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

--- a/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Fri Dec 11 15:06:12 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Fri Dec 11 15:35:29 2009 +0100
@@ -1,6631 +1,6631 @@
 #2 := false
-decl up_6 :: (-> T4 T2 bool)
-decl ?x47!7 :: (-> T2 T2)
-decl ?x75!20 :: T2
-#2235 := ?x75!20
-#5912 := (?x47!7 ?x75!20)
-decl uf_23 :: T4
-#187 := uf_23
-#16889 := (up_6 uf_23 #5912)
-decl uf_2 :: (-> T1 T2)
+#52 := 0::int
+decl uf_10 :: (-> T1 int)
 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
-#179 := uf_22
-#4603 := (uf_1 uf_22 uf_22)
-#10571 := (uf_3 #4603)
-#15148 := (uf_1 #10571 ?x75!20)
-#15931 := (uf_3 #15148)
-#16881 := (uf_1 #5912 #15931)
-#19932 := (uf_2 #16881)
+#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)
 decl uf_7 :: (-> T4 T2 T5 T4)
 decl uf_8 :: T5
 #33 := uf_8
-decl uf_15 :: T4
-#110 := uf_15
-#11533 := (uf_7 uf_15 #10571 uf_8)
-#27162 := (up_6 #11533 #19932)
-#27198 := (not #27162)
-#16890 := (not #16889)
-#27320 := (iff #16890 #27198)
-#27318 := (iff #16889 #27162)
-#27316 := (iff #27162 #16889)
-#27304 := (= #19932 #5912)
-#20977 := (= #5912 #19932)
-#11 := (:var 0 T2)
-#10 := (:var 1 T2)
-#12 := (uf_1 #10 #11)
-#4070 := (pattern #12)
-#16 := (uf_2 #12)
-#317 := (= #10 #16)
-#4077 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #4070) #317)
-#321 := (forall (vars (?x4 T2) (?x5 T2)) #317)
-#4080 := (iff #321 #4077)
-#4078 := (iff #317 #317)
-#4079 := [refl]: #4078
-#4081 := [quant-intro #4079]: #4080
-#1731 := (~ #321 #321)
-#1765 := (~ #317 #317)
-#1766 := [refl]: #1765
-#1732 := [nnf-pos #1766]: #1731
-#17 := (= #16 #10)
-#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
-#322 := (iff #18 #321)
-#319 := (iff #17 #317)
-#320 := [rewrite]: #319
-#323 := [quant-intro #320]: #322
-#316 := [asserted]: #18
-#326 := [mp #316 #323]: #321
-#1767 := [mp~ #326 #1732]: #321
-#4082 := [mp #1767 #4081]: #4077
-#8504 := (not #4077)
-#20954 := (or #8504 #20977)
-#20968 := [quant-inst]: #20954
-#27303 := [unit-resolution #20968 #4082]: #20977
-#27305 := [symm #27303]: #27304
-#13612 := (= #11533 uf_23)
-#188 := (uf_7 uf_15 uf_22 uf_8)
-#7202 := (= #188 uf_23)
-#189 := (= uf_23 #188)
-#2239 := (uf_1 #11 ?x75!20)
-#4360 := (pattern #2239)
-decl uf_24 :: (-> T2 int)
-#196 := (uf_24 #11)
-#4300 := (pattern #196)
-#206 := (up_6 uf_23 #11)
-#4326 := (pattern #206)
-#52 := 0::int
-decl uf_10 :: (-> T1 int)
-#2240 := (uf_10 #2239)
-#2236 := (uf_24 ?x75!20)
-#1127 := -1::int
-#2237 := (* -1::int #2236)
-#2834 := (+ #2237 #2240)
-#2835 := (+ #196 #2834)
-#2838 := (= #2835 0::int)
-#3400 := (not #2838)
-#2238 := (+ #196 #2237)
-#2243 := (>= #2238 0::int)
-#213 := (not #206)
-#3401 := (or #213 #2243 #3400)
-#4361 := (forall (vars (?x76 T2)) (:pat #4326 #4300 #4360) #3401)
-#4366 := (not #4361)
-#87 := (uf_1 #11 #10)
-#4155 := (pattern #87)
-#216 := (uf_24 #10)
-#1407 := (* -1::int #216)
-#1408 := (+ #196 #1407)
-#88 := (uf_10 #87)
-#1433 := (+ #88 #1408)
-#1431 := (>= #1433 0::int)
-#1142 := (* -1::int #88)
-decl uf_9 :: int
-#53 := uf_9
-#1143 := (+ uf_9 #1142)
-#1144 := (<= #1143 0::int)
-#3392 := (or #213 #1144 #1431)
-#4352 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #4155) #3392)
-#4357 := (not #4352)
-decl uf_11 :: T2
-#64 := uf_11
-#2810 := (= uf_11 ?x75!20)
-#2247 := (+ uf_9 #2237)
-#2248 := (<= #2247 0::int)
-#4369 := (or #2248 #2810 #4357 #4366)
-#4372 := (not #4369)
-decl ?x71!19 :: T2
-#2206 := ?x71!19
-decl ?x72!18 :: T2
-#2205 := ?x72!18
-#2211 := (uf_1 ?x72!18 ?x71!19)
-#2212 := (uf_10 #2211)
-#2215 := (* -1::int #2212)
-#2209 := (uf_24 ?x72!18)
-#2796 := (* -1::int #2209)
-#2797 := (+ #2796 #2215)
-#2207 := (uf_24 ?x71!19)
-#2798 := (+ #2207 #2797)
-#2799 := (<= #2798 0::int)
-#2219 := (up_6 uf_23 ?x72!18)
-#3355 := (not #2219)
-#2216 := (+ uf_9 #2215)
-#2217 := (<= #2216 0::int)
-#3370 := (or #2217 #3355 #2799)
-#3375 := (not #3370)
-#4375 := (or #3375 #4372)
-#4378 := (not #4375)
-#4343 := (pattern #196 #216)
-#1406 := (>= #1408 0::int)
-#214 := (up_6 uf_23 #10)
-#3332 := (not #214)
-#3347 := (or #206 #3332 #1406)
-#4344 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4343) #3347)
-#4349 := (not #4344)
-#4381 := (or #4349 #4378)
-#4384 := (not #4381)
+#8048 := (uf_7 uf_15 #6904 uf_8)
+#13996 := (up_6 #8048 ?x75!20)
+#14006 := (iff #13996 #14001)
+#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)
+#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)
+#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
-#2180 := ?x68!16
-#2184 := (uf_24 ?x68!16)
-#2770 := (* -1::int #2184)
+#1976 := ?x68!16
+#1980 := (uf_24 ?x68!16)
+#2517 := (* -1::int #1980)
 decl ?x67!17 :: T2
-#2181 := ?x67!17
-#2182 := (uf_24 ?x67!17)
-#2771 := (+ #2182 #2770)
-#2772 := (<= #2771 0::int)
-#2188 := (up_6 uf_23 ?x68!16)
-#2187 := (up_6 uf_23 ?x67!17)
-#3309 := (not #2187)
-#3324 := (or #3309 #2188 #2772)
-#3329 := (not #3324)
-#4387 := (or #3329 #4384)
-#4390 := (not #4387)
-#1397 := (>= #196 0::int)
-#4335 := (forall (vars (?x65 T2)) (:pat #4300) #1397)
-#4340 := (not #4335)
-#4393 := (or #4340 #4390)
-#4396 := (not #4393)
+#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
-#2165 := ?x65!15
-#2166 := (uf_24 ?x65!15)
-#2167 := (>= #2166 0::int)
-#2168 := (not #2167)
-#4399 := (or #2168 #4396)
-#4402 := (not #4399)
-#209 := (uf_24 uf_11)
-#210 := (= #209 0::int)
-#1394 := (not #210)
-#4405 := (or #1394 #4402)
-#4408 := (not #4405)
-#4411 := (or #1394 #4408)
-#4414 := (not #4411)
-decl uf_4 :: (-> T3 T2 int)
-decl uf_14 :: T3
-#104 := uf_14
-#107 := (uf_4 uf_14 #11)
-#4179 := (pattern #107)
-#688 := (= #107 #196)
-#705 := (or #213 #688)
-#4327 := (forall (vars (?x63 T2)) (:pat #4326 #4179 #4300) #705)
-#4332 := (not #4327)
-#4417 := (or #4332 #4414)
-#4420 := (not #4417)
+#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
-#2141 := ?x63!14
-#2143 := (uf_4 uf_14 ?x63!14)
-#2142 := (uf_24 ?x63!14)
-#2747 := (= #2142 #2143)
-#2145 := (up_6 uf_23 ?x63!14)
-#2146 := (not #2145)
-#2750 := (or #2146 #2747)
-#2753 := (not #2750)
-#4423 := (or #2753 #4420)
-#4426 := (not #4423)
-#1382 := (* -1::int #196)
-#1383 := (+ #107 #1382)
-#1381 := (>= #1383 0::int)
-#4318 := (forall (vars (?x61 T2)) (:pat #4179 #4300) #1381)
-#4323 := (not #4318)
-#4429 := (or #4323 #4426)
-#4432 := (not #4429)
+#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
-#2123 := ?x61!13
-#2126 := (uf_4 uf_14 ?x61!13)
-#2737 := (* -1::int #2126)
-#2124 := (uf_24 ?x61!13)
-#2738 := (+ #2124 #2737)
-#2739 := (<= #2738 0::int)
-#2744 := (not #2739)
-#4435 := (or #2744 #4432)
-#4438 := (not #4435)
-#190 := (uf_1 uf_22 #11)
-#4301 := (pattern #190)
-#191 := (uf_10 #190)
-#1520 := (+ #191 #1382)
-#182 := (uf_4 uf_14 uf_22)
-#1521 := (+ #182 #1520)
-#1522 := (= #1521 0::int)
-#1351 := (* -1::int #191)
-#1357 := (* -1::int #182)
-#1358 := (+ #1357 #1351)
-#1359 := (+ #107 #1358)
-#1360 := (<= #1359 0::int)
-#1352 := (+ uf_9 #1351)
-#1353 := (<= #1352 0::int)
-#3301 := (or #1353 #1360 #1522)
-#4310 := (forall (vars (?x59 T2)) (:pat #4301 #4179 #4300) #3301)
-#4315 := (not #4310)
-#3281 := (or #1353 #1360)
-#3282 := (not #3281)
-#3285 := (or #688 #3282)
-#4302 := (forall (vars (?x60 T2)) (:pat #4179 #4300 #4301) #3285)
-#4307 := (not #4302)
+#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
-#2100 := ?x48!12
-#2106 := (up_6 uf_15 ?x48!12)
-#2101 := (uf_4 uf_14 ?x48!12)
-#2102 := (* -1::int #2101)
-#2103 := (+ uf_9 #2102)
-#2104 := (<= #2103 0::int)
-#1547 := (+ uf_9 #1357)
-#1548 := (<= #1547 0::int)
-#111 := (up_6 uf_15 #11)
-#4221 := (pattern #111)
-#1535 := (+ #107 #1357)
-#1534 := (>= #1535 0::int)
-#1538 := (or #111 #1534)
-#4292 := (forall (vars (?x58 T2)) (:pat #4221 #4179) #1538)
-#4297 := (not #4292)
-#888 := (not #189)
-#180 := (up_6 uf_15 uf_22)
-#4441 := (or #180 #888 #4297 #1548 #2104 #2106 #4307 #4315 #4438)
-#4444 := (not #4441)
+#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
-#2034 := ?x53!11
+#1827 := ?x53!11
 decl ?x54!10 :: T2
-#2033 := ?x54!10
-#2039 := (uf_1 ?x54!10 ?x53!11)
-#2040 := (uf_10 #2039)
-#2047 := (* -1::int #2040)
+#1826 := ?x54!10
+#1832 := (uf_1 ?x54!10 ?x53!11)
+#1833 := (uf_10 #1832)
+#1840 := (* -1::int #1833)
 decl uf_19 :: T3
-#141 := uf_19
-#2037 := (uf_4 uf_19 ?x54!10)
-#2043 := (* -1::int #2037)
-#2694 := (+ #2043 #2047)
-#2035 := (uf_4 uf_19 ?x53!11)
-#2695 := (+ #2035 #2694)
-#2696 := (<= #2695 0::int)
-#2048 := (+ uf_9 #2047)
-#2049 := (<= #2048 0::int)
-#2044 := (+ uf_9 #2043)
-#2045 := (<= #2044 0::int)
-#3245 := (or #2045 #2049 #2696)
-#3250 := (not #3245)
-#149 := (uf_4 uf_19 #10)
-#1264 := (* -1::int #149)
-#146 := (uf_4 uf_19 #11)
-#1265 := (+ #146 #1264)
-#1271 := (+ #88 #1265)
-#1294 := (>= #1271 0::int)
-#1251 := (* -1::int #146)
-#1252 := (+ uf_9 #1251)
-#1253 := (<= #1252 0::int)
-#3213 := (or #1144 #1253 #1294)
-#4254 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #4155) #3213)
-#4259 := (not #4254)
-#161 := (uf_4 uf_19 uf_11)
-#162 := (= #161 0::int)
-#4262 := (or #162 #4259)
-#4265 := (not #4262)
-#4268 := (or #4265 #3250)
-#4271 := (not #4268)
-#4230 := (pattern #146)
+#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)
-#2010 := (?x50!9 #11)
-#2013 := (uf_1 #2010 #11)
-#2014 := (uf_10 #2013)
-#2664 := (* -1::int #2014)
-#2011 := (uf_4 uf_19 #2010)
-#2647 := (* -1::int #2011)
-#2665 := (+ #2647 #2664)
-#2666 := (+ #146 #2665)
-#2667 := (= #2666 0::int)
-#3183 := (not #2667)
-#2648 := (+ #146 #2647)
-#2649 := (<= #2648 0::int)
-#3184 := (or #2649 #3183)
-#3185 := (not #3184)
+#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)
-#3191 := (or #65 #1253 #3185)
-#4246 := (forall (vars (?x49 T2)) (:pat #4230) #3191)
-#4251 := (not #4246)
-#4274 := (or #4251 #4271)
-#4277 := (not #4274)
+#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
-#1970 := ?x49!8
-#1974 := (uf_1 #11 ?x49!8)
-#4231 := (pattern #1974)
-#1975 := (uf_10 #1974)
-#1971 := (uf_4 uf_19 ?x49!8)
-#1972 := (* -1::int #1971)
-#2617 := (+ #1972 #1975)
-#2618 := (+ #146 #2617)
-#2621 := (= #2618 0::int)
-#3147 := (not #2621)
-#1973 := (+ #146 #1972)
-#1978 := (>= #1973 0::int)
-#3148 := (or #1978 #3147)
-#4232 := (forall (vars (?x50 T2)) (:pat #4230 #4231) #3148)
-#4237 := (not #4232)
-#2593 := (= uf_11 ?x49!8)
-#1982 := (+ uf_9 #1972)
-#1983 := (<= #1982 0::int)
-#4240 := (or #1983 #2593 #4237)
-#4243 := (not #4240)
-#4280 := (or #4243 #4277)
-#4283 := (not #4280)
-#1206 := (* -1::int #107)
-#1207 := (+ uf_9 #1206)
-#1208 := (<= #1207 0::int)
-#3133 := (or #111 #1208)
-#4222 := (forall (vars (?x48 T2)) (:pat #4221 #4179) #3133)
-#4227 := (not #4222)
-#509 := (= uf_14 uf_19)
-#614 := (not #509)
+#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
-#136 := uf_16
-#506 := (= uf_15 uf_16)
-#632 := (not #506)
+#145 := uf_16
+#530 := (= uf_15 uf_16)
+#3022 := (not #530)
 decl uf_21 :: T3
-#144 := uf_21
+#153 := uf_21
 decl uf_20 :: T3
-#143 := uf_20
-#145 := (= uf_20 uf_21)
-#605 := (not #145)
+#152 := uf_20
+#154 := (= uf_20 uf_21)
+#3021 := (not #154)
 decl uf_18 :: T2
-#139 := uf_18
+#148 := uf_18
 decl uf_17 :: T2
-#138 := uf_17
-#140 := (= uf_17 uf_18)
-#623 := (not #140)
-#4286 := (or #623 #605 #632 #614 #4227 #4283)
-#4289 := (not #4286)
-#4447 := (or #4289 #4444)
-#4450 := (not #4447)
-#1934 := (?x47!7 #11)
-#1935 := (uf_4 uf_14 #1934)
-#2552 := (* -1::int #1935)
-#2567 := (+ #107 #2552)
-#2568 := (<= #2567 0::int)
-#1939 := (uf_1 #1934 #11)
-#1940 := (uf_10 #1939)
-#2553 := (* -1::int #1940)
-#2554 := (+ #2552 #2553)
-#2555 := (+ #107 #2554)
-#2556 := (= #2555 0::int)
-#3117 := (not #2556)
-#1943 := (up_6 uf_15 #1934)
-#3116 := (not #1943)
-#3118 := (or #3116 #3117 #2568)
-#3119 := (not #3118)
-#3125 := (or #65 #1208 #3119)
-#4213 := (forall (vars (?x46 T2)) (:pat #4179) #3125)
-#4218 := (not #4213)
+#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)
-#4131 := (pattern #66)
+#3886 := (pattern #66)
 decl ?x38!6 :: (-> T2 T2)
-#1907 := (?x38!6 #11)
-#1911 := (uf_12 #1907)
-#2511 := (* -1::int #1911)
-#1908 := (uf_1 #1907 #11)
-#1909 := (uf_10 #1908)
-#2528 := (* -1::int #1909)
-#2529 := (+ #2528 #2511)
-#2530 := (+ #66 #2529)
-#2531 := (= #2530 0::int)
-#3089 := (not #2531)
-#2512 := (+ #66 #2511)
-#2513 := (<= #2512 0::int)
+#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)
-#1917 := (up_13 #1907)
-#3088 := (not #1917)
-#3090 := (or #3088 #2513 #3089)
-#3091 := (not #3090)
-#1168 := (* -1::int #66)
-#1169 := (+ uf_9 #1168)
-#1170 := (<= #1169 0::int)
-#3097 := (or #65 #1170 #3091)
-#4205 := (forall (vars (?x37 T2)) (:pat #4131) #3097)
-#4210 := (not #4205)
-#113 := (up_6 uf_15 #10)
-#4196 := (pattern #111 #113)
-#115 := (uf_4 uf_14 #10)
-#1220 := (* -1::int #115)
-#1221 := (+ #107 #1220)
-#1224 := (>= #1221 0::int)
-#3054 := (not #113)
-#3069 := (or #111 #3054 #1224)
-#4197 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #4196) #3069)
-#4202 := (not #4197)
-#1222 := (+ #88 #1221)
-#1602 := (>= #1222 0::int)
-#112 := (not #111)
-#3046 := (or #112 #1144 #1602)
-#4188 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #4155) #3046)
-#4193 := (not #4188)
-#1625 := (>= #107 0::int)
-#4180 := (forall (vars (?x41 T2)) (:pat #4179) #1625)
-#4185 := (not #4180)
-#105 := (uf_4 uf_14 uf_11)
-#106 := (= #105 0::int)
-#1636 := (not #106)
-#4453 := (or #1636 #4185 #4193 #4202 #4210 #4218 #4450)
-#4456 := (not #4453)
+#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
-#1863 := ?x37!5
-#1864 := (uf_1 #11 ?x37!5)
-#4164 := (pattern #1864)
+#1636 := ?x37!5
+#1637 := (uf_1 #11 ?x37!5)
+#3925 := (pattern #1637)
 #74 := (up_13 #11)
-#4124 := (pattern #74)
-#1866 := (uf_12 ?x37!5)
-#1867 := (* -1::int #1866)
-#1865 := (uf_10 #1864)
-#2479 := (+ #1865 #1867)
-#2480 := (+ #66 #2479)
-#2483 := (= #2480 0::int)
-#3007 := (not #2483)
-#1871 := (+ #66 #1867)
-#1872 := (>= #1871 0::int)
+#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)
-#3008 := (or #75 #1872 #3007)
-#4165 := (forall (vars (?x38 T2)) (:pat #4124 #4131 #4164) #3008)
-#4170 := (not #4165)
-#2455 := (= uf_11 ?x37!5)
-#1876 := (+ uf_9 #1867)
-#1877 := (<= #1876 0::int)
-#4173 := (or #1877 #2455 #4170)
-#4176 := (not #4173)
-#4459 := (or #4176 #4456)
-#4462 := (not #4459)
-#83 := (uf_12 #10)
-#1130 := (* -1::int #83)
-#1157 := (+ #1130 #88)
-#1158 := (+ #66 #1157)
-#1155 := (>= #1158 0::int)
-#2999 := (or #75 #1144 #1155)
-#4156 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #4155) #2999)
-#4161 := (not #4156)
-#4465 := (or #4161 #4462)
-#4468 := (not #4465)
+#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
-#1833 := ?x34!3
-#1840 := (uf_12 ?x34!3)
+#1606 := ?x34!3
+#1613 := (uf_12 ?x34!3)
 decl ?x33!4 :: T2
-#1834 := ?x33!4
-#1837 := (uf_12 ?x33!4)
-#1838 := (* -1::int #1837)
-#2442 := (+ #1838 #1840)
-#1835 := (uf_1 ?x34!3 ?x33!4)
-#1836 := (uf_10 #1835)
-#2443 := (+ #1836 #2442)
-#2446 := (>= #2443 0::int)
-#1847 := (up_13 ?x34!3)
-#2962 := (not #1847)
-#1843 := (* -1::int #1836)
-#1844 := (+ uf_9 #1843)
-#1845 := (<= #1844 0::int)
-#2977 := (or #1845 #2962 #2446)
-#8241 := [hypothesis]: #1847
-#4125 := (forall (vars (?x26 T2)) (:pat #4124) #75)
-#76 := (forall (vars (?x26 T2)) #75)
-#4128 := (iff #76 #4125)
-#4126 := (iff #75 #75)
-#4127 := [refl]: #4126
-#4129 := [quant-intro #4127]: #4128
-#1747 := (~ #76 #76)
-#1784 := (~ #75 #75)
-#1785 := [refl]: #1784
-#1748 := [nnf-pos #1785]: #1747
+#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)
-#1694 := (or #70 #67)
-#1697 := (forall (vars (?x24 T2)) #1694)
-#1700 := (not #1697)
-#1628 := (forall (vars (?x41 T2)) #1625)
-#1631 := (not #1628)
-#114 := (and #112 #113)
-#454 := (not #114)
-#1616 := (or #454 #1224)
-#1619 := (forall (vars (?x42 T2) (?x43 T2)) #1616)
-#1622 := (not #1619)
-#1145 := (not #1144)
-#1594 := (and #111 #1145)
-#1599 := (not #1594)
-#1605 := (or #1599 #1602)
-#1608 := (forall (vars (?x44 T2) (?x45 T2)) #1605)
-#1611 := (not #1608)
-#1541 := (forall (vars (?x58 T2)) #1538)
-#1544 := (not #1541)
-#1361 := (not #1360)
-#1354 := (not #1353)
-#1364 := (and #1354 #1361)
-#1517 := (not #1364)
-#1525 := (or #1517 #1522)
-#1528 := (forall (vars (?x59 T2)) #1525)
-#1531 := (not #1528)
-#1455 := (= #1433 0::int)
-#1458 := (not #1406)
-#1467 := (and #206 #1458 #1455)
-#1472 := (exists (vars (?x76 T2)) #1467)
-#1444 := (+ uf_9 #1382)
-#1445 := (<= #1444 0::int)
-#1446 := (not #1445)
-#1449 := (and #70 #1446)
-#1452 := (not #1449)
-#1475 := (or #1452 #1472)
-#1478 := (forall (vars (?x75 T2)) #1475)
-#1423 := (and #206 #1145)
-#1428 := (not #1423)
-#1435 := (or #1428 #1431)
-#1438 := (forall (vars (?x71 T2) (?x72 T2)) #1435)
-#1441 := (not #1438)
-#1481 := (or #1441 #1478)
-#1484 := (and #1438 #1481)
-#215 := (and #213 #214)
-#716 := (not #215)
-#1411 := (or #716 #1406)
-#1414 := (forall (vars (?x67 T2) (?x68 T2)) #1411)
-#1417 := (not #1414)
-#1487 := (or #1417 #1484)
-#1490 := (and #1414 #1487)
-#1400 := (forall (vars (?x65 T2)) #1397)
-#1403 := (not #1400)
-#1493 := (or #1403 #1490)
-#1496 := (and #1400 #1493)
-#1499 := (or #1394 #1496)
-#1502 := (and #210 #1499)
-#710 := (forall (vars (?x63 T2)) #705)
-#846 := (not #710)
-#1505 := (or #846 #1502)
-#1508 := (and #710 #1505)
-#1386 := (forall (vars (?x61 T2)) #1381)
-#1389 := (not #1386)
-#1511 := (or #1389 #1508)
-#1514 := (and #1386 #1511)
-#1370 := (or #688 #1364)
-#1375 := (forall (vars (?x60 T2)) #1370)
-#1378 := (not #1375)
-#1209 := (not #1208)
-#1325 := (and #112 #1209)
-#1328 := (exists (vars (?x48 T2)) #1325)
-#1559 := (not #1328)
-#1583 := (or #180 #888 #1559 #1378 #1514 #1531 #1544 #1548)
-#1254 := (not #1253)
-#1288 := (and #1145 #1254)
-#1291 := (not #1288)
-#1297 := (or #1291 #1294)
-#1300 := (forall (vars (?x53 T2) (?x54 T2)) #1297)
-#1303 := (not #1300)
-#1311 := (or #162 #1303)
-#1316 := (and #1300 #1311)
-#1269 := (= #1271 0::int)
-#1263 := (>= #1265 0::int)
-#1266 := (not #1263)
-#1273 := (and #1266 #1269)
-#1276 := (exists (vars (?x50 T2)) #1273)
-#1257 := (and #70 #1254)
-#1260 := (not #1257)
-#1279 := (or #1260 #1276)
-#1282 := (forall (vars (?x49 T2)) #1279)
-#1285 := (not #1282)
-#1319 := (or #1285 #1316)
-#1322 := (and #1282 #1319)
-#1346 := (or #623 #605 #632 #614 #1322 #1328)
-#1588 := (and #1346 #1583)
-#1225 := (not #1224)
-#1218 := (= #1222 0::int)
-#1234 := (and #111 #1218 #1225)
-#1239 := (exists (vars (?x47 T2)) #1234)
-#1212 := (and #70 #1209)
-#1215 := (not #1212)
-#1242 := (or #1215 #1239)
-#1245 := (forall (vars (?x46 T2)) #1242)
-#1248 := (not #1245)
-#1180 := (= #1158 0::int)
-#1131 := (+ #66 #1130)
-#1129 := (>= #1131 0::int)
-#1183 := (not #1129)
-#1192 := (and #74 #1183 #1180)
-#1197 := (exists (vars (?x38 T2)) #1192)
-#1171 := (not #1170)
-#1174 := (and #70 #1171)
-#1177 := (not #1174)
-#1200 := (or #1177 #1197)
-#1203 := (forall (vars (?x37 T2)) #1200)
-#1639 := (not #1203)
-#1660 := (or #1636 #1639 #1248 #1588 #1611 #1622 #1631)
-#1665 := (and #1203 #1660)
-#1148 := (and #74 #1145)
-#1151 := (not #1148)
-#1159 := (or #1151 #1155)
-#1162 := (forall (vars (?x33 T2) (?x34 T2)) #1159)
-#1165 := (not #1162)
-#1668 := (or #1165 #1665)
-#1671 := (and #1162 #1668)
-#81 := (up_13 #10)
-#82 := (and #75 #81)
-#430 := (not #82)
-#1133 := (or #430 #1129)
-#1136 := (forall (vars (?x29 T2) (?x30 T2)) #1133)
-#1139 := (not #1136)
-#1674 := (or #1139 #1671)
-#1677 := (and #1136 #1674)
-#1120 := (>= #66 0::int)
-#1121 := (forall (vars (?x27 T2)) #1120)
-#1124 := (not #1121)
-#1680 := (or #1124 #1677)
-#1683 := (and #1121 #1680)
-#77 := (uf_12 uf_11)
-#78 := (= #77 0::int)
-#1115 := (not #78)
-#1686 := (or #1115 #1683)
-#1689 := (and #78 #1686)
-#413 := (= uf_9 #66)
-#419 := (or #65 #413)
-#424 := (forall (vars (?x25 T2)) #419)
-#1084 := (not #424)
-#1075 := (not #76)
-#1712 := (or #1075 #1084 #1689 #1700)
-#1717 := (not #1712)
-#1 := true
-#234 := (implies false true)
-#221 := (+ #196 #88)
-#228 := (= #216 #221)
-#229 := (and #206 #228)
-#227 := (< #196 #216)
-#230 := (and #227 #229)
-#231 := (exists (vars (?x76 T2)) #230)
-#225 := (< #196 uf_9)
-#226 := (and #70 #225)
-#232 := (implies #226 #231)
-#233 := (forall (vars (?x75 T2)) #232)
-#235 := (implies #233 #234)
-#236 := (and #233 #235)
-#222 := (<= #216 #221)
-#89 := (< #88 uf_9)
-#220 := (and #206 #89)
-#223 := (implies #220 #222)
-#224 := (forall (vars (?x71 T2) (?x72 T2)) #223)
-#237 := (implies #224 #236)
-#238 := (and #224 #237)
-#217 := (<= #216 #196)
-#218 := (implies #215 #217)
-#219 := (forall (vars (?x67 T2) (?x68 T2)) #218)
-#239 := (implies #219 #238)
-#240 := (and #219 #239)
-#211 := (<= 0::int #196)
-#212 := (forall (vars (?x65 T2)) #211)
-#241 := (implies #212 #240)
-#242 := (and #212 #241)
-#243 := (implies #210 #242)
-#244 := (and #210 #243)
-#245 := (implies true #244)
-#246 := (implies true #245)
-#201 := (= #196 #107)
-#207 := (implies #206 #201)
-#208 := (forall (vars (?x63 T2)) #207)
-#247 := (implies #208 #246)
-#248 := (and #208 #247)
-#204 := (<= #196 #107)
-#205 := (forall (vars (?x61 T2)) #204)
-#249 := (implies #205 #248)
-#250 := (and #205 #249)
-#193 := (+ #182 #191)
-#194 := (< #193 #107)
-#192 := (< #191 uf_9)
-#195 := (and #192 #194)
-#200 := (not #195)
-#202 := (implies #200 #201)
-#203 := (forall (vars (?x60 T2)) #202)
-#251 := (implies #203 #250)
-#197 := (= #196 #193)
-#198 := (implies #195 #197)
-#199 := (forall (vars (?x59 T2)) #198)
-#252 := (implies #199 #251)
-#253 := (implies #189 #252)
-#184 := (<= #182 #107)
-#185 := (implies #112 #184)
-#186 := (forall (vars (?x58 T2)) #185)
-#254 := (implies #186 #253)
-#183 := (< #182 uf_9)
-#255 := (implies #183 #254)
-#181 := (not #180)
-#256 := (implies #181 #255)
-#124 := (< #107 uf_9)
-#133 := (and #112 #124)
-#134 := (exists (vars (?x48 T2)) #133)
-#257 := (implies #134 #256)
-#258 := (implies true #257)
-#259 := (implies true #258)
-#163 := (implies #162 true)
-#164 := (and #162 #163)
-#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)
-#165 := (implies #160 #164)
-#166 := (and #160 #165)
-#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)
-#167 := (implies #156 #166)
-#168 := (and #156 #167)
-#169 := (implies true #168)
-#170 := (implies #145 #169)
-#142 := (= uf_19 uf_14)
-#171 := (implies #142 #170)
-#172 := (implies #140 #171)
-#137 := (= uf_16 uf_15)
-#173 := (implies #137 #172)
-#174 := (implies true #173)
-#175 := (implies true #174)
-#135 := (not #134)
-#176 := (implies #135 #175)
-#177 := (implies true #176)
-#178 := (implies true #177)
-#260 := (and #178 #259)
-#261 := (implies true #260)
-#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)
-#262 := (implies #132 #261)
-#121 := (<= #115 #120)
-#119 := (and #111 #89)
-#122 := (implies #119 #121)
-#123 := (forall (vars (?x44 T2) (?x45 T2)) #122)
-#263 := (implies #123 #262)
-#116 := (<= #115 #107)
-#117 := (implies #114 #116)
-#118 := (forall (vars (?x42 T2) (?x43 T2)) #117)
-#264 := (implies #118 #263)
-#108 := (<= 0::int #107)
-#109 := (forall (vars (?x41 T2)) #108)
-#265 := (implies #109 #264)
-#266 := (implies #106 #265)
-#267 := (implies true #266)
-#268 := (implies true #267)
-#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)
-#269 := (implies #103 #268)
-#270 := (and #103 #269)
-#92 := (<= #83 #91)
-#90 := (and #74 #89)
-#93 := (implies #90 #92)
-#94 := (forall (vars (?x33 T2) (?x34 T2)) #93)
-#271 := (implies #94 #270)
-#272 := (and #94 #271)
-#84 := (<= #83 #66)
-#85 := (implies #82 #84)
-#86 := (forall (vars (?x29 T2) (?x30 T2)) #85)
-#273 := (implies #86 #272)
-#274 := (and #86 #273)
-#79 := (<= 0::int #66)
-#80 := (forall (vars (?x27 T2)) #79)
-#275 := (implies #80 #274)
-#276 := (and #80 #275)
-#277 := (implies #78 #276)
-#278 := (and #78 #277)
-#279 := (implies true #278)
-#280 := (implies #76 #279)
+#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)
+#990 := (not #987)
+#1459 := (or #990 #1456)
+#1462 := (and #987 #1459)
+#85 := (and #75 #84)
+#432 := (not #85)
+#958 := (or #432 #954)
+#961 := (forall (vars (?x29 T2) (?x30 T2)) #958)
+#964 := (not #961)
+#1465 := (or #964 #1462)
+#1468 := (and #961 #1465)
+#946 := (forall (vars (?x27 T2)) #945)
+#949 := (not #946)
+#1471 := (or #949 #1468)
+#1474 := (and #946 #1471)
+#1477 := (or #940 #1474)
+#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)
+#243 := (forall (vars (?x75 T2)) #242)
+#232 := (<= #226 #231)
+#92 := (< #91 uf_9)
+#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)
+#221 := (<= 0::int #199)
+#222 := (forall (vars (?x65 T2)) #221)
+#248 := (implies #222 #247)
+#249 := (and #222 #248)
+#250 := (implies #220 #249)
+#251 := (and #220 #250)
+#204 := (= #199 #110)
+#217 := (implies #216 #204)
+#218 := (forall (vars (?x63 T2)) #217)
+#252 := (implies #218 #251)
+#253 := (and #218 #252)
+#214 := (<= #199 #110)
+#215 := (forall (vars (?x61 T2)) #214)
+#254 := (implies #215 #253)
+#255 := (and #215 #254)
+#196 := (+ #185 #194)
+#197 := (< #196 #110)
+#195 := (< #194 uf_9)
+#198 := (and #195 #197)
+#203 := (not #198)
+#205 := (implies #203 #204)
+#206 := (forall (vars (?x60 T2)) #205)
+#200 := (= #199 #196)
+#201 := (implies #198 #200)
+#202 := (forall (vars (?x59 T2)) #201)
+#207 := (and #202 #206)
+#208 := (and #192 #207)
+#187 := (<= #185 #110)
+#188 := (implies #115 #187)
+#189 := (forall (vars (?x58 T2)) #188)
+#209 := (and #189 #208)
+#186 := (< #185 uf_9)
+#210 := (and #186 #209)
+#211 := (and #184 #210)
+#127 := (< #110 uf_9)
+#142 := (and #115 #127)
+#143 := (exists (vars (?x48 T2)) #142)
+#212 := (and #143 #211)
+#213 := (and true #212)
+#256 := (implies #213 #255)
+#165 := (+ #160 #91)
+#172 := (<= #163 #165)
+#161 := (< #160 uf_9)
+#171 := (and #161 #92)
+#173 := (implies #171 #172)
+#174 := (forall (vars (?x53 T2) (?x54 T2)) #173)
+#177 := (implies #174 #176)
+#178 := (and #174 #177)
+#166 := (= #163 #165)
+#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)
+#179 := (implies #170 #178)
+#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)
+#181 := (implies #159 #180)
+#257 := (and #181 #256)
+#123 := (+ #110 #91)
+#130 := (= #118 #123)
+#131 := (and #114 #130)
+#129 := (< #110 #118)
+#132 := (and #129 #131)
+#133 := (exists (vars (?x47 T2)) #132)
+#128 := (and #70 #127)
+#134 := (implies #128 #133)
+#135 := (forall (vars (?x46 T2)) #134)
+#124 := (<= #118 #123)
+#122 := (and #114 #92)
+#125 := (implies #122 #124)
+#126 := (forall (vars (?x44 T2) (?x45 T2)) #125)
+#136 := (and #126 #135)
+#119 := (<= #118 #110)
+#120 := (implies #117 #119)
+#121 := (forall (vars (?x42 T2) (?x43 T2)) #120)
+#137 := (and #121 #136)
+#111 := (<= 0::int #110)
+#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)
+#103 := (and #100 #102)
+#104 := (exists (vars (?x38 T2)) #103)
+#98 := (< #66 uf_9)
+#99 := (and #70 #98)
+#105 := (implies #99 #104)
+#106 := (forall (vars (?x37 T2)) #105)
+#141 := (and #106 #140)
+#258 := (implies #141 #257)
+#259 := (and #106 #258)
+#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)
+#87 := (<= #86 #66)
+#88 := (implies #85 #87)
+#89 := (forall (vars (?x29 T2) (?x30 T2)) #88)
+#262 := (implies #89 #261)
+#263 := (and #89 #262)
+#82 := (<= 0::int #66)
+#83 := (forall (vars (?x27 T2)) #82)
+#264 := (implies #83 #263)
+#265 := (and #83 #264)
+#266 := (implies #81 #265)
+#267 := (and #81 #266)
 #71 := (= #66 uf_9)
 #72 := (implies #70 #71)
 #73 := (forall (vars (?x25 T2)) #72)
-#281 := (implies #73 #280)
+#77 := (and #73 #76)
 #68 := (implies #65 #67)
 #69 := (forall (vars (?x24 T2)) #68)
-#282 := (implies #69 #281)
-#283 := (implies true #282)
-#284 := (implies true #283)
-#285 := (not #284)
-#1720 := (iff #285 #1717)
-#726 := (+ #88 #196)
-#744 := (= #216 #726)
-#747 := (and #206 #744)
-#750 := (and #227 #747)
-#753 := (exists (vars (?x76 T2)) #750)
-#759 := (not #226)
-#760 := (or #759 #753)
-#765 := (forall (vars (?x75 T2)) #760)
-#729 := (<= #216 #726)
-#723 := (and #89 #206)
-#735 := (not #723)
-#736 := (or #735 #729)
-#741 := (forall (vars (?x71 T2) (?x72 T2)) #736)
-#787 := (not #741)
-#788 := (or #787 #765)
-#793 := (and #741 #788)
-#717 := (or #716 #217)
-#720 := (forall (vars (?x67 T2) (?x68 T2)) #717)
-#799 := (not #720)
-#800 := (or #799 #793)
-#805 := (and #720 #800)
-#811 := (not #212)
-#812 := (or #811 #805)
-#817 := (and #212 #812)
-#713 := (= 0::int #209)
-#823 := (not #713)
-#824 := (or #823 #817)
-#829 := (and #713 #824)
-#847 := (or #846 #829)
-#852 := (and #710 #847)
-#858 := (not #205)
-#859 := (or #858 #852)
-#864 := (and #205 #859)
-#694 := (or #195 #688)
-#699 := (forall (vars (?x60 T2)) #694)
-#870 := (not #699)
-#871 := (or #870 #864)
-#674 := (= #193 #196)
-#680 := (or #200 #674)
-#685 := (forall (vars (?x59 T2)) #680)
-#879 := (not #685)
-#880 := (or #879 #871)
-#889 := (or #888 #880)
-#668 := (or #111 #184)
-#671 := (forall (vars (?x58 T2)) #668)
-#897 := (not #671)
-#898 := (or #897 #889)
-#906 := (not #183)
-#907 := (or #906 #898)
-#915 := (or #180 #907)
-#923 := (or #135 #915)
-#554 := (= 0::int #161)
-#512 := (+ #88 #146)
-#539 := (<= #149 #512)
-#536 := (and #89 #147)
-#545 := (not #536)
-#546 := (or #545 #539)
-#551 := (forall (vars (?x53 T2) (?x54 T2)) #546)
-#574 := (not #551)
-#575 := (or #574 #554)
-#580 := (and #551 #575)
-#515 := (= #149 #512)
-#518 := (and #150 #515)
-#521 := (exists (vars (?x50 T2)) #518)
-#527 := (not #148)
-#528 := (or #527 #521)
-#533 := (forall (vars (?x49 T2)) #528)
-#586 := (not #533)
-#587 := (or #586 #580)
-#592 := (and #533 #587)
-#606 := (or #605 #592)
-#615 := (or #614 #606)
-#624 := (or #623 #615)
-#633 := (or #632 #624)
-#652 := (or #134 #633)
-#939 := (and #652 #923)
-#464 := (+ #88 #107)
-#482 := (= #115 #464)
-#485 := (and #111 #482)
-#488 := (and #126 #485)
-#491 := (exists (vars (?x47 T2)) #488)
-#497 := (not #125)
-#498 := (or #497 #491)
-#503 := (forall (vars (?x46 T2)) #498)
-#952 := (not #503)
-#953 := (or #952 #939)
-#467 := (<= #115 #464)
-#461 := (and #89 #111)
-#473 := (not #461)
-#474 := (or #473 #467)
-#479 := (forall (vars (?x44 T2) (?x45 T2)) #474)
-#961 := (not #479)
-#962 := (or #961 #953)
-#455 := (or #454 #116)
-#458 := (forall (vars (?x42 T2) (?x43 T2)) #455)
-#970 := (not #458)
-#971 := (or #970 #962)
-#979 := (not #109)
-#980 := (or #979 #971)
-#451 := (= 0::int #105)
-#988 := (not #451)
-#989 := (or #988 #980)
-#444 := (not #96)
-#445 := (or #444 #101)
-#448 := (forall (vars (?x37 T2)) #445)
-#1008 := (not #448)
-#1009 := (or #1008 #989)
-#1014 := (and #448 #1009)
-#437 := (not #90)
-#438 := (or #437 #92)
-#441 := (forall (vars (?x33 T2) (?x34 T2)) #438)
-#1020 := (not #441)
-#1021 := (or #1020 #1014)
-#1026 := (and #441 #1021)
-#431 := (or #430 #84)
-#434 := (forall (vars (?x29 T2) (?x30 T2)) #431)
-#1032 := (not #434)
-#1033 := (or #1032 #1026)
-#1038 := (and #434 #1033)
-#1044 := (not #80)
-#1045 := (or #1044 #1038)
-#1050 := (and #80 #1045)
-#427 := (= 0::int #77)
-#1056 := (not #427)
-#1057 := (or #1056 #1050)
-#1062 := (and #427 #1057)
-#1076 := (or #1075 #1062)
-#1085 := (or #1084 #1076)
-#399 := (= 0::int #66)
-#405 := (or #70 #399)
-#410 := (forall (vars (?x24 T2)) #405)
-#1093 := (not #410)
-#1094 := (or #1093 #1085)
-#1110 := (not #1094)
-#1718 := (iff #1110 #1717)
-#1715 := (iff #1094 #1712)
-#1703 := (or #1075 #1689)
-#1706 := (or #1084 #1703)
-#1709 := (or #1700 #1706)
-#1713 := (iff #1709 #1712)
-#1714 := [rewrite]: #1713
-#1710 := (iff #1094 #1709)
-#1707 := (iff #1085 #1706)
-#1704 := (iff #1076 #1703)
-#1690 := (iff #1062 #1689)
-#1687 := (iff #1057 #1686)
-#1684 := (iff #1050 #1683)
-#1681 := (iff #1045 #1680)
-#1678 := (iff #1038 #1677)
-#1675 := (iff #1033 #1674)
-#1672 := (iff #1026 #1671)
-#1669 := (iff #1021 #1668)
-#1666 := (iff #1014 #1665)
-#1663 := (iff #1009 #1660)
-#1642 := (or #1248 #1588)
-#1645 := (or #1611 #1642)
-#1648 := (or #1622 #1645)
-#1651 := (or #1631 #1648)
-#1654 := (or #1636 #1651)
-#1657 := (or #1639 #1654)
-#1661 := (iff #1657 #1660)
-#1662 := [rewrite]: #1661
-#1658 := (iff #1009 #1657)
-#1655 := (iff #989 #1654)
-#1652 := (iff #980 #1651)
-#1649 := (iff #971 #1648)
-#1646 := (iff #962 #1645)
-#1643 := (iff #953 #1642)
-#1589 := (iff #939 #1588)
-#1586 := (iff #923 #1583)
-#1562 := (or #1378 #1514)
-#1565 := (or #1531 #1562)
-#1568 := (or #888 #1565)
-#1571 := (or #1544 #1568)
-#1574 := (or #1548 #1571)
-#1577 := (or #180 #1574)
-#1580 := (or #1559 #1577)
-#1584 := (iff #1580 #1583)
-#1585 := [rewrite]: #1584
-#1581 := (iff #923 #1580)
-#1578 := (iff #915 #1577)
-#1575 := (iff #907 #1574)
-#1572 := (iff #898 #1571)
-#1569 := (iff #889 #1568)
-#1566 := (iff #880 #1565)
-#1563 := (iff #871 #1562)
-#1515 := (iff #864 #1514)
-#1512 := (iff #859 #1511)
-#1509 := (iff #852 #1508)
-#1506 := (iff #847 #1505)
-#1503 := (iff #829 #1502)
-#1500 := (iff #824 #1499)
-#1497 := (iff #817 #1496)
-#1494 := (iff #812 #1493)
-#1491 := (iff #805 #1490)
-#1488 := (iff #800 #1487)
-#1485 := (iff #793 #1484)
-#1482 := (iff #788 #1481)
-#1479 := (iff #765 #1478)
-#1476 := (iff #760 #1475)
-#1473 := (iff #753 #1472)
-#1470 := (iff #750 #1467)
-#1461 := (and #206 #1455)
-#1464 := (and #1458 #1461)
-#1468 := (iff #1464 #1467)
-#1469 := [rewrite]: #1468
-#1465 := (iff #750 #1464)
-#1462 := (iff #747 #1461)
-#1456 := (iff #744 #1455)
-#1457 := [rewrite]: #1456
-#1463 := [monotonicity #1457]: #1462
-#1459 := (iff #227 #1458)
-#1460 := [rewrite]: #1459
-#1466 := [monotonicity #1460 #1463]: #1465
-#1471 := [trans #1466 #1469]: #1470
-#1474 := [quant-intro #1471]: #1473
-#1453 := (iff #759 #1452)
-#1450 := (iff #226 #1449)
-#1447 := (iff #225 #1446)
-#1448 := [rewrite]: #1447
-#1451 := [monotonicity #1448]: #1450
-#1454 := [monotonicity #1451]: #1453
-#1477 := [monotonicity #1454 #1474]: #1476
-#1480 := [quant-intro #1477]: #1479
-#1442 := (iff #787 #1441)
-#1439 := (iff #741 #1438)
-#1436 := (iff #736 #1435)
-#1432 := (iff #729 #1431)
-#1434 := [rewrite]: #1432
-#1429 := (iff #735 #1428)
-#1426 := (iff #723 #1423)
-#1420 := (and #1145 #206)
-#1424 := (iff #1420 #1423)
-#1425 := [rewrite]: #1424
-#1421 := (iff #723 #1420)
-#1146 := (iff #89 #1145)
-#1147 := [rewrite]: #1146
-#1422 := [monotonicity #1147]: #1421
-#1427 := [trans #1422 #1425]: #1426
-#1430 := [monotonicity #1427]: #1429
-#1437 := [monotonicity #1430 #1434]: #1436
-#1440 := [quant-intro #1437]: #1439
-#1443 := [monotonicity #1440]: #1442
-#1483 := [monotonicity #1443 #1480]: #1482
-#1486 := [monotonicity #1440 #1483]: #1485
-#1418 := (iff #799 #1417)
-#1415 := (iff #720 #1414)
-#1412 := (iff #717 #1411)
-#1409 := (iff #217 #1406)
-#1410 := [rewrite]: #1409
-#1413 := [monotonicity #1410]: #1412
-#1416 := [quant-intro #1413]: #1415
-#1419 := [monotonicity #1416]: #1418
-#1489 := [monotonicity #1419 #1486]: #1488
-#1492 := [monotonicity #1416 #1489]: #1491
-#1404 := (iff #811 #1403)
-#1401 := (iff #212 #1400)
-#1398 := (iff #211 #1397)
+#78 := (and #69 #77)
+#79 := (and true #78)
+#268 := (implies #79 #267)
+#269 := (not #268)
+#1489 := (iff #269 #1486)
+#721 := (+ #91 #199)
+#739 := (= #226 #721)
+#742 := (and #216 #739)
+#745 := (and #237 #742)
+#748 := (exists (vars (?x76 T2)) #745)
+#754 := (not #236)
+#755 := (or #754 #748)
+#760 := (forall (vars (?x75 T2)) #755)
+#724 := (<= #226 #721)
+#718 := (and #92 #216)
+#730 := (not #718)
+#731 := (or #730 #724)
+#736 := (forall (vars (?x71 T2) (?x72 T2)) #731)
+#766 := (not #736)
+#767 := (or #766 #760)
+#772 := (and #736 #767)
+#712 := (or #711 #227)
+#715 := (forall (vars (?x67 T2) (?x68 T2)) #712)
+#778 := (not #715)
+#779 := (or #778 #772)
+#784 := (and #715 #779)
+#790 := (not #222)
+#791 := (or #790 #784)
+#796 := (and #222 #791)
+#708 := (= 0::int #219)
+#802 := (not #708)
+#803 := (or #802 #796)
+#808 := (and #708 #803)
+#815 := (or #814 #808)
+#820 := (and #705 #815)
+#826 := (not #215)
+#827 := (or #826 #820)
+#832 := (and #215 #827)
+#664 := (or #198 #658)
+#669 := (forall (vars (?x60 T2)) #664)
+#644 := (= #196 #199)
+#650 := (or #203 #644)
+#655 := (forall (vars (?x59 T2)) #650)
+#672 := (and #655 #669)
+#675 := (and #192 #672)
+#638 := (or #114 #187)
+#641 := (forall (vars (?x58 T2)) #638)
+#678 := (and #641 #675)
+#681 := (and #186 #678)
+#684 := (and #184 #681)
+#687 := (and #143 #684)
+#838 := (not #687)
+#839 := (or #838 #832)
+#602 := (= 0::int #175)
+#560 := (+ #91 #160)
+#587 := (<= #163 #560)
+#584 := (and #92 #161)
+#593 := (not #584)
+#594 := (or #593 #587)
+#599 := (forall (vars (?x53 T2) (?x54 T2)) #594)
+#608 := (not #599)
+#609 := (or #608 #602)
+#614 := (and #599 #609)
+#563 := (= #163 #560)
+#566 := (and #164 #563)
+#569 := (exists (vars (?x50 T2)) #566)
+#575 := (not #162)
+#576 := (or #575 #569)
+#581 := (forall (vars (?x49 T2)) #576)
+#620 := (not #581)
+#621 := (or #620 #614)
+#626 := (and #581 #621)
+#539 := (and #154 #533)
+#544 := (and #149 #539)
+#547 := (and #530 #544)
+#550 := (and #144 #547)
+#632 := (not #550)
+#633 := (or #632 #626)
+#844 := (and #633 #839)
+#466 := (+ #91 #110)
+#484 := (= #118 #466)
+#487 := (and #114 #484)
+#490 := (and #129 #487)
+#493 := (exists (vars (?x47 T2)) #490)
+#499 := (not #128)
+#500 := (or #499 #493)
+#505 := (forall (vars (?x46 T2)) #500)
+#469 := (<= #118 #466)
+#463 := (and #92 #114)
+#475 := (not #463)
+#476 := (or #475 #469)
+#481 := (forall (vars (?x44 T2) (?x45 T2)) #476)
+#508 := (and #481 #505)
+#457 := (or #456 #119)
+#460 := (forall (vars (?x42 T2) (?x43 T2)) #457)
+#511 := (and #460 #508)
+#514 := (and #112 #511)
+#453 := (= 0::int #108)
+#517 := (and #453 #514)
+#446 := (not #99)
+#447 := (or #446 #104)
+#450 := (forall (vars (?x37 T2)) #447)
+#527 := (and #450 #517)
+#850 := (not #527)
+#851 := (or #850 #844)
+#856 := (and #450 #851)
+#439 := (not #93)
+#440 := (or #439 #95)
+#443 := (forall (vars (?x33 T2) (?x34 T2)) #440)
+#862 := (not #443)
+#863 := (or #862 #856)
+#868 := (and #443 #863)
+#433 := (or #432 #87)
+#436 := (forall (vars (?x29 T2) (?x30 T2)) #433)
+#874 := (not #436)
+#875 := (or #874 #868)
+#880 := (and #436 #875)
+#886 := (not #83)
+#887 := (or #886 #880)
+#892 := (and #83 #887)
+#429 := (= 0::int #80)
+#898 := (not #429)
+#899 := (or #898 #892)
+#904 := (and #429 #899)
+#414 := (and #76 #408)
+#383 := (= 0::int #66)
+#389 := (or #70 #383)
+#394 := (forall (vars (?x24 T2)) #389)
+#419 := (and #394 #414)
+#910 := (not #419)
+#911 := (or #910 #904)
+#916 := (not #911)
+#1487 := (iff #916 #1486)
+#1484 := (iff #911 #1483)
+#1481 := (iff #904 #1480)
+#1478 := (iff #899 #1477)
+#1475 := (iff #892 #1474)
+#1472 := (iff #887 #1471)
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+#1466 := (iff #875 #1465)
+#1463 := (iff #868 #1462)
+#1460 := (iff #863 #1459)
+#1457 := (iff #856 #1456)
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+#1451 := (iff #844 #1450)
+#1448 := (iff #839 #1447)
+#1445 := (iff #832 #1444)
+#1442 := (iff #827 #1441)
+#1439 := (iff #820 #1438)
+#1436 := (iff #815 #1435)
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+#1430 := (iff #803 #1429)
+#1427 := (iff #796 #1426)
+#1424 := (iff #791 #1423)
+#1421 := (iff #784 #1420)
+#1418 := (iff #779 #1417)
+#1415 := (iff #772 #1414)
+#1412 := (iff #767 #1411)
+#1409 := (iff #760 #1408)
+#1406 := (iff #755 #1405)
+#1403 := (iff #748 #1402)
+#1400 := (iff #745 #1397)
+#1391 := (and #216 #1385)
+#1394 := (and #1388 #1391)
+#1398 := (iff #1394 #1397)
 #1399 := [rewrite]: #1398
-#1402 := [quant-intro #1399]: #1401
-#1405 := [monotonicity #1402]: #1404
-#1495 := [monotonicity #1405 #1492]: #1494
-#1498 := [monotonicity #1402 #1495]: #1497
-#1395 := (iff #823 #1394)
-#1392 := (iff #713 #210)
-#1393 := [rewrite]: #1392
-#1396 := [monotonicity #1393]: #1395
-#1501 := [monotonicity #1396 #1498]: #1500
-#1504 := [monotonicity #1393 #1501]: #1503
-#1507 := [monotonicity #1504]: #1506
-#1510 := [monotonicity #1507]: #1509
-#1390 := (iff #858 #1389)
-#1387 := (iff #205 #1386)
-#1384 := (iff #204 #1381)
-#1385 := [rewrite]: #1384
-#1388 := [quant-intro #1385]: #1387
-#1391 := [monotonicity #1388]: #1390
-#1513 := [monotonicity #1391 #1510]: #1512
-#1516 := [monotonicity #1388 #1513]: #1515
-#1379 := (iff #870 #1378)
-#1376 := (iff #699 #1375)
-#1373 := (iff #694 #1370)
-#1367 := (or #1364 #688)
-#1371 := (iff #1367 #1370)
-#1372 := [rewrite]: #1371
-#1368 := (iff #694 #1367)
-#1365 := (iff #195 #1364)
-#1362 := (iff #194 #1361)
-#1363 := [rewrite]: #1362
-#1355 := (iff #192 #1354)
-#1356 := [rewrite]: #1355
-#1366 := [monotonicity #1356 #1363]: #1365
-#1369 := [monotonicity #1366]: #1368
-#1374 := [trans #1369 #1372]: #1373
-#1377 := [quant-intro #1374]: #1376
-#1380 := [monotonicity #1377]: #1379
-#1564 := [monotonicity #1380 #1516]: #1563
-#1532 := (iff #879 #1531)
-#1529 := (iff #685 #1528)
-#1526 := (iff #680 #1525)
-#1523 := (iff #674 #1522)
-#1524 := [rewrite]: #1523
-#1518 := (iff #200 #1517)
-#1519 := [monotonicity #1366]: #1518
-#1527 := [monotonicity #1519 #1524]: #1526
-#1530 := [quant-intro #1527]: #1529
-#1533 := [monotonicity #1530]: #1532
-#1567 := [monotonicity #1533 #1564]: #1566
-#1570 := [monotonicity #1567]: #1569
-#1545 := (iff #897 #1544)
-#1542 := (iff #671 #1541)
-#1539 := (iff #668 #1538)
-#1536 := (iff #184 #1534)
-#1537 := [rewrite]: #1536
-#1540 := [monotonicity #1537]: #1539
-#1543 := [quant-intro #1540]: #1542
-#1546 := [monotonicity #1543]: #1545
-#1573 := [monotonicity #1546 #1570]: #1572
-#1557 := (iff #906 #1548)
-#1549 := (not #1548)
-#1552 := (not #1549)
-#1555 := (iff #1552 #1548)
-#1556 := [rewrite]: #1555
-#1553 := (iff #906 #1552)
-#1550 := (iff #183 #1549)
-#1551 := [rewrite]: #1550
-#1554 := [monotonicity #1551]: #1553
-#1558 := [trans #1554 #1556]: #1557
-#1576 := [monotonicity #1558 #1573]: #1575
-#1579 := [monotonicity #1576]: #1578
-#1560 := (iff #135 #1559)
-#1329 := (iff #134 #1328)
-#1326 := (iff #133 #1325)
-#1210 := (iff #124 #1209)
-#1211 := [rewrite]: #1210
-#1327 := [monotonicity #1211]: #1326
-#1330 := [quant-intro #1327]: #1329
-#1561 := [monotonicity #1330]: #1560
-#1582 := [monotonicity #1561 #1579]: #1581
-#1587 := [trans #1582 #1585]: #1586
-#1349 := (iff #652 #1346)
-#1331 := (or #605 #1322)
-#1334 := (or #614 #1331)
-#1337 := (or #623 #1334)
-#1340 := (or #632 #1337)
-#1343 := (or #1328 #1340)
-#1347 := (iff #1343 #1346)
-#1348 := [rewrite]: #1347
-#1344 := (iff #652 #1343)
-#1341 := (iff #633 #1340)
-#1338 := (iff #624 #1337)
-#1335 := (iff #615 #1334)
-#1332 := (iff #606 #1331)
-#1323 := (iff #592 #1322)
-#1320 := (iff #587 #1319)
-#1317 := (iff #580 #1316)
-#1314 := (iff #575 #1311)
-#1308 := (or #1303 #162)
-#1312 := (iff #1308 #1311)
-#1313 := [rewrite]: #1312
-#1309 := (iff #575 #1308)
-#1306 := (iff #554 #162)
-#1307 := [rewrite]: #1306
-#1304 := (iff #574 #1303)
-#1301 := (iff #551 #1300)
-#1298 := (iff #546 #1297)
-#1295 := (iff #539 #1294)
-#1296 := [rewrite]: #1295
-#1292 := (iff #545 #1291)
-#1289 := (iff #536 #1288)
-#1255 := (iff #147 #1254)
-#1256 := [rewrite]: #1255
-#1290 := [monotonicity #1147 #1256]: #1289
-#1293 := [monotonicity #1290]: #1292
-#1299 := [monotonicity #1293 #1296]: #1298
-#1302 := [quant-intro #1299]: #1301
-#1305 := [monotonicity #1302]: #1304
-#1310 := [monotonicity #1305 #1307]: #1309
-#1315 := [trans #1310 #1313]: #1314
-#1318 := [monotonicity #1302 #1315]: #1317
-#1286 := (iff #586 #1285)
-#1283 := (iff #533 #1282)
-#1280 := (iff #528 #1279)
-#1277 := (iff #521 #1276)
-#1274 := (iff #518 #1273)
-#1270 := (iff #515 #1269)
-#1272 := [rewrite]: #1270
-#1267 := (iff #150 #1266)
-#1268 := [rewrite]: #1267
-#1275 := [monotonicity #1268 #1272]: #1274
-#1278 := [quant-intro #1275]: #1277
-#1261 := (iff #527 #1260)
-#1258 := (iff #148 #1257)
-#1259 := [monotonicity #1256]: #1258
-#1262 := [monotonicity #1259]: #1261
-#1281 := [monotonicity #1262 #1278]: #1280
-#1284 := [quant-intro #1281]: #1283
-#1287 := [monotonicity #1284]: #1286
-#1321 := [monotonicity #1287 #1318]: #1320
-#1324 := [monotonicity #1284 #1321]: #1323
-#1333 := [monotonicity #1324]: #1332
-#1336 := [monotonicity #1333]: #1335
-#1339 := [monotonicity #1336]: #1338
-#1342 := [monotonicity #1339]: #1341
-#1345 := [monotonicity #1330 #1342]: #1344
-#1350 := [trans #1345 #1348]: #1349
-#1590 := [monotonicity #1350 #1587]: #1589
-#1249 := (iff #952 #1248)
-#1246 := (iff #503 #1245)
-#1243 := (iff #498 #1242)
-#1240 := (iff #491 #1239)
-#1237 := (iff #488 #1234)
-#1228 := (and #111 #1218)
-#1231 := (and #1225 #1228)
-#1235 := (iff #1231 #1234)
-#1236 := [rewrite]: #1235
-#1232 := (iff #488 #1231)
-#1229 := (iff #485 #1228)
-#1219 := (iff #482 #1218)
-#1223 := [rewrite]: #1219
-#1230 := [monotonicity #1223]: #1229
-#1226 := (iff #126 #1225)
-#1227 := [rewrite]: #1226
-#1233 := [monotonicity #1227 #1230]: #1232
-#1238 := [trans #1233 #1236]: #1237
-#1241 := [quant-intro #1238]: #1240
-#1216 := (iff #497 #1215)
-#1213 := (iff #125 #1212)
-#1214 := [monotonicity #1211]: #1213
-#1217 := [monotonicity #1214]: #1216
-#1244 := [monotonicity #1217 #1241]: #1243
-#1247 := [quant-intro #1244]: #1246
-#1250 := [monotonicity #1247]: #1249
-#1644 := [monotonicity #1250 #1590]: #1643
-#1612 := (iff #961 #1611)
-#1609 := (iff #479 #1608)
-#1606 := (iff #474 #1605)
-#1603 := (iff #467 #1602)
-#1604 := [rewrite]: #1603
-#1600 := (iff #473 #1599)
-#1597 := (iff #461 #1594)
-#1591 := (and #1145 #111)
-#1595 := (iff #1591 #1594)
-#1596 := [rewrite]: #1595
-#1592 := (iff #461 #1591)
-#1593 := [monotonicity #1147]: #1592
-#1598 := [trans #1593 #1596]: #1597
-#1601 := [monotonicity #1598]: #1600
-#1607 := [monotonicity #1601 #1604]: #1606
-#1610 := [quant-intro #1607]: #1609
-#1613 := [monotonicity #1610]: #1612
-#1647 := [monotonicity #1613 #1644]: #1646
-#1623 := (iff #970 #1622)
-#1620 := (iff #458 #1619)
-#1617 := (iff #455 #1616)
-#1614 := (iff #116 #1224)
-#1615 := [rewrite]: #1614
-#1618 := [monotonicity #1615]: #1617
-#1621 := [quant-intro #1618]: #1620
-#1624 := [monotonicity #1621]: #1623
-#1650 := [monotonicity #1624 #1647]: #1649
-#1632 := (iff #979 #1631)
-#1629 := (iff #109 #1628)
-#1626 := (iff #108 #1625)
-#1627 := [rewrite]: #1626
-#1630 := [quant-intro #1627]: #1629
-#1633 := [monotonicity #1630]: #1632
-#1653 := [monotonicity #1633 #1650]: #1652
-#1637 := (iff #988 #1636)
-#1634 := (iff #451 #106)
-#1635 := [rewrite]: #1634
-#1638 := [monotonicity #1635]: #1637
-#1656 := [monotonicity #1638 #1653]: #1655
-#1640 := (iff #1008 #1639)
-#1204 := (iff #448 #1203)
-#1201 := (iff #445 #1200)
-#1198 := (iff #101 #1197)
-#1195 := (iff #100 #1192)
-#1186 := (and #74 #1180)
-#1189 := (and #1183 #1186)
-#1193 := (iff #1189 #1192)
-#1194 := [rewrite]: #1193
-#1190 := (iff #100 #1189)
-#1187 := (iff #99 #1186)
-#1181 := (iff #98 #1180)
-#1182 := [rewrite]: #1181
-#1188 := [monotonicity #1182]: #1187
-#1184 := (iff #97 #1183)
-#1185 := [rewrite]: #1184
-#1191 := [monotonicity #1185 #1188]: #1190
-#1196 := [trans #1191 #1194]: #1195
-#1199 := [quant-intro #1196]: #1198
-#1178 := (iff #444 #1177)
-#1175 := (iff #96 #1174)
-#1172 := (iff #95 #1171)
-#1173 := [rewrite]: #1172
-#1176 := [monotonicity #1173]: #1175
-#1179 := [monotonicity #1176]: #1178
-#1202 := [monotonicity #1179 #1199]: #1201
-#1205 := [quant-intro #1202]: #1204
-#1641 := [monotonicity #1205]: #1640
-#1659 := [monotonicity #1641 #1656]: #1658
-#1664 := [trans #1659 #1662]: #1663
-#1667 := [monotonicity #1205 #1664]: #1666
-#1166 := (iff #1020 #1165)
-#1163 := (iff #441 #1162)
-#1160 := (iff #438 #1159)
-#1154 := (iff #92 #1155)
-#1156 := [rewrite]: #1154
-#1152 := (iff #437 #1151)
-#1149 := (iff #90 #1148)
-#1150 := [monotonicity #1147]: #1149
-#1153 := [monotonicity #1150]: #1152
-#1161 := [monotonicity #1153 #1156]: #1160
-#1164 := [quant-intro #1161]: #1163
-#1167 := [monotonicity #1164]: #1166
-#1670 := [monotonicity #1167 #1667]: #1669
-#1673 := [monotonicity #1164 #1670]: #1672
-#1140 := (iff #1032 #1139)
-#1137 := (iff #434 #1136)
-#1134 := (iff #431 #1133)
-#1128 := (iff #84 #1129)
-#1132 := [rewrite]: #1128
-#1135 := [monotonicity #1132]: #1134
-#1138 := [quant-intro #1135]: #1137
-#1141 := [monotonicity #1138]: #1140
-#1676 := [monotonicity #1141 #1673]: #1675
-#1679 := [monotonicity #1138 #1676]: #1678
-#1125 := (iff #1044 #1124)
-#1122 := (iff #80 #1121)
-#1118 := (iff #79 #1120)
-#1119 := [rewrite]: #1118
-#1123 := [quant-intro #1119]: #1122
-#1126 := [monotonicity #1123]: #1125
-#1682 := [monotonicity #1126 #1679]: #1681
-#1685 := [monotonicity #1123 #1682]: #1684
-#1116 := (iff #1056 #1115)
-#1113 := (iff #427 #78)
-#1114 := [rewrite]: #1113
-#1117 := [monotonicity #1114]: #1116
-#1688 := [monotonicity #1117 #1685]: #1687
-#1691 := [monotonicity #1114 #1688]: #1690
-#1705 := [monotonicity #1691]: #1704
-#1708 := [monotonicity #1705]: #1707
-#1701 := (iff #1093 #1700)
-#1698 := (iff #410 #1697)
-#1695 := (iff #405 #1694)
-#1692 := (iff #399 #67)
-#1693 := [rewrite]: #1692
-#1696 := [monotonicity #1693]: #1695
-#1699 := [quant-intro #1696]: #1698
-#1702 := [monotonicity #1699]: #1701
-#1711 := [monotonicity #1702 #1708]: #1710
-#1716 := [trans #1711 #1714]: #1715
-#1719 := [monotonicity #1716]: #1718
-#1111 := (iff #285 #1110)
-#1108 := (iff #284 #1094)
-#1099 := (implies true #1094)
-#1102 := (iff #1099 #1094)
+#1395 := (iff #745 #1394)
+#1392 := (iff #742 #1391)
+#1386 := (iff #739 #1385)
+#1387 := [rewrite]: #1386
+#1393 := [monotonicity #1387]: #1392
+#1389 := (iff #237 #1388)
+#1390 := [rewrite]: #1389
+#1396 := [monotonicity #1390 #1393]: #1395
+#1401 := [trans #1396 #1399]: #1400
+#1404 := [quant-intro #1401]: #1403
+#1383 := (iff #754 #1382)
+#1380 := (iff #236 #1379)
+#1377 := (iff #235 #1376)
+#1378 := [rewrite]: #1377
+#1381 := [monotonicity #1378]: #1380
+#1384 := [monotonicity #1381]: #1383
+#1407 := [monotonicity #1384 #1404]: #1406
+#1410 := [quant-intro #1407]: #1409
+#1372 := (iff #766 #1371)
+#1369 := (iff #736 #1368)
+#1366 := (iff #731 #1365)
+#1362 := (iff #724 #1361)
+#1364 := [rewrite]: #1362
+#1359 := (iff #730 #1358)
+#1356 := (iff #718 #1353)
+#1350 := (and #970 #216)
+#1354 := (iff #1350 #1353)
+#1355 := [rewrite]: #1354
+#1351 := (iff #718 #1350)
+#971 := (iff #92 #970)
+#972 := [rewrite]: #971
+#1352 := [monotonicity #972]: #1351
+#1357 := [trans #1352 #1355]: #1356
+#1360 := [monotonicity #1357]: #1359
+#1367 := [monotonicity #1360 #1364]: #1366
+#1370 := [quant-intro #1367]: #1369
+#1373 := [monotonicity #1370]: #1372
+#1413 := [monotonicity #1373 #1410]: #1412
+#1416 := [monotonicity #1370 #1413]: #1415
+#1348 := (iff #778 #1347)
+#1345 := (iff #715 #1344)
+#1342 := (iff #712 #1341)
+#1339 := (iff #227 #1336)
+#1340 := [rewrite]: #1339
+#1343 := [monotonicity #1340]: #1342
+#1346 := [quant-intro #1343]: #1345
+#1349 := [monotonicity #1346]: #1348
+#1419 := [monotonicity #1349 #1416]: #1418
+#1422 := [monotonicity #1346 #1419]: #1421
+#1334 := (iff #790 #1333)
+#1331 := (iff #222 #1330)
+#1328 := (iff #221 #1327)
+#1329 := [rewrite]: #1328
+#1332 := [quant-intro #1329]: #1331
+#1335 := [monotonicity #1332]: #1334
+#1425 := [monotonicity #1335 #1422]: #1424
+#1428 := [monotonicity #1332 #1425]: #1427
+#1325 := (iff #802 #1324)
+#1322 := (iff #708 #220)
+#1323 := [rewrite]: #1322
+#1326 := [monotonicity #1323]: #1325
+#1431 := [monotonicity #1326 #1428]: #1430
+#1434 := [monotonicity #1323 #1431]: #1433
+#1437 := [monotonicity #1434]: #1436
+#1440 := [monotonicity #1437]: #1439
+#1320 := (iff #826 #1319)
+#1317 := (iff #215 #1316)
+#1314 := (iff #214 #1312)
+#1315 := [rewrite]: #1314
+#1318 := [quant-intro #1315]: #1317
+#1321 := [monotonicity #1318]: #1320
+#1443 := [monotonicity #1321 #1440]: #1442
+#1446 := [monotonicity #1318 #1443]: #1445
+#1310 := (iff #838 #1309)
+#1307 := (iff #687 #1304)
+#1286 := (and #1257 #1268)
+#1289 := (and #192 #1286)
+#1292 := (and #1278 #1289)
+#1295 := (and #1283 #1292)
+#1298 := (and #184 #1295)
+#1301 := (and #1135 #1298)
+#1305 := (iff #1301 #1304)
+#1306 := [rewrite]: #1305
+#1302 := (iff #687 #1301)
+#1299 := (iff #684 #1298)
+#1296 := (iff #681 #1295)
+#1293 := (iff #678 #1292)
+#1290 := (iff #675 #1289)
+#1287 := (iff #672 #1286)
+#1269 := (iff #669 #1268)
+#1266 := (iff #664 #1263)
+#1260 := (or #1242 #658)
+#1264 := (iff #1260 #1263)
+#1265 := [rewrite]: #1264
+#1261 := (iff #664 #1260)
+#1243 := (iff #198 #1242)
+#1240 := (iff #197 #1239)
+#1241 := [rewrite]: #1240
+#1233 := (iff #195 #1232)
+#1234 := [rewrite]: #1233
+#1244 := [monotonicity #1234 #1241]: #1243
+#1262 := [monotonicity #1244]: #1261
+#1267 := [trans #1262 #1265]: #1266
+#1270 := [quant-intro #1267]: #1269
+#1258 := (iff #655 #1257)
+#1255 := (iff #650 #1254)
+#1252 := (iff #644 #1251)
+#1253 := [rewrite]: #1252
+#1246 := (iff #203 #1245)
+#1247 := [monotonicity #1244]: #1246
+#1256 := [monotonicity #1247 #1253]: #1255
+#1259 := [quant-intro #1256]: #1258
+#1288 := [monotonicity #1259 #1270]: #1287
+#1291 := [monotonicity #1288]: #1290
+#1279 := (iff #641 #1278)
+#1276 := (iff #638 #1275)
+#1273 := (iff #187 #1271)
+#1274 := [rewrite]: #1273
+#1277 := [monotonicity #1274]: #1276
+#1280 := [quant-intro #1277]: #1279
+#1294 := [monotonicity #1280 #1291]: #1293
+#1284 := (iff #186 #1283)
+#1285 := [rewrite]: #1284
+#1297 := [monotonicity #1285 #1294]: #1296
+#1300 := [monotonicity #1297]: #1299
+#1136 := (iff #143 #1135)
+#1133 := (iff #142 #1132)
+#1058 := (iff #127 #1057)
+#1059 := [rewrite]: #1058
+#1134 := [monotonicity #1059]: #1133
+#1137 := [quant-intro #1134]: #1136
+#1303 := [monotonicity #1137 #1300]: #1302
+#1308 := [trans #1303 #1306]: #1307
+#1311 := [monotonicity #1308]: #1310
+#1449 := [monotonicity #1311 #1446]: #1448
+#1227 := (iff #633 #1226)
+#1224 := (iff #626 #1223)
+#1221 := (iff #621 #1220)
+#1218 := (iff #614 #1217)
+#1215 := (iff #609 #1212)
+#1209 := (or #1204 #176)
+#1213 := (iff #1209 #1212)
+#1214 := [rewrite]: #1213
+#1210 := (iff #609 #1209)
+#1207 := (iff #602 #176)
+#1208 := [rewrite]: #1207
+#1205 := (iff #608 #1204)
+#1202 := (iff #599 #1201)
+#1199 := (iff #594 #1198)
+#1196 := (iff #587 #1195)
+#1197 := [rewrite]: #1196
+#1193 := (iff #593 #1192)
+#1190 := (iff #584 #1189)
+#1156 := (iff #161 #1155)
+#1157 := [rewrite]: #1156
+#1191 := [monotonicity #972 #1157]: #1190
+#1194 := [monotonicity #1191]: #1193
+#1200 := [monotonicity #1194 #1197]: #1199
+#1203 := [quant-intro #1200]: #1202
+#1206 := [monotonicity #1203]: #1205
+#1211 := [monotonicity #1206 #1208]: #1210
+#1216 := [trans #1211 #1214]: #1215
+#1219 := [monotonicity #1203 #1216]: #1218
+#1187 := (iff #620 #1186)
+#1184 := (iff #581 #1183)
+#1181 := (iff #576 #1180)
+#1178 := (iff #569 #1177)
+#1175 := (iff #566 #1174)
+#1171 := (iff #563 #1170)
+#1173 := [rewrite]: #1171
+#1168 := (iff #164 #1167)
+#1169 := [rewrite]: #1168
+#1176 := [monotonicity #1169 #1173]: #1175
+#1179 := [quant-intro #1176]: #1178
+#1162 := (iff #575 #1161)
+#1159 := (iff #162 #1158)
+#1160 := [monotonicity #1157]: #1159
+#1163 := [monotonicity #1160]: #1162
+#1182 := [monotonicity #1163 #1179]: #1181
+#1185 := [quant-intro #1182]: #1184
+#1188 := [monotonicity #1185]: #1187
+#1222 := [monotonicity #1188 #1219]: #1221
+#1225 := [monotonicity #1185 #1222]: #1224
+#1150 := (iff #632 #1149)
+#1147 := (iff #550 #1144)
+#1141 := (and #1138 #547)
+#1145 := (iff #1141 #1144)
+#1146 := [rewrite]: #1145
+#1142 := (iff #550 #1141)
+#1139 := (iff #144 #1138)
+#1140 := [monotonicity #1137]: #1139
+#1143 := [monotonicity #1140]: #1142
+#1148 := [trans #1143 #1146]: #1147
+#1151 := [monotonicity #1148]: #1150
+#1228 := [monotonicity #1151 #1225]: #1227
+#1452 := [monotonicity #1228 #1449]: #1451
+#1130 := (iff #850 #1129)
+#1127 := (iff #527 #1124)
+#1109 := (and #1051 #1090)
+#1112 := (and #1098 #1109)
+#1115 := (and #1104 #1112)
+#1118 := (and #109 #1115)
+#1121 := (and #1028 #1118)
+#1125 := (iff #1121 #1124)
+#1126 := [rewrite]: #1125
+#1122 := (iff #527 #1121)
+#1119 := (iff #517 #1118)
+#1116 := (iff #514 #1115)
+#1113 := (iff #511 #1112)
+#1110 := (iff #508 #1109)
+#1091 := (iff #505 #1090)
+#1088 := (iff #500 #1087)
+#1085 := (iff #493 #1084)
+#1082 := (iff #490 #1079)
+#1073 := (and #114 #1066)
+#1076 := (and #1070 #1073)
+#1080 := (iff #1076 #1079)
+#1081 := [rewrite]: #1080
+#1077 := (iff #490 #1076)
+#1074 := (iff #487 #1073)
+#1067 := (iff #484 #1066)
+#1068 := [rewrite]: #1067
+#1075 := [monotonicity #1068]: #1074
+#1071 := (iff #129 #1070)
+#1072 := [rewrite]: #1071
+#1078 := [monotonicity #1072 #1075]: #1077
+#1083 := [trans #1078 #1081]: #1082
+#1086 := [quant-intro #1083]: #1085
+#1064 := (iff #499 #1063)
+#1061 := (iff #128 #1060)
+#1062 := [monotonicity #1059]: #1061
+#1065 := [monotonicity #1062]: #1064
+#1089 := [monotonicity #1065 #1086]: #1088
+#1092 := [quant-intro #1089]: #1091
+#1052 := (iff #481 #1051)
+#1049 := (iff #476 #1048)
+#1042 := (iff #469 #1043)
+#1044 := [rewrite]: #1042
+#1040 := (iff #475 #1039)
+#1037 := (iff #463 #1034)
+#1031 := (and #970 #114)
+#1035 := (iff #1031 #1034)
+#1036 := [rewrite]: #1035
+#1032 := (iff #463 #1031)
+#1033 := [monotonicity #972]: #1032
+#1038 := [trans #1033 #1036]: #1037
+#1041 := [monotonicity #1038]: #1040
+#1050 := [monotonicity #1041 #1044]: #1049
+#1053 := [quant-intro #1050]: #1052
+#1111 := [monotonicity #1053 #1092]: #1110
+#1099 := (iff #460 #1098)
+#1096 := (iff #457 #1095)
+#1093 := (iff #119 #1069)
+#1094 := [rewrite]: #1093
+#1097 := [monotonicity #1094]: #1096
+#1100 := [quant-intro #1097]: #1099
+#1114 := [monotonicity #1100 #1111]: #1113
+#1105 := (iff #112 #1104)
+#1102 := (iff #111 #1101)
 #1103 := [rewrite]: #1102
-#1106 := (iff #284 #1099)
-#1104 := (iff #283 #1094)
-#1100 := (iff #283 #1099)
-#1097 := (iff #282 #1094)
-#1090 := (implies #410 #1085)
-#1095 := (iff #1090 #1094)
-#1096 := [rewrite]: #1095
-#1091 := (iff #282 #1090)
-#1088 := (iff #281 #1085)
-#1081 := (implies #424 #1076)
-#1086 := (iff #1081 #1085)
-#1087 := [rewrite]: #1086
-#1082 := (iff #281 #1081)
-#1079 := (iff #280 #1076)
-#1072 := (implies #76 #1062)
-#1077 := (iff #1072 #1076)
-#1078 := [rewrite]: #1077
-#1073 := (iff #280 #1072)
-#1070 := (iff #279 #1062)
-#1065 := (implies true #1062)
-#1068 := (iff #1065 #1062)
-#1069 := [rewrite]: #1068
-#1066 := (iff #279 #1065)
-#1063 := (iff #278 #1062)
-#1060 := (iff #277 #1057)
-#1053 := (implies #427 #1050)
-#1058 := (iff #1053 #1057)
-#1059 := [rewrite]: #1058
-#1054 := (iff #277 #1053)
-#1051 := (iff #276 #1050)
-#1048 := (iff #275 #1045)
-#1041 := (implies #80 #1038)
-#1046 := (iff #1041 #1045)
-#1047 := [rewrite]: #1046
-#1042 := (iff #275 #1041)
-#1039 := (iff #274 #1038)
-#1036 := (iff #273 #1033)
-#1029 := (implies #434 #1026)
-#1034 := (iff #1029 #1033)
-#1035 := [rewrite]: #1034
-#1030 := (iff #273 #1029)
-#1027 := (iff #272 #1026)
-#1024 := (iff #271 #1021)
-#1017 := (implies #441 #1014)
-#1022 := (iff #1017 #1021)
-#1023 := [rewrite]: #1022
-#1018 := (iff #271 #1017)
-#1015 := (iff #270 #1014)
-#1012 := (iff #269 #1009)
-#1005 := (implies #448 #989)
-#1010 := (iff #1005 #1009)
-#1011 := [rewrite]: #1010
-#1006 := (iff #269 #1005)
-#1003 := (iff #268 #989)
-#994 := (implies true #989)
-#997 := (iff #994 #989)
+#1106 := [quant-intro #1103]: #1105
+#1117 := [monotonicity #1106 #1114]: #1116
+#1107 := (iff #453 #109)
+#1108 := [rewrite]: #1107
+#1120 := [monotonicity #1108 #1117]: #1119
+#1029 := (iff #450 #1028)
+#1026 := (iff #447 #1025)
+#1023 := (iff #104 #1022)
+#1020 := (iff #103 #1017)
+#1011 := (and #74 #1005)
+#1014 := (and #1008 #1011)
+#1018 := (iff #1014 #1017)
+#1019 := [rewrite]: #1018
+#1015 := (iff #103 #1014)
+#1012 := (iff #102 #1011)
+#1006 := (iff #101 #1005)
+#1007 := [rewrite]: #1006
+#1013 := [monotonicity #1007]: #1012
+#1009 := (iff #100 #1008)
+#1010 := [rewrite]: #1009
+#1016 := [monotonicity #1010 #1013]: #1015
+#1021 := [trans #1016 #1019]: #1020
+#1024 := [quant-intro #1021]: #1023
+#1003 := (iff #446 #1002)
+#1000 := (iff #99 #999)
+#997 := (iff #98 #996)
 #998 := [rewrite]: #997
-#1001 := (iff #268 #994)
-#999 := (iff #267 #989)
-#995 := (iff #267 #994)
-#992 := (iff #266 #989)
-#985 := (implies #451 #980)
-#990 := (iff #985 #989)
-#991 := [rewrite]: #990
-#986 := (iff #266 #985)
-#983 := (iff #265 #980)
-#976 := (implies #109 #971)
-#981 := (iff #976 #980)
-#982 := [rewrite]: #981
-#977 := (iff #265 #976)
-#974 := (iff #264 #971)
-#967 := (implies #458 #962)
-#972 := (iff #967 #971)
-#973 := [rewrite]: #972
-#968 := (iff #264 #967)
-#965 := (iff #263 #962)
-#958 := (implies #479 #953)
-#963 := (iff #958 #962)
-#964 := [rewrite]: #963
-#959 := (iff #263 #958)
-#956 := (iff #262 #953)
-#949 := (implies #503 #939)
-#954 := (iff #949 #953)
-#955 := [rewrite]: #954
-#950 := (iff #262 #949)
-#947 := (iff #261 #939)
-#942 := (implies true #939)
-#945 := (iff #942 #939)
-#946 := [rewrite]: #945
-#943 := (iff #261 #942)
-#940 := (iff #260 #939)
-#937 := (iff #259 #923)
-#928 := (implies true #923)
-#931 := (iff #928 #923)
+#1001 := [monotonicity #998]: #1000
+#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
+#1455 := [monotonicity #1131 #1452]: #1454
+#1458 := [monotonicity #1030 #1455]: #1457
+#991 := (iff #862 #990)
+#988 := (iff #443 #987)
+#985 := (iff #440 #984)
+#979 := (iff #95 #980)
+#981 := [rewrite]: #979
+#977 := (iff #439 #976)
+#974 := (iff #93 #973)
+#975 := [monotonicity #972]: #974
+#978 := [monotonicity #975]: #977
+#986 := [monotonicity #978 #981]: #985
+#989 := [quant-intro #986]: #988
+#992 := [monotonicity #989]: #991
+#1461 := [monotonicity #992 #1458]: #1460
+#1464 := [monotonicity #989 #1461]: #1463
+#965 := (iff #874 #964)
+#962 := (iff #436 #961)
+#959 := (iff #433 #958)
+#953 := (iff #87 #954)
+#957 := [rewrite]: #953
+#960 := [monotonicity #957]: #959
+#963 := [quant-intro #960]: #962
+#966 := [monotonicity #963]: #965
+#1467 := [monotonicity #966 #1464]: #1466
+#1470 := [monotonicity #963 #1467]: #1469
+#950 := (iff #886 #949)
+#947 := (iff #83 #946)
+#943 := (iff #82 #945)
+#944 := [rewrite]: #943
+#948 := [quant-intro #944]: #947
+#951 := [monotonicity #948]: #950
+#1473 := [monotonicity #951 #1470]: #1472
+#1476 := [monotonicity #948 #1473]: #1475
+#941 := (iff #898 #940)
+#938 := (iff #429 #81)
+#939 := [rewrite]: #938
+#942 := [monotonicity #939]: #941
+#1479 := [monotonicity #942 #1476]: #1478
+#1482 := [monotonicity #939 #1479]: #1481
+#936 := (iff #910 #935)
+#933 := (iff #419 #930)
+#927 := (and #924 #414)
+#931 := (iff #927 #930)
 #932 := [rewrite]: #931
-#935 := (iff #259 #928)
-#933 := (iff #258 #923)
-#929 := (iff #258 #928)
-#926 := (iff #257 #923)
-#920 := (implies #134 #915)
-#924 := (iff #920 #923)
-#925 := [rewrite]: #924
-#921 := (iff #257 #920)
-#918 := (iff #256 #915)
-#912 := (implies #181 #907)
-#916 := (iff #912 #915)
-#917 := [rewrite]: #916
-#913 := (iff #256 #912)
-#910 := (iff #255 #907)
-#903 := (implies #183 #898)
-#908 := (iff #903 #907)
-#909 := [rewrite]: #908
-#904 := (iff #255 #903)
-#901 := (iff #254 #898)
-#894 := (implies #671 #889)
-#899 := (iff #894 #898)
-#900 := [rewrite]: #899
-#895 := (iff #254 #894)
-#892 := (iff #253 #889)
-#885 := (implies #189 #880)
-#890 := (iff #885 #889)
-#891 := [rewrite]: #890
-#886 := (iff #253 #885)
-#883 := (iff #252 #880)
-#876 := (implies #685 #871)
-#881 := (iff #876 #880)
-#882 := [rewrite]: #881
-#877 := (iff #252 #876)
-#874 := (iff #251 #871)
-#867 := (implies #699 #864)
-#872 := (iff #867 #871)
-#873 := [rewrite]: #872
-#868 := (iff #251 #867)
-#865 := (iff #250 #864)
-#862 := (iff #249 #859)
-#855 := (implies #205 #852)
-#860 := (iff #855 #859)
-#861 := [rewrite]: #860
-#856 := (iff #249 #855)
-#853 := (iff #248 #852)
-#850 := (iff #247 #847)
-#843 := (implies #710 #829)
-#848 := (iff #843 #847)
-#849 := [rewrite]: #848
-#844 := (iff #247 #843)
-#841 := (iff #246 #829)
-#832 := (implies true #829)
-#835 := (iff #832 #829)
-#836 := [rewrite]: #835
-#839 := (iff #246 #832)
-#837 := (iff #245 #829)
-#833 := (iff #245 #832)
-#830 := (iff #244 #829)
-#827 := (iff #243 #824)
-#820 := (implies #713 #817)
-#825 := (iff #820 #824)
-#826 := [rewrite]: #825
-#821 := (iff #243 #820)
-#818 := (iff #242 #817)
-#815 := (iff #241 #812)
-#808 := (implies #212 #805)
-#813 := (iff #808 #812)
-#814 := [rewrite]: #813
-#809 := (iff #241 #808)
-#806 := (iff #240 #805)
-#803 := (iff #239 #800)
-#796 := (implies #720 #793)
-#801 := (iff #796 #800)
-#802 := [rewrite]: #801
-#797 := (iff #239 #796)
-#794 := (iff #238 #793)
-#791 := (iff #237 #788)
-#784 := (implies #741 #765)
-#789 := (iff #784 #788)
-#790 := [rewrite]: #789
-#785 := (iff #237 #784)
-#782 := (iff #236 #765)
-#777 := (and #765 true)
-#780 := (iff #777 #765)
+#928 := (iff #419 #927)
+#925 := (iff #394 #924)
+#922 := (iff #389 #921)
+#919 := (iff #383 #67)
+#920 := [rewrite]: #919
+#923 := [monotonicity #920]: #922
+#926 := [quant-intro #923]: #925
+#929 := [monotonicity #926]: #928
+#934 := [trans #929 #932]: #933
+#937 := [monotonicity #934]: #936
+#1485 := [monotonicity #937 #1482]: #1484
+#1488 := [monotonicity #1485]: #1487
+#917 := (iff #269 #916)
+#914 := (iff #268 #911)
+#907 := (implies #419 #904)
+#912 := (iff #907 #911)
+#913 := [rewrite]: #912
+#908 := (iff #268 #907)
+#905 := (iff #267 #904)
+#902 := (iff #266 #899)
+#895 := (implies #429 #892)
+#900 := (iff #895 #899)
+#901 := [rewrite]: #900
+#896 := (iff #266 #895)
+#893 := (iff #265 #892)
+#890 := (iff #264 #887)
+#883 := (implies #83 #880)
+#888 := (iff #883 #887)
+#889 := [rewrite]: #888
+#884 := (iff #264 #883)
+#881 := (iff #263 #880)
+#878 := (iff #262 #875)
+#871 := (implies #436 #868)
+#876 := (iff #871 #875)
+#877 := [rewrite]: #876
+#872 := (iff #262 #871)
+#869 := (iff #261 #868)
+#866 := (iff #260 #863)
+#859 := (implies #443 #856)
+#864 := (iff #859 #863)
+#865 := [rewrite]: #864
+#860 := (iff #260 #859)
+#857 := (iff #259 #856)
+#854 := (iff #258 #851)
+#847 := (implies #527 #844)
+#852 := (iff #847 #851)
+#853 := [rewrite]: #852
+#848 := (iff #258 #847)
+#845 := (iff #257 #844)
+#842 := (iff #256 #839)
+#835 := (implies #687 #832)
+#840 := (iff #835 #839)
+#841 := [rewrite]: #840
+#836 := (iff #256 #835)
+#833 := (iff #255 #832)
+#830 := (iff #254 #827)
+#823 := (implies #215 #820)
+#828 := (iff #823 #827)
+#829 := [rewrite]: #828
+#824 := (iff #254 #823)
+#821 := (iff #253 #820)
+#818 := (iff #252 #815)
+#811 := (implies #705 #808)
+#816 := (iff #811 #815)
+#817 := [rewrite]: #816
+#812 := (iff #252 #811)
+#809 := (iff #251 #808)
+#806 := (iff #250 #803)
+#799 := (implies #708 #796)
+#804 := (iff #799 #803)
+#805 := [rewrite]: #804
+#800 := (iff #250 #799)
+#797 := (iff #249 #796)
+#794 := (iff #248 #791)
+#787 := (implies #222 #784)
+#792 := (iff #787 #791)
+#793 := [rewrite]: #792
+#788 := (iff #248 #787)
+#785 := (iff #247 #784)
+#782 := (iff #246 #779)
+#775 := (implies #715 #772)
+#780 := (iff #775 #779)
 #781 := [rewrite]: #780
-#778 := (iff #236 #777)
-#775 := (iff #235 true)
-#770 := (implies #765 true)
-#773 := (iff #770 true)
-#774 := [rewrite]: #773
-#771 := (iff #235 #770)
-#768 := (iff #234 true)
+#776 := (iff #246 #775)
+#773 := (iff #245 #772)
+#770 := (iff #244 #767)
+#763 := (implies #736 #760)
+#768 := (iff #763 #767)
 #769 := [rewrite]: #768
-#766 := (iff #233 #765)
-#763 := (iff #232 #760)
-#756 := (implies #226 #753)
-#761 := (iff #756 #760)
-#762 := [rewrite]: #761
-#757 := (iff #232 #756)
-#754 := (iff #231 #753)
-#751 := (iff #230 #750)
-#748 := (iff #229 #747)
-#745 := (iff #228 #744)
-#727 := (= #221 #726)
-#728 := [rewrite]: #727
-#746 := [monotonicity #728]: #745
-#749 := [monotonicity #746]: #748
-#752 := [monotonicity #749]: #751
-#755 := [quant-intro #752]: #754
-#758 := [monotonicity #755]: #757
-#764 := [trans #758 #762]: #763
-#767 := [quant-intro #764]: #766
-#772 := [monotonicity #767 #769]: #771
-#776 := [trans #772 #774]: #775
-#779 := [monotonicity #767 #776]: #778
-#783 := [trans #779 #781]: #782
-#742 := (iff #224 #741)
-#739 := (iff #223 #736)
-#732 := (implies #723 #729)
-#737 := (iff #732 #736)
-#738 := [rewrite]: #737
-#733 := (iff #223 #732)
-#730 := (iff #222 #729)
-#731 := [monotonicity #728]: #730
-#724 := (iff #220 #723)
-#725 := [rewrite]: #724
-#734 := [monotonicity #725 #731]: #733
-#740 := [trans #734 #738]: #739
-#743 := [quant-intro #740]: #742
-#786 := [monotonicity #743 #783]: #785
-#792 := [trans #786 #790]: #791
-#795 := [monotonicity #743 #792]: #794
-#721 := (iff #219 #720)
-#718 := (iff #218 #717)
-#719 := [rewrite]: #718
-#722 := [quant-intro #719]: #721
-#798 := [monotonicity #722 #795]: #797
-#804 := [trans #798 #802]: #803
-#807 := [monotonicity #722 #804]: #806
-#810 := [monotonicity #807]: #809
-#816 := [trans #810 #814]: #815
-#819 := [monotonicity #816]: #818
-#714 := (iff #210 #713)
-#715 := [rewrite]: #714
-#822 := [monotonicity #715 #819]: #821
-#828 := [trans #822 #826]: #827
-#831 := [monotonicity #715 #828]: #830
+#764 := (iff #244 #763)
+#761 := (iff #243 #760)
+#758 := (iff #242 #755)
+#751 := (implies #236 #748)
+#756 := (iff #751 #755)
+#757 := [rewrite]: #756
+#752 := (iff #242 #751)
+#749 := (iff #241 #748)
+#746 := (iff #240 #745)
+#743 := (iff #239 #742)
+#740 := (iff #238 #739)
+#722 := (= #231 #721)
+#723 := [rewrite]: #722
+#741 := [monotonicity #723]: #740
+#744 := [monotonicity #741]: #743
+#747 := [monotonicity #744]: #746
+#750 := [quant-intro #747]: #749
+#753 := [monotonicity #750]: #752
+#759 := [trans #753 #757]: #758
+#762 := [quant-intro #759]: #761
+#737 := (iff #234 #736)
+#734 := (iff #233 #731)
+#727 := (implies #718 #724)
+#732 := (iff #727 #731)
+#733 := [rewrite]: #732
+#728 := (iff #233 #727)
+#725 := (iff #232 #724)
+#726 := [monotonicity #723]: #725
+#719 := (iff #230 #718)
+#720 := [rewrite]: #719
+#729 := [monotonicity #720 #726]: #728
+#735 := [trans #729 #733]: #734
+#738 := [quant-intro #735]: #737
+#765 := [monotonicity #738 #762]: #764
+#771 := [trans #765 #769]: #770
+#774 := [monotonicity #738 #771]: #773
+#716 := (iff #229 #715)
+#713 := (iff #228 #712)
+#714 := [rewrite]: #713
+#717 := [quant-intro #714]: #716
+#777 := [monotonicity #717 #774]: #776
+#783 := [trans #777 #781]: #782
+#786 := [monotonicity #717 #783]: #785
+#789 := [monotonicity #786]: #788
+#795 := [trans #789 #793]: #794
+#798 := [monotonicity #795]: #797
+#709 := (iff #220 #708)
+#710 := [rewrite]: #709
+#801 := [monotonicity #710 #798]: #800
+#807 := [trans #801 #805]: #806
+#810 := [monotonicity #710 #807]: #809
+#706 := (iff #218 #705)
+#703 := (iff #217 #700)
+#697 := (implies #216 #658)
+#701 := (iff #697 #700)
+#702 := [rewrite]: #701
+#698 := (iff #217 #697)
+#659 := (iff #204 #658)
+#660 := [rewrite]: #659
+#699 := [monotonicity #660]: #698
+#704 := [trans #699 #702]: #703
+#707 := [quant-intro #704]: #706
+#813 := [monotonicity #707 #810]: #812
+#819 := [trans #813 #817]: #818
+#822 := [monotonicity #707 #819]: #821
+#825 := [monotonicity #822]: #824
+#831 := [trans #825 #829]: #830
 #834 := [monotonicity #831]: #833
-#838 := [trans #834 #836]: #837
-#840 := [monotonicity #838]: #839
-#842 := [trans #840 #836]: #841
-#711 := (iff #208 #710)
-#708 := (iff #207 #705)
-#702 := (implies #206 #688)
-#706 := (iff #702 #705)
-#707 := [rewrite]: #706
-#703 := (iff #207 #702)
-#689 := (iff #201 #688)
-#690 := [rewrite]: #689
-#704 := [monotonicity #690]: #703
-#709 := [trans #704 #707]: #708
-#712 := [quant-intro #709]: #711
-#845 := [monotonicity #712 #842]: #844
-#851 := [trans #845 #849]: #850
-#854 := [monotonicity #712 #851]: #853
-#857 := [monotonicity #854]: #856
-#863 := [trans #857 #861]: #862
-#866 := [monotonicity #863]: #865
-#700 := (iff #203 #699)
-#697 := (iff #202 #694)
-#691 := (implies #200 #688)
-#695 := (iff #691 #694)
-#696 := [rewrite]: #695
-#692 := (iff #202 #691)
-#693 := [monotonicity #690]: #692
-#698 := [trans #693 #696]: #697
-#701 := [quant-intro #698]: #700
-#869 := [monotonicity #701 #866]: #868
-#875 := [trans #869 #873]: #874
-#686 := (iff #199 #685)
-#683 := (iff #198 #680)
-#677 := (implies #195 #674)
-#681 := (iff #677 #680)
-#682 := [rewrite]: #681
-#678 := (iff #198 #677)
-#675 := (iff #197 #674)
-#676 := [rewrite]: #675
-#679 := [monotonicity #676]: #678
-#684 := [trans #679 #682]: #683
-#687 := [quant-intro #684]: #686
-#878 := [monotonicity #687 #875]: #877
-#884 := [trans #878 #882]: #883
-#887 := [monotonicity #884]: #886
-#893 := [trans #887 #891]: #892
-#672 := (iff #186 #671)
-#669 := (iff #185 #668)
-#670 := [rewrite]: #669
-#673 := [quant-intro #670]: #672
-#896 := [monotonicity #673 #893]: #895
-#902 := [trans #896 #900]: #901
-#905 := [monotonicity #902]: #904
-#911 := [trans #905 #909]: #910
-#914 := [monotonicity #911]: #913
-#919 := [trans #914 #917]: #918
-#922 := [monotonicity #919]: #921
-#927 := [trans #922 #925]: #926
-#930 := [monotonicity #927]: #929
-#934 := [trans #930 #932]: #933
-#936 := [monotonicity #934]: #935
-#938 := [trans #936 #932]: #937
-#666 := (iff #178 #652)
-#657 := (implies true #652)
-#660 := (iff #657 #652)
-#661 := [rewrite]: #660
-#664 := (iff #178 #657)
-#662 := (iff #177 #652)
-#658 := (iff #177 #657)
-#655 := (iff #176 #652)
-#649 := (implies #135 #633)
-#653 := (iff #649 #652)
-#654 := [rewrite]: #653
-#650 := (iff #176 #649)
-#647 := (iff #175 #633)
-#638 := (implies true #633)
-#641 := (iff #638 #633)
-#642 := [rewrite]: #641
-#645 := (iff #175 #638)
-#643 := (iff #174 #633)
-#639 := (iff #174 #638)
-#636 := (iff #173 #633)
-#629 := (implies #506 #624)
+#695 := (iff #213 #687)
+#690 := (and true #687)
+#693 := (iff #690 #687)
+#694 := [rewrite]: #693
+#691 := (iff #213 #690)
+#688 := (iff #212 #687)
+#685 := (iff #211 #684)
+#682 := (iff #210 #681)
+#679 := (iff #209 #678)
+#676 := (iff #208 #675)
+#673 := (iff #207 #672)
+#670 := (iff #206 #669)
+#667 := (iff #205 #664)
+#661 := (implies #203 #658)
+#665 := (iff #661 #664)
+#666 := [rewrite]: #665
+#662 := (iff #205 #661)
+#663 := [monotonicity #660]: #662
+#668 := [trans #663 #666]: #667
+#671 := [quant-intro #668]: #670
+#656 := (iff #202 #655)
+#653 := (iff #201 #650)
+#647 := (implies #198 #644)
+#651 := (iff #647 #650)
+#652 := [rewrite]: #651
+#648 := (iff #201 #647)
+#645 := (iff #200 #644)
+#646 := [rewrite]: #645
+#649 := [monotonicity #646]: #648
+#654 := [trans #649 #652]: #653
+#657 := [quant-intro #654]: #656
+#674 := [monotonicity #657 #671]: #673
+#677 := [monotonicity #674]: #676
+#642 := (iff #189 #641)
+#639 := (iff #188 #638)
+#640 := [rewrite]: #639
+#643 := [quant-intro #640]: #642
+#680 := [monotonicity #643 #677]: #679
+#683 := [monotonicity #680]: #682
+#686 := [monotonicity #683]: #685
+#689 := [monotonicity #686]: #688
+#692 := [monotonicity #689]: #691
+#696 := [trans #692 #694]: #695
+#837 := [monotonicity #696 #834]: #836
+#843 := [trans #837 #841]: #842
+#636 := (iff #181 #633)
+#629 := (implies #550 #626)
 #634 := (iff #629 #633)
 #635 := [rewrite]: #634
-#630 := (iff #173 #629)
-#627 := (iff #172 #624)
-#620 := (implies #140 #615)
-#625 := (iff #620 #624)
-#626 := [rewrite]: #625
-#621 := (iff #172 #620)
-#618 := (iff #171 #615)
-#611 := (implies #509 #606)
-#616 := (iff #611 #615)
-#617 := [rewrite]: #616
-#612 := (iff #171 #611)
-#609 := (iff #170 #606)
-#602 := (implies #145 #592)
-#607 := (iff #602 #606)
-#608 := [rewrite]: #607
-#603 := (iff #170 #602)
-#600 := (iff #169 #592)
-#595 := (implies true #592)
-#598 := (iff #595 #592)
-#599 := [rewrite]: #598
-#596 := (iff #169 #595)
-#593 := (iff #168 #592)
-#590 := (iff #167 #587)
-#583 := (implies #533 #580)
-#588 := (iff #583 #587)
-#589 := [rewrite]: #588
-#584 := (iff #167 #583)
-#581 := (iff #166 #580)
-#578 := (iff #165 #575)
-#571 := (implies #551 #554)
-#576 := (iff #571 #575)
-#577 := [rewrite]: #576
-#572 := (iff #165 #571)
-#569 := (iff #164 #554)
-#564 := (and #554 true)
-#567 := (iff #564 #554)
-#568 := [rewrite]: #567
-#565 := (iff #164 #564)
-#562 := (iff #163 true)
-#557 := (implies #554 true)
-#560 := (iff #557 true)
-#561 := [rewrite]: #560
-#558 := (iff #163 #557)
-#555 := (iff #162 #554)
-#556 := [rewrite]: #555
-#559 := [monotonicity #556]: #558
-#563 := [trans #559 #561]: #562
-#566 := [monotonicity #556 #563]: #565
-#570 := [trans #566 #568]: #569
-#552 := (iff #160 #551)
-#549 := (iff #159 #546)
-#542 := (implies #536 #539)
-#547 := (iff #542 #546)
-#548 := [rewrite]: #547
-#543 := (iff #159 #542)
-#540 := (iff #158 #539)
-#513 := (= #151 #512)
-#514 := [rewrite]: #513
-#541 := [monotonicity #514]: #540
-#537 := (iff #157 #536)
-#538 := [rewrite]: #537
-#544 := [monotonicity #538 #541]: #543
-#550 := [trans #544 #548]: #549
-#553 := [quant-intro #550]: #552
-#573 := [monotonicity #553 #570]: #572
-#579 := [trans #573 #577]: #578
-#582 := [monotonicity #553 #579]: #581
-#534 := (iff #156 #533)
-#531 := (iff #155 #528)
-#524 := (implies #148 #521)
-#529 := (iff #524 #528)
-#530 := [rewrite]: #529
-#525 := (iff #155 #524)
-#522 := (iff #154 #521)
-#519 := (iff #153 #518)
-#516 := (iff #152 #515)
-#517 := [monotonicity #514]: #516
-#520 := [monotonicity #517]: #519
-#523 := [quant-intro #520]: #522
-#526 := [monotonicity #523]: #525
-#532 := [trans #526 #530]: #531
-#535 := [quant-intro #532]: #534
-#585 := [monotonicity #535 #582]: #584
-#591 := [trans #585 #589]: #590
-#594 := [monotonicity #535 #591]: #593
-#597 := [monotonicity #594]: #596
-#601 := [trans #597 #599]: #600
-#604 := [monotonicity #601]: #603
-#610 := [trans #604 #608]: #609
-#510 := (iff #142 #509)
-#511 := [rewrite]: #510
-#613 := [monotonicity #511 #610]: #612
-#619 := [trans #613 #617]: #618
-#622 := [monotonicity #619]: #621
-#628 := [trans #622 #626]: #627
-#507 := (iff #137 #506)
-#508 := [rewrite]: #507
-#631 := [monotonicity #508 #628]: #630
+#630 := (iff #181 #629)
+#627 := (iff #180 #626)
+#624 := (iff #179 #621)
+#617 := (implies #581 #614)
+#622 := (iff #617 #621)
+#623 := [rewrite]: #622
+#618 := (iff #179 #617)
+#615 := (iff #178 #614)
+#612 := (iff #177 #609)
+#605 := (implies #599 #602)
+#610 := (iff #605 #609)
+#611 := [rewrite]: #610
+#606 := (iff #177 #605)
+#603 := (iff #176 #602)
+#604 := [rewrite]: #603
+#600 := (iff #174 #599)
+#597 := (iff #173 #594)
+#590 := (implies #584 #587)
+#595 := (iff #590 #594)
+#596 := [rewrite]: #595
+#591 := (iff #173 #590)
+#588 := (iff #172 #587)
+#561 := (= #165 #560)
+#562 := [rewrite]: #561
+#589 := [monotonicity #562]: #588
+#585 := (iff #171 #584)
+#586 := [rewrite]: #585
+#592 := [monotonicity #586 #589]: #591
+#598 := [trans #592 #596]: #597
+#601 := [quant-intro #598]: #600
+#607 := [monotonicity #601 #604]: #606
+#613 := [trans #607 #611]: #612
+#616 := [monotonicity #601 #613]: #615
+#582 := (iff #170 #581)
+#579 := (iff #169 #576)
+#572 := (implies #162 #569)
+#577 := (iff #572 #576)
+#578 := [rewrite]: #577
+#573 := (iff #169 #572)
+#570 := (iff #168 #569)
+#567 := (iff #167 #566)
+#564 := (iff #166 #563)
+#565 := [monotonicity #562]: #564
+#568 := [monotonicity #565]: #567
+#571 := [quant-intro #568]: #570
+#574 := [monotonicity #571]: #573
+#580 := [trans #574 #578]: #579
+#583 := [quant-intro #580]: #582
+#619 := [monotonicity #583 #616]: #618
+#625 := [trans #619 #623]: #624
+#628 := [monotonicity #583 #625]: #627
+#558 := (iff #159 #550)
+#553 := (and true #550)
+#556 := (iff #553 #550)
+#557 := [rewrite]: #556
+#554 := (iff #159 #553)
+#551 := (iff #158 #550)
+#548 := (iff #157 #547)
+#545 := (iff #156 #544)
+#542 := (iff #155 #539)
+#536 := (and #533 #154)
+#540 := (iff #536 #539)
+#541 := [rewrite]: #540
+#537 := (iff #155 #536)
+#534 := (iff #151 #533)
+#535 := [rewrite]: #534
+#538 := [monotonicity #535]: #537
+#543 := [trans #538 #541]: #542
+#546 := [monotonicity #543]: #545
+#531 := (iff #146 #530)
+#532 := [rewrite]: #531
+#549 := [monotonicity #532 #546]: #548
+#552 := [monotonicity #549]: #551
+#555 := [monotonicity #552]: #554
+#559 := [trans #555 #557]: #558
+#631 := [monotonicity #559 #628]: #630
 #637 := [trans #631 #635]: #636
-#640 := [monotonicity #637]: #639
-#644 := [trans #640 #642]: #643
-#646 := [monotonicity #644]: #645
-#648 := [trans #646 #642]: #647
-#651 := [monotonicity #648]: #650
-#656 := [trans #651 #654]: #655
-#659 := [monotonicity #656]: #658
-#663 := [trans #659 #661]: #662
-#665 := [monotonicity #663]: #664
-#667 := [trans #665 #661]: #666
-#941 := [monotonicity #667 #938]: #940
-#944 := [monotonicity #941]: #943
-#948 := [trans #944 #946]: #947
-#504 := (iff #132 #503)
-#501 := (iff #131 #498)
-#494 := (implies #125 #491)
-#499 := (iff #494 #498)
-#500 := [rewrite]: #499
-#495 := (iff #131 #494)
-#492 := (iff #130 #491)
-#489 := (iff #129 #488)
-#486 := (iff #128 #485)
-#483 := (iff #127 #482)
-#465 := (= #120 #464)
-#466 := [rewrite]: #465
-#484 := [monotonicity #466]: #483
-#487 := [monotonicity #484]: #486
-#490 := [monotonicity #487]: #489
-#493 := [quant-intro #490]: #492
-#496 := [monotonicity #493]: #495
-#502 := [trans #496 #500]: #501
-#505 := [quant-intro #502]: #504
-#951 := [monotonicity #505 #948]: #950
-#957 := [trans #951 #955]: #956
-#480 := (iff #123 #479)
-#477 := (iff #122 #474)
-#470 := (implies #461 #467)
-#475 := (iff #470 #474)
-#476 := [rewrite]: #475
-#471 := (iff #122 #470)
-#468 := (iff #121 #467)
-#469 := [monotonicity #466]: #468
-#462 := (iff #119 #461)
-#463 := [rewrite]: #462
-#472 := [monotonicity #463 #469]: #471
-#478 := [trans #472 #476]: #477
-#481 := [quant-intro #478]: #480
-#960 := [monotonicity #481 #957]: #959
-#966 := [trans #960 #964]: #965
-#459 := (iff #118 #458)
-#456 := (iff #117 #455)
-#457 := [rewrite]: #456
-#460 := [quant-intro #457]: #459
-#969 := [monotonicity #460 #966]: #968
-#975 := [trans #969 #973]: #974
-#978 := [monotonicity #975]: #977
-#984 := [trans #978 #982]: #983
-#452 := (iff #106 #451)
-#453 := [rewrite]: #452
-#987 := [monotonicity #453 #984]: #986
-#993 := [trans #987 #991]: #992
-#996 := [monotonicity #993]: #995
-#1000 := [trans #996 #998]: #999
-#1002 := [monotonicity #1000]: #1001
-#1004 := [trans #1002 #998]: #1003
-#449 := (iff #103 #448)
-#446 := (iff #102 #445)
-#447 := [rewrite]: #446
-#450 := [quant-intro #447]: #449
-#1007 := [monotonicity #450 #1004]: #1006
-#1013 := [trans #1007 #1011]: #1012
-#1016 := [monotonicity #450 #1013]: #1015
-#442 := (iff #94 #441)
-#439 := (iff #93 #438)
-#440 := [rewrite]: #439
-#443 := [quant-intro #440]: #442
-#1019 := [monotonicity #443 #1016]: #1018
-#1025 := [trans #1019 #1023]: #1024
-#1028 := [monotonicity #443 #1025]: #1027
-#435 := (iff #86 #434)
-#432 := (iff #85 #431)
-#433 := [rewrite]: #432
-#436 := [quant-intro #433]: #435
-#1031 := [monotonicity #436 #1028]: #1030
-#1037 := [trans #1031 #1035]: #1036
-#1040 := [monotonicity #436 #1037]: #1039
-#1043 := [monotonicity #1040]: #1042
-#1049 := [trans #1043 #1047]: #1048
-#1052 := [monotonicity #1049]: #1051
-#428 := (iff #78 #427)
-#429 := [rewrite]: #428
-#1055 := [monotonicity #429 #1052]: #1054
-#1061 := [trans #1055 #1059]: #1060
-#1064 := [monotonicity #429 #1061]: #1063
-#1067 := [monotonicity #1064]: #1066
-#1071 := [trans #1067 #1069]: #1070
-#1074 := [monotonicity #1071]: #1073
-#1080 := [trans #1074 #1078]: #1079
-#425 := (iff #73 #424)
-#422 := (iff #72 #419)
-#416 := (implies #70 #413)
-#420 := (iff #416 #419)
-#421 := [rewrite]: #420
-#417 := (iff #72 #416)
-#414 := (iff #71 #413)
-#415 := [rewrite]: #414
-#418 := [monotonicity #415]: #417
-#423 := [trans #418 #421]: #422
-#426 := [quant-intro #423]: #425
-#1083 := [monotonicity #426 #1080]: #1082
-#1089 := [trans #1083 #1087]: #1088
-#411 := (iff #69 #410)
-#408 := (iff #68 #405)
-#402 := (implies #65 #399)
-#406 := (iff #402 #405)
-#407 := [rewrite]: #406
-#403 := (iff #68 #402)
-#400 := (iff #67 #399)
-#401 := [rewrite]: #400
-#404 := [monotonicity #401]: #403
-#409 := [trans #404 #407]: #408
-#412 := [quant-intro #409]: #411
-#1092 := [monotonicity #412 #1089]: #1091
-#1098 := [trans #1092 #1096]: #1097
-#1101 := [monotonicity #1098]: #1100
-#1105 := [trans #1101 #1103]: #1104
-#1107 := [monotonicity #1105]: #1106
-#1109 := [trans #1107 #1103]: #1108
-#1112 := [monotonicity #1109]: #1111
-#1721 := [trans #1112 #1719]: #1720
-#398 := [asserted]: #285
-#1722 := [mp #398 #1721]: #1717
-#1723 := [not-or-elim #1722]: #76
-#1786 := [mp~ #1723 #1748]: #76
-#4130 := [mp #1786 #4129]: #4125
-#5292 := (not #4125)
-#5293 := (or #5292 #2962)
-#5294 := [quant-inst]: #5293
-#8242 := [unit-resolution #5294 #4130 #8241]: false
-#8245 := [lemma #8242]: #2962
-#3719 := (or #2977 #1847)
-#4054 := [def-axiom]: #3719
-#10109 := [unit-resolution #4054 #8245]: #2977
-#2982 := (not #2977)
-#4471 := (or #2982 #4468)
-#4474 := (not #4471)
-#4146 := (pattern #74 #81)
-#2408 := (not #81)
-#2954 := (or #74 #2408 #1129)
-#4147 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #4146) #2954)
-#4152 := (not #4147)
-#4477 := (or #4152 #4474)
-#4480 := (not #4477)
-decl ?x30!1 :: T2
-#1808 := ?x30!1
-#1812 := (uf_12 ?x30!1)
-#2423 := (* -1::int #1812)
-decl ?x29!2 :: T2
-#1809 := ?x29!2
-#1810 := (uf_12 ?x29!2)
-#2424 := (+ #1810 #2423)
-#2425 := (<= #2424 0::int)
-#1816 := (up_13 ?x30!1)
-#1815 := (up_13 ?x29!2)
-#2058 := (not #1815)
-#2132 := (or #2058 #1816 #2425)
-#8816 := [hypothesis]: #1815
-#5238 := (or #5292 #2058)
-#5267 := [quant-inst]: #5238
-#8817 := [unit-resolution #5267 #4130 #8816]: false
-#8818 := [lemma #8817]: #2058
-#3648 := (or #2132 #1815)
-#3733 := [def-axiom]: #3648
-#10110 := [unit-resolution #3733 #8818]: #2132
-#1948 := (not #2132)
-#4483 := (or #1948 #4480)
-#4486 := (not #4483)
-#4138 := (forall (vars (?x27 T2)) (:pat #4131) #1120)
-#4143 := (not #4138)
-#4489 := (or #4143 #4486)
-#4492 := (not #4489)
-decl ?x27!0 :: T2
-#1793 := ?x27!0
-#1794 := (uf_12 ?x27!0)
-#1795 := (>= #1794 0::int)
-#1796 := (not #1795)
-#4495 := (or #1796 #4492)
-#4498 := (not #4495)
-#4501 := (or #1115 #4498)
-#4504 := (not #4501)
-#4511 := (forall (vars (?x24 T2)) (:pat #4131) #1694)
-#4514 := (iff #1697 #4511)
-#4512 := (iff #1694 #1694)
-#4513 := [refl]: #4512
-#4515 := [quant-intro #4513]: #4514
-#2226 := (~ #1697 #1697)
-#2022 := (~ #1694 #1694)
-#2023 := [refl]: #2022
-#2227 := [nnf-pos #2023]: #2226
-#1727 := [not-or-elim #1722]: #1697
-#2057 := [mp~ #1727 #2227]: #1697
-#4516 := [mp #2057 #4515]: #4511
-#5053 := [hypothesis]: #1115
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-#4998 := (= uf_11 uf_11)
-#4996 := (not #4998)
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-#5008 := (iff #4998 true)
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-#5061 := [trans #5011 #8737]: #5012
-#5052 := [monotonicity #5061]: #5062
-#5071 := [trans #5052 #5064]: #5070
-#5079 := [monotonicity #5071]: #5078
-#5104 := [trans #5079 #5103]: #5078
-#5077 := [quant-inst]: #5076
-#5105 := [mp #5077 #5104]: #5075
-#5060 := [unit-resolution #5105 #5053 #4516]: false
-#5109 := [lemma #5060]: #78
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-#3352 := (forall (vars (?x67 T2) (?x68 T2)) #3347)
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-#3447 := (or #1403 #3446)
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-#3501 := (or #180 #888 #1544 #1548 #2104 #2106 #3498 #3499 #3500)
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-#3275 := (or #623 #605 #632 #614 #3273 #3274)
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-#3025 := (not #3019)
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+#480 := [trans #474 #478]: #479
+#483 := [quant-intro #480]: #482
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+#461 := (iff #121 #460)
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+#855 := [trans #849 #853]: #854
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+#867 := [trans #861 #865]: #866
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+#434 := (iff #88 #433)
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+#427 := (iff #79 #419)
+#422 := (and true #419)
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+#407 := [trans #402 #405]: #406
+#410 := [quant-intro #407]: #409
+#413 := [monotonicity #410]: #412
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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)
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+#4980 := [trans #4977 #4979]: #4976
+#4970 := [quant-inst]: #4975
+#4990 := [mp #4970 #4980]: #4974
+#4993 := [unit-resolution #4990 #3898 #4992]: false
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 #3027 := (not #3026)
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-#4354 := [refl]: #4353
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-#4374 := [monotonicity #4371]: #4373
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-#4398 := [monotonicity #4395]: #4397
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-#4404 := [monotonicity #4401]: #4403
-#4407 := [monotonicity #4404]: #4406
-#4410 := [monotonicity #4407]: #4409
-#4413 := [monotonicity #4410]: #4412
-#4416 := [monotonicity #4413]: #4415
-#4333 := (iff #846 #4332)
-#4330 := (iff #710 #4327)
-#4328 := (iff #705 #705)
-#4329 := [refl]: #4328
-#4331 := [quant-intro #4329]: #4330
-#4334 := [monotonicity #4331]: #4333
-#4419 := [monotonicity #4334 #4416]: #4418
-#4422 := [monotonicity #4419]: #4421
-#4425 := [monotonicity #4422]: #4424
-#4428 := [monotonicity #4425]: #4427
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-#4321 := (iff #1386 #4318)
-#4319 := (iff #1381 #1381)
-#4320 := [refl]: #4319
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-#4325 := [monotonicity #4322]: #4324
-#4431 := [monotonicity #4325 #4428]: #4430
-#4434 := [monotonicity #4431]: #4433
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-#4440 := [monotonicity #4437]: #4439
-#4316 := (iff #3499 #4315)
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-#4312 := [refl]: #4311
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-#4303 := (iff #3285 #3285)
-#4304 := [refl]: #4303
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-#4298 := (iff #1544 #4297)
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-#4294 := [refl]: #4293
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-#4443 := [monotonicity #4299 #4309 #4317 #4440]: #4442
-#4446 := [monotonicity #4443]: #4445
-#4290 := (iff #3276 #4289)
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-#4256 := [refl]: #4255
-#4258 := [quant-intro #4256]: #4257
+#3260 := (or #3027 #3255)
+#3272 := (not #3260)
+#2877 := (forall (vars (?x46 T2)) #2872)
+#3271 := (not #2877)
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+#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)
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+#3275 := (iff #3263 #3274)
+#3276 := [rewrite]: #3275
+#3264 := (iff #2658 #3263)
+#3261 := (iff #2649 #3260)
+#3258 := (iff #2644 #3255)
+#3246 := (and #184 #192 #3051 #3057 #1278 #1283 #1891 #1893 #3243)
+#3256 := (iff #3246 #3255)
+#3257 := [rewrite]: #3256
+#3247 := (iff #2644 #3246)
+#3244 := (iff #2638 #3243)
+#3241 := (iff #2635 #3238)
+#3233 := (and #1316 #3230)
+#3239 := (iff #3233 #3238)
+#3240 := [rewrite]: #3239
+#3234 := (iff #2635 #3233)
+#3231 := (iff #2632 #3230)
+#3228 := (iff #2629 #3225)
+#3220 := (and #705 #3217)
+#3226 := (iff #3220 #3225)
+#3227 := [rewrite]: #3226
+#3221 := (iff #2629 #3220)
+#3218 := (iff #2626 #3217)
+#3215 := (iff #2623 #3212)
+#3207 := (and #220 #3204)
+#3213 := (iff #3207 #3212)
+#3214 := [rewrite]: #3213
+#3208 := (iff #2623 #3207)
+#3205 := (iff #2620 #3204)
+#3202 := (iff #2617 #3199)
+#3194 := (and #1330 #3191)
+#3200 := (iff #3194 #3199)
+#3201 := [rewrite]: #3200
+#3195 := (iff #2617 #3194)
+#3192 := (iff #2614 #3191)
+#3189 := (iff #2611 #3186)
+#3180 := (and #3103 #3177)
+#3187 := (iff #3180 #3186)
+#3188 := [rewrite]: #3187
+#3181 := (iff #2611 #3180)
+#3178 := (iff #2608 #3177)
+#3175 := (iff #2603 #3172)
+#3166 := (and #3148 #2045 #2560 #3163)
+#3173 := (iff #3166 #3172)
+#3174 := [rewrite]: #3173
+#3167 := (iff #2603 #3166)
+#3164 := (iff #2594 #3163)
+#3161 := (iff #2591 #3152)
+#3153 := (not #3152)
+#3156 := (not #3153)
+#3159 := (iff #3156 #3152)
+#3160 := [rewrite]: #3159
+#3157 := (iff #2591 #3156)
+#3154 := (iff #2588 #3153)
+#3155 := [rewrite]: #3154
+#3158 := [monotonicity #3155]: #3157
+#3162 := [trans #3158 #3160]: #3161
+#3165 := [quant-intro #3162]: #3164
+#3149 := (iff #1368 #3148)
+#3146 := (iff #1365 #3143)
+#3129 := (or #223 #969)
+#3140 := (or #3129 #1361)
+#3144 := (iff #3140 #3143)
+#3145 := [rewrite]: #3144
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+#3138 := (iff #1358 #3129)
+#3130 := (not #3129)
+#3133 := (not #3130)
+#3136 := (iff #3133 #3129)
+#3137 := [rewrite]: #3136
+#3134 := (iff #1358 #3133)
+#3131 := (iff #1353 #3130)
+#3132 := [rewrite]: #3131
+#3135 := [monotonicity #3132]: #3134
+#3139 := [trans #3135 #3137]: #3138
+#3142 := [monotonicity #3139]: #3141
+#3147 := [trans #3142 #3145]: #3146
+#3150 := [quant-intro #3147]: #3149
+#3168 := [monotonicity #3150 #3165]: #3167
+#3176 := [trans #3168 #3174]: #3175
+#3127 := (iff #2554 #3126)
+#3124 := (iff #2551 #3121)
+#3107 := (or #2013 #3106)
+#3118 := (or #3107 #2546)
+#3122 := (iff #3118 #3121)
+#3123 := [rewrite]: #3122
+#3119 := (iff #2551 #3118)
+#3116 := (iff #2533 #3107)
+#3108 := (not #3107)
+#3111 := (not #3108)
+#3114 := (iff #3111 #3107)
+#3115 := [rewrite]: #3114
+#3112 := (iff #2533 #3111)
+#3109 := (iff #2530 #3108)
+#3110 := [rewrite]: #3109
+#3113 := [monotonicity #3110]: #3112
+#3117 := [trans #3113 #3115]: #3116
+#3120 := [monotonicity #3117]: #3119
+#3125 := [trans #3120 #3123]: #3124
+#3128 := [monotonicity #3125]: #3127
+#3179 := [monotonicity #3128 #3176]: #3178
+#3104 := (iff #1344 #3103)
+#3101 := (iff #1341 #3098)
+#3084 := (or #216 #3083)
+#3095 := (or #3084 #1336)
+#3099 := (iff #3095 #3098)
+#3100 := [rewrite]: #3099
+#3096 := (iff #1341 #3095)
+#3093 := (iff #711 #3084)
+#3085 := (not #3084)
+#3088 := (not #3085)
+#3091 := (iff #3088 #3084)
+#3092 := [rewrite]: #3091
+#3089 := (iff #711 #3088)
+#3086 := (iff #225 #3085)
+#3087 := [rewrite]: #3086
+#3090 := [monotonicity #3087]: #3089
+#3094 := [trans #3090 #3092]: #3093
+#3097 := [monotonicity #3094]: #3096
+#3102 := [trans #3097 #3100]: #3101
+#3105 := [quant-intro #3102]: #3104
+#3182 := [monotonicity #3105 #3179]: #3181
+#3190 := [trans #3182 #3188]: #3189
+#3081 := (iff #2527 #3080)
+#3078 := (iff #2524 #3075)
+#3061 := (or #3060 #1984)
+#3072 := (or #3061 #2519)
+#3076 := (iff #3072 #3075)
+#3077 := [rewrite]: #3076
+#3073 := (iff #2524 #3072)
+#3070 := (iff #2508 #3061)
+#3062 := (not #3061)
+#3065 := (not #3062)
+#3068 := (iff #3065 #3061)
+#3069 := [rewrite]: #3068
+#3066 := (iff #2508 #3065)
+#3063 := (iff #2505 #3062)
+#3064 := [rewrite]: #3063
+#3067 := [monotonicity #3064]: #3066
+#3071 := [trans #3067 #3069]: #3070
+#3074 := [monotonicity #3071]: #3073
+#3079 := [trans #3074 #3077]: #3078
+#3082 := [monotonicity #3079]: #3081
+#3193 := [monotonicity #3082 #3190]: #3192
+#3196 := [monotonicity #3193]: #3195
+#3203 := [trans #3196 #3201]: #3202
+#3206 := [monotonicity #3203]: #3205
+#3209 := [monotonicity #3206]: #3208
+#3216 := [trans #3209 #3214]: #3215
+#3219 := [monotonicity #3216]: #3218
+#3222 := [monotonicity #3219]: #3221
+#3229 := [trans #3222 #3227]: #3228
+#3232 := [monotonicity #3229]: #3231
+#3235 := [monotonicity #3232]: #3234
+#3242 := [trans #3235 #3240]: #3241
+#3245 := [monotonicity #3242]: #3244
+#3058 := (iff #1268 #3057)
+#3055 := (iff #1263 #3054)
+#3034 := (iff #1242 #3033)
+#3035 := [rewrite]: #3034
+#3056 := [monotonicity #3035]: #3055
+#3059 := [quant-intro #3056]: #3058
+#3052 := (iff #1257 #3051)
+#3049 := (iff #1254 #3046)
+#3043 := (or #3032 #1251)
 #3047 := (iff #3043 #3046)
 #3048 := [rewrite]: #3047
-#3044 := (iff #1605 #3043)
-#3041 := (iff #1599 #3032)
-#3033 := (not #3032)
+#3044 := (iff #1254 #3043)
+#3041 := (iff #1245 #3032)
 #3036 := (not #3033)
 #3039 := (iff #3036 #3032)
 #3040 := [rewrite]: #3039
-#3037 := (iff #1599 #3036)
-#3034 := (iff #1594 #3033)
-#3035 := [rewrite]: #3034
+#3037 := (iff #1245 #3036)
 #3038 := [monotonicity #3035]: #3037
 #3042 := [trans #3038 #3040]: #3041
 #3045 := [monotonicity #3042]: #3044
 #3050 := [trans #3045 #3048]: #3049
 #3053 := [quant-intro #3050]: #3052
-#3512 := [monotonicity #3053 #3076 #3104 #3132 #3509]: #3511
-#3523 := [trans #3512 #3521]: #3522
-#3030 := (iff #2498 #3027)
-#3022 := (and #1878 #2458 #3019)
-#3028 := (iff #3022 #3027)
+#3248 := [monotonicity #3053 #3059 #3245]: #3247
+#3259 := [trans #3248 #3257]: #3258
+#3030 := (iff #2473 #3027)
+#3017 := (and #149 #154 #530 #533 #2891 #3014)
+#3028 := (iff #3017 #3027)
 #3029 := [rewrite]: #3028
-#3023 := (iff #2498 #3022)
-#3020 := (iff #2492 #3019)
-#3017 := (iff #2489 #3008)
-#3009 := (not #3008)
-#3012 := (not #3009)
-#3015 := (iff #3012 #3008)
-#3016 := [rewrite]: #3015
-#3013 := (iff #2489 #3012)
-#3010 := (iff #2486 #3009)
+#3018 := (iff #2473 #3017)
+#3015 := (iff #2467 #3014)
+#3012 := (iff #2464 #3009)
+#3003 := (and #2943 #3000)
+#3010 := (iff #3003 #3009)
 #3011 := [rewrite]: #3010
-#3014 := [monotonicity #3011]: #3013
-#3018 := [trans #3014 #3016]: #3017
-#3021 := [quant-intro #3018]: #3020
-#3024 := [monotonicity #3021]: #3023
-#3031 := [trans #3024 #3029]: #3030
-#3526 := [monotonicity #3031 #3523]: #3525
-#3005 := (iff #1162 #3004)
-#3002 := (iff #1159 #2999)
-#2985 := (or #75 #1144)
-#2996 := (or #2985 #1155)
-#3000 := (iff #2996 #2999)
-#3001 := [rewrite]: #3000
-#2997 := (iff #1159 #2996)
-#2994 := (iff #1151 #2985)
-#2986 := (not #2985)
-#2989 := (not #2986)
-#2992 := (iff #2989 #2985)
-#2993 := [rewrite]: #2992
-#2990 := (iff #1151 #2989)
-#2987 := (iff #1148 #2986)
-#2988 := [rewrite]: #2987
-#2991 := [monotonicity #2988]: #2990
-#2995 := [trans #2991 #2993]: #2994
-#2998 := [monotonicity #2995]: #2997
-#3003 := [trans #2998 #3001]: #3002
-#3006 := [quant-intro #3003]: #3005
-#3529 := [monotonicity #3006 #3526]: #3528
-#3537 := [trans #3529 #3535]: #3536
-#2983 := (iff #2452 #2982)
-#2980 := (iff #2449 #2977)
-#2963 := (or #1845 #2962)
-#2974 := (or #2963 #2446)
-#2978 := (iff #2974 #2977)
-#2979 := [rewrite]: #2978
-#2975 := (iff #2449 #2974)
-#2972 := (iff #2439 #2963)
-#2964 := (not #2963)
-#2967 := (not #2964)
-#2970 := (iff #2967 #2963)
-#2971 := [rewrite]: #2970
-#2968 := (iff #2439 #2967)
-#2965 := (iff #2436 #2964)
-#2966 := [rewrite]: #2965
-#2969 := [monotonicity #2966]: #2968
-#2973 := [trans #2969 #2971]: #2972
-#2976 := [monotonicity #2973]: #2975
-#2981 := [trans #2976 #2979]: #2980
+#3004 := (iff #2464 #3003)
+#3001 := (iff #2459 #3000)
+#2998 := (iff #2453 #2997)
+#2995 := (iff #2450 #2992)
+#2978 := (or #1838 #1842)
+#2989 := (or #2978 #2445)
+#2993 := (iff #2989 #2992)
+#2994 := [rewrite]: #2993
+#2990 := (iff #2450 #2989)
+#2987 := (iff #2433 #2978)
+#2979 := (not #2978)
+#2982 := (not #2979)
+#2985 := (iff #2982 #2978)
+#2986 := [rewrite]: #2985
+#2983 := (iff #2433 #2982)
+#2980 := (iff #2430 #2979)
+#2981 := [rewrite]: #2980
 #2984 := [monotonicity #2981]: #2983
-#3540 := [monotonicity #2984 #3537]: #3539
-#2960 := (iff #1136 #2959)
-#2957 := (iff #1133 #2954)
-#2940 := (or #74 #2408)
-#2951 := (or #2940 #1129)
-#2955 := (iff #2951 #2954)
-#2956 := [rewrite]: #2955
-#2952 := (iff #1133 #2951)
-#2949 := (iff #430 #2940)
-#2941 := (not #2940)
-#2944 := (not #2941)
-#2947 := (iff #2944 #2940)
-#2948 := [rewrite]: #2947
-#2945 := (iff #430 #2944)
-#2942 := (iff #82 #2941)
-#2943 := [rewrite]: #2942
-#2946 := [monotonicity #2943]: #2945
-#2950 := [trans #2946 #2948]: #2949
-#2953 := [monotonicity #2950]: #2952
-#2958 := [trans #2953 #2956]: #2957
-#2961 := [quant-intro #2958]: #2960
-#3543 := [monotonicity #2961 #3540]: #3542
-#3551 := [trans #3543 #3549]: #3550
-#2111 := (iff #2433 #1948)
-#1825 := (iff #2430 #2132)
-#1799 := (or #2058 #1816)
-#2197 := (or #1799 #2425)
-#2133 := (iff #2197 #2132)
-#1824 := [rewrite]: #2133
-#2171 := (iff #2430 #2197)
-#1855 := (iff #2414 #1799)
-#1755 := (not #1799)
-#1921 := (not #1755)
-#2152 := (iff #1921 #1799)
-#1854 := [rewrite]: #2152
-#1922 := (iff #2414 #1921)
-#1756 := (iff #2411 #1755)
-#1800 := [rewrite]: #1756
-#2151 := [monotonicity #1800]: #1922
-#2196 := [trans #2151 #1854]: #1855
-#2172 := [monotonicity #2196]: #2171
-#1947 := [trans #2172 #1824]: #1825
-#2112 := [monotonicity #1947]: #2111
-#3554 := [monotonicity #2112 #3551]: #3553
-#3557 := [monotonicity #3554]: #3556
-#3564 := [trans #3557 #3562]: #3563
-#3567 := [monotonicity #3564]: #3566
-#3570 := [monotonicity #3567]: #3569
-#3577 := [trans #3570 #3575]: #3576
-#3580 := [monotonicity #3577]: #3579
-#2241 := (+ #2240 #2238)
-#2242 := (= #2241 0::int)
-#2245 := (and #206 #2244 #2242)
-#2262 := (not #2245)
-#2265 := (forall (vars (?x76 T2)) #2262)
-#2250 := (= ?x75!20 uf_11)
-#2251 := (not #2250)
-#2252 := (and #2251 #2249)
-#2253 := (not #2252)
-#2259 := (not #2253)
-#2269 := (and #2259 #2265)
-#2274 := (and #1438 #2269)
-#2208 := (* -1::int #2207)
-#2210 := (+ #2209 #2208)
-#2213 := (+ #2212 #2210)
-#2214 := (>= #2213 0::int)
-#2220 := (and #2219 #2218)
-#2221 := (not #2220)
-#2222 := (or #2221 #2214)
-#2223 := (not #2222)
-#2278 := (or #2223 #2274)
-#2282 := (and #1414 #2278)
-#2183 := (* -1::int #2182)
-#2185 := (+ #2184 #2183)
-#2186 := (>= #2185 0::int)
-#2190 := (and #2189 #2187)
-#2191 := (not #2190)
-#2192 := (or #2191 #2186)
-#2193 := (not #2192)
-#2286 := (or #2193 #2282)
-#2290 := (and #1400 #2286)
-#2294 := (or #2168 #2290)
-#2162 := (not #1394)
-#2298 := (and #2162 #2294)
-#2302 := (or #1394 #2298)
-#2306 := (and #710 #2302)
-#2144 := (= #2143 #2142)
-#2147 := (or #2146 #2144)
-#2148 := (not #2147)
-#2310 := (or #2148 #2306)
-#2314 := (and #1386 #2310)
-#2125 := (* -1::int #2124)
-#2127 := (+ #2126 #2125)
-#2128 := (>= #2127 0::int)
-#2129 := (not #2128)
-#2318 := (or #2129 #2314)
-#2108 := (and #2107 #2105)
-#2097 := (not #888)
-#2338 := (and #181 #2097 #2108 #1375 #2318 #1528 #1541 #1549)
-#2036 := (* -1::int #2035)
-#2038 := (+ #2037 #2036)
-#2041 := (+ #2040 #2038)
-#2042 := (>= #2041 0::int)
-#2051 := (and #2050 #2046)
-#2052 := (not #2051)
-#2053 := (or #2052 #2042)
-#2054 := (not #2053)
-#2073 := (or #2054 #2069)
-#2012 := (+ #2011 #1251)
-#2015 := (+ #2014 #2012)
-#2016 := (= #2015 0::int)
-#2017 := (>= #2012 0::int)
-#2018 := (not #2017)
-#2019 := (and #2018 #2016)
-#2024 := (or #1260 #2019)
-#2027 := (forall (vars (?x49 T2)) #2024)
-#2077 := (and #2027 #2073)
-#1976 := (+ #1975 #1973)
-#1977 := (= #1976 0::int)
-#1980 := (and #1979 #1977)
-#1996 := (not #1980)
-#1999 := (forall (vars (?x50 T2)) #1996)
-#1985 := (= ?x49!8 uf_11)
-#1986 := (not #1985)
-#1987 := (and #1986 #1984)
-#1988 := (not #1987)
-#1993 := (not #1988)
-#2003 := (and #1993 #1999)
-#2081 := (or #2003 #2077)
-#1967 := (not #614)
-#1964 := (not #632)
-#1961 := (not #605)
-#1958 := (not #623)
-#2091 := (and #1958 #1961 #1964 #1967 #2081 #2088)
-#2342 := (or #2091 #2338)
-#1936 := (+ #1935 #1206)
-#1937 := (>= #1936 0::int)
-#1938 := (not #1937)
-#1941 := (+ #1940 #1936)
-#1942 := (= #1941 0::int)
-#1944 := (and #1943 #1942 #1938)
-#1949 := (or #1215 #1944)
-#1952 := (forall (vars (?x46 T2)) #1949)
-#1910 := (+ #1168 #1909)
-#1912 := (+ #1911 #1910)
-#1913 := (= #1912 0::int)
-#1914 := (+ #1911 #1168)
-#1915 := (>= #1914 0::int)
-#1916 := (not #1915)
-#1918 := (and #1917 #1916 #1913)
-#1923 := (or #1177 #1918)
-#1926 := (forall (vars (?x37 T2)) #1923)
-#1902 := (not #1636)
-#2367 := (and #1902 #1926 #1952 #2342 #1608 #1619 #1628)
-#1868 := (+ #1867 #1865)
-#1869 := (+ #66 #1868)
-#1870 := (= #1869 0::int)
-#1874 := (and #74 #1873 #1870)
-#1890 := (not #1874)
-#1893 := (forall (vars (?x38 T2)) #1890)
-#1879 := (= ?x37!5 uf_11)
-#1880 := (not #1879)
-#1881 := (and #1880 #1878)
-#1882 := (not #1881)
-#1887 := (not #1882)
-#1897 := (and #1887 #1893)
-#2371 := (or #1897 #2367)
-#2375 := (and #1162 #2371)
-#1839 := (+ #1838 #1836)
-#1841 := (+ #1840 #1839)
-#1842 := (>= #1841 0::int)
-#1848 := (and #1847 #1846)
-#1849 := (not #1848)
-#1850 := (or #1849 #1842)
-#1851 := (not #1850)
-#2379 := (or #1851 #2375)
-#2383 := (and #1136 #2379)
-#1811 := (* -1::int #1810)
-#1813 := (+ #1812 #1811)
-#1814 := (>= #1813 0::int)
-#1818 := (and #1817 #1815)
-#1819 := (not #1818)
-#1820 := (or #1819 #1814)
-#1821 := (not #1820)
-#2387 := (or #1821 #2383)
-#2391 := (and #1121 #2387)
-#2395 := (or #1796 #2391)
-#1751 := (not #1115)
-#2399 := (and #1751 #2395)
-#2403 := (or #1115 #2399)
-#2938 := (iff #2403 #2937)
-#2935 := (iff #2399 #2934)
-#2932 := (iff #2395 #2931)
-#2929 := (iff #2391 #2928)
-#2926 := (iff #2387 #2925)
-#2923 := (iff #2383 #2922)
-#2920 := (iff #2379 #2919)
-#2917 := (iff #2375 #2916)
-#2914 := (iff #2371 #2913)
-#2911 := (iff #2367 #2908)
-#2905 := (and #106 #2542 #2582 #2902 #1608 #1619 #1628)
-#2909 := (iff #2905 #2908)
-#2910 := [rewrite]: #2909
-#2906 := (iff #2367 #2905)
-#2903 := (iff #2342 #2902)
-#2900 := (iff #2338 #2897)
-#2894 := (and #181 #189 #2108 #1375 #2891 #1528 #1541 #1549)
-#2898 := (iff #2894 #2897)
-#2899 := [rewrite]: #2898
-#2895 := (iff #2338 #2894)
-#2892 := (iff #2318 #2891)
-#2889 := (iff #2314 #2888)
-#2886 := (iff #2310 #2885)
-#2883 := (iff #2306 #2882)
-#2880 := (iff #2302 #2879)
-#2877 := (iff #2298 #2876)
-#2874 := (iff #2294 #2873)
-#2871 := (iff #2290 #2870)
-#2868 := (iff #2286 #2867)
-#2865 := (iff #2282 #2864)
-#2862 := (iff #2278 #2861)
-#2859 := (iff #2274 #2856)
-#2819 := (and #2249 #2813)
-#2850 := (and #2819 #2847)
-#2853 := (and #1438 #2850)
-#2857 := (iff #2853 #2856)
-#2858 := [rewrite]: #2857
-#2854 := (iff #2274 #2853)
-#2851 := (iff #2269 #2850)
-#2848 := (iff #2265 #2847)
-#2845 := (iff #2262 #2844)
-#2842 := (iff #2245 #2841)
-#2839 := (iff #2242 #2838)
-#2836 := (= #2241 #2835)
-#2837 := [rewrite]: #2836
-#2840 := [monotonicity #2837]: #2839
-#2843 := [monotonicity #2840]: #2842
-#2846 := [monotonicity #2843]: #2845
-#2849 := [quant-intro #2846]: #2848
-#2832 := (iff #2259 #2819)
-#2824 := (not #2819)
-#2827 := (not #2824)
-#2830 := (iff #2827 #2819)
-#2831 := [rewrite]: #2830
-#2828 := (iff #2259 #2827)
-#2825 := (iff #2253 #2824)
-#2822 := (iff #2252 #2819)
-#2816 := (and #2813 #2249)
-#2820 := (iff #2816 #2819)
-#2821 := [rewrite]: #2820
-#2817 := (iff #2252 #2816)
-#2814 := (iff #2251 #2813)
-#2811 := (iff #2250 #2810)
-#2812 := [rewrite]: #2811
+#2988 := [trans #2984 #2986]: #2987
+#2991 := [monotonicity #2988]: #2990
+#2996 := [trans #2991 #2994]: #2995
+#2999 := [monotonicity #2996]: #2998
+#2976 := (iff #1862 #2973)
+#2968 := (and #1852 #2965)
+#2974 := (iff #2968 #2973)
+#2975 := [rewrite]: #2974
+#2969 := (iff #1862 #2968)
+#2966 := (iff #1201 #2965)
+#2963 := (iff #1198 #2960)
+#2946 := (or #969 #1154)
+#2957 := (or #2946 #1195)
+#2961 := (iff #2957 #2960)
+#2962 := [rewrite]: #2961
+#2958 := (iff #1198 #2957)
+#2955 := (iff #1192 #2946)
+#2947 := (not #2946)
+#2950 := (not #2947)
+#2953 := (iff #2950 #2946)
+#2954 := [rewrite]: #2953
+#2951 := (iff #1192 #2950)
+#2948 := (iff #1189 #2947)
+#2949 := [rewrite]: #2948
+#2952 := [monotonicity #2949]: #2951
+#2956 := [trans #2952 #2954]: #2955
+#2959 := [monotonicity #2956]: #2958
+#2964 := [trans #2959 #2962]: #2963
+#2967 := [quant-intro #2964]: #2966
+#2970 := [monotonicity #2967]: #2969
+#2977 := [trans #2970 #2975]: #2976
+#3002 := [monotonicity #2977 #2999]: #3001
+#2944 := (iff #2427 #2943)
+#2941 := (iff #2424 #2938)
+#2919 := (or #65 #1154)
+#2935 := (or #2919 #2932)
+#2939 := (iff #2935 #2938)
+#2940 := [rewrite]: #2939
+#2936 := (iff #2424 #2935)
+#2933 := (iff #2421 #2932)
+#2934 := [rewrite]: #2933
+#2928 := (iff #1161 #2919)
+#2920 := (not #2919)
+#2923 := (not #2920)
+#2926 := (iff #2923 #2919)
+#2927 := [rewrite]: #2926
+#2924 := (iff #1161 #2923)
+#2921 := (iff #1158 #2920)
+#2922 := [rewrite]: #2921
+#2925 := [monotonicity #2922]: #2924
+#2929 := [trans #2925 #2927]: #2928
+#2937 := [monotonicity #2929 #2934]: #2936
+#2942 := [trans #2937 #2940]: #2941
+#2945 := [quant-intro #2942]: #2944
+#3005 := [monotonicity #2945 #3002]: #3004
+#3013 := [trans #3005 #3011]: #3012
+#2917 := (iff #2385 #2914)
+#2909 := (and #1777 #2345 #2906)
+#2915 := (iff #2909 #2914)
+#2916 := [rewrite]: #2915
+#2910 := (iff #2385 #2909)
+#2907 := (iff #2379 #2906)
+#2904 := (iff #2376 #2895)
+#2896 := (not #2895)
+#2899 := (not #2896)
+#2902 := (iff #2899 #2895)
+#2903 := [rewrite]: #2902
+#2900 := (iff #2376 #2899)
+#2897 := (iff #2373 #2896)
+#2898 := [rewrite]: #2897
+#2901 := [monotonicity #2898]: #2900
+#2905 := [trans #2901 #2903]: #2904
+#2908 := [quant-intro #2905]: #2907
+#2911 := [monotonicity #2908]: #2910
+#2918 := [trans #2911 #2916]: #2917
+#3016 := [monotonicity #2918 #3013]: #3015
+#2892 := (iff #1754 #2891)
+#2889 := (iff #1751 #2880)
+#2881 := (not #2880)
+#2884 := (not #2881)
+#2887 := (iff #2884 #2880)
+#2888 := [rewrite]: #2887
+#2885 := (iff #1751 #2884)
+#2882 := (iff #1132 #2881)
+#2883 := [rewrite]: #2882
+#2886 := [monotonicity #2883]: #2885
+#2890 := [trans #2886 #2888]: #2889
+#2893 := [quant-intro #2890]: #2892
+#3019 := [monotonicity #2893 #3016]: #3018
+#3031 := [trans #3019 #3029]: #3030
+#3262 := [monotonicity #3031 #3259]: #3261
+#2878 := (iff #2339 #2877)
+#2875 := (iff #2336 #2872)
+#2852 := (or #65 #1056)
+#2869 := (or #2852 #2866)
+#2873 := (iff #2869 #2872)
+#2874 := [rewrite]: #2873
+#2870 := (iff #2336 #2869)
+#2867 := (iff #2333 #2866)
+#2868 := [rewrite]: #2867
+#2861 := (iff #1063 #2852)
+#2853 := (not #2852)
+#2856 := (not #2853)
+#2859 := (iff #2856 #2852)
+#2860 := [rewrite]: #2859
+#2857 := (iff #1063 #2856)
+#2854 := (iff #1060 #2853)
+#2855 := [rewrite]: #2854
+#2858 := [monotonicity #2855]: #2857
+#2862 := [trans #2858 #2860]: #2861
+#2871 := [monotonicity #2862 #2868]: #2870
+#2876 := [trans #2871 #2874]: #2875
+#2879 := [quant-intro #2876]: #2878
+#2850 := (iff #2299 #2849)
+#2847 := (iff #2296 #2844)
+#2824 := (or #65 #995)
+#2841 := (or #2824 #2838)
+#2845 := (iff #2841 #2844)
+#2846 := [rewrite]: #2845
+#2842 := (iff #2296 #2841)
+#2839 := (iff #2293 #2838)
+#2840 := [rewrite]: #2839
+#2833 := (iff #1002 #2824)
+#2825 := (not #2824)
+#2828 := (not #2825)
+#2831 := (iff #2828 #2824)
+#2832 := [rewrite]: #2831
+#2829 := (iff #1002 #2828)
+#2826 := (iff #999 #2825)
+#2827 := [rewrite]: #2826
+#2830 := [monotonicity #2827]: #2829
+#2834 := [trans #2830 #2832]: #2833
+#2843 := [monotonicity #2834 #2840]: #2842
+#2848 := [trans #2843 #2846]: #2847
+#2851 := [quant-intro #2848]: #2850
+#2822 := (iff #1098 #2821)
+#2819 := (iff #1095 #2816)
+#2802 := (or #114 #2801)
+#2813 := (or #2802 #1069)
+#2817 := (iff #2813 #2816)
+#2818 := [rewrite]: #2817
+#2814 := (iff #1095 #2813)
+#2811 := (iff #456 #2802)
+#2803 := (not #2802)
+#2806 := (not #2803)
+#2809 := (iff #2806 #2802)
+#2810 := [rewrite]: #2809
+#2807 := (iff #456 #2806)
+#2804 := (iff #117 #2803)
+#2805 := [rewrite]: #2804
+#2808 := [monotonicity #2805]: #2807
+#2812 := [trans #2808 #2810]: #2811
 #2815 := [monotonicity #2812]: #2814
-#2818 := [monotonicity #2815]: #2817
-#2823 := [trans #2818 #2821]: #2822
-#2826 := [monotonicity #2823]: #2825
-#2829 := [monotonicity #2826]: #2828
-#2833 := [trans #2829 #2831]: #2832
-#2852 := [monotonicity #2833 #2849]: #2851
-#2855 := [monotonicity #2852]: #2854
-#2860 := [trans #2855 #2858]: #2859
-#2808 := (iff #2223 #2807)
-#2805 := (iff #2222 #2804)
-#2802 := (iff #2214 #2799)
-#2789 := (+ #2209 #2212)
-#2790 := (+ #2208 #2789)
-#2793 := (>= #2790 0::int)
-#2800 := (iff #2793 #2799)
-#2801 := [rewrite]: #2800
-#2794 := (iff #2214 #2793)
-#2791 := (= #2213 #2790)
-#2792 := [rewrite]: #2791
-#2795 := [monotonicity #2792]: #2794
-#2803 := [trans #2795 #2801]: #2802
-#2787 := (iff #2221 #2786)
-#2784 := (iff #2220 #2783)
-#2785 := [rewrite]: #2784
-#2788 := [monotonicity #2785]: #2787
-#2806 := [monotonicity #2788 #2803]: #2805
-#2809 := [monotonicity #2806]: #2808
-#2863 := [monotonicity #2809 #2860]: #2862
-#2866 := [monotonicity #2863]: #2865
-#2781 := (iff #2193 #2780)
-#2778 := (iff #2192 #2777)
-#2775 := (iff #2186 #2772)
-#2764 := (+ #2183 #2184)
-#2767 := (>= #2764 0::int)
-#2773 := (iff #2767 #2772)
-#2774 := [rewrite]: #2773
-#2768 := (iff #2186 #2767)
-#2765 := (= #2185 #2764)
-#2766 := [rewrite]: #2765
-#2769 := [monotonicity #2766]: #2768
-#2776 := [trans #2769 #2774]: #2775
-#2762 := (iff #2191 #2761)
-#2759 := (iff #2190 #2758)
-#2760 := [rewrite]: #2759
-#2763 := [monotonicity #2760]: #2762
-#2779 := [monotonicity #2763 #2776]: #2778
-#2782 := [monotonicity #2779]: #2781
-#2869 := [monotonicity #2782 #2866]: #2868
-#2872 := [monotonicity #2869]: #2871
-#2875 := [monotonicity #2872]: #2874
-#2756 := (iff #2162 #210)
-#2757 := [rewrite]: #2756
-#2878 := [monotonicity #2757 #2875]: #2877
-#2881 := [monotonicity #2878]: #2880
-#2884 := [monotonicity #2881]: #2883
-#2754 := (iff #2148 #2753)
-#2751 := (iff #2147 #2750)
-#2748 := (iff #2144 #2747)
-#2749 := [rewrite]: #2748
-#2752 := [monotonicity #2749]: #2751
-#2755 := [monotonicity #2752]: #2754
-#2887 := [monotonicity #2755 #2884]: #2886
-#2890 := [monotonicity #2887]: #2889
-#2745 := (iff #2129 #2744)
-#2742 := (iff #2128 #2739)
-#2731 := (+ #2125 #2126)
-#2734 := (>= #2731 0::int)
-#2740 := (iff #2734 #2739)
-#2741 := [rewrite]: #2740
-#2735 := (iff #2128 #2734)
-#2732 := (= #2127 #2731)
-#2733 := [rewrite]: #2732
-#2736 := [monotonicity #2733]: #2735
-#2743 := [trans #2736 #2741]: #2742
-#2746 := [monotonicity #2743]: #2745
-#2893 := [monotonicity #2746 #2890]: #2892
-#2729 := (iff #2097 #189)
-#2730 := [rewrite]: #2729
-#2896 := [monotonicity #2730 #2893]: #2895
-#2901 := [trans #2896 #2899]: #2900
-#2727 := (iff #2091 #2724)
-#2721 := (and #140 #145 #506 #509 #2718 #2088)
+#2820 := [trans #2815 #2818]: #2819
+#2823 := [quant-intro #2820]: #2822
+#2799 := (iff #1051 #2798)
+#2796 := (iff #1048 #2793)
+#2779 := (or #115 #969)
+#2790 := (or #2779 #1043)
+#2794 := (iff #2790 #2793)
+#2795 := [rewrite]: #2794
+#2791 := (iff #1048 #2790)
+#2788 := (iff #1039 #2779)
+#2780 := (not #2779)
+#2783 := (not #2780)
+#2786 := (iff #2783 #2779)
+#2787 := [rewrite]: #2786
+#2784 := (iff #1039 #2783)
+#2781 := (iff #1034 #2780)
+#2782 := [rewrite]: #2781
+#2785 := [monotonicity #2782]: #2784
+#2789 := [trans #2785 #2787]: #2788
+#2792 := [monotonicity #2789]: #2791
+#2797 := [trans #2792 #2795]: #2796
+#2800 := [quant-intro #2797]: #2799
+#3265 := [monotonicity #2800 #2823 #2851 #2879 #3262]: #3264
+#3278 := [trans #3265 #3276]: #3277
+#2777 := (iff #2257 #2774)
+#2769 := (and #1651 #2217 #2766)
+#2775 := (iff #2769 #2774)
+#2776 := [rewrite]: #2775
+#2770 := (iff #2257 #2769)
+#2767 := (iff #2251 #2766)
+#2764 := (iff #2248 #2755)
+#2756 := (not #2755)
+#2759 := (not #2756)
+#2762 := (iff #2759 #2755)
+#2763 := [rewrite]: #2762
+#2760 := (iff #2248 #2759)
+#2757 := (iff #2245 #2756)
+#2758 := [rewrite]: #2757
+#2761 := [monotonicity #2758]: #2760
+#2765 := [trans #2761 #2763]: #2764
+#2768 := [quant-intro #2765]: #2767
+#2771 := [monotonicity #2768]: #2770
+#2778 := [trans #2771 #2776]: #2777
+#3281 := [monotonicity #2778 #3278]: #3280
+#2752 := (iff #987 #2751)
+#2749 := (iff #984 #2746)
+#2732 := (or #75 #969)
+#2743 := (or #2732 #980)
+#2747 := (iff #2743 #2746)
+#2748 := [rewrite]: #2747
+#2744 := (iff #984 #2743)
+#2741 := (iff #976 #2732)
+#2733 := (not #2732)
+#2736 := (not #2733)
+#2739 := (iff #2736 #2732)
+#2740 := [rewrite]: #2739
+#2737 := (iff #976 #2736)
+#2734 := (iff #973 #2733)
+#2735 := [rewrite]: #2734
+#2738 := [monotonicity #2735]: #2737
+#2742 := [trans #2738 #2740]: #2741
+#2745 := [monotonicity #2742]: #2744
+#2750 := [trans #2745 #2748]: #2749
+#2753 := [quant-intro #2750]: #2752
+#3284 := [monotonicity #2753 #3281]: #3283
+#3292 := [trans #3284 #3290]: #3291
+#2730 := (iff #2211 #2729)
+#2727 := (iff #2208 #2724)
+#2710 := (or #1618 #2709)
+#2721 := (or #2710 #2205)
 #2725 := (iff #2721 #2724)
 #2726 := [rewrite]: #2725
-#2722 := (iff #2091 #2721)
-#2719 := (iff #2081 #2718)
-#2716 := (iff #2077 #2715)
-#2713 := (iff #2073 #2710)
-#2707 := (or #2704 #2069)
-#2711 := (iff #2707 #2710)
-#2712 := [rewrite]: #2711
-#2708 := (iff #2073 #2707)
-#2705 := (iff #2054 #2704)
-#2702 := (iff #2053 #2701)
-#2699 := (iff #2042 #2696)
-#2687 := (+ #2037 #2040)
-#2688 := (+ #2036 #2687)
-#2691 := (>= #2688 0::int)
-#2697 := (iff #2691 #2696)
-#2698 := [rewrite]: #2697
-#2692 := (iff #2042 #2691)
-#2689 := (= #2041 #2688)
-#2690 := [rewrite]: #2689
+#2722 := (iff #2208 #2721)
+#2719 := (iff #2198 #2710)
+#2711 := (not #2710)
+#2714 := (not #2711)
+#2717 := (iff #2714 #2710)
+#2718 := [rewrite]: #2717
+#2715 := (iff #2198 #2714)
+#2712 := (iff #2195 #2711)
+#2713 := [rewrite]: #2712
+#2716 := [monotonicity #2713]: #2715
+#2720 := [trans #2716 #2718]: #2719
+#2723 := [monotonicity #2720]: #2722
+#2728 := [trans #2723 #2726]: #2727
+#2731 := [monotonicity #2728]: #2730
+#3295 := [monotonicity #2731 #3292]: #3294
+#2707 := (iff #961 #2706)
+#2704 := (iff #958 #2701)
+#1721 := (or #74 #1898)
+#2698 := (or #1721 #954)
+#2702 := (iff #2698 #2701)
+#2703 := [rewrite]: #2702
+#2699 := (iff #958 #2698)
+#2696 := (iff #432 #1721)
+#1722 := (not #1721)
+#2691 := (not #1722)
+#2694 := (iff #2691 #1721)
+#2695 := [rewrite]: #2694
+#2692 := (iff #432 #2691)
+#2167 := (iff #85 #1722)
+#2690 := [rewrite]: #2167
 #2693 := [monotonicity #2690]: #2692
-#2700 := [trans #2693 #2698]: #2699
-#2685 := (iff #2052 #2684)
-#2682 := (iff #2051 #2681)
-#2683 := [rewrite]: #2682
-#2686 := [monotonicity #2683]: #2685
-#2703 := [monotonicity #2686 #2700]: #2702
-#2706 := [monotonicity #2703]: #2705
-#2709 := [monotonicity #2706]: #2708
-#2714 := [trans #2709 #2712]: #2713
-#2679 := (iff #2027 #2678)
-#2676 := (iff #2024 #2675)
-#2673 := (iff #2019 #2672)
-#2670 := (iff #2016 #2667)
-#2657 := (+ #2011 #2014)
-#2658 := (+ #1251 #2657)
-#2661 := (= #2658 0::int)
-#2668 := (iff #2661 #2667)
-#2669 := [rewrite]: #2668
-#2662 := (iff #2016 #2661)
-#2659 := (= #2015 #2658)
+#2697 := [trans #2693 #2695]: #2696
+#2700 := [monotonicity #2697]: #2699
+#2705 := [trans #2700 #2703]: #2704
+#2708 := [quant-intro #2705]: #2707
+#3298 := [monotonicity #2708 #3295]: #3297
+#3306 := [trans #3298 #3304]: #3305
+#2023 := (iff #2192 #2022)
+#1694 := (iff #2189 #1948)
+#1598 := (or #1597 #1589)
+#1572 := (or #1598 #2184)
+#1850 := (iff #1572 #1948)
+#1851 := [rewrite]: #1850
+#1573 := (iff #2189 #1572)
+#1992 := (iff #2173 #1598)
+#1967 := (not #1598)
+#1929 := (not #1967)
+#1815 := (iff #1929 #1598)
+#1816 := [rewrite]: #1815
+#1627 := (iff #2173 #1929)
+#1968 := (iff #2170 #1967)
+#1928 := [rewrite]: #1968
+#1628 := [monotonicity #1928]: #1627
+#1993 := [trans #1628 #1816]: #1992
+#1947 := [monotonicity #1993]: #1573
+#1695 := [trans #1947 #1851]: #1694
+#1897 := [monotonicity #1695]: #2023
+#3309 := [monotonicity #1897 #3306]: #3308
+#3312 := [monotonicity #3309]: #3311
+#3319 := [trans #3312 #3317]: #3318
+#3322 := [monotonicity #3319]: #3321
+#3325 := [monotonicity #3322]: #3324
+#3332 := [trans #3325 #3330]: #3331
+#3335 := [monotonicity #3332]: #3334
+#2037 := (+ #2036 #2034)
+#2038 := (= #2037 0::int)
+#2041 := (and #216 #2040 #2038)
+#2058 := (not #2041)
+#2061 := (forall (vars (?x76 T2)) #2058)
+#2046 := (= ?x75!20 uf_11)
+#2047 := (not #2046)
+#2048 := (and #2047 #2045)
+#2049 := (not #2048)
+#2055 := (not #2049)
+#2065 := (and #2055 #2061)
+#2070 := (and #1368 #2065)
+#2004 := (* -1::int #2003)
+#2006 := (+ #2005 #2004)
+#2009 := (+ #2008 #2006)
+#2010 := (>= #2009 0::int)
+#2016 := (and #2015 #2014)
+#2017 := (not #2016)
+#2018 := (or #2017 #2010)
+#2019 := (not #2018)
+#2074 := (or #2019 #2070)
+#2078 := (and #1344 #2074)
+#1979 := (* -1::int #1978)
+#1981 := (+ #1980 #1979)
+#1982 := (>= #1981 0::int)
+#1986 := (and #1985 #1983)
+#1987 := (not #1986)
+#1988 := (or #1987 #1982)
+#1989 := (not #1988)
+#2082 := (or #1989 #2078)
+#2086 := (and #1330 #2082)
+#2090 := (or #1964 #2086)
+#1958 := (not #1324)
+#2094 := (and #1958 #2090)
+#2098 := (or #1324 #2094)
+#2102 := (and #705 #2098)
+#1940 := (= #1939 #1938)
+#1943 := (or #1942 #1940)
+#1944 := (not #1943)
+#2106 := (or #1944 #2102)
+#2110 := (and #1316 #2106)
+#1921 := (* -1::int #1920)
+#1923 := (+ #1922 #1921)
+#1924 := (>= #1923 0::int)
+#1925 := (not #1924)
+#2114 := (or #1925 #2110)
+#1894 := (and #1893 #1891)
+#1913 := (and #184 #192 #1894 #1257 #1268 #1278 #1283)
+#2118 := (and #1913 #2114)
+#1829 := (* -1::int #1828)
+#1831 := (+ #1830 #1829)
+#1834 := (+ #1833 #1831)
+#1835 := (>= #1834 0::int)
+#1844 := (and #1843 #1839)
+#1845 := (not #1844)
+#1846 := (or #1845 #1835)
+#1847 := (not #1846)
+#1866 := (or #1847 #1862)
+#1805 := (+ #1804 #1152)
+#1808 := (+ #1807 #1805)
+#1809 := (= #1808 0::int)
+#1810 := (>= #1805 0::int)
+#1811 := (not #1810)
+#1812 := (and #1811 #1809)
+#1817 := (or #1161 #1812)
+#1820 := (forall (vars (?x49 T2)) #1817)
+#1870 := (and #1820 #1866)
+#1769 := (+ #1768 #1766)
+#1770 := (= #1769 0::int)
+#1773 := (and #1772 #1770)
+#1789 := (not #1773)
+#1792 := (forall (vars (?x50 T2)) #1789)
+#1778 := (= ?x49!8 uf_11)
+#1779 := (not #1778)
+#1780 := (and #1779 #1777)
+#1781 := (not #1780)
+#1786 := (not #1781)
+#1796 := (and #1786 #1792)
+#1874 := (or #1796 #1870)
+#1757 := (and #149 #154 #530 #533 #1754)
+#1878 := (and #1757 #1874)
+#2122 := (or #1878 #2118)
+#1710 := (+ #1709 #1054)
+#1711 := (>= #1710 0::int)
+#1712 := (not #1711)
+#1715 := (+ #1714 #1710)
+#1716 := (= #1715 0::int)
+#1718 := (and #1717 #1716 #1712)
+#1723 := (or #1063 #1718)
+#1726 := (forall (vars (?x46 T2)) #1723)
+#1683 := (+ #993 #1682)
+#1685 := (+ #1684 #1683)
+#1686 := (= #1685 0::int)
+#1687 := (+ #1684 #993)
+#1688 := (>= #1687 0::int)
+#1689 := (not #1688)
+#1691 := (and #1690 #1689 #1686)
+#1696 := (or #1002 #1691)
+#1699 := (forall (vars (?x37 T2)) #1696)
+#1737 := (and #109 #1699 #1051 #1726 #1098 #1104)
+#2126 := (and #1737 #2122)
+#1641 := (+ #1640 #1638)
+#1642 := (+ #66 #1641)
+#1643 := (= #1642 0::int)
+#1647 := (and #74 #1646 #1643)
+#1664 := (not #1647)
+#1667 := (forall (vars (?x38 T2)) #1664)
+#1652 := (= ?x37!5 uf_11)
+#1653 := (not #1652)
+#1654 := (and #1653 #1651)
+#1655 := (not #1654)
+#1661 := (not #1655)
+#1671 := (and #1661 #1667)
+#2130 := (or #1671 #2126)
+#2134 := (and #987 #2130)
+#1612 := (+ #1611 #1609)
+#1614 := (+ #1613 #1612)
+#1615 := (>= #1614 0::int)
+#1621 := (and #1620 #1619)
+#1622 := (not #1621)
+#1623 := (or #1622 #1615)
+#1624 := (not #1623)
+#2138 := (or #1624 #2134)
+#2142 := (and #961 #2138)
+#1584 := (* -1::int #1583)
+#1586 := (+ #1585 #1584)
+#1587 := (>= #1586 0::int)
+#1591 := (and #1590 #1588)
+#1592 := (not #1591)
+#1593 := (or #1592 #1587)
+#1594 := (not #1593)
+#2146 := (or #1594 #2142)
+#2150 := (and #946 #2146)
+#2154 := (or #1569 #2150)
+#1523 := (not #940)
+#2158 := (and #1523 #2154)
+#2162 := (or #940 #2158)
+#2688 := (iff #2162 #2687)
+#2685 := (iff #2158 #2684)
+#2682 := (iff #2154 #2681)
+#2679 := (iff #2150 #2678)
+#2676 := (iff #2146 #2675)
+#2673 := (iff #2142 #2672)
+#2670 := (iff #2138 #2669)
+#2667 := (iff #2134 #2666)
+#2664 := (iff #2130 #2663)
+#2661 := (iff #2126 #2658)
+#2652 := (and #109 #2299 #1051 #2339 #1098 #1104)
+#2655 := (and #2652 #2649)
+#2659 := (iff #2655 #2658)
 #2660 := [rewrite]: #2659
-#2663 := [monotonicity #2660]: #2662
-#2671 := [trans #2663 #2669]: #2670
-#2655 := (iff #2018 #2654)
-#2652 := (iff #2017 #2649)
-#2641 := (+ #1251 #2011)
-#2644 := (>= #2641 0::int)
-#2650 := (iff #2644 #2649)
-#2651 := [rewrite]: #2650
-#2645 := (iff #2017 #2644)
-#2642 := (= #2012 #2641)
-#2643 := [rewrite]: #2642
-#2646 := [monotonicity #2643]: #2645
-#2653 := [trans #2646 #2651]: #2652
-#2656 := [monotonicity #2653]: #2655
-#2674 := [monotonicity #2656 #2671]: #2673
-#2677 := [monotonicity #2674]: #2676
-#2680 := [quant-intro #2677]: #2679
-#2717 := [monotonicity #2680 #2714]: #2716
-#2639 := (iff #2003 #2636)
-#2602 := (and #1984 #2596)
-#2633 := (and #2602 #2630)
-#2637 := (iff #2633 #2636)
-#2638 := [rewrite]: #2637
-#2634 := (iff #2003 #2633)
-#2631 := (iff #1999 #2630)
-#2628 := (iff #1996 #2627)
-#2625 := (iff #1980 #2624)
-#2622 := (iff #1977 #2621)
-#2619 := (= #1976 #2618)
-#2620 := [rewrite]: #2619
-#2623 := [monotonicity #2620]: #2622
-#2626 := [monotonicity #2623]: #2625
-#2629 := [monotonicity #2626]: #2628
-#2632 := [quant-intro #2629]: #2631
-#2615 := (iff #1993 #2602)
-#2607 := (not #2602)
-#2610 := (not #2607)
-#2613 := (iff #2610 #2602)
-#2614 := [rewrite]: #2613
-#2611 := (iff #1993 #2610)
-#2608 := (iff #1988 #2607)
-#2605 := (iff #1987 #2602)
-#2599 := (and #2596 #1984)
-#2603 := (iff #2599 #2602)
-#2604 := [rewrite]: #2603
-#2600 := (iff #1987 #2599)
-#2597 := (iff #1986 #2596)
-#2594 := (iff #1985 #2593)
-#2595 := [rewrite]: #2594
-#2598 := [monotonicity #2595]: #2597
-#2601 := [monotonicity #2598]: #2600
-#2606 := [trans #2601 #2604]: #2605
-#2609 := [monotonicity #2606]: #2608
-#2612 := [monotonicity #2609]: #2611
-#2616 := [trans #2612 #2614]: #2615
-#2635 := [monotonicity #2616 #2632]: #2634
-#2640 := [trans #2635 #2638]: #2639
-#2720 := [monotonicity #2640 #2717]: #2719
-#2591 := (iff #1967 #509)
-#2592 := [rewrite]: #2591
-#2589 := (iff #1964 #506)
-#2590 := [rewrite]: #2589
-#2587 := (iff #1961 #145)
-#2588 := [rewrite]: #2587
-#2585 := (iff #1958 #140)
-#2586 := [rewrite]: #2585
-#2723 := [monotonicity #2586 #2588 #2590 #2592 #2720]: #2722
-#2728 := [trans #2723 #2726]: #2727
-#2904 := [monotonicity #2728 #2901]: #2903
-#2583 := (iff #1952 #2582)
-#2580 := (iff #1949 #2579)
-#2577 := (iff #1944 #2576)
-#2574 := (iff #1938 #2573)
-#2571 := (iff #1937 #2568)
-#2561 := (+ #1206 #1935)
-#2564 := (>= #2561 0::int)
-#2569 := (iff #2564 #2568)
-#2570 := [rewrite]: #2569
-#2565 := (iff #1937 #2564)
-#2562 := (= #1936 #2561)
-#2563 := [rewrite]: #2562
-#2566 := [monotonicity #2563]: #2565
-#2572 := [trans #2566 #2570]: #2571
-#2575 := [monotonicity #2572]: #2574
-#2559 := (iff #1942 #2556)
-#2545 := (+ #1935 #1940)
-#2546 := (+ #1206 #2545)
-#2549 := (= #2546 0::int)
-#2557 := (iff #2549 #2556)
-#2558 := [rewrite]: #2557
-#2550 := (iff #1942 #2549)
-#2547 := (= #1941 #2546)
+#2656 := (iff #2126 #2655)
+#2650 := (iff #2122 #2649)
+#2647 := (iff #2118 #2644)
+#2641 := (and #1913 #2638)
+#2645 := (iff #2641 #2644)
+#2646 := [rewrite]: #2645
+#2642 := (iff #2118 #2641)
+#2639 := (iff #2114 #2638)
+#2636 := (iff #2110 #2635)
+#2633 := (iff #2106 #2632)
+#2630 := (iff #2102 #2629)
+#2627 := (iff #2098 #2626)
+#2624 := (iff #2094 #2623)
+#2621 := (iff #2090 #2620)
+#2618 := (iff #2086 #2617)
+#2615 := (iff #2082 #2614)
+#2612 := (iff #2078 #2611)
+#2609 := (iff #2074 #2608)
+#2606 := (iff #2070 #2603)
+#2566 := (and #2045 #2560)
+#2597 := (and #2566 #2594)
+#2600 := (and #1368 #2597)
+#2604 := (iff #2600 #2603)
+#2605 := [rewrite]: #2604
+#2601 := (iff #2070 #2600)
+#2598 := (iff #2065 #2597)
+#2595 := (iff #2061 #2594)
+#2592 := (iff #2058 #2591)
+#2589 := (iff #2041 #2588)
+#2586 := (iff #2038 #2585)
+#2583 := (= #2037 #2582)
+#2584 := [rewrite]: #2583
+#2587 := [monotonicity #2584]: #2586
+#2590 := [monotonicity #2587]: #2589
+#2593 := [monotonicity #2590]: #2592
+#2596 := [quant-intro #2593]: #2595
+#2579 := (iff #2055 #2566)
+#2571 := (not #2566)
+#2574 := (not #2571)
+#2577 := (iff #2574 #2566)
+#2578 := [rewrite]: #2577
+#2575 := (iff #2055 #2574)
+#2572 := (iff #2049 #2571)
+#2569 := (iff #2048 #2566)
+#2563 := (and #2560 #2045)
+#2567 := (iff #2563 #2566)
+#2568 := [rewrite]: #2567
+#2564 := (iff #2048 #2563)
+#2561 := (iff #2047 #2560)
+#2558 := (iff #2046 #2557)
+#2559 := [rewrite]: #2558
+#2562 := [monotonicity #2559]: #2561
+#2565 := [monotonicity #2562]: #2564
+#2570 := [trans #2565 #2568]: #2569
+#2573 := [monotonicity #2570]: #2572
+#2576 := [monotonicity #2573]: #2575
+#2580 := [trans #2576 #2578]: #2579
+#2599 := [monotonicity #2580 #2596]: #2598
+#2602 := [monotonicity #2599]: #2601
+#2607 := [trans #2602 #2605]: #2606
+#2555 := (iff #2019 #2554)
+#2552 := (iff #2018 #2551)
+#2549 := (iff #2010 #2546)
+#2536 := (+ #2005 #2008)
+#2537 := (+ #2004 #2536)
+#2540 := (>= #2537 0::int)
+#2547 := (iff #2540 #2546)
 #2548 := [rewrite]: #2547
-#2551 := [monotonicity #2548]: #2550
-#2560 := [trans #2551 #2558]: #2559
-#2578 := [monotonicity #2560 #2575]: #2577
-#2581 := [monotonicity #2578]: #2580
-#2584 := [quant-intro #2581]: #2583
-#2543 := (iff #1926 #2542)
-#2540 := (iff #1923 #2539)
-#2537 := (iff #1918 #2536)
-#2534 := (iff #1913 #2531)
-#2521 := (+ #1909 #1911)
-#2522 := (+ #1168 #2521)
-#2525 := (= #2522 0::int)
-#2532 := (iff #2525 #2531)
-#2533 := [rewrite]: #2532
-#2526 := (iff #1913 #2525)
-#2523 := (= #1912 #2522)
-#2524 := [rewrite]: #2523
-#2527 := [monotonicity #2524]: #2526
-#2535 := [trans #2527 #2533]: #2534
-#2519 := (iff #1916 #2518)
-#2516 := (iff #1915 #2513)
-#2505 := (+ #1168 #1911)
-#2508 := (>= #2505 0::int)
-#2514 := (iff #2508 #2513)
-#2515 := [rewrite]: #2514
-#2509 := (iff #1915 #2508)
-#2506 := (= #1914 #2505)
+#2541 := (iff #2010 #2540)
+#2538 := (= #2009 #2537)
+#2539 := [rewrite]: #2538
+#2542 := [monotonicity #2539]: #2541
+#2550 := [trans #2542 #2548]: #2549
+#2534 := (iff #2017 #2533)
+#2531 := (iff #2016 #2530)
+#2532 := [rewrite]: #2531
+#2535 := [monotonicity #2532]: #2534
+#2553 := [monotonicity #2535 #2550]: #2552
+#2556 := [monotonicity #2553]: #2555
+#2610 := [monotonicity #2556 #2607]: #2609
+#2613 := [monotonicity #2610]: #2612
+#2528 := (iff #1989 #2527)
+#2525 := (iff #1988 #2524)
+#2522 := (iff #1982 #2519)
+#2511 := (+ #1979 #1980)
+#2514 := (>= #2511 0::int)
+#2520 := (iff #2514 #2519)
+#2521 := [rewrite]: #2520
+#2515 := (iff #1982 #2514)
+#2512 := (= #1981 #2511)
+#2513 := [rewrite]: #2512
+#2516 := [monotonicity #2513]: #2515
+#2523 := [trans #2516 #2521]: #2522
+#2509 := (iff #1987 #2508)
+#2506 := (iff #1986 #2505)
 #2507 := [rewrite]: #2506
 #2510 := [monotonicity #2507]: #2509
-#2517 := [trans #2510 #2515]: #2516
-#2520 := [monotonicity #2517]: #2519
-#2538 := [monotonicity #2520 #2535]: #2537
-#2541 := [monotonicity #2538]: #2540
-#2544 := [quant-intro #2541]: #2543
-#2503 := (iff #1902 #106)
+#2526 := [monotonicity #2510 #2523]: #2525
+#2529 := [monotonicity #2526]: #2528
+#2616 := [monotonicity #2529 #2613]: #2615
+#2619 := [monotonicity #2616]: #2618
+#2622 := [monotonicity #2619]: #2621
+#2503 := (iff #1958 #220)
 #2504 := [rewrite]: #2503
-#2907 := [monotonicity #2504 #2544 #2584 #2904]: #2906
-#2912 := [trans #2907 #2910]: #2911
-#2501 := (iff #1897 #2498)
-#2464 := (and #1878 #2458)
-#2495 := (and #2464 #2492)
-#2499 := (iff #2495 #2498)
-#2500 := [rewrite]: #2499
-#2496 := (iff #1897 #2495)
-#2493 := (iff #1893 #2492)
-#2490 := (iff #1890 #2489)
-#2487 := (iff #1874 #2486)
-#2484 := (iff #1870 #2483)
-#2481 := (= #1869 #2480)
-#2482 := [rewrite]: #2481
-#2485 := [monotonicity #2482]: #2484
-#2488 := [monotonicity #2485]: #2487
-#2491 := [monotonicity #2488]: #2490
-#2494 := [quant-intro #2491]: #2493
-#2477 := (iff #1887 #2464)
-#2469 := (not #2464)
-#2472 := (not #2469)
-#2475 := (iff #2472 #2464)
-#2476 := [rewrite]: #2475
-#2473 := (iff #1887 #2472)
-#2470 := (iff #1882 #2469)
-#2467 := (iff #1881 #2464)
-#2461 := (and #2458 #1878)
-#2465 := (iff #2461 #2464)
-#2466 := [rewrite]: #2465
-#2462 := (iff #1881 #2461)
-#2459 := (iff #1880 #2458)
-#2456 := (iff #1879 #2455)
-#2457 := [rewrite]: #2456
-#2460 := [monotonicity #2457]: #2459
-#2463 := [monotonicity #2460]: #2462
-#2468 := [trans #2463 #2466]: #2467
-#2471 := [monotonicity #2468]: #2470
-#2474 := [monotonicity #2471]: #2473
-#2478 := [trans #2474 #2476]: #2477
-#2497 := [monotonicity #2478 #2494]: #2496
-#2502 := [trans #2497 #2500]: #2501
-#2915 := [monotonicity #2502 #2912]: #2914
-#2918 := [monotonicity #2915]: #2917
-#2453 := (iff #1851 #2452)
-#2450 := (iff #1850 #2449)
-#2447 := (iff #1842 #2446)
-#2444 := (= #1841 #2443)
-#2445 := [rewrite]: #2444
-#2448 := [monotonicity #2445]: #2447
-#2440 := (iff #1849 #2439)
-#2437 := (iff #1848 #2436)
-#2438 := [rewrite]: #2437
-#2441 := [monotonicity #2438]: #2440
-#2451 := [monotonicity #2441 #2448]: #2450
-#2454 := [monotonicity #2451]: #2453
-#2921 := [monotonicity #2454 #2918]: #2920
-#2924 := [monotonicity #2921]: #2923
-#2434 := (iff #1821 #2433)
-#2431 := (iff #1820 #2430)
-#2428 := (iff #1814 #2425)
-#2417 := (+ #1811 #1812)
-#2420 := (>= #2417 0::int)
-#2426 := (iff #2420 #2425)
-#2427 := [rewrite]: #2426
-#2421 := (iff #1814 #2420)
-#2418 := (= #1813 #2417)
-#2419 := [rewrite]: #2418
-#2422 := [monotonicity #2419]: #2421
-#2429 := [trans #2422 #2427]: #2428
-#2415 := (iff #1819 #2414)
-#2412 := (iff #1818 #2411)
-#2413 := [rewrite]: #2412
-#2416 := [monotonicity #2413]: #2415
-#2432 := [monotonicity #2416 #2429]: #2431
+#2625 := [monotonicity #2504 #2622]: #2624
+#2628 := [monotonicity #2625]: #2627
+#2631 := [monotonicity #2628]: #2630
+#2501 := (iff #1944 #2500)
+#2498 := (iff #1943 #2497)
+#2495 := (iff #1940 #2494)
+#2496 := [rewrite]: #2495
+#2499 := [monotonicity #2496]: #2498
+#2502 := [monotonicity #2499]: #2501
+#2634 := [monotonicity #2502 #2631]: #2633
+#2637 := [monotonicity #2634]: #2636
+#2492 := (iff #1925 #2491)
+#2489 := (iff #1924 #2486)
+#2478 := (+ #1921 #1922)
+#2481 := (>= #2478 0::int)
+#2487 := (iff #2481 #2486)
+#2488 := [rewrite]: #2487
+#2482 := (iff #1924 #2481)
+#2479 := (= #1923 #2478)
+#2480 := [rewrite]: #2479
+#2483 := [monotonicity #2480]: #2482
+#2490 := [trans #2483 #2488]: #2489
+#2493 := [monotonicity #2490]: #2492
+#2640 := [monotonicity #2493 #2637]: #2639
+#2643 := [monotonicity #2640]: #2642
+#2648 := [trans #2643 #2646]: #2647
+#2476 := (iff #1878 #2473)
+#2470 := (and #1757 #2467)
+#2474 := (iff #2470 #2473)
+#2475 := [rewrite]: #2474
+#2471 := (iff #1878 #2470)
+#2468 := (iff #1874 #2467)
+#2465 := (iff #1870 #2464)
+#2462 := (iff #1866 #2459)
+#2456 := (or #2453 #1862)
+#2460 := (iff #2456 #2459)
+#2461 := [rewrite]: #2460
+#2457 := (iff #1866 #2456)
+#2454 := (iff #1847 #2453)
+#2451 := (iff #1846 #2450)
+#2448 := (iff #1835 #2445)
+#2436 := (+ #1830 #1833)
+#2437 := (+ #1829 #2436)
+#2440 := (>= #2437 0::int)
+#2446 := (iff #2440 #2445)
+#2447 := [rewrite]: #2446
+#2441 := (iff #1835 #2440)
+#2438 := (= #1834 #2437)
+#2439 := [rewrite]: #2438
+#2442 := [monotonicity #2439]: #2441
+#2449 := [trans #2442 #2447]: #2448
+#2434 := (iff #1845 #2433)
+#2431 := (iff #1844 #2430)
+#2432 := [rewrite]: #2431
 #2435 := [monotonicity #2432]: #2434
-#2927 := [monotonicity #2435 #2924]: #2926
-#2930 := [monotonicity #2927]: #2929
-#2933 := [monotonicity #2930]: #2932
-#2409 := (iff #1751 #78)
-#2410 := [rewrite]: #2409
-#2936 := [monotonicity #2410 #2933]: #2935
-#2939 := [monotonicity #2936]: #2938
-#1725 := (not #1689)
-#2404 := (~ #1725 #2403)
-#2400 := (not #1686)
-#2401 := (~ #2400 #2399)
-#2396 := (not #1683)
-#2397 := (~ #2396 #2395)
-#2392 := (not #1680)
-#2393 := (~ #2392 #2391)
-#2388 := (not #1677)
-#2389 := (~ #2388 #2387)
-#2384 := (not #1674)
-#2385 := (~ #2384 #2383)
-#2380 := (not #1671)
-#2381 := (~ #2380 #2379)
-#2376 := (not #1668)
-#2377 := (~ #2376 #2375)
-#2372 := (not #1665)
-#2373 := (~ #2372 #2371)
-#2368 := (not #1660)
-#2369 := (~ #2368 #2367)
-#2364 := (not #1631)
-#2365 := (~ #2364 #1628)
-#2362 := (~ #1628 #1628)
-#2360 := (~ #1625 #1625)
-#2361 := [refl]: #2360
-#2363 := [nnf-pos #2361]: #2362
-#2366 := [nnf-neg #2363]: #2365
-#2357 := (not #1622)
-#2358 := (~ #2357 #1619)
-#2355 := (~ #1619 #1619)
-#2353 := (~ #1616 #1616)
-#2354 := [refl]: #2353
-#2356 := [nnf-pos #2354]: #2355
-#2359 := [nnf-neg #2356]: #2358
-#2350 := (not #1611)
-#2351 := (~ #2350 #1608)
-#2348 := (~ #1608 #1608)
-#2346 := (~ #1605 #1605)
-#2347 := [refl]: #2346
-#2349 := [nnf-pos #2347]: #2348
-#2352 := [nnf-neg #2349]: #2351
-#2343 := (not #1588)
-#2344 := (~ #2343 #2342)
-#2339 := (not #1583)
-#2340 := (~ #2339 #2338)
-#2336 := (~ #1549 #1549)
-#2337 := [refl]: #2336
-#2333 := (not #1544)
-#2334 := (~ #2333 #1541)
-#2331 := (~ #1541 #1541)
-#2329 := (~ #1538 #1538)
-#2330 := [refl]: #2329
-#2332 := [nnf-pos #2330]: #2331
-#2335 := [nnf-neg #2332]: #2334
-#2326 := (not #1531)
-#2327 := (~ #2326 #1528)
-#2324 := (~ #1528 #1528)
-#2322 := (~ #1525 #1525)
-#2323 := [refl]: #2322
-#2325 := [nnf-pos #2323]: #2324
-#2328 := [nnf-neg #2325]: #2327
-#2319 := (not #1514)
-#2320 := (~ #2319 #2318)
-#2315 := (not #1511)
-#2316 := (~ #2315 #2314)
-#2311 := (not #1508)
-#2312 := (~ #2311 #2310)
-#2307 := (not #1505)
-#2308 := (~ #2307 #2306)
-#2303 := (not #1502)
-#2304 := (~ #2303 #2302)
-#2299 := (not #1499)
-#2300 := (~ #2299 #2298)
-#2295 := (not #1496)
-#2296 := (~ #2295 #2294)
-#2291 := (not #1493)
-#2292 := (~ #2291 #2290)
-#2287 := (not #1490)
-#2288 := (~ #2287 #2286)
-#2283 := (not #1487)
-#2284 := (~ #2283 #2282)
-#2279 := (not #1484)
-#2280 := (~ #2279 #2278)
-#2275 := (not #1481)
-#2276 := (~ #2275 #2274)
-#2256 := (not #1478)
-#2272 := (~ #2256 #2269)
-#2246 := (exists (vars (?x76 T2)) #2245)
-#2254 := (or #2253 #2246)
-#2255 := (not #2254)
-#2270 := (~ #2255 #2269)
-#2266 := (not #2246)
-#2267 := (~ #2266 #2265)
-#2263 := (~ #2262 #2262)
-#2264 := [refl]: #2263
-#2268 := [nnf-neg #2264]: #2267
-#2260 := (~ #2259 #2259)
-#2261 := [refl]: #2260
-#2271 := [nnf-neg #2261 #2268]: #2270
-#2257 := (~ #2256 #2255)
-#2258 := [sk]: #2257
-#2273 := [trans #2258 #2271]: #2272
-#2232 := (not #1441)
-#2233 := (~ #2232 #1438)
-#2230 := (~ #1438 #1438)
-#2228 := (~ #1435 #1435)
-#2229 := [refl]: #2228
-#2231 := [nnf-pos #2229]: #2230
-#2234 := [nnf-neg #2231]: #2233
-#2277 := [nnf-neg #2234 #2273]: #2276
-#2224 := (~ #1441 #2223)
-#2225 := [sk]: #2224
-#2281 := [nnf-neg #2225 #2277]: #2280
-#2202 := (not #1417)
-#2203 := (~ #2202 #1414)
-#2200 := (~ #1414 #1414)
-#2198 := (~ #1411 #1411)
-#2199 := [refl]: #2198
-#2201 := [nnf-pos #2199]: #2200
-#2204 := [nnf-neg #2201]: #2203
-#2285 := [nnf-neg #2204 #2281]: #2284
-#2194 := (~ #1417 #2193)
-#2195 := [sk]: #2194
-#2289 := [nnf-neg #2195 #2285]: #2288
-#2177 := (not #1403)
-#2178 := (~ #2177 #1400)
-#2175 := (~ #1400 #1400)
-#2173 := (~ #1397 #1397)
-#2174 := [refl]: #2173
-#2176 := [nnf-pos #2174]: #2175
-#2179 := [nnf-neg #2176]: #2178
-#2293 := [nnf-neg #2179 #2289]: #2292
-#2169 := (~ #1403 #2168)
-#2170 := [sk]: #2169
-#2297 := [nnf-neg #2170 #2293]: #2296
-#2163 := (~ #2162 #2162)
-#2164 := [refl]: #2163
-#2301 := [nnf-neg #2164 #2297]: #2300
-#2160 := (~ #1394 #1394)
-#2161 := [refl]: #2160
-#2305 := [nnf-neg #2161 #2301]: #2304
-#2157 := (not #846)
-#2158 := (~ #2157 #710)
-#2155 := (~ #710 #710)
-#2153 := (~ #705 #705)
-#2154 := [refl]: #2153
-#2156 := [nnf-pos #2154]: #2155
-#2159 := [nnf-neg #2156]: #2158
-#2309 := [nnf-neg #2159 #2305]: #2308
-#2149 := (~ #846 #2148)
-#2150 := [sk]: #2149
-#2313 := [nnf-neg #2150 #2309]: #2312
-#2138 := (not #1389)
-#2139 := (~ #2138 #1386)
-#2136 := (~ #1386 #1386)
-#2134 := (~ #1381 #1381)
-#2135 := [refl]: #2134
-#2137 := [nnf-pos #2135]: #2136
-#2140 := [nnf-neg #2137]: #2139
-#2317 := [nnf-neg #2140 #2313]: #2316
-#2130 := (~ #1389 #2129)
-#2131 := [sk]: #2130
-#2321 := [nnf-neg #2131 #2317]: #2320
-#2120 := (not #1378)
-#2121 := (~ #2120 #1375)
-#2118 := (~ #1375 #1375)
-#2116 := (~ #1370 #1370)
-#2117 := [refl]: #2116
-#2119 := [nnf-pos #2117]: #2118
-#2122 := [nnf-neg #2119]: #2121
-#2113 := (not #1559)
-#2114 := (~ #2113 #2108)
-#2109 := (~ #1328 #2108)
-#2110 := [sk]: #2109
-#2115 := [nnf-neg #2110]: #2114
-#2098 := (~ #2097 #2097)
-#2099 := [refl]: #2098
-#2095 := (~ #181 #181)
-#2096 := [refl]: #2095
-#2341 := [nnf-neg #2096 #2099 #2115 #2122 #2321 #2328 #2335 #2337]: #2340
-#2092 := (not #1346)
-#2093 := (~ #2092 #2091)
-#2089 := (~ #1559 #2088)
-#2086 := (~ #2085 #2085)
-#2087 := [refl]: #2086
-#2090 := [nnf-neg #2087]: #2089
-#2082 := (not #1322)
-#2083 := (~ #2082 #2081)
-#2078 := (not #1319)
-#2079 := (~ #2078 #2077)
-#2074 := (not #1316)
-#2075 := (~ #2074 #2073)
-#2070 := (not #1311)
-#2071 := (~ #2070 #2069)
-#2066 := (not #1303)
-#2067 := (~ #2066 #1300)
-#2064 := (~ #1300 #1300)
-#2062 := (~ #1297 #1297)
-#2063 := [refl]: #2062
-#2065 := [nnf-pos #2063]: #2064
-#2068 := [nnf-neg #2065]: #2067
-#2060 := (~ #2059 #2059)
-#2061 := [refl]: #2060
-#2072 := [nnf-neg #2061 #2068]: #2071
-#2055 := (~ #1303 #2054)
-#2056 := [sk]: #2055
-#2076 := [nnf-neg #2056 #2072]: #2075
-#2030 := (not #1285)
-#2031 := (~ #2030 #2027)
-#2028 := (~ #1282 #2027)
-#2025 := (~ #1279 #2024)
-#2020 := (~ #1276 #2019)
+#2452 := [monotonicity #2435 #2449]: #2451
+#2455 := [monotonicity #2452]: #2454
+#2458 := [monotonicity #2455]: #2457
+#2463 := [trans #2458 #2461]: #2462
+#2428 := (iff #1820 #2427)
+#2425 := (iff #1817 #2424)
+#2422 := (iff #1812 #2421)
+#2419 := (iff #1809 #2416)
+#2406 := (+ #1804 #1807)
+#2407 := (+ #1152 #2406)
+#2410 := (= #2407 0::int)
+#2417 := (iff #2410 #2416)
+#2418 := [rewrite]: #2417
+#2411 := (iff #1809 #2410)
+#2408 := (= #1808 #2407)
+#2409 := [rewrite]: #2408
+#2412 := [monotonicity #2409]: #2411
+#2420 := [trans #2412 #2418]: #2419
+#2404 := (iff #1811 #2403)
+#2401 := (iff #1810 #2398)
+#2390 := (+ #1152 #1804)
+#2393 := (>= #2390 0::int)
+#2399 := (iff #2393 #2398)
+#2400 := [rewrite]: #2399
+#2394 := (iff #1810 #2393)
+#2391 := (= #1805 #2390)
+#2392 := [rewrite]: #2391
+#2395 := [monotonicity #2392]: #2394
+#2402 := [trans #2395 #2400]: #2401
+#2405 := [monotonicity #2402]: #2404
+#2423 := [monotonicity #2405 #2420]: #2422
+#2426 := [monotonicity #2423]: #2425
+#2429 := [quant-intro #2426]: #2428
+#2466 := [monotonicity #2429 #2463]: #2465
+#2388 := (iff #1796 #2385)
+#2351 := (and #1777 #2345)
+#2382 := (and #2351 #2379)
+#2386 := (iff #2382 #2385)
+#2387 := [rewrite]: #2386
+#2383 := (iff #1796 #2382)
+#2380 := (iff #1792 #2379)
+#2377 := (iff #1789 #2376)
+#2374 := (iff #1773 #2373)
+#2371 := (iff #1770 #2370)
+#2368 := (= #1769 #2367)
+#2369 := [rewrite]: #2368
+#2372 := [monotonicity #2369]: #2371
+#2375 := [monotonicity #2372]: #2374
+#2378 := [monotonicity #2375]: #2377
+#2381 := [quant-intro #2378]: #2380
+#2364 := (iff #1786 #2351)
+#2356 := (not #2351)
+#2359 := (not #2356)
+#2362 := (iff #2359 #2351)
+#2363 := [rewrite]: #2362
+#2360 := (iff #1786 #2359)
+#2357 := (iff #1781 #2356)
+#2354 := (iff #1780 #2351)
+#2348 := (and #2345 #1777)
+#2352 := (iff #2348 #2351)
+#2353 := [rewrite]: #2352
+#2349 := (iff #1780 #2348)
+#2346 := (iff #1779 #2345)
+#2343 := (iff #1778 #2342)
+#2344 := [rewrite]: #2343
+#2347 := [monotonicity #2344]: #2346
+#2350 := [monotonicity #2347]: #2349
+#2355 := [trans #2350 #2353]: #2354
+#2358 := [monotonicity #2355]: #2357
+#2361 := [monotonicity #2358]: #2360
+#2365 := [trans #2361 #2363]: #2364
+#2384 := [monotonicity #2365 #2381]: #2383
+#2389 := [trans #2384 #2387]: #2388
+#2469 := [monotonicity #2389 #2466]: #2468
+#2472 := [monotonicity #2469]: #2471
+#2477 := [trans #2472 #2475]: #2476
+#2651 := [monotonicity #2477 #2648]: #2650
+#2653 := (iff #1737 #2652)
+#2340 := (iff #1726 #2339)
+#2337 := (iff #1723 #2336)
+#2334 := (iff #1718 #2333)
+#2331 := (iff #1712 #2330)
+#2328 := (iff #1711 #2325)
+#2318 := (+ #1054 #1709)
+#2321 := (>= #2318 0::int)
+#2326 := (iff #2321 #2325)
+#2327 := [rewrite]: #2326
+#2322 := (iff #1711 #2321)
+#2319 := (= #1710 #2318)
+#2320 := [rewrite]: #2319
+#2323 := [monotonicity #2320]: #2322
+#2329 := [trans #2323 #2327]: #2328
+#2332 := [monotonicity #2329]: #2331
+#2316 := (iff #1716 #2313)
+#2302 := (+ #1709 #1714)
+#2303 := (+ #1054 #2302)
+#2306 := (= #2303 0::int)
+#2314 := (iff #2306 #2313)
+#2315 := [rewrite]: #2314
+#2307 := (iff #1716 #2306)
+#2304 := (= #1715 #2303)
+#2305 := [rewrite]: #2304
+#2308 := [monotonicity #2305]: #2307
+#2317 := [trans #2308 #2315]: #2316
+#2335 := [monotonicity #2317 #2332]: #2334
+#2338 := [monotonicity #2335]: #2337
+#2341 := [quant-intro #2338]: #2340
+#2300 := (iff #1699 #2299)
+#2297 := (iff #1696 #2296)
+#2294 := (iff #1691 #2293)
+#2291 := (iff #1686 #2288)
+#2278 := (+ #1682 #1684)
+#2279 := (+ #993 #2278)
+#2282 := (= #2279 0::int)
+#2289 := (iff #2282 #2288)
+#2290 := [rewrite]: #2289
+#2283 := (iff #1686 #2282)
+#2280 := (= #1685 #2279)
+#2281 := [rewrite]: #2280
+#2284 := [monotonicity #2281]: #2283
+#2292 := [trans #2284 #2290]: #2291
+#2276 := (iff #1689 #2275)
+#2273 := (iff #1688 #2270)
+#2262 := (+ #993 #1684)
+#2265 := (>= #2262 0::int)
+#2271 := (iff #2265 #2270)
+#2272 := [rewrite]: #2271
+#2266 := (iff #1688 #2265)
+#2263 := (= #1687 #2262)
+#2264 := [rewrite]: #2263
+#2267 := [monotonicity #2264]: #2266
+#2274 := [trans #2267 #2272]: #2273
+#2277 := [monotonicity #2274]: #2276
+#2295 := [monotonicity #2277 #2292]: #2294
+#2298 := [monotonicity #2295]: #2297
+#2301 := [quant-intro #2298]: #2300
+#2654 := [monotonicity #2301 #2341]: #2653
+#2657 := [monotonicity #2654 #2651]: #2656
+#2662 := [trans #2657 #2660]: #2661
+#2260 := (iff #1671 #2257)
+#2223 := (and #1651 #2217)
+#2254 := (and #2223 #2251)
+#2258 := (iff #2254 #2257)
+#2259 := [rewrite]: #2258
+#2255 := (iff #1671 #2254)
+#2252 := (iff #1667 #2251)
+#2249 := (iff #1664 #2248)
+#2246 := (iff #1647 #2245)
+#2243 := (iff #1643 #2242)
+#2240 := (= #1642 #2239)
+#2241 := [rewrite]: #2240
+#2244 := [monotonicity #2241]: #2243
+#2247 := [monotonicity #2244]: #2246
+#2250 := [monotonicity #2247]: #2249
+#2253 := [quant-intro #2250]: #2252
+#2236 := (iff #1661 #2223)
+#2228 := (not #2223)
+#2231 := (not #2228)
+#2234 := (iff #2231 #2223)
+#2235 := [rewrite]: #2234
+#2232 := (iff #1661 #2231)
+#2229 := (iff #1655 #2228)
+#2226 := (iff #1654 #2223)
+#2220 := (and #2217 #1651)
+#2224 := (iff #2220 #2223)
+#2225 := [rewrite]: #2224
+#2221 := (iff #1654 #2220)
+#2218 := (iff #1653 #2217)
+#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
-#2008 := (~ #1260 #1260)
-#2009 := [refl]: #2008
-#2026 := [monotonicity #2009 #2021]: #2025
-#2029 := [nnf-pos #2026]: #2028
-#2032 := [nnf-neg #2029]: #2031
-#2080 := [nnf-neg #2032 #2076]: #2079
-#2006 := (~ #1285 #2003)
-#1981 := (exists (vars (?x50 T2)) #1980)
-#1989 := (or #1988 #1981)
-#1990 := (not #1989)
-#2004 := (~ #1990 #2003)
-#2000 := (not #1981)
-#2001 := (~ #2000 #1999)
-#1997 := (~ #1996 #1996)
-#1998 := [refl]: #1997
-#2002 := [nnf-neg #1998]: #2001
-#1994 := (~ #1993 #1993)
+#2077 := [nnf-neg #2021 #2073]: #2076
+#1998 := (not #1347)
+#1999 := (~ #1998 #1344)
+#1996 := (~ #1344 #1344)
+#1994 := (~ #1341 #1341)
 #1995 := [refl]: #1994
-#2005 := [nnf-neg #1995 #2002]: #2004
-#1991 := (~ #1285 #1990)
-#1992 := [sk]: #1991
-#2007 := [trans #1992 #2005]: #2006
-#2084 := [nnf-neg #2007 #2080]: #2083
-#1968 := (~ #1967 #1967)
-#1969 := [refl]: #1968
-#1965 := (~ #1964 #1964)
-#1966 := [refl]: #1965
-#1962 := (~ #1961 #1961)
-#1963 := [refl]: #1962
+#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
-#2094 := [nnf-neg #1960 #1963 #1966 #1969 #2084 #2090]: #2093
-#2345 := [nnf-neg #2094 #2341]: #2344
-#1955 := (not #1248)
-#1956 := (~ #1955 #1952)
-#1953 := (~ #1245 #1952)
-#1950 := (~ #1242 #1949)
-#1945 := (~ #1239 #1944)
+#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
-#1932 := (~ #1215 #1215)
-#1933 := [refl]: #1932
-#1951 := [monotonicity #1933 #1946]: #1950
-#1954 := [nnf-pos #1951]: #1953
-#1957 := [nnf-neg #1954]: #1956
-#1929 := (not #1639)
-#1930 := (~ #1929 #1926)
-#1927 := (~ #1203 #1926)
-#1924 := (~ #1200 #1923)
-#1919 := (~ #1197 #1918)
-#1920 := [sk]: #1919
-#1905 := (~ #1177 #1177)
-#1906 := [refl]: #1905
-#1925 := [monotonicity #1906 #1920]: #1924
-#1928 := [nnf-pos #1925]: #1927
-#1931 := [nnf-neg #1928]: #1930
-#1903 := (~ #1902 #1902)
+#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
-#2370 := [nnf-neg #1904 #1931 #1957 #2345 #2352 #2359 #2366]: #2369
-#1900 := (~ #1639 #1897)
-#1875 := (exists (vars (?x38 T2)) #1874)
-#1883 := (or #1882 #1875)
-#1884 := (not #1883)
-#1898 := (~ #1884 #1897)
-#1894 := (not #1875)
-#1895 := (~ #1894 #1893)
-#1891 := (~ #1890 #1890)
-#1892 := [refl]: #1891
-#1896 := [nnf-neg #1892]: #1895
-#1888 := (~ #1887 #1887)
-#1889 := [refl]: #1888
-#1899 := [nnf-neg #1889 #1896]: #1898
-#1885 := (~ #1639 #1884)
-#1886 := [sk]: #1885
-#1901 := [trans #1886 #1899]: #1900
-#2374 := [nnf-neg #1901 #2370]: #2373
-#1860 := (not #1165)
-#1861 := (~ #1860 #1162)
-#1858 := (~ #1162 #1162)
-#1856 := (~ #1159 #1159)
-#1857 := [refl]: #1856
-#1859 := [nnf-pos #1857]: #1858
-#1862 := [nnf-neg #1859]: #1861
-#2378 := [nnf-neg #1862 #2374]: #2377
-#1852 := (~ #1165 #1851)
-#1853 := [sk]: #1852
-#2382 := [nnf-neg #1853 #2378]: #2381
-#1830 := (not #1139)
-#1831 := (~ #1830 #1136)
-#1828 := (~ #1136 #1136)
-#1826 := (~ #1133 #1133)
-#1827 := [refl]: #1826
-#1829 := [nnf-pos #1827]: #1828
-#1832 := [nnf-neg #1829]: #1831
-#2386 := [nnf-neg #1832 #2382]: #2385
-#1822 := (~ #1139 #1821)
-#1823 := [sk]: #1822
-#2390 := [nnf-neg #1823 #2386]: #2389
-#1805 := (not #1124)
-#1806 := (~ #1805 #1121)
-#1803 := (~ #1121 #1121)
-#1801 := (~ #1120 #1120)
+#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
-#1804 := [nnf-pos #1802]: #1803
-#1807 := [nnf-neg #1804]: #1806
-#2394 := [nnf-neg #1807 #2390]: #2393
-#1797 := (~ #1124 #1796)
-#1798 := [sk]: #1797
-#2398 := [nnf-neg #1798 #2394]: #2397
-#1752 := (~ #1751 #1751)
-#1792 := [refl]: #1752
-#2402 := [nnf-neg #1792 #2398]: #2401
-#1790 := (~ #1115 #1115)
+#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
-#2405 := [nnf-neg #1791 #2402]: #2404
-#1726 := [not-or-elim #1722]: #1725
-#2406 := [mp~ #1726 #2405]: #2403
-#2407 := [mp #2406 #2939]: #2937
-#3581 := [mp #2407 #3580]: #3578
-#4510 := [mp #3581 #4509]: #4507
-#10108 := [unit-resolution #4510 #5109]: #4504
-#3836 := (or #4501 #4495)
-#3679 := [def-axiom]: #3836
-#10111 := [unit-resolution #3679 #10108]: #4495
-#10112 := (or #4498 #4492)
-#3753 := (* -1::int #1794)
-#3720 := (+ uf_9 #3753)
-#3722 := (<= #3720 0::int)
-#3827 := (= uf_9 #1794)
-#3801 := (= uf_11 ?x27!0)
-#3650 := (not #3801)
-#3649 := (= #1794 0::int)
-#4542 := (not #3649)
-#4541 := [hypothesis]: #1796
-#4593 := (or #4542 #1795)
-#4594 := [th-lemma]: #4593
-#4595 := [unit-resolution #4594 #4541]: #4542
-#3660 := (or #3659 #3649 #3650)
-#3816 := (= ?x27!0 uf_11)
-#3651 := (not #3816)
-#3652 := (or #3651 #3649)
-#3661 := (or #3659 #3652)
-#4532 := (iff #3661 #3660)
-#3674 := (or #3649 #3650)
-#4533 := (or #3659 #3674)
-#4536 := (iff #4533 #3660)
-#4537 := [rewrite]: #4536
-#4534 := (iff #3661 #4533)
-#3672 := (iff #3652 #3674)
-#4518 := (or #3650 #3649)
-#3658 := (iff #4518 #3674)
-#3655 := [rewrite]: #3658
-#3673 := (iff #3652 #4518)
-#3653 := (iff #3651 #3650)
-#3799 := (iff #3816 #3801)
-#3802 := [rewrite]: #3799
-#4517 := [monotonicity #3802]: #3653
-#3665 := [monotonicity #4517]: #3673
-#3656 := [trans #3665 #3655]: #3672
-#4535 := [monotonicity #3656]: #4534
-#4538 := [trans #4535 #4537]: #4532
-#3657 := [quant-inst]: #3661
-#4539 := [mp #3657 #4538]: #3660
-#4596 := [unit-resolution #4539 #4516 #4595]: #3650
-#3784 := (or #3801 #3827)
-#4132 := (forall (vars (?x25 T2)) (:pat #4131) #419)
-#4135 := (iff #424 #4132)
-#4133 := (iff #419 #419)
-#4134 := [refl]: #4133
-#4136 := [quant-intro #4134]: #4135
-#1749 := (~ #424 #424)
-#1787 := (~ #419 #419)
+#1795 := [nnf-neg #1791]: #1794
+#1787 := (~ #1786 #1786)
 #1788 := [refl]: #1787
-#1750 := [nnf-pos #1788]: #1749
-#1724 := [not-or-elim #1722]: #424
-#1789 := [mp~ #1724 #1750]: #424
-#4137 := [mp #1789 #4136]: #4132
-#3787 := (not #4132)
-#3788 := (or #3787 #3801 #3827)
-#3819 := (or #3816 #3827)
-#3789 := (or #3787 #3819)
-#3751 := (iff #3789 #3788)
-#3791 := (or #3787 #3784)
-#3742 := (iff #3791 #3788)
-#3749 := [rewrite]: #3742
-#3748 := (iff #3789 #3791)
-#3786 := (iff #3819 #3784)
-#3800 := [monotonicity #3802]: #3786
-#3750 := [monotonicity #3800]: #3748
-#3752 := [trans #3750 #3749]: #3751
-#3790 := [quant-inst]: #3789
-#3743 := [mp #3790 #3752]: #3788
-#4597 := [unit-resolution #3743 #4137]: #3784
-#4598 := [unit-resolution #4597 #4596]: #3827
-#4599 := (not #3827)
-#4600 := (or #4599 #3722)
-#4601 := [th-lemma]: #4600
-#4581 := [unit-resolution #4601 #4598]: #3722
-#4540 := (<= #1794 0::int)
-#4582 := (or #4540 #1795)
-#4583 := [th-lemma]: #4582
-#4584 := [unit-resolution #4583 #4541]: #4540
-#349 := (<= uf_9 0::int)
-#350 := (not #349)
+#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)
-#351 := (iff #54 #350)
-#352 := [rewrite]: #351
-#345 := [asserted]: #54
-#353 := [mp #345 #352]: #350
-#4585 := [th-lemma #353 #4584 #4581]: false
-#4580 := [lemma #4585]: #1795
-#3831 := (or #4498 #1796 #4492)
-#3832 := [def-axiom]: #3831
-#10113 := [unit-resolution #3832 #4580]: #10112
-#10114 := [unit-resolution #10113 #10111]: #4492
-#3855 := (or #4489 #4483)
-#3856 := [def-axiom]: #3855
-#10107 := [unit-resolution #3856 #10114]: #4483
-#3850 := (or #4486 #1948 #4480)
-#3851 := [def-axiom]: #3850
-#10115 := [unit-resolution #3851 #10107]: #4483
-#10116 := [unit-resolution #10115 #10110]: #4480
-#3876 := (or #4477 #4471)
-#3877 := [def-axiom]: #3876
-#10117 := [unit-resolution #3877 #10116]: #4471
-#3872 := (or #4474 #2982 #4468)
-#3873 := [def-axiom]: #3872
-#10118 := [unit-resolution #3873 #10117 #10109]: #4468
-#3860 := (or #4465 #4459)
-#3861 := [def-axiom]: #3860
-#10119 := [unit-resolution #3861 #10118]: #4459
-#10121 := (or #4462 #4456)
-#4588 := [hypothesis]: #4176
-#4058 := (or #4173 #2458)
-#4059 := [def-axiom]: #4058
-#4725 := [unit-resolution #4059 #4588]: #2458
-#4673 := (= uf_9 #1866)
-#4816 := (not #4673)
-#3725 := (or #4173 #1878)
-#4057 := [def-axiom]: #3725
-#4726 := [unit-resolution #4057 #4588]: #1878
-#4826 := (or #4816 #1877)
-#4827 := [th-lemma]: #4826
-#4828 := [unit-resolution #4827 #4726]: #4816
-#4847 := (or #4673 #2455)
-#4817 := [hypothesis]: #4816
-#4818 := [hypothesis]: #2458
-#4730 := (or #3787 #2455 #4673)
-#4674 := (or #1879 #4673)
-#4731 := (or #3787 #4674)
-#4717 := (iff #4731 #4730)
-#4727 := (or #2455 #4673)
-#4733 := (or #3787 #4727)
-#4715 := (iff #4733 #4730)
-#4716 := [rewrite]: #4715
-#4713 := (iff #4731 #4733)
-#4728 := (iff #4674 #4727)
-#4729 := [monotonicity #2457]: #4728
-#4714 := [monotonicity #4729]: #4713
-#4712 := [trans #4714 #4716]: #4717
-#4732 := [quant-inst]: #4731
-#4718 := [mp #4732 #4712]: #4730
-#4819 := [unit-resolution #4718 #4137 #4818 #4817]: false
-#4849 := [lemma #4819]: #4847
-#4829 := [unit-resolution #4849 #4828 #4725]: false
-#4830 := [lemma #4829]: #4173
-#3894 := (or #4462 #4176 #4456)
-#3904 := [def-axiom]: #3894
-#10122 := [unit-resolution #3904 #4830]: #10121
-#10123 := [unit-resolution #10122 #10119]: #4456
-#3889 := (or #4453 #4447)
-#3848 := [def-axiom]: #3889
-#10335 := [unit-resolution #3848 #10123]: #4447
-#3682 := (not #2696)
-#3925 := (or #4453 #106)
-#3921 := [def-axiom]: #3925
-#10124 := [unit-resolution #3921 #10123]: #106
-#8213 := (= #161 #105)
-#4974 := [hypothesis]: #4289
-#3741 := (or #4286 #509)
-#4023 := [def-axiom]: #3741
-#4975 := [unit-resolution #4023 #4974]: #509
-#8228 := [symm #4975]: #142
-#8026 := [monotonicity #8228]: #8213
-#4825 := [trans #8026 #10124]: #162
-#3701 := (or #4262 #2059)
-#3702 := [def-axiom]: #3701
-#7196 := [unit-resolution #3702 #4825]: #4262
-#4028 := (or #4286 #4280)
-#4017 := [def-axiom]: #4028
-#8815 := [unit-resolution #4017 #4974]: #4280
-#10558 := (or #4240 #614)
-#8833 := (?x47!7 ?x49!8)
-#8906 := (uf_4 uf_19 #8833)
-#8925 := (* -1::int #8906)
-#8828 := (uf_4 uf_14 #8833)
-#9957 := (+ #8828 #8925)
-#9963 := (>= #9957 0::int)
-#9956 := (= #8828 #8906)
-#10507 := (= #8906 #8828)
-#6339 := [hypothesis]: #509
-#10506 := [symm #6339]: #142
-#10508 := [monotonicity #10506]: #10507
-#10509 := [symm #10508]: #9956
-#10510 := (not #9956)
-#10505 := (or #10510 #9963)
-#10511 := [th-lemma]: #10505
-#10512 := [unit-resolution #10511 #10509]: #9963
-#8834 := (* -1::int #8828)
-#8675 := (uf_4 uf_14 ?x49!8)
-#8835 := (+ #8675 #8834)
-#8836 := (<= #8835 0::int)
-#8878 := (not #8836)
-#8859 := (up_6 uf_15 #8833)
-#8860 := (not #8859)
-#8837 := (uf_1 #8833 ?x49!8)
-#8838 := (uf_10 #8837)
-#8854 := (* -1::int #8838)
-#8855 := (+ #8834 #8854)
-#8856 := (+ #8675 #8855)
-#8857 := (= #8856 0::int)
-#8858 := (not #8857)
-#8843 := (or #8836 #8858 #8860)
-#8846 := (not #8843)
-#8810 := (* -1::int #8675)
-#8823 := (+ uf_9 #8810)
-#8811 := (<= #8823 0::int)
-#9028 := (not #8811)
-#10513 := [hypothesis]: #4243
-#3711 := (or #4240 #1984)
-#3716 := [def-axiom]: #3711
-#10514 := [unit-resolution #3716 #10513]: #1984
-#9024 := (+ #1971 #8810)
-#9021 := (>= #9024 0::int)
-#9023 := (= #1971 #8675)
-#10515 := (= #8675 #1971)
-#10516 := [monotonicity #6339]: #10515
-#10517 := [symm #10516]: #9023
-#10518 := (not #9023)
-#10519 := (or #10518 #9021)
-#10520 := [th-lemma]: #10519
-#10521 := [unit-resolution #10520 #10517]: #9021
-#9020 := (not #9021)
-#9029 := (or #9028 #9020 #1983)
-#9025 := [hypothesis]: #1984
-#9022 := [hypothesis]: #8811
-#9026 := [hypothesis]: #9021
-#9027 := [th-lemma #9026 #9022 #9025]: false
-#8827 := [lemma #9027]: #9029
-#10522 := [unit-resolution #8827 #10521 #10514]: #9028
-#10532 := (or #8811 #8846)
-#4052 := (or #4240 #2596)
-#3712 := [def-axiom]: #4052
-#10523 := [unit-resolution #3712 #10513]: #2596
-#3914 := (or #4453 #4213)
-#3882 := [def-axiom]: #3914
-#10531 := [unit-resolution #3882 #10123]: #4213
-#8851 := (or #4218 #2593 #8811 #8846)
-#8861 := (or #8860 #8858 #8836)
-#8862 := (not #8861)
-#8842 := (or #1985 #8811 #8862)
-#8864 := (or #4218 #8842)
-#8870 := (iff #8864 #8851)
-#8848 := (or #2593 #8811 #8846)
-#8866 := (or #4218 #8848)
-#8863 := (iff #8866 #8851)
-#8869 := [rewrite]: #8863
-#8867 := (iff #8864 #8866)
-#8849 := (iff #8842 #8848)
-#8841 := (iff #8862 #8846)
-#8844 := (iff #8861 #8843)
-#8845 := [rewrite]: #8844
-#8847 := [monotonicity #8845]: #8841
-#8850 := [monotonicity #2595 #8847]: #8849
-#8868 := [monotonicity #8850]: #8867
-#8871 := [trans #8868 #8869]: #8870
-#8865 := [quant-inst]: #8864
-#8872 := [mp #8865 #8871]: #8851
-#10533 := [unit-resolution #8872 #10531 #10523]: #10532
-#10534 := [unit-resolution #10533 #10522]: #8846
-#8876 := (or #8843 #8878)
-#8879 := [def-axiom]: #8876
-#10535 := [unit-resolution #8879 #10534]: #8878
-#8920 := (+ #1971 #8925)
-#8937 := (<= #8920 0::int)
-#8982 := (+ #8854 #8925)
-#8983 := (+ #1971 #8982)
-#9001 := (= #8983 0::int)
-#9173 := (<= #8983 0::int)
-#9960 := (<= #9957 0::int)
-#10536 := (or #10510 #9960)
-#10537 := [th-lemma]: #10536
-#10538 := [unit-resolution #10537 #10509]: #9960
-#8873 := (<= #8856 0::int)
-#8880 := (or #8843 #8857)
-#8881 := [def-axiom]: #8880
-#10539 := [unit-resolution #8881 #10534]: #8857
-#10540 := (or #8858 #8873)
-#10541 := [th-lemma]: #10540
-#10542 := [unit-resolution #10541 #10539]: #8873
-#9019 := (<= #9024 0::int)
-#10543 := (or #10518 #9019)
-#10544 := [th-lemma]: #10543
-#10545 := [unit-resolution #10544 #10517]: #9019
-#10185 := (not #9960)
-#10187 := (not #8873)
-#10186 := (not #9019)
-#10188 := (or #9173 #10186 #10187 #10185)
-#10148 := [hypothesis]: #9960
-#10149 := [hypothesis]: #8873
-#10151 := [hypothesis]: #9019
-#10152 := (not #9173)
-#10153 := [hypothesis]: #10152
-#10154 := [th-lemma #10153 #10151 #10149 #10148]: false
-#10189 := [lemma #10154]: #10188
-#10546 := [unit-resolution #10189 #10545 #10542 #10538]: #9173
-#9157 := (>= #8983 0::int)
-#8877 := (>= #8856 0::int)
-#10547 := (or #8858 #8877)
-#10548 := [th-lemma]: #10547
-#10549 := [unit-resolution #10548 #10539]: #8877
-#10528 := (not #9963)
-#10096 := (not #8877)
-#10529 := (or #9157 #9020 #10096 #10528)
-#10524 := [hypothesis]: #9963
-#10027 := [hypothesis]: #8877
-#10525 := (not #9157)
-#10526 := [hypothesis]: #10525
-#10527 := [th-lemma #10526 #9026 #10027 #10524]: false
-#10530 := [lemma #10527]: #10529
-#10550 := [unit-resolution #10530 #10521 #10549 #10512]: #9157
-#10551 := (or #9001 #10152 #10525)
-#10552 := [th-lemma]: #10551
-#10553 := [unit-resolution #10552 #10550 #10546]: #9001
-#9000 := (not #9001)
-#9007 := (or #8937 #9000)
-#4053 := (or #4240 #4232)
-#3696 := [def-axiom]: #4053
-#10554 := [unit-resolution #3696 #10513]: #4232
-#9111 := (or #4237 #8937 #9000)
-#8904 := (+ #1972 #8838)
-#8907 := (+ #8906 #8904)
-#8908 := (= #8907 0::int)
-#8909 := (not #8908)
-#8910 := (+ #8906 #1972)
-#8914 := (>= #8910 0::int)
-#8915 := (or #8914 #8909)
-#9120 := (or #4237 #8915)
-#9170 := (iff #9120 #9111)
-#9167 := (or #4237 #9007)
-#9113 := (iff #9167 #9111)
-#9169 := [rewrite]: #9113
-#9168 := (iff #9120 #9167)
-#9008 := (iff #8915 #9007)
-#9005 := (iff #8909 #9000)
-#9004 := (iff #8908 #9001)
-#8975 := (+ #8838 #8906)
-#8976 := (+ #1972 #8975)
-#8979 := (= #8976 0::int)
-#9002 := (iff #8979 #9001)
-#9003 := [rewrite]: #9002
-#8980 := (iff #8908 #8979)
-#8977 := (= #8907 #8976)
-#8978 := [rewrite]: #8977
-#8981 := [monotonicity #8978]: #8980
-#8999 := [trans #8981 #9003]: #9004
-#9006 := [monotonicity #8999]: #9005
-#8946 := (iff #8914 #8937)
-#8916 := (+ #1972 #8906)
-#8922 := (>= #8916 0::int)
-#8938 := (iff #8922 #8937)
-#8945 := [rewrite]: #8938
-#8923 := (iff #8914 #8922)
-#8918 := (= #8910 #8916)
-#8921 := [rewrite]: #8918
-#8924 := [monotonicity #8921]: #8923
-#8947 := [trans #8924 #8945]: #8946
-#9009 := [monotonicity #8947 #9006]: #9008
-#9112 := [monotonicity #9009]: #9168
-#9171 := [trans #9112 #9169]: #9170
-#9121 := [quant-inst]: #9120
-#9172 := [mp #9121 #9171]: #9111
-#10555 := [unit-resolution #9172 #10554]: #9007
-#10556 := [unit-resolution #10555 #10553]: #8937
-#10557 := [th-lemma #10521 #10556 #10535 #10512]: false
-#10559 := [lemma #10557]: #10558
-#8829 := [unit-resolution #10559 #4975]: #4240
-#4030 := (or #4283 #4243 #4277)
-#4034 := [def-axiom]: #4030
-#8830 := [unit-resolution #4034 #8829 #8815]: #4277
-#3761 := (or #4274 #4268)
-#3654 := [def-axiom]: #3761
-#8831 := [unit-resolution #3654 #8830]: #4268
-#4036 := (or #4271 #4265 #3250)
-#3758 := [def-axiom]: #4036
-#8832 := [unit-resolution #3758 #8831 #7196]: #3250
-#4045 := (or #3245 #3682)
-#4047 := [def-axiom]: #4045
-#8875 := [unit-resolution #4047 #8832]: #3682
-#3852 := (or #4453 #4188)
-#3907 := [def-axiom]: #3852
-#10131 := [unit-resolution #3907 #10123]: #4188
-#4042 := (or #3245 #2046)
-#4043 := [def-axiom]: #4042
-#8882 := [unit-resolution #4043 #8832]: #2046
-#4038 := (or #3245 #2050)
-#4044 := [def-axiom]: #4038
-#8883 := [unit-resolution #4044 #8832]: #2050
-#4959 := (or #4286 #2045 #4193 #2049 #2696)
-#4978 := (uf_4 uf_14 ?x53!11)
-#4972 := (= #2035 #4978)
-#4976 := (= #4978 #2035)
-#4971 := [monotonicity #4975]: #4976
-#4977 := [symm #4971]: #4972
-#4979 := (* -1::int #4978)
-#6252 := (+ #2035 #4979)
-#6267 := (<= #6252 0::int)
-#6377 := (not #6267)
-#6280 := [hypothesis]: #3682
-#6333 := [hypothesis]: #2050
-#6336 := [hypothesis]: #4188
-#6338 := [hypothesis]: #2046
-#4027 := (or #4286 #4222)
-#4024 := [def-axiom]: #4027
-#4930 := [unit-resolution #4024 #4974]: #4222
-#6383 := (or #6377 #2045 #4227 #4193 #2049 #2696 #614)
-#5295 := (uf_4 uf_14 ?x54!10)
-#5296 := (* -1::int #5295)
-#5291 := (+ uf_9 #5296)
-#5297 := (<= #5291 0::int)
-#5298 := (up_6 uf_15 ?x54!10)
-#5736 := (not #5298)
-#5668 := (+ #4979 #5295)
-#5669 := (+ #2040 #5668)
-#5661 := (>= #5669 0::int)
-#6283 := (not #5661)
-#6285 := (+ #2037 #5296)
-#6297 := (>= #6285 0::int)
-#6284 := (= #2037 #5295)
-#6298 := (= #5295 #2037)
-#6296 := [monotonicity #6339]: #6298
-#6299 := [symm #6296]: #6284
-#6300 := (not #6284)
-#6301 := (or #6300 #6297)
-#6330 := [th-lemma]: #6301
-#6331 := [unit-resolution #6330 #6299]: #6297
-#6281 := [hypothesis]: #6267
-#6378 := (not #6297)
-#6379 := (or #6283 #6377 #2696 #6378)
-#6279 := [hypothesis]: #6297
-#6276 := [hypothesis]: #5661
-#6282 := [th-lemma #6276 #6281 #6280 #6279]: false
-#6380 := [lemma #6282]: #6379
-#6332 := [unit-resolution #6380 #6281 #6280 #6331]: #6283
-#6337 := (or #5736 #5661)
-#5758 := (or #4193 #2049 #5736 #5661)
-#5694 := (+ #5295 #4979)
-#5695 := (+ #2040 #5694)
-#5735 := (>= #5695 0::int)
-#5667 := (or #5736 #2049 #5735)
-#5763 := (or #4193 #5667)
-#6028 := (iff #5763 #5758)
-#5759 := (or #2049 #5736 #5661)
-#5765 := (or #4193 #5759)
-#5998 := (iff #5765 #5758)
-#5999 := [rewrite]: #5998
-#5766 := (iff #5763 #5765)
-#5762 := (iff #5667 #5759)
-#5687 := (or #5736 #2049 #5661)
-#5760 := (iff #5687 #5759)
-#5761 := [rewrite]: #5760
-#5690 := (iff #5667 #5687)
-#5688 := (iff #5735 #5661)
-#5670 := (= #5695 #5669)
-#5671 := [rewrite]: #5670
-#5689 := [monotonicity #5671]: #5688
-#5691 := [monotonicity #5689]: #5690
-#5757 := [trans #5691 #5761]: #5762
-#5767 := [monotonicity #5757]: #5766
-#6029 := [trans #5767 #5999]: #6028
-#5764 := [quant-inst]: #5763
-#6030 := [mp #5764 #6029]: #5758
-#6266 := [unit-resolution #6030 #6336 #6333]: #6337
-#6278 := [unit-resolution #6266 #6332]: #5736
-#5300 := (or #5297 #5298)
-#6257 := [hypothesis]: #4222
-#5326 := (or #4227 #5297 #5298)
-#5299 := (or #5298 #5297)
-#5327 := (or #4227 #5299)
-#5333 := (iff #5327 #5326)
-#5329 := (or #4227 #5300)
-#5331 := (iff #5329 #5326)
-#5332 := [rewrite]: #5331
-#5324 := (iff #5327 #5329)
-#5301 := (iff #5299 #5300)
-#5325 := [rewrite]: #5301
-#5330 := [monotonicity #5325]: #5324
-#5334 := [trans #5330 #5332]: #5333
-#5328 := [quant-inst]: #5327
-#5382 := [mp #5328 #5334]: #5326
-#6381 := [unit-resolution #5382 #6257]: #5300
-#6376 := [unit-resolution #6381 #6278]: #5297
-#6382 := [th-lemma #6331 #6376 #6338]: false
-#6384 := [lemma #6382]: #6383
-#4955 := [unit-resolution #6384 #4930 #6338 #6336 #6333 #6280 #4975]: #6377
-#4956 := (not #4972)
-#4957 := (or #4956 #6267)
-#4958 := [th-lemma]: #4957
-#4929 := [unit-resolution #4958 #4955 #4977]: false
-#4954 := [lemma #4929]: #4959
-#8884 := [unit-resolution #4954 #8883 #8882 #10131 #4974 #8875]: false
-#8887 := [lemma #8884]: #4286
-#3923 := (or #4450 #4289 #4444)
-#3924 := [def-axiom]: #3923
-#10456 := [unit-resolution #3924 #8887 #10335]: #4444
-#3945 := (or #4441 #189)
-#3931 := [def-axiom]: #3945
-#10469 := [unit-resolution #3931 #10456]: #189
-#10470 := [symm #10469]: #7202
-#13610 := (= #11533 #188)
-#13435 := (= #10571 uf_22)
-#10572 := (= uf_22 #10571)
+#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)
+#4795 := (or #3998 #4719)
+#4793 := (iff #4795 #4792)
+#4630 := (or #3998 #4786)
+#4679 := (iff #4630 #4792)
+#4788 := [rewrite]: #4679
+#4631 := (iff #4795 #4630)
+#4787 := (iff #4719 #4786)
+#4782 := (iff #4717 #4784)
+#4776 := (iff #4716 #4773)
+#4757 := (+ #4354 #4714)
+#4758 := (+ #1765 #4757)
+#4769 := (= #4758 0::int)
+#4774 := (iff #4769 #4773)
+#4775 := [rewrite]: #4774
+#4770 := (iff #4716 #4769)
+#4767 := (= #4715 #4758)
+#4768 := [rewrite]: #4767
+#4771 := [monotonicity #4768]: #4770
+#4783 := [trans #4771 #4775]: #4776
+#4785 := [monotonicity #4783]: #4782
+#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
+#5358 := [unit-resolution #5425 #5357 #5342 #5281 #5336 #5341 #5338 #5310 #5269]: false
+#5354 := [lemma #5358]: #5359
+#6215 := [unit-resolution #5354 #6214]: #4205
+#3700 := (or #4202 #192)
+#3686 := [def-axiom]: #3700
+#7417 := [unit-resolution #3686 #6215]: #192
+#7413 := [symm #7417]: #7418
+#8694 := (= #8048 #191)
+#9757 := (= #6904 uf_22)
+#6905 := (= uf_22 #6904)
+#12 := (uf_1 #10 #11)
+#3825 := (pattern #12)
 #13 := (uf_3 #12)
-#309 := (= #11 #13)
-#4071 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #4070) #309)
-#313 := (forall (vars (?x2 T2) (?x3 T2)) #309)
-#4074 := (iff #313 #4071)
-#4072 := (iff #309 #309)
-#4073 := [refl]: #4072
-#4075 := [quant-intro #4073]: #4074
-#1730 := (~ #313 #313)
-#1762 := (~ #309 #309)
-#1763 := [refl]: #1762
-#1728 := [nnf-pos #1763]: #1730
+#293 := (= #11 #13)
+#3826 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #3825) #293)
+#297 := (forall (vars (?x2 T2) (?x3 T2)) #293)
+#3829 := (iff #297 #3826)
+#3827 := (iff #293 #293)
+#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)
-#314 := (iff #15 #313)
-#311 := (iff #14 #309)
-#312 := [rewrite]: #311
-#315 := [quant-intro #312]: #314
-#308 := [asserted]: #15
-#318 := [mp #308 #315]: #313
-#1764 := [mp~ #318 #1728]: #313
-#4076 := [mp #1764 #4075]: #4071
-#7845 := (not #4071)
-#10578 := (or #7845 #10572)
-#10579 := [quant-inst]: #10578
-#13434 := [unit-resolution #10579 #4076]: #10572
-#13436 := [symm #13434]: #13435
-#13611 := [monotonicity #13436]: #13610
-#13613 := [trans #13611 #10470]: #13612
-#27317 := [monotonicity #13613 #27305]: #27316
-#27319 := [symm #27317]: #27318
-#27321 := [monotonicity #27319]: #27320
-#27315 := [hypothesis]: #16890
-#27322 := [mp #27315 #27321]: #27198
-#27164 := (= #10571 #19932)
-#25982 := (up_6 uf_15 #19932)
-#27170 := (or #25982 #27164)
-#27175 := (iff #27162 #27170)
-#30 := (:var 1 T5)
-#20 := (:var 2 T2)
-#29 := (:var 3 T4)
-#31 := (uf_7 #29 #20 #30)
-#32 := (up_6 #31 #11)
-#4090 := (pattern #32)
-#35 := (up_6 #29 #11)
-#34 := (= #30 uf_8)
-#24 := (= #11 #20)
-#36 := (ite #24 #34 #35)
-#37 := (iff #32 #36)
-#4091 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4090) #37)
-#38 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #37)
-#4094 := (iff #38 #4091)
-#4092 := (iff #37 #37)
-#4093 := [refl]: #4092
-#4095 := [quant-intro #4093]: #4094
-#1735 := (~ #38 #38)
-#1771 := (~ #37 #37)
-#1772 := [refl]: #1771
-#1736 := [nnf-pos #1772]: #1735
-#325 := [asserted]: #38
-#1773 := [mp~ #325 #1736]: #38
-#4096 := [mp #1773 #4095]: #4091
-#6627 := (not #4091)
-#27178 := (or #6627 #27175)
-#3770 := (= uf_8 uf_8)
-#27158 := (= #19932 #10571)
-#27159 := (ite #27158 #3770 #25982)
-#27163 := (iff #27162 #27159)
-#27179 := (or #6627 #27163)
-#27181 := (iff #27179 #27178)
-#27183 := (iff #27178 #27178)
-#27184 := [rewrite]: #27183
-#27176 := (iff #27163 #27175)
-#27173 := (iff #27159 #27170)
-#27167 := (ite #27164 true #25982)
-#27171 := (iff #27167 #27170)
-#27172 := [rewrite]: #27171
-#27168 := (iff #27159 #27167)
-#3773 := (iff #3770 true)
-#3762 := [rewrite]: #3773
-#27165 := (iff #27158 #27164)
-#27166 := [rewrite]: #27165
-#27169 := [monotonicity #27166 #3762]: #27168
-#27174 := [trans #27169 #27172]: #27173
-#27177 := [monotonicity #27174]: #27176
-#27182 := [monotonicity #27177]: #27181
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-#27180 := [quant-inst]: #27179
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-#5924 := (up_6 uf_15 #5912)
-#27308 := (iff #5924 #25982)
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-#5918 := (uf_10 #5917)
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-#5920 := (+ #5914 #5919)
-#5650 := (uf_4 uf_14 ?x75!20)
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-#5922 := (= #5921 0::int)
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-#5916 := (<= #5915 0::int)
-#5931 := (or #5916 #5923 #5925)
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-#5680 := (* -1::int #5650)
-#5928 := (+ uf_9 #5680)
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-#4010 := (or #3324 #4009)
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-#13689 := (or #3324 #2772)
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-#6526 := (uf_10 #6525)
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-#6552 := (+ #182 #6551)
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-#6492 := (uf_4 uf_14 ?x68!16)
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-#6545 := (+ #182 #6544)
-#6546 := (>= #6545 0::int)
-#6530 := (* -1::int #6526)
-#6534 := (+ uf_9 #6530)
-#6535 := (<= #6534 0::int)
-#6581 := (or #6535 #6546)
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-#6578 := (= #2184 #6492)
-#9424 := (not #6578)
-#6510 := (+ #2184 #6509)
-#13145 := (>= #6510 0::int)
-#13450 := (not #13145)
-#13018 := (= ?x67!17 #10571)
-#6294 := (up_6 uf_15 ?x67!17)
-#13025 := (or #6294 #13018)
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-#13019 := (ite #13018 #3770 #6294)
-#13021 := (iff #13020 #13019)
-#12985 := (or #6627 #13021)
-#12987 := (iff #12985 #12984)
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-#13022 := (ite #13018 true #6294)
-#13026 := (iff #13022 #13025)
-#13027 := [rewrite]: #13026
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-#13024 := [monotonicity #3762]: #13023
-#13029 := [trans #13024 #13027]: #13028
-#13032 := [monotonicity #13029]: #13031
-#12988 := [monotonicity #13032]: #12987
-#12990 := [trans #12988 #12989]: #12987
-#12986 := [quant-inst]: #12985
-#12991 := [mp #12986 #12990]: #12984
-#13478 := [unit-resolution #12991 #4096]: #13030
-#11491 := (iff #2187 #13020)
-#13479 := (iff #13020 #2187)
-#11490 := [monotonicity #13613]: #13479
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-#3864 := (or #3324 #2187)
-#3865 := [def-axiom]: #3864
-#6614 := [unit-resolution #3865 #6611]: #2187
-#13625 := [mp #6614 #13624]: #13020
-#13051 := (not #13020)
-#13048 := (not #13030)
-#13052 := (or #13048 #13051 #13025)
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-#13626 := [unit-resolution #13053 #13625 #13478]: #13025
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-#6322 := (+ #182 #6509)
-#6323 := (<= #6322 0::int)
-#3838 := (up_6 uf_15 ?x68!16)
-#12920 := (not #3838)
-#12850 := (= ?x68!16 #10571)
-#12856 := (or #3838 #12850)
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-#12885 := (iff #12852 #12856)
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-#12851 := (ite #12850 #3770 #3838)
-#12853 := (iff #12852 #12851)
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-#12890 := (iff #12888 #12882)
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-#12883 := (iff #12851 #12856)
-#12848 := (ite #12850 true #3838)
-#12857 := (iff #12848 #12856)
-#12858 := [rewrite]: #12857
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-#12884 := [trans #12855 #12858]: #12883
-#12887 := [monotonicity #12884]: #12886
-#12891 := [monotonicity #12887]: #12890
-#12918 := [trans #12891 #12917]: #12890
-#12889 := [quant-inst]: #12888
-#12919 := [mp #12889 #12918]: #12882
-#13654 := [unit-resolution #12919 #4096]: #12885
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-#13653 := (iff #2189 #12955)
-#13657 := (iff #2188 #12852)
-#13655 := (iff #12852 #2188)
-#13656 := [monotonicity #13613]: #13655
-#13658 := [symm #13656]: #13657
-#13659 := [monotonicity #13658]: #13653
-#4007 := (or #3324 #2189)
-#4008 := [def-axiom]: #4007
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-#13660 := [mp #6613 #13659]: #12955
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-#6343 := (+ #1357 #6492)
-#6346 := (>= #6343 0::int)
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-#6344 := (= #6340 #6343)
-#6345 := [rewrite]: #6344
-#6348 := [monotonicity #6345]: #6347
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-#13181 := [monotonicity #6329]: #13173
-#13185 := [trans #13181 #13183]: #13184
-#13179 := [quant-inst]: #13174
-#13187 := [mp #13179 #13185]: #13176
-#13663 := [unit-resolution #13187 #10883]: #6327
-#10648 := [unit-resolution #13663 #13662]: #6323
-#13045 := (not #13025)
-#13449 := (not #6323)
-#13468 := (or #13450 #2772 #13449 #13045)
-#4615 := (uf_24 uf_22)
-#4656 := (* -1::int #4615)
-#6243 := (+ #2182 #4656)
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-#6648 := (>= #6642 0::int)
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-#6542 := (iff #6533 #6541)
-#6539 := (= #6532 #6538)
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-#6543 := [monotonicity #6540]: #6542
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-#13101 := (or #4315 #6535 #6546 #6555)
-#6527 := (+ #6526 #2770)
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-#6536 := (or #6535 #6533 #6529)
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-#13120 := (iff #13102 #13101)
-#13104 := (or #4315 #6558)
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-#13119 := [rewrite]: #13118
-#13116 := (iff #13102 #13104)
-#6559 := (iff #6536 #6558)
-#6556 := (iff #6529 #6555)
-#6553 := (= #6528 #6552)
-#6554 := [rewrite]: #6553
-#6557 := [monotonicity #6554]: #6556
-#6560 := [monotonicity #6550 #6557]: #6559
-#13117 := [monotonicity #6560]: #13116
-#13115 := [trans #13117 #13119]: #13120
-#13103 := [quant-inst]: #13102
-#13121 := [mp #13103 #13115]: #13101
-#13456 := [unit-resolution #13121 #10914]: #6558
-#13457 := [unit-resolution #13456 #13455 #13454 #13524]: false
-#13475 := [lemma #13457]: #13474
-#13577 := [unit-resolution #13475 #13477]: #6555
-#13677 := (or #13523 #13122)
-#13678 := [th-lemma]: #13677
-#13679 := [unit-resolution #13678 #13577]: #13122
-#13013 := (uf_1 #10571 ?x68!16)
-#13014 := (uf_10 #13013)
-#13149 := (* -1::int #13014)
-#13526 := (+ #6526 #13149)
-#13530 := (>= #13526 0::int)
-#13525 := (= #6526 #13014)
-#13534 := (= #13014 #6526)
-#13532 := (= #13013 #6525)
-#13533 := [monotonicity #13436]: #13532
-#13535 := [monotonicity #13533]: #13534
-#13536 := [symm #13535]: #13525
-#13537 := (not #13525)
-#13538 := (or #13537 #13530)
-#13539 := [th-lemma]: #13538
-#13540 := [unit-resolution #13539 #13536]: #13530
-#13499 := (<= #13014 0::int)
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-#12922 := (not #12850)
-#12923 := (or #12856 #12922)
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-#13680 := [unit-resolution #12924 #13661]: #12922
+#298 := (iff #15 #297)
+#295 := (iff #14 #293)
+#296 := [rewrite]: #295
+#299 := [quant-intro #296]: #298
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+#6321 := (or #5007 #6905)
+#6319 := [quant-inst]: #6321
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+#9758 := [symm #9756]: #9757
+#8603 := [monotonicity #9758]: #8694
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+#30523 := [monotonicity #8592]: #30522
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+#30519 := [hypothesis]: #30518
+#10337 := (or #9640 #10311)
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+#8831 := (= ?x63!14 uf_22)
+#8074 := (= ?x63!14 #6904)
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+#8269 := (<= #8213 0::int)
+#7863 := (up_6 uf_15 ?x63!14)
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+#8128 := (iff #8055 #8073)
+#8076 := (or #6010 #8128)
+#8075 := (ite #8074 #5970 #7863)
+#8051 := (iff #8073 #8075)
+#8160 := (or #6010 #8051)
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+#8140 := (iff #8051 #8128)
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+#8122 := (iff #8051 #8126)
+#8124 := (iff #8075 #8055)
+#8052 := (ite #8074 true #7863)
+#8123 := (iff #8052 #8055)
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+#8054 := [monotonicity #5976]: #8053
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+#8127 := [monotonicity #8125]: #8122
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+#7891 := (uf_1 uf_22 ?x63!14)
+#7892 := (uf_10 #7891)
+#7831 := (* -1::int #1939)
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+#7912 := (>= #7911 0::int)
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+#7928 := (or #4076 #2494 #7946)
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+#7944 := (iff #7940 #7943)
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+#7908 := (iff #7899 #7907)
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+#7909 := [monotonicity #7906]: #7908
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+#9020 := [unit-resolution #7582 #6216 #8506]: #7946
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+#6768 := (not #8055)
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+#9705 := (uf_4 uf_14 #8339)
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+#8358 := (uf_4 uf_14 #6904)
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+#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)
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+#8309 := (or #8159 #8299)
 #56 := (uf_10 #12)
-#385 := (<= #56 0::int)
-#386 := (not #385)
+#57 := (= #56 0::int)
 #55 := (= #10 #11)
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-#4121 := (iff #392 #4118)
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-#1745 := (~ #392 #392)
-#1744 := (~ #389 #389)
-#1782 := [refl]: #1744
-#1746 := [nnf-pos #1782]: #1745
-#61 := (< 0::int #56)
 #60 := (not #55)
-#62 := (implies #60 #61)
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-#388 := [rewrite]: #387
-#391 := [monotonicity #388]: #390
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-#381 := [rewrite]: #380
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-#13503 := (iff #13501 #12850)
-#13504 := [rewrite]: #13503
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-#13518 := [mp #13510 #13517]: #13508
-#13681 := [unit-resolution #13518 #4123 #13680]: #13500
-#13552 := (not #13122)
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-#13543 := [hypothesis]: #13122
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-#13684 := [unit-resolution #13047 #13683 #13626]: #13018
-#13685 := [trans #13684 #13436]: #6295
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-#7566 := (uf_10 #7565)
-#6801 := (* -1::int #2143)
-#7652 := (+ #6801 #7566)
-#7653 := (+ #182 #7652)
-#7726 := (>= #7653 0::int)
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-#7567 := (* -1::int #7566)
-#7569 := (+ uf_9 #7567)
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-#7787 := (or #4307 #2747 #7720)
-#7561 := (+ #1357 #7567)
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-#7752 := [rewrite]: #7751
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-#7470 := (= #7568 #7469)
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-#7392 := [trans #7812 #7809]: #6906
-#7789 := [quant-inst]: #7783
-#7572 := [mp #7789 #7392]: #7787
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-#8277 := (= uf_22 ?x63!14)
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-#9109 := (or #8348 #7726)
-#7497 := (+ #182 #6801)
-#8974 := (>= #7497 0::int)
-#8973 := (= #182 #2143)
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-#8218 := (= ?x63!14 uf_22)
-#9035 := [hypothesis]: #8277
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-#9040 := [monotonicity #9036]: #9039
-#9072 := [symm #9040]: #8973
-#9073 := (not #8973)
-#9074 := (or #9073 #8974)
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-#8497 := (>= #7566 0::int)
-#8487 := (= #7566 0::int)
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-#57 := (= #56 0::int)
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-#372 := (forall (vars (?x20 T2) (?x21 T2)) #369)
-#4115 := (iff #372 #4112)
-#4113 := (iff #369 #369)
-#4114 := [refl]: #4113
-#4116 := [quant-intro #4114]: #4115
-#1741 := (~ #372 #372)
-#1780 := (~ #369 #369)
-#1781 := [refl]: #1780
-#1742 := [nnf-pos #1781]: #1741
+#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
 #58 := (implies #55 #57)
 #59 := (forall (vars (?x20 T2) (?x21 T2)) #58)
-#375 := (iff #59 #372)
-#348 := (= 0::int #56)
-#359 := (or #60 #348)
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-#373 := (iff #364 #372)
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-#365 := (iff #59 #364)
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-#357 := (iff #58 #356)
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-#355 := [rewrite]: #354
-#358 := [monotonicity #355]: #357
-#363 := [trans #358 #361]: #362
-#366 := [quant-intro #363]: #365
-#376 := [trans #366 #374]: #375
-#346 := [asserted]: #59
-#377 := [mp #346 #376]: #372
-#1743 := [mp~ #377 #1742]: #372
-#4117 := [mp #1743 #4116]: #4112
-#7157 := (not #4112)
-#8491 := (or #7157 #8348 #8487)
-#8492 := (or #7157 #8488)
-#8494 := (iff #8492 #8491)
-#8495 := [rewrite]: #8494
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-#8496 := [mp #8493 #8495]: #8491
-#9075 := [unit-resolution #8496 #4117]: #8488
-#9076 := [unit-resolution #9075 #9035]: #8487
-#9104 := (not #8487)
-#9105 := (or #9104 #8497)
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-#9106 := [unit-resolution #9071 #9076]: #8497
-#9103 := [th-lemma #9106 #10210 #9066]: false
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-#7253 := (up_6 uf_15 ?x63!14)
-#8282 := (or #7253 #8277)
-#8262 := (up_6 #188 ?x63!14)
-#8295 := (iff #8262 #8282)
-#8298 := (or #6627 #8295)
-#8219 := (ite #8218 #3770 #7253)
-#8276 := (iff #8262 #8219)
-#8293 := (or #6627 #8276)
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-#8303 := [rewrite]: #8302
-#8296 := (iff #8276 #8295)
-#8285 := (iff #8219 #8282)
-#8280 := (ite #8277 true #7253)
-#8283 := (iff #8280 #8282)
-#8284 := [rewrite]: #8283
-#8275 := (iff #8219 #8280)
-#8278 := (iff #8218 #8277)
-#8279 := [rewrite]: #8278
-#8281 := [monotonicity #8279 #3762]: #8275
-#8294 := [trans #8281 #8284]: #8285
-#8297 := [monotonicity #8294]: #8296
-#8301 := [monotonicity #8297]: #8300
-#8335 := [trans #8301 #8303]: #8300
-#8299 := [quant-inst]: #8293
-#8336 := [mp #8299 #8335]: #8298
-#8642 := [unit-resolution #8336 #4096]: #8295
-#8763 := (iff #2145 #8262)
-#8755 := (iff #8262 #2145)
-#10471 := [monotonicity #10470]: #8755
-#10474 := [symm #10471]: #8763
-#4014 := (or #2750 #2145)
-#4015 := [def-axiom]: #4014
-#10468 := [unit-resolution #4015 #10460]: #2145
-#10560 := [mp #10468 #10474]: #8262
-#8379 := (not #8262)
-#8376 := (not #8295)
-#8380 := (or #8376 #8379 #8282)
-#8375 := [def-axiom]: #8380
-#10561 := [unit-resolution #8375 #10560 #8642]: #8282
-#8351 := (not #8282)
-#10563 := (or #8277 #7726 #8617 #8351)
-#10231 := (or #8277 #7726 #4202 #8617 #8351)
-#8489 := (uf_3 #7565)
-#10159 := (uf_4 uf_14 #8489)
-#10160 := (* -1::int #10159)
-#8614 := (uf_4 uf_14 #8498)
-#10161 := (+ #8614 #10160)
-#10162 := (>= #10161 0::int)
-#10163 := (up_6 uf_15 #8489)
-#10201 := (iff #7253 #10163)
-#10199 := (iff #10163 #7253)
-#10197 := (= #8489 ?x63!14)
-#8490 := (= ?x63!14 #8489)
-#8500 := (or #7845 #8490)
-#8501 := [quant-inst]: #8500
-#10196 := [unit-resolution #8501 #4076]: #8490
-#10198 := [symm #10196]: #10197
-#10200 := [monotonicity #10198]: #10199
-#10202 := [symm #10200]: #10201
-#10193 := [hypothesis]: #8282
-#10194 := [hypothesis]: #8348
-#8352 := (or #8351 #7253 #8277)
-#8353 := [def-axiom]: #8352
-#10195 := [unit-resolution #8353 #10194 #10193]: #7253
-#10203 := [mp #10195 #10202]: #10163
-#10164 := (not #10163)
-#10207 := (or #10162 #10164)
-#10204 := (not #8617)
-#10205 := [hypothesis]: #10204
-#10206 := [hypothesis]: #4197
-#10169 := (or #4202 #8617 #10162 #10164)
-#10165 := (or #8617 #10164 #10162)
-#10170 := (or #4202 #10165)
-#10177 := (iff #10170 #10169)
-#10166 := (or #8617 #10162 #10164)
-#10172 := (or #4202 #10166)
-#10175 := (iff #10172 #10169)
-#10176 := [rewrite]: #10175
-#10173 := (iff #10170 #10172)
-#10167 := (iff #10165 #10166)
-#10168 := [rewrite]: #10167
-#10174 := [monotonicity #10168]: #10173
-#10178 := [trans #10174 #10176]: #10177
-#10171 := [quant-inst]: #10170
-#10179 := [mp #10171 #10178]: #10169
-#10208 := [unit-resolution #10179 #10206 #10205]: #10207
-#10209 := [unit-resolution #10208 #10203]: #10162
-#8246 := (<= #7566 0::int)
-#8247 := (not #8246)
-#8249 := (or #8247 #8277)
-#8252 := (or #7140 #8247 #8277)
-#8248 := (or #8277 #8247)
-#8253 := (or #7140 #8248)
-#8311 := (iff #8253 #8252)
-#8304 := (or #7140 #8249)
-#8307 := (iff #8304 #8252)
-#8308 := [rewrite]: #8307
-#8305 := (iff #8253 #8304)
-#8250 := (iff #8248 #8249)
-#8251 := [rewrite]: #8250
-#8306 := [monotonicity #8251]: #8305
-#8436 := [trans #8306 #8308]: #8311
-#8255 := [quant-inst]: #8253
-#8486 := [mp #8255 #8436]: #8252
-#10211 := [unit-resolution #8486 #4123]: #8249
-#10212 := [unit-resolution #10211 #10194]: #8247
-#10213 := (or #8497 #8246)
-#10214 := [th-lemma]: #10213
-#10215 := [unit-resolution #10214 #10212]: #8497
-#10184 := (+ #2143 #10160)
-#10191 := (<= #10184 0::int)
-#10183 := (= #2143 #10159)
-#10216 := (= #10159 #2143)
-#10217 := [monotonicity #10198]: #10216
-#10218 := [symm #10217]: #10183
-#10219 := (not #10183)
-#10220 := (or #10219 #10191)
-#10221 := [th-lemma]: #10220
-#10222 := [unit-resolution #10221 #10218]: #10191
-#8625 := (* -1::int #8614)
-#8892 := (+ #182 #8625)
-#8905 := (>= #8892 0::int)
-#8891 := (= #182 #8614)
-#10223 := (= #8614 #182)
-#8787 := (= #8498 uf_22)
-#8788 := [symm #8783]: #8787
-#10224 := [monotonicity #8788]: #10223
-#10225 := [symm #10224]: #8891
-#10226 := (not #8891)
-#10227 := (or #10226 #8905)
-#10228 := [th-lemma]: #10227
-#10229 := [unit-resolution #10228 #10225]: #8905
-#10230 := [th-lemma #10229 #10222 #10215 #10210 #10209]: false
-#10232 := [lemma #10230]: #10231
-#10564 := [unit-resolution #10232 #10562]: #10563
-#10565 := [unit-resolution #10564 #10561 #10467 #10466]: #8617
-#10568 := [mp #10565 #10567]: #180
-#10569 := [unit-resolution #10457 #10568]: false
-#10570 := [lemma #10569]: #2750
-#3957 := (or #4429 #4423)
-#3958 := [def-axiom]: #3957
-#10917 := [unit-resolution #3958 #10916]: #4423
-#3953 := (or #4426 #2753 #4420)
-#3954 := [def-axiom]: #3953
-#10918 := [unit-resolution #3954 #10917]: #4423
-#10919 := [unit-resolution #10918 #10570]: #4420
-#11065 := (or #4417 #4396)
-#3926 := (or #4453 #4180)
-#3906 := [def-axiom]: #3926
-#9067 := [unit-resolution #3906 #10123]: #4180
-#7840 := (or #4417 #888 #4315 #4307 #4185 #4396 #1636)
-#4734 := (>= #182 0::int)
-#7810 := [hypothesis]: #4180
-#6390 := (or #4185 #4734)
-#6391 := [quant-inst]: #6390
-#7811 := [unit-resolution #6391 #7810]: #4734
-#7291 := (uf_1 uf_22 ?x65!15)
-#7292 := (uf_10 #7291)
-#4945 := (* -1::int #2166)
-#7344 := (+ #4945 #7292)
-#7345 := (+ #182 #7344)
-#7389 := (<= #7345 0::int)
-#7362 := (= #7345 0::int)
-#6919 := (uf_4 uf_14 ?x65!15)
-#7124 := (* -1::int #6919)
-#7338 := (+ #7124 #7292)
-#7339 := (+ #182 #7338)
-#7340 := (>= #7339 0::int)
-#7434 := (not #7340)
-#7295 := (* -1::int #7292)
-#7299 := (+ uf_9 #7295)
-#7350 := (<= #7299 0::int)
-#7440 := (or #7340 #7350)
-#7445 := (not #7440)
-#6927 := (= #2166 #6919)
-#8448 := (not #6927)
-#7125 := (+ #2166 #7124)
-#7959 := (>= #7125 0::int)
-#7967 := (not #7959)
-#7578 := (>= #6919 0::int)
-#7581 := (or #4185 #7578)
-#7576 := [quant-inst]: #7581
-#7815 := [unit-resolution #7576 #7810]: #7578
-#7816 := [hypothesis]: #4393
-#7817 := [hypothesis]: #4420
-#3962 := (or #4417 #4411)
-#3966 := [def-axiom]: #3962
-#7818 := [unit-resolution #3966 #7817]: #4411
-#4798 := (= #105 #209)
-#7837 := (iff #4798 #210)
-#7836 := [commutativity]: #1392
-#7829 := (iff #4798 #713)
-#7814 := [hypothesis]: #106
-#7835 := [monotonicity #7814]: #7829
-#7838 := [trans #7835 #7836]: #7837
-#4810 := (<= #105 0::int)
-#7819 := (or #1636 #4810)
-#7830 := [th-lemma]: #7819
-#7831 := [unit-resolution #7830 #7814]: #4810
-#7201 := [hypothesis]: #189
-#3964 := (or #4417 #4327)
-#3965 := [def-axiom]: #3964
-#7832 := [unit-resolution #3965 #7817]: #4327
-#7250 := (not #4734)
-#7249 := (not #4810)
-#7251 := (or #4798 #7249 #7250 #888 #4332 #4307)
-#4756 := (uf_1 uf_22 uf_11)
-#4757 := (uf_10 #4756)
-#7072 := (<= #4757 0::int)
-#7073 := (not #7072)
-#4695 := (= uf_11 uf_22)
-#6917 := (not #4695)
-#4739 := (up_6 uf_15 uf_11)
-#7422 := (or #4695 #4739)
-#6926 := (not #7422)
-#7417 := (up_6 #188 uf_11)
-#7427 := (iff #7417 #7422)
-#3826 := (or #6627 #7427)
-#7416 := (ite #4695 #3770 #4739)
-#7418 := (iff #7417 #7416)
-#6907 := (or #6627 #7418)
-#6903 := (iff #6907 #3826)
-#6910 := (iff #3826 #3826)
-#6911 := [rewrite]: #6910
-#7428 := (iff #7418 #7427)
-#7425 := (iff #7416 #7422)
-#7419 := (ite #4695 true #4739)
-#7423 := (iff #7419 #7422)
-#7424 := [rewrite]: #7423
-#7420 := (iff #7416 #7419)
-#7421 := [monotonicity #3762]: #7420
-#7426 := [trans #7421 #7424]: #7425
-#7429 := [monotonicity #7426]: #7428
-#6909 := [monotonicity #7429]: #6903
-#6912 := [trans #6909 #6911]: #6903
-#6908 := [quant-inst]: #6907
-#6913 := [mp #6908 #6912]: #3826
-#7172 := [unit-resolution #6913 #4096]: #7427
-#6931 := (not #7417)
-#4884 := (up_6 uf_23 uf_11)
-#4885 := (not #4884)
-#7258 := (iff #4885 #6931)
-#7256 := (iff #4884 #7417)
-#7204 := (iff #7417 #4884)
-#7203 := [symm #7201]: #7202
-#7205 := [monotonicity #7203]: #7204
-#7257 := [symm #7205]: #7256
-#7259 := [monotonicity #7257]: #7258
-#7173 := (not #4798)
-#7198 := [hypothesis]: #7173
-#4887 := (or #4798 #4885)
-#7199 := [hypothesis]: #4327
-#6803 := (or #4332 #4798 #4885)
-#4886 := (or #4885 #4798)
-#6818 := (or #4332 #4886)
-#6809 := (iff #6818 #6803)
-#6817 := (or #4332 #4887)
-#6807 := (iff #6817 #6803)
-#6808 := [rewrite]: #6807
-#6820 := (iff #6818 #6817)
-#4888 := (iff #4886 #4887)
-#4889 := [rewrite]: #4888
-#6806 := [monotonicity #4889]: #6820
-#6810 := [trans #6806 #6808]: #6809
-#6819 := [quant-inst]: #6818
-#6805 := [mp #6819 #6810]: #6803
-#7200 := [unit-resolution #6805 #7199]: #4887
-#7195 := [unit-resolution #7200 #7198]: #4885
-#7260 := [mp #7195 #7259]: #6931
-#6929 := (not #7427)
-#6930 := (or #6929 #7417 #6926)
-#6925 := [def-axiom]: #6930
-#7261 := [unit-resolution #6925 #7260 #7172]: #6926
-#6918 := (or #7422 #6917)
-#6916 := [def-axiom]: #6918
-#7262 := [unit-resolution #6916 #7261]: #6917
-#7075 := (or #4695 #7073)
-#7078 := (or #7140 #4695 #7073)
-#4693 := (= uf_22 uf_11)
-#7074 := (or #4693 #7073)
-#7079 := (or #7140 #7074)
-#7067 := (iff #7079 #7078)
-#7063 := (or #7140 #7075)
-#7066 := (iff #7063 #7078)
-#7061 := [rewrite]: #7066
-#7064 := (iff #7079 #7063)
-#7076 := (iff #7074 #7075)
-#4696 := (iff #4693 #4695)
-#4697 := [rewrite]: #4696
-#7077 := [monotonicity #4697]: #7076
-#7065 := [monotonicity #7077]: #7064
-#7068 := [trans #7065 #7061]: #7067
-#7062 := [quant-inst]: #7079
-#7069 := [mp #7062 #7068]: #7078
-#7263 := [unit-resolution #7069 #4123]: #7075
-#7264 := [unit-resolution #7263 #7262]: #7073
-#4761 := (* -1::int #4757)
-#4762 := (+ #1357 #4761)
-#4763 := (+ #105 #4762)
-#4764 := (<= #4763 0::int)
-#6619 := (not #4764)
-#4765 := (+ uf_9 #4761)
-#4766 := (<= #4765 0::int)
-#4800 := (or #4764 #4766)
-#4803 := (not #4800)
-#4806 := (or #4798 #4803)
-#6415 := (or #4307 #4798 #4803)
-#4796 := (or #4766 #4764)
-#4797 := (not #4796)
-#4799 := (or #4798 #4797)
-#6444 := (or #4307 #4799)
-#6449 := (iff #6444 #6415)
-#6446 := (or #4307 #4806)
-#6443 := (iff #6446 #6415)
-#6448 := [rewrite]: #6443
-#6441 := (iff #6444 #6446)
-#4807 := (iff #4799 #4806)
-#4804 := (iff #4797 #4803)
-#4801 := (iff #4796 #4800)
-#4802 := [rewrite]: #4801
-#4805 := [monotonicity #4802]: #4804
-#4808 := [monotonicity #4805]: #4807
-#6447 := [monotonicity #4808]: #6441
-#6450 := [trans #6447 #6448]: #6449
-#6445 := [quant-inst]: #6444
-#6451 := [mp #6445 #6450]: #6415
-#7244 := [unit-resolution #6451 #6843]: #4806
-#7245 := [unit-resolution #7244 #7198]: #4803
-#6620 := (or #4800 #6619)
-#6621 := [def-axiom]: #6620
-#7246 := [unit-resolution #6621 #7245]: #6619
-#7247 := [hypothesis]: #4734
-#7248 := [hypothesis]: #4810
-#7243 := [th-lemma #7248 #7247 #7246 #7264]: false
-#7252 := [lemma #7243]: #7251
-#7833 := [unit-resolution #7252 #7832 #7811 #7201 #7831 #6843]: #4798
-#7834 := [mp #7833 #7838]: #210
-#3961 := (or #4414 #1394 #4408)
-#3963 := [def-axiom]: #3961
-#7839 := [unit-resolution #3963 #7834 #7818]: #4408
-#3968 := (or #4405 #4399)
-#3970 := [def-axiom]: #3968
-#7850 := [unit-resolution #3970 #7839]: #4399
-#3982 := (or #4402 #2168 #4396)
-#3976 := [def-axiom]: #3982
-#7851 := [unit-resolution #3976 #7850 #7816]: #2168
-#8005 := (not #7578)
-#8006 := (or #7967 #2167 #8005)
-#7964 := [hypothesis]: #7578
-#7965 := [hypothesis]: #7959
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-#7966 := [th-lemma #8460 #7965 #7964]: false
-#8007 := [lemma #7966]: #8006
-#7852 := [unit-resolution #8007 #7851 #7815]: #7967
-#7885 := (or #8448 #7959)
-#7881 := [hypothesis]: #7967
-#7882 := [hypothesis]: #6927
-#7886 := [th-lemma]: #7885
-#7887 := [unit-resolution #7886 #7882 #7881]: false
-#7888 := [lemma #7887]: #7885
-#7879 := [unit-resolution #7888 #7852]: #8448
-#7448 := (or #6927 #7445)
-#7451 := (or #4307 #6927 #7445)
-#7296 := (+ #1357 #7295)
-#7297 := (+ #6919 #7296)
-#7298 := (<= #7297 0::int)
-#7393 := (or #7350 #7298)
-#7394 := (not #7393)
-#6920 := (= #6919 #2166)
-#7395 := (or #6920 #7394)
-#7452 := (or #4307 #7395)
-#7432 := (iff #7452 #7451)
-#7454 := (or #4307 #7448)
-#7457 := (iff #7454 #7451)
-#7431 := [rewrite]: #7457
-#7455 := (iff #7452 #7454)
-#7449 := (iff #7395 #7448)
-#7446 := (iff #7394 #7445)
-#7443 := (iff #7393 #7440)
-#7396 := (or #7350 #7340)
-#7441 := (iff #7396 #7440)
-#7442 := [rewrite]: #7441
-#7397 := (iff #7393 #7396)
-#7337 := (iff #7298 #7340)
-#7352 := (+ #6919 #7295)
-#7353 := (+ #1357 #7352)
-#7356 := (<= #7353 0::int)
-#7341 := (iff #7356 #7340)
-#7342 := [rewrite]: #7341
-#7357 := (iff #7298 #7356)
-#7354 := (= #7297 #7353)
-#7355 := [rewrite]: #7354
-#7358 := [monotonicity #7355]: #7357
-#7343 := [trans #7358 #7342]: #7337
-#7439 := [monotonicity #7343]: #7397
-#7444 := [trans #7439 #7442]: #7443
-#7447 := [monotonicity #7444]: #7446
-#6928 := (iff #6920 #6927)
-#6932 := [rewrite]: #6928
-#7450 := [monotonicity #6932 #7447]: #7449
-#7456 := [monotonicity #7450]: #7455
-#7430 := [trans #7456 #7431]: #7432
-#7453 := [quant-inst]: #7452
-#7433 := [mp #7453 #7430]: #7451
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-#7435 := (or #7440 #7434)
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-#7402 := (or #7340 #7350 #7362)
-#7407 := (or #4315 #7340 #7350 #7362)
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-#7294 := (+ #182 #7293)
-#7289 := (= #7294 0::int)
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-#7415 := (iff #7408 #7407)
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-#7403 := (iff #7399 #7402)
-#7404 := [rewrite]: #7403
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-#7363 := (iff #7289 #7362)
-#7346 := (= #7294 #7345)
-#7347 := [rewrite]: #7346
-#7398 := [monotonicity #7347]: #7363
-#7401 := [monotonicity #7343 #7398]: #7400
-#7406 := [trans #7401 #7404]: #7405
-#7412 := [monotonicity #7406]: #7411
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-#7409 := [quant-inst]: #7408
-#7391 := [mp #7409 #7390]: #7407
-#8454 := [unit-resolution #7391 #6847]: #7402
-#7713 := [unit-resolution #8454 #7884 #7878]: #7362
-#8456 := (not #7362)
-#8457 := (or #8456 #7389)
-#8458 := [th-lemma]: #8457
-#7714 := [unit-resolution #8458 #7713]: #7389
-#7790 := (>= #7292 0::int)
-#7701 := (<= #7292 0::int)
-#7702 := (not #7701)
-#7603 := (= uf_22 ?x65!15)
-#7464 := (not #7603)
-#7505 := (up_6 uf_15 ?x65!15)
-#7628 := (or #7505 #7603)
-#4543 := (not #7628)
-#7584 := (up_6 #188 ?x65!15)
-#7611 := (iff #7584 #7628)
-#7612 := (or #6627 #7611)
-#7597 := (= ?x65!15 uf_22)
-#7598 := (ite #7597 #3770 #7505)
-#7599 := (iff #7584 #7598)
-#7607 := (or #6627 #7599)
-#7614 := (iff #7607 #7612)
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-#7468 := [rewrite]: #7467
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-#7606 := (ite #7603 true #7505)
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-#7602 := (iff #7598 #7606)
-#7604 := (iff #7597 #7603)
-#7605 := [rewrite]: #7604
-#7620 := [monotonicity #7605 #3762]: #7602
-#7610 := [trans #7620 #7586]: #7609
-#7585 := [monotonicity #7610]: #7627
-#7615 := [monotonicity #7585]: #7614
-#7460 := [trans #7615 #7468]: #7614
-#7613 := [quant-inst]: #7607
-#7461 := [mp #7613 #7460]: #7612
-#7705 := [unit-resolution #7461 #4096]: #7611
-#7575 := (not #7584)
-#4948 := (up_6 uf_23 ?x65!15)
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-#7912 := (iff #4949 #7575)
-#7910 := (iff #4948 #7584)
-#7908 := (iff #7584 #4948)
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-#7911 := [symm #7909]: #7910
-#7907 := [monotonicity #7911]: #7912
-#6933 := (or #4949 #6927)
-#6943 := (or #4332 #4949 #6927)
-#6921 := (or #4949 #6920)
-#6944 := (or #4332 #6921)
-#7042 := (iff #6944 #6943)
-#7039 := (or #4332 #6933)
-#7036 := (iff #7039 #6943)
-#7037 := [rewrite]: #7036
-#7040 := (iff #6944 #7039)
-#6934 := (iff #6921 #6933)
-#6935 := [monotonicity #6932]: #6934
-#7041 := [monotonicity #6935]: #7040
-#7043 := [trans #7041 #7037]: #7042
-#7038 := [quant-inst]: #6944
-#7044 := [mp #7038 #7043]: #6943
-#7700 := [unit-resolution #7044 #7832]: #6933
-#7880 := [unit-resolution #7700 #7879]: #4949
-#7913 := [mp #7880 #7907]: #7575
-#7471 := (not #7611)
-#7574 := (or #7471 #7584 #4543)
-#3825 := [def-axiom]: #7574
-#7914 := [unit-resolution #3825 #7913 #7705]: #4543
-#7465 := (or #7628 #7464)
-#7466 := [def-axiom]: #7465
-#7915 := [unit-resolution #7466 #7914]: #7464
-#7703 := (or #7603 #7702)
-#7750 := (or #7140 #7603 #7702)
-#7754 := (or #7140 #7703)
-#7757 := (iff #7754 #7750)
-#7758 := [rewrite]: #7757
-#7756 := [quant-inst]: #7754
-#7759 := [mp #7756 #7758]: #7750
-#7916 := [unit-resolution #7759 #4123]: #7703
-#7917 := [unit-resolution #7916 #7915]: #7702
-#7661 := (or #7790 #7701)
-#7662 := [th-lemma]: #7661
-#7711 := [unit-resolution #7662 #7917]: #7790
-#7712 := [th-lemma #7711 #7851 #7714 #7811]: false
-#7918 := [lemma #7712]: #7840
-#11066 := [unit-resolution #7918 #10914 #10462 #9067 #10469 #10124]: #11065
-#11067 := [unit-resolution #11066 #10919]: #4396
-#3987 := (or #4393 #4387)
-#3988 := [def-axiom]: #3987
-#27286 := [unit-resolution #3988 #11067]: #4387
-#3986 := (or #4390 #3329 #4384)
-#3978 := [def-axiom]: #3986
-#27289 := [unit-resolution #3978 #27286]: #4387
-#27290 := [unit-resolution #27289 #13940]: #4384
-#3900 := (or #4381 #4375)
-#3901 := [def-axiom]: #3900
-#27291 := [unit-resolution #3901 #27290]: #4375
-#27292 := (or #4378 #4372)
-#7000 := (uf_1 uf_22 ?x71!19)
-#7001 := (uf_10 #7000)
-#6954 := (uf_4 uf_14 ?x71!19)
-#6984 := (* -1::int #6954)
-#7019 := (+ #6984 #7001)
-#7020 := (+ #182 #7019)
-#7021 := (>= #7020 0::int)
-#18941 := (not #7021)
-#7005 := (* -1::int #7001)
-#19226 := (+ #2212 #7005)
-#19230 := (>= #19226 0::int)
-#19225 := (= #2212 #7001)
-#19092 := (= #2211 #7000)
-#5993 := (= ?x72!18 uf_22)
-#15489 := (= ?x72!18 #10571)
-#5992 := (up_6 uf_15 ?x72!18)
-#6705 := (not #5992)
-#5963 := (uf_4 uf_14 ?x72!18)
-#7080 := (+ #5963 #6984)
-#7081 := (+ #2212 #7080)
-#7082 := (>= #7081 0::int)
-#19649 := (not #7082)
-#6985 := (+ #2207 #6984)
-#6986 := (<= #6985 0::int)
-#18752 := (or #4323 #6986)
-#6976 := (+ #6954 #2208)
-#6977 := (>= #6976 0::int)
-#18750 := (or #4323 #6977)
-#18782 := (iff #18750 #18752)
-#18807 := (iff #18752 #18752)
-#18838 := [rewrite]: #18807
-#6989 := (iff #6977 #6986)
-#6978 := (+ #2208 #6954)
-#6981 := (>= #6978 0::int)
-#6987 := (iff #6981 #6986)
-#6988 := [rewrite]: #6987
-#6982 := (iff #6977 #6981)
-#6979 := (= #6976 #6978)
-#6980 := [rewrite]: #6979
-#6983 := [monotonicity #6980]: #6982
-#6990 := [trans #6983 #6988]: #6989
-#18837 := [monotonicity #6990]: #18782
-#18839 := [trans #18837 #18838]: #18782
-#18781 := [quant-inst]: #18750
-#18834 := [mp #18781 #18839]: #18752
-#19630 := [unit-resolution #18834 #10924]: #6986
-#3844 := (not #2799)
-#19636 := [hypothesis]: #3375
-#3845 := (or #3370 #3844)
-#3998 := [def-axiom]: #3845
-#19637 := [unit-resolution #3998 #19636]: #3844
-#6055 := (* -1::int #5963)
-#6056 := (+ #2209 #6055)
-#17904 := (>= #6056 0::int)
-#5968 := (= #2209 #5963)
-#4013 := (or #3370 #2219)
-#3842 := [def-axiom]: #4013
-#19638 := [unit-resolution #3842 #19636]: #2219
-#10920 := [unit-resolution #3965 #10919]: #4327
-#16950 := (or #4332 #3355 #5968)
-#5964 := (= #5963 #2209)
-#5967 := (or #3355 #5964)
-#16945 := (or #4332 #5967)
-#17123 := (iff #16945 #16950)
-#5971 := (or #3355 #5968)
-#16952 := (or #4332 #5971)
-#16954 := (iff #16952 #16950)
-#16815 := [rewrite]: #16954
-#16953 := (iff #16945 #16952)
-#5972 := (iff #5967 #5971)
-#5969 := (iff #5964 #5968)
-#5970 := [rewrite]: #5969
-#5973 := [monotonicity #5970]: #5972
-#16949 := [monotonicity #5973]: #16953
-#17124 := [trans #16949 #16815]: #17123
-#16951 := [quant-inst]: #16945
-#17131 := [mp #16951 #17124]: #16950
-#19604 := [unit-resolution #17131 #10920 #19638]: #5968
-#19640 := (not #5968)
-#19647 := (or #19640 #17904)
-#19648 := [th-lemma]: #19647
-#19646 := [unit-resolution #19648 #19604]: #17904
-#19668 := (not #6986)
-#19667 := (not #17904)
-#19669 := (or #19649 #19667 #19668 #2799)
-#19674 := [th-lemma]: #19669
-#19675 := [unit-resolution #19674 #19646 #19637 #19630]: #19649
-#19673 := (or #6705 #7082)
-#4012 := (or #3370 #2218)
-#4006 := [def-axiom]: #4012
-#19664 := [unit-resolution #4006 #19636]: #2218
-#18969 := (or #4193 #2217 #6705 #7082)
-#7083 := (or #6705 #2217 #7082)
-#18974 := (or #4193 #7083)
-#18875 := (iff #18974 #18969)
-#7084 := (or #2217 #6705 #7082)
-#18976 := (or #4193 #7084)
-#18944 := (iff #18976 #18969)
-#18874 := [rewrite]: #18944
-#18977 := (iff #18974 #18976)
-#7085 := (iff #7083 #7084)
-#7086 := [rewrite]: #7085
-#18943 := [monotonicity #7086]: #18977
-#18873 := [trans #18943 #18874]: #18875
-#18975 := [quant-inst]: #18974
-#18942 := [mp #18975 #18873]: #18969
-#18871 := [unit-resolution #18942 #10131 #19664]: #19673
-#19651 := [unit-resolution #18871 #19675]: #6705
-#15504 := (or #5992 #15489)
-#15499 := (up_6 #11533 ?x72!18)
-#15509 := (iff #15499 #15504)
-#17157 := (or #6627 #15509)
-#15490 := (ite #15489 #3770 #5992)
-#15500 := (iff #15499 #15490)
-#17130 := (or #6627 #15500)
-#17160 := (iff #17130 #17157)
-#17164 := (iff #17157 #17157)
-#17122 := [rewrite]: #17164
-#15510 := (iff #15500 #15509)
-#15507 := (iff #15490 #15504)
-#15501 := (ite #15489 true #5992)
-#15505 := (iff #15501 #15504)
-#15506 := [rewrite]: #15505
-#15502 := (iff #15490 #15501)
-#15503 := [monotonicity #3762]: #15502
-#15508 := [trans #15503 #15506]: #15507
-#15511 := [monotonicity #15508]: #15510
-#17158 := [monotonicity #15511]: #17160
-#17165 := [trans #17158 #17122]: #17160
-#17159 := [quant-inst]: #17130
-#17166 := [mp #17159 #17165]: #17157
-#19656 := [unit-resolution #17166 #4096]: #15509
-#19655 := (iff #2219 #15499)
-#19650 := (iff #15499 #2219)
-#19657 := [monotonicity #13613]: #19650
-#19665 := [symm #19657]: #19655
-#19666 := [mp #19638 #19665]: #15499
-#17221 := (not #15499)
-#17223 := (not #15509)
-#17226 := (or #17223 #17221 #15504)
-#17227 := [def-axiom]: #17226
-#19660 := [unit-resolution #17227 #19666 #19656]: #15504
-#17201 := (not #15504)
-#17222 := (or #17201 #5992 #15489)
-#17217 := [def-axiom]: #17222
-#19635 := [unit-resolution #17217 #19660 #19651]: #15489
-#19038 := [trans #19635 #13436]: #5993
-#19241 := [monotonicity #19038]: #19092
-#19355 := [monotonicity #19241]: #19225
-#19410 := (not #19225)
-#18872 := (or #19410 #19230)
-#19416 := [th-lemma]: #18872
-#19513 := [unit-resolution #19416 #19355]: #19230
-#7165 := (uf_2 #2211)
-#7171 := (uf_4 uf_14 #7165)
-#7185 := (* -1::int #7171)
-#7186 := (+ #182 #7185)
-#7187 := (<= #7186 0::int)
-#19218 := (= #182 #7171)
-#19098 := (= #7171 #182)
-#19114 := (= #7165 uf_22)
-#19115 := (= #7165 #10571)
-#19577 := (= #7165 ?x72!18)
-#7166 := (= ?x72!18 #7165)
-#19027 := (or #8504 #7166)
-#19028 := [quant-inst]: #19027
-#19514 := [unit-resolution #19028 #4082]: #7166
-#19578 := [symm #19514]: #19577
-#19116 := [trans #19578 #19635]: #19115
-#19205 := [trans #19116 #13436]: #19114
-#19206 := [monotonicity #19205]: #19098
-#19213 := [symm #19206]: #19218
-#19214 := (not #19218)
-#19207 := (or #19214 #7187)
-#19215 := [th-lemma]: #19207
-#19583 := [unit-resolution #19215 #19213]: #7187
-#19048 := (+ #5963 #7185)
-#19031 := (>= #19048 0::int)
-#19047 := (= #5963 #7171)
-#19592 := [monotonicity #19514]: #19047
-#19803 := (not #19047)
-#19804 := (or #19803 #19031)
-#19805 := [th-lemma]: #19804
-#19806 := [unit-resolution #19805 #19592]: #19031
-#19929 := (not #19230)
-#19808 := (not #19031)
-#19807 := (not #7187)
-#19809 := (or #18941 #19668 #2799 #19807 #19808 #19667 #19929)
-#19810 := [th-lemma]: #19809
-#19811 := [unit-resolution #19810 #19630 #19646 #19637 #19806 #19583 #19513]: #18941
-#7009 := (+ uf_9 #7005)
-#7010 := (<= #7009 0::int)
-#18939 := (not #7010)
-#19930 := (or #18939 #19929 #2217)
-#19925 := [hypothesis]: #2218
-#19926 := [hypothesis]: #7010
-#19927 := [hypothesis]: #19230
-#19928 := [th-lemma #19927 #19926 #19925]: false
-#19931 := [lemma #19928]: #19930
-#19837 := [unit-resolution #19931 #19513 #19664]: #18939
-#7026 := (+ #2208 #7001)
-#7027 := (+ #182 #7026)
-#7030 := (= #7027 0::int)
-#19841 := (not #7030)
-#18789 := (>= #7027 0::int)
-#19838 := (not #18789)
-#19839 := (or #19838 #2799 #19807 #19808 #19667 #19929)
-#19835 := [th-lemma]: #19839
-#19836 := [unit-resolution #19835 #19646 #19637 #19806 #19583 #19513]: #19838
-#19842 := (or #19841 #18789)
-#19843 := [th-lemma]: #19842
-#19840 := [unit-resolution #19843 #19836]: #19841
-#7033 := (or #7010 #7021 #7030)
-#18840 := (or #4315 #7010 #7021 #7030)
-#7002 := (+ #7001 #2208)
-#7003 := (+ #182 #7002)
-#7004 := (= #7003 0::int)
-#7006 := (+ #1357 #7005)
-#7007 := (+ #6954 #7006)
-#7008 := (<= #7007 0::int)
-#7011 := (or #7010 #7008 #7004)
-#18841 := (or #4315 #7011)
-#18786 := (iff #18841 #18840)
-#18900 := (or #4315 #7033)
-#18780 := (iff #18900 #18840)
-#18785 := [rewrite]: #18780
-#18784 := (iff #18841 #18900)
-#7034 := (iff #7011 #7033)
-#7031 := (iff #7004 #7030)
-#7028 := (= #7003 #7027)
-#7029 := [rewrite]: #7028
-#7032 := [monotonicity #7029]: #7031
-#7024 := (iff #7008 #7021)
-#7012 := (+ #6954 #7005)
-#7013 := (+ #1357 #7012)
-#7016 := (<= #7013 0::int)
-#7022 := (iff #7016 #7021)
-#7023 := [rewrite]: #7022
-#7017 := (iff #7008 #7016)
-#7014 := (= #7007 #7013)
-#7015 := [rewrite]: #7014
-#7018 := [monotonicity #7015]: #7017
-#7025 := [trans #7018 #7023]: #7024
-#7035 := [monotonicity #7025 #7032]: #7034
-#18779 := [monotonicity #7035]: #18784
-#18783 := [trans #18779 #18785]: #18786
-#18905 := [quant-inst]: #18841
-#18787 := [mp #18905 #18783]: #18840
-#19844 := [unit-resolution #18787 #10914]: #7033
-#19845 := [unit-resolution #19844 #19840 #19837 #19811]: false
-#19871 := [lemma #19845]: #3370
-#3897 := (or #4378 #3375 #4372)
-#3898 := [def-axiom]: #3897
-#27293 := [unit-resolution #3898 #19871]: #27292
-#27294 := [unit-resolution #27293 #27291]: #4372
-#4002 := (or #4369 #2249)
-#4000 := [def-axiom]: #4002
-#27295 := [unit-resolution #4000 #27294]: #2249
-#5681 := (+ #2236 #5680)
-#18550 := (>= #5681 0::int)
-#5655 := (= #2236 #5650)
-#3846 := (or #4369 #4361)
-#3994 := [def-axiom]: #3846
-#27296 := [unit-resolution #3994 #27294]: #4361
-#18659 := (or #5655 #4366)
-#15149 := (uf_10 #15148)
-#15175 := (* -1::int #15149)
-#11814 := (uf_24 #10571)
-#11812 := (* -1::int #11814)
-#15176 := (+ #11812 #15175)
-#15177 := (+ #2236 #15176)
-#15830 := (>= #15177 0::int)
-#5696 := (uf_1 uf_22 ?x75!20)
-#5697 := (uf_10 #5696)
-#15921 := (+ #5697 #15175)
-#15923 := (>= #15921 0::int)
-#15920 := (= #5697 #15149)
-#18516 := (= #15149 #5697)
-#18514 := (= #15148 #5696)
-#18515 := [monotonicity #13436]: #18514
-#18517 := [monotonicity #18515]: #18516
-#18518 := [symm #18517]: #15920
-#18513 := (not #15920)
-#18519 := (or #18513 #15923)
-#18520 := [th-lemma]: #18519
-#18521 := [unit-resolution #18520 #18518]: #15923
-#11766 := (+ #4615 #11812)
-#8751 := (>= #11766 0::int)
-#8693 := (= #4615 #11814)
-#18522 := (= #11814 #4615)
-#18523 := [monotonicity #13436]: #18522
-#18530 := [symm #18523]: #8693
-#18531 := (not #8693)
-#18529 := (or #18531 #8751)
-#18532 := [th-lemma]: #18529
-#18533 := [unit-resolution #18532 #18530]: #8751
-#5722 := (+ #2237 #5697)
-#5723 := (+ #182 #5722)
-#15649 := (<= #5723 0::int)
-#5726 := (= #5723 0::int)
-#5701 := (* -1::int #5697)
-#5705 := (+ uf_9 #5701)
-#5706 := (<= #5705 0::int)
-#15666 := (not #5706)
-#5715 := (+ #5680 #5697)
-#5716 := (+ #182 #5715)
-#5717 := (>= #5716 0::int)
-#5748 := (or #5706 #5717)
-#5751 := (not #5748)
-#18607 := (not #5655)
-#18534 := [hypothesis]: #18607
-#5754 := (or #5655 #5751)
-#15653 := (or #4307 #5655 #5751)
-#5702 := (+ #1357 #5701)
-#5703 := (+ #5650 #5702)
-#5704 := (<= #5703 0::int)
-#5745 := (or #5706 #5704)
-#5746 := (not #5745)
-#5651 := (= #5650 #2236)
-#5747 := (or #5651 #5746)
-#15654 := (or #4307 #5747)
-#15663 := (iff #15654 #15653)
-#15656 := (or #4307 #5754)
-#15659 := (iff #15656 #15653)
-#15660 := [rewrite]: #15659
-#15657 := (iff #15654 #15656)
-#5755 := (iff #5747 #5754)
-#5752 := (iff #5746 #5751)
-#5749 := (iff #5745 #5748)
-#5720 := (iff #5704 #5717)
-#5708 := (+ #5650 #5701)
-#5709 := (+ #1357 #5708)
-#5712 := (<= #5709 0::int)
-#5718 := (iff #5712 #5717)
-#5719 := [rewrite]: #5718
-#5713 := (iff #5704 #5712)
-#5710 := (= #5703 #5709)
-#5711 := [rewrite]: #5710
-#5714 := [monotonicity #5711]: #5713
-#5721 := [trans #5714 #5719]: #5720
-#5750 := [monotonicity #5721]: #5749
-#5753 := [monotonicity #5750]: #5752
-#5656 := (iff #5651 #5655)
-#5657 := [rewrite]: #5656
-#5756 := [monotonicity #5657 #5753]: #5755
-#15658 := [monotonicity #5756]: #15657
-#15664 := [trans #15658 #15660]: #15663
-#15655 := [quant-inst]: #15654
-#15665 := [mp #15655 #15664]: #15653
-#18538 := [unit-resolution #15665 #10462]: #5754
-#18539 := [unit-resolution #18538 #18534]: #5751
-#15667 := (or #5748 #15666)
-#15697 := [def-axiom]: #15667
-#18542 := [unit-resolution #15697 #18539]: #15666
-#15813 := (not #5717)
-#15814 := (or #5748 #15813)
-#15815 := [def-axiom]: #15814
-#18543 := [unit-resolution #15815 #18539]: #15813
-#5729 := (or #5706 #5717 #5726)
-#15441 := (or #4315 #5706 #5717 #5726)
-#5698 := (+ #5697 #2237)
-#5699 := (+ #182 #5698)
-#5700 := (= #5699 0::int)
-#5707 := (or #5706 #5704 #5700)
-#15442 := (or #4315 #5707)
-#15615 := (iff #15442 #15441)
-#15466 := (or #4315 #5729)
-#15594 := (iff #15466 #15441)
-#15595 := [rewrite]: #15594
-#15497 := (iff #15442 #15466)
-#5730 := (iff #5707 #5729)
-#5727 := (iff #5700 #5726)
-#5724 := (= #5699 #5723)
-#5725 := [rewrite]: #5724
-#5728 := [monotonicity #5725]: #5727
-#5731 := [monotonicity #5721 #5728]: #5730
-#15498 := [monotonicity #5731]: #15497
-#15638 := [trans #15498 #15595]: #15615
-#15465 := [quant-inst]: #15442
-#15639 := [mp #15465 #15638]: #15441
-#18579 := [unit-resolution #15639 #10914]: #5729
-#18580 := [unit-resolution #18579 #18543 #18542]: #5726
-#18581 := (not #5726)
-#18582 := (or #18581 #15649)
-#18583 := [th-lemma]: #18582
-#18584 := [unit-resolution #18583 #18580]: #15649
-#18588 := (not #15923)
-#18587 := (not #4858)
-#18586 := (not #8751)
-#18585 := (not #15649)
-#18589 := (or #15830 #18585 #18586 #18587 #18588)
-#18590 := [th-lemma]: #18589
-#18591 := [unit-resolution #18590 #18584 #18533 #10925 #18521]: #15830
-#15829 := (<= #15177 0::int)
-#15922 := (<= #15921 0::int)
-#18592 := (or #18513 #15922)
-#18593 := [th-lemma]: #18592
-#18594 := [unit-resolution #18593 #18518]: #15922
-#9376 := (<= #4857 0::int)
-#4616 := (= #182 #4615)
-#4865 := (up_6 uf_23 uf_22)
-#3772 := (up_6 #188 uf_22)
-#10910 := (iff #3772 #4865)
-#10908 := (iff #4865 #3772)
-#10909 := [monotonicity #10469]: #10908
-#10911 := [symm #10909]: #10910
+#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
+#30551 := [unit-resolution #20894 #30550]: #21628
+#22445 := (not #10499)
+#21601 := (or #10509 #22445)
+#19500 := [def-axiom]: #21601
+#30552 := [unit-resolution #19500 #30550]: #22445
+#10680 := (or #10470 #10499 #10649)
+#22909 := (or #4068 #10470 #10499 #10649)
+#10641 := (+ #10441 #2033)
+#10642 := (+ #185 #10641)
+#10643 := (= #10642 0::int)
+#10650 := (or #10470 #10468 #10643)
+#22907 := (or #4068 #10650)
+#21602 := (iff #22907 #22909)
+#22692 := (or #4068 #10680)
+#22690 := (iff #22692 #22909)
+#22915 := [rewrite]: #22690
+#22680 := (iff #22907 #22692)
+#10681 := (iff #10650 #10680)
+#10679 := (iff #10643 #10649)
+#10677 := (= #10642 #10676)
+#10678 := [rewrite]: #10677
+#10674 := [monotonicity #10678]: #10679
+#10682 := [monotonicity #10508 #10674]: #10681
+#22900 := [monotonicity #10682]: #22680
+#21458 := [trans #22900 #22915]: #21602
+#22696 := [quant-inst]: #22907
+#21404 := [mp #22696 #21458]: #22909
+#30553 := [unit-resolution #21404 #6220]: #10680
+#30554 := [unit-resolution #30553 #30552 #30551]: #10649
+#30555 := (not #10649)
+#30556 := (or #30555 #22250)
+#30557 := [th-lemma]: #30556
+#30558 := [unit-resolution #30557 #30554]: #22250
+#30563 := (not #23144)
+#30562 := (not #5876)
+#23491 := (not #6249)
+#30561 := (not #7614)
+#30560 := (not #22250)
+#30564 := (or #30559 #30560 #30561 #23491 #30562 #30273 #30563)
+#30565 := [th-lemma]: #30564
+#30566 := [unit-resolution #30565 #30558 #30548 #22632 #30545 #30541 #30532]: #30559
+#10720 := (+ #7883 #10732)
+#10721 := (+ #2032 #10720)
+#10722 := (= #10721 0::int)
+#17953 := (>= #10721 0::int)
+#30567 := (or #17953 #30560 #30561 #23491 #30562 #30563)
+#30568 := [th-lemma]: #30567
+#30569 := [unit-resolution #30568 #30558 #30548 #22632 #30545 #30541]: #17953
+#17886 := (<= #10721 0::int)
+#17849 := (<= #17909 0::int)
+#30570 := (or #30538 #17849)
+#30571 := [th-lemma]: #30570
+#30572 := [unit-resolution #30571 #30537]: #17849
+#5875 := (<= #5855 0::int)
+#5902 := (<= #5901 0::int)
+#23487 := (not #5879)
+#23488 := (or #23487 #5902)
+#23489 := [th-lemma]: #23488
+#23490 := [unit-resolution #23489 #8605]: #5902
+#23492 := (not #5902)
+#23493 := (or #5875 #23491 #23492)
+#23494 := [th-lemma]: #23493
+#23495 := [unit-resolution #23494 #23490 #22632]: #5875
+#7859 := (<= #7858 0::int)
+#23500 := (or #23499 #7859)
+#23501 := [th-lemma]: #23500
+#23502 := [unit-resolution #23501 #23498]: #7859
+#22934 := (>= #10676 0::int)
+#30573 := (or #30555 #22934)
+#30574 := [th-lemma]: #30573
+#30575 := [unit-resolution #30574 #30554]: #22934
+#30579 := (not #17849)
+#30578 := (not #5875)
+#30577 := (not #7859)
+#30576 := (not #22934)
+#30580 := (or #17886 #30576 #30577 #5907 #30578 #30579)
+#30581 := [th-lemma]: #30580
+#30582 := [unit-resolution #30581 #30575 #23502 #23495 #9692 #30572]: #17886
+#30584 := (not #17953)
+#30583 := (not #17886)
+#30585 := (or #10722 #30583 #30584)
+#30586 := [th-lemma]: #30585
+#30587 := [unit-resolution #30586 #30582 #30569]: #10722
+#10725 := (not #10722)
+#30589 := (or #10697 #10725)
+#8020 := (up_6 uf_23 #6904)
+#5971 := (up_6 #191 uf_22)
+#29386 := (iff #5971 #8020)
+#29384 := (iff #8020 #5971)
+#29385 := [monotonicity #7417 #9758]: #29384
+#29387 := [symm #29385]: #29386
 #46 := (:var 0 T5)
 #45 := (:var 2 T4)
 #47 := (uf_7 #45 #10 #46)
-#4105 := (pattern #47)
-#335 := (= uf_8 #46)
+#3860 := (pattern #47)
+#319 := (= uf_8 #46)
 #48 := (up_6 #47 #10)
-#339 := (iff #48 #335)
-#4106 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4105) #339)
-#342 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #339)
-#4109 := (iff #342 #4106)
-#4107 := (iff #339 #339)
-#4108 := [refl]: #4107
-#4110 := [quant-intro #4108]: #4109
-#1739 := (~ #342 #342)
-#1777 := (~ #339 #339)
-#1778 := [refl]: #1777
-#1740 := [nnf-pos #1778]: #1739
+#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
 #49 := (= #46 uf_8)
 #50 := (iff #48 #49)
 #51 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #50)
-#343 := (iff #51 #342)
-#340 := (iff #50 #339)
-#337 := (iff #49 #335)
-#338 := [rewrite]: #337
-#341 := [monotonicity #338]: #340
-#344 := [quant-intro #341]: #343
-#334 := [asserted]: #51
-#347 := [mp #334 #344]: #342
-#1779 := [mp~ #347 #1740]: #342
-#4111 := [mp #1779 #4110]: #4106
-#8930 := (not #4106)
-#8932 := (or #8930 #3772)
-#3771 := (iff #3772 #3770)
-#8926 := (or #8930 #3771)
-#8933 := (iff #8926 #8932)
-#8935 := (iff #8932 #8932)
-#8936 := [rewrite]: #8935
-#3757 := (iff #3771 #3772)
-#3763 := (iff #3772 true)
-#3765 := (iff #3763 #3772)
-#3766 := [rewrite]: #3765
-#3764 := (iff #3771 #3763)
-#3756 := [monotonicity #3762]: #3764
-#3767 := [trans #3756 #3766]: #3757
-#8934 := [monotonicity #3767]: #8933
-#8931 := [trans #8934 #8936]: #8933
-#8927 := [quant-inst]: #8926
-#9499 := [mp #8927 #8931]: #8932
-#10907 := [unit-resolution #9499 #4111]: #3772
-#10912 := [mp #10907 #10911]: #4865
-#4866 := (not #4865)
-#4870 := (or #4616 #4866)
-#10280 := (or #4332 #4616 #4866)
-#4869 := (or #4866 #4616)
-#10281 := (or #4332 #4869)
-#10339 := (iff #10281 #10280)
-#10282 := (or #4332 #4870)
-#10337 := (iff #10282 #10280)
-#10338 := [rewrite]: #10337
-#10283 := (iff #10281 #10282)
-#4871 := (iff #4869 #4870)
-#4872 := [rewrite]: #4871
-#10336 := [monotonicity #4872]: #10283
-#10341 := [trans #10336 #10338]: #10339
-#10279 := [quant-inst]: #10281
-#10342 := [mp #10279 #10341]: #10280
-#10921 := [unit-resolution #10342 #10920]: #4870
-#10922 := [unit-resolution #10921 #10912]: #4616
-#9432 := (not #4616)
-#9433 := (or #9432 #9376)
-#9434 := [th-lemma]: #9433
-#10923 := [unit-resolution #9434 #10922]: #9376
-#11761 := (<= #11766 0::int)
-#18595 := (or #18531 #11761)
-#18596 := [th-lemma]: #18595
-#18597 := [unit-resolution #18596 #18530]: #11761
-#15650 := (>= #5723 0::int)
-#18571 := (or #18581 #15650)
-#18572 := [th-lemma]: #18571
-#18570 := [unit-resolution #18572 #18580]: #15650
-#18576 := (not #15922)
-#18575 := (not #9376)
-#18574 := (not #11761)
-#18573 := (not #15650)
-#18577 := (or #15829 #18573 #18574 #18575 #18576)
-#18578 := [th-lemma]: #18577
-#17865 := [unit-resolution #18578 #18570 #18597 #10923 #18594]: #15829
-#15178 := (= #15177 0::int)
-#15183 := (not #15178)
-#15085 := (+ #2236 #11812)
-#15163 := (<= #15085 0::int)
-#18640 := (not #15163)
-#17249 := (uf_3 #5917)
-#18036 := (uf_1 #10571 #17249)
-#18037 := (uf_10 #18036)
-#18039 := (* -1::int #18037)
-#18208 := (+ #5697 #18039)
-#18250 := (>= #18208 0::int)
-#18205 := (= #5697 #18037)
-#18060 := (= #18037 #5697)
-#18054 := (= #18036 #5696)
-#17915 := (= #17249 ?x75!20)
-#17250 := (= ?x75!20 #17249)
-#17253 := (or #7845 #17250)
-#17254 := [quant-inst]: #17253
-#17866 := [unit-resolution #17254 #4076]: #17250
-#17916 := [symm #17866]: #17915
-#18059 := [monotonicity #13436 #17916]: #18054
-#18063 := [monotonicity #18059]: #18060
-#18064 := [symm #18063]: #18205
-#18065 := (not #18205)
-#18068 := (or #18065 #18250)
-#18126 := [th-lemma]: #18068
-#18127 := [unit-resolution #18126 #18064]: #18250
-#18137 := (<= #18037 0::int)
-#18138 := (not #18137)
-#18556 := (= #10571 #17249)
-#17987 := (not #18556)
-#18551 := (up_6 uf_15 #17249)
-#18562 := (or #18551 #18556)
-#18015 := (not #18562)
-#18554 := (up_6 #11533 #17249)
-#18567 := (iff #18554 #18562)
-#17962 := (or #6627 #18567)
-#18552 := (= #17249 #10571)
-#18553 := (ite #18552 #3770 #18551)
-#18555 := (iff #18554 #18553)
-#17963 := (or #6627 #18555)
-#17965 := (iff #17963 #17962)
-#17981 := (iff #17962 #17962)
-#17982 := [rewrite]: #17981
-#18568 := (iff #18555 #18567)
-#18565 := (iff #18553 #18562)
-#18559 := (ite #18556 true #18551)
-#18563 := (iff #18559 #18562)
-#18564 := [rewrite]: #18563
-#18560 := (iff #18553 #18559)
-#18557 := (iff #18552 #18556)
-#18558 := [rewrite]: #18557
-#18561 := [monotonicity #18558 #3762]: #18560
-#18566 := [trans #18561 #18564]: #18565
-#18569 := [monotonicity #18566]: #18568
-#17980 := [monotonicity #18569]: #17965
-#17983 := [trans #17980 #17982]: #17965
-#17964 := [quant-inst]: #17963
-#17984 := [mp #17964 #17983]: #17962
-#18426 := [unit-resolution #17984 #4096]: #18567
-#18020 := (not #18554)
-#5037 := (up_6 uf_23 ?x75!20)
-#5038 := (not #5037)
-#18541 := (iff #5038 #18020)
-#18441 := (iff #5037 #18554)
-#18430 := (iff #18554 #5037)
-#18431 := [monotonicity #13613 #17916]: #18430
-#18540 := [symm #18431]: #18441
-#18544 := [monotonicity #18540]: #18541
-#5658 := (or #5038 #5655)
-#15006 := (or #4332 #5038 #5655)
-#5654 := (or #5038 #5651)
-#15007 := (or #4332 #5654)
-#15427 := (iff #15007 #15006)
-#15242 := (or #4332 #5658)
-#15290 := (iff #15242 #15006)
-#15291 := [rewrite]: #15290
-#15251 := (iff #15007 #15242)
-#5659 := (iff #5654 #5658)
-#5660 := [monotonicity #5657]: #5659
-#15252 := [monotonicity #5660]: #15251
-#15428 := [trans #15252 #15291]: #15427
-#15241 := [quant-inst]: #15007
-#15429 := [mp #15241 #15428]: #15006
-#18605 := [unit-resolution #15429 #10920]: #5658
-#18427 := [unit-resolution #18605 #18534]: #5038
-#18545 := [mp #18427 #18544]: #18020
-#18018 := (not #18567)
-#18019 := (or #18018 #18554 #18015)
-#18014 := [def-axiom]: #18019
-#18546 := [unit-resolution #18014 #18545 #18426]: #18015
-#17988 := (or #18562 #17987)
-#17989 := [def-axiom]: #17988
-#18549 := [unit-resolution #17989 #18546]: #17987
-#18153 := (or #18138 #18556)
-#18155 := (or #7140 #18138 #18556)
-#18152 := (or #18556 #18138)
-#18156 := (or #7140 #18152)
-#18170 := (iff #18156 #18155)
-#18162 := (or #7140 #18153)
-#18164 := (iff #18162 #18155)
-#18165 := [rewrite]: #18164
-#18160 := (iff #18156 #18162)
-#18151 := (iff #18152 #18153)
-#18154 := [rewrite]: #18151
-#18163 := [monotonicity #18154]: #18160
-#18171 := [trans #18163 #18165]: #18170
-#18161 := [quant-inst]: #18156
-#18169 := [mp #18161 #18171]: #18155
-#18638 := [unit-resolution #18169 #4123]: #18153
-#18639 := [unit-resolution #18638 #18549]: #18138
-#18641 := (not #18250)
-#18642 := (or #18640 #18585 #18586 #18587 #18137 #18641)
-#18643 := [th-lemma]: #18642
-#18644 := [unit-resolution #18643 #18584 #18533 #10925 #18639 #18127]: #18640
-#18651 := (or #15163 #15183)
-#11817 := (up_6 uf_23 #10571)
-#18647 := (iff #3772 #11817)
-#18645 := (iff #11817 #3772)
-#18646 := [monotonicity #10469 #13436]: #18645
-#18648 := [symm #18646]: #18647
-#18649 := [mp #10907 #18648]: #11817
-#18650 := [hypothesis]: #4361
-#11821 := (not #11817)
-#15818 := (or #4366 #11821 #15163 #15183)
-#15150 := (+ #2237 #15149)
-#15151 := (+ #11814 #15150)
-#15152 := (= #15151 0::int)
-#15153 := (not #15152)
-#15154 := (+ #11814 #2237)
-#15155 := (>= #15154 0::int)
-#15156 := (or #11821 #15155 #15153)
-#15819 := (or #4366 #15156)
-#15826 := (iff #15819 #15818)
-#15186 := (or #11821 #15163 #15183)
-#15821 := (or #4366 #15186)
-#15824 := (iff #15821 #15818)
-#15825 := [rewrite]: #15824
-#15822 := (iff #15819 #15821)
-#15187 := (iff #15156 #15186)
-#15184 := (iff #15153 #15183)
-#15181 := (iff #15152 #15178)
-#15168 := (+ #11814 #15149)
-#15169 := (+ #2237 #15168)
-#15172 := (= #15169 0::int)
-#15179 := (iff #15172 #15178)
-#15180 := [rewrite]: #15179
-#15173 := (iff #15152 #15172)
-#15170 := (= #15151 #15169)
-#15171 := [rewrite]: #15170
-#15174 := [monotonicity #15171]: #15173
-#15182 := [trans #15174 #15180]: #15181
-#15185 := [monotonicity #15182]: #15184
-#15166 := (iff #15155 #15163)
-#15157 := (+ #2237 #11814)
-#15160 := (>= #15157 0::int)
-#15164 := (iff #15160 #15163)
-#15165 := [rewrite]: #15164
-#15161 := (iff #15155 #15160)
-#15158 := (= #15154 #15157)
-#15159 := [rewrite]: #15158
-#15162 := [monotonicity #15159]: #15161
-#15167 := [trans #15162 #15165]: #15166
-#15188 := [monotonicity #15167 #15185]: #15187
-#15823 := [monotonicity #15188]: #15822
-#15827 := [trans #15823 #15825]: #15826
-#15820 := [quant-inst]: #15819
-#15828 := [mp #15820 #15827]: #15818
-#18652 := [unit-resolution #15828 #18650 #18649]: #18651
-#18653 := [unit-resolution #18652 #18644]: #15183
-#18655 := (not #15830)
-#18654 := (not #15829)
-#18656 := (or #15178 #18654 #18655)
-#18657 := [th-lemma]: #18656
-#18658 := [unit-resolution #18657 #18653 #17865 #18591]: false
-#18660 := [lemma #18658]: #18659
-#27297 := [unit-resolution #18660 #27296]: #5655
-#18608 := (or #18607 #18550)
-#18609 := [th-lemma]: #18608
-#27298 := [unit-resolution #18609 #27297]: #18550
-#22669 := (not #18550)
-#22675 := (or #22674 #22669 #2248)
-#22670 := [hypothesis]: #2249
-#22671 := [hypothesis]: #18550
-#22672 := [hypothesis]: #5929
-#22673 := [th-lemma #22672 #22671 #22670]: false
-#22676 := [lemma #22673]: #22675
-#27299 := [unit-resolution #22676 #27298 #27295]: #22674
-#4003 := (or #4369 #2813)
-#3885 := [def-axiom]: #4003
-#27300 := [unit-resolution #3885 #27294]: #2813
-#16375 := (or #4218 #2810 #5929 #5934)
-#5926 := (or #5925 #5923 #5916)
-#5927 := (not #5926)
-#5930 := (or #2250 #5929 #5927)
-#16398 := (or #4218 #5930)
-#16553 := (iff #16398 #16375)
-#5937 := (or #2810 #5929 #5934)
-#16114 := (or #4218 #5937)
-#16503 := (iff #16114 #16375)
-#16391 := [rewrite]: #16503
-#16534 := (iff #16398 #16114)
-#5938 := (iff #5930 #5937)
-#5935 := (iff #5927 #5934)
-#5932 := (iff #5926 #5931)
-#5933 := [rewrite]: #5932
-#5936 := [monotonicity #5933]: #5935
-#5939 := [monotonicity #2812 #5936]: #5938
-#16550 := [monotonicity #5939]: #16534
-#16502 := [trans #16550 #16391]: #16553
-#16396 := [quant-inst]: #16398
-#16533 := [mp #16396 #16502]: #16375
-#27301 := [unit-resolution #16533 #10531 #27300 #27299]: #5934
-#16782 := (or #5931 #5924)
-#16643 := [def-axiom]: #16782
-#27302 := [unit-resolution #16643 #27301]: #5924
-#27310 := [mp #27302 #27309]: #25982
-#25983 := (not #25982)
-#27187 := (or #27170 #25983)
-#27188 := [def-axiom]: #27187
-#27311 := [unit-resolution #27188 #27310]: #27170
-#27192 := (not #27170)
-#27196 := (or #27195 #27162 #27192)
-#27197 := [def-axiom]: #27196
-#27313 := [unit-resolution #27197 #27311]: #27312
-#27314 := [unit-resolution #27313 #27285]: #27162
-#27323 := [unit-resolution #27314 #27322]: false
-#27324 := [lemma #27323]: #16889
-#16887 := (uf_24 #5912)
-#16906 := (* -1::int #16887)
-#17099 := (+ #2236 #16906)
-#17100 := (<= #17099 0::int)
-#22648 := (not #17100)
-#15991 := (not #5916)
-#16678 := (or #5931 #15991)
-#16501 := [def-axiom]: #16678
-#22641 := [unit-resolution #16501 #27301]: #15991
-#16907 := (+ #5913 #16906)
-#16908 := (>= #16907 0::int)
-#16989 := (or #4323 #16908)
-#16027 := [quant-inst]: #16989
-#22647 := [unit-resolution #16027 #10924]: #16908
-#22633 := (not #16908)
-#23110 := (or #22648 #5916 #22669 #22633)
-#22643 := [th-lemma]: #23110
-#18144 := [unit-resolution #22643 #27298 #22647 #22641]: #22648
-#17066 := (+ #5919 #16906)
-#17067 := (+ #2236 #17066)
-#17110 := (= #17067 0::int)
-#20033 := (>= #17067 0::int)
-#9449 := (>= #5921 0::int)
-#16586 := (or #5931 #5922)
-#16707 := [def-axiom]: #16586
-#16131 := [unit-resolution #16707 #27301]: #5922
-#21450 := (or #5923 #9449)
-#21454 := [th-lemma]: #21450
-#23041 := [unit-resolution #21454 #16131]: #9449
-#23063 := (not #9449)
-#23122 := (or #20033 #23063 #22669 #22633)
-#23065 := [th-lemma]: #23122
-#23044 := [unit-resolution #23065 #23041 #22647 #27298]: #20033
-#17068 := (<= #17067 0::int)
-#22638 := (<= #16907 0::int)
-#16888 := (= #5913 #16887)
-#16892 := (or #16888 #16890)
-#17827 := (or #4332 #16888 #16890)
-#16891 := (or #16890 #16888)
-#18121 := (or #4332 #16891)
-#16026 := (iff #18121 #17827)
-#18876 := (or #4332 #16892)
-#19063 := (iff #18876 #17827)
-#19159 := [rewrite]: #19063
-#19153 := (iff #18121 #18876)
-#16893 := (iff #16891 #16892)
-#16894 := [rewrite]: #16893
-#17533 := [monotonicity #16894]: #19153
-#19171 := [trans #17533 #19159]: #16026
-#19129 := [quant-inst]: #18121
-#17856 := [mp #19129 #19171]: #17827
-#18906 := [unit-resolution #17856 #10920]: #16892
-#23139 := [unit-resolution #18906 #27324]: #16888
-#23113 := (not #16888)
-#23108 := (or #23113 #22638)
-#23136 := [th-lemma]: #23108
-#23104 := [unit-resolution #23136 #23139]: #22638
-#5682 := (<= #5681 0::int)
-#20530 := (not #5682)
-#20531 := [hypothesis]: #20530
-#20442 := (or #4323 #5682)
-#5672 := (+ #5650 #2237)
-#5673 := (>= #5672 0::int)
-#20459 := (or #4323 #5673)
-#20466 := (iff #20459 #20442)
-#20473 := (iff #20442 #20442)
-#20476 := [rewrite]: #20473
-#5685 := (iff #5673 #5682)
-#5674 := (+ #2237 #5650)
-#5677 := (>= #5674 0::int)
-#5683 := (iff #5677 #5682)
-#5684 := [rewrite]: #5683
-#5678 := (iff #5673 #5677)
-#5675 := (= #5672 #5674)
-#5676 := [rewrite]: #5675
-#5679 := [monotonicity #5676]: #5678
-#5686 := [trans #5679 #5684]: #5685
-#20472 := [monotonicity #5686]: #20466
-#20477 := [trans #20472 #20476]: #20466
-#20465 := [quant-inst]: #20459
-#20527 := [mp #20465 #20477]: #20442
-#20526 := [unit-resolution #20527 #10924 #20531]: false
-#20532 := [lemma #20526]: #5682
-#15989 := (<= #5921 0::int)
-#23166 := (or #5923 #15989)
-#23129 := [th-lemma]: #23166
-#23111 := [unit-resolution #23129 #16131]: #15989
-#23142 := (not #22638)
-#23025 := (not #15989)
-#23268 := (or #17068 #23025 #20530 #23142)
-#23150 := [th-lemma]: #23268
-#23164 := [unit-resolution #23150 #23111 #20532 #23104]: #17068
-#23270 := (not #20033)
-#23269 := (not #17068)
-#23148 := (or #17110 #23269 #23270)
-#23146 := [th-lemma]: #23148
-#23271 := [unit-resolution #23146 #23164 #23044]: #17110
-#17115 := (not #17110)
-#17118 := (or #16890 #17100 #17115)
-#19968 := (or #4366 #16890 #17100 #17115)
-#17087 := (+ #2237 #5918)
-#17088 := (+ #16887 #17087)
-#17089 := (= #17088 0::int)
-#17090 := (not #17089)
-#17051 := (+ #16887 #2237)
-#17091 := (>= #17051 0::int)
-#17092 := (or #16890 #17091 #17090)
-#19969 := (or #4366 #17092)
-#19939 := (iff #19969 #19968)
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-#20227 := (iff #19969 #19962)
-#17119 := (iff #17092 #17118)
-#17116 := (iff #17090 #17115)
-#17113 := (iff #17089 #17110)
-#17059 := (+ #5918 #16887)
-#17060 := (+ #2237 #17059)
-#17107 := (= #17060 0::int)
-#17111 := (iff #17107 #17110)
-#17112 := [rewrite]: #17111
-#17108 := (iff #17089 #17107)
-#17105 := (= #17088 #17060)
-#17106 := [rewrite]: #17105
-#17109 := [monotonicity #17106]: #17108
-#17114 := [trans #17109 #17112]: #17113
-#17117 := [monotonicity #17114]: #17116
-#17103 := (iff #17091 #17100)
-#17093 := (+ #2237 #16887)
-#17096 := (>= #17093 0::int)
-#17101 := (iff #17096 #17100)
-#17102 := [rewrite]: #17101
-#17097 := (iff #17091 #17096)
-#17094 := (= #17051 #17093)
-#17095 := [rewrite]: #17094
-#17098 := [monotonicity #17095]: #17097
-#17104 := [trans #17098 #17102]: #17103
-#17120 := [monotonicity #17104 #17117]: #17119
-#20114 := [monotonicity #17120]: #20227
-#20212 := [trans #20114 #19963]: #19939
-#19967 := [quant-inst]: #19969
-#20005 := [mp #19967 #20212]: #19968
-#23170 := [unit-resolution #20005 #27296]: #17118
-[unit-resolution #23170 #23271 #18144 #27324]: false
+#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
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+#5984 := (not #3861)
+#5985 := (or #5984 #5971)
+#5974 := (iff #5971 #5970)
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+#5988 := (iff #5986 #5985)
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+#5977 := (iff #5971 true)
+#5980 := (iff #5977 #5971)
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+#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)
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+#22994 := (iff #22922 #23013)
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+#22955 := (iff #22980 #23013)
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+#22906 := (iff #22922 #22980)
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+#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)
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+#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
+#22699 := (or #8450 #22691)
+#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)
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+#23443 := (or #10438 #8788)
+#22944 := (or #10438 #23491 #8788 #22695)
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+#8933 := (or #8794 #8929)
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+#9007 := (or #9033 #9032)
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+#13134 := (iff #13122 #12859)
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+#23445 := [unit-resolution #13151 #3872]: #9009
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+#17852 := [lemma #11092]: #8450
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+#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
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+#25450 := [mp #25444 #25449]: #220
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+#13489 := [unit-resolution #3721 #13486]: #4172
+#3716 := (or #4175 #1324 #4169)
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+#25451 := [unit-resolution #3718 #13489]: #4172
+#25452 := [unit-resolution #25451 #25450]: #4169
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+#3725 := [def-axiom]: #3723
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+#25454 := (or #4163 #4157)
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+#8407 := (uf_4 uf_14 ?x65!15)
+#8699 := (>= #8407 0::int)
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+#8438 := (* -1::int #8407)
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+#8763 := (>= #8439 0::int)
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+#8455 := (uf_10 #8454)
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+#8499 := (not #8461)
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+#8479 := (or #8461 #8474)
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+#8485 := (or #8412 #8482)
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+#8462 := (or #8461 #8459)
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+#8497 := [trans #8493 #8495]: #8496
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+#8518 := (or #8461 #8474 #8515)
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+#9052 := (= #8904 #8455)
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+#8872 := (iff #8862 #8867)
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+#8860 := (ite #8859 #5970 #8612)
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+#8870 := (iff #8860 #8867)
+#8864 := (ite #8859 true #8612)
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+#8423 := [monotonicity #8417]: #8422
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+#8420 := [quant-inst]: #8419
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+#9073 := [mp #9062 #9072]: #8896
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+#25456 := [unit-resolution #25455 #25453]: #4157
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+#6336 := (ite #6333 true #6328)
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+#7498 := [unit-resolution #6715 #7497]: #6702
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+#3765 := (or #3075 #3764)
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+#7500 := [unit-resolution #3759 #7415]: #3764
+#7343 := (not #6697)
+#7344 := (or #7041 #2519 #7343 #6266)
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+#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
 unsat