merged
authorhuffman
Sun, 19 Dec 2010 17:39:20 -0800
changeset 41293 59949cf040cb
parent 41292 2b7bc8d9fd6e (current diff)
parent 41283 f9dd7a95158f (diff)
child 41294 53df0095b5e4
merged
--- a/src/FOL/ex/Locale_Test/Locale_Test1.thy	Sun Dec 19 17:37:19 2010 -0800
+++ b/src/FOL/ex/Locale_Test/Locale_Test1.thy	Sun Dec 19 17:39:20 2010 -0800
@@ -156,6 +156,8 @@
     end;
 *}
 
+local_setup {* Config.put show_hyps true *}
+
 ML {*
   check_syntax @{context} @{thm d1_def} "d1(?x) <-> ~ p2(p1(?x))";
   check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
@@ -695,7 +697,69 @@
 locale mixin_thy_merge = le: reflexive le + le': reflexive le' for le le'
 
 
-subsection {* Interpretation in proofs *}
+subsection {* Mixins in sublocale *}
+
+text {* Simulate a specification of left groups where unit and inverse are defined
+  rather than specified.  This is possible, but not in FOL, due to the lack of a
+  selection operator. *}
+
+axiomatization glob_one and glob_inv
+  where glob_lone: "prod(glob_one(prod), x) = x"
+    and glob_linv: "prod(glob_inv(prod, x), x) = glob_one(prod)"
+
+locale dgrp = semi
+begin
+
+definition one where "one = glob_one(prod)"
+
+lemma lone: "one ** x = x"
+  unfolding one_def by (rule glob_lone)
+
+definition inv where "inv(x) = glob_inv(prod, x)"
+
+lemma linv: "inv(x) ** x = one"
+  unfolding one_def inv_def by (rule glob_linv)
+
+end
+
+sublocale lgrp < "def": dgrp
+  where one_equation: "dgrp.one(prod) = one" and inv_equation: "dgrp.inv(prod, x) = inv(x)"
+proof -
+  show "dgrp(prod)" by unfold_locales
+  from this interpret d: dgrp .
+  -- Unit
+  have "dgrp.one(prod) = glob_one(prod)" by (rule d.one_def)
+  also have "... = glob_one(prod) ** one" by (simp add: rone)
+  also have "... = one" by (simp add: glob_lone)
+  finally show "dgrp.one(prod) = one" .
+  -- Inverse
+  then have "dgrp.inv(prod, x) ** x = inv(x) ** x" by (simp add: glob_linv d.linv linv)
+  then show "dgrp.inv(prod, x) = inv(x)" by (simp add: rcancel)
+qed
+
+print_locale! lgrp
+
+context lgrp begin
+
+text {* Equations stored in target *}
+
+lemma "dgrp.one(prod) = one" by (rule one_equation)
+lemma "dgrp.inv(prod, x) = inv(x)" by (rule inv_equation)
+
+text {* Mixins applied *}
+
+lemma "one = glob_one(prod)" by (rule one_def)
+lemma "inv(x) = glob_inv(prod, x)" by (rule inv_def)
+
+end
+
+text {* Interpreted versions *}
+
+lemma "0 = glob_one (op +)" by (rule int.def.one_def)
+lemma "- x = glob_inv(op +, x)" by (rule int.def.inv_def)
+
+
+section {* Interpretation in proofs *}
 
 lemma True
 proof
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Dec 19 17:37:19 2010 -0800
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Dec 19 17:39:20 2010 -0800
@@ -1,4 +1,4 @@
-2bcca4894d12c21351a258c93ec6b00e790bb1de 7195 0
+b9c818fc8db5c62ae4864b1c933f204656ce6c70 7184 0
 #2 := false
 decl f13 :: (-> S5 S3 Int)
 decl f22 :: S3
@@ -9,883 +9,878 @@
 decl f10 :: S3
 #56 := f10
 #99 := (f13 f14 f10)
-#7797 := (= #99 #174)
-#7825 := (= #174 #99)
-#6086 := (= f22 f10)
-#6088 := (= f10 f22)
+#7788 := (= #99 #174)
+#7816 := (= #174 #99)
+#6077 := (= f22 f10)
+#6079 := (= f10 f22)
 decl f3 :: (-> S2 S3 S1)
 decl ?v1!7 :: (-> S3 S3)
-#6069 := (?v1!7 f22)
+#6060 := (?v1!7 f22)
 decl f15 :: S2
 #104 := f15
-#6081 := (f3 f15 #6069)
+#6072 := (f3 f15 #6060)
 decl f1 :: S1
 #4 := f1
-#6082 := (= f1 #6081)
-#6083 := (not #6082)
+#6073 := (= f1 #6072)
+#6074 := (not #6073)
 #44 := 0::Int
 decl f9 :: (-> S4 Int)
 decl f5 :: (-> S3 S3 S4)
-#6074 := (f5 #6069 f22)
-#6075 := (f9 #6074)
-#1208 := -1::Int
-#6076 := (* -1::Int #6075)
-#6070 := (f13 f14 #6069)
-#6071 := (* -1::Int #6070)
-#6077 := (+ #6071 #6076)
-#6078 := (+ #174 #6077)
-#6079 := (= #6078 0::Int)
-#6080 := (not #6079)
-#6072 := (+ #174 #6071)
-#6073 := (<= #6072 0::Int)
-#6091 := (or #6073 #6080 #6083)
+#6065 := (f5 #6060 f22)
+#6066 := (f9 #6065)
+#1199 := -1::Int
+#6067 := (* -1::Int #6066)
+#6061 := (f13 f14 #6060)
+#6062 := (* -1::Int #6061)
+#6068 := (+ #6062 #6067)
+#6069 := (+ #174 #6068)
+#6070 := (= #6069 0::Int)
+#6071 := (not #6070)
+#6063 := (+ #174 #6062)
+#6064 := (<= #6063 0::Int)
+#6082 := (or #6064 #6071 #6074)
 decl f24 :: (-> S3 Int)
 decl ?v0!15 :: S3
-#2273 := ?v0!15
-#2274 := (f24 ?v0!15)
-#2275 := (>= #2274 0::Int)
-#2276 := (not #2275)
+#2264 := ?v0!15
+#2265 := (f24 ?v0!15)
+#2266 := (>= #2265 0::Int)
+#2267 := (not #2266)
 decl ?v0!20 :: S3
-#2346 := ?v0!20
+#2337 := ?v0!20
 #12 := (:var 0 S3)
-#2350 := (f5 #12 ?v0!20)
-#4454 := (pattern #2350)
-#189 := (f24 #12)
-#4394 := (pattern #189)
+#2341 := (f5 #12 ?v0!20)
+#4445 := (pattern #2341)
+#188 := (f24 #12)
+#4385 := (pattern #188)
 decl f23 :: S2
 #179 := f23
-#199 := (f3 f23 #12)
-#4420 := (pattern #199)
-#2351 := (f9 #2350)
-#2347 := (f24 ?v0!20)
-#2348 := (* -1::Int #2347)
-#2950 := (+ #2348 #2351)
-#2951 := (+ #189 #2950)
-#2954 := (= #2951 0::Int)
-#3516 := (not #2954)
-#2349 := (+ #189 #2348)
-#2354 := (>= #2349 0::Int)
-#807 := (= f1 #199)
-#813 := (not #807)
-#3517 := (or #813 #2354 #3516)
-#4455 := (forall (vars (?v1 S3)) (:pat #4420 #4394 #4454) #3517)
-#4460 := (not #4455)
+#198 := (f3 f23 #12)
+#4411 := (pattern #198)
+#2342 := (f9 #2341)
+#2338 := (f24 ?v0!20)
+#2339 := (* -1::Int #2338)
+#2941 := (+ #2339 #2342)
+#2942 := (+ #188 #2941)
+#2945 := (= #2942 0::Int)
+#3507 := (not #2945)
+#2340 := (+ #188 #2339)
+#2345 := (>= #2340 0::Int)
+#798 := (= f1 #198)
+#804 := (not #798)
+#3508 := (or #804 #2345 #3507)
+#4446 := (forall (vars (?v1 S3)) (:pat #4411 #4385 #4445) #3508)
+#4451 := (not #4446)
 #23 := (:var 1 S3)
 #81 := (f5 #12 #23)
-#4249 := (pattern #81)
-#211 := (f24 #23)
-#1503 := (* -1::Int #211)
-#1504 := (+ #189 #1503)
+#4240 := (pattern #81)
+#210 := (f24 #23)
+#1494 := (* -1::Int #210)
+#1495 := (+ #188 #1494)
 #82 := (f9 #81)
-#1534 := (+ #82 #1504)
-#1532 := (>= #1534 0::Int)
-#1231 := (* -1::Int #82)
+#1525 := (+ #82 #1495)
+#1523 := (>= #1525 0::Int)
+#1222 := (* -1::Int #82)
 decl f8 :: Int
 #45 := f8
-#1234 := (+ f8 #1231)
-#1235 := (<= #1234 0::Int)
-#3508 := (or #813 #1235 #1532)
-#4446 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3508)
-#4451 := (not #4446)
-#2926 := (= f10 ?v0!20)
-#2358 := (+ f8 #2348)
-#2359 := (<= #2358 0::Int)
-#4463 := (or #2359 #2926 #4451 #4460)
-#4466 := (not #4463)
+#1225 := (+ f8 #1222)
+#1226 := (<= #1225 0::Int)
+#3499 := (or #804 #1226 #1523)
+#4437 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3499)
+#4442 := (not #4437)
+#2917 := (= f10 ?v0!20)
+#2349 := (+ f8 #2339)
+#2350 := (<= #2349 0::Int)
+#4454 := (or #2350 #2917 #4442 #4451)
+#4457 := (not #4454)
 decl ?v0!19 :: S3
-#2316 := ?v0!19
+#2307 := ?v0!19
 decl ?v1!18 :: S3
-#2315 := ?v1!18
-#2321 := (f5 ?v1!18 ?v0!19)
-#2322 := (f9 #2321)
-#2325 := (* -1::Int #2322)
-#2319 := (f24 ?v1!18)
-#2912 := (* -1::Int #2319)
-#2913 := (+ #2912 #2325)
-#2317 := (f24 ?v0!19)
-#2914 := (+ #2317 #2913)
-#2915 := (<= #2914 0::Int)
-#2329 := (f3 f23 ?v1!18)
-#2330 := (= f1 #2329)
-#3471 := (not #2330)
-#2326 := (+ f8 #2325)
-#2327 := (<= #2326 0::Int)
-#3486 := (or #2327 #3471 #2915)
-#3491 := (not #3486)
-#4469 := (or #3491 #4466)
-#4472 := (not #4469)
-#4437 := (pattern #189 #211)
-#1502 := (>= #1504 0::Int)
-#208 := (f3 f23 #23)
-#827 := (= f1 #208)
-#3448 := (not #827)
-#3463 := (or #807 #3448 #1502)
-#4438 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4437) #3463)
-#4443 := (not #4438)
-#4475 := (or #4443 #4472)
-#4478 := (not #4475)
+#2306 := ?v1!18
+#2312 := (f5 ?v1!18 ?v0!19)
+#2313 := (f9 #2312)
+#2316 := (* -1::Int #2313)
+#2310 := (f24 ?v1!18)
+#2903 := (* -1::Int #2310)
+#2904 := (+ #2903 #2316)
+#2308 := (f24 ?v0!19)
+#2905 := (+ #2308 #2904)
+#2906 := (<= #2905 0::Int)
+#2320 := (f3 f23 ?v1!18)
+#2321 := (= f1 #2320)
+#3462 := (not #2321)
+#2317 := (+ f8 #2316)
+#2318 := (<= #2317 0::Int)
+#3477 := (or #2318 #3462 #2906)
+#3482 := (not #3477)
+#4460 := (or #3482 #4457)
+#4463 := (not #4460)
+#4428 := (pattern #188 #210)
+#1493 := (>= #1495 0::Int)
+#207 := (f3 f23 #23)
+#818 := (= f1 #207)
+#3439 := (not #818)
+#3454 := (or #798 #3439 #1493)
+#4429 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4428) #3454)
+#4434 := (not #4429)
+#4466 := (or #4434 #4463)
+#4469 := (not #4466)
 decl ?v1!16 :: S3
-#2288 := ?v1!16
-#2292 := (f24 ?v1!16)
-#2886 := (* -1::Int #2292)
+#2279 := ?v1!16
+#2283 := (f24 ?v1!16)
+#2877 := (* -1::Int #2283)
 decl ?v0!17 :: S3
-#2289 := ?v0!17
-#2290 := (f24 ?v0!17)
-#2887 := (+ #2290 #2886)
-#2888 := (<= #2887 0::Int)
-#2297 := (f3 f23 ?v1!16)
-#2298 := (= f1 #2297)
-#2295 := (f3 f23 ?v0!17)
-#2296 := (= f1 #2295)
-#3425 := (not #2296)
-#3440 := (or #3425 #2298 #2888)
-#3445 := (not #3440)
-#4481 := (or #3445 #4478)
-#4484 := (not #4481)
-#1493 := (>= #189 0::Int)
-#4429 := (forall (vars (?v0 S3)) (:pat #4394) #1493)
-#4434 := (not #4429)
-#4487 := (or #4434 #4484)
+#2280 := ?v0!17
+#2281 := (f24 ?v0!17)
+#2878 := (+ #2281 #2877)
+#2879 := (<= #2878 0::Int)
+#2288 := (f3 f23 ?v1!16)
+#2289 := (= f1 #2288)
+#2286 := (f3 f23 ?v0!17)
+#2287 := (= f1 #2286)
+#3416 := (not #2287)
+#3431 := (or #3416 #2289 #2879)
+#3436 := (not #3431)
+#4472 := (or #3436 #4469)
+#4475 := (not #4472)
+#1484 := (>= #188 0::Int)
+#4420 := (forall (vars (?v0 S3)) (:pat #4385) #1484)
+#4425 := (not #4420)
+#4478 := (or #4425 #4475)
 decl f6 :: (-> S4 S3)
 decl f7 :: (-> S4 S3)
-#5995 := (f5 f22 f22)
-#7211 := (f7 #5995)
-#14211 := (f5 #7211 ?v0!20)
-#24392 := (f7 #14211)
-#14774 := (?v1!7 ?v0!20)
-#24669 := (f5 #14774 #24392)
-#25042 := (f6 #24669)
-#26213 := (f3 f15 #25042)
-#26214 := (= f1 #26213)
-#14786 := (f3 f15 #14774)
-#27706 := (= #14786 #26213)
-#27703 := (= #26213 #14786)
-#29051 := (= #25042 #14774)
-#14779 := (f5 #14774 ?v0!20)
-#19038 := (f6 #14779)
-#26818 := (= #19038 #14774)
-#19043 := (= #14774 #19038)
+#5986 := (f5 f22 f22)
+#7202 := (f7 #5986)
+#14202 := (f5 #7202 ?v0!20)
+#24383 := (f7 #14202)
+#14765 := (?v1!7 ?v0!20)
+#24660 := (f5 #14765 #24383)
+#25033 := (f6 #24660)
+#26204 := (f3 f15 #25033)
+#26205 := (= f1 #26204)
+#14777 := (f3 f15 #14765)
+#27697 := (= #14777 #26204)
+#27694 := (= #26204 #14777)
+#29042 := (= #25033 #14765)
+#14770 := (f5 #14765 ?v0!20)
+#19029 := (f6 #14770)
+#26809 := (= #19029 #14765)
+#19034 := (= #14765 #19029)
 #37 := (f5 #23 #12)
-#4193 := (pattern #37)
+#4184 := (pattern #37)
 #41 := (f6 #37)
-#344 := (= #23 #41)
-#4200 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #344)
-#348 := (forall (vars (?v0 S3) (?v1 S3)) #344)
-#4203 := (iff #348 #4200)
-#4201 := (iff #344 #344)
-#4202 := [refl]: #4201
-#4204 := [quant-intro #4202]: #4203
-#1848 := (~ #348 #348)
-#1878 := (~ #344 #344)
-#1879 := [refl]: #1878
-#1849 := [nnf-pos #1879]: #1848
+#343 := (= #23 #41)
+#4191 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #343)
+#347 := (forall (vars (?v0 S3) (?v1 S3)) #343)
+#4194 := (iff #347 #4191)
+#4192 := (iff #343 #343)
+#4193 := [refl]: #4192
+#4195 := [quant-intro #4193]: #4194
+#1839 := (~ #347 #347)
+#1869 := (~ #343 #343)
+#1870 := [refl]: #1869
+#1840 := [nnf-pos #1870]: #1839
 #42 := (= #41 #23)
 #43 := (forall (vars (?v0 S3) (?v1 S3)) #42)
-#349 := (iff #43 #348)
-#346 := (iff #42 #344)
-#347 := [rewrite]: #346
-#350 := [quant-intro #347]: #349
-#343 := [asserted]: #43
-#353 := [mp #343 #350]: #348
-#1880 := [mp~ #353 #1849]: #348
-#4205 := [mp #1880 #4204]: #4200
-#6829 := (not #4200)
-#8630 := (or #6829 #19043)
-#13594 := [quant-inst #14774 #2346]: #8630
-#26774 := [unit-resolution #13594 #4205]: #19043
-#26816 := [symm #26774]: #26818
-#26826 := (= #25042 #19038)
-#26823 := (= #24669 #14779)
-#27255 := (= #24392 ?v0!20)
-#19042 := (f7 #14779)
-#25094 := (= #19042 ?v0!20)
-#19037 := (= ?v0!20 #19042)
+#348 := (iff #43 #347)
+#345 := (iff #42 #343)
+#346 := [rewrite]: #345
+#349 := [quant-intro #346]: #348
+#342 := [asserted]: #43
+#352 := [mp #342 #349]: #347
+#1871 := [mp~ #352 #1840]: #347
+#4196 := [mp #1871 #4195]: #4191
+#6820 := (not #4191)
+#8621 := (or #6820 #19034)
+#13585 := [quant-inst #14765 #2337]: #8621
+#26765 := [unit-resolution #13585 #4196]: #19034
+#26807 := [symm #26765]: #26809
+#26817 := (= #25033 #19029)
+#26814 := (= #24660 #14770)
+#27246 := (= #24383 ?v0!20)
+#19033 := (f7 #14770)
+#25085 := (= #19033 ?v0!20)
+#19028 := (= ?v0!20 #19033)
 #38 := (f7 #37)
-#336 := (= #12 #38)
-#4194 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #336)
-#340 := (forall (vars (?v0 S3) (?v1 S3)) #336)
-#4197 := (iff #340 #4194)
-#4195 := (iff #336 #336)
-#4196 := [refl]: #4195
-#4198 := [quant-intro #4196]: #4197
-#1846 := (~ #340 #340)
-#1875 := (~ #336 #336)
-#1876 := [refl]: #1875
-#1847 := [nnf-pos #1876]: #1846
+#335 := (= #12 #38)
+#4185 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #335)
+#339 := (forall (vars (?v0 S3) (?v1 S3)) #335)
+#4188 := (iff #339 #4185)
+#4186 := (iff #335 #335)
+#4187 := [refl]: #4186
+#4189 := [quant-intro #4187]: #4188
+#1837 := (~ #339 #339)
+#1866 := (~ #335 #335)
+#1867 := [refl]: #1866
+#1838 := [nnf-pos #1867]: #1837
 #39 := (= #38 #12)
 #40 := (forall (vars (?v0 S3) (?v1 S3)) #39)
-#341 := (iff #40 #340)
-#338 := (iff #39 #336)
-#339 := [rewrite]: #338
-#342 := [quant-intro #339]: #341
-#335 := [asserted]: #40
-#345 := [mp #335 #342]: #340
-#1877 := [mp~ #345 #1847]: #340
-#4199 := [mp #1877 #4198]: #4194
-#6824 := (not #4194)
-#19044 := (or #6824 #19037)
-#19045 := [quant-inst #14774 #2346]: #19044
-#25093 := [unit-resolution #19045 #4199]: #19037
-#25095 := [symm #25093]: #25094
-#26795 := (= #24392 #19042)
-#23180 := (f5 #7211 #19042)
-#23299 := (f7 #23180)
-#26807 := (= #23299 #19042)
-#23305 := (= #19042 #23299)
-#26717 := (or #6824 #23305)
-#26720 := [quant-inst #7211 #19042]: #26717
-#26803 := [unit-resolution #26720 #4199]: #23305
-#26808 := [symm #26803]: #26807
-#26804 := (= #24392 #23299)
-#26801 := (= #23299 #24392)
-#26799 := (= #23180 #14211)
-#14131 := (f5 f22 ?v0!20)
-#26773 := (= #14131 #14211)
-#24028 := (= #14211 #14131)
-#7784 := (= #7211 f22)
-#7212 := (= f22 #7211)
-#7263 := (or #6824 #7212)
-#7264 := [quant-inst #170 #170]: #7263
-#7789 := [unit-resolution #7264 #4199]: #7212
-#7790 := [symm #7789]: #7784
-#24029 := [monotonicity #7790]: #24028
-#26715 := [symm #24029]: #26773
-#26777 := (= #23180 #14131)
-#26776 := (= #14131 #23180)
-#26752 := [monotonicity #7789 #25093]: #26776
-#26778 := [symm #26752]: #26777
-#26802 := [trans #26778 #26715]: #26799
-#26805 := [monotonicity #26802]: #26801
-#26806 := [symm #26805]: #26804
-#26822 := [trans #26806 #26808]: #26795
-#26796 := [trans #26822 #25095]: #27255
-#26824 := [monotonicity #26796]: #26823
-#26817 := [monotonicity #26824]: #26826
-#26819 := [trans #26817 #26816]: #29051
-#26814 := [monotonicity #26819]: #27703
-#26828 := [symm #26814]: #27706
-#14787 := (= f1 #14786)
-#14788 := (not #14787)
-#14780 := (f9 #14779)
-#14781 := (* -1::Int #14780)
-#14775 := (f13 f14 #14774)
-#14776 := (* -1::Int #14775)
-#14782 := (+ #14776 #14781)
-#14074 := (f13 f14 ?v0!20)
-#14783 := (+ #14074 #14782)
-#14784 := (= #14783 0::Int)
-#14785 := (not #14784)
-#14777 := (+ #14074 #14776)
-#14778 := (<= #14777 0::Int)
-#14794 := (or #14778 #14785 #14788)
-#14797 := (not #14794)
-#14115 := (* -1::Int #14074)
-#14791 := (+ f8 #14115)
-#14792 := (<= #14791 0::Int)
-#21435 := (not #14792)
-#2360 := (not #2359)
-#19783 := [hypothesis]: #2360
-#14116 := (+ #2347 #14115)
-#19567 := (>= #14116 0::Int)
-#14085 := (= #2347 #14074)
-#14132 := (f9 #14131)
-#14150 := (+ #14115 #14132)
-#14151 := (+ #174 #14150)
-#14152 := (>= #14151 0::Int)
-#14136 := (* -1::Int #14132)
-#14140 := (+ f8 #14136)
-#14141 := (<= #14140 0::Int)
-#14183 := (or #14141 #14152)
-#4490 := (not #4487)
-#1453 := (* -1::Int #174)
-#5913 := (+ #99 #1453)
-#7798 := (<= #5913 0::Int)
-#27734 := (or #6073 #2359)
-#25047 := (= #14774 #25042)
-#23337 := (or #6829 #25047)
-#23338 := [quant-inst #14774 #24392]: #23337
-#28984 := [unit-resolution #23338 #4205]: #25047
-#29062 := [symm #28984]: #29051
-#27698 := [monotonicity #29062]: #27703
-#27718 := [symm #27698]: #27706
-#6118 := (not #6073)
-#10074 := [hypothesis]: #6118
-#23174 := (or #14152 #6073)
-#11114 := (or #2275 #6073)
-#7536 := (f13 f14 ?v0!15)
-#7757 := (>= #7536 0::Int)
+#340 := (iff #40 #339)
+#337 := (iff #39 #335)
+#338 := [rewrite]: #337
+#341 := [quant-intro #338]: #340
+#334 := [asserted]: #40
+#344 := [mp #334 #341]: #339
+#1868 := [mp~ #344 #1838]: #339
+#4190 := [mp #1868 #4189]: #4185
+#6815 := (not #4185)
+#19035 := (or #6815 #19028)
+#19036 := [quant-inst #14765 #2337]: #19035
+#25084 := [unit-resolution #19036 #4190]: #19028
+#25086 := [symm #25084]: #25085
+#26786 := (= #24383 #19033)
+#23171 := (f5 #7202 #19033)
+#23290 := (f7 #23171)
+#26798 := (= #23290 #19033)
+#23296 := (= #19033 #23290)
+#26708 := (or #6815 #23296)
+#26711 := [quant-inst #7202 #19033]: #26708
+#26794 := [unit-resolution #26711 #4190]: #23296
+#26799 := [symm #26794]: #26798
+#26795 := (= #24383 #23290)
+#26792 := (= #23290 #24383)
+#26790 := (= #23171 #14202)
+#14122 := (f5 f22 ?v0!20)
+#26764 := (= #14122 #14202)
+#24019 := (= #14202 #14122)
+#7775 := (= #7202 f22)
+#7203 := (= f22 #7202)
+#7254 := (or #6815 #7203)
+#7255 := [quant-inst #170 #170]: #7254
+#7780 := [unit-resolution #7255 #4190]: #7203
+#7781 := [symm #7780]: #7775
+#24020 := [monotonicity #7781]: #24019
+#26706 := [symm #24020]: #26764
+#26768 := (= #23171 #14122)
+#26767 := (= #14122 #23171)
+#26743 := [monotonicity #7780 #25084]: #26767
+#26769 := [symm #26743]: #26768
+#26793 := [trans #26769 #26706]: #26790
+#26796 := [monotonicity #26793]: #26792
+#26797 := [symm #26796]: #26795
+#26813 := [trans #26797 #26799]: #26786
+#26787 := [trans #26813 #25086]: #27246
+#26815 := [monotonicity #26787]: #26814
+#26808 := [monotonicity #26815]: #26817
+#26810 := [trans #26808 #26807]: #29042
+#26805 := [monotonicity #26810]: #27694
+#26819 := [symm #26805]: #27697
+#14778 := (= f1 #14777)
+#14779 := (not #14778)
+#14771 := (f9 #14770)
+#14772 := (* -1::Int #14771)
+#14766 := (f13 f14 #14765)
+#14767 := (* -1::Int #14766)
+#14773 := (+ #14767 #14772)
+#14065 := (f13 f14 ?v0!20)
+#14774 := (+ #14065 #14773)
+#14775 := (= #14774 0::Int)
+#14776 := (not #14775)
+#14768 := (+ #14065 #14767)
+#14769 := (<= #14768 0::Int)
+#14785 := (or #14769 #14776 #14779)
+#14788 := (not #14785)
+#14106 := (* -1::Int #14065)
+#14782 := (+ f8 #14106)
+#14783 := (<= #14782 0::Int)
+#21426 := (not #14783)
+#2351 := (not #2350)
+#19774 := [hypothesis]: #2351
+#14107 := (+ #2338 #14106)
+#19558 := (>= #14107 0::Int)
+#14076 := (= #2338 #14065)
+#14123 := (f9 #14122)
+#14141 := (+ #14106 #14123)
+#14142 := (+ #174 #14141)
+#14143 := (>= #14142 0::Int)
+#14127 := (* -1::Int #14123)
+#14131 := (+ f8 #14127)
+#14132 := (<= #14131 0::Int)
+#14174 := (or #14132 #14143)
+#4481 := (not #4478)
+#1444 := (* -1::Int #174)
+#5904 := (+ #99 #1444)
+#7789 := (<= #5904 0::Int)
+#27725 := (or #6064 #2350)
+#25038 := (= #14765 #25033)
+#23328 := (or #6820 #25038)
+#23329 := [quant-inst #14765 #24383]: #23328
+#28975 := [unit-resolution #23329 #4196]: #25038
+#29053 := [symm #28975]: #29042
+#27689 := [monotonicity #29053]: #27694
+#27709 := [symm #27689]: #27697
+#6109 := (not #6064)
+#10065 := [hypothesis]: #6109
+#23165 := (or #14143 #6064)
+#11105 := (or #2266 #6064)
+#7527 := (f13 f14 ?v0!15)
+#7748 := (>= #7527 0::Int)
 #101 := (f13 f14 #12)
-#4273 := (pattern #101)
-#1736 := (>= #101 0::Int)
-#4274 := (forall (vars (?v0 S3)) (:pat #4273) #1736)
-#4493 := (or #2276 #4490)
-#4496 := (not #4493)
-#203 := (f24 f10)
-#204 := (= #203 0::Int)
-#1490 := (not #204)
-#4499 := (or #1490 #4496)
-#4502 := (not #4499)
-#4505 := (or #1490 #4502)
-#4508 := (not #4505)
-#793 := (= #101 #189)
-#814 := (or #793 #813)
-#4421 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4420) #814)
-#4426 := (not #4421)
-#4511 := (or #4426 #4508)
-#4514 := (not #4511)
+#4264 := (pattern #101)
+#1727 := (>= #101 0::Int)
+#4265 := (forall (vars (?v0 S3)) (:pat #4264) #1727)
+#4484 := (or #2267 #4481)
+#4487 := (not #4484)
+#202 := (f24 f10)
+#203 := (= #202 0::Int)
+#1481 := (not #203)
+#4490 := (or #1481 #4487)
+#4493 := (not #4490)
+#4496 := (or #1481 #4493)
+#4499 := (not #4496)
+#784 := (= #101 #188)
+#805 := (or #784 #804)
+#4412 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4411) #805)
+#4417 := (not #4412)
+#4502 := (or #4417 #4499)
+#4505 := (not #4502)
 decl ?v0!14 :: S3
-#2248 := ?v0!14
-#2253 := (f13 f14 ?v0!14)
-#2252 := (f24 ?v0!14)
-#2858 := (= #2252 #2253)
-#2249 := (f3 f23 ?v0!14)
-#2250 := (= f1 #2249)
-#2251 := (not #2250)
-#2864 := (or #2251 #2858)
-#2869 := (not #2864)
-#4517 := (or #2869 #4514)
-#4520 := (not #4517)
-#1478 := (* -1::Int #189)
-#1479 := (+ #101 #1478)
-#1477 := (>= #1479 0::Int)
-#4412 := (forall (vars (?v0 S3)) (:pat #4273 #4394) #1477)
-#4417 := (not #4412)
-#4523 := (or #4417 #4520)
-#4526 := (not #4523)
+#2239 := ?v0!14
+#2244 := (f13 f14 ?v0!14)
+#2243 := (f24 ?v0!14)
+#2849 := (= #2243 #2244)
+#2240 := (f3 f23 ?v0!14)
+#2241 := (= f1 #2240)
+#2242 := (not #2241)
+#2855 := (or #2242 #2849)
+#2860 := (not #2855)
+#4508 := (or #2860 #4505)
+#4511 := (not #4508)
+#1469 := (* -1::Int #188)
+#1470 := (+ #101 #1469)
+#1468 := (>= #1470 0::Int)
+#4403 := (forall (vars (?v0 S3)) (:pat #4264 #4385) #1468)
+#4408 := (not #4403)
+#4514 := (or #4408 #4511)
+#4517 := (not #4514)
 decl ?v0!13 :: S3
-#2230 := ?v0!13
-#2233 := (f13 f14 ?v0!13)
-#2848 := (* -1::Int #2233)
-#2231 := (f24 ?v0!13)
-#2849 := (+ #2231 #2848)
-#2850 := (<= #2849 0::Int)
-#2855 := (not #2850)
-#4529 := (or #2855 #4526)
-#4532 := (not #4529)
-#183 := (f5 f22 #12)
-#4395 := (pattern #183)
-#184 := (f9 #183)
-#1621 := (+ #184 #1478)
-#1622 := (+ #174 #1621)
-#1623 := (= #1622 0::Int)
-#1447 := (* -1::Int #184)
-#1454 := (+ #1453 #1447)
-#1455 := (+ #101 #1454)
-#1456 := (<= #1455 0::Int)
-#1448 := (+ f8 #1447)
-#1449 := (<= #1448 0::Int)
-#3417 := (or #1449 #1456 #1623)
-#4404 := (forall (vars (?v0 S3)) (:pat #4395 #4273 #4394) #3417)
-#4409 := (not #4404)
-#3397 := (or #1449 #1456)
-#3398 := (not #3397)
-#3401 := (or #793 #3398)
-#4396 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4395) #3401)
-#4401 := (not #4396)
+#2221 := ?v0!13
+#2224 := (f13 f14 ?v0!13)
+#2839 := (* -1::Int #2224)
+#2222 := (f24 ?v0!13)
+#2840 := (+ #2222 #2839)
+#2841 := (<= #2840 0::Int)
+#2846 := (not #2841)
+#4520 := (or #2846 #4517)
+#4523 := (not #4520)
+#182 := (f5 f22 #12)
+#4386 := (pattern #182)
+#183 := (f9 #182)
+#1612 := (+ #183 #1469)
+#1613 := (+ #174 #1612)
+#1614 := (= #1613 0::Int)
+#1438 := (* -1::Int #183)
+#1445 := (+ #1444 #1438)
+#1446 := (+ #101 #1445)
+#1447 := (<= #1446 0::Int)
+#1439 := (+ f8 #1438)
+#1440 := (<= #1439 0::Int)
+#3408 := (or #1440 #1447 #1614)
+#4395 := (forall (vars (?v0 S3)) (:pat #4386 #4264 #4385) #3408)
+#4400 := (not #4395)
+#3388 := (or #1440 #1447)
+#3389 := (not #3388)
+#3392 := (or #784 #3389)
+#4387 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4386) #3392)
+#4392 := (not #4387)
 decl ?v0!12 :: S3
-#2206 := ?v0!12
-#2212 := (f3 f15 ?v0!12)
-#2213 := (= f1 #2212)
-#2207 := (f13 f14 ?v0!12)
-#2208 := (* -1::Int #2207)
-#2209 := (+ f8 #2208)
-#2210 := (<= #2209 0::Int)
-#1653 := (+ f8 #1453)
-#1654 := (<= #1653 0::Int)
+#2197 := ?v0!12
+#2203 := (f3 f15 ?v0!12)
+#2204 := (= f1 #2203)
+#2198 := (f13 f14 ?v0!12)
+#2199 := (* -1::Int #2198)
+#2200 := (+ f8 #2199)
+#2201 := (<= #2200 0::Int)
+#1644 := (+ f8 #1444)
+#1645 := (<= #1644 0::Int)
 #105 := (f3 f15 #12)
-#4315 := (pattern #105)
-#1636 := (+ #101 #1453)
-#1635 := (>= #1636 0::Int)
-#533 := (= f1 #105)
-#1642 := (or #533 #1635)
-#4386 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #1642)
-#4391 := (not #4386)
+#4306 := (pattern #105)
+#1627 := (+ #101 #1444)
+#1626 := (>= #1627 0::Int)
+#532 := (= f1 #105)
+#1633 := (or #532 #1626)
+#4377 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #1633)
+#4382 := (not #4377)
+#171 := (f3 f15 f22)
+#753 := (= f1 #171)
 decl f4 :: (-> S2 S3 S1 S2)
-#773 := (f4 f15 f22 f1)
-#776 := (= f23 #773)
-#995 := (not #776)
-#171 := (f3 f15 f22)
-#754 := (= f1 #171)
-#4535 := (or #754 #995 #4391 #1654 #2210 #2213 #4401 #4409 #4532)
-#4538 := (not #4535)
+#180 := (f4 f15 f22 f1)
+#181 := (= f23 #180)
+#986 := (not #181)
+#4526 := (or #986 #753 #4382 #1645 #2201 #2204 #4392 #4400 #4523)
+#4529 := (not #4526)
 decl ?v0!11 :: S3
-#2140 := ?v0!11
+#2131 := ?v0!11
 decl ?v1!10 :: S3
-#2139 := ?v1!10
-#2145 := (f5 ?v1!10 ?v0!11)
-#2146 := (f9 #2145)
-#2153 := (* -1::Int #2146)
+#2130 := ?v1!10
+#2136 := (f5 ?v1!10 ?v0!11)
+#2137 := (f9 #2136)
+#2144 := (* -1::Int #2137)
 decl f19 :: S5
 #137 := f19
-#2143 := (f13 f19 ?v1!10)
-#2149 := (* -1::Int #2143)
-#2805 := (+ #2149 #2153)
-#2141 := (f13 f19 ?v0!11)
-#2806 := (+ #2141 #2805)
-#2807 := (<= #2806 0::Int)
-#2154 := (+ f8 #2153)
-#2155 := (<= #2154 0::Int)
-#2150 := (+ f8 #2149)
-#2151 := (<= #2150 0::Int)
-#3361 := (or #2151 #2155 #2807)
-#3366 := (not #3361)
+#2134 := (f13 f19 ?v1!10)
+#2140 := (* -1::Int #2134)
+#2796 := (+ #2140 #2144)
+#2132 := (f13 f19 ?v0!11)
+#2797 := (+ #2132 #2796)
+#2798 := (<= #2797 0::Int)
+#2145 := (+ f8 #2144)
+#2146 := (<= #2145 0::Int)
+#2141 := (+ f8 #2140)
+#2142 := (<= #2141 0::Int)
+#3352 := (or #2142 #2146 #2798)
+#3357 := (not #3352)
 #145 := (f13 f19 #23)
-#1355 := (* -1::Int #145)
+#1346 := (* -1::Int #145)
 #142 := (f13 f19 #12)
-#1356 := (+ #142 #1355)
-#1362 := (+ #82 #1356)
-#1385 := (>= #1362 0::Int)
-#1342 := (* -1::Int #142)
-#1343 := (+ f8 #1342)
-#1344 := (<= #1343 0::Int)
-#3329 := (or #1235 #1344 #1385)
-#4348 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3329)
-#4353 := (not #4348)
+#1347 := (+ #142 #1346)
+#1353 := (+ #82 #1347)
+#1376 := (>= #1353 0::Int)
+#1333 := (* -1::Int #142)
+#1334 := (+ f8 #1333)
+#1335 := (<= #1334 0::Int)
+#3320 := (or #1226 #1335 #1376)
+#4339 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3320)
+#4344 := (not #4339)
 #157 := (f13 f19 f10)
 #158 := (= #157 0::Int)
-#4356 := (or #158 #4353)
-#4359 := (not #4356)
-#4362 := (or #4359 #3366)
-#4365 := (not #4362)
-#4324 := (pattern #142)
+#4347 := (or #158 #4344)
+#4350 := (not #4347)
+#4353 := (or #4350 #3357)
+#4356 := (not #4353)
+#4315 := (pattern #142)
 decl ?v1!9 :: (-> S3 S3)
-#2116 := (?v1!9 #12)
-#2119 := (f5 #2116 #12)
-#2120 := (f9 #2119)
-#2775 := (* -1::Int #2120)
-#2117 := (f13 f19 #2116)
-#2758 := (* -1::Int #2117)
-#2776 := (+ #2758 #2775)
-#2777 := (+ #142 #2776)
-#2778 := (= #2777 0::Int)
-#3299 := (not #2778)
-#2759 := (+ #142 #2758)
-#2760 := (<= #2759 0::Int)
-#3300 := (or #2760 #3299)
-#3301 := (not #3300)
+#2107 := (?v1!9 #12)
+#2110 := (f5 #2107 #12)
+#2111 := (f9 #2110)
+#2766 := (* -1::Int #2111)
+#2108 := (f13 f19 #2107)
+#2749 := (* -1::Int #2108)
+#2767 := (+ #2749 #2766)
+#2768 := (+ #142 #2767)
+#2769 := (= #2768 0::Int)
+#3290 := (not #2769)
+#2750 := (+ #142 #2749)
+#2751 := (<= #2750 0::Int)
+#3291 := (or #2751 #3290)
+#3292 := (not #3291)
 #57 := (= #12 f10)
-#3307 := (or #57 #1344 #3301)
-#4340 := (forall (vars (?v0 S3)) (:pat #4324) #3307)
-#4345 := (not #4340)
-#4368 := (or #4345 #4365)
-#4371 := (not #4368)
+#3298 := (or #57 #1335 #3292)
+#4331 := (forall (vars (?v0 S3)) (:pat #4315) #3298)
+#4336 := (not #4331)
+#4359 := (or #4336 #4356)
+#4362 := (not #4359)
 decl ?v0!8 :: S3
-#2076 := ?v0!8
-#2080 := (f5 #12 ?v0!8)
-#4325 := (pattern #2080)
-#2081 := (f9 #2080)
-#2077 := (f13 f19 ?v0!8)
-#2078 := (* -1::Int #2077)
-#2728 := (+ #2078 #2081)
-#2729 := (+ #142 #2728)
-#2732 := (= #2729 0::Int)
-#3263 := (not #2732)
-#2079 := (+ #142 #2078)
-#2084 := (>= #2079 0::Int)
-#3264 := (or #2084 #3263)
-#4326 := (forall (vars (?v1 S3)) (:pat #4324 #4325) #3264)
-#4331 := (not #4326)
-#2704 := (= f10 ?v0!8)
-#2088 := (+ f8 #2078)
-#2089 := (<= #2088 0::Int)
-#4334 := (or #2089 #2704 #4331)
-#4337 := (not #4334)
-#4374 := (or #4337 #4371)
-#4377 := (not #4374)
-#1297 := (* -1::Int #101)
-#1298 := (+ f8 #1297)
-#1299 := (<= #1298 0::Int)
-#3249 := (or #533 #1299)
-#4316 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #3249)
-#4321 := (not #4316)
-#624 := (= f14 f19)
-#715 := (not #624)
+#2067 := ?v0!8
+#2071 := (f5 #12 ?v0!8)
+#4316 := (pattern #2071)
+#2072 := (f9 #2071)
+#2068 := (f13 f19 ?v0!8)
+#2069 := (* -1::Int #2068)
+#2719 := (+ #2069 #2072)
+#2720 := (+ #142 #2719)
+#2723 := (= #2720 0::Int)
+#3254 := (not #2723)
+#2070 := (+ #142 #2069)
+#2075 := (>= #2070 0::Int)
+#3255 := (or #2075 #3254)
+#4317 := (forall (vars (?v1 S3)) (:pat #4315 #4316) #3255)
+#4322 := (not #4317)
+#2695 := (= f10 ?v0!8)
+#2079 := (+ f8 #2069)
+#2080 := (<= #2079 0::Int)
+#4325 := (or #2080 #2695 #4322)
+#4328 := (not #4325)
+#4365 := (or #4328 #4362)
+#4368 := (not #4365)
+#1288 := (* -1::Int #101)
+#1289 := (+ f8 #1288)
+#1290 := (<= #1289 0::Int)
+#3240 := (or #532 #1290)
+#4307 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #3240)
+#4312 := (not #4307)
+#623 := (= f14 f19)
+#714 := (not #623)
 decl f16 :: S2
 #132 := f16
-#621 := (= f15 f16)
-#733 := (not #621)
+#620 := (= f15 f16)
+#732 := (not #620)
 decl f21 :: S5
 #140 := f21
 decl f20 :: S5
 #139 := f20
 #141 := (= f20 f21)
-#706 := (not #141)
+#705 := (not #141)
 decl f18 :: S3
 #135 := f18
 decl f17 :: S3
 #134 := f17
 #136 := (= f17 f18)
-#724 := (not #136)
-#4380 := (or #724 #706 #733 #715 #4321 #4377)
-#4383 := (not #4380)
-#4541 := (or #4383 #4538)
-#4544 := (not #4541)
-#2039 := (?v1!7 #12)
-#2040 := (f13 f14 #2039)
-#2663 := (* -1::Int #2040)
-#2678 := (+ #101 #2663)
-#2679 := (<= #2678 0::Int)
-#2044 := (f5 #2039 #12)
-#2045 := (f9 #2044)
-#2664 := (* -1::Int #2045)
-#2665 := (+ #2663 #2664)
-#2666 := (+ #101 #2665)
-#2667 := (= #2666 0::Int)
-#3233 := (not #2667)
-#2048 := (f3 f15 #2039)
-#2049 := (= f1 #2048)
-#3232 := (not #2049)
-#3234 := (or #3232 #3233 #2679)
-#3235 := (not #3234)
-#3241 := (or #57 #1299 #3235)
-#4307 := (forall (vars (?v0 S3)) (:pat #4273) #3241)
-#4312 := (not #4307)
+#723 := (not #136)
+#4371 := (or #723 #705 #732 #714 #4312 #4368)
+#4374 := (not #4371)
+#4532 := (or #4374 #4529)
+#4535 := (not #4532)
+#2030 := (?v1!7 #12)
+#2031 := (f13 f14 #2030)
+#2654 := (* -1::Int #2031)
+#2669 := (+ #101 #2654)
+#2670 := (<= #2669 0::Int)
+#2035 := (f5 #2030 #12)
+#2036 := (f9 #2035)
+#2655 := (* -1::Int #2036)
+#2656 := (+ #2654 #2655)
+#2657 := (+ #101 #2656)
+#2658 := (= #2657 0::Int)
+#3224 := (not #2658)
+#2039 := (f3 f15 #2030)
+#2040 := (= f1 #2039)
+#3223 := (not #2040)
+#3225 := (or #3223 #3224 #2670)
+#3226 := (not #3225)
+#3232 := (or #57 #1290 #3226)
+#4298 := (forall (vars (?v0 S3)) (:pat #4264) #3232)
+#4303 := (not #4298)
 decl f11 :: (-> S3 Int)
 #58 := (f11 #12)
-#4218 := (pattern #58)
+#4209 := (pattern #58)
 decl ?v1!6 :: (-> S3 S3)
-#2011 := (?v1!6 #12)
-#2015 := (f11 #2011)
-#2622 := (* -1::Int #2015)
-#2012 := (f5 #2011 #12)
-#2013 := (f9 #2012)
-#2639 := (* -1::Int #2013)
-#2640 := (+ #2639 #2622)
-#2641 := (+ #58 #2640)
-#2642 := (= #2641 0::Int)
-#3205 := (not #2642)
-#2623 := (+ #58 #2622)
-#2624 := (<= #2623 0::Int)
+#2002 := (?v1!6 #12)
+#2006 := (f11 #2002)
+#2613 := (* -1::Int #2006)
+#2003 := (f5 #2002 #12)
+#2004 := (f9 #2003)
+#2630 := (* -1::Int #2004)
+#2631 := (+ #2630 #2613)
+#2632 := (+ #58 #2631)
+#2633 := (= #2632 0::Int)
+#3196 := (not #2633)
+#2614 := (+ #58 #2613)
+#2615 := (<= #2614 0::Int)
 decl f12 :: (-> S3 S1)
-#2021 := (f12 #2011)
-#2022 := (= f1 #2021)
-#3204 := (not #2022)
-#3206 := (or #3204 #2624 #3205)
-#3207 := (not #3206)
-#1259 := (* -1::Int #58)
-#1260 := (+ f8 #1259)
-#1261 := (<= #1260 0::Int)
-#3213 := (or #57 #1261 #3207)
-#4299 := (forall (vars (?v0 S3)) (:pat #4218) #3213)
-#4304 := (not #4299)
+#2012 := (f12 #2002)
+#2013 := (= f1 #2012)
+#3195 := (not #2013)
+#3197 := (or #3195 #2615 #3196)
+#3198 := (not #3197)
+#1250 := (* -1::Int #58)
+#1251 := (+ f8 #1250)
+#1252 := (<= #1251 0::Int)
+#3204 := (or #57 #1252 #3198)
+#4290 := (forall (vars (?v0 S3)) (:pat #4209) #3204)
+#4295 := (not #4290)
 #108 := (f3 f15 #23)
-#4290 := (pattern #105 #108)
+#4281 := (pattern #105 #108)
 #111 := (f13 f14 #23)
-#1311 := (* -1::Int #111)
-#1312 := (+ #101 #1311)
-#1315 := (>= #1312 0::Int)
-#539 := (= f1 #108)
-#3170 := (not #539)
-#3185 := (or #533 #3170 #1315)
-#4291 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4290) #3185)
-#4296 := (not #4291)
-#1313 := (+ #82 #1312)
-#1708 := (>= #1313 0::Int)
-#536 := (not #533)
-#3162 := (or #536 #1235 #1708)
-#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3162)
+#1302 := (* -1::Int #111)
+#1303 := (+ #101 #1302)
+#1306 := (>= #1303 0::Int)
+#538 := (= f1 #108)
+#3161 := (not #538)
+#3176 := (or #532 #3161 #1306)
+#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4281) #3176)
 #4287 := (not #4282)
-#4279 := (not #4274)
+#1304 := (+ #82 #1303)
+#1699 := (>= #1304 0::Int)
+#535 := (not #532)
+#3153 := (or #535 #1226 #1699)
+#4273 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3153)
+#4278 := (not #4273)
+#4270 := (not #4265)
 #100 := (= #99 0::Int)
-#1747 := (not #100)
-#4547 := (or #1747 #4279 #4287 #4296 #4304 #4312 #4544)
-#4550 := (not #4547)
+#1738 := (not #100)
+#4538 := (or #1738 #4270 #4278 #4287 #4295 #4303 #4535)
+#4541 := (not #4538)
 decl ?v0!5 :: S3
-#1967 := ?v0!5
-#1968 := (f5 #12 ?v0!5)
-#4258 := (pattern #1968)
+#1958 := ?v0!5
+#1959 := (f5 #12 ?v0!5)
+#4249 := (pattern #1959)
 #66 := (f12 #12)
-#4225 := (pattern #66)
-#1970 := (f11 ?v0!5)
-#1971 := (* -1::Int #1970)
-#1969 := (f9 #1968)
-#2590 := (+ #1969 #1971)
-#2591 := (+ #58 #2590)
-#2594 := (= #2591 0::Int)
-#3123 := (not #2594)
-#1975 := (+ #58 #1971)
-#1976 := (>= #1975 0::Int)
-#454 := (= f1 #66)
-#457 := (not #454)
-#3124 := (or #457 #1976 #3123)
-#4259 := (forall (vars (?v1 S3)) (:pat #4225 #4218 #4258) #3124)
-#4264 := (not #4259)
-#2566 := (= f10 ?v0!5)
-#1980 := (+ f8 #1971)
-#1981 := (<= #1980 0::Int)
-#4267 := (or #1981 #2566 #4264)
-#4270 := (not #4267)
-#4553 := (or #4270 #4550)
-#4556 := (not #4553)
-#77 := (f11 #23)
-#1211 := (* -1::Int #77)
-#1232 := (+ #1211 #82)
-#1233 := (+ #58 #1232)
-#1230 := (>= #1233 0::Int)
-#3115 := (or #457 #1230 #1235)
-#4250 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3115)
+#4216 := (pattern #66)
+#1961 := (f11 ?v0!5)
+#1962 := (* -1::Int #1961)
+#1960 := (f9 #1959)
+#2581 := (+ #1960 #1962)
+#2582 := (+ #58 #2581)
+#2585 := (= #2582 0::Int)
+#3114 := (not #2585)
+#1966 := (+ #58 #1962)
+#1967 := (>= #1966 0::Int)
+#453 := (= f1 #66)
+#456 := (not #453)
+#3115 := (or #456 #1967 #3114)
+#4250 := (forall (vars (?v1 S3)) (:pat #4216 #4209 #4249) #3115)
 #4255 := (not #4250)
-#4559 := (or #4255 #4556)
-#4562 := (not #4559)
+#2557 := (= f10 ?v0!5)
+#1971 := (+ f8 #1962)
+#1972 := (<= #1971 0::Int)
+#4258 := (or #1972 #2557 #4255)
+#4261 := (not #4258)
+#4544 := (or #4261 #4541)
+#4547 := (not #4544)
+#77 := (f11 #23)
+#1202 := (* -1::Int #77)
+#1223 := (+ #1202 #82)
+#1224 := (+ #58 #1223)
+#1221 := (>= #1224 0::Int)
+#3106 := (or #456 #1221 #1226)
+#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3106)
+#4246 := (not #4241)
+#4550 := (or #4246 #4547)
+#4553 := (not #4550)
 decl ?v1!3 :: S3
-#1936 := ?v1!3
-#1951 := (f11 ?v1!3)
+#1927 := ?v1!3
+#1942 := (f11 ?v1!3)
 decl ?v0!4 :: S3
-#1937 := ?v0!4
-#1948 := (f11 ?v0!4)
-#1949 := (* -1::Int #1948)
-#2547 := (+ #1949 #1951)
-#1938 := (f5 ?v1!3 ?v0!4)
-#1939 := (f9 #1938)
-#2548 := (+ #1939 #2547)
-#2551 := (>= #2548 0::Int)
-#1944 := (f12 ?v1!3)
-#1945 := (= f1 #1944)
-#3078 := (not #1945)
+#1928 := ?v0!4
+#1939 := (f11 ?v0!4)
 #1940 := (* -1::Int #1939)
-#1941 := (+ f8 #1940)
-#1942 := (<= #1941 0::Int)
-#3093 := (or #1942 #3078 #2551)
-#5222 := [hypothesis]: #1945
-#4226 := (forall (vars (?v0 S3)) (:pat #4225) #457)
-#460 := (forall (vars (?v0 S3)) #457)
-#4229 := (iff #460 #4226)
-#4227 := (iff #457 #457)
-#4228 := [refl]: #4227
-#4230 := [quant-intro #4228]: #4229
-#1858 := (~ #460 #460)
-#1888 := (~ #457 #457)
-#1889 := [refl]: #1888
-#1859 := [nnf-pos #1889]: #1858
+#2538 := (+ #1940 #1942)
+#1929 := (f5 ?v1!3 ?v0!4)
+#1930 := (f9 #1929)
+#2539 := (+ #1930 #2538)
+#2542 := (>= #2539 0::Int)
+#1935 := (f12 ?v1!3)
+#1936 := (= f1 #1935)
+#3069 := (not #1936)
+#1931 := (* -1::Int #1930)
+#1932 := (+ f8 #1931)
+#1933 := (<= #1932 0::Int)
+#3084 := (or #1933 #3069 #2542)
+#5213 := [hypothesis]: #1936
+#4217 := (forall (vars (?v0 S3)) (:pat #4216) #456)
+#459 := (forall (vars (?v0 S3)) #456)
+#4220 := (iff #459 #4217)
+#4218 := (iff #456 #456)
+#4219 := [refl]: #4218
+#4221 := [quant-intro #4219]: #4220
+#1849 := (~ #459 #459)
+#1879 := (~ #456 #456)
+#1880 := [refl]: #1879
+#1850 := [nnf-pos #1880]: #1849
 #59 := (= #58 0::Int)
 #62 := (not #57)
-#1805 := (or #62 #59)
-#1808 := (forall (vars (?v0 S3)) #1805)
-#1811 := (not #1808)
-#1739 := (forall (vars (?v0 S3)) #1736)
-#1742 := (not #1739)
-#542 := (and #536 #539)
-#548 := (not #542)
-#1725 := (or #548 #1315)
-#1730 := (forall (vars (?v0 S3) (?v1 S3)) #1725)
+#1796 := (or #62 #59)
+#1799 := (forall (vars (?v0 S3)) #1796)
+#1802 := (not #1799)
+#1730 := (forall (vars (?v0 S3)) #1727)
 #1733 := (not #1730)
-#1236 := (not #1235)
-#1700 := (and #533 #1236)
-#1705 := (not #1700)
-#1711 := (or #1705 #1708)
-#1714 := (forall (vars (?v0 S3) (?v1 S3)) #1711)
-#1717 := (not #1714)
-#1647 := (forall (vars (?v0 S3)) #1642)
-#1650 := (not #1647)
-#1457 := (not #1456)
-#1450 := (not #1449)
-#1460 := (and #1450 #1457)
-#1618 := (not #1460)
-#1626 := (or #1618 #1623)
-#1629 := (forall (vars (?v0 S3)) #1626)
-#1632 := (not #1629)
-#1556 := (= #1534 0::Int)
-#1559 := (not #1502)
-#1568 := (and #807 #1559 #1556)
-#1573 := (exists (vars (?v1 S3)) #1568)
-#1545 := (+ f8 #1478)
-#1546 := (<= #1545 0::Int)
-#1547 := (not #1546)
-#1550 := (and #62 #1547)
-#1553 := (not #1550)
-#1576 := (or #1553 #1573)
-#1579 := (forall (vars (?v0 S3)) #1576)
-#1524 := (and #807 #1236)
-#1529 := (not #1524)
-#1536 := (or #1529 #1532)
-#1539 := (forall (vars (?v0 S3) (?v1 S3)) #1536)
-#1542 := (not #1539)
-#1582 := (or #1542 #1579)
-#1585 := (and #1539 #1582)
-#830 := (and #813 #827)
-#836 := (not #830)
-#1510 := (or #836 #1502)
-#1515 := (forall (vars (?v0 S3) (?v1 S3)) #1510)
-#1518 := (not #1515)
-#1588 := (or #1518 #1585)
-#1591 := (and #1515 #1588)
-#1496 := (forall (vars (?v0 S3)) #1493)
-#1499 := (not #1496)
-#1594 := (or #1499 #1591)
-#1597 := (and #1496 #1594)
-#1600 := (or #1490 #1597)
-#1603 := (and #204 #1600)
-#819 := (forall (vars (?v0 S3)) #814)
-#953 := (not #819)
-#1606 := (or #953 #1603)
-#1609 := (and #819 #1606)
-#1482 := (forall (vars (?v0 S3)) #1477)
-#1485 := (not #1482)
-#1612 := (or #1485 #1609)
-#1615 := (and #1482 #1612)
-#1466 := (or #793 #1460)
-#1471 := (forall (vars (?v0 S3)) #1466)
-#1474 := (not #1471)
-#1300 := (not #1299)
-#1419 := (and #536 #1300)
-#1424 := (exists (vars (?v0 S3)) #1419)
-#1665 := (not #1424)
-#1689 := (or #754 #995 #1665 #1474 #1615 #1632 #1650 #1654)
-#1345 := (not #1344)
-#1379 := (and #1236 #1345)
-#1382 := (not #1379)
-#1388 := (or #1382 #1385)
-#1391 := (forall (vars (?v0 S3) (?v1 S3)) #1388)
-#1394 := (not #1391)
-#1402 := (or #158 #1394)
-#1407 := (and #1391 #1402)
-#1360 := (= #1362 0::Int)
-#1354 := (>= #1356 0::Int)
-#1357 := (not #1354)
-#1364 := (and #1357 #1360)
-#1367 := (exists (vars (?v1 S3)) #1364)
-#1348 := (and #62 #1345)
-#1351 := (not #1348)
-#1370 := (or #1351 #1367)
-#1373 := (forall (vars (?v0 S3)) #1370)
-#1376 := (not #1373)
-#1410 := (or #1376 #1407)
-#1413 := (and #1373 #1410)
-#1442 := (or #724 #706 #733 #715 #1413 #1424)
-#1694 := (and #1442 #1689)
-#1316 := (not #1315)
-#1309 := (= #1313 0::Int)
-#1325 := (and #533 #1309 #1316)
-#1330 := (exists (vars (?v1 S3)) #1325)
-#1303 := (and #62 #1300)
-#1306 := (not #1303)
-#1333 := (or #1306 #1330)
-#1336 := (forall (vars (?v0 S3)) #1333)
-#1339 := (not #1336)
-#1271 := (= #1233 0::Int)
-#1212 := (+ #58 #1211)
-#1210 := (>= #1212 0::Int)
-#1274 := (not #1210)
-#1283 := (and #454 #1274 #1271)
-#1288 := (exists (vars (?v1 S3)) #1283)
-#1262 := (not #1261)
-#1265 := (and #62 #1262)
-#1268 := (not #1265)
-#1291 := (or #1268 #1288)
-#1294 := (forall (vars (?v0 S3)) #1291)
-#1750 := (not #1294)
-#1771 := (or #1747 #1750 #1339 #1694 #1717 #1733 #1742)
-#1776 := (and #1294 #1771)
-#1242 := (and #454 #1236)
-#1247 := (not #1242)
-#1250 := (or #1230 #1247)
-#1253 := (forall (vars (?v0 S3) (?v1 S3)) #1250)
-#1256 := (not #1253)
-#1779 := (or #1256 #1776)
-#1782 := (and #1253 #1779)
+#541 := (and #535 #538)
+#547 := (not #541)
+#1716 := (or #547 #1306)
+#1721 := (forall (vars (?v0 S3) (?v1 S3)) #1716)
+#1724 := (not #1721)
+#1227 := (not #1226)
+#1691 := (and #532 #1227)
+#1696 := (not #1691)
+#1702 := (or #1696 #1699)
+#1705 := (forall (vars (?v0 S3) (?v1 S3)) #1702)
+#1708 := (not #1705)
+#1638 := (forall (vars (?v0 S3)) #1633)
+#1641 := (not #1638)
+#1448 := (not #1447)
+#1441 := (not #1440)
+#1451 := (and #1441 #1448)
+#1609 := (not #1451)
+#1617 := (or #1609 #1614)
+#1620 := (forall (vars (?v0 S3)) #1617)
+#1623 := (not #1620)
+#1547 := (= #1525 0::Int)
+#1550 := (not #1493)
+#1559 := (and #798 #1550 #1547)
+#1564 := (exists (vars (?v1 S3)) #1559)
+#1536 := (+ f8 #1469)
+#1537 := (<= #1536 0::Int)
+#1538 := (not #1537)
+#1541 := (and #62 #1538)
+#1544 := (not #1541)
+#1567 := (or #1544 #1564)
+#1570 := (forall (vars (?v0 S3)) #1567)
+#1515 := (and #798 #1227)
+#1520 := (not #1515)
+#1527 := (or #1520 #1523)
+#1530 := (forall (vars (?v0 S3) (?v1 S3)) #1527)
+#1533 := (not #1530)
+#1573 := (or #1533 #1570)
+#1576 := (and #1530 #1573)
+#821 := (and #804 #818)
+#827 := (not #821)
+#1501 := (or #827 #1493)
+#1506 := (forall (vars (?v0 S3) (?v1 S3)) #1501)
+#1509 := (not #1506)
+#1579 := (or #1509 #1576)
+#1582 := (and #1506 #1579)
+#1487 := (forall (vars (?v0 S3)) #1484)
+#1490 := (not #1487)
+#1585 := (or #1490 #1582)
+#1588 := (and #1487 #1585)
+#1591 := (or #1481 #1588)
+#1594 := (and #203 #1591)
+#810 := (forall (vars (?v0 S3)) #805)
+#944 := (not #810)
+#1597 := (or #944 #1594)
+#1600 := (and #810 #1597)
+#1473 := (forall (vars (?v0 S3)) #1468)
+#1476 := (not #1473)
+#1603 := (or #1476 #1600)
+#1606 := (and #1473 #1603)
+#1457 := (or #784 #1451)
+#1462 := (forall (vars (?v0 S3)) #1457)
+#1465 := (not #1462)
+#1291 := (not #1290)
+#1410 := (and #535 #1291)
+#1415 := (exists (vars (?v0 S3)) #1410)
+#1656 := (not #1415)
+#1680 := (or #986 #753 #1656 #1465 #1606 #1623 #1641 #1645)
+#1336 := (not #1335)
+#1370 := (and #1227 #1336)
+#1373 := (not #1370)
+#1379 := (or #1373 #1376)
+#1382 := (forall (vars (?v0 S3) (?v1 S3)) #1379)
+#1385 := (not #1382)
+#1393 := (or #158 #1385)
+#1398 := (and #1382 #1393)
+#1351 := (= #1353 0::Int)
+#1345 := (>= #1347 0::Int)
+#1348 := (not #1345)
+#1355 := (and #1348 #1351)
+#1358 := (exists (vars (?v1 S3)) #1355)
+#1339 := (and #62 #1336)
+#1342 := (not #1339)
+#1361 := (or #1342 #1358)
+#1364 := (forall (vars (?v0 S3)) #1361)
+#1367 := (not #1364)
+#1401 := (or #1367 #1398)
+#1404 := (and #1364 #1401)
+#1433 := (or #723 #705 #732 #714 #1404 #1415)
+#1685 := (and #1433 #1680)
+#1307 := (not #1306)
+#1300 := (= #1304 0::Int)
+#1316 := (and #532 #1300 #1307)
+#1321 := (exists (vars (?v1 S3)) #1316)
+#1294 := (and #62 #1291)
+#1297 := (not #1294)
+#1324 := (or #1297 #1321)
+#1327 := (forall (vars (?v0 S3)) #1324)
+#1330 := (not #1327)
+#1262 := (= #1224 0::Int)
+#1203 := (+ #58 #1202)
+#1201 := (>= #1203 0::Int)
+#1265 := (not #1201)
+#1274 := (and #453 #1265 #1262)
+#1279 := (exists (vars (?v1 S3)) #1274)
+#1253 := (not #1252)
+#1256 := (and #62 #1253)
+#1259 := (not #1256)
+#1282 := (or #1259 #1279)
+#1285 := (forall (vars (?v0 S3)) #1282)
+#1741 := (not #1285)
+#1762 := (or #1738 #1741 #1330 #1685 #1708 #1724 #1733)
+#1767 := (and #1285 #1762)
+#1233 := (and #453 #1227)
+#1238 := (not #1233)
+#1241 := (or #1221 #1238)
+#1244 := (forall (vars (?v0 S3) (?v1 S3)) #1241)
+#1247 := (not #1244)
+#1770 := (or #1247 #1767)
+#1773 := (and #1244 #1770)
 #74 := (f12 #23)
-#466 := (= f1 #74)
-#469 := (and #457 #466)
-#475 := (not #469)
-#1217 := (or #475 #1210)
-#1222 := (forall (vars (?v0 S3) (?v1 S3)) #1217)
-#1225 := (not #1222)
-#1785 := (or #1225 #1782)
-#1788 := (and #1222 #1785)
-#1201 := (>= #58 0::Int)
-#1202 := (forall (vars (?v0 S3)) #1201)
-#1205 := (not #1202)
-#1791 := (or #1205 #1788)
-#1794 := (and #1202 #1791)
+#465 := (= f1 #74)
+#468 := (and #456 #465)
+#474 := (not #468)
+#1208 := (or #474 #1201)
+#1213 := (forall (vars (?v0 S3) (?v1 S3)) #1208)
+#1216 := (not #1213)
+#1776 := (or #1216 #1773)
+#1779 := (and #1213 #1776)
+#1192 := (>= #58 0::Int)
+#1193 := (forall (vars (?v0 S3)) #1192)
+#1196 := (not #1193)
+#1782 := (or #1196 #1779)
+#1785 := (and #1193 #1782)
 #70 := (f11 f10)
 #71 := (= #70 0::Int)
-#1196 := (not #71)
-#1797 := (or #1196 #1794)
-#1800 := (and #71 #1797)
-#1160 := (not #460)
-#440 := (= f8 #58)
-#446 := (or #57 #440)
-#451 := (forall (vars (?v0 S3)) #446)
-#1169 := (not #451)
-#1823 := (or #1169 #1160 #1800 #1811)
-#1828 := (not #1823)
+#1187 := (not #71)
+#1788 := (or #1187 #1785)
+#1791 := (and #71 #1788)
+#1151 := (not #459)
+#439 := (= f8 #58)
+#445 := (or #57 #439)
+#450 := (forall (vars (?v0 S3)) #445)
+#1160 := (not #450)
+#1814 := (or #1160 #1151 #1791 #1802)
+#1819 := (not #1814)
 #1 := true
-#216 := (+ #189 #82)
-#223 := (= #211 #216)
-#200 := (= #199 f1)
-#224 := (and #200 #223)
-#222 := (< #189 #211)
-#225 := (and #222 #224)
-#226 := (exists (vars (?v1 S3)) #225)
-#220 := (< #189 f8)
-#221 := (and #62 #220)
-#227 := (implies #221 #226)
-#228 := (forall (vars (?v0 S3)) #227)
-#229 := (and #228 true)
-#217 := (<= #211 #216)
+#215 := (+ #188 #82)
+#222 := (= #210 #215)
+#199 := (= #198 f1)
+#223 := (and #199 #222)
+#221 := (< #188 #210)
+#224 := (and #221 #223)
+#225 := (exists (vars (?v1 S3)) #224)
+#219 := (< #188 f8)
+#220 := (and #62 #219)
+#226 := (implies #220 #225)
+#227 := (forall (vars (?v0 S3)) #226)
+#228 := (and #227 true)
+#216 := (<= #210 #215)
 #83 := (< #82 f8)
-#215 := (and #200 #83)
-#218 := (implies #215 #217)
-#219 := (forall (vars (?v0 S3) (?v1 S3)) #218)
-#230 := (implies #219 #229)
-#231 := (and #219 #230)
-#212 := (<= #211 #189)
-#209 := (= #208 f1)
-#207 := (not #200)
-#210 := (and #207 #209)
-#213 := (implies #210 #212)
-#214 := (forall (vars (?v0 S3) (?v1 S3)) #213)
-#232 := (implies #214 #231)
-#233 := (and #214 #232)
-#205 := (<= 0::Int #189)
-#206 := (forall (vars (?v0 S3)) #205)
-#234 := (implies #206 #233)
-#235 := (and #206 #234)
-#236 := (implies #204 #235)
-#237 := (and #204 #236)
-#194 := (= #189 #101)
-#201 := (implies #200 #194)
-#202 := (forall (vars (?v0 S3)) #201)
-#238 := (implies #202 #237)
-#239 := (and #202 #238)
-#197 := (<= #189 #101)
-#198 := (forall (vars (?v0 S3)) #197)
-#240 := (implies #198 #239)
-#241 := (and #198 #240)
-#186 := (+ #174 #184)
-#187 := (< #186 #101)
-#185 := (< #184 f8)
-#188 := (and #185 #187)
-#193 := (not #188)
-#195 := (implies #193 #194)
-#196 := (forall (vars (?v0 S3)) #195)
-#242 := (implies #196 #241)
-#190 := (= #189 #186)
-#191 := (implies #188 #190)
-#192 := (forall (vars (?v0 S3)) #191)
-#243 := (implies #192 #242)
-decl f2 :: S1
-#5 := f2
-#180 := (ite true f1 f2)
-#181 := (f4 f15 f22 #180)
-#182 := (= f23 #181)
-#244 := (implies #182 #243)
+#214 := (and #199 #83)
+#217 := (implies #214 #216)
+#218 := (forall (vars (?v0 S3) (?v1 S3)) #217)
+#229 := (implies #218 #228)
+#230 := (and #218 #229)
+#211 := (<= #210 #188)
+#208 := (= #207 f1)
+#206 := (not #199)
+#209 := (and #206 #208)
+#212 := (implies #209 #211)
+#213 := (forall (vars (?v0 S3) (?v1 S3)) #212)
+#231 := (implies #213 #230)
+#232 := (and #213 #231)
+#204 := (<= 0::Int #188)
+#205 := (forall (vars (?v0 S3)) #204)
+#233 := (implies #205 #232)
+#234 := (and #205 #233)
+#235 := (implies #203 #234)
+#236 := (and #203 #235)
+#193 := (= #188 #101)
+#200 := (implies #199 #193)
+#201 := (forall (vars (?v0 S3)) #200)
+#237 := (implies #201 #236)
+#238 := (and #201 #237)
+#196 := (<= #188 #101)
+#197 := (forall (vars (?v0 S3)) #196)
+#239 := (implies #197 #238)
+#240 := (and #197 #239)
+#185 := (+ #174 #183)
+#186 := (< #185 #101)
+#184 := (< #183 f8)
+#187 := (and #184 #186)
+#192 := (not #187)
+#194 := (implies #192 #193)
+#195 := (forall (vars (?v0 S3)) #194)
+#241 := (implies #195 #240)
+#189 := (= #188 #185)
+#190 := (implies #187 #189)
+#191 := (forall (vars (?v0 S3)) #190)
+#242 := (implies #191 #241)
+#243 := (implies #181 #242)
 #176 := (<= #174 #101)
 #106 := (= #105 f1)
 #107 := (not #106)
 #177 := (implies #107 #176)
 #178 := (forall (vars (?v0 S3)) #177)
-#245 := (implies #178 #244)
+#244 := (implies #178 #243)
 #175 := (< #174 f8)
-#246 := (implies #175 #245)
+#245 := (implies #175 #244)
 #172 := (= #171 f1)
 #173 := (not #172)
-#247 := (implies #173 #246)
+#246 := (implies #173 #245)
 #120 := (< #101 f8)
 #129 := (and #107 #120)
 #130 := (exists (vars (?v0 S3)) #129)
-#248 := (implies #130 #247)
-#249 := (implies true #248)
+#247 := (implies #130 #246)
+#248 := (implies true #247)
 #159 := (and #158 true)
 #147 := (+ #142 #82)
 #154 := (<= #145 #147)
@@ -913,7 +908,7 @@
 #131 := (not #130)
 #168 := (implies #131 #167)
 #169 := (implies true #168)
-#250 := (and #169 #249)
+#249 := (and #169 #248)
 #116 := (+ #101 #82)
 #123 := (= #111 #116)
 #124 := (and #106 #123)
@@ -923,23 +918,23 @@
 #121 := (and #62 #120)
 #127 := (implies #121 #126)
 #128 := (forall (vars (?v0 S3)) #127)
-#251 := (implies #128 #250)
+#250 := (implies #128 #249)
 #117 := (<= #111 #116)
 #115 := (and #106 #83)
 #118 := (implies #115 #117)
 #119 := (forall (vars (?v0 S3) (?v1 S3)) #118)
-#252 := (implies #119 #251)
+#251 := (implies #119 #250)
 #112 := (<= #111 #101)
 #109 := (= #108 f1)
 #110 := (and #107 #109)
 #113 := (implies #110 #112)
 #114 := (forall (vars (?v0 S3) (?v1 S3)) #113)
-#253 := (implies #114 #252)
+#252 := (implies #114 #251)
 #102 := (<= 0::Int #101)
 #103 := (forall (vars (?v0 S3)) #102)
-#254 := (implies #103 #253)
-#255 := (implies #100 #254)
-#256 := (implies true #255)
+#253 := (implies #103 #252)
+#254 := (implies #100 #253)
+#255 := (implies true #254)
 #85 := (+ #58 #82)
 #92 := (= #77 #85)
 #67 := (= #66 f1)
@@ -951,3880 +946,3874 @@
 #90 := (and #62 #89)
 #96 := (implies #90 #95)
 #97 := (forall (vars (?v0 S3)) #96)
-#257 := (implies #97 #256)
-#258 := (and #97 #257)
+#256 := (implies #97 #255)
+#257 := (and #97 #256)
 #86 := (<= #77 #85)
 #84 := (and #67 #83)
 #87 := (implies #84 #86)
 #88 := (forall (vars (?v0 S3) (?v1 S3)) #87)
-#259 := (implies #88 #258)
-#260 := (and #88 #259)
+#258 := (implies #88 #257)
+#259 := (and #88 #258)
 #78 := (<= #77 #58)
 #75 := (= #74 f1)
 #68 := (not #67)
 #76 := (and #68 #75)
 #79 := (implies #76 #78)
 #80 := (forall (vars (?v0 S3) (?v1 S3)) #79)
-#261 := (implies #80 #260)
-#262 := (and #80 #261)
+#260 := (implies #80 #259)
+#261 := (and #80 #260)
 #72 := (<= 0::Int #58)
 #73 := (forall (vars (?v0 S3)) #72)
-#263 := (implies #73 #262)
-#264 := (and #73 #263)
-#265 := (implies #71 #264)
-#266 := (and #71 #265)
+#262 := (implies #73 #261)
+#263 := (and #73 #262)
+#264 := (implies #71 #263)
+#265 := (and #71 #264)
 #69 := (forall (vars (?v0 S3)) #68)
-#267 := (implies #69 #266)
+#266 := (implies #69 #265)
 #63 := (= #58 f8)
 #64 := (implies #62 #63)
 #65 := (forall (vars (?v0 S3)) #64)
-#268 := (implies #65 #267)
+#267 := (implies #65 #266)
 #60 := (implies #57 #59)
 #61 := (forall (vars (?v0 S3)) #60)
-#269 := (implies #61 #268)
-#270 := (implies true #269)
-#271 := (not #270)
-#1831 := (iff #271 #1828)
-#853 := (+ #82 #189)
-#871 := (= #211 #853)
-#874 := (and #807 #871)
-#877 := (and #222 #874)
-#880 := (exists (vars (?v1 S3)) #877)
-#886 := (not #221)
-#887 := (or #886 #880)
-#892 := (forall (vars (?v0 S3)) #887)
-#856 := (<= #211 #853)
-#848 := (and #83 #807)
-#862 := (not #848)
-#863 := (or #862 #856)
-#868 := (forall (vars (?v0 S3) (?v1 S3)) #863)
-#905 := (not #868)
-#906 := (or #905 #892)
-#911 := (and #868 #906)
-#837 := (or #212 #836)
-#842 := (forall (vars (?v0 S3) (?v1 S3)) #837)
-#917 := (not #842)
-#918 := (or #917 #911)
-#923 := (and #842 #918)
-#929 := (not #206)
-#930 := (or #929 #923)
-#935 := (and #206 #930)
-#822 := (= 0::Int #203)
-#941 := (not #822)
-#942 := (or #941 #935)
-#947 := (and #822 #942)
-#954 := (or #953 #947)
-#959 := (and #819 #954)
-#965 := (not #198)
-#966 := (or #965 #959)
-#971 := (and #198 #966)
-#799 := (or #188 #793)
-#804 := (forall (vars (?v0 S3)) #799)
-#977 := (not #804)
-#978 := (or #977 #971)
-#779 := (= #186 #189)
-#785 := (or #193 #779)
-#790 := (forall (vars (?v0 S3)) #785)
-#986 := (not #790)
+#268 := (implies #61 #267)
+#269 := (implies true #268)
+#270 := (not #269)
+#1822 := (iff #270 #1819)
+#844 := (+ #82 #188)
+#862 := (= #210 #844)
+#865 := (and #798 #862)
+#868 := (and #221 #865)
+#871 := (exists (vars (?v1 S3)) #868)
+#877 := (not #220)
+#878 := (or #877 #871)
+#883 := (forall (vars (?v0 S3)) #878)
+#847 := (<= #210 #844)
+#839 := (and #83 #798)
+#853 := (not #839)
+#854 := (or #853 #847)
+#859 := (forall (vars (?v0 S3) (?v1 S3)) #854)
+#896 := (not #859)
+#897 := (or #896 #883)
+#902 := (and #859 #897)
+#828 := (or #211 #827)
+#833 := (forall (vars (?v0 S3) (?v1 S3)) #828)
+#908 := (not #833)
+#909 := (or #908 #902)
+#914 := (and #833 #909)
+#920 := (not #205)
+#921 := (or #920 #914)
+#926 := (and #205 #921)
+#813 := (= 0::Int #202)
+#932 := (not #813)
+#933 := (or #932 #926)
+#938 := (and #813 #933)
+#945 := (or #944 #938)
+#950 := (and #810 #945)
+#956 := (not #197)
+#957 := (or #956 #950)
+#962 := (and #197 #957)
+#790 := (or #187 #784)
+#795 := (forall (vars (?v0 S3)) #790)
+#968 := (not #795)
+#969 := (or #968 #962)
+#770 := (= #185 #188)
+#776 := (or #192 #770)
+#781 := (forall (vars (?v0 S3)) #776)
+#977 := (not #781)
+#978 := (or #977 #969)
 #987 := (or #986 #978)
+#762 := (or #176 #532)
+#767 := (forall (vars (?v0 S3)) #762)
+#995 := (not #767)
 #996 := (or #995 #987)
-#763 := (or #176 #533)
-#768 := (forall (vars (?v0 S3)) #763)
-#1004 := (not #768)
+#1004 := (not #175)
 #1005 := (or #1004 #996)
-#1013 := (not #175)
-#1014 := (or #1013 #1005)
-#1022 := (or #754 #1014)
-#610 := (and #120 #536)
-#615 := (exists (vars (?v0 S3)) #610)
-#618 := (not #615)
-#1030 := (or #618 #1022)
-#669 := (= 0::Int #157)
-#627 := (+ #82 #142)
-#654 := (<= #145 #627)
-#651 := (and #83 #143)
-#660 := (not #651)
-#661 := (or #660 #654)
-#666 := (forall (vars (?v0 S3) (?v1 S3)) #661)
-#682 := (not #666)
-#683 := (or #682 #669)
-#688 := (and #666 #683)
-#630 := (= #145 #627)
-#633 := (and #146 #630)
-#636 := (exists (vars (?v1 S3)) #633)
-#642 := (not #144)
-#643 := (or #642 #636)
-#648 := (forall (vars (?v0 S3)) #643)
-#694 := (not #648)
-#695 := (or #694 #688)
-#700 := (and #648 #695)
-#707 := (or #706 #700)
-#716 := (or #715 #707)
-#725 := (or #724 #716)
-#734 := (or #733 #725)
-#742 := (or #615 #734)
-#1042 := (and #742 #1030)
-#565 := (+ #82 #101)
-#583 := (= #111 #565)
-#586 := (and #533 #583)
-#589 := (and #122 #586)
-#592 := (exists (vars (?v1 S3)) #589)
-#598 := (not #121)
-#599 := (or #598 #592)
-#604 := (forall (vars (?v0 S3)) #599)
-#1048 := (not #604)
-#1049 := (or #1048 #1042)
-#568 := (<= #111 #565)
-#560 := (and #83 #533)
-#574 := (not #560)
-#575 := (or #574 #568)
-#580 := (forall (vars (?v0 S3) (?v1 S3)) #575)
-#1057 := (not #580)
+#1013 := (or #753 #1005)
+#609 := (and #120 #535)
+#614 := (exists (vars (?v0 S3)) #609)
+#617 := (not #614)
+#1021 := (or #617 #1013)
+#668 := (= 0::Int #157)
+#626 := (+ #82 #142)
+#653 := (<= #145 #626)
+#650 := (and #83 #143)
+#659 := (not #650)
+#660 := (or #659 #653)
+#665 := (forall (vars (?v0 S3) (?v1 S3)) #660)
+#681 := (not #665)
+#682 := (or #681 #668)
+#687 := (and #665 #682)
+#629 := (= #145 #626)
+#632 := (and #146 #629)
+#635 := (exists (vars (?v1 S3)) #632)
+#641 := (not #144)
+#642 := (or #641 #635)
+#647 := (forall (vars (?v0 S3)) #642)
+#693 := (not #647)
+#694 := (or #693 #687)
+#699 := (and #647 #694)
+#706 := (or #705 #699)
+#715 := (or #714 #706)
+#724 := (or #723 #715)
+#733 := (or #732 #724)
+#741 := (or #614 #733)
+#1033 := (and #741 #1021)
+#564 := (+ #82 #101)
+#582 := (= #111 #564)
+#585 := (and #532 #582)
+#588 := (and #122 #585)
+#591 := (exists (vars (?v1 S3)) #588)
+#597 := (not #121)
+#598 := (or #597 #591)
+#603 := (forall (vars (?v0 S3)) #598)
+#1039 := (not #603)
+#1040 := (or #1039 #1033)
+#567 := (<= #111 #564)
+#559 := (and #83 #532)
+#573 := (not #559)
+#574 := (or #573 #567)
+#579 := (forall (vars (?v0 S3) (?v1 S3)) #574)
+#1048 := (not #579)
+#1049 := (or #1048 #1040)
+#548 := (or #112 #547)
+#553 := (forall (vars (?v0 S3) (?v1 S3)) #548)
+#1057 := (not #553)
 #1058 := (or #1057 #1049)
-#549 := (or #112 #548)
-#554 := (forall (vars (?v0 S3) (?v1 S3)) #549)
-#1066 := (not #554)
+#1066 := (not #103)
 #1067 := (or #1066 #1058)
-#1075 := (not #103)
+#529 := (= 0::Int #99)
+#1075 := (not #529)
 #1076 := (or #1075 #1067)
-#530 := (= 0::Int #99)
-#1084 := (not #530)
-#1085 := (or #1084 #1076)
-#507 := (and #92 #454)
-#512 := (and #91 #507)
-#515 := (exists (vars (?v1 S3)) #512)
-#521 := (not #90)
-#522 := (or #521 #515)
-#527 := (forall (vars (?v0 S3)) #522)
-#1100 := (not #527)
-#1101 := (or #1100 #1085)
-#1106 := (and #527 #1101)
-#487 := (and #83 #454)
-#495 := (not #487)
-#496 := (or #86 #495)
-#501 := (forall (vars (?v0 S3) (?v1 S3)) #496)
-#1112 := (not #501)
-#1113 := (or #1112 #1106)
-#1118 := (and #501 #1113)
-#476 := (or #78 #475)
-#481 := (forall (vars (?v0 S3) (?v1 S3)) #476)
-#1124 := (not #481)
-#1125 := (or #1124 #1118)
-#1130 := (and #481 #1125)
-#1136 := (not #73)
-#1137 := (or #1136 #1130)
-#1142 := (and #73 #1137)
-#463 := (= 0::Int #70)
-#1148 := (not #463)
-#1149 := (or #1148 #1142)
-#1154 := (and #463 #1149)
-#1161 := (or #1160 #1154)
+#506 := (and #92 #453)
+#511 := (and #91 #506)
+#514 := (exists (vars (?v1 S3)) #511)
+#520 := (not #90)
+#521 := (or #520 #514)
+#526 := (forall (vars (?v0 S3)) #521)
+#1091 := (not #526)
+#1092 := (or #1091 #1076)
+#1097 := (and #526 #1092)
+#486 := (and #83 #453)
+#494 := (not #486)
+#495 := (or #86 #494)
+#500 := (forall (vars (?v0 S3) (?v1 S3)) #495)
+#1103 := (not #500)
+#1104 := (or #1103 #1097)
+#1109 := (and #500 #1104)
+#475 := (or #78 #474)
+#480 := (forall (vars (?v0 S3) (?v1 S3)) #475)
+#1115 := (not #480)
+#1116 := (or #1115 #1109)
+#1121 := (and #480 #1116)
+#1127 := (not #73)
+#1128 := (or #1127 #1121)
+#1133 := (and #73 #1128)
+#462 := (= 0::Int #70)
+#1139 := (not #462)
+#1140 := (or #1139 #1133)
+#1145 := (and #462 #1140)
+#1152 := (or #1151 #1145)
+#1161 := (or #1160 #1152)
+#425 := (= 0::Int #58)
+#431 := (or #62 #425)
+#436 := (forall (vars (?v0 S3)) #431)
+#1169 := (not #436)
 #1170 := (or #1169 #1161)
-#426 := (= 0::Int #58)
-#432 := (or #62 #426)
-#437 := (forall (vars (?v0 S3)) #432)
-#1178 := (not #437)
-#1179 := (or #1178 #1170)
-#1191 := (not #1179)
-#1829 := (iff #1191 #1828)
-#1826 := (iff #1179 #1823)
-#1814 := (or #1160 #1800)
-#1817 := (or #1169 #1814)
-#1820 := (or #1811 #1817)
-#1824 := (iff #1820 #1823)
-#1825 := [rewrite]: #1824
-#1821 := (iff #1179 #1820)
-#1818 := (iff #1170 #1817)
-#1815 := (iff #1161 #1814)
-#1801 := (iff #1154 #1800)
-#1798 := (iff #1149 #1797)
-#1795 := (iff #1142 #1794)
-#1792 := (iff #1137 #1791)
-#1789 := (iff #1130 #1788)
-#1786 := (iff #1125 #1785)
-#1783 := (iff #1118 #1782)
-#1780 := (iff #1113 #1779)
-#1777 := (iff #1106 #1776)
-#1774 := (iff #1101 #1771)
-#1753 := (or #1339 #1694)
-#1756 := (or #1717 #1753)
-#1759 := (or #1733 #1756)
-#1762 := (or #1742 #1759)
-#1765 := (or #1747 #1762)
-#1768 := (or #1750 #1765)
-#1772 := (iff #1768 #1771)
-#1773 := [rewrite]: #1772
-#1769 := (iff #1101 #1768)
-#1766 := (iff #1085 #1765)
-#1763 := (iff #1076 #1762)
-#1760 := (iff #1067 #1759)
-#1757 := (iff #1058 #1756)
-#1754 := (iff #1049 #1753)
-#1695 := (iff #1042 #1694)
-#1692 := (iff #1030 #1689)
-#1668 := (or #1474 #1615)
-#1671 := (or #1632 #1668)
-#1674 := (or #995 #1671)
-#1677 := (or #1650 #1674)
-#1680 := (or #1654 #1677)
-#1683 := (or #754 #1680)
-#1686 := (or #1665 #1683)
-#1690 := (iff #1686 #1689)
-#1691 := [rewrite]: #1690
-#1687 := (iff #1030 #1686)
-#1684 := (iff #1022 #1683)
-#1681 := (iff #1014 #1680)
-#1678 := (iff #1005 #1677)
-#1675 := (iff #996 #1674)
-#1672 := (iff #987 #1671)
-#1669 := (iff #978 #1668)
-#1616 := (iff #971 #1615)
-#1613 := (iff #966 #1612)
-#1610 := (iff #959 #1609)
-#1607 := (iff #954 #1606)
-#1604 := (iff #947 #1603)
-#1601 := (iff #942 #1600)
-#1598 := (iff #935 #1597)
-#1595 := (iff #930 #1594)
-#1592 := (iff #923 #1591)
-#1589 := (iff #918 #1588)
-#1586 := (iff #911 #1585)
-#1583 := (iff #906 #1582)
-#1580 := (iff #892 #1579)
-#1577 := (iff #887 #1576)
-#1574 := (iff #880 #1573)
-#1571 := (iff #877 #1568)
-#1562 := (and #807 #1556)
-#1565 := (and #1559 #1562)
-#1569 := (iff #1565 #1568)
-#1570 := [rewrite]: #1569
-#1566 := (iff #877 #1565)
-#1563 := (iff #874 #1562)
-#1557 := (iff #871 #1556)
-#1558 := [rewrite]: #1557
-#1564 := [monotonicity #1558]: #1563
-#1560 := (iff #222 #1559)
+#1182 := (not #1170)
+#1820 := (iff #1182 #1819)
+#1817 := (iff #1170 #1814)
+#1805 := (or #1151 #1791)
+#1808 := (or #1160 #1805)
+#1811 := (or #1802 #1808)
+#1815 := (iff #1811 #1814)
+#1816 := [rewrite]: #1815
+#1812 := (iff #1170 #1811)
+#1809 := (iff #1161 #1808)
+#1806 := (iff #1152 #1805)
+#1792 := (iff #1145 #1791)
+#1789 := (iff #1140 #1788)
+#1786 := (iff #1133 #1785)
+#1783 := (iff #1128 #1782)
+#1780 := (iff #1121 #1779)
+#1777 := (iff #1116 #1776)
+#1774 := (iff #1109 #1773)
+#1771 := (iff #1104 #1770)
+#1768 := (iff #1097 #1767)
+#1765 := (iff #1092 #1762)
+#1744 := (or #1330 #1685)
+#1747 := (or #1708 #1744)
+#1750 := (or #1724 #1747)
+#1753 := (or #1733 #1750)
+#1756 := (or #1738 #1753)
+#1759 := (or #1741 #1756)
+#1763 := (iff #1759 #1762)
+#1764 := [rewrite]: #1763
+#1760 := (iff #1092 #1759)
+#1757 := (iff #1076 #1756)
+#1754 := (iff #1067 #1753)
+#1751 := (iff #1058 #1750)
+#1748 := (iff #1049 #1747)
+#1745 := (iff #1040 #1744)
+#1686 := (iff #1033 #1685)
+#1683 := (iff #1021 #1680)
+#1659 := (or #1465 #1606)
+#1662 := (or #1623 #1659)
+#1665 := (or #986 #1662)
+#1668 := (or #1641 #1665)
+#1671 := (or #1645 #1668)
+#1674 := (or #753 #1671)
+#1677 := (or #1656 #1674)
+#1681 := (iff #1677 #1680)
+#1682 := [rewrite]: #1681
+#1678 := (iff #1021 #1677)
+#1675 := (iff #1013 #1674)
+#1672 := (iff #1005 #1671)
+#1669 := (iff #996 #1668)
+#1666 := (iff #987 #1665)
+#1663 := (iff #978 #1662)
+#1660 := (iff #969 #1659)
+#1607 := (iff #962 #1606)
+#1604 := (iff #957 #1603)
+#1601 := (iff #950 #1600)
+#1598 := (iff #945 #1597)
+#1595 := (iff #938 #1594)
+#1592 := (iff #933 #1591)
+#1589 := (iff #926 #1588)
+#1586 := (iff #921 #1585)
+#1583 := (iff #914 #1582)
+#1580 := (iff #909 #1579)
+#1577 := (iff #902 #1576)
+#1574 := (iff #897 #1573)
+#1571 := (iff #883 #1570)
+#1568 := (iff #878 #1567)
+#1565 := (iff #871 #1564)
+#1562 := (iff #868 #1559)
+#1553 := (and #798 #1547)
+#1556 := (and #1550 #1553)
+#1560 := (iff #1556 #1559)
 #1561 := [rewrite]: #1560
-#1567 := [monotonicity #1561 #1564]: #1566
-#1572 := [trans #1567 #1570]: #1571
-#1575 := [quant-intro #1572]: #1574
-#1554 := (iff #886 #1553)
-#1551 := (iff #221 #1550)
-#1548 := (iff #220 #1547)
+#1557 := (iff #868 #1556)
+#1554 := (iff #865 #1553)
+#1548 := (iff #862 #1547)
 #1549 := [rewrite]: #1548
-#1552 := [monotonicity #1549]: #1551
-#1555 := [monotonicity #1552]: #1554
-#1578 := [monotonicity #1555 #1575]: #1577
-#1581 := [quant-intro #1578]: #1580
-#1543 := (iff #905 #1542)
-#1540 := (iff #868 #1539)
-#1537 := (iff #863 #1536)
-#1533 := (iff #856 #1532)
-#1535 := [rewrite]: #1533
-#1530 := (iff #862 #1529)
-#1527 := (iff #848 #1524)
-#1521 := (and #1236 #807)
-#1525 := (iff #1521 #1524)
-#1526 := [rewrite]: #1525
-#1522 := (iff #848 #1521)
-#1237 := (iff #83 #1236)
-#1238 := [rewrite]: #1237
-#1523 := [monotonicity #1238]: #1522
-#1528 := [trans #1523 #1526]: #1527
-#1531 := [monotonicity #1528]: #1530
-#1538 := [monotonicity #1531 #1535]: #1537
-#1541 := [quant-intro #1538]: #1540
-#1544 := [monotonicity #1541]: #1543
-#1584 := [monotonicity #1544 #1581]: #1583
-#1587 := [monotonicity #1541 #1584]: #1586
-#1519 := (iff #917 #1518)
-#1516 := (iff #842 #1515)
-#1513 := (iff #837 #1510)
-#1507 := (or #1502 #836)
-#1511 := (iff #1507 #1510)
-#1512 := [rewrite]: #1511
-#1508 := (iff #837 #1507)
-#1505 := (iff #212 #1502)
-#1506 := [rewrite]: #1505
-#1509 := [monotonicity #1506]: #1508
-#1514 := [trans #1509 #1512]: #1513
-#1517 := [quant-intro #1514]: #1516
-#1520 := [monotonicity #1517]: #1519
-#1590 := [monotonicity #1520 #1587]: #1589
-#1593 := [monotonicity #1517 #1590]: #1592
-#1500 := (iff #929 #1499)
-#1497 := (iff #206 #1496)
-#1494 := (iff #205 #1493)
-#1495 := [rewrite]: #1494
-#1498 := [quant-intro #1495]: #1497
-#1501 := [monotonicity #1498]: #1500
-#1596 := [monotonicity #1501 #1593]: #1595
-#1599 := [monotonicity #1498 #1596]: #1598
-#1491 := (iff #941 #1490)
-#1488 := (iff #822 #204)
-#1489 := [rewrite]: #1488
+#1555 := [monotonicity #1549]: #1554
+#1551 := (iff #221 #1550)
+#1552 := [rewrite]: #1551
+#1558 := [monotonicity #1552 #1555]: #1557
+#1563 := [trans #1558 #1561]: #1562
+#1566 := [quant-intro #1563]: #1565
+#1545 := (iff #877 #1544)
+#1542 := (iff #220 #1541)
+#1539 := (iff #219 #1538)
+#1540 := [rewrite]: #1539
+#1543 := [monotonicity #1540]: #1542
+#1546 := [monotonicity #1543]: #1545
+#1569 := [monotonicity #1546 #1566]: #1568
+#1572 := [quant-intro #1569]: #1571
+#1534 := (iff #896 #1533)
+#1531 := (iff #859 #1530)
+#1528 := (iff #854 #1527)
+#1524 := (iff #847 #1523)
+#1526 := [rewrite]: #1524
+#1521 := (iff #853 #1520)
+#1518 := (iff #839 #1515)
+#1512 := (and #1227 #798)
+#1516 := (iff #1512 #1515)
+#1517 := [rewrite]: #1516
+#1513 := (iff #839 #1512)
+#1228 := (iff #83 #1227)
+#1229 := [rewrite]: #1228
+#1514 := [monotonicity #1229]: #1513
+#1519 := [trans #1514 #1517]: #1518
+#1522 := [monotonicity #1519]: #1521
+#1529 := [monotonicity #1522 #1526]: #1528
+#1532 := [quant-intro #1529]: #1531
+#1535 := [monotonicity #1532]: #1534
+#1575 := [monotonicity #1535 #1572]: #1574
+#1578 := [monotonicity #1532 #1575]: #1577
+#1510 := (iff #908 #1509)
+#1507 := (iff #833 #1506)
+#1504 := (iff #828 #1501)
+#1498 := (or #1493 #827)
+#1502 := (iff #1498 #1501)
+#1503 := [rewrite]: #1502
+#1499 := (iff #828 #1498)
+#1496 := (iff #211 #1493)
+#1497 := [rewrite]: #1496
+#1500 := [monotonicity #1497]: #1499
+#1505 := [trans #1500 #1503]: #1504
+#1508 := [quant-intro #1505]: #1507
+#1511 := [monotonicity #1508]: #1510
+#1581 := [monotonicity #1511 #1578]: #1580
+#1584 := [monotonicity #1508 #1581]: #1583
+#1491 := (iff #920 #1490)
+#1488 := (iff #205 #1487)
+#1485 := (iff #204 #1484)
+#1486 := [rewrite]: #1485
+#1489 := [quant-intro #1486]: #1488
 #1492 := [monotonicity #1489]: #1491
-#1602 := [monotonicity #1492 #1599]: #1601
-#1605 := [monotonicity #1489 #1602]: #1604
-#1608 := [monotonicity #1605]: #1607
-#1611 := [monotonicity #1608]: #1610
-#1486 := (iff #965 #1485)
-#1483 := (iff #198 #1482)
-#1480 := (iff #197 #1477)
-#1481 := [rewrite]: #1480
-#1484 := [quant-intro #1481]: #1483
-#1487 := [monotonicity #1484]: #1486
-#1614 := [monotonicity #1487 #1611]: #1613
-#1617 := [monotonicity #1484 #1614]: #1616
-#1475 := (iff #977 #1474)
-#1472 := (iff #804 #1471)
-#1469 := (iff #799 #1466)
-#1463 := (or #1460 #793)
-#1467 := (iff #1463 #1466)
-#1468 := [rewrite]: #1467
-#1464 := (iff #799 #1463)
-#1461 := (iff #188 #1460)
-#1458 := (iff #187 #1457)
+#1587 := [monotonicity #1492 #1584]: #1586
+#1590 := [monotonicity #1489 #1587]: #1589
+#1482 := (iff #932 #1481)
+#1479 := (iff #813 #203)
+#1480 := [rewrite]: #1479
+#1483 := [monotonicity #1480]: #1482
+#1593 := [monotonicity #1483 #1590]: #1592
+#1596 := [monotonicity #1480 #1593]: #1595
+#1599 := [monotonicity #1596]: #1598
+#1602 := [monotonicity #1599]: #1601
+#1477 := (iff #956 #1476)
+#1474 := (iff #197 #1473)
+#1471 := (iff #196 #1468)
+#1472 := [rewrite]: #1471
+#1475 := [quant-intro #1472]: #1474
+#1478 := [monotonicity #1475]: #1477
+#1605 := [monotonicity #1478 #1602]: #1604
+#1608 := [monotonicity #1475 #1605]: #1607
+#1466 := (iff #968 #1465)
+#1463 := (iff #795 #1462)
+#1460 := (iff #790 #1457)
+#1454 := (or #1451 #784)
+#1458 := (iff #1454 #1457)
 #1459 := [rewrite]: #1458
-#1451 := (iff #185 #1450)
-#1452 := [rewrite]: #1451
-#1462 := [monotonicity #1452 #1459]: #1461
-#1465 := [monotonicity #1462]: #1464
-#1470 := [trans #1465 #1468]: #1469
-#1473 := [quant-intro #1470]: #1472
-#1476 := [monotonicity #1473]: #1475
-#1670 := [monotonicity #1476 #1617]: #1669
-#1633 := (iff #986 #1632)
-#1630 := (iff #790 #1629)
-#1627 := (iff #785 #1626)
-#1624 := (iff #779 #1623)
-#1625 := [rewrite]: #1624
-#1619 := (iff #193 #1618)
-#1620 := [monotonicity #1462]: #1619
-#1628 := [monotonicity #1620 #1625]: #1627
-#1631 := [quant-intro #1628]: #1630
-#1634 := [monotonicity #1631]: #1633
-#1673 := [monotonicity #1634 #1670]: #1672
+#1455 := (iff #790 #1454)
+#1452 := (iff #187 #1451)
+#1449 := (iff #186 #1448)
+#1450 := [rewrite]: #1449
+#1442 := (iff #184 #1441)
+#1443 := [rewrite]: #1442
+#1453 := [monotonicity #1443 #1450]: #1452
+#1456 := [monotonicity #1453]: #1455
+#1461 := [trans #1456 #1459]: #1460
+#1464 := [quant-intro #1461]: #1463
+#1467 := [monotonicity #1464]: #1466
+#1661 := [monotonicity #1467 #1608]: #1660
+#1624 := (iff #977 #1623)
+#1621 := (iff #781 #1620)
+#1618 := (iff #776 #1617)
+#1615 := (iff #770 #1614)
+#1616 := [rewrite]: #1615
+#1610 := (iff #192 #1609)
+#1611 := [monotonicity #1453]: #1610
+#1619 := [monotonicity #1611 #1616]: #1618
+#1622 := [quant-intro #1619]: #1621
+#1625 := [monotonicity #1622]: #1624
+#1664 := [monotonicity #1625 #1661]: #1663
+#1667 := [monotonicity #1664]: #1666
+#1642 := (iff #995 #1641)
+#1639 := (iff #767 #1638)
+#1636 := (iff #762 #1633)
+#1630 := (or #1626 #532)
+#1634 := (iff #1630 #1633)
+#1635 := [rewrite]: #1634
+#1631 := (iff #762 #1630)
+#1628 := (iff #176 #1626)
+#1629 := [rewrite]: #1628
+#1632 := [monotonicity #1629]: #1631
+#1637 := [trans #1632 #1635]: #1636
+#1640 := [quant-intro #1637]: #1639
+#1643 := [monotonicity #1640]: #1642
+#1670 := [monotonicity #1643 #1667]: #1669
+#1654 := (iff #1004 #1645)
+#1646 := (not #1645)
+#1649 := (not #1646)
+#1652 := (iff #1649 #1645)
+#1653 := [rewrite]: #1652
+#1650 := (iff #1004 #1649)
+#1647 := (iff #175 #1646)
+#1648 := [rewrite]: #1647
+#1651 := [monotonicity #1648]: #1650
+#1655 := [trans #1651 #1653]: #1654
+#1673 := [monotonicity #1655 #1670]: #1672
 #1676 := [monotonicity #1673]: #1675
-#1651 := (iff #1004 #1650)
-#1648 := (iff #768 #1647)
-#1645 := (iff #763 #1642)
-#1639 := (or #1635 #533)
-#1643 := (iff #1639 #1642)
-#1644 := [rewrite]: #1643
-#1640 := (iff #763 #1639)
-#1637 := (iff #176 #1635)
-#1638 := [rewrite]: #1637
-#1641 := [monotonicity #1638]: #1640
-#1646 := [trans #1641 #1644]: #1645
-#1649 := [quant-intro #1646]: #1648
-#1652 := [monotonicity #1649]: #1651
-#1679 := [monotonicity #1652 #1676]: #1678
-#1663 := (iff #1013 #1654)
-#1655 := (not #1654)
-#1658 := (not #1655)
-#1661 := (iff #1658 #1654)
-#1662 := [rewrite]: #1661
-#1659 := (iff #1013 #1658)
-#1656 := (iff #175 #1655)
-#1657 := [rewrite]: #1656
-#1660 := [monotonicity #1657]: #1659
-#1664 := [trans #1660 #1662]: #1663
-#1682 := [monotonicity #1664 #1679]: #1681
-#1685 := [monotonicity #1682]: #1684
-#1666 := (iff #618 #1665)
-#1425 := (iff #615 #1424)
-#1422 := (iff #610 #1419)
-#1416 := (and #1300 #536)
-#1420 := (iff #1416 #1419)
-#1421 := [rewrite]: #1420
-#1417 := (iff #610 #1416)
-#1301 := (iff #120 #1300)
-#1302 := [rewrite]: #1301
-#1418 := [monotonicity #1302]: #1417
-#1423 := [trans #1418 #1421]: #1422
-#1426 := [quant-intro #1423]: #1425
-#1667 := [monotonicity #1426]: #1666
-#1688 := [monotonicity #1667 #1685]: #1687
-#1693 := [trans #1688 #1691]: #1692
-#1445 := (iff #742 #1442)
-#1427 := (or #706 #1413)
-#1430 := (or #715 #1427)
-#1433 := (or #724 #1430)
-#1436 := (or #733 #1433)
-#1439 := (or #1424 #1436)
-#1443 := (iff #1439 #1442)
-#1444 := [rewrite]: #1443
-#1440 := (iff #742 #1439)
-#1437 := (iff #734 #1436)
-#1434 := (iff #725 #1433)
-#1431 := (iff #716 #1430)
-#1428 := (iff #707 #1427)
-#1414 := (iff #700 #1413)
-#1411 := (iff #695 #1410)
-#1408 := (iff #688 #1407)
-#1405 := (iff #683 #1402)
-#1399 := (or #1394 #158)
-#1403 := (iff #1399 #1402)
-#1404 := [rewrite]: #1403
-#1400 := (iff #683 #1399)
-#1397 := (iff #669 #158)
-#1398 := [rewrite]: #1397
-#1395 := (iff #682 #1394)
-#1392 := (iff #666 #1391)
-#1389 := (iff #661 #1388)
-#1386 := (iff #654 #1385)
-#1387 := [rewrite]: #1386
-#1383 := (iff #660 #1382)
-#1380 := (iff #651 #1379)
-#1346 := (iff #143 #1345)
-#1347 := [rewrite]: #1346
-#1381 := [monotonicity #1238 #1347]: #1380
-#1384 := [monotonicity #1381]: #1383
-#1390 := [monotonicity #1384 #1387]: #1389
-#1393 := [quant-intro #1390]: #1392
-#1396 := [monotonicity #1393]: #1395
-#1401 := [monotonicity #1396 #1398]: #1400
-#1406 := [trans #1401 #1404]: #1405
-#1409 := [monotonicity #1393 #1406]: #1408
-#1377 := (iff #694 #1376)
-#1374 := (iff #648 #1373)
-#1371 := (iff #643 #1370)
-#1368 := (iff #636 #1367)
-#1365 := (iff #633 #1364)
-#1361 := (iff #630 #1360)
-#1363 := [rewrite]: #1361
-#1358 := (iff #146 #1357)
-#1359 := [rewrite]: #1358
-#1366 := [monotonicity #1359 #1363]: #1365
-#1369 := [quant-intro #1366]: #1368
-#1352 := (iff #642 #1351)
-#1349 := (iff #144 #1348)
-#1350 := [monotonicity #1347]: #1349
-#1353 := [monotonicity #1350]: #1352
-#1372 := [monotonicity #1353 #1369]: #1371
-#1375 := [quant-intro #1372]: #1374
-#1378 := [monotonicity #1375]: #1377
-#1412 := [monotonicity #1378 #1409]: #1411
-#1415 := [monotonicity #1375 #1412]: #1414
-#1429 := [monotonicity #1415]: #1428
-#1432 := [monotonicity #1429]: #1431
-#1435 := [monotonicity #1432]: #1434
-#1438 := [monotonicity #1435]: #1437
-#1441 := [monotonicity #1426 #1438]: #1440
-#1446 := [trans #1441 #1444]: #1445
-#1696 := [monotonicity #1446 #1693]: #1695
-#1340 := (iff #1048 #1339)
-#1337 := (iff #604 #1336)
-#1334 := (iff #599 #1333)
-#1331 := (iff #592 #1330)
-#1328 := (iff #589 #1325)
-#1319 := (and #533 #1309)
-#1322 := (and #1316 #1319)
-#1326 := (iff #1322 #1325)
-#1327 := [rewrite]: #1326
-#1323 := (iff #589 #1322)
-#1320 := (iff #586 #1319)
-#1310 := (iff #583 #1309)
-#1314 := [rewrite]: #1310
-#1321 := [monotonicity #1314]: #1320
-#1317 := (iff #122 #1316)
+#1657 := (iff #617 #1656)
+#1416 := (iff #614 #1415)
+#1413 := (iff #609 #1410)
+#1407 := (and #1291 #535)
+#1411 := (iff #1407 #1410)
+#1412 := [rewrite]: #1411
+#1408 := (iff #609 #1407)
+#1292 := (iff #120 #1291)
+#1293 := [rewrite]: #1292
+#1409 := [monotonicity #1293]: #1408
+#1414 := [trans #1409 #1412]: #1413
+#1417 := [quant-intro #1414]: #1416
+#1658 := [monotonicity #1417]: #1657
+#1679 := [monotonicity #1658 #1676]: #1678
+#1684 := [trans #1679 #1682]: #1683
+#1436 := (iff #741 #1433)
+#1418 := (or #705 #1404)
+#1421 := (or #714 #1418)
+#1424 := (or #723 #1421)
+#1427 := (or #732 #1424)
+#1430 := (or #1415 #1427)
+#1434 := (iff #1430 #1433)
+#1435 := [rewrite]: #1434
+#1431 := (iff #741 #1430)
+#1428 := (iff #733 #1427)
+#1425 := (iff #724 #1424)
+#1422 := (iff #715 #1421)
+#1419 := (iff #706 #1418)
+#1405 := (iff #699 #1404)
+#1402 := (iff #694 #1401)
+#1399 := (iff #687 #1398)
+#1396 := (iff #682 #1393)
+#1390 := (or #1385 #158)
+#1394 := (iff #1390 #1393)
+#1395 := [rewrite]: #1394
+#1391 := (iff #682 #1390)
+#1388 := (iff #668 #158)
+#1389 := [rewrite]: #1388
+#1386 := (iff #681 #1385)
+#1383 := (iff #665 #1382)
+#1380 := (iff #660 #1379)
+#1377 := (iff #653 #1376)
+#1378 := [rewrite]: #1377
+#1374 := (iff #659 #1373)
+#1371 := (iff #650 #1370)
+#1337 := (iff #143 #1336)
+#1338 := [rewrite]: #1337
+#1372 := [monotonicity #1229 #1338]: #1371
+#1375 := [monotonicity #1372]: #1374
+#1381 := [monotonicity #1375 #1378]: #1380
+#1384 := [quant-intro #1381]: #1383
+#1387 := [monotonicity #1384]: #1386
+#1392 := [monotonicity #1387 #1389]: #1391
+#1397 := [trans #1392 #1395]: #1396
+#1400 := [monotonicity #1384 #1397]: #1399
+#1368 := (iff #693 #1367)
+#1365 := (iff #647 #1364)
+#1362 := (iff #642 #1361)
+#1359 := (iff #635 #1358)
+#1356 := (iff #632 #1355)
+#1352 := (iff #629 #1351)
+#1354 := [rewrite]: #1352
+#1349 := (iff #146 #1348)
+#1350 := [rewrite]: #1349
+#1357 := [monotonicity #1350 #1354]: #1356
+#1360 := [quant-intro #1357]: #1359
+#1343 := (iff #641 #1342)
+#1340 := (iff #144 #1339)
+#1341 := [monotonicity #1338]: #1340
+#1344 := [monotonicity #1341]: #1343
+#1363 := [monotonicity #1344 #1360]: #1362
+#1366 := [quant-intro #1363]: #1365
+#1369 := [monotonicity #1366]: #1368
+#1403 := [monotonicity #1369 #1400]: #1402
+#1406 := [monotonicity #1366 #1403]: #1405
+#1420 := [monotonicity #1406]: #1419
+#1423 := [monotonicity #1420]: #1422
+#1426 := [monotonicity #1423]: #1425
+#1429 := [monotonicity #1426]: #1428
+#1432 := [monotonicity #1417 #1429]: #1431
+#1437 := [trans #1432 #1435]: #1436
+#1687 := [monotonicity #1437 #1684]: #1686
+#1331 := (iff #1039 #1330)
+#1328 := (iff #603 #1327)
+#1325 := (iff #598 #1324)
+#1322 := (iff #591 #1321)
+#1319 := (iff #588 #1316)
+#1310 := (and #532 #1300)
+#1313 := (and #1307 #1310)
+#1317 := (iff #1313 #1316)
 #1318 := [rewrite]: #1317
-#1324 := [monotonicity #1318 #1321]: #1323
-#1329 := [trans #1324 #1327]: #1328
-#1332 := [quant-intro #1329]: #1331
-#1307 := (iff #598 #1306)
-#1304 := (iff #121 #1303)
-#1305 := [monotonicity #1302]: #1304
-#1308 := [monotonicity #1305]: #1307
-#1335 := [monotonicity #1308 #1332]: #1334
-#1338 := [quant-intro #1335]: #1337
-#1341 := [monotonicity #1338]: #1340
-#1755 := [monotonicity #1341 #1696]: #1754
-#1718 := (iff #1057 #1717)
-#1715 := (iff #580 #1714)
-#1712 := (iff #575 #1711)
-#1709 := (iff #568 #1708)
-#1710 := [rewrite]: #1709
-#1706 := (iff #574 #1705)
-#1703 := (iff #560 #1700)
-#1697 := (and #1236 #533)
-#1701 := (iff #1697 #1700)
-#1702 := [rewrite]: #1701
-#1698 := (iff #560 #1697)
-#1699 := [monotonicity #1238]: #1698
-#1704 := [trans #1699 #1702]: #1703
-#1707 := [monotonicity #1704]: #1706
-#1713 := [monotonicity #1707 #1710]: #1712
-#1716 := [quant-intro #1713]: #1715
-#1719 := [monotonicity #1716]: #1718
-#1758 := [monotonicity #1719 #1755]: #1757
+#1314 := (iff #588 #1313)
+#1311 := (iff #585 #1310)
+#1301 := (iff #582 #1300)
+#1305 := [rewrite]: #1301
+#1312 := [monotonicity #1305]: #1311
+#1308 := (iff #122 #1307)
+#1309 := [rewrite]: #1308
+#1315 := [monotonicity #1309 #1312]: #1314
+#1320 := [trans #1315 #1318]: #1319
+#1323 := [quant-intro #1320]: #1322
+#1298 := (iff #597 #1297)
+#1295 := (iff #121 #1294)
+#1296 := [monotonicity #1293]: #1295
+#1299 := [monotonicity #1296]: #1298
+#1326 := [monotonicity #1299 #1323]: #1325
+#1329 := [quant-intro #1326]: #1328
+#1332 := [monotonicity #1329]: #1331
+#1746 := [monotonicity #1332 #1687]: #1745
+#1709 := (iff #1048 #1708)
+#1706 := (iff #579 #1705)
+#1703 := (iff #574 #1702)
+#1700 := (iff #567 #1699)
+#1701 := [rewrite]: #1700
+#1697 := (iff #573 #1696)
+#1694 := (iff #559 #1691)
+#1688 := (and #1227 #532)
+#1692 := (iff #1688 #1691)
+#1693 := [rewrite]: #1692
+#1689 := (iff #559 #1688)
+#1690 := [monotonicity #1229]: #1689
+#1695 := [trans #1690 #1693]: #1694
+#1698 := [monotonicity #1695]: #1697
+#1704 := [monotonicity #1698 #1701]: #1703
+#1707 := [quant-intro #1704]: #1706
+#1710 := [monotonicity #1707]: #1709
+#1749 := [monotonicity #1710 #1746]: #1748
+#1725 := (iff #1057 #1724)
+#1722 := (iff #553 #1721)
+#1719 := (iff #548 #1716)
+#1713 := (or #1306 #547)
+#1717 := (iff #1713 #1716)
+#1718 := [rewrite]: #1717
+#1714 := (iff #548 #1713)
+#1711 := (iff #112 #1306)
+#1712 := [rewrite]: #1711
+#1715 := [monotonicity #1712]: #1714
+#1720 := [trans #1715 #1718]: #1719
+#1723 := [quant-intro #1720]: #1722
+#1726 := [monotonicity #1723]: #1725
+#1752 := [monotonicity #1726 #1749]: #1751
 #1734 := (iff #1066 #1733)
-#1731 := (iff #554 #1730)
-#1728 := (iff #549 #1725)
-#1722 := (or #1315 #548)
-#1726 := (iff #1722 #1725)
-#1727 := [rewrite]: #1726
-#1723 := (iff #549 #1722)
-#1720 := (iff #112 #1315)
-#1721 := [rewrite]: #1720
-#1724 := [monotonicity #1721]: #1723
-#1729 := [trans #1724 #1727]: #1728
+#1731 := (iff #103 #1730)
+#1728 := (iff #102 #1727)
+#1729 := [rewrite]: #1728
 #1732 := [quant-intro #1729]: #1731
 #1735 := [monotonicity #1732]: #1734
-#1761 := [monotonicity #1735 #1758]: #1760
-#1743 := (iff #1075 #1742)
-#1740 := (iff #103 #1739)
-#1737 := (iff #102 #1736)
-#1738 := [rewrite]: #1737
-#1741 := [quant-intro #1738]: #1740
-#1744 := [monotonicity #1741]: #1743
-#1764 := [monotonicity #1744 #1761]: #1763
-#1748 := (iff #1084 #1747)
-#1745 := (iff #530 #100)
-#1746 := [rewrite]: #1745
-#1749 := [monotonicity #1746]: #1748
-#1767 := [monotonicity #1749 #1764]: #1766
-#1751 := (iff #1100 #1750)
-#1295 := (iff #527 #1294)
-#1292 := (iff #522 #1291)
-#1289 := (iff #515 #1288)
-#1286 := (iff #512 #1283)
-#1277 := (and #1271 #454)
-#1280 := (and #1274 #1277)
-#1284 := (iff #1280 #1283)
-#1285 := [rewrite]: #1284
-#1281 := (iff #512 #1280)
-#1278 := (iff #507 #1277)
-#1272 := (iff #92 #1271)
-#1273 := [rewrite]: #1272
-#1279 := [monotonicity #1273]: #1278
-#1275 := (iff #91 #1274)
+#1755 := [monotonicity #1735 #1752]: #1754
+#1739 := (iff #1075 #1738)
+#1736 := (iff #529 #100)
+#1737 := [rewrite]: #1736
+#1740 := [monotonicity #1737]: #1739
+#1758 := [monotonicity #1740 #1755]: #1757
+#1742 := (iff #1091 #1741)
+#1286 := (iff #526 #1285)
+#1283 := (iff #521 #1282)
+#1280 := (iff #514 #1279)
+#1277 := (iff #511 #1274)
+#1268 := (and #1262 #453)
+#1271 := (and #1265 #1268)
+#1275 := (iff #1271 #1274)
 #1276 := [rewrite]: #1275
-#1282 := [monotonicity #1276 #1279]: #1281
-#1287 := [trans #1282 #1285]: #1286
-#1290 := [quant-intro #1287]: #1289
-#1269 := (iff #521 #1268)
-#1266 := (iff #90 #1265)
-#1263 := (iff #89 #1262)
+#1272 := (iff #511 #1271)
+#1269 := (iff #506 #1268)
+#1263 := (iff #92 #1262)
 #1264 := [rewrite]: #1263
-#1267 := [monotonicity #1264]: #1266
-#1270 := [monotonicity #1267]: #1269
-#1293 := [monotonicity #1270 #1290]: #1292
-#1296 := [quant-intro #1293]: #1295
-#1752 := [monotonicity #1296]: #1751
-#1770 := [monotonicity #1752 #1767]: #1769
-#1775 := [trans #1770 #1773]: #1774
-#1778 := [monotonicity #1296 #1775]: #1777
-#1257 := (iff #1112 #1256)
-#1254 := (iff #501 #1253)
-#1251 := (iff #496 #1250)
-#1248 := (iff #495 #1247)
-#1245 := (iff #487 #1242)
-#1239 := (and #1236 #454)
-#1243 := (iff #1239 #1242)
-#1244 := [rewrite]: #1243
-#1240 := (iff #487 #1239)
-#1241 := [monotonicity #1238]: #1240
-#1246 := [trans #1241 #1244]: #1245
+#1270 := [monotonicity #1264]: #1269
+#1266 := (iff #91 #1265)
+#1267 := [rewrite]: #1266
+#1273 := [monotonicity #1267 #1270]: #1272
+#1278 := [trans #1273 #1276]: #1277
+#1281 := [quant-intro #1278]: #1280
+#1260 := (iff #520 #1259)
+#1257 := (iff #90 #1256)
+#1254 := (iff #89 #1253)
+#1255 := [rewrite]: #1254
+#1258 := [monotonicity #1255]: #1257
+#1261 := [monotonicity #1258]: #1260
+#1284 := [monotonicity #1261 #1281]: #1283
+#1287 := [quant-intro #1284]: #1286
+#1743 := [monotonicity #1287]: #1742
+#1761 := [monotonicity #1743 #1758]: #1760
+#1766 := [trans #1761 #1764]: #1765
+#1769 := [monotonicity #1287 #1766]: #1768
+#1248 := (iff #1103 #1247)
+#1245 := (iff #500 #1244)
+#1242 := (iff #495 #1241)
+#1239 := (iff #494 #1238)
+#1236 := (iff #486 #1233)
+#1230 := (and #1227 #453)
+#1234 := (iff #1230 #1233)
+#1235 := [rewrite]: #1234
+#1231 := (iff #486 #1230)
+#1232 := [monotonicity #1229]: #1231
+#1237 := [trans #1232 #1235]: #1236
+#1240 := [monotonicity #1237]: #1239
+#1220 := (iff #86 #1221)
+#1219 := [rewrite]: #1220
+#1243 := [monotonicity #1219 #1240]: #1242
+#1246 := [quant-intro #1243]: #1245
 #1249 := [monotonicity #1246]: #1248
-#1229 := (iff #86 #1230)
-#1228 := [rewrite]: #1229
-#1252 := [monotonicity #1228 #1249]: #1251
-#1255 := [quant-intro #1252]: #1254
-#1258 := [monotonicity #1255]: #1257
-#1781 := [monotonicity #1258 #1778]: #1780
-#1784 := [monotonicity #1255 #1781]: #1783
-#1226 := (iff #1124 #1225)
-#1223 := (iff #481 #1222)
-#1220 := (iff #476 #1217)
-#1214 := (or #1210 #475)
-#1218 := (iff #1214 #1217)
-#1219 := [rewrite]: #1218
-#1215 := (iff #476 #1214)
-#1209 := (iff #78 #1210)
-#1213 := [rewrite]: #1209
-#1216 := [monotonicity #1213]: #1215
-#1221 := [trans #1216 #1219]: #1220
-#1224 := [quant-intro #1221]: #1223
-#1227 := [monotonicity #1224]: #1226
-#1787 := [monotonicity #1227 #1784]: #1786
-#1790 := [monotonicity #1224 #1787]: #1789
-#1206 := (iff #1136 #1205)
-#1203 := (iff #73 #1202)
-#1199 := (iff #72 #1201)
-#1200 := [rewrite]: #1199
-#1204 := [quant-intro #1200]: #1203
+#1772 := [monotonicity #1249 #1769]: #1771
+#1775 := [monotonicity #1246 #1772]: #1774
+#1217 := (iff #1115 #1216)
+#1214 := (iff #480 #1213)
+#1211 := (iff #475 #1208)
+#1205 := (or #1201 #474)
+#1209 := (iff #1205 #1208)
+#1210 := [rewrite]: #1209
+#1206 := (iff #475 #1205)
+#1200 := (iff #78 #1201)
+#1204 := [rewrite]: #1200
 #1207 := [monotonicity #1204]: #1206
-#1793 := [monotonicity #1207 #1790]: #1792
-#1796 := [monotonicity #1204 #1793]: #1795
-#1197 := (iff #1148 #1196)
-#1194 := (iff #463 #71)
-#1195 := [rewrite]: #1194
+#1212 := [trans #1207 #1210]: #1211
+#1215 := [quant-intro #1212]: #1214
+#1218 := [monotonicity #1215]: #1217
+#1778 := [monotonicity #1218 #1775]: #1777
+#1781 := [monotonicity #1215 #1778]: #1780
+#1197 := (iff #1127 #1196)
+#1194 := (iff #73 #1193)
+#1190 := (iff #72 #1192)
+#1191 := [rewrite]: #1190
+#1195 := [quant-intro #1191]: #1194
 #1198 := [monotonicity #1195]: #1197
-#1799 := [monotonicity #1198 #1796]: #1798
-#1802 := [monotonicity #1195 #1799]: #1801
-#1816 := [monotonicity #1802]: #1815
-#1819 := [monotonicity #1816]: #1818
-#1812 := (iff #1178 #1811)
-#1809 := (iff #437 #1808)
-#1806 := (iff #432 #1805)
-#1803 := (iff #426 #59)
-#1804 := [rewrite]: #1803
-#1807 := [monotonicity #1804]: #1806
-#1810 := [quant-intro #1807]: #1809
-#1813 := [monotonicity #1810]: #1812
-#1822 := [monotonicity #1813 #1819]: #1821
-#1827 := [trans #1822 #1825]: #1826
-#1830 := [monotonicity #1827]: #1829
-#1192 := (iff #271 #1191)
-#1189 := (iff #270 #1179)
-#1184 := (implies true #1179)
-#1187 := (iff #1184 #1179)
-#1188 := [rewrite]: #1187
-#1185 := (iff #270 #1184)
-#1182 := (iff #269 #1179)
-#1175 := (implies #437 #1170)
-#1180 := (iff #1175 #1179)
-#1181 := [rewrite]: #1180
+#1784 := [monotonicity #1198 #1781]: #1783
+#1787 := [monotonicity #1195 #1784]: #1786
+#1188 := (iff #1139 #1187)
+#1185 := (iff #462 #71)
+#1186 := [rewrite]: #1185
+#1189 := [monotonicity #1186]: #1188
+#1790 := [monotonicity #1189 #1787]: #1789
+#1793 := [monotonicity #1186 #1790]: #1792
+#1807 := [monotonicity #1793]: #1806
+#1810 := [monotonicity #1807]: #1809
+#1803 := (iff #1169 #1802)
+#1800 := (iff #436 #1799)
+#1797 := (iff #431 #1796)
+#1794 := (iff #425 #59)
+#1795 := [rewrite]: #1794
+#1798 := [monotonicity #1795]: #1797
+#1801 := [quant-intro #1798]: #1800
+#1804 := [monotonicity #1801]: #1803
+#1813 := [monotonicity #1804 #1810]: #1812
+#1818 := [trans #1813 #1816]: #1817
+#1821 := [monotonicity #1818]: #1820
+#1183 := (iff #270 #1182)
+#1180 := (iff #269 #1170)
+#1175 := (implies true #1170)
+#1178 := (iff #1175 #1170)
+#1179 := [rewrite]: #1178
 #1176 := (iff #269 #1175)
 #1173 := (iff #268 #1170)
-#1166 := (implies #451 #1161)
+#1166 := (implies #436 #1161)
 #1171 := (iff #1166 #1170)
 #1172 := [rewrite]: #1171
 #1167 := (iff #268 #1166)
 #1164 := (iff #267 #1161)
-#1157 := (implies #460 #1154)
+#1157 := (implies #450 #1152)
 #1162 := (iff #1157 #1161)
 #1163 := [rewrite]: #1162
 #1158 := (iff #267 #1157)
-#1155 := (iff #266 #1154)
-#1152 := (iff #265 #1149)
-#1145 := (implies #463 #1142)
-#1150 := (iff #1145 #1149)
-#1151 := [rewrite]: #1150
+#1155 := (iff #266 #1152)
+#1148 := (implies #459 #1145)
+#1153 := (iff #1148 #1152)
+#1154 := [rewrite]: #1153
+#1149 := (iff #266 #1148)
 #1146 := (iff #265 #1145)
-#1143 := (iff #264 #1142)
-#1140 := (iff #263 #1137)
-#1133 := (implies #73 #1130)
-#1138 := (iff #1133 #1137)
-#1139 := [rewrite]: #1138
+#1143 := (iff #264 #1140)
+#1136 := (implies #462 #1133)
+#1141 := (iff #1136 #1140)
+#1142 := [rewrite]: #1141
+#1137 := (iff #264 #1136)
 #1134 := (iff #263 #1133)
-#1131 := (iff #262 #1130)
-#1128 := (iff #261 #1125)
-#1121 := (implies #481 #1118)
-#1126 := (iff #1121 #1125)
-#1127 := [rewrite]: #1126
+#1131 := (iff #262 #1128)
+#1124 := (implies #73 #1121)
+#1129 := (iff #1124 #1128)
+#1130 := [rewrite]: #1129
+#1125 := (iff #262 #1124)
 #1122 := (iff #261 #1121)
-#1119 := (iff #260 #1118)
-#1116 := (iff #259 #1113)
-#1109 := (implies #501 #1106)
-#1114 := (iff #1109 #1113)
-#1115 := [rewrite]: #1114
+#1119 := (iff #260 #1116)
+#1112 := (implies #480 #1109)
+#1117 := (iff #1112 #1116)
+#1118 := [rewrite]: #1117
+#1113 := (iff #260 #1112)
 #1110 := (iff #259 #1109)
-#1107 := (iff #258 #1106)
-#1104 := (iff #257 #1101)
-#1097 := (implies #527 #1085)
-#1102 := (iff #1097 #1101)
-#1103 := [rewrite]: #1102
+#1107 := (iff #258 #1104)
+#1100 := (implies #500 #1097)
+#1105 := (iff #1100 #1104)
+#1106 := [rewrite]: #1105
+#1101 := (iff #258 #1100)
 #1098 := (iff #257 #1097)
-#1095 := (iff #256 #1085)
-#1090 := (implies true #1085)
-#1093 := (iff #1090 #1085)
+#1095 := (iff #256 #1092)
+#1088 := (implies #526 #1076)
+#1093 := (iff #1088 #1092)
 #1094 := [rewrite]: #1093
-#1091 := (iff #256 #1090)
-#1088 := (iff #255 #1085)
-#1081 := (implies #530 #1076)
-#1086 := (iff #1081 #1085)
-#1087 := [rewrite]: #1086
+#1089 := (iff #256 #1088)
+#1086 := (iff #255 #1076)
+#1081 := (implies true #1076)
+#1084 := (iff #1081 #1076)
+#1085 := [rewrite]: #1084
 #1082 := (iff #255 #1081)
 #1079 := (iff #254 #1076)
-#1072 := (implies #103 #1067)
+#1072 := (implies #529 #1067)
 #1077 := (iff #1072 #1076)
 #1078 := [rewrite]: #1077
 #1073 := (iff #254 #1072)
 #1070 := (iff #253 #1067)
-#1063 := (implies #554 #1058)
+#1063 := (implies #103 #1058)
 #1068 := (iff #1063 #1067)
 #1069 := [rewrite]: #1068
 #1064 := (iff #253 #1063)
 #1061 := (iff #252 #1058)
-#1054 := (implies #580 #1049)
+#1054 := (implies #553 #1049)
 #1059 := (iff #1054 #1058)
 #1060 := [rewrite]: #1059
 #1055 := (iff #252 #1054)
 #1052 := (iff #251 #1049)
-#1045 := (implies #604 #1042)
+#1045 := (implies #579 #1040)
 #1050 := (iff #1045 #1049)
 #1051 := [rewrite]: #1050
 #1046 := (iff #251 #1045)
-#1043 := (iff #250 #1042)
-#1040 := (iff #249 #1030)
-#1035 := (implies true #1030)
-#1038 := (iff #1035 #1030)
-#1039 := [rewrite]: #1038
-#1036 := (iff #249 #1035)
-#1033 := (iff #248 #1030)
-#1027 := (implies #615 #1022)
-#1031 := (iff #1027 #1030)
-#1032 := [rewrite]: #1031
-#1028 := (iff #248 #1027)
-#1025 := (iff #247 #1022)
-#757 := (not #754)
-#1019 := (implies #757 #1014)
-#1023 := (iff #1019 #1022)
-#1024 := [rewrite]: #1023
-#1020 := (iff #247 #1019)
-#1017 := (iff #246 #1014)
-#1010 := (implies #175 #1005)
-#1015 := (iff #1010 #1014)
-#1016 := [rewrite]: #1015
+#1043 := (iff #250 #1040)
+#1036 := (implies #603 #1033)
+#1041 := (iff #1036 #1040)
+#1042 := [rewrite]: #1041
+#1037 := (iff #250 #1036)
+#1034 := (iff #249 #1033)
+#1031 := (iff #248 #1021)
+#1026 := (implies true #1021)
+#1029 := (iff #1026 #1021)
+#1030 := [rewrite]: #1029
+#1027 := (iff #248 #1026)
+#1024 := (iff #247 #1021)
+#1018 := (implies #614 #1013)
+#1022 := (iff #1018 #1021)
+#1023 := [rewrite]: #1022
+#1019 := (iff #247 #1018)
+#1016 := (iff #246 #1013)
+#756 := (not #753)
+#1010 := (implies #756 #1005)
+#1014 := (iff #1010 #1013)
+#1015 := [rewrite]: #1014
 #1011 := (iff #246 #1010)
 #1008 := (iff #245 #1005)
-#1001 := (implies #768 #996)
+#1001 := (implies #175 #996)
 #1006 := (iff #1001 #1005)
 #1007 := [rewrite]: #1006
 #1002 := (iff #245 #1001)
 #999 := (iff #244 #996)
-#992 := (implies #776 #987)
+#992 := (implies #767 #987)
 #997 := (iff #992 #996)
 #998 := [rewrite]: #997
 #993 := (iff #244 #992)
 #990 := (iff #243 #987)
-#983 := (implies #790 #978)
+#983 := (implies #181 #978)
 #988 := (iff #983 #987)
 #989 := [rewrite]: #988
 #984 := (iff #243 #983)
 #981 := (iff #242 #978)
-#974 := (implies #804 #971)
+#974 := (implies #781 #969)
 #979 := (iff #974 #978)
 #980 := [rewrite]: #979
 #975 := (iff #242 #974)
-#972 := (iff #241 #971)
-#969 := (iff #240 #966)
-#962 := (implies #198 #959)
-#967 := (iff #962 #966)
-#968 := [rewrite]: #967
+#972 := (iff #241 #969)
+#965 := (implies #795 #962)
+#970 := (iff #965 #969)
+#971 := [rewrite]: #970
+#966 := (iff #241 #965)
 #963 := (iff #240 #962)
-#960 := (iff #239 #959)
-#957 := (iff #238 #954)
-#950 := (implies #819 #947)
-#955 := (iff #950 #954)
-#956 := [rewrite]: #955
+#960 := (iff #239 #957)
+#953 := (implies #197 #950)
+#958 := (iff #953 #957)
+#959 := [rewrite]: #958
+#954 := (iff #239 #953)
 #951 := (iff #238 #950)
-#948 := (iff #237 #947)
-#945 := (iff #236 #942)
-#938 := (implies #822 #935)
-#943 := (iff #938 #942)
-#944 := [rewrite]: #943
+#948 := (iff #237 #945)
+#941 := (implies #810 #938)
+#946 := (iff #941 #945)
+#947 := [rewrite]: #946
+#942 := (iff #237 #941)
 #939 := (iff #236 #938)
-#936 := (iff #235 #935)
-#933 := (iff #234 #930)
-#926 := (implies #206 #923)
-#931 := (iff #926 #930)
-#932 := [rewrite]: #931
+#936 := (iff #235 #933)
+#929 := (implies #813 #926)
+#934 := (iff #929 #933)
+#935 := [rewrite]: #934
+#930 := (iff #235 #929)
 #927 := (iff #234 #926)
-#924 := (iff #233 #923)
-#921 := (iff #232 #918)
-#914 := (implies #842 #911)
-#919 := (iff #914 #918)
-#920 := [rewrite]: #919
+#924 := (iff #233 #921)
+#917 := (implies #205 #914)
+#922 := (iff #917 #921)
+#923 := [rewrite]: #922
+#918 := (iff #233 #917)
 #915 := (iff #232 #914)
-#912 := (iff #231 #911)
-#909 := (iff #230 #906)
-#902 := (implies #868 #892)
-#907 := (iff #902 #906)
-#908 := [rewrite]: #907
+#912 := (iff #231 #909)
+#905 := (implies #833 #902)
+#910 := (iff #905 #909)
+#911 := [rewrite]: #910
+#906 := (iff #231 #905)
 #903 := (iff #230 #902)
-#900 := (iff #229 #892)
-#895 := (and #892 true)
-#898 := (iff #895 #892)
+#900 := (iff #229 #897)
+#893 := (implies #859 #883)
+#898 := (iff #893 #897)
 #899 := [rewrite]: #898
-#896 := (iff #229 #895)
-#893 := (iff #228 #892)
-#890 := (iff #227 #887)
-#883 := (implies #221 #880)
-#888 := (iff #883 #887)
-#889 := [rewrite]: #888
+#894 := (iff #229 #893)
+#891 := (iff #228 #883)
+#886 := (and #883 true)
+#889 := (iff #886 #883)
+#890 := [rewrite]: #889
+#887 := (iff #228 #886)
 #884 := (iff #227 #883)
-#881 := (iff #226 #880)
-#878 := (iff #225 #877)
-#875 := (iff #224 #874)
-#872 := (iff #223 #871)
-#854 := (= #216 #853)
-#855 := [rewrite]: #854
-#873 := [monotonicity #855]: #872
-#808 := (iff #200 #807)
-#809 := [rewrite]: #808
-#876 := [monotonicity #809 #873]: #875
-#879 := [monotonicity #876]: #878
-#882 := [quant-intro #879]: #881
-#885 := [monotonicity #882]: #884
-#891 := [trans #885 #889]: #890
-#894 := [quant-intro #891]: #893
-#897 := [monotonicity #894]: #896
-#901 := [trans #897 #899]: #900
-#869 := (iff #219 #868)
-#866 := (iff #218 #863)
-#859 := (implies #848 #856)
-#864 := (iff #859 #863)
-#865 := [rewrite]: #864
+#881 := (iff #226 #878)
+#874 := (implies #220 #871)
+#879 := (iff #874 #878)
+#880 := [rewrite]: #879
+#875 := (iff #226 #874)
+#872 := (iff #225 #871)
+#869 := (iff #224 #868)
+#866 := (iff #223 #865)
+#863 := (iff #222 #862)
+#845 := (= #215 #844)
+#846 := [rewrite]: #845
+#864 := [monotonicity #846]: #863
+#799 := (iff #199 #798)
+#800 := [rewrite]: #799
+#867 := [monotonicity #800 #864]: #866
+#870 := [monotonicity #867]: #869
+#873 := [quant-intro #870]: #872
+#876 := [monotonicity #873]: #875
+#882 := [trans #876 #880]: #881
+#885 := [quant-intro #882]: #884
+#888 := [monotonicity #885]: #887
+#892 := [trans #888 #890]: #891
 #860 := (iff #218 #859)
-#857 := (iff #217 #856)
-#858 := [monotonicity #855]: #857
-#851 := (iff #215 #848)
-#845 := (and #807 #83)
-#849 := (iff #845 #848)
-#850 := [rewrite]: #849
-#846 := (iff #215 #845)
-#847 := [monotonicity #809]: #846
-#852 := [trans #847 #850]: #851
-#861 := [monotonicity #852 #858]: #860
-#867 := [trans #861 #865]: #866
-#870 := [quant-intro #867]: #869
-#904 := [monotonicity #870 #901]: #903
-#910 := [trans #904 #908]: #909
-#913 := [monotonicity #870 #910]: #912
-#843 := (iff #214 #842)
-#840 := (iff #213 #837)
-#833 := (implies #830 #212)
-#838 := (iff #833 #837)
-#839 := [rewrite]: #838
+#857 := (iff #217 #854)
+#850 := (implies #839 #847)
+#855 := (iff #850 #854)
+#856 := [rewrite]: #855
+#851 := (iff #217 #850)
+#848 := (iff #216 #847)
+#849 := [monotonicity #846]: #848
+#842 := (iff #214 #839)
+#836 := (and #798 #83)
+#840 := (iff #836 #839)
+#841 := [rewrite]: #840
+#837 := (iff #214 #836)
+#838 := [monotonicity #800]: #837
+#843 := [trans #838 #841]: #842
+#852 := [monotonicity #843 #849]: #851
+#858 := [trans #852 #856]: #857
+#861 := [quant-intro #858]: #860
+#895 := [monotonicity #861 #892]: #894
+#901 := [trans #895 #899]: #900
+#904 := [monotonicity #861 #901]: #903
 #834 := (iff #213 #833)
-#831 := (iff #210 #830)
-#828 := (iff #209 #827)
-#829 := [rewrite]: #828
-#825 := (iff #207 #813)
-#826 := [monotonicity #809]: #825
-#832 := [monotonicity #826 #829]: #831
-#835 := [monotonicity #832]: #834
-#841 := [trans #835 #839]: #840
-#844 := [quant-intro #841]: #843
-#916 := [monotonicity #844 #913]: #915
-#922 := [trans #916 #920]: #921
-#925 := [monotonicity #844 #922]: #924
+#831 := (iff #212 #828)
+#824 := (implies #821 #211)
+#829 := (iff #824 #828)
+#830 := [rewrite]: #829
+#825 := (iff #212 #824)
+#822 := (iff #209 #821)
+#819 := (iff #208 #818)
+#820 := [rewrite]: #819
+#816 := (iff #206 #804)
+#817 := [monotonicity #800]: #816
+#823 := [monotonicity #817 #820]: #822
+#826 := [monotonicity #823]: #825
+#832 := [trans #826 #830]: #831
+#835 := [quant-intro #832]: #834
+#907 := [monotonicity #835 #904]: #906
+#913 := [trans #907 #911]: #912
+#916 := [monotonicity #835 #913]: #915
+#919 := [monotonicity #916]: #918
+#925 := [trans #919 #923]: #924
 #928 := [monotonicity #925]: #927
-#934 := [trans #928 #932]: #933
-#937 := [monotonicity #934]: #936
-#823 := (iff #204 #822)
-#824 := [rewrite]: #823
-#940 := [monotonicity #824 #937]: #939
-#946 := [trans #940 #944]: #945
-#949 := [monotonicity #824 #946]: #948
-#820 := (iff #202 #819)
-#817 := (iff #201 #814)
-#810 := (implies #807 #793)
-#815 := (iff #810 #814)
-#816 := [rewrite]: #815
+#814 := (iff #203 #813)
+#815 := [rewrite]: #814
+#931 := [monotonicity #815 #928]: #930
+#937 := [trans #931 #935]: #936
+#940 := [monotonicity #815 #937]: #939
 #811 := (iff #201 #810)
-#794 := (iff #194 #793)
-#795 := [rewrite]: #794
-#812 := [monotonicity #809 #795]: #811
-#818 := [trans #812 #816]: #817
-#821 := [quant-intro #818]: #820
-#952 := [monotonicity #821 #949]: #951
-#958 := [trans #952 #956]: #957
-#961 := [monotonicity #821 #958]: #960
+#808 := (iff #200 #805)
+#801 := (implies #798 #784)
+#806 := (iff #801 #805)
+#807 := [rewrite]: #806
+#802 := (iff #200 #801)
+#785 := (iff #193 #784)
+#786 := [rewrite]: #785
+#803 := [monotonicity #800 #786]: #802
+#809 := [trans #803 #807]: #808
+#812 := [quant-intro #809]: #811
+#943 := [monotonicity #812 #940]: #942
+#949 := [trans #943 #947]: #948
+#952 := [monotonicity #812 #949]: #951
+#955 := [monotonicity #952]: #954
+#961 := [trans #955 #959]: #960
 #964 := [monotonicity #961]: #963
-#970 := [trans #964 #968]: #969
-#973 := [monotonicity #970]: #972
-#805 := (iff #196 #804)
-#802 := (iff #195 #799)
-#796 := (implies #193 #793)
-#800 := (iff #796 #799)
-#801 := [rewrite]: #800
-#797 := (iff #195 #796)
-#798 := [monotonicity #795]: #797
-#803 := [trans #798 #801]: #802
-#806 := [quant-intro #803]: #805
-#976 := [monotonicity #806 #973]: #975
-#982 := [trans #976 #980]: #981
-#791 := (iff #192 #790)
-#788 := (iff #191 #785)
-#782 := (implies #188 #779)
-#786 := (iff #782 #785)
-#787 := [rewrite]: #786
-#783 := (iff #191 #782)
-#780 := (iff #190 #779)
-#781 := [rewrite]: #780
-#784 := [monotonicity #781]: #783
-#789 := [trans #784 #787]: #788
-#792 := [quant-intro #789]: #791
-#985 := [monotonicity #792 #982]: #984
-#991 := [trans #985 #989]: #990
-#777 := (iff #182 #776)
-#774 := (= #181 #773)
-#771 := (= #180 f1)
+#796 := (iff #195 #795)
+#793 := (iff #194 #790)
+#787 := (implies #192 #784)
+#791 := (iff #787 #790)
+#792 := [rewrite]: #791
+#788 := (iff #194 #787)
+#789 := [monotonicity #786]: #788
+#794 := [trans #789 #792]: #793
+#797 := [quant-intro #794]: #796
+#967 := [monotonicity #797 #964]: #966
+#973 := [trans #967 #971]: #972
+#782 := (iff #191 #781)
+#779 := (iff #190 #776)
+#773 := (implies #187 #770)
+#777 := (iff #773 #776)
+#778 := [rewrite]: #777
+#774 := (iff #190 #773)
+#771 := (iff #189 #770)
 #772 := [rewrite]: #771
 #775 := [monotonicity #772]: #774
-#778 := [monotonicity #775]: #777
-#994 := [monotonicity #778 #991]: #993
+#780 := [trans #775 #778]: #779
+#783 := [quant-intro #780]: #782
+#976 := [monotonicity #783 #973]: #975
+#982 := [trans #976 #980]: #981
+#985 := [monotonicity #982]: #984
+#991 := [trans #985 #989]: #990
+#768 := (iff #178 #767)
+#765 := (iff #177 #762)
+#759 := (implies #535 #176)
+#763 := (iff #759 #762)
+#764 := [rewrite]: #763
+#760 := (iff #177 #759)
+#536 := (iff #107 #535)
+#533 := (iff #106 #532)
+#534 := [rewrite]: #533
+#537 := [monotonicity #534]: #536
+#761 := [monotonicity #537]: #760
+#766 := [trans #761 #764]: #765
+#769 := [quant-intro #766]: #768
+#994 := [monotonicity #769 #991]: #993
 #1000 := [trans #994 #998]: #999
-#769 := (iff #178 #768)
-#766 := (iff #177 #763)
-#760 := (implies #536 #176)
-#764 := (iff #760 #763)
-#765 := [rewrite]: #764
-#761 := (iff #177 #760)
-#537 := (iff #107 #536)
-#534 := (iff #106 #533)
-#535 := [rewrite]: #534
-#538 := [monotonicity #535]: #537
-#762 := [monotonicity #538]: #761
-#767 := [trans #762 #765]: #766
-#770 := [quant-intro #767]: #769
-#1003 := [monotonicity #770 #1000]: #1002
+#1003 := [monotonicity #1000]: #1002
 #1009 := [trans #1003 #1007]: #1008
-#1012 := [monotonicity #1009]: #1011
-#1018 := [trans #1012 #1016]: #1017
-#758 := (iff #173 #757)
-#755 := (iff #172 #754)
-#756 := [rewrite]: #755
-#759 := [monotonicity #756]: #758
-#1021 := [monotonicity #759 #1018]: #1020
-#1026 := [trans #1021 #1024]: #1025
-#616 := (iff #130 #615)
-#613 := (iff #129 #610)
-#607 := (and #536 #120)
-#611 := (iff #607 #610)
-#612 := [rewrite]: #611
-#608 := (iff #129 #607)
-#609 := [monotonicity #538]: #608
-#614 := [trans #609 #612]: #613
-#617 := [quant-intro #614]: #616
-#1029 := [monotonicity #617 #1026]: #1028
-#1034 := [trans #1029 #1032]: #1033
-#1037 := [monotonicity #1034]: #1036
-#1041 := [trans #1037 #1039]: #1040
-#752 := (iff #169 #742)
-#747 := (implies true #742)
-#750 := (iff #747 #742)
-#751 := [rewrite]: #750
-#748 := (iff #169 #747)
-#745 := (iff #168 #742)
-#739 := (implies #618 #734)
-#743 := (iff #739 #742)
-#744 := [rewrite]: #743
-#740 := (iff #168 #739)
-#737 := (iff #167 #734)
-#730 := (implies #621 #725)
-#735 := (iff #730 #734)
-#736 := [rewrite]: #735
-#731 := (iff #167 #730)
-#728 := (iff #166 #725)
-#721 := (implies #136 #716)
-#726 := (iff #721 #725)
-#727 := [rewrite]: #726
-#722 := (iff #166 #721)
-#719 := (iff #165 #716)
-#712 := (implies #624 #707)
-#717 := (iff #712 #716)
-#718 := [rewrite]: #717
-#713 := (iff #165 #712)
-#710 := (iff #164 #707)
-#703 := (implies #141 #700)
-#708 := (iff #703 #707)
-#709 := [rewrite]: #708
-#704 := (iff #164 #703)
-#701 := (iff #163 #700)
-#698 := (iff #162 #695)
-#691 := (implies #648 #688)
-#696 := (iff #691 #695)
-#697 := [rewrite]: #696
-#692 := (iff #162 #691)
-#689 := (iff #161 #688)
-#686 := (iff #160 #683)
-#679 := (implies #666 #669)
-#684 := (iff #679 #683)
-#685 := [rewrite]: #684
-#680 := (iff #160 #679)
-#677 := (iff #159 #669)
-#672 := (and #669 true)
-#675 := (iff #672 #669)
-#676 := [rewrite]: #675
-#673 := (iff #159 #672)
-#670 := (iff #158 #669)
-#671 := [rewrite]: #670
-#674 := [monotonicity #671]: #673
-#678 := [trans #674 #676]: #677
-#667 := (iff #156 #666)
-#664 := (iff #155 #661)
-#657 := (implies #651 #654)
-#662 := (iff #657 #661)
-#663 := [rewrite]: #662
-#658 := (iff #155 #657)
-#655 := (iff #154 #654)
-#628 := (= #147 #627)
-#629 := [rewrite]: #628
-#656 := [monotonicity #629]: #655
-#652 := (iff #153 #651)
-#653 := [rewrite]: #652
-#659 := [monotonicity #653 #656]: #658
-#665 := [trans #659 #663]: #664
-#668 := [quant-intro #665]: #667
-#681 := [monotonicity #668 #678]: #680
-#687 := [trans #681 #685]: #686
-#690 := [monotonicity #668 #687]: #689
-#649 := (iff #152 #648)
-#646 := (iff #151 #643)
-#639 := (implies #144 #636)
-#644 := (iff #639 #643)
-#645 := [rewrite]: #644
-#640 := (iff #151 #639)
-#637 := (iff #150 #636)
-#634 := (iff #149 #633)
-#631 := (iff #148 #630)
-#632 := [monotonicity #629]: #631
-#635 := [monotonicity #632]: #634
-#638 := [quant-intro #635]: #637
-#641 := [monotonicity #638]: #640
-#647 := [trans #641 #645]: #646
-#650 := [quant-intro #647]: #649
-#693 := [monotonicity #650 #690]: #692
-#699 := [trans #693 #697]: #698
-#702 := [monotonicity #650 #699]: #701
-#705 := [monotonicity #702]: #704
-#711 := [trans #705 #709]: #710
-#625 := (iff #138 #624)
-#626 := [rewrite]: #625
-#714 := [monotonicity #626 #711]: #713
-#720 := [trans #714 #718]: #719
-#723 := [monotonicity #720]: #722
-#729 := [trans #723 #727]: #728
-#622 := (iff #133 #621)
-#623 := [rewrite]: #622
-#732 := [monotonicity #623 #729]: #731
-#738 := [trans #732 #736]: #737
-#619 := (iff #131 #618)
-#620 := [monotonicity #617]: #619
-#741 := [monotonicity #620 #738]: #740
-#746 := [trans #741 #744]: #745
-#749 := [monotonicity #746]: #748
-#753 := [trans #749 #751]: #752
-#1044 := [monotonicity #753 #1041]: #1043
-#605 := (iff #128 #604)
-#602 := (iff #127 #599)
-#595 := (implies #121 #592)
-#600 := (iff #595 #599)
-#601 := [rewrite]: #600
-#596 := (iff #127 #595)
-#593 := (iff #126 #592)
-#590 := (iff #125 #589)
-#587 := (iff #124 #586)
-#584 := (iff #123 #583)
-#566 := (= #116 #565)
-#567 := [rewrite]: #566
-#585 := [monotonicity #567]: #584
-#588 := [monotonicity #535 #585]: #587
-#591 := [monotonicity #588]: #590
-#594 := [quant-intro #591]: #593
-#597 := [monotonicity #594]: #596
-#603 := [trans #597 #601]: #602
-#606 := [quant-intro #603]: #605
-#1047 := [monotonicity #606 #1044]: #1046
+#757 := (iff #173 #756)
+#754 := (iff #172 #753)
+#755 := [rewrite]: #754
+#758 := [monotonicity #755]: #757
+#1012 := [monotonicity #758 #1009]: #1011
+#1017 := [trans #1012 #1015]: #1016
+#615 := (iff #130 #614)
+#612 := (iff #129 #609)
+#606 := (and #535 #120)
+#610 := (iff #606 #609)
+#611 := [rewrite]: #610
+#607 := (iff #129 #606)
+#608 := [monotonicity #537]: #607
+#613 := [trans #608 #611]: #612
+#616 := [quant-intro #613]: #615
+#1020 := [monotonicity #616 #1017]: #1019
+#1025 := [trans #1020 #1023]: #1024
+#1028 := [monotonicity #1025]: #1027
+#1032 := [trans #1028 #1030]: #1031
+#751 := (iff #169 #741)
+#746 := (implies true #741)
+#749 := (iff #746 #741)
+#750 := [rewrite]: #749
+#747 := (iff #169 #746)
+#744 := (iff #168 #741)
+#738 := (implies #617 #733)
+#742 := (iff #738 #741)
+#743 := [rewrite]: #742
+#739 := (iff #168 #738)
+#736 := (iff #167 #733)
+#729 := (implies #620 #724)
+#734 := (iff #729 #733)
+#735 := [rewrite]: #734
+#730 := (iff #167 #729)
+#727 := (iff #166 #724)
+#720 := (implies #136 #715)
+#725 := (iff #720 #724)
+#726 := [rewrite]: #725
+#721 := (iff #166 #720)
+#718 := (iff #165 #715)
+#711 := (implies #623 #706)
+#716 := (iff #711 #715)
+#717 := [rewrite]: #716
+#712 := (iff #165 #711)
+#709 := (iff #164 #706)
+#702 := (implies #141 #699)
+#707 := (iff #702 #706)
+#708 := [rewrite]: #707
+#703 := (iff #164 #702)
+#700 := (iff #163 #699)
+#697 := (iff #162 #694)
+#690 := (implies #647 #687)
+#695 := (iff #690 #694)
+#696 := [rewrite]: #695
+#691 := (iff #162 #690)
+#688 := (iff #161 #687)
+#685 := (iff #160 #682)
+#678 := (implies #665 #668)
+#683 := (iff #678 #682)
+#684 := [rewrite]: #683
+#679 := (iff #160 #678)
+#676 := (iff #159 #668)
+#671 := (and #668 true)
+#674 := (iff #671 #668)
+#675 := [rewrite]: #674
+#672 := (iff #159 #671)
+#669 := (iff #158 #668)
+#670 := [rewrite]: #669
+#673 := [monotonicity #670]: #672
+#677 := [trans #673 #675]: #676
+#666 := (iff #156 #665)
+#663 := (iff #155 #660)
+#656 := (implies #650 #653)
+#661 := (iff #656 #660)
+#662 := [rewrite]: #661
+#657 := (iff #155 #656)
+#654 := (iff #154 #653)
+#627 := (= #147 #626)
+#628 := [rewrite]: #627
+#655 := [monotonicity #628]: #654
+#651 := (iff #153 #650)
+#652 := [rewrite]: #651
+#658 := [monotonicity #652 #655]: #657
+#664 := [trans #658 #662]: #663
+#667 := [quant-intro #664]: #666
+#680 := [monotonicity #667 #677]: #679
+#686 := [trans #680 #684]: #685
+#689 := [monotonicity #667 #686]: #688
+#648 := (iff #152 #647)
+#645 := (iff #151 #642)
+#638 := (implies #144 #635)
+#643 := (iff #638 #642)
+#644 := [rewrite]: #643
+#639 := (iff #151 #638)
+#636 := (iff #150 #635)
+#633 := (iff #149 #632)
+#630 := (iff #148 #629)
+#631 := [monotonicity #628]: #630
+#634 := [monotonicity #631]: #633
+#637 := [quant-intro #634]: #636
+#640 := [monotonicity #637]: #639
+#646 := [trans #640 #644]: #645
+#649 := [quant-intro #646]: #648
+#692 := [monotonicity #649 #689]: #691
+#698 := [trans #692 #696]: #697
+#701 := [monotonicity #649 #698]: #700
+#704 := [monotonicity #701]: #703
+#710 := [trans #704 #708]: #709
+#624 := (iff #138 #623)
+#625 := [rewrite]: #624
+#713 := [monotonicity #625 #710]: #712
+#719 := [trans #713 #717]: #718
+#722 := [monotonicity #719]: #721
+#728 := [trans #722 #726]: #727
+#621 := (iff #133 #620)
+#622 := [rewrite]: #621
+#731 := [monotonicity #622 #728]: #730
+#737 := [trans #731 #735]: #736
+#618 := (iff #131 #617)
+#619 := [monotonicity #616]: #618
+#740 := [monotonicity #619 #737]: #739
+#745 := [trans #740 #743]: #744
+#748 := [monotonicity #745]: #747
+#752 := [trans #748 #750]: #751
+#1035 := [monotonicity #752 #1032]: #1034
+#604 := (iff #128 #603)
+#601 := (iff #127 #598)
+#594 := (implies #121 #591)
+#599 := (iff #594 #598)
+#600 := [rewrite]: #599
+#595 := (iff #127 #594)
+#592 := (iff #126 #591)
+#589 := (iff #125 #588)
+#586 := (iff #124 #585)
+#583 := (iff #123 #582)
+#565 := (= #116 #564)
+#566 := [rewrite]: #565
+#584 := [monotonicity #566]: #583
+#587 := [monotonicity #534 #584]: #586
+#590 := [monotonicity #587]: #589
+#593 := [quant-intro #590]: #592
+#596 := [monotonicity #593]: #595
+#602 := [trans #596 #600]: #601
+#605 := [quant-intro #602]: #604
+#1038 := [monotonicity #605 #1035]: #1037
+#1044 := [trans #1038 #1042]: #1043
+#580 := (iff #119 #579)
+#577 := (iff #118 #574)
+#570 := (implies #559 #567)
+#575 := (iff #570 #574)
+#576 := [rewrite]: #575
+#571 := (iff #118 #570)
+#568 := (iff #117 #567)
+#569 := [monotonicity #566]: #568
+#562 := (iff #115 #559)
+#556 := (and #532 #83)
+#560 := (iff #556 #559)
+#561 := [rewrite]: #560
+#557 := (iff #115 #556)
+#558 := [monotonicity #534]: #557
+#563 := [trans #558 #561]: #562
+#572 := [monotonicity #563 #569]: #571
+#578 := [trans #572 #576]: #577
+#581 := [quant-intro #578]: #580
+#1047 := [monotonicity #581 #1044]: #1046
 #1053 := [trans #1047 #1051]: #1052
-#581 := (iff #119 #580)
-#578 := (iff #118 #575)
-#571 := (implies #560 #568)
-#576 := (iff #571 #575)
-#577 := [rewrite]: #576
-#572 := (iff #118 #571)
-#569 := (iff #117 #568)
-#570 := [monotonicity #567]: #569
-#563 := (iff #115 #560)
-#557 := (and #533 #83)
-#561 := (iff #557 #560)
-#562 := [rewrite]: #561
-#558 := (iff #115 #557)
-#559 := [monotonicity #535]: #558
-#564 := [trans #559 #562]: #563
-#573 := [monotonicity #564 #570]: #572
-#579 := [trans #573 #577]: #578
-#582 := [quant-intro #579]: #581
-#1056 := [monotonicity #582 #1053]: #1055
+#554 := (iff #114 #553)
+#551 := (iff #113 #548)
+#544 := (implies #541 #112)
+#549 := (iff #544 #548)
+#550 := [rewrite]: #549
+#545 := (iff #113 #544)
+#542 := (iff #110 #541)
+#539 := (iff #109 #538)
+#540 := [rewrite]: #539
+#543 := [monotonicity #537 #540]: #542
+#546 := [monotonicity #543]: #545
+#552 := [trans #546 #550]: #551
+#555 := [quant-intro #552]: #554
+#1056 := [monotonicity #555 #1053]: #1055
 #1062 := [trans #1056 #1060]: #1061
-#555 := (iff #114 #554)
-#552 := (iff #113 #549)
-#545 := (implies #542 #112)
-#550 := (iff #545 #549)
-#551 := [rewrite]: #550
-#546 := (iff #113 #545)
-#543 := (iff #110 #542)
-#540 := (iff #109 #539)
-#541 := [rewrite]: #540
-#544 := [monotonicity #538 #541]: #543
-#547 := [monotonicity #544]: #546
-#553 := [trans #547 #551]: #552
-#556 := [quant-intro #553]: #555
-#1065 := [monotonicity #556 #1062]: #1064
+#1065 := [monotonicity #1062]: #1064
 #1071 := [trans #1065 #1069]: #1070
-#1074 := [monotonicity #1071]: #1073
+#530 := (iff #100 #529)
+#531 := [rewrite]: #530
+#1074 := [monotonicity #531 #1071]: #1073
 #1080 := [trans #1074 #1078]: #1079
-#531 := (iff #100 #530)
-#532 := [rewrite]: #531
-#1083 := [monotonicity #532 #1080]: #1082
-#1089 := [trans #1083 #1087]: #1088
-#1092 := [monotonicity #1089]: #1091
-#1096 := [trans #1092 #1094]: #1095
-#528 := (iff #97 #527)
-#525 := (iff #96 #522)
-#518 := (implies #90 #515)
-#523 := (iff #518 #522)
-#524 := [rewrite]: #523
-#519 := (iff #96 #518)
-#516 := (iff #95 #515)
-#513 := (iff #94 #512)
-#510 := (iff #93 #507)
-#504 := (and #454 #92)
-#508 := (iff #504 #507)
-#509 := [rewrite]: #508
-#505 := (iff #93 #504)
-#455 := (iff #67 #454)
-#456 := [rewrite]: #455
-#506 := [monotonicity #456]: #505
-#511 := [trans #506 #509]: #510
-#514 := [monotonicity #511]: #513
-#517 := [quant-intro #514]: #516
-#520 := [monotonicity #517]: #519
-#526 := [trans #520 #524]: #525
-#529 := [quant-intro #526]: #528
-#1099 := [monotonicity #529 #1096]: #1098
-#1105 := [trans #1099 #1103]: #1104
-#1108 := [monotonicity #529 #1105]: #1107
-#502 := (iff #88 #501)
-#499 := (iff #87 #496)
-#492 := (implies #487 #86)
-#497 := (iff #492 #496)
-#498 := [rewrite]: #497
-#493 := (iff #87 #492)
-#490 := (iff #84 #487)
-#484 := (and #454 #83)
-#488 := (iff #484 #487)
-#489 := [rewrite]: #488
-#485 := (iff #84 #484)
-#486 := [monotonicity #456]: #485
-#491 := [trans #486 #489]: #490
-#494 := [monotonicity #491]: #493
-#500 := [trans #494 #498]: #499
-#503 := [quant-intro #500]: #502
-#1111 := [monotonicity #503 #1108]: #1110
-#1117 := [trans #1111 #1115]: #1116
-#1120 := [monotonicity #503 #1117]: #1119
-#482 := (iff #80 #481)
-#479 := (iff #79 #476)
-#472 := (implies #469 #78)
-#477 := (iff #472 #476)
-#478 := [rewrite]: #477
-#473 := (iff #79 #472)
-#470 := (iff #76 #469)
-#467 := (iff #75 #466)
-#468 := [rewrite]: #467
-#458 := (iff #68 #457)
-#459 := [monotonicity #456]: #458
-#471 := [monotonicity #459 #468]: #470
-#474 := [monotonicity #471]: #473
-#480 := [trans #474 #478]: #479
-#483 := [quant-intro #480]: #482
-#1123 := [monotonicity #483 #1120]: #1122
-#1129 := [trans #1123 #1127]: #1128
-#1132 := [monotonicity #483 #1129]: #1131
+#1083 := [monotonicity #1080]: #1082
+#1087 := [trans #1083 #1085]: #1086
+#527 := (iff #97 #526)
+#524 := (iff #96 #521)
+#517 := (implies #90 #514)
+#522 := (iff #517 #521)
+#523 := [rewrite]: #522
+#518 := (iff #96 #517)
+#515 := (iff #95 #514)
+#512 := (iff #94 #511)
+#509 := (iff #93 #506)
+#503 := (and #453 #92)
+#507 := (iff #503 #506)
+#508 := [rewrite]: #507
+#504 := (iff #93 #503)
+#454 := (iff #67 #453)
+#455 := [rewrite]: #454
+#505 := [monotonicity #455]: #504
+#510 := [trans #505 #508]: #509
+#513 := [monotonicity #510]: #512
+#516 := [quant-intro #513]: #515
+#519 := [monotonicity #516]: #518
+#525 := [trans #519 #523]: #524
+#528 := [quant-intro #525]: #527
+#1090 := [monotonicity #528 #1087]: #1089
+#1096 := [trans #1090 #1094]: #1095
+#1099 := [monotonicity #528 #1096]: #1098
+#501 := (iff #88 #500)
+#498 := (iff #87 #495)
+#491 := (implies #486 #86)
+#496 := (iff #491 #495)
+#497 := [rewrite]: #496
+#492 := (iff #87 #491)
+#489 := (iff #84 #486)
+#483 := (and #453 #83)
+#487 := (iff #483 #486)
+#488 := [rewrite]: #487
+#484 := (iff #84 #483)
+#485 := [monotonicity #455]: #484
+#490 := [trans #485 #488]: #489
+#493 := [monotonicity #490]: #492
+#499 := [trans #493 #497]: #498
+#502 := [quant-intro #499]: #501
+#1102 := [monotonicity #502 #1099]: #1101
+#1108 := [trans #1102 #1106]: #1107
+#1111 := [monotonicity #502 #1108]: #1110
+#481 := (iff #80 #480)
+#478 := (iff #79 #475)
+#471 := (implies #468 #78)
+#476 := (iff #471 #475)
+#477 := [rewrite]: #476
+#472 := (iff #79 #471)
+#469 := (iff #76 #468)
+#466 := (iff #75 #465)
+#467 := [rewrite]: #466
+#457 := (iff #68 #456)
+#458 := [monotonicity #455]: #457
+#470 := [monotonicity #458 #467]: #469
+#473 := [monotonicity #470]: #472
+#479 := [trans #473 #477]: #478
+#482 := [quant-intro #479]: #481
+#1114 := [monotonicity #482 #1111]: #1113
+#1120 := [trans #1114 #1118]: #1119
+#1123 := [monotonicity #482 #1120]: #1122
+#1126 := [monotonicity #1123]: #1125
+#1132 := [trans #1126 #1130]: #1131
 #1135 := [monotonicity #1132]: #1134
-#1141 := [trans #1135 #1139]: #1140
-#1144 := [monotonicity #1141]: #1143
-#464 := (iff #71 #463)
-#465 := [rewrite]: #464
-#1147 := [monotonicity #465 #1144]: #1146
-#1153 := [trans #1147 #1151]: #1152
-#1156 := [monotonicity #465 #1153]: #1155
-#461 := (iff #69 #460)
-#462 := [quant-intro #459]: #461
-#1159 := [monotonicity #462 #1156]: #1158
+#463 := (iff #71 #462)
+#464 := [rewrite]: #463
+#1138 := [monotonicity #464 #1135]: #1137
+#1144 := [trans #1138 #1142]: #1143
+#1147 := [monotonicity #464 #1144]: #1146
+#460 := (iff #69 #459)
+#461 := [quant-intro #458]: #460
+#1150 := [monotonicity #461 #1147]: #1149
+#1156 := [trans #1150 #1154]: #1155
+#451 := (iff #65 #450)
+#448 := (iff #64 #445)
+#442 := (implies #62 #439)
+#446 := (iff #442 #445)
+#447 := [rewrite]: #446
+#443 := (iff #64 #442)
+#440 := (iff #63 #439)
+#441 := [rewrite]: #440
+#444 := [monotonicity #441]: #443
+#449 := [trans #444 #447]: #448
+#452 := [quant-intro #449]: #451
+#1159 := [monotonicity #452 #1156]: #1158
 #1165 := [trans #1159 #1163]: #1164
-#452 := (iff #65 #451)
-#449 := (iff #64 #446)
-#443 := (implies #62 #440)
-#447 := (iff #443 #446)
-#448 := [rewrite]: #447
-#444 := (iff #64 #443)
-#441 := (iff #63 #440)
-#442 := [rewrite]: #441
-#445 := [monotonicity #442]: #444
-#450 := [trans #445 #448]: #449
-#453 := [quant-intro #450]: #452
-#1168 := [monotonicity #453 #1165]: #1167
+#437 := (iff #61 #436)
+#434 := (iff #60 #431)
+#428 := (implies #57 #425)
+#432 := (iff #428 #431)
+#433 := [rewrite]: #432
+#429 := (iff #60 #428)
+#426 := (iff #59 #425)
+#427 := [rewrite]: #426
+#430 := [monotonicity #427]: #429
+#435 := [trans #430 #433]: #434
+#438 := [quant-intro #435]: #437
+#1168 := [monotonicity #438 #1165]: #1167
 #1174 := [trans #1168 #1172]: #1173
-#438 := (iff #61 #437)
-#435 := (iff #60 #432)
-#429 := (implies #57 #426)
-#433 := (iff #429 #432)
-#434 := [rewrite]: #433
-#430 := (iff #60 #429)
-#427 := (iff #59 #426)
-#428 := [rewrite]: #427
-#431 := [monotonicity #428]: #430
-#436 := [trans #431 #434]: #435
-#439 := [quant-intro #436]: #438
-#1177 := [monotonicity #439 #1174]: #1176
-#1183 := [trans #1177 #1181]: #1182
-#1186 := [monotonicity #1183]: #1185
-#1190 := [trans #1186 #1188]: #1189
-#1193 := [monotonicity #1190]: #1192
-#1832 := [trans #1193 #1830]: #1831
-#425 := [asserted]: #271
-#1833 := [mp #425 #1832]: #1828
-#1835 := [not-or-elim #1833]: #460
-#1890 := [mp~ #1835 #1859]: #460
-#4231 := [mp #1890 #4230]: #4226
-#5529 := (not #4226)
-#5530 := (or #5529 #3078)
-#5525 := [quant-inst #1936]: #5530
-#5337 := [unit-resolution #5525 #4231 #5222]: false
-#5345 := [lemma #5337]: #3078
-#3845 := (or #3093 #1945)
-#3849 := [def-axiom]: #3845
-#6495 := [unit-resolution #3849 #5345]: #3093
-#3098 := (not #3093)
-#4565 := (or #3098 #4562)
-#4568 := (not #4565)
-#4240 := (pattern #66 #74)
-#2519 := (not #466)
-#3070 := (or #454 #2519 #1210)
-#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3070)
-#4246 := (not #4241)
-#4571 := (or #4246 #4568)
-#4574 := (not #4571)
+#1177 := [monotonicity #1174]: #1176
+#1181 := [trans #1177 #1179]: #1180
+#1184 := [monotonicity #1181]: #1183
+#1823 := [trans #1184 #1821]: #1822
+#424 := [asserted]: #270
+#1824 := [mp #424 #1823]: #1819
+#1826 := [not-or-elim #1824]: #459
+#1881 := [mp~ #1826 #1850]: #459
+#4222 := [mp #1881 #4221]: #4217
+#5520 := (not #4217)
+#5521 := (or #5520 #3069)
+#5516 := [quant-inst #1927]: #5521
+#5328 := [unit-resolution #5516 #4222 #5213]: false
+#5336 := [lemma #5328]: #3069
+#3836 := (or #3084 #1936)
+#3840 := [def-axiom]: #3836
+#6486 := [unit-resolution #3840 #5336]: #3084
+#3089 := (not #3084)
+#4556 := (or #3089 #4553)
+#4559 := (not #4556)
+#4231 := (pattern #66 #74)
+#2510 := (not #465)
+#3061 := (or #453 #2510 #1201)
+#4232 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4231) #3061)
+#4237 := (not #4232)
+#4562 := (or #4237 #4559)
+#4565 := (not #4562)
 decl ?v1!1 :: S3
-#1909 := ?v1!1
-#1913 := (f11 ?v1!1)
-#2534 := (* -1::Int #1913)
+#1900 := ?v1!1
+#1904 := (f11 ?v1!1)
+#2525 := (* -1::Int #1904)
 decl ?v0!2 :: S3
-#1910 := ?v0!2
-#1911 := (f11 ?v0!2)
-#2535 := (+ #1911 #2534)
-#2536 := (<= #2535 0::Int)
-#1918 := (f12 ?v1!1)
-#1919 := (= f1 #1918)
-#1916 := (f12 ?v0!2)
-#1917 := (= f1 #1916)
-#2054 := (not #1917)
-#2026 := (or #2054 #1919 #2536)
-#1928 := (not #2026)
-#4577 := (or #1928 #4574)
-#4580 := (not #4577)
-#4232 := (forall (vars (?v0 S3)) (:pat #4218) #1201)
-#4237 := (not #4232)
-#4583 := (or #4237 #4580)
-#4586 := (not #4583)
+#1901 := ?v0!2
+#1902 := (f11 ?v0!2)
+#2526 := (+ #1902 #2525)
+#2527 := (<= #2526 0::Int)
+#1909 := (f12 ?v1!1)
+#1910 := (= f1 #1909)
+#1907 := (f12 ?v0!2)
+#1908 := (= f1 #1907)
+#2210 := (not #1908)
+#2119 := (or #2210 #1910 #2527)
+#2018 := (not #2119)
+#4568 := (or #2018 #4565)
+#4571 := (not #4568)
+#4223 := (forall (vars (?v0 S3)) (:pat #4209) #1192)
+#4228 := (not #4223)
+#4574 := (or #4228 #4571)
+#4577 := (not #4574)
 decl ?v0!0 :: S3
-#1894 := ?v0!0
-#1895 := (f11 ?v0!0)
-#1896 := (>= #1895 0::Int)
-#1897 := (not #1896)
-#4589 := (or #1897 #4586)
-#4592 := (not #4589)
-#4595 := (or #1196 #4592)
-#4598 := (not #4595)
-#4605 := (forall (vars (?v0 S3)) (:pat #4218) #1805)
-#4608 := (iff #1808 #4605)
-#4606 := (iff #1805 #1805)
-#4607 := [refl]: #4606
-#4609 := [quant-intro #4607]: #4608
-#1958 := (~ #1808 #1808)
-#1900 := (~ #1805 #1805)
-#1901 := [refl]: #1900
-#1959 := [nnf-pos #1901]: #1958
-#1838 := [not-or-elim #1833]: #1808
-#2053 := [mp~ #1838 #1959]: #1808
-#4610 := [mp #2053 #4609]: #4605
-#5324 := [hypothesis]: #1196
-#4784 := (not #4605)
-#5260 := (or #4784 #71)
-#5144 := (= f10 f10)
-#5145 := (not #5144)
-#5147 := (or #5145 #71)
-#5228 := (or #4784 #5147)
-#5262 := (iff #5228 #5260)
-#5264 := (iff #5260 #5260)
-#5259 := [rewrite]: #5264
-#5233 := (iff #5147 #71)
-#5201 := (or false #71)
-#5229 := (iff #5201 #71)
-#5232 := [rewrite]: #5229
-#5202 := (iff #5147 #5201)
-#5199 := (iff #5145 false)
-#5196 := (not true)
-#5193 := (iff #5196 false)
-#5194 := [rewrite]: #5193
-#5197 := (iff #5145 #5196)
-#5148 := (iff #5144 true)
-#5195 := [rewrite]: #5148
-#5198 := [monotonicity #5195]: #5197
-#5200 := [trans #5198 #5194]: #5199
-#5203 := [monotonicity #5200]: #5202
-#5234 := [trans #5203 #5232]: #5233
-#5263 := [monotonicity #5234]: #5262
-#5269 := [trans #5263 #5259]: #5262
-#5261 := [quant-inst #56]: #5228
-#5295 := [mp #5261 #5269]: #5260
-#5325 := [unit-resolution #5295 #5324 #4610]: false
-#5320 := [lemma #5325]: #71
-#4601 := (or #1196 #4598)
-#3528 := (forall (vars (?v1 S3)) #3517)
-#3535 := (not #3528)
-#3513 := (forall (vars (?v0 S3) (?v1 S3)) #3508)
-#3534 := (not #3513)
-#3536 := (or #2359 #2926 #3534 #3535)
-#3537 := (not #3536)
-#3542 := (or #3491 #3537)
-#3549 := (not #3542)
-#3468 := (forall (vars (?v0 S3) (?v1 S3)) #3463)
-#3548 := (not #3468)
-#3550 := (or #3548 #3549)
-#3551 := (not #3550)
-#3556 := (or #3445 #3551)
-#3562 := (not #3556)
-#3563 := (or #1499 #3562)
-#3564 := (not #3563)
-#3569 := (or #2276 #3564)
-#3575 := (not #3569)
-#3576 := (or #1490 #3575)
-#3577 := (not #3576)
-#3582 := (or #1490 #3577)
-#3588 := (not #3582)
-#3589 := (or #953 #3588)
-#3590 := (not #3589)
-#3595 := (or #2869 #3590)
-#3601 := (not #3595)
-#3602 := (or #1485 #3601)
-#3603 := (not #3602)
-#3608 := (or #2855 #3603)
-#3616 := (not #3608)
-#3422 := (forall (vars (?v0 S3)) #3417)
-#3615 := (not #3422)
-#3404 := (forall (vars (?v0 S3)) #3401)
-#3614 := (not #3404)
-#3617 := (or #754 #995 #1650 #1654 #2210 #2213 #3614 #3615 #3616)
-#3618 := (not #3617)
-#3334 := (forall (vars (?v0 S3) (?v1 S3)) #3329)
-#3340 := (not #3334)
-#3341 := (or #158 #3340)
-#3342 := (not #3341)
-#3369 := (or #3342 #3366)
-#3376 := (not #3369)
-#3312 := (forall (vars (?v0 S3)) #3307)
-#3375 := (not #3312)
-#3377 := (or #3375 #3376)
-#3378 := (not #3377)
-#3275 := (forall (vars (?v1 S3)) #3264)
-#3281 := (not #3275)
-#3282 := (or #2089 #2704 #3281)
-#3283 := (not #3282)
-#3383 := (or #3283 #3378)
-#3390 := (not #3383)
-#3260 := (forall (vars (?v0 S3)) #3249)
-#3389 := (not #3260)
-#3391 := (or #724 #706 #733 #715 #3389 #3390)
-#3392 := (not #3391)
-#3623 := (or #3392 #3618)
-#3633 := (not #3623)
-#3246 := (forall (vars (?v0 S3)) #3241)
-#3632 := (not #3246)
-#3218 := (forall (vars (?v0 S3)) #3213)
-#3631 := (not #3218)
-#3190 := (forall (vars (?v0 S3) (?v1 S3)) #3185)
-#3630 := (not #3190)
-#3167 := (forall (vars (?v0 S3) (?v1 S3)) #3162)
-#3629 := (not #3167)
-#3634 := (or #1747 #1742 #3629 #3630 #3631 #3632 #3633)
-#3635 := (not #3634)
-#3135 := (forall (vars (?v1 S3)) #3124)
-#3141 := (not #3135)
-#3142 := (or #1981 #2566 #3141)
-#3143 := (not #3142)
-#3640 := (or #3143 #3635)
-#3647 := (not #3640)
-#3120 := (forall (vars (?v0 S3) (?v1 S3)) #3115)
-#3646 := (not #3120)
-#3648 := (or #3646 #3647)
-#3649 := (not #3648)
-#3654 := (or #3098 #3649)
-#3661 := (not #3654)
-#3075 := (forall (vars (?v0 S3) (?v1 S3)) #3070)
-#3660 := (not #3075)
-#3662 := (or #3660 #3661)
-#3663 := (not #3662)
-#3668 := (or #1928 #3663)
-#3674 := (not #3668)
-#3675 := (or #1205 #3674)
-#3676 := (not #3675)
-#3681 := (or #1897 #3676)
-#3687 := (not #3681)
-#3688 := (or #1196 #3687)
-#3689 := (not #3688)
-#3694 := (or #1196 #3689)
-#4602 := (iff #3694 #4601)
-#4599 := (iff #3689 #4598)
-#4596 := (iff #3688 #4595)
-#4593 := (iff #3687 #4592)
-#4590 := (iff #3681 #4589)
-#4587 := (iff #3676 #4586)
-#4584 := (iff #3675 #4583)
-#4581 := (iff #3674 #4580)
-#4578 := (iff #3668 #4577)
-#4575 := (iff #3663 #4574)
-#4572 := (iff #3662 #4571)
-#4569 := (iff #3661 #4568)
+#1885 := ?v0!0
+#1886 := (f11 ?v0!0)
+#1887 := (>= #1886 0::Int)
+#1888 := (not #1887)
+#4580 := (or #1888 #4577)
+#4583 := (not #4580)
+#4586 := (or #1187 #4583)
+#4589 := (not #4586)
+#4596 := (forall (vars (?v0 S3)) (:pat #4209) #1796)
+#4599 := (iff #1799 #4596)
+#4597 := (iff #1796 #1796)
+#4598 := [refl]: #4597
+#4600 := [quant-intro #4598]: #4599
+#2044 := (~ #1799 #1799)
+#1891 := (~ #1796 #1796)
+#1892 := [refl]: #1891
+#2045 := [nnf-pos #1892]: #2044
+#1829 := [not-or-elim #1824]: #1799
+#2209 := [mp~ #1829 #2045]: #1799
+#4601 := [mp #2209 #4600]: #4596
+#5315 := [hypothesis]: #1187
+#4775 := (not #4596)
+#5251 := (or #4775 #71)
+#5135 := (= f10 f10)
+#5136 := (not #5135)
+#5138 := (or #5136 #71)
+#5219 := (or #4775 #5138)
+#5253 := (iff #5219 #5251)
+#5255 := (iff #5251 #5251)
+#5250 := [rewrite]: #5255
+#5224 := (iff #5138 #71)
+#5192 := (or false #71)
+#5220 := (iff #5192 #71)
+#5223 := [rewrite]: #5220
+#5193 := (iff #5138 #5192)
+#5190 := (iff #5136 false)
+#5187 := (not true)
+#5184 := (iff #5187 false)
+#5185 := [rewrite]: #5184
+#5188 := (iff #5136 #5187)
+#5139 := (iff #5135 true)
+#5186 := [rewrite]: #5139
+#5189 := [monotonicity #5186]: #5188
+#5191 := [trans #5189 #5185]: #5190
+#5194 := [monotonicity #5191]: #5193
+#5225 := [trans #5194 #5223]: #5224
+#5254 := [monotonicity #5225]: #5253
+#5260 := [trans #5254 #5250]: #5253
+#5252 := [quant-inst #56]: #5219
+#5286 := [mp #5252 #5260]: #5251
+#5316 := [unit-resolution #5286 #5315 #4601]: false
+#5311 := [lemma #5316]: #71
+#4592 := (or #1187 #4589)
+#3519 := (forall (vars (?v1 S3)) #3508)
+#3526 := (not #3519)
+#3504 := (forall (vars (?v0 S3) (?v1 S3)) #3499)
+#3525 := (not #3504)
+#3527 := (or #2350 #2917 #3525 #3526)
+#3528 := (not #3527)
+#3533 := (or #3482 #3528)
+#3540 := (not #3533)
+#3459 := (forall (vars (?v0 S3) (?v1 S3)) #3454)
+#3539 := (not #3459)
+#3541 := (or #3539 #3540)
+#3542 := (not #3541)
+#3547 := (or #3436 #3542)
+#3553 := (not #3547)
+#3554 := (or #1490 #3553)
+#3555 := (not #3554)
+#3560 := (or #2267 #3555)
+#3566 := (not #3560)
+#3567 := (or #1481 #3566)
+#3568 := (not #3567)
+#3573 := (or #1481 #3568)
+#3579 := (not #3573)
+#3580 := (or #944 #3579)
+#3581 := (not #3580)
+#3586 := (or #2860 #3581)
+#3592 := (not #3586)
+#3593 := (or #1476 #3592)
+#3594 := (not #3593)
+#3599 := (or #2846 #3594)
+#3607 := (not #3599)
+#3413 := (forall (vars (?v0 S3)) #3408)
+#3606 := (not #3413)
+#3395 := (forall (vars (?v0 S3)) #3392)
+#3605 := (not #3395)
+#3608 := (or #986 #753 #1641 #1645 #2201 #2204 #3605 #3606 #3607)
+#3609 := (not #3608)
+#3325 := (forall (vars (?v0 S3) (?v1 S3)) #3320)
+#3331 := (not #3325)
+#3332 := (or #158 #3331)
+#3333 := (not #3332)
+#3360 := (or #3333 #3357)
+#3367 := (not #3360)
+#3303 := (forall (vars (?v0 S3)) #3298)
+#3366 := (not #3303)
+#3368 := (or #3366 #3367)
+#3369 := (not #3368)
+#3266 := (forall (vars (?v1 S3)) #3255)
+#3272 := (not #3266)
+#3273 := (or #2080 #2695 #3272)
+#3274 := (not #3273)
+#3374 := (or #3274 #3369)
+#3381 := (not #3374)
+#3251 := (forall (vars (?v0 S3)) #3240)
+#3380 := (not #3251)
+#3382 := (or #723 #705 #732 #714 #3380 #3381)
+#3383 := (not #3382)
+#3614 := (or #3383 #3609)
+#3624 := (not #3614)
+#3237 := (forall (vars (?v0 S3)) #3232)
+#3623 := (not #3237)
+#3209 := (forall (vars (?v0 S3)) #3204)
+#3622 := (not #3209)
+#3181 := (forall (vars (?v0 S3) (?v1 S3)) #3176)
+#3621 := (not #3181)
+#3158 := (forall (vars (?v0 S3) (?v1 S3)) #3153)
+#3620 := (not #3158)
+#3625 := (or #1738 #1733 #3620 #3621 #3622 #3623 #3624)
+#3626 := (not #3625)
+#3126 := (forall (vars (?v1 S3)) #3115)
+#3132 := (not #3126)
+#3133 := (or #1972 #2557 #3132)
+#3134 := (not #3133)
+#3631 := (or #3134 #3626)
+#3638 := (not #3631)
+#3111 := (forall (vars (?v0 S3) (?v1 S3)) #3106)
+#3637 := (not #3111)
+#3639 := (or #3637 #3638)
+#3640 := (not #3639)
+#3645 := (or #3089 #3640)
+#3652 := (not #3645)
+#3066 := (forall (vars (?v0 S3) (?v1 S3)) #3061)
+#3651 := (not #3066)
+#3653 := (or #3651 #3652)
+#3654 := (not #3653)
+#3659 := (or #2018 #3654)
+#3665 := (not #3659)
+#3666 := (or #1196 #3665)
+#3667 := (not #3666)
+#3672 := (or #1888 #3667)
+#3678 := (not #3672)
+#3679 := (or #1187 #3678)
+#3680 := (not #3679)
+#3685 := (or #1187 #3680)
+#4593 := (iff #3685 #4592)
+#4590 := (iff #3680 #4589)
+#4587 := (iff #3679 #4586)
+#4584 := (iff #3678 #4583)
+#4581 := (iff #3672 #4580)
+#4578 := (iff #3667 #4577)
+#4575 := (iff #3666 #4574)
+#4572 := (iff #3665 #4571)
+#4569 := (iff #3659 #4568)
 #4566 := (iff #3654 #4565)
-#4563 := (iff #3649 #4562)
-#4560 := (iff #3648 #4559)
-#4557 := (iff #3647 #4556)
+#4563 := (iff #3653 #4562)
+#4560 := (iff #3652 #4559)
+#4557 := (iff #3645 #4556)
 #4554 := (iff #3640 #4553)
-#4551 := (iff #3635 #4550)
-#4548 := (iff #3634 #4547)
-#4545 := (iff #3633 #4544)
-#4542 := (iff #3623 #4541)
-#4539 := (iff #3618 #4538)
-#4536 := (iff #3617 #4535)
-#4533 := (iff #3616 #4532)
-#4530 := (iff #3608 #4529)
-#4527 := (iff #3603 #4526)
-#4524 := (iff #3602 #4523)
-#4521 := (iff #3601 #4520)
-#4518 := (iff #3595 #4517)
-#4515 := (iff #3590 #4514)
-#4512 := (iff #3589 #4511)
-#4509 := (iff #3588 #4508)
-#4506 := (iff #3582 #4505)
-#4503 := (iff #3577 #4502)
-#4500 := (iff #3576 #4499)
-#4497 := (iff #3575 #4496)
-#4494 := (iff #3569 #4493)
-#4491 := (iff #3564 #4490)
-#4488 := (iff #3563 #4487)
-#4485 := (iff #3562 #4484)
-#4482 := (iff #3556 #4481)
-#4479 := (iff #3551 #4478)
-#4476 := (iff #3550 #4475)
-#4473 := (iff #3549 #4472)
+#4551 := (iff #3639 #4550)
+#4548 := (iff #3638 #4547)
+#4545 := (iff #3631 #4544)
+#4542 := (iff #3626 #4541)
+#4539 := (iff #3625 #4538)
+#4536 := (iff #3624 #4535)
+#4533 := (iff #3614 #4532)
+#4530 := (iff #3609 #4529)
+#4527 := (iff #3608 #4526)
+#4524 := (iff #3607 #4523)
+#4521 := (iff #3599 #4520)
+#4518 := (iff #3594 #4517)
+#4515 := (iff #3593 #4514)
+#4512 := (iff #3592 #4511)
+#4509 := (iff #3586 #4508)
+#4506 := (iff #3581 #4505)
+#4503 := (iff #3580 #4502)
+#4500 := (iff #3579 #4499)
+#4497 := (iff #3573 #4496)
+#4494 := (iff #3568 #4493)
+#4491 := (iff #3567 #4490)
+#4488 := (iff #3566 #4487)
+#4485 := (iff #3560 #4484)
+#4482 := (iff #3555 #4481)
+#4479 := (iff #3554 #4478)
+#4476 := (iff #3553 #4475)
+#4473 := (iff #3547 #4472)
 #4470 := (iff #3542 #4469)
-#4467 := (iff #3537 #4466)
-#4464 := (iff #3536 #4463)
-#4461 := (iff #3535 #4460)
-#4458 := (iff #3528 #4455)
-#4456 := (iff #3517 #3517)
-#4457 := [refl]: #4456
-#4459 := [quant-intro #4457]: #4458
-#4462 := [monotonicity #4459]: #4461
-#4452 := (iff #3534 #4451)
-#4449 := (iff #3513 #4446)
+#4467 := (iff #3541 #4466)
+#4464 := (iff #3540 #4463)
+#4461 := (iff #3533 #4460)
+#4458 := (iff #3528 #4457)
+#4455 := (iff #3527 #4454)
+#4452 := (iff #3526 #4451)
+#4449 := (iff #3519 #4446)
 #4447 := (iff #3508 #3508)
 #4448 := [refl]: #4447
 #4450 := [quant-intro #4448]: #4449
 #4453 := [monotonicity #4450]: #4452
-#4465 := [monotonicity #4453 #4462]: #4464
-#4468 := [monotonicity #4465]: #4467
-#4471 := [monotonicity #4468]: #4470
-#4474 := [monotonicity #4471]: #4473
-#4444 := (iff #3548 #4443)
-#4441 := (iff #3468 #4438)
-#4439 := (iff #3463 #3463)
-#4440 := [refl]: #4439
-#4442 := [quant-intro #4440]: #4441
-#4445 := [monotonicity #4442]: #4444
-#4477 := [monotonicity #4445 #4474]: #4476
-#4480 := [monotonicity #4477]: #4479
-#4483 := [monotonicity #4480]: #4482
-#4486 := [monotonicity #4483]: #4485
-#4435 := (iff #1499 #4434)
-#4432 := (iff #1496 #4429)
-#4430 := (iff #1493 #1493)
+#4443 := (iff #3525 #4442)
+#4440 := (iff #3504 #4437)
+#4438 := (iff #3499 #3499)
+#4439 := [refl]: #4438
+#4441 := [quant-intro #4439]: #4440
+#4444 := [monotonicity #4441]: #4443
+#4456 := [monotonicity #4444 #4453]: #4455
+#4459 := [monotonicity #4456]: #4458
+#4462 := [monotonicity #4459]: #4461
+#4465 := [monotonicity #4462]: #4464
+#4435 := (iff #3539 #4434)
+#4432 := (iff #3459 #4429)
+#4430 := (iff #3454 #3454)
 #4431 := [refl]: #4430
 #4433 := [quant-intro #4431]: #4432
 #4436 := [monotonicity #4433]: #4435
-#4489 := [monotonicity #4436 #4486]: #4488
+#4468 := [monotonicity #4436 #4465]: #4467
+#4471 := [monotonicity #4468]: #4470
+#4474 := [monotonicity #4471]: #4473
+#4477 := [monotonicity #4474]: #4476
+#4426 := (iff #1490 #4425)
+#4423 := (iff #1487 #4420)
+#4421 := (iff #1484 #1484)
+#4422 := [refl]: #4421
+#4424 := [quant-intro #4422]: #4423
+#4427 := [monotonicity #4424]: #4426
+#4480 := [monotonicity #4427 #4477]: #4479
+#4483 := [monotonicity #4480]: #4482
+#4486 := [monotonicity #4483]: #4485
+#4489 := [monotonicity #4486]: #4488
 #4492 := [monotonicity #4489]: #4491
 #4495 := [monotonicity #4492]: #4494
 #4498 := [monotonicity #4495]: #4497
 #4501 := [monotonicity #4498]: #4500
-#4504 := [monotonicity #4501]: #4503
-#4507 := [monotonicity #4504]: #4506
-#4510 := [monotonicity #4507]: #4509
-#4427 := (iff #953 #4426)
-#4424 := (iff #819 #4421)
-#4422 := (iff #814 #814)
-#4423 := [refl]: #4422
-#4425 := [quant-intro #4423]: #4424
-#4428 := [monotonicity #4425]: #4427
-#4513 := [monotonicity #4428 #4510]: #4512
-#4516 := [monotonicity #4513]: #4515
-#4519 := [monotonicity #4516]: #4518
-#4522 := [monotonicity #4519]: #4521
-#4418 := (iff #1485 #4417)
-#4415 := (iff #1482 #4412)
-#4413 := (iff #1477 #1477)
+#4418 := (iff #944 #4417)
+#4415 := (iff #810 #4412)
+#4413 := (iff #805 #805)
 #4414 := [refl]: #4413
 #4416 := [quant-intro #4414]: #4415
 #4419 := [monotonicity #4416]: #4418
-#4525 := [monotonicity #4419 #4522]: #4524
-#4528 := [monotonicity #4525]: #4527
+#4504 := [monotonicity #4419 #4501]: #4503
+#4507 := [monotonicity #4504]: #4506
+#4510 := [monotonicity #4507]: #4509
+#4513 := [monotonicity #4510]: #4512
+#4409 := (iff #1476 #4408)
+#4406 := (iff #1473 #4403)
+#4404 := (iff #1468 #1468)
+#4405 := [refl]: #4404
+#4407 := [quant-intro #4405]: #4406
+#4410 := [monotonicity #4407]: #4409
+#4516 := [monotonicity #4410 #4513]: #4515
+#4519 := [monotonicity #4516]: #4518
+#4522 := [monotonicity #4519]: #4521
+#4525 := [monotonicity #4522]: #4524
+#4401 := (iff #3606 #4400)
+#4398 := (iff #3413 #4395)
+#4396 := (iff #3408 #3408)
+#4397 := [refl]: #4396
+#4399 := [quant-intro #4397]: #4398
+#4402 := [monotonicity #4399]: #4401
+#4393 := (iff #3605 #4392)
+#4390 := (iff #3395 #4387)
+#4388 := (iff #3392 #3392)
+#4389 := [refl]: #4388
+#4391 := [quant-intro #4389]: #4390
+#4394 := [monotonicity #4391]: #4393
+#4383 := (iff #1641 #4382)
+#4380 := (iff #1638 #4377)
+#4378 := (iff #1633 #1633)
+#4379 := [refl]: #4378
+#4381 := [quant-intro #4379]: #4380
+#4384 := [monotonicity #4381]: #4383
+#4528 := [monotonicity #4384 #4394 #4402 #4525]: #4527
 #4531 := [monotonicity #4528]: #4530
-#4534 := [monotonicity #4531]: #4533
-#4410 := (iff #3615 #4409)
-#4407 := (iff #3422 #4404)
-#4405 := (iff #3417 #3417)
-#4406 := [refl]: #4405
-#4408 := [quant-intro #4406]: #4407
-#4411 := [monotonicity #4408]: #4410
-#4402 := (iff #3614 #4401)
-#4399 := (iff #3404 #4396)
-#4397 := (iff #3401 #3401)
-#4398 := [refl]: #4397
-#4400 := [quant-intro #4398]: #4399
-#4403 := [monotonicity #4400]: #4402
-#4392 := (iff #1650 #4391)
-#4389 := (iff #1647 #4386)
-#4387 := (iff #1642 #1642)
-#4388 := [refl]: #4387
-#4390 := [quant-intro #4388]: #4389
-#4393 := [monotonicity #4390]: #4392
-#4537 := [monotonicity #4393 #4403 #4411 #4534]: #4536
-#4540 := [monotonicity #4537]: #4539
-#4384 := (iff #3392 #4383)
-#4381 := (iff #3391 #4380)
-#4378 := (iff #3390 #4377)
 #4375 := (iff #3383 #4374)
-#4372 := (iff #3378 #4371)
-#4369 := (iff #3377 #4368)
-#4366 := (iff #3376 #4365)
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 #4363 := (iff #3369 #4362)
-#4360 := (iff #3342 #4359)
-#4357 := (iff #3341 #4356)
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-#4351 := (iff #3334 #4348)
-#4349 := (iff #3329 #3329)
-#4350 := [refl]: #4349
-#4352 := [quant-intro #4350]: #4351
+#4360 := (iff #3368 #4359)
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+#4340 := (iff #3320 #3320)
+#4341 := [refl]: #4340
+#4343 := [quant-intro #4341]: #4342
+#4346 := [monotonicity #4343]: #4345
+#4349 := [monotonicity #4346]: #4348
+#4352 := [monotonicity #4349]: #4351
 #4355 := [monotonicity #4352]: #4354
 #4358 := [monotonicity #4355]: #4357
-#4361 := [monotonicity #4358]: #4360
+#4337 := (iff #3366 #4336)
+#4334 := (iff #3303 #4331)
+#4332 := (iff #3298 #3298)
+#4333 := [refl]: #4332
+#4335 := [quant-intro #4333]: #4334
+#4338 := [monotonicity #4335]: #4337
+#4361 := [monotonicity #4338 #4358]: #4360
 #4364 := [monotonicity #4361]: #4363
-#4367 := [monotonicity #4364]: #4366
-#4346 := (iff #3375 #4345)
-#4343 := (iff #3312 #4340)
-#4341 := (iff #3307 #3307)
-#4342 := [refl]: #4341
-#4344 := [quant-intro #4342]: #4343
-#4347 := [monotonicity #4344]: #4346
-#4370 := [monotonicity #4347 #4367]: #4369
-#4373 := [monotonicity #4370]: #4372
-#4338 := (iff #3283 #4337)
-#4335 := (iff #3282 #4334)
-#4332 := (iff #3281 #4331)
-#4329 := (iff #3275 #4326)
-#4327 := (iff #3264 #3264)
-#4328 := [refl]: #4327
-#4330 := [quant-intro #4328]: #4329
-#4333 := [monotonicity #4330]: #4332
-#4336 := [monotonicity #4333]: #4335
-#4339 := [monotonicity #4336]: #4338
-#4376 := [monotonicity #4339 #4373]: #4375
-#4379 := [monotonicity #4376]: #4378
-#4322 := (iff #3389 #4321)
-#4319 := (iff #3260 #4316)
-#4317 := (iff #3249 #3249)
-#4318 := [refl]: #4317
-#4320 := [quant-intro #4318]: #4319
-#4323 := [monotonicity #4320]: #4322
-#4382 := [monotonicity #4323 #4379]: #4381
-#4385 := [monotonicity #4382]: #4384
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-#4308 := (iff #3241 #3241)
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 #4309 := [refl]: #4308
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-#4300 := (iff #3213 #3213)
-#4301 := [refl]: #4300
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-#4285 := (iff #3167 #4282)
-#4283 := (iff #3162 #3162)
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 #4284 := [refl]: #4283
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 #4272 := [monotonicity #4269]: #4271
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 #4243 := [refl]: #4242
 #4245 := [quant-intro #4243]: #4244
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 #4234 := [refl]: #4233
 #4236 := [quant-intro #4234]: #4235
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 #4588 := [monotonicity #4585]: #4587
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 #4594 := [monotonicity #4591]: #4593
-#4597 := [monotonicity #4594]: #4596
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-#3507 := [monotonicity #3504]: #3506
-#3512 := [trans #3507 #3510]: #3511
-#3515 := [quant-intro #3512]: #3514
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+#2826 := (and #136 #141 #620 #623 #2185 #2820)
+#3009 := (or #2826 #3004)
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+#2678 := (and #2040 #2658 #2675)
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+#2620 := (not #2615)
+#2638 := (and #2013 #2620 #2633)
+#2641 := (or #1259 #2638)
+#2644 := (forall (vars (?v0 S3)) #2641)
+#3015 := (and #100 #1705 #1721 #1730 #2644 #2684 #3009)
+#1968 := (not #1967)
+#2588 := (and #453 #1968 #2585)
+#2591 := (not #2588)
+#2594 := (forall (vars (?v1 S3)) #2591)
+#2560 := (not #2557)
+#1973 := (not #1972)
+#2600 := (and #1973 #2560 #2594)
+#3020 := (or #2600 #3015)
+#3023 := (and #1244 #3020)
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+#2545 := (and #1934 #1936)
+#2548 := (not #2545)
+#2551 := (or #2542 #2548)
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+#3026 := (or #2554 #3023)
+#3029 := (and #1213 #3026)
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+#2516 := (not #2513)
+#2532 := (or #2516 #2527)
+#2535 := (not #2532)
+#3032 := (or #2535 #3029)
+#3035 := (and #1193 #3032)
+#3038 := (or #1888 #3035)
+#3041 := (and #71 #3038)
+#3044 := (or #1187 #3041)
+#3686 := (iff #3044 #3685)
+#3683 := (iff #3041 #3680)
+#3675 := (and #71 #3672)
+#3681 := (iff #3675 #3680)
+#3682 := [rewrite]: #3681
+#3676 := (iff #3041 #3675)
+#3673 := (iff #3038 #3672)
+#3670 := (iff #3035 #3667)
+#3662 := (and #1193 #3659)
+#3668 := (iff #3662 #3667)
+#3669 := [rewrite]: #3668
+#3663 := (iff #3035 #3662)
+#3660 := (iff #3032 #3659)
+#3657 := (iff #3029 #3654)
+#3648 := (and #3066 #3645)
+#3655 := (iff #3648 #3654)
+#3656 := [rewrite]: #3655
+#3649 := (iff #3029 #3648)
+#3646 := (iff #3026 #3645)
+#3643 := (iff #3023 #3640)
+#3634 := (and #3111 #3631)
+#3641 := (iff #3634 #3640)
+#3642 := [rewrite]: #3641
+#3635 := (iff #3023 #3634)
+#3632 := (iff #3020 #3631)
+#3629 := (iff #3015 #3626)
+#3617 := (and #100 #3158 #3181 #1730 #3209 #3237 #3614)
+#3627 := (iff #3617 #3626)
+#3628 := [rewrite]: #3627
+#3618 := (iff #3015 #3617)
+#3615 := (iff #3009 #3614)
+#3612 := (iff #3004 #3609)
+#3602 := (and #181 #756 #3395 #3413 #1638 #1646 #2202 #2205 #3599)
+#3610 := (iff #3602 #3609)
+#3611 := [rewrite]: #3610
+#3603 := (iff #3004 #3602)
+#3600 := (iff #2998 #3599)
+#3597 := (iff #2995 #3594)
+#3589 := (and #1473 #3586)
+#3595 := (iff #3589 #3594)
+#3596 := [rewrite]: #3595
+#3590 := (iff #2995 #3589)
+#3587 := (iff #2992 #3586)
+#3584 := (iff #2989 #3581)
+#3576 := (and #810 #3573)
+#3582 := (iff #3576 #3581)
+#3583 := [rewrite]: #3582
+#3577 := (iff #2989 #3576)
+#3574 := (iff #2986 #3573)
+#3571 := (iff #2983 #3568)
+#3563 := (and #203 #3560)
+#3569 := (iff #3563 #3568)
+#3570 := [rewrite]: #3569
+#3564 := (iff #2983 #3563)
+#3561 := (iff #2980 #3560)
+#3558 := (iff #2977 #3555)
+#3550 := (and #1487 #3547)
+#3556 := (iff #3550 #3555)
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+#3548 := (iff #2974 #3547)
+#3545 := (iff #2971 #3542)
+#3536 := (and #3459 #3533)
+#3543 := (iff #3536 #3542)
+#3544 := [rewrite]: #3543
+#3537 := (iff #2971 #3536)
+#3534 := (iff #2968 #3533)
+#3531 := (iff #2963 #3528)
+#3522 := (and #3504 #2351 #2920 #3519)
+#3529 := (iff #3522 #3528)
+#3530 := [rewrite]: #3529
+#3523 := (iff #2963 #3522)
+#3520 := (iff #2954 #3519)
+#3517 := (iff #2951 #3508)
+#3509 := (not #3508)
+#3512 := (not #3509)
+#3515 := (iff #3512 #3508)
+#3516 := [rewrite]: #3515
+#3513 := (iff #2951 #3512)
+#3510 := (iff #2948 #3509)
+#3511 := [rewrite]: #3510
+#3514 := [monotonicity #3511]: #3513
+#3518 := [trans #3514 #3516]: #3517
+#3521 := [quant-intro #3518]: #3520
+#3505 := (iff #1530 #3504)
+#3502 := (iff #1527 #3499)
+#3485 := (or #804 #1226)
+#3496 := (or #3485 #1523)
+#3500 := (iff #3496 #3499)
+#3501 := [rewrite]: #3500
+#3497 := (iff #1527 #3496)
+#3494 := (iff #1520 #3485)
+#3486 := (not #3485)
+#3489 := (not #3486)
+#3492 := (iff #3489 #3485)
+#3493 := [rewrite]: #3492
+#3490 := (iff #1520 #3489)
+#3487 := (iff #1515 #3486)
 #3488 := [rewrite]: #3487
-#3484 := (iff #2920 #3483)
-#3481 := (iff #2902 #3472)
-#3473 := (not #3472)
-#3476 := (not #3473)
-#3479 := (iff #3476 #3472)
-#3480 := [rewrite]: #3479
-#3477 := (iff #2902 #3476)
-#3474 := (iff #2899 #3473)
-#3475 := [rewrite]: #3474
-#3478 := [monotonicity #3475]: #3477
-#3482 := [trans #3478 #3480]: #3481
-#3485 := [monotonicity #3482]: #3484
-#3490 := [trans #3485 #3488]: #3489
-#3493 := [monotonicity #3490]: #3492
-#3544 := [monotonicity #3493 #3541]: #3543
-#3469 := (iff #1515 #3468)
-#3466 := (iff #1510 #3463)
-#3449 := (or #807 #3448)
-#3460 := (or #3449 #1502)
-#3464 := (iff #3460 #3463)
-#3465 := [rewrite]: #3464
-#3461 := (iff #1510 #3460)
-#3458 := (iff #836 #3449)
-#3450 := (not #3449)
-#3453 := (not #3450)
-#3456 := (iff #3453 #3449)
-#3457 := [rewrite]: #3456
-#3454 := (iff #836 #3453)
-#3451 := (iff #830 #3450)
-#3452 := [rewrite]: #3451
-#3455 := [monotonicity #3452]: #3454
-#3459 := [trans #3455 #3457]: #3458
-#3462 := [monotonicity #3459]: #3461
-#3467 := [trans #3462 #3465]: #3466
-#3470 := [quant-intro #3467]: #3469
-#3547 := [monotonicity #3470 #3544]: #3546
-#3555 := [trans #3547 #3553]: #3554
-#3446 := (iff #2896 #3445)
-#3443 := (iff #2893 #3440)
-#3426 := (or #3425 #2298)
-#3437 := (or #3426 #2888)
-#3441 := (iff #3437 #3440)
-#3442 := [rewrite]: #3441
-#3438 := (iff #2893 #3437)
-#3435 := (iff #2877 #3426)
-#3427 := (not #3426)
-#3430 := (not #3427)
-#3433 := (iff #3430 #3426)
-#3434 := [rewrite]: #3433
-#3431 := (iff #2877 #3430)
-#3428 := (iff #2874 #3427)
-#3429 := [rewrite]: #3428
-#3432 := [monotonicity #3429]: #3431
-#3436 := [trans #3432 #3434]: #3435
-#3439 := [monotonicity #3436]: #3438
-#3444 := [trans #3439 #3442]: #3443
-#3447 := [monotonicity #3444]: #3446
-#3558 := [monotonicity #3447 #3555]: #3557
-#3561 := [monotonicity #3558]: #3560
-#3568 := [trans #3561 #3566]: #3567
-#3571 := [monotonicity #3568]: #3570
-#3574 := [monotonicity #3571]: #3573
-#3581 := [trans #3574 #3579]: #3580
-#3584 := [monotonicity #3581]: #3583
-#3587 := [monotonicity #3584]: #3586
-#3594 := [trans #3587 #3592]: #3593
-#3597 := [monotonicity #3594]: #3596
-#3600 := [monotonicity #3597]: #3599
-#3607 := [trans #3600 #3605]: #3606
-#3610 := [monotonicity #3607]: #3609
-#3423 := (iff #1629 #3422)
-#3420 := (iff #1626 #3417)
-#3414 := (or #3397 #1623)
-#3418 := (iff #3414 #3417)
-#3419 := [rewrite]: #3418
-#3415 := (iff #1626 #3414)
-#3412 := (iff #1618 #3397)
-#3407 := (not #3398)
-#3410 := (iff #3407 #3397)
-#3411 := [rewrite]: #3410
-#3408 := (iff #1618 #3407)
-#3399 := (iff #1460 #3398)
-#3400 := [rewrite]: #3399
-#3409 := [monotonicity #3400]: #3408
-#3413 := [trans #3409 #3411]: #3412
-#3416 := [monotonicity #3413]: #3415
-#3421 := [trans #3416 #3419]: #3420
-#3424 := [quant-intro #3421]: #3423
-#3405 := (iff #1471 #3404)
-#3402 := (iff #1466 #3401)
-#3403 := [monotonicity #3400]: #3402
-#3406 := [quant-intro #3403]: #3405
-#3613 := [monotonicity #3406 #3424 #3610]: #3612
-#3622 := [trans #3613 #3620]: #3621
-#3395 := (iff #2835 #3392)
-#3386 := (and #136 #141 #621 #624 #3260 #3383)
-#3393 := (iff #3386 #3392)
-#3394 := [rewrite]: #3393
-#3387 := (iff #2835 #3386)
-#3384 := (iff #2829 #3383)
-#3381 := (iff #2826 #3378)
-#3372 := (and #3312 #3369)
-#3379 := (iff #3372 #3378)
-#3380 := [rewrite]: #3379
-#3373 := (iff #2826 #3372)
-#3370 := (iff #2821 #3369)
-#3367 := (iff #2815 #3366)
-#3364 := (iff #2812 #3361)
-#3347 := (or #2151 #2155)
-#3358 := (or #3347 #2807)
-#3362 := (iff #3358 #3361)
-#3363 := [rewrite]: #3362
-#3359 := (iff #2812 #3358)
-#3356 := (iff #2795 #3347)
-#3348 := (not #3347)
-#3351 := (not #3348)
-#3354 := (iff #3351 #3347)
-#3355 := [rewrite]: #3354
-#3352 := (iff #2795 #3351)
-#3349 := (iff #2792 #3348)
-#3350 := [rewrite]: #3349
-#3353 := [monotonicity #3350]: #3352
-#3357 := [trans #3353 #3355]: #3356
-#3360 := [monotonicity #3357]: #3359
-#3365 := [trans #3360 #3363]: #3364
-#3368 := [monotonicity #3365]: #3367
-#3345 := (iff #2175 #3342)
-#3337 := (and #2165 #3334)
-#3343 := (iff #3337 #3342)
-#3344 := [rewrite]: #3343
-#3338 := (iff #2175 #3337)
-#3335 := (iff #1391 #3334)
-#3332 := (iff #1388 #3329)
-#3315 := (or #1235 #1344)
-#3326 := (or #3315 #1385)
-#3330 := (iff #3326 #3329)
-#3331 := [rewrite]: #3330
-#3327 := (iff #1388 #3326)
-#3324 := (iff #1382 #3315)
-#3316 := (not #3315)
-#3319 := (not #3316)
-#3322 := (iff #3319 #3315)
-#3323 := [rewrite]: #3322
-#3320 := (iff #1382 #3319)
-#3317 := (iff #1379 #3316)
-#3318 := [rewrite]: #3317
-#3321 := [monotonicity #3318]: #3320
-#3325 := [trans #3321 #3323]: #3324
-#3328 := [monotonicity #3325]: #3327
-#3333 := [trans #3328 #3331]: #3332
-#3336 := [quant-intro #3333]: #3335
-#3339 := [monotonicity #3336]: #3338
-#3346 := [trans #3339 #3344]: #3345
-#3371 := [monotonicity #3346 #3368]: #3370
-#3313 := (iff #2789 #3312)
-#3310 := (iff #2786 #3307)
-#3288 := (or #57 #1344)
-#3304 := (or #3288 #3301)
-#3308 := (iff #3304 #3307)
+#3491 := [monotonicity #3488]: #3490
+#3495 := [trans #3491 #3493]: #3494
+#3498 := [monotonicity #3495]: #3497
+#3503 := [trans #3498 #3501]: #3502
+#3506 := [quant-intro #3503]: #3505
+#3524 := [monotonicity #3506 #3521]: #3523
+#3532 := [trans #3524 #3530]: #3531
+#3483 := (iff #2914 #3482)
+#3480 := (iff #2911 #3477)
+#3463 := (or #2318 #3462)
+#3474 := (or #3463 #2906)
+#3478 := (iff #3474 #3477)
+#3479 := [rewrite]: #3478
+#3475 := (iff #2911 #3474)
+#3472 := (iff #2893 #3463)
+#3464 := (not #3463)
+#3467 := (not #3464)
+#3470 := (iff #3467 #3463)
+#3471 := [rewrite]: #3470
+#3468 := (iff #2893 #3467)
+#3465 := (iff #2890 #3464)
+#3466 := [rewrite]: #3465
+#3469 := [monotonicity #3466]: #3468
+#3473 := [trans #3469 #3471]: #3472
+#3476 := [monotonicity #3473]: #3475
+#3481 := [trans #3476 #3479]: #3480
+#3484 := [monotonicity #3481]: #3483
+#3535 := [monotonicity #3484 #3532]: #3534
+#3460 := (iff #1506 #3459)
+#3457 := (iff #1501 #3454)
+#3440 := (or #798 #3439)
+#3451 := (or #3440 #1493)
+#3455 := (iff #3451 #3454)
+#3456 := [rewrite]: #3455
+#3452 := (iff #1501 #3451)
+#3449 := (iff #827 #3440)
+#3441 := (not #3440)
+#3444 := (not #3441)
+#3447 := (iff #3444 #3440)
+#3448 := [rewrite]: #3447
+#3445 := (iff #827 #3444)
+#3442 := (iff #821 #3441)
+#3443 := [rewrite]: #3442
+#3446 := [monotonicity #3443]: #3445
+#3450 := [trans #3446 #3448]: #3449
+#3453 := [monotonicity #3450]: #3452
+#3458 := [trans #3453 #3456]: #3457
+#3461 := [quant-intro #3458]: #3460
+#3538 := [monotonicity #3461 #3535]: #3537
+#3546 := [trans #3538 #3544]: #3545
+#3437 := (iff #2887 #3436)
+#3434 := (iff #2884 #3431)
+#3417 := (or #3416 #2289)
+#3428 := (or #3417 #2879)
+#3432 := (iff #3428 #3431)
+#3433 := [rewrite]: #3432
+#3429 := (iff #2884 #3428)
+#3426 := (iff #2868 #3417)
+#3418 := (not #3417)
+#3421 := (not #3418)
+#3424 := (iff #3421 #3417)
+#3425 := [rewrite]: #3424
+#3422 := (iff #2868 #3421)
+#3419 := (iff #2865 #3418)
+#3420 := [rewrite]: #3419
+#3423 := [monotonicity #3420]: #3422
+#3427 := [trans #3423 #3425]: #3426
+#3430 := [monotonicity #3427]: #3429
+#3435 := [trans #3430 #3433]: #3434
+#3438 := [monotonicity #3435]: #3437
+#3549 := [monotonicity #3438 #3546]: #3548
+#3552 := [monotonicity #3549]: #3551
+#3559 := [trans #3552 #3557]: #3558
+#3562 := [monotonicity #3559]: #3561
+#3565 := [monotonicity #3562]: #3564
+#3572 := [trans #3565 #3570]: #3571
+#3575 := [monotonicity #3572]: #3574
+#3578 := [monotonicity #3575]: #3577
+#3585 := [trans #3578 #3583]: #3584
+#3588 := [monotonicity #3585]: #3587
+#3591 := [monotonicity #3588]: #3590
+#3598 := [trans #3591 #3596]: #3597
+#3601 := [monotonicity #3598]: #3600
+#3414 := (iff #1620 #3413)
+#3411 := (iff #1617 #3408)
+#3405 := (or #3388 #1614)
+#3409 := (iff #3405 #3408)
+#3410 := [rewrite]: #3409
+#3406 := (iff #1617 #3405)
+#3403 := (iff #1609 #3388)
+#3398 := (not #3389)
+#3401 := (iff #3398 #3388)
+#3402 := [rewrite]: #3401
+#3399 := (iff #1609 #3398)
+#3390 := (iff #1451 #3389)
+#3391 := [rewrite]: #3390
+#3400 := [monotonicity #3391]: #3399
+#3404 := [trans #3400 #3402]: #3403
+#3407 := [monotonicity #3404]: #3406
+#3412 := [trans #3407 #3410]: #3411
+#3415 := [quant-intro #3412]: #3414
+#3396 := (iff #1462 #3395)
+#3393 := (iff #1457 #3392)
+#3394 := [monotonicity #3391]: #3393
+#3397 := [quant-intro #3394]: #3396
+#3604 := [monotonicity #3397 #3415 #3601]: #3603
+#3613 := [trans #3604 #3611]: #3612
+#3386 := (iff #2826 #3383)
+#3377 := (and #136 #141 #620 #623 #3251 #3374)
+#3384 := (iff #3377 #3383)
+#3385 := [rewrite]: #3384
+#3378 := (iff #2826 #3377)
+#3375 := (iff #2820 #3374)
+#3372 := (iff #2817 #3369)
+#3363 := (and #3303 #3360)
+#3370 := (iff #3363 #3369)
+#3371 := [rewrite]: #3370
+#3364 := (iff #2817 #3363)
+#3361 := (iff #2812 #3360)
+#3358 := (iff #2806 #3357)
+#3355 := (iff #2803 #3352)
+#3338 := (or #2142 #2146)
+#3349 := (or #3338 #2798)
+#3353 := (iff #3349 #3352)
+#3354 := [rewrite]: #3353
+#3350 := (iff #2803 #3349)
+#3347 := (iff #2786 #3338)
+#3339 := (not #3338)
+#3342 := (not #3339)
+#3345 := (iff #3342 #3338)
+#3346 := [rewrite]: #3345
+#3343 := (iff #2786 #3342)
+#3340 := (iff #2783 #3339)
+#3341 := [rewrite]: #3340
+#3344 := [monotonicity #3341]: #3343
+#3348 := [trans #3344 #3346]: #3347
+#3351 := [monotonicity #3348]: #3350
+#3356 := [trans #3351 #3354]: #3355
+#3359 := [monotonicity #3356]: #3358
+#3336 := (iff #2166 #3333)
+#3328 := (and #2156 #3325)
+#3334 := (iff #3328 #3333)
+#3335 := [rewrite]: #3334
+#3329 := (iff #2166 #3328)
+#3326 := (iff #1382 #3325)
+#3323 := (iff #1379 #3320)
+#3306 := (or #1226 #1335)
+#3317 := (or #3306 #1376)
+#3321 := (iff #3317 #3320)
+#3322 := [rewrite]: #3321
+#3318 := (iff #1379 #3317)
+#3315 := (iff #1373 #3306)
+#3307 := (not #3306)
+#3310 := (not #3307)
+#3313 := (iff #3310 #3306)
+#3314 := [rewrite]: #3313
+#3311 := (iff #1373 #3310)
+#3308 := (iff #1370 #3307)
 #3309 := [rewrite]: #3308
-#3305 := (iff #2786 #3304)
-#3302 := (iff #2783 #3301)
-#3303 := [rewrite]: #3302
-#3297 := (iff #1351 #3288)
-#3289 := (not #3288)
-#3292 := (not #3289)
-#3295 := (iff #3292 #3288)
-#3296 := [rewrite]: #3295
-#3293 := (iff #1351 #3292)
-#3290 := (iff #1348 #3289)
-#3291 := [rewrite]: #3290
-#3294 := [monotonicity #3291]: #3293
-#3298 := [trans #3294 #3296]: #3297
-#3306 := [monotonicity #3298 #3303]: #3305
-#3311 := [trans #3306 #3309]: #3310
-#3314 := [quant-intro #3311]: #3313
-#3374 := [monotonicity #3314 #3371]: #3373
-#3382 := [trans #3374 #3380]: #3381
-#3286 := (iff #2747 #3283)
-#3278 := (and #2090 #2707 #3275)
-#3284 := (iff #3278 #3283)
-#3285 := [rewrite]: #3284
-#3279 := (iff #2747 #3278)
-#3276 := (iff #2741 #3275)
-#3273 := (iff #2738 #3264)
-#3265 := (not #3264)
-#3268 := (not #3265)
-#3271 := (iff #3268 #3264)
-#3272 := [rewrite]: #3271
-#3269 := (iff #2738 #3268)
-#3266 := (iff #2735 #3265)
-#3267 := [rewrite]: #3266
-#3270 := [monotonicity #3267]: #3269
-#3274 := [trans #3270 #3272]: #3273
-#3277 := [quant-intro #3274]: #3276
-#3280 := [monotonicity #3277]: #3279
-#3287 := [trans #3280 #3285]: #3286
-#3385 := [monotonicity #3287 #3382]: #3384
-#3261 := (iff #2194 #3260)
-#3258 := (iff #2191 #3249)
-#3250 := (not #3249)
-#3253 := (not #3250)
-#3256 := (iff #3253 #3249)
-#3257 := [rewrite]: #3256
-#3254 := (iff #2191 #3253)
-#3251 := (iff #1419 #3250)
-#3252 := [rewrite]: #3251
-#3255 := [monotonicity #3252]: #3254
-#3259 := [trans #3255 #3257]: #3258
-#3262 := [quant-intro #3259]: #3261
-#3388 := [monotonicity #3262 #3385]: #3387
-#3396 := [trans #3388 #3394]: #3395
-#3625 := [monotonicity #3396 #3622]: #3624
-#3247 := (iff #2693 #3246)
-#3244 := (iff #2690 #3241)
-#3221 := (or #57 #1299)
-#3238 := (or #3221 #3235)
-#3242 := (iff #3238 #3241)
+#3312 := [monotonicity #3309]: #3311
+#3316 := [trans #3312 #3314]: #3315
+#3319 := [monotonicity #3316]: #3318
+#3324 := [trans #3319 #3322]: #3323
+#3327 := [quant-intro #3324]: #3326
+#3330 := [monotonicity #3327]: #3329
+#3337 := [trans #3330 #3335]: #3336
+#3362 := [monotonicity #3337 #3359]: #3361
+#3304 := (iff #2780 #3303)
+#3301 := (iff #2777 #3298)
+#3279 := (or #57 #1335)
+#3295 := (or #3279 #3292)
+#3299 := (iff #3295 #3298)
+#3300 := [rewrite]: #3299
+#3296 := (iff #2777 #3295)
+#3293 := (iff #2774 #3292)
+#3294 := [rewrite]: #3293
+#3288 := (iff #1342 #3279)
+#3280 := (not #3279)
+#3283 := (not #3280)
+#3286 := (iff #3283 #3279)
+#3287 := [rewrite]: #3286
+#3284 := (iff #1342 #3283)
+#3281 := (iff #1339 #3280)
+#3282 := [rewrite]: #3281
+#3285 := [monotonicity #3282]: #3284
+#3289 := [trans #3285 #3287]: #3288
+#3297 := [monotonicity #3289 #3294]: #3296
+#3302 := [trans #3297 #3300]: #3301
+#3305 := [quant-intro #3302]: #3304
+#3365 := [monotonicity #3305 #3362]: #3364
+#3373 := [trans #3365 #3371]: #3372
+#3277 := (iff #2738 #3274)
+#3269 := (and #2081 #2698 #3266)
+#3275 := (iff #3269 #3274)
+#3276 := [rewrite]: #3275
+#3270 := (iff #2738 #3269)
+#3267 := (iff #2732 #3266)
+#3264 := (iff #2729 #3255)
+#3256 := (not #3255)
+#3259 := (not #3256)
+#3262 := (iff #3259 #3255)
+#3263 := [rewrite]: #3262
+#3260 := (iff #2729 #3259)
+#3257 := (iff #2726 #3256)
+#3258 := [rewrite]: #3257
+#3261 := [monotonicity #3258]: #3260
+#3265 := [trans #3261 #3263]: #3264
+#3268 := [quant-intro #3265]: #3267
+#3271 := [monotonicity #3268]: #3270
+#3278 := [trans #3271 #3276]: #3277
+#3376 := [monotonicity #3278 #3373]: #3375
+#3252 := (iff #2185 #3251)
+#3249 := (iff #2182 #3240)
+#3241 := (not #3240)
+#3244 := (not #3241)
+#3247 := (iff #3244 #3240)
+#3248 := [rewrite]: #3247
+#3245 := (iff #2182 #3244)
+#3242 := (iff #1410 #3241)
 #3243 := [rewrite]: #3242
-#3239 := (iff #2690 #3238)
-#3236 := (iff #2687 #3235)
-#3237 := [rewrite]: #3236
-#3230 := (iff #1306 #3221)
-#3222 := (not #3221)
-#3225 := (not #3222)
-#3228 := (iff #3225 #3221)
-#3229 := [rewrite]: #3228
-#3226 := (iff #1306 #3225)
-#3223 := (iff #1303 #3222)
-#3224 := [rewrite]: #3223
-#3227 := [monotonicity #3224]: #3226
-#3231 := [trans #3227 #3229]: #3230
-#3240 := [monotonicity #3231 #3237]: #3239
-#3245 := [trans #3240 #3243]: #3244
-#3248 := [quant-intro #3245]: #3247
-#3219 := (iff #2653 #3218)
-#3216 := (iff #2650 #3213)
-#3193 := (or #57 #1261)
-#3210 := (or #3193 #3207)
-#3214 := (iff #3210 #3213)
+#3246 := [monotonicity #3243]: #3245
+#3250 := [trans #3246 #3248]: #3249
+#3253 := [quant-intro #3250]: #3252
+#3379 := [monotonicity #3253 #3376]: #3378
+#3387 := [trans #3379 #3385]: #3386
+#3616 := [monotonicity #3387 #3613]: #3615
+#3238 := (iff #2684 #3237)
+#3235 := (iff #2681 #3232)
+#3212 := (or #57 #1290)
+#3229 := (or #3212 #3226)
+#3233 := (iff #3229 #3232)
+#3234 := [rewrite]: #3233
+#3230 := (iff #2681 #3229)
+#3227 := (iff #2678 #3226)
+#3228 := [rewrite]: #3227
+#3221 := (iff #1297 #3212)
+#3213 := (not #3212)
+#3216 := (not #3213)
+#3219 := (iff #3216 #3212)
+#3220 := [rewrite]: #3219
+#3217 := (iff #1297 #3216)
+#3214 := (iff #1294 #3213)
 #3215 := [rewrite]: #3214
-#3211 := (iff #2650 #3210)
-#3208 := (iff #2647 #3207)
-#3209 := [rewrite]: #3208
-#3202 := (iff #1268 #3193)
-#3194 := (not #3193)
-#3197 := (not #3194)
-#3200 := (iff #3197 #3193)
-#3201 := [rewrite]: #3200
-#3198 := (iff #1268 #3197)
-#3195 := (iff #1265 #3194)
-#3196 := [rewrite]: #3195
-#3199 := [monotonicity #3196]: #3198
-#3203 := [trans #3199 #3201]: #3202
-#3212 := [monotonicity #3203 #3209]: #3211
-#3217 := [trans #3212 #3215]: #3216
-#3220 := [quant-intro #3217]: #3219
-#3191 := (iff #1730 #3190)
-#3188 := (iff #1725 #3185)
-#3171 := (or #533 #3170)
-#3182 := (or #3171 #1315)
-#3186 := (iff #3182 #3185)
+#3218 := [monotonicity #3215]: #3217
+#3222 := [trans #3218 #3220]: #3221
+#3231 := [monotonicity #3222 #3228]: #3230
+#3236 := [trans #3231 #3234]: #3235
+#3239 := [quant-intro #3236]: #3238
+#3210 := (iff #2644 #3209)
+#3207 := (iff #2641 #3204)
+#3184 := (or #57 #1252)
+#3201 := (or #3184 #3198)
+#3205 := (iff #3201 #3204)
+#3206 := [rewrite]: #3205
+#3202 := (iff #2641 #3201)
+#3199 := (iff #2638 #3198)
+#3200 := [rewrite]: #3199
+#3193 := (iff #1259 #3184)
+#3185 := (not #3184)
+#3188 := (not #3185)
+#3191 := (iff #3188 #3184)
+#3192 := [rewrite]: #3191
+#3189 := (iff #1259 #3188)
+#3186 := (iff #1256 #3185)
 #3187 := [rewrite]: #3186
-#3183 := (iff #1725 #3182)
-#3180 := (iff #548 #3171)
-#3172 := (not #3171)
-#3175 := (not #3172)
-#3178 := (iff #3175 #3171)
-#3179 := [rewrite]: #3178
-#3176 := (iff #548 #3175)
-#3173 := (iff #542 #3172)
-#3174 := [rewrite]: #3173
-#3177 := [monotonicity #3174]: #3176
-#3181 := [trans #3177 #3179]: #3180
-#3184 := [monotonicity #3181]: #3183
-#3189 := [trans #3184 #3187]: #3188
-#3192 := [quant-intro #3189]: #3191
-#3168 := (iff #1714 #3167)
-#3165 := (iff #1711 #3162)
-#3148 := (or #536 #1235)
-#3159 := (or #3148 #1708)
-#3163 := (iff #3159 #3162)
-#3164 := [rewrite]: #3163
-#3160 := (iff #1711 #3159)
-#3157 := (iff #1705 #3148)
-#3149 := (not #3148)
-#3152 := (not #3149)
-#3155 := (iff #3152 #3148)
-#3156 := [rewrite]: #3155
-#3153 := (iff #1705 #3152)
-#3150 := (iff #1700 #3149)
-#3151 := [rewrite]: #3150
-#3154 := [monotonicity #3151]: #3153
-#3158 := [trans #3154 #3156]: #3157
-#3161 := [monotonicity #3158]: #3160
-#3166 := [trans #3161 #3164]: #3165
-#3169 := [quant-intro #3166]: #3168
-#3628 := [monotonicity #3169 #3192 #3220 #3248 #3625]: #3627
-#3639 := [trans #3628 #3637]: #3638
-#3146 := (iff #2609 #3143)
-#3138 := (and #1982 #2569 #3135)
-#3144 := (iff #3138 #3143)
-#3145 := [rewrite]: #3144
-#3139 := (iff #2609 #3138)
-#3136 := (iff #2603 #3135)
-#3133 := (iff #2600 #3124)
-#3125 := (not #3124)
-#3128 := (not #3125)
-#3131 := (iff #3128 #3124)
-#3132 := [rewrite]: #3131
-#3129 := (iff #2600 #3128)
-#3126 := (iff #2597 #3125)
-#3127 := [rewrite]: #3126
-#3130 := [monotonicity #3127]: #3129
-#3134 := [trans #3130 #3132]: #3133
-#3137 := [quant-intro #3134]: #3136
-#3140 := [monotonicity #3137]: #3139
-#3147 := [trans #3140 #3145]: #3146
-#3642 := [monotonicity #3147 #3639]: #3641
-#3121 := (iff #1253 #3120)
-#3118 := (iff #1250 #3115)
-#3101 := (or #457 #1235)
-#3112 := (or #1230 #3101)
-#3116 := (iff #3112 #3115)
-#3117 := [rewrite]: #3116
-#3113 := (iff #1250 #3112)
-#3110 := (iff #1247 #3101)
-#3102 := (not #3101)
-#3105 := (not #3102)
-#3108 := (iff #3105 #3101)
-#3109 := [rewrite]: #3108
-#3106 := (iff #1247 #3105)
-#3103 := (iff #1242 #3102)
-#3104 := [rewrite]: #3103
-#3107 := [monotonicity #3104]: #3106
-#3111 := [trans #3107 #3109]: #3110
-#3114 := [monotonicity #3111]: #3113
-#3119 := [trans #3114 #3117]: #3118
-#3122 := [quant-intro #3119]: #3121
-#3645 := [monotonicity #3122 #3642]: #3644
-#3653 := [trans #3645 #3651]: #3652
-#3099 := (iff #2563 #3098)
-#3096 := (iff #2560 #3093)
-#3079 := (or #1942 #3078)
-#3090 := (or #2551 #3079)
-#3094 := (iff #3090 #3093)
+#3190 := [monotonicity #3187]: #3189
+#3194 := [trans #3190 #3192]: #3193
+#3203 := [monotonicity #3194 #3200]: #3202
+#3208 := [trans #3203 #3206]: #3207
+#3211 := [quant-intro #3208]: #3210
+#3182 := (iff #1721 #3181)
+#3179 := (iff #1716 #3176)
+#3162 := (or #532 #3161)
+#3173 := (or #3162 #1306)
+#3177 := (iff #3173 #3176)
+#3178 := [rewrite]: #3177
+#3174 := (iff #1716 #3173)
+#3171 := (iff #547 #3162)
+#3163 := (not #3162)
+#3166 := (not #3163)
+#3169 := (iff #3166 #3162)
+#3170 := [rewrite]: #3169
+#3167 := (iff #547 #3166)
+#3164 := (iff #541 #3163)
+#3165 := [rewrite]: #3164
+#3168 := [monotonicity #3165]: #3167
+#3172 := [trans #3168 #3170]: #3171
+#3175 := [monotonicity #3172]: #3174
+#3180 := [trans #3175 #3178]: #3179
+#3183 := [quant-intro #3180]: #3182
+#3159 := (iff #1705 #3158)
+#3156 := (iff #1702 #3153)
+#3139 := (or #535 #1226)
+#3150 := (or #3139 #1699)
+#3154 := (iff #3150 #3153)
+#3155 := [rewrite]: #3154
+#3151 := (iff #1702 #3150)
+#3148 := (iff #1696 #3139)
+#3140 := (not #3139)
+#3143 := (not #3140)
+#3146 := (iff #3143 #3139)
+#3147 := [rewrite]: #3146
+#3144 := (iff #1696 #3143)
+#3141 := (iff #1691 #3140)
+#3142 := [rewrite]: #3141
+#3145 := [monotonicity #3142]: #3144
+#3149 := [trans #3145 #3147]: #3148
+#3152 := [monotonicity #3149]: #3151
+#3157 := [trans #3152 #3155]: #3156
+#3160 := [quant-intro #3157]: #3159
+#3619 := [monotonicity #3160 #3183 #3211 #3239 #3616]: #3618
+#3630 := [trans #3619 #3628]: #3629
+#3137 := (iff #2600 #3134)
+#3129 := (and #1973 #2560 #3126)
+#3135 := (iff #3129 #3134)
+#3136 := [rewrite]: #3135
+#3130 := (iff #2600 #3129)
+#3127 := (iff #2594 #3126)
+#3124 := (iff #2591 #3115)
+#3116 := (not #3115)
+#3119 := (not #3116)
+#3122 := (iff #3119 #3115)
+#3123 := [rewrite]: #3122
+#3120 := (iff #2591 #3119)
+#3117 := (iff #2588 #3116)
+#3118 := [rewrite]: #3117
+#3121 := [monotonicity #3118]: #3120
+#3125 := [trans #3121 #3123]: #3124
+#3128 := [quant-intro #3125]: #3127
+#3131 := [monotonicity #3128]: #3130
+#3138 := [trans #3131 #3136]: #3137
+#3633 := [monotonicity #3138 #3630]: #3632
+#3112 := (iff #1244 #3111)
+#3109 := (iff #1241 #3106)
+#3092 := (or #456 #1226)
+#3103 := (or #1221 #3092)
+#3107 := (iff #3103 #3106)
+#3108 := [rewrite]: #3107
+#3104 := (iff #1241 #3103)
+#3101 := (iff #1238 #3092)
+#3093 := (not #3092)
+#3096 := (not #3093)
+#3099 := (iff #3096 #3092)
+#3100 := [rewrite]: #3099
+#3097 := (iff #1238 #3096)
+#3094 := (iff #1233 #3093)
 #3095 := [rewrite]: #3094
-#3091 := (iff #2560 #3090)
-#3088 := (iff #2557 #3079)
-#3080 := (not #3079)
-#3083 := (not #3080)
-#3086 := (iff #3083 #3079)
-#3087 := [rewrite]: #3086
-#3084 := (iff #2557 #3083)
-#3081 := (iff #2554 #3080)
-#3082 := [rewrite]: #3081
-#3085 := [monotonicity #3082]: #3084
-#3089 := [trans #3085 #3087]: #3088
-#3092 := [monotonicity #3089]: #3091
-#3097 := [trans #3092 #3095]: #3096
-#3100 := [monotonicity #3097]: #3099
-#3656 := [monotonicity #3100 #3653]: #3655
-#3076 := (iff #1222 #3075)
-#3073 := (iff #1217 #3070)
-#3056 := (or #454 #2519)
-#3067 := (or #3056 #1210)
-#3071 := (iff #3067 #3070)
-#3072 := [rewrite]: #3071
-#3068 := (iff #1217 #3067)
-#3065 := (iff #475 #3056)
-#3057 := (not #3056)
-#3060 := (not #3057)
-#3063 := (iff #3060 #3056)
-#3064 := [rewrite]: #3063
-#3061 := (iff #475 #3060)
-#3058 := (iff #469 #3057)
-#3059 := [rewrite]: #3058
-#3062 := [monotonicity #3059]: #3061
-#3066 := [trans #3062 #3064]: #3065
-#3069 := [monotonicity #3066]: #3068
-#3074 := [trans #3069 #3072]: #3073
-#3077 := [quant-intro #3074]: #3076
-#3659 := [monotonicity #3077 #3656]: #3658
-#3667 := [trans #3659 #3665]: #3666
-#2218 := (iff #2544 #1928)
-#2280 := (iff #2541 #2026)
-#2239 := (or #2054 #1919)
-#2338 := (or #2239 #2536)
-#2027 := (iff #2338 #2026)
-#2279 := [rewrite]: #2027
-#2306 := (iff #2541 #2338)
-#2260 := (iff #2525 #2239)
-#1864 := (not #2239)
-#2128 := (not #1864)
-#2164 := (iff #2128 #2239)
-#2259 := [rewrite]: #2164
-#2129 := (iff #2525 #2128)
-#1865 := (iff #2522 #1864)
-#2240 := [rewrite]: #1865
-#2163 := [monotonicity #2240]: #2129
-#2337 := [trans #2163 #2259]: #2260
-#2307 := [monotonicity #2337]: #2306
-#1927 := [trans #2307 #2279]: #2280
-#2219 := [monotonicity #1927]: #2218
-#3670 := [monotonicity #2219 #3667]: #3669
-#3673 := [monotonicity #3670]: #3672
-#3680 := [trans #3673 #3678]: #3679
-#3683 := [monotonicity #3680]: #3682
-#3686 := [monotonicity #3683]: #3685
-#3693 := [trans #3686 #3691]: #3692
-#3696 := [monotonicity #3693]: #3695
-#2352 := (+ #2351 #2349)
-#2353 := (= #2352 0::Int)
-#2356 := (and #807 #2355 #2353)
-#2373 := (not #2356)
-#2376 := (forall (vars (?v1 S3)) #2373)
-#2361 := (= ?v0!20 f10)
-#2362 := (not #2361)
-#2363 := (and #2362 #2360)
-#2364 := (not #2363)
-#2370 := (not #2364)
-#2380 := (and #2370 #2376)
-#2385 := (and #1539 #2380)
-#2318 := (* -1::Int #2317)
-#2320 := (+ #2319 #2318)
-#2323 := (+ #2322 #2320)
-#2324 := (>= #2323 0::Int)
-#2331 := (and #2330 #2328)
-#2332 := (not #2331)
-#2333 := (or #2332 #2324)
-#2334 := (not #2333)
-#2389 := (or #2334 #2385)
-#2393 := (and #1515 #2389)
-#2291 := (* -1::Int #2290)
-#2293 := (+ #2292 #2291)
-#2294 := (>= #2293 0::Int)
-#2300 := (and #2299 #2296)
-#2301 := (not #2300)
-#2302 := (or #2301 #2294)
-#2303 := (not #2302)
-#2397 := (or #2303 #2393)
-#2401 := (and #1496 #2397)
-#2405 := (or #2276 #2401)
-#2270 := (not #1490)
-#2409 := (and #2270 #2405)
-#2413 := (or #1490 #2409)
-#2417 := (and #819 #2413)
-#2254 := (= #2253 #2252)
-#2255 := (or #2254 #2251)
-#2256 := (not #2255)
-#2421 := (or #2256 #2417)
-#2425 := (and #1482 #2421)
-#2232 := (* -1::Int #2231)
-#2234 := (+ #2233 #2232)
-#2235 := (>= #2234 0::Int)
-#2236 := (not #2235)
-#2429 := (or #2236 #2425)
-#2215 := (and #2214 #2211)
-#2203 := (not #995)
-#2449 := (and #757 #2203 #2215 #1471 #2429 #1629 #1647 #1655)
-#2142 := (* -1::Int #2141)
-#2144 := (+ #2143 #2142)
-#2147 := (+ #2146 #2144)
-#2148 := (>= #2147 0::Int)
-#2157 := (and #2156 #2152)
-#2158 := (not #2157)
-#2159 := (or #2158 #2148)
-#2160 := (not #2159)
-#2179 := (or #2160 #2175)
-#2118 := (+ #2117 #1342)
-#2121 := (+ #2120 #2118)
-#2122 := (= #2121 0::Int)
-#2123 := (>= #2118 0::Int)
-#2124 := (not #2123)
-#2125 := (and #2124 #2122)
-#2130 := (or #1351 #2125)
-#2133 := (forall (vars (?v0 S3)) #2130)
-#2183 := (and #2133 #2179)
-#2082 := (+ #2081 #2079)
-#2083 := (= #2082 0::Int)
-#2086 := (and #2085 #2083)
-#2102 := (not #2086)
-#2105 := (forall (vars (?v1 S3)) #2102)
-#2091 := (= ?v0!8 f10)
-#2092 := (not #2091)
-#2093 := (and #2092 #2090)
-#2094 := (not #2093)
-#2099 := (not #2094)
-#2109 := (and #2099 #2105)
-#2187 := (or #2109 #2183)
-#2073 := (not #715)
-#2070 := (not #733)
-#2067 := (not #706)
-#2064 := (not #724)
-#2197 := (and #2064 #2067 #2070 #2073 #2187 #2194)
-#2453 := (or #2197 #2449)
-#2041 := (+ #2040 #1297)
-#2042 := (>= #2041 0::Int)
-#2043 := (not #2042)
-#2046 := (+ #2045 #2041)
-#2047 := (= #2046 0::Int)
-#2050 := (and #2049 #2047 #2043)
-#2055 := (or #1306 #2050)
-#2058 := (forall (vars (?v0 S3)) #2055)
-#2014 := (+ #1259 #2013)
-#2016 := (+ #2015 #2014)
-#2017 := (= #2016 0::Int)
-#2018 := (+ #2015 #1259)
-#2019 := (>= #2018 0::Int)
-#2020 := (not #2019)
-#2023 := (and #2022 #2020 #2017)
-#2028 := (or #1268 #2023)
-#2031 := (forall (vars (?v0 S3)) #2028)
-#2006 := (not #1747)
-#2478 := (and #2006 #2031 #2058 #2453 #1714 #1730 #1739)
-#1972 := (+ #1971 #1969)
-#1973 := (+ #58 #1972)
-#1974 := (= #1973 0::Int)
-#1978 := (and #454 #1977 #1974)
-#1994 := (not #1978)
-#1997 := (forall (vars (?v1 S3)) #1994)
-#1983 := (= ?v0!5 f10)
-#1984 := (not #1983)
-#1985 := (and #1984 #1982)
-#1986 := (not #1985)
-#1991 := (not #1986)
-#2001 := (and #1991 #1997)
-#2482 := (or #2001 #2478)
-#2486 := (and #1253 #2482)
-#1946 := (and #1945 #1943)
-#1947 := (not #1946)
-#1950 := (+ #1949 #1939)
-#1952 := (+ #1951 #1950)
-#1953 := (>= #1952 0::Int)
-#1954 := (or #1953 #1947)
-#1955 := (not #1954)
-#2490 := (or #1955 #2486)
-#2494 := (and #1222 #2490)
-#1912 := (* -1::Int #1911)
-#1914 := (+ #1913 #1912)
-#1915 := (>= #1914 0::Int)
-#1921 := (and #1920 #1917)
-#1922 := (not #1921)
-#1923 := (or #1922 #1915)
-#1924 := (not #1923)
-#2498 := (or #1924 #2494)
-#2502 := (and #1202 #2498)
-#2506 := (or #1897 #2502)
-#1860 := (not #1196)
-#2510 := (and #1860 #2506)
-#2514 := (or #1196 #2510)
-#3054 := (iff #2514 #3053)
-#3051 := (iff #2510 #3050)
-#3048 := (iff #2506 #3047)
-#3045 := (iff #2502 #3044)
-#3042 := (iff #2498 #3041)
-#3039 := (iff #2494 #3038)
-#3036 := (iff #2490 #3035)
-#3033 := (iff #2486 #3032)
-#3030 := (iff #2482 #3029)
-#3027 := (iff #2478 #3024)
-#3021 := (and #100 #2653 #2693 #3018 #1714 #1730 #1739)
-#3025 := (iff #3021 #3024)
-#3026 := [rewrite]: #3025
-#3022 := (iff #2478 #3021)
-#3019 := (iff #2453 #3018)
-#3016 := (iff #2449 #3013)
-#3010 := (and #757 #776 #2215 #1471 #3007 #1629 #1647 #1655)
-#3014 := (iff #3010 #3013)
-#3015 := [rewrite]: #3014
-#3011 := (iff #2449 #3010)
-#3008 := (iff #2429 #3007)
-#3005 := (iff #2425 #3004)
-#3002 := (iff #2421 #3001)
-#2999 := (iff #2417 #2998)
-#2996 := (iff #2413 #2995)
-#2993 := (iff #2409 #2992)
-#2990 := (iff #2405 #2989)
-#2987 := (iff #2401 #2986)
-#2984 := (iff #2397 #2983)
-#2981 := (iff #2393 #2980)
-#2978 := (iff #2389 #2977)
-#2975 := (iff #2385 #2972)
-#2935 := (and #2360 #2929)
-#2966 := (and #2935 #2963)
-#2969 := (and #1539 #2966)
-#2973 := (iff #2969 #2972)
-#2974 := [rewrite]: #2973
-#2970 := (iff #2385 #2969)
-#2967 := (iff #2380 #2966)
-#2964 := (iff #2376 #2963)
-#2961 := (iff #2373 #2960)
-#2958 := (iff #2356 #2957)
-#2955 := (iff #2353 #2954)
-#2952 := (= #2352 #2951)
-#2953 := [rewrite]: #2952
-#2956 := [monotonicity #2953]: #2955
-#2959 := [monotonicity #2956]: #2958
+#3098 := [monotonicity #3095]: #3097
+#3102 := [trans #3098 #3100]: #3101
+#3105 := [monotonicity #3102]: #3104
+#3110 := [trans #3105 #3108]: #3109
+#3113 := [quant-intro #3110]: #3112
+#3636 := [monotonicity #3113 #3633]: #3635
+#3644 := [trans #3636 #3642]: #3643
+#3090 := (iff #2554 #3089)
+#3087 := (iff #2551 #3084)
+#3070 := (or #1933 #3069)
+#3081 := (or #2542 #3070)
+#3085 := (iff #3081 #3084)
+#3086 := [rewrite]: #3085
+#3082 := (iff #2551 #3081)
+#3079 := (iff #2548 #3070)
+#3071 := (not #3070)
+#3074 := (not #3071)
+#3077 := (iff #3074 #3070)
+#3078 := [rewrite]: #3077
+#3075 := (iff #2548 #3074)
+#3072 := (iff #2545 #3071)
+#3073 := [rewrite]: #3072
+#3076 := [monotonicity #3073]: #3075
+#3080 := [trans #3076 #3078]: #3079
+#3083 := [monotonicity #3080]: #3082
+#3088 := [trans #3083 #3086]: #3087
+#3091 := [monotonicity #3088]: #3090
+#3647 := [monotonicity #3091 #3644]: #3646
+#3067 := (iff #1213 #3066)
+#3064 := (iff #1208 #3061)
+#3047 := (or #453 #2510)
+#3058 := (or #3047 #1201)
+#3062 := (iff #3058 #3061)
+#3063 := [rewrite]: #3062
+#3059 := (iff #1208 #3058)
+#3056 := (iff #474 #3047)
+#3048 := (not #3047)
+#3051 := (not #3048)
+#3054 := (iff #3051 #3047)
+#3055 := [rewrite]: #3054
+#3052 := (iff #474 #3051)
+#3049 := (iff #468 #3048)
+#3050 := [rewrite]: #3049
+#3053 := [monotonicity #3050]: #3052
+#3057 := [trans #3053 #3055]: #3056
+#3060 := [monotonicity #3057]: #3059
+#3065 := [trans #3060 #3063]: #3064
+#3068 := [quant-intro #3065]: #3067
+#3650 := [monotonicity #3068 #3647]: #3649
+#3658 := [trans #3650 #3656]: #3657
+#2250 := (iff #2535 #2018)
+#2329 := (iff #2532 #2119)
+#2297 := (or #2210 #1910)
+#2231 := (or #2297 #2527)
+#2120 := (iff #2231 #2119)
+#2328 := [rewrite]: #2120
+#1918 := (iff #2532 #2231)
+#2271 := (iff #2516 #2297)
+#1855 := (not #2297)
+#2154 := (not #1855)
+#1950 := (iff #2154 #2297)
+#2270 := [rewrite]: #1950
+#2155 := (iff #2516 #2154)
+#1856 := (iff #2513 #1855)
+#2298 := [rewrite]: #1856
+#1949 := [monotonicity #2298]: #2155
+#2230 := [trans #1949 #2270]: #2271
+#1919 := [monotonicity #2230]: #1918
+#2017 := [trans #1919 #2328]: #2329
+#2251 := [monotonicity #2017]: #2250
+#3661 := [monotonicity #2251 #3658]: #3660
+#3664 := [monotonicity #3661]: #3663
+#3671 := [trans #3664 #3669]: #3670
+#3674 := [monotonicity #3671]: #3673
+#3677 := [monotonicity #3674]: #3676
+#3684 := [trans #3677 #3682]: #3683
+#3687 := [monotonicity #3684]: #3686
+#2343 := (+ #2342 #2340)
+#2344 := (= #2343 0::Int)
+#2347 := (and #798 #2346 #2344)
+#2364 := (not #2347)
+#2367 := (forall (vars (?v1 S3)) #2364)
+#2352 := (= ?v0!20 f10)
+#2353 := (not #2352)
+#2354 := (and #2353 #2351)
+#2355 := (not #2354)
+#2361 := (not #2355)
+#2371 := (and #2361 #2367)
+#2376 := (and #1530 #2371)
+#2309 := (* -1::Int #2308)
+#2311 := (+ #2310 #2309)
+#2314 := (+ #2313 #2311)
+#2315 := (>= #2314 0::Int)
+#2322 := (and #2321 #2319)
+#2323 := (not #2322)
+#2324 := (or #2323 #2315)
+#2325 := (not #2324)
+#2380 := (or #2325 #2376)
+#2384 := (and #1506 #2380)
+#2282 := (* -1::Int #2281)
+#2284 := (+ #2283 #2282)
+#2285 := (>= #2284 0::Int)
+#2291 := (and #2290 #2287)
+#2292 := (not #2291)
+#2293 := (or #2292 #2285)
+#2294 := (not #2293)
+#2388 := (or #2294 #2384)
+#2392 := (and #1487 #2388)
+#2396 := (or #2267 #2392)
+#2261 := (not #1481)
+#2400 := (and #2261 #2396)
+#2404 := (or #1481 #2400)
+#2408 := (and #810 #2404)
+#2245 := (= #2244 #2243)
+#2246 := (or #2245 #2242)
+#2247 := (not #2246)
+#2412 := (or #2247 #2408)
+#2416 := (and #1473 #2412)
+#2223 := (* -1::Int #2222)
+#2225 := (+ #2224 #2223)
+#2226 := (>= #2225 0::Int)
+#2227 := (not #2226)
+#2420 := (or #2227 #2416)
+#2206 := (and #2205 #2202)
+#2192 := (not #986)
+#2440 := (and #2192 #756 #2206 #1462 #2420 #1620 #1638 #1646)
+#2133 := (* -1::Int #2132)
+#2135 := (+ #2134 #2133)
+#2138 := (+ #2137 #2135)
+#2139 := (>= #2138 0::Int)
+#2148 := (and #2147 #2143)
+#2149 := (not #2148)
+#2150 := (or #2149 #2139)
+#2151 := (not #2150)
+#2170 := (or #2151 #2166)
+#2109 := (+ #2108 #1333)
+#2112 := (+ #2111 #2109)
+#2113 := (= #2112 0::Int)
+#2114 := (>= #2109 0::Int)
+#2115 := (not #2114)
+#2116 := (and #2115 #2113)
+#2121 := (or #1342 #2116)
+#2124 := (forall (vars (?v0 S3)) #2121)
+#2174 := (and #2124 #2170)
+#2073 := (+ #2072 #2070)
+#2074 := (= #2073 0::Int)
+#2077 := (and #2076 #2074)
+#2093 := (not #2077)
+#2096 := (forall (vars (?v1 S3)) #2093)
+#2082 := (= ?v0!8 f10)
+#2083 := (not #2082)
+#2084 := (and #2083 #2081)
+#2085 := (not #2084)
+#2090 := (not #2085)
+#2100 := (and #2090 #2096)
+#2178 := (or #2100 #2174)
+#2064 := (not #714)
+#2061 := (not #732)
+#2058 := (not #705)
+#2055 := (not #723)
+#2188 := (and #2055 #2058 #2061 #2064 #2178 #2185)
+#2444 := (or #2188 #2440)
+#2032 := (+ #2031 #1288)
+#2033 := (>= #2032 0::Int)
+#2034 := (not #2033)
+#2037 := (+ #2036 #2032)
+#2038 := (= #2037 0::Int)
+#2041 := (and #2040 #2038 #2034)
+#2046 := (or #1297 #2041)
+#2049 := (forall (vars (?v0 S3)) #2046)
+#2005 := (+ #1250 #2004)
+#2007 := (+ #2006 #2005)
+#2008 := (= #2007 0::Int)
+#2009 := (+ #2006 #1250)
+#2010 := (>= #2009 0::Int)
+#2011 := (not #2010)
+#2014 := (and #2013 #2011 #2008)
+#2019 := (or #1259 #2014)
+#2022 := (forall (vars (?v0 S3)) #2019)
+#1997 := (not #1738)
+#2469 := (and #1997 #2022 #2049 #2444 #1705 #1721 #1730)
+#1963 := (+ #1962 #1960)
+#1964 := (+ #58 #1963)
+#1965 := (= #1964 0::Int)
+#1969 := (and #453 #1968 #1965)
+#1985 := (not #1969)
+#1988 := (forall (vars (?v1 S3)) #1985)
+#1974 := (= ?v0!5 f10)
+#1975 := (not #1974)
+#1976 := (and #1975 #1973)
+#1977 := (not #1976)
+#1982 := (not #1977)
+#1992 := (and #1982 #1988)
+#2473 := (or #1992 #2469)
+#2477 := (and #1244 #2473)
+#1937 := (and #1936 #1934)
+#1938 := (not #1937)
+#1941 := (+ #1940 #1930)
+#1943 := (+ #1942 #1941)
+#1944 := (>= #1943 0::Int)
+#1945 := (or #1944 #1938)
+#1946 := (not #1945)
+#2481 := (or #1946 #2477)
+#2485 := (and #1213 #2481)
+#1903 := (* -1::Int #1902)
+#1905 := (+ #1904 #1903)
+#1906 := (>= #1905 0::Int)
+#1912 := (and #1911 #1908)
+#1913 := (not #1912)
+#1914 := (or #1913 #1906)
+#1915 := (not #1914)
+#2489 := (or #1915 #2485)
+#2493 := (and #1193 #2489)
+#2497 := (or #1888 #2493)
+#1851 := (not #1187)
+#2501 := (and #1851 #2497)
+#2505 := (or #1187 #2501)
+#3045 := (iff #2505 #3044)
+#3042 := (iff #2501 #3041)
+#3039 := (iff #2497 #3038)
+#3036 := (iff #2493 #3035)
+#3033 := (iff #2489 #3032)
+#3030 := (iff #2485 #3029)
+#3027 := (iff #2481 #3026)
+#3024 := (iff #2477 #3023)
+#3021 := (iff #2473 #3020)
+#3018 := (iff #2469 #3015)
+#3012 := (and #100 #2644 #2684 #3009 #1705 #1721 #1730)
+#3016 := (iff #3012 #3015)
+#3017 := [rewrite]: #3016
+#3013 := (iff #2469 #3012)
+#3010 := (iff #2444 #3009)
+#3007 := (iff #2440 #3004)
+#3001 := (and #181 #756 #2206 #1462 #2998 #1620 #1638 #1646)
+#3005 := (iff #3001 #3004)
+#3006 := [rewrite]: #3005
+#3002 := (iff #2440 #3001)
+#2999 := (iff #2420 #2998)
+#2996 := (iff #2416 #2995)
+#2993 := (iff #2412 #2992)
+#2990 := (iff #2408 #2989)
+#2987 := (iff #2404 #2986)
+#2984 := (iff #2400 #2983)
+#2981 := (iff #2396 #2980)
+#2978 := (iff #2392 #2977)
+#2975 := (iff #2388 #2974)
+#2972 := (iff #2384 #2971)
+#2969 := (iff #2380 #2968)
+#2966 := (iff #2376 #2963)
+#2926 := (and #2351 #2920)
+#2957 := (and #2926 #2954)
+#2960 := (and #1530 #2957)
+#2964 := (iff #2960 #2963)
+#2965 := [rewrite]: #2964
+#2961 := (iff #2376 #2960)
+#2958 := (iff #2371 #2957)
+#2955 := (iff #2367 #2954)
+#2952 := (iff #2364 #2951)
+#2949 := (iff #2347 #2948)
+#2946 := (iff #2344 #2945)
+#2943 := (= #2343 #2942)
+#2944 := [rewrite]: #2943
+#2947 := [monotonicity #2944]: #2946
+#2950 := [monotonicity #2947]: #2949
+#2953 := [monotonicity #2950]: #2952
+#2956 := [quant-intro #2953]: #2955
+#2939 := (iff #2361 #2926)
+#2931 := (not #2926)
+#2934 := (not #2931)
+#2937 := (iff #2934 #2926)
+#2938 := [rewrite]: #2937
+#2935 := (iff #2361 #2934)
+#2932 := (iff #2355 #2931)
+#2929 := (iff #2354 #2926)
+#2923 := (and #2920 #2351)
+#2927 := (iff #2923 #2926)
+#2928 := [rewrite]: #2927
+#2924 := (iff #2354 #2923)
+#2921 := (iff #2353 #2920)
+#2918 := (iff #2352 #2917)
+#2919 := [rewrite]: #2918
+#2922 := [monotonicity #2919]: #2921
+#2925 := [monotonicity #2922]: #2924
+#2930 := [trans #2925 #2928]: #2929
+#2933 := [monotonicity #2930]: #2932
+#2936 := [monotonicity #2933]: #2935
+#2940 := [trans #2936 #2938]: #2939
+#2959 := [monotonicity #2940 #2956]: #2958
 #2962 := [monotonicity #2959]: #2961
-#2965 := [quant-intro #2962]: #2964
-#2948 := (iff #2370 #2935)
-#2940 := (not #2935)
-#2943 := (not #2940)
-#2946 := (iff #2943 #2935)
-#2947 := [rewrite]: #2946
-#2944 := (iff #2370 #2943)
-#2941 := (iff #2364 #2940)
-#2938 := (iff #2363 #2935)
-#2932 := (and #2929 #2360)
-#2936 := (iff #2932 #2935)
-#2937 := [rewrite]: #2936
-#2933 := (iff #2363 #2932)
-#2930 := (iff #2362 #2929)
-#2927 := (iff #2361 #2926)
-#2928 := [rewrite]: #2927
-#2931 := [monotonicity #2928]: #2930
-#2934 := [monotonicity #2931]: #2933
-#2939 := [trans #2934 #2937]: #2938
-#2942 := [monotonicity #2939]: #2941
-#2945 := [monotonicity #2942]: #2944
-#2949 := [trans #2945 #2947]: #2948
-#2968 := [monotonicity #2949 #2965]: #2967
-#2971 := [monotonicity #2968]: #2970
-#2976 := [trans #2971 #2974]: #2975
-#2924 := (iff #2334 #2923)
-#2921 := (iff #2333 #2920)
-#2918 := (iff #2324 #2915)
-#2905 := (+ #2319 #2322)
-#2906 := (+ #2318 #2905)
-#2909 := (>= #2906 0::Int)
-#2916 := (iff #2909 #2915)
-#2917 := [rewrite]: #2916
-#2910 := (iff #2324 #2909)
-#2907 := (= #2323 #2906)
+#2967 := [trans #2962 #2965]: #2966
+#2915 := (iff #2325 #2914)
+#2912 := (iff #2324 #2911)
+#2909 := (iff #2315 #2906)
+#2896 := (+ #2310 #2313)
+#2897 := (+ #2309 #2896)
+#2900 := (>= #2897 0::Int)
+#2907 := (iff #2900 #2906)
 #2908 := [rewrite]: #2907
-#2911 := [monotonicity #2908]: #2910
-#2919 := [trans #2911 #2917]: #2918
-#2903 := (iff #2332 #2902)
-#2900 := (iff #2331 #2899)
-#2901 := [rewrite]: #2900
-#2904 := [monotonicity #2901]: #2903
-#2922 := [monotonicity #2904 #2919]: #2921
-#2925 := [monotonicity #2922]: #2924
-#2979 := [monotonicity #2925 #2976]: #2978
+#2901 := (iff #2315 #2900)
+#2898 := (= #2314 #2897)
+#2899 := [rewrite]: #2898
+#2902 := [monotonicity #2899]: #2901
+#2910 := [trans #2902 #2908]: #2909
+#2894 := (iff #2323 #2893)
+#2891 := (iff #2322 #2890)
+#2892 := [rewrite]: #2891
+#2895 := [monotonicity #2892]: #2894
+#2913 := [monotonicity #2895 #2910]: #2912
+#2916 := [monotonicity #2913]: #2915
+#2970 := [monotonicity #2916 #2967]: #2969
+#2973 := [monotonicity #2970]: #2972
+#2888 := (iff #2294 #2887)
+#2885 := (iff #2293 #2884)
+#2882 := (iff #2285 #2879)
+#2871 := (+ #2282 #2283)
+#2874 := (>= #2871 0::Int)
+#2880 := (iff #2874 #2879)
+#2881 := [rewrite]: #2880
+#2875 := (iff #2285 #2874)
+#2872 := (= #2284 #2871)
+#2873 := [rewrite]: #2872
+#2876 := [monotonicity #2873]: #2875
+#2883 := [trans #2876 #2881]: #2882
+#2869 := (iff #2292 #2868)
+#2866 := (iff #2291 #2865)
+#2867 := [rewrite]: #2866
+#2870 := [monotonicity #2867]: #2869
+#2886 := [monotonicity #2870 #2883]: #2885
+#2889 := [monotonicity #2886]: #2888
+#2976 := [monotonicity #2889 #2973]: #2975
+#2979 := [monotonicity #2976]: #2978
 #2982 := [monotonicity #2979]: #2981
-#2897 := (iff #2303 #2896)
-#2894 := (iff #2302 #2893)
-#2891 := (iff #2294 #2888)
-#2880 := (+ #2291 #2292)
-#2883 := (>= #2880 0::Int)
-#2889 := (iff #2883 #2888)
-#2890 := [rewrite]: #2889
-#2884 := (iff #2294 #2883)
-#2881 := (= #2293 #2880)
-#2882 := [rewrite]: #2881
-#2885 := [monotonicity #2882]: #2884
-#2892 := [trans #2885 #2890]: #2891
-#2878 := (iff #2301 #2877)
-#2875 := (iff #2300 #2874)
-#2876 := [rewrite]: #2875
-#2879 := [monotonicity #2876]: #2878
-#2895 := [monotonicity #2879 #2892]: #2894
-#2898 := [monotonicity #2895]: #2897
-#2985 := [monotonicity #2898 #2982]: #2984
+#2863 := (iff #2261 #203)
+#2864 := [rewrite]: #2863
+#2985 := [monotonicity #2864 #2982]: #2984
 #2988 := [monotonicity #2985]: #2987
 #2991 := [monotonicity #2988]: #2990
-#2872 := (iff #2270 #204)
-#2873 := [rewrite]: #2872
-#2994 := [monotonicity #2873 #2991]: #2993
+#2861 := (iff #2247 #2860)
+#2858 := (iff #2246 #2855)
+#2852 := (or #2849 #2242)
+#2856 := (iff #2852 #2855)
+#2857 := [rewrite]: #2856
+#2853 := (iff #2246 #2852)
+#2850 := (iff #2245 #2849)
+#2851 := [rewrite]: #2850
+#2854 := [monotonicity #2851]: #2853
+#2859 := [trans #2854 #2857]: #2858
+#2862 := [monotonicity #2859]: #2861
+#2994 := [monotonicity #2862 #2991]: #2993
 #2997 := [monotonicity #2994]: #2996
-#3000 := [monotonicity #2997]: #2999
-#2870 := (iff #2256 #2869)
-#2867 := (iff #2255 #2864)
-#2861 := (or #2858 #2251)
-#2865 := (iff #2861 #2864)
-#2866 := [rewrite]: #2865
-#2862 := (iff #2255 #2861)
-#2859 := (iff #2254 #2858)
-#2860 := [rewrite]: #2859
-#2863 := [monotonicity #2860]: #2862
-#2868 := [trans #2863 #2866]: #2867
-#2871 := [monotonicity #2868]: #2870
-#3003 := [monotonicity #2871 #3000]: #3002
-#3006 := [monotonicity #3003]: #3005
-#2856 := (iff #2236 #2855)
-#2853 := (iff #2235 #2850)
-#2842 := (+ #2232 #2233)
-#2845 := (>= #2842 0::Int)
-#2851 := (iff #2845 #2850)
-#2852 := [rewrite]: #2851
-#2846 := (iff #2235 #2845)
-#2843 := (= #2234 #2842)
-#2844 := [rewrite]: #2843
-#2847 := [monotonicity #2844]: #2846
-#2854 := [trans #2847 #2852]: #2853
-#2857 := [monotonicity #2854]: #2856
-#3009 := [monotonicity #2857 #3006]: #3008
-#2840 := (iff #2203 #776)
-#2841 := [rewrite]: #2840
-#3012 := [monotonicity #2841 #3009]: #3011
-#3017 := [trans #3012 #3015]: #3016
-#2838 := (iff #2197 #2835)
-#2832 := (and #136 #141 #621 #624 #2829 #2194)
-#2836 := (iff #2832 #2835)
-#2837 := [rewrite]: #2836
-#2833 := (iff #2197 #2832)
-#2830 := (iff #2187 #2829)
-#2827 := (iff #2183 #2826)
-#2824 := (iff #2179 #2821)
-#2818 := (or #2815 #2175)
-#2822 := (iff #2818 #2821)
-#2823 := [rewrite]: #2822
-#2819 := (iff #2179 #2818)
-#2816 := (iff #2160 #2815)
-#2813 := (iff #2159 #2812)
-#2810 := (iff #2148 #2807)
-#2798 := (+ #2143 #2146)
-#2799 := (+ #2142 #2798)
-#2802 := (>= #2799 0::Int)
-#2808 := (iff #2802 #2807)
-#2809 := [rewrite]: #2808
-#2803 := (iff #2148 #2802)
-#2800 := (= #2147 #2799)
-#2801 := [rewrite]: #2800
-#2804 := [monotonicity #2801]: #2803
-#2811 := [trans #2804 #2809]: #2810
-#2796 := (iff #2158 #2795)
-#2793 := (iff #2157 #2792)
-#2794 := [rewrite]: #2793
-#2797 := [monotonicity #2794]: #2796
-#2814 := [monotonicity #2797 #2811]: #2813
-#2817 := [monotonicity #2814]: #2816
-#2820 := [monotonicity #2817]: #2819
-#2825 := [trans #2820 #2823]: #2824
-#2790 := (iff #2133 #2789)
-#2787 := (iff #2130 #2786)
-#2784 := (iff #2125 #2783)
-#2781 := (iff #2122 #2778)
-#2768 := (+ #2117 #2120)
-#2769 := (+ #1342 #2768)
-#2772 := (= #2769 0::Int)
-#2779 := (iff #2772 #2778)
-#2780 := [rewrite]: #2779
-#2773 := (iff #2122 #2772)
-#2770 := (= #2121 #2769)
+#2847 := (iff #2227 #2846)
+#2844 := (iff #2226 #2841)
+#2833 := (+ #2223 #2224)
+#2836 := (>= #2833 0::Int)
+#2842 := (iff #2836 #2841)
+#2843 := [rewrite]: #2842
+#2837 := (iff #2226 #2836)
+#2834 := (= #2225 #2833)
+#2835 := [rewrite]: #2834
+#2838 := [monotonicity #2835]: #2837
+#2845 := [trans #2838 #2843]: #2844
+#2848 := [monotonicity #2845]: #2847
+#3000 := [monotonicity #2848 #2997]: #2999
+#2831 := (iff #2192 #181)
+#2832 := [rewrite]: #2831
+#3003 := [monotonicity #2832 #3000]: #3002
+#3008 := [trans #3003 #3006]: #3007
+#2829 := (iff #2188 #2826)
+#2823 := (and #136 #141 #620 #623 #2820 #2185)
+#2827 := (iff #2823 #2826)
+#2828 := [rewrite]: #2827
+#2824 := (iff #2188 #2823)
+#2821 := (iff #2178 #2820)
+#2818 := (iff #2174 #2817)
+#2815 := (iff #2170 #2812)
+#2809 := (or #2806 #2166)
+#2813 := (iff #2809 #2812)
+#2814 := [rewrite]: #2813
+#2810 := (iff #2170 #2809)
+#2807 := (iff #2151 #2806)
+#2804 := (iff #2150 #2803)
+#2801 := (iff #2139 #2798)
+#2789 := (+ #2134 #2137)
+#2790 := (+ #2133 #2789)
+#2793 := (>= #2790 0::Int)
+#2799 := (iff #2793 #2798)
+#2800 := [rewrite]: #2799
+#2794 := (iff #2139 #2793)
+#2791 := (= #2138 #2790)
+#2792 := [rewrite]: #2791
+#2795 := [monotonicity #2792]: #2794
+#2802 := [trans #2795 #2800]: #2801
+#2787 := (iff #2149 #2786)
+#2784 := (iff #2148 #2783)
+#2785 := [rewrite]: #2784
+#2788 := [monotonicity #2785]: #2787
+#2805 := [monotonicity #2788 #2802]: #2804
+#2808 := [monotonicity #2805]: #2807
+#2811 := [monotonicity #2808]: #2810
+#2816 := [trans #2811 #2814]: #2815
+#2781 := (iff #2124 #2780)
+#2778 := (iff #2121 #2777)
+#2775 := (iff #2116 #2774)
+#2772 := (iff #2113 #2769)
+#2759 := (+ #2108 #2111)
+#2760 := (+ #1333 #2759)
+#2763 := (= #2760 0::Int)
+#2770 := (iff #2763 #2769)
 #2771 := [rewrite]: #2770
-#2774 := [monotonicity #2771]: #2773
-#2782 := [trans #2774 #2780]: #2781
-#2766 := (iff #2124 #2765)
-#2763 := (iff #2123 #2760)
-#2752 := (+ #1342 #2117)
-#2755 := (>= #2752 0::Int)
-#2761 := (iff #2755 #2760)
+#2764 := (iff #2113 #2763)
+#2761 := (= #2112 #2760)
 #2762 := [rewrite]: #2761
-#2756 := (iff #2123 #2755)
-#2753 := (= #2118 #2752)
-#2754 := [rewrite]: #2753
-#2757 := [monotonicity #2754]: #2756
-#2764 := [trans #2757 #2762]: #2763
-#2767 := [monotonicity #2764]: #2766
-#2785 := [monotonicity #2767 #2782]: #2784
-#2788 := [monotonicity #2785]: #2787
-#2791 := [quant-intro #2788]: #2790
-#2828 := [monotonicity #2791 #2825]: #2827
-#2750 := (iff #2109 #2747)
-#2713 := (and #2090 #2707)
-#2744 := (and #2713 #2741)
-#2748 := (iff #2744 #2747)
-#2749 := [rewrite]: #2748
-#2745 := (iff #2109 #2744)
-#2742 := (iff #2105 #2741)
-#2739 := (iff #2102 #2738)
-#2736 := (iff #2086 #2735)
-#2733 := (iff #2083 #2732)
-#2730 := (= #2082 #2729)
-#2731 := [rewrite]: #2730
-#2734 := [monotonicity #2731]: #2733
-#2737 := [monotonicity #2734]: #2736
-#2740 := [monotonicity #2737]: #2739
-#2743 := [quant-intro #2740]: #2742
-#2726 := (iff #2099 #2713)
-#2718 := (not #2713)
-#2721 := (not #2718)
-#2724 := (iff #2721 #2713)
-#2725 := [rewrite]: #2724
-#2722 := (iff #2099 #2721)
-#2719 := (iff #2094 #2718)
-#2716 := (iff #2093 #2713)
-#2710 := (and #2707 #2090)
-#2714 := (iff #2710 #2713)
-#2715 := [rewrite]: #2714
-#2711 := (iff #2093 #2710)
-#2708 := (iff #2092 #2707)
-#2705 := (iff #2091 #2704)
+#2765 := [monotonicity #2762]: #2764
+#2773 := [trans #2765 #2771]: #2772
+#2757 := (iff #2115 #2756)
+#2754 := (iff #2114 #2751)
+#2743 := (+ #1333 #2108)
+#2746 := (>= #2743 0::Int)
+#2752 := (iff #2746 #2751)
+#2753 := [rewrite]: #2752
+#2747 := (iff #2114 #2746)
+#2744 := (= #2109 #2743)
+#2745 := [rewrite]: #2744
+#2748 := [monotonicity #2745]: #2747
+#2755 := [trans #2748 #2753]: #2754
+#2758 := [monotonicity #2755]: #2757
+#2776 := [monotonicity #2758 #2773]: #2775
+#2779 := [monotonicity #2776]: #2778
+#2782 := [quant-intro #2779]: #2781
+#2819 := [monotonicity #2782 #2816]: #2818
+#2741 := (iff #2100 #2738)
+#2704 := (and #2081 #2698)
+#2735 := (and #2704 #2732)
+#2739 := (iff #2735 #2738)
+#2740 := [rewrite]: #2739
+#2736 := (iff #2100 #2735)
+#2733 := (iff #2096 #2732)
+#2730 := (iff #2093 #2729)
+#2727 := (iff #2077 #2726)
+#2724 := (iff #2074 #2723)
+#2721 := (= #2073 #2720)
+#2722 := [rewrite]: #2721
+#2725 := [monotonicity #2722]: #2724
+#2728 := [monotonicity #2725]: #2727
+#2731 := [monotonicity #2728]: #2730
+#2734 := [quant-intro #2731]: #2733
+#2717 := (iff #2090 #2704)
+#2709 := (not #2704)
+#2712 := (not #2709)
+#2715 := (iff #2712 #2704)
+#2716 := [rewrite]: #2715
+#2713 := (iff #2090 #2712)
+#2710 := (iff #2085 #2709)
+#2707 := (iff #2084 #2704)
+#2701 := (and #2698 #2081)
+#2705 := (iff #2701 #2704)
 #2706 := [rewrite]: #2705
-#2709 := [monotonicity #2706]: #2708
-#2712 := [monotonicity #2709]: #2711
-#2717 := [trans #2712 #2715]: #2716
-#2720 := [monotonicity #2717]: #2719
-#2723 := [monotonicity #2720]: #2722
-#2727 := [trans #2723 #2725]: #2726
-#2746 := [monotonicity #2727 #2743]: #2745
-#2751 := [trans #2746 #2749]: #2750
-#2831 := [monotonicity #2751 #2828]: #2830
-#2702 := (iff #2073 #624)
-#2703 := [rewrite]: #2702
-#2700 := (iff #2070 #621)
-#2701 := [rewrite]: #2700
-#2698 := (iff #2067 #141)
-#2699 := [rewrite]: #2698
-#2696 := (iff #2064 #136)
+#2702 := (iff #2084 #2701)
+#2699 := (iff #2083 #2698)
+#2696 := (iff #2082 #2695)
 #2697 := [rewrite]: #2696
-#2834 := [monotonicity #2697 #2699 #2701 #2703 #2831]: #2833
-#2839 := [trans #2834 #2837]: #2838
-#3020 := [monotonicity #2839 #3017]: #3019
-#2694 := (iff #2058 #2693)
-#2691 := (iff #2055 #2690)
-#2688 := (iff #2050 #2687)
-#2685 := (iff #2043 #2684)
-#2682 := (iff #2042 #2679)
-#2672 := (+ #1297 #2040)
-#2675 := (>= #2672 0::Int)
-#2680 := (iff #2675 #2679)
-#2681 := [rewrite]: #2680
-#2676 := (iff #2042 #2675)
-#2673 := (= #2041 #2672)
-#2674 := [rewrite]: #2673
+#2700 := [monotonicity #2697]: #2699
+#2703 := [monotonicity #2700]: #2702
+#2708 := [trans #2703 #2706]: #2707
+#2711 := [monotonicity #2708]: #2710
+#2714 := [monotonicity #2711]: #2713
+#2718 := [trans #2714 #2716]: #2717
+#2737 := [monotonicity #2718 #2734]: #2736
+#2742 := [trans #2737 #2740]: #2741
+#2822 := [monotonicity #2742 #2819]: #2821
+#2693 := (iff #2064 #623)
+#2694 := [rewrite]: #2693
+#2691 := (iff #2061 #620)
+#2692 := [rewrite]: #2691
+#2689 := (iff #2058 #141)
+#2690 := [rewrite]: #2689
+#2687 := (iff #2055 #136)
+#2688 := [rewrite]: #2687
+#2825 := [monotonicity #2688 #2690 #2692 #2694 #2822]: #2824
+#2830 := [trans #2825 #2828]: #2829
+#3011 := [monotonicity #2830 #3008]: #3010
+#2685 := (iff #2049 #2684)
+#2682 := (iff #2046 #2681)
+#2679 := (iff #2041 #2678)
+#2676 := (iff #2034 #2675)
+#2673 := (iff #2033 #2670)
+#2663 := (+ #1288 #2031)
+#2666 := (>= #2663 0::Int)
+#2671 := (iff #2666 #2670)
+#2672 := [rewrite]: #2671
+#2667 := (iff #2033 #2666)
+#2664 := (= #2032 #2663)
+#2665 := [rewrite]: #2664
+#2668 := [monotonicity #2665]: #2667
+#2674 := [trans #2668 #2672]: #2673
 #2677 := [monotonicity #2674]: #2676
-#2683 := [trans #2677 #2681]: #2682
-#2686 := [monotonicity #2683]: #2685
-#2670 := (iff #2047 #2667)
-#2656 := (+ #2040 #2045)
-#2657 := (+ #1297 #2656)
-#2660 := (= #2657 0::Int)
-#2668 := (iff #2660 #2667)
-#2669 := [rewrite]: #2668
-#2661 := (iff #2047 #2660)
-#2658 := (= #2046 #2657)
-#2659 := [rewrite]: #2658
-#2662 := [monotonicity #2659]: #2661
-#2671 := [trans #2662 #2669]: #2670
-#2689 := [monotonicity #2671 #2686]: #2688
-#2692 := [monotonicity #2689]: #2691
-#2695 := [quant-intro #2692]: #2694
-#2654 := (iff #2031 #2653)
-#2651 := (iff #2028 #2650)
-#2648 := (iff #2023 #2647)
-#2645 := (iff #2017 #2642)
-#2632 := (+ #2013 #2015)
-#2633 := (+ #1259 #2632)
-#2636 := (= #2633 0::Int)
-#2643 := (iff #2636 #2642)
-#2644 := [rewrite]: #2643
-#2637 := (iff #2017 #2636)
-#2634 := (= #2016 #2633)
+#2661 := (iff #2038 #2658)
+#2647 := (+ #2031 #2036)
+#2648 := (+ #1288 #2647)
+#2651 := (= #2648 0::Int)
+#2659 := (iff #2651 #2658)
+#2660 := [rewrite]: #2659
+#2652 := (iff #2038 #2651)
+#2649 := (= #2037 #2648)
+#2650 := [rewrite]: #2649
+#2653 := [monotonicity #2650]: #2652
+#2662 := [trans #2653 #2660]: #2661
+#2680 := [monotonicity #2662 #2677]: #2679
+#2683 := [monotonicity #2680]: #2682
+#2686 := [quant-intro #2683]: #2685
+#2645 := (iff #2022 #2644)
+#2642 := (iff #2019 #2641)
+#2639 := (iff #2014 #2638)
+#2636 := (iff #2008 #2633)
+#2623 := (+ #2004 #2006)
+#2624 := (+ #1250 #2623)
+#2627 := (= #2624 0::Int)
+#2634 := (iff #2627 #2633)
 #2635 := [rewrite]: #2634
-#2638 := [monotonicity #2635]: #2637
-#2646 := [trans #2638 #2644]: #2645
-#2630 := (iff #2020 #2629)
-#2627 := (iff #2019 #2624)
-#2616 := (+ #1259 #2015)
-#2619 := (>= #2616 0::Int)
-#2625 := (iff #2619 #2624)
+#2628 := (iff #2008 #2627)
+#2625 := (= #2007 #2624)
 #2626 := [rewrite]: #2625
-#2620 := (iff #2019 #2619)
-#2617 := (= #2018 #2616)
-#2618 := [rewrite]: #2617
-#2621 := [monotonicity #2618]: #2620
-#2628 := [trans #2621 #2626]: #2627
-#2631 := [monotonicity #2628]: #2630
-#2649 := [monotonicity #2631 #2646]: #2648
-#2652 := [monotonicity #2649]: #2651
-#2655 := [quant-intro #2652]: #2654
-#2614 := (iff #2006 #100)
-#2615 := [rewrite]: #2614
-#3023 := [monotonicity #2615 #2655 #2695 #3020]: #3022
-#3028 := [trans #3023 #3026]: #3027
-#2612 := (iff #2001 #2609)
-#2575 := (and #1982 #2569)
-#2606 := (and #2575 #2603)
-#2610 := (iff #2606 #2609)
-#2611 := [rewrite]: #2610
-#2607 := (iff #2001 #2606)
-#2604 := (iff #1997 #2603)
-#2601 := (iff #1994 #2600)
-#2598 := (iff #1978 #2597)
-#2595 := (iff #1974 #2594)
-#2592 := (= #1973 #2591)
-#2593 := [rewrite]: #2592
-#2596 := [monotonicity #2593]: #2595
-#2599 := [monotonicity #2596]: #2598
-#2602 := [monotonicity #2599]: #2601
-#2605 := [quant-intro #2602]: #2604
-#2588 := (iff #1991 #2575)
-#2580 := (not #2575)
-#2583 := (not #2580)
-#2586 := (iff #2583 #2575)
-#2587 := [rewrite]: #2586
-#2584 := (iff #1991 #2583)
-#2581 := (iff #1986 #2580)
-#2578 := (iff #1985 #2575)
-#2572 := (and #2569 #1982)
-#2576 := (iff #2572 #2575)
-#2577 := [rewrite]: #2576
-#2573 := (iff #1985 #2572)
-#2570 := (iff #1984 #2569)
-#2567 := (iff #1983 #2566)
+#2629 := [monotonicity #2626]: #2628
+#2637 := [trans #2629 #2635]: #2636
+#2621 := (iff #2011 #2620)
+#2618 := (iff #2010 #2615)
+#2607 := (+ #1250 #2006)
+#2610 := (>= #2607 0::Int)
+#2616 := (iff #2610 #2615)
+#2617 := [rewrite]: #2616
+#2611 := (iff #2010 #2610)
+#2608 := (= #2009 #2607)
+#2609 := [rewrite]: #2608
+#2612 := [monotonicity #2609]: #2611
+#2619 := [trans #2612 #2617]: #2618
+#2622 := [monotonicity #2619]: #2621
+#2640 := [monotonicity #2622 #2637]: #2639
+#2643 := [monotonicity #2640]: #2642
+#2646 := [quant-intro #2643]: #2645
+#2605 := (iff #1997 #100)
+#2606 := [rewrite]: #2605
+#3014 := [monotonicity #2606 #2646 #2686 #3011]: #3013
+#3019 := [trans #3014 #3017]: #3018
+#2603 := (iff #1992 #2600)
+#2566 := (and #1973 #2560)
+#2597 := (and #2566 #2594)
+#2601 := (iff #2597 #2600)
+#2602 := [rewrite]: #2601
+#2598 := (iff #1992 #2597)
+#2595 := (iff #1988 #2594)
+#2592 := (iff #1985 #2591)
+#2589 := (iff #1969 #2588)
+#2586 := (iff #1965 #2585)
+#2583 := (= #1964 #2582)
+#2584 := [rewrite]: #2583
+#2587 := [monotonicity #2584]: #2586
+#2590 := [monotonicity #2587]: #2589
+#2593 := [monotonicity #2590]: #2592
+#2596 := [quant-intro #2593]: #2595
+#2579 := (iff #1982 #2566)
+#2571 := (not #2566)
+#2574 := (not #2571)
+#2577 := (iff #2574 #2566)
+#2578 := [rewrite]: #2577
+#2575 := (iff #1982 #2574)
+#2572 := (iff #1977 #2571)
+#2569 := (iff #1976 #2566)
+#2563 := (and #2560 #1973)
+#2567 := (iff #2563 #2566)
 #2568 := [rewrite]: #2567
-#2571 := [monotonicity #2568]: #2570
-#2574 := [monotonicity #2571]: #2573
-#2579 := [trans #2574 #2577]: #2578
-#2582 := [monotonicity #2579]: #2581
-#2585 := [monotonicity #2582]: #2584
-#2589 := [trans #2585 #2587]: #2588
-#2608 := [monotonicity #2589 #2605]: #2607
-#2613 := [trans #2608 #2611]: #2612
-#3031 := [monotonicity #2613 #3028]: #3030
-#3034 := [monotonicity #3031]: #3033
-#2564 := (iff #1955 #2563)
-#2561 := (iff #1954 #2560)
-#2558 := (iff #1947 #2557)
+#2564 := (iff #1976 #2563)
+#2561 := (iff #1975 #2560)
+#2558 := (iff #1974 #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
+#2604 := [trans #2599 #2602]: #2603
+#3022 := [monotonicity #2604 #3019]: #3021
+#3025 := [monotonicity #3022]: #3024
 #2555 := (iff #1946 #2554)
-#2556 := [rewrite]: #2555
-#2559 := [monotonicity #2556]: #2558
-#2552 := (iff #1953 #2551)
-#2549 := (= #1952 #2548)
-#2550 := [rewrite]: #2549
-#2553 := [monotonicity #2550]: #2552
-#2562 := [monotonicity #2553 #2559]: #2561
-#2565 := [monotonicity #2562]: #2564
-#3037 := [monotonicity #2565 #3034]: #3036
+#2552 := (iff #1945 #2551)
+#2549 := (iff #1938 #2548)
+#2546 := (iff #1937 #2545)
+#2547 := [rewrite]: #2546
+#2550 := [monotonicity #2547]: #2549
+#2543 := (iff #1944 #2542)
+#2540 := (= #1943 #2539)
+#2541 := [rewrite]: #2540
+#2544 := [monotonicity #2541]: #2543
+#2553 := [monotonicity #2544 #2550]: #2552
+#2556 := [monotonicity #2553]: #2555
+#3028 := [monotonicity #2556 #3025]: #3027
+#3031 := [monotonicity #3028]: #3030
+#2536 := (iff #1915 #2535)
+#2533 := (iff #1914 #2532)
+#2530 := (iff #1906 #2527)
+#2519 := (+ #1903 #1904)
+#2522 := (>= #2519 0::Int)
+#2528 := (iff #2522 #2527)
+#2529 := [rewrite]: #2528
+#2523 := (iff #1906 #2522)
+#2520 := (= #1905 #2519)
+#2521 := [rewrite]: #2520
+#2524 := [monotonicity #2521]: #2523
+#2531 := [trans #2524 #2529]: #2530
+#2517 := (iff #1913 #2516)
+#2514 := (iff #1912 #2513)
+#2515 := [rewrite]: #2514
+#2518 := [monotonicity #2515]: #2517
+#2534 := [monotonicity #2518 #2531]: #2533
+#2537 := [monotonicity #2534]: #2536
+#3034 := [monotonicity #2537 #3031]: #3033
+#3037 := [monotonicity #3034]: #3036
 #3040 := [monotonicity #3037]: #3039
-#2545 := (iff #1924 #2544)
-#2542 := (iff #1923 #2541)
-#2539 := (iff #1915 #2536)
-#2528 := (+ #1912 #1913)
-#2531 := (>= #2528 0::Int)
-#2537 := (iff #2531 #2536)
-#2538 := [rewrite]: #2537
-#2532 := (iff #1915 #2531)
-#2529 := (= #1914 #2528)
-#2530 := [rewrite]: #2529
-#2533 := [monotonicity #2530]: #2532
-#2540 := [trans #2533 #2538]: #2539
-#2526 := (iff #1922 #2525)
-#2523 := (iff #1921 #2522)
-#2524 := [rewrite]: #2523
-#2527 := [monotonicity #2524]: #2526
-#2543 := [monotonicity #2527 #2540]: #2542
-#2546 := [monotonicity #2543]: #2545
-#3043 := [monotonicity #2546 #3040]: #3042
+#2511 := (iff #1851 #71)
+#2512 := [rewrite]: #2511
+#3043 := [monotonicity #2512 #3040]: #3042
 #3046 := [monotonicity #3043]: #3045
-#3049 := [monotonicity #3046]: #3048
-#2520 := (iff #1860 #71)
-#2521 := [rewrite]: #2520
-#3052 := [monotonicity #2521 #3049]: #3051
-#3055 := [monotonicity #3052]: #3054
-#1836 := (not #1800)
-#2515 := (~ #1836 #2514)
-#2511 := (not #1797)
-#2512 := (~ #2511 #2510)
-#2507 := (not #1794)
-#2508 := (~ #2507 #2506)
-#2503 := (not #1791)
-#2504 := (~ #2503 #2502)
-#2499 := (not #1788)
-#2500 := (~ #2499 #2498)
-#2495 := (not #1785)
-#2496 := (~ #2495 #2494)
-#2491 := (not #1782)
-#2492 := (~ #2491 #2490)
-#2487 := (not #1779)
-#2488 := (~ #2487 #2486)
-#2483 := (not #1776)
-#2484 := (~ #2483 #2482)
-#2479 := (not #1771)
-#2480 := (~ #2479 #2478)
-#2475 := (not #1742)
-#2476 := (~ #2475 #1739)
-#2473 := (~ #1739 #1739)
-#2471 := (~ #1736 #1736)
-#2472 := [refl]: #2471
-#2474 := [nnf-pos #2472]: #2473
-#2477 := [nnf-neg #2474]: #2476
-#2468 := (not #1733)
-#2469 := (~ #2468 #1730)
-#2466 := (~ #1730 #1730)
-#2464 := (~ #1725 #1725)
-#2465 := [refl]: #2464
-#2467 := [nnf-pos #2465]: #2466
-#2470 := [nnf-neg #2467]: #2469
-#2461 := (not #1717)
-#2462 := (~ #2461 #1714)
-#2459 := (~ #1714 #1714)
-#2457 := (~ #1711 #1711)
-#2458 := [refl]: #2457
-#2460 := [nnf-pos #2458]: #2459
-#2463 := [nnf-neg #2460]: #2462
-#2454 := (not #1694)
-#2455 := (~ #2454 #2453)
-#2450 := (not #1689)
-#2451 := (~ #2450 #2449)
-#2447 := (~ #1655 #1655)
-#2448 := [refl]: #2447
-#2444 := (not #1650)
-#2445 := (~ #2444 #1647)
-#2442 := (~ #1647 #1647)
-#2440 := (~ #1642 #1642)
-#2441 := [refl]: #2440
-#2443 := [nnf-pos #2441]: #2442
-#2446 := [nnf-neg #2443]: #2445
-#2437 := (not #1632)
-#2438 := (~ #2437 #1629)
-#2435 := (~ #1629 #1629)
-#2433 := (~ #1626 #1626)
-#2434 := [refl]: #2433
-#2436 := [nnf-pos #2434]: #2435
-#2439 := [nnf-neg #2436]: #2438
-#2430 := (not #1615)
-#2431 := (~ #2430 #2429)
-#2426 := (not #1612)
-#2427 := (~ #2426 #2425)
-#2422 := (not #1609)
-#2423 := (~ #2422 #2421)
-#2418 := (not #1606)
-#2419 := (~ #2418 #2417)
-#2414 := (not #1603)
-#2415 := (~ #2414 #2413)
-#2410 := (not #1600)
-#2411 := (~ #2410 #2409)
-#2406 := (not #1597)
-#2407 := (~ #2406 #2405)
-#2402 := (not #1594)
-#2403 := (~ #2402 #2401)
-#2398 := (not #1591)
-#2399 := (~ #2398 #2397)
-#2394 := (not #1588)
-#2395 := (~ #2394 #2393)
-#2390 := (not #1585)
-#2391 := (~ #2390 #2389)
-#2386 := (not #1582)
-#2387 := (~ #2386 #2385)
-#2367 := (not #1579)
-#2383 := (~ #2367 #2380)
-#2357 := (exists (vars (?v1 S3)) #2356)
-#2365 := (or #2364 #2357)
-#2366 := (not #2365)
-#2381 := (~ #2366 #2380)
-#2377 := (not #2357)
+#1827 := (not #1791)
+#2506 := (~ #1827 #2505)
+#2502 := (not #1788)
+#2503 := (~ #2502 #2501)
+#2498 := (not #1785)
+#2499 := (~ #2498 #2497)
+#2494 := (not #1782)
+#2495 := (~ #2494 #2493)
+#2490 := (not #1779)
+#2491 := (~ #2490 #2489)
+#2486 := (not #1776)
+#2487 := (~ #2486 #2485)
+#2482 := (not #1773)
+#2483 := (~ #2482 #2481)
+#2478 := (not #1770)
+#2479 := (~ #2478 #2477)
+#2474 := (not #1767)
+#2475 := (~ #2474 #2473)
+#2470 := (not #1762)
+#2471 := (~ #2470 #2469)
+#2466 := (not #1733)
+#2467 := (~ #2466 #1730)
+#2464 := (~ #1730 #1730)
+#2462 := (~ #1727 #1727)
+#2463 := [refl]: #2462
+#2465 := [nnf-pos #2463]: #2464
+#2468 := [nnf-neg #2465]: #2467
+#2459 := (not #1724)
+#2460 := (~ #2459 #1721)
+#2457 := (~ #1721 #1721)
+#2455 := (~ #1716 #1716)
+#2456 := [refl]: #2455
+#2458 := [nnf-pos #2456]: #2457
+#2461 := [nnf-neg #2458]: #2460
+#2452 := (not #1708)
+#2453 := (~ #2452 #1705)
+#2450 := (~ #1705 #1705)
+#2448 := (~ #1702 #1702)
+#2449 := [refl]: #2448
+#2451 := [nnf-pos #2449]: #2450
+#2454 := [nnf-neg #2451]: #2453
+#2445 := (not #1685)
+#2446 := (~ #2445 #2444)
+#2441 := (not #1680)
+#2442 := (~ #2441 #2440)
+#2438 := (~ #1646 #1646)
+#2439 := [refl]: #2438
+#2435 := (not #1641)
+#2436 := (~ #2435 #1638)
+#2433 := (~ #1638 #1638)
+#2431 := (~ #1633 #1633)
+#2432 := [refl]: #2431
+#2434 := [nnf-pos #2432]: #2433
+#2437 := [nnf-neg #2434]: #2436
+#2428 := (not #1623)
+#2429 := (~ #2428 #1620)
+#2426 := (~ #1620 #1620)
+#2424 := (~ #1617 #1617)
+#2425 := [refl]: #2424
+#2427 := [nnf-pos #2425]: #2426
+#2430 := [nnf-neg #2427]: #2429
+#2421 := (not #1606)
+#2422 := (~ #2421 #2420)
+#2417 := (not #1603)
+#2418 := (~ #2417 #2416)
+#2413 := (not #1600)
+#2414 := (~ #2413 #2412)
+#2409 := (not #1597)
+#2410 := (~ #2409 #2408)
+#2405 := (not #1594)
+#2406 := (~ #2405 #2404)
+#2401 := (not #1591)
+#2402 := (~ #2401 #2400)
+#2397 := (not #1588)
+#2398 := (~ #2397 #2396)
+#2393 := (not #1585)
+#2394 := (~ #2393 #2392)
+#2389 := (not #1582)
+#2390 := (~ #2389 #2388)
+#2385 := (not #1579)
+#2386 := (~ #2385 #2384)
+#2381 := (not #1576)
+#2382 := (~ #2381 #2380)
+#2377 := (not #1573)
 #2378 := (~ #2377 #2376)
-#2374 := (~ #2373 #2373)
-#2375 := [refl]: #2374
-#2379 := [nnf-neg #2375]: #2378
-#2371 := (~ #2370 #2370)
-#2372 := [refl]: #2371
-#2382 := [nnf-neg #2372 #2379]: #2381
-#2368 := (~ #2367 #2366)
-#2369 := [sk]: #2368
-#2384 := [trans #2369 #2382]: #2383
-#2343 := (not #1542)
-#2344 := (~ #2343 #1539)
-#2341 := (~ #1539 #1539)
-#2339 := (~ #1536 #1536)
-#2340 := [refl]: #2339
-#2342 := [nnf-pos #2340]: #2341
-#2345 := [nnf-neg #2342]: #2344
-#2388 := [nnf-neg #2345 #2384]: #2387
-#2335 := (~ #1542 #2334)
-#2336 := [sk]: #2335
-#2392 := [nnf-neg #2336 #2388]: #2391
-#2312 := (not #1518)
-#2313 := (~ #2312 #1515)
-#2310 := (~ #1515 #1515)
-#2308 := (~ #1510 #1510)
-#2309 := [refl]: #2308
-#2311 := [nnf-pos #2309]: #2310
-#2314 := [nnf-neg #2311]: #2313
-#2396 := [nnf-neg #2314 #2392]: #2395
-#2304 := (~ #1518 #2303)
-#2305 := [sk]: #2304
-#2400 := [nnf-neg #2305 #2396]: #2399
-#2285 := (not #1499)
-#2286 := (~ #2285 #1496)
-#2283 := (~ #1496 #1496)
-#2281 := (~ #1493 #1493)
-#2282 := [refl]: #2281
-#2284 := [nnf-pos #2282]: #2283
-#2287 := [nnf-neg #2284]: #2286
-#2404 := [nnf-neg #2287 #2400]: #2403
-#2277 := (~ #1499 #2276)
-#2278 := [sk]: #2277
-#2408 := [nnf-neg #2278 #2404]: #2407
-#2271 := (~ #2270 #2270)
-#2272 := [refl]: #2271
-#2412 := [nnf-neg #2272 #2408]: #2411
-#2268 := (~ #1490 #1490)
-#2269 := [refl]: #2268
-#2416 := [nnf-neg #2269 #2412]: #2415
-#2265 := (not #953)
-#2266 := (~ #2265 #819)
-#2263 := (~ #819 #819)
-#2261 := (~ #814 #814)
-#2262 := [refl]: #2261
-#2264 := [nnf-pos #2262]: #2263
-#2267 := [nnf-neg #2264]: #2266
-#2420 := [nnf-neg #2267 #2416]: #2419
-#2257 := (~ #953 #2256)
-#2258 := [sk]: #2257
-#2424 := [nnf-neg #2258 #2420]: #2423
-#2245 := (not #1485)
-#2246 := (~ #2245 #1482)
-#2243 := (~ #1482 #1482)
-#2241 := (~ #1477 #1477)
-#2242 := [refl]: #2241
-#2244 := [nnf-pos #2242]: #2243
-#2247 := [nnf-neg #2244]: #2246
-#2428 := [nnf-neg #2247 #2424]: #2427
-#2237 := (~ #1485 #2236)
-#2238 := [sk]: #2237
-#2432 := [nnf-neg #2238 #2428]: #2431
-#2227 := (not #1474)
-#2228 := (~ #2227 #1471)
-#2225 := (~ #1471 #1471)
-#2223 := (~ #1466 #1466)
-#2224 := [refl]: #2223
-#2226 := [nnf-pos #2224]: #2225
-#2229 := [nnf-neg #2226]: #2228
-#2220 := (not #1665)
-#2221 := (~ #2220 #2215)
-#2216 := (~ #1424 #2215)
-#2217 := [sk]: #2216
-#2222 := [nnf-neg #2217]: #2221
-#2204 := (~ #2203 #2203)
-#2205 := [refl]: #2204
-#2201 := (~ #757 #757)
-#2202 := [refl]: #2201
-#2452 := [nnf-neg #2202 #2205 #2222 #2229 #2432 #2439 #2446 #2448]: #2451
-#2198 := (not #1442)
-#2199 := (~ #2198 #2197)
-#2195 := (~ #1665 #2194)
-#2192 := (~ #2191 #2191)
-#2193 := [refl]: #2192
-#2196 := [nnf-neg #2193]: #2195
-#2188 := (not #1413)
-#2189 := (~ #2188 #2187)
-#2184 := (not #1410)
-#2185 := (~ #2184 #2183)
-#2180 := (not #1407)
-#2181 := (~ #2180 #2179)
-#2176 := (not #1402)
-#2177 := (~ #2176 #2175)
-#2172 := (not #1394)
-#2173 := (~ #2172 #1391)
-#2170 := (~ #1391 #1391)
-#2168 := (~ #1388 #1388)
-#2169 := [refl]: #2168
-#2171 := [nnf-pos #2169]: #2170
-#2174 := [nnf-neg #2171]: #2173
-#2166 := (~ #2165 #2165)
-#2167 := [refl]: #2166
-#2178 := [nnf-neg #2167 #2174]: #2177
-#2161 := (~ #1394 #2160)
-#2162 := [sk]: #2161
-#2182 := [nnf-neg #2162 #2178]: #2181
-#2136 := (not #1376)
-#2137 := (~ #2136 #2133)
-#2134 := (~ #1373 #2133)
-#2131 := (~ #1370 #2130)
-#2126 := (~ #1367 #2125)
-#2127 := [sk]: #2126
-#2114 := (~ #1351 #1351)
-#2115 := [refl]: #2114
-#2132 := [monotonicity #2115 #2127]: #2131
-#2135 := [nnf-pos #2132]: #2134
-#2138 := [nnf-neg #2135]: #2137
-#2186 := [nnf-neg #2138 #2182]: #2185
-#2112 := (~ #1376 #2109)
-#2087 := (exists (vars (?v1 S3)) #2086)
-#2095 := (or #2094 #2087)
-#2096 := (not #2095)
-#2110 := (~ #2096 #2109)
-#2106 := (not #2087)
-#2107 := (~ #2106 #2105)
-#2103 := (~ #2102 #2102)
-#2104 := [refl]: #2103
-#2108 := [nnf-neg #2104]: #2107
-#2100 := (~ #2099 #2099)
-#2101 := [refl]: #2100
-#2111 := [nnf-neg #2101 #2108]: #2110
-#2097 := (~ #1376 #2096)
-#2098 := [sk]: #2097
-#2113 := [trans #2098 #2111]: #2112
-#2190 := [nnf-neg #2113 #2186]: #2189
-#2074 := (~ #2073 #2073)
-#2075 := [refl]: #2074
-#2071 := (~ #2070 #2070)
-#2072 := [refl]: #2071
-#2068 := (~ #2067 #2067)
-#2069 := [refl]: #2068
+#2358 := (not #1570)
+#2374 := (~ #2358 #2371)
+#2348 := (exists (vars (?v1 S3)) #2347)
+#2356 := (or #2355 #2348)
+#2357 := (not #2356)
+#2372 := (~ #2357 #2371)
+#2368 := (not #2348)
+#2369 := (~ #2368 #2367)
+#2365 := (~ #2364 #2364)
+#2366 := [refl]: #2365
+#2370 := [nnf-neg #2366]: #2369
+#2362 := (~ #2361 #2361)
+#2363 := [refl]: #2362
+#2373 := [nnf-neg #2363 #2370]: #2372
+#2359 := (~ #2358 #2357)
+#2360 := [sk]: #2359
+#2375 := [trans #2360 #2373]: #2374
+#2334 := (not #1533)
+#2335 := (~ #2334 #1530)
+#2332 := (~ #1530 #1530)
+#2330 := (~ #1527 #1527)
+#2331 := [refl]: #2330
+#2333 := [nnf-pos #2331]: #2332
+#2336 := [nnf-neg #2333]: #2335
+#2379 := [nnf-neg #2336 #2375]: #2378
+#2326 := (~ #1533 #2325)
+#2327 := [sk]: #2326
+#2383 := [nnf-neg #2327 #2379]: #2382
+#2303 := (not #1509)
+#2304 := (~ #2303 #1506)
+#2301 := (~ #1506 #1506)
+#2299 := (~ #1501 #1501)
+#2300 := [refl]: #2299
+#2302 := [nnf-pos #2300]: #2301
+#2305 := [nnf-neg #2302]: #2304
+#2387 := [nnf-neg #2305 #2383]: #2386
+#2295 := (~ #1509 #2294)
+#2296 := [sk]: #2295
+#2391 := [nnf-neg #2296 #2387]: #2390
+#2276 := (not #1490)
+#2277 := (~ #2276 #1487)
+#2274 := (~ #1487 #1487)
+#2272 := (~ #1484 #1484)
+#2273 := [refl]: #2272
+#2275 := [nnf-pos #2273]: #2274
+#2278 := [nnf-neg #2275]: #2277
+#2395 := [nnf-neg #2278 #2391]: #2394
+#2268 := (~ #1490 #2267)
+#2269 := [sk]: #2268
+#2399 := [nnf-neg #2269 #2395]: #2398
+#2262 := (~ #2261 #2261)
+#2263 := [refl]: #2262
+#2403 := [nnf-neg #2263 #2399]: #2402
+#2259 := (~ #1481 #1481)
+#2260 := [refl]: #2259
+#2407 := [nnf-neg #2260 #2403]: #2406
+#2256 := (not #944)
+#2257 := (~ #2256 #810)
+#2254 := (~ #810 #810)
+#2252 := (~ #805 #805)
+#2253 := [refl]: #2252
+#2255 := [nnf-pos #2253]: #2254
+#2258 := [nnf-neg #2255]: #2257
+#2411 := [nnf-neg #2258 #2407]: #2410
+#2248 := (~ #944 #2247)
+#2249 := [sk]: #2248
+#2415 := [nnf-neg #2249 #2411]: #2414
+#2236 := (not #1476)
+#2237 := (~ #2236 #1473)
+#2234 := (~ #1473 #1473)
+#2232 := (~ #1468 #1468)
+#2233 := [refl]: #2232
+#2235 := [nnf-pos #2233]: #2234
+#2238 := [nnf-neg #2235]: #2237
+#2419 := [nnf-neg #2238 #2415]: #2418
+#2228 := (~ #1476 #2227)
+#2229 := [sk]: #2228
+#2423 := [nnf-neg #2229 #2419]: #2422
+#2218 := (not #1465)
+#2219 := (~ #2218 #1462)
+#2216 := (~ #1462 #1462)
+#2214 := (~ #1457 #1457)
+#2215 := [refl]: #2214
+#2217 := [nnf-pos #2215]: #2216
+#2220 := [nnf-neg #2217]: #2219
+#2211 := (not #1656)
+#2212 := (~ #2211 #2206)
+#2207 := (~ #1415 #2206)
+#2208 := [sk]: #2207
+#2213 := [nnf-neg #2208]: #2212
+#2195 := (~ #756 #756)
+#2196 := [refl]: #2195
+#2193 := (~ #2192 #2192)
+#2194 := [refl]: #2193
+#2443 := [nnf-neg #2194 #2196 #2213 #2220 #2423 #2430 #2437 #2439]: #2442
+#2189 := (not #1433)
+#2190 := (~ #2189 #2188)
+#2186 := (~ #1656 #2185)
+#2183 := (~ #2182 #2182)
+#2184 := [refl]: #2183
+#2187 := [nnf-neg #2184]: #2186
+#2179 := (not #1404)
+#2180 := (~ #2179 #2178)
+#2175 := (not #1401)
+#2176 := (~ #2175 #2174)
+#2171 := (not #1398)
+#2172 := (~ #2171 #2170)
+#2167 := (not #1393)
+#2168 := (~ #2167 #2166)
+#2163 := (not #1385)
+#2164 := (~ #2163 #1382)
+#2161 := (~ #1382 #1382)
+#2159 := (~ #1379 #1379)
+#2160 := [refl]: #2159
+#2162 := [nnf-pos #2160]: #2161
+#2165 := [nnf-neg #2162]: #2164
+#2157 := (~ #2156 #2156)
+#2158 := [refl]: #2157
+#2169 := [nnf-neg #2158 #2165]: #2168
+#2152 := (~ #1385 #2151)
+#2153 := [sk]: #2152
+#2173 := [nnf-neg #2153 #2169]: #2172
+#2127 := (not #1367)
+#2128 := (~ #2127 #2124)
+#2125 := (~ #1364 #2124)
+#2122 := (~ #1361 #2121)
+#2117 := (~ #1358 #2116)
+#2118 := [sk]: #2117
+#2105 := (~ #1342 #1342)
+#2106 := [refl]: #2105
+#2123 := [monotonicity #2106 #2118]: #2122
+#2126 := [nnf-pos #2123]: #2125
+#2129 := [nnf-neg #2126]: #2128
+#2177 := [nnf-neg #2129 #2173]: #2176
+#2103 := (~ #1367 #2100)
+#2078 := (exists (vars (?v1 S3)) #2077)
+#2086 := (or #2085 #2078)
+#2087 := (not #2086)
+#2101 := (~ #2087 #2100)
+#2097 := (not #2078)
+#2098 := (~ #2097 #2096)
+#2094 := (~ #2093 #2093)
+#2095 := [refl]: #2094
+#2099 := [nnf-neg #2095]: #2098
+#2091 := (~ #2090 #2090)
+#2092 := [refl]: #2091
+#2102 := [nnf-neg #2092 #2099]: #2101
+#2088 := (~ #1367 #2087)
+#2089 := [sk]: #2088
+#2104 := [trans #2089 #2102]: #2103
+#2181 := [nnf-neg #2104 #2177]: #2180
 #2065 := (~ #2064 #2064)
 #2066 := [refl]: #2065
-#2200 := [nnf-neg #2066 #2069 #2072 #2075 #2190 #2196]: #2199
-#2456 := [nnf-neg #2200 #2452]: #2455
-#2061 := (not #1339)
-#2062 := (~ #2061 #2058)
-#2059 := (~ #1336 #2058)
-#2056 := (~ #1333 #2055)
-#2051 := (~ #1330 #2050)
-#2052 := [sk]: #2051
-#2037 := (~ #1306 #1306)
-#2038 := [refl]: #2037
-#2057 := [monotonicity #2038 #2052]: #2056
-#2060 := [nnf-pos #2057]: #2059
-#2063 := [nnf-neg #2060]: #2062
-#2034 := (not #1750)
-#2035 := (~ #2034 #2031)
-#2032 := (~ #1294 #2031)
-#2029 := (~ #1291 #2028)
-#2024 := (~ #1288 #2023)
-#2025 := [sk]: #2024
-#2009 := (~ #1268 #1268)
-#2010 := [refl]: #2009
-#2030 := [monotonicity #2010 #2025]: #2029
-#2033 := [nnf-pos #2030]: #2032
-#2036 := [nnf-neg #2033]: #2035
-#2007 := (~ #2006 #2006)
-#2008 := [refl]: #2007
-#2481 := [nnf-neg #2008 #2036 #2063 #2456 #2463 #2470 #2477]: #2480
-#2004 := (~ #1750 #2001)
-#1979 := (exists (vars (?v1 S3)) #1978)
-#1987 := (or #1986 #1979)
-#1988 := (not #1987)
-#2002 := (~ #1988 #2001)
-#1998 := (not #1979)
-#1999 := (~ #1998 #1997)
-#1995 := (~ #1994 #1994)
-#1996 := [refl]: #1995
-#2000 := [nnf-neg #1996]: #1999
-#1992 := (~ #1991 #1991)
-#1993 := [refl]: #1992
-#2003 := [nnf-neg #1993 #2000]: #2002
-#1989 := (~ #1750 #1988)
-#1990 := [sk]: #1989
-#2005 := [trans #1990 #2003]: #2004
-#2485 := [nnf-neg #2005 #2481]: #2484
-#1964 := (not #1256)
-#1965 := (~ #1964 #1253)
-#1962 := (~ #1253 #1253)
-#1960 := (~ #1250 #1250)
-#1961 := [refl]: #1960
-#1963 := [nnf-pos #1961]: #1962
-#1966 := [nnf-neg #1963]: #1965
-#2489 := [nnf-neg #1966 #2485]: #2488
-#1956 := (~ #1256 #1955)
-#1957 := [sk]: #1956
-#2493 := [nnf-neg #1957 #2489]: #2492
-#1933 := (not #1225)
-#1934 := (~ #1933 #1222)
-#1931 := (~ #1222 #1222)
-#1929 := (~ #1217 #1217)
-#1930 := [refl]: #1929
-#1932 := [nnf-pos #1930]: #1931
-#1935 := [nnf-neg #1932]: #1934
-#2497 := [nnf-neg #1935 #2493]: #2496
-#1925 := (~ #1225 #1924)
-#1926 := [sk]: #1925
-#2501 := [nnf-neg #1926 #2497]: #2500
-#1906 := (not #1205)
-#1907 := (~ #1906 #1202)
-#1904 := (~ #1202 #1202)
-#1902 := (~ #1201 #1201)
-#1903 := [refl]: #1902
-#1905 := [nnf-pos #1903]: #1904
-#1908 := [nnf-neg #1905]: #1907
-#2505 := [nnf-neg #1908 #2501]: #2504
-#1898 := (~ #1205 #1897)
-#1899 := [sk]: #1898
-#2509 := [nnf-neg #1899 #2505]: #2508
-#1861 := (~ #1860 #1860)
-#1893 := [refl]: #1861
-#2513 := [nnf-neg #1893 #2509]: #2512
-#1891 := (~ #1196 #1196)
-#1892 := [refl]: #1891
-#2516 := [nnf-neg #1892 #2513]: #2515
-#1837 := [not-or-elim #1833]: #1836
-#2517 := [mp~ #1837 #2516]: #2514
-#2518 := [mp #2517 #3055]: #3053
-#3697 := [mp #2518 #3696]: #3694
-#4604 := [mp #3697 #4603]: #4601
-#6496 := [unit-resolution #4604 #5320]: #4598
-#3943 := (or #4595 #4589)
-#3944 := [def-axiom]: #3943
-#6497 := [unit-resolution #3944 #6496]: #4589
-#6498 := (or #4592 #4586)
-#5107 := [hypothesis]: #1897
-#5106 := (<= #1895 0::Int)
-#4721 := (or #5106 #1896)
-#5139 := [th-lemma arith farkas 1 1]: #4721
-#5140 := [unit-resolution #5139 #5107]: #5106
-#5099 := (not #5106)
-#5114 := (or #5099 #1896)
-#355 := (<= f8 0::Int)
-#356 := (not #355)
+#2062 := (~ #2061 #2061)
+#2063 := [refl]: #2062
+#2059 := (~ #2058 #2058)
+#2060 := [refl]: #2059
+#2056 := (~ #2055 #2055)
+#2057 := [refl]: #2056
+#2191 := [nnf-neg #2057 #2060 #2063 #2066 #2181 #2187]: #2190
+#2447 := [nnf-neg #2191 #2443]: #2446
+#2052 := (not #1330)
+#2053 := (~ #2052 #2049)
+#2050 := (~ #1327 #2049)
+#2047 := (~ #1324 #2046)
+#2042 := (~ #1321 #2041)
+#2043 := [sk]: #2042
+#2028 := (~ #1297 #1297)
+#2029 := [refl]: #2028
+#2048 := [monotonicity #2029 #2043]: #2047
+#2051 := [nnf-pos #2048]: #2050
+#2054 := [nnf-neg #2051]: #2053
+#2025 := (not #1741)
+#2026 := (~ #2025 #2022)
+#2023 := (~ #1285 #2022)
+#2020 := (~ #1282 #2019)
+#2015 := (~ #1279 #2014)
+#2016 := [sk]: #2015
+#2000 := (~ #1259 #1259)
+#2001 := [refl]: #2000
+#2021 := [monotonicity #2001 #2016]: #2020
+#2024 := [nnf-pos #2021]: #2023
+#2027 := [nnf-neg #2024]: #2026
+#1998 := (~ #1997 #1997)
+#1999 := [refl]: #1998
+#2472 := [nnf-neg #1999 #2027 #2054 #2447 #2454 #2461 #2468]: #2471
+#1995 := (~ #1741 #1992)
+#1970 := (exists (vars (?v1 S3)) #1969)
+#1978 := (or #1977 #1970)
+#1979 := (not #1978)
+#1993 := (~ #1979 #1992)
+#1989 := (not #1970)
+#1990 := (~ #1989 #1988)
+#1986 := (~ #1985 #1985)
+#1987 := [refl]: #1986
+#1991 := [nnf-neg #1987]: #1990
+#1983 := (~ #1982 #1982)
+#1984 := [refl]: #1983
+#1994 := [nnf-neg #1984 #1991]: #1993
+#1980 := (~ #1741 #1979)
+#1981 := [sk]: #1980
+#1996 := [trans #1981 #1994]: #1995
+#2476 := [nnf-neg #1996 #2472]: #2475
+#1955 := (not #1247)
+#1956 := (~ #1955 #1244)
+#1953 := (~ #1244 #1244)
+#1951 := (~ #1241 #1241)
+#1952 := [refl]: #1951
+#1954 := [nnf-pos #1952]: #1953
+#1957 := [nnf-neg #1954]: #1956
+#2480 := [nnf-neg #1957 #2476]: #2479
+#1947 := (~ #1247 #1946)
+#1948 := [sk]: #1947
+#2484 := [nnf-neg #1948 #2480]: #2483
+#1924 := (not #1216)
+#1925 := (~ #1924 #1213)
+#1922 := (~ #1213 #1213)
+#1920 := (~ #1208 #1208)
+#1921 := [refl]: #1920
+#1923 := [nnf-pos #1921]: #1922
+#1926 := [nnf-neg #1923]: #1925
+#2488 := [nnf-neg #1926 #2484]: #2487
+#1916 := (~ #1216 #1915)
+#1917 := [sk]: #1916
+#2492 := [nnf-neg #1917 #2488]: #2491
+#1897 := (not #1196)
+#1898 := (~ #1897 #1193)
+#1895 := (~ #1193 #1193)
+#1893 := (~ #1192 #1192)
+#1894 := [refl]: #1893
+#1896 := [nnf-pos #1894]: #1895
+#1899 := [nnf-neg #1896]: #1898
+#2496 := [nnf-neg #1899 #2492]: #2495
+#1889 := (~ #1196 #1888)
+#1890 := [sk]: #1889
+#2500 := [nnf-neg #1890 #2496]: #2499
+#1852 := (~ #1851 #1851)
+#1884 := [refl]: #1852
+#2504 := [nnf-neg #1884 #2500]: #2503
+#1882 := (~ #1187 #1187)
+#1883 := [refl]: #1882
+#2507 := [nnf-neg #1883 #2504]: #2506
+#1828 := [not-or-elim #1824]: #1827
+#2508 := [mp~ #1828 #2507]: #2505
+#2509 := [mp #2508 #3046]: #3044
+#3688 := [mp #2509 #3687]: #3685
+#4595 := [mp #3688 #4594]: #4592
+#6487 := [unit-resolution #4595 #5311]: #4589
+#3934 := (or #4586 #4580)
+#3935 := [def-axiom]: #3934
+#6488 := [unit-resolution #3935 #6487]: #4580
+#6489 := (or #4583 #4577)
+#5098 := [hypothesis]: #1888
+#5097 := (<= #1886 0::Int)
+#4712 := (or #5097 #1887)
+#5130 := [th-lemma arith farkas 1 1]: #4712
+#5131 := [unit-resolution #5130 #5098]: #5097
+#5090 := (not #5097)
+#5105 := (or #5090 #1887)
+#354 := (<= f8 0::Int)
+#355 := (not #354)
 #46 := (< 0::Int f8)
-#357 := (iff #46 #356)
-#358 := [rewrite]: #357
-#351 := [asserted]: #46
-#359 := [mp #351 #358]: #356
-#4718 := (* -1::Int #1895)
-#4719 := (+ f8 #4718)
-#4720 := (<= #4719 0::Int)
-#3933 := (= f8 #1895)
-#3912 := (= f10 ?v0!0)
-#4911 := (not #3912)
-#4908 := (= #1895 0::Int)
-#5108 := (not #4908)
-#5109 := (or #5108 #1896)
-#5110 := [th-lemma arith triangle-eq]: #5109
-#5090 := [unit-resolution #5110 #5107]: #5108
-#4917 := (or #4784 #4911 #4908)
-#3932 := (= ?v0!0 f10)
-#4909 := (not #3932)
-#4910 := (or #4909 #4908)
-#4648 := (or #4784 #4910)
-#5103 := (iff #4648 #4917)
-#4715 := (or #4911 #4908)
-#4934 := (or #4784 #4715)
-#4980 := (iff #4934 #4917)
-#5102 := [rewrite]: #4980
-#4978 := (iff #4648 #4934)
-#4716 := (iff #4910 #4715)
-#4914 := (iff #4909 #4911)
-#3914 := (iff #3932 #3912)
-#3915 := [rewrite]: #3914
-#4915 := [monotonicity #3915]: #4914
-#4783 := [monotonicity #4915]: #4716
-#4979 := [monotonicity #4783]: #4978
-#5104 := [trans #4979 #5102]: #5103
-#4931 := [quant-inst #1894]: #4648
-#5105 := [mp #4931 #5104]: #4917
-#5091 := [unit-resolution #5105 #4610 #5090]: #4911
-#3927 := (or #3912 #3933)
-#4219 := (forall (vars (?v0 S3)) (:pat #4218) #446)
-#4222 := (iff #451 #4219)
-#4220 := (iff #446 #446)
-#4221 := [refl]: #4220
-#4223 := [quant-intro #4221]: #4222
-#1856 := (~ #451 #451)
-#1885 := (~ #446 #446)
-#1886 := [refl]: #1885
-#1857 := [nnf-pos #1886]: #1856
-#1834 := [not-or-elim #1833]: #451
-#1887 := [mp~ #1834 #1857]: #451
-#4224 := [mp #1887 #4223]: #4219
-#3923 := (not #4219)
-#3916 := (or #3923 #3912 #3933)
-#3922 := (or #3932 #3933)
-#3924 := (or #3923 #3922)
-#4662 := (iff #3924 #3916)
-#3909 := (or #3923 #3927)
-#4646 := (iff #3909 #3916)
-#4661 := [rewrite]: #4646
-#4644 := (iff #3924 #3909)
-#3918 := (iff #3922 #3927)
-#3919 := [monotonicity #3915]: #3918
-#4645 := [monotonicity #3919]: #4644
-#4643 := [trans #4645 #4661]: #4662
-#3907 := [quant-inst #1894]: #3924
-#4717 := [mp #3907 #4643]: #3916
-#5092 := [unit-resolution #4717 #4224]: #3927
-#5093 := [unit-resolution #5092 #5091]: #3933
-#5094 := (not #3933)
-#5089 := (or #5094 #4720)
-#5095 := [th-lemma arith triangle-eq]: #5089
-#5096 := [unit-resolution #5095 #5093]: #4720
-#5097 := [hypothesis]: #5106
-#5098 := [th-lemma arith farkas 1 -1 1 #5097 #5096 #359]: false
-#5115 := [lemma #5098]: #5114
-#5141 := [unit-resolution #5115 #5140 #5107]: false
-#5142 := [lemma #5141]: #1896
-#3938 := (or #4592 #1897 #4586)
-#3939 := [def-axiom]: #3938
-#6499 := [unit-resolution #3939 #5142]: #6498
-#6500 := [unit-resolution #6499 #6497]: #4586
-#3962 := (or #4583 #4577)
-#3963 := [def-axiom]: #3962
-#6501 := [unit-resolution #3963 #6500]: #4577
-#5817 := [hypothesis]: #1917
-#5330 := (or #5529 #2054)
-#5335 := [quant-inst #1910]: #5330
-#5818 := [unit-resolution #5335 #4231 #5817]: false
-#5819 := [lemma #5818]: #2054
-#3755 := (or #2026 #1917)
-#3842 := [def-axiom]: #3755
-#6502 := [unit-resolution #3842 #5819]: #2026
-#3956 := (or #4580 #1928 #4574)
-#3958 := [def-axiom]: #3956
-#6503 := [unit-resolution #3958 #6502 #6501]: #4574
-#3983 := (or #4571 #4565)
-#3984 := [def-axiom]: #3983
-#6504 := [unit-resolution #3984 #6503]: #4565
-#3979 := (or #4568 #3098 #4562)
-#3980 := [def-axiom]: #3979
-#6505 := [unit-resolution #3980 #6504 #6495]: #4562
-#3993 := (or #4559 #4553)
-#4014 := [def-axiom]: #3993
-#6506 := [unit-resolution #4014 #6505]: #4553
-#5790 := (= f8 #1970)
-#5854 := (not #5790)
-#5852 := [hypothesis]: #4270
-#4159 := (or #4267 #1982)
-#3833 := [def-axiom]: #4159
-#5853 := [unit-resolution #3833 #5852]: #1982
-#5855 := (or #5854 #1981)
-#5856 := [th-lemma arith triangle-eq]: #5855
-#5857 := [unit-resolution #5856 #5853]: #5854
-#3834 := (or #4267 #2569)
-#4166 := [def-axiom]: #3834
-#5858 := [unit-resolution #4166 #5852]: #2569
-#5810 := (or #3923 #2566 #5790)
-#5791 := (or #1983 #5790)
-#5805 := (or #3923 #5791)
-#5669 := (iff #5805 #5810)
-#5807 := (or #2566 #5790)
-#5812 := (or #3923 #5807)
-#5815 := (iff #5812 #5810)
-#5668 := [rewrite]: #5815
-#5813 := (iff #5805 #5812)
-#5808 := (iff #5791 #5807)
-#5809 := [monotonicity #2568]: #5808
-#5814 := [monotonicity #5809]: #5813
-#5670 := [trans #5814 #5668]: #5669
-#5811 := [quant-inst #1967]: #5805
-#5475 := [mp #5811 #5670]: #5810
-#5859 := [unit-resolution #5475 #4224 #5858 #5857]: false
-#5860 := [lemma #5859]: #4267
-#4001 := (or #4556 #4270 #4550)
-#4002 := [def-axiom]: #4001
-#6507 := [unit-resolution #4002 #5860 #6506]: #4550
-#4034 := (or #4547 #4274)
-#4030 := [def-axiom]: #4034
-#7121 := [unit-resolution #4030 #6507]: #4274
-#9553 := (or #4279 #7757)
-#9554 := [quant-inst #2273]: #9553
-#9580 := [unit-resolution #9554 #7121]: #7757
-#7570 := (* -1::Int #7536)
-#7571 := (+ #2274 #7570)
-#9581 := (>= #7571 0::Int)
-#7539 := (= #2274 #7536)
-#10087 := [hypothesis]: #2276
-#11985 := (or #7539 #2275 #6073)
-#9988 := (f5 #7211 ?v0!15)
-#9989 := (f9 #9988)
-#9990 := (* -1::Int #9989)
-#7586 := (f5 f22 ?v0!15)
-#7587 := (f9 #7586)
-#10058 := (+ #7587 #9990)
-#10062 := (>= #10058 0::Int)
-#10057 := (= #7587 #9989)
-#10065 := (= #9989 #7587)
-#10063 := (= #9988 #7586)
-#10064 := [monotonicity #7790]: #10063
-#10066 := [monotonicity #10064]: #10065
-#10067 := [symm #10066]: #10057
-#10068 := (not #10057)
-#10069 := (or #10068 #10062)
-#10070 := [th-lemma arith triangle-eq]: #10069
-#10071 := [unit-resolution #10070 #10067]: #10062
-#7968 := (f5 #6069 #7211)
-#8217 := (f6 #7968)
-#9081 := (f13 f14 #8217)
-#9082 := (* -1::Int #9081)
-#9455 := (+ #6070 #9082)
-#9457 := (>= #9455 0::Int)
-#9861 := (= #6070 #9081)
-#8218 := (= #6069 #8217)
-#8389 := (or #6829 #8218)
-#8390 := [quant-inst #6069 #7211]: #8389
-#9280 := [unit-resolution #8390 #4205]: #8218
-#11947 := [monotonicity #9280]: #9861
-#11945 := (not #9861)
-#11948 := (or #11945 #9457)
-#11949 := [th-lemma arith triangle-eq]: #11948
-#11950 := [unit-resolution #11949 #11947]: #9457
-#10866 := (+ #99 #9082)
-#10878 := (<= #10866 0::Int)
-#10875 := (= #99 #9081)
-#11956 := (= #9081 #99)
-#10697 := (= #8217 f10)
-#7317 := (= #6069 f10)
-#7319 := (= f10 #6069)
-#7298 := (?v1!7 #6069)
-#7310 := (f3 f15 #7298)
-#7311 := (= f1 #7310)
-#7312 := (not #7311)
-#7303 := (f5 #7298 #6069)
-#7304 := (f9 #7303)
-#7305 := (* -1::Int #7304)
-#7299 := (f13 f14 #7298)
-#7300 := (* -1::Int #7299)
-#7306 := (+ #7300 #7305)
-#7307 := (+ #6070 #7306)
-#7308 := (= #7307 0::Int)
-#7309 := (not #7308)
-#7301 := (+ #6070 #7300)
-#7302 := (<= #7301 0::Int)
-#7322 := (or #7302 #7309 #7312)
-#9607 := (or #2275 #6073 #7302)
-#8251 := (not #7302)
-#10072 := [hypothesis]: #8251
-#10110 := (or #7539 #2275 #6073 #7302)
-#9125 := (>= #7299 0::Int)
-#9128 := (or #4279 #9125)
-#9299 := [quant-inst #7298]: #9128
-#10073 := [unit-resolution #9299 #7121]: #9125
-#7561 := (* -1::Int #2274)
-#7612 := (+ #7561 #7587)
-#7613 := (+ #174 #7612)
-#9497 := (<= #7613 0::Int)
-#7616 := (= #7613 0::Int)
-#7591 := (* -1::Int #7587)
-#7595 := (+ f8 #7591)
-#7596 := (<= #7595 0::Int)
-#9510 := (not #7596)
-#7605 := (+ #7570 #7587)
-#7606 := (+ #174 #7605)
-#7607 := (>= #7606 0::Int)
-#7638 := (or #7596 #7607)
-#7641 := (not #7638)
-#10075 := (not #7539)
-#10076 := [hypothesis]: #10075
-#7644 := (or #7539 #7641)
-#5788 := (or #4547 #4538)
-#4722 := (?v1!7 ?v0!8)
-#4998 := (f13 f19 #4722)
-#5011 := (* -1::Int #4998)
-#4723 := (f13 f14 #4722)
-#5231 := (+ #4723 #5011)
-#5236 := (>= #5231 0::Int)
-#5230 := (= #4723 #4998)
-#5720 := (= #4998 #4723)
-#5715 := [hypothesis]: #4535
-#5716 := [hypothesis]: #4550
-#4023 := (or #4547 #4541)
-#3991 := [def-axiom]: #4023
-#5717 := [unit-resolution #3991 #5716]: #4541
-#4028 := (or #4544 #4383 #4538)
-#4029 := [def-axiom]: #4028
-#5718 := [unit-resolution #4029 #5717 #5715]: #4383
-#4134 := (or #4380 #624)
-#4135 := [def-axiom]: #4134
-#5719 := [unit-resolution #4135 #5718]: #624
-#5714 := [symm #5719]: #138
-#5721 := [monotonicity #5714]: #5720
-#5722 := [symm #5721]: #5230
-#5723 := (not #5230)
-#5724 := (or #5723 #5236)
-#5737 := [th-lemma arith triangle-eq]: #5724
-#5738 := [unit-resolution #5737 #5722]: #5236
-#4705 := (* -1::Int #4723)
-#4655 := (f13 f14 ?v0!8)
-#4706 := (+ #4655 #4705)
-#4707 := (<= #4706 0::Int)
-#4888 := (not #4707)
-#4714 := (f3 f15 #4722)
-#4785 := (= f1 #4714)
-#4786 := (not #4785)
-#4708 := (f5 #4722 ?v0!8)
-#4709 := (f9 #4708)
-#4704 := (* -1::Int #4709)
-#4790 := (+ #4704 #4705)
-#4791 := (+ #4655 #4790)
-#4773 := (= #4791 0::Int)
-#4776 := (not #4773)
-#4781 := (or #4707 #4776 #4786)
-#4855 := (not #4781)
-#4656 := (* -1::Int #4655)
-#4657 := (+ f8 #4656)
-#4637 := (<= #4657 0::Int)
-#4993 := (not #4637)
-#4136 := (or #4380 #4374)
-#4133 := [def-axiom]: #4136
-#5739 := [unit-resolution #4133 #5718]: #4374
-#4032 := (or #4547 #100)
-#4033 := [def-axiom]: #4032
-#5740 := [unit-resolution #4033 #5716]: #100
-#5741 := (= #157 #99)
-#5736 := [monotonicity #5714]: #5741
-#5742 := [trans #5736 #5740]: #158
-#4146 := (or #4356 #2165)
-#3809 := [def-axiom]: #4146
-#5743 := [unit-resolution #3809 #5742]: #4356
-#4035 := (or #4547 #4282)
-#4015 := [def-axiom]: #4035
-#5744 := [unit-resolution #4015 #5716]: #4282
-#3850 := (or #4380 #4316)
-#4132 := [def-axiom]: #3850
-#5745 := [unit-resolution #4132 #5718]: #4316
-#4976 := (or #3361 #4321 #4287 #715)
-#4949 := [hypothesis]: #3366
-#4149 := (or #3361 #2152)
-#4150 := [def-axiom]: #4149
-#4950 := [unit-resolution #4150 #4949]: #2152
-#4724 := (f13 f14 ?v1!10)
-#4725 := (* -1::Int #4724)
-#4726 := (+ f8 #4725)
-#4727 := (<= #4726 0::Int)
-#4728 := (f3 f15 ?v1!10)
-#4729 := (= f1 #4728)
-#4800 := (not #4729)
-#3837 := (f13 f14 ?v0!11)
-#3838 := (* -1::Int #3837)
-#4802 := (+ #3838 #4724)
-#4803 := (+ #2146 #4802)
-#4806 := (>= #4803 0::Int)
-#4959 := (not #4806)
-#4933 := (+ #2143 #4725)
-#4935 := (>= #4933 0::Int)
-#4932 := (= #2143 #4724)
-#4937 := (= #4724 #2143)
-#4936 := [hypothesis]: #624
-#4938 := [monotonicity #4936]: #4937
-#4939 := [symm #4938]: #4932
-#4940 := (not #4932)
-#4941 := (or #4940 #4935)
-#4942 := [th-lemma arith triangle-eq]: #4941
-#4943 := [unit-resolution #4942 #4939]: #4935
-#4147 := (not #2807)
-#4153 := (or #3361 #4147)
-#3791 := [def-axiom]: #4153
-#4944 := [unit-resolution #3791 #4949]: #4147
-#4926 := (+ #2141 #3838)
-#4930 := (<= #4926 0::Int)
-#4925 := (= #2141 #3837)
-#4947 := (= #3837 #2141)
-#4948 := [monotonicity #4936]: #4947
-#4951 := [symm #4948]: #4925
-#4952 := (not #4925)
-#4953 := (or #4952 #4930)
-#4964 := [th-lemma arith triangle-eq]: #4953
-#4965 := [unit-resolution #4964 #4951]: #4930
-#4961 := (not #4935)
-#4960 := (not #4930)
-#4962 := (or #4959 #4960 #2807 #4961)
-#4954 := [hypothesis]: #4935
-#4955 := [hypothesis]: #4147
-#4956 := [hypothesis]: #4930
-#4957 := [hypothesis]: #4806
-#4958 := [th-lemma arith farkas 1 -1 1 1 #4957 #4956 #4955 #4954]: false
-#4963 := [lemma #4958]: #4962
-#4966 := [unit-resolution #4963 #4965 #4944 #4943]: #4959
-#4969 := (or #4800 #4806)
-#4151 := (or #3361 #2156)
-#4152 := [def-axiom]: #4151
-#4967 := [unit-resolution #4152 #4949]: #2156
-#4968 := [hypothesis]: #4282
-#4817 := (or #4287 #2155 #4800 #4806)
-#4795 := (+ #4724 #3838)
-#4796 := (+ #2146 #4795)
-#4799 := (>= #4796 0::Int)
-#4801 := (or #4800 #2155 #4799)
-#4818 := (or #4287 #4801)
-#4825 := (iff #4818 #4817)
-#4812 := (or #2155 #4800 #4806)
-#4820 := (or #4287 #4812)
-#4823 := (iff #4820 #4817)
-#4824 := [rewrite]: #4823
-#4821 := (iff #4818 #4820)
-#4815 := (iff #4801 #4812)
-#4809 := (or #4800 #2155 #4806)
-#4813 := (iff #4809 #4812)
-#4814 := [rewrite]: #4813
-#4810 := (iff #4801 #4809)
-#4807 := (iff #4799 #4806)
-#4804 := (= #4796 #4803)
+#356 := (iff #46 #355)
+#357 := [rewrite]: #356
+#350 := [asserted]: #46
+#358 := [mp #350 #357]: #355
+#4709 := (* -1::Int #1886)
+#4710 := (+ f8 #4709)
+#4711 := (<= #4710 0::Int)
+#3924 := (= f8 #1886)
+#3903 := (= f10 ?v0!0)
+#4902 := (not #3903)
+#4899 := (= #1886 0::Int)
+#5099 := (not #4899)
+#5100 := (or #5099 #1887)
+#5101 := [th-lemma arith triangle-eq]: #5100
+#5081 := [unit-resolution #5101 #5098]: #5099
+#4908 := (or #4775 #4902 #4899)
+#3923 := (= ?v0!0 f10)
+#4900 := (not #3923)
+#4901 := (or #4900 #4899)
+#4639 := (or #4775 #4901)
+#5094 := (iff #4639 #4908)
+#4706 := (or #4902 #4899)
+#4925 := (or #4775 #4706)
+#4971 := (iff #4925 #4908)
+#5093 := [rewrite]: #4971
+#4969 := (iff #4639 #4925)
+#4707 := (iff #4901 #4706)
+#4905 := (iff #4900 #4902)
+#3905 := (iff #3923 #3903)
+#3906 := [rewrite]: #3905
+#4906 := [monotonicity #3906]: #4905
+#4774 := [monotonicity #4906]: #4707
+#4970 := [monotonicity #4774]: #4969
+#5095 := [trans #4970 #5093]: #5094
+#4922 := [quant-inst #1885]: #4639
+#5096 := [mp #4922 #5095]: #4908
+#5082 := [unit-resolution #5096 #4601 #5081]: #4902
+#3918 := (or #3903 #3924)
+#4210 := (forall (vars (?v0 S3)) (:pat #4209) #445)
+#4213 := (iff #450 #4210)
+#4211 := (iff #445 #445)
+#4212 := [refl]: #4211
+#4214 := [quant-intro #4212]: #4213
+#1847 := (~ #450 #450)
+#1876 := (~ #445 #445)
+#1877 := [refl]: #1876
+#1848 := [nnf-pos #1877]: #1847
+#1825 := [not-or-elim #1824]: #450
+#1878 := [mp~ #1825 #1848]: #450
+#4215 := [mp #1878 #4214]: #4210
+#3914 := (not #4210)
+#3907 := (or #3914 #3903 #3924)
+#3913 := (or #3923 #3924)
+#3915 := (or #3914 #3913)
+#4653 := (iff #3915 #3907)
+#3900 := (or #3914 #3918)
+#4637 := (iff #3900 #3907)
+#4652 := [rewrite]: #4637
+#4635 := (iff #3915 #3900)
+#3909 := (iff #3913 #3918)
+#3910 := [monotonicity #3906]: #3909
+#4636 := [monotonicity #3910]: #4635
+#4634 := [trans #4636 #4652]: #4653
+#3898 := [quant-inst #1885]: #3915
+#4708 := [mp #3898 #4634]: #3907
+#5083 := [unit-resolution #4708 #4215]: #3918
+#5084 := [unit-resolution #5083 #5082]: #3924
+#5085 := (not #3924)
+#5080 := (or #5085 #4711)
+#5086 := [th-lemma arith triangle-eq]: #5080
+#5087 := [unit-resolution #5086 #5084]: #4711
+#5088 := [hypothesis]: #5097
+#5089 := [th-lemma arith farkas 1 -1 1 #5088 #5087 #358]: false
+#5106 := [lemma #5089]: #5105
+#5132 := [unit-resolution #5106 #5131 #5098]: false
+#5133 := [lemma #5132]: #1887
+#3929 := (or #4583 #1888 #4577)
+#3930 := [def-axiom]: #3929
+#6490 := [unit-resolution #3930 #5133]: #6489
+#6491 := [unit-resolution #6490 #6488]: #4577
+#3953 := (or #4574 #4568)
+#3954 := [def-axiom]: #3953
+#6492 := [unit-resolution #3954 #6491]: #4568
+#5808 := [hypothesis]: #1908
+#5321 := (or #5520 #2210)
+#5326 := [quant-inst #1901]: #5321
+#5809 := [unit-resolution #5326 #4222 #5808]: false
+#5810 := [lemma #5809]: #2210
+#3746 := (or #2119 #1908)
+#3833 := [def-axiom]: #3746
+#6493 := [unit-resolution #3833 #5810]: #2119
+#3947 := (or #4571 #2018 #4565)
+#3949 := [def-axiom]: #3947
+#6494 := [unit-resolution #3949 #6493 #6492]: #4565
+#3974 := (or #4562 #4556)
+#3975 := [def-axiom]: #3974
+#6495 := [unit-resolution #3975 #6494]: #4556
+#3970 := (or #4559 #3089 #4553)
+#3971 := [def-axiom]: #3970
+#6496 := [unit-resolution #3971 #6495 #6486]: #4553
+#3984 := (or #4550 #4544)
+#4005 := [def-axiom]: #3984
+#6497 := [unit-resolution #4005 #6496]: #4544
+#5781 := (= f8 #1961)
+#5845 := (not #5781)
+#5843 := [hypothesis]: #4261
+#4150 := (or #4258 #1973)
+#3824 := [def-axiom]: #4150
+#5844 := [unit-resolution #3824 #5843]: #1973
+#5846 := (or #5845 #1972)
+#5847 := [th-lemma arith triangle-eq]: #5846
+#5848 := [unit-resolution #5847 #5844]: #5845
+#3825 := (or #4258 #2560)
+#4157 := [def-axiom]: #3825
+#5849 := [unit-resolution #4157 #5843]: #2560
+#5801 := (or #3914 #2557 #5781)
+#5782 := (or #1974 #5781)
+#5796 := (or #3914 #5782)
+#5660 := (iff #5796 #5801)
+#5798 := (or #2557 #5781)
+#5803 := (or #3914 #5798)
+#5806 := (iff #5803 #5801)
+#5659 := [rewrite]: #5806
+#5804 := (iff #5796 #5803)
+#5799 := (iff #5782 #5798)
+#5800 := [monotonicity #2559]: #5799
+#5805 := [monotonicity #5800]: #5804
+#5661 := [trans #5805 #5659]: #5660
+#5802 := [quant-inst #1958]: #5796
+#5466 := [mp #5802 #5661]: #5801
+#5850 := [unit-resolution #5466 #4215 #5849 #5848]: false
+#5851 := [lemma #5850]: #4258
+#3992 := (or #4547 #4261 #4541)
+#3993 := [def-axiom]: #3992
+#6498 := [unit-resolution #3993 #5851 #6497]: #4541
+#4025 := (or #4538 #4265)
+#4021 := [def-axiom]: #4025
+#7112 := [unit-resolution #4021 #6498]: #4265
+#9544 := (or #4270 #7748)
+#9545 := [quant-inst #2264]: #9544
+#9571 := [unit-resolution #9545 #7112]: #7748
+#7561 := (* -1::Int #7527)
+#7562 := (+ #2265 #7561)
+#9572 := (>= #7562 0::Int)
+#7530 := (= #2265 #7527)
+#10078 := [hypothesis]: #2267
+#11976 := (or #7530 #2266 #6064)
+#9979 := (f5 #7202 ?v0!15)
+#9980 := (f9 #9979)
+#9981 := (* -1::Int #9980)
+#7577 := (f5 f22 ?v0!15)
+#7578 := (f9 #7577)
+#10049 := (+ #7578 #9981)
+#10053 := (>= #10049 0::Int)
+#10048 := (= #7578 #9980)
+#10056 := (= #9980 #7578)
+#10054 := (= #9979 #7577)
+#10055 := [monotonicity #7781]: #10054
+#10057 := [monotonicity #10055]: #10056
+#10058 := [symm #10057]: #10048
+#10059 := (not #10048)
+#10060 := (or #10059 #10053)
+#10061 := [th-lemma arith triangle-eq]: #10060
+#10062 := [unit-resolution #10061 #10058]: #10053
+#7959 := (f5 #6060 #7202)
+#8208 := (f6 #7959)
+#9072 := (f13 f14 #8208)
+#9073 := (* -1::Int #9072)
+#9446 := (+ #6061 #9073)
+#9448 := (>= #9446 0::Int)
+#9852 := (= #6061 #9072)
+#8209 := (= #6060 #8208)
+#8380 := (or #6820 #8209)
+#8381 := [quant-inst #6060 #7202]: #8380
+#9271 := [unit-resolution #8381 #4196]: #8209
+#11938 := [monotonicity #9271]: #9852
+#11936 := (not #9852)
+#11939 := (or #11936 #9448)
+#11940 := [th-lemma arith triangle-eq]: #11939
+#11941 := [unit-resolution #11940 #11938]: #9448
+#10857 := (+ #99 #9073)
+#10869 := (<= #10857 0::Int)
+#10866 := (= #99 #9072)
+#11947 := (= #9072 #99)
+#10688 := (= #8208 f10)
+#7308 := (= #6060 f10)
+#7310 := (= f10 #6060)
+#7289 := (?v1!7 #6060)
+#7301 := (f3 f15 #7289)
+#7302 := (= f1 #7301)
+#7303 := (not #7302)
+#7294 := (f5 #7289 #6060)
+#7295 := (f9 #7294)
+#7296 := (* -1::Int #7295)
+#7290 := (f13 f14 #7289)
+#7291 := (* -1::Int #7290)
+#7297 := (+ #7291 #7296)
+#7298 := (+ #6061 #7297)
+#7299 := (= #7298 0::Int)
+#7300 := (not #7299)
+#7292 := (+ #6061 #7291)
+#7293 := (<= #7292 0::Int)
+#7313 := (or #7293 #7300 #7303)
+#9598 := (or #2266 #6064 #7293)
+#8242 := (not #7293)
+#10063 := [hypothesis]: #8242
+#10101 := (or #7530 #2266 #6064 #7293)
+#9116 := (>= #7290 0::Int)
+#9119 := (or #4270 #9116)
+#9290 := [quant-inst #7289]: #9119
+#10064 := [unit-resolution #9290 #7112]: #9116
+#7552 := (* -1::Int #2265)
+#7603 := (+ #7552 #7578)
+#7604 := (+ #174 #7603)
+#9488 := (<= #7604 0::Int)
+#7607 := (= #7604 0::Int)
+#7582 := (* -1::Int #7578)
+#7586 := (+ f8 #7582)
+#7587 := (<= #7586 0::Int)
+#9501 := (not #7587)
+#7596 := (+ #7561 #7578)
+#7597 := (+ #174 #7596)
+#7598 := (>= #7597 0::Int)
+#7629 := (or #7587 #7598)
+#7632 := (not #7629)
+#10066 := (not #7530)
+#10067 := [hypothesis]: #10066
+#7635 := (or #7530 #7632)
+#5779 := (or #4538 #4529)
+#4713 := (?v1!7 ?v0!8)
+#4989 := (f13 f19 #4713)
+#5002 := (* -1::Int #4989)
+#4714 := (f13 f14 #4713)
+#5222 := (+ #4714 #5002)
+#5227 := (>= #5222 0::Int)
+#5221 := (= #4714 #4989)
+#5711 := (= #4989 #4714)
+#5706 := [hypothesis]: #4526
+#5707 := [hypothesis]: #4541
+#4014 := (or #4538 #4532)
+#3982 := [def-axiom]: #4014
+#5708 := [unit-resolution #3982 #5707]: #4532
+#4019 := (or #4535 #4374 #4529)
+#4020 := [def-axiom]: #4019
+#5709 := [unit-resolution #4020 #5708 #5706]: #4374
+#4125 := (or #4371 #623)
+#4126 := [def-axiom]: #4125
+#5710 := [unit-resolution #4126 #5709]: #623
+#5705 := [symm #5710]: #138
+#5712 := [monotonicity #5705]: #5711
+#5713 := [symm #5712]: #5221
+#5714 := (not #5221)
+#5715 := (or #5714 #5227)
+#5728 := [th-lemma arith triangle-eq]: #5715
+#5729 := [unit-resolution #5728 #5713]: #5227
+#4696 := (* -1::Int #4714)
+#4646 := (f13 f14 ?v0!8)
+#4697 := (+ #4646 #4696)
+#4698 := (<= #4697 0::Int)
+#4879 := (not #4698)
+#4705 := (f3 f15 #4713)
+#4776 := (= f1 #4705)
+#4777 := (not #4776)
+#4699 := (f5 #4713 ?v0!8)
+#4700 := (f9 #4699)
+#4695 := (* -1::Int #4700)
+#4781 := (+ #4695 #4696)
+#4782 := (+ #4646 #4781)
+#4764 := (= #4782 0::Int)
+#4767 := (not #4764)
+#4772 := (or #4698 #4767 #4777)
+#4846 := (not #4772)
+#4647 := (* -1::Int #4646)
+#4648 := (+ f8 #4647)
+#4628 := (<= #4648 0::Int)
+#4984 := (not #4628)
+#4127 := (or #4371 #4365)
+#4124 := [def-axiom]: #4127
+#5730 := [unit-resolution #4124 #5709]: #4365
+#4023 := (or #4538 #100)
+#4024 := [def-axiom]: #4023
+#5731 := [unit-resolution #4024 #5707]: #100
+#5732 := (= #157 #99)
+#5727 := [monotonicity #5705]: #5732
+#5733 := [trans #5727 #5731]: #158
+#4137 := (or #4347 #2156)
+#3800 := [def-axiom]: #4137
+#5734 := [unit-resolution #3800 #5733]: #4347
+#4026 := (or #4538 #4273)
+#4006 := [def-axiom]: #4026
+#5735 := [unit-resolution #4006 #5707]: #4273
+#3841 := (or #4371 #4307)
+#4123 := [def-axiom]: #3841
+#5736 := [unit-resolution #4123 #5709]: #4307
+#4967 := (or #3352 #4312 #4278 #714)
+#4940 := [hypothesis]: #3357
+#4140 := (or #3352 #2143)
+#4141 := [def-axiom]: #4140
+#4941 := [unit-resolution #4141 #4940]: #2143
+#4715 := (f13 f14 ?v1!10)
+#4716 := (* -1::Int #4715)
+#4717 := (+ f8 #4716)
+#4718 := (<= #4717 0::Int)
+#4719 := (f3 f15 ?v1!10)
+#4720 := (= f1 #4719)
+#4791 := (not #4720)
+#3828 := (f13 f14 ?v0!11)
+#3829 := (* -1::Int #3828)
+#4793 := (+ #3829 #4715)
+#4794 := (+ #2137 #4793)
+#4797 := (>= #4794 0::Int)
+#4950 := (not #4797)
+#4924 := (+ #2134 #4716)
+#4926 := (>= #4924 0::Int)
+#4923 := (= #2134 #4715)
+#4928 := (= #4715 #2134)
+#4927 := [hypothesis]: #623
+#4929 := [monotonicity #4927]: #4928
+#4930 := [symm #4929]: #4923
+#4931 := (not #4923)
+#4932 := (or #4931 #4926)
+#4933 := [th-lemma arith triangle-eq]: #4932
+#4934 := [unit-resolution #4933 #4930]: #4926
+#4138 := (not #2798)
+#4144 := (or #3352 #4138)
+#3782 := [def-axiom]: #4144
+#4935 := [unit-resolution #3782 #4940]: #4138
+#4917 := (+ #2132 #3829)
+#4921 := (<= #4917 0::Int)
+#4916 := (= #2132 #3828)
+#4938 := (= #3828 #2132)
+#4939 := [monotonicity #4927]: #4938
+#4942 := [symm #4939]: #4916
+#4943 := (not #4916)
+#4944 := (or #4943 #4921)
+#4955 := [th-lemma arith triangle-eq]: #4944
+#4956 := [unit-resolution #4955 #4942]: #4921
+#4952 := (not #4926)
+#4951 := (not #4921)
+#4953 := (or #4950 #4951 #2798 #4952)
+#4945 := [hypothesis]: #4926
+#4946 := [hypothesis]: #4138
+#4947 := [hypothesis]: #4921
+#4948 := [hypothesis]: #4797
+#4949 := [th-lemma arith farkas 1 -1 1 1 #4948 #4947 #4946 #4945]: false
+#4954 := [lemma #4949]: #4953
+#4957 := [unit-resolution #4954 #4956 #4935 #4934]: #4950
+#4960 := (or #4791 #4797)
+#4142 := (or #3352 #2147)
+#4143 := [def-axiom]: #4142
+#4958 := [unit-resolution #4143 #4940]: #2147
+#4959 := [hypothesis]: #4273
+#4808 := (or #4278 #2146 #4791 #4797)
+#4786 := (+ #4715 #3829)
+#4787 := (+ #2137 #4786)
+#4790 := (>= #4787 0::Int)
+#4792 := (or #4791 #2146 #4790)
+#4809 := (or #4278 #4792)
+#4816 := (iff #4809 #4808)
+#4803 := (or #2146 #4791 #4797)
+#4811 := (or #4278 #4803)
+#4814 := (iff #4811 #4808)
+#4815 := [rewrite]: #4814
+#4812 := (iff #4809 #4811)
+#4806 := (iff #4792 #4803)
+#4800 := (or #4791 #2146 #4797)
+#4804 := (iff #4800 #4803)
 #4805 := [rewrite]: #4804
-#4808 := [monotonicity #4805]: #4807
-#4811 := [monotonicity #4808]: #4810
-#4816 := [trans #4811 #4814]: #4815
-#4822 := [monotonicity #4816]: #4821
-#4826 := [trans #4822 #4824]: #4825
-#4819 := [quant-inst #2140 #2139]: #4818
-#4827 := [mp #4819 #4826]: #4817
-#4970 := [unit-resolution #4827 #4968 #4967]: #4969
-#4971 := [unit-resolution #4970 #4966]: #4800
-#4731 := (or #4727 #4729)
-#4972 := [hypothesis]: #4316
-#4734 := (or #4321 #4727 #4729)
-#4730 := (or #4729 #4727)
-#4735 := (or #4321 #4730)
-#4742 := (iff #4735 #4734)
-#4737 := (or #4321 #4731)
-#4740 := (iff #4737 #4734)
-#4741 := [rewrite]: #4740
-#4738 := (iff #4735 #4737)
-#4732 := (iff #4730 #4731)
-#4733 := [rewrite]: #4732
-#4739 := [monotonicity #4733]: #4738
-#4743 := [trans #4739 #4741]: #4742
-#4736 := [quant-inst #2139]: #4735
-#4744 := [mp #4736 #4743]: #4734
-#4973 := [unit-resolution #4744 #4972]: #4731
-#4974 := [unit-resolution #4973 #4971]: #4727
-#4975 := [th-lemma arith farkas 1 -1 1 #4943 #4974 #4950]: false
-#4977 := [lemma #4975]: #4976
-#5746 := [unit-resolution #4977 #5745 #5744 #5719]: #3361
-#4158 := (or #4365 #4359 #3366)
-#4144 := [def-axiom]: #4158
-#5747 := [unit-resolution #4144 #5746 #5743]: #4365
-#3868 := (or #4368 #4362)
-#3869 := [def-axiom]: #3868
-#5748 := [unit-resolution #3869 #5747]: #4368
-#4138 := (or #4377 #4337 #4371)
-#4142 := [def-axiom]: #4138
-#5749 := [unit-resolution #4142 #5748 #5739]: #4337
-#4170 := (or #4334 #2090)
-#4160 := [def-axiom]: #4170
-#5750 := [unit-resolution #4160 #5749]: #2090
-#4986 := (+ #2077 #4656)
-#4988 := (>= #4986 0::Int)
-#4985 := (= #2077 #4655)
-#5413 := (= #4655 #2077)
-#5751 := [monotonicity #5719]: #5413
-#5752 := [symm #5751]: #4985
-#5416 := (not #4985)
-#5421 := (or #5416 #4988)
-#5422 := [th-lemma arith triangle-eq]: #5421
-#5753 := [unit-resolution #5422 #5752]: #4988
-#4994 := (not #4988)
-#4995 := (or #4993 #4994 #2089)
-#4989 := [hypothesis]: #2090
-#4990 := [hypothesis]: #4637
-#4991 := [hypothesis]: #4988
-#4992 := [th-lemma arith farkas 1 -1 1 #4991 #4990 #4989]: false
-#4996 := [lemma #4992]: #4995
-#5754 := [unit-resolution #4996 #5753 #5750]: #4993
-#5764 := (or #4637 #4855)
-#3820 := (or #4334 #2707)
-#3825 := [def-axiom]: #3820
-#5762 := [unit-resolution #3825 #5749]: #2707
-#4022 := (or #4547 #4307)
-#4017 := [def-axiom]: #4022
-#5763 := [unit-resolution #4017 #5716]: #4307
-#4860 := (or #4312 #2704 #4637 #4855)
-#4710 := (+ #4705 #4704)
-#4711 := (+ #4655 #4710)
-#4712 := (= #4711 0::Int)
-#4713 := (not #4712)
-#4787 := (or #4786 #4713 #4707)
-#4788 := (not #4787)
-#4789 := (or #2091 #4637 #4788)
-#4861 := (or #4312 #4789)
-#4884 := (iff #4861 #4860)
-#4858 := (or #2704 #4637 #4855)
-#4863 := (or #4312 #4858)
-#4882 := (iff #4863 #4860)
-#4883 := [rewrite]: #4882
-#4879 := (iff #4861 #4863)
-#4853 := (iff #4789 #4858)
-#4856 := (iff #4788 #4855)
-#4798 := (iff #4787 #4781)
-#4778 := (or #4786 #4776 #4707)
-#4782 := (iff #4778 #4781)
-#4797 := [rewrite]: #4782
-#4779 := (iff #4787 #4778)
-#4777 := (iff #4713 #4776)
-#4774 := (iff #4712 #4773)
-#4792 := (= #4711 #4791)
-#4793 := [rewrite]: #4792
-#4775 := [monotonicity #4793]: #4774
-#4772 := [monotonicity #4775]: #4777
-#4780 := [monotonicity #4772]: #4779
-#4854 := [trans #4780 #4797]: #4798
-#4857 := [monotonicity #4854]: #4856
-#4859 := [monotonicity #2706 #4857]: #4853
-#4881 := [monotonicity #4859]: #4879
-#4885 := [trans #4881 #4883]: #4884
-#4862 := [quant-inst #2076]: #4861
-#4880 := [mp #4862 #4885]: #4860
-#5765 := [unit-resolution #4880 #5763 #5762]: #5764
-#5766 := [unit-resolution #5765 #5754]: #4855
-#4889 := (or #4781 #4888)
-#4890 := [def-axiom]: #4889
-#5767 := [unit-resolution #4890 #5766]: #4888
-#5012 := (+ #2077 #5011)
-#5013 := (<= #5012 0::Int)
-#5025 := (+ #4704 #5011)
-#5026 := (+ #2077 #5025)
-#5027 := (= #5026 0::Int)
-#5049 := (<= #5026 0::Int)
-#5235 := (<= #5231 0::Int)
-#5768 := (or #5723 #5235)
+#4801 := (iff #4792 #4800)
+#4798 := (iff #4790 #4797)
+#4795 := (= #4787 #4794)
+#4796 := [rewrite]: #4795
+#4799 := [monotonicity #4796]: #4798
+#4802 := [monotonicity #4799]: #4801
+#4807 := [trans #4802 #4805]: #4806
+#4813 := [monotonicity #4807]: #4812
+#4817 := [trans #4813 #4815]: #4816
+#4810 := [quant-inst #2131 #2130]: #4809
+#4818 := [mp #4810 #4817]: #4808
+#4961 := [unit-resolution #4818 #4959 #4958]: #4960
+#4962 := [unit-resolution #4961 #4957]: #4791
+#4722 := (or #4718 #4720)
+#4963 := [hypothesis]: #4307
+#4725 := (or #4312 #4718 #4720)
+#4721 := (or #4720 #4718)
+#4726 := (or #4312 #4721)
+#4733 := (iff #4726 #4725)
+#4728 := (or #4312 #4722)
+#4731 := (iff #4728 #4725)
+#4732 := [rewrite]: #4731
+#4729 := (iff #4726 #4728)
+#4723 := (iff #4721 #4722)
+#4724 := [rewrite]: #4723
+#4730 := [monotonicity #4724]: #4729
+#4734 := [trans #4730 #4732]: #4733
+#4727 := [quant-inst #2130]: #4726
+#4735 := [mp #4727 #4734]: #4725
+#4964 := [unit-resolution #4735 #4963]: #4722
+#4965 := [unit-resolution #4964 #4962]: #4718
+#4966 := [th-lemma arith farkas 1 -1 1 #4934 #4965 #4941]: false
+#4968 := [lemma #4966]: #4967
+#5737 := [unit-resolution #4968 #5736 #5735 #5710]: #3352
+#4149 := (or #4356 #4350 #3357)
+#4135 := [def-axiom]: #4149
+#5738 := [unit-resolution #4135 #5737 #5734]: #4356
+#3859 := (or #4359 #4353)
+#3860 := [def-axiom]: #3859
+#5739 := [unit-resolution #3860 #5738]: #4359
+#4129 := (or #4368 #4328 #4362)
+#4133 := [def-axiom]: #4129
+#5740 := [unit-resolution #4133 #5739 #5730]: #4328
+#4161 := (or #4325 #2081)
+#4151 := [def-axiom]: #4161
+#5741 := [unit-resolution #4151 #5740]: #2081
+#4977 := (+ #2068 #4647)
+#4979 := (>= #4977 0::Int)
+#4976 := (= #2068 #4646)
+#5404 := (= #4646 #2068)
+#5742 := [monotonicity #5710]: #5404
+#5743 := [symm #5742]: #4976
+#5407 := (not #4976)
+#5412 := (or #5407 #4979)
+#5413 := [th-lemma arith triangle-eq]: #5412
+#5744 := [unit-resolution #5413 #5743]: #4979
+#4985 := (not #4979)
+#4986 := (or #4984 #4985 #2080)
+#4980 := [hypothesis]: #2081
+#4981 := [hypothesis]: #4628
+#4982 := [hypothesis]: #4979
+#4983 := [th-lemma arith farkas 1 -1 1 #4982 #4981 #4980]: false
+#4987 := [lemma #4983]: #4986
+#5745 := [unit-resolution #4987 #5744 #5741]: #4984
+#5755 := (or #4628 #4846)
+#3811 := (or #4325 #2698)
+#3816 := [def-axiom]: #3811
+#5753 := [unit-resolution #3816 #5740]: #2698
+#4013 := (or #4538 #4298)
+#4008 := [def-axiom]: #4013
+#5754 := [unit-resolution #4008 #5707]: #4298
+#4851 := (or #4303 #2695 #4628 #4846)
+#4701 := (+ #4696 #4695)
+#4702 := (+ #4646 #4701)
+#4703 := (= #4702 0::Int)
+#4704 := (not #4703)
+#4778 := (or #4777 #4704 #4698)
+#4779 := (not #4778)
+#4780 := (or #2082 #4628 #4779)
+#4852 := (or #4303 #4780)
+#4875 := (iff #4852 #4851)
+#4849 := (or #2695 #4628 #4846)
+#4854 := (or #4303 #4849)
+#4873 := (iff #4854 #4851)
+#4874 := [rewrite]: #4873
+#4870 := (iff #4852 #4854)
+#4844 := (iff #4780 #4849)
+#4847 := (iff #4779 #4846)
+#4789 := (iff #4778 #4772)
+#4769 := (or #4777 #4767 #4698)
+#4773 := (iff #4769 #4772)
+#4788 := [rewrite]: #4773
+#4770 := (iff #4778 #4769)
+#4768 := (iff #4704 #4767)
+#4765 := (iff #4703 #4764)
+#4783 := (= #4702 #4782)
+#4784 := [rewrite]: #4783
+#4766 := [monotonicity #4784]: #4765
+#4763 := [monotonicity #4766]: #4768
+#4771 := [monotonicity #4763]: #4770
+#4845 := [trans #4771 #4788]: #4789
+#4848 := [monotonicity #4845]: #4847
+#4850 := [monotonicity #2697 #4848]: #4844
+#4872 := [monotonicity #4850]: #4870
+#4876 := [trans #4872 #4874]: #4875
+#4853 := [quant-inst #2067]: #4852
+#4871 := [mp #4853 #4876]: #4851
+#5756 := [unit-resolution #4871 #5754 #5753]: #5755
+#5757 := [unit-resolution #5756 #5745]: #4846
+#4880 := (or #4772 #4879)
+#4881 := [def-axiom]: #4880
+#5758 := [unit-resolution #4881 #5757]: #4879
+#5003 := (+ #2068 #5002)
+#5004 := (<= #5003 0::Int)
+#5016 := (+ #4695 #5002)
+#5017 := (+ #2068 #5016)
+#5018 := (= #5017 0::Int)
+#5040 := (<= #5017 0::Int)
+#5226 := (<= #5222 0::Int)
+#5759 := (or #5714 #5226)
+#5760 := [th-lemma arith triangle-eq]: #5759
+#5761 := [unit-resolution #5760 #5713]: #5226
+#4877 := (<= #4782 0::Int)
+#4896 := (or #4772 #4764)
+#4898 := [def-axiom]: #4896
+#5762 := [unit-resolution #4898 #5757]: #4764
+#5763 := (or #4767 #4877)
+#5764 := [th-lemma arith triangle-eq]: #5763
+#5765 := [unit-resolution #5764 #5762]: #4877
+#4978 := (<= #4977 0::Int)
+#5408 := (or #5407 #4978)
+#5409 := [th-lemma arith triangle-eq]: #5408
+#5766 := [unit-resolution #5409 #5743]: #4978
+#5350 := (not #5226)
+#5349 := (not #4877)
+#5348 := (not #4978)
+#5351 := (or #5040 #5348 #5349 #5350)
+#5342 := [hypothesis]: #5226
+#5343 := [hypothesis]: #4877
+#5344 := [hypothesis]: #4978
+#5345 := (not #5040)
+#5346 := [hypothesis]: #5345
+#5347 := [th-lemma arith farkas -1 1 1 1 #5346 #5344 #5343 #5342]: false
+#5352 := [lemma #5347]: #5351
+#5767 := [unit-resolution #5352 #5766 #5765 #5761]: #5040
+#5041 := (>= #5017 0::Int)
+#4878 := (>= #4782 0::Int)
+#5768 := (or #4767 #4878)
 #5769 := [th-lemma arith triangle-eq]: #5768
-#5770 := [unit-resolution #5769 #5722]: #5235
-#4886 := (<= #4791 0::Int)
-#4905 := (or #4781 #4773)
-#4907 := [def-axiom]: #4905
-#5771 := [unit-resolution #4907 #5766]: #4773
-#5772 := (or #4776 #4886)
+#5770 := [unit-resolution #5769 #5762]: #4878
+#5750 := (not #5227)
+#5390 := (not #4878)
+#5751 := (or #5041 #4985 #5390 #5750)
+#5746 := [hypothesis]: #5227
+#5386 := [hypothesis]: #4878
+#5747 := (not #5041)
+#5748 := [hypothesis]: #5747
+#5749 := [th-lemma arith farkas -1 1 1 1 #5748 #4982 #5386 #5746]: false
+#5752 := [lemma #5749]: #5751
+#5771 := [unit-resolution #5752 #5744 #5770 #5729]: #5041
+#5772 := (or #5018 #5345 #5747)
 #5773 := [th-lemma arith triangle-eq]: #5772
-#5774 := [unit-resolution #5773 #5771]: #4886
-#4987 := (<= #4986 0::Int)
-#5417 := (or #5416 #4987)
-#5418 := [th-lemma arith triangle-eq]: #5417
-#5775 := [unit-resolution #5418 #5752]: #4987
-#5359 := (not #5235)
-#5358 := (not #4886)
-#5357 := (not #4987)
-#5360 := (or #5049 #5357 #5358 #5359)
-#5351 := [hypothesis]: #5235
-#5352 := [hypothesis]: #4886
-#5353 := [hypothesis]: #4987
-#5354 := (not #5049)
-#5355 := [hypothesis]: #5354
-#5356 := [th-lemma arith farkas -1 1 1 1 #5355 #5353 #5352 #5351]: false
-#5361 := [lemma #5356]: #5360
-#5776 := [unit-resolution #5361 #5775 #5774 #5770]: #5049
-#5050 := (>= #5026 0::Int)
-#4887 := (>= #4791 0::Int)
-#5777 := (or #4776 #4887)
-#5778 := [th-lemma arith triangle-eq]: #5777
-#5779 := [unit-resolution #5778 #5771]: #4887
-#5759 := (not #5236)
-#5399 := (not #4887)
-#5760 := (or #5050 #4994 #5399 #5759)
-#5755 := [hypothesis]: #5236
-#5395 := [hypothesis]: #4887
-#5756 := (not #5050)
-#5757 := [hypothesis]: #5756
-#5758 := [th-lemma arith farkas -1 1 1 1 #5757 #4991 #5395 #5755]: false
-#5761 := [lemma #5758]: #5760
-#5780 := [unit-resolution #5761 #5753 #5779 #5738]: #5050
-#5781 := (or #5027 #5354 #5756)
-#5782 := [th-lemma arith triangle-eq]: #5781
-#5783 := [unit-resolution #5782 #5780 #5776]: #5027
-#5032 := (not #5027)
-#5035 := (or #5013 #5032)
-#4161 := (or #4334 #4326)
-#3821 := [def-axiom]: #4161
-#5784 := [unit-resolution #3821 #5749]: #4326
-#5038 := (or #4331 #5013 #5032)
-#4997 := (+ #2078 #4709)
-#4999 := (+ #4998 #4997)
-#5000 := (= #4999 0::Int)
-#5001 := (not #5000)
-#5002 := (+ #4998 #2078)
-#5003 := (>= #5002 0::Int)
-#5004 := (or #5003 #5001)
-#5039 := (or #4331 #5004)
-#5046 := (iff #5039 #5038)
-#5041 := (or #4331 #5035)
-#5044 := (iff #5041 #5038)
-#5045 := [rewrite]: #5044
-#5042 := (iff #5039 #5041)
-#5036 := (iff #5004 #5035)
-#5033 := (iff #5001 #5032)
-#5030 := (iff #5000 #5027)
-#5018 := (+ #4709 #4998)
-#5019 := (+ #2078 #5018)
-#5022 := (= #5019 0::Int)
-#5028 := (iff #5022 #5027)
-#5029 := [rewrite]: #5028
-#5023 := (iff #5000 #5022)
-#5020 := (= #4999 #5019)
-#5021 := [rewrite]: #5020
-#5024 := [monotonicity #5021]: #5023
-#5031 := [trans #5024 #5029]: #5030
-#5034 := [monotonicity #5031]: #5033
-#5016 := (iff #5003 #5013)
-#5005 := (+ #2078 #4998)
-#5008 := (>= #5005 0::Int)
-#5014 := (iff #5008 #5013)
-#5015 := [rewrite]: #5014
-#5009 := (iff #5003 #5008)
-#5006 := (= #5002 #5005)
-#5007 := [rewrite]: #5006
-#5010 := [monotonicity #5007]: #5009
-#5017 := [trans #5010 #5015]: #5016
-#5037 := [monotonicity #5017 #5034]: #5036
-#5043 := [monotonicity #5037]: #5042
-#5047 := [trans #5043 #5045]: #5046
-#5040 := [quant-inst #4722]: #5039
-#5048 := [mp #5040 #5047]: #5038
-#5785 := [unit-resolution #5048 #5784]: #5035
-#5786 := [unit-resolution #5785 #5783]: #5013
-#5787 := [th-lemma arith farkas 1 -1 1 1 #5753 #5786 #5767 #5738]: false
-#5789 := [lemma #5787]: #5788
-#6508 := [unit-resolution #5789 #6507]: #4538
-#4044 := (or #4535 #4396)
-#4039 := [def-axiom]: #4044
-#6509 := [unit-resolution #4039 #6508]: #4396
-#9499 := (or #4401 #7539 #7641)
-#7592 := (+ #1453 #7591)
-#7593 := (+ #7536 #7592)
-#7594 := (<= #7593 0::Int)
-#7635 := (or #7596 #7594)
-#7636 := (not #7635)
-#7537 := (= #7536 #2274)
-#7637 := (or #7537 #7636)
-#9500 := (or #4401 #7637)
-#9507 := (iff #9500 #9499)
-#9502 := (or #4401 #7644)
-#9505 := (iff #9502 #9499)
-#9506 := [rewrite]: #9505
-#9503 := (iff #9500 #9502)
-#7645 := (iff #7637 #7644)
-#7642 := (iff #7636 #7641)
-#7639 := (iff #7635 #7638)
-#7610 := (iff #7594 #7607)
-#7598 := (+ #7536 #7591)
-#7599 := (+ #1453 #7598)
-#7602 := (<= #7599 0::Int)
-#7608 := (iff #7602 #7607)
-#7609 := [rewrite]: #7608
-#7603 := (iff #7594 #7602)
-#7600 := (= #7593 #7599)
-#7601 := [rewrite]: #7600
-#7604 := [monotonicity #7601]: #7603
-#7611 := [trans #7604 #7609]: #7610
-#7640 := [monotonicity #7611]: #7639
-#7643 := [monotonicity #7640]: #7642
-#7540 := (iff #7537 #7539)
-#7541 := [rewrite]: #7540
-#7646 := [monotonicity #7541 #7643]: #7645
-#9504 := [monotonicity #7646]: #9503
-#9508 := [trans #9504 #9506]: #9507
-#9501 := [quant-inst #2273]: #9500
-#9509 := [mp #9501 #9508]: #9499
-#10077 := [unit-resolution #9509 #6509]: #7644
-#10078 := [unit-resolution #10077 #10076]: #7641
-#9511 := (or #7638 #9510)
-#9512 := [def-axiom]: #9511
-#10079 := [unit-resolution #9512 #10078]: #9510
-#9513 := (not #7607)
-#9514 := (or #7638 #9513)
-#9515 := [def-axiom]: #9514
-#10080 := [unit-resolution #9515 #10078]: #9513
-#7619 := (or #7596 #7607 #7616)
-#4045 := (or #4535 #4404)
-#4018 := [def-axiom]: #4045
-#6513 := [unit-resolution #4018 #6508]: #4404
-#9486 := (or #4409 #7596 #7607 #7616)
-#7588 := (+ #7587 #7561)
-#7589 := (+ #174 #7588)
-#7590 := (= #7589 0::Int)
-#7597 := (or #7596 #7594 #7590)
-#9487 := (or #4409 #7597)
-#9494 := (iff #9487 #9486)
-#9489 := (or #4409 #7619)
-#9492 := (iff #9489 #9486)
-#9493 := [rewrite]: #9492
-#9490 := (iff #9487 #9489)
-#7620 := (iff #7597 #7619)
-#7617 := (iff #7590 #7616)
-#7614 := (= #7589 #7613)
-#7615 := [rewrite]: #7614
-#7618 := [monotonicity #7615]: #7617
-#7621 := [monotonicity #7611 #7618]: #7620
-#9491 := [monotonicity #7621]: #9490
-#9495 := [trans #9491 #9493]: #9494
-#9488 := [quant-inst #2273]: #9487
-#9496 := [mp #9488 #9495]: #9486
-#10081 := [unit-resolution #9496 #6513]: #7619
-#10082 := [unit-resolution #10081 #10080 #10079]: #7616
-#10083 := (not #7616)
-#10084 := (or #10083 #9497)
-#10085 := [th-lemma arith triangle-eq]: #10084
-#10086 := [unit-resolution #10085 #10082]: #9497
-#10050 := (>= #9989 0::Int)
-#10025 := (<= #9989 0::Int)
-#10026 := (not #10025)
-#9949 := (= ?v0!15 #7211)
-#9968 := (not #9949)
-#7668 := (f3 f15 ?v0!15)
-#7669 := (= f1 #7668)
-#5891 := (f3 #773 f22)
-#5892 := (= f1 #5891)
-#9952 := (ite #9949 #5892 #7669)
-#9967 := (not #9952)
-#8442 := (f4 f15 #7211 #5891)
-#9946 := (f3 #8442 ?v0!15)
-#9947 := (= f1 #9946)
-#9955 := (iff #9947 #9952)
+#5774 := [unit-resolution #5773 #5771 #5767]: #5018
+#5023 := (not #5018)
+#5026 := (or #5004 #5023)
+#4152 := (or #4325 #4317)
+#3812 := [def-axiom]: #4152
+#5775 := [unit-resolution #3812 #5740]: #4317
+#5029 := (or #4322 #5004 #5023)
+#4988 := (+ #2069 #4700)
+#4990 := (+ #4989 #4988)
+#4991 := (= #4990 0::Int)
+#4992 := (not #4991)
+#4993 := (+ #4989 #2069)
+#4994 := (>= #4993 0::Int)
+#4995 := (or #4994 #4992)
+#5030 := (or #4322 #4995)
+#5037 := (iff #5030 #5029)
+#5032 := (or #4322 #5026)
+#5035 := (iff #5032 #5029)
+#5036 := [rewrite]: #5035
+#5033 := (iff #5030 #5032)
+#5027 := (iff #4995 #5026)
+#5024 := (iff #4992 #5023)
+#5021 := (iff #4991 #5018)
+#5009 := (+ #4700 #4989)
+#5010 := (+ #2069 #5009)
+#5013 := (= #5010 0::Int)
+#5019 := (iff #5013 #5018)
+#5020 := [rewrite]: #5019
+#5014 := (iff #4991 #5013)
+#5011 := (= #4990 #5010)
+#5012 := [rewrite]: #5011
+#5015 := [monotonicity #5012]: #5014
+#5022 := [trans #5015 #5020]: #5021
+#5025 := [monotonicity #5022]: #5024
+#5007 := (iff #4994 #5004)
+#4996 := (+ #2069 #4989)
+#4999 := (>= #4996 0::Int)
+#5005 := (iff #4999 #5004)
+#5006 := [rewrite]: #5005
+#5000 := (iff #4994 #4999)
+#4997 := (= #4993 #4996)
+#4998 := [rewrite]: #4997
+#5001 := [monotonicity #4998]: #5000
+#5008 := [trans #5001 #5006]: #5007
+#5028 := [monotonicity #5008 #5025]: #5027
+#5034 := [monotonicity #5028]: #5033
+#5038 := [trans #5034 #5036]: #5037
+#5031 := [quant-inst #4713]: #5030
+#5039 := [mp #5031 #5038]: #5029
+#5776 := [unit-resolution #5039 #5775]: #5026
+#5777 := [unit-resolution #5776 #5774]: #5004
+#5778 := [th-lemma arith farkas 1 -1 1 1 #5744 #5777 #5758 #5729]: false
+#5780 := [lemma #5778]: #5779
+#6499 := [unit-resolution #5780 #6498]: #4529
+#4035 := (or #4526 #4387)
+#4030 := [def-axiom]: #4035
+#6500 := [unit-resolution #4030 #6499]: #4387
+#9490 := (or #4392 #7530 #7632)
+#7583 := (+ #1444 #7582)
+#7584 := (+ #7527 #7583)
+#7585 := (<= #7584 0::Int)
+#7626 := (or #7587 #7585)
+#7627 := (not #7626)
+#7528 := (= #7527 #2265)
+#7628 := (or #7528 #7627)
+#9491 := (or #4392 #7628)
+#9498 := (iff #9491 #9490)
+#9493 := (or #4392 #7635)
+#9496 := (iff #9493 #9490)
+#9497 := [rewrite]: #9496
+#9494 := (iff #9491 #9493)
+#7636 := (iff #7628 #7635)
+#7633 := (iff #7627 #7632)
+#7630 := (iff #7626 #7629)
+#7601 := (iff #7585 #7598)
+#7589 := (+ #7527 #7582)
+#7590 := (+ #1444 #7589)
+#7593 := (<= #7590 0::Int)
+#7599 := (iff #7593 #7598)
+#7600 := [rewrite]: #7599
+#7594 := (iff #7585 #7593)
+#7591 := (= #7584 #7590)
+#7592 := [rewrite]: #7591
+#7595 := [monotonicity #7592]: #7594
+#7602 := [trans #7595 #7600]: #7601
+#7631 := [monotonicity #7602]: #7630
+#7634 := [monotonicity #7631]: #7633
+#7531 := (iff #7528 #7530)
+#7532 := [rewrite]: #7531
+#7637 := [monotonicity #7532 #7634]: #7636
+#9495 := [monotonicity #7637]: #9494
+#9499 := [trans #9495 #9497]: #9498
+#9492 := [quant-inst #2264]: #9491
+#9500 := [mp #9492 #9499]: #9490
+#10068 := [unit-resolution #9500 #6500]: #7635
+#10069 := [unit-resolution #10068 #10067]: #7632
+#9502 := (or #7629 #9501)
+#9503 := [def-axiom]: #9502
+#10070 := [unit-resolution #9503 #10069]: #9501
+#9504 := (not #7598)
+#9505 := (or #7629 #9504)
+#9506 := [def-axiom]: #9505
+#10071 := [unit-resolution #9506 #10069]: #9504
+#7610 := (or #7587 #7598 #7607)
+#4036 := (or #4526 #4395)
+#4009 := [def-axiom]: #4036
+#6504 := [unit-resolution #4009 #6499]: #4395
+#9477 := (or #4400 #7587 #7598 #7607)
+#7579 := (+ #7578 #7552)
+#7580 := (+ #174 #7579)
+#7581 := (= #7580 0::Int)
+#7588 := (or #7587 #7585 #7581)
+#9478 := (or #4400 #7588)
+#9485 := (iff #9478 #9477)
+#9480 := (or #4400 #7610)
+#9483 := (iff #9480 #9477)
+#9484 := [rewrite]: #9483
+#9481 := (iff #9478 #9480)
+#7611 := (iff #7588 #7610)
+#7608 := (iff #7581 #7607)
+#7605 := (= #7580 #7604)
+#7606 := [rewrite]: #7605
+#7609 := [monotonicity #7606]: #7608
+#7612 := [monotonicity #7602 #7609]: #7611
+#9482 := [monotonicity #7612]: #9481
+#9486 := [trans #9482 #9484]: #9485
+#9479 := [quant-inst #2264]: #9478
+#9487 := [mp #9479 #9486]: #9477
+#10072 := [unit-resolution #9487 #6504]: #7610
+#10073 := [unit-resolution #10072 #10071 #10070]: #7607
+#10074 := (not #7607)
+#10075 := (or #10074 #9488)
+#10076 := [th-lemma arith triangle-eq]: #10075
+#10077 := [unit-resolution #10076 #10073]: #9488
+#10041 := (>= #9980 0::Int)
+#10016 := (<= #9980 0::Int)
+#10017 := (not #10016)
+#9940 := (= ?v0!15 #7202)
+#9959 := (not #9940)
+#7659 := (f3 f15 ?v0!15)
+#7660 := (= f1 #7659)
+#5882 := (f3 #180 f22)
+#5883 := (= f1 #5882)
+#9943 := (ite #9940 #5883 #7660)
+#9958 := (not #9943)
+#8433 := (f4 f15 #7202 #5882)
+#9937 := (f3 #8433 ?v0!15)
+#9938 := (= f1 #9937)
+#9946 := (iff #9938 #9943)
 #10 := (:var 1 S1)
 #9 := (:var 2 S3)
 #8 := (:var 3 S2)
 #11 := (f4 #8 #9 #10)
 #13 := (f3 #11 #12)
-#4171 := (pattern #13)
+#4162 := (pattern #13)
 #17 := (f3 #8 #12)
-#301 := (= f1 #17)
-#298 := (= f1 #10)
-#295 := (= #9 #12)
-#304 := (ite #295 #298 #301)
-#292 := (= f1 #13)
-#307 := (iff #292 #304)
-#4172 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4171) #307)
-#310 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #307)
-#4175 := (iff #310 #4172)
-#4173 := (iff #307 #307)
-#4174 := [refl]: #4173
-#4176 := [quant-intro #4174]: #4175
-#1868 := (~ #310 #310)
-#1866 := (~ #307 #307)
-#1867 := [refl]: #1866
-#1869 := [nnf-pos #1867]: #1868
+#300 := (= f1 #17)
+#297 := (= f1 #10)
+#294 := (= #9 #12)
+#303 := (ite #294 #297 #300)
+#291 := (= f1 #13)
+#306 := (iff #291 #303)
+#4163 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4162) #306)
+#309 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #306)
+#4166 := (iff #309 #4163)
+#4164 := (iff #306 #306)
+#4165 := [refl]: #4164
+#4167 := [quant-intro #4165]: #4166
+#1859 := (~ #309 #309)
+#1857 := (~ #306 #306)
+#1858 := [refl]: #1857
+#1860 := [nnf-pos #1858]: #1859
 #18 := (= #17 f1)
 #16 := (= #10 f1)
 #15 := (= #12 #9)
@@ -4832,2365 +4821,2365 @@
 #14 := (= #13 f1)
 #20 := (iff #14 #19)
 #21 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #20)
-#311 := (iff #21 #310)
-#308 := (iff #20 #307)
-#305 := (iff #19 #304)
-#302 := (iff #18 #301)
-#303 := [rewrite]: #302
-#299 := (iff #16 #298)
-#300 := [rewrite]: #299
-#296 := (iff #15 #295)
-#297 := [rewrite]: #296
-#306 := [monotonicity #297 #300 #303]: #305
-#293 := (iff #14 #292)
-#294 := [rewrite]: #293
-#309 := [monotonicity #294 #306]: #308
-#312 := [quant-intro #309]: #311
-#291 := [asserted]: #21
-#315 := [mp #291 #312]: #310
-#1840 := [mp~ #315 #1869]: #310
-#4177 := [mp #1840 #4176]: #4172
-#6290 := (not #4172)
-#9958 := (or #6290 #9955)
-#9944 := (= #7211 ?v0!15)
-#9945 := (ite #9944 #5892 #7669)
-#9948 := (iff #9947 #9945)
-#9959 := (or #6290 #9948)
-#9961 := (iff #9959 #9958)
-#9963 := (iff #9958 #9958)
-#9964 := [rewrite]: #9963
-#9956 := (iff #9948 #9955)
-#9953 := (iff #9945 #9952)
-#9950 := (iff #9944 #9949)
-#9951 := [rewrite]: #9950
-#9954 := [monotonicity #9951]: #9953
-#9957 := [monotonicity #9954]: #9956
-#9962 := [monotonicity #9957]: #9961
-#9965 := [trans #9962 #9964]: #9961
-#9960 := [quant-inst #104 #7211 #5891 #2273]: #9959
-#9966 := [mp #9960 #9965]: #9958
-#10088 := [unit-resolution #9966 #4177]: #9955
-#9981 := (not #9947)
-#7533 := (f3 f23 ?v0!15)
-#7534 := (= f1 #7533)
-#7535 := (not #7534)
-#10097 := (iff #7535 #9981)
-#10095 := (iff #7534 #9947)
-#10093 := (iff #9947 #7534)
-#10091 := (= #9946 #7533)
-#9285 := (= #8442 f23)
-#7004 := (= #773 f23)
-#4053 := (or #4535 #776)
-#4048 := [def-axiom]: #4053
-#6998 := [unit-resolution #4048 #6508]: #776
-#7005 := [symm #6998]: #7004
-#9283 := (= #8442 #773)
-#7000 := (= #5891 f1)
+#310 := (iff #21 #309)
+#307 := (iff #20 #306)
+#304 := (iff #19 #303)
+#301 := (iff #18 #300)
+#302 := [rewrite]: #301
+#298 := (iff #16 #297)
+#299 := [rewrite]: #298
+#295 := (iff #15 #294)
+#296 := [rewrite]: #295
+#305 := [monotonicity #296 #299 #302]: #304
+#292 := (iff #14 #291)
+#293 := [rewrite]: #292
+#308 := [monotonicity #293 #305]: #307
+#311 := [quant-intro #308]: #310
+#290 := [asserted]: #21
+#314 := [mp #290 #311]: #309
+#1831 := [mp~ #314 #1860]: #309
+#4168 := [mp #1831 #4167]: #4163
+#6281 := (not #4163)
+#9949 := (or #6281 #9946)
+#9935 := (= #7202 ?v0!15)
+#9936 := (ite #9935 #5883 #7660)
+#9939 := (iff #9938 #9936)
+#9950 := (or #6281 #9939)
+#9952 := (iff #9950 #9949)
+#9954 := (iff #9949 #9949)
+#9955 := [rewrite]: #9954
+#9947 := (iff #9939 #9946)
+#9944 := (iff #9936 #9943)
+#9941 := (iff #9935 #9940)
+#9942 := [rewrite]: #9941
+#9945 := [monotonicity #9942]: #9944
+#9948 := [monotonicity #9945]: #9947
+#9953 := [monotonicity #9948]: #9952
+#9956 := [trans #9953 #9955]: #9952
+#9951 := [quant-inst #104 #7202 #5882 #2264]: #9950
+#9957 := [mp #9951 #9956]: #9949
+#10079 := [unit-resolution #9957 #4168]: #9946
+#9972 := (not #9938)
+#7524 := (f3 f23 ?v0!15)
+#7525 := (= f1 #7524)
+#7526 := (not #7525)
+#10088 := (iff #7526 #9972)
+#10086 := (iff #7525 #9938)
+#10084 := (iff #9938 #7525)
+#10082 := (= #9937 #7524)
+#9276 := (= #8433 f23)
+#6995 := (= #180 f23)
+#4042 := (or #4526 #181)
+#4043 := [def-axiom]: #4042
+#6989 := [unit-resolution #4043 #6499]: #181
+#6996 := [symm #6989]: #6995
+#9274 := (= #8433 #180)
+#6991 := (= #5882 f1)
 #24 := (:var 0 S1)
 #22 := (:var 2 S2)
 #25 := (f4 #22 #23 #24)
-#4178 := (pattern #25)
-#318 := (= f1 #24)
+#4169 := (pattern #25)
+#317 := (= f1 #24)
 #26 := (f3 #25 #23)
-#314 := (= f1 #26)
-#321 := (iff #314 #318)
-#4179 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4178) #321)
-#324 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #321)
-#4182 := (iff #324 #4179)
-#4180 := (iff #321 #321)
-#4181 := [refl]: #4180
-#4183 := [quant-intro #4181]: #4182
-#1842 := (~ #324 #324)
-#1841 := (~ #321 #321)
-#1870 := [refl]: #1841
-#1843 := [nnf-pos #1870]: #1842
+#313 := (= f1 #26)
+#320 := (iff #313 #317)
+#4170 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4169) #320)
+#323 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #320)
+#4173 := (iff #323 #4170)
+#4171 := (iff #320 #320)
+#4172 := [refl]: #4171
+#4174 := [quant-intro #4172]: #4173
+#1833 := (~ #323 #323)
+#1832 := (~ #320 #320)
+#1861 := [refl]: #1832
+#1834 := [nnf-pos #1861]: #1833
 #28 := (= #24 f1)
 #27 := (= #26 f1)
 #29 := (iff #27 #28)
 #30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #29)
-#325 := (iff #30 #324)
-#322 := (iff #29 #321)
-#319 := (iff #28 #318)
-#320 := [rewrite]: #319
-#316 := (iff #27 #314)
-#317 := [rewrite]: #316
-#323 := [monotonicity #317 #320]: #322
-#326 := [quant-intro #323]: #325
-#313 := [asserted]: #30
-#329 := [mp #313 #326]: #324
-#1871 := [mp~ #329 #1843]: #324
-#4184 := [mp #1871 #4183]: #4179
-#5903 := (not #4179)
-#5904 := (or #5903 #5892)
-#5890 := (= f1 f1)
-#5893 := (iff #5892 #5890)
-#5905 := (or #5903 #5893)
-#5907 := (iff #5905 #5904)
-#5909 := (iff #5904 #5904)
-#5910 := [rewrite]: #5909
-#5901 := (iff #5893 #5892)
-#5896 := (iff #5892 true)
-#5899 := (iff #5896 #5892)
-#5900 := [rewrite]: #5899
-#5897 := (iff #5893 #5896)
-#5894 := (iff #5890 true)
-#5895 := [rewrite]: #5894
-#5898 := [monotonicity #5895]: #5897
-#5902 := [trans #5898 #5900]: #5901
-#5908 := [monotonicity #5902]: #5907
-#5911 := [trans #5908 #5910]: #5907
-#5906 := [quant-inst #104 #170 #4]: #5905
-#5912 := [mp #5906 #5911]: #5904
-#6999 := [unit-resolution #5912 #4184]: #5892
-#7001 := [symm #6999]: #7000
-#9284 := [monotonicity #7790 #7001]: #9283
-#9286 := [trans #9284 #7005]: #9285
-#10092 := [monotonicity #9286]: #10091
-#10094 := [monotonicity #10092]: #10093
-#10096 := [symm #10094]: #10095
-#10098 := [monotonicity #10096]: #10097
-#7545 := (or #7535 #7539)
-#4019 := (or #4535 #4529)
-#4020 := [def-axiom]: #4019
-#7096 := [unit-resolution #4020 #6508]: #4529
-#6311 := (f5 f22 ?v0!13)
-#6312 := (f9 #6311)
-#6337 := (+ #2232 #6312)
-#6338 := (+ #174 #6337)
-#6359 := (>= #6338 0::Int)
-#6341 := (= #6338 0::Int)
-#6316 := (* -1::Int #6312)
-#6320 := (+ f8 #6316)
-#6321 := (<= #6320 0::Int)
-#6388 := (not #6321)
-#6330 := (+ #2848 #6312)
-#6331 := (+ #174 #6330)
-#6332 := (>= #6331 0::Int)
-#6367 := (or #6321 #6332)
-#6370 := (not #6367)
-#6364 := (= #2231 #2233)
-#6489 := (not #6364)
-#6488 := [hypothesis]: #2855
-#6492 := (or #6489 #2850)
-#6493 := [th-lemma arith triangle-eq]: #6492
-#6494 := [unit-resolution #6493 #6488]: #6489
-#6376 := (or #4401 #6364 #6370)
-#6317 := (+ #1453 #6316)
-#6318 := (+ #2233 #6317)
-#6319 := (<= #6318 0::Int)
-#6360 := (or #6321 #6319)
-#6361 := (not #6360)
-#6362 := (= #2233 #2231)
-#6363 := (or #6362 #6361)
-#6377 := (or #4401 #6363)
-#6384 := (iff #6377 #6376)
-#6373 := (or #6364 #6370)
-#6379 := (or #4401 #6373)
-#6382 := (iff #6379 #6376)
-#6383 := [rewrite]: #6382
-#6380 := (iff #6377 #6379)
-#6374 := (iff #6363 #6373)
-#6371 := (iff #6361 #6370)
-#6368 := (iff #6360 #6367)
-#6335 := (iff #6319 #6332)
-#6323 := (+ #2233 #6316)
-#6324 := (+ #1453 #6323)
-#6327 := (<= #6324 0::Int)
-#6333 := (iff #6327 #6332)
-#6334 := [rewrite]: #6333
-#6328 := (iff #6319 #6327)
-#6325 := (= #6318 #6324)
-#6326 := [rewrite]: #6325
-#6329 := [monotonicity #6326]: #6328
-#6336 := [trans #6329 #6334]: #6335
-#6369 := [monotonicity #6336]: #6368
-#6372 := [monotonicity #6369]: #6371
-#6365 := (iff #6362 #6364)
-#6366 := [rewrite]: #6365
-#6375 := [monotonicity #6366 #6372]: #6374
-#6381 := [monotonicity #6375]: #6380
-#6385 := [trans #6381 #6383]: #6384
-#6378 := [quant-inst #2230]: #6377
-#6386 := [mp #6378 #6385]: #6376
-#6510 := [unit-resolution #6386 #6509 #6494]: #6370
-#6389 := (or #6367 #6388)
-#6390 := [def-axiom]: #6389
-#6511 := [unit-resolution #6390 #6510]: #6388
-#6391 := (not #6332)
-#6392 := (or #6367 #6391)
-#6393 := [def-axiom]: #6392
-#6512 := [unit-resolution #6393 #6510]: #6391
-#6344 := (or #6321 #6332 #6341)
-#6347 := (or #4409 #6321 #6332 #6341)
-#6313 := (+ #6312 #2232)
-#6314 := (+ #174 #6313)
-#6315 := (= #6314 0::Int)
-#6322 := (or #6321 #6319 #6315)
-#6348 := (or #4409 #6322)
-#6355 := (iff #6348 #6347)
-#6350 := (or #4409 #6344)
-#6353 := (iff #6350 #6347)
-#6354 := [rewrite]: #6353
-#6351 := (iff #6348 #6350)
-#6345 := (iff #6322 #6344)
-#6342 := (iff #6315 #6341)
-#6339 := (= #6314 #6338)
-#6340 := [rewrite]: #6339
-#6343 := [monotonicity #6340]: #6342
-#6346 := [monotonicity #6336 #6343]: #6345
-#6352 := [monotonicity #6346]: #6351
-#6356 := [trans #6352 #6354]: #6355
-#6349 := [quant-inst #2230]: #6348
-#6357 := [mp #6349 #6356]: #6347
-#6514 := [unit-resolution #6357 #6513]: #6344
-#6515 := [unit-resolution #6514 #6512 #6511]: #6341
-#6516 := (not #6341)
-#6517 := (or #6516 #6359)
-#6518 := [th-lemma arith triangle-eq]: #6517
-#6519 := [unit-resolution #6518 #6515]: #6359
-#6387 := (>= #2849 0::Int)
-#6520 := (or #6387 #2850)
-#6521 := [th-lemma arith farkas 1 1]: #6520
-#6522 := [unit-resolution #6521 #6488]: #6387
-#6523 := [th-lemma arith farkas 1 -1 1 #6522 #6512 #6519]: false
-#6524 := [lemma #6523]: #2850
-#4049 := (or #4532 #2855 #4526)
-#4050 := [def-axiom]: #4049
-#7097 := [unit-resolution #4050 #6524 #7096]: #4526
-#4064 := (or #4523 #4517)
-#4065 := [def-axiom]: #4064
-#7098 := [unit-resolution #4065 #7097]: #4517
-#6879 := (= #174 #2253)
-#6696 := (= f22 ?v0!14)
-#6526 := (f3 f15 ?v0!14)
-#6527 := (= f1 #6526)
-#6697 := (ite #6696 #5892 #6527)
-#6269 := (f4 f15 f22 #5891)
-#6700 := (f3 #6269 ?v0!14)
-#6701 := (= f1 #6700)
-#6703 := (iff #6697 #6701)
-#6706 := (or #6290 #6703)
-#6702 := (iff #6701 #6697)
-#6707 := (or #6290 #6702)
-#6709 := (iff #6707 #6706)
-#6711 := (iff #6706 #6706)
-#6712 := [rewrite]: #6711
-#6704 := (iff #6702 #6703)
-#6705 := [rewrite]: #6704
-#6710 := [monotonicity #6705]: #6709
-#6713 := [trans #6710 #6712]: #6709
-#6708 := [quant-inst #104 #170 #5891 #2248]: #6707
-#6714 := [mp #6708 #6713]: #6706
-#6996 := [unit-resolution #6714 #4177]: #6703
-#7012 := (= #2249 #6700)
-#7008 := (= #6700 #2249)
-#7006 := (= #6269 f23)
-#7002 := (= #6269 #773)
-#7003 := [monotonicity #7001]: #7002
-#7007 := [trans #7003 #7005]: #7006
-#7009 := [monotonicity #7007]: #7008
-#7013 := [symm #7009]: #7012
-#6994 := [hypothesis]: #2869
-#4127 := (or #2864 #2250)
-#4128 := [def-axiom]: #4127
-#6997 := [unit-resolution #4128 #6994]: #2250
-#7014 := [trans #6997 #7013]: #6701
-#6727 := (not #6701)
-#6726 := (not #6703)
-#6728 := (or #6726 #6697 #6727)
-#6729 := [def-axiom]: #6728
-#7015 := [unit-resolution #6729 #7014 #6996]: #6697
-#6555 := (f5 f22 ?v0!14)
-#6556 := (f9 #6555)
-#6486 := (* -1::Int #2253)
-#6573 := (+ #6486 #6556)
-#6574 := (+ #174 #6573)
-#6575 := (>= #6574 0::Int)
-#6603 := (not #6575)
-#6557 := (* -1::Int #6556)
-#6561 := (+ f8 #6557)
-#6562 := (<= #6561 0::Int)
-#6580 := (or #6562 #6575)
-#6583 := (not #6580)
-#4123 := (not #2858)
-#4124 := (or #2864 #4123)
-#4129 := [def-axiom]: #4124
-#6995 := [unit-resolution #4129 #6994]: #4123
-#6589 := (or #4401 #2858 #6583)
-#6558 := (+ #1453 #6557)
-#6559 := (+ #2253 #6558)
-#6560 := (<= #6559 0::Int)
-#6563 := (or #6562 #6560)
-#6564 := (not #6563)
-#6565 := (or #2254 #6564)
-#6590 := (or #4401 #6565)
-#6597 := (iff #6590 #6589)
-#6586 := (or #2858 #6583)
-#6592 := (or #4401 #6586)
-#6595 := (iff #6592 #6589)
-#6596 := [rewrite]: #6595
-#6593 := (iff #6590 #6592)
-#6587 := (iff #6565 #6586)
-#6584 := (iff #6564 #6583)
-#6581 := (iff #6563 #6580)
-#6578 := (iff #6560 #6575)
-#6566 := (+ #2253 #6557)
-#6567 := (+ #1453 #6566)
-#6570 := (<= #6567 0::Int)
-#6576 := (iff #6570 #6575)
-#6577 := [rewrite]: #6576
-#6571 := (iff #6560 #6570)
-#6568 := (= #6559 #6567)
-#6569 := [rewrite]: #6568
-#6572 := [monotonicity #6569]: #6571
-#6579 := [trans #6572 #6577]: #6578
-#6582 := [monotonicity #6579]: #6581
-#6585 := [monotonicity #6582]: #6584
-#6588 := [monotonicity #2860 #6585]: #6587
-#6594 := [monotonicity #6588]: #6593
-#6598 := [trans #6594 #6596]: #6597
-#6591 := [quant-inst #2248]: #6590
-#6599 := [mp #6591 #6598]: #6589
-#7016 := [unit-resolution #6599 #6509 #6995]: #6583
-#6604 := (or #6580 #6603)
-#6605 := [def-axiom]: #6604
-#7017 := [unit-resolution #6605 #7016]: #6603
-#6715 := (not #6697)
-#6941 := (or #6696 #6575 #6715)
-#6822 := (f6 #6555)
-#6832 := (f13 f14 #6822)
-#6847 := (* -1::Int #6832)
-#6887 := (+ #174 #6847)
-#6889 := (>= #6887 0::Int)
-#6886 := (= #174 #6832)
-#6893 := (= #6832 #174)
-#6891 := (= #6822 f22)
-#6823 := (= f22 #6822)
-#6830 := (or #6829 #6823)
-#6831 := [quant-inst #170 #2248]: #6830
-#6890 := [unit-resolution #6831 #4205]: #6823
-#6892 := [symm #6890]: #6891
-#6894 := [monotonicity #6892]: #6893
-#6895 := [symm #6894]: #6886
-#6896 := (not #6886)
-#6897 := (or #6896 #6889)
-#6898 := [th-lemma arith triangle-eq]: #6897
-#6899 := [unit-resolution #6898 #6895]: #6889
-#6900 := [hypothesis]: #6603
-#6819 := (>= #6556 0::Int)
-#6773 := (<= #6556 0::Int)
-#6774 := (not #6773)
-#6716 := (not #6696)
-#6901 := [hypothesis]: #6716
-#6779 := (or #6696 #6774)
+#324 := (iff #30 #323)
+#321 := (iff #29 #320)
+#318 := (iff #28 #317)
+#319 := [rewrite]: #318
+#315 := (iff #27 #313)
+#316 := [rewrite]: #315
+#322 := [monotonicity #316 #319]: #321
+#325 := [quant-intro #322]: #324
+#312 := [asserted]: #30
+#328 := [mp #312 #325]: #323
+#1862 := [mp~ #328 #1834]: #323
+#4175 := [mp #1862 #4174]: #4170
+#5894 := (not #4170)
+#5895 := (or #5894 #5883)
+#5881 := (= f1 f1)
+#5884 := (iff #5883 #5881)
+#5896 := (or #5894 #5884)
+#5898 := (iff #5896 #5895)
+#5900 := (iff #5895 #5895)
+#5901 := [rewrite]: #5900
+#5892 := (iff #5884 #5883)
+#5887 := (iff #5883 true)
+#5890 := (iff #5887 #5883)
+#5891 := [rewrite]: #5890
+#5888 := (iff #5884 #5887)
+#5885 := (iff #5881 true)
+#5886 := [rewrite]: #5885
+#5889 := [monotonicity #5886]: #5888
+#5893 := [trans #5889 #5891]: #5892
+#5899 := [monotonicity #5893]: #5898
+#5902 := [trans #5899 #5901]: #5898
+#5897 := [quant-inst #104 #170 #4]: #5896
+#5903 := [mp #5897 #5902]: #5895
+#6990 := [unit-resolution #5903 #4175]: #5883
+#6992 := [symm #6990]: #6991
+#9275 := [monotonicity #7781 #6992]: #9274
+#9277 := [trans #9275 #6996]: #9276
+#10083 := [monotonicity #9277]: #10082
+#10085 := [monotonicity #10083]: #10084
+#10087 := [symm #10085]: #10086
+#10089 := [monotonicity #10087]: #10088
+#7536 := (or #7526 #7530)
+#4010 := (or #4526 #4520)
+#4011 := [def-axiom]: #4010
+#7087 := [unit-resolution #4011 #6499]: #4520
+#6302 := (f5 f22 ?v0!13)
+#6303 := (f9 #6302)
+#6328 := (+ #2223 #6303)
+#6329 := (+ #174 #6328)
+#6350 := (>= #6329 0::Int)
+#6332 := (= #6329 0::Int)
+#6307 := (* -1::Int #6303)
+#6311 := (+ f8 #6307)
+#6312 := (<= #6311 0::Int)
+#6379 := (not #6312)
+#6321 := (+ #2839 #6303)
+#6322 := (+ #174 #6321)
+#6323 := (>= #6322 0::Int)
+#6358 := (or #6312 #6323)
+#6361 := (not #6358)
+#6355 := (= #2222 #2224)
+#6480 := (not #6355)
+#6479 := [hypothesis]: #2846
+#6483 := (or #6480 #2841)
+#6484 := [th-lemma arith triangle-eq]: #6483
+#6485 := [unit-resolution #6484 #6479]: #6480
+#6367 := (or #4392 #6355 #6361)
+#6308 := (+ #1444 #6307)
+#6309 := (+ #2224 #6308)
+#6310 := (<= #6309 0::Int)
+#6351 := (or #6312 #6310)
+#6352 := (not #6351)
+#6353 := (= #2224 #2222)
+#6354 := (or #6353 #6352)
+#6368 := (or #4392 #6354)
+#6375 := (iff #6368 #6367)
+#6364 := (or #6355 #6361)
+#6370 := (or #4392 #6364)
+#6373 := (iff #6370 #6367)
+#6374 := [rewrite]: #6373
+#6371 := (iff #6368 #6370)
+#6365 := (iff #6354 #6364)
+#6362 := (iff #6352 #6361)
+#6359 := (iff #6351 #6358)
+#6326 := (iff #6310 #6323)
+#6314 := (+ #2224 #6307)
+#6315 := (+ #1444 #6314)
+#6318 := (<= #6315 0::Int)
+#6324 := (iff #6318 #6323)
+#6325 := [rewrite]: #6324
+#6319 := (iff #6310 #6318)
+#6316 := (= #6309 #6315)
+#6317 := [rewrite]: #6316
+#6320 := [monotonicity #6317]: #6319
+#6327 := [trans #6320 #6325]: #6326
+#6360 := [monotonicity #6327]: #6359
+#6363 := [monotonicity #6360]: #6362
+#6356 := (iff #6353 #6355)
+#6357 := [rewrite]: #6356
+#6366 := [monotonicity #6357 #6363]: #6365
+#6372 := [monotonicity #6366]: #6371
+#6376 := [trans #6372 #6374]: #6375
+#6369 := [quant-inst #2221]: #6368
+#6377 := [mp #6369 #6376]: #6367
+#6501 := [unit-resolution #6377 #6500 #6485]: #6361
+#6380 := (or #6358 #6379)
+#6381 := [def-axiom]: #6380
+#6502 := [unit-resolution #6381 #6501]: #6379
+#6382 := (not #6323)
+#6383 := (or #6358 #6382)
+#6384 := [def-axiom]: #6383
+#6503 := [unit-resolution #6384 #6501]: #6382
+#6335 := (or #6312 #6323 #6332)
+#6338 := (or #4400 #6312 #6323 #6332)
+#6304 := (+ #6303 #2223)
+#6305 := (+ #174 #6304)
+#6306 := (= #6305 0::Int)
+#6313 := (or #6312 #6310 #6306)
+#6339 := (or #4400 #6313)
+#6346 := (iff #6339 #6338)
+#6341 := (or #4400 #6335)
+#6344 := (iff #6341 #6338)
+#6345 := [rewrite]: #6344
+#6342 := (iff #6339 #6341)
+#6336 := (iff #6313 #6335)
+#6333 := (iff #6306 #6332)
+#6330 := (= #6305 #6329)
+#6331 := [rewrite]: #6330
+#6334 := [monotonicity #6331]: #6333
+#6337 := [monotonicity #6327 #6334]: #6336
+#6343 := [monotonicity #6337]: #6342
+#6347 := [trans #6343 #6345]: #6346
+#6340 := [quant-inst #2221]: #6339
+#6348 := [mp #6340 #6347]: #6338
+#6505 := [unit-resolution #6348 #6504]: #6335
+#6506 := [unit-resolution #6505 #6503 #6502]: #6332
+#6507 := (not #6332)
+#6508 := (or #6507 #6350)
+#6509 := [th-lemma arith triangle-eq]: #6508
+#6510 := [unit-resolution #6509 #6506]: #6350
+#6378 := (>= #2840 0::Int)
+#6511 := (or #6378 #2841)
+#6512 := [th-lemma arith farkas 1 1]: #6511
+#6513 := [unit-resolution #6512 #6479]: #6378
+#6514 := [th-lemma arith farkas 1 -1 1 #6513 #6503 #6510]: false
+#6515 := [lemma #6514]: #2841
+#4040 := (or #4523 #2846 #4517)
+#4041 := [def-axiom]: #4040
+#7088 := [unit-resolution #4041 #6515 #7087]: #4517
+#4055 := (or #4514 #4508)
+#4056 := [def-axiom]: #4055
+#7089 := [unit-resolution #4056 #7088]: #4508
+#6870 := (= #174 #2244)
+#6687 := (= f22 ?v0!14)
+#6517 := (f3 f15 ?v0!14)
+#6518 := (= f1 #6517)
+#6688 := (ite #6687 #5883 #6518)
+#6260 := (f4 f15 f22 #5882)
+#6691 := (f3 #6260 ?v0!14)
+#6692 := (= f1 #6691)
+#6694 := (iff #6688 #6692)
+#6697 := (or #6281 #6694)
+#6693 := (iff #6692 #6688)
+#6698 := (or #6281 #6693)
+#6700 := (iff #6698 #6697)
+#6702 := (iff #6697 #6697)
+#6703 := [rewrite]: #6702
+#6695 := (iff #6693 #6694)
+#6696 := [rewrite]: #6695
+#6701 := [monotonicity #6696]: #6700
+#6704 := [trans #6701 #6703]: #6700
+#6699 := [quant-inst #104 #170 #5882 #2239]: #6698
+#6705 := [mp #6699 #6704]: #6697
+#6987 := [unit-resolution #6705 #4168]: #6694
+#7003 := (= #2240 #6691)
+#6999 := (= #6691 #2240)
+#6997 := (= #6260 f23)
+#6993 := (= #6260 #180)
+#6994 := [monotonicity #6992]: #6993
+#6998 := [trans #6994 #6996]: #6997
+#7000 := [monotonicity #6998]: #6999
+#7004 := [symm #7000]: #7003
+#6985 := [hypothesis]: #2860
+#4118 := (or #2855 #2241)
+#4119 := [def-axiom]: #4118
+#6988 := [unit-resolution #4119 #6985]: #2241
+#7005 := [trans #6988 #7004]: #6692
+#6718 := (not #6692)
+#6717 := (not #6694)
+#6719 := (or #6717 #6688 #6718)
+#6720 := [def-axiom]: #6719
+#7006 := [unit-resolution #6720 #7005 #6987]: #6688
+#6546 := (f5 f22 ?v0!14)
+#6547 := (f9 #6546)
+#6477 := (* -1::Int #2244)
+#6564 := (+ #6477 #6547)
+#6565 := (+ #174 #6564)
+#6566 := (>= #6565 0::Int)
+#6594 := (not #6566)
+#6548 := (* -1::Int #6547)
+#6552 := (+ f8 #6548)
+#6553 := (<= #6552 0::Int)
+#6571 := (or #6553 #6566)
+#6574 := (not #6571)
+#4114 := (not #2849)
+#4115 := (or #2855 #4114)
+#4120 := [def-axiom]: #4115
+#6986 := [unit-resolution #4120 #6985]: #4114
+#6580 := (or #4392 #2849 #6574)
+#6549 := (+ #1444 #6548)
+#6550 := (+ #2244 #6549)
+#6551 := (<= #6550 0::Int)
+#6554 := (or #6553 #6551)
+#6555 := (not #6554)
+#6556 := (or #2245 #6555)
+#6581 := (or #4392 #6556)
+#6588 := (iff #6581 #6580)
+#6577 := (or #2849 #6574)
+#6583 := (or #4392 #6577)
+#6586 := (iff #6583 #6580)
+#6587 := [rewrite]: #6586
+#6584 := (iff #6581 #6583)
+#6578 := (iff #6556 #6577)
+#6575 := (iff #6555 #6574)
+#6572 := (iff #6554 #6571)
+#6569 := (iff #6551 #6566)
+#6557 := (+ #2244 #6548)
+#6558 := (+ #1444 #6557)
+#6561 := (<= #6558 0::Int)
+#6567 := (iff #6561 #6566)
+#6568 := [rewrite]: #6567
+#6562 := (iff #6551 #6561)
+#6559 := (= #6550 #6558)
+#6560 := [rewrite]: #6559
+#6563 := [monotonicity #6560]: #6562
+#6570 := [trans #6563 #6568]: #6569
+#6573 := [monotonicity #6570]: #6572
+#6576 := [monotonicity #6573]: #6575
+#6579 := [monotonicity #2851 #6576]: #6578
+#6585 := [monotonicity #6579]: #6584
+#6589 := [trans #6585 #6587]: #6588
+#6582 := [quant-inst #2239]: #6581
+#6590 := [mp #6582 #6589]: #6580
+#7007 := [unit-resolution #6590 #6500 #6986]: #6574
+#6595 := (or #6571 #6594)
+#6596 := [def-axiom]: #6595
+#7008 := [unit-resolution #6596 #7007]: #6594
+#6706 := (not #6688)
+#6932 := (or #6687 #6566 #6706)
+#6813 := (f6 #6546)
+#6823 := (f13 f14 #6813)
+#6838 := (* -1::Int #6823)
+#6878 := (+ #174 #6838)
+#6880 := (>= #6878 0::Int)
+#6877 := (= #174 #6823)
+#6884 := (= #6823 #174)
+#6882 := (= #6813 f22)
+#6814 := (= f22 #6813)
+#6821 := (or #6820 #6814)
+#6822 := [quant-inst #170 #2239]: #6821
+#6881 := [unit-resolution #6822 #4196]: #6814
+#6883 := [symm #6881]: #6882
+#6885 := [monotonicity #6883]: #6884
+#6886 := [symm #6885]: #6877
+#6887 := (not #6877)
+#6888 := (or #6887 #6880)
+#6889 := [th-lemma arith triangle-eq]: #6888
+#6890 := [unit-resolution #6889 #6886]: #6880
+#6891 := [hypothesis]: #6594
+#6810 := (>= #6547 0::Int)
+#6764 := (<= #6547 0::Int)
+#6765 := (not #6764)
+#6707 := (not #6687)
+#6892 := [hypothesis]: #6707
+#6770 := (or #6687 #6765)
 #48 := (f9 #37)
-#407 := (<= #48 0::Int)
-#408 := (not #407)
-#354 := (= #12 #23)
-#414 := (or #354 #408)
-#4212 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #414)
-#419 := (forall (vars (?v0 S3) (?v1 S3)) #414)
-#4215 := (iff #419 #4212)
-#4213 := (iff #414 #414)
-#4214 := [refl]: #4213
-#4216 := [quant-intro #4214]: #4215
-#1854 := (~ #419 #419)
-#1853 := (~ #414 #414)
-#1883 := [refl]: #1853
-#1855 := [nnf-pos #1883]: #1854
+#406 := (<= #48 0::Int)
+#407 := (not #406)
+#353 := (= #12 #23)
+#413 := (or #353 #407)
+#4203 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #413)
+#418 := (forall (vars (?v0 S3) (?v1 S3)) #413)
+#4206 := (iff #418 #4203)
+#4204 := (iff #413 #413)
+#4205 := [refl]: #4204
+#4207 := [quant-intro #4205]: #4206
+#1845 := (~ #418 #418)
+#1844 := (~ #413 #413)
+#1874 := [refl]: #1844
+#1846 := [nnf-pos #1874]: #1845
 #53 := (< 0::Int #48)
 #47 := (= #23 #12)
 #52 := (not #47)
 #54 := (implies #52 #53)
 #55 := (forall (vars (?v0 S3) (?v1 S3)) #54)
-#422 := (iff #55 #419)
-#399 := (or #53 #354)
-#404 := (forall (vars (?v0 S3) (?v1 S3)) #399)
-#420 := (iff #404 #419)
-#417 := (iff #399 #414)
-#411 := (or #408 #354)
-#415 := (iff #411 #414)
-#416 := [rewrite]: #415
-#412 := (iff #399 #411)
-#409 := (iff #53 #408)
-#410 := [rewrite]: #409
-#413 := [monotonicity #410]: #412
-#418 := [trans #413 #416]: #417
-#421 := [quant-intro #418]: #420
-#405 := (iff #55 #404)
-#402 := (iff #54 #399)
-#368 := (not #354)
-#396 := (implies #368 #53)
-#400 := (iff #396 #399)
-#401 := [rewrite]: #400
-#397 := (iff #54 #396)
-#394 := (iff #52 #368)
-#360 := (iff #47 #354)
-#361 := [rewrite]: #360
-#395 := [monotonicity #361]: #394
-#398 := [monotonicity #395]: #397
-#403 := [trans #398 #401]: #402
-#406 := [quant-intro #403]: #405
-#423 := [trans #406 #421]: #422
-#393 := [asserted]: #55
-#424 := [mp #393 #423]: #419
-#1884 := [mp~ #424 #1855]: #419
-#4217 := [mp #1884 #4216]: #4212
-#6782 := (not #4212)
-#6783 := (or #6782 #6696 #6774)
-#6775 := (= ?v0!14 f22)
-#6776 := (or #6775 #6774)
-#6784 := (or #6782 #6776)
-#6791 := (iff #6784 #6783)
-#6786 := (or #6782 #6779)
-#6789 := (iff #6786 #6783)
-#6790 := [rewrite]: #6789
-#6787 := (iff #6784 #6786)
-#6780 := (iff #6776 #6779)
-#6777 := (iff #6775 #6696)
-#6778 := [rewrite]: #6777
-#6781 := [monotonicity #6778]: #6780
-#6788 := [monotonicity #6781]: #6787
-#6792 := [trans #6788 #6790]: #6791
-#6785 := [quant-inst #170 #2248]: #6784
-#6793 := [mp #6785 #6792]: #6783
-#6902 := [unit-resolution #6793 #4217]: #6779
-#6903 := [unit-resolution #6902 #6901]: #6774
-#6904 := (or #6819 #6773)
-#6905 := [th-lemma arith farkas 1 1]: #6904
-#6906 := [unit-resolution #6905 #6903]: #6819
-#6820 := (f7 #6555)
-#6827 := (f13 f14 #6820)
-#6828 := (* -1::Int #6827)
-#6877 := (+ #2253 #6828)
-#6884 := (<= #6877 0::Int)
-#6876 := (= #2253 #6827)
-#6910 := (= #6827 #2253)
-#6908 := (= #6820 ?v0!14)
-#6821 := (= ?v0!14 #6820)
-#6825 := (or #6824 #6821)
-#6826 := [quant-inst #170 #2248]: #6825
-#6907 := [unit-resolution #6826 #4199]: #6821
-#6909 := [symm #6907]: #6908
-#6911 := [monotonicity #6909]: #6910
-#6912 := [symm #6911]: #6876
-#6913 := (not #6876)
-#6914 := (or #6913 #6884)
-#6915 := [th-lemma arith triangle-eq]: #6914
-#6916 := [unit-resolution #6915 #6912]: #6884
-#6848 := (+ #6827 #6847)
-#6849 := (<= #6848 0::Int)
-#6835 := (f3 f15 #6820)
-#6836 := (= f1 #6835)
-#6923 := (= #6526 #6835)
-#6919 := (= #6835 #6526)
-#6920 := [monotonicity #6909]: #6919
-#6924 := [symm #6920]: #6923
-#6917 := [hypothesis]: #6697
-#6719 := (or #6715 #6696 #6527)
-#6720 := [def-axiom]: #6719
-#6918 := [unit-resolution #6720 #6901 #6917]: #6527
-#6925 := [trans #6918 #6924]: #6836
-#6838 := (f3 f15 #6822)
-#6839 := (= f1 #6838)
-#6933 := (not #6839)
-#6934 := (iff #757 #6933)
-#6931 := (iff #754 #6839)
-#6929 := (iff #6839 #754)
-#6927 := (= #6838 #171)
-#6928 := [monotonicity #6892]: #6927
-#6930 := [monotonicity #6928]: #6929
-#6932 := [symm #6930]: #6931
-#6935 := [monotonicity #6932]: #6934
-#4051 := (or #4535 #757)
-#4052 := [def-axiom]: #4051
-#6926 := [unit-resolution #4052 #6508]: #757
-#6936 := [mp #6926 #6935]: #6933
-#6837 := (not #6836)
-#6857 := (or #6837 #6839 #6849)
-#3961 := (or #4547 #4291)
-#4016 := [def-axiom]: #3961
-#6937 := [unit-resolution #4016 #6507]: #4291
-#6862 := (or #4296 #6837 #6839 #6849)
-#6833 := (+ #6832 #6828)
-#6834 := (>= #6833 0::Int)
-#6840 := (or #6839 #6837 #6834)
-#6863 := (or #4296 #6840)
-#6870 := (iff #6863 #6862)
-#6865 := (or #4296 #6857)
-#6868 := (iff #6865 #6862)
-#6869 := [rewrite]: #6868
-#6866 := (iff #6863 #6865)
-#6860 := (iff #6840 #6857)
-#6854 := (or #6839 #6837 #6849)
-#6858 := (iff #6854 #6857)
-#6859 := [rewrite]: #6858
-#6855 := (iff #6840 #6854)
-#6852 := (iff #6834 #6849)
-#6841 := (+ #6828 #6832)
-#6844 := (>= #6841 0::Int)
-#6850 := (iff #6844 #6849)
-#6851 := [rewrite]: #6850
-#6845 := (iff #6834 #6844)
-#6842 := (= #6833 #6841)
-#6843 := [rewrite]: #6842
-#6846 := [monotonicity #6843]: #6845
-#6853 := [trans #6846 #6851]: #6852
-#6856 := [monotonicity #6853]: #6855
-#6861 := [trans #6856 #6859]: #6860
-#6867 := [monotonicity #6861]: #6866
-#6871 := [trans #6867 #6869]: #6870
-#6864 := [quant-inst #6820 #6822]: #6863
-#6872 := [mp #6864 #6871]: #6862
-#6938 := [unit-resolution #6872 #6937]: #6857
-#6939 := [unit-resolution #6938 #6936 #6925]: #6849
-#6940 := [th-lemma arith farkas 1 1 1 -1 1 #6939 #6916 #6906 #6900 #6899]: false
-#6942 := [lemma #6940]: #6941
-#7018 := [unit-resolution #6942 #7017 #7015]: #6696
-#7042 := [monotonicity #7018]: #6879
-#7040 := (= #2252 #174)
-#7038 := (= #174 #2252)
-#6795 := (= #6556 0::Int)
-#6802 := (or #6716 #6795)
+#421 := (iff #55 #418)
+#398 := (or #53 #353)
+#403 := (forall (vars (?v0 S3) (?v1 S3)) #398)
+#419 := (iff #403 #418)
+#416 := (iff #398 #413)
+#410 := (or #407 #353)
+#414 := (iff #410 #413)
+#415 := [rewrite]: #414
+#411 := (iff #398 #410)
+#408 := (iff #53 #407)
+#409 := [rewrite]: #408
+#412 := [monotonicity #409]: #411
+#417 := [trans #412 #415]: #416
+#420 := [quant-intro #417]: #419
+#404 := (iff #55 #403)
+#401 := (iff #54 #398)
+#367 := (not #353)
+#395 := (implies #367 #53)
+#399 := (iff #395 #398)
+#400 := [rewrite]: #399
+#396 := (iff #54 #395)
+#393 := (iff #52 #367)
+#359 := (iff #47 #353)
+#360 := [rewrite]: #359
+#394 := [monotonicity #360]: #393
+#397 := [monotonicity #394]: #396
+#402 := [trans #397 #400]: #401
+#405 := [quant-intro #402]: #404
+#422 := [trans #405 #420]: #421
+#392 := [asserted]: #55
+#423 := [mp #392 #422]: #418
+#1875 := [mp~ #423 #1846]: #418
+#4208 := [mp #1875 #4207]: #4203
+#6773 := (not #4203)
+#6774 := (or #6773 #6687 #6765)
+#6766 := (= ?v0!14 f22)
+#6767 := (or #6766 #6765)
+#6775 := (or #6773 #6767)
+#6782 := (iff #6775 #6774)
+#6777 := (or #6773 #6770)
+#6780 := (iff #6777 #6774)
+#6781 := [rewrite]: #6780
+#6778 := (iff #6775 #6777)
+#6771 := (iff #6767 #6770)
+#6768 := (iff #6766 #6687)
+#6769 := [rewrite]: #6768
+#6772 := [monotonicity #6769]: #6771
+#6779 := [monotonicity #6772]: #6778
+#6783 := [trans #6779 #6781]: #6782
+#6776 := [quant-inst #170 #2239]: #6775
+#6784 := [mp #6776 #6783]: #6774
+#6893 := [unit-resolution #6784 #4208]: #6770
+#6894 := [unit-resolution #6893 #6892]: #6765
+#6895 := (or #6810 #6764)
+#6896 := [th-lemma arith farkas 1 1]: #6895
+#6897 := [unit-resolution #6896 #6894]: #6810
+#6811 := (f7 #6546)
+#6818 := (f13 f14 #6811)
+#6819 := (* -1::Int #6818)
+#6868 := (+ #2244 #6819)
+#6875 := (<= #6868 0::Int)
+#6867 := (= #2244 #6818)
+#6901 := (= #6818 #2244)
+#6899 := (= #6811 ?v0!14)
+#6812 := (= ?v0!14 #6811)
+#6816 := (or #6815 #6812)
+#6817 := [quant-inst #170 #2239]: #6816
+#6898 := [unit-resolution #6817 #4190]: #6812
+#6900 := [symm #6898]: #6899
+#6902 := [monotonicity #6900]: #6901
+#6903 := [symm #6902]: #6867
+#6904 := (not #6867)
+#6905 := (or #6904 #6875)
+#6906 := [th-lemma arith triangle-eq]: #6905
+#6907 := [unit-resolution #6906 #6903]: #6875
+#6839 := (+ #6818 #6838)
+#6840 := (<= #6839 0::Int)
+#6826 := (f3 f15 #6811)
+#6827 := (= f1 #6826)
+#6914 := (= #6517 #6826)
+#6910 := (= #6826 #6517)
+#6911 := [monotonicity #6900]: #6910
+#6915 := [symm #6911]: #6914
+#6908 := [hypothesis]: #6688
+#6710 := (or #6706 #6687 #6518)
+#6711 := [def-axiom]: #6710
+#6909 := [unit-resolution #6711 #6892 #6908]: #6518
+#6916 := [trans #6909 #6915]: #6827
+#6829 := (f3 f15 #6813)
+#6830 := (= f1 #6829)
+#6924 := (not #6830)
+#6925 := (iff #756 #6924)
+#6922 := (iff #753 #6830)
+#6920 := (iff #6830 #753)
+#6918 := (= #6829 #171)
+#6919 := [monotonicity #6883]: #6918
+#6921 := [monotonicity #6919]: #6920
+#6923 := [symm #6921]: #6922
+#6926 := [monotonicity #6923]: #6925
+#4044 := (or #4526 #756)
+#4039 := [def-axiom]: #4044
+#6917 := [unit-resolution #4039 #6499]: #756
+#6927 := [mp #6917 #6926]: #6924
+#6828 := (not #6827)
+#6848 := (or #6828 #6830 #6840)
+#3952 := (or #4538 #4282)
+#4007 := [def-axiom]: #3952
+#6928 := [unit-resolution #4007 #6498]: #4282
+#6853 := (or #4287 #6828 #6830 #6840)
+#6824 := (+ #6823 #6819)
+#6825 := (>= #6824 0::Int)
+#6831 := (or #6830 #6828 #6825)
+#6854 := (or #4287 #6831)
+#6861 := (iff #6854 #6853)
+#6856 := (or #4287 #6848)
+#6859 := (iff #6856 #6853)
+#6860 := [rewrite]: #6859
+#6857 := (iff #6854 #6856)
+#6851 := (iff #6831 #6848)
+#6845 := (or #6830 #6828 #6840)
+#6849 := (iff #6845 #6848)
+#6850 := [rewrite]: #6849
+#6846 := (iff #6831 #6845)
+#6843 := (iff #6825 #6840)
+#6832 := (+ #6819 #6823)
+#6835 := (>= #6832 0::Int)
+#6841 := (iff #6835 #6840)
+#6842 := [rewrite]: #6841
+#6836 := (iff #6825 #6835)
+#6833 := (= #6824 #6832)
+#6834 := [rewrite]: #6833
+#6837 := [monotonicity #6834]: #6836
+#6844 := [trans #6837 #6842]: #6843
+#6847 := [monotonicity #6844]: #6846
+#6852 := [trans #6847 #6850]: #6851
+#6858 := [monotonicity #6852]: #6857
+#6862 := [trans #6858 #6860]: #6861
+#6855 := [quant-inst #6811 #6813]: #6854
+#6863 := [mp #6855 #6862]: #6853
+#6929 := [unit-resolution #6863 #6928]: #6848
+#6930 := [unit-resolution #6929 #6927 #6916]: #6840
+#6931 := [th-lemma arith farkas 1 1 1 -1 1 #6930 #6907 #6897 #6891 #6890]: false
+#6933 := [lemma #6931]: #6932
+#7009 := [unit-resolution #6933 #7008 #7006]: #6687
+#7033 := [monotonicity #7009]: #6870
+#7031 := (= #2243 #174)
+#7029 := (= #174 #2243)
+#6786 := (= #6547 0::Int)
+#6793 := (or #6707 #6786)
 #49 := (= #48 0::Int)
-#382 := (or #49 #368)
-#4206 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #382)
-#387 := (forall (vars (?v0 S3) (?v1 S3)) #382)
-#4209 := (iff #387 #4206)
-#4207 := (iff #382 #382)
-#4208 := [refl]: #4207
-#4210 := [quant-intro #4208]: #4209
-#1850 := (~ #387 #387)
-#1881 := (~ #382 #382)
-#1882 := [refl]: #1881
-#1851 := [nnf-pos #1882]: #1850
+#381 := (or #49 #367)
+#4197 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #381)
+#386 := (forall (vars (?v0 S3) (?v1 S3)) #381)
+#4200 := (iff #386 #4197)
+#4198 := (iff #381 #381)
+#4199 := [refl]: #4198
+#4201 := [quant-intro #4199]: #4200
+#1841 := (~ #386 #386)
+#1872 := (~ #381 #381)
+#1873 := [refl]: #1872
+#1842 := [nnf-pos #1873]: #1841
 #50 := (implies #47 #49)
 #51 := (forall (vars (?v0 S3) (?v1 S3)) #50)
-#390 := (iff #51 #387)
-#362 := (= 0::Int #48)
-#369 := (or #368 #362)
-#374 := (forall (vars (?v0 S3) (?v1 S3)) #369)
-#388 := (iff #374 #387)
-#385 := (iff #369 #382)
-#379 := (or #368 #49)
-#383 := (iff #379 #382)
-#384 := [rewrite]: #383
-#380 := (iff #369 #379)
-#377 := (iff #362 #49)
-#378 := [rewrite]: #377
-#381 := [monotonicity #378]: #380
-#386 := [trans #381 #384]: #385
-#389 := [quant-intro #386]: #388
-#375 := (iff #51 #374)
-#372 := (iff #50 #369)
-#365 := (implies #354 #362)
-#370 := (iff #365 #369)
-#371 := [rewrite]: #370
-#366 := (iff #50 #365)
-#363 := (iff #49 #362)
-#364 := [rewrite]: #363
-#367 := [monotonicity #361 #364]: #366
-#373 := [trans #367 #371]: #372
-#376 := [quant-intro #373]: #375
-#391 := [trans #376 #389]: #390
-#352 := [asserted]: #51
-#392 := [mp #352 #391]: #387
-#1852 := [mp~ #392 #1851]: #387
-#4211 := [mp #1852 #4210]: #4206
-#6807 := (not #4206)
-#6808 := (or #6807 #6716 #6795)
-#6794 := (not #6775)
-#6796 := (or #6795 #6794)
-#6809 := (or #6807 #6796)
-#6816 := (iff #6809 #6808)
-#6811 := (or #6807 #6802)
-#6814 := (iff #6811 #6808)
-#6815 := [rewrite]: #6814
-#6812 := (iff #6809 #6811)
-#6805 := (iff #6796 #6802)
-#6799 := (or #6795 #6716)
-#6803 := (iff #6799 #6802)
-#6804 := [rewrite]: #6803
-#6800 := (iff #6796 #6799)
-#6797 := (iff #6794 #6716)
-#6798 := [monotonicity #6778]: #6797
-#6801 := [monotonicity #6798]: #6800
-#6806 := [trans #6801 #6804]: #6805
-#6813 := [monotonicity #6806]: #6812
-#6817 := [trans #6813 #6815]: #6816
-#6810 := [quant-inst #170 #2248]: #6809
-#6818 := [mp #6810 #6817]: #6808
-#7019 := [unit-resolution #6818 #4211]: #6802
-#7020 := [unit-resolution #7019 #7018]: #6795
-#7021 := (not #6795)
-#7022 := (or #7021 #6773)
-#7023 := [th-lemma arith triangle-eq]: #7022
-#7024 := [unit-resolution #7023 #7020]: #6773
-#7025 := (or #7021 #6819)
-#7026 := [th-lemma arith triangle-eq]: #7025
-#7027 := [unit-resolution #7026 #7020]: #6819
-#6424 := (* -1::Int #2252)
-#6612 := (+ #6424 #6556)
-#6613 := (+ #174 #6612)
-#6633 := (<= #6613 0::Int)
-#6616 := (= #6613 0::Int)
-#6600 := (not #6562)
-#6601 := (or #6580 #6600)
-#6602 := [def-axiom]: #6601
-#7028 := [unit-resolution #6602 #7016]: #6600
-#6619 := (or #6562 #6575 #6616)
-#6622 := (or #4409 #6562 #6575 #6616)
-#6608 := (+ #6556 #6424)
-#6609 := (+ #174 #6608)
-#6610 := (= #6609 0::Int)
-#6611 := (or #6562 #6560 #6610)
-#6623 := (or #4409 #6611)
-#6630 := (iff #6623 #6622)
-#6625 := (or #4409 #6619)
-#6628 := (iff #6625 #6622)
-#6629 := [rewrite]: #6628
-#6626 := (iff #6623 #6625)
-#6620 := (iff #6611 #6619)
-#6617 := (iff #6610 #6616)
-#6614 := (= #6609 #6613)
-#6615 := [rewrite]: #6614
-#6618 := [monotonicity #6615]: #6617
-#6621 := [monotonicity #6579 #6618]: #6620
-#6627 := [monotonicity #6621]: #6626
-#6631 := [trans #6627 #6629]: #6630
-#6624 := [quant-inst #2248]: #6623
-#6632 := [mp #6624 #6631]: #6622
-#7029 := [unit-resolution #6632 #6513]: #6619
-#7030 := [unit-resolution #7029 #7017 #7028]: #6616
-#7031 := (not #6616)
-#7032 := (or #7031 #6633)
-#7033 := [th-lemma arith triangle-eq]: #7032
-#7034 := [unit-resolution #7033 #7030]: #6633
-#6634 := (>= #6613 0::Int)
-#7035 := (or #7031 #6634)
-#7036 := [th-lemma arith triangle-eq]: #7035
-#7037 := [unit-resolution #7036 #7030]: #6634
-#7039 := [th-lemma ar