updated SMT certificates

--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Fri Dec 17 14:36:33 2010 +0100
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Fri Dec 17 14:59:06 2010 +0100
@@ -1,7198 +1,7196 @@
-4a18f08eb054c06c0e0f108571305a91f86ae528 7197 0
+2bcca4894d12c21351a258c93ec6b00e790bb1de 7195 0
 #2 := false
-decl f14 :: (-> S6 S3 Int)
-decl f23 :: S3
-#171 := f23
-decl f15 :: S6
-#99 := f15
-#175 := (f14 f15 f23)
-decl f11 :: S3
-#57 := f11
-#100 := (f14 f15 f11)
-#7798 := (= #100 #175)
-#7826 := (= #175 #100)
-#6087 := (= f23 f11)
-#6089 := (= f11 f23)
+decl f13 :: (-> S5 S3 Int)
+decl f22 :: S3
+#170 := f22
+decl f14 :: S5
+#98 := f14
+#174 := (f13 f14 f22)
+decl f10 :: S3
+#56 := f10
+#99 := (f13 f14 f10)
+#7797 := (= #99 #174)
+#7825 := (= #174 #99)
+#6086 := (= f22 f10)
+#6088 := (= f10 f22)
 decl f3 :: (-> S2 S3 S1)
 decl ?v1!7 :: (-> S3 S3)
-#6070 := (?v1!7 f23)
-decl f16 :: S2
-#105 := f16
-#6082 := (f3 f16 #6070)
+#6069 := (?v1!7 f22)
+decl f15 :: S2
+#104 := f15
+#6081 := (f3 f15 #6069)
 decl f1 :: S1
 #4 := f1
-#6083 := (= f1 #6082)
-#6084 := (not #6083)
-#45 := 0::Int
-decl f10 :: (-> S5 Int)
-decl f6 :: (-> S3 S3 S5)
-#6075 := (f6 #6070 f23)
-#6076 := (f10 #6075)
-#1209 := -1::Int
-#6077 := (* -1::Int #6076)
-#6071 := (f14 f15 #6070)
-#6072 := (* -1::Int #6071)
-#6078 := (+ #6072 #6077)
-#6079 := (+ #175 #6078)
-#6080 := (= #6079 0::Int)
-#6081 := (not #6080)
-#6073 := (+ #175 #6072)
-#6074 := (<= #6073 0::Int)
-#6092 := (or #6074 #6081 #6084)
-decl f25 :: (-> S3 Int)
+#6082 := (= f1 #6081)
+#6083 := (not #6082)
+#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)
+decl f24 :: (-> S3 Int)
 decl ?v0!15 :: S3
-#2274 := ?v0!15
-#2275 := (f25 ?v0!15)
-#2276 := (>= #2275 0::Int)
-#2277 := (not #2276)
+#2273 := ?v0!15
+#2274 := (f24 ?v0!15)
+#2275 := (>= #2274 0::Int)
+#2276 := (not #2275)
 decl ?v0!20 :: S3
-#2347 := ?v0!20
-#13 := (:var 0 S3)
-#2351 := (f6 #13 ?v0!20)
-#4455 := (pattern #2351)
-#190 := (f25 #13)
-#4395 := (pattern #190)
-decl f24 :: S2
-#180 := f24
-#200 := (f3 f24 #13)
-#4421 := (pattern #200)
-#2352 := (f10 #2351)
-#2348 := (f25 ?v0!20)
-#2349 := (* -1::Int #2348)
-#2951 := (+ #2349 #2352)
-#2952 := (+ #190 #2951)
-#2955 := (= #2952 0::Int)
-#3517 := (not #2955)
-#2350 := (+ #190 #2349)
-#2355 := (>= #2350 0::Int)
-#808 := (= f1 #200)
-#814 := (not #808)
-#3518 := (or #814 #2355 #3517)
-#4456 := (forall (vars (?v1 S3)) (:pat #4421 #4395 #4455) #3518)
-#4461 := (not #4456)
-#24 := (:var 1 S3)
-#82 := (f6 #13 #24)
-#4250 := (pattern #82)
-#212 := (f25 #24)
-#1504 := (* -1::Int #212)
-#1505 := (+ #190 #1504)
-#83 := (f10 #82)
-#1535 := (+ #83 #1505)
-#1533 := (>= #1535 0::Int)
-#1232 := (* -1::Int #83)
-decl f9 :: Int
-#46 := f9
-#1235 := (+ f9 #1232)
-#1236 := (<= #1235 0::Int)
-#3509 := (or #814 #1236 #1533)
-#4447 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3509)
-#4452 := (not #4447)
-#2927 := (= f11 ?v0!20)
-#2359 := (+ f9 #2349)
-#2360 := (<= #2359 0::Int)
-#4464 := (or #2360 #2927 #4452 #4461)
-#4467 := (not #4464)
+#2346 := ?v0!20
+#12 := (:var 0 S3)
+#2350 := (f5 #12 ?v0!20)
+#4454 := (pattern #2350)
+#189 := (f24 #12)
+#4394 := (pattern #189)
+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)
+#23 := (:var 1 S3)
+#81 := (f5 #12 #23)
+#4249 := (pattern #81)
+#211 := (f24 #23)
+#1503 := (* -1::Int #211)
+#1504 := (+ #189 #1503)
+#82 := (f9 #81)
+#1534 := (+ #82 #1504)
+#1532 := (>= #1534 0::Int)
+#1231 := (* -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)
 decl ?v0!19 :: S3
-#2317 := ?v0!19
+#2316 := ?v0!19
 decl ?v1!18 :: S3
-#2316 := ?v1!18
-#2322 := (f6 ?v1!18 ?v0!19)
-#2323 := (f10 #2322)
-#2326 := (* -1::Int #2323)
-#2320 := (f25 ?v1!18)
-#2913 := (* -1::Int #2320)
-#2914 := (+ #2913 #2326)
-#2318 := (f25 ?v0!19)
-#2915 := (+ #2318 #2914)
-#2916 := (<= #2915 0::Int)
-#2330 := (f3 f24 ?v1!18)
-#2331 := (= f1 #2330)
-#3472 := (not #2331)
-#2327 := (+ f9 #2326)
-#2328 := (<= #2327 0::Int)
-#3487 := (or #2328 #3472 #2916)
-#3492 := (not #3487)
-#4470 := (or #3492 #4467)
-#4473 := (not #4470)
-#4438 := (pattern #190 #212)
-#1503 := (>= #1505 0::Int)
-#209 := (f3 f24 #24)
-#828 := (= f1 #209)
-#3449 := (not #828)
-#3464 := (or #808 #3449 #1503)
-#4439 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4438) #3464)
-#4444 := (not #4439)
-#4476 := (or #4444 #4473)
-#4479 := (not #4476)
+#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)
 decl ?v1!16 :: S3
-#2289 := ?v1!16
-#2293 := (f25 ?v1!16)
-#2887 := (* -1::Int #2293)
+#2288 := ?v1!16
+#2292 := (f24 ?v1!16)
+#2886 := (* -1::Int #2292)
 decl ?v0!17 :: S3
-#2290 := ?v0!17
-#2291 := (f25 ?v0!17)
-#2888 := (+ #2291 #2887)
-#2889 := (<= #2888 0::Int)
-#2298 := (f3 f24 ?v1!16)
-#2299 := (= f1 #2298)
-#2296 := (f3 f24 ?v0!17)
-#2297 := (= f1 #2296)
-#3426 := (not #2297)
-#3441 := (or #3426 #2299 #2889)
-#3446 := (not #3441)
-#4482 := (or #3446 #4479)
-#4485 := (not #4482)
-#1494 := (>= #190 0::Int)
-#4430 := (forall (vars (?v0 S3)) (:pat #4395) #1494)
-#4435 := (not #4430)
-#4488 := (or #4435 #4485)
-decl f7 :: (-> S5 S3)
-decl f8 :: (-> S5 S3)
-#5996 := (f6 f23 f23)
-#7212 := (f8 #5996)
-#14212 := (f6 #7212 ?v0!20)
-#24393 := (f8 #14212)
-#14775 := (?v1!7 ?v0!20)
-#24670 := (f6 #14775 #24393)
-#25043 := (f7 #24670)
-#26214 := (f3 f16 #25043)
-#26215 := (= f1 #26214)
-#14787 := (f3 f16 #14775)
-#27707 := (= #14787 #26214)
-#27704 := (= #26214 #14787)
-#29052 := (= #25043 #14775)
-#14780 := (f6 #14775 ?v0!20)
-#19039 := (f7 #14780)
-#26819 := (= #19039 #14775)
-#19044 := (= #14775 #19039)
-#38 := (f6 #24 #13)
-#4194 := (pattern #38)
-#42 := (f7 #38)
-#345 := (= #24 #42)
-#4201 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #345)
-#349 := (forall (vars (?v0 S3) (?v1 S3)) #345)
-#4204 := (iff #349 #4201)
-#4202 := (iff #345 #345)
-#4203 := [refl]: #4202
-#4205 := [quant-intro #4203]: #4204
-#1849 := (~ #349 #349)
-#1879 := (~ #345 #345)
-#1880 := [refl]: #1879
-#1850 := [nnf-pos #1880]: #1849
-#43 := (= #42 #24)
-#44 := (forall (vars (?v0 S3) (?v1 S3)) #43)
-#350 := (iff #44 #349)
-#347 := (iff #43 #345)
-#348 := [rewrite]: #347
-#351 := [quant-intro #348]: #350
-#344 := [asserted]: #44
-#354 := [mp #344 #351]: #349
-#1881 := [mp~ #354 #1850]: #349
-#4206 := [mp #1881 #4205]: #4201
-#6830 := (not #4201)
-#8631 := (or #6830 #19044)
-#13595 := [quant-inst #14775 #2347]: #8631
-#26775 := [unit-resolution #13595 #4206]: #19044
-#26817 := [symm #26775]: #26819
-#26827 := (= #25043 #19039)
-#26824 := (= #24670 #14780)
-#27256 := (= #24393 ?v0!20)
-#19043 := (f8 #14780)
-#25095 := (= #19043 ?v0!20)
-#19038 := (= ?v0!20 #19043)
-#39 := (f8 #38)
-#337 := (= #13 #39)
-#4195 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #337)
-#341 := (forall (vars (?v0 S3) (?v1 S3)) #337)
-#4198 := (iff #341 #4195)
-#4196 := (iff #337 #337)
-#4197 := [refl]: #4196
-#4199 := [quant-intro #4197]: #4198
-#1847 := (~ #341 #341)
-#1876 := (~ #337 #337)
-#1877 := [refl]: #1876
-#1848 := [nnf-pos #1877]: #1847
-#40 := (= #39 #13)
-#41 := (forall (vars (?v0 S3) (?v1 S3)) #40)
-#342 := (iff #41 #341)
-#339 := (iff #40 #337)
-#340 := [rewrite]: #339
-#343 := [quant-intro #340]: #342
-#336 := [asserted]: #41
-#346 := [mp #336 #343]: #341
-#1878 := [mp~ #346 #1848]: #341
-#4200 := [mp #1878 #4199]: #4195
-#6825 := (not #4195)
-#19045 := (or #6825 #19038)
-#19046 := [quant-inst #14775 #2347]: #19045
-#25094 := [unit-resolution #19046 #4200]: #19038
-#25096 := [symm #25094]: #25095
-#26796 := (= #24393 #19043)
-#23181 := (f6 #7212 #19043)
-#23300 := (f8 #23181)
-#26808 := (= #23300 #19043)
-#23306 := (= #19043 #23300)
-#26718 := (or #6825 #23306)
-#26721 := [quant-inst #7212 #19043]: #26718
-#26804 := [unit-resolution #26721 #4200]: #23306
-#26809 := [symm #26804]: #26808
-#26805 := (= #24393 #23300)
-#26802 := (= #23300 #24393)
-#26800 := (= #23181 #14212)
-#14132 := (f6 f23 ?v0!20)
-#26774 := (= #14132 #14212)
-#24029 := (= #14212 #14132)
-#7785 := (= #7212 f23)
-#7213 := (= f23 #7212)
-#7264 := (or #6825 #7213)
-#7265 := [quant-inst #171 #171]: #7264
-#7790 := [unit-resolution #7265 #4200]: #7213
-#7791 := [symm #7790]: #7785
-#24030 := [monotonicity #7791]: #24029
-#26716 := [symm #24030]: #26774
-#26778 := (= #23181 #14132)
-#26777 := (= #14132 #23181)
-#26753 := [monotonicity #7790 #25094]: #26777
-#26779 := [symm #26753]: #26778
-#26803 := [trans #26779 #26716]: #26800
-#26806 := [monotonicity #26803]: #26802
-#26807 := [symm #26806]: #26805
-#26823 := [trans #26807 #26809]: #26796
-#26797 := [trans #26823 #25096]: #27256
-#26825 := [monotonicity #26797]: #26824
-#26818 := [monotonicity #26825]: #26827
-#26820 := [trans #26818 #26817]: #29052
-#26815 := [monotonicity #26820]: #27704
-#26829 := [symm #26815]: #27707
-#14788 := (= f1 #14787)
-#14789 := (not #14788)
-#14781 := (f10 #14780)
-#14782 := (* -1::Int #14781)
-#14776 := (f14 f15 #14775)
-#14777 := (* -1::Int #14776)
-#14783 := (+ #14777 #14782)
-#14075 := (f14 f15 ?v0!20)
-#14784 := (+ #14075 #14783)
-#14785 := (= #14784 0::Int)
-#14786 := (not #14785)
-#14778 := (+ #14075 #14777)
-#14779 := (<= #14778 0::Int)
-#14795 := (or #14779 #14786 #14789)
-#14798 := (not #14795)
-#14116 := (* -1::Int #14075)
-#14792 := (+ f9 #14116)
-#14793 := (<= #14792 0::Int)
-#21436 := (not #14793)
-#2361 := (not #2360)
-#19784 := [hypothesis]: #2361
-#14117 := (+ #2348 #14116)
-#19568 := (>= #14117 0::Int)
-#14086 := (= #2348 #14075)
-#14133 := (f10 #14132)
-#14151 := (+ #14116 #14133)
-#14152 := (+ #175 #14151)
-#14153 := (>= #14152 0::Int)
-#14137 := (* -1::Int #14133)
-#14141 := (+ f9 #14137)
-#14142 := (<= #14141 0::Int)
-#14184 := (or #14142 #14153)
-#4491 := (not #4488)
-#1454 := (* -1::Int #175)
-#5914 := (+ #100 #1454)
-#7799 := (<= #5914 0::Int)
-#27735 := (or #6074 #2360)
-#25048 := (= #14775 #25043)
-#23338 := (or #6830 #25048)
-#23339 := [quant-inst #14775 #24393]: #23338
-#28985 := [unit-resolution #23339 #4206]: #25048
-#29063 := [symm #28985]: #29052
-#27699 := [monotonicity #29063]: #27704
-#27719 := [symm #27699]: #27707
-#6119 := (not #6074)
-#10075 := [hypothesis]: #6119
-#23175 := (or #14153 #6074)
-#11115 := (or #2276 #6074)
-#7537 := (f14 f15 ?v0!15)
-#7758 := (>= #7537 0::Int)
-#102 := (f14 f15 #13)
-#4274 := (pattern #102)
-#1737 := (>= #102 0::Int)
-#4275 := (forall (vars (?v0 S3)) (:pat #4274) #1737)
-#4494 := (or #2277 #4491)
-#4497 := (not #4494)
-#204 := (f25 f11)
-#205 := (= #204 0::Int)
-#1491 := (not #205)
-#4500 := (or #1491 #4497)
-#4503 := (not #4500)
-#4506 := (or #1491 #4503)
-#4509 := (not #4506)
-#794 := (= #102 #190)
-#815 := (or #794 #814)
-#4422 := (forall (vars (?v0 S3)) (:pat #4274 #4395 #4421) #815)
-#4427 := (not #4422)
-#4512 := (or #4427 #4509)
-#4515 := (not #4512)
+#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)
+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)
+#37 := (f5 #23 #12)
+#4193 := (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
+#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)
+#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
+#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)
+#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)
 decl ?v0!14 :: S3
-#2249 := ?v0!14
-#2254 := (f14 f15 ?v0!14)
-#2253 := (f25 ?v0!14)
-#2859 := (= #2253 #2254)
-#2250 := (f3 f24 ?v0!14)
-#2251 := (= f1 #2250)
-#2252 := (not #2251)
-#2865 := (or #2252 #2859)
-#2870 := (not #2865)
-#4518 := (or #2870 #4515)
-#4521 := (not #4518)
-#1479 := (* -1::Int #190)
-#1480 := (+ #102 #1479)
-#1478 := (>= #1480 0::Int)
-#4413 := (forall (vars (?v0 S3)) (:pat #4274 #4395) #1478)
-#4418 := (not #4413)
-#4524 := (or #4418 #4521)
-#4527 := (not #4524)
+#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)
 decl ?v0!13 :: S3
-#2231 := ?v0!13
-#2234 := (f14 f15 ?v0!13)
-#2849 := (* -1::Int #2234)
-#2232 := (f25 ?v0!13)
-#2850 := (+ #2232 #2849)
-#2851 := (<= #2850 0::Int)
-#2856 := (not #2851)
-#4530 := (or #2856 #4527)
-#4533 := (not #4530)
-#184 := (f6 f23 #13)
-#4396 := (pattern #184)
-#185 := (f10 #184)
-#1622 := (+ #185 #1479)
-#1623 := (+ #175 #1622)
-#1624 := (= #1623 0::Int)
-#1448 := (* -1::Int #185)
-#1455 := (+ #1454 #1448)
-#1456 := (+ #102 #1455)
-#1457 := (<= #1456 0::Int)
-#1449 := (+ f9 #1448)
-#1450 := (<= #1449 0::Int)
-#3418 := (or #1450 #1457 #1624)
-#4405 := (forall (vars (?v0 S3)) (:pat #4396 #4274 #4395) #3418)
-#4410 := (not #4405)
-#3398 := (or #1450 #1457)
-#3399 := (not #3398)
-#3402 := (or #794 #3399)
-#4397 := (forall (vars (?v0 S3)) (:pat #4274 #4395 #4396) #3402)
-#4402 := (not #4397)
+#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)
 decl ?v0!12 :: S3
-#2207 := ?v0!12
-#2213 := (f3 f16 ?v0!12)
-#2214 := (= f1 #2213)
-#2208 := (f14 f15 ?v0!12)
-#2209 := (* -1::Int #2208)
-#2210 := (+ f9 #2209)
-#2211 := (<= #2210 0::Int)
-#1654 := (+ f9 #1454)
-#1655 := (<= #1654 0::Int)
-#106 := (f3 f16 #13)
-#4316 := (pattern #106)
-#1637 := (+ #102 #1454)
-#1636 := (>= #1637 0::Int)
-#534 := (= f1 #106)
-#1643 := (or #534 #1636)
-#4387 := (forall (vars (?v0 S3)) (:pat #4316 #4274) #1643)
-#4392 := (not #4387)
-decl f4 :: (-> S4 S2 S3 S1 S2)
-decl f5 :: S4
-#8 := f5
-#774 := (f4 f5 f16 f23 f1)
-#777 := (= f24 #774)
-#996 := (not #777)
-#172 := (f3 f16 f23)
-#755 := (= f1 #172)
-#4536 := (or #755 #996 #4392 #1655 #2211 #2214 #4402 #4410 #4533)
-#4539 := (not #4536)
+#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)
+#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)
+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)
 decl ?v0!11 :: S3
-#2141 := ?v0!11
+#2140 := ?v0!11
 decl ?v1!10 :: S3
-#2140 := ?v1!10
-#2146 := (f6 ?v1!10 ?v0!11)
-#2147 := (f10 #2146)
-#2154 := (* -1::Int #2147)
-decl f20 :: S6
-#138 := f20
-#2144 := (f14 f20 ?v1!10)
-#2150 := (* -1::Int #2144)
-#2806 := (+ #2150 #2154)
-#2142 := (f14 f20 ?v0!11)
-#2807 := (+ #2142 #2806)
-#2808 := (<= #2807 0::Int)
-#2155 := (+ f9 #2154)
-#2156 := (<= #2155 0::Int)
-#2151 := (+ f9 #2150)
-#2152 := (<= #2151 0::Int)
-#3362 := (or #2152 #2156 #2808)
-#3367 := (not #3362)
-#146 := (f14 f20 #24)
-#1356 := (* -1::Int #146)
-#143 := (f14 f20 #13)
-#1357 := (+ #143 #1356)
-#1363 := (+ #83 #1357)
-#1386 := (>= #1363 0::Int)
-#1343 := (* -1::Int #143)
-#1344 := (+ f9 #1343)
-#1345 := (<= #1344 0::Int)
-#3330 := (or #1236 #1345 #1386)
-#4349 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3330)
-#4354 := (not #4349)
-#158 := (f14 f20 f11)
-#159 := (= #158 0::Int)
-#4357 := (or #159 #4354)
-#4360 := (not #4357)
-#4363 := (or #4360 #3367)
-#4366 := (not #4363)
-#4325 := (pattern #143)
+#2139 := ?v1!10
+#2145 := (f5 ?v1!10 ?v0!11)
+#2146 := (f9 #2145)
+#2153 := (* -1::Int #2146)
+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)
+#145 := (f13 f19 #23)
+#1355 := (* -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)
+#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)
 decl ?v1!9 :: (-> S3 S3)
-#2117 := (?v1!9 #13)
-#2120 := (f6 #2117 #13)
-#2121 := (f10 #2120)
-#2776 := (* -1::Int #2121)
-#2118 := (f14 f20 #2117)
-#2759 := (* -1::Int #2118)
-#2777 := (+ #2759 #2776)
-#2778 := (+ #143 #2777)
-#2779 := (= #2778 0::Int)
-#3300 := (not #2779)
-#2760 := (+ #143 #2759)
-#2761 := (<= #2760 0::Int)
-#3301 := (or #2761 #3300)
-#3302 := (not #3301)
-#58 := (= #13 f11)
-#3308 := (or #58 #1345 #3302)
-#4341 := (forall (vars (?v0 S3)) (:pat #4325) #3308)
-#4346 := (not #4341)
-#4369 := (or #4346 #4366)
-#4372 := (not #4369)
+#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)
+#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)
 decl ?v0!8 :: S3
-#2077 := ?v0!8
-#2081 := (f6 #13 ?v0!8)
-#4326 := (pattern #2081)
-#2082 := (f10 #2081)
-#2078 := (f14 f20 ?v0!8)
-#2079 := (* -1::Int #2078)
-#2729 := (+ #2079 #2082)
-#2730 := (+ #143 #2729)
-#2733 := (= #2730 0::Int)
-#3264 := (not #2733)
-#2080 := (+ #143 #2079)
-#2085 := (>= #2080 0::Int)
-#3265 := (or #2085 #3264)
-#4327 := (forall (vars (?v1 S3)) (:pat #4325 #4326) #3265)
-#4332 := (not #4327)
-#2705 := (= f11 ?v0!8)
-#2089 := (+ f9 #2079)
-#2090 := (<= #2089 0::Int)
-#4335 := (or #2090 #2705 #4332)
-#4338 := (not #4335)
-#4375 := (or #4338 #4372)
-#4378 := (not #4375)
-#1298 := (* -1::Int #102)
-#1299 := (+ f9 #1298)
-#1300 := (<= #1299 0::Int)
-#3250 := (or #534 #1300)
-#4317 := (forall (vars (?v0 S3)) (:pat #4316 #4274) #3250)
-#4322 := (not #4317)
-#625 := (= f15 f20)
-#716 := (not #625)
-decl f17 :: S2
-#133 := f17
-#622 := (= f16 f17)
-#734 := (not #622)
-decl f22 :: S6
-#141 := f22
-decl f21 :: S6
+#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)
+decl f16 :: S2
+#132 := f16
+#621 := (= f15 f16)
+#733 := (not #621)
+decl f21 :: S5
 #140 := f21
-#142 := (= f21 f22)
-#707 := (not #142)
-decl f19 :: S3
-#136 := f19
+decl f20 :: S5
+#139 := f20
+#141 := (= f20 f21)
+#706 := (not #141)
 decl f18 :: S3
 #135 := f18
-#137 := (= f18 f19)
-#725 := (not #137)
-#4381 := (or #725 #707 #734 #716 #4322 #4378)
-#4384 := (not #4381)
-#4542 := (or #4384 #4539)
-#4545 := (not #4542)
-#2040 := (?v1!7 #13)
-#2041 := (f14 f15 #2040)
-#2664 := (* -1::Int #2041)
-#2679 := (+ #102 #2664)
-#2680 := (<= #2679 0::Int)
-#2045 := (f6 #2040 #13)
-#2046 := (f10 #2045)
-#2665 := (* -1::Int #2046)
-#2666 := (+ #2664 #2665)
-#2667 := (+ #102 #2666)
-#2668 := (= #2667 0::Int)
-#3234 := (not #2668)
-#2049 := (f3 f16 #2040)
-#2050 := (= f1 #2049)
-#3233 := (not #2050)
-#3235 := (or #3233 #3234 #2680)
-#3236 := (not #3235)
-#3242 := (or #58 #1300 #3236)
-#4308 := (forall (vars (?v0 S3)) (:pat #4274) #3242)
-#4313 := (not #4308)
-decl f12 :: (-> S3 Int)
-#59 := (f12 #13)
-#4219 := (pattern #59)
+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)
+decl f11 :: (-> S3 Int)
+#58 := (f11 #12)
+#4218 := (pattern #58)
 decl ?v1!6 :: (-> S3 S3)
-#2012 := (?v1!6 #13)
-#2016 := (f12 #2012)
-#2623 := (* -1::Int #2016)
-#2013 := (f6 #2012 #13)
-#2014 := (f10 #2013)
-#2640 := (* -1::Int #2014)
-#2641 := (+ #2640 #2623)
-#2642 := (+ #59 #2641)
-#2643 := (= #2642 0::Int)
-#3206 := (not #2643)
-#2624 := (+ #59 #2623)
-#2625 := (<= #2624 0::Int)
-decl f13 :: (-> S3 S1)
-#2022 := (f13 #2012)
-#2023 := (= f1 #2022)
-#3205 := (not #2023)
-#3207 := (or #3205 #2625 #3206)
-#3208 := (not #3207)
-#1260 := (* -1::Int #59)
-#1261 := (+ f9 #1260)
-#1262 := (<= #1261 0::Int)
-#3214 := (or #58 #1262 #3208)
-#4300 := (forall (vars (?v0 S3)) (:pat #4219) #3214)
-#4305 := (not #4300)
-#109 := (f3 f16 #24)
-#4291 := (pattern #106 #109)
-#112 := (f14 f15 #24)
-#1312 := (* -1::Int #112)
-#1313 := (+ #102 #1312)
-#1316 := (>= #1313 0::Int)
-#540 := (= f1 #109)
-#3171 := (not #540)
-#3186 := (or #534 #3171 #1316)
-#4292 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4291) #3186)
-#4297 := (not #4292)
-#1314 := (+ #83 #1313)
-#1709 := (>= #1314 0::Int)
-#537 := (not #534)
-#3163 := (or #537 #1236 #1709)
-#4283 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3163)
-#4288 := (not #4283)
-#4280 := (not #4275)
-#101 := (= #100 0::Int)
-#1748 := (not #101)
-#4548 := (or #1748 #4280 #4288 #4297 #4305 #4313 #4545)
-#4551 := (not #4548)
+#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)
+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)
+#108 := (f3 f15 #23)
+#4290 := (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)
+#4287 := (not #4282)
+#4279 := (not #4274)
+#100 := (= #99 0::Int)
+#1747 := (not #100)
+#4547 := (or #1747 #4279 #4287 #4296 #4304 #4312 #4544)
+#4550 := (not #4547)
 decl ?v0!5 :: S3
-#1968 := ?v0!5
-#1969 := (f6 #13 ?v0!5)
-#4259 := (pattern #1969)
-#67 := (f13 #13)
-#4226 := (pattern #67)
-#1971 := (f12 ?v0!5)
-#1972 := (* -1::Int #1971)
-#1970 := (f10 #1969)
-#2591 := (+ #1970 #1972)
-#2592 := (+ #59 #2591)
-#2595 := (= #2592 0::Int)
-#3124 := (not #2595)
-#1976 := (+ #59 #1972)
-#1977 := (>= #1976 0::Int)
-#455 := (= f1 #67)
-#458 := (not #455)
-#3125 := (or #458 #1977 #3124)
-#4260 := (forall (vars (?v1 S3)) (:pat #4226 #4219 #4259) #3125)
-#4265 := (not #4260)
-#2567 := (= f11 ?v0!5)
-#1981 := (+ f9 #1972)
-#1982 := (<= #1981 0::Int)
-#4268 := (or #1982 #2567 #4265)
-#4271 := (not #4268)
-#4554 := (or #4271 #4551)
-#4557 := (not #4554)
-#78 := (f12 #24)
-#1212 := (* -1::Int #78)
-#1233 := (+ #1212 #83)
-#1234 := (+ #59 #1233)
-#1231 := (>= #1234 0::Int)
-#3116 := (or #458 #1231 #1236)
-#4251 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3116)
-#4256 := (not #4251)
-#4560 := (or #4256 #4557)
-#4563 := (not #4560)
+#1967 := ?v0!5
+#1968 := (f5 #12 ?v0!5)
+#4258 := (pattern #1968)
+#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)
+#4255 := (not #4250)
+#4559 := (or #4255 #4556)
+#4562 := (not #4559)
 decl ?v1!3 :: S3
-#1937 := ?v1!3
-#1952 := (f12 ?v1!3)
+#1936 := ?v1!3
+#1951 := (f11 ?v1!3)
 decl ?v0!4 :: S3
-#1938 := ?v0!4
-#1949 := (f12 ?v0!4)
-#1950 := (* -1::Int #1949)
-#2548 := (+ #1950 #1952)
-#1939 := (f6 ?v1!3 ?v0!4)
-#1940 := (f10 #1939)
-#2549 := (+ #1940 #2548)
-#2552 := (>= #2549 0::Int)
-#1945 := (f13 ?v1!3)
-#1946 := (= f1 #1945)
-#3079 := (not #1946)
-#1941 := (* -1::Int #1940)
-#1942 := (+ f9 #1941)
-#1943 := (<= #1942 0::Int)
-#3094 := (or #1943 #3079 #2552)
-#5223 := [hypothesis]: #1946
-#4227 := (forall (vars (?v0 S3)) (:pat #4226) #458)
-#461 := (forall (vars (?v0 S3)) #458)
-#4230 := (iff #461 #4227)
-#4228 := (iff #458 #458)
-#4229 := [refl]: #4228
-#4231 := [quant-intro #4229]: #4230
-#1859 := (~ #461 #461)
-#1889 := (~ #458 #458)
-#1890 := [refl]: #1889
-#1860 := [nnf-pos #1890]: #1859
-#60 := (= #59 0::Int)
-#63 := (not #58)
-#1806 := (or #63 #60)
-#1809 := (forall (vars (?v0 S3)) #1806)
-#1812 := (not #1809)
-#1740 := (forall (vars (?v0 S3)) #1737)
-#1743 := (not #1740)
-#543 := (and #537 #540)
-#549 := (not #543)
-#1726 := (or #549 #1316)
-#1731 := (forall (vars (?v0 S3) (?v1 S3)) #1726)
-#1734 := (not #1731)
-#1237 := (not #1236)
-#1701 := (and #534 #1237)
-#1706 := (not #1701)
-#1712 := (or #1706 #1709)
-#1715 := (forall (vars (?v0 S3) (?v1 S3)) #1712)
-#1718 := (not #1715)
-#1648 := (forall (vars (?v0 S3)) #1643)
-#1651 := (not #1648)
-#1458 := (not #1457)
-#1451 := (not #1450)
-#1461 := (and #1451 #1458)
-#1619 := (not #1461)
-#1627 := (or #1619 #1624)
-#1630 := (forall (vars (?v0 S3)) #1627)
-#1633 := (not #1630)
-#1557 := (= #1535 0::Int)
-#1560 := (not #1503)
-#1569 := (and #808 #1560 #1557)
-#1574 := (exists (vars (?v1 S3)) #1569)
-#1546 := (+ f9 #1479)
-#1547 := (<= #1546 0::Int)
-#1548 := (not #1547)
-#1551 := (and #63 #1548)
-#1554 := (not #1551)
-#1577 := (or #1554 #1574)
-#1580 := (forall (vars (?v0 S3)) #1577)
-#1525 := (and #808 #1237)
-#1530 := (not #1525)
-#1537 := (or #1530 #1533)
-#1540 := (forall (vars (?v0 S3) (?v1 S3)) #1537)
-#1543 := (not #1540)
-#1583 := (or #1543 #1580)
-#1586 := (and #1540 #1583)
-#831 := (and #814 #828)
-#837 := (not #831)
-#1511 := (or #837 #1503)
-#1516 := (forall (vars (?v0 S3) (?v1 S3)) #1511)
-#1519 := (not #1516)
-#1589 := (or #1519 #1586)
-#1592 := (and #1516 #1589)
-#1497 := (forall (vars (?v0 S3)) #1494)
-#1500 := (not #1497)
-#1595 := (or #1500 #1592)
-#1598 := (and #1497 #1595)
-#1601 := (or #1491 #1598)
-#1604 := (and #205 #1601)
-#820 := (forall (vars (?v0 S3)) #815)
-#954 := (not #820)
-#1607 := (or #954 #1604)
-#1610 := (and #820 #1607)
-#1483 := (forall (vars (?v0 S3)) #1478)
-#1486 := (not #1483)
-#1613 := (or #1486 #1610)
-#1616 := (and #1483 #1613)
-#1467 := (or #794 #1461)
-#1472 := (forall (vars (?v0 S3)) #1467)
-#1475 := (not #1472)
-#1301 := (not #1300)
-#1420 := (and #537 #1301)
-#1425 := (exists (vars (?v0 S3)) #1420)
-#1666 := (not #1425)
-#1690 := (or #755 #996 #1666 #1475 #1616 #1633 #1651 #1655)
-#1346 := (not #1345)
-#1380 := (and #1237 #1346)
-#1383 := (not #1380)
-#1389 := (or #1383 #1386)
-#1392 := (forall (vars (?v0 S3) (?v1 S3)) #1389)
-#1395 := (not #1392)
-#1403 := (or #159 #1395)
-#1408 := (and #1392 #1403)
-#1361 := (= #1363 0::Int)
-#1355 := (>= #1357 0::Int)
-#1358 := (not #1355)
-#1365 := (and #1358 #1361)
-#1368 := (exists (vars (?v1 S3)) #1365)
-#1349 := (and #63 #1346)
-#1352 := (not #1349)
-#1371 := (or #1352 #1368)
-#1374 := (forall (vars (?v0 S3)) #1371)
-#1377 := (not #1374)
-#1411 := (or #1377 #1408)
-#1414 := (and #1374 #1411)
-#1443 := (or #725 #707 #734 #716 #1414 #1425)
-#1695 := (and #1443 #1690)
-#1317 := (not #1316)
-#1310 := (= #1314 0::Int)
-#1326 := (and #534 #1310 #1317)
-#1331 := (exists (vars (?v1 S3)) #1326)
-#1304 := (and #63 #1301)
-#1307 := (not #1304)
-#1334 := (or #1307 #1331)
-#1337 := (forall (vars (?v0 S3)) #1334)
-#1340 := (not #1337)
-#1272 := (= #1234 0::Int)
-#1213 := (+ #59 #1212)
-#1211 := (>= #1213 0::Int)
-#1275 := (not #1211)
-#1284 := (and #455 #1275 #1272)
-#1289 := (exists (vars (?v1 S3)) #1284)
-#1263 := (not #1262)
-#1266 := (and #63 #1263)
-#1269 := (not #1266)
-#1292 := (or #1269 #1289)
-#1295 := (forall (vars (?v0 S3)) #1292)
-#1751 := (not #1295)
-#1772 := (or #1748 #1751 #1340 #1695 #1718 #1734 #1743)
-#1777 := (and #1295 #1772)
-#1243 := (and #455 #1237)
-#1248 := (not #1243)
-#1251 := (or #1231 #1248)
-#1254 := (forall (vars (?v0 S3) (?v1 S3)) #1251)
-#1257 := (not #1254)
-#1780 := (or #1257 #1777)
-#1783 := (and #1254 #1780)
-#75 := (f13 #24)
-#467 := (= f1 #75)
-#470 := (and #458 #467)
-#476 := (not #470)
-#1218 := (or #476 #1211)
-#1223 := (forall (vars (?v0 S3) (?v1 S3)) #1218)
-#1226 := (not #1223)
-#1786 := (or #1226 #1783)
-#1789 := (and #1223 #1786)
-#1202 := (>= #59 0::Int)
-#1203 := (forall (vars (?v0 S3)) #1202)
-#1206 := (not #1203)
-#1792 := (or #1206 #1789)
-#1795 := (and #1203 #1792)
-#71 := (f12 f11)
-#72 := (= #71 0::Int)
-#1197 := (not #72)
-#1798 := (or #1197 #1795)
-#1801 := (and #72 #1798)
-#1161 := (not #461)
-#441 := (= f9 #59)
-#447 := (or #58 #441)
-#452 := (forall (vars (?v0 S3)) #447)
-#1170 := (not #452)
-#1824 := (or #1170 #1161 #1801 #1812)
-#1829 := (not #1824)
+#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)
+#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
+#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)
+#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)
+#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)
+#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)
 #1 := true
-#217 := (+ #190 #83)
-#224 := (= #212 #217)
-#201 := (= #200 f1)
-#225 := (and #201 #224)
-#223 := (< #190 #212)
-#226 := (and #223 #225)
-#227 := (exists (vars (?v1 S3)) #226)
-#221 := (< #190 f9)
-#222 := (and #63 #221)
-#228 := (implies #222 #227)
-#229 := (forall (vars (?v0 S3)) #228)
-#230 := (and #229 true)
-#218 := (<= #212 #217)
-#84 := (< #83 f9)
-#216 := (and #201 #84)
-#219 := (implies #216 #218)
-#220 := (forall (vars (?v0 S3) (?v1 S3)) #219)
-#231 := (implies #220 #230)
-#232 := (and #220 #231)
-#213 := (<= #212 #190)
-#210 := (= #209 f1)
-#208 := (not #201)
-#211 := (and #208 #210)
-#214 := (implies #211 #213)
-#215 := (forall (vars (?v0 S3) (?v1 S3)) #214)
-#233 := (implies #215 #232)
-#234 := (and #215 #233)
-#206 := (<= 0::Int #190)
-#207 := (forall (vars (?v0 S3)) #206)
-#235 := (implies #207 #234)
-#236 := (and #207 #235)
-#237 := (implies #205 #236)
-#238 := (and #205 #237)
-#195 := (= #190 #102)
-#202 := (implies #201 #195)
-#203 := (forall (vars (?v0 S3)) #202)
-#239 := (implies #203 #238)
-#240 := (and #203 #239)
-#198 := (<= #190 #102)
-#199 := (forall (vars (?v0 S3)) #198)
-#241 := (implies #199 #240)
-#242 := (and #199 #241)
-#187 := (+ #175 #185)
-#188 := (< #187 #102)
-#186 := (< #185 f9)
-#189 := (and #186 #188)
-#194 := (not #189)
-#196 := (implies #194 #195)
-#197 := (forall (vars (?v0 S3)) #196)
-#243 := (implies #197 #242)
-#191 := (= #190 #187)
-#192 := (implies #189 #191)
-#193 := (forall (vars (?v0 S3)) #192)
-#244 := (implies #193 #243)
+#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)
+#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
-#181 := (ite true f1 f2)
-#182 := (f4 f5 f16 f23 #181)
-#183 := (= f24 #182)
-#245 := (implies #183 #244)
-#177 := (<= #175 #102)
-#107 := (= #106 f1)
-#108 := (not #107)
-#178 := (implies #108 #177)
-#179 := (forall (vars (?v0 S3)) #178)
-#246 := (implies #179 #245)
-#176 := (< #175 f9)
-#247 := (implies #176 #246)
-#173 := (= #172 f1)
-#174 := (not #173)
-#248 := (implies #174 #247)
-#121 := (< #102 f9)
-#130 := (and #108 #121)
-#131 := (exists (vars (?v0 S3)) #130)
-#249 := (implies #131 #248)
-#250 := (implies true #249)
-#160 := (and #159 true)
-#148 := (+ #143 #83)
-#155 := (<= #146 #148)
-#144 := (< #143 f9)
-#154 := (and #144 #84)
-#156 := (implies #154 #155)
-#157 := (forall (vars (?v0 S3) (?v1 S3)) #156)
-#161 := (implies #157 #160)
-#162 := (and #157 #161)
-#149 := (= #146 #148)
-#147 := (< #143 #146)
-#150 := (and #147 #149)
-#151 := (exists (vars (?v1 S3)) #150)
-#145 := (and #63 #144)
-#152 := (implies #145 #151)
-#153 := (forall (vars (?v0 S3)) #152)
-#163 := (implies #153 #162)
-#164 := (and #153 #163)
-#165 := (implies #142 #164)
-#139 := (= f20 f15)
-#166 := (implies #139 #165)
-#167 := (implies #137 #166)
-#134 := (= f17 f16)
-#168 := (implies #134 #167)
-#132 := (not #131)
-#169 := (implies #132 #168)
-#170 := (implies true #169)
-#251 := (and #170 #250)
-#117 := (+ #102 #83)
-#124 := (= #112 #117)
-#125 := (and #107 #124)
-#123 := (< #102 #112)
-#126 := (and #123 #125)
-#127 := (exists (vars (?v1 S3)) #126)
-#122 := (and #63 #121)
-#128 := (implies #122 #127)
-#129 := (forall (vars (?v0 S3)) #128)
-#252 := (implies #129 #251)
-#118 := (<= #112 #117)
-#116 := (and #107 #84)
-#119 := (implies #116 #118)
-#120 := (forall (vars (?v0 S3) (?v1 S3)) #119)
-#253 := (implies #120 #252)
-#113 := (<= #112 #102)
-#110 := (= #109 f1)
-#111 := (and #108 #110)
-#114 := (implies #111 #113)
-#115 := (forall (vars (?v0 S3) (?v1 S3)) #114)
-#254 := (implies #115 #253)
-#103 := (<= 0::Int #102)
-#104 := (forall (vars (?v0 S3)) #103)
-#255 := (implies #104 #254)
-#256 := (implies #101 #255)
-#257 := (implies true #256)
-#86 := (+ #59 #83)
-#93 := (= #78 #86)
-#68 := (= #67 f1)
-#94 := (and #68 #93)
-#92 := (< #59 #78)
-#95 := (and #92 #94)
-#96 := (exists (vars (?v1 S3)) #95)
-#90 := (< #59 f9)
-#91 := (and #63 #90)
-#97 := (implies #91 #96)
-#98 := (forall (vars (?v0 S3)) #97)
-#258 := (implies #98 #257)
-#259 := (and #98 #258)
-#87 := (<= #78 #86)
-#85 := (and #68 #84)
-#88 := (implies #85 #87)
-#89 := (forall (vars (?v0 S3) (?v1 S3)) #88)
-#260 := (implies #89 #259)
-#261 := (and #89 #260)
-#79 := (<= #78 #59)
-#76 := (= #75 f1)
-#69 := (not #68)
-#77 := (and #69 #76)
-#80 := (implies #77 #79)
-#81 := (forall (vars (?v0 S3) (?v1 S3)) #80)
-#262 := (implies #81 #261)
-#263 := (and #81 #262)
-#73 := (<= 0::Int #59)
-#74 := (forall (vars (?v0 S3)) #73)
-#264 := (implies #74 #263)
-#265 := (and #74 #264)
-#266 := (implies #72 #265)
-#267 := (and #72 #266)
-#70 := (forall (vars (?v0 S3)) #69)
-#268 := (implies #70 #267)
-#64 := (= #59 f9)
-#65 := (implies #63 #64)
-#66 := (forall (vars (?v0 S3)) #65)
-#269 := (implies #66 #268)
-#61 := (implies #58 #60)
-#62 := (forall (vars (?v0 S3)) #61)
-#270 := (implies #62 #269)
-#271 := (implies true #270)
-#272 := (not #271)
-#1832 := (iff #272 #1829)
-#854 := (+ #83 #190)
-#872 := (= #212 #854)
-#875 := (and #808 #872)
-#878 := (and #223 #875)
-#881 := (exists (vars (?v1 S3)) #878)
-#887 := (not #222)
-#888 := (or #887 #881)
-#893 := (forall (vars (?v0 S3)) #888)
-#857 := (<= #212 #854)
-#849 := (and #84 #808)
-#863 := (not #849)
-#864 := (or #863 #857)
-#869 := (forall (vars (?v0 S3) (?v1 S3)) #864)
-#906 := (not #869)
-#907 := (or #906 #893)
-#912 := (and #869 #907)
-#838 := (or #213 #837)
-#843 := (forall (vars (?v0 S3) (?v1 S3)) #838)
-#918 := (not #843)
-#919 := (or #918 #912)
-#924 := (and #843 #919)
-#930 := (not #207)
-#931 := (or #930 #924)
-#936 := (and #207 #931)
-#823 := (= 0::Int #204)
-#942 := (not #823)
-#943 := (or #942 #936)
-#948 := (and #823 #943)
-#955 := (or #954 #948)
-#960 := (and #820 #955)
-#966 := (not #199)
-#967 := (or #966 #960)
-#972 := (and #199 #967)
-#800 := (or #189 #794)
-#805 := (forall (vars (?v0 S3)) #800)
-#978 := (not #805)
-#979 := (or #978 #972)
-#780 := (= #187 #190)
-#786 := (or #194 #780)
-#791 := (forall (vars (?v0 S3)) #786)
-#987 := (not #791)
-#988 := (or #987 #979)
-#997 := (or #996 #988)
-#764 := (or #177 #534)
-#769 := (forall (vars (?v0 S3)) #764)
-#1005 := (not #769)
-#1006 := (or #1005 #997)
-#1014 := (not #176)
-#1015 := (or #1014 #1006)
-#1023 := (or #755 #1015)
-#611 := (and #121 #537)
-#616 := (exists (vars (?v0 S3)) #611)
-#619 := (not #616)
-#1031 := (or #619 #1023)
-#670 := (= 0::Int #158)
-#628 := (+ #83 #143)
-#655 := (<= #146 #628)
-#652 := (and #84 #144)
-#661 := (not #652)
-#662 := (or #661 #655)
-#667 := (forall (vars (?v0 S3) (?v1 S3)) #662)
-#683 := (not #667)
-#684 := (or #683 #670)
-#689 := (and #667 #684)
-#631 := (= #146 #628)
-#634 := (and #147 #631)
-#637 := (exists (vars (?v1 S3)) #634)
-#643 := (not #145)
-#644 := (or #643 #637)
-#649 := (forall (vars (?v0 S3)) #644)
-#695 := (not #649)
-#696 := (or #695 #689)
-#701 := (and #649 #696)
-#708 := (or #707 #701)
-#717 := (or #716 #708)
-#726 := (or #725 #717)
-#735 := (or #734 #726)
-#743 := (or #616 #735)
-#1043 := (and #743 #1031)
-#566 := (+ #83 #102)
-#584 := (= #112 #566)
-#587 := (and #534 #584)
-#590 := (and #123 #587)
-#593 := (exists (vars (?v1 S3)) #590)
-#599 := (not #122)
-#600 := (or #599 #593)
-#605 := (forall (vars (?v0 S3)) #600)
-#1049 := (not #605)
-#1050 := (or #1049 #1043)
-#569 := (<= #112 #566)
-#561 := (and #84 #534)
-#575 := (not #561)
-#576 := (or #575 #569)
-#581 := (forall (vars (?v0 S3) (?v1 S3)) #576)
-#1058 := (not #581)
-#1059 := (or #1058 #1050)
-#550 := (or #113 #549)
-#555 := (forall (vars (?v0 S3) (?v1 S3)) #550)
-#1067 := (not #555)
-#1068 := (or #1067 #1059)
-#1076 := (not #104)
-#1077 := (or #1076 #1068)
-#531 := (= 0::Int #100)
-#1085 := (not #531)
-#1086 := (or #1085 #1077)
-#508 := (and #93 #455)
-#513 := (and #92 #508)
-#516 := (exists (vars (?v1 S3)) #513)
-#522 := (not #91)
-#523 := (or #522 #516)
-#528 := (forall (vars (?v0 S3)) #523)
-#1101 := (not #528)
-#1102 := (or #1101 #1086)
-#1107 := (and #528 #1102)
-#488 := (and #84 #455)
-#496 := (not #488)
-#497 := (or #87 #496)
-#502 := (forall (vars (?v0 S3) (?v1 S3)) #497)
-#1113 := (not #502)
-#1114 := (or #1113 #1107)
-#1119 := (and #502 #1114)
-#477 := (or #79 #476)
-#482 := (forall (vars (?v0 S3) (?v1 S3)) #477)
-#1125 := (not #482)
-#1126 := (or #1125 #1119)
-#1131 := (and #482 #1126)
-#1137 := (not #74)
-#1138 := (or #1137 #1131)
-#1143 := (and #74 #1138)
-#464 := (= 0::Int #71)
-#1149 := (not #464)
-#1150 := (or #1149 #1143)
-#1155 := (and #464 #1150)
-#1162 := (or #1161 #1155)
-#1171 := (or #1170 #1162)
-#427 := (= 0::Int #59)
-#433 := (or #63 #427)
-#438 := (forall (vars (?v0 S3)) #433)
-#1179 := (not #438)
-#1180 := (or #1179 #1171)
-#1192 := (not #1180)
-#1830 := (iff #1192 #1829)
-#1827 := (iff #1180 #1824)
-#1815 := (or #1161 #1801)
-#1818 := (or #1170 #1815)
-#1821 := (or #1812 #1818)
-#1825 := (iff #1821 #1824)
-#1826 := [rewrite]: #1825
-#1822 := (iff #1180 #1821)
-#1819 := (iff #1171 #1818)
-#1816 := (iff #1162 #1815)
-#1802 := (iff #1155 #1801)
-#1799 := (iff #1150 #1798)
-#1796 := (iff #1143 #1795)
-#1793 := (iff #1138 #1792)
-#1790 := (iff #1131 #1789)
-#1787 := (iff #1126 #1786)
-#1784 := (iff #1119 #1783)
-#1781 := (iff #1114 #1780)
-#1778 := (iff #1107 #1777)
-#1775 := (iff #1102 #1772)
-#1754 := (or #1340 #1695)
-#1757 := (or #1718 #1754)
-#1760 := (or #1734 #1757)
-#1763 := (or #1743 #1760)
-#1766 := (or #1748 #1763)
-#1769 := (or #1751 #1766)
-#1773 := (iff #1769 #1772)
-#1774 := [rewrite]: #1773
-#1770 := (iff #1102 #1769)
-#1767 := (iff #1086 #1766)
-#1764 := (iff #1077 #1763)
-#1761 := (iff #1068 #1760)
-#1758 := (iff #1059 #1757)
-#1755 := (iff #1050 #1754)
-#1696 := (iff #1043 #1695)
-#1693 := (iff #1031 #1690)
-#1669 := (or #1475 #1616)
-#1672 := (or #1633 #1669)
-#1675 := (or #996 #1672)
-#1678 := (or #1651 #1675)
-#1681 := (or #1655 #1678)
-#1684 := (or #755 #1681)
-#1687 := (or #1666 #1684)
-#1691 := (iff #1687 #1690)
-#1692 := [rewrite]: #1691
-#1688 := (iff #1031 #1687)
-#1685 := (iff #1023 #1684)
-#1682 := (iff #1015 #1681)
-#1679 := (iff #1006 #1678)
-#1676 := (iff #997 #1675)
-#1673 := (iff #988 #1672)
-#1670 := (iff #979 #1669)
-#1617 := (iff #972 #1616)
-#1614 := (iff #967 #1613)
-#1611 := (iff #960 #1610)
-#1608 := (iff #955 #1607)
-#1605 := (iff #948 #1604)
-#1602 := (iff #943 #1601)
-#1599 := (iff #936 #1598)
-#1596 := (iff #931 #1595)
-#1593 := (iff #924 #1592)
-#1590 := (iff #919 #1589)
-#1587 := (iff #912 #1586)
-#1584 := (iff #907 #1583)
-#1581 := (iff #893 #1580)
-#1578 := (iff #888 #1577)
-#1575 := (iff #881 #1574)
-#1572 := (iff #878 #1569)
-#1563 := (and #808 #1557)
-#1566 := (and #1560 #1563)
-#1570 := (iff #1566 #1569)
-#1571 := [rewrite]: #1570
-#1567 := (iff #878 #1566)
-#1564 := (iff #875 #1563)
-#1558 := (iff #872 #1557)
-#1559 := [rewrite]: #1558
-#1565 := [monotonicity #1559]: #1564
-#1561 := (iff #223 #1560)
-#1562 := [rewrite]: #1561
-#1568 := [monotonicity #1562 #1565]: #1567
-#1573 := [trans #1568 #1571]: #1572
-#1576 := [quant-intro #1573]: #1575
-#1555 := (iff #887 #1554)
-#1552 := (iff #222 #1551)
-#1549 := (iff #221 #1548)
-#1550 := [rewrite]: #1549
-#1553 := [monotonicity #1550]: #1552
-#1556 := [monotonicity #1553]: #1555
-#1579 := [monotonicity #1556 #1576]: #1578
-#1582 := [quant-intro #1579]: #1581
-#1544 := (iff #906 #1543)
-#1541 := (iff #869 #1540)
-#1538 := (iff #864 #1537)
-#1534 := (iff #857 #1533)
-#1536 := [rewrite]: #1534
-#1531 := (iff #863 #1530)
-#1528 := (iff #849 #1525)
-#1522 := (and #1237 #808)
-#1526 := (iff #1522 #1525)
-#1527 := [rewrite]: #1526
-#1523 := (iff #849 #1522)
-#1238 := (iff #84 #1237)
-#1239 := [rewrite]: #1238
-#1524 := [monotonicity #1239]: #1523
-#1529 := [trans #1524 #1527]: #1528
-#1532 := [monotonicity #1529]: #1531
-#1539 := [monotonicity #1532 #1536]: #1538
-#1542 := [quant-intro #1539]: #1541
-#1545 := [monotonicity #1542]: #1544
-#1585 := [monotonicity #1545 #1582]: #1584
-#1588 := [monotonicity #1542 #1585]: #1587
-#1520 := (iff #918 #1519)
-#1517 := (iff #843 #1516)
-#1514 := (iff #838 #1511)
-#1508 := (or #1503 #837)
-#1512 := (iff #1508 #1511)
-#1513 := [rewrite]: #1512
-#1509 := (iff #838 #1508)
-#1506 := (iff #213 #1503)
-#1507 := [rewrite]: #1506
-#1510 := [monotonicity #1507]: #1509
-#1515 := [trans #1510 #1513]: #1514
-#1518 := [quant-intro #1515]: #1517
-#1521 := [monotonicity #1518]: #1520
-#1591 := [monotonicity #1521 #1588]: #1590
-#1594 := [monotonicity #1518 #1591]: #1593
-#1501 := (iff #930 #1500)
-#1498 := (iff #207 #1497)
-#1495 := (iff #206 #1494)
-#1496 := [rewrite]: #1495
-#1499 := [quant-intro #1496]: #1498
-#1502 := [monotonicity #1499]: #1501
-#1597 := [monotonicity #1502 #1594]: #1596
-#1600 := [monotonicity #1499 #1597]: #1599
-#1492 := (iff #942 #1491)
-#1489 := (iff #823 #205)
-#1490 := [rewrite]: #1489
-#1493 := [monotonicity #1490]: #1492
-#1603 := [monotonicity #1493 #1600]: #1602
-#1606 := [monotonicity #1490 #1603]: #1605
-#1609 := [monotonicity #1606]: #1608
-#1612 := [monotonicity #1609]: #1611
-#1487 := (iff #966 #1486)
-#1484 := (iff #199 #1483)
-#1481 := (iff #198 #1478)
-#1482 := [rewrite]: #1481
-#1485 := [quant-intro #1482]: #1484
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-#871 := [quant-intro #868]: #870
-#905 := [monotonicity #871 #902]: #904
-#911 := [trans #905 #909]: #910
-#914 := [monotonicity #871 #911]: #913
-#844 := (iff #215 #843)
-#841 := (iff #214 #838)
-#834 := (implies #831 #213)
-#839 := (iff #834 #838)
-#840 := [rewrite]: #839
-#835 := (iff #214 #834)
-#832 := (iff #211 #831)
-#829 := (iff #210 #828)
-#830 := [rewrite]: #829
-#826 := (iff #208 #814)
-#827 := [monotonicity #810]: #826
-#833 := [monotonicity #827 #830]: #832
-#836 := [monotonicity #833]: #835
-#842 := [trans #836 #840]: #841
-#845 := [quant-intro #842]: #844
-#917 := [monotonicity #845 #914]: #916
-#923 := [trans #917 #921]: #922
-#926 := [monotonicity #845 #923]: #925
-#929 := [monotonicity #926]: #928
-#935 := [trans #929 #933]: #934
-#938 := [monotonicity #935]: #937
-#824 := (iff #205 #823)
-#825 := [rewrite]: #824
-#941 := [monotonicity #825 #938]: #940
-#947 := [trans #941 #945]: #946
-#950 := [monotonicity #825 #947]: #949
-#821 := (iff #203 #820)
-#818 := (iff #202 #815)
-#811 := (implies #808 #794)
-#816 := (iff #811 #815)
-#817 := [rewrite]: #816
-#812 := (iff #202 #811)
-#795 := (iff #195 #794)
-#796 := [rewrite]: #795
-#813 := [monotonicity #810 #796]: #812
-#819 := [trans #813 #817]: #818
-#822 := [quant-intro #819]: #821
-#953 := [monotonicity #822 #950]: #952
-#959 := [trans #953 #957]: #958
-#962 := [monotonicity #822 #959]: #961
-#965 := [monotonicity #962]: #964
-#971 := [trans #965 #969]: #970
-#974 := [monotonicity #971]: #973
-#806 := (iff #197 #805)
-#803 := (iff #196 #800)
-#797 := (implies #194 #794)
-#801 := (iff #797 #800)
-#802 := [rewrite]: #801
-#798 := (iff #196 #797)
-#799 := [monotonicity #796]: #798
-#804 := [trans #799 #802]: #803
-#807 := [quant-intro #804]: #806
-#977 := [monotonicity #807 #974]: #976
-#983 := [trans #977 #981]: #982
-#792 := (iff #193 #791)
-#789 := (iff #192 #786)
-#783 := (implies #189 #780)
-#787 := (iff #783 #786)
-#788 := [rewrite]: #787
-#784 := (iff #192 #783)
-#781 := (iff #191 #780)
-#782 := [rewrite]: #781
-#785 := [monotonicity #782]: #784
-#790 := [trans #785 #788]: #789
-#793 := [quant-intro #790]: #792
-#986 := [monotonicity #793 #983]: #985
-#992 := [trans #986 #990]: #991
-#778 := (iff #183 #777)
-#775 := (= #182 #774)
-#772 := (= #181 f1)
-#773 := [rewrite]: #772
-#776 := [monotonicity #773]: #775
-#779 := [monotonicity #776]: #778
-#995 := [monotonicity #779 #992]: #994
-#1001 := [trans #995 #999]: #1000
-#770 := (iff #179 #769)
-#767 := (iff #178 #764)
-#761 := (implies #537 #177)
-#765 := (iff #761 #764)
-#766 := [rewrite]: #765
-#762 := (iff #178 #761)
-#538 := (iff #108 #537)
-#535 := (iff #107 #534)
-#536 := [rewrite]: #535
-#539 := [monotonicity #536]: #538
-#763 := [monotonicity #539]: #762
-#768 := [trans #763 #766]: #767
-#771 := [quant-intro #768]: #770
-#1004 := [monotonicity #771 #1001]: #1003
-#1010 := [trans #1004 #1008]: #1009
-#1013 := [monotonicity #1010]: #1012
-#1019 := [trans #1013 #1017]: #1018
-#759 := (iff #174 #758)
-#756 := (iff #173 #755)
-#757 := [rewrite]: #756
-#760 := [monotonicity #757]: #759
-#1022 := [monotonicity #760 #1019]: #1021
-#1027 := [trans #1022 #1025]: #1026
-#617 := (iff #131 #616)
-#614 := (iff #130 #611)
-#608 := (and #537 #121)
-#612 := (iff #608 #611)
-#613 := [rewrite]: #612
-#609 := (iff #130 #608)
-#610 := [monotonicity #539]: #609
-#615 := [trans #610 #613]: #614
-#618 := [quant-intro #615]: #617
-#1030 := [monotonicity #618 #1027]: #1029
-#1035 := [trans #1030 #1033]: #1034
-#1038 := [monotonicity #1035]: #1037
-#1042 := [trans #1038 #1040]: #1041
-#753 := (iff #170 #743)
-#748 := (implies true #743)
-#751 := (iff #748 #743)
-#752 := [rewrite]: #751
-#749 := (iff #170 #748)
-#746 := (iff #169 #743)
-#740 := (implies #619 #735)
-#744 := (iff #740 #743)
-#745 := [rewrite]: #744
-#741 := (iff #169 #740)
-#738 := (iff #168 #735)
-#731 := (implies #622 #726)
-#736 := (iff #731 #735)
-#737 := [rewrite]: #736
-#732 := (iff #168 #731)
-#729 := (iff #167 #726)
-#722 := (implies #137 #717)
-#727 := (iff #722 #726)
-#728 := [rewrite]: #727
-#723 := (iff #167 #722)
-#720 := (iff #166 #717)
-#713 := (implies #625 #708)
-#718 := (iff #713 #717)
-#719 := [rewrite]: #718
-#714 := (iff #166 #713)
-#711 := (iff #165 #708)
-#704 := (implies #142 #701)
-#709 := (iff #704 #708)
-#710 := [rewrite]: #709
-#705 := (iff #165 #704)
-#702 := (iff #164 #701)
-#699 := (iff #163 #696)
-#692 := (implies #649 #689)
-#697 := (iff #692 #696)
-#698 := [rewrite]: #697
-#693 := (iff #163 #692)
-#690 := (iff #162 #689)
-#687 := (iff #161 #684)
-#680 := (implies #667 #670)
-#685 := (iff #680 #684)
-#686 := [rewrite]: #685
-#681 := (iff #161 #680)
-#678 := (iff #160 #670)
-#673 := (and #670 true)
-#676 := (iff #673 #670)
-#677 := [rewrite]: #676
-#674 := (iff #160 #673)
-#671 := (iff #159 #670)
-#672 := [rewrite]: #671
-#675 := [monotonicity #672]: #674
-#679 := [trans #675 #677]: #678
-#668 := (iff #157 #667)
-#665 := (iff #156 #662)
-#658 := (implies #652 #655)
-#663 := (iff #658 #662)
-#664 := [rewrite]: #663
-#659 := (iff #156 #658)
-#656 := (iff #155 #655)
-#629 := (= #148 #628)
-#630 := [rewrite]: #629
-#657 := [monotonicity #630]: #656
-#653 := (iff #154 #652)
-#654 := [rewrite]: #653
-#660 := [monotonicity #654 #657]: #659
-#666 := [trans #660 #664]: #665
-#669 := [quant-intro #666]: #668
-#682 := [monotonicity #669 #679]: #681
-#688 := [trans #682 #686]: #687
-#691 := [monotonicity #669 #688]: #690
-#650 := (iff #153 #649)
-#647 := (iff #152 #644)
-#640 := (implies #145 #637)
-#645 := (iff #640 #644)
-#646 := [rewrite]: #645
-#641 := (iff #152 #640)
-#638 := (iff #151 #637)
-#635 := (iff #150 #634)
-#632 := (iff #149 #631)
-#633 := [monotonicity #630]: #632
-#636 := [monotonicity #633]: #635
-#639 := [quant-intro #636]: #638
-#642 := [monotonicity #639]: #641
-#648 := [trans #642 #646]: #647
-#651 := [quant-intro #648]: #650
-#694 := [monotonicity #651 #691]: #693
-#700 := [trans #694 #698]: #699
-#703 := [monotonicity #651 #700]: #702
-#706 := [monotonicity #703]: #705
-#712 := [trans #706 #710]: #711
-#626 := (iff #139 #625)
-#627 := [rewrite]: #626
-#715 := [monotonicity #627 #712]: #714
-#721 := [trans #715 #719]: #720
-#724 := [monotonicity #721]: #723
-#730 := [trans #724 #728]: #729
-#623 := (iff #134 #622)
-#624 := [rewrite]: #623
-#733 := [monotonicity #624 #730]: #732
-#739 := [trans #733 #737]: #738
-#620 := (iff #132 #619)
-#621 := [monotonicity #618]: #620
-#742 := [monotonicity #621 #739]: #741
-#747 := [trans #742 #745]: #746
-#750 := [monotonicity #747]: #749
-#754 := [trans #750 #752]: #753
-#1045 := [monotonicity #754 #1042]: #1044
-#606 := (iff #129 #605)
-#603 := (iff #128 #600)
-#596 := (implies #122 #593)
-#601 := (iff #596 #600)
-#602 := [rewrite]: #601
-#597 := (iff #128 #596)
-#594 := (iff #127 #593)
-#591 := (iff #126 #590)
-#588 := (iff #125 #587)
-#585 := (iff #124 #584)
-#567 := (= #117 #566)
-#568 := [rewrite]: #567
-#586 := [monotonicity #568]: #585
-#589 := [monotonicity #536 #586]: #588
-#592 := [monotonicity #589]: #591
-#595 := [quant-intro #592]: #594
-#598 := [monotonicity #595]: #597
-#604 := [trans #598 #602]: #603
-#607 := [quant-intro #604]: #606
-#1048 := [monotonicity #607 #1045]: #1047
-#1054 := [trans #1048 #1052]: #1053
-#582 := (iff #120 #581)
-#579 := (iff #119 #576)
-#572 := (implies #561 #569)
-#577 := (iff #572 #576)
-#578 := [rewrite]: #577
-#573 := (iff #119 #572)
-#570 := (iff #118 #569)
-#571 := [monotonicity #568]: #570
-#564 := (iff #116 #561)
-#558 := (and #534 #84)
-#562 := (iff #558 #561)
-#563 := [rewrite]: #562
-#559 := (iff #116 #558)
-#560 := [monotonicity #536]: #559
-#565 := [trans #560 #563]: #564
-#574 := [monotonicity #565 #571]: #573
-#580 := [trans #574 #578]: #579
-#583 := [quant-intro #580]: #582
-#1057 := [monotonicity #583 #1054]: #1056
-#1063 := [trans #1057 #1061]: #1062
-#556 := (iff #115 #555)
-#553 := (iff #114 #550)
-#546 := (implies #543 #113)
-#551 := (iff #546 #550)
-#552 := [rewrite]: #551
-#547 := (iff #114 #546)
-#544 := (iff #111 #543)
-#541 := (iff #110 #540)
-#542 := [rewrite]: #541
-#545 := [monotonicity #539 #542]: #544
-#548 := [monotonicity #545]: #547
-#554 := [trans #548 #552]: #553
-#557 := [quant-intro #554]: #556
-#1066 := [monotonicity #557 #1063]: #1065
-#1072 := [trans #1066 #1070]: #1071
-#1075 := [monotonicity #1072]: #1074
-#1081 := [trans #1075 #1079]: #1080
-#532 := (iff #101 #531)
-#533 := [rewrite]: #532
-#1084 := [monotonicity #533 #1081]: #1083
-#1090 := [trans #1084 #1088]: #1089
-#1093 := [monotonicity #1090]: #1092
-#1097 := [trans #1093 #1095]: #1096
-#529 := (iff #98 #528)
-#526 := (iff #97 #523)
-#519 := (implies #91 #516)
-#524 := (iff #519 #523)
-#525 := [rewrite]: #524
-#520 := (iff #97 #519)
-#517 := (iff #96 #516)
-#514 := (iff #95 #513)
-#511 := (iff #94 #508)
-#505 := (and #455 #93)
-#509 := (iff #505 #508)
-#510 := [rewrite]: #509
-#506 := (iff #94 #505)
-#456 := (iff #68 #455)
-#457 := [rewrite]: #456
-#507 := [monotonicity #457]: #506
-#512 := [trans #507 #510]: #511
-#515 := [monotonicity #512]: #514
-#518 := [quant-intro #515]: #517
-#521 := [monotonicity #518]: #520
-#527 := [trans #521 #525]: #526
-#530 := [quant-intro #527]: #529
-#1100 := [monotonicity #530 #1097]: #1099
-#1106 := [trans #1100 #1104]: #1105
-#1109 := [monotonicity #530 #1106]: #1108
-#503 := (iff #89 #502)
-#500 := (iff #88 #497)
-#493 := (implies #488 #87)
-#498 := (iff #493 #497)
-#499 := [rewrite]: #498
-#494 := (iff #88 #493)
-#491 := (iff #85 #488)
-#485 := (and #455 #84)
-#489 := (iff #485 #488)
-#490 := [rewrite]: #489
-#486 := (iff #85 #485)
-#487 := [monotonicity #457]: #486
-#492 := [trans #487 #490]: #491
-#495 := [monotonicity #492]: #494
-#501 := [trans #495 #499]: #500
-#504 := [quant-intro #501]: #503
-#1112 := [monotonicity #504 #1109]: #1111
-#1118 := [trans #1112 #1116]: #1117
-#1121 := [monotonicity #504 #1118]: #1120
-#483 := (iff #81 #482)
-#480 := (iff #80 #477)
-#473 := (implies #470 #79)
-#478 := (iff #473 #477)
-#479 := [rewrite]: #478
-#474 := (iff #80 #473)
-#471 := (iff #77 #470)
-#468 := (iff #76 #467)
-#469 := [rewrite]: #468
-#459 := (iff #69 #458)
-#460 := [monotonicity #457]: #459
-#472 := [monotonicity #460 #469]: #471
-#475 := [monotonicity #472]: #474
-#481 := [trans #475 #479]: #480
-#484 := [quant-intro #481]: #483
-#1124 := [monotonicity #484 #1121]: #1123
-#1130 := [trans #1124 #1128]: #1129
-#1133 := [monotonicity #484 #1130]: #1132
-#1136 := [monotonicity #1133]: #1135
-#1142 := [trans #1136 #1140]: #1141
-#1145 := [monotonicity #1142]: #1144
-#465 := (iff #72 #464)
-#466 := [rewrite]: #465
-#1148 := [monotonicity #466 #1145]: #1147
-#1154 := [trans #1148 #1152]: #1153
-#1157 := [monotonicity #466 #1154]: #1156
-#462 := (iff #70 #461)
-#463 := [quant-intro #460]: #462
-#1160 := [monotonicity #463 #1157]: #1159
-#1166 := [trans #1160 #1164]: #1165
-#453 := (iff #66 #452)
-#450 := (iff #65 #447)
-#444 := (implies #63 #441)
-#448 := (iff #444 #447)
-#449 := [rewrite]: #448
-#445 := (iff #65 #444)
-#442 := (iff #64 #441)
-#443 := [rewrite]: #442
-#446 := [monotonicity #443]: #445
-#451 := [trans #446 #449]: #450
-#454 := [quant-intro #451]: #453
-#1169 := [monotonicity #454 #1166]: #1168
-#1175 := [trans #1169 #1173]: #1174
-#439 := (iff #62 #438)
-#436 := (iff #61 #433)
-#430 := (implies #58 #427)
-#434 := (iff #430 #433)
-#435 := [rewrite]: #434
-#431 := (iff #61 #430)
-#428 := (iff #60 #427)
-#429 := [rewrite]: #428
-#432 := [monotonicity #429]: #431
-#437 := [trans #432 #435]: #436
-#440 := [quant-intro #437]: #439
-#1178 := [monotonicity #440 #1175]: #1177
-#1184 := [trans #1178 #1182]: #1183
-#1187 := [monotonicity #1184]: #1186
-#1191 := [trans #1187 #1189]: #1190
-#1194 := [monotonicity #1191]: #1193
-#1833 := [trans #1194 #1831]: #1832
-#426 := [asserted]: #272
-#1834 := [mp #426 #1833]: #1829
-#1836 := [not-or-elim #1834]: #461
-#1891 := [mp~ #1836 #1860]: #461
-#4232 := [mp #1891 #4231]: #4227
-#5530 := (not #4227)
-#5531 := (or #5530 #3079)
-#5526 := [quant-inst #1937]: #5531
-#5338 := [unit-resolution #5526 #4232 #5223]: false
-#5346 := [lemma #5338]: #3079
-#3846 := (or #3094 #1946)
-#3850 := [def-axiom]: #3846
-#6496 := [unit-resolution #3850 #5346]: #3094
-#3099 := (not #3094)
-#4566 := (or #3099 #4563)
-#4569 := (not #4566)
-#4241 := (pattern #67 #75)
-#2520 := (not #467)
-#3071 := (or #455 #2520 #1211)
-#4242 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4241) #3071)
-#4247 := (not #4242)
-#4572 := (or #4247 #4569)
-#4575 := (not #4572)
+#180 := (ite true f1 f2)
+#181 := (f4 f15 f22 #180)
+#182 := (= f23 #181)
+#244 := (implies #182 #243)
+#176 := (<= #174 #101)
+#106 := (= #105 f1)
+#107 := (not #106)
+#177 := (implies #107 #176)
+#178 := (forall (vars (?v0 S3)) #177)
+#245 := (implies #178 #244)
+#175 := (< #174 f8)
+#246 := (implies #175 #245)
+#172 := (= #171 f1)
+#173 := (not #172)
+#247 := (implies #173 #246)
+#120 := (< #101 f8)
+#129 := (and #107 #120)
+#130 := (exists (vars (?v0 S3)) #129)
+#248 := (implies #130 #247)
+#249 := (implies true #248)
+#159 := (and #158 true)
+#147 := (+ #142 #82)
+#154 := (<= #145 #147)
+#143 := (< #142 f8)
+#153 := (and #143 #83)
+#155 := (implies #153 #154)
+#156 := (forall (vars (?v0 S3) (?v1 S3)) #155)
+#160 := (implies #156 #159)
+#161 := (and #156 #160)
+#148 := (= #145 #147)
+#146 := (< #142 #145)
+#149 := (and #146 #148)
+#150 := (exists (vars (?v1 S3)) #149)
+#144 := (and #62 #143)
+#151 := (implies #144 #150)
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+#162 := (implies #152 #161)
+#163 := (and #152 #162)
+#164 := (implies #141 #163)
+#138 := (= f19 f14)
+#165 := (implies #138 #164)
+#166 := (implies #136 #165)
+#133 := (= f16 f15)
+#167 := (implies #133 #166)
+#131 := (not #130)
+#168 := (implies #131 #167)
+#169 := (implies true #168)
+#250 := (and #169 #249)
+#116 := (+ #101 #82)
+#123 := (= #111 #116)
+#124 := (and #106 #123)
+#122 := (< #101 #111)
+#125 := (and #122 #124)
+#126 := (exists (vars (?v1 S3)) #125)
+#121 := (and #62 #120)
+#127 := (implies #121 #126)
+#128 := (forall (vars (?v0 S3)) #127)
+#251 := (implies #128 #250)
+#117 := (<= #111 #116)
+#115 := (and #106 #83)
+#118 := (implies #115 #117)
+#119 := (forall (vars (?v0 S3) (?v1 S3)) #118)
+#252 := (implies #119 #251)
+#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)
+#102 := (<= 0::Int #101)
+#103 := (forall (vars (?v0 S3)) #102)
+#254 := (implies #103 #253)
+#255 := (implies #100 #254)
+#256 := (implies true #255)
+#85 := (+ #58 #82)
+#92 := (= #77 #85)
+#67 := (= #66 f1)
+#93 := (and #67 #92)
+#91 := (< #58 #77)
+#94 := (and #91 #93)
+#95 := (exists (vars (?v1 S3)) #94)
+#89 := (< #58 f8)
+#90 := (and #62 #89)
+#96 := (implies #90 #95)
+#97 := (forall (vars (?v0 S3)) #96)
+#257 := (implies #97 #256)
+#258 := (and #97 #257)
+#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)
+#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)
+#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)
+#69 := (forall (vars (?v0 S3)) #68)
+#267 := (implies #69 #266)
+#63 := (= #58 f8)
+#64 := (implies #62 #63)
+#65 := (forall (vars (?v0 S3)) #64)
+#268 := (implies #65 #267)
+#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)
+#987 := (or #986 #978)
+#996 := (or #995 #987)
+#763 := (or #176 #533)
+#768 := (forall (vars (?v0 S3)) #763)
+#1004 := (not #768)
+#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)
+#1058 := (or #1057 #1049)
+#549 := (or #112 #548)
+#554 := (forall (vars (?v0 S3) (?v1 S3)) #549)
+#1066 := (not #554)
+#1067 := (or #1066 #1058)
+#1075 := (not #103)
+#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)
+#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)
+#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)
+#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
+#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)
+#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
+#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)
+#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
+#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
+#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)
+#1276 := [rewrite]: #1275
+#1282 := [monotonicity #1276 #1279]: #1281
+#1287 := [trans #1282 #1285]: #1286
+#1290 := [quant-intro #1287]: #1289
+#1269 := (iff #521 #1268)
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+#1255 := [quant-intro #1252]: #1254
+#1258 := [monotonicity #1255]: #1257
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+#1221 := [trans #1216 #1219]: #1220
+#1224 := [quant-intro #1221]: #1223
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+#1813 := [monotonicity #1810]: #1812
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+#844 := [quant-intro #841]: #843
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+#922 := [trans #916 #920]: #921
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+#605 := (iff #128 #604)
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+#584 := (iff #123 #583)
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+#591 := [monotonicity #588]: #590
+#594 := [quant-intro #591]: #593
+#597 := [monotonicity #594]: #596
+#603 := [trans #597 #601]: #602
+#606 := [quant-intro #603]: #605
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+#1053 := [trans #1047 #1051]: #1052
+#581 := (iff #119 #580)
+#578 := (iff #118 #575)
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+#577 := [rewrite]: #576
+#572 := (iff #118 #571)
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+#563 := (iff #115 #560)
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+#561 := (iff #557 #560)
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+#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
+#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
+#1071 := [trans #1065 #1069]: #1070
+#1074 := [monotonicity #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
+#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
+#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
+#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)
 decl ?v1!1 :: S3
-#1910 := ?v1!1
-#1914 := (f12 ?v1!1)
-#2535 := (* -1::Int #1914)
+#1909 := ?v1!1
+#1913 := (f11 ?v1!1)
+#2534 := (* -1::Int #1913)
 decl ?v0!2 :: S3
-#1911 := ?v0!2
-#1912 := (f12 ?v0!2)
-#2536 := (+ #1912 #2535)
-#2537 := (<= #2536 0::Int)
-#1919 := (f13 ?v1!1)
-#1920 := (= f1 #1919)
-#1917 := (f13 ?v0!2)
-#1918 := (= f1 #1917)
-#2308 := (not #1918)
-#2338 := (or #2308 #1920 #2537)
-#2130 := (not #2338)
-#4578 := (or #2130 #4575)
-#4581 := (not #4578)
-#4233 := (forall (vars (?v0 S3)) (:pat #4219) #1202)
-#4238 := (not #4233)
-#4584 := (or #4238 #4581)
-#4587 := (not #4584)
+#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)
 decl ?v0!0 :: S3
-#1895 := ?v0!0
-#1896 := (f12 ?v0!0)
-#1897 := (>= #1896 0::Int)
-#1898 := (not #1897)
-#4590 := (or #1898 #4587)
-#4593 := (not #4590)
-#4596 := (or #1197 #4593)
-#4599 := (not #4596)
-#4606 := (forall (vars (?v0 S3)) (:pat #4219) #1806)
-#4609 := (iff #1809 #4606)
-#4607 := (iff #1806 #1806)
-#4608 := [refl]: #4607
-#4610 := [quant-intro #4608]: #4609
-#2219 := (~ #1809 #1809)
-#1901 := (~ #1806 #1806)
-#1902 := [refl]: #1901
-#2220 := [nnf-pos #1902]: #2219
-#1839 := [not-or-elim #1834]: #1809
-#2307 := [mp~ #1839 #2220]: #1809
-#4611 := [mp #2307 #4610]: #4606
-#5325 := [hypothesis]: #1197
-#4785 := (not #4606)
-#5261 := (or #4785 #72)
-#5145 := (= f11 f11)
-#5146 := (not #5145)
-#5148 := (or #5146 #72)
-#5229 := (or #4785 #5148)
-#5263 := (iff #5229 #5261)
-#5265 := (iff #5261 #5261)
-#5260 := [rewrite]: #5265
-#5234 := (iff #5148 #72)
-#5202 := (or false #72)
-#5230 := (iff #5202 #72)
-#5233 := [rewrite]: #5230
-#5203 := (iff #5148 #5202)
-#5200 := (iff #5146 false)
-#5197 := (not true)
-#5194 := (iff #5197 false)
-#5195 := [rewrite]: #5194
-#5198 := (iff #5146 #5197)
-#5149 := (iff #5145 true)
-#5196 := [rewrite]: #5149
-#5199 := [monotonicity #5196]: #5198
-#5201 := [trans #5199 #5195]: #5200
-#5204 := [monotonicity #5201]: #5203
-#5235 := [trans #5204 #5233]: #5234
-#5264 := [monotonicity #5235]: #5263
-#5270 := [trans #5264 #5260]: #5263
-#5262 := [quant-inst #57]: #5229
-#5296 := [mp #5262 #5270]: #5261
-#5326 := [unit-resolution #5296 #5325 #4611]: false
-#5321 := [lemma #5326]: #72
-#4602 := (or #1197 #4599)
-#3529 := (forall (vars (?v1 S3)) #3518)
-#3536 := (not #3529)
-#3514 := (forall (vars (?v0 S3) (?v1 S3)) #3509)
-#3535 := (not #3514)
-#3537 := (or #2360 #2927 #3535 #3536)
-#3538 := (not #3537)
-#3543 := (or #3492 #3538)
-#3550 := (not #3543)
-#3469 := (forall (vars (?v0 S3) (?v1 S3)) #3464)
-#3549 := (not #3469)
-#3551 := (or #3549 #3550)
-#3552 := (not #3551)
-#3557 := (or #3446 #3552)
-#3563 := (not #3557)
-#3564 := (or #1500 #3563)
-#3565 := (not #3564)
-#3570 := (or #2277 #3565)
-#3576 := (not #3570)
-#3577 := (or #1491 #3576)
-#3578 := (not #3577)
-#3583 := (or #1491 #3578)
-#3589 := (not #3583)
-#3590 := (or #954 #3589)
-#3591 := (not #3590)
-#3596 := (or #2870 #3591)
-#3602 := (not #3596)
-#3603 := (or #1486 #3602)
-#3604 := (not #3603)
-#3609 := (or #2856 #3604)
-#3617 := (not #3609)
-#3423 := (forall (vars (?v0 S3)) #3418)
-#3616 := (not #3423)
-#3405 := (forall (vars (?v0 S3)) #3402)
-#3615 := (not #3405)
-#3618 := (or #755 #996 #1651 #1655 #2211 #2214 #3615 #3616 #3617)
-#3619 := (not #3618)
-#3335 := (forall (vars (?v0 S3) (?v1 S3)) #3330)
-#3341 := (not #3335)
-#3342 := (or #159 #3341)
-#3343 := (not #3342)
-#3370 := (or #3343 #3367)
-#3377 := (not #3370)
-#3313 := (forall (vars (?v0 S3)) #3308)
-#3376 := (not #3313)
-#3378 := (or #3376 #3377)
-#3379 := (not #3378)
-#3276 := (forall (vars (?v1 S3)) #3265)
-#3282 := (not #3276)
-#3283 := (or #2090 #2705 #3282)
-#3284 := (not #3283)
-#3384 := (or #3284 #3379)
-#3391 := (not #3384)
-#3261 := (forall (vars (?v0 S3)) #3250)
-#3390 := (not #3261)
-#3392 := (or #725 #707 #734 #716 #3390 #3391)
-#3393 := (not #3392)
-#3624 := (or #3393 #3619)
-#3634 := (not #3624)
-#3247 := (forall (vars (?v0 S3)) #3242)
-#3633 := (not #3247)
-#3219 := (forall (vars (?v0 S3)) #3214)
-#3632 := (not #3219)
-#3191 := (forall (vars (?v0 S3) (?v1 S3)) #3186)
-#3631 := (not #3191)
-#3168 := (forall (vars (?v0 S3) (?v1 S3)) #3163)
-#3630 := (not #3168)
-#3635 := (or #1748 #1743 #3630 #3631 #3632 #3633 #3634)
-#3636 := (not #3635)
-#3136 := (forall (vars (?v1 S3)) #3125)
-#3142 := (not #3136)
-#3143 := (or #1982 #2567 #3142)
-#3144 := (not #3143)
-#3641 := (or #3144 #3636)
-#3648 := (not #3641)
-#3121 := (forall (vars (?v0 S3) (?v1 S3)) #3116)
-#3647 := (not #3121)
-#3649 := (or #3647 #3648)
-#3650 := (not #3649)
-#3655 := (or #3099 #3650)
-#3662 := (not #3655)
-#3076 := (forall (vars (?v0 S3) (?v1 S3)) #3071)
-#3661 := (not #3076)
-#3663 := (or #3661 #3662)
-#3664 := (not #3663)
-#3669 := (or #2130 #3664)
-#3675 := (not #3669)
-#3676 := (or #1206 #3675)
-#3677 := (not #3676)
-#3682 := (or #1898 #3677)
-#3688 := (not #3682)
-#3689 := (or #1197 #3688)
-#3690 := (not #3689)
-#3695 := (or #1197 #3690)
-#4603 := (iff #3695 #4602)
-#4600 := (iff #3690 #4599)
-#4597 := (iff #3689 #4596)
-#4594 := (iff #3688 #4593)
-#4591 := (iff #3682 #4590)
-#4588 := (iff #3677 #4587)
-#4585 := (iff #3676 #4584)
-#4582 := (iff #3675 #4581)
-#4579 := (iff #3669 #4578)
-#4576 := (iff #3664 #4575)
-#4573 := (iff #3663 #4572)
-#4570 := (iff #3662 #4569)
-#4567 := (iff #3655 #4566)
-#4564 := (iff #3650 #4563)
-#4561 := (iff #3649 #4560)
-#4558 := (iff #3648 #4557)
-#4555 := (iff #3641 #4554)
-#4552 := (iff #3636 #4551)
-#4549 := (iff #3635 #4548)
-#4546 := (iff #3634 #4545)
-#4543 := (iff #3624 #4542)
-#4540 := (iff #3619 #4539)
-#4537 := (iff #3618 #4536)
-#4534 := (iff #3617 #4533)
-#4531 := (iff #3609 #4530)
-#4528 := (iff #3604 #4527)
-#4525 := (iff #3603 #4524)
-#4522 := (iff #3602 #4521)
-#4519 := (iff #3596 #4518)
-#4516 := (iff #3591 #4515)
-#4513 := (iff #3590 #4512)
-#4510 := (iff #3589 #4509)
-#4507 := (iff #3583 #4506)
-#4504 := (iff #3578 #4503)
-#4501 := (iff #3577 #4500)
-#4498 := (iff #3576 #4497)
-#4495 := (iff #3570 #4494)
-#4492 := (iff #3565 #4491)
-#4489 := (iff #3564 #4488)
-#4486 := (iff #3563 #4485)
-#4483 := (iff #3557 #4482)
-#4480 := (iff #3552 #4479)
-#4477 := (iff #3551 #4476)
-#4474 := (iff #3550 #4473)
-#4471 := (iff #3543 #4470)
-#4468 := (iff #3538 #4467)
-#4465 := (iff #3537 #4464)
-#4462 := (iff #3536 #4461)
-#4459 := (iff #3529 #4456)
-#4457 := (iff #3518 #3518)
-#4458 := [refl]: #4457
-#4460 := [quant-intro #4458]: #4459
-#4463 := [monotonicity #4460]: #4462
-#4453 := (iff #3535 #4452)
-#4450 := (iff #3514 #4447)
-#4448 := (iff #3509 #3509)
-#4449 := [refl]: #4448
-#4451 := [quant-intro #4449]: #4450
-#4454 := [monotonicity #4451]: #4453
-#4466 := [monotonicity #4454 #4463]: #4465
-#4469 := [monotonicity #4466]: #4468
-#4472 := [monotonicity #4469]: #4471
-#4475 := [monotonicity #4472]: #4474
-#4445 := (iff #3549 #4444)
-#4442 := (iff #3469 #4439)
-#4440 := (iff #3464 #3464)
-#4441 := [refl]: #4440
-#4443 := [quant-intro #4441]: #4442
-#4446 := [monotonicity #4443]: #4445
-#4478 := [monotonicity #4446 #4475]: #4477
-#4481 := [monotonicity #4478]: #4480
-#4484 := [monotonicity #4481]: #4483
-#4487 := [monotonicity #4484]: #4486
-#4436 := (iff #1500 #4435)
-#4433 := (iff #1497 #4430)
-#4431 := (iff #1494 #1494)
-#4432 := [refl]: #4431
-#4434 := [quant-intro #4432]: #4433
-#4437 := [monotonicity #4434]: #4436
-#4490 := [monotonicity #4437 #4487]: #4489
-#4493 := [monotonicity #4490]: #4492
-#4496 := [monotonicity #4493]: #4495
-#4499 := [monotonicity #4496]: #4498
-#4502 := [monotonicity #4499]: #4501
-#4505 := [monotonicity #4502]: #4504
-#4508 := [monotonicity #4505]: #4507
-#4511 := [monotonicity #4508]: #4510
-#4428 := (iff #954 #4427)
-#4425 := (iff #820 #4422)
-#4423 := (iff #815 #815)
-#4424 := [refl]: #4423
-#4426 := [quant-intro #4424]: #4425
-#4429 := [monotonicity #4426]: #4428
-#4514 := [monotonicity #4429 #4511]: #4513
-#4517 := [monotonicity #4514]: #4516
-#4520 := [monotonicity #4517]: #4519
-#4523 := [monotonicity #4520]: #4522
-#4419 := (iff #1486 #4418)
-#4416 := (iff #1483 #4413)
-#4414 := (iff #1478 #1478)
-#4415 := [refl]: #4414
-#4417 := [quant-intro #4415]: #4416
-#4420 := [monotonicity #4417]: #4419
-#4526 := [monotonicity #4420 #4523]: #4525
-#4529 := [monotonicity #4526]: #4528
-#4532 := [monotonicity #4529]: #4531
-#4535 := [monotonicity #4532]: #4534
-#4411 := (iff #3616 #4410)
-#4408 := (iff #3423 #4405)
-#4406 := (iff #3418 #3418)
-#4407 := [refl]: #4406
-#4409 := [quant-intro #4407]: #4408
-#4412 := [monotonicity #4409]: #4411
-#4403 := (iff #3615 #4402)
-#4400 := (iff #3405 #4397)
-#4398 := (iff #3402 #3402)
-#4399 := [refl]: #4398
-#4401 := [quant-intro #4399]: #4400
-#4404 := [monotonicity #4401]: #4403
-#4393 := (iff #1651 #4392)
-#4390 := (iff #1648 #4387)
-#4388 := (iff #1643 #1643)
-#4389 := [refl]: #4388
-#4391 := [quant-intro #4389]: #4390
-#4394 := [monotonicity #4391]: #4393
-#4538 := [monotonicity #4394 #4404 #4412 #4535]: #4537
-#4541 := [monotonicity #4538]: #4540
-#4385 := (iff #3393 #4384)
-#4382 := (iff #3392 #4381)
-#4379 := (iff #3391 #4378)
-#4376 := (iff #3384 #4375)
-#4373 := (iff #3379 #4372)
-#4370 := (iff #3378 #4369)
-#4367 := (iff #3377 #4366)
-#4364 := (iff #3370 #4363)
-#4361 := (iff #3343 #4360)
-#4358 := (iff #3342 #4357)
-#4355 := (iff #3341 #4354)
-#4352 := (iff #3335 #4349)
-#4350 := (iff #3330 #3330)
-#4351 := [refl]: #4350
-#4353 := [quant-intro #4351]: #4352
-#4356 := [monotonicity #4353]: #4355
-#4359 := [monotonicity #4356]: #4358
-#4362 := [monotonicity #4359]: #4361
-#4365 := [monotonicity #4362]: #4364
-#4368 := [monotonicity #4365]: #4367
-#4347 := (iff #3376 #4346)
-#4344 := (iff #3313 #4341)
-#4342 := (iff #3308 #3308)
-#4343 := [refl]: #4342
-#4345 := [quant-intro #4343]: #4344
-#4348 := [monotonicity #4345]: #4347
-#4371 := [monotonicity #4348 #4368]: #4370
-#4374 := [monotonicity #4371]: #4373
-#4339 := (iff #3284 #4338)
-#4336 := (iff #3283 #4335)
-#4333 := (iff #3282 #4332)
-#4330 := (iff #3276 #4327)
-#4328 := (iff #3265 #3265)
-#4329 := [refl]: #4328
-#4331 := [quant-intro #4329]: #4330
-#4334 := [monotonicity #4331]: #4333
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-#3386 := [monotonicity #3288 #3383]: #3385
-#3262 := (iff #2195 #3261)
-#3259 := (iff #2192 #3250)
-#3251 := (not #3250)
-#3254 := (not #3251)
-#3257 := (iff #3254 #3250)
-#3258 := [rewrite]: #3257
-#3255 := (iff #2192 #3254)
-#3252 := (iff #1420 #3251)
-#3253 := [rewrite]: #3252
-#3256 := [monotonicity #3253]: #3255
-#3260 := [trans #3256 #3258]: #3259
-#3263 := [quant-intro #3260]: #3262
-#3389 := [monotonicity #3263 #3386]: #3388
-#3397 := [trans #3389 #3395]: #3396
-#3626 := [monotonicity #3397 #3623]: #3625
-#3248 := (iff #2694 #3247)
-#3245 := (iff #2691 #3242)
-#3222 := (or #58 #1300)
-#3239 := (or #3222 #3236)
-#3243 := (iff #3239 #3242)
-#3244 := [rewrite]: #3243
-#3240 := (iff #2691 #3239)
-#3237 := (iff #2688 #3236)
-#3238 := [rewrite]: #3237
-#3231 := (iff #1307 #3222)
-#3223 := (not #3222)
-#3226 := (not #3223)
-#3229 := (iff #3226 #3222)
-#3230 := [rewrite]: #3229
-#3227 := (iff #1307 #3226)
-#3224 := (iff #1304 #3223)
-#3225 := [rewrite]: #3224
-#3228 := [monotonicity #3225]: #3227
-#3232 := [trans #3228 #3230]: #3231
-#3241 := [monotonicity #3232 #3238]: #3240
-#3246 := [trans #3241 #3244]: #3245
-#3249 := [quant-intro #3246]: #3248
-#3220 := (iff #2654 #3219)
-#3217 := (iff #2651 #3214)
-#3194 := (or #58 #1262)
-#3211 := (or #3194 #3208)
-#3215 := (iff #3211 #3214)
-#3216 := [rewrite]: #3215
-#3212 := (iff #2651 #3211)
-#3209 := (iff #2648 #3208)
-#3210 := [rewrite]: #3209
-#3203 := (iff #1269 #3194)
-#3195 := (not #3194)
-#3198 := (not #3195)
-#3201 := (iff #3198 #3194)
-#3202 := [rewrite]: #3201
-#3199 := (iff #1269 #3198)
-#3196 := (iff #1266 #3195)
-#3197 := [rewrite]: #3196
-#3200 := [monotonicity #3197]: #3199
-#3204 := [trans #3200 #3202]: #3203
-#3213 := [monotonicity #3204 #3210]: #3212
-#3218 := [trans #3213 #3216]: #3217
-#3221 := [quant-intro #3218]: #3220
-#3192 := (iff #1731 #3191)
-#3189 := (iff #1726 #3186)
-#3172 := (or #534 #3171)
-#3183 := (or #3172 #1316)
-#3187 := (iff #3183 #3186)
-#3188 := [rewrite]: #3187
-#3184 := (iff #1726 #3183)
-#3181 := (iff #549 #3172)
-#3173 := (not #3172)
-#3176 := (not #3173)
-#3179 := (iff #3176 #3172)
-#3180 := [rewrite]: #3179
-#3177 := (iff #549 #3176)
-#3174 := (iff #543 #3173)
-#3175 := [rewrite]: #3174
-#3178 := [monotonicity #3175]: #3177
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-#3185 := [monotonicity #3182]: #3184
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-#3193 := [quant-intro #3190]: #3192
-#3169 := (iff #1715 #3168)
-#3166 := (iff #1712 #3163)
-#3149 := (or #537 #1236)
-#3160 := (or #3149 #1709)
-#3164 := (iff #3160 #3163)
-#3165 := [rewrite]: #3164
-#3161 := (iff #1712 #3160)
-#3158 := (iff #1706 #3149)
-#3150 := (not #3149)
-#3153 := (not #3150)
-#3156 := (iff #3153 #3149)
-#3157 := [rewrite]: #3156
-#3154 := (iff #1706 #3153)
-#3151 := (iff #1701 #3150)
-#3152 := [rewrite]: #3151
-#3155 := [monotonicity #3152]: #3154
-#3159 := [trans #3155 #3157]: #3158
-#3162 := [monotonicity #3159]: #3161
-#3167 := [trans #3162 #3165]: #3166
-#3170 := [quant-intro #3167]: #3169
-#3629 := [monotonicity #3170 #3193 #3221 #3249 #3626]: #3628
-#3640 := [trans #3629 #3638]: #3639
-#3147 := (iff #2610 #3144)
-#3139 := (and #1983 #2570 #3136)
-#3145 := (iff #3139 #3144)
-#3146 := [rewrite]: #3145
-#3140 := (iff #2610 #3139)
-#3137 := (iff #2604 #3136)
-#3134 := (iff #2601 #3125)
-#3126 := (not #3125)
-#3129 := (not #3126)
-#3132 := (iff #3129 #3125)
-#3133 := [rewrite]: #3132
-#3130 := (iff #2601 #3129)
-#3127 := (iff #2598 #3126)
-#3128 := [rewrite]: #3127
-#3131 := [monotonicity #3128]: #3130
-#3135 := [trans #3131 #3133]: #3134
-#3138 := [quant-intro #3135]: #3137
-#3141 := [monotonicity #3138]: #3140
-#3148 := [trans #3141 #3146]: #3147
-#3643 := [monotonicity #3148 #3640]: #3642
-#3122 := (iff #1254 #3121)
-#3119 := (iff #1251 #3116)
-#3102 := (or #458 #1236)
-#3113 := (or #1231 #3102)
-#3117 := (iff #3113 #3116)
-#3118 := [rewrite]: #3117
-#3114 := (iff #1251 #3113)
-#3111 := (iff #1248 #3102)
-#3103 := (not #3102)
-#3106 := (not #3103)
-#3109 := (iff #3106 #3102)
-#3110 := [rewrite]: #3109
-#3107 := (iff #1248 #3106)
-#3104 := (iff #1243 #3103)
-#3105 := [rewrite]: #3104
-#3108 := [monotonicity #3105]: #3107
-#3112 := [trans #3108 #3110]: #3111
-#3115 := [monotonicity #3112]: #3114
-#3120 := [trans #3115 #3118]: #3119
-#3123 := [quant-intro #3120]: #3122
-#3646 := [monotonicity #3123 #3643]: #3645
-#3654 := [trans #3646 #3652]: #3653
-#3100 := (iff #2564 #3099)
-#3097 := (iff #2561 #3094)
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-#3095 := (iff #3091 #3094)
-#3096 := [rewrite]: #3095
-#3092 := (iff #2561 #3091)
-#3089 := (iff #2558 #3080)
-#3081 := (not #3080)
-#3084 := (not #3081)
-#3087 := (iff #3084 #3080)
-#3088 := [rewrite]: #3087
-#3085 := (iff #2558 #3084)
-#3082 := (iff #2555 #3081)
-#3083 := [rewrite]: #3082
-#3086 := [monotonicity #3083]: #3085
-#3090 := [trans #3086 #3088]: #3089
-#3093 := [monotonicity #3090]: #3092
-#3098 := [trans #3093 #3096]: #3097
-#3101 := [monotonicity #3098]: #3100
-#3657 := [monotonicity #3101 #3654]: #3656
-#3077 := (iff #1223 #3076)
-#3074 := (iff #1218 #3071)
-#3057 := (or #455 #2520)
-#3068 := (or #3057 #1211)
-#3072 := (iff #3068 #3071)
-#3073 := [rewrite]: #3072
-#3069 := (iff #1218 #3068)
-#3066 := (iff #476 #3057)
-#3058 := (not #3057)
-#3061 := (not #3058)
-#3064 := (iff #3061 #3057)
-#3065 := [rewrite]: #3064
-#3062 := (iff #476 #3061)
-#3059 := (iff #470 #3058)
-#3060 := [rewrite]: #3059
-#3063 := [monotonicity #3060]: #3062
-#3067 := [trans #3063 #3065]: #3066
-#3070 := [monotonicity #3067]: #3069
-#3075 := [trans #3070 #3073]: #3074
-#3078 := [quant-intro #3075]: #3077
-#3660 := [monotonicity #3078 #3657]: #3659
-#3668 := [trans #3660 #3666]: #3667
-#2260 := (iff #2545 #2130)
-#2241 := (iff #2542 #2338)
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-#2240 := [rewrite]: #2339
-#2280 := (iff #2542 #2165)
-#1960 := (iff #2526 #1928)
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-#2027 := (not #1865)
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-#1959 := [rewrite]: #2055
-#2028 := (iff #2526 #2027)
-#1866 := (iff #2523 #1865)
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-#2054 := [monotonicity #1929]: #2028
-#2164 := [trans #2054 #1959]: #1960
-#2281 := [monotonicity #2164]: #2280
-#2129 := [trans #2281 #2240]: #2241
-#2261 := [monotonicity #2129]: #2260
-#3671 := [monotonicity #2261 #3668]: #3670
-#3674 := [monotonicity #3671]: #3673
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-#3684 := [monotonicity #3681]: #3683
-#3687 := [monotonicity #3684]: #3686
-#3694 := [trans #3687 #3692]: #3693
-#3697 := [monotonicity #3694]: #3696
-#2353 := (+ #2352 #2350)
-#2354 := (= #2353 0::Int)
-#2357 := (and #808 #2356 #2354)
-#2374 := (not #2357)
-#2377 := (forall (vars (?v1 S3)) #2374)
-#2362 := (= ?v0!20 f11)
-#2363 := (not #2362)
-#2364 := (and #2363 #2361)
-#2365 := (not #2364)
-#2371 := (not #2365)
-#2381 := (and #2371 #2377)
-#2386 := (and #1540 #2381)
-#2319 := (* -1::Int #2318)
-#2321 := (+ #2320 #2319)
-#2324 := (+ #2323 #2321)
-#2325 := (>= #2324 0::Int)
-#2332 := (and #2331 #2329)
-#2333 := (not #2332)
-#2334 := (or #2333 #2325)
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-#2390 := (or #2335 #2386)
-#2394 := (and #1516 #2390)
-#2292 := (* -1::Int #2291)
-#2294 := (+ #2293 #2292)
-#2295 := (>= #2294 0::Int)
-#2301 := (and #2300 #2297)
-#2302 := (not #2301)
-#2303 := (or #2302 #2295)
-#2304 := (not #2303)
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-#2271 := (not #1491)
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-#2414 := (or #1491 #2410)
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-#2255 := (= #2254 #2253)
-#2256 := (or #2255 #2252)
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-#2426 := (and #1483 #2422)
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-#2236 := (>= #2235 0::Int)
-#2237 := (not #2236)
-#2430 := (or #2237 #2426)
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-#2143 := (* -1::Int #2142)
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-#2149 := (>= #2148 0::Int)
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-#2160 := (or #2159 #2149)
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-#2123 := (= #2122 0::Int)
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-#2083 := (+ #2082 #2080)
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-#2100 := (not #2095)
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-#2043 := (>= #2042 0::Int)
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-#2047 := (+ #2046 #2042)
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-#2015 := (+ #1260 #2014)
-#2017 := (+ #2016 #2015)
-#2018 := (= #2017 0::Int)
-#2019 := (+ #2016 #1260)
-#2020 := (>= #2019 0::Int)
-#2021 := (not #2020)
-#2024 := (and #2023 #2021 #2018)
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-#1973 := (+ #1972 #1970)
-#1974 := (+ #59 #1973)
-#1975 := (= #1974 0::Int)
-#1979 := (and #455 #1978 #1975)
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-#1984 := (= ?v0!5 f11)
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-#1986 := (and #1985 #1983)
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-#1992 := (not #1987)
-#2002 := (and #1992 #1998)
-#2483 := (or #2002 #2479)
-#2487 := (and #1254 #2483)
-#1947 := (and #1946 #1944)
-#1948 := (not #1947)
-#1951 := (+ #1950 #1940)
-#1953 := (+ #1952 #1951)
-#1954 := (>= #1953 0::Int)
-#1955 := (or #1954 #1948)
-#1956 := (not #1955)
-#2491 := (or #1956 #2487)
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-#1913 := (* -1::Int #1912)
-#1915 := (+ #1914 #1913)
-#1916 := (>= #1915 0::Int)
-#1922 := (and #1921 #1918)
-#1923 := (not #1922)
-#1924 := (or #1923 #1916)
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-#3011 := (and #758 #777 #2216 #1472 #3008 #1630 #1648 #1656)
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-#3012 := (iff #2450 #3011)
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-#3000 := (iff #2418 #2999)
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-#2956 := (iff #2354 #2955)
-#2953 := (= #2353 #2952)
-#2954 := [rewrite]: #2953
-#2957 := [monotonicity #2954]: #2956
-#2960 := [monotonicity #2957]: #2959
-#2963 := [monotonicity #2960]: #2962
-#2966 := [quant-intro #2963]: #2965
-#2949 := (iff #2371 #2936)
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-#2944 := (not #2941)
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-#2948 := [rewrite]: #2947
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-#2934 := (iff #2364 #2933)
-#2931 := (iff #2363 #2930)
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-#2929 := [rewrite]: #2928
-#2932 := [monotonicity #2929]: #2931
-#2935 := [monotonicity #2932]: #2934
-#2940 := [trans #2935 #2938]: #2939
-#2943 := [monotonicity #2940]: #2942
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-#2969 := [monotonicity #2950 #2966]: #2968
-#2972 := [monotonicity #2969]: #2971
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-#2925 := (iff #2335 #2924)
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-#2919 := (iff #2325 #2916)
-#2906 := (+ #2320 #2323)
-#2907 := (+ #2319 #2906)
-#2910 := (>= #2907 0::Int)
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-#2918 := [rewrite]: #2917
-#2911 := (iff #2325 #2910)
-#2908 := (= #2324 #2907)
-#2909 := [rewrite]: #2908
-#2912 := [monotonicity #2909]: #2911
-#2920 := [trans #2912 #2918]: #2919
-#2904 := (iff #2333 #2903)
-#2901 := (iff #2332 #2900)
-#2902 := [rewrite]: #2901
-#2905 := [monotonicity #2902]: #2904
-#2923 := [monotonicity #2905 #2920]: #2922
-#2926 := [monotonicity #2923]: #2925
-#2980 := [monotonicity #2926 #2977]: #2979
-#2983 := [monotonicity #2980]: #2982
-#2898 := (iff #2304 #2897)
-#2895 := (iff #2303 #2894)
-#2892 := (iff #2295 #2889)
-#2881 := (+ #2292 #2293)
-#2884 := (>= #2881 0::Int)
-#2890 := (iff #2884 #2889)
-#2891 := [rewrite]: #2890
-#2885 := (iff #2295 #2884)
-#2882 := (= #2294 #2881)
-#2883 := [rewrite]: #2882
-#2886 := [monotonicity #2883]: #2885
-#2893 := [trans #2886 #2891]: #2892
-#2879 := (iff #2302 #2878)
-#2876 := (iff #2301 #2875)
-#2877 := [rewrite]: #2876
-#2880 := [monotonicity #2877]: #2879
-#2896 := [monotonicity #2880 #2893]: #2895
-#2899 := [monotonicity #2896]: #2898
-#2986 := [monotonicity #2899 #2983]: #2985
-#2989 := [monotonicity #2986]: #2988
-#2992 := [monotonicity #2989]: #2991
-#2873 := (iff #2271 #205)
-#2874 := [rewrite]: #2873
-#2995 := [monotonicity #2874 #2992]: #2994
-#2998 := [monotonicity #2995]: #2997
-#3001 := [monotonicity #2998]: #3000
-#2871 := (iff #2257 #2870)
-#2868 := (iff #2256 #2865)
-#2862 := (or #2859 #2252)
-#2866 := (iff #2862 #2865)
-#2867 := [rewrite]: #2866
-#2863 := (iff #2256 #2862)
-#2860 := (iff #2255 #2859)
-#2861 := [rewrite]: #2860
-#2864 := [monotonicity #2861]: #2863
-#2869 := [trans #2864 #2867]: #2868
-#2872 := [monotonicity #2869]: #2871
-#3004 := [monotonicity #2872 #3001]: #3003
-#3007 := [monotonicity #3004]: #3006
-#2857 := (iff #2237 #2856)
-#2854 := (iff #2236 #2851)
-#2843 := (+ #2233 #2234)
-#2846 := (>= #2843 0::Int)
-#2852 := (iff #2846 #2851)
-#2853 := [rewrite]: #2852
-#2847 := (iff #2236 #2846)
-#2844 := (= #2235 #2843)
-#2845 := [rewrite]: #2844
-#2848 := [monotonicity #2845]: #2847
-#2855 := [trans #2848 #2853]: #2854
-#2858 := [monotonicity #2855]: #2857
-#3010 := [monotonicity #2858 #3007]: #3009
-#2841 := (iff #2204 #777)
-#2842 := [rewrite]: #2841
-#3013 := [monotonicity #2842 #3010]: #3012
-#3018 := [trans #3013 #3016]: #3017
-#2839 := (iff #2198 #2836)
-#2833 := (and #137 #142 #622 #625 #2830 #2195)
-#2837 := (iff #2833 #2836)
-#2838 := [rewrite]: #2837
-#2834 := (iff #2198 #2833)
-#2831 := (iff #2188 #2830)
-#2828 := (iff #2184 #2827)
-#2825 := (iff #2180 #2822)
-#2819 := (or #2816 #2176)
-#2823 := (iff #2819 #2822)
-#2824 := [rewrite]: #2823
-#2820 := (iff #2180 #2819)
-#2817 := (iff #2161 #2816)
-#2814 := (iff #2160 #2813)
-#2811 := (iff #2149 #2808)
-#2799 := (+ #2144 #2147)
-#2800 := (+ #2143 #2799)
-#2803 := (>= #2800 0::Int)
-#2809 := (iff #2803 #2808)
-#2810 := [rewrite]: #2809
-#2804 := (iff #2149 #2803)
-#2801 := (= #2148 #2800)
-#2802 := [rewrite]: #2801
-#2805 := [monotonicity #2802]: #2804
-#2812 := [trans #2805 #2810]: #2811
-#2797 := (iff #2159 #2796)
-#2794 := (iff #2158 #2793)
-#2795 := [rewrite]: #2794
-#2798 := [monotonicity #2795]: #2797
-#2815 := [monotonicity #2798 #2812]: #2814
-#2818 := [monotonicity #2815]: #2817
-#2821 := [monotonicity #2818]: #2820
-#2826 := [trans #2821 #2824]: #2825
-#2791 := (iff #2134 #2790)
-#2788 := (iff #2131 #2787)
-#2785 := (iff #2126 #2784)
-#2782 := (iff #2123 #2779)
-#2769 := (+ #2118 #2121)
-#2770 := (+ #1343 #2769)
-#2773 := (= #2770 0::Int)
-#2780 := (iff #2773 #2779)
-#2781 := [rewrite]: #2780
-#2774 := (iff #2123 #2773)
-#2771 := (= #2122 #2770)
-#2772 := [rewrite]: #2771
-#2775 := [monotonicity #2772]: #2774
-#2783 := [trans #2775 #2781]: #2782
-#2767 := (iff #2125 #2766)
-#2764 := (iff #2124 #2761)
-#2753 := (+ #1343 #2118)
-#2756 := (>= #2753 0::Int)
-#2762 := (iff #2756 #2761)
-#2763 := [rewrite]: #2762
-#2757 := (iff #2124 #2756)
-#2754 := (= #2119 #2753)
-#2755 := [rewrite]: #2754
-#2758 := [monotonicity #2755]: #2757
-#2765 := [trans #2758 #2763]: #2764
-#2768 := [monotonicity #2765]: #2767
-#2786 := [monotonicity #2768 #2783]: #2785
-#2789 := [monotonicity #2786]: #2788
-#2792 := [quant-intro #2789]: #2791
-#2829 := [monotonicity #2792 #2826]: #2828
-#2751 := (iff #2110 #2748)
-#2714 := (and #2091 #2708)
-#2745 := (and #2714 #2742)
-#2749 := (iff #2745 #2748)
-#2750 := [rewrite]: #2749
-#2746 := (iff #2110 #2745)
-#2743 := (iff #2106 #2742)
-#2740 := (iff #2103 #2739)
-#2737 := (iff #2087 #2736)
-#2734 := (iff #2084 #2733)
-#2731 := (= #2083 #2730)
-#2732 := [rewrite]: #2731
-#2735 := [monotonicity #2732]: #2734
-#2738 := [monotonicity #2735]: #2737
-#2741 := [monotonicity #2738]: #2740
-#2744 := [quant-intro #2741]: #2743
-#2727 := (iff #2100 #2714)
-#2719 := (not #2714)
-#2722 := (not #2719)
-#2725 := (iff #2722 #2714)
-#2726 := [rewrite]: #2725
-#2723 := (iff #2100 #2722)
-#2720 := (iff #2095 #2719)
-#2717 := (iff #2094 #2714)
-#2711 := (and #2708 #2091)
-#2715 := (iff #2711 #2714)
-#2716 := [rewrite]: #2715
-#2712 := (iff #2094 #2711)
-#2709 := (iff #2093 #2708)
-#2706 := (iff #2092 #2705)
-#2707 := [rewrite]: #2706
-#2710 := [monotonicity #2707]: #2709
-#2713 := [monotonicity #2710]: #2712
-#2718 := [trans #2713 #2716]: #2717
-#2721 := [monotonicity #2718]: #2720
-#2724 := [monotonicity #2721]: #2723
-#2728 := [trans #2724 #2726]: #2727
-#2747 := [monotonicity #2728 #2744]: #2746
-#2752 := [trans #2747 #2750]: #2751
-#2832 := [monotonicity #2752 #2829]: #2831
-#2703 := (iff #2074 #625)
-#2704 := [rewrite]: #2703
-#2701 := (iff #2071 #622)
-#2702 := [rewrite]: #2701
-#2699 := (iff #2068 #142)
-#2700 := [rewrite]: #2699
-#2697 := (iff #2065 #137)
-#2698 := [rewrite]: #2697
-#2835 := [monotonicity #2698 #2700 #2702 #2704 #2832]: #2834
-#2840 := [trans #2835 #2838]: #2839
-#3021 := [monotonicity #2840 #3018]: #3020
-#2695 := (iff #2059 #2694)
-#2692 := (iff #2056 #2691)
-#2689 := (iff #2051 #2688)
-#2686 := (iff #2044 #2685)
-#2683 := (iff #2043 #2680)
-#2673 := (+ #1298 #2041)
-#2676 := (>= #2673 0::Int)
-#2681 := (iff #2676 #2680)
-#2682 := [rewrite]: #2681
-#2677 := (iff #2043 #2676)
-#2674 := (= #2042 #2673)
-#2675 := [rewrite]: #2674
-#2678 := [monotonicity #2675]: #2677
-#2684 := [trans #2678 #2682]: #2683
-#2687 := [monotonicity #2684]: #2686
-#2671 := (iff #2048 #2668)
-#2657 := (+ #2041 #2046)
-#2658 := (+ #1298 #2657)
-#2661 := (= #2658 0::Int)
-#2669 := (iff #2661 #2668)
-#2670 := [rewrite]: #2669
-#2662 := (iff #2048 #2661)
-#2659 := (= #2047 #2658)
-#2660 := [rewrite]: #2659
-#2663 := [monotonicity #2660]: #2662
-#2672 := [trans #2663 #2670]: #2671
-#2690 := [monotonicity #2672 #2687]: #2689
-#2693 := [monotonicity #2690]: #2692
-#2696 := [quant-intro #2693]: #2695
-#2655 := (iff #2032 #2654)
-#2652 := (iff #2029 #2651)
-#2649 := (iff #2024 #2648)
-#2646 := (iff #2018 #2643)
-#2633 := (+ #2014 #2016)
-#2634 := (+ #1260 #2633)
-#2637 := (= #2634 0::Int)
-#2644 := (iff #2637 #2643)
-#2645 := [rewrite]: #2644
-#2638 := (iff #2018 #2637)
-#2635 := (= #2017 #2634)
-#2636 := [rewrite]: #2635
-#2639 := [monotonicity #2636]: #2638
-#2647 := [trans #2639 #2645]: #2646
-#2631 := (iff #2021 #2630)
-#2628 := (iff #2020 #2625)
-#2617 := (+ #1260 #2016)
-#2620 := (>= #2617 0::Int)
-#2626 := (iff #2620 #2625)
-#2627 := [rewrite]: #2626
-#2621 := (iff #2020 #2620)
-#2618 := (= #2019 #2617)
-#2619 := [rewrite]: #2618
-#2622 := [monotonicity #2619]: #2621
-#2629 := [trans #2622 #2627]: #2628
-#2632 := [monotonicity #2629]: #2631
-#2650 := [monotonicity #2632 #2647]: #2649
-#2653 := [monotonicity #2650]: #2652
-#2656 := [quant-intro #2653]: #2655
-#2615 := (iff #2007 #101)
-#2616 := [rewrite]: #2615
-#3024 := [monotonicity #2616 #2656 #2696 #3021]: #3023
-#3029 := [trans #3024 #3027]: #3028
-#2613 := (iff #2002 #2610)
-#2576 := (and #1983 #2570)
-#2607 := (and #2576 #2604)
-#2611 := (iff #2607 #2610)
-#2612 := [rewrite]: #2611
-#2608 := (iff #2002 #2607)
-#2605 := (iff #1998 #2604)
-#2602 := (iff #1995 #2601)
-#2599 := (iff #1979 #2598)
-#2596 := (iff #1975 #2595)
-#2593 := (= #1974 #2592)
-#2594 := [rewrite]: #2593
-#2597 := [monotonicity #2594]: #2596
-#2600 := [monotonicity #2597]: #2599
-#2603 := [monotonicity #2600]: #2602
-#2606 := [quant-intro #2603]: #2605
-#2589 := (iff #1992 #2576)
-#2581 := (not #2576)
-#2584 := (not #2581)
-#2587 := (iff #2584 #2576)
-#2588 := [rewrite]: #2587
-#2585 := (iff #1992 #2584)
-#2582 := (iff #1987 #2581)
-#2579 := (iff #1986 #2576)
-#2573 := (and #2570 #1983)
-#2577 := (iff #2573 #2576)
-#2578 := [rewrite]: #2577
-#2574 := (iff #1986 #2573)
-#2571 := (iff #1985 #2570)
-#2568 := (iff #1984 #2567)
-#2569 := [rewrite]: #2568
-#2572 := [monotonicity #2569]: #2571
-#2575 := [monotonicity #2572]: #2574
-#2580 := [trans #2575 #2578]: #2579
-#2583 := [monotonicity #2580]: #2582
-#2586 := [monotonicity #2583]: #2585
-#2590 := [trans #2586 #2588]: #2589
-#2609 := [monotonicity #2590 #2606]: #2608
-#2614 := [trans #2609 #2612]: #2613
-#3032 := [monotonicity #2614 #3029]: #3031
-#3035 := [monotonicity #3032]: #3034
-#2565 := (iff #1956 #2564)
-#2562 := (iff #1955 #2561)
-#2559 := (iff #1948 #2558)
-#2556 := (iff #1947 #2555)
-#2557 := [rewrite]: #2556
-#2560 := [monotonicity #2557]: #2559
-#2553 := (iff #1954 #2552)
-#2550 := (= #1953 #2549)
-#2551 := [rewrite]: #2550
-#2554 := [monotonicity #2551]: #2553
-#2563 := [monotonicity #2554 #2560]: #2562
-#2566 := [monotonicity #2563]: #2565
-#3038 := [monotonicity #2566 #3035]: #3037
-#3041 := [monotonicity #3038]: #3040
-#2546 := (iff #1925 #2545)
-#2543 := (iff #1924 #2542)
-#2540 := (iff #1916 #2537)
-#2529 := (+ #1913 #1914)
-#2532 := (>= #2529 0::Int)
-#2538 := (iff #2532 #2537)
-#2539 := [rewrite]: #2538
-#2533 := (iff #1916 #2532)
-#2530 := (= #1915 #2529)
-#2531 := [rewrite]: #2530
-#2534 := [monotonicity #2531]: #2533
-#2541 := [trans #2534 #2539]: #2540
-#2527 := (iff #1923 #2526)
-#2524 := (iff #1922 #2523)
-#2525 := [rewrite]: #2524
-#2528 := [monotonicity #2525]: #2527
-#2544 := [monotonicity #2528 #2541]: #2543
-#2547 := [monotonicity #2544]: #2546
-#3044 := [monotonicity #2547 #3041]: #3043
-#3047 := [monotonicity #3044]: #3046
-#3050 := [monotonicity #3047]: #3049
-#2521 := (iff #1861 #72)
-#2522 := [rewrite]: #2521
-#3053 := [monotonicity #2522 #3050]: #3052
-#3056 := [monotonicity #3053]: #3055
-#1837 := (not #1801)
-#2516 := (~ #1837 #2515)
-#2512 := (not #1798)
-#2513 := (~ #2512 #2511)
-#2508 := (not #1795)
-#2509 := (~ #2508 #2507)
-#2504 := (not #1792)
-#2505 := (~ #2504 #2503)
-#2500 := (not #1789)
-#2501 := (~ #2500 #2499)
-#2496 := (not #1786)
-#2497 := (~ #2496 #2495)
-#2492 := (not #1783)
-#2493 := (~ #2492 #2491)
-#2488 := (not #1780)
-#2489 := (~ #2488 #2487)
-#2484 := (not #1777)
-#2485 := (~ #2484 #2483)
-#2480 := (not #1772)
-#2481 := (~ #2480 #2479)
-#2476 := (not #1743)
-#2477 := (~ #2476 #1740)
-#2474 := (~ #1740 #1740)
-#2472 := (~ #1737 #1737)
-#2473 := [refl]: #2472
-#2475 := [nnf-pos #2473]: #2474
-#2478 := [nnf-neg #2475]: #2477
-#2469 := (not #1734)
-#2470 := (~ #2469 #1731)
-#2467 := (~ #1731 #1731)
-#2465 := (~ #1726 #1726)
-#2466 := [refl]: #2465
-#2468 := [nnf-pos #2466]: #2467
-#2471 := [nnf-neg #2468]: #2470
-#2462 := (not #1718)
-#2463 := (~ #2462 #1715)
-#2460 := (~ #1715 #1715)
-#2458 := (~ #1712 #1712)
-#2459 := [refl]: #2458
-#2461 := [nnf-pos #2459]: #2460
-#2464 := [nnf-neg #2461]: #2463
-#2455 := (not #1695)
-#2456 := (~ #2455 #2454)
-#2451 := (not #1690)
-#2452 := (~ #2451 #2450)
-#2448 := (~ #1656 #1656)
-#2449 := [refl]: #2448
-#2445 := (not #1651)
-#2446 := (~ #2445 #1648)
-#2443 := (~ #1648 #1648)
-#2441 := (~ #1643 #1643)
-#2442 := [refl]: #2441
-#2444 := [nnf-pos #2442]: #2443
-#2447 := [nnf-neg #2444]: #2446
-#2438 := (not #1633)
-#2439 := (~ #2438 #1630)
-#2436 := (~ #1630 #1630)
-#2434 := (~ #1627 #1627)
-#2435 := [refl]: #2434
-#2437 := [nnf-pos #2435]: #2436
-#2440 := [nnf-neg #2437]: #2439
-#2431 := (not #1616)
-#2432 := (~ #2431 #2430)
-#2427 := (not #1613)
-#2428 := (~ #2427 #2426)
-#2423 := (not #1610)
-#2424 := (~ #2423 #2422)
-#2419 := (not #1607)
-#2420 := (~ #2419 #2418)
-#2415 := (not #1604)
-#2416 := (~ #2415 #2414)
-#2411 := (not #1601)
-#2412 := (~ #2411 #2410)
-#2407 := (not #1598)
-#2408 := (~ #2407 #2406)
-#2403 := (not #1595)
-#2404 := (~ #2403 #2402)
-#2399 := (not #1592)
-#2400 := (~ #2399 #2398)
-#2395 := (not #1589)
-#2396 := (~ #2395 #2394)
-#2391 := (not #1586)
-#2392 := (~ #2391 #2390)
-#2387 := (not #1583)
-#2388 := (~ #2387 #2386)
-#2368 := (not #1580)
-#2384 := (~ #2368 #2381)
-#2358 := (exists (vars (?v1 S3)) #2357)
-#2366 := (or #2365 #2358)
-#2367 := (not #2366)
-#2382 := (~ #2367 #2381)
-#2378 := (not #2358)
-#2379 := (~ #2378 #2377)
-#2375 := (~ #2374 #2374)
-#2376 := [refl]: #2375
-#2380 := [nnf-neg #2376]: #2379
-#2372 := (~ #2371 #2371)
-#2373 := [refl]: #2372
-#2383 := [nnf-neg #2373 #2380]: #2382
-#2369 := (~ #2368 #2367)
-#2370 := [sk]: #2369
-#2385 := [trans #2370 #2383]: #2384
-#2344 := (not #1543)
-#2345 := (~ #2344 #1540)
-#2342 := (~ #1540 #1540)
-#2340 := (~ #1537 #1537)
-#2341 := [refl]: #2340
-#2343 := [nnf-pos #2341]: #2342
-#2346 := [nnf-neg #2343]: #2345
-#2389 := [nnf-neg #2346 #2385]: #2388
-#2336 := (~ #1543 #2335)
-#2337 := [sk]: #2336
-#2393 := [nnf-neg #2337 #2389]: #2392
-#2313 := (not #1519)
-#2314 := (~ #2313 #1516)
-#2311 := (~ #1516 #1516)
-#2309 := (~ #1511 #1511)
-#2310 := [refl]: #2309
-#2312 := [nnf-pos #2310]: #2311
-#2315 := [nnf-neg #2312]: #2314
-#2397 := [nnf-neg #2315 #2393]: #2396
-#2305 := (~ #1519 #2304)
-#2306 := [sk]: #2305
-#2401 := [nnf-neg #2306 #2397]: #2400
-#2286 := (not #1500)
-#2287 := (~ #2286 #1497)
-#2284 := (~ #1497 #1497)
-#2282 := (~ #1494 #1494)
-#2283 := [refl]: #2282
-#2285 := [nnf-pos #2283]: #2284
-#2288 := [nnf-neg #2285]: #2287
-#2405 := [nnf-neg #2288 #2401]: #2404
-#2278 := (~ #1500 #2277)
-#2279 := [sk]: #2278
-#2409 := [nnf-neg #2279 #2405]: #2408
-#2272 := (~ #2271 #2271)
-#2273 := [refl]: #2272
-#2413 := [nnf-neg #2273 #2409]: #2412
-#2269 := (~ #1491 #1491)
-#2270 := [refl]: #2269
-#2417 := [nnf-neg #2270 #2413]: #2416
-#2266 := (not #954)
-#2267 := (~ #2266 #820)
-#2264 := (~ #820 #820)
-#2262 := (~ #815 #815)
-#2263 := [refl]: #2262
-#2265 := [nnf-pos #2263]: #2264
-#2268 := [nnf-neg #2265]: #2267
-#2421 := [nnf-neg #2268 #2417]: #2420
-#2258 := (~ #954 #2257)
-#2259 := [sk]: #2258
-#2425 := [nnf-neg #2259 #2421]: #2424
-#2246 := (not #1486)
-#2247 := (~ #2246 #1483)
-#2244 := (~ #1483 #1483)
-#2242 := (~ #1478 #1478)
-#2243 := [refl]: #2242
-#2245 := [nnf-pos #2243]: #2244
-#2248 := [nnf-neg #2245]: #2247
-#2429 := [nnf-neg #2248 #2425]: #2428
-#2238 := (~ #1486 #2237)
-#2239 := [sk]: #2238
-#2433 := [nnf-neg #2239 #2429]: #2432
-#2228 := (not #1475)
-#2229 := (~ #2228 #1472)
-#2226 := (~ #1472 #1472)
-#2224 := (~ #1467 #1467)
-#2225 := [refl]: #2224
-#2227 := [nnf-pos #2225]: #2226
-#2230 := [nnf-neg #2227]: #2229
-#2221 := (not #1666)
-#2222 := (~ #2221 #2216)
-#2217 := (~ #1425 #2216)
-#2218 := [sk]: #2217
-#2223 := [nnf-neg #2218]: #2222
-#2205 := (~ #2204 #2204)
-#2206 := [refl]: #2205
-#2202 := (~ #758 #758)
-#2203 := [refl]: #2202
-#2453 := [nnf-neg #2203 #2206 #2223 #2230 #2433 #2440 #2447 #2449]: #2452
-#2199 := (not #1443)
-#2200 := (~ #2199 #2198)
-#2196 := (~ #1666 #2195)
-#2193 := (~ #2192 #2192)
-#2194 := [refl]: #2193
-#2197 := [nnf-neg #2194]: #2196
-#2189 := (not #1414)
-#2190 := (~ #2189 #2188)
-#2185 := (not #1411)
-#2186 := (~ #2185 #2184)
-#2181 := (not #1408)
-#2182 := (~ #2181 #2180)
-#2177 := (not #1403)
-#2178 := (~ #2177 #2176)
-#2173 := (not #1395)
-#2174 := (~ #2173 #1392)
-#2171 := (~ #1392 #1392)
-#2169 := (~ #1389 #1389)
-#2170 := [refl]: #2169
-#2172 := [nnf-pos #2170]: #2171
-#2175 := [nnf-neg #2172]: #2174
-#2167 := (~ #2166 #2166)
-#2168 := [refl]: #2167
-#2179 := [nnf-neg #2168 #2175]: #2178
-#2162 := (~ #1395 #2161)
-#2163 := [sk]: #2162
-#2183 := [nnf-neg #2163 #2179]: #2182
-#2137 := (not #1377)
-#2138 := (~ #2137 #2134)
-#2135 := (~ #1374 #2134)
-#2132 := (~ #1371 #2131)
-#2127 := (~ #1368 #2126)
-#2128 := [sk]: #2127
-#2115 := (~ #1352 #1352)
-#2116 := [refl]: #2115
-#2133 := [monotonicity #2116 #2128]: #2132
-#2136 := [nnf-pos #2133]: #2135
-#2139 := [nnf-neg #2136]: #2138
-#2187 := [nnf-neg #2139 #2183]: #2186
-#2113 := (~ #1377 #2110)
-#2088 := (exists (vars (?v1 S3)) #2087)
-#2096 := (or #2095 #2088)
-#2097 := (not #2096)
-#2111 := (~ #2097 #2110)
-#2107 := (not #2088)
-#2108 := (~ #2107 #2106)
-#2104 := (~ #2103 #2103)
-#2105 := [refl]: #2104
-#2109 := [nnf-neg #2105]: #2108
-#2101 := (~ #2100 #2100)
-#2102 := [refl]: #2101
-#2112 := [nnf-neg #2102 #2109]: #2111
-#2098 := (~ #1377 #2097)
-#2099 := [sk]: #2098
-#2114 := [trans #2099 #2112]: #2113
-#2191 := [nnf-neg #2114 #2187]: #2190
-#2075 := (~ #2074 #2074)
-#2076 := [refl]: #2075
-#2072 := (~ #2071 #2071)
-#2073 := [refl]: #2072
-#2069 := (~ #2068 #2068)
-#2070 := [refl]: #2069
-#2066 := (~ #2065 #2065)
-#2067 := [refl]: #2066
-#2201 := [nnf-neg #2067 #2070 #2073 #2076 #2191 #2197]: #2200
-#2457 := [nnf-neg #2201 #2453]: #2456
-#2062 := (not #1340)
-#2063 := (~ #2062 #2059)
-#2060 := (~ #1337 #2059)
-#2057 := (~ #1334 #2056)
-#2052 := (~ #1331 #2051)
-#2053 := [sk]: #2052
-#2038 := (~ #1307 #1307)
-#2039 := [refl]: #2038
-#2058 := [monotonicity #2039 #2053]: #2057
-#2061 := [nnf-pos #2058]: #2060
-#2064 := [nnf-neg #2061]: #2063
-#2035 := (not #1751)
-#2036 := (~ #2035 #2032)
-#2033 := (~ #1295 #2032)
-#2030 := (~ #1292 #2029)
-#2025 := (~ #1289 #2024)
-#2026 := [sk]: #2025
-#2010 := (~ #1269 #1269)
-#2011 := [refl]: #2010
-#2031 := [monotonicity #2011 #2026]: #2030
-#2034 := [nnf-pos #2031]: #2033
-#2037 := [nnf-neg #2034]: #2036
-#2008 := (~ #2007 #2007)
-#2009 := [refl]: #2008
-#2482 := [nnf-neg #2009 #2037 #2064 #2457 #2464 #2471 #2478]: #2481
-#2005 := (~ #1751 #2002)
-#1980 := (exists (vars (?v1 S3)) #1979)
-#1988 := (or #1987 #1980)
-#1989 := (not #1988)
-#2003 := (~ #1989 #2002)
-#1999 := (not #1980)
-#2000 := (~ #1999 #1998)
-#1996 := (~ #1995 #1995)
-#1997 := [refl]: #1996
-#2001 := [nnf-neg #1997]: #2000
-#1993 := (~ #1992 #1992)
-#1994 := [refl]: #1993
-#2004 := [nnf-neg #1994 #2001]: #2003
-#1990 := (~ #1751 #1989)
-#1991 := [sk]: #1990
-#2006 := [trans #1991 #2004]: #2005
-#2486 := [nnf-neg #2006 #2482]: #2485
-#1965 := (not #1257)
-#1966 := (~ #1965 #1254)
-#1963 := (~ #1254 #1254)
-#1961 := (~ #1251 #1251)
-#1962 := [refl]: #1961
-#1964 := [nnf-pos #1962]: #1963
-#1967 := [nnf-neg #1964]: #1966
-#2490 := [nnf-neg #1967 #2486]: #2489
-#1957 := (~ #1257 #1956)
-#1958 := [sk]: #1957
-#2494 := [nnf-neg #1958 #2490]: #2493
-#1934 := (not #1226)
-#1935 := (~ #1934 #1223)
-#1932 := (~ #1223 #1223)
-#1930 := (~ #1218 #1218)
-#1931 := [refl]: #1930
-#1933 := [nnf-pos #1931]: #1932
-#1936 := [nnf-neg #1933]: #1935
-#2498 := [nnf-neg #1936 #2494]: #2497
-#1926 := (~ #1226 #1925)
-#1927 := [sk]: #1926
-#2502 := [nnf-neg #1927 #2498]: #2501
-#1907 := (not #1206)
-#1908 := (~ #1907 #1203)
-#1905 := (~ #1203 #1203)
-#1903 := (~ #1202 #1202)
-#1904 := [refl]: #1903
-#1906 := [nnf-pos #1904]: #1905
-#1909 := [nnf-neg #1906]: #1908
-#2506 := [nnf-neg #1909 #2502]: #2505
-#1899 := (~ #1206 #1898)
-#1900 := [sk]: #1899
-#2510 := [nnf-neg #1900 #2506]: #2509
-#1862 := (~ #1861 #1861)
-#1894 := [refl]: #1862
-#2514 := [nnf-neg #1894 #2510]: #2513
-#1892 := (~ #1197 #1197)
-#1893 := [refl]: #1892
-#2517 := [nnf-neg #1893 #2514]: #2516
-#1838 := [not-or-elim #1834]: #1837
-#2518 := [mp~ #1838 #2517]: #2515
-#2519 := [mp #2518 #3056]: #3054
-#3698 := [mp #2519 #3697]: #3695
-#4605 := [mp #3698 #4604]: #4602
-#6497 := [unit-resolution #4605 #5321]: #4599
-#3944 := (or #4596 #4590)
-#3945 := [def-axiom]: #3944
-#6498 := [unit-resolution #3945 #6497]: #4590
-#6499 := (or #4593 #4587)
-#5108 := [hypothesis]: #1898
-#5107 := (<= #1896 0::Int)
-#4722 := (or #5107 #1897)
-#5140 := [th-lemma arith farkas 1 1]: #4722
-#5141 := [unit-resolution #5140 #5108]: #5107
-#5100 := (not #5107)
-#5115 := (or #5100 #1897)
-#356 := (<= f9 0::Int)
-#357 := (not #356)
-#47 := (< 0::Int f9)
-#358 := (iff #47 #357)
-#359 := [rewrite]: #358
-#352 := [asserted]: #47
-#360 := [mp #352 #359]: #357
-#4719 := (* -1::Int #1896)
-#4720 := (+ f9 #4719)
-#4721 := (<= #4720 0::Int)
-#3934 := (= f9 #1896)
-#3913 := (= f11 ?v0!0)
-#4912 := (not #3913)
-#4909 := (= #1896 0::Int)
-#5109 := (not #4909)
-#5110 := (or #5109 #1897)
-#5111 := [th-lemma arith triangle-eq]: #5110
-#5091 := [unit-resolution #5111 #5108]: #5109
-#4918 := (or #4785 #4912 #4909)
-#3933 := (= ?v0!0 f11)
-#4910 := (not #3933)
-#4911 := (or #4910 #4909)
-#4649 := (or #4785 #4911)
-#5104 := (iff #4649 #4918)
-#4716 := (or #4912 #4909)
-#4935 := (or #4785 #4716)
-#4981 := (iff #4935 #4918)
-#5103 := [rewrite]: #4981
-#4979 := (iff #4649 #4935)
-#4717 := (iff #4911 #4716)
-#4915 := (iff #4910 #4912)
-#3915 := (iff #3933 #3913)
-#3916 := [rewrite]: #3915
-#4916 := [monotonicity #3916]: #4915
-#4784 := [monotonicity #4916]: #4717
-#4980 := [monotonicity #4784]: #4979
-#5105 := [trans #4980 #5103]: #5104
-#4932 := [quant-inst #1895]: #4649
-#5106 := [mp #4932 #5105]: #4918
-#5092 := [unit-resolution #5106 #4611 #5091]: #4912
-#3928 := (or #3913 #3934)
-#4220 := (forall (vars (?v0 S3)) (:pat #4219) #447)
-#4223 := (iff #452 #4220)
-#4221 := (iff #447 #447)
-#4222 := [refl]: #4221
-#4224 := [quant-intro #4222]: #4223
-#1857 := (~ #452 #452)
-#1886 := (~ #447 #447)
-#1887 := [refl]: #1886
-#1858 := [nnf-pos #1887]: #1857
-#1835 := [not-or-elim #1834]: #452
-#1888 := [mp~ #1835 #1858]: #452
-#4225 := [mp #1888 #4224]: #4220
-#3924 := (not #4220)
-#3917 := (or #3924 #3913 #3934)
-#3923 := (or #3933 #3934)
-#3925 := (or #3924 #3923)
-#4663 := (iff #3925 #3917)
-#3910 := (or #3924 #3928)
-#4647 := (iff #3910 #3917)
-#4662 := [rewrite]: #4647
-#4645 := (iff #3925 #3910)
-#3919 := (iff #3923 #3928)
-#3920 := [monotonicity #3916]: #3919
-#4646 := [monotonicity #3920]: #4645
-#4644 := [trans #4646 #4662]: #4663
-#3908 := [quant-inst #1895]: #3925
-#4718 := [mp #3908 #4644]: #3917
-#5093 := [unit-resolution #4718 #4225]: #3928
-#5094 := [unit-resolution #5093 #5092]: #3934
-#5095 := (not #3934)
-#5090 := (or #5095 #4721)
-#5096 := [th-lemma arith triangle-eq]: #5090
-#5097 := [unit-resolution #5096 #5094]: #4721
-#5098 := [hypothesis]: #5107
-#5099 := [th-lemma arith farkas 1 -1 1 #5098 #5097 #360]: false
-#5116 := [lemma #5099]: #5115
-#5142 := [unit-resolution #5116 #5141 #5108]: false
-#5143 := [lemma #5142]: #1897
-#3939 := (or #4593 #1898 #4587)
-#3940 := [def-axiom]: #3939
-#6500 := [unit-resolution #3940 #5143]: #6499
-#6501 := [unit-resolution #6500 #6498]: #4587
-#3963 := (or #4584 #4578)
-#3964 := [def-axiom]: #3963
-#6502 := [unit-resolution #3964 #6501]: #4578
-#5818 := [hypothesis]: #1918
-#5331 := (or #5530 #2308)
-#5336 := [quant-inst #1911]: #5331
-#5819 := [unit-resolution #5336 #4232 #5818]: false
-#5820 := [lemma #5819]: #2308
-#3756 := (or #2338 #1918)
-#3843 := [def-axiom]: #3756
-#6503 := [unit-resolution #3843 #5820]: #2338
-#3957 := (or #4581 #2130 #4575)
-#3959 := [def-axiom]: #3957
-#6504 := [unit-resolution #3959 #6503 #6502]: #4575
-#3984 := (or #4572 #4566)
-#3985 := [def-axiom]: #3984
-#6505 := [unit-resolution #3985 #6504]: #4566
-#3980 := (or #4569 #3099 #4563)
-#3981 := [def-axiom]: #3980
-#6506 := [unit-resolution #3981 #6505 #6496]: #4563
-#3994 := (or #4560 #4554)
-#4015 := [def-axiom]: #3994
-#6507 := [unit-resolution #4015 #6506]: #4554
-#5791 := (= f9 #1971)
-#5855 := (not #5791)
-#5853 := [hypothesis]: #4271
-#4160 := (or #4268 #1983)
-#3834 := [def-axiom]: #4160
-#5854 := [unit-resolution #3834 #5853]: #1983
-#5856 := (or #5855 #1982)
-#5857 := [th-lemma arith triangle-eq]: #5856
-#5858 := [unit-resolution #5857 #5854]: #5855
-#3835 := (or #4268 #2570)
-#4167 := [def-axiom]: #3835
-#5859 := [unit-resolution #4167 #5853]: #2570
-#5811 := (or #3924 #2567 #5791)
-#5792 := (or #1984 #5791)
-#5806 := (or #3924 #5792)
-#5670 := (iff #5806 #5811)
-#5808 := (or #2567 #5791)
-#5813 := (or #3924 #5808)
-#5816 := (iff #5813 #5811)
-#5669 := [rewrite]: #5816
-#5814 := (iff #5806 #5813)
-#5809 := (iff #5792 #5808)
-#5810 := [monotonicity #2569]: #5809
-#5815 := [monotonicity #5810]: #5814
-#5671 := [trans #5815 #5669]: #5670
-#5812 := [quant-inst #1968]: #5806
-#5476 := [mp #5812 #5671]: #5811
-#5860 := [unit-resolution #5476 #4225 #5859 #5858]: false
-#5861 := [lemma #5860]: #4268
-#4002 := (or #4557 #4271 #4551)
-#4003 := [def-axiom]: #4002
-#6508 := [unit-resolution #4003 #5861 #6507]: #4551
-#4035 := (or #4548 #4275)
-#4031 := [def-axiom]: #4035
-#7122 := [unit-resolution #4031 #6508]: #4275
-#9554 := (or #4280 #7758)
-#9555 := [quant-inst #2274]: #9554
-#9581 := [unit-resolution #9555 #7122]: #7758
-#7571 := (* -1::Int #7537)
-#7572 := (+ #2275 #7571)
-#9582 := (>= #7572 0::Int)
-#7540 := (= #2275 #7537)
-#10088 := [hypothesis]: #2277
-#11986 := (or #7540 #2276 #6074)
-#9989 := (f6 #7212 ?v0!15)
-#9990 := (f10 #9989)
-#9991 := (* -1::Int #9990)
-#7587 := (f6 f23 ?v0!15)
-#7588 := (f10 #7587)
-#10059 := (+ #7588 #9991)
-#10063 := (>= #10059 0::Int)
-#10058 := (= #7588 #9990)
-#10066 := (= #9990 #7588)
-#10064 := (= #9989 #7587)
-#10065 := [monotonicity #7791]: #10064
-#10067 := [monotonicity #10065]: #10066
-#10068 := [symm #10067]: #10058
-#10069 := (not #10058)
-#10070 := (or #10069 #10063)
-#10071 := [th-lemma arith triangle-eq]: #10070
-#10072 := [unit-resolution #10071 #10068]: #10063
-#7969 := (f6 #6070 #7212)
-#8218 := (f7 #7969)
-#9082 := (f14 f15 #8218)
-#9083 := (* -1::Int #9082)
-#9456 := (+ #6071 #9083)
-#9458 := (>= #9456 0::Int)
-#9862 := (= #6071 #9082)
-#8219 := (= #6070 #8218)
-#8390 := (or #6830 #8219)
-#8391 := [quant-inst #6070 #7212]: #8390
-#9281 := [unit-resolution #8391 #4206]: #8219
-#11948 := [monotonicity #9281]: #9862
-#11946 := (not #9862)
-#11949 := (or #11946 #9458)
-#11950 := [th-lemma arith triangle-eq]: #11949
-#11951 := [unit-resolution #11950 #11948]: #9458
-#10867 := (+ #100 #9083)
-#10879 := (<= #10867 0::Int)
-#10876 := (= #100 #9082)
-#11957 := (= #9082 #100)
-#10698 := (= #8218 f11)
-#7318 := (= #6070 f11)
-#7320 := (= f11 #6070)
-#7299 := (?v1!7 #6070)
-#7311 := (f3 f16 #7299)
-#7312 := (= f1 #7311)
-#7313 := (not #7312)
-#7304 := (f6 #7299 #6070)
-#7305 := (f10 #7304)
-#7306 := (* -1::Int #7305)
-#7300 := (f14 f15 #7299)
-#7301 := (* -1::Int #7300)
-#7307 := (+ #7301 #7306)
-#7308 := (+ #6071 #7307)
-#7309 := (= #7308 0::Int)
-#7310 := (not #7309)
-#7302 := (+ #6071 #7301)
-#7303 := (<= #7302 0::Int)
-#7323 := (or #7303 #7310 #7313)
-#9608 := (or #2276 #6074 #7303)
-#8252 := (not #7303)
-#10073 := [hypothesis]: #8252
-#10111 := (or #7540 #2276 #6074 #7303)
-#9126 := (>= #7300 0::Int)
-#9129 := (or #4280 #9126)
-#9300 := [quant-inst #7299]: #9129
-#10074 := [unit-resolution #9300 #7122]: #9126
-#7562 := (* -1::Int #2275)
-#7613 := (+ #7562 #7588)
-#7614 := (+ #175 #7613)
-#9498 := (<= #7614 0::Int)
-#7617 := (= #7614 0::Int)
-#7592 := (* -1::Int #7588)
-#7596 := (+ f9 #7592)
-#7597 := (<= #7596 0::Int)
-#9511 := (not #7597)
-#7606 := (+ #7571 #7588)
-#7607 := (+ #175 #7606)
-#7608 := (>= #7607 0::Int)
-#7639 := (or #7597 #7608)
-#7642 := (not #7639)
-#10076 := (not #7540)
-#10077 := [hypothesis]: #10076
-#7645 := (or #7540 #7642)
-#5789 := (or #4548 #4539)
-#4723 := (?v1!7 ?v0!8)
-#4999 := (f14 f20 #4723)
-#5012 := (* -1::Int #4999)
-#4724 := (f14 f15 #4723)
-#5232 := (+ #4724 #5012)
-#5237 := (>= #5232 0::Int)
-#5231 := (= #4724 #4999)
-#5721 := (= #4999 #4724)
-#5716 := [hypothesis]: #4536
-#5717 := [hypothesis]: #4551
-#4024 := (or #4548 #4542)
-#3992 := [def-axiom]: #4024
-#5718 := [unit-resolution #3992 #5717]: #4542
-#4029 := (or #4545 #4384 #4539)
-#4030 := [def-axiom]: #4029
-#5719 := [unit-resolution #4030 #5718 #5716]: #4384
-#4135 := (or #4381 #625)
-#4136 := [def-axiom]: #4135
-#5720 := [unit-resolution #4136 #5719]: #625
-#5715 := [symm #5720]: #139
-#5722 := [monotonicity #5715]: #5721
-#5723 := [symm #5722]: #5231
-#5724 := (not #5231)
-#5725 := (or #5724 #5237)
-#5738 := [th-lemma arith triangle-eq]: #5725
-#5739 := [unit-resolution #5738 #5723]: #5237
-#4706 := (* -1::Int #4724)
-#4656 := (f14 f15 ?v0!8)
-#4707 := (+ #4656 #4706)
-#4708 := (<= #4707 0::Int)
-#4889 := (not #4708)
-#4715 := (f3 f16 #4723)
-#4786 := (= f1 #4715)
-#4787 := (not #4786)
-#4709 := (f6 #4723 ?v0!8)
-#4710 := (f10 #4709)
-#4705 := (* -1::Int #4710)
-#4791 := (+ #4705 #4706)
-#4792 := (+ #4656 #4791)
-#4774 := (= #4792 0::Int)
-#4777 := (not #4774)
-#4782 := (or #4708 #4777 #4787)
-#4856 := (not #4782)
-#4657 := (* -1::Int #4656)
-#4658 := (+ f9 #4657)
-#4638 := (<= #4658 0::Int)
-#4994 := (not #4638)
-#4137 := (or #4381 #4375)
-#4134 := [def-axiom]: #4137
-#5740 := [unit-resolution #4134 #5719]: #4375
-#4033 := (or #4548 #101)
-#4034 := [def-axiom]: #4033
-#5741 := [unit-resolution #4034 #5717]: #101
-#5742 := (= #158 #100)
-#5737 := [monotonicity #5715]: #5742
-#5743 := [trans #5737 #5741]: #159
-#4147 := (or #4357 #2166)
-#3810 := [def-axiom]: #4147
-#5744 := [unit-resolution #3810 #5743]: #4357
-#4036 := (or #4548 #4283)
-#4016 := [def-axiom]: #4036
-#5745 := [unit-resolution #4016 #5717]: #4283
-#3851 := (or #4381 #4317)
-#4133 := [def-axiom]: #3851
-#5746 := [unit-resolution #4133 #5719]: #4317
-#4977 := (or #3362 #4322 #4288 #716)
-#4950 := [hypothesis]: #3367
-#4150 := (or #3362 #2153)
-#4151 := [def-axiom]: #4150
-#4951 := [unit-resolution #4151 #4950]: #2153
-#4725 := (f14 f15 ?v1!10)
-#4726 := (* -1::Int #4725)
-#4727 := (+ f9 #4726)
-#4728 := (<= #4727 0::Int)
-#4729 := (f3 f16 ?v1!10)
-#4730 := (= f1 #4729)
-#4801 := (not #4730)
-#3838 := (f14 f15 ?v0!11)
-#3839 := (* -1::Int #3838)
-#4803 := (+ #3839 #4725)
-#4804 := (+ #2147 #4803)
-#4807 := (>= #4804 0::Int)
-#4960 := (not #4807)
-#4934 := (+ #2144 #4726)
-#4936 := (>= #4934 0::Int)
-#4933 := (= #2144 #4725)
-#4938 := (= #4725 #2144)
-#4937 := [hypothesis]: #625
-#4939 := [monotonicity #4937]: #4938
-#4940 := [symm #4939]: #4933
-#4941 := (not #4933)
-#4942 := (or #4941 #4936)
-#4943 := [th-lemma arith triangle-eq]: #4942
-#4944 := [unit-resolution #4943 #4940]: #4936
-#4148 := (not #2808)
-#4154 := (or #3362 #4148)
-#3792 := [def-axiom]: #4154
-#4945 := [unit-resolution #3792 #4950]: #4148
-#4927 := (+ #2142 #3839)
-#4931 := (<= #4927 0::Int)
-#4926 := (= #2142 #3838)
-#4948 := (= #3838 #2142)
-#4949 := [monotonicity #4937]: #4948
-#4952 := [symm #4949]: #4926
-#4953 := (not #4926)
-#4954 := (or #4953 #4931)
-#4965 := [th-lemma arith triangle-eq]: #4954
-#4966 := [unit-resolution #4965 #4952]: #4931
-#4962 := (not #4936)
-#4961 := (not #4931)
-#4963 := (or #4960 #4961 #2808 #4962)
-#4955 := [hypothesis]: #4936
-#4956 := [hypothesis]: #4148
-#4957 := [hypothesis]: #4931
-#4958 := [hypothesis]: #4807
-#4959 := [th-lemma arith farkas 1 -1 1 1 #4958 #4957 #4956 #4955]: false
-#4964 := [lemma #4959]: #4963
-#4967 := [unit-resolution #4964 #4966 #4945 #4944]: #4960
-#4970 := (or #4801 #4807)
-#4152 := (or #3362 #2157)
-#4153 := [def-axiom]: #4152
-#4968 := [unit-resolution #4153 #4950]: #2157
-#4969 := [hypothesis]: #4283
-#4818 := (or #4288 #2156 #4801 #4807)
-#4796 := (+ #4725 #3839)
-#4797 := (+ #2147 #4796)
-#4800 := (>= #4797 0::Int)
-#4802 := (or #4801 #2156 #4800)
-#4819 := (or #4288 #4802)
-#4826 := (iff #4819 #4818)
-#4813 := (or #2156 #4801 #4807)
-#4821 := (or #4288 #4813)
-#4824 := (iff #4821 #4818)
-#4825 := [rewrite]: #4824
-#4822 := (iff #4819 #4821)
-#4816 := (iff #4802 #4813)
-#4810 := (or #4801 #2156 #4807)
-#4814 := (iff #4810 #4813)
-#4815 := [rewrite]: #4814
-#4811 := (iff #4802 #4810)
-#4808 := (iff #4800 #4807)
-#4805 := (= #4797 #4804)
-#4806 := [rewrite]: #4805
-#4809 := [monotonicity #4806]: #4808
-#4812 := [monotonicity #4809]: #4811
-#4817 := [trans #4812 #4815]: #4816
-#4823 := [monotonicity #4817]: #4822
-#4827 := [trans #4823 #4825]: #4826
-#4820 := [quant-inst #2141 #2140]: #4819
-#4828 := [mp #4820 #4827]: #4818
-#4971 := [unit-resolution #4828 #4969 #4968]: #4970
-#4972 := [unit-resolution #4971 #4967]: #4801
-#4732 := (or #4728 #4730)
-#4973 := [hypothesis]: #4317
-#4735 := (or #4322 #4728 #4730)
-#4731 := (or #4730 #4728)
-#4736 := (or #4322 #4731)
-#4743 := (iff #4736 #4735)
-#4738 := (or #4322 #4732)
-#4741 := (iff #4738 #4735)
-#4742 := [rewrite]: #4741
-#4739 := (iff #4736 #4738)
-#4733 := (iff #4731 #4732)
-#4734 := [rewrite]: #4733
-#4740 := [monotonicity #4734]: #4739
-#4744 := [trans #4740 #4742]: #4743
-#4737 := [quant-inst #2140]: #4736
-#4745 := [mp #4737 #4744]: #4735
-#4974 := [unit-resolution #4745 #4973]: #4732
-#4975 := [unit-resolution #4974 #4972]: #4728
-#4976 := [th-lemma arith farkas 1 -1 1 #4944 #4975 #4951]: false
-#4978 := [lemma #4976]: #4977
-#5747 := [unit-resolution #4978 #5746 #5745 #5720]: #3362
-#4159 := (or #4366 #4360 #3367)
-#4145 := [def-axiom]: #4159
-#5748 := [unit-resolution #4145 #5747 #5744]: #4366
-#3869 := (or #4369 #4363)
-#3870 := [def-axiom]: #3869
-#5749 := [unit-resolution #3870 #5748]: #4369
-#4139 := (or #4378 #4338 #4372)
-#4143 := [def-axiom]: #4139
-#5750 := [unit-resolution #4143 #5749 #5740]: #4338
-#4171 := (or #4335 #2091)
-#4161 := [def-axiom]: #4171
-#5751 := [unit-resolution #4161 #5750]: #2091
-#4987 := (+ #2078 #4657)
-#4989 := (>= #4987 0::Int)
-#4986 := (= #2078 #4656)
-#5414 := (= #4656 #2078)
-#5752 := [monotonicity #5720]: #5414
-#5753 := [symm #5752]: #4986
-#5417 := (not #4986)
-#5422 := (or #5417 #4989)
-#5423 := [th-lemma arith triangle-eq]: #5422
-#5754 := [unit-resolution #5423 #5753]: #4989
-#4995 := (not #4989)
-#4996 := (or #4994 #4995 #2090)
-#4990 := [hypothesis]: #2091
-#4991 := [hypothesis]: #4638
-#4992 := [hypothesis]: #4989
-#4993 := [th-lemma arith farkas 1 -1 1 #4992 #4991 #4990]: false
-#4997 := [lemma #4993]: #4996
-#5755 := [unit-resolution #4997 #5754 #5751]: #4994
-#5765 := (or #4638 #4856)
-#3821 := (or #4335 #2708)
-#3826 := [def-axiom]: #3821
-#5763 := [unit-resolution #3826 #5750]: #2708
-#4023 := (or #4548 #4308)
-#4018 := [def-axiom]: #4023
-#5764 := [unit-resolution #4018 #5717]: #4308
-#4861 := (or #4313 #2705 #4638 #4856)
-#4711 := (+ #4706 #4705)
-#4712 := (+ #4656 #4711)
-#4713 := (= #4712 0::Int)
-#4714 := (not #4713)
-#4788 := (or #4787 #4714 #4708)
-#4789 := (not #4788)
-#4790 := (or #2092 #4638 #4789)
-#4862 := (or #4313 #4790)
-#4885 := (iff #4862 #4861)
-#4859 := (or #2705 #4638 #4856)
-#4864 := (or #4313 #4859)
-#4883 := (iff #4864 #4861)
-#4884 := [rewrite]: #4883
-#4880 := (iff #4862 #4864)
-#4854 := (iff #4790 #4859)
-#4857 := (iff #4789 #4856)
-#4799 := (iff #4788 #4782)
-#4779 := (or #4787 #4777 #4708)
-#4783 := (iff #4779 #4782)
-#4798 := [rewrite]: #4783
-#4780 := (iff #4788 #4779)
-#4778 := (iff #4714 #4777)
-#4775 := (iff #4713 #4774)
-#4793 := (= #4712 #4792)
-#4794 := [rewrite]: #4793
-#4776 := [monotonicity #4794]: #4775
-#4773 := [monotonicity #4776]: #4778
-#4781 := [monotonicity #4773]: #4780
-#4855 := [trans #4781 #4798]: #4799
-#4858 := [monotonicity #4855]: #4857
-#4860 := [monotonicity #2707 #4858]: #4854
-#4882 := [monotonicity #4860]: #4880
-#4886 := [trans #4882 #4884]: #4885
-#4863 := [quant-inst #2077]: #4862
-#4881 := [mp #4863 #4886]: #4861
-#5766 := [unit-resolution #4881 #5764 #5763]: #5765
-#5767 := [unit-resolution #5766 #5755]: #4856
-#4890 := (or #4782 #4889)
-#4891 := [def-axiom]: #4890
-#5768 := [unit-resolution #4891 #5767]: #4889
-#5013 := (+ #2078 #5012)
-#5014 := (<= #5013 0::Int)
-#5026 := (+ #4705 #5012)
-#5027 := (+ #2078 #5026)
-#5028 := (= #5027 0::Int)
-#5050 := (<= #5027 0::Int)
-#5236 := (<= #5232 0::Int)
-#5769 := (or #5724 #5236)
-#5770 := [th-lemma arith triangle-eq]: #5769
-#5771 := [unit-resolution #5770 #5723]: #5236
-#4887 := (<= #4792 0::Int)
-#4906 := (or #4782 #4774)
-#4908 := [def-axiom]: #4906
-#5772 := [unit-resolution #4908 #5767]: #4774
-#5773 := (or #4777 #4887)
-#5774 := [th-lemma arith triangle-eq]: #5773
-#5775 := [unit-resolution #5774 #5772]: #4887
-#4988 := (<= #4987 0::Int)
-#5418 := (or #5417 #4988)
-#5419 := [th-lemma arith triangle-eq]: #5418
-#5776 := [unit-resolution #5419 #5753]: #4988
-#5360 := (not #5236)
-#5359 := (not #4887)
-#5358 := (not #4988)
-#5361 := (or #5050 #5358 #5359 #5360)
-#5352 := [hypothesis]: #5236
-#5353 := [hypothesis]: #4887
-#5354 := [hypothesis]: #4988
-#5355 := (not #5050)
-#5356 := [hypothesis]: #5355
-#5357 := [th-lemma arith farkas -1 1 1 1 #5356 #5354 #5353 #5352]: false
-#5362 := [lemma #5357]: #5361
-#5777 := [unit-resolution #5362 #5776 #5775 #5771]: #5050
-#5051 := (>= #5027 0::Int)
-#4888 := (>= #4792 0::Int)
-#5778 := (or #4777 #4888)
-#5779 := [th-lemma arith triangle-eq]: #5778
-#5780 := [unit-resolution #5779 #5772]: #4888
-#5760 := (not #5237)
-#5400 := (not #4888)
-#5761 := (or #5051 #4995 #5400 #5760)
-#5756 := [hypothesis]: #5237
-#5396 := [hypothesis]: #4888
-#5757 := (not #5051)
-#5758 := [hypothesis]: #5757
-#5759 := [th-lemma arith farkas -1 1 1 1 #5758 #4992 #5396 #5756]: false
-#5762 := [lemma #5759]: #5761
-#5781 := [unit-resolution #5762 #5754 #5780 #5739]: #5051
-#5782 := (or #5028 #5355 #5757)
-#5783 := [th-lemma arith triangle-eq]: #5782
-#5784 := [unit-resolution #5783 #5781 #5777]: #5028
-#5033 := (not #5028)
-#5036 := (or #5014 #5033)
-#4162 := (or #4335 #4327)
-#3822 := [def-axiom]: #4162
-#5785 := [unit-resolution #3822 #5750]: #4327
-#5039 := (or #4332 #5014 #5033)
-#4998 := (+ #2079 #4710)
-#5000 := (+ #4999 #4998)
-#5001 := (= #5000 0::Int)
-#5002 := (not #5001)
-#5003 := (+ #4999 #2079)
-#5004 := (>= #5003 0::Int)
-#5005 := (or #5004 #5002)
-#5040 := (or #4332 #5005)
-#5047 := (iff #5040 #5039)
-#5042 := (or #4332 #5036)
-#5045 := (iff #5042 #5039)
-#5046 := [rewrite]: #5045
-#5043 := (iff #5040 #5042)
-#5037 := (iff #5005 #5036)
-#5034 := (iff #5002 #5033)
-#5031 := (iff #5001 #5028)
-#5019 := (+ #4710 #4999)
-#5020 := (+ #2079 #5019)
-#5023 := (= #5020 0::Int)
-#5029 := (iff #5023 #5028)
-#5030 := [rewrite]: #5029
-#5024 := (iff #5001 #5023)
-#5021 := (= #5000 #5020)
-#5022 := [rewrite]: #5021
-#5025 := [monotonicity #5022]: #5024
-#5032 := [trans #5025 #5030]: #5031
-#5035 := [monotonicity #5032]: #5034
-#5017 := (iff #5004 #5014)
-#5006 := (+ #2079 #4999)
-#5009 := (>= #5006 0::Int)
-#5015 := (iff #5009 #5014)
-#5016 := [rewrite]: #5015
-#5010 := (iff #5004 #5009)
-#5007 := (= #5003 #5006)
-#5008 := [rewrite]: #5007
-#5011 := [monotonicity #5008]: #5010
-#5018 := [trans #5011 #5016]: #5017
-#5038 := [monotonicity #5018 #5035]: #5037
-#5044 := [monotonicity #5038]: #5043
-#5048 := [trans #5044 #5046]: #5047
-#5041 := [quant-inst #4723]: #5040
-#5049 := [mp #5041 #5048]: #5039
-#5786 := [unit-resolution #5049 #5785]: #5036
-#5787 := [unit-resolution #5786 #5784]: #5014
-#5788 := [th-lemma arith farkas 1 -1 1 1 #5754 #5787 #5768 #5739]: false
-#5790 := [lemma #5788]: #5789
-#6509 := [unit-resolution #5790 #6508]: #4539
-#4045 := (or #4536 #4397)
-#4040 := [def-axiom]: #4045
-#6510 := [unit-resolution #4040 #6509]: #4397
-#9500 := (or #4402 #7540 #7642)
-#7593 := (+ #1454 #7592)
-#7594 := (+ #7537 #7593)
-#7595 := (<= #7594 0::Int)
-#7636 := (or #7597 #7595)
-#7637 := (not #7636)
-#7538 := (= #7537 #2275)
-#7638 := (or #7538 #7637)
-#9501 := (or #4402 #7638)
-#9508 := (iff #9501 #9500)
-#9503 := (or #4402 #7645)
-#9506 := (iff #9503 #9500)
-#9507 := [rewrite]: #9506
-#9504 := (iff #9501 #9503)
-#7646 := (iff #7638 #7645)
-#7643 := (iff #7637 #7642)
-#7640 := (iff #7636 #7639)
-#7611 := (iff #7595 #7608)
-#7599 := (+ #7537 #7592)
-#7600 := (+ #1454 #7599)
-#7603 := (<= #7600 0::Int)
-#7609 := (iff #7603 #7608)
-#7610 := [rewrite]: #7609
-#7604 := (iff #7595 #7603)
-#7601 := (= #7594 #7600)
-#7602 := [rewrite]: #7601
-#7605 := [monotonicity #7602]: #7604
-#7612 := [trans #7605 #7610]: #7611
-#7641 := [monotonicity #7612]: #7640
-#7644 := [monotonicity #7641]: #7643
-#7541 := (iff #7538 #7540)
-#7542 := [rewrite]: #7541
-#7647 := [monotonicity #7542 #7644]: #7646
-#9505 := [monotonicity #7647]: #9504
-#9509 := [trans #9505 #9507]: #9508
-#9502 := [quant-inst #2274]: #9501
-#9510 := [mp #9502 #9509]: #9500
-#10078 := [unit-resolution #9510 #6510]: #7645
-#10079 := [unit-resolution #10078 #10077]: #7642
-#9512 := (or #7639 #9511)
-#9513 := [def-axiom]: #9512
-#10080 := [unit-resolution #9513 #10079]: #9511
-#9514 := (not #7608)
-#9515 := (or #7639 #9514)
-#9516 := [def-axiom]: #9515
-#10081 := [unit-resolution #9516 #10079]: #9514
-#7620 := (or #7597 #7608 #7617)
-#4046 := (or #4536 #4405)
-#4019 := [def-axiom]: #4046
-#6514 := [unit-resolution #4019 #6509]: #4405
-#9487 := (or #4410 #7597 #7608 #7617)
-#7589 := (+ #7588 #7562)
-#7590 := (+ #175 #7589)
-#7591 := (= #7590 0::Int)
-#7598 := (or #7597 #7595 #7591)
-#9488 := (or #4410 #7598)
-#9495 := (iff #9488 #9487)
-#9490 := (or #4410 #7620)
-#9493 := (iff #9490 #9487)
-#9494 := [rewrite]: #9493
-#9491 := (iff #9488 #9490)
-#7621 := (iff #7598 #7620)
-#7618 := (iff #7591 #7617)
-#7615 := (= #7590 #7614)
-#7616 := [rewrite]: #7615
-#7619 := [monotonicity #7616]: #7618
-#7622 := [monotonicity #7612 #7619]: #7621
-#9492 := [monotonicity #7622]: #9491
-#9496 := [trans #9492 #9494]: #9495
-#9489 := [quant-inst #2274]: #9488
-#9497 := [mp #9489 #9496]: #9487
-#10082 := [unit-resolution #9497 #6514]: #7620
-#10083 := [unit-resolution #10082 #10081 #10080]: #7617
-#10084 := (not #7617)
-#10085 := (or #10084 #9498)
-#10086 := [th-lemma arith triangle-eq]: #10085
-#10087 := [unit-resolution #10086 #10083]: #9498
-#10051 := (>= #9990 0::Int)
-#10026 := (<= #9990 0::Int)
-#10027 := (not #10026)
-#9950 := (= ?v0!15 #7212)
-#9969 := (not #9950)
-#7669 := (f3 f16 ?v0!15)
-#7670 := (= f1 #7669)
-#5892 := (f3 #774 f23)
-#5893 := (= f1 #5892)
-#9953 := (ite #9950 #5893 #7670)
-#9968 := (not #9953)
-#8443 := (f4 f5 f16 #7212 #5892)
-#9947 := (f3 #8443 ?v0!15)
-#9948 := (= f1 #9947)
-#9956 := (iff #9948 #9953)
-#11 := (:var 1 S1)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#4172 := (pattern #14)
-#18 := (f3 #9 #13)
-#302 := (= f1 #18)
-#299 := (= f1 #11)
-#296 := (= #10 #13)
-#305 := (ite #296 #299 #302)
-#293 := (= f1 #14)
-#308 := (iff #293 #305)
-#4173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4172) #308)
-#311 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #308)
-#4176 := (iff #311 #4173)
-#4174 := (iff #308 #308)
-#4175 := [refl]: #4174
-#4177 := [quant-intro #4175]: #4176
-#1869 := (~ #311 #311)
-#1867 := (~ #308 #308)
-#1868 := [refl]: #1867
-#1870 := [nnf-pos #1868]: #1869
-#19 := (= #18 f1)
-#17 := (= #11 f1)
-#16 := (= #13 #10)
-#20 := (ite #16 #17 #19)
-#15 := (= #14 f1)
-#21 := (iff #15 #20)
-#22 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #21)
-#312 := (iff #22 #311)
-#309 := (iff #21 #308)
-#306 := (iff #20 #305)
-#303 := (iff #19 #302)
-#304 := [rewrite]: #303
-#300 := (iff #17 #299)
-#301 := [rewrite]: #300
-#297 := (iff #16 #296)
-#298 := [rewrite]: #297
-#307 := [monotonicity #298 #301 #304]: #306
-#294 := (iff #15 #293)
-#295 := [rewrite]: #294
-#310 := [monotonicity #295 #307]: #309
-#313 := [quant-intro #310]: #312
-#292 := [asserted]: #22
-#316 := [mp #292 #313]: #311
-#1841 := [mp~ #316 #1870]: #311
-#4178 := [mp #1841 #4177]: #4173
-#6291 := (not #4173)
-#9959 := (or #6291 #9956)
-#9945 := (= #7212 ?v0!15)
-#9946 := (ite #9945 #5893 #7670)
-#9949 := (iff #9948 #9946)
-#9960 := (or #6291 #9949)
-#9962 := (iff #9960 #9959)
-#9964 := (iff #9959 #9959)
-#9965 := [rewrite]: #9964
-#9957 := (iff #9949 #9956)
-#9954 := (iff #9946 #9953)
-#9951 := (iff #9945 #9950)
-#9952 := [rewrite]: #9951
-#9955 := [monotonicity #9952]: #9954
-#9958 := [monotonicity #9955]: #9957
-#9963 := [monotonicity #9958]: #9962
-#9966 := [trans #9963 #9965]: #9962
-#9961 := [quant-inst #105 #7212 #5892 #2274]: #9960
-#9967 := [mp #9961 #9966]: #9959
-#10089 := [unit-resolution #9967 #4178]: #9956
-#9982 := (not #9948)
-#7534 := (f3 f24 ?v0!15)
-#7535 := (= f1 #7534)
-#7536 := (not #7535)
-#10098 := (iff #7536 #9982)
-#10096 := (iff #7535 #9948)
-#10094 := (iff #9948 #7535)
-#10092 := (= #9947 #7534)
-#9286 := (= #8443 f24)
-#7005 := (= #774 f24)
-#4054 := (or #4536 #777)
-#4049 := [def-axiom]: #4054
-#6999 := [unit-resolution #4049 #6509]: #777
-#7006 := [symm #6999]: #7005
-#9284 := (= #8443 #774)
-#7001 := (= #5892 f1)
-#25 := (:var 0 S1)
-#23 := (:var 2 S2)
-#26 := (f4 f5 #23 #24 #25)
-#4179 := (pattern #26)
-#319 := (= f1 #25)
-#27 := (f3 #26 #24)
-#315 := (= f1 #27)
-#322 := (iff #315 #319)
-#4180 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4179) #322)
-#325 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #322)
-#4183 := (iff #325 #4180)
-#4181 := (iff #322 #322)
-#4182 := [refl]: #4181
-#4184 := [quant-intro #4182]: #4183
-#1843 := (~ #325 #325)
-#1842 := (~ #322 #322)
-#1871 := [refl]: #1842
-#1844 := [nnf-pos #1871]: #1843
-#29 := (= #25 f1)
-#28 := (= #27 f1)
-#30 := (iff #28 #29)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #30)
-#326 := (iff #31 #325)
-#323 := (iff #30 #322)
-#320 := (iff #29 #319)
-#321 := [rewrite]: #320
-#317 := (iff #28 #315)
-#318 := [rewrite]: #317
-#324 := [monotonicity #318 #321]: #323
-#327 := [quant-intro #324]: #326
-#314 := [asserted]: #31
-#330 := [mp #314 #327]: #325
-#1872 := [mp~ #330 #1844]: #325
-#4185 := [mp #1872 #4184]: #4180
-#5904 := (not #4180)
-#5905 := (or #5904 #5893)
-#5891 := (= f1 f1)
-#5894 := (iff #5893 #5891)
-#5906 := (or #5904 #5894)
-#5908 := (iff #5906 #5905)
-#5910 := (iff #5905 #5905)
-#5911 := [rewrite]: #5910
-#5902 := (iff #5894 #5893)
-#5897 := (iff #5893 true)
-#5900 := (iff #5897 #5893)
-#5901 := [rewrite]: #5900
-#5898 := (iff #5894 #5897)
-#5895 := (iff #5891 true)
-#5896 := [rewrite]: #5895
-#5899 := [monotonicity #5896]: #5898
-#5903 := [trans #5899 #5901]: #5902
-#5909 := [monotonicity #5903]: #5908
-#5912 := [trans #5909 #5911]: #5908
-#5907 := [quant-inst #105 #171 #4]: #5906
-#5913 := [mp #5907 #5912]: #5905
-#7000 := [unit-resolution #5913 #4185]: #5893
-#7002 := [symm #7000]: #7001
-#9285 := [monotonicity #7791 #7002]: #9284
-#9287 := [trans #9285 #7006]: #9286
-#10093 := [monotonicity #9287]: #10092
-#10095 := [monotonicity #10093]: #10094
-#10097 := [symm #10095]: #10096
-#10099 := [monotonicity #10097]: #10098
-#7546 := (or #7536 #7540)
-#4020 := (or #4536 #4530)
-#4021 := [def-axiom]: #4020
-#7097 := [unit-resolution #4021 #6509]: #4530
-#6312 := (f6 f23 ?v0!13)
-#6313 := (f10 #6312)
-#6338 := (+ #2233 #6313)
-#6339 := (+ #175 #6338)
-#6360 := (>= #6339 0::Int)
-#6342 := (= #6339 0::Int)
-#6317 := (* -1::Int #6313)
-#6321 := (+ f9 #6317)
-#6322 := (<= #6321 0::Int)
-#6389 := (not #6322)
-#6331 := (+ #2849 #6313)
-#6332 := (+ #175 #6331)
-#6333 := (>= #6332 0::Int)
-#6368 := (or #6322 #6333)
-#6371 := (not #6368)
-#6365 := (= #2232 #2234)
-#6490 := (not #6365)
-#6489 := [hypothesis]: #2856
-#6493 := (or #6490 #2851)
-#6494 := [th-lemma arith triangle-eq]: #6493
-#6495 := [unit-resolution #6494 #6489]: #6490
-#6377 := (or #4402 #6365 #6371)
-#6318 := (+ #1454 #6317)
-#6319 := (+ #2234 #6318)
-#6320 := (<= #6319 0::Int)
-#6361 := (or #6322 #6320)
-#6362 := (not #6361)
-#6363 := (= #2234 #2232)
-#6364 := (or #6363 #6362)
-#6378 := (or #4402 #6364)
-#6385 := (iff #6378 #6377)
-#6374 := (or #6365 #6371)
-#6380 := (or #4402 #6374)
-#6383 := (iff #6380 #6377)
-#6384 := [rewrite]: #6383
-#6381 := (iff #6378 #6380)
-#6375 := (iff #6364 #6374)
-#6372 := (iff #6362 #6371)
-#6369 := (iff #6361 #6368)
-#6336 := (iff #6320 #6333)
-#6324 := (+ #2234 #6317)
-#6325 := (+ #1454 #6324)
-#6328 := (<= #6325 0::Int)
-#6334 := (iff #6328 #6333)
-#6335 := [rewrite]: #6334
-#6329 := (iff #6320 #6328)
-#6326 := (= #6319 #6325)
-#6327 := [rewrite]: #6326
-#6330 := [monotonicity #6327]: #6329
-#6337 := [trans #6330 #6335]: #6336
-#6370 := [monotonicity #6337]: #6369
-#6373 := [monotonicity #6370]: #6372
-#6366 := (iff #6363 #6365)
-#6367 := [rewrite]: #6366
-#6376 := [monotonicity #6367 #6373]: #6375
-#6382 := [monotonicity #6376]: #6381
-#6386 := [trans #6382 #6384]: #6385
-#6379 := [quant-inst #2231]: #6378
-#6387 := [mp #6379 #6386]: #6377
-#6511 := [unit-resolution #6387 #6510 #6495]: #6371
-#6390 := (or #6368 #6389)
-#6391 := [def-axiom]: #6390
-#6512 := [unit-resolution #6391 #6511]: #6389
-#6392 := (not #6333)
-#6393 := (or #6368 #6392)
-#6394 := [def-axiom]: #6393
-#6513 := [unit-resolution #6394 #6511]: #6392
-#6345 := (or #6322 #6333 #6342)
-#6348 := (or #4410 #6322 #6333 #6342)
-#6314 := (+ #6313 #2233)
-#6315 := (+ #175 #6314)
-#6316 := (= #6315 0::Int)
-#6323 := (or #6322 #6320 #6316)
-#6349 := (or #4410 #6323)
-#6356 := (iff #6349 #6348)
-#6351 := (or #4410 #6345)
-#6354 := (iff #6351 #6348)
-#6355 := [rewrite]: #6354
-#6352 := (iff #6349 #6351)
-#6346 := (iff #6323 #6345)
-#6343 := (iff #6316 #6342)
-#6340 := (= #6315 #6339)
-#6341 := [rewrite]: #6340
-#6344 := [monotonicity #6341]: #6343
-#6347 := [monotonicity #6337 #6344]: #6346
-#6353 := [monotonicity #6347]: #6352
-#6357 := [trans #6353 #6355]: #6356
-#6350 := [quant-inst #2231]: #6349
-#6358 := [mp #6350 #6357]: #6348
-#6515 := [unit-resolution #6358 #6514]: #6345
-#6516 := [unit-resolution #6515 #6513 #6512]: #6342
-#6517 := (not #6342)
-#6518 := (or #6517 #6360)
-#6519 := [th-lemma arith triangle-eq]: #6518
-#6520 := [unit-resolution #6519 #6516]: #6360
-#6388 := (>= #2850 0::Int)
-#6521 := (or #6388 #2851)
-#6522 := [th-lemma arith farkas 1 1]: #6521
-#6523 := [unit-resolution #6522 #6489]: #6388
-#6524 := [th-lemma arith farkas 1 -1 1 #6523 #6513 #6520]: false
-#6525 := [lemma #6524]: #2851
-#4050 := (or #4533 #2856 #4527)
-#4051 := [def-axiom]: #4050
-#7098 := [unit-resolution #4051 #6525 #7097]: #4527
-#4065 := (or #4524 #4518)
-#4066 := [def-axiom]: #4065
-#7099 := [unit-resolution #4066 #7098]: #4518
-#6880 := (= #175 #2254)
-#6697 := (= f23 ?v0!14)
-#6527 := (f3 f16 ?v0!14)
-#6528 := (= f1 #6527)
-#6698 := (ite #6697 #5893 #6528)
-#6270 := (f4 f5 f16 f23 #5892)
-#6701 := (f3 #6270 ?v0!14)
-#6702 := (= f1 #6701)
-#6704 := (iff #6698 #6702)
-#6707 := (or #6291 #6704)
-#6703 := (iff #6702 #6698)
-#6708 := (or #6291 #6703)
-#6710 := (iff #6708 #6707)
-#6712 := (iff #6707 #6707)
-#6713 := [rewrite]: #6712
-#6705 := (iff #6703 #6704)
-#6706 := [rewrite]: #6705
-#6711 := [monotonicity #6706]: #6710
-#6714 := [trans #6711 #6713]: #6710
-#6709 := [quant-inst #105 #171 #5892 #2249]: #6708
-#6715 := [mp #6709 #6714]: #6707
-#6997 := [unit-resolution #6715 #4178]: #6704
-#7013 := (= #2250 #6701)
-#7009 := (= #6701 #2250)
-#7007 := (= #6270 f24)
-#7003 := (= #6270 #774)
-#7004 := [monotonicity #7002]: #7003
-#7008 := [trans #7004 #7006]: #7007
-#7010 := [monotonicity #7008]: #7009
-#7014 := [symm #7010]: #7013
-#6995 := [hypothesis]: #2870
-#4128 := (or #2865 #2251)
-#4129 := [def-axiom]: #4128
-#6998 := [unit-resolution #4129 #6995]: #2251
-#7015 := [trans #6998 #7014]: #6702
-#6728 := (not #6702)
-#6727 := (not #6704)
-#6729 := (or #6727 #6698 #6728)
-#6730 := [def-axiom]: #6729
-#7016 := [unit-resolution #6730 #7015 #6997]: #6698
-#6556 := (f6 f23 ?v0!14)
-#6557 := (f10 #6556)
-#6487 := (* -1::Int #2254)
-#6574 := (+ #6487 #6557)
-#6575 := (+ #175 #6574)
-#6576 := (>= #6575 0::Int)
-#6604 := (not #6576)
-#6558 := (* -1::Int #6557)
-#6562 := (+ f9 #6558)
-#6563 := (<= #6562 0::Int)
-#6581 := (or #6563 #6576)
-#6584 := (not #6581)
-#4124 := (not #2859)
-#4125 := (or #2865 #4124)
-#4130 := [def-axiom]: #4125
-#6996 := [unit-resolution #4130 #6995]: #4124
-#6590 := (or #4402 #2859 #6584)
-#6559 := (+ #1454 #6558)
-#6560 := (+ #2254 #6559)
-#6561 := (<= #6560 0::Int)
-#6564 := (or #6563 #6561)
-#6565 := (not #6564)
-#6566 := (or #2255 #6565)
-#6591 := (or #4402 #6566)
-#6598 := (iff #6591 #6590)
-#6587 := (or #2859 #6584)
-#6593 := (or #4402 #6587)
-#6596 := (iff #6593 #6590)
-#6597 := [rewrite]: #6596
-#6594 := (iff #6591 #6593)
-#6588 := (iff #6566 #6587)
-#6585 := (iff #6565 #6584)
-#6582 := (iff #6564 #6581)
-#6579 := (iff #6561 #6576)
-#6567 := (+ #2254 #6558)
-#6568 := (+ #1454 #6567)
-#6571 := (<= #6568 0::Int)
-#6577 := (iff #6571 #6576)
-#6578 := [rewrite]: #6577
-#6572 := (iff #6561 #6571)
-#6569 := (= #6560 #6568)
-#6570 := [rewrite]: #6569
-#6573 := [monotonicity #6570]: #6572
-#6580 := [trans #6573 #6578]: #6579
-#6583 := [monotonicity #6580]: #6582
-#6586 := [monotonicity #6583]: #6585
-#6589 := [monotonicity #2861 #6586]: #6588
-#6595 := [monotonicity #6589]: #6594
-#6599 := [trans #6595 #6597]: #6598
-#6592 := [quant-inst #2249]: #6591
-#6600 := [mp #6592 #6599]: #6590
-#7017 := [unit-resolution #6600 #6510 #6996]: #6584
-#6605 := (or #6581 #6604)
-#6606 := [def-axiom]: #6605
-#7018 := [unit-resolution #6606 #7017]: #6604
-#6716 := (not #6698)
-#6942 := (or #6697 #6576 #6716)
-#6823 := (f7 #6556)
-#6833 := (f14 f15 #6823)
-#6848 := (* -1::Int #6833)
-#6888 := (+ #175 #6848)
-#6890 := (>= #6888 0::Int)
-#6887 := (= #175 #6833)
-#6894 := (= #6833 #175)
-#6892 := (= #6823 f23)
-#6824 := (= f23 #6823)
-#6831 := (or #6830 #6824)
-#6832 := [quant-inst #171 #2249]: #6831
-#6891 := [unit-resolution #6832 #4206]: #6824
-#6893 := [symm #6891]: #6892
-#6895 := [monotonicity #6893]: #6894
-#6896 := [symm #6895]: #6887
-#6897 := (not #6887)
-#6898 := (or #6897 #6890)
-#6899 := [th-lemma arith triangle-eq]: #6898
-#6900 := [unit-resolution #6899 #6896]: #6890
-#6901 := [hypothesis]: #6604
-#6820 := (>= #6557 0::Int)
-#6774 := (<= #6557 0::Int)
-#6775 := (not #6774)
-#6717 := (not #6697)
-#6902 := [hypothesis]: #6717
-#6780 := (or #6697 #6775)
-#49 := (f10 #38)
-#408 := (<= #49 0::Int)
-#409 := (not #408)
-#355 := (= #13 #24)
-#415 := (or #355 #409)
-#4213 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #415)
-#420 := (forall (vars (?v0 S3) (?v1 S3)) #415)
-#4216 := (iff #420 #4213)
-#4214 := (iff #415 #415)
-#4215 := [refl]: #4214
-#4217 := [quant-intro #4215]: #4216
-#1855 := (~ #420 #420)
-#1854 := (~ #415 #415)
-#1884 := [refl]: #1854
-#1856 := [nnf-pos #1884]: #1855
-#54 := (< 0::Int #49)
-#48 := (= #24 #13)
-#53 := (not #48)
-#55 := (implies #53 #54)
-#56 := (forall (vars (?v0 S3) (?v1 S3)) #55)
-#423 := (iff #56 #420)
-#400 := (or #54 #355)
-#405 := (forall (vars (?v0 S3) (?v1 S3)) #400)
-#421 := (iff #405 #420)
-#418 := (iff #400 #415)
-#412 := (or #409 #355)
-#416 := (iff #412 #415)
-#417 := [rewrite]: #416
-#413 := (iff #400 #412)
-#410 := (iff #54 #409)
-#411 := [rewrite]: #410
-#414 := [monotonicity #411]: #413
-#419 := [trans #414 #417]: #418
-#422 := [quant-intro #419]: #421
-#406 := (iff #56 #405)
-#403 := (iff #55 #400)
-#369 := (not #355)
-#397 := (implies #369 #54)
-#401 := (iff #397 #400)
-#402 := [rewrite]: #401
-#398 := (iff #55 #397)
-#395 := (iff #53 #369)
-#361 := (iff #48 #355)
-#362 := [rewrite]: #361
-#396 := [monotonicity #362]: #395
-#399 := [monotonicity #396]: #398
-#404 := [trans #399 #402]: #403
-#407 := [quant-intro #404]: #406
-#424 := [trans #407 #422]: #423
-#394 := [asserted]: #56
-#425 := [mp #394 #424]: #420
-#1885 := [mp~ #425 #1856]: #420
-#4218 := [mp #1885 #4217]: #4213
-#6783 := (not #4213)
-#6784 := (or #6783 #6697 #6775)
-#6776 := (= ?v0!14 f23)
-#6777 := (or #6776 #6775)
-#6785 := (or #6783 #6777)
-#6792 := (iff #6785 #6784)
-#6787 := (or #6783 #6780)
-#6790 := (iff #6787 #6784)
-#6791 := [rewrite]: #6790
-#6788 := (iff #6785 #6787)
-#6781 := (iff #6777 #6780)
-#6778 := (iff #6776 #6697)
-#6779 := [rewrite]: #6778
-#6782 := [monotonicity #6779]: #6781
-#6789 := [monotonicity #6782]: #6788
-#6793 := [trans #6789 #6791]: #6792
-#6786 := [quant-inst #171 #2249]: #6785
-#6794 := [mp #6786 #6793]: #6784
-#6903 := [unit-resolution #6794 #4218]: #6780
-#6904 := [unit-resolution #6903 #6902]: #6775
-#6905 := (or #6820 #6774)
-#6906 := [th-lemma arith farkas 1 1]: #6905
-#6907 := [unit-resolution #6906 #6904]: #6820
-#6821 := (f8 #6556)
-#6828 := (f14 f15 #6821)
-#6829 := (* -1::Int #6828)
-#6878 := (+ #2254 #6829)
-#6885 := (<= #6878 0::Int)
-#6877 := (= #2254 #6828)
-#6911 := (= #6828 #2254)
-#6909 := (= #6821 ?v0!14)
-#6822 := (= ?v0!14 #6821)
-#6826 := (or #6825 #6822)
-#6827 := [quant-inst #171 #2249]: #6826
-#6908 := [unit-resolution #6827 #4200]: #6822
-#6910 := [symm #6908]: #6909
-#6912 := [monotonicity #6910]: #6911
-#6913 := [symm #6912]: #6877
-#6914 := (not #6877)
-#6915 := (or #6914 #6885)
-#6916 := [th-lemma arith triangle-eq]: #6915
-#6917 := [unit-resolution #6916 #6913]: #6885
-#6849 := (+ #6828 #6848)
-#6850 := (<= #6849 0::Int)
-#6836 := (f3 f16 #6821)
-#6837 := (= f1 #6836)
-#6924 := (= #6527 #6836)
-#6920 := (= #6836 #6527)
-#6921 := [monotonicity #6910]: #6920
-#6925 := [symm #6921]: #6924
-#6918 := [hypothesis]: #6698
-#6720 := (or #6716 #6697 #6528)
-#6721 := [def-axiom]: #6720
-#6919 := [unit-resolution #6721 #6902 #6918]: #6528
-#6926 := [trans #6919 #6925]: #6837
-#6839 := (f3 f16 #6823)
-#6840 := (= f1 #6839)
-#6934 := (not #6840)
-#6935 := (iff #758 #6934)
-#6932 := (iff #755 #6840)
-#6930 := (iff #6840 #755)
-#6928 := (= #6839 #172)
-#6929 := [monotonicity #6893]: #6928
-#6931 := [monotonicity #6929]: #6930
-#6933 := [symm #6931]: #6932
-#6936 := [monotonicity #6933]: #6935
-#4052 := (or #4536 #758)
-#4053 := [def-axiom]: #4052
-#6927 := [unit-resolution #4053 #6509]: #758
-#6937 := [mp #6927 #6936]: #6934
-#6838 := (not #6837)
-#6858 := (or #6838 #6840 #6850)
-#3962 := (or #4548 #4292)
-#4017 := [def-axiom]: #3962
-#6938 := [unit-resolution #4017 #6508]: #4292
-#6863 := (or #4297 #6838 #6840 #6850)
-#6834 := (+ #6833 #6829)
-#6835 := (>= #6834 0::Int)
-#6841 := (or #6840 #6838 #6835)
-#6864 := (or #4297 #6841)
-#6871 := (iff #6864 #6863)
-#6866 := (or #4297 #6858)
-#6869 := (iff #6866 #6863)
-#6870 := [rewrite]: #6869
-#6867 := (iff #6864 #6866)
-#6861 := (iff #6841 #6858)
-#6855 := (or #6840 #6838 #6850)
-#6859 := (iff #6855 #6858)
-#6860 := [rewrite]: #6859
-#6856 := (iff #6841 #6855)
-#6853 := (iff #6835 #6850)
-#6842 := (+ #6829 #6833)
-#6845 := (>= #6842 0::Int)
-#6851 := (iff #6845 #6850)
-#6852 := [rewrite]: #6851
-#6846 := (iff #6835 #6845)
-#6843 := (= #6834 #6842)
-#6844 := [rewrite]: #6843
-#6847 := [monotonicity #6844]: #6846
-#6854 := [trans #6847 #6852]: #6853
-#6857 := [monotonicity #6854]: #6856
-#6862 := [trans #6857 #6860]: #6861
-#6868 := [monotonicity #6862]: #6867
-#6872 := [trans #6868 #6870]: #6871
-#6865 := [quant-inst #6821 #6823]: #6864
-#6873 := [mp #6865 #6872]: #6863
-#6939 := [unit-resolution #6873 #6938]: #6858
-#6940 := [unit-resolution #6939 #6937 #6926]: #6850
-#6941 := [th-lemma arith farkas 1 1 1 -1 1 #6940 #6917 #6907 #6901 #6900]: false
-#6943 := [lemma #6941]: #6942
-#7019 := [unit-resolution #6943 #7018 #7016]: #6697
-#7043 := [monotonicity #7019]: #6880
-#7041 := (= #2253 #175)
-#7039 := (= #175 #2253)
-#6796 := (= #6557 0::Int)
-#6803 := (or #6717 #6796)
-#50 := (= #49 0::Int)
-#383 := (or #50 #369)
-#4207 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #383)
-#388 := (forall (vars (?v0 S3) (?v1 S3)) #383)
-#4210 := (iff #388 #4207)
-#4208 := (iff #383 #383)
-#4209 := [refl]: #4208
-#4211 := [quant-intro #4209]: #4210
-#1851 := (~ #388 #388)
-#1882 := (~ #383 #383)
-#1883 := [refl]: #1882
-#1852 := [nnf-pos #1883]: #1851
-#51 := (implies #48 #50)
-#52 := (forall (vars (?v0 S3) (?v1 S3)) #51)
-#391 := (iff #52 #388)
-#363 := (= 0::Int #49)
-#370 := (or #369 #363)
-#375 := (forall (vars (?v0 S3) (?v1 S3)) #370)
-#389 := (iff #375 #388)
-#386 := (iff #370 #383)
-#380 := (or #369 #50)
-#384 := (iff #380 #383)
-#385 := [rewrite]: #384
-#381 := (iff #370 #380)
-#378 := (iff #363 #50)
-#379 := [rewrite]: #378
-#382 := [monotonicity #379]: #381
-#387 := [trans #382 #385]: #386
-#390 := [quant-intro #387]: #389
-#376 := (iff #52 #375)
-#373 := (iff #51 #370)
-#366 := (implies #355 #363)
-#371 := (iff #366 #370)
-#372 := [rewrite]: #371
-#367 := (iff #51 #366)
-#364 := (iff #50 #363)
-#365 := [rewrite]: #364
-#368 := [monotonicity #362 #365]: #367
-#374 := [trans #368 #372]: #373
-#377 := [quant-intro #374]: #376
-#392 := [trans #377 #390]: #391
-#353 := [asserted]: #52
-#393 := [mp #353 #392]: #388
-#1853 := [mp~ #393 #1852]: #388
-#4212 := [mp #1853 #4211]: #4207
-#6808 := (not #4207)
-#6809 := (or #6808 #6717 #6796)
-#6795 := (not #6776)
-#6797 := (or #6796 #6795)
-#6810 := (or #6808 #6797)
-#6817 := (iff #6810 #6809)
-#6812 := (or #6808 #6803)
-#6815 := (iff #6812 #6809)
-#6816 := [rewrite]: #6815
-#6813 := (iff #6810 #6812)
-#6806 := (iff #6797 #6803)
-#6800 := (or #6796 #6717)
-#6804 := (iff #6800 #6803)
-#6805 := [rewrite]: #6804
-#6801 := (iff #6797 #6800)
-#6798 := (iff #6795 #6717)
-#6799 := [monotonicity #6779]: #6798
-#6802 := [monotonicity #6799]: #6801
-#6807 := [trans #6802 #6805]: #6806
-#6814 := [monotonicity #6807]: #6813
-#6818 := [trans #6814 #6816]: #6817
-#6811 := [quant-inst #171 #2249]: #6810
-#6819 := [mp #6811 #6818]: #6809
-#7020 := [unit-resolution #6819 #4212]: #6803
-#7021 := [unit-resolution #7020 #7019]: #6796
-#7022 := (not #6796)
-#7023 := (or #7022 #6774)
-#7024 := [th-lemma arith triangle-eq]: #7023
-#7025 := [unit-resolution #7024 #7021]: #6774
-#7026 := (or #7022 #6820)
-#7027 := [th-lemma arith triangle-eq]: #7026
-#7028 := [unit-resolution #7027 #7021]: #6820
-#6425 := (* -1::Int #2253)
-#6613 := (+ #6425 #6557)
-#6614 := (+ #175 #6613)
-#6634 := (<= #6614 0::Int)
-#6617 := (= #6614 0::Int)
-#6601 := (not #6563)
-#6602 := (or #6581 #6601)
-#6603 := [def-axiom]: #6602
-#7029 := [unit-resolution #6603 #7017]: #6601
-#6620 := (or #6563 #6576 #6617)
-#6623 := (or #4410 #6563 #6576 #6617)
-#6609 := (+ #6557 #6425)
-#6610 := (+ #175 #6609)
-#6611 := (= #6610 0::Int)
-#6612 := (or #6563 #6561 #6611)
-#6624 := (or #4410 #6612)
-#6631 := (iff #6624 #6623)
-#6626 := (or #4410 #6620)
-#6629 := (iff #6626 #6623)
-#6630 := [rewrite]: #6629
-#6627 := (iff #6624 #6626)
-#6621 := (iff #6612 #6620)
-#6618 := (iff #6611 #6617)
-#6615 := (= #6610 #6614)
-#6616 := [rewrite]: #6615
-#6619 := [monotonicity #6616]: #6618
-#6622 := [monotonicity #6580 #6619]: #6621
-#6628 := [monotonicity #6622]: #6627
-#6632 := [trans #6628 #6630]: #6631
-#6625 := [quant-inst #2249]: #6624
-#6633 := [mp #6625 #6632]: #6623
-#7030 := [unit-resolution #6633 #6514]: #6620
-#7031 := [unit-resolution #7030 #7018 #7029]: #6617
-#7032 := (not #6617)
-#7033 := (or #7032 #6634)
-#7034 := [th-lemma arith triangle-eq]: #7033
-#7035 := [unit-resolution #7034 #7031]: #6634
-#6635 := (>= #6614 0::Int)
-#7036 := (or #7032 #6635)
-#7037 := [th-lemma arith triangle-eq]: #7036
-#7038 := [unit-resolution #7037 #7031]: #6635
-#7040 := [th-lemma arith eq-propagate 1 1 -1 -1 #7038 #7035 #7028 #7025]: #7039
-#7042 := [symm #7040]: #7041
-#7044 := [trans #7042 #7043]: #2859
-#7045 := [unit-resolution #6996 #7044]: false
-#7046 := [lemma #7045]: #2865
-#4061 := (or #4521 #2870 #4515)
-#4062 := [def-axiom]: #4061
-#7100 := [unit-resolution #4062 #7046 #7099]: #4515
-#4071 := (or #4512 #4422)
-#4073 := [def-axiom]: #4071
-#7101 := [unit-resolution #4073 #7100]: #4422
-#9467 := (or #4427 #7536 #7540)
-#7539 := (or #7538 #7536)
-#9468 := (or #4427 #7539)
-#9475 := (iff #9468 #9467)
-#9470 := (or #4427 #7546)
-#9473 := (iff #9470 #9467)
-#9474 := [rewrite]: #9473
-#9471 := (iff #9468 #9470)
-#7549 := (iff #7539 #7546)
-#7543 := (or #7540 #7536)
-#7547 := (iff #7543 #7546)
-#7548 := [rewrite]: #7547
-#7544 := (iff #7539 #7543)
-#7545 := [monotonicity #7542]: #7544
-#7550 := [trans #7545 #7548]: #7549
-#9472 := [monotonicity #7550]: #9471
-#9476 := [trans #9472 #9474]: #9475
-#9469 := [quant-inst #2274]: #9468
-#9477 := [mp #9469 #9476]: #9467
-#10090 := [unit-resolution #9477 #7101]: #7546
-#10091 := [unit-resolution #10090 #10077]: #7536
-#10100 := [mp #10091 #10099]: #9982
-#9979 := (not #9956)
-#9980 := (or #9979 #9948 #9968)
-#9981 := [def-axiom]: #9980
-#10101 := [unit-resolution #9981 #10100 #10089]: #9968
-#10102 := (or #9953 #9969)
-#6305 := (not #5893)
-#9974 := (or #9953 #9969 #6305)
-#9975 := [def-axiom]: #9974
-#10103 := [unit-resolution #9975 #7000]: #10102
-#10104 := [unit-resolution #10103 #10101]: #9969
-#10028 := (or #9950 #10027)
-#10031 := (or #6783 #9950 #10027)
-#10032 := (or #6783 #10028)
-#10034 := (iff #10032 #10031)
-#10035 := [rewrite]: #10034
-#10033 := [quant-inst #7212 #2274]: #10032
-#10036 := [mp #10033 #10035]: #10031
-#10105 := [unit-resolution #10036 #4218]: #10028
-#10106 := [unit-resolution #10105 #10104]: #10027
-#10107 := (or #10051 #10026)
-#10108 := [th-lemma arith farkas 1 1]: #10107
-#10109 := [unit-resolution #10108 #10106]: #10051
-#10110 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10109 #10088 #10087 #10075 #10074 #10073 #10072]: false
-#10112 := [lemma #10110]: #10111
-#9587 := [unit-resolution #10112 #10088 #10075 #10073]: #7540
-#9588 := (or #10076 #9582)
-#9589 := [th-lemma arith triangle-eq]: #9588
-#9590 := [unit-resolution #9589 #9587]: #9582
-#9591 := [th-lemma arith farkas -1 1 1 #10088 #9590 #9581]: false
-#9609 := [lemma #9591]: #9608
-#11953 := [unit-resolution #9609 #10088 #10075]: #7303
-#9480 := (or #7323 #8252)
-#9478 := [def-axiom]: #9480
-#11954 := [unit-resolution #9478 #11953]: #7323
-#7326 := (not #7323)
-#12704 := (or #7320 #7326)
-#7316 := (+ f9 #6072)
-#7317 := (<= #7316 0::Int)
-#12698 := (not #7317)
-#12701 := (or #12698 #6074)
-#4037 := (or #4536 #1656)
-#4038 := [def-axiom]: #4037
-#7831 := [unit-resolution #4038 #6509]: #1656
-#12699 := (or #12698 #1655 #6074)
-#12700 := [th-lemma arith assign-bounds 1 1]: #12699
-#12702 := [unit-resolution #12700 #7831]: #12701
-#12703 := [unit-resolution #12702 #10075]: #12698
-#12666 := [unit-resolution #4018 #6508]: #4308
-#9212 := (or #4313 #7317 #7320 #7326)
-#7314 := (or #7313 #7310 #7303)
-#7315 := (not #7314)
-#7319 := (or #7318 #7317 #7315)
-#9449 := (or #4313 #7319)
-#9462 := (iff #9449 #9212)
-#7332 := (or #7317 #7320 #7326)
-#9455 := (or #4313 #7332)
-#9460 := (iff #9455 #9212)
-#9461 := [rewrite]: #9460
-#9457 := (iff #9449 #9455)
-#7335 := (iff #7319 #7332)
-#7329 := (or #7320 #7317 #7326)
-#7333 := (iff #7329 #7332)
-#7334 := [rewrite]: #7333
-#7330 := (iff #7319 #7329)
-#7327 := (iff #7315 #7326)
-#7324 := (iff #7314 #7323)
-#7325 := [rewrite]: #7324
-#7328 := [monotonicity #7325]: #7327
-#7321 := (iff #7318 #7320)
-#7322 := [rewrite]: #7321
-#7331 := [monotonicity #7322 #7328]: #7330
-#7336 := [trans #7331 #7334]: #7335
-#9459 := [monotonicity #7336]: #9457
-#9463 := [trans #9459 #9461]: #9462
-#9454 := [quant-inst #6070]: #9449
-#9479 := [mp #9454 #9463]: #9212
-#12705 := [unit-resolution #9479 #12666 #12703]: #12704
-#11952 := [unit-resolution #12705 #11954]: #7320
-#11955 := [symm #11952]: #7318
-#9282 := (= #8218 #6070)
-#9283 := [symm #9281]: #9282
-#11956 := [trans #9283 #11955]: #10698
-#11958 := [monotonicity #11956]: #11957
-#11959 := [symm #11958]: #10876
-#11945 := (not #10876)
-#11960 := (or #11945 #10879)
-#11961 := [th-lemma arith triangle-eq]: #11960
-#11962 := [unit-resolution #11961 #11959]: #10879
-#3918 := (>= #100 0::Int)
-#7124 := [unit-resolution #4034 #6508]: #101
-#6990 := (or #1748 #3918)
-#6991 := [th-lemma arith triangle-eq]: #6990
-#6992 := [unit-resolution #6991 #7124]: #3918
-#11982 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10109 #10088 #10087 #10075 #6992 #11962 #11951 #10072]: false
-#11987 := [lemma #11982]: #11986
-#11110 := [unit-resolution #11987 #10088 #10075]: #7540
-#11964 := (not #9582)
-#11918 := [hypothesis]: #11964
-#11919 := [hypothesis]: #7540
-#11920 := [unit-resolution #9589 #11919 #11918]: false
-#11921 := [lemma #11920]: #9588
-#11111 := [unit-resolution #11921 #11110]: #9582
-#11114 := [th-lemma arith farkas -1 1 1 #10088 #11111 #9581]: false
-#11113 := [lemma #11114]: #11115
-#23131 := [unit-resolution #11113 #10075]: #2276
-#4074 := (or #4512 #4506)
-#4075 := [def-axiom]: #4074
-#12709 := [unit-resolution #4075 #7100]: #4506
-#5933 := (= #100 #204)
-#12713 := (iff #5933 #205)
-#12712 := [commutativity]: #1489
-#12710 := (iff #5933 #823)
-#12711 := [monotonicity #7124]: #12710
-#12714 := [trans #12711 #12712]: #12713
-#5917 := (f6 f23 f11)
-#5918 := (f10 #5917)
-#7060 := (<= #5918 0::Int)
-#7061 := (not #7060)
-#6768 := (not #6089)
-#3935 := (f3 f16 f11)
-#3938 := (= f1 #3935)
-#6719 := (ite #6089 #5893 #3938)
-#6767 := (not #6719)
-#6699 := (f3 #6270 f11)
-#6700 := (= f1 #6699)
-#6724 := (iff #6700 #6719)
-#6731 := (or #6291 #6724)
-#6684 := (ite #6087 #5893 #3938)
-#6718 := (iff #6700 #6684)
-#6732 := (or #6291 #6718)
-#6734 := (iff #6732 #6731)
-#6736 := (iff #6731 #6731)
-#6764 := [rewrite]: #6736
-#6725 := (iff #6718 #6724)
-#6722 := (iff #6684 #6719)
-#6090 := (iff #6087 #6089)
-#6091 := [rewrite]: #6090
-#6723 := [monotonicity #6091]: #6722
-#6726 := [monotonicity #6723]: #6725
-#6735 := [monotonicity #6726]: #6734
-#6765 := [trans #6735 #6764]: #6734
-#6733 := [quant-inst #105 #171 #5892 #57]: #6732
-#6766 := [mp #6733 #6765]: #6731
-#7092 := [unit-resolution #6766 #4178]: #6724
-#6984 := (not #6700)
-#6359 := (f3 f24 f11)
-#6477 := (= f1 #6359)
-#6546 := (not #6477)
-#7110 := (iff #6546 #6984)
-#7108 := (iff #6477 #6700)
-#7106 := (iff #6700 #6477)
-#7104 := (= #6699 #6359)
-#7105 := [monotonicity #7008]: #7104
-#7107 := [monotonicity #7105]: #7106
-#7109 := [symm #7107]: #7108
-#7111 := [monotonicity #7109]: #7110
-#7093 := (not #5933)
-#7096 := [hypothesis]: #7093
-#6547 := (or #5933 #6546)
-#6550 := (or #4427 #5933 #6546)
-#6545 := (or #4427 #6547)
-#6552 := (iff #6545 #6550)
-#6553 := [rewrite]: #6552
-#6551 := [quant-inst #57]: #6545
-#6554 := [mp #6551 #6553]: #6550
-#7102 := [unit-resolution #6554 #7101]: #6547
-#7103 := [unit-resolution #7102 #7096]: #6546
-#7112 := [mp #7103 #7111]: #6984
-#6987 := (not #6724)
-#6988 := (or #6987 #6700 #6767)
-#6989 := [def-axiom]: #6988
-#7113 := [unit-resolution #6989 #7112 #7092]: #6767
-#7114 := (or #6719 #6768)
-#6772 := (or #6719 #6768 #6305)
-#6773 := [def-axiom]: #6772
-#7115 := [unit-resolution #6773 #7000]: #7114
-#7116 := [unit-resolution #7115 #7113]: #6768
-#7062 := (or #6089 #7061)
-#7065 := (or #6783 #6089 #7061)
-#7066 := (or #6783 #7062)
-#7068 := (iff #7066 #7065)
-#7069 := [rewrite]: #7068
-#7067 := [quant-inst #171 #57]: #7066
-#7070 := [mp #7067 #7069]: #7065
-#7117 := [unit-resolution #7070 #4218]: #7062
-#7118 := [unit-resolution #7117 #7116]: #7061
-#5925 := (* -1::Int #5918)
-#5926 := (+ #1454 #5925)
-#5927 := (+ #100 #5926)
-#5928 := (<= #5927 0::Int)
-#5955 := (not #5928)
-#5929 := (+ f9 #5925)
-#5930 := (<= #5929 0::Int)
-#5935 := (or #5928 #5930)
-#5938 := (not #5935)
-#5941 := (or #5933 #5938)
-#5944 := (or #4402 #5933 #5938)
-#5931 := (or #5930 #5928)
-#5932 := (not #5931)
-#5934 := (or #5933 #5932)
-#5945 := (or #4402 #5934)
-#5952 := (iff #5945 #5944)
-#5947 := (or #4402 #5941)
-#5950 := (iff #5947 #5944)
-#5951 := [rewrite]: #5950
-#5948 := (iff #5945 #5947)
-#5942 := (iff #5934 #5941)
-#5939 := (iff #5932 #5938)
-#5936 := (iff #5931 #5935)
-#5937 := [rewrite]: #5936
-#5940 := [monotonicity #5937]: #5939
-#5943 := [monotonicity #5940]: #5942
-#5949 := [monotonicity #5943]: #5948
-#5953 := [trans #5949 #5951]: #5952
-#5946 := [quant-inst #57]: #5945
-#5954 := [mp #5946 #5953]: #5944
-#7119 := [unit-resolution #5954 #6510]: #5941
-#7120 := [unit-resolution #7119 #7096]: #5938
-#5956 := (or #5935 #5955)
-#5957 := [def-axiom]: #5956
-#7121 := [unit-resolution #5957 #7120]: #5955
-#6128 := (>= #175 0::Int)
-#6131 := (or #4280 #6128)
-#6132 := [quant-inst #171]: #6131
-#7123 := [unit-resolution #6132 #7122]: #6128
-#3921 := (<= #100 0::Int)
-#7125 := (or #1748 #3921)
-#7126 := [th-lemma arith triangle-eq]: #7125
-#7127 := [unit-resolution #7126 #7124]: #3921
-#7128 := [th-lemma arith farkas 1 1 1 1 #7127 #7123 #7121 #7118]: false
-#7129 := [lemma #7128]: #5933
-#12715 := [mp #7129 #12714]: #205
-#4084 := (or #4509 #1491 #4503)
-#4070 := [def-axiom]: #4084
-#12716 := [unit-resolution #4070 #12715 #12709]: #4503
-#4093 := (or #4500 #4494)
-#4077 := [def-axiom]: #4093
-#12717 := [unit-resolution #4077 #12716]: #4494
-#4090 := (or #4497 #2277 #4491)
-#4091 := [def-axiom]: #4090
-#12718 := [unit-resolution #4091 #12717]: #4494
-#23132 := [unit-resolution #12718 #23131]: #4491
-#4085 := (or #4488 #4482)
-#4087 := [def-axiom]: #4085
-#23140 := [unit-resolution #4087 #23132]: #4482
-#12721 := (or #4485 #4479)
-#10289 := [hypothesis]: #3446
-#3974 := (or #3441 #2300)
-#3975 := [def-axiom]: #3974
-#9759 := [unit-resolution #3975 #10289]: #2300
-#10380 := (or #3441 #2299)
-#10565 := (f6 #7212 ?v1!16)
-#10566 := (f10 #10565)
-#10583 := (* -1::Int #10566)
-#8692 := (f6 f23 ?v1!16)
-#8693 := (f10 #8692)
-#10586 := (+ #8693 #10583)
-#10588 := (>= #10586 0::Int)
-#10582 := (= #8693 #10566)
-#10593 := (= #10566 #8693)
-#10591 := (= #10565 #8692)
-#10592 := [monotonicity #7791]: #10591
-#10594 := [monotonicity #10592]: #10593
-#10595 := [symm #10594]: #10582
-#10596 := (not #10582)
-#10597 := (or #10596 #10588)
-#10598 := [th-lemma arith triangle-eq]: #10597
-#10599 := [unit-resolution #10598 #10595]: #10588
-#6008 := (f25 f23)
-#6049 := (* -1::Int #6008)
-#6418 := (+ #175 #6049)
-#6419 := (>= #6418 0::Int)
-#4063 := (or #4524 #4413)
-#4064 := [def-axiom]: #4063
-#8194 := [unit-resolution #4064 #7098]: #4413
-#6423 := (or #4418 #6419)
-#6424 := [quant-inst #171]: #6423
-#8195 := [unit-resolution #6424 #8194]: #6419
-#4117 := (not #2889)
-#4118 := (or #3441 #4117)
-#4119 := [def-axiom]: #4118
-#10292 := [unit-resolution #4119 #10289]: #4117
-#10224 := (+ #2291 #6049)
-#10225 := (<= #10224 0::Int)
-#10213 := (= #2291 #6008)
-#10481 := (= ?v0!17 f23)
-#8518 := (= ?v0!17 #7212)
-#8511 := (f3 f16 ?v0!17)
-#8512 := (= f1 #8511)
-#8521 := (ite #8518 #5893 #8512)
-#8515 := (f3 #8443 ?v0!17)
-#8516 := (= f1 #8515)
-#8524 := (iff #8516 #8521)
-#9712 := (or #6291 #8524)
-#8513 := (= #7212 ?v0!17)
-#8514 := (ite #8513 #5893 #8512)
-#8517 := (iff #8516 #8514)
-#9707 := (or #6291 #8517)
-#9714 := (iff #9707 #9712)
-#9716 := (iff #9712 #9712)
-#9717 := [rewrite]: #9716
-#8525 := (iff #8517 #8524)
-#8522 := (iff #8514 #8521)
-#8519 := (iff #8513 #8518)
-#8520 := [rewrite]: #8519
-#8523 := [monotonicity #8520]: #8522
-#8526 := [monotonicity #8523]: #8525
-#9715 := [monotonicity #8526]: #9714
-#9723 := [trans #9715 #9717]: #9714
-#9713 := [quant-inst #105 #7212 #5892 #2290]: #9707
-#9724 := [mp #9713 #9723]: #9712
-#10293 := [unit-resolution #9724 #4178]: #8524
-#10322 := (= #2296 #8515)
-#10295 := (= #8515 #2296)
-#10232 := [monotonicity #9287]: #10295
-#10323 := [symm #10232]: #10322
-#4132 := (or #3441 #2297)
-#3973 := [def-axiom]: #4132
-#10294 := [unit-resolution #3973 #10289]: #2297
-#10324 := [trans #10294 #10323]: #8516
-#9733 := (not #8516)
-#9736 := (not #8524)
-#9739 := (or #9736 #9733 #8521)
-#9740 := [def-axiom]: #9739
-#10325 := [unit-resolution #9740 #10324 #10293]: #8521
-#9732 := (not #8512)
-#8486 := (f14 f15 ?v0!17)
-#8568 := (* -1::Int #8486)
-#7514 := (f14 f15 #7212)
-#10487 := (+ #7514 #8568)
-#10488 := (>= #10487 0::Int)
-#10613 := (not #10488)
-#8447 := (= ?v1!16 #7212)
-#9617 := (not #8447)
-#8439 := (f3 f16 ?v1!16)
-#8440 := (= f1 #8439)
-#8450 := (ite #8447 #5893 #8440)
-#9616 := (not #8450)
-#8444 := (f3 #8443 ?v1!16)
-#8445 := (= f1 #8444)
-#8453 := (iff #8445 #8450)
-#9585 := (or #6291 #8453)
-#8441 := (= #7212 ?v1!16)
-#8442 := (ite #8441 #5893 #8440)
-#8446 := (iff #8445 #8442)
-#9586 := (or #6291 #8446)
-#9611 := (iff #9586 #9585)
-#9607 := (iff #9585 #9585)
-#9613 := [rewrite]: #9607
-#8454 := (iff #8446 #8453)
-#8451 := (iff #8442 #8450)
-#8448 := (iff #8441 #8447)
-#8449 := [rewrite]: #8448
-#8452 := [monotonicity #8449]: #8451
-#8455 := [monotonicity #8452]: #8454
-#9612 := [monotonicity #8455]: #9611
-#9614 := [trans #9612 #9613]: #9611
-#9610 := [quant-inst #105 #7212 #5892 #2289]: #9586
-#9615 := [mp #9610 #9614]: #9585
-#10326 := [unit-resolution #9615 #4178]: #8453
-#9649 := (not #8445)
-#10334 := (iff #2300 #9649)
-#10332 := (iff #2299 #8445)
-#10330 := (iff #8445 #2299)
-#10328 := (= #8444 #2298)
-#10329 := [monotonicity #9287]: #10328
-#10331 := [monotonicity #10329]: #10330
-#10333 := [symm #10331]: #10332
-#10335 := [monotonicity #10333]: #10334
-#10327 := [hypothesis]: #2300
-#10336 := [mp #10327 #10335]: #9649
-#9641 := (not #8453)
-#9642 := (or #9641 #8445 #9616)
-#9648 := [def-axiom]: #9642
-#10337 := [unit-resolution #9648 #10336 #10326]: #9616
-#10338 := (or #8450 #9617)
-#9637 := (or #8450 #9617 #6305)
-#9632 := [def-axiom]: #9637
-#10339 := [unit-resolution #9632 #7000]: #10338
-#10340 := [unit-resolution #10339 #10337]: #9617
-#8665 := (f14 f15 ?v1!16)
-#8676 := (* -1::Int #8665)
-#8924 := (+ #175 #8676)
-#8925 := (<= #8924 0::Int)
-#9638 := (not #8440)
-#9639 := (or #8450 #8447 #9638)
-#9640 := [def-axiom]: #9639
-#10309 := [unit-resolution #9640 #10340 #10337]: #9638
-#8930 := (or #8440 #8925)
-#4055 := (or #4536 #4387)
-#4041 := [def-axiom]: #4055
-#10314 := [unit-resolution #4041 #6509]: #4387
-#9985 := (or #4392 #8440 #8925)
-#8913 := (+ #8665 #1454)
-#8914 := (>= #8913 0::Int)
-#8917 := (or #8440 #8914)
-#9986 := (or #4392 #8917)
-#10021 := (iff #9986 #9985)
-#10017 := (or #4392 #8930)
-#10020 := (iff #10017 #9985)
-#10015 := [rewrite]: #10020
-#10018 := (iff #9986 #10017)
-#8931 := (iff #8917 #8930)
-#8928 := (iff #8914 #8925)
-#8918 := (+ #1454 #8665)
-#8921 := (>= #8918 0::Int)
-#8926 := (iff #8921 #8925)
-#8927 := [rewrite]: #8926
-#8922 := (iff #8914 #8921)
-#8919 := (= #8913 #8918)
-#8920 := [rewrite]: #8919
-#8923 := [monotonicity #8920]: #8922
-#8929 := [trans #8923 #8927]: #8928
-#8932 := [monotonicity #8929]: #8931
-#10019 := [monotonicity #8932]: #10018
-#10022 := [trans #10019 #10015]: #10021
-#10016 := [quant-inst #2289]: #9986
-#10023 := [mp #10016 #10022]: #9985
-#10308 := [unit-resolution #10023 #10314]: #8930
-#10315 := [unit-resolution #10308 #10309]: #8925
-#10587 := (not #8925)
-#10634 := (or #10613 #10587 #2889 #8447)
-#8718 := (+ #2887 #8693)
-#8719 := (+ #175 #8718)
-#8722 := (= #8719 0::Int)
-#10619 := (not #8722)
-#9836 := (<= #8719 0::Int)
-#10612 := (not #9836)
-#10600 := [hypothesis]: #9617
-#10602 := [hypothesis]: #4117
-#10589 := [hypothesis]: #10488
-#10614 := (or #10612 #2889 #10613 #8447)
-#10590 := [hypothesis]: #9836
-#10567 := (<= #10566 0::Int)
-#10568 := (not #10567)
-#10572 := (or #6783 #8447 #10568)
-#10569 := (or #8447 #10568)
-#10573 := (or #6783 #10569)
-#10575 := (iff #10573 #10572)
-#10576 := [rewrite]: #10575
-#10574 := [quant-inst #7212 #2289]: #10573
-#10577 := [mp #10574 #10576]: #10572
-#10601 := [unit-resolution #10577 #4218 #10600]: #10568
-#8569 := (+ #2291 #8568)
-#8570 := (<= #8569 0::Int)
-#9749 := (or #4418 #8570)
-#8558 := (+ #8486 #2292)
-#8559 := (>= #8558 0::Int)
-#9752 := (or #4418 #8559)
-#9767 := (iff #9752 #9749)
-#9769 := (iff #9749 #9749)
-#9770 := [rewrite]: #9769
-#8573 := (iff #8559 #8570)
-#8562 := (+ #2292 #8486)
-#8565 := (>= #8562 0::Int)
-#8571 := (iff #8565 #8570)
-#8572 := [rewrite]: #8571
-#8566 := (iff #8559 #8565)
-#8563 := (= #8558 #8562)
-#8564 := [rewrite]: #8563
-#8567 := [monotonicity #8564]: #8566
-#8574 := [trans #8567 #8572]: #8573
-#9768 := [monotonicity #8574]: #9767
-#9771 := [trans #9768 #9770]: #9767
-#9766 := [quant-inst #2290]: #9752
-#9772 := [mp #9766 #9771]: #9749
-#10603 := [unit-resolution #9772 #8194]: #8570
-#7530 := (* -1::Int #7514)
-#8424 := (+ #175 #7530)
-#8430 := (>= #8424 0::Int)
-#7337 := (= #175 #7514)
-#10604 := (= #7514 #175)
-#10605 := [monotonicity #7791]: #10604
-#10606 := [symm #10605]: #7337
-#10607 := (not #7337)
-#10608 := (or #10607 #8430)
-#10609 := [th-lemma arith triangle-eq]: #10608
-#10610 := [unit-resolution #10609 #10606]: #8430
-#10611 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10610 #10603 #10602 #10601 #10599 #10590 #10589]: false
-#10615 := [lemma #10611]: #10614
-#10618 := [unit-resolution #10615 #10589 #10602 #10600]: #10612
-#10620 := (or #10619 #9836)
-#10621 := [th-lemma arith triangle-eq]: #10620
-#10622 := [unit-resolution #10621 #10618]: #10619
-#8697 := (* -1::Int #8693)
-#8701 := (+ f9 #8697)
-#8702 := (<= #8701 0::Int)
-#9850 := (not #8702)
-#8711 := (+ #8676 #8693)
-#8712 := (+ #175 #8711)
-#8713 := (>= #8712 0::Int)
-#8748 := (or #8702 #8713)
-#8751 := (not #8748)
-#8745 := (= #2293 #8665)
-#10624 := (not #8745)
-#8677 := (+ #2293 #8676)
-#9849 := (>= #8677 0::Int)
-#10585 := (not #9849)
-#10580 := [hypothesis]: #8925
-#10616 := (or #10585 #2889 #10587 #10613)
-#10581 := [hypothesis]: #9849
-#10584 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10610 #10603 #10602 #10581 #10580 #10589]: false
-#10617 := [lemma #10584]: #10616
-#10623 := [unit-resolution #10617 #10589 #10580 #10602]: #10585
-#10625 := (or #10624 #9849)
-#10626 := [th-lemma arith triangle-eq]: #10625
-#10627 := [unit-resolution #10626 #10623]: #10624
-#8754 := (or #8745 #8751)
-#9838 := (or #4402 #8745 #8751)
-#8698 := (+ #1454 #8697)
-#8699 := (+ #8665 #8698)
-#8700 := (<= #8699 0::Int)
-#8741 := (or #8702 #8700)
-#8742 := (not #8741)
-#8743 := (= #8665 #2293)
-#8744 := (or #8743 #8742)
-#9839 := (or #4402 #8744)
-#9846 := (iff #9839 #9838)
-#9840 := (or #4402 #8754)
-#9843 := (iff #9840 #9838)
-#9844 := [rewrite]: #9843
-#9841 := (iff #9839 #9840)
-#8755 := (iff #8744 #8754)
-#8752 := (iff #8742 #8751)
-#8749 := (iff #8741 #8748)
-#8716 := (iff #8700 #8713)
-#8704 := (+ #8665 #8697)
-#8705 := (+ #1454 #8704)
-#8708 := (<= #8705 0::Int)
-#8714 := (iff #8708 #8713)
-#8715 := [rewrite]: #8714
-#8709 := (iff #8700 #8708)
-#8706 := (= #8699 #8705)
-#8707 := [rewrite]: #8706
-#8710 := [monotonicity #8707]: #8709
-#8717 := [trans #8710 #8715]: #8716
-#8750 := [monotonicity #8717]: #8749
-#8753 := [monotonicity #8750]: #8752
-#8746 := (iff #8743 #8745)
-#8747 := [rewrite]: #8746
-#8756 := [monotonicity #8747 #8753]: #8755
-#9842 := [monotonicity #8756]: #9841
-#9847 := [trans #9842 #9844]: #9846
-#9818 := [quant-inst #2289]: #9839
-#9848 := [mp #9818 #9847]: #9838
-#10628 := [unit-resolution #9848 #6510]: #8754
-#10629 := [unit-resolution #10628 #10627]: #8751
-#9845 := (or #8748 #9850)
-#9851 := [def-axiom]: #9845
-#10630 := [unit-resolution #9851 #10629]: #9850
-#9852 := (not #8713)
-#9853 := (or #8748 #9852)
-#9854 := [def-axiom]: #9853
-#10631 := [unit-resolution #9854 #10629]: #9852
-#8725 := (or #8702 #8713 #8722)
-#9824 := (or #4410 #8702 #8713 #8722)
-#8694 := (+ #8693 #2887)
-#8695 := (+ #175 #8694)
-#8696 := (= #8695 0::Int)
-#8703 := (or #8702 #8700 #8696)
-#9825 := (or #4410 #8703)
-#9831 := (iff #9825 #9824)
-#9827 := (or #4410 #8725)
-#9829 := (iff #9827 #9824)
-#9830 := [rewrite]: #9829
-#9822 := (iff #9825 #9827)
-#8726 := (iff #8703 #8725)
-#8723 := (iff #8696 #8722)
-#8720 := (= #8695 #8719)
-#8721 := [rewrite]: #8720
-#8724 := [monotonicity #8721]: #8723
-#8727 := [monotonicity #8717 #8724]: #8726
-#9828 := [monotonicity #8727]: #9822
-#9832 := [trans #9828 #9830]: #9831
-#9826 := [quant-inst #2289]: #9825
-#9835 := [mp #9826 #9832]: #9824
-#10632 := [unit-resolution #9835 #6514]: #8725
-#10633 := [unit-resolution #10632 #10631 #10630 #10622]: false
-#10635 := [lemma #10633]: #10634
-#10316 := [unit-resolution #10635 #10315 #10292 #10340]: #10613
-#10311 := (or #9732 #10488)
-#10296 := [hypothesis]: #10613
-#10298 := [hypothesis]: #8512
-#7516 := (f3 f16 #7212)
-#7517 := (= f1 #7516)
-#10304 := (not #7517)
-#10305 := (iff #758 #10304)
-#10297 := (iff #755 #7517)
-#10301 := (iff #7517 #755)
-#10299 := (= #7516 #172)
-#10300 := [monotonicity #7791]: #10299
-#10302 := [monotonicity #10300]: #10301
-#10303 := [symm #10302]: #10297
-#10306 := [monotonicity #10303]: #10305
-#10307 := [mp #6927 #10306]: #10304
-#10234 := (or #4297 #7517 #9732 #10488)
-#10495 := (or #7517 #9732 #10488)
-#10240 := (or #4297 #10495)
-#10242 := (iff #10240 #10234)
-#10243 := [rewrite]: #10242
-#10241 := [quant-inst #2290 #7212]: #10240
-#10244 := [mp #10241 #10243]: #10234
-#10310 := [unit-resolution #10244 #6938 #10307 #10298 #10296]: false
-#10312 := [lemma #10310]: #10311
-#10317 := [unit-resolution #10312 #10316]: #9732
-#9725 := (not #8521)
-#9728 := (or #9725 #8518 #8512)
-#9729 := [def-axiom]: #9728
-#10318 := [unit-resolution #9729 #10317 #10325]: #8518
-#10319 := [trans #10318 #7791]: #10481
-#10320 := [monotonicity #10319]: #10213
-#10347 := (not #10213)
-#10348 := (or #10347 #10225)
-#10346 := [th-lemma arith triangle-eq]: #10348
-#10349 := [unit-resolution #10346 #10320]: #10225
-#10351 := (not #6419)
-#10350 := (not #10225)
-#10356 := (or #10585 #10350 #2889 #10587 #10351)
-#10357 := [th-lemma arith assign-bounds -1 1 -1 1]: #10356
-#10355 := [unit-resolution #10357 #10292 #8195 #10315 #10349]: #10585
-#10358 := [unit-resolution #10626 #10355]: #10624
-#10359 := [unit-resolution #10628 #10358]: #8751
-#10184 := (or #8748 #8722)
-#10180 := [hypothesis]: #10619
-#10181 := [hypothesis]: #8751
-#10182 := [unit-resolution #9851 #10181]: #9850
-#10177 := [unit-resolution #9854 #10181]: #9852
-#10183 := [unit-resolution #10632 #10177 #10182 #10180]: false
-#10185 := [lemma #10183]: #10184
-#10360 := [unit-resolution #10185 #10359]: #8722
-#10377 := [unit-resolution #10621 #10360]: #9836
-#10378 := [unit-resolution #10577 #4218 #10340]: #10568
-#10379 := [th-lemma arith farkas 1 1 1 1 1 1 #10378 #10377 #10349 #10292 #8195 #10599]: false
-#10381 := [lemma #10379]: #10380
-#9760 := [unit-resolution #10381 #9759 #10289]: false
-#9761 := [lemma #9760]: #3441
-#4107 := (or #4485 #3446 #4479)
-#4094 := [def-axiom]: #4107
-#12722 := [unit-resolution #4094 #9761]: #12721
-#23133 := [unit-resolution #12722 #23140]: #4479
-#4001 := (or #4476 #4470)
-#4009 := [def-axiom]: #4001
-#23134 := [unit-resolution #4009 #23133]: #4470
-#23135 := (or #4473 #4467)
-#14672 := (f6 f23 ?v0!19)
-#14673 := (f10 #14672)
-#14468 := (f14 f15 ?v0!19)
-#14604 := (* -1::Int #14468)
-#14720 := (+ #14604 #14673)
-#14721 := (+ #175 #14720)
-#14722 := (>= #14721 0::Int)
-#14961 := (not #14722)
-#14676 := (* -1::Int #14673)
-#15460 := (+ #2323 #14676)
-#15461 := (>= #15460 0::Int)
-#15459 := (= #2323 #14673)
-#15669 := (= #2322 #14672)
-#15696 := (= ?v1!18 f23)
-#13666 := (= ?v1!18 #7212)
-#13659 := (f3 f16 ?v1!18)
-#13660 := (= f1 #13659)
-#13803 := (not #13660)
-#13799 := (f14 f15 ?v1!18)
-#14924 := (+ #13799 #14604)
-#14925 := (+ #2323 #14924)
-#14920 := (>= #14925 0::Int)
-#15620 := (not #14920)
-#14605 := (+ #2318 #14604)
-#14606 := (<= #14605 0::Int)
-#14819 := (or #4418 #14606)
-#14571 := (+ #14468 #2319)
-#14598 := (>= #14571 0::Int)
-#14820 := (or #4418 #14598)
-#14822 := (iff #14820 #14819)
-#14824 := (iff #14819 #14819)
-#14825 := [rewrite]: #14824
-#14623 := (iff #14598 #14606)
-#14599 := (+ #2319 #14468)
-#14602 := (>= #14599 0::Int)
-#14607 := (iff #14602 #14606)
-#14622 := [rewrite]: #14607
-#14597 := (iff #14598 #14602)
-#14600 := (= #14571 #14599)
-#14601 := [rewrite]: #14600
-#14603 := [monotonicity #14601]: #14597
-#14624 := [trans #14603 #14622]: #14623
-#14823 := [monotonicity #14624]: #14822
-#14773 := [trans #14823 #14825]: #14822
-#14821 := [quant-inst #2317]: #14820
-#14892 := [mp #14821 #14773]: #14819
-#15609 := [unit-resolution #14892 #8194]: #14606
-#4123 := (not #2916)
-#15610 := [hypothesis]: #3492
-#3952 := (or #3487 #4123)
-#3954 := [def-axiom]: #3952
-#15608 := [unit-resolution #3954 #15610]: #4123
-#13816 := (* -1::Int #13799)
-#13817 := (+ #2320 #13816)
-#13545 := (>= #13817 0::Int)
-#13885 := (= #2320 #13799)
-#4122 := (or #3487 #2331)
-#4116 := [def-axiom]: #4122
-#15611 := [unit-resolution #4116 #15610]: #2331
-#13777 := (or #4427 #3472 #13885)
-#13883 := (= #13799 #2320)
-#13753 := (or #13883 #3472)
-#13778 := (or #4427 #13753)
-#13800 := (iff #13778 #13777)
-#13751 := (or #3472 #13885)
-#13792 := (or #4427 #13751)
-#13802 := (iff #13792 #13777)
-#13794 := [rewrite]: #13802
-#13797 := (iff #13778 #13792)
-#13759 := (iff #13753 #13751)
-#13754 := (or #13885 #3472)
-#13757 := (iff #13754 #13751)
-#13758 := [rewrite]: #13757
-#13755 := (iff #13753 #13754)
-#13886 := (iff #13883 #13885)
-#13887 := [rewrite]: #13886
-#13756 := [monotonicity #13887]: #13755
-#13760 := [trans #13756 #13758]: #13759
-#13801 := [monotonicity #13760]: #13797
-#13804 := [trans #13801 #13794]: #13800
-#13796 := [quant-inst #2316]: #13778
-#13805 := [mp #13796 #13804]: #13777
-#15616 := [unit-resolution #13805 #7101 #15611]: #13885
-#15617 := (not #13885)
-#15618 := (or #15617 #13545)
-#15602 := [th-lemma arith triangle-eq]: #15618
-#15619 := [unit-resolution #15602 #15616]: #13545
-#15615 := (not #14606)
-#15612 := (not #13545)
-#15621 := (or #15620 #15612 #15615 #2916)
-#15623 := [th-lemma arith assign-bounds 1 -1 1]: #15621
-#15624 := [unit-resolution #15623 #15619 #15608 #15609]: #15620
-#15629 := (or #13803 #14920)
-#4115 := (or #3487 #2329)
-#4121 := [def-axiom]: #4115
-#15627 := [unit-resolution #4121 #15610]: #2329
-#15628 := [unit-resolution #4016 #6508]: #4283
-#13312 := (or #4288 #2328 #13803 #14920)
-#14926 := (or #13803 #2328 #14920)
-#13541 := (or #4288 #14926)
-#15127 := (iff #13541 #13312)
-#14927 := (or #2328 #13803 #14920)
-#13547 := (or #4288 #14927)
-#15125 := (iff #13547 #13312)
-#15126 := [rewrite]: #15125
-#13649 := (iff #13541 #13547)
-#14928 := (iff #14926 #14927)
-#14929 := [rewrite]: #14928
-#15124 := [monotonicity #14929]: #13649
-#15128 := [trans #15124 #15126]: #15127
-#13544 := [quant-inst #2317 #2316]: #13541
-#15129 := [mp #13544 #15128]: #13312
-#15622 := [unit-resolution #15129 #15628 #15627]: #15629
-#15630 := [unit-resolution #15622 #15624]: #13803
-#13669 := (ite #13666 #5893 #13660)
-#13663 := (f3 #8443 ?v1!18)
-#13664 := (= f1 #13663)
-#13672 := (iff #13664 #13669)
-#15013 := (or #6291 #13672)
-#13661 := (= #7212 ?v1!18)
-#13662 := (ite #13661 #5893 #13660)
-#13665 := (iff #13664 #13662)
-#15018 := (or #6291 #13665)
-#14891 := (iff #15018 #15013)
-#15044 := (iff #15013 #15013)
-#15045 := [rewrite]: #15044
-#13673 := (iff #13665 #13672)
-#13670 := (iff #13662 #13669)
-#13667 := (iff #13661 #13666)
-#13668 := [rewrite]: #13667
-#13671 := [monotonicity #13668]: #13670
-#13674 := [monotonicity #13671]: #13673
-#15020 := [monotonicity #13674]: #14891
-#15061 := [trans #15020 #15045]: #14891
-#15019 := [quant-inst #105 #7212 #5892 #2316]: #15018
-#14890 := [mp #15019 #15061]: #15013
-#15631 := [unit-resolution #14890 #4178]: #13672
-#15691 := (= #2330 #13663)
-#15625 := (= #13663 #2330)
-#15626 := [monotonicity #9287]: #15625
-#15693 := [symm #15626]: #15691
-#15694 := [trans #15611 #15693]: #13664
-#13238 := (not #13664)
-#12831 := (not #13672)
-#12789 := (or #12831 #13238 #13669)
-#13251 := [def-axiom]: #12789
-#15695 := [unit-resolution #13251 #15694 #15631]: #13669
-#15062 := (not #13669)
-#15060 := (or #15062 #13666 #13660)
-#15068 := [def-axiom]: #15060
-#15689 := [unit-resolution #15068 #15695 #15630]: #13666
-#15668 := [trans #15689 #7791]: #15696
-#15667 := [monotonicity #15668]: #15669
-#15671 := [monotonicity #15667]: #15459
-#15673 := (not #15459)
-#15674 := (or #15673 #15461)
-#15675 := [th-lemma arith triangle-eq]: #15674
-#15670 := [unit-resolution #15675 #15671]: #15461
-#15239 := (+ #2320 #6049)
-#15241 := (>= #15239 0::Int)
-#15451 := (= #2320 #6008)
-#15762 := [monotonicity #15668]: #15451
-#15672 := (not #15451)
-#15768 := (or #15672 #15241)
-#15769 := [th-lemma arith triangle-eq]: #15768
-#15770 := [unit-resolution #15769 #15762]: #15241
-#6675 := (<= #6418 0::Int)
-#6009 := (= #175 #6008)
-#6548 := (f3 f24 f23)
-#6549 := (= f1 #6548)
-#8185 := (= #5892 #6548)
-#8183 := (= #6548 #5892)
-#8184 := [monotonicity #6999]: #8183
-#8186 := [symm #8184]: #8185
-#8187 := [trans #7000 #8186]: #6549
-#6555 := (not #6549)
-#6607 := (or #6009 #6555)
-#6688 := (or #4427 #6009 #6555)
-#6689 := (or #4427 #6607)
-#6691 := (iff #6689 #6688)
-#6692 := [rewrite]: #6691
-#6690 := [quant-inst #171]: #6689
-#6693 := [mp #6690 #6692]: #6688
-#8188 := [unit-resolution #6693 #7101]: #6607
-#8189 := [unit-resolution #8188 #8187]: #6009
-#8190 := (not #6009)
-#8191 := (or #8190 #6675)
-#8192 := [th-lemma arith triangle-eq]: #8191
-#8193 := [unit-resolution #8192 #8189]: #6675
-#16340 := (not #15461)
-#12653 := (not #6675)
-#15771 := (not #15241)
-#15767 := (or #14961 #15615 #2916 #15771 #12653 #16340)
-#15775 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15767
-#15776 := [unit-resolution #15775 #15609 #8193 #15770 #15608 #15670]: #14961
-#14680 := (+ f9 #14676)
-#14732 := (<= #14680 0::Int)
-#15015 := (not #14732)
-#16341 := (or #15015 #16340 #2328)
-#16337 := [hypothesis]: #2329
-#16332 := [hypothesis]: #14732
-#16338 := [hypothesis]: #15461
-#16339 := [th-lemma arith farkas 1 -1 1 #16338 #16332 #16337]: false
-#16342 := [lemma #16339]: #16341
-#15777 := [unit-resolution #16342 #15670 #15627]: #15015
-#14726 := (+ #2319 #14673)
-#14727 := (+ #175 #14726)
-#14744 := (= #14727 0::Int)
-#15812 := (not #14744)
-#14858 := (>= #14727 0::Int)
-#15773 := (not #14858)
-#15794 := (or #15773 #2916 #15771 #12653 #16340)
-#15806 := [th-lemma arith assign-bounds 1 1 -1 1]: #15794
-#15807 := [unit-resolution #15806 #15770 #8193 #15608 #15670]: #15773
-#15813 := (or #15812 #14858)
-#15814 := [th-lemma arith triangle-eq]: #15813
-#15848 := [unit-resolution #15814 #15807]: #15812
-#14769 := (or #14722 #14732 #14744)
-#14893 := (or #4410 #14722 #14732 #14744)
-#14674 := (+ #14673 #2319)
-#14675 := (+ #175 #14674)
-#14670 := (= #14675 0::Int)
-#14677 := (+ #1454 #14676)
-#14678 := (+ #14468 #14677)
-#14679 := (<= #14678 0::Int)
-#14733 := (or #14732 #14679 #14670)
-#14894 := (or #4410 #14733)
-#14861 := (iff #14894 #14893)
-#14896 := (or #4410 #14769)
-#14859 := (iff #14896 #14893)
-#14860 := [rewrite]: #14859
-#14922 := (iff #14894 #14896)
-#14771 := (iff #14733 #14769)
-#14766 := (or #14732 #14722 #14744)
-#14764 := (iff #14766 #14769)
-#14770 := [rewrite]: #14764
-#14767 := (iff #14733 #14766)
-#14745 := (iff #14670 #14744)
-#14728 := (= #14675 #14727)
-#14729 := [rewrite]: #14728
-#14765 := [monotonicity #14729]: #14745
-#14719 := (iff #14679 #14722)
-#14734 := (+ #14468 #14676)
-#14735 := (+ #1454 #14734)
-#14738 := (<= #14735 0::Int)
-#14723 := (iff #14738 #14722)
-#14724 := [rewrite]: #14723
-#14739 := (iff #14679 #14738)
-#14736 := (= #14678 #14735)
-#14737 := [rewrite]: #14736
-#14740 := [monotonicity #14737]: #14739
-#14725 := [trans #14740 #14724]: #14719
-#14768 := [monotonicity #14725 #14765]: #14767
-#14772 := [trans #14768 #14770]: #14771
-#14923 := [monotonicity #14772]: #14922
-#14921 := [trans #14923 #14860]: #14861
-#14895 := [quant-inst #2317]: #14894
-#14862 := [mp #14895 #14921]: #14893
-#15846 := [unit-resolution #14862 #6514]: #14769
-#15847 := [unit-resolution #15846 #15848 #15777 #15776]: false
-#15843 := [lemma #15847]: #3487
-#3990 := (or #4473 #3492 #4467)
-#4005 := [def-axiom]: #3990
-#23150 := [unit-resolution #4005 #15843]: #23135
-#23151 := [unit-resolution #23150 #23134]: #4467
-#4109 := (or #4464 #2361)
-#4111 := [def-axiom]: #4109
-#23152 := [unit-resolution #4111 #23151]: #2361
-#23153 := (= #9082 #6071)
-#23154 := [monotonicity #9283]: #23153
-#23156 := [symm #23154]: #9862
-#23157 := [unit-resolution #11950 #23156]: #9458
-#9819 := (<= #9456 0::Int)
-#23149 := (or #11946 #9819)
-#23155 := [th-lemma arith triangle-eq]: #23149
-#23158 := [unit-resolution #23155 #23156]: #9819
-#23159 := (not #9819)
-#23165 := (or #10879 #23159)
-#7359 := (>= #6071 0::Int)
-#7297 := (not #7359)
-#7298 := [hypothesis]: #7297
-#7979 := (or #4280 #7359)
-#7980 := [quant-inst #6070]: #7979
-#7485 := [unit-resolution #7980 #7122 #7298]: false
-#7489 := [lemma #7485]: #7359
-#7054 := (not #3921)
-#23160 := (or #10879 #7054 #7297 #23159)
-#23162 := [th-lemma arith assign-bounds -1 1 -1]: #23160
-#23166 := [unit-resolution #23162 #7489 #7127]: #23165
-#23164 := [unit-resolution #23166 #23158]: #10879
-#3996 := (or #4464 #4456)
-#3997 := [def-axiom]: #3996
-#23167 := [unit-resolution #3997 #23151]: #4456
-#24106 := (or #14184 #4461)
-#8779 := (f25 #7212)
-#9545 := (* -1::Int #8779)
-#14039 := (+ #2348 #9545)
-#14227 := (<= #14039 0::Int)
-#10165 := (f3 f24 #7212)
-#10166 := (= f1 #10165)
-#11811 := (= #5892 #10165)
-#11804 := (= #10165 #5892)
-#11810 := [monotonicity #6999 #7791]: #11804
-#11812 := [symm #11810]: #11811
-#11813 := [trans #7000 #11812]: #10166
-#14213 := (f10 #14212)
-#14239 := (* -1::Int #14213)
-#14240 := (+ #9545 #14239)
-#14241 := (+ #2348 #14240)
-#14242 := (= #14241 0::Int)
-#15157 := (>= #14241 0::Int)
-#14158 := (+ #2349 #14133)
-#14159 := (+ #175 #14158)
-#14428 := (<= #14159 0::Int)
-#14162 := (= #14159 0::Int)
-#14187 := (not #14184)
-#21312 := [hypothesis]: #14187
-#21317 := (or #14184 #14162)
-#21306 := (not #14162)
-#21307 := [hypothesis]: #21306
-#12473 := (not #14142)
-#12480 := (or #14184 #12473)
-#12481 := [def-axiom]: #12480
-#21313 := [unit-resolution #12481 #21312]: #12473
-#12470 := (not #14153)
-#12479 := (or #14184 #12470)
-#12482 := [def-axiom]: #12479
-#21314 := [unit-resolution #12482 #21312]: #12470
-#14165 := (or #14142 #14153 #14162)
-#12412 := (or #4410 #14142 #14153 #14162)
-#14134 := (+ #14133 #2349)
-#14135 := (+ #175 #14134)
-#14136 := (= #14135 0::Int)
-#14138 := (+ #1454 #14137)
-#14139 := (+ #14075 #14138)
-#14140 := (<= #14139 0::Int)
-#14143 := (or #14142 #14140 #14136)
-#12436 := (or #4410 #14143)
-#12441 := (iff #12436 #12412)
-#12409 := (or #4410 #14165)
-#12440 := (iff #12409 #12412)
-#12435 := [rewrite]: #12440
-#12438 := (iff #12436 #12409)
-#14166 := (iff #14143 #14165)
-#14163 := (iff #14136 #14162)
-#14160 := (= #14135 #14159)
-#14161 := [rewrite]: #14160
-#14164 := [monotonicity #14161]: #14163
-#14156 := (iff #14140 #14153)
-#14144 := (+ #14075 #14137)
-#14145 := (+ #1454 #14144)
-#14148 := (<= #14145 0::Int)
-#14154 := (iff #14148 #14153)
-#14155 := [rewrite]: #14154
-#14149 := (iff #14140 #14148)
-#14146 := (= #14139 #14145)
-#14147 := [rewrite]: #14146
-#14150 := [monotonicity #14147]: #14149
-#14157 := [trans #14150 #14155]: #14156
-#14167 := [monotonicity #14157 #14164]: #14166
-#12439 := [monotonicity #14167]: #12438
-#12443 := [trans #12439 #12435]: #12441
-#12437 := [quant-inst #2347]: #12436
-#12444 := [mp #12437 #12443]: #12412
-#21315 := [unit-resolution #12444 #6514]: #14165
-#21316 := [unit-resolution #21315 #21314 #21313 #21307]: false
-#21318 := [lemma #21316]: #21317
-#24023 := [unit-resolution #21318 #21312]: #14162
-#24024 := (or #21306 #14428)
-#24025 := [th-lemma arith triangle-eq]: #24024
-#24026 := [unit-resolution #24025 #24023]: #14428
-#17685 := (not #14428)
-#24047 := (or #15157 #17685)
-#9546 := (+ #6008 #9545)
-#7446 := (>= #9546 0::Int)
-#9544 := (= #6008 #8779)
-#11875 := (= #8779 #6008)
-#11876 := [monotonicity #7791]: #11875
-#11877 := [symm #11876]: #9544
-#11878 := (not #9544)
-#24021 := (or #11878 #7446)
-#24027 := [th-lemma arith triangle-eq]: #24021
-#24028 := [unit-resolution #24027 #11877]: #7446
-#13354 := (+ #14133 #14239)
-#13587 := (>= #13354 0::Int)
-#7924 := (= #14133 #14213)
-#24031 := (= #14213 #14133)
-#24038 := [monotonicity #24030]: #24031
-#24039 := [symm #24038]: #7924
-#24037 := (not #7924)
-#24040 := (or #24037 #13587)
-#24041 := [th-lemma arith triangle-eq]: #24040
-#24042 := [unit-resolution #24041 #24039]: #13587
-#24045 := (not #13587)
-#24044 := (not #7446)
-#24043 := (or #15157 #24044 #10351 #24045 #17685)
-#24046 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24043
-#24048 := [unit-resolution #24046 #24042 #24028 #8195]: #24047
-#24036 := [unit-resolution #24048 #24026]: #15157
-#15135 := (<= #14241 0::Int)
-#14429 := (>= #14159 0::Int)
-#24049 := (or #21306 #14429)
-#24050 := [th-lemma arith triangle-eq]: #24049
-#24051 := [unit-resolution #24050 #24023]: #14429
-#24055 := (not #14429)
-#24059 := (or #15135 #24055)
-#9547 := (<= #9546 0::Int)
-#11879 := (or #11878 #9547)
-#11880 := [th-lemma arith triangle-eq]: #11879
-#11881 := [unit-resolution #11880 #11877]: #9547
-#13355 := (<= #13354 0::Int)
-#24052 := (or #24037 #13355)
-#24035 := [th-lemma arith triangle-eq]: #24052
-#24053 := [unit-resolution #24035 #24039]: #13355
-#24054 := (not #13355)
-#12652 := (not #9547)
-#24056 := (or #15135 #12652 #12653 #24054 #24055)
-#24057 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24056
-#24060 := [unit-resolution #24057 #24053 #11881 #8193]: #24059
-#24061 := [unit-resolution #24060 #24051]: #15135
-#24063 := (not #15157)
-#24062 := (not #15135)
-#24058 := (or #14242 #24062 #24063)
-#24064 := [th-lemma arith triangle-eq]: #24058
-#24065 := [unit-resolution #24064 #24061 #24036]: #14242
-#14247 := (not #14242)
-#10178 := (not #10166)
-#14250 := (or #10178 #14227 #14247)
-#24066 := [hypothesis]: #4456
-#12778 := (or #4461 #10178 #14227 #14247)
-#14214 := (+ #2349 #14213)
-#14215 := (+ #8779 #14214)
-#14216 := (= #14215 0::Int)
-#14217 := (not #14216)
-#14218 := (+ #8779 #2349)
-#14219 := (>= #14218 0::Int)
-#14220 := (or #10178 #14219 #14217)
-#12785 := (or #4461 #14220)
-#12838 := (iff #12785 #12778)
-#12849 := (or #4461 #14250)
-#12872 := (iff #12849 #12778)
-#12878 := [rewrite]: #12872
-#12876 := (iff #12785 #12849)
-#14251 := (iff #14220 #14250)
-#14248 := (iff #14217 #14247)
-#14245 := (iff #14216 #14242)
-#14232 := (+ #8779 #14213)
-#14233 := (+ #2349 #14232)
-#14236 := (= #14233 0::Int)
-#14243 := (iff #14236 #14242)
-#14244 := [rewrite]: #14243
-#14237 := (iff #14216 #14236)
-#14234 := (= #14215 #14233)
-#14235 := [rewrite]: #14234
-#14238 := [monotonicity #14235]: #14237
-#14246 := [trans #14238 #14244]: #14245
-#14249 := [monotonicity #14246]: #14248
-#14230 := (iff #14219 #14227)
-#14221 := (+ #2349 #8779)
-#14224 := (>= #14221 0::Int)
-#14228 := (iff #14224 #14227)
-#14229 := [rewrite]: #14228
-#14225 := (iff #14219 #14224)
-#14222 := (= #14218 #14221)
-#14223 := [rewrite]: #14222
-#14226 := [monotonicity #14223]: #14225
-#14231 := [trans #14226 #14229]: #14230
-#14252 := [monotonicity #14231 #14249]: #14251
-#12877 := [monotonicity #14252]: #12876
-#12904 := [trans #12877 #12878]: #12838
-#12842 := [quant-inst #7212]: #12785
-#12905 := [mp #12842 #12904]: #12778
-#24067 := [unit-resolution #12905 #24066]: #14250
-#24068 := [unit-resolution #24067 #24065 #11813]: #14227
-#12488 := (f6 f11 ?v0!20)
-#17156 := (f8 #12488)
-#22317 := (f6 #7212 #17156)
-#22326 := (f10 #22317)
-#22329 := (* -1::Int #22326)
-#22458 := (+ #14133 #22329)
-#17192 := (>= #22458 0::Int)
-#17178 := (= #14133 #22326)
-#24069 := (= #22326 #14133)
-#24073 := (= #22317 #14132)
-#24071 := (= #17156 ?v0!20)
-#17157 := (= ?v0!20 #17156)
-#17180 := (or #6825 #17157)
-#17181 := [quant-inst #57 #2347]: #17180
-#24070 := [unit-resolution #17181 #4200]: #17157
-#24072 := [symm #24070]: #24071
-#24074 := [monotonicity #7791 #24072]: #24073
-#24075 := [monotonicity #24074]: #24069
-#24076 := [symm #24075]: #17178
-#24077 := (not #17178)
-#24078 := (or #24077 #17192)
-#24079 := [th-lemma arith triangle-eq]: #24078
-#24081 := [unit-resolution #24079 #24076]: #17192
-#22385 := (<= #22326 0::Int)
-#22365 := (not #22385)
-#22368 := (= #7212 #17156)
-#22398 := (not #22368)
-#20555 := (f3 f16 #17156)
-#20572 := (= f1 #20555)
-#23982 := (ite #22368 #5893 #20572)
-#24002 := (not #23982)
-#23983 := (f3 #8443 #17156)
-#23988 := (= f1 #23983)
-#23990 := (iff #23982 #23988)
-#23994 := (or #6291 #23990)
-#23989 := (iff #23988 #23982)
-#23995 := (or #6291 #23989)
-#23997 := (iff #23995 #23994)
-#23993 := (iff #23994 #23994)
-#23999 := [rewrite]: #23993
-#23991 := (iff #23989 #23990)
-#23992 := [rewrite]: #23991
-#23998 := [monotonicity #23992]: #23997
-#24000 := [trans #23998 #23999]: #23997
-#23996 := [quant-inst #105 #7212 #5892 #17156]: #23995
-#24001 := [mp #23996 #24000]: #23994
-#24082 := [unit-resolution #24001 #4178]: #23990
-#24014 := (not #23988)
-#10247 := (f3 f24 ?v0!20)
-#10248 := (= f1 #10247)
-#10249 := (not #10248)
-#24095 := (iff #10249 #24014)
-#24093 := (iff #10248 #23988)
-#24090 := (iff #23988 #10248)
-#24088 := (= #23983 #10247)
-#24089 := [monotonicity #9287 #24072]: #24088
-#24092 := [monotonicity #24089]: #24090
-#24094 := [symm #24092]: #24093
-#24096 := [monotonicity #24094]: #24095
-#24709 := (not #14086)
-#21437 := (not #19568)
-#24083 := (or #14153 #21437 #24045 #24062 #24044 #10351)
-#24084 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24083
-#24085 := [unit-resolution #24084 #24061 #24042 #21314 #24028 #8195]: #21437
-#24710 := (or #24709 #19568)
-#24697 := [hypothesis]: #21437
-#24698 := [hypothesis]: #14086
-#24711 := [th-lemma arith triangle-eq]: #24710
-#24712 := [unit-resolution #24711 #24698 #24697]: false
-#24713 := [lemma #24712]: #24710
-#24080 := [unit-resolution #24713 #24085]: #24709
-#14092 := (or #10249 #14086)
-#12335 := (or #4427 #10249 #14086)
-#14082 := (= #14075 #2348)
-#14085 := (or #14082 #10249)
-#12375 := (or #4427 #14085)
-#12383 := (iff #12375 #12335)
-#12378 := (or #4427 #14092)
-#12380 := (iff #12378 #12335)
-#12382 := [rewrite]: #12380
-#12379 := (iff #12375 #12378)
-#14095 := (iff #14085 #14092)
-#14089 := (or #14086 #10249)
-#14093 := (iff #14089 #14092)
-#14094 := [rewrite]: #14093
-#14090 := (iff #14085 #14089)
-#14087 := (iff #14082 #14086)
-#14088 := [rewrite]: #14087
-#14091 := [monotonicity #14088]: #14090
-#14096 := [trans #14091 #14094]: #14095
-#12374 := [monotonicity #14096]: #12379
-#12384 := [trans #12374 #12382]: #12383
-#12377 := [quant-inst #2347]: #12375
-#12403 := [mp #12377 #12384]: #12335
-#24086 := [unit-resolution #12403 #7101]: #14092
-#24087 := [unit-resolution #24086 #24080]: #10249
-#24091 := [mp #24087 #24096]: #24014
-#24013 := (not #23990)
-#24016 := (or #24013 #24002 #23988)
-#24017 := [def-axiom]: #24016
-#24097 := [unit-resolution #24017 #24091 #24082]: #24002
-#24098 := (or #23982 #22398)
-#24009 := (or #23982 #22398 #6305)
-#24010 := [def-axiom]: #24009
-#24099 := [unit-resolution #24010 #7000]: #24098
-#24100 := [unit-resolution #24099 #24097]: #22398
-#22370 := (or #22368 #22365)
-#23959 := (or #6783 #22368 #22365)
-#22366 := (= #17156 #7212)
-#22367 := (or #22366 #22365)
-#23960 := (or #6783 #22367)
-#23967 := (iff #23960 #23959)
-#23962 := (or #6783 #22370)
-#23965 := (iff #23962 #23959)
-#23966 := [rewrite]: #23965
-#23963 := (iff #23960 #23962)
-#22371 := (iff #22367 #22370)
-#22369 := (iff #22366 #22368)
-#22364 := [rewrite]: #22369
-#22372 := [monotonicity #22364]: #22371
-#23964 := [monotonicity #22372]: #23963
-#23968 := [trans #23964 #23966]: #23967
-#23961 := [quant-inst #7212 #17156]: #23960
-#23969 := [mp #23961 #23968]: #23959
-#24101 := [unit-resolution #23969 #4218]: #22370
-#24104 := [unit-resolution #24101 #24100]: #22365
-#24105 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24028 #8195 #24104 #24081 #24026 #24068]: false
-#24107 := [lemma #24105]: #24106
-#23168 := [unit-resolution #24107 #23167]: #14184
-#23148 := [hypothesis]: #12470
-#12483 := (or #14187 #14142 #14153)
-#12484 := [def-axiom]: #12483
-#23161 := [unit-resolution #12484 #23148 #23168]: #14142
-#14190 := (or #14086 #14187)
-#12445 := (or #4402 #14086 #14187)
-#14181 := (or #14142 #14140)
-#14182 := (not #14181)
-#14183 := (or #14082 #14182)
-#12464 := (or #4402 #14183)
-#12469 := (iff #12464 #12445)
-#12442 := (or #4402 #14190)
-#12468 := (iff #12442 #12445)
-#12463 := [rewrite]: #12468
-#12466 := (iff #12464 #12442)
-#14191 := (iff #14183 #14190)
-#14188 := (iff #14182 #14187)
-#14185 := (iff #14181 #14184)
-#14186 := [monotonicity #14157]: #14185
-#14189 := [monotonicity #14186]: #14188
-#14192 := [monotonicity #14088 #14189]: #14191
-#12467 := [monotonicity #14192]: #12466
-#12471 := [trans #12467 #12463]: #12469
-#12465 := [quant-inst #2347]: #12464
-#12472 := [mp #12465 #12471]: #12445
-#23169 := [unit-resolution #12472 #6510]: #14190
-#23147 := [unit-resolution #23169 #23168]: #14086
-#23170 := [unit-resolution #24713 #23147]: #19568
-#23171 := [unit-resolution #24084 #23148 #24042 #23170 #24028 #8195]: #24062
-#23163 := (or #15135 #15157)
-#23172 := [th-lemma arith farkas 1 1]: #23163
-#23173 := [unit-resolution #23172 #23171]: #15157
-#23174 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24053 #23173 #11881 #8193 #23161 #10075 #23164 #23157 #6992 #23152]: false
-#23176 := [lemma #23174]: #23175
-#27692 := [unit-resolution #23176 #10075]: #14153
-#27697 := [unit-resolution #12482 #27692]: #14184
-#27709 := [unit-resolution #12472 #6510 #27697]: #14086
-#27710 := [unit-resolution #24711 #27709]: #19568
-#21438 := (or #21436 #21437 #2360)
-#21431 := [hypothesis]: #19568
-#21432 := [hypothesis]: #14793
-#21435 := [th-lemma arith farkas -1 1 1 #21432 #21431 #19784]: false
-#21439 := [lemma #21435]: #21438
-#27711 := [unit-resolution #21439 #27710 #19784]: #21436
-#4112 := (or #4464 #2930)
-#4110 := [def-axiom]: #4112
-#27712 := [unit-resolution #4110 #23151]: #2930
-#24436 := (or #4313 #2927 #14793 #14798)
-#14790 := (or #14789 #14786 #14779)
-#14791 := (not #14790)
-#14794 := (or #2362 #14793 #14791)
-#24445 := (or #4313 #14794)
-#24451 := (iff #24445 #24436)
-#14801 := (or #2927 #14793 #14798)
-#24442 := (or #4313 #14801)
-#24450 := (iff #24442 #24436)
-#24446 := [rewrite]: #24450
-#24441 := (iff #24445 #24442)
-#14802 := (iff #14794 #14801)
-#14799 := (iff #14791 #14798)
-#14796 := (iff #14790 #14795)
-#14797 := [rewrite]: #14796
-#14800 := [monotonicity #14797]: #14799
-#14803 := [monotonicity #2929 #14800]: #14802
-#24448 := [monotonicity #14803]: #24441
-#24440 := [trans #24448 #24446]: #24451
-#24447 := [quant-inst #2347]: #24445
-#24463 := [mp #24447 #24440]: #24436
-#27714 := [unit-resolution #24463 #12666 #27712 #27711]: #14798
-#24467 := (or #14795 #14788)
-#24453 := [def-axiom]: #24467
-#27679 := [unit-resolution #24453 #27714]: #14788
-#27720 := [trans #27679 #27719]: #26215
-#26243 := (not #26215)
-#15537 := (>= #14784 0::Int)
-#24465 := (or #14795 #14785)
-#24466 := [def-axiom]: #24465
-#27716 := [unit-resolution #24466 #27714]: #14785
-#27717 := (or #14786 #15537)
-#27715 := [th-lemma arith triangle-eq]: #27717
-#27718 := [unit-resolution #27715 #27716]: #15537
-#24449 := (not #14779)
-#24464 := (or #14795 #24449)
-#24443 := [def-axiom]: #24464
-#27700 := [unit-resolution #24443 #27714]: #24449
-#15513 := (<= #14784 0::Int)
-#27698 := (or #14786 #15513)
-#27701 := [th-lemma arith triangle-eq]: #27698
-#27702 := [unit-resolution #27701 #27716]: #15513
-#28965 := (not #15537)
-#29082 := (not #15513)
-#29113 := (or #26243 #29082 #4461 #14779 #21437 #28965)
-#21417 := (f25 #14775)
-#21447 := (* -1::Int #21417)
-#21658 := (+ #14782 #21447)
-#21659 := (+ #2348 #21658)
-#17956 := (<= #21659 0::Int)
-#29065 := (not #17956)
-#18267 := (>= #21659 0::Int)
-#21448 := (+ #14776 #21447)
-#21449 := (>= #21448 0::Int)
-#25333 := (or #4418 #21449)
-#25340 := [quant-inst #14775]: #25333
-#28970 := [unit-resolution #25340 #8194]: #21449
-#28962 := [hypothesis]: #15537
-#28967 := (not #21449)
-#28968 := (or #18267 #28965 #21437 #28967)
-#28964 := [th-lemma arith assign-bounds -1 -1 -1]: #28968
-#28963 := [unit-resolution #28964 #28962 #21431 #28970]: #18267
-#21660 := (= #21659 0::Int)
-#21665 := (not #21660)
-#21645 := (+ #2348 #21447)
-#21646 := (<= #21645 0::Int)
-#28966 := (not #21646)
-#28969 := [hypothesis]: #24449
-#28986 := (or #28966 #14779 #21437 #28967)
-#29000 := [th-lemma arith assign-bounds -1 -1 -1]: #28986
-#29043 := [unit-resolution #29000 #28969 #21431 #28970]: #28966
-#21430 := (f3 f24 #14775)
-#21410 := (= f1 #21430)
-#25159 := (f3 f24 #25043)
-#25148 := (= f1 #25159)
-#29044 := (iff #25148 #21410)
-#29047 := (iff #21410 #25148)
-#29046 := (= #21430 #25159)
-#29001 := [monotonicity #28985]: #29046
-#29042 := [monotonicity #29001]: #29047
-#29050 := [symm #29042]: #29044
-#30427 := (= #7212 #25043)
-#30421 := (ite #30427 #5893 #26215)
-#30489 := [hypothesis]: #26215
-#30493 := (or #30421 #26243)
-#30465 := (not #30421)
-#30485 := [hypothesis]: #30465
-#30466 := (not #30427)
-#30486 := (or #30421 #30466)
-#30471 := (or #30421 #30466 #6305)
-#30472 := [def-axiom]: #30471
-#30487 := [unit-resolution #30472 #7000]: #30486
-#30488 := [unit-resolution #30487 #30485]: #30466
-#30490 := (or #30421 #30427)
-#30473 := (or #30421 #30427 #26243)
-#30474 := [def-axiom]: #30473
-#30491 := [unit-resolution #30474 #30489]: #30490
-#30492 := [unit-resolution #30491 #30488 #30485]: false
-#30494 := [lemma #30492]: #30493
-#28984 := [unit-resolution #30494 #30489]: #30421
-#30260 := (or #25148 #30465)
-#30450 := (f3 #8443 #25043)
-#30255 := (= #30450 #25159)
-#30251 := (= #25159 #30450)
-#18325 := (= f24 #8443)
-#18226 := (= #774 #8443)
-#18327 := [symm #9285]: #18226
-#18324 := [trans #6999 #18327]: #18325
-#30252 := [monotonicity #18324]: #30251
-#30257 := [symm #30252]: #30255
-#30451 := (= f1 #30450)
-#30453 := (iff #30421 #30451)
-#30195 := (or #6291 #30453)
-#30452 := (iff #30451 #30421)
-#30193 := (or #6291 #30452)
-#30200 := (iff #30193 #30195)
-#30202 := (iff #30195 #30195)
-#30191 := [rewrite]: #30202
-#30454 := (iff #30452 #30453)
-#30455 := [rewrite]: #30454
-#30201 := [monotonicity #30455]: #30200
-#30203 := [trans #30201 #30191]: #30200
-#30199 := [quant-inst #105 #7212 #5892 #25043]: #30193
-#30204 := [mp #30199 #30203]: #30195
-#30247 := [unit-resolution #30204 #4178]: #30453
-#30205 := (not #30453)
-#30249 := (or #30205 #30451)
-#30248 := [hypothesis]: #30421
-#30210 := (or #30205 #30465 #30451)
-#30211 := [def-axiom]: #30210
-#30250 := [unit-resolution #30211 #30248]: #30249
-#30241 := [unit-resolution #30250 #30247]: #30451
-#30258 := [trans #30241 #30257]: #25148
-#25160 := (not #25148)
-#30242 := [hypothesis]: #25160
-#30259 := [unit-resolution #30242 #30258]: false
-#30261 := [lemma #30259]: #30260
-#29045 := [unit-resolution #30261 #28984]: #25148
-#29051 := [mp #29045 #29050]: #21410
-#21416 := (not #21410)
-#21668 := (or #21416 #21646 #21665)
-#16841 := (or #4461 #21416 #21646 #21665)
-#21632 := (+ #2349 #14781)
-#21633 := (+ #21417 #21632)
-#21634 := (= #21633 0::Int)
-#21635 := (not #21634)
-#21636 := (+ #21417 #2349)
-#21637 := (>= #21636 0::Int)
-#21638 := (or #21416 #21637 #21635)
-#16842 := (or #4461 #21638)
-#16875 := (iff #16842 #16841)
-#16855 := (or #4461 #21668)
-#16858 := (iff #16855 #16841)
-#16853 := [rewrite]: #16858
-#16856 := (iff #16842 #16855)
-#21669 := (iff #21638 #21668)
-#21666 := (iff #21635 #21665)
-#21663 := (iff #21634 #21660)
-#21651 := (+ #14781 #21417)
-#21652 := (+ #2349 #21651)
-#21655 := (= #21652 0::Int)
-#21661 := (iff #21655 #21660)
-#21662 := [rewrite]: #21661
-#21656 := (iff #21634 #21655)
-#21653 := (= #21633 #21652)
-#21654 := [rewrite]: #21653
-#21657 := [monotonicity #21654]: #21656
-#21664 := [trans #21657 #21662]: #21663
-#21667 := [monotonicity #21664]: #21666
-#21649 := (iff #21637 #21646)
-#21639 := (+ #2349 #21417)
-#21642 := (>= #21639 0::Int)
-#21647 := (iff #21642 #21646)
-#21648 := [rewrite]: #21647
-#21643 := (iff #21637 #21642)
-#21640 := (= #21636 #21639)
-#21641 := [rewrite]: #21640
-#21644 := [monotonicity #21641]: #21643
-#21650 := [trans #21644 #21648]: #21649
-#21670 := [monotonicity #21650 #21667]: #21669
-#16863 := [monotonicity #21670]: #16856
-#16860 := [trans #16863 #16853]: #16875
-#16854 := [quant-inst #14775]: #16842
-#16904 := [mp #16854 #16860]: #16841
-#29062 := [unit-resolution #16904 #24066]: #21668
-#29060 := [unit-resolution #29062 #29051 #29043]: #21665
-#29049 := (not #18267)
-#29061 := (or #21660 #29065 #29049)
-#29064 := [th-lemma arith triangle-eq]: #29061
-#29072 := [unit-resolution #29064 #29060 #28963]: #29065
-#25330 := (<= #21448 0::Int)
-#21418 := (= #14776 #21417)
-#26210 := (f14 f15 #25043)
-#25149 := (f25 #25043)
-#26949 := (= #25149 #26210)
-#29156 := (iff #26949 #21418)
-#29078 := (= #21417 #14776)
-#29070 := (iff #29078 #21418)
-#29155 := [commutativity]: #29070
-#29081 := (iff #26949 #29078)
-#29079 := (= #26210 #14776)
-#29048 := [monotonicity #29063]: #29079
-#29074 := (= #25149 #21417)
-#24501 := (= #21417 #25149)
-#29080 := [monotonicity #28985]: #24501
-#29071 := [symm #29080]: #29074
-#29083 := [monotonicity #29071 #29048]: #29081
-#29154 := [trans #29083 #29155]: #29156
-#26989 := (or #25160 #26949)
-#26992 := (or #4427 #25160 #26949)
-#26983 := (= #26210 #25149)
-#27002 := (or #26983 #25160)
-#27009 := (or #4427 #27002)
-#27014 := (iff #27009 #26992)
-#27011 := (or #4427 #26989)
-#26967 := (iff #27011 #26992)
-#27013 := [rewrite]: #26967
-#27004 := (iff #27009 #27011)
-#27005 := (iff #27002 #26989)
-#26982 := (or #26949 #25160)
-#26990 := (iff #26982 #26989)
-#26991 := [rewrite]: #26990
-#26988 := (iff #27002 #26982)
-#26986 := (iff #26983 #26949)
-#26948 := [rewrite]: #26986
-#26987 := [monotonicity #26948]: #26988
-#27008 := [trans #26987 #26991]: #27005
-#27012 := [monotonicity #27008]: #27004
-#26966 := [trans #27012 #27013]: #27014
-#27010 := [quant-inst #25043]: #27009
-#27016 := [mp #27010 #26966]: #26992
-#29073 := [unit-resolution #27016 #7101]: #26989
-#29069 := [unit-resolution #29073 #29045]: #26949
-#29157 := [mp #29069 #29154]: #21418
-#29158 := (not #21418)
-#29159 := (or #29158 #25330)
-#29119 := [th-lemma arith triangle-eq]: #29159
-#29152 := [unit-resolution #29119 #29157]: #25330
-#14118 := (<= #14117 0::Int)
-#13522 := (or #4418 #14118)
-#14108 := (+ #14075 #2349)
-#14109 := (>= #14108 0::Int)
-#13552 := (or #4418 #14109)
-#13519 := (iff #13552 #13522)
-#13568 := (iff #13522 #13522)
-#13576 := [rewrite]: #13568
-#14121 := (iff #14109 #14118)
-#14110 := (+ #2349 #14075)
-#14113 := (>= #14110 0::Int)
-#14119 := (iff #14113 #14118)
-#14120 := [rewrite]: #14119
-#14114 := (iff #14109 #14113)
-#14111 := (= #14108 #14110)
-#14112 := [rewrite]: #14111
-#14115 := [monotonicity #14112]: #14114
-#14122 := [trans #14115 #14120]: #14121
-#13571 := [monotonicity #14122]: #13519
-#13579 := [trans #13571 #13576]: #13519
-#13562 := [quant-inst #2347]: #13552
-#13577 := [mp #13562 #13579]: #13522
-#29111 := [unit-resolution #13577 #8194]: #14118
-#29160 := [hypothesis]: #15513
-#29110 := [th-lemma arith farkas -1 -1 -1 1 #29160 #29111 #29152 #29072]: false
-#29114 := [lemma #29110]: #29113
-#27703 := [unit-resolution #29114 #27702 #23167 #27700 #27710 #27718]: #26243
-#27721 := [unit-resolution #27703 #27720]: false
-#27736 := [lemma #27721]: #27735
-#26719 := [unit-resolution #27736 #19784]: #6074
-#6120 := (or #6092 #6119)
-#6121 := [def-axiom]: #6120
-#26720 := [unit-resolution #6121 #26719]: #6092
-#6095 := (not #6092)
-#12667 := (or #6089 #6095)
-#6106 := (or #4313 #1655 #6089 #6095)
-#6085 := (or #6084 #6081 #6074)
-#6086 := (not #6085)
-#6088 := (or #6087 #1655 #6086)
-#6107 := (or #4313 #6088)
-#6114 := (iff #6107 #6106)
-#6101 := (or #1655 #6089 #6095)
-#6109 := (or #4313 #6101)
-#6112 := (iff #6109 #6106)
-#6113 := [rewrite]: #6112
-#6110 := (iff #6107 #6109)
-#6104 := (iff #6088 #6101)
-#6098 := (or #6089 #1655 #6095)
-#6102 := (iff #6098 #6101)
-#6103 := [rewrite]: #6102
-#6099 := (iff #6088 #6098)
-#6096 := (iff #6086 #6095)
-#6093 := (iff #6085 #6092)
-#6094 := [rewrite]: #6093
-#6097 := [monotonicity #6094]: #6096
-#6100 := [monotonicity #6091 #6097]: #6099
-#6105 := [trans #6100 #6103]: #6104
-#6111 := [monotonicity #6105]: #6110
-#6115 := [trans #6111 #6113]: #6114
-#6108 := [quant-inst #171]: #6107
-#6116 := [mp #6108 #6115]: #6106
-#12668 := [unit-resolution #6116 #12666 #7831]: #12667
-#26766 := [unit-resolution #12668 #26720]: #6089
-#26767 := [symm #26766]: #6087
-#26763 := [monotonicity #26767]: #7826
-#26770 := [symm #26763]: #7798
-#7793 := (not #7798)
-#7823 := (or #7793 #7799)
-#7829 := [th-lemma arith triangle-eq]: #7823
-#26765 := [unit-resolution #7829 #26770]: #7799
-#9970 := (not #7799)
-#8365 := (or #2276 #9970)
-#9901 := (not #9498)
-#9583 := [hypothesis]: #7799
-#9655 := (or #9901 #2276 #9970)
-#10029 := (= #9990 0::Int)
-#9976 := (not #10029)
-#9786 := (not #10051)
-#9584 := [hypothesis]: #9498
-#6993 := (not #3918)
-#9900 := (not #10063)
-#9973 := (or #9786 #9900 #2276 #9901 #6993 #9970)
-#9893 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9973
-#9899 := [unit-resolution #9893 #9584 #6992 #10072 #10088 #9583]: #9786
-#9860 := (or #9976 #10051)
-#9972 := [th-lemma arith triangle-eq]: #9860
-#9654 := [unit-resolution #9972 #9899]: #9976
-#9971 := (or #10026 #9900 #2276 #9901 #6993 #9970)
-#10042 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9971
-#10043 := [unit-resolution #10042 #9584 #6992 #10088 #10072 #9583]: #10026
-#9864 := [unit-resolution #10036 #4218 #10043]: #9950
-#9529 := (or #6808 #9969 #10029)
-#10030 := (or #10029 #9969)
-#9548 := (or #6808 #10030)
-#9802 := (iff #9548 #9529)
-#10037 := (or #9969 #10029)
-#9499 := (or #6808 #10037)
-#9536 := (iff #9499 #9529)
-#9801 := [rewrite]: #9536
-#9538 := (iff #9548 #9499)
-#10038 := (iff #10030 #10037)
-#10039 := [rewrite]: #10038
-#9542 := [monotonicity #10039]: #9538
-#9803 := [trans #9542 #9801]: #9802
-#9540 := [quant-inst #7212 #2274]: #9548
-#9762 := [mp #9540 #9803]: #9529
-#9863 := [unit-resolution #9762 #4212 #9864 #9654]: false
-#10143 := [lemma #9863]: #9655
-#9535 := [unit-resolution #10143 #10088 #9583]: #9901
-#9539 := [unit-resolution #10086 #9535]: #10084
-#8428 := (or #7639 #7617)
-#9099 := [hypothesis]: #10084
-#8425 := [hypothesis]: #7642
-#8427 := [unit-resolution #9513 #8425]: #9511
-#8467 := [unit-resolution #9516 #8425]: #9514
-#8468 := [unit-resolution #10082 #8467 #8427 #9099]: false
-#9344 := [lemma #8468]: #8428
-#9758 := [unit-resolution #9344 #9539]: #7639
-#9800 := [unit-resolution #10078 #9758]: #7540
-#9756 := [unit-resolution #11921 #9800]: #9582
-#9898 := [th-lemma arith farkas 1 -1 1 #9581 #10088 #9756]: false
-#8323 := [lemma #9898]: #8365
-#26771 := [unit-resolution #8323 #26765]: #2276
-#26769 := [unit-resolution #12718 #26771]: #4491
-#26772 := [unit-resolution #4087 #26769]: #4482
-#26768 := [unit-resolution #12722 #26772]: #4479
-#26773 := [unit-resolution #4009 #26768]: #4470
-#26781 := [unit-resolution #23150 #26773]: #4467
-#26783 := [unit-resolution #3997 #26781]: #4456
-#26780 := [unit-resolution #24107 #26783]: #14184
-#26784 := [unit-resolution #12472 #6510 #26780]: #14086
-#26782 := [unit-resolution #24711 #26784]: #19568
-#26798 := [unit-resolution #21439 #26782 #19784]: #21436
-#26801 := [unit-resolution #4110 #26781]: #2930
-#26793 := [unit-resolution #24463 #12666 #26801 #26798]: #14798
-#26776 := [unit-resolution #24453 #26793]: #14788
-#26835 := [trans #26776 #26829]: #26215
-#26799 := [unit-resolution #24466 #26793]: #14785
-#26794 := [unit-resolution #27701 #26799]: #15513
-#26792 := [unit-resolution #24443 #26793]: #24449
-#26795 := [unit-resolution #27715 #26799]: #15537
-#26791 := [unit-resolution #29114 #26795 #26783 #26792 #26782 #26794]: #26243
-#26830 := [unit-resolution #26791 #26835]: false
-#26831 := [lemma #26830]: #2360
-#8230 := [unit-resolution #4111 #26831]: #4464
-#8234 := [unit-resolution #23150 #8230]: #4473
-#8320 := [unit-resolution #4009 #8234]: #4476
-#8239 := [unit-resolution #12722 #8320]: #4485
-#8243 := [unit-resolution #4087 #8239]: #4488
-#8249 := [unit-resolution #12718 #8243]: #2277
-#8343 := [unit-resolution #11113 #8249]: #6074
-#8368 := [unit-resolution #6121 #8343]: #6092
-#8286 := [unit-resolution #12668 #8368]: #6089
-#8426 := [symm #8286]: #6087
-#8355 := [monotonicity #8426]: #7826
-#8359 := [symm #8355]: #7798
-#8361 := [unit-resolution #8323 #8249]: #9970
-[unit-resolution #7829 #8361 #8359]: false
+#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)
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+#3547 := [monotonicity #3470 #3544]: #3546
+#3555 := [trans #3547 #3553]: #3554
+#3446 := (iff #2896 #3445)
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+#3426 := (or #3425 #2298)
+#3437 := (or #3426 #2888)
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+#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
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+#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)
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+#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)
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+#3357 := [trans #3353 #3355]: #3356
+#3360 := [monotonicity #3357]: #3359
+#3365 := [trans #3360 #3363]: #3364
+#3368 := [monotonicity #3365]: #3367
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+#3337 := (and #2165 #3334)
+#3343 := (iff #3337 #3342)
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+#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)
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+#3311 := [trans #3306 #3309]: #3310
+#3314 := [quant-intro #3311]: #3313
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+#3277 := [quant-intro #3274]: #3276
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+#3287 := [trans #3280 #3285]: #3286
+#3385 := [monotonicity #3287 #3382]: #3384
+#3261 := (iff #2194 #3260)
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+#3262 := [quant-intro #3259]: #3261
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+#3114 := [monotonicity #3111]: #3113
+#3119 := [trans #3114 #3117]: #3118
+#3122 := [quant-intro #3119]: #3121
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+#3089 := [trans #3085 #3087]: #3088
+#3092 := [monotonicity #3089]: #3091
+#3097 := [trans #3092 #3095]: #3096
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+#3073 := (iff #1217 #3070)
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+#3066 := [trans #3062 #3064]: #3065
+#3069 := [monotonicity #3066]: #3068
+#3074 := [trans #3069 #3072]: #3073
+#3077 := [quant-intro #3074]: #3076
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+#3696 := [monotonicity #3693]: #3695
+#2352 := (+ #2351 #2349)
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+#2091 := (= ?v0!8 f10)
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+#2453 := (or #2197 #2449)
+#2041 := (+ #2040 #1297)
+#2042 := (>= #2041 0::Int)
+#2043 := (not #2042)
+#2046 := (+ #2045 #2041)
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+#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)
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+#2006 := (not #1747)
+#2478 := (and #2006 #2031 #2058 #2453 #1714 #1730 #1739)
+#1972 := (+ #1971 #1969)
+#1973 := (+ #58 #1972)
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+#1978 := (and #454 #1977 #1974)
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+#1983 := (= ?v0!5 f10)
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+#2001 := (and #1991 #1997)
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+#1947 := (not #1946)
+#1950 := (+ #1949 #1939)
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+#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
+#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)
+#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
+#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
+#2988 := [monotonicity #2985]: #2987
+#2991 := [monotonicity #2988]: #2990
+#2872 := (iff #2270 #204)
+#2873 := [rewrite]: #2872
+#2994 := [monotonicity #2873 #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)
+#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)
+#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)
+#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)
+#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
+#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)
+#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)
+#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)
+#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)
+#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
+#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
+#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)
+#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
+#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)
+#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)
+#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)
+#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)
+#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)
+#10 := (:var 1 S1)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#4171 := (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
+#18 := (= #17 f1)
+#16 := (= #10 f1)
+#15 := (= #12 #9)
+#19 := (ite #15 #16 #18)
+#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)
+#24 := (:var 0 S1)
+#22 := (:var 2 S2)
+#25 := (f4 #22 #23 #24)
+#4178 := (pattern #25)
+#318 := (= 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
+#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)
+#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
+#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)
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+#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
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+#7040 := (= #2252 #174)
+#7038 := (= #174 #2252)
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+#49 := (= #48 0::Int)
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+#4207 := (iff #382 #382)
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+#4210 := [quant-intro #4208]: #4209
+#1850 := (~ #387 #387)
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+#383 := (iff #379 #382)
+#384 := [rewrite]: #383
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+#381 := [monotonicity #378]: #380
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+#375 := (iff #51 #374)
+#372 := (iff #50 #369)
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+#370 := (iff #365 #369)
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+#363 := (iff #49 #362)
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+#373 := [trans #367 #371]: #372
+#376 := [quant-intro #373]: #375
+#391 := [trans #376 #389]: #390
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+#392 := [mp #352 #391]: #387
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+#6816 := (iff #6809 #6808)
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+#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)
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+#6616 := (= #6613 0::Int)
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+#6601 := (or #6580 #6600)
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+#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)
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+#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)
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+#7036 := [th-lemma arith triangle-eq]: #7035
+#7037 := [unit-resolution #7036 #7030]: #6634
+#7039 := [th-lemma arith eq-propagate 1 1 -1 -1 #7037 #7034 #7027 #7024]: #7038
+#7041 := [symm #7039]: #7040
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+#7045 := [lemma #7044]: #2864
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+#7099 := [unit-resolution #4061 #7045 #7098]: #4514
+#4070 := (or #4511 #4421)
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+#7100 := [unit-resolution #4072 #7099]: #4421
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+#7538 := (or #7537 #7535)
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+#9474 := (iff #9467 #9466)
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+#9473 := [rewrite]: #9472
+#9470 := (iff #9467 #9469)
+#7548 := (iff #7538 #7545)
+#7542 := (or #7539 #7535)
+#7546 := (iff #7542 #7545)
+#7547 := [rewrite]: #7546
+#7543 := (iff #7538 #7542)
+#7544 := [monotonicity #7541]: #7543
+#7549 := [trans #7544 #7547]: #7548
+#9471 := [monotonicity #7549]: #9470
+#9475 := [trans #9471 #9473]: #9474
+#9468 := [quant-inst #2273]: #9467
+#9476 := [mp #9468 #9475]: #9466
+#10089 := [unit-resolution #9476 #7100]: #7545
+#10090 := [unit-resolution #10089 #10076]: #7535
+#10099 := [mp #10090 #10098]: #9981
+#9978 := (not #9955)
+#9979 := (or #9978 #9947 #9967)
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+#10101 := (or #9952 #9968)
+#6304 := (not #5892)
+#9973 := (or #9952 #9968 #6304)
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+#10102 := [unit-resolution #9974 #6999]: #10101
+#10103 := [unit-resolution #10102 #10100]: #9968
+#10027 := (or #9949 #10026)
+#10030 := (or #6782 #9949 #10026)
+#10031 := (or #6782 #10027)
+#10033 := (iff #10031 #10030)
+#10034 := [rewrite]: #10033
+#10032 := [quant-inst #7211 #2273]: #10031
+#10035 := [mp #10032 #10034]: #10030
+#10104 := [unit-resolution #10035 #4217]: #10027
+#10105 := [unit-resolution #10104 #10103]: #10026
+#10106 := (or #10050 #10025)
+#10107 := [th-lemma arith farkas 1 1]: #10106
+#10108 := [unit-resolution #10107 #10105]: #10050
+#10109 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10108 #10087 #10086 #10074 #10073 #10072 #10071]: false
+#10111 := [lemma #10109]: #10110
+#9586 := [unit-resolution #10111 #10087 #10074 #10072]: #7539
+#9587 := (or #10075 #9581)
+#9588 := [th-lemma arith triangle-eq]: #9587
+#9589 := [unit-resolution #9588 #9586]: #9581
+#9590 := [th-lemma arith farkas -1 1 1 #10087 #9589 #9580]: false
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+#11952 := [unit-resolution #9608 #10087 #10074]: #7302
+#9479 := (or #7322 #8251)
+#9477 := [def-axiom]: #9479
+#11953 := [unit-resolution #9477 #11952]: #7322
+#7325 := (not #7322)
+#12703 := (or #7319 #7325)
+#7315 := (+ f8 #6071)
+#7316 := (<= #7315 0::Int)
+#12697 := (not #7316)
+#12700 := (or #12697 #6073)
+#4036 := (or #4535 #1655)
+#4037 := [def-axiom]: #4036
+#7830 := [unit-resolution #4037 #6508]: #1655
+#12698 := (or #12697 #1654 #6073)
+#12699 := [th-lemma arith assign-bounds 1 1]: #12698
+#12701 := [unit-resolution #12699 #7830]: #12700
+#12702 := [unit-resolution #12701 #10074]: #12697
+#12665 := [unit-resolution #4017 #6507]: #4307
+#9211 := (or #4312 #7316 #7319 #7325)
+#7313 := (or #7312 #7309 #7302)
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+#7318 := (or #7317 #7316 #7314)
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+#9461 := (iff #9448 #9211)
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+#7332 := (iff #7328 #7331)
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+#7329 := (iff #7318 #7328)
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+#7323 := (iff #7313 #7322)
+#7324 := [rewrite]: #7323
+#7327 := [monotonicity #7324]: #7326
+#7320 := (iff #7317 #7319)
+#7321 := [rewrite]: #7320
+#7330 := [monotonicity #7321 #7327]: #7329
+#7335 := [trans #7330 #7333]: #7334
+#9458 := [monotonicity #7335]: #9456
+#9462 := [trans #9458 #9460]: #9461
+#9453 := [quant-inst #6069]: #9448
+#9478 := [mp #9453 #9462]: #9211
+#12704 := [unit-resolution #9478 #12665 #12702]: #12703
+#11951 := [unit-resolution #12704 #11953]: #7319
+#11954 := [symm #11951]: #7317
+#9281 := (= #8217 #6069)
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+#11957 := [monotonicity #11955]: #11956
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+#11959 := (or #11944 #10878)
+#11960 := [th-lemma arith triangle-eq]: #11959
+#11961 := [unit-resolution #11960 #11958]: #10878
+#3917 := (>= #99 0::Int)
+#7123 := [unit-resolution #4033 #6507]: #100
+#6989 := (or #1747 #3917)
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+#11981 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10108 #10087 #10086 #10074 #6991 #11961 #11950 #10071]: false
+#11986 := [lemma #11981]: #11985
+#11109 := [unit-resolution #11986 #10087 #10074]: #7539
+#11963 := (not #9581)
+#11917 := [hypothesis]: #11963
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+#11919 := [unit-resolution #9588 #11918 #11917]: false
+#11920 := [lemma #11919]: #9587
+#11110 := [unit-resolution #11920 #11109]: #9581
+#11113 := [th-lemma arith farkas -1 1 1 #10087 #11110 #9580]: false
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+#4073 := (or #4511 #4505)
+#4074 := [def-axiom]: #4073
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+#5932 := (= #99 #203)
+#12712 := (iff #5932 #204)
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+#12710 := [monotonicity #7123]: #12709
+#12713 := [trans #12710 #12711]: #12712
+#5916 := (f5 f22 f10)
+#5917 := (f9 #5916)
+#7059 := (<= #5917 0::Int)
+#7060 := (not #7059)
+#6767 := (not #6088)
+#3934 := (f3 f15 f10)
+#3937 := (= f1 #3934)
+#6718 := (ite #6088 #5892 #3937)
+#6766 := (not #6718)
+#6698 := (f3 #6269 f10)
+#6699 := (= f1 #6698)
+#6723 := (iff #6699 #6718)
+#6730 := (or #6290 #6723)
+#6683 := (ite #6086 #5892 #3937)
+#6717 := (iff #6699 #6683)
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+#6733 := (iff #6731 #6730)
+#6735 := (iff #6730 #6730)
+#6763 := [rewrite]: #6735
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+#6089 := (iff #6086 #6088)
+#6090 := [rewrite]: #6089
+#6722 := [monotonicity #6090]: #6721
+#6725 := [monotonicity #6722]: #6724
+#6734 := [monotonicity #6725]: #6733
+#6764 := [trans #6734 #6763]: #6733
+#6732 := [quant-inst #104 #170 #5891 #56]: #6731
+#6765 := [mp #6732 #6764]: #6730
+#7091 := [unit-resolution #6765 #4177]: #6723
+#6983 := (not #6699)
+#6358 := (f3 f23 f10)
+#6476 := (= f1 #6358)
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+#6546 := (or #5932 #6545)
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+#6544 := (or #4426 #6546)
+#6551 := (iff #6544 #6549)
+#6552 := [rewrite]: #6551
+#6550 := [quant-inst #56]: #6544
+#6553 := [mp #6550 #6552]: #6549
+#7101 := [unit-resolution #6553 #7100]: #6546
+#7102 := [unit-resolution #7101 #7095]: #6545
+#7111 := [mp #7102 #7110]: #6983
+#6986 := (not #6723)
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+#7115 := [unit-resolution #7114 #7112]: #6767
+#7061 := (or #6088 #7060)
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+#7065 := (or #6782 #7061)
+#7067 := (iff #7065 #7064)
+#7068 := [rewrite]: #7067
+#7066 := [quant-inst #170 #56]: #7065
+#7069 := [mp #7066 #7068]: #7064
+#7116 := [unit-resolution #7069 #4217]: #7061
+#7117 := [unit-resolution #7116 #7115]: #7060
+#5924 := (* -1::Int #5917)
+#5925 := (+ #1453 #5924)
+#5926 := (+ #99 #5925)
+#5927 := (<= #5926 0::Int)
+#5954 := (not #5927)
+#5928 := (+ f8 #5924)
+#5929 := (<= #5928 0::Int)
+#5934 := (or #5927 #5929)
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+#5947 := (iff #5944 #5946)
+#5941 := (iff #5933 #5940)
+#5938 := (iff #5931 #5937)
+#5935 := (iff #5930 #5934)
+#5936 := [rewrite]: #5935
+#5939 := [monotonicity #5936]: #5938
+#5942 := [monotonicity #5939]: #5941
+#5948 := [monotonicity #5942]: #5947
+#5952 := [trans #5948 #5950]: #5951
+#5945 := [quant-inst #56]: #5944
+#5953 := [mp #5945 #5952]: #5943
+#7118 := [unit-resolution #5953 #6509]: #5940
+#7119 := [unit-resolution #7118 #7095]: #5937
+#5955 := (or #5934 #5954)
+#5956 := [def-axiom]: #5955
+#7120 := [unit-resolution #5956 #7119]: #5954
+#6127 := (>= #174 0::Int)
+#6130 := (or #4279 #6127)
+#6131 := [quant-inst #170]: #6130
+#7122 := [unit-resolution #6131 #7121]: #6127
+#3920 := (<= #99 0::Int)
+#7124 := (or #1747 #3920)
+#7125 := [th-lemma arith triangle-eq]: #7124
+#7126 := [unit-resolution #7125 #7123]: #3920
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+#12714 := [mp #7128 #12713]: #204
+#4083 := (or #4508 #1490 #4502)
+#4069 := [def-axiom]: #4083
+#12715 := [unit-resolution #4069 #12714 #12708]: #4502
+#4092 := (or #4499 #4493)
+#4076 := [def-axiom]: #4092
+#12716 := [unit-resolution #4076 #12715]: #4493
+#4089 := (or #4496 #2276 #4490)
+#4090 := [def-axiom]: #4089
+#12717 := [unit-resolution #4090 #12716]: #4493
+#23131 := [unit-resolution #12717 #23130]: #4490
+#4084 := (or #4487 #4481)
+#4086 := [def-axiom]: #4084
+#23139 := [unit-resolution #4086 #23131]: #4481
+#12720 := (or #4484 #4478)
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+#3973 := (or #3440 #2299)
+#3974 := [def-axiom]: #3973
+#9758 := [unit-resolution #3974 #10288]: #2299
+#10379 := (or #3440 #2298)
+#10564 := (f5 #7211 ?v1!16)
+#10565 := (f9 #10564)
+#10582 := (* -1::Int #10565)
+#8691 := (f5 f22 ?v1!16)
+#8692 := (f9 #8691)
+#10585 := (+ #8692 #10582)
+#10587 := (>= #10585 0::Int)
+#10581 := (= #8692 #10565)
+#10592 := (= #10565 #8692)
+#10590 := (= #10564 #8691)
+#10591 := [monotonicity #7790]: #10590
+#10593 := [monotonicity #10591]: #10592
+#10594 := [symm #10593]: #10581
+#10595 := (not #10581)
+#10596 := (or #10595 #10587)
+#10597 := [th-lemma arith triangle-eq]: #10596
+#10598 := [unit-resolution #10597 #10594]: #10587
+#6007 := (f24 f22)
+#6048 := (* -1::Int #6007)
+#6417 := (+ #174 #6048)
+#6418 := (>= #6417 0::Int)
+#4062 := (or #4523 #4412)
+#4063 := [def-axiom]: #4062
+#8193 := [unit-resolution #4063 #7097]: #4412
+#6422 := (or #4417 #6418)
+#6423 := [quant-inst #170]: #6422
+#8194 := [unit-resolution #6423 #8193]: #6418
+#4116 := (not #2888)
+#4117 := (or #3440 #4116)
+#4118 := [def-axiom]: #4117
+#10291 := [unit-resolution #4118 #10288]: #4116
+#10223 := (+ #2290 #6048)
+#10224 := (<= #10223 0::Int)
+#10212 := (= #2290 #6007)
+#10480 := (= ?v0!17 f22)
+#8517 := (= ?v0!17 #7211)
+#8510 := (f3 f15 ?v0!17)
+#8511 := (= f1 #8510)
+#8520 := (ite #8517 #5892 #8511)
+#8514 := (f3 #8442 ?v0!17)
+#8515 := (= f1 #8514)
+#8523 := (iff #8515 #8520)
+#9711 := (or #6290 #8523)
+#8512 := (= #7211 ?v0!17)
+#8513 := (ite #8512 #5892 #8511)
+#8516 := (iff #8515 #8513)
+#9706 := (or #6290 #8516)
+#9713 := (iff #9706 #9711)
+#9715 := (iff #9711 #9711)
+#9716 := [rewrite]: #9715
+#8524 := (iff #8516 #8523)
+#8521 := (iff #8513 #8520)
+#8518 := (iff #8512 #8517)
+#8519 := [rewrite]: #8518
+#8522 := [monotonicity #8519]: #8521
+#8525 := [monotonicity #8522]: #8524
+#9714 := [monotonicity #8525]: #9713
+#9722 := [trans #9714 #9716]: #9713
+#9712 := [quant-inst #104 #7211 #5891 #2289]: #9706
+#9723 := [mp #9712 #9722]: #9711
+#10292 := [unit-resolution #9723 #4177]: #8523
+#10321 := (= #2295 #8514)
+#10294 := (= #8514 #2295)
+#10231 := [monotonicity #9286]: #10294
+#10322 := [symm #10231]: #10321
+#4131 := (or #3440 #2296)
+#3972 := [def-axiom]: #4131
+#10293 := [unit-resolution #3972 #10288]: #2296
+#10323 := [trans #10293 #10322]: #8515
+#9732 := (not #8515)
+#9735 := (not #8523)
+#9738 := (or #9735 #9732 #8520)
+#9739 := [def-axiom]: #9738
+#10324 := [unit-resolution #9739 #10323 #10292]: #8520
+#9731 := (not #8511)
+#8485 := (f13 f14 ?v0!17)
+#8567 := (* -1::Int #8485)
+#7513 := (f13 f14 #7211)
+#10486 := (+ #7513 #8567)
+#10487 := (>= #10486 0::Int)
+#10612 := (not #10487)
+#8446 := (= ?v1!16 #7211)
+#9616 := (not #8446)
+#8438 := (f3 f15 ?v1!16)
+#8439 := (= f1 #8438)
+#8449 := (ite #8446 #5892 #8439)
+#9615 := (not #8449)
+#8443 := (f3 #8442 ?v1!16)
+#8444 := (= f1 #8443)
+#8452 := (iff #8444 #8449)
+#9584 := (or #6290 #8452)
+#8440 := (= #7211 ?v1!16)
+#8441 := (ite #8440 #5892 #8439)
+#8445 := (iff #8444 #8441)
+#9585 := (or #6290 #8445)
+#9610 := (iff #9585 #9584)
+#9606 := (iff #9584 #9584)
+#9612 := [rewrite]: #9606
+#8453 := (iff #8445 #8452)
+#8450 := (iff #8441 #8449)
+#8447 := (iff #8440 #8446)
+#8448 := [rewrite]: #8447
+#8451 := [monotonicity #8448]: #8450
+#8454 := [monotonicity #8451]: #8453
+#9611 := [monotonicity #8454]: #9610
+#9613 := [trans #9611 #9612]: #9610
+#9609 := [quant-inst #104 #7211 #5891 #2288]: #9585
+#9614 := [mp #9609 #9613]: #9584
+#10325 := [unit-resolution #9614 #4177]: #8452
+#9648 := (not #8444)
+#10333 := (iff #2299 #9648)
+#10331 := (iff #2298 #8444)
+#10329 := (iff #8444 #2298)
+#10327 := (= #8443 #2297)
+#10328 := [monotonicity #9286]: #10327
+#10330 := [monotonicity #10328]: #10329
+#10332 := [symm #10330]: #10331
+#10334 := [monotonicity #10332]: #10333
+#10326 := [hypothesis]: #2299
+#10335 := [mp #10326 #10334]: #9648
+#9640 := (not #8452)
+#9641 := (or #9640 #8444 #9615)
+#9647 := [def-axiom]: #9641
+#10336 := [unit-resolution #9647 #10335 #10325]: #9615
+#10337 := (or #8449 #9616)
+#9636 := (or #8449 #9616 #6304)
+#9631 := [def-axiom]: #9636
+#10338 := [unit-resolution #9631 #6999]: #10337
+#10339 := [unit-resolution #10338 #10336]: #9616
+#8664 := (f13 f14 ?v1!16)
+#8675 := (* -1::Int #8664)
+#8923 := (+ #174 #8675)
+#8924 := (<= #8923 0::Int)
+#9637 := (not #8439)
+#9638 := (or #8449 #8446 #9637)
+#9639 := [def-axiom]: #9638
+#10308 := [unit-resolution #9639 #10339 #10336]: #9637
+#8929 := (or #8439 #8924)
+#4054 := (or #4535 #4386)
+#4040 := [def-axiom]: #4054
+#10313 := [unit-resolution #4040 #6508]: #4386
+#9984 := (or #4391 #8439 #8924)
+#8912 := (+ #8664 #1453)
+#8913 := (>= #8912 0::Int)
+#8916 := (or #8439 #8913)
+#9985 := (or #4391 #8916)
+#10020 := (iff #9985 #9984)
+#10016 := (or #4391 #8929)
+#10019 := (iff #10016 #9984)
+#10014 := [rewrite]: #10019
+#10017 := (iff #9985 #10016)
+#8930 := (iff #8916 #8929)
+#8927 := (iff #8913 #8924)
+#8917 := (+ #1453 #8664)
+#8920 := (>= #8917 0::Int)
+#8925 := (iff #8920 #8924)
+#8926 := [rewrite]: #8925
+#8921 := (iff #8913 #8920)
+#8918 := (= #8912 #8917)
+#8919 := [rewrite]: #8918
+#8922 := [monotonicity #8919]: #8921
+#8928 := [trans #8922 #8926]: #8927
+#8931 := [monotonicity #8928]: #8930
+#10018 := [monotonicity #8931]: #10017
+#10021 := [trans #10018 #10014]: #10020
+#10015 := [quant-inst #2288]: #9985
+#10022 := [mp #10015 #10021]: #9984
+#10307 := [unit-resolution #10022 #10313]: #8929
+#10314 := [unit-resolution #10307 #10308]: #8924
+#10586 := (not #8924)
+#10633 := (or #10612 #10586 #2888 #8446)
+#8717 := (+ #2886 #8692)
+#8718 := (+ #174 #8717)
+#8721 := (= #8718 0::Int)
+#10618 := (not #8721)
+#9835 := (<= #8718 0::Int)
+#10611 := (not #9835)
+#10599 := [hypothesis]: #9616
+#10601 := [hypothesis]: #4116
+#10588 := [hypothesis]: #10487
+#10613 := (or #10611 #2888 #10612 #8446)
+#10589 := [hypothesis]: #9835
+#10566 := (<= #10565 0::Int)
+#10567 := (not #10566)
+#10571 := (or #6782 #8446 #10567)
+#10568 := (or #8446 #10567)
+#10572 := (or #6782 #10568)
+#10574 := (iff #10572 #10571)
+#10575 := [rewrite]: #10574
+#10573 := [quant-inst #7211 #2288]: #10572
+#10576 := [mp #10573 #10575]: #10571
+#10600 := [unit-resolution #10576 #4217 #10599]: #10567
+#8568 := (+ #2290 #8567)
+#8569 := (<= #8568 0::Int)
+#9748 := (or #4417 #8569)
+#8557 := (+ #8485 #2291)
+#8558 := (>= #8557 0::Int)
+#9751 := (or #4417 #8558)
+#9766 := (iff #9751 #9748)
+#9768 := (iff #9748 #9748)
+#9769 := [rewrite]: #9768
+#8572 := (iff #8558 #8569)
+#8561 := (+ #2291 #8485)
+#8564 := (>= #8561 0::Int)
+#8570 := (iff #8564 #8569)
+#8571 := [rewrite]: #8570
+#8565 := (iff #8558 #8564)
+#8562 := (= #8557 #8561)
+#8563 := [rewrite]: #8562
+#8566 := [monotonicity #8563]: #8565
+#8573 := [trans #8566 #8571]: #8572
+#9767 := [monotonicity #8573]: #9766
+#9770 := [trans #9767 #9769]: #9766
+#9765 := [quant-inst #2289]: #9751
+#9771 := [mp #9765 #9770]: #9748
+#10602 := [unit-resolution #9771 #8193]: #8569
+#7529 := (* -1::Int #7513)
+#8423 := (+ #174 #7529)
+#8429 := (>= #8423 0::Int)
+#7336 := (= #174 #7513)
+#10603 := (= #7513 #174)
+#10604 := [monotonicity #7790]: #10603
+#10605 := [symm #10604]: #7336
+#10606 := (not #7336)
+#10607 := (or #10606 #8429)
+#10608 := [th-lemma arith triangle-eq]: #10607
+#10609 := [unit-resolution #10608 #10605]: #8429
+#10610 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10609 #10602 #10601 #10600 #10598 #10589 #10588]: false
+#10614 := [lemma #10610]: #10613
+#10617 := [unit-resolution #10614 #10588 #10601 #10599]: #10611
+#10619 := (or #10618 #9835)
+#10620 := [th-lemma arith triangle-eq]: #10619
+#10621 := [unit-resolution #10620 #10617]: #10618
+#8696 := (* -1::Int #8692)
+#8700 := (+ f8 #8696)
+#8701 := (<= #8700 0::Int)
+#9849 := (not #8701)
+#8710 := (+ #8675 #8692)
+#8711 := (+ #174 #8710)
+#8712 := (>= #8711 0::Int)
+#8747 := (or #8701 #8712)
+#8750 := (not #8747)
+#8744 := (= #2292 #8664)
+#10623 := (not #8744)
+#8676 := (+ #2292 #8675)
+#9848 := (>= #8676 0::Int)
+#10584 := (not #9848)
+#10579 := [hypothesis]: #8924
+#10615 := (or #10584 #2888 #10586 #10612)
+#10580 := [hypothesis]: #9848
+#10583 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10609 #10602 #10601 #10580 #10579 #10588]: false
+#10616 := [lemma #10583]: #10615
+#10622 := [unit-resolution #10616 #10588 #10579 #10601]: #10584
+#10624 := (or #10623 #9848)
+#10625 := [th-lemma arith triangle-eq]: #10624
+#10626 := [unit-resolution #10625 #10622]: #10623
+#8753 := (or #8744 #8750)
+#9837 := (or #4401 #8744 #8750)
+#8697 := (+ #1453 #8696)
+#8698 := (+ #8664 #8697)
+#8699 := (<= #8698 0::Int)
+#8740 := (or #8701 #8699)
+#8741 := (not #8740)
+#8742 := (= #8664 #2292)
+#8743 := (or #8742 #8741)
+#9838 := (or #4401 #8743)
+#9845 := (iff #9838 #9837)
+#9839 := (or #4401 #8753)
+#9842 := (iff #9839 #9837)
+#9843 := [rewrite]: #9842
+#9840 := (iff #9838 #9839)
+#8754 := (iff #8743 #8753)
+#8751 := (iff #8741 #8750)
+#8748 := (iff #8740 #8747)
+#8715 := (iff #8699 #8712)
+#8703 := (+ #8664 #8696)
+#8704 := (+ #1453 #8703)
+#8707 := (<= #8704 0::Int)
+#8713 := (iff #8707 #8712)
+#8714 := [rewrite]: #8713
+#8708 := (iff #8699 #8707)
+#8705 := (= #8698 #8704)
+#8706 := [rewrite]: #8705
+#8709 := [monotonicity #8706]: #8708
+#8716 := [trans #8709 #8714]: #8715
+#8749 := [monotonicity #8716]: #8748
+#8752 := [monotonicity #8749]: #8751
+#8745 := (iff #8742 #8744)
+#8746 := [rewrite]: #8745
+#8755 := [monotonicity #8746 #8752]: #8754
+#9841 := [monotonicity #8755]: #9840
+#9846 := [trans #9841 #9843]: #9845
+#9817 := [quant-inst #2288]: #9838
+#9847 := [mp #9817 #9846]: #9837
+#10627 := [unit-resolution #9847 #6509]: #8753
+#10628 := [unit-resolution #10627 #10626]: #8750
+#9844 := (or #8747 #9849)
+#9850 := [def-axiom]: #9844
+#10629 := [unit-resolution #9850 #10628]: #9849
+#9851 := (not #8712)
+#9852 := (or #8747 #9851)
+#9853 := [def-axiom]: #9852
+#10630 := [unit-resolution #9853 #10628]: #9851
+#8724 := (or #8701 #8712 #8721)
+#9823 := (or #4409 #8701 #8712 #8721)
+#8693 := (+ #8692 #2886)
+#8694 := (+ #174 #8693)
+#8695 := (= #8694 0::Int)
+#8702 := (or #8701 #8699 #8695)
+#9824 := (or #4409 #8702)
+#9830 := (iff #9824 #9823)
+#9826 := (or #4409 #8724)
+#9828 := (iff #9826 #9823)
+#9829 := [rewrite]: #9828
+#9821 := (iff #9824 #9826)
+#8725 := (iff #8702 #8724)
+#8722 := (iff #8695 #8721)
+#8719 := (= #8694 #8718)
+#8720 := [rewrite]: #8719
+#8723 := [monotonicity #8720]: #8722
+#8726 := [monotonicity #8716 #8723]: #8725
+#9827 := [monotonicity #8726]: #9821
+#9831 := [trans #9827 #9829]: #9830
+#9825 := [quant-inst #2288]: #9824
+#9834 := [mp #9825 #9831]: #9823
+#10631 := [unit-resolution #9834 #6513]: #8724
+#10632 := [unit-resolution #10631 #10630 #10629 #10621]: false
+#10634 := [lemma #10632]: #10633
+#10315 := [unit-resolution #10634 #10314 #10291 #10339]: #10612
+#10310 := (or #9731 #10487)
+#10295 := [hypothesis]: #10612
+#10297 := [hypothesis]: #8511
+#7515 := (f3 f15 #7211)
+#7516 := (= f1 #7515)
+#10303 := (not #7516)
+#10304 := (iff #757 #10303)
+#10296 := (iff #754 #7516)
+#10300 := (iff #7516 #754)
+#10298 := (= #7515 #171)
+#10299 := [monotonicity #7790]: #10298
+#10301 := [monotonicity #10299]: #10300
+#10302 := [symm #10301]: #10296
+#10305 := [monotonicity #10302]: #10304
+#10306 := [mp #6926 #10305]: #10303
+#10233 := (or #4296 #7516 #9731 #10487)
+#10494 := (or #7516 #9731 #10487)
+#10239 := (or #4296 #10494)
+#10241 := (iff #10239 #10233)
+#10242 := [rewrite]: #10241
+#10240 := [quant-inst #2289 #7211]: #10239
+#10243 := [mp #10240 #10242]: #10233
+#10309 := [unit-resolution #10243 #6937 #10306 #10297 #10295]: false
+#10311 := [lemma #10309]: #10310
+#10316 := [unit-resolution #10311 #10315]: #9731
+#9724 := (not #8520)
+#9727 := (or #9724 #8517 #8511)
+#9728 := [def-axiom]: #9727
+#10317 := [unit-resolution #9728 #10316 #10324]: #8517
+#10318 := [trans #10317 #7790]: #10480
+#10319 := [monotonicity #10318]: #10212
+#10346 := (not #10212)
+#10347 := (or #10346 #10224)
+#10345 := [th-lemma arith triangle-eq]: #10347
+#10348 := [unit-resolution #10345 #10319]: #10224
+#10350 := (not #6418)
+#10349 := (not #10224)
+#10355 := (or #10584 #10349 #2888 #10586 #10350)
+#10356 := [th-lemma arith assign-bounds -1 1 -1 1]: #10355
+#10354 := [unit-resolution #10356 #10291 #8194 #10314 #10348]: #10584
+#10357 := [unit-resolution #10625 #10354]: #10623
+#10358 := [unit-resolution #10627 #10357]: #8750
+#10183 := (or #8747 #8721)
+#10179 := [hypothesis]: #10618
+#10180 := [hypothesis]: #8750
+#10181 := [unit-resolution #9850 #10180]: #9849
+#10176 := [unit-resolution #9853 #10180]: #9851
+#10182 := [unit-resolution #10631 #10176 #10181 #10179]: false
+#10184 := [lemma #10182]: #10183
+#10359 := [unit-resolution #10184 #10358]: #8721
+#10376 := [unit-resolution #10620 #10359]: #9835
+#10377 := [unit-resolution #10576 #4217 #10339]: #10567
+#10378 := [th-lemma arith farkas 1 1 1 1 1 1 #10377 #10376 #10348 #10291 #8194 #10598]: false
+#10380 := [lemma #10378]: #10379
+#9759 := [unit-resolution #10380 #9758 #10288]: false
+#9760 := [lemma #9759]: #3440
+#4106 := (or #4484 #3445 #4478)
+#4093 := [def-axiom]: #4106
+#12721 := [unit-resolution #4093 #9760]: #12720
+#23132 := [unit-resolution #12721 #23139]: #4478
+#4000 := (or #4475 #4469)
+#4008 := [def-axiom]: #4000
+#23133 := [unit-resolution #4008 #23132]: #4469
+#23134 := (or #4472 #4466)
+#14671 := (f5 f22 ?v0!19)
+#14672 := (f9 #14671)
+#14467 := (f13 f14 ?v0!19)
+#14603 := (* -1::Int #14467)
+#14719 := (+ #14603 #14672)
+#14720 := (+ #174 #14719)
+#14721 := (>= #14720 0::Int)
+#14960 := (not #14721)
+#14675 := (* -1::Int #14672)
+#15459 := (+ #2322 #14675)
+#15460 := (>= #15459 0::Int)
+#15458 := (= #2322 #14672)
+#15668 := (= #2321 #14671)
+#15695 := (= ?v1!18 f22)
+#13665 := (= ?v1!18 #7211)
+#13658 := (f3 f15 ?v1!18)
+#13659 := (= f1 #13658)
+#13802 := (not #13659)
+#13798 := (f13 f14 ?v1!18)
+#14923 := (+ #13798 #14603)
+#14924 := (+ #2322 #14923)
+#14919 := (>= #14924 0::Int)
+#15619 := (not #14919)
+#14604 := (+ #2317 #14603)
+#14605 := (<= #14604 0::Int)
+#14818 := (or #4417 #14605)
+#14570 := (+ #14467 #2318)
+#14597 := (>= #14570 0::Int)
+#14819 := (or #4417 #14597)
+#14821 := (iff #14819 #14818)
+#14823 := (iff #14818 #14818)
+#14824 := [rewrite]: #14823
+#14622 := (iff #14597 #14605)
+#14598 := (+ #2318 #14467)
+#14601 := (>= #14598 0::Int)
+#14606 := (iff #14601 #14605)
+#14621 := [rewrite]: #14606
+#14596 := (iff #14597 #14601)
+#14599 := (= #14570 #14598)
+#14600 := [rewrite]: #14599
+#14602 := [monotonicity #14600]: #14596
+#14623 := [trans #14602 #14621]: #14622
+#14822 := [monotonicity #14623]: #14821
+#14772 := [trans #14822 #14824]: #14821
+#14820 := [quant-inst #2316]: #14819
+#14891 := [mp #14820 #14772]: #14818
+#15608 := [unit-resolution #14891 #8193]: #14605
+#4122 := (not #2915)
+#15609 := [hypothesis]: #3491
+#3951 := (or #3486 #4122)
+#3953 := [def-axiom]: #3951
+#15607 := [unit-resolution #3953 #15609]: #4122
+#13815 := (* -1::Int #13798)
+#13816 := (+ #2319 #13815)
+#13544 := (>= #13816 0::Int)
+#13884 := (= #2319 #13798)
+#4121 := (or #3486 #2330)
+#4115 := [def-axiom]: #4121
+#15610 := [unit-resolution #4115 #15609]: #2330
+#13776 := (or #4426 #3471 #13884)
+#13882 := (= #13798 #2319)
+#13752 := (or #13882 #3471)
+#13777 := (or #4426 #13752)
+#13799 := (iff #13777 #13776)
+#13750 := (or #3471 #13884)
+#13791 := (or #4426 #13750)
+#13801 := (iff #13791 #13776)
+#13793 := [rewrite]: #13801
+#13796 := (iff #13777 #13791)
+#13758 := (iff #13752 #13750)
+#13753 := (or #13884 #3471)
+#13756 := (iff #13753 #13750)
+#13757 := [rewrite]: #13756
+#13754 := (iff #13752 #13753)
+#13885 := (iff #13882 #13884)
+#13886 := [rewrite]: #13885
+#13755 := [monotonicity #13886]: #13754
+#13759 := [trans #13755 #13757]: #13758
+#13800 := [monotonicity #13759]: #13796
+#13803 := [trans #13800 #13793]: #13799
+#13795 := [quant-inst #2315]: #13777
+#13804 := [mp #13795 #13803]: #13776
+#15615 := [unit-resolution #13804 #7100 #15610]: #13884
+#15616 := (not #13884)
+#15617 := (or #15616 #13544)
+#15601 := [th-lemma arith triangle-eq]: #15617
+#15618 := [unit-resolution #15601 #15615]: #13544
+#15614 := (not #14605)
+#15611 := (not #13544)
+#15620 := (or #15619 #15611 #15614 #2915)
+#15622 := [th-lemma arith assign-bounds 1 -1 1]: #15620
+#15623 := [unit-resolution #15622 #15618 #15607 #15608]: #15619
+#15628 := (or #13802 #14919)
+#4114 := (or #3486 #2328)
+#4120 := [def-axiom]: #4114
+#15626 := [unit-resolution #4120 #15609]: #2328
+#15627 := [unit-resolution #4015 #6507]: #4282
+#13311 := (or #4287 #2327 #13802 #14919)
+#14925 := (or #13802 #2327 #14919)
+#13540 := (or #4287 #14925)
+#15126 := (iff #13540 #13311)
+#14926 := (or #2327 #13802 #14919)
+#13546 := (or #4287 #14926)
+#15124 := (iff #13546 #13311)
+#15125 := [rewrite]: #15124
+#13648 := (iff #13540 #13546)
+#14927 := (iff #14925 #14926)
+#14928 := [rewrite]: #14927
+#15123 := [monotonicity #14928]: #13648
+#15127 := [trans #15123 #15125]: #15126
+#13543 := [quant-inst #2316 #2315]: #13540
+#15128 := [mp #13543 #15127]: #13311
+#15621 := [unit-resolution #15128 #15627 #15626]: #15628
+#15629 := [unit-resolution #15621 #15623]: #13802
+#13668 := (ite #13665 #5892 #13659)
+#13662 := (f3 #8442 ?v1!18)
+#13663 := (= f1 #13662)
+#13671 := (iff #13663 #13668)
+#15012 := (or #6290 #13671)
+#13660 := (= #7211 ?v1!18)
+#13661 := (ite #13660 #5892 #13659)
+#13664 := (iff #13663 #13661)
+#15017 := (or #6290 #13664)
+#14890 := (iff #15017 #15012)
+#15043 := (iff #15012 #15012)
+#15044 := [rewrite]: #15043
+#13672 := (iff #13664 #13671)
+#13669 := (iff #13661 #13668)
+#13666 := (iff #13660 #13665)
+#13667 := [rewrite]: #13666
+#13670 := [monotonicity #13667]: #13669
+#13673 := [monotonicity #13670]: #13672
+#15019 := [monotonicity #13673]: #14890
+#15060 := [trans #15019 #15044]: #14890
+#15018 := [quant-inst #104 #7211 #5891 #2315]: #15017
+#14889 := [mp #15018 #15060]: #15012
+#15630 := [unit-resolution #14889 #4177]: #13671
+#15690 := (= #2329 #13662)
+#15624 := (= #13662 #2329)
+#15625 := [monotonicity #9286]: #15624
+#15692 := [symm #15625]: #15690
+#15693 := [trans #15610 #15692]: #13663
+#13237 := (not #13663)
+#12830 := (not #13671)
+#12788 := (or #12830 #13237 #13668)
+#13250 := [def-axiom]: #12788
+#15694 := [unit-resolution #13250 #15693 #15630]: #13668
+#15061 := (not #13668)
+#15059 := (or #15061 #13665 #13659)
+#15067 := [def-axiom]: #15059
+#15688 := [unit-resolution #15067 #15694 #15629]: #13665
+#15667 := [trans #15688 #7790]: #15695
+#15666 := [monotonicity #15667]: #15668
+#15670 := [monotonicity #15666]: #15458
+#15672 := (not #15458)
+#15673 := (or #15672 #15460)
+#15674 := [th-lemma arith triangle-eq]: #15673
+#15669 := [unit-resolution #15674 #15670]: #15460
+#15238 := (+ #2319 #6048)
+#15240 := (>= #15238 0::Int)
+#15450 := (= #2319 #6007)
+#15761 := [monotonicity #15667]: #15450
+#15671 := (not #15450)
+#15767 := (or #15671 #15240)
+#15768 := [th-lemma arith triangle-eq]: #15767
+#15769 := [unit-resolution #15768 #15761]: #15240
+#6674 := (<= #6417 0::Int)
+#6008 := (= #174 #6007)
+#6547 := (f3 f23 f22)
+#6548 := (= f1 #6547)
+#8184 := (= #5891 #6547)
+#8182 := (= #6547 #5891)
+#8183 := [monotonicity #6998]: #8182
+#8185 := [symm #8183]: #8184
+#8186 := [trans #6999 #8185]: #6548
+#6554 := (not #6548)
+#6606 := (or #6008 #6554)
+#6687 := (or #4426 #6008 #6554)
+#6688 := (or #4426 #6606)
+#6690 := (iff #6688 #6687)
+#6691 := [rewrite]: #6690
+#6689 := [quant-inst #170]: #6688
+#6692 := [mp #6689 #6691]: #6687
+#8187 := [unit-resolution #6692 #7100]: #6606
+#8188 := [unit-resolution #8187 #8186]: #6008
+#8189 := (not #6008)
+#8190 := (or #8189 #6674)
+#8191 := [th-lemma arith triangle-eq]: #8190
+#8192 := [unit-resolution #8191 #8188]: #6674
+#16339 := (not #15460)
+#12652 := (not #6674)
+#15770 := (not #15240)
+#15766 := (or #14960 #15614 #2915 #15770 #12652 #16339)
+#15774 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15766
+#15775 := [unit-resolution #15774 #15608 #8192 #15769 #15607 #15669]: #14960
+#14679 := (+ f8 #14675)
+#14731 := (<= #14679 0::Int)
+#15014 := (not #14731)
+#16340 := (or #15014 #16339 #2327)
+#16336 := [hypothesis]: #2328
+#16331 := [hypothesis]: #14731
+#16337 := [hypothesis]: #15460
+#16338 := [th-lemma arith farkas 1 -1 1 #16337 #16331 #16336]: false
+#16341 := [lemma #16338]: #16340
+#15776 := [unit-resolution #16341 #15669 #15626]: #15014
+#14725 := (+ #2318 #14672)
+#14726 := (+ #174 #14725)
+#14743 := (= #14726 0::Int)
+#15811 := (not #14743)
+#14857 := (>= #14726 0::Int)
+#15772 := (not #14857)
+#15793 := (or #15772 #2915 #15770 #12652 #16339)
+#15805 := [th-lemma arith assign-bounds 1 1 -1 1]: #15793
+#15806 := [unit-resolution #15805 #15769 #8192 #15607 #15669]: #15772
+#15812 := (or #15811 #14857)
+#15813 := [th-lemma arith triangle-eq]: #15812
+#15847 := [unit-resolution #15813 #15806]: #15811
+#14768 := (or #14721 #14731 #14743)
+#14892 := (or #4409 #14721 #14731 #14743)
+#14673 := (+ #14672 #2318)
+#14674 := (+ #174 #14673)
+#14669 := (= #14674 0::Int)
+#14676 := (+ #1453 #14675)
+#14677 := (+ #14467 #14676)
+#14678 := (<= #14677 0::Int)
+#14732 := (or #14731 #14678 #14669)
+#14893 := (or #4409 #14732)
+#14860 := (iff #14893 #14892)
+#14895 := (or #4409 #14768)
+#14858 := (iff #14895 #14892)
+#14859 := [rewrite]: #14858
+#14921 := (iff #14893 #14895)
+#14770 := (iff #14732 #14768)
+#14765 := (or #14731 #14721 #14743)
+#14763 := (iff #14765 #14768)
+#14769 := [rewrite]: #14763
+#14766 := (iff #14732 #14765)
+#14744 := (iff #14669 #14743)
+#14727 := (= #14674 #14726)
+#14728 := [rewrite]: #14727
+#14764 := [monotonicity #14728]: #14744
+#14718 := (iff #14678 #14721)
+#14733 := (+ #14467 #14675)
+#14734 := (+ #1453 #14733)
+#14737 := (<= #14734 0::Int)
+#14722 := (iff #14737 #14721)
+#14723 := [rewrite]: #14722
+#14738 := (iff #14678 #14737)
+#14735 := (= #14677 #14734)
+#14736 := [rewrite]: #14735
+#14739 := [monotonicity #14736]: #14738
+#14724 := [trans #14739 #14723]: #14718
+#14767 := [monotonicity #14724 #14764]: #14766
+#14771 := [trans #14767 #14769]: #14770
+#14922 := [monotonicity #14771]: #14921
+#14920 := [trans #14922 #14859]: #14860
+#14894 := [quant-inst #2316]: #14893
+#14861 := [mp #14894 #14920]: #14892
+#15845 := [unit-resolution #14861 #6513]: #14768
+#15846 := [unit-resolution #15845 #15847 #15776 #15775]: false
+#15842 := [lemma #15846]: #3486
+#3989 := (or #4472 #3491 #4466)
+#4004 := [def-axiom]: #3989
+#23149 := [unit-resolution #4004 #15842]: #23134
+#23150 := [unit-resolution #23149 #23133]: #4466
+#4108 := (or #4463 #2360)
+#4110 := [def-axiom]: #4108
+#23151 := [unit-resolution #4110 #23150]: #2360
+#23152 := (= #9081 #6070)
+#23153 := [monotonicity #9282]: #23152
+#23155 := [symm #23153]: #9861
+#23156 := [unit-resolution #11949 #23155]: #9457
+#9818 := (<= #9455 0::Int)
+#23148 := (or #11945 #9818)
+#23154 := [th-lemma arith triangle-eq]: #23148
+#23157 := [unit-resolution #23154 #23155]: #9818
+#23158 := (not #9818)
+#23164 := (or #10878 #23158)
+#7358 := (>= #6070 0::Int)
+#7296 := (not #7358)
+#7297 := [hypothesis]: #7296
+#7978 := (or #4279 #7358)
+#7979 := [quant-inst #6069]: #7978
+#7484 := [unit-resolution #7979 #7121 #7297]: false
+#7488 := [lemma #7484]: #7358
+#7053 := (not #3920)
+#23159 := (or #10878 #7053 #7296 #23158)
+#23161 := [th-lemma arith assign-bounds -1 1 -1]: #23159
+#23165 := [unit-resolution #23161 #7488 #7126]: #23164
+#23163 := [unit-resolution #23165 #23157]: #10878
+#3995 := (or #4463 #4455)
+#3996 := [def-axiom]: #3995
+#23166 := [unit-resolution #3996 #23150]: #4455
+#24105 := (or #14183 #4460)
+#8778 := (f24 #7211)
+#9544 := (* -1::Int #8778)
+#14038 := (+ #2347 #9544)
+#14226 := (<= #14038 0::Int)
+#10164 := (f3 f23 #7211)
+#10165 := (= f1 #10164)
+#11810 := (= #5891 #10164)
+#11803 := (= #10164 #5891)
+#11809 := [monotonicity #6998 #7790]: #11803
+#11811 := [symm #11809]: #11810
+#11812 := [trans #6999 #11811]: #10165
+#14212 := (f9 #14211)
+#14238 := (* -1::Int #14212)
+#14239 := (+ #9544 #14238)
+#14240 := (+ #2347 #14239)
+#14241 := (= #14240 0::Int)
+#15156 := (>= #14240 0::Int)
+#14157 := (+ #2348 #14132)
+#14158 := (+ #174 #14157)
+#14427 := (<= #14158 0::Int)
+#14161 := (= #14158 0::Int)
+#14186 := (not #14183)
+#21311 := [hypothesis]: #14186
+#21316 := (or #14183 #14161)
+#21305 := (not #14161)
+#21306 := [hypothesis]: #21305
+#12472 := (not #14141)
+#12479 := (or #14183 #12472)
+#12480 := [def-axiom]: #12479
+#21312 := [unit-resolution #12480 #21311]: #12472
+#12469 := (not #14152)
+#12478 := (or #14183 #12469)
+#12481 := [def-axiom]: #12478
+#21313 := [unit-resolution #12481 #21311]: #12469
+#14164 := (or #14141 #14152 #14161)
+#12411 := (or #4409 #14141 #14152 #14161)
+#14133 := (+ #14132 #2348)
+#14134 := (+ #174 #14133)
+#14135 := (= #14134 0::Int)
+#14137 := (+ #1453 #14136)
+#14138 := (+ #14074 #14137)
+#14139 := (<= #14138 0::Int)
+#14142 := (or #14141 #14139 #14135)
+#12435 := (or #4409 #14142)
+#12440 := (iff #12435 #12411)
+#12408 := (or #4409 #14164)
+#12439 := (iff #12408 #12411)
+#12434 := [rewrite]: #12439
+#12437 := (iff #12435 #12408)
+#14165 := (iff #14142 #14164)
+#14162 := (iff #14135 #14161)
+#14159 := (= #14134 #14158)
+#14160 := [rewrite]: #14159
+#14163 := [monotonicity #14160]: #14162
+#14155 := (iff #14139 #14152)
+#14143 := (+ #14074 #14136)
+#14144 := (+ #1453 #14143)
+#14147 := (<= #14144 0::Int)
+#14153 := (iff #14147 #14152)
+#14154 := [rewrite]: #14153
+#14148 := (iff #14139 #14147)
+#14145 := (= #14138 #14144)
+#14146 := [rewrite]: #14145
+#14149 := [monotonicity #14146]: #14148
+#14156 := [trans #14149 #14154]: #14155
+#14166 := [monotonicity #14156 #14163]: #14165
+#12438 := [monotonicity #14166]: #12437
+#12442 := [trans #12438 #12434]: #12440
+#12436 := [quant-inst #2346]: #12435
+#12443 := [mp #12436 #12442]: #12411
+#21314 := [unit-resolution #12443 #6513]: #14164
+#21315 := [unit-resolution #21314 #21313 #21312 #21306]: false
+#21317 := [lemma #21315]: #21316
+#24022 := [unit-resolution #21317 #21311]: #14161
+#24023 := (or #21305 #14427)
+#24024 := [th-lemma arith triangle-eq]: #24023
+#24025 := [unit-resolution #24024 #24022]: #14427
+#17684 := (not #14427)
+#24046 := (or #15156 #17684)
+#9545 := (+ #6007 #9544)
+#7445 := (>= #9545 0::Int)
+#9543 := (= #6007 #8778)
+#11874 := (= #8778 #6007)
+#11875 := [monotonicity #7790]: #11874
+#11876 := [symm #11875]: #9543
+#11877 := (not #9543)
+#24020 := (or #11877 #7445)
+#24026 := [th-lemma arith triangle-eq]: #24020
+#24027 := [unit-resolution #24026 #11876]: #7445
+#13353 := (+ #14132 #14238)
+#13586 := (>= #13353 0::Int)
+#7923 := (= #14132 #14212)
+#24030 := (= #14212 #14132)
+#24037 := [monotonicity #24029]: #24030
+#24038 := [symm #24037]: #7923
+#24036 := (not #7923)
+#24039 := (or #24036 #13586)
+#24040 := [th-lemma arith triangle-eq]: #24039
+#24041 := [unit-resolution #24040 #24038]: #13586
+#24044 := (not #13586)
+#24043 := (not #7445)
+#24042 := (or #15156 #24043 #10350 #24044 #17684)
+#24045 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24042
+#24047 := [unit-resolution #24045 #24041 #24027 #8194]: #24046
+#24035 := [unit-resolution #24047 #24025]: #15156
+#15134 := (<= #14240 0::Int)
+#14428 := (>= #14158 0::Int)
+#24048 := (or #21305 #14428)
+#24049 := [th-lemma arith triangle-eq]: #24048
+#24050 := [unit-resolution #24049 #24022]: #14428
+#24054 := (not #14428)
+#24058 := (or #15134 #24054)
+#9546 := (<= #9545 0::Int)
+#11878 := (or #11877 #9546)
+#11879 := [th-lemma arith triangle-eq]: #11878
+#11880 := [unit-resolution #11879 #11876]: #9546
+#13354 := (<= #13353 0::Int)
+#24051 := (or #24036 #13354)
+#24034 := [th-lemma arith triangle-eq]: #24051
+#24052 := [unit-resolution #24034 #24038]: #13354
+#24053 := (not #13354)
+#12651 := (not #9546)
+#24055 := (or #15134 #12651 #12652 #24053 #24054)
+#24056 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24055
+#24059 := [unit-resolution #24056 #24052 #11880 #8192]: #24058
+#24060 := [unit-resolution #24059 #24050]: #15134
+#24062 := (not #15156)
+#24061 := (not #15134)
+#24057 := (or #14241 #24061 #24062)
+#24063 := [th-lemma arith triangle-eq]: #24057
+#24064 := [unit-resolution #24063 #24060 #24035]: #14241
+#14246 := (not #14241)
+#10177 := (not #10165)
+#14249 := (or #10177 #14226 #14246)
+#24065 := [hypothesis]: #4455
+#12777 := (or #4460 #10177 #14226 #14246)
+#14213 := (+ #2348 #14212)
+#14214 := (+ #8778 #14213)
+#14215 := (= #14214 0::Int)
+#14216 := (not #14215)
+#14217 := (+ #8778 #2348)
+#14218 := (>= #14217 0::Int)
+#14219 := (or #10177 #14218 #14216)
+#12784 := (or #4460 #14219)
+#12837 := (iff #12784 #12777)
+#12848 := (or #4460 #14249)
+#12871 := (iff #12848 #12777)
+#12877 := [rewrite]: #12871
+#12875 := (iff #12784 #12848)
+#14250 := (iff #14219 #14249)
+#14247 := (iff #14216 #14246)
+#14244 := (iff #14215 #14241)
+#14231 := (+ #8778 #14212)
+#14232 := (+ #2348 #14231)
+#14235 := (= #14232 0::Int)
+#14242 := (iff #14235 #14241)
+#14243 := [rewrite]: #14242
+#14236 := (iff #14215 #14235)
+#14233 := (= #14214 #14232)
+#14234 := [rewrite]: #14233
+#14237 := [monotonicity #14234]: #14236
+#14245 := [trans #14237 #14243]: #14244
+#14248 := [monotonicity #14245]: #14247
+#14229 := (iff #14218 #14226)
+#14220 := (+ #2348 #8778)
+#14223 := (>= #14220 0::Int)
+#14227 := (iff #14223 #14226)
+#14228 := [rewrite]: #14227
+#14224 := (iff #14218 #14223)
+#14221 := (= #14217 #14220)
+#14222 := [rewrite]: #14221
+#14225 := [monotonicity #14222]: #14224
+#14230 := [trans #14225 #14228]: #14229
+#14251 := [monotonicity #14230 #14248]: #14250
+#12876 := [monotonicity #14251]: #12875
+#12903 := [trans #12876 #12877]: #12837
+#12841 := [quant-inst #7211]: #12784
+#12904 := [mp #12841 #12903]: #12777
+#24066 := [unit-resolution #12904 #24065]: #14249
+#24067 := [unit-resolution #24066 #24064 #11812]: #14226
+#12487 := (f5 f10 ?v0!20)
+#17155 := (f7 #12487)
+#22316 := (f5 #7211 #17155)
+#22325 := (f9 #22316)
+#22328 := (* -1::Int #22325)
+#22457 := (+ #14132 #22328)
+#17191 := (>= #22457 0::Int)
+#17177 := (= #14132 #22325)
+#24068 := (= #22325 #14132)
+#24072 := (= #22316 #14131)
+#24070 := (= #17155 ?v0!20)
+#17156 := (= ?v0!20 #17155)
+#17179 := (or #6824 #17156)
+#17180 := [quant-inst #56 #2346]: #17179
+#24069 := [unit-resolution #17180 #4199]: #17156
+#24071 := [symm #24069]: #24070
+#24073 := [monotonicity #7790 #24071]: #24072
+#24074 := [monotonicity #24073]: #24068
+#24075 := [symm #24074]: #17177
+#24076 := (not #17177)
+#24077 := (or #24076 #17191)
+#24078 := [th-lemma arith triangle-eq]: #24077
+#24080 := [unit-resolution #24078 #24075]: #17191
+#22384 := (<= #22325 0::Int)
+#22364 := (not #22384)
+#22367 := (= #7211 #17155)
+#22397 := (not #22367)
+#20554 := (f3 f15 #17155)
+#20571 := (= f1 #20554)
+#23981 := (ite #22367 #5892 #20571)
+#24001 := (not #23981)
+#23982 := (f3 #8442 #17155)
+#23987 := (= f1 #23982)
+#23989 := (iff #23981 #23987)
+#23993 := (or #6290 #23989)
+#23988 := (iff #23987 #23981)
+#23994 := (or #6290 #23988)
+#23996 := (iff #23994 #23993)
+#23992 := (iff #23993 #23993)
+#23998 := [rewrite]: #23992
+#23990 := (iff #23988 #23989)
+#23991 := [rewrite]: #23990
+#23997 := [monotonicity #23991]: #23996
+#23999 := [trans #23997 #23998]: #23996
+#23995 := [quant-inst #104 #7211 #5891 #17155]: #23994
+#24000 := [mp #23995 #23999]: #23993
+#24081 := [unit-resolution #24000 #4177]: #23989
+#24013 := (not #23987)
+#10246 := (f3 f23 ?v0!20)
+#10247 := (= f1 #10246)
+#10248 := (not #10247)
+#24094 := (iff #10248 #24013)
+#24092 := (iff #10247 #23987)
+#24089 := (iff #23987 #10247)
+#24087 := (= #23982 #10246)
+#24088 := [monotonicity #9286 #24071]: #24087
+#24091 := [monotonicity #24088]: #24089
+#24093 := [symm #24091]: #24092
+#24095 := [monotonicity #24093]: #24094
+#24708 := (not #14085)
+#21436 := (not #19567)
+#24082 := (or #14152 #21436 #24044 #24061 #24043 #10350)
+#24083 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24082
+#24084 := [unit-resolution #24083 #24060 #24041 #21313 #24027 #8194]: #21436
+#24709 := (or #24708 #19567)
+#24696 := [hypothesis]: #21436
+#24697 := [hypothesis]: #14085
+#24710 := [th-lemma arith triangle-eq]: #24709
+#24711 := [unit-resolution #24710 #24697 #24696]: false
+#24712 := [lemma #24711]: #24709
+#24079 := [unit-resolution #24712 #24084]: #24708
+#14091 := (or #10248 #14085)
+#12334 := (or #4426 #10248 #14085)
+#14081 := (= #14074 #2347)
+#14084 := (or #14081 #10248)
+#12374 := (or #4426 #14084)
+#12382 := (iff #12374 #12334)
+#12377 := (or #4426 #14091)
+#12379 := (iff #12377 #12334)
+#12381 := [rewrite]: #12379
+#12378 := (iff #12374 #12377)
+#14094 := (iff #14084 #14091)
+#14088 := (or #14085 #10248)
+#14092 := (iff #14088 #14091)
+#14093 := [rewrite]: #14092
+#14089 := (iff #14084 #14088)
+#14086 := (iff #14081 #14085)
+#14087 := [rewrite]: #14086
+#14090 := [monotonicity #14087]: #14089
+#14095 := [trans #14090 #14093]: #14094
+#12373 := [monotonicity #14095]: #12378
+#12383 := [trans #12373 #12381]: #12382
+#12376 := [quant-inst #2346]: #12374
+#12402 := [mp #12376 #12383]: #12334
+#24085 := [unit-resolution #12402 #7100]: #14091
+#24086 := [unit-resolution #24085 #24079]: #10248
+#24090 := [mp #24086 #24095]: #24013
+#24012 := (not #23989)
+#24015 := (or #24012 #24001 #23987)
+#24016 := [def-axiom]: #24015
+#24096 := [unit-resolution #24016 #24090 #24081]: #24001
+#24097 := (or #23981 #22397)
+#24008 := (or #23981 #22397 #6304)
+#24009 := [def-axiom]: #24008
+#24098 := [unit-resolution #24009 #6999]: #24097
+#24099 := [unit-resolution #24098 #24096]: #22397
+#22369 := (or #22367 #22364)
+#23958 := (or #6782 #22367 #22364)
+#22365 := (= #17155 #7211)
+#22366 := (or #22365 #22364)
+#23959 := (or #6782 #22366)
+#23966 := (iff #23959 #23958)
+#23961 := (or #6782 #22369)
+#23964 := (iff #23961 #23958)
+#23965 := [rewrite]: #23964
+#23962 := (iff #23959 #23961)
+#22370 := (iff #22366 #22369)
+#22368 := (iff #22365 #22367)
+#22363 := [rewrite]: #22368
+#22371 := [monotonicity #22363]: #22370
+#23963 := [monotonicity #22371]: #23962
+#23967 := [trans #23963 #23965]: #23966
+#23960 := [quant-inst #7211 #17155]: #23959
+#23968 := [mp #23960 #23967]: #23958
+#24100 := [unit-resolution #23968 #4217]: #22369
+#24103 := [unit-resolution #24100 #24099]: #22364
+#24104 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24027 #8194 #24103 #24080 #24025 #24067]: false
+#24106 := [lemma #24104]: #24105
+#23167 := [unit-resolution #24106 #23166]: #14183
+#23147 := [hypothesis]: #12469
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+#12483 := [def-axiom]: #12482
+#23160 := [unit-resolution #12483 #23147 #23167]: #14141
+#14189 := (or #14085 #14186)
+#12444 := (or #4401 #14085 #14186)
+#14180 := (or #14141 #14139)
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+#14182 := (or #14081 #14181)
+#12463 := (or #4401 #14182)
+#12468 := (iff #12463 #12444)
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+#12467 := (iff #12441 #12444)
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+#12465 := (iff #12463 #12441)
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+#14187 := (iff #14181 #14186)
+#14184 := (iff #14180 #14183)
+#14185 := [monotonicity #14156]: #14184
+#14188 := [monotonicity #14185]: #14187
+#14191 := [monotonicity #14087 #14188]: #14190
+#12466 := [monotonicity #14191]: #12465
+#12470 := [trans #12466 #12462]: #12468
+#12464 := [quant-inst #2346]: #12463
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+#23169 := [unit-resolution #24712 #23146]: #19567
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+#27708 := [unit-resolution #12471 #6509 #27696]: #14085
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+#21430 := [hypothesis]: #19567
+#21431 := [hypothesis]: #14792
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+#27710 := [unit-resolution #21438 #27709 #19783]: #21435
+#4111 := (or #4463 #2929)
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+#27711 := [unit-resolution #4109 #23150]: #2929
+#24435 := (or #4312 #2926 #14792 #14797)
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+#14790 := (not #14789)
+#14793 := (or #2361 #14792 #14790)
+#24444 := (or #4312 #14793)
+#24450 := (iff #24444 #24435)
+#14800 := (or #2926 #14792 #14797)
+#24441 := (or #4312 #14800)
+#24449 := (iff #24441 #24435)
+#24445 := [rewrite]: #24449
+#24440 := (iff #24444 #24441)
+#14801 := (iff #14793 #14800)
+#14798 := (iff #14790 #14797)
+#14795 := (iff #14789 #14794)
+#14796 := [rewrite]: #14795
+#14799 := [monotonicity #14796]: #14798
+#14802 := [monotonicity #2928 #14799]: #14801
+#24447 := [monotonicity #14802]: #24440
+#24439 := [trans #24447 #24445]: #24450
+#24446 := [quant-inst #2346]: #24444
+#24462 := [mp #24446 #24439]: #24435
+#27713 := [unit-resolution #24462 #12665 #27711 #27710]: #14797
+#24466 := (or #14794 #14787)
+#24452 := [def-axiom]: #24466
+#27678 := [unit-resolution #24452 #27713]: #14787
+#27719 := [trans #27678 #27718]: #26214
+#26242 := (not #26214)
+#15536 := (>= #14783 0::Int)
+#24464 := (or #14794 #14784)
+#24465 := [def-axiom]: #24464
+#27715 := [unit-resolution #24465 #27713]: #14784
+#27716 := (or #14785 #15536)
+#27714 := [th-lemma arith triangle-eq]: #27716
+#27717 := [unit-resolution #27714 #27715]: #15536
+#24448 := (not #14778)
+#24463 := (or #14794 #24448)
+#24442 := [def-axiom]: #24463
+#27699 := [unit-resolution #24442 #27713]: #24448
+#15512 := (<= #14783 0::Int)
+#27697 := (or #14785 #15512)
+#27700 := [th-lemma arith triangle-eq]: #27697
+#27701 := [unit-resolution #27700 #27715]: #15512
+#28964 := (not #15536)
+#29081 := (not #15512)
+#29112 := (or #26242 #29081 #4460 #14778 #21436 #28964)
+#21416 := (f24 #14774)
+#21446 := (* -1::Int #21416)
+#21657 := (+ #14781 #21446)
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+#21447 := (+ #14775 #21446)
+#21448 := (>= #21447 0::Int)
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+#28967 := (or #18266 #28964 #21436 #28966)
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+#21659 := (= #21658 0::Int)
+#21664 := (not #21659)
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+#21429 := (f3 f23 #14774)
+#21409 := (= f1 #21429)
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+#29043 := (iff #25147 #21409)
+#29046 := (iff #21409 #25147)
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+#29049 := [symm #29041]: #29043
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+#30420 := (ite #30426 #5892 #26214)
+#30488 := [hypothesis]: #26214
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+#30487 := [unit-resolution #30486 #30484]: #30465
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+#30449 := (f3 #8442 #25042)
+#30254 := (= #30449 #25158)
+#30250 := (= #25158 #30449)
+#18324 := (= f23 #8442)
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+#18326 := [symm #9284]: #18225
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+#21646 := (iff #21641 #21645)
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+#29080 := (iff #26948 #29077)
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+#26986 := [monotonicity #26947]: #26987
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+#27011 := [monotonicity #27007]: #27003
+#26965 := [trans #27011 #27012]: #27013
+#27009 := [quant-inst #25042]: #27008
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+#14121 := [trans #14114 #14119]: #14120
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+#29159 := [hypothesis]: #15512
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+#6110 := [monotonicity #6104]: #6109
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+#9899 := (not #10062)
+#9972 := (or #9785 #9899 #2275 #9900 #6992 #9969)
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+#9898 := [unit-resolution #9892 #9583 #6991 #10071 #10087 #9582]: #9785
+#9859 := (or #9975 #10050)
+#9971 := [th-lemma arith triangle-eq]: #9859
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+#9970 := (or #10025 #9899 #2275 #9900 #6992 #9969)
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+#10042 := [unit-resolution #10041 #9583 #6991 #10087 #10071 #9582]: #10025
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+#9528 := (or #6807 #9968 #10028)
+#10029 := (or #10028 #9968)
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+#9535 := (iff #9498 #9528)
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+#10037 := (iff #10029 #10036)
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+#9802 := [trans #9541 #9800]: #9801
+#9539 := [quant-inst #7211 #2273]: #9547
+#9761 := [mp #9539 #9802]: #9528
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+#10142 := [lemma #9862]: #9654
+#9534 := [unit-resolution #10142 #10087 #9582]: #9900
+#9538 := [unit-resolution #10085 #9534]: #10083
+#8427 := (or #7638 #7616)
+#9098 := [hypothesis]: #10083
+#8424 := [hypothesis]: #7641
+#8426 := [unit-resolution #9512 #8424]: #9510
+#8466 := [unit-resolution #9515 #8424]: #9513
+#8467 := [unit-resolution #10081 #8466 #8426 #9098]: false
+#9343 := [lemma #8467]: #8427
+#9757 := [unit-resolution #9343 #9538]: #7638
+#9799 := [unit-resolution #10077 #9757]: #7539
+#9755 := [unit-resolution #11920 #9799]: #9581
+#9897 := [th-lemma arith farkas 1 -1 1 #9580 #10087 #9755]: false
+#8322 := [lemma #9897]: #8364
+#26770 := [unit-resolution #8322 #26764]: #2275
+#26768 := [unit-resolution #12717 #26770]: #4490
+#26771 := [unit-resolution #4086 #26768]: #4481
+#26767 := [unit-resolution #12721 #26771]: #4478
+#26772 := [unit-resolution #4008 #26767]: #4469
+#26780 := [unit-resolution #23149 #26772]: #4466
+#26782 := [unit-resolution #3996 #26780]: #4455
+#26779 := [unit-resolution #24106 #26782]: #14183
+#26783 := [unit-resolution #12471 #6509 #26779]: #14085
+#26781 := [unit-resolution #24710 #26783]: #19567
+#26797 := [unit-resolution #21438 #26781 #19783]: #21435
+#26800 := [unit-resolution #4109 #26780]: #2929
+#26792 := [unit-resolution #24462 #12665 #26800 #26797]: #14797
+#26775 := [unit-resolution #24452 #26792]: #14787
+#26834 := [trans #26775 #26828]: #26214
+#26798 := [unit-resolution #24465 #26792]: #14784
+#26793 := [unit-resolution #27700 #26798]: #15512
+#26791 := [unit-resolution #24442 #26792]: #24448
+#26794 := [unit-resolution #27714 #26798]: #15536
+#26790 := [unit-resolution #29113 #26794 #26782 #26791 #26781 #26793]: #26242
+#26829 := [unit-resolution #26790 #26834]: false
+#26830 := [lemma #26829]: #2359
+#8229 := [unit-resolution #4110 #26830]: #4463
+#8233 := [unit-resolution #23149 #8229]: #4472
+#8319 := [unit-resolution #4008 #8233]: #4475
+#8238 := [unit-resolution #12721 #8319]: #4484
+#8242 := [unit-resolution #4086 #8238]: #4487
+#8248 := [unit-resolution #12717 #8242]: #2276
+#8342 := [unit-resolution #11112 #8248]: #6073
+#8367 := [unit-resolution #6120 #8342]: #6091
+#8285 := [unit-resolution #12667 #8367]: #6088
+#8425 := [symm #8285]: #6086
+#8354 := [monotonicity #8425]: #7825
+#8358 := [symm #8354]: #7797
+#8360 := [unit-resolution #8322 #8248]: #9969
+[unit-resolution #7828 #8360 #8358]: false
 unsat

--- a/src/HOL/Multivariate_Analysis/Integration.certs	Fri Dec 17 14:36:33 2010 +0100
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Fri Dec 17 14:59:06 2010 +0100
@@ -1,275 +1,275 @@
-57b03a56df49326094be4946646336bc93948572 272 0
+8d81ff6f41bc1cff9f5c6454ee204d147f8e27b7 272 0
 #2 := false
-#46 := 0::Real
-decl f16 :: (-> S3 S9 Real)
-decl f17 :: S9
-#41 := f17
+#48 := 0::Real
+decl f17 :: (-> S3 S10 Real)
+decl f18 :: S10
+#43 := f18
 decl f4 :: S3
 #8 := f4
-#56 := (f16 f4 f17)
-#92 := -1::Real
-#136 := (* -1::Real #56)
+#58 := (f17 f4 f18)
+#94 := -1::Real
+#138 := (* -1::Real #58)
 decl f5 :: (-> S4 S5 Real)
 decl f8 :: S5
 #14 := f8
+decl f20 :: S4
+#54 := f20
+#55 := (f5 f20 f8)
+#139 := (+ #55 #138)
+#122 := (* -1::Real #55)
+#129 := (+ #122 #58)
+#189 := (<= #139 0::Real)
+#196 := (ite #189 #129 #139)
+#372 := (* -1::Real #196)
+#373 := (+ #129 #372)
+#374 := (<= #373 0::Real)
+#356 := (= #129 #196)
 decl f19 :: S4
-#52 := f19
-#53 := (f5 f19 f8)
-#137 := (+ #53 #136)
-#120 := (* -1::Real #53)
-#127 := (+ #120 #56)
-#187 := (<= #137 0::Real)
-#194 := (ite #187 #127 #137)
-#370 := (* -1::Real #194)
-#371 := (+ #127 #370)
-#372 := (<= #371 0::Real)
-#354 := (= #127 #194)
-decl f18 :: S4
-#43 := f18
-#44 := (f5 f18 f8)
+#45 := f19
+#46 := (f5 f19 f8)
 decl f9 :: S3
 #18 := f9
-#42 := (f16 f9 f17)
-#103 := (* -1::Real #42)
-#104 := (+ #103 #44)
-#93 := (* -1::Real #44)
-#94 := (+ #42 #93)
-#222 := (>= #94 0::Real)
-#229 := (ite #222 #94 #104)
-#366 := (* -1::Real #229)
-#369 := (+ #104 #366)
-#373 := (<= #369 0::Real)
-#361 := (= #104 #229)
-#223 := (not #222)
-#374 := [hypothesis]: #222
-#180 := (+ #42 #136)
-#181 := (<= #180 0::Real)
-#205 := -3::Real
-#240 := (* -3::Real #229)
-#241 := (+ #120 #240)
-#242 := (+ #44 #241)
-#243 := (<= #242 0::Real)
-#206 := (* -3::Real #194)
-#207 := (+ #120 #206)
-#208 := (+ #44 #207)
-#209 := (<= #208 0::Real)
-#184 := (not #181)
-#262 := (or #184 #209 #243)
-#267 := (not #262)
-#63 := (<= #42 #56)
-#64 := (implies #63 false)
-#54 := (- #44 #53)
-#50 := 3::Real
-#57 := (- #56 #53)
-#59 := (- #57)
-#58 := (< #57 0::Real)
-#60 := (ite #58 #59 #57)
-#61 := (* #60 3::Real)
-#62 := (< #61 #54)
-#65 := (implies #62 #64)
-#45 := (- #42 #44)
-#48 := (- #45)
-#47 := (< #45 0::Real)
-#49 := (ite #47 #48 #45)
-#51 := (* #49 3::Real)
-#55 := (< #51 #54)
-#66 := (implies #55 #65)
-#67 := (not #66)
-#270 := (iff #67 #267)
-#121 := (+ #44 #120)
-#130 := (< #127 0::Real)
-#142 := (ite #130 #137 #127)
-#148 := (* 3::Real #142)
-#153 := (< #148 #121)
-#162 := (not #153)
-#156 := (not #63)
-#163 := (or #156 #162)
-#97 := (< #94 0::Real)
-#109 := (ite #97 #104 #94)
-#115 := (* 3::Real #109)
-#124 := (< #115 #121)
-#171 := (not #124)
-#172 := (or #171 #163)
-#177 := (not #172)
-#268 := (iff #177 #267)
-#265 := (iff #172 #262)
-#256 := (or #184 #209)
-#259 := (or #243 #256)
-#263 := (iff #259 #262)
-#264 := [rewrite]: #263
-#260 := (iff #172 #259)
-#257 := (iff #163 #256)
-#220 := (iff #162 #209)
-#210 := (not #209)
-#215 := (not #210)
-#218 := (iff #215 #209)
-#219 := [rewrite]: #218
-#216 := (iff #162 #215)
-#213 := (iff #153 #210)
-#199 := (* 3::Real #194)
-#202 := (< #199 #121)
-#211 := (iff #202 #210)
-#212 := [rewrite]: #211
-#203 := (iff #153 #202)
-#200 := (= #148 #199)
-#197 := (= #142 #194)
-#188 := (not #187)
-#191 := (ite #188 #137 #127)
-#195 := (= #191 #194)
-#196 := [rewrite]: #195
-#192 := (= #142 #191)
-#189 := (iff #130 #188)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#198 := [trans #193 #196]: #197
-#201 := [monotonicity #198]: #200
-#204 := [monotonicity #201]: #203
-#214 := [trans #204 #212]: #213
-#217 := [monotonicity #214]: #216
-#221 := [trans #217 #219]: #220
-#185 := (iff #156 #184)
-#182 := (iff #63 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#258 := [monotonicity #186 #221]: #257
-#254 := (iff #171 #243)
-#244 := (not #243)
-#249 := (not #244)
-#252 := (iff #249 #243)
-#253 := [rewrite]: #252
-#250 := (iff #171 #249)
-#247 := (iff #124 #244)
-#234 := (* 3::Real #229)
-#237 := (< #234 #121)
-#245 := (iff #237 #244)
-#246 := [rewrite]: #245
-#238 := (iff #124 #237)
-#235 := (= #115 #234)
-#232 := (= #109 #229)
-#226 := (ite #223 #104 #94)
-#230 := (= #226 #229)
-#231 := [rewrite]: #230
-#227 := (= #109 #226)
-#224 := (iff #97 #223)
-#225 := [rewrite]: #224
-#228 := [monotonicity #225]: #227
-#233 := [trans #228 #231]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#248 := [trans #239 #246]: #247
-#251 := [monotonicity #248]: #250
-#255 := [trans #251 #253]: #254
-#261 := [monotonicity #255 #258]: #260
-#266 := [trans #261 #264]: #265
-#269 := [monotonicity #266]: #268
-#178 := (iff #67 #177)
-#175 := (iff #66 #172)
-#168 := (implies #124 #163)
-#173 := (iff #168 #172)
-#174 := [rewrite]: #173
-#169 := (iff #66 #168)
-#166 := (iff #65 #163)
-#159 := (implies #153 #156)
-#164 := (iff #159 #163)
-#165 := [rewrite]: #164
-#160 := (iff #65 #159)
-#157 := (iff #64 #156)
-#158 := [rewrite]: #157
-#154 := (iff #62 #153)
-#122 := (= #54 #121)
-#123 := [rewrite]: #122
-#151 := (= #61 #148)
-#145 := (* #142 3::Real)
-#149 := (= #145 #148)
-#150 := [rewrite]: #149
-#146 := (= #61 #145)
-#143 := (= #60 #142)
-#128 := (= #57 #127)
-#129 := [rewrite]: #128
-#140 := (= #59 #137)
-#133 := (- #127)
-#138 := (= #133 #137)
-#139 := [rewrite]: #138
-#134 := (= #59 #133)
-#135 := [monotonicity #129]: #134
-#141 := [trans #135 #139]: #140
-#131 := (iff #58 #130)
-#132 := [monotonicity #129]: #131
-#144 := [monotonicity #132 #141 #129]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#155 := [monotonicity #152 #123]: #154
-#161 := [monotonicity #155 #158]: #160
-#167 := [trans #161 #165]: #166
-#125 := (iff #55 #124)
-#118 := (= #51 #115)
-#112 := (* #109 3::Real)
-#116 := (= #112 #115)
-#117 := [rewrite]: #116
-#113 := (= #51 #112)
-#110 := (= #49 #109)
-#95 := (= #45 #94)
-#96 := [rewrite]: #95
-#107 := (= #48 #104)
-#100 := (- #94)
-#105 := (= #100 #104)
-#106 := [rewrite]: #105
-#101 := (= #48 #100)
-#102 := [monotonicity #96]: #101
-#108 := [trans #102 #106]: #107
-#98 := (iff #47 #97)
-#99 := [monotonicity #96]: #98
-#111 := [monotonicity #99 #108 #96]: #110
-#114 := [monotonicity #111]: #113
-#119 := [trans #114 #117]: #118
-#126 := [monotonicity #119 #123]: #125
-#170 := [monotonicity #126 #167]: #169
-#176 := [trans #170 #174]: #175
-#179 := [monotonicity #176]: #178
-#271 := [trans #179 #269]: #270
-#91 := [asserted]: #67
-#272 := [mp #91 #271]: #267
-#273 := [not-or-elim #272]: #181
-#275 := [not-or-elim #272]: #244
-#367 := (+ #94 #366)
-#368 := (<= #367 0::Real)
-#360 := (= #94 #229)
-#362 := (or #223 #360)
-#363 := [def-axiom]: #362
-#386 := [unit-resolution #363 #374]: #360
-#387 := (not #360)
-#388 := (or #387 #368)
-#389 := [th-lemma arith triangle-eq]: #388
-#390 := [unit-resolution #389 #386]: #368
-#382 := (or #188 #223)
-#375 := [hypothesis]: #187
-#274 := [not-or-elim #272]: #210
-#356 := (or #188 #354)
-#357 := [def-axiom]: #356
-#376 := [unit-resolution #357 #375]: #354
-#377 := (not #354)
-#378 := (or #377 #372)
-#379 := [th-lemma arith triangle-eq]: #378
-#380 := [unit-resolution #379 #376]: #372
-#381 := [th-lemma arith farkas -1 -3 1 -2 1 #273 #380 #274 #375 #374]: false
-#383 := [lemma #381]: #382
-#391 := [unit-resolution #383 #374]: #188
-#392 := [th-lemma arith farkas 1/4 -3/4 1/4 -1/4 1 #391 #390 #275 #273 #374]: false
-#393 := [lemma #392]: #223
-#364 := (or #222 #361)
+#44 := (f17 f9 f18)
+#105 := (* -1::Real #44)
+#106 := (+ #105 #46)
+#95 := (* -1::Real #46)
+#96 := (+ #44 #95)
+#224 := (>= #96 0::Real)
+#231 := (ite #224 #96 #106)
+#368 := (* -1::Real #231)
+#371 := (+ #106 #368)
+#375 := (<= #371 0::Real)
+#363 := (= #106 #231)
+#225 := (not #224)
+#376 := [hypothesis]: #224
+#182 := (+ #44 #138)
+#183 := (<= #182 0::Real)
+#207 := -3::Real
+#242 := (* -3::Real #231)
+#243 := (+ #122 #242)
+#244 := (+ #46 #243)
+#245 := (<= #244 0::Real)
+#208 := (* -3::Real #196)
+#209 := (+ #122 #208)
+#210 := (+ #46 #209)
+#211 := (<= #210 0::Real)
+#186 := (not #183)
+#264 := (or #186 #211 #245)
+#269 := (not #264)
+#65 := (<= #44 #58)
+#66 := (implies #65 false)
+#56 := (- #46 #55)
+#52 := 3::Real
+#59 := (- #58 #55)
+#61 := (- #59)
+#60 := (< #59 0::Real)
+#62 := (ite #60 #61 #59)
+#63 := (* #62 3::Real)
+#64 := (< #63 #56)
+#67 := (implies #64 #66)
+#47 := (- #44 #46)
+#50 := (- #47)
+#49 := (< #47 0::Real)
+#51 := (ite #49 #50 #47)
+#53 := (* #51 3::Real)
+#57 := (< #53 #56)
+#68 := (implies #57 #67)
+#69 := (not #68)
+#272 := (iff #69 #269)
+#123 := (+ #46 #122)
+#132 := (< #129 0::Real)
+#144 := (ite #132 #139 #129)
+#150 := (* 3::Real #144)
+#155 := (< #150 #123)
+#164 := (not #155)
+#158 := (not #65)
+#165 := (or #158 #164)
+#99 := (< #96 0::Real)
+#111 := (ite #99 #106 #96)
+#117 := (* 3::Real #111)
+#126 := (< #117 #123)
+#173 := (not #126)
+#174 := (or #173 #165)
+#179 := (not #174)
+#270 := (iff #179 #269)
+#267 := (iff #174 #264)
+#258 := (or #186 #211)
+#261 := (or #245 #258)
+#265 := (iff #261 #264)
+#266 := [rewrite]: #265
+#262 := (iff #174 #261)
+#259 := (iff #165 #258)
+#222 := (iff #164 #211)
+#212 := (not #211)
+#217 := (not #212)
+#220 := (iff #217 #211)
+#221 := [rewrite]: #220
+#218 := (iff #164 #217)
+#215 := (iff #155 #212)
+#201 := (* 3::Real #196)
+#204 := (< #201 #123)
+#213 := (iff #204 #212)
+#214 := [rewrite]: #213
+#205 := (iff #155 #204)
+#202 := (= #150 #201)
+#199 := (= #144 #196)
+#190 := (not #189)
+#193 := (ite #190 #139 #129)
+#197 := (= #193 #196)
+#198 := [rewrite]: #197
+#194 := (= #144 #193)
+#191 := (iff #132 #190)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#200 := [trans #195 #198]: #199
+#203 := [monotonicity #200]: #202
+#206 := [monotonicity #203]: #205
+#216 := [trans #206 #214]: #215
+#219 := [monotonicity #216]: #218
+#223 := [trans #219 #221]: #222
+#187 := (iff #158 #186)
+#184 := (iff #65 #183)
+#185 := [rewrite]: #184
+#188 := [monotonicity #185]: #187
+#260 := [monotonicity #188 #223]: #259
+#256 := (iff #173 #245)
+#246 := (not #245)
+#251 := (not #246)
+#254 := (iff #251 #245)
+#255 := [rewrite]: #254
+#252 := (iff #173 #251)
+#249 := (iff #126 #246)
+#236 := (* 3::Real #231)
+#239 := (< #236 #123)
+#247 := (iff #239 #246)
+#248 := [rewrite]: #247
+#240 := (iff #126 #239)
+#237 := (= #117 #236)
+#234 := (= #111 #231)
+#228 := (ite #225 #106 #96)
+#232 := (= #228 #231)
+#233 := [rewrite]: #232
+#229 := (= #111 #228)
+#226 := (iff #99 #225)
+#227 := [rewrite]: #226
+#230 := [monotonicity #227]: #229
+#235 := [trans #230 #233]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#250 := [trans #241 #248]: #249
+#253 := [monotonicity #250]: #252
+#257 := [trans #253 #255]: #256
+#263 := [monotonicity #257 #260]: #262
+#268 := [trans #263 #266]: #267
+#271 := [monotonicity #268]: #270
+#180 := (iff #69 #179)
+#177 := (iff #68 #174)
+#170 := (implies #126 #165)
+#175 := (iff #170 #174)
+#176 := [rewrite]: #175
+#171 := (iff #68 #170)
+#168 := (iff #67 #165)
+#161 := (implies #155 #158)
+#166 := (iff #161 #165)
+#167 := [rewrite]: #166
+#162 := (iff #67 #161)
+#159 := (iff #66 #158)
+#160 := [rewrite]: #159
+#156 := (iff #64 #155)
+#124 := (= #56 #123)
+#125 := [rewrite]: #124
+#153 := (= #63 #150)
+#147 := (* #144 3::Real)
+#151 := (= #147 #150)
+#152 := [rewrite]: #151
+#148 := (= #63 #147)
+#145 := (= #62 #144)
+#130 := (= #59 #129)
+#131 := [rewrite]: #130
+#142 := (= #61 #139)
+#135 := (- #129)
+#140 := (= #135 #139)
+#141 := [rewrite]: #140
+#136 := (= #61 #135)
+#137 := [monotonicity #131]: #136
+#143 := [trans #137 #141]: #142
+#133 := (iff #60 #132)
+#134 := [monotonicity #131]: #133
+#146 := [monotonicity #134 #143 #131]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#157 := [monotonicity #154 #125]: #156
+#163 := [monotonicity #157 #160]: #162
+#169 := [trans #163 #167]: #168
+#127 := (iff #57 #126)
+#120 := (= #53 #117)
+#114 := (* #111 3::Real)
+#118 := (= #114 #117)
+#119 := [rewrite]: #118
+#115 := (= #53 #114)
+#112 := (= #51 #111)
+#97 := (= #47 #96)
+#98 := [rewrite]: #97
+#109 := (= #50 #106)
+#102 := (- #96)
+#107 := (= #102 #106)
+#108 := [rewrite]: #107
+#103 := (= #50 #102)
+#104 := [monotonicity #98]: #103
+#110 := [trans #104 #108]: #109
+#100 := (iff #49 #99)
+#101 := [monotonicity #98]: #100
+#113 := [monotonicity #101 #110 #98]: #112
+#116 := [monotonicity #113]: #115
+#121 := [trans #116 #119]: #120
+#128 := [monotonicity #121 #125]: #127
+#172 := [monotonicity #128 #169]: #171
+#178 := [trans #172 #176]: #177
+#181 := [monotonicity #178]: #180
+#273 := [trans #181 #271]: #272
+#93 := [asserted]: #69
+#274 := [mp #93 #273]: #269
+#275 := [not-or-elim #274]: #183
+#277 := [not-or-elim #274]: #246
+#369 := (+ #96 #368)
+#370 := (<= #369 0::Real)
+#362 := (= #96 #231)
+#364 := (or #225 #362)
 #365 := [def-axiom]: #364
-#394 := [unit-resolution #365 #393]: #361
-#395 := (not #361)
-#396 := (or #395 #373)
-#397 := [th-lemma arith triangle-eq]: #396
-#398 := [unit-resolution #397 #394]: #373
-#399 := (not #373)
-#400 := (or #187 #399 #243 #184 #222)
-#401 := [th-lemma arith assign-bounds 3 1 1 2]: #400
-#402 := [unit-resolution #401 #273 #393 #275 #398]: #187
-#403 := [unit-resolution #357 #402]: #354
-#404 := [unit-resolution #379 #403]: #372
-[th-lemma arith farkas 2 2/3 1 1 1/3 1 #398 #275 #273 #393 #274 #404]: false
+#388 := [unit-resolution #365 #376]: #362
+#389 := (not #362)
+#390 := (or #389 #370)
+#391 := [th-lemma arith triangle-eq]: #390
+#392 := [unit-resolution #391 #388]: #370
+#384 := (or #190 #225)
+#377 := [hypothesis]: #189
+#276 := [not-or-elim #274]: #212
+#358 := (or #190 #356)
+#359 := [def-axiom]: #358
+#378 := [unit-resolution #359 #377]: #356
+#379 := (not #356)
+#380 := (or #379 #374)
+#381 := [th-lemma arith triangle-eq]: #380
+#382 := [unit-resolution #381 #378]: #374
+#383 := [th-lemma arith farkas -1 -3 1 -2 1 #275 #382 #276 #377 #376]: false
+#385 := [lemma #383]: #384
+#393 := [unit-resolution #385 #376]: #190
+#394 := [th-lemma arith farkas 1/4 -3/4 1/4 -1/4 1 #393 #392 #277 #275 #376]: false
+#395 := [lemma #394]: #225
+#366 := (or #224 #363)
+#367 := [def-axiom]: #366
+#396 := [unit-resolution #367 #395]: #363
+#397 := (not #363)
+#398 := (or #397 #375)
+#399 := [th-lemma arith triangle-eq]: #398
+#400 := [unit-resolution #399 #396]: #375
+#401 := (not #375)
+#402 := (or #189 #401 #245 #186 #224)
+#403 := [th-lemma arith assign-bounds 3 1 1 2]: #402
+#404 := [unit-resolution #403 #275 #395 #277 #400]: #189
+#405 := [unit-resolution #359 #404]: #356
+#406 := [unit-resolution #381 #405]: #374
+[th-lemma arith farkas 2 2/3 1 1 1/3 1 #400 #277 #275 #395 #276 #406]: false
 unsat
 a66e77fbacece8ec9b71617769b478381e4da6e9 349 0
 #2 := false

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Fri Dec 17 14:36:33 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Fri Dec 17 14:59:06 2010 +0100
@@ -12981,199 +12981,198 @@
 #104 := [not-or-elim #101]: #103
 [unit-resolution #104 #576]: false
 unsat
-60ddd77de436db09ff8cc70aa2e0eff7e14b8798 193 0
[phone]f04e63dea2f01d8f4ea201edb55fb97e 192 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
+decl f5 :: S3
+#26 := f5
+decl f8 :: S2
+#34 := f8
+#40 := (f3 f8 f5)
+decl f4 :: (-> S2 S3 S4 S2)
+decl f10 :: S4
+#37 := f10
+decl f7 :: S3
+#30 := f7
+decl f9 :: S4
+#35 := f9
 decl f6 :: S3
 #27 := f6
-decl f9 :: S2
-#35 := f9
-#41 := (f3 f9 f6)
-decl f4 :: (-> S5 S2 S3 S4 S2)
-decl f11 :: S4
-#38 := f11
-decl f8 :: S3
-#31 := f8
-decl f10 :: S4
-#36 := f10
-decl f7 :: S3
-#28 := f7
-decl f5 :: S5
-#8 := f5
-#37 := (f4 f5 f9 f7 f10)
-#39 := (f4 f5 #37 f8 f11)
-#40 := (f3 #39 f6)
-#42 := (= #40 #41)
-#243 := (f3 #37 f7)
-#234 := (f4 f5 f9 f7 #243)
-#572 := (f3 #234 f6)
-#575 := (= #572 #41)
-#580 := (= #41 #572)
-#576 := (= #243 #572)
-#29 := (= f6 f7)
-#581 := (ite #29 #576 #580)
-#13 := (:var 0 S3)
-#11 := (:var 1 S4)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#595 := (pattern #14)
-#16 := (f3 #9 #13)
-#120 := (= #14 #16)
-#119 := (= #11 #14)
-#65 := (= #10 #13)
-#105 := (ite #65 #119 #120)
-#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105)
-#112 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105)
-#599 := (iff #112 #596)
-#597 := (iff #105 #105)
-#598 := [refl]: #597
-#600 := [quant-intro #598]: #599
-#68 := (ite #65 #11 #16)
-#71 := (= #14 #68)
-#74 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #71)
-#109 := (iff #74 #112)
-#106 := (iff #71 #105)
-#111 := [rewrite]: #106
-#110 := [quant-intro #111]: #109
-#115 := (~ #74 #74)
-#113 := (~ #71 #71)
-#114 := [refl]: #113
-#116 := [nnf-pos #114]: #115
-#15 := (= #13 #10)
-#17 := (ite #15 #11 #16)
-#18 := (= #14 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18)
-#75 := (iff #19 #74)
-#72 := (iff #18 #71)
-#69 := (= #17 #68)
-#66 := (iff #15 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#76 := [quant-intro #73]: #75
-#64 := [asserted]: #19
-#79 := [mp #64 #76]: #74
-#101 := [mp~ #79 #116]: #74
-#107 := [mp #101 #110]: #112
-#601 := [mp #107 #600]: #596
-#270 := (not #596)
-#568 := (or #270 #581)
-#571 := (= f7 f6)
-#577 := (ite #571 #576 #575)
-#569 := (or #270 #577)
-#291 := (iff #569 #568)
-#293 := (iff #568 #568)
-#279 := [rewrite]: #293
-#579 := (iff #577 #581)
-#218 := (iff #575 #580)
-#219 := [rewrite]: #218
-#213 := (iff #571 #29)
-#578 := [rewrite]: #213
-#582 := [monotonicity #578 #219]: #579
-#292 := [monotonicity #582]: #291
-#294 := [trans #292 #279]: #291
-#275 := [quant-inst #35 #28 #243 #27]: #569
-#185 := [mp #275 #294]: #568
-#530 := [unit-resolution #185 #601]: #581
-#564 := (not #581)
-#517 := (or #564 #580)
-#30 := (not #29)
-#32 := (= f6 f8)
-#33 := (not #32)
-#34 := (and #30 #33)
-#86 := (not #34)
-#88 := (or #86 #42)
-#91 := (not #88)
-#43 := (implies #34 #42)
-#44 := (not #43)
-#92 := (iff #44 #91)
-#89 := (iff #43 #88)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#85 := [asserted]: #44
-#96 := [mp #85 #93]: #91
-#94 := [not-or-elim #96]: #34
-#95 := [and-elim #94]: #30
-#288 := (or #564 #29 #580)
-#562 := [def-axiom]: #288
-#519 := [unit-resolution #562 #95]: #517
-#511 := [unit-resolution #519 #530]: #580
-#513 := [symm #511]: #575
-#514 := (= #40 #572)
-#177 := (f3 #37 f6)
-#523 := (= #177 #572)
-#522 := (= #572 #177)
-#529 := (= #234 #37)
-#435 := (= #243 f10)
-#586 := (= f10 #243)
-#22 := (:var 0 S4)
-#21 := (:var 1 S3)
-#20 := (:var 2 S2)
-#23 := (f4 f5 #20 #21 #22)
-#602 := (pattern #23)
-#24 := (f3 #23 #21)
-#78 := (= #22 #24)
-#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #602) #78)
-#82 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #78)
-#606 := (iff #82 #603)
-#604 := (iff #78 #78)
-#605 := [refl]: #604
-#607 := [quant-intro #605]: #606
-#103 := (~ #82 #82)
-#102 := (~ #78 #78)
-#117 := [refl]: #102
-#104 := [nnf-pos #117]: #103
-#25 := (= #24 #22)
-#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25)
-#83 := (iff #26 #82)
-#80 := (iff #25 #78)
-#81 := [rewrite]: #80
-#84 := [quant-intro #81]: #83
-#77 := [asserted]: #26
-#87 := [mp #77 #84]: #82
-#118 := [mp~ #87 #104]: #82
-#608 := [mp #118 #607]: #603
-#231 := (not #603)
-#232 := (or #231 #586)
-#233 := [quant-inst #35 #28 #36]: #232
-#434 := [unit-resolution #233 #608]: #586
-#436 := [symm #434]: #435
-#526 := [monotonicity #436]: #529
-#518 := [monotonicity #526]: #522
-#512 := [symm #518]: #523
-#264 := (= #40 #177)
-#178 := (= f11 #40)
-#268 := (ite #32 #178 #264)
-#267 := (or #270 #268)
-#265 := (= f8 f6)
-#179 := (ite #265 #178 #264)
-#271 := (or #270 #179)
-#587 := (iff #271 #267)
-#244 := (iff #267 #267)
-#376 := [rewrite]: #244
-#269 := (iff #179 #268)
-#266 := (iff #265 #32)
-#257 := [rewrite]: #266
-#197 := [monotonicity #257]: #269
-#589 := [monotonicity #197]: #587
-#583 := [trans #589 #376]: #587
-#250 := [quant-inst #37 #31 #38 #27]: #271
-#255 := [mp #250 #583]: #267
-#508 := [unit-resolution #255 #601]: #268
-#256 := (not #268)
-#510 := (or #256 #264)
-#97 := [and-elim #94]: #33
-#592 := (or #256 #32 #264)
-#593 := [def-axiom]: #592
-#520 := [unit-resolution #593 #97]: #510
-#521 := [unit-resolution #520 #508]: #264
-#515 := [trans #521 #512]: #514
-#509 := [trans #515 #513]: #42
-#98 := (not #42)
-#99 := [not-or-elim #96]: #98
-[unit-resolution #99 #509]: false
+#36 := (f4 f8 f6 f9)
+#38 := (f4 #36 f7 f10)
+#39 := (f3 #38 f5)
+#41 := (= #39 #40)
+#242 := (f3 #36 f6)
+#233 := (f4 f8 f6 #242)
+#571 := (f3 #233 f5)
+#574 := (= #571 #40)
+#579 := (= #40 #571)
+#575 := (= #242 #571)
+#28 := (= f5 f6)
+#580 := (ite #28 #575 #579)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#594 := (pattern #13)
+#15 := (f3 #8 #12)
+#119 := (= #13 #15)
+#118 := (= #10 #13)
+#64 := (= #9 #12)
+#104 := (ite #64 #118 #119)
+#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#111 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
+#598 := (iff #111 #595)
+#596 := (iff #104 #104)
+#597 := [refl]: #596
+#599 := [quant-intro #597]: #598
+#67 := (ite #64 #10 #15)
+#70 := (= #13 #67)
+#73 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #70)
+#108 := (iff #73 #111)
+#105 := (iff #70 #104)
+#110 := [rewrite]: #105
+#109 := [quant-intro #110]: #108
+#114 := (~ #73 #73)
+#112 := (~ #70 #70)
+#113 := [refl]: #112
+#115 := [nnf-pos #113]: #114
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#74 := (iff #18 #73)
+#71 := (iff #17 #70)
+#68 := (= #16 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#75 := [quant-intro #72]: #74
+#63 := [asserted]: #18
+#78 := [mp #63 #75]: #73
+#100 := [mp~ #78 #115]: #73
+#106 := [mp #100 #109]: #111
+#600 := [mp #106 #599]: #595
+#269 := (not #595)
+#567 := (or #269 #580)
+#570 := (= f6 f5)
+#576 := (ite #570 #575 #574)
+#568 := (or #269 #576)
+#290 := (iff #568 #567)
+#292 := (iff #567 #567)
+#278 := [rewrite]: #292
+#578 := (iff #576 #580)
+#217 := (iff #574 #579)
+#218 := [rewrite]: #217
+#212 := (iff #570 #28)
+#577 := [rewrite]: #212
+#581 := [monotonicity #577 #218]: #578
+#291 := [monotonicity #581]: #290
+#293 := [trans #291 #278]: #290
+#274 := [quant-inst #34 #27 #242 #26]: #568
+#184 := [mp #274 #293]: #567
+#529 := [unit-resolution #184 #600]: #580
+#563 := (not #580)
+#516 := (or #563 #579)
+#29 := (not #28)
+#31 := (= f5 f7)
+#32 := (not #31)
+#33 := (and #29 #32)
+#85 := (not #33)
+#87 := (or #85 #41)
+#90 := (not #87)
+#42 := (implies #33 #41)
+#43 := (not #42)
+#91 := (iff #43 #90)
+#88 := (iff #42 #87)
+#89 := [rewrite]: #88
+#92 := [monotonicity #89]: #91
+#84 := [asserted]: #43
+#95 := [mp #84 #92]: #90
+#93 := [not-or-elim #95]: #33
+#94 := [and-elim #93]: #29
+#287 := (or #563 #28 #579)
+#561 := [def-axiom]: #287
+#518 := [unit-resolution #561 #94]: #516
+#510 := [unit-resolution #518 #529]: #579
+#512 := [symm #510]: #574
+#513 := (= #39 #571)
+#176 := (f3 #36 f5)
+#522 := (= #176 #571)
+#521 := (= #571 #176)
+#528 := (= #233 #36)
+#434 := (= #242 f9)
+#585 := (= f9 #242)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#601 := (pattern #22)
+#23 := (f3 #22 #20)
+#77 := (= #21 #23)
+#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #77)
+#81 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #77)
+#602 := (iff #81 #603)
+#605 := (iff #603 #603)
+#606 := [rewrite]: #605
+#604 := [rewrite]: #602
+#607 := [trans #604 #606]: #602
+#102 := (~ #81 #81)
+#101 := (~ #77 #77)
+#116 := [refl]: #101
+#103 := [nnf-pos #116]: #102
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#82 := (iff #25 #81)
+#79 := (iff #24 #77)
+#80 := [rewrite]: #79
+#83 := [quant-intro #80]: #82
+#76 := [asserted]: #25
+#86 := [mp #76 #83]: #81
+#117 := [mp~ #86 #103]: #81
+#608 := [mp #117 #607]: #603
+#230 := (not #603)
+#231 := (or #230 #585)
+#232 := [quant-inst #34 #27 #35]: #231
+#433 := [unit-resolution #232 #608]: #585
+#435 := [symm #433]: #434
+#525 := [monotonicity #435]: #528
+#517 := [monotonicity #525]: #521
+#511 := [symm #517]: #522
+#263 := (= #39 #176)
+#177 := (= f10 #39)
+#267 := (ite #31 #177 #263)
+#266 := (or #269 #267)
+#264 := (= f7 f5)
+#178 := (ite #264 #177 #263)
+#270 := (or #269 #178)
+#586 := (iff #270 #266)
+#243 := (iff #266 #266)
+#375 := [rewrite]: #243
+#268 := (iff #178 #267)
+#265 := (iff #264 #31)
+#256 := [rewrite]: #265
+#196 := [monotonicity #256]: #268
+#588 := [monotonicity #196]: #586
+#582 := [trans #588 #375]: #586
+#249 := [quant-inst #36 #30 #37 #26]: #270
+#254 := [mp #249 #582]: #266
+#507 := [unit-resolution #254 #600]: #267
+#255 := (not #267)
+#509 := (or #255 #263)
+#96 := [and-elim #93]: #32
+#591 := (or #255 #31 #263)
+#592 := [def-axiom]: #591
+#519 := [unit-resolution #592 #96]: #509
+#520 := [unit-resolution #519 #507]: #263
+#514 := [trans #520 #511]: #513
+#508 := [trans #514 #512]: #41
+#97 := (not #41)
+#98 := [not-or-elim #95]: #97
+[unit-resolution #98 #508]: false
 unsat
 10c4eb4ff6b9f0c880cfc3af0cd433a1ff110114 96 0
 #2 := false
@@ -14299,82 +14298,82 @@
 unsat
 8f8fbc61d0925864fffd8945e68a0401b7416686 1 0
 unsat
-4bafa9f250d1b4853cae936d5a014474439d5625 76 0
-#2 := false
-decl f3 :: (-> Int S1)
-#129 := 1::Int
-#130 := (f3 1::Int)
+a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0
+#2 := false
+decl f28 :: (-> Int S1)
+#107 := 1::Int
+#108 := (f28 1::Int)
 decl f1 :: S1
 #4 := f1
-#460 := (= f1 #130)
-#464 := (not #460)
-#131 := (= #130 f1)
-#132 := (not #131)
-#465 := (iff #132 #464)
-#462 := (iff #131 #460)
-#463 := [rewrite]: #462
-#466 := [monotonicity #463]: #465
-#459 := [asserted]: #132
-#469 := [mp #459 #466]: #464
-#8 := (:var 0 Int)
-#9 := (f3 #8)
-#997 := (pattern #9)
-#153 := (= f1 #9)
-#998 := (forall (vars (?v0 Int)) (:pat #997) #153)
-#176 := (forall (vars (?v0 Int)) #153)
-#1001 := (iff #176 #998)
-#999 := (iff #153 #153)
-#1000 := [refl]: #999
-#1002 := [quant-intro #1000]: #1001
-#497 := (~ #176 #176)
-#495 := (~ #153 #153)
-#496 := [refl]: #495
-#498 := [nnf-pos #496]: #497
-decl f4 :: (-> S2 S1)
-decl f5 :: (-> Int S2 S2)
-decl f6 :: S2
-#11 := f6
-#12 := (f5 #8 f6)
-#13 := (f4 #12)
-#14 := (= #13 f1)
-#15 := (not #14)
-#16 := (or #14 #15)
-#10 := (= #9 f1)
-#17 := (and #10 #16)
-#18 := (forall (vars (?v0 Int)) #17)
-#177 := (iff #18 #176)
-#174 := (iff #17 #153)
+#382 := (= f1 #108)
+#386 := (not #382)
+#109 := (= #108 f1)
+#110 := (not #109)
+#387 := (iff #110 #386)
+#384 := (iff #109 #382)
+#385 := [rewrite]: #384
+#388 := [monotonicity #385]: #387
+#381 := [asserted]: #110
+#391 := [mp #381 #388]: #386
+#96 := (:var 0 Int)
+#97 := (f28 #96)
+#965 := (pattern #97)
+#354 := (= f1 #97)
+#966 := (forall (vars (?v0 Int)) (:pat #965) #354)
+#378 := (forall (vars (?v0 Int)) #354)
+#969 := (iff #378 #966)
+#967 := (iff #354 #354)
+#968 := [refl]: #967
+#970 := [quant-intro #968]: #969
+#407 := (~ #378 #378)
+#437 := (~ #354 #354)
+#438 := [refl]: #437
+#408 := [nnf-pos #438]: #407
+decl f3 :: (-> S2 S1)
+decl f29 :: (-> Int S2 S2)
+decl f30 :: S2
+#99 := f30
+#100 := (f29 #96 f30)
+#101 := (f3 #100)
+#102 := (= #101 f1)
+#103 := (not #102)
+#104 := (or #102 #103)
+#98 := (= #97 f1)
+#105 := (and #98 #104)
+#106 := (forall (vars (?v0 Int)) #105)
+#379 := (iff #106 #378)
+#376 := (iff #105 #354)
 #1 := true
-#169 := (and #153 true)
-#172 := (iff #169 #153)
-#173 := [rewrite]: #172
-#170 := (iff #17 #169)
-#167 := (iff #16 true)
-#156 := (= f1 #13)
-#159 := (not #156)
-#162 := (or #156 #159)
-#165 := (iff #162 true)
-#166 := [rewrite]: #165
-#163 := (iff #16 #162)
-#160 := (iff #15 #159)
-#157 := (iff #14 #156)
-#158 := [rewrite]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #158 #161]: #163
-#168 := [trans #164 #166]: #167
-#154 := (iff #10 #153)
-#155 := [rewrite]: #154
-#171 := [monotonicity #155 #168]: #170
-#175 := [trans #171 #173]: #174
-#178 := [quant-intro #175]: #177
-#152 := [asserted]: #18
-#181 := [mp #152 #178]: #176
-#468 := [mp~ #181 #498]: #176
-#1003 := [mp #468 #1002]: #998
-#582 := (not #998)
-#667 := (or #582 #460)
-#668 := [quant-inst #129]: #667
-[unit-resolution #668 #1003 #469]: false
+#371 := (and #354 true)
+#374 := (iff #371 #354)
+#375 := [rewrite]: #374
+#372 := (iff #105 #371)
+#369 := (iff #104 true)
+#358 := (= f1 #101)
+#361 := (not #358)
+#364 := (or #358 #361)
+#367 := (iff #364 true)
+#368 := [rewrite]: #367
+#365 := (iff #104 #364)
+#362 := (iff #103 #361)
+#359 := (iff #102 #358)
+#360 := [rewrite]: #359
+#363 := [monotonicity #360]: #362
+#366 := [monotonicity #360 #363]: #365
+#370 := [trans #366 #368]: #369
+#356 := (iff #98 #354)
+#357 := [rewrite]: #356
+#373 := [monotonicity #357 #370]: #372
+#377 := [trans #373 #375]: #376
+#380 := [quant-intro #377]: #379
+#353 := [asserted]: #106
+#383 := [mp #353 #380]: #378
+#439 := [mp~ #383 #408]: #378
+#971 := [mp #439 #970]: #966
+#494 := (not #966)
+#579 := (or #494 #382)
+#580 := [quant-inst #107]: #579
+[unit-resolution #580 #971 #391]: false
 unsat
 e4dd068db00f152c179631d20d9af452dbe0f45d 439 0
 #2 := false
@@ -14816,80 +14815,3 @@
 #287 := [mp #270 #284]: #282
 [unit-resolution #287 #630]: false
 unsat
-a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0
-#2 := false
-decl f28 :: (-> Int S1)
-#107 := 1::Int
-#108 := (f28 1::Int)
-decl f1 :: S1
-#4 := f1
-#382 := (= f1 #108)
-#386 := (not #382)
-#109 := (= #108 f1)
-#110 := (not #109)
-#387 := (iff #110 #386)
-#384 := (iff #109 #382)
-#385 := [rewrite]: #384
-#388 := [monotonicity #385]: #387
-#381 := [asserted]: #110
-#391 := [mp #381 #388]: #386
-#96 := (:var 0 Int)
-#97 := (f28 #96)
-#965 := (pattern #97)
-#354 := (= f1 #97)
-#966 := (forall (vars (?v0 Int)) (:pat #965) #354)
-#378 := (forall (vars (?v0 Int)) #354)
-#969 := (iff #378 #966)
-#967 := (iff #354 #354)
-#968 := [refl]: #967
-#970 := [quant-intro #968]: #969
-#407 := (~ #378 #378)
-#437 := (~ #354 #354)
-#438 := [refl]: #437
-#408 := [nnf-pos #438]: #407
-decl f3 :: (-> S2 S1)
-decl f29 :: (-> Int S2 S2)
-decl f30 :: S2
-#99 := f30
-#100 := (f29 #96 f30)
-#101 := (f3 #100)
-#102 := (= #101 f1)
-#103 := (not #102)
-#104 := (or #102 #103)
-#98 := (= #97 f1)
-#105 := (and #98 #104)
-#106 := (forall (vars (?v0 Int)) #105)
-#379 := (iff #106 #378)
-#376 := (iff #105 #354)
-#1 := true
-#371 := (and #354 true)
-#374 := (iff #371 #354)
-#375 := [rewrite]: #374
-#372 := (iff #105 #371)
-#369 := (iff #104 true)
-#358 := (= f1 #101)
-#361 := (not #358)
-#364 := (or #358 #361)
-#367 := (iff #364 true)
-#368 := [rewrite]: #367
-#365 := (iff #104 #364)
-#362 := (iff #103 #361)
-#359 := (iff #102 #358)
-#360 := [rewrite]: #359
-#363 := [monotonicity #360]: #362
-#366 := [monotonicity #360 #363]: #365
-#370 := [trans #366 #368]: #369
-#356 := (iff #98 #354)
-#357 := [rewrite]: #356
-#373 := [monotonicity #357 #370]: #372
-#377 := [trans #373 #375]: #376
-#380 := [quant-intro #377]: #379
-#353 := [asserted]: #106
-#383 := [mp #353 #380]: #378
-#439 := [mp~ #383 #408]: #378
-#971 := [mp #439 #970]: #966
-#494 := (not #966)
-#579 := (or #494 #382)
-#580 := [quant-inst #107]: #579
-[unit-resolution #580 #971 #391]: false
-unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Fri Dec 17 14:36:33 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Fri Dec 17 14:59:06 2010 +0100
@@ -51097,597 +51097,591 @@
 #244 := [quant-inst #28 #24 #29 #25]: #253
 [unit-resolution #244 #588 #165]: false
 unsat
-3a3e28b9a1ce272e3a845bbcea7eeac5abc8f586 159 0
+57b1778e367cf6f6921505d440f3fc4fb8332587 158 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
+decl f5 :: S3
+#26 := f5
+decl f4 :: (-> S2 S3 S4 S2)
+decl f9 :: S4
+#33 := f9
 decl f6 :: S3
 #27 := f6
-decl f4 :: (-> S5 S2 S3 S4 S2)
-decl f10 :: S4
-#34 := f10
-decl f7 :: S3
-#28 := f7
-decl f9 :: S4
-#32 := f9
-decl f8 :: S2
+decl f8 :: S4
 #31 := f8
-decl f5 :: S5
-#8 := f5
-#33 := (f4 f5 f8 f6 f9)
-#35 := (f4 f5 #33 f7 f10)
-#36 := (f3 #35 f6)
-#81 := (= f9 #36)
-#177 := (f3 #33 f6)
-#264 := (= #36 #177)
-#581 := (iff #264 #81)
-#218 := (iff #81 #264)
-#571 := (= #177 #36)
-#578 := (iff #571 #264)
-#580 := [commutativity]: #578
-#577 := (iff #81 #571)
-#243 := (= f9 #177)
-#22 := (:var 0 S4)
-#21 := (:var 1 S3)
-#20 := (:var 2 S2)
-#23 := (f4 f5 #20 #21 #22)
-#602 := (pattern #23)
-#24 := (f3 #23 #21)
-#73 := (= #22 #24)
-#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #602) #73)
-#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #73)
-#606 := (iff #77 #603)
-#604 := (iff #73 #73)
-#605 := [refl]: #604
-#607 := [quant-intro #605]: #606
-#103 := (~ #77 #77)
-#102 := (~ #73 #73)
-#115 := [refl]: #102
-#104 := [nnf-pos #115]: #103
-#25 := (= #24 #22)
-#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25)
-#78 := (iff #26 #77)
-#75 := (iff #25 #73)
-#76 := [rewrite]: #75
-#79 := [quant-intro #76]: #78
-#72 := [asserted]: #26
-#82 := [mp #72 #79]: #77
-#116 := [mp~ #82 #104]: #77
-#608 := [mp #116 #607]: #603
-#570 := (not #603)
-#231 := (or #570 #243)
-#232 := [quant-inst #31 #27 #32]: #231
-#576 := [unit-resolution #232 #608]: #243
-#213 := [monotonicity #576]: #577
-#219 := [trans #213 #580]: #218
-#579 := [symm #219]: #581
-#178 := (= f10 #36)
-#29 := (= f6 f7)
-#268 := (ite #29 #178 #264)
-#13 := (:var 0 S3)
-#11 := (:var 1 S4)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#595 := (pattern #14)
-#16 := (f3 #9 #13)
-#118 := (= #14 #16)
-#117 := (= #11 #14)
-#60 := (= #10 #13)
-#105 := (ite #60 #117 #118)
-#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105)
-#599 := (iff #110 #596)
-#597 := (iff #105 #105)
-#598 := [refl]: #597
-#600 := [quant-intro #598]: #599
-#63 := (ite #60 #11 #16)
-#66 := (= #14 #63)
-#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66)
-#107 := (iff #69 #110)
-#106 := (iff #66 #105)
-#109 := [rewrite]: #106
-#108 := [quant-intro #109]: #107
-#113 := (~ #69 #69)
-#111 := (~ #66 #66)
-#112 := [refl]: #111
-#114 := [nnf-pos #112]: #113
-#15 := (= #13 #10)
-#17 := (ite #15 #11 #16)
-#18 := (= #14 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18)
-#70 := (iff #19 #69)
-#67 := (iff #18 #66)
-#64 := (= #17 #63)
-#61 := (iff #15 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#71 := [quant-intro #68]: #70
-#59 := [asserted]: #19
-#74 := [mp #59 #71]: #69
-#101 := [mp~ #74 #114]: #69
-#119 := [mp #101 #108]: #110
-#601 := [mp #119 #600]: #596
-#270 := (not #596)
-#267 := (or #270 #268)
-#265 := (= f7 f6)
-#179 := (ite #265 #178 #264)
-#271 := (or #270 #179)
-#587 := (iff #271 #267)
-#244 := (iff #267 #267)
-#376 := [rewrite]: #244
-#269 := (iff #179 #268)
-#266 := (iff #265 #29)
-#257 := [rewrite]: #266
-#197 := [monotonicity #257]: #269
-#589 := [monotonicity #197]: #587
-#583 := [trans #589 #376]: #587
-#250 := [quant-inst #33 #28 #34 #27]: #271
-#255 := [mp #250 #583]: #267
-#233 := [unit-resolution #255 #601]: #268
-#256 := (not #268)
-#234 := (or #256 #264)
-#30 := (not #29)
-#88 := (or #29 #81)
-#93 := (not #88)
-#37 := (= #36 f9)
-#38 := (implies #30 #37)
-#39 := (not #38)
-#94 := (iff #39 #93)
-#91 := (iff #38 #88)
-#85 := (implies #30 #81)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #38 #85)
-#83 := (iff #37 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#92 := [trans #87 #90]: #91
-#95 := [monotonicity #92]: #94
-#80 := [asserted]: #39
-#98 := [mp #80 #95]: #93
-#96 := [not-or-elim #98]: #30
-#592 := (or #256 #29 #264)
-#593 := [def-axiom]: #592
-#574 := [unit-resolution #593 #96]: #234
-#575 := [unit-resolution #574 #233]: #264
-#582 := [mp #575 #579]: #81
-#97 := (not #81)
-#99 := [not-or-elim #98]: #97
-[unit-resolution #99 #582]: false
-unsat
-9624532c2fce6f30c8a21e62aa8e557532aee6d5 113 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f7 :: S3
-#28 := f7
-decl f4 :: (-> S5 S2 S3 S4 S2)
-decl f10 :: S4
-#34 := f10
-decl f9 :: S4
-#32 := f9
-decl f6 :: S3
-#27 := f6
-decl f8 :: S2
-#31 := f8
-decl f5 :: S5
-#8 := f5
-#33 := (f4 f5 f8 f6 f9)
-#35 := (f4 f5 #33 f7 f10)
-#36 := (f3 #35 f7)
-#81 := (= f10 #36)
-#97 := (not #81)
-#29 := (= f6 f7)
-#88 := (or #29 #81)
-#93 := (not #88)
-#37 := (= #36 f10)
-#30 := (not #29)
-#38 := (implies #30 #37)
-#39 := (not #38)
-#94 := (iff #39 #93)
-#91 := (iff #38 #88)
-#85 := (implies #30 #81)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #38 #85)
-#83 := (iff #37 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#92 := [trans #87 #90]: #91
-#95 := [monotonicity #92]: #94
-#80 := [asserted]: #39
-#98 := [mp #80 #95]: #93
-#99 := [not-or-elim #98]: #97
-#13 := (:var 0 S3)
-#11 := (:var 1 S4)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#595 := (pattern #14)
-#16 := (f3 #9 #13)
-#118 := (= #14 #16)
-#117 := (= #11 #14)
-#60 := (= #10 #13)
-#105 := (ite #60 #117 #118)
-#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105)
-#599 := (iff #110 #596)
-#597 := (iff #105 #105)
-#598 := [refl]: #597
-#600 := [quant-intro #598]: #599
-#63 := (ite #60 #11 #16)
-#66 := (= #14 #63)
-#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66)
-#107 := (iff #69 #110)
-#106 := (iff #66 #105)
-#109 := [rewrite]: #106
-#108 := [quant-intro #109]: #107
-#113 := (~ #69 #69)
-#111 := (~ #66 #66)
-#112 := [refl]: #111
-#114 := [nnf-pos #112]: #113
-#15 := (= #13 #10)
-#17 := (ite #15 #11 #16)
-#18 := (= #14 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18)
-#70 := (iff #19 #69)
-#67 := (iff #18 #66)
-#64 := (= #17 #63)
-#61 := (iff #15 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#71 := [quant-intro #68]: #70
-#59 := [asserted]: #19
-#74 := [mp #59 #71]: #69
-#101 := [mp~ #74 #114]: #69
-#119 := [mp #101 #108]: #110
-#601 := [mp #119 #600]: #596
-#250 := (not #596)
-#587 := (or #250 #81)
-#177 := (f3 #33 f7)
-#264 := (= #36 #177)
-#178 := (= f7 f7)
-#265 := (ite #178 #81 #264)
-#589 := (or #250 #265)
-#376 := (iff #589 #587)
-#255 := (iff #587 #587)
-#256 := [rewrite]: #255
-#267 := (iff #265 #81)
-#1 := true
-#257 := (ite true #81 #264)
-#197 := (iff #257 #81)
-#270 := [rewrite]: #197
-#268 := (iff #265 #257)
-#179 := (iff #178 true)
-#266 := [rewrite]: #179
-#269 := [monotonicity #266]: #268
-#271 := [trans #269 #270]: #267
-#583 := [monotonicity #271]: #376
-#590 := [trans #583 #256]: #376
-#244 := [quant-inst #33 #28 #34 #28]: #589
-#591 := [mp #244 #590]: #587
-[unit-resolution #591 #601 #99]: false
-unsat
-c87329d6ba7c190d060550d5a4c2a90769f50212 125 0
+decl f7 :: S2
+#30 := f7
+#32 := (f4 f7 f5 f8)
+#34 := (f4 #32 f6 f9)
+#35 := (f3 #34 f5)
+#80 := (= f8 #35)
+#176 := (f3 #32 f5)
+#263 := (= #35 #176)
+#580 := (iff #263 #80)
+#217 := (iff #80 #263)
+#570 := (= #176 #35)
+#577 := (iff #570 #263)
+#579 := [commutativity]: #577
+#576 := (iff #80 #570)
+#242 := (= f8 #176)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#601 := (pattern #22)
+#23 := (f3 #22 #20)
+#72 := (= #21 #23)
+#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #72)
+#76 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #72)
+#602 := (iff #76 #603)
+#605 := (iff #603 #603)
+#606 := [rewrite]: #605
+#604 := [rewrite]: #602
+#607 := [trans #604 #606]: #602
+#102 := (~ #76 #76)
+#101 := (~ #72 #72)
+#114 := [refl]: #101
+#103 := [nnf-pos #114]: #102
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#77 := (iff #25 #76)
+#74 := (iff #24 #72)
+#75 := [rewrite]: #74
+#78 := [quant-intro #75]: #77
+#71 := [asserted]: #25
+#81 := [mp #71 #78]: #76
+#115 := [mp~ #81 #103]: #76
+#608 := [mp #115 #607]: #603
+#569 := (not #603)
+#230 := (or #569 #242)
+#231 := [quant-inst #30 #26 #31]: #230
+#575 := [unit-resolution #231 #608]: #242
+#212 := [monotonicity #575]: #576
+#218 := [trans #212 #579]: #217
+#578 := [symm #218]: #580
+#177 := (= f9 #35)
+#28 := (= f5 f6)
+#267 := (ite #28 #177 #263)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#594 := (pattern #13)
+#15 := (f3 #8 #12)
+#117 := (= #13 #15)
+#116 := (= #10 #13)
+#59 := (= #9 #12)
+#104 := (ite #59 #116 #117)
+#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
+#598 := (iff #109 #595)
+#596 := (iff #104 #104)
+#597 := [refl]: #596
+#599 := [quant-intro #597]: #598
+#62 := (ite #59 #10 #15)
+#65 := (= #13 #62)
+#68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65)
+#106 := (iff #68 #109)
+#105 := (iff #65 #104)
+#108 := [rewrite]: #105
+#107 := [quant-intro #108]: #106
+#112 := (~ #68 #68)
+#110 := (~ #65 #65)
+#111 := [refl]: #110
+#113 := [nnf-pos #111]: #112
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#69 := (iff #18 #68)
+#66 := (iff #17 #65)
+#63 := (= #16 #62)
+#60 := (iff #14 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#70 := [quant-intro #67]: #69
+#58 := [asserted]: #18
+#73 := [mp #58 #70]: #68
+#100 := [mp~ #73 #113]: #68
+#118 := [mp #100 #107]: #109
+#600 := [mp #118 #599]: #595
+#269 := (not #595)
+#266 := (or #269 #267)
+#264 := (= f6 f5)
+#178 := (ite #264 #177 #263)
+#270 := (or #269 #178)
+#586 := (iff #270 #266)
+#243 := (iff #266 #266)
+#375 := [rewrite]: #243
+#268 := (iff #178 #267)
+#265 := (iff #264 #28)
+#256 := [rewrite]: #265
+#196 := [monotonicity #256]: #268
+#588 := [monotonicity #196]: #586
+#582 := [trans #588 #375]: #586
+#249 := [quant-inst #32 #27 #33 #26]: #270
+#254 := [mp #249 #582]: #266
+#232 := [unit-resolution #254 #600]: #267
+#255 := (not #267)
+#233 := (or #255 #263)
+#29 := (not #28)
+#87 := (or #28 #80)
+#92 := (not #87)
+#36 := (= #35 f8)
+#37 := (implies #29 #36)
+#38 := (not #37)
+#93 := (iff #38 #92)
+#90 := (iff #37 #87)
+#84 := (implies #29 #80)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #37 #84)
+#82 := (iff #36 #80)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [monotonicity #91]: #93
+#79 := [asserted]: #38
+#97 := [mp #79 #94]: #92
+#95 := [not-or-elim #97]: #29
+#591 := (or #255 #28 #263)
+#592 := [def-axiom]: #591
+#573 := [unit-resolution #592 #95]: #233
+#574 := [unit-resolution #573 #232]: #263
+#581 := [mp #574 #578]: #80
+#96 := (not #80)
+#98 := [not-or-elim #97]: #96
+[unit-resolution #98 #581]: false
+unsat
+c5924477e9186eb5df53c29cfb676c83a60e811c 111 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f6 :: S3
 #27 := f6
-decl f4 :: (-> S5 S2 S3 S4 S2)
-decl f10 :: S4
-#33 := f10
-decl f7 :: S3
-#28 := f7
+decl f4 :: (-> S2 S3 S4 S2)
 decl f9 :: S4
-#31 := f9
-decl f8 :: S2
-#30 := f8
-decl f5 :: S5
-#8 := f5
-#32 := (f4 f5 f8 f6 f9)
-#34 := (f4 f5 #32 f7 f10)
+#33 := f9
+decl f8 :: S4
+#31 := f8
+decl f5 :: S3
+#26 := f5
+decl f7 :: S2
+#30 := f7
+#32 := (f4 f7 f5 f8)
+#34 := (f4 #32 f6 f9)
 #35 := (f3 #34 f6)
-#80 := (= f10 #35)
-#264 := (f3 #34 f7)
-#572 := (= #264 #35)
-#586 := (= #35 #264)
-#29 := (= f6 f7)
-#87 := (not #29)
-#88 := (or #87 #80)
-#93 := (not #88)
-#36 := (= #35 f10)
+#80 := (= f9 #35)
+#96 := (not #80)
+#28 := (= f5 f6)
+#87 := (or #28 #80)
+#92 := (not #87)
+#36 := (= #35 f9)
+#29 := (not #28)
 #37 := (implies #29 #36)
 #38 := (not #37)
-#94 := (iff #38 #93)
-#91 := (iff #37 #88)
+#93 := (iff #38 #92)
+#90 := (iff #37 #87)
 #84 := (implies #29 #80)
-#89 := (iff #84 #88)
-#90 := [rewrite]: #89
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
 #85 := (iff #37 #84)
 #82 := (iff #36 #80)
 #83 := [rewrite]: #82
 #86 := [monotonicity #83]: #85
-#92 := [trans #86 #90]: #91
-#95 := [monotonicity #92]: #94
+#91 := [trans #86 #89]: #90
+#94 := [monotonicity #91]: #93
 #79 := [asserted]: #38
-#98 := [mp #79 #95]: #93
-#96 := [not-or-elim #98]: #29
-#234 := [monotonicity #96]: #586
-#573 := [symm #234]: #572
-#265 := (= f10 #264)
-#13 := (:var 0 S3)
-#11 := (:var 1 S4)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#595 := (pattern #14)
-#16 := (f3 #9 #13)
-#118 := (= #14 #16)
-#117 := (= #11 #14)
-#59 := (= #10 #13)
-#105 := (ite #59 #117 #118)
-#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105)
-#599 := (iff #110 #596)
-#597 := (iff #105 #105)
-#598 := [refl]: #597
-#600 := [quant-intro #598]: #599
-#62 := (ite #59 #11 #16)
-#65 := (= #14 #62)
+#97 := [mp #79 #94]: #92
+#98 := [not-or-elim #97]: #96
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#594 := (pattern #13)
+#15 := (f3 #8 #12)
+#117 := (= #13 #15)
+#116 := (= #10 #13)
+#59 := (= #9 #12)
+#104 := (ite #59 #116 #117)
+#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
+#598 := (iff #109 #595)
+#596 := (iff #104 #104)
+#597 := [refl]: #596
+#599 := [quant-intro #597]: #598
+#62 := (ite #59 #10 #15)
+#65 := (= #13 #62)
 #68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65)
-#107 := (iff #68 #110)
-#106 := (iff #65 #105)
-#109 := [rewrite]: #106
-#108 := [quant-intro #109]: #107
-#113 := (~ #68 #68)
-#111 := (~ #65 #65)
-#112 := [refl]: #111
-#114 := [nnf-pos #112]: #113
-#15 := (= #13 #10)
-#17 := (ite #15 #11 #16)
-#18 := (= #14 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18)
-#69 := (iff #19 #68)
-#66 := (iff #18 #65)
-#63 := (= #17 #62)
-#60 := (iff #15 #59)
+#106 := (iff #68 #109)
+#105 := (iff #65 #104)
+#108 := [rewrite]: #105
+#107 := [quant-intro #108]: #106
+#112 := (~ #68 #68)
+#110 := (~ #65 #65)
+#111 := [refl]: #110
+#113 := [nnf-pos #111]: #112
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#69 := (iff #18 #68)
+#66 := (iff #17 #65)
+#63 := (= #16 #62)
+#60 := (iff #14 #59)
 #61 := [rewrite]: #60
 #64 := [monotonicity #61]: #63
 #67 := [monotonicity #64]: #66
 #70 := [quant-intro #67]: #69
-#58 := [asserted]: #19
+#58 := [asserted]: #18
 #73 := [mp #58 #70]: #68
-#101 := [mp~ #73 #114]: #68
-#119 := [mp #101 #108]: #110
-#601 := [mp #119 #600]: #596
-#583 := (not #596)
-#255 := (or #583 #265)
-#177 := (f3 #32 f7)
-#178 := (= #264 #177)
-#179 := (= f7 f7)
-#266 := (ite #179 #265 #178)
-#256 := (or #583 #266)
-#591 := (iff #256 #255)
-#593 := (iff #255 #255)
-#588 := [rewrite]: #593
-#244 := (iff #266 #265)
-#269 := (= #177 #264)
-#1 := true
-#267 := (ite true #265 #269)
-#587 := (iff #267 #265)
-#589 := [rewrite]: #587
-#271 := (iff #266 #267)
-#197 := (iff #178 #269)
-#270 := [rewrite]: #197
-#257 := (iff #179 true)
-#268 := [rewrite]: #257
-#250 := [monotonicity #268 #270]: #271
-#376 := [trans #250 #589]: #244
-#592 := [monotonicity #376]: #591
-#594 := [trans #592 #588]: #591
-#590 := [quant-inst #32 #28 #33 #28]: #256
-#584 := [mp #590 #594]: #255
-#243 := [unit-resolution #584 #601]: #265
-#574 := [trans #243 #573]: #80
-#97 := (not #80)
-#99 := [not-or-elim #98]: #97
-[unit-resolution #99 #574]: false
-unsat
-1d21028f73bdc0aae30ff8eb56a63829018f8e82 191 0
+#100 := [mp~ #73 #113]: #68
+#118 := [mp #100 #107]: #109
+#600 := [mp #118 #599]: #595
+#249 := (not #595)
+#586 := (or #249 #80)
+#176 := (f3 #32 f6)
+#263 := (= #35 #176)
+#177 := (= f6 f6)
+#264 := (ite #177 #80 #263)
+#588 := (or #249 #264)
+#375 := (iff #588 #586)
+#254 := (iff #586 #586)
+#255 := [rewrite]: #254
+#266 := (iff #264 #80)
+#1 := true
+#256 := (ite true #80 #263)
+#196 := (iff #256 #80)
+#269 := [rewrite]: #196
+#267 := (iff #264 #256)
+#178 := (iff #177 true)
+#265 := [rewrite]: #178
+#268 := [monotonicity #265]: #267
+#270 := [trans #268 #269]: #266
+#582 := [monotonicity #270]: #375
+#589 := [trans #582 #255]: #375
+#243 := [quant-inst #32 #27 #33 #27]: #588
+#590 := [mp #243 #589]: #586
+[unit-resolution #590 #600 #98]: false
+unsat
+7e28540fd0d4f5814439be9d6e362d0c1457f76e 123 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
-decl f8 :: S3
-#29 := f8
-decl f9 :: S2
-#31 := f9
-#37 := (f3 f9 f8)
-decl f4 :: (-> S5 S2 S3 S4 S2)
-decl f11 :: S4
-#34 := f11
+decl f5 :: S3
+#26 := f5
+decl f4 :: (-> S2 S3 S4 S2)
+decl f9 :: S4
+#32 := f9
+decl f6 :: S3
+#27 := f6
+decl f8 :: S4
+#30 := f8
+decl f7 :: S2
+#29 := f7
+#31 := (f4 f7 f5 f8)
+#33 := (f4 #31 f6 f9)
+#34 := (f3 #33 f5)
+#79 := (= f9 #34)
+#263 := (f3 #33 f6)
+#571 := (= #263 #34)
+#585 := (= #34 #263)
+#28 := (= f5 f6)
+#86 := (not #28)
+#87 := (or #86 #79)
+#92 := (not #87)
+#35 := (= #34 f9)
+#36 := (implies #28 #35)
+#37 := (not #36)
+#93 := (iff #37 #92)
+#90 := (iff #36 #87)
+#83 := (implies #28 #79)
+#88 := (iff #83 #87)
+#89 := [rewrite]: #88
+#84 := (iff #36 #83)
+#81 := (iff #35 #79)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#91 := [trans #85 #89]: #90
+#94 := [monotonicity #91]: #93
+#78 := [asserted]: #37
+#97 := [mp #78 #94]: #92
+#95 := [not-or-elim #97]: #28
+#233 := [monotonicity #95]: #585
+#572 := [symm #233]: #571
+#264 := (= f9 #263)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#594 := (pattern #13)
+#15 := (f3 #8 #12)
+#117 := (= #13 #15)
+#116 := (= #10 #13)
+#58 := (= #9 #12)
+#104 := (ite #58 #116 #117)
+#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
+#598 := (iff #109 #595)
+#596 := (iff #104 #104)
+#597 := [refl]: #596
+#599 := [quant-intro #597]: #598
+#61 := (ite #58 #10 #15)
+#64 := (= #13 #61)
+#67 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #64)
+#106 := (iff #67 #109)
+#105 := (iff #64 #104)
+#108 := [rewrite]: #105
+#107 := [quant-intro #108]: #106
+#112 := (~ #67 #67)
+#110 := (~ #64 #64)
+#111 := [refl]: #110
+#113 := [nnf-pos #111]: #112
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#68 := (iff #18 #67)
+#65 := (iff #17 #64)
+#62 := (= #16 #61)
+#59 := (iff #14 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63]: #65
+#69 := [quant-intro #66]: #68
+#57 := [asserted]: #18
+#72 := [mp #57 #69]: #67
+#100 := [mp~ #72 #113]: #67
+#118 := [mp #100 #107]: #109
+#600 := [mp #118 #599]: #595
+#582 := (not #595)
+#254 := (or #582 #264)
+#176 := (f3 #31 f6)
+#177 := (= #263 #176)
+#178 := (= f6 f6)
+#265 := (ite #178 #264 #177)
+#255 := (or #582 #265)
+#590 := (iff #255 #254)
+#592 := (iff #254 #254)
+#587 := [rewrite]: #592
+#243 := (iff #265 #264)
+#268 := (= #176 #263)
+#1 := true
+#266 := (ite true #264 #268)
+#586 := (iff #266 #264)
+#588 := [rewrite]: #586
+#270 := (iff #265 #266)
+#196 := (iff #177 #268)
+#269 := [rewrite]: #196
+#256 := (iff #178 true)
+#267 := [rewrite]: #256
+#249 := [monotonicity #267 #269]: #270
+#375 := [trans #249 #588]: #243
+#591 := [monotonicity #375]: #590
+#593 := [trans #591 #587]: #590
+#589 := [quant-inst #31 #27 #32 #27]: #255
+#583 := [mp #589 #593]: #254
+#242 := [unit-resolution #583 #600]: #264
+#573 := [trans #242 #572]: #79
+#96 := (not #79)
+#98 := [not-or-elim #97]: #96
+[unit-resolution #98 #573]: false
+unsat
+6e80c9c78d8fedc6d33345078567183b7c70457d 190 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
 decl f7 :: S3
 #28 := f7
+decl f8 :: S2
+#30 := f8
+#36 := (f3 f8 f7)
+decl f4 :: (-> S2 S3 S4 S2)
 decl f10 :: S4
-#32 := f10
+#33 := f10
 decl f6 :: S3
 #27 := f6
-decl f5 :: S5
-#8 := f5
-#33 := (f4 f5 f9 f6 f10)
-#35 := (f4 f5 #33 f7 f11)
-#36 := (f3 #35 f8)
-#38 := (= #36 #37)
-#587 := (f3 #33 f6)
-#571 := (f4 f5 f9 f6 #587)
-#207 := (f3 #571 f8)
-#212 := (= #207 #37)
-#563 := (= #37 #207)
-#573 := (= #207 #587)
-#172 := (= f6 f8)
-#286 := (ite #172 #573 #563)
-#13 := (:var 0 S3)
-#11 := (:var 1 S4)
-#10 := (:var 2 S3)
-#9 := (:var 3 S2)
-#12 := (f4 f5 #9 #10 #11)
-#14 := (f3 #12 #13)
-#589 := (pattern #14)
-#16 := (f3 #9 #13)
-#112 := (= #14 #16)
-#111 := (= #11 #14)
-#61 := (= #10 #13)
-#99 := (ite #61 #111 #112)
-#590 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #589) #99)
-#104 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #99)
-#593 := (iff #104 #590)
-#591 := (iff #99 #99)
-#592 := [refl]: #591
-#594 := [quant-intro #592]: #593
-#64 := (ite #61 #11 #16)
-#67 := (= #14 #64)
-#70 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #67)
-#101 := (iff #70 #104)
-#100 := (iff #67 #99)
-#103 := [rewrite]: #100
-#102 := [quant-intro #103]: #101
-#107 := (~ #70 #70)
-#105 := (~ #67 #67)
-#106 := [refl]: #105
-#108 := [nnf-pos #106]: #107
-#15 := (= #13 #10)
-#17 := (ite #15 #11 #16)
-#18 := (= #14 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18)
-#71 := (iff #19 #70)
-#68 := (iff #18 #67)
-#65 := (= #17 #64)
-#62 := (iff #15 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [quant-intro #69]: #71
-#60 := [asserted]: #19
-#75 := [mp #60 #72]: #70
-#95 := [mp~ #75 #108]: #70
-#113 := [mp #95 #102]: #104
-#595 := [mp #113 #594]: #590
-#588 := (not #590)
-#288 := (or #588 #286)
-#213 := (= #587 #207)
-#575 := (ite #172 #213 #212)
-#179 := (or #588 #575)
-#559 := (iff #179 #288)
-#282 := (iff #288 #288)
-#556 := [rewrite]: #282
-#287 := (iff #575 #286)
-#269 := (iff #212 #563)
-#285 := [rewrite]: #269
-#576 := (iff #213 #573)
-#562 := [rewrite]: #576
-#273 := [monotonicity #562 #285]: #287
-#281 := [monotonicity #273]: #559
-#560 := [trans #281 #556]: #559
-#558 := [quant-inst #31 #27 #587 #29]: #179
-#557 := [mp #558 #560]: #288
-#517 := [unit-resolution #557 #595]: #286
-#561 := (not #286)
-#508 := (or #561 #563)
-#259 := (not #172)
-#173 := (= f7 f8)
-#260 := (not #173)
-#171 := (= f6 f7)
+decl f9 :: S4
+#31 := f9
+decl f5 :: S3
+#26 := f5
+#32 := (f4 f8 f5 f9)
+#34 := (f4 #32 f6 f10)
+#35 := (f3 #34 f7)
+#37 := (= #35 #36)
+#586 := (f3 #32 f5)
+#570 := (f4 f8 f5 #586)
+#206 := (f3 #570 f7)
+#211 := (= #206 #36)
+#562 := (= #36 #206)
+#572 := (= #206 #586)
+#171 := (= f5 f7)
+#285 := (ite #171 #572 #562)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#588 := (pattern #13)
+#15 := (f3 #8 #12)
+#111 := (= #13 #15)
+#110 := (= #10 #13)
+#60 := (= #9 #12)
+#98 := (ite #60 #110 #111)
+#589 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #588) #98)
+#103 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #98)
+#592 := (iff #103 #589)
+#590 := (iff #98 #98)
+#591 := [refl]: #590
+#593 := [quant-intro #591]: #592
+#63 := (ite #60 #10 #15)
+#66 := (= #13 #63)
+#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66)
+#100 := (iff #69 #103)
+#99 := (iff #66 #98)
+#102 := [rewrite]: #99
+#101 := [quant-intro #102]: #100
+#106 := (~ #69 #69)
+#104 := (~ #66 #66)
+#105 := [refl]: #104
+#107 := [nnf-pos #105]: #106
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#70 := (iff #18 #69)
+#67 := (iff #17 #66)
+#64 := (= #16 #63)
+#61 := (iff #14 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#71 := [quant-intro #68]: #70
+#59 := [asserted]: #18
+#74 := [mp #59 #71]: #69
+#94 := [mp~ #74 #107]: #69
+#112 := [mp #94 #101]: #103
+#594 := [mp #112 #593]: #589
+#587 := (not #589)
+#287 := (or #587 #285)
+#212 := (= #586 #206)
+#574 := (ite #171 #212 #211)
+#178 := (or #587 #574)
+#558 := (iff #178 #287)
+#281 := (iff #287 #287)
+#555 := [rewrite]: #281
+#286 := (iff #574 #285)
+#268 := (iff #211 #562)
+#284 := [rewrite]: #268
+#575 := (iff #212 #572)
+#561 := [rewrite]: #575
+#272 := [monotonicity #561 #284]: #286
+#280 := [monotonicity #272]: #558
+#559 := [trans #280 #555]: #558
+#557 := [quant-inst #30 #26 #586 #28]: #178
+#556 := [mp #557 #559]: #287
+#516 := [unit-resolution #556 #594]: #285
+#560 := (not #285)
+#507 := (or #560 #562)
 #258 := (not #171)
-#251 := (and #258 #259 #260)
-#30 := (distinct f6 f7 f8)
-#82 := (not #30)
-#84 := (or #82 #38)
-#87 := (not #84)
-#39 := (implies #30 #38)
-#40 := (not #39)
-#88 := (iff #40 #87)
-#85 := (iff #39 #84)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#81 := [asserted]: #40
-#92 := [mp #81 #89]: #87
-#90 := [not-or-elim #92]: #30
-#238 := (or #82 #251)
-#370 := [def-axiom]: #238
-#506 := [unit-resolution #370 #90]: #251
-#262 := (not #251)
-#264 := (or #262 #259)
-#261 := [def-axiom]: #264
-#507 := [unit-resolution #261 #506]: #259
-#272 := (or #561 #172 #563)
-#274 := [def-axiom]: #272
-#509 := [unit-resolution #274 #507]: #508
-#503 := [unit-resolution #509 #517]: #563
-#487 := [symm #503]: #212
-#488 := (= #36 #207)
-#250 := (f3 #33 f8)
-#496 := (= #250 #207)
-#499 := (= #207 #250)
-#516 := (= #571 #33)
-#514 := (= #587 f10)
-#582 := (= f10 #587)
-#22 := (:var 0 S4)
-#21 := (:var 1 S3)
-#20 := (:var 2 S2)
-#23 := (f4 f5 #20 #21 #22)
-#596 := (pattern #23)
-#24 := (f3 #23 #21)
-#74 := (= #22 #24)
-#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #596) #74)
-#78 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #74)
-#600 := (iff #78 #597)
-#598 := (iff #74 #74)
-#599 := [refl]: #598
-#601 := [quant-intro #599]: #600
-#97 := (~ #78 #78)
-#96 := (~ #74 #74)
-#109 := [refl]: #96
-#98 := [nnf-pos #109]: #97
-#25 := (= #24 #22)
-#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25)
-#79 := (iff #26 #78)
-#76 := (iff #25 #74)
-#77 := [rewrite]: #76
-#80 := [quant-intro #77]: #79
-#73 := [asserted]: #26
-#83 := [mp #73 #80]: #78
-#110 := [mp~ #83 #98]: #78
-#602 := [mp #110 #601]: #597
-#569 := (not #597)
-#570 := (or #569 #582)
-#565 := [quant-inst #31 #27 #32]: #570
-#504 := [unit-resolution #565 #602]: #582
-#515 := [symm #504]: #514
-#512 := [monotonicity #515]: #516
-#500 := [monotonicity #512]: #499
-#501 := [symm #500]: #496
-#584 := (= #36 #250)
-#585 := (= f11 #36)
-#586 := (ite #173 #585 #584)
-#578 := (or #588 #586)
-#236 := [quant-inst #33 #28 #34 #29]: #578
-#510 := [unit-resolution #236 #595]: #586
-#241 := (not #586)
-#495 := (or #241 #584)
-#265 := (or #262 #260)
-#244 := [def-axiom]: #265
-#494 := [unit-resolution #244 #506]: #260
-#580 := (or #241 #173 #584)
-#221 := [def-axiom]: #580
-#497 := [unit-resolution #221 #494]: #495
-#498 := [unit-resolution #497 #510]: #584
-#490 := [trans #498 #501]: #488
-#491 := [trans #490 #487]: #38
-#91 := (not #38)
-#93 := [not-or-elim #92]: #91
-[unit-resolution #93 #491]: false
+#172 := (= f6 f7)
+#259 := (not #172)
+#170 := (= f5 f6)
+#257 := (not #170)
+#250 := (and #257 #258 #259)
+#29 := (distinct f5 f6 f7)
+#81 := (not #29)
+#83 := (or #81 #37)
+#86 := (not #83)
+#38 := (implies #29 #37)
+#39 := (not #38)
+#87 := (iff #39 #86)
+#84 := (iff #38 #83)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#80 := [asserted]: #39
+#91 := [mp #80 #88]: #86
+#89 := [not-or-elim #91]: #29
+#237 := (or #81 #250)
+#369 := [def-axiom]: #237
+#505 := [unit-resolution #369 #89]: #250
+#261 := (not #250)
+#263 := (or #261 #258)
+#260 := [def-axiom]: #263
+#506 := [unit-resolution #260 #505]: #258
+#271 := (or #560 #171 #562)
+#273 := [def-axiom]: #271
+#508 := [unit-resolution #273 #506]: #507
+#502 := [unit-resolution #508 #516]: #562
+#486 := [symm #502]: #211
+#487 := (= #35 #206)
+#249 := (f3 #32 f7)
+#495 := (= #249 #206)
+#498 := (= #206 #249)
+#515 := (= #570 #32)
+#513 := (= #586 f9)
+#581 := (= f9 #586)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#595 := (pattern #22)
+#23 := (f3 #22 #20)
+#73 := (= #21 #23)
+#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #595) #73)
+#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #73)
+#596 := (iff #77 #597)
+#599 := (iff #597 #597)
+#600 := [rewrite]: #599
+#598 := [rewrite]: #596
+#601 := [trans #598 #600]: #596
+#96 := (~ #77 #77)
+#95 := (~ #73 #73)
+#108 := [refl]: #95
+#97 := [nnf-pos #108]: #96
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#78 := (iff #25 #77)
+#75 := (iff #24 #73)
+#76 := [rewrite]: #75
+#79 := [quant-intro #76]: #78
+#72 := [asserted]: #25
+#82 := [mp #72 #79]: #77
+#109 := [mp~ #82 #97]: #77
+#602 := [mp #109 #601]: #597
+#568 := (not #597)
+#569 := (or #568 #581)
+#564 := [quant-inst #30 #26 #31]: #569
+#503 := [unit-resolution #564 #602]: #581
+#514 := [symm #503]: #513
+#511 := [monotonicity #514]: #515
+#499 := [monotonicity #511]: #498
+#500 := [symm #499]: #495
+#583 := (= #35 #249)
+#584 := (= f10 #35)
+#585 := (ite #172 #584 #583)
+#577 := (or #587 #585)
+#235 := [quant-inst #32 #27 #33 #28]: #577
+#509 := [unit-resolution #235 #594]: #585
+#240 := (not #585)
+#494 := (or #240 #583)
+#264 := (or #261 #259)
+#243 := [def-axiom]: #264
+#493 := [unit-resolution #243 #505]: #259
+#579 := (or #240 #172 #583)
+#220 := [def-axiom]: #579
+#496 := [unit-resolution #220 #493]: #494
+#497 := [unit-resolution #496 #509]: #583
+#489 := [trans #497 #500]: #487
+#490 := [trans #489 #486]: #37
+#90 := (not #37)
+#92 := [not-or-elim #91]: #90
+[unit-resolution #92 #490]: false
 unsat
 a8479ddc219a8a1f70834d2e3bfa9595c2e54d48 31 0
 #2 := false
@@ -52500,267 +52494,265 @@
 #637 := [unit-resolution #308 #293]: #636
 [unit-resolution #637 #635 #634]: false
 unsat
-5515b772fc370cead501436e9e655f396708da26 261 0
+8df9cadd28b79979ba76c3dfed467a1319648283 259 0
 #2 := false
 decl f5 :: (-> S4 S5 S1)
-decl f13 :: S5
-#48 := f13
-decl f11 :: S4
-#44 := f11
-#628 := (f5 f11 f13)
-decl f1 :: S1
-#4 := f1
-#341 := (= f1 #628)
-decl f12 :: S4
-#45 := f12
-#339 := (f5 f12 f13)
-#336 := (= f1 #339)
-#626 := (or #336 #341)
-decl f6 :: (-> S6 S4 S4 S4)
-decl f7 :: S6
-#20 := f7
-#46 := (f6 f7 f11 f12)
-#313 := (f5 #46 f13)
-#445 := (= f1 #313)
-#620 := (iff #445 #626)
-#586 := (not #620)
-#598 := (not #626)
-#610 := (not #341)
+decl f12 :: S5
+#47 := f12
 decl f10 :: S4
 #43 := f10
-#641 := (f5 f10 f13)
-#642 := (= f1 #641)
-#488 := (or #341 #642)
-#613 := (not #488)
-#51 := (f6 f7 f10 f11)
-#340 := (f5 #51 f13)
-#319 := (= f1 #340)
-#596 := (iff #319 #488)
-#588 := (not #596)
-#581 := [hypothesis]: #588
-#24 := (:var 0 S5)
-#22 := (:var 1 S4)
-#21 := (:var 2 S4)
-#23 := (f6 f7 #21 #22)
-#25 := (f5 #23 #24)
-#671 := (pattern #25)
-#29 := (f5 #22 #24)
-#103 := (= f1 #29)
-#27 := (f5 #21 #24)
-#100 := (= f1 #27)
-#106 := (or #100 #103)
-#96 := (= f1 #25)
-#109 := (iff #96 #106)
-#672 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #671) #109)
-#112 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #109)
-#675 := (iff #112 #672)
-#673 := (iff #109 #109)
-#674 := [refl]: #673
-#676 := [quant-intro #674]: #675
-#158 := (~ #112 #112)
-#157 := (~ #109 #109)
-#172 := [refl]: #157
-#159 := [nnf-pos #172]: #158
-#30 := (= #29 f1)
-#28 := (= #27 f1)
-#31 := (or #28 #30)
-#26 := (= #25 f1)
-#32 := (iff #26 #31)
-#33 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #32)
-#113 := (iff #33 #112)
-#110 := (iff #32 #109)
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#105 := [rewrite]: #104
-#101 := (iff #28 #100)
-#102 := [rewrite]: #101
-#108 := [monotonicity #102 #105]: #107
-#98 := (iff #26 #96)
-#99 := [rewrite]: #98
-#111 := [monotonicity #99 #108]: #110
-#114 := [quant-intro #111]: #113
-#95 := [asserted]: #33
-#117 := [mp #95 #114]: #112
-#173 := [mp~ #117 #159]: #112
-#677 := [mp #173 #676]: #672
-#652 := (not #672)
-#594 := (or #652 #596)
-#605 := (or #642 #341)
-#487 := (iff #319 #605)
-#597 := (or #652 #487)
-#497 := (iff #597 #594)
-#500 := (iff #594 #594)
-#493 := [rewrite]: #500
-#498 := (iff #487 #596)
-#489 := (iff #605 #488)
-#448 := [rewrite]: #489
-#593 := [monotonicity #448]: #498
-#499 := [monotonicity #593]: #497
-#501 := [trans #499 #493]: #497
-#482 := [quant-inst #43 #44 #48]: #597
-#502 := [mp #482 #501]: #594
-#582 := [unit-resolution #502 #677 #581]: false
-#583 := [lemma #582]: #596
-#659 := (not #319)
-#656 := (or #319 #336)
-#653 := (not #656)
-#52 := (f6 f7 #51 f12)
-#53 := (f5 #52 f13)
-#139 := (= f1 #53)
-#335 := (not #139)
-#47 := (f6 f7 f10 #46)
-#49 := (f5 #47 f13)
-#135 := (= f1 #49)
-#148 := (not #135)
-#584 := [hypothesis]: #148
-#334 := (or #139 #135)
-#149 := (iff #139 #148)
-#54 := (= #53 f1)
-#50 := (= #49 f1)
-#55 := (iff #50 #54)
-#56 := (not #55)
-#152 := (iff #56 #149)
-#142 := (iff #135 #139)
-#145 := (not #142)
-#150 := (iff #145 #149)
-#151 := [rewrite]: #150
-#146 := (iff #56 #145)
-#143 := (iff #55 #142)
-#140 := (iff #54 #139)
-#141 := [rewrite]: #140
-#137 := (iff #50 #135)
-#138 := [rewrite]: #137
-#144 := [monotonicity #138 #141]: #143
-#147 := [monotonicity #144]: #146
-#153 := [trans #147 #151]: #152
-#134 := [asserted]: #56
-#156 := [mp #134 #153]: #149
-#246 := (not #149)
-#333 := (or #139 #135 #246)
-#247 := [def-axiom]: #333
-#248 := [unit-resolution #247 #156]: #334
-#578 := [unit-resolution #248 #584]: #139
-#569 := (or #335 #656)
-#658 := (iff #139 #656)
-#324 := (or #652 #658)
-#325 := [quant-inst #51 #45 #48]: #324
-#585 := [unit-resolution #325 #677]: #658
-#654 := (not #658)
-#296 := (or #654 #335 #656)
-#639 := [def-axiom]: #296
-#570 := [unit-resolution #639 #585]: #569
-#572 := [unit-resolution #570 #578]: #656
-#662 := (not #336)
-#602 := (or #652 #620)
-#625 := (or #341 #336)
-#629 := (iff #445 #625)
-#622 := (or #652 #629)
-#617 := (iff #622 #602)
-#624 := (iff #602 #602)
-#465 := [rewrite]: #624
-#621 := (iff #629 #620)
-#630 := (iff #625 #626)
-#619 := [rewrite]: #630
-#616 := [monotonicity #619]: #621
-#618 := [monotonicity #616]: #617
-#466 := [trans #618 #465]: #617
-#623 := [quant-inst #44 #45 #48]: #622
-#467 := [mp #623 #466]: #602
-#573 := [unit-resolution #467 #677]: #620
-#563 := (or #586 #598)
-#361 := (not #445)
-#645 := (or #445 #642)
-#634 := (not #645)
-#575 := (or #135 #634)
-#282 := (iff #135 #645)
-#287 := (or #652 #282)
-#643 := (or #642 #445)
-#644 := (iff #135 #643)
-#288 := (or #652 #644)
-#648 := (iff #288 #287)
-#637 := (iff #287 #287)
-#638 := [rewrite]: #637
-#647 := (iff #644 #282)
-#640 := (iff #643 #645)
-#646 := [rewrite]: #640
-#649 := [monotonicity #646]: #647
-#651 := [monotonicity #649]: #648
-#344 := [trans #651 #638]: #648
-#650 := [quant-inst #43 #46 #48]: #288
-#360 := [mp #650 #344]: #287
-#574 := [unit-resolution #360 #677]: #282
-#631 := (not #282)
-#635 := (or #631 #135 #634)
-#632 := [def-axiom]: #635
-#571 := [unit-resolution #632 #574]: #575
-#576 := [unit-resolution #571 #584]: #634
-#362 := (or #645 #361)
-#348 := [def-axiom]: #362
-#562 := [unit-resolution #348 #576]: #361
-#580 := (or #586 #445 #598)
-#577 := [def-axiom]: #580
-#565 := [unit-resolution #577 #562]: #563
-#566 := [unit-resolution #565 #573]: #598
-#609 := (or #626 #662)
-#503 := [def-axiom]: #609
-#567 := [unit-resolution #503 #566]: #662
-#311 := (or #653 #319 #336)
-#316 := [def-axiom]: #311
-#564 := [unit-resolution #316 #567 #572]: #319
-#363 := (not #642)
-#254 := (or #645 #363)
-#633 := [def-axiom]: #254
-#568 := [unit-resolution #633 #576]: #363
-#504 := (or #626 #610)
-#505 := [def-axiom]: #504
-#548 := [unit-resolution #505 #566]: #610
-#614 := (or #613 #341 #642)
-#608 := [def-axiom]: #614
-#549 := [unit-resolution #608 #548 #568]: #613
-#446 := (or #588 #659 #488)
-#447 := [def-axiom]: #446
-#551 := [unit-resolution #447 #549 #564 #583]: false
-#552 := [lemma #551]: #135
-#338 := (or #335 #148)
-#326 := (or #335 #148 #246)
-#337 := [def-axiom]: #326
-#266 := [unit-resolution #337 #156]: #338
-#553 := [unit-resolution #266 #552]: #335
-#554 := (or #139 #653)
-#312 := (or #654 #139 #653)
-#655 := [def-axiom]: #312
-#555 := [unit-resolution #655 #585]: #554
-#556 := [unit-resolution #555 #553]: #653
-#660 := (or #656 #659)
-#661 := [def-axiom]: #660
-#557 := [unit-resolution #661 #556]: #659
-#615 := (or #588 #319 #613)
-#444 := [def-axiom]: #615
-#558 := [unit-resolution #444 #557 #583]: #613
-#611 := (or #488 #610)
-#612 := [def-axiom]: #611
-#559 := [unit-resolution #612 #558]: #610
-#657 := (or #656 #662)
-#663 := [def-axiom]: #657
-#560 := [unit-resolution #663 #556]: #662
-#595 := (or #598 #336 #341)
-#599 := [def-axiom]: #595
-#550 := [unit-resolution #599 #560 #559]: #598
-#561 := (or #148 #645)
-#636 := (or #631 #148 #645)
-#345 := [def-axiom]: #636
-#539 := [unit-resolution #345 #574]: #561
-#540 := [unit-resolution #539 #552]: #645
-#606 := (or #488 #363)
-#607 := [def-axiom]: #606
-#542 := [unit-resolution #607 #558]: #363
-#356 := (or #634 #445 #642)
-#357 := [def-axiom]: #356
-#543 := [unit-resolution #357 #542 #540]: #445
-#579 := (or #586 #361 #626)
-#589 := [def-axiom]: #579
-#544 := [unit-resolution #589 #543 #550]: #586
-[unit-resolution #467 #677 #544]: false
+#627 := (f5 f10 f12)
+decl f1 :: S1
+#4 := f1
+#340 := (= f1 #627)
+decl f11 :: S4
+#44 := f11
+#338 := (f5 f11 f12)
+#335 := (= f1 #338)
+#625 := (or #335 #340)
+decl f6 :: (-> S4 S4 S4)
+#45 := (f6 f10 f11)
+#312 := (f5 #45 f12)
+#444 := (= f1 #312)
+#619 := (iff #444 #625)
+#585 := (not #619)
+#597 := (not #625)
+#609 := (not #340)
+decl f9 :: S4
+#42 := f9
+#640 := (f5 f9 f12)
+#641 := (= f1 #640)
+#487 := (or #340 #641)
+#612 := (not #487)
+#50 := (f6 f9 f10)
+#339 := (f5 #50 f12)
+#318 := (= f1 #339)
+#595 := (iff #318 #487)
+#587 := (not #595)
+#580 := [hypothesis]: #587
+#23 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#22 := (f6 #20 #21)
+#24 := (f5 #22 #23)
+#670 := (pattern #24)
+#28 := (f5 #21 #23)
+#102 := (= f1 #28)
+#26 := (f5 #20 #23)
+#99 := (= f1 #26)
+#105 := (or #99 #102)
+#95 := (= f1 #24)
+#108 := (iff #95 #105)
+#671 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #670) #108)
+#111 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #108)
+#674 := (iff #111 #671)
+#672 := (iff #108 #108)
+#673 := [refl]: #672
+#675 := [quant-intro #673]: #674
+#157 := (~ #111 #111)
+#156 := (~ #108 #108)
+#171 := [refl]: #156
+#158 := [nnf-pos #171]: #157
+#29 := (= #28 f1)
+#27 := (= #26 f1)
+#30 := (or #27 #29)
+#25 := (= #24 f1)
+#31 := (iff #25 #30)
+#32 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #31)
+#112 := (iff #32 #111)
+#109 := (iff #31 #108)
+#106 := (iff #30 #105)
+#103 := (iff #29 #102)
+#104 := [rewrite]: #103
+#100 := (iff #27 #99)
+#101 := [rewrite]: #100
+#107 := [monotonicity #101 #104]: #106
+#97 := (iff #25 #95)
+#98 := [rewrite]: #97
+#110 := [monotonicity #98 #107]: #109
+#113 := [quant-intro #110]: #112
+#94 := [asserted]: #32
+#116 := [mp #94 #113]: #111
+#172 := [mp~ #116 #158]: #111
+#676 := [mp #172 #675]: #671
+#651 := (not #671)
+#593 := (or #651 #595)
+#604 := (or #641 #340)
+#486 := (iff #318 #604)
+#596 := (or #651 #486)
+#496 := (iff #596 #593)
+#499 := (iff #593 #593)
+#492 := [rewrite]: #499
+#497 := (iff #486 #595)
+#488 := (iff #604 #487)
+#447 := [rewrite]: #488
+#592 := [monotonicity #447]: #497
+#498 := [monotonicity #592]: #496
+#500 := [trans #498 #492]: #496
+#481 := [quant-inst #42 #43 #47]: #596
+#501 := [mp #481 #500]: #593
+#581 := [unit-resolution #501 #676 #580]: false
+#582 := [lemma #581]: #595
+#658 := (not #318)
+#655 := (or #318 #335)
+#652 := (not #655)
+#51 := (f6 #50 f11)
+#52 := (f5 #51 f12)
+#138 := (= f1 #52)
+#334 := (not #138)
+#46 := (f6 f9 #45)
+#48 := (f5 #46 f12)
+#134 := (= f1 #48)
+#147 := (not #134)
+#583 := [hypothesis]: #147
+#333 := (or #138 #134)
+#148 := (iff #138 #147)
+#53 := (= #52 f1)
+#49 := (= #48 f1)
+#54 := (iff #49 #53)
+#55 := (not #54)
+#151 := (iff #55 #148)
+#141 := (iff #134 #138)
+#144 := (not #141)
+#149 := (iff #144 #148)
+#150 := [rewrite]: #149
+#145 := (iff #55 #144)
+#142 := (iff #54 #141)
+#139 := (iff #53 #138)
+#140 := [rewrite]: #139
+#136 := (iff #49 #134)
+#137 := [rewrite]: #136
+#143 := [monotonicity #137 #140]: #142
+#146 := [monotonicity #143]: #145
+#152 := [trans #146 #150]: #151
+#133 := [asserted]: #55
+#155 := [mp #133 #152]: #148
+#245 := (not #148)
+#332 := (or #138 #134 #245)
+#246 := [def-axiom]: #332
+#247 := [unit-resolution #246 #155]: #333
+#577 := [unit-resolution #247 #583]: #138
+#568 := (or #334 #655)
+#657 := (iff #138 #655)
+#323 := (or #651 #657)
+#324 := [quant-inst #50 #44 #47]: #323
+#584 := [unit-resolution #324 #676]: #657
+#653 := (not #657)
+#295 := (or #653 #334 #655)
+#638 := [def-axiom]: #295
+#569 := [unit-resolution #638 #584]: #568
+#571 := [unit-resolution #569 #577]: #655
+#661 := (not #335)
+#601 := (or #651 #619)
+#624 := (or #340 #335)
+#628 := (iff #444 #624)
+#621 := (or #651 #628)
+#616 := (iff #621 #601)
+#623 := (iff #601 #601)
+#464 := [rewrite]: #623
+#620 := (iff #628 #619)
+#629 := (iff #624 #625)
+#618 := [rewrite]: #629
+#615 := [monotonicity #618]: #620
+#617 := [monotonicity #615]: #616
+#465 := [trans #617 #464]: #616
+#622 := [quant-inst #43 #44 #47]: #621
+#466 := [mp #622 #465]: #601
+#572 := [unit-resolution #466 #676]: #619
+#562 := (or #585 #597)
+#360 := (not #444)
+#644 := (or #444 #641)
+#633 := (not #644)
+#574 := (or #134 #633)
+#281 := (iff #134 #644)
+#286 := (or #651 #281)
+#642 := (or #641 #444)
+#643 := (iff #134 #642)
+#287 := (or #651 #643)
+#647 := (iff #287 #286)
+#636 := (iff #286 #286)
+#637 := [rewrite]: #636
+#646 := (iff #643 #281)
+#639 := (iff #642 #644)
+#645 := [rewrite]: #639
+#648 := [monotonicity #645]: #646
+#650 := [monotonicity #648]: #647
+#343 := [trans #650 #637]: #647
+#649 := [quant-inst #42 #45 #47]: #287
+#359 := [mp #649 #343]: #286
+#573 := [unit-resolution #359 #676]: #281
+#630 := (not #281)
+#634 := (or #630 #134 #633)
+#631 := [def-axiom]: #634
+#570 := [unit-resolution #631 #573]: #574
+#575 := [unit-resolution #570 #583]: #633
+#361 := (or #644 #360)
+#347 := [def-axiom]: #361
+#561 := [unit-resolution #347 #575]: #360
+#579 := (or #585 #444 #597)
+#576 := [def-axiom]: #579
+#564 := [unit-resolution #576 #561]: #562
+#565 := [unit-resolution #564 #572]: #597
+#608 := (or #625 #661)
+#502 := [def-axiom]: #608
+#566 := [unit-resolution #502 #565]: #661
+#310 := (or #652 #318 #335)
+#315 := [def-axiom]: #310
+#563 := [unit-resolution #315 #566 #571]: #318
+#362 := (not #641)
+#253 := (or #644 #362)
+#632 := [def-axiom]: #253
+#567 := [unit-resolution #632 #575]: #362
+#503 := (or #625 #609)
+#504 := [def-axiom]: #503
+#547 := [unit-resolution #504 #565]: #609
+#613 := (or #612 #340 #641)
+#607 := [def-axiom]: #613
+#548 := [unit-resolution #607 #547 #567]: #612
+#445 := (or #587 #658 #487)
+#446 := [def-axiom]: #445
+#550 := [unit-resolution #446 #548 #563 #582]: false
+#551 := [lemma #550]: #134
+#337 := (or #334 #147)
+#325 := (or #334 #147 #245)
+#336 := [def-axiom]: #325
+#265 := [unit-resolution #336 #155]: #337
+#552 := [unit-resolution #265 #551]: #334
+#553 := (or #138 #652)
+#311 := (or #653 #138 #652)
+#654 := [def-axiom]: #311
+#554 := [unit-resolution #654 #584]: #553
+#555 := [unit-resolution #554 #552]: #652
+#659 := (or #655 #658)
+#660 := [def-axiom]: #659
+#556 := [unit-resolution #660 #555]: #658
+#614 := (or #587 #318 #612)
+#443 := [def-axiom]: #614
+#557 := [unit-resolution #443 #556 #582]: #612
+#610 := (or #487 #609)
+#611 := [def-axiom]: #610
+#558 := [unit-resolution #611 #557]: #609
+#656 := (or #655 #661)
+#662 := [def-axiom]: #656
+#559 := [unit-resolution #662 #555]: #661
+#594 := (or #597 #335 #340)
+#598 := [def-axiom]: #594
+#549 := [unit-resolution #598 #559 #558]: #597
+#560 := (or #147 #644)
+#635 := (or #630 #147 #644)
+#344 := [def-axiom]: #635
+#538 := [unit-resolution #344 #573]: #560
+#539 := [unit-resolution #538 #551]: #644
+#605 := (or #487 #362)
+#606 := [def-axiom]: #605
+#541 := [unit-resolution #606 #557]: #362
+#355 := (or #633 #444 #641)
+#356 := [def-axiom]: #355
+#542 := [unit-resolution #356 #541 #539]: #444
+#578 := (or #585 #360 #625)
+#588 := [def-axiom]: #578
+#543 := [unit-resolution #588 #542 #549]: #585
+[unit-resolution #466 #676 #543]: false
 unsat
 e18331b7b676705a2856a4af405fce965b0fd82f 153 0
 #2 := false
@@ -53532,288 +53524,286 @@
 #642 := [unit-resolution #294 #632]: #280
 [unit-resolution #642 #279 #641]: false
 unsat
-875452e11949675636517f32afdb052ad9456477 282 0
+2197c1dae16f488eb4bfcbae6c35e5ab268a4235 280 0
 #2 := false
 decl f3 :: (-> S2 S3 S1)
-decl f13 :: S3
-#48 := f13
-decl f4 :: (-> S4 S2 S2 S2)
-decl f11 :: S2
-#44 := f11
+decl f12 :: S3
+#47 := f12
+decl f4 :: (-> S2 S2 S2)
 decl f10 :: S2
 #43 := f10
-decl f5 :: S4
-#8 := f5
-#51 := (f4 f5 f10 f11)
-#319 := (f3 #51 f13)
-decl f1 :: S1
-#4 := f1
-#656 := (= f1 #319)
-#254 := (f3 f11 f13)
-#633 := (= f1 #254)
-#630 := (not #633)
-#344 := (f3 f10 f13)
-#360 := (= f1 #344)
-#361 := (not #360)
-#619 := (or #361 #630)
-#620 := (not #619)
-#616 := (iff #620 #656)
-#587 := (not #616)
-decl f12 :: S2
-#45 := f12
-#339 := (f3 f12 f13)
-#336 := (= f1 #339)
-#340 := (not #336)
-#489 := (or #340 #630)
-#498 := (not #489)
-#46 := (f4 f5 f11 f12)
-#651 := (f3 #46 f13)
-#637 := (= f1 #651)
-#499 := (iff #498 #637)
-#592 := (not #499)
-#572 := [hypothesis]: #592
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#9 := (:var 2 S2)
-#11 := (f4 f5 #9 #10)
-#13 := (f3 #11 #12)
-#664 := (pattern #13)
-#17 := (f3 #10 #12)
-#83 := (= f1 #17)
-#181 := (not #83)
-#15 := (f3 #9 #12)
-#80 := (= f1 #15)
-#180 := (not #80)
-#164 := (or #180 #181)
-#165 := (not #164)
-#77 := (= f1 #13)
-#182 := (iff #77 #165)
-#665 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #664) #182)
-#185 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #182)
-#668 := (iff #185 #665)
-#666 := (iff #182 #182)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#86 := (and #80 #83)
-#89 := (iff #77 #86)
-#92 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #89)
-#186 := (iff #92 #185)
-#183 := (iff #89 #182)
-#166 := (iff #86 #165)
-#167 := [rewrite]: #166
-#184 := [monotonicity #167]: #183
-#187 := [quant-intro #184]: #186
-#170 := (~ #92 #92)
-#168 := (~ #89 #89)
-#169 := [refl]: #168
-#171 := [nnf-pos #169]: #170
-#18 := (= #17 f1)
-#16 := (= #15 f1)
-#19 := (and #16 #18)
-#14 := (= #13 f1)
-#20 := (iff #14 #19)
-#21 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #20)
-#93 := (iff #21 #92)
-#90 := (iff #20 #89)
-#87 := (iff #19 #86)
-#84 := (iff #18 #83)
-#85 := [rewrite]: #84
-#81 := (iff #16 #80)
-#82 := [rewrite]: #81
-#88 := [monotonicity #82 #85]: #87
-#78 := (iff #14 #77)
-#79 := [rewrite]: #78
-#91 := [monotonicity #79 #88]: #90
-#94 := [quant-intro #91]: #93
-#76 := [asserted]: #21
-#97 := [mp #76 #94]: #92
-#155 := [mp~ #97 #171]: #92
-#188 := [mp #155 #187]: #185
-#670 := [mp #188 #669]: #665
-#311 := (not #665)
-#503 := (or #311 #499)
-#605 := (or #630 #340)
-#487 := (not #605)
-#488 := (iff #637 #487)
-#504 := (or #311 #488)
-#598 := (iff #504 #503)
-#599 := (iff #503 #503)
-#586 := [rewrite]: #599
-#501 := (iff #488 #499)
-#597 := (iff #637 #498)
-#500 := (iff #597 #499)
-#493 := [rewrite]: #500
-#482 := (iff #488 #597)
-#593 := (iff #487 #498)
-#448 := (iff #605 #489)
-#596 := [rewrite]: #448
-#594 := [monotonicity #596]: #593
-#497 := [monotonicity #594]: #482
-#502 := [trans #497 #493]: #501
-#595 := [monotonicity #502]: #598
-#588 := [trans #595 #586]: #598
-#505 := [quant-inst #44 #45 #48]: #504
-#580 := [mp #505 #588]: #503
-#573 := [unit-resolution #580 #670 #572]: false
-#574 := [lemma #573]: #499
-#638 := (not #637)
-#362 := (or #361 #638)
-#348 := (not #362)
-#47 := (f4 f5 f10 #46)
-#49 := (f3 #47 f13)
-#135 := (= f1 #49)
-#148 := (not #135)
-#575 := [hypothesis]: #148
-#576 := (or #135 #362)
-#363 := (iff #135 #348)
-#634 := (or #311 #363)
-#356 := [quant-inst #43 #46 #48]: #634
-#571 := [unit-resolution #356 #670]: #363
-#346 := (not #363)
-#347 := (or #346 #135 #362)
-#349 := [def-axiom]: #347
-#562 := [unit-resolution #349 #571]: #576
-#563 := [unit-resolution #562 #575]: #362
-#602 := (or #311 #616)
-#621 := (iff #656 #620)
-#618 := (or #311 #621)
-#623 := (iff #618 #602)
-#466 := (iff #602 #602)
-#467 := [rewrite]: #466
-#617 := (iff #621 #616)
-#622 := [rewrite]: #617
-#465 := [monotonicity #622]: #623
-#609 := [trans #465 #467]: #623
-#624 := [quant-inst #43 #44 #48]: #618
-#610 := [mp #624 #609]: #602
-#565 := [unit-resolution #610 #670]: #616
-#551 := (or #587 #620)
-#658 := (not #656)
-#324 := (or #340 #658)
-#660 := (not #324)
-#52 := (f4 f5 #51 f12)
-#53 := (f3 #52 f13)
-#139 := (= f1 #53)
-#334 := (or #139 #135)
-#149 := (iff #139 #148)
-#54 := (= #53 f1)
-#50 := (= #49 f1)
-#55 := (iff #50 #54)
-#56 := (not #55)
-#152 := (iff #56 #149)
-#142 := (iff #135 #139)
-#145 := (not #142)
-#150 := (iff #145 #149)
-#151 := [rewrite]: #150
-#146 := (iff #56 #145)
-#143 := (iff #55 #142)
-#140 := (iff #54 #139)
-#141 := [rewrite]: #140
-#137 := (iff #50 #135)
-#138 := [rewrite]: #137
-#144 := [monotonicity #138 #141]: #143
-#147 := [monotonicity #144]: #146
-#153 := [trans #147 #151]: #152
-#134 := [asserted]: #56
-#156 := [mp #134 #153]: #149
-#246 := (not #149)
-#333 := (or #139 #135 #246)
-#247 := [def-axiom]: #333
-#248 := [unit-resolution #247 #156]: #334
-#566 := [unit-resolution #248 #575]: #139
-#335 := (not #139)
-#564 := (or #335 #660)
-#657 := (iff #139 #660)
-#316 := (or #311 #657)
-#313 := (or #658 #340)
-#445 := (not #313)
-#652 := (iff #139 #445)
-#654 := (or #311 #652)
-#655 := (iff #654 #316)
-#639 := (iff #316 #316)
-#300 := [rewrite]: #639
-#663 := (iff #652 #657)
-#661 := (iff #445 #660)
-#325 := (iff #313 #324)
-#659 := [rewrite]: #325
-#662 := [monotonicity #659]: #661
-#653 := [monotonicity #662]: #663
-#296 := [monotonicity #653]: #655
-#301 := [trans #296 #300]: #655
-#312 := [quant-inst #51 #45 #48]: #654
-#302 := [mp #312 #301]: #316
-#567 := [unit-resolution #302 #670]: #657
-#640 := (not #657)
-#647 := (or #640 #335 #660)
-#649 := [def-axiom]: #647
-#568 := [unit-resolution #649 #567]: #564
-#548 := [unit-resolution #568 #566]: #660
-#642 := (or #324 #656)
-#643 := [def-axiom]: #642
-#549 := [unit-resolution #643 #548]: #656
-#581 := (or #587 #620 #658)
-#582 := [def-axiom]: #581
-#552 := [unit-resolution #582 #549]: #551
-#553 := [unit-resolution #552 #565]: #620
-#611 := (or #619 #360)
-#577 := [def-axiom]: #611
-#554 := [unit-resolution #577 #553]: #360
-#636 := (or #348 #361 #638)
-#345 := [def-axiom]: #636
-#555 := [unit-resolution #345 #554 #563]: #638
-#303 := (or #324 #336)
-#641 := [def-axiom]: #303
-#556 := [unit-resolution #641 #548]: #336
-#579 := (or #619 #633)
-#589 := [def-axiom]: #579
-#557 := [unit-resolution #589 #553]: #633
-#614 := (or #498 #340 #630)
-#608 := [def-axiom]: #614
-#558 := [unit-resolution #608 #557 #556]: #498
-#446 := (or #592 #489 #637)
-#447 := [def-axiom]: #446
-#559 := [unit-resolution #447 #558 #555 #574]: false
-#560 := [lemma #559]: #135
-#550 := (or #148 #348)
-#627 := (or #346 #148 #348)
-#628 := [def-axiom]: #627
-#561 := [unit-resolution #628 #571]: #550
-#539 := [unit-resolution #561 #560]: #348
-#635 := (or #362 #637)
-#632 := [def-axiom]: #635
-#540 := [unit-resolution #632 #539]: #637
-#615 := (or #592 #498 #638)
-#444 := [def-axiom]: #615
-#542 := [unit-resolution #444 #540 #574]: #498
-#607 := (or #489 #633)
-#613 := [def-axiom]: #607
-#543 := [unit-resolution #613 #542]: #633
-#357 := (or #362 #360)
-#631 := [def-axiom]: #357
-#544 := [unit-resolution #631 #539]: #360
-#590 := (or #620 #361 #630)
-#591 := [def-axiom]: #590
-#545 := [unit-resolution #591 #544 #543]: #620
-#338 := (or #335 #148)
-#326 := (or #335 #148 #246)
-#337 := [def-axiom]: #326
-#266 := [unit-resolution #337 #156]: #338
-#546 := [unit-resolution #266 #560]: #335
-#541 := (or #139 #324)
-#646 := (or #640 #139 #324)
-#282 := [def-axiom]: #646
-#547 := [unit-resolution #282 #567]: #541
-#533 := [unit-resolution #547 #546]: #324
-#612 := (or #489 #336)
-#606 := [def-axiom]: #612
-#529 := [unit-resolution #606 #542]: #336
-#644 := (or #660 #340 #658)
-#645 := [def-axiom]: #644
-#530 := [unit-resolution #645 #529 #533]: #658
-#583 := (or #587 #619 #656)
-#584 := [def-axiom]: #583
-#531 := [unit-resolution #584 #530 #545]: #587
-[unit-resolution #610 #670 #531]: false
+decl f9 :: S2
+#42 := f9
+#50 := (f4 f9 f10)
+#318 := (f3 #50 f12)
+decl f1 :: S1
+#4 := f1
+#655 := (= f1 #318)
+#253 := (f3 f10 f12)
+#632 := (= f1 #253)
+#629 := (not #632)
+#343 := (f3 f9 f12)
+#359 := (= f1 #343)
+#360 := (not #359)
+#618 := (or #360 #629)
+#619 := (not #618)
+#615 := (iff #619 #655)
+#586 := (not #615)
+decl f11 :: S2
+#44 := f11
+#338 := (f3 f11 f12)
+#335 := (= f1 #338)
+#339 := (not #335)
+#488 := (or #339 #629)
+#497 := (not #488)
+#45 := (f4 f10 f11)
+#650 := (f3 #45 f12)
+#636 := (= f1 #650)
+#498 := (iff #497 #636)
+#591 := (not #498)
+#571 := [hypothesis]: #591
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#10 := (f4 #8 #9)
+#12 := (f3 #10 #11)
+#663 := (pattern #12)
+#16 := (f3 #9 #11)
+#82 := (= f1 #16)
+#180 := (not #82)
+#14 := (f3 #8 #11)
+#79 := (= f1 #14)
+#179 := (not #79)
+#163 := (or #179 #180)
+#164 := (not #163)
+#76 := (= f1 #12)
+#181 := (iff #76 #164)
+#664 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #663) #181)
+#184 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #181)
+#667 := (iff #184 #664)
+#665 := (iff #181 #181)
+#666 := [refl]: #665
+#668 := [quant-intro #666]: #667
+#85 := (and #79 #82)
+#88 := (iff #76 #85)
+#91 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #88)
+#185 := (iff #91 #184)
+#182 := (iff #88 #181)
+#165 := (iff #85 #164)
+#166 := [rewrite]: #165
+#183 := [monotonicity #166]: #182
+#186 := [quant-intro #183]: #185
+#169 := (~ #91 #91)
+#167 := (~ #88 #88)
+#168 := [refl]: #167
+#170 := [nnf-pos #168]: #169
+#17 := (= #16 f1)
+#15 := (= #14 f1)
+#18 := (and #15 #17)
+#13 := (= #12 f1)
+#19 := (iff #13 #18)
+#20 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #19)
+#92 := (iff #20 #91)
+#89 := (iff #19 #88)
+#86 := (iff #18 #85)
+#83 := (iff #17 #82)
+#84 := [rewrite]: #83
+#80 := (iff #15 #79)
+#81 := [rewrite]: #80
+#87 := [monotonicity #81 #84]: #86
+#77 := (iff #13 #76)
+#78 := [rewrite]: #77
+#90 := [monotonicity #78 #87]: #89
+#93 := [quant-intro #90]: #92
+#75 := [asserted]: #20
+#96 := [mp #75 #93]: #91
+#154 := [mp~ #96 #170]: #91
+#187 := [mp #154 #186]: #184
+#669 := [mp #187 #668]: #664
+#310 := (not #664)
+#502 := (or #310 #498)
+#604 := (or #629 #339)
+#486 := (not #604)
+#487 := (iff #636 #486)
+#503 := (or #310 #487)
+#597 := (iff #503 #502)
+#598 := (iff #502 #502)
+#585 := [rewrite]: #598
+#500 := (iff #487 #498)
+#596 := (iff #636 #497)
+#499 := (iff #596 #498)
+#492 := [rewrite]: #499
+#481 := (iff #487 #596)
+#592 := (iff #486 #497)
+#447 := (iff #604 #488)
+#595 := [rewrite]: #447
+#593 := [monotonicity #595]: #592
+#496 := [monotonicity #593]: #481
+#501 := [trans #496 #492]: #500
+#594 := [monotonicity #501]: #597
+#587 := [trans #594 #585]: #597
+#504 := [quant-inst #43 #44 #47]: #503
+#579 := [mp #504 #587]: #502
+#572 := [unit-resolution #579 #669 #571]: false
+#573 := [lemma #572]: #498
+#637 := (not #636)
+#361 := (or #360 #637)
+#347 := (not #361)
+#46 := (f4 f9 #45)
+#48 := (f3 #46 f12)
+#134 := (= f1 #48)
+#147 := (not #134)
+#574 := [hypothesis]: #147
+#575 := (or #134 #361)
+#362 := (iff #134 #347)
+#633 := (or #310 #362)
+#355 := [quant-inst #42 #45 #47]: #633
+#570 := [unit-resolution #355 #669]: #362
+#345 := (not #362)
+#346 := (or #345 #134 #361)
+#348 := [def-axiom]: #346
+#561 := [unit-resolution #348 #570]: #575
+#562 := [unit-resolution #561 #574]: #361
+#601 := (or #310 #615)
+#620 := (iff #655 #619)
+#617 := (or #310 #620)
+#622 := (iff #617 #601)
+#465 := (iff #601 #601)
+#466 := [rewrite]: #465
+#616 := (iff #620 #615)
+#621 := [rewrite]: #616
+#464 := [monotonicity #621]: #622
+#608 := [trans #464 #466]: #622
+#623 := [quant-inst #42 #43 #47]: #617
+#609 := [mp #623 #608]: #601
+#564 := [unit-resolution #609 #669]: #615
+#550 := (or #586 #619)
+#657 := (not #655)
+#323 := (or #339 #657)
+#659 := (not #323)
+#51 := (f4 #50 f11)
+#52 := (f3 #51 f12)
+#138 := (= f1 #52)
+#333 := (or #138 #134)
+#148 := (iff #138 #147)
+#53 := (= #52 f1)
+#49 := (= #48 f1)
+#54 := (iff #49 #53)
+#55 := (not #54)
+#151 := (iff #55 #148)
+#141 := (iff #134 #138)
+#144 := (not #141)
+#149 := (iff #144 #148)
+#150 := [rewrite]: #149
+#145 := (iff #55 #144)
+#142 := (iff #54 #141)
+#139 := (iff #53 #138)
+#140 := [rewrite]: #139
+#136 := (iff #49 #134)
+#137 := [rewrite]: #136
+#143 := [monotonicity #137 #140]: #142
+#146 := [monotonicity #143]: #145
+#152 := [trans #146 #150]: #151
+#133 := [asserted]: #55
+#155 := [mp #133 #152]: #148
+#245 := (not #148)
+#332 := (or #138 #134 #245)
+#246 := [def-axiom]: #332
+#247 := [unit-resolution #246 #155]: #333
+#565 := [unit-resolution #247 #574]: #138
+#334 := (not #138)
+#563 := (or #334 #659)
+#656 := (iff #138 #659)
+#315 := (or #310 #656)
+#312 := (or #657 #339)
+#444 := (not #312)
+#651 := (iff #138 #444)
+#653 := (or #310 #651)
+#654 := (iff #653 #315)
+#638 := (iff #315 #315)
+#299 := [rewrite]: #638
+#662 := (iff #651 #656)
+#660 := (iff #444 #659)
+#324 := (iff #312 #323)
+#658 := [rewrite]: #324
+#661 := [monotonicity #658]: #660
+#652 := [monotonicity #661]: #662
+#295 := [monotonicity #652]: #654
+#300 := [trans #295 #299]: #654
+#311 := [quant-inst #50 #44 #47]: #653
+#301 := [mp #311 #300]: #315
+#566 := [unit-resolution #301 #669]: #656
+#639 := (not #656)
+#646 := (or #639 #334 #659)
+#648 := [def-axiom]: #646
+#567 := [unit-resolution #648 #566]: #563
+#547 := [unit-resolution #567 #565]: #659
+#641 := (or #323 #655)
+#642 := [def-axiom]: #641
+#548 := [unit-resolution #642 #547]: #655
+#580 := (or #586 #619 #657)
+#581 := [def-axiom]: #580
+#551 := [unit-resolution #581 #548]: #550
+#552 := [unit-resolution #551 #564]: #619
+#610 := (or #618 #359)
+#576 := [def-axiom]: #610
+#553 := [unit-resolution #576 #552]: #359
+#635 := (or #347 #360 #637)
+#344 := [def-axiom]: #635
+#554 := [unit-resolution #344 #553 #562]: #637
+#302 := (or #323 #335)
+#640 := [def-axiom]: #302
+#555 := [unit-resolution #640 #547]: #335
+#578 := (or #618 #632)
+#588 := [def-axiom]: #578
+#556 := [unit-resolution #588 #552]: #632
+#613 := (or #497 #339 #629)
+#607 := [def-axiom]: #613
+#557 := [unit-resolution #607 #556 #555]: #497
+#445 := (or #591 #488 #636)
+#446 := [def-axiom]: #445
+#558 := [unit-resolution #446 #557 #554 #573]: false
+#559 := [lemma #558]: #134
+#549 := (or #147 #347)
+#626 := (or #345 #147 #347)
+#627 := [def-axiom]: #626
+#560 := [unit-resolution #627 #570]: #549
+#538 := [unit-resolution #560 #559]: #347
+#634 := (or #361 #636)
+#631 := [def-axiom]: #634
+#539 := [unit-resolution #631 #538]: #636
+#614 := (or #591 #497 #637)
+#443 := [def-axiom]: #614
+#541 := [unit-resolution #443 #539 #573]: #497
+#606 := (or #488 #632)
+#612 := [def-axiom]: #606
+#542 := [unit-resolution #612 #541]: #632
+#356 := (or #361 #359)
+#630 := [def-axiom]: #356
+#543 := [unit-resolution #630 #538]: #359
+#589 := (or #619 #360 #629)
+#590 := [def-axiom]: #589
+#544 := [unit-resolution #590 #543 #542]: #619
+#337 := (or #334 #147)
+#325 := (or #334 #147 #245)
+#336 := [def-axiom]: #325
+#265 := [unit-resolution #336 #155]: #337
+#545 := [unit-resolution #265 #559]: #334
+#540 := (or #138 #323)
+#645 := (or #639 #138 #323)
+#281 := [def-axiom]: #645
+#546 := [unit-resolution #281 #566]: #540
+#532 := [unit-resolution #546 #545]: #323
+#611 := (or #488 #335)
+#605 := [def-axiom]: #611
+#528 := [unit-resolution #605 #541]: #335
+#643 := (or #659 #339 #657)
+#644 := [def-axiom]: #643
+#529 := [unit-resolution #644 #528 #532]: #657
+#582 := (or #586 #618 #655)
+#583 := [def-axiom]: #582
+#530 := [unit-resolution #583 #529 #544]: #586
+[unit-resolution #609 #669 #530]: false
 unsat
 2b2ce778241d0cd9017eb9658fd16ee31fe3f28e 18 0
 #2 := false