# HG changeset patch # User boehmes # Date 1292781321 -3600 # Node ID a4d1b5eef12e144d8509c67426ff505b287e5111 # Parent 679118e35378f95c5c66f3bb675e85339b4367c2 updated SMT certificates diff -r 679118e35378 -r a4d1b5eef12e src/HOL/Boogie/Examples/Boogie_Dijkstra.certs --- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs Sun Dec 19 18:55:21 2010 +0100 @@ -1,4 +1,4 @@ -2bcca4894d12c21351a258c93ec6b00e790bb1de 7195 0 +b9c818fc8db5c62ae4864b1c933f204656ce6c70 7184 0 #2 := false decl f13 :: (-> S5 S3 Int) decl f22 :: S3 @@ -9,883 +9,878 @@ decl f10 :: S3 #56 := f10 #99 := (f13 f14 f10) -#7797 := (= #99 #174) -#7825 := (= #174 #99) -#6086 := (= f22 f10) -#6088 := (= f10 f22) +#7788 := (= #99 #174) +#7816 := (= #174 #99) +#6077 := (= f22 f10) +#6079 := (= f10 f22) decl f3 :: (-> S2 S3 S1) decl ?v1!7 :: (-> S3 S3) -#6069 := (?v1!7 f22) +#6060 := (?v1!7 f22) decl f15 :: S2 #104 := f15 -#6081 := (f3 f15 #6069) +#6072 := (f3 f15 #6060) decl f1 :: S1 #4 := f1 -#6082 := (= f1 #6081) -#6083 := (not #6082) +#6073 := (= f1 #6072) +#6074 := (not #6073) #44 := 0::Int decl f9 :: (-> S4 Int) decl f5 :: (-> S3 S3 S4) -#6074 := (f5 #6069 f22) -#6075 := (f9 #6074) -#1208 := -1::Int -#6076 := (* -1::Int #6075) -#6070 := (f13 f14 #6069) -#6071 := (* -1::Int #6070) -#6077 := (+ #6071 #6076) -#6078 := (+ #174 #6077) -#6079 := (= #6078 0::Int) -#6080 := (not #6079) -#6072 := (+ #174 #6071) -#6073 := (<= #6072 0::Int) -#6091 := (or #6073 #6080 #6083) +#6065 := (f5 #6060 f22) +#6066 := (f9 #6065) +#1199 := -1::Int +#6067 := (* -1::Int #6066) +#6061 := (f13 f14 #6060) +#6062 := (* -1::Int #6061) +#6068 := (+ #6062 #6067) +#6069 := (+ #174 #6068) +#6070 := (= #6069 0::Int) +#6071 := (not #6070) +#6063 := (+ #174 #6062) +#6064 := (<= #6063 0::Int) +#6082 := (or #6064 #6071 #6074) decl f24 :: (-> S3 Int) decl ?v0!15 :: S3 -#2273 := ?v0!15 -#2274 := (f24 ?v0!15) -#2275 := (>= #2274 0::Int) -#2276 := (not #2275) +#2264 := ?v0!15 +#2265 := (f24 ?v0!15) +#2266 := (>= #2265 0::Int) +#2267 := (not #2266) decl ?v0!20 :: S3 -#2346 := ?v0!20 +#2337 := ?v0!20 #12 := (:var 0 S3) -#2350 := (f5 #12 ?v0!20) -#4454 := (pattern #2350) -#189 := (f24 #12) -#4394 := (pattern #189) +#2341 := (f5 #12 ?v0!20) +#4445 := (pattern #2341) +#188 := (f24 #12) +#4385 := (pattern #188) decl f23 :: S2 #179 := f23 -#199 := (f3 f23 #12) -#4420 := (pattern #199) -#2351 := (f9 #2350) -#2347 := (f24 ?v0!20) -#2348 := (* -1::Int #2347) -#2950 := (+ #2348 #2351) -#2951 := (+ #189 #2950) -#2954 := (= #2951 0::Int) -#3516 := (not #2954) -#2349 := (+ #189 #2348) -#2354 := (>= #2349 0::Int) -#807 := (= f1 #199) -#813 := (not #807) -#3517 := (or #813 #2354 #3516) -#4455 := (forall (vars (?v1 S3)) (:pat #4420 #4394 #4454) #3517) -#4460 := (not #4455) +#198 := (f3 f23 #12) +#4411 := (pattern #198) +#2342 := (f9 #2341) +#2338 := (f24 ?v0!20) +#2339 := (* -1::Int #2338) +#2941 := (+ #2339 #2342) +#2942 := (+ #188 #2941) +#2945 := (= #2942 0::Int) +#3507 := (not #2945) +#2340 := (+ #188 #2339) +#2345 := (>= #2340 0::Int) +#798 := (= f1 #198) +#804 := (not #798) +#3508 := (or #804 #2345 #3507) +#4446 := (forall (vars (?v1 S3)) (:pat #4411 #4385 #4445) #3508) +#4451 := (not #4446) #23 := (:var 1 S3) #81 := (f5 #12 #23) -#4249 := (pattern #81) -#211 := (f24 #23) -#1503 := (* -1::Int #211) -#1504 := (+ #189 #1503) +#4240 := (pattern #81) +#210 := (f24 #23) +#1494 := (* -1::Int #210) +#1495 := (+ #188 #1494) #82 := (f9 #81) -#1534 := (+ #82 #1504) -#1532 := (>= #1534 0::Int) -#1231 := (* -1::Int #82) +#1525 := (+ #82 #1495) +#1523 := (>= #1525 0::Int) +#1222 := (* -1::Int #82) decl f8 :: Int #45 := f8 -#1234 := (+ f8 #1231) -#1235 := (<= #1234 0::Int) -#3508 := (or #813 #1235 #1532) -#4446 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3508) -#4451 := (not #4446) -#2926 := (= f10 ?v0!20) -#2358 := (+ f8 #2348) -#2359 := (<= #2358 0::Int) -#4463 := (or #2359 #2926 #4451 #4460) -#4466 := (not #4463) +#1225 := (+ f8 #1222) +#1226 := (<= #1225 0::Int) +#3499 := (or #804 #1226 #1523) +#4437 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3499) +#4442 := (not #4437) +#2917 := (= f10 ?v0!20) +#2349 := (+ f8 #2339) +#2350 := (<= #2349 0::Int) +#4454 := (or #2350 #2917 #4442 #4451) +#4457 := (not #4454) decl ?v0!19 :: S3 -#2316 := ?v0!19 +#2307 := ?v0!19 decl ?v1!18 :: S3 -#2315 := ?v1!18 -#2321 := (f5 ?v1!18 ?v0!19) -#2322 := (f9 #2321) -#2325 := (* -1::Int #2322) -#2319 := (f24 ?v1!18) -#2912 := (* -1::Int #2319) -#2913 := (+ #2912 #2325) -#2317 := (f24 ?v0!19) -#2914 := (+ #2317 #2913) -#2915 := (<= #2914 0::Int) -#2329 := (f3 f23 ?v1!18) -#2330 := (= f1 #2329) -#3471 := (not #2330) -#2326 := (+ f8 #2325) -#2327 := (<= #2326 0::Int) -#3486 := (or #2327 #3471 #2915) -#3491 := (not #3486) -#4469 := (or #3491 #4466) -#4472 := (not #4469) -#4437 := (pattern #189 #211) -#1502 := (>= #1504 0::Int) -#208 := (f3 f23 #23) -#827 := (= f1 #208) -#3448 := (not #827) -#3463 := (or #807 #3448 #1502) -#4438 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4437) #3463) -#4443 := (not #4438) -#4475 := (or #4443 #4472) -#4478 := (not #4475) +#2306 := ?v1!18 +#2312 := (f5 ?v1!18 ?v0!19) +#2313 := (f9 #2312) +#2316 := (* -1::Int #2313) +#2310 := (f24 ?v1!18) +#2903 := (* -1::Int #2310) +#2904 := (+ #2903 #2316) +#2308 := (f24 ?v0!19) +#2905 := (+ #2308 #2904) +#2906 := (<= #2905 0::Int) +#2320 := (f3 f23 ?v1!18) +#2321 := (= f1 #2320) +#3462 := (not #2321) +#2317 := (+ f8 #2316) +#2318 := (<= #2317 0::Int) +#3477 := (or #2318 #3462 #2906) +#3482 := (not #3477) +#4460 := (or #3482 #4457) +#4463 := (not #4460) +#4428 := (pattern #188 #210) +#1493 := (>= #1495 0::Int) +#207 := (f3 f23 #23) +#818 := (= f1 #207) +#3439 := (not #818) +#3454 := (or #798 #3439 #1493) +#4429 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4428) #3454) +#4434 := (not #4429) +#4466 := (or #4434 #4463) +#4469 := (not #4466) decl ?v1!16 :: S3 -#2288 := ?v1!16 -#2292 := (f24 ?v1!16) -#2886 := (* -1::Int #2292) +#2279 := ?v1!16 +#2283 := (f24 ?v1!16) +#2877 := (* -1::Int #2283) decl ?v0!17 :: S3 -#2289 := ?v0!17 -#2290 := (f24 ?v0!17) -#2887 := (+ #2290 #2886) -#2888 := (<= #2887 0::Int) -#2297 := (f3 f23 ?v1!16) -#2298 := (= f1 #2297) -#2295 := (f3 f23 ?v0!17) -#2296 := (= f1 #2295) -#3425 := (not #2296) -#3440 := (or #3425 #2298 #2888) -#3445 := (not #3440) -#4481 := (or #3445 #4478) -#4484 := (not #4481) -#1493 := (>= #189 0::Int) -#4429 := (forall (vars (?v0 S3)) (:pat #4394) #1493) -#4434 := (not #4429) -#4487 := (or #4434 #4484) +#2280 := ?v0!17 +#2281 := (f24 ?v0!17) +#2878 := (+ #2281 #2877) +#2879 := (<= #2878 0::Int) +#2288 := (f3 f23 ?v1!16) +#2289 := (= f1 #2288) +#2286 := (f3 f23 ?v0!17) +#2287 := (= f1 #2286) +#3416 := (not #2287) +#3431 := (or #3416 #2289 #2879) +#3436 := (not #3431) +#4472 := (or #3436 #4469) +#4475 := (not #4472) +#1484 := (>= #188 0::Int) +#4420 := (forall (vars (?v0 S3)) (:pat #4385) #1484) +#4425 := (not #4420) +#4478 := (or #4425 #4475) decl f6 :: (-> S4 S3) decl f7 :: (-> S4 S3) -#5995 := (f5 f22 f22) -#7211 := (f7 #5995) -#14211 := (f5 #7211 ?v0!20) -#24392 := (f7 #14211) -#14774 := (?v1!7 ?v0!20) -#24669 := (f5 #14774 #24392) -#25042 := (f6 #24669) -#26213 := (f3 f15 #25042) -#26214 := (= f1 #26213) -#14786 := (f3 f15 #14774) -#27706 := (= #14786 #26213) -#27703 := (= #26213 #14786) -#29051 := (= #25042 #14774) -#14779 := (f5 #14774 ?v0!20) -#19038 := (f6 #14779) -#26818 := (= #19038 #14774) -#19043 := (= #14774 #19038) +#5986 := (f5 f22 f22) +#7202 := (f7 #5986) +#14202 := (f5 #7202 ?v0!20) +#24383 := (f7 #14202) +#14765 := (?v1!7 ?v0!20) +#24660 := (f5 #14765 #24383) +#25033 := (f6 #24660) +#26204 := (f3 f15 #25033) +#26205 := (= f1 #26204) +#14777 := (f3 f15 #14765) +#27697 := (= #14777 #26204) +#27694 := (= #26204 #14777) +#29042 := (= #25033 #14765) +#14770 := (f5 #14765 ?v0!20) +#19029 := (f6 #14770) +#26809 := (= #19029 #14765) +#19034 := (= #14765 #19029) #37 := (f5 #23 #12) -#4193 := (pattern #37) +#4184 := (pattern #37) #41 := (f6 #37) -#344 := (= #23 #41) -#4200 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #344) -#348 := (forall (vars (?v0 S3) (?v1 S3)) #344) -#4203 := (iff #348 #4200) -#4201 := (iff #344 #344) -#4202 := [refl]: #4201 -#4204 := [quant-intro #4202]: #4203 -#1848 := (~ #348 #348) -#1878 := (~ #344 #344) -#1879 := [refl]: #1878 -#1849 := [nnf-pos #1879]: #1848 +#343 := (= #23 #41) +#4191 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #343) +#347 := (forall (vars (?v0 S3) (?v1 S3)) #343) +#4194 := (iff #347 #4191) +#4192 := (iff #343 #343) +#4193 := [refl]: #4192 +#4195 := [quant-intro #4193]: #4194 +#1839 := (~ #347 #347) +#1869 := (~ #343 #343) +#1870 := [refl]: #1869 +#1840 := [nnf-pos #1870]: #1839 #42 := (= #41 #23) #43 := (forall (vars (?v0 S3) (?v1 S3)) #42) -#349 := (iff #43 #348) -#346 := (iff #42 #344) -#347 := [rewrite]: #346 -#350 := [quant-intro #347]: #349 -#343 := [asserted]: #43 -#353 := [mp #343 #350]: #348 -#1880 := [mp~ #353 #1849]: #348 -#4205 := [mp #1880 #4204]: #4200 -#6829 := (not #4200) -#8630 := (or #6829 #19043) -#13594 := [quant-inst #14774 #2346]: #8630 -#26774 := [unit-resolution #13594 #4205]: #19043 -#26816 := [symm #26774]: #26818 -#26826 := (= #25042 #19038) -#26823 := (= #24669 #14779) -#27255 := (= #24392 ?v0!20) -#19042 := (f7 #14779) -#25094 := (= #19042 ?v0!20) -#19037 := (= ?v0!20 #19042) +#348 := (iff #43 #347) +#345 := (iff #42 #343) +#346 := [rewrite]: #345 +#349 := [quant-intro #346]: #348 +#342 := [asserted]: #43 +#352 := [mp #342 #349]: #347 +#1871 := [mp~ #352 #1840]: #347 +#4196 := [mp #1871 #4195]: #4191 +#6820 := (not #4191) +#8621 := (or #6820 #19034) +#13585 := [quant-inst #14765 #2337]: #8621 +#26765 := [unit-resolution #13585 #4196]: #19034 +#26807 := [symm #26765]: #26809 +#26817 := (= #25033 #19029) +#26814 := (= #24660 #14770) +#27246 := (= #24383 ?v0!20) +#19033 := (f7 #14770) +#25085 := (= #19033 ?v0!20) +#19028 := (= ?v0!20 #19033) #38 := (f7 #37) -#336 := (= #12 #38) -#4194 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #336) -#340 := (forall (vars (?v0 S3) (?v1 S3)) #336) -#4197 := (iff #340 #4194) -#4195 := (iff #336 #336) -#4196 := [refl]: #4195 -#4198 := [quant-intro #4196]: #4197 -#1846 := (~ #340 #340) -#1875 := (~ #336 #336) -#1876 := [refl]: #1875 -#1847 := [nnf-pos #1876]: #1846 +#335 := (= #12 #38) +#4185 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #335) +#339 := (forall (vars (?v0 S3) (?v1 S3)) #335) +#4188 := (iff #339 #4185) +#4186 := (iff #335 #335) +#4187 := [refl]: #4186 +#4189 := [quant-intro #4187]: #4188 +#1837 := (~ #339 #339) +#1866 := (~ #335 #335) +#1867 := [refl]: #1866 +#1838 := [nnf-pos #1867]: #1837 #39 := (= #38 #12) #40 := (forall (vars (?v0 S3) (?v1 S3)) #39) -#341 := (iff #40 #340) -#338 := (iff #39 #336) -#339 := [rewrite]: #338 -#342 := [quant-intro #339]: #341 -#335 := [asserted]: #40 -#345 := [mp #335 #342]: #340 -#1877 := [mp~ #345 #1847]: #340 -#4199 := [mp #1877 #4198]: #4194 -#6824 := (not #4194) -#19044 := (or #6824 #19037) -#19045 := [quant-inst #14774 #2346]: #19044 -#25093 := [unit-resolution #19045 #4199]: #19037 -#25095 := [symm #25093]: #25094 -#26795 := (= #24392 #19042) -#23180 := (f5 #7211 #19042) -#23299 := (f7 #23180) -#26807 := (= #23299 #19042) -#23305 := (= #19042 #23299) -#26717 := (or #6824 #23305) -#26720 := [quant-inst #7211 #19042]: #26717 -#26803 := [unit-resolution #26720 #4199]: #23305 -#26808 := [symm #26803]: #26807 -#26804 := (= #24392 #23299) -#26801 := (= #23299 #24392) -#26799 := (= #23180 #14211) -#14131 := (f5 f22 ?v0!20) -#26773 := (= #14131 #14211) -#24028 := (= #14211 #14131) -#7784 := (= #7211 f22) -#7212 := (= f22 #7211) -#7263 := (or #6824 #7212) -#7264 := [quant-inst #170 #170]: #7263 -#7789 := [unit-resolution #7264 #4199]: #7212 -#7790 := [symm #7789]: #7784 -#24029 := [monotonicity #7790]: #24028 -#26715 := [symm #24029]: #26773 -#26777 := (= #23180 #14131) -#26776 := (= #14131 #23180) -#26752 := [monotonicity #7789 #25093]: #26776 -#26778 := [symm #26752]: #26777 -#26802 := [trans #26778 #26715]: #26799 -#26805 := [monotonicity #26802]: #26801 -#26806 := [symm #26805]: #26804 -#26822 := [trans #26806 #26808]: #26795 -#26796 := [trans #26822 #25095]: #27255 -#26824 := [monotonicity #26796]: #26823 -#26817 := [monotonicity #26824]: #26826 -#26819 := [trans #26817 #26816]: #29051 -#26814 := [monotonicity #26819]: #27703 -#26828 := [symm #26814]: #27706 -#14787 := (= f1 #14786) -#14788 := (not #14787) -#14780 := (f9 #14779) -#14781 := (* -1::Int #14780) -#14775 := (f13 f14 #14774) -#14776 := (* -1::Int #14775) -#14782 := (+ #14776 #14781) -#14074 := (f13 f14 ?v0!20) -#14783 := (+ #14074 #14782) -#14784 := (= #14783 0::Int) -#14785 := (not #14784) -#14777 := (+ #14074 #14776) -#14778 := (<= #14777 0::Int) -#14794 := (or #14778 #14785 #14788) -#14797 := (not #14794) -#14115 := (* -1::Int #14074) -#14791 := (+ f8 #14115) -#14792 := (<= #14791 0::Int) -#21435 := (not #14792) -#2360 := (not #2359) -#19783 := [hypothesis]: #2360 -#14116 := (+ #2347 #14115) -#19567 := (>= #14116 0::Int) -#14085 := (= #2347 #14074) -#14132 := (f9 #14131) -#14150 := (+ #14115 #14132) -#14151 := (+ #174 #14150) -#14152 := (>= #14151 0::Int) -#14136 := (* -1::Int #14132) -#14140 := (+ f8 #14136) -#14141 := (<= #14140 0::Int) -#14183 := (or #14141 #14152) -#4490 := (not #4487) -#1453 := (* -1::Int #174) -#5913 := (+ #99 #1453) -#7798 := (<= #5913 0::Int) -#27734 := (or #6073 #2359) -#25047 := (= #14774 #25042) -#23337 := (or #6829 #25047) -#23338 := [quant-inst #14774 #24392]: #23337 -#28984 := [unit-resolution #23338 #4205]: #25047 -#29062 := [symm #28984]: #29051 -#27698 := [monotonicity #29062]: #27703 -#27718 := [symm #27698]: #27706 -#6118 := (not #6073) -#10074 := [hypothesis]: #6118 -#23174 := (or #14152 #6073) -#11114 := (or #2275 #6073) -#7536 := (f13 f14 ?v0!15) -#7757 := (>= #7536 0::Int) +#340 := (iff #40 #339) +#337 := (iff #39 #335) +#338 := [rewrite]: #337 +#341 := [quant-intro #338]: #340 +#334 := [asserted]: #40 +#344 := [mp #334 #341]: #339 +#1868 := [mp~ #344 #1838]: #339 +#4190 := [mp #1868 #4189]: #4185 +#6815 := (not #4185) +#19035 := (or #6815 #19028) +#19036 := [quant-inst #14765 #2337]: #19035 +#25084 := [unit-resolution #19036 #4190]: #19028 +#25086 := [symm #25084]: #25085 +#26786 := (= #24383 #19033) +#23171 := (f5 #7202 #19033) +#23290 := (f7 #23171) +#26798 := (= #23290 #19033) +#23296 := (= #19033 #23290) +#26708 := (or #6815 #23296) +#26711 := [quant-inst #7202 #19033]: #26708 +#26794 := [unit-resolution #26711 #4190]: #23296 +#26799 := [symm #26794]: #26798 +#26795 := (= #24383 #23290) +#26792 := (= #23290 #24383) +#26790 := (= #23171 #14202) +#14122 := (f5 f22 ?v0!20) +#26764 := (= #14122 #14202) +#24019 := (= #14202 #14122) +#7775 := (= #7202 f22) +#7203 := (= f22 #7202) +#7254 := (or #6815 #7203) +#7255 := [quant-inst #170 #170]: #7254 +#7780 := [unit-resolution #7255 #4190]: #7203 +#7781 := [symm #7780]: #7775 +#24020 := [monotonicity #7781]: #24019 +#26706 := [symm #24020]: #26764 +#26768 := (= #23171 #14122) +#26767 := (= #14122 #23171) +#26743 := [monotonicity #7780 #25084]: #26767 +#26769 := [symm #26743]: #26768 +#26793 := [trans #26769 #26706]: #26790 +#26796 := [monotonicity #26793]: #26792 +#26797 := [symm #26796]: #26795 +#26813 := [trans #26797 #26799]: #26786 +#26787 := [trans #26813 #25086]: #27246 +#26815 := [monotonicity #26787]: #26814 +#26808 := [monotonicity #26815]: #26817 +#26810 := [trans #26808 #26807]: #29042 +#26805 := [monotonicity #26810]: #27694 +#26819 := [symm #26805]: #27697 +#14778 := (= f1 #14777) +#14779 := (not #14778) +#14771 := (f9 #14770) +#14772 := (* -1::Int #14771) +#14766 := (f13 f14 #14765) +#14767 := (* -1::Int #14766) +#14773 := (+ #14767 #14772) +#14065 := (f13 f14 ?v0!20) +#14774 := (+ #14065 #14773) +#14775 := (= #14774 0::Int) +#14776 := (not #14775) +#14768 := (+ #14065 #14767) +#14769 := (<= #14768 0::Int) +#14785 := (or #14769 #14776 #14779) +#14788 := (not #14785) +#14106 := (* -1::Int #14065) +#14782 := (+ f8 #14106) +#14783 := (<= #14782 0::Int) +#21426 := (not #14783) +#2351 := (not #2350) +#19774 := [hypothesis]: #2351 +#14107 := (+ #2338 #14106) +#19558 := (>= #14107 0::Int) +#14076 := (= #2338 #14065) +#14123 := (f9 #14122) +#14141 := (+ #14106 #14123) +#14142 := (+ #174 #14141) +#14143 := (>= #14142 0::Int) +#14127 := (* -1::Int #14123) +#14131 := (+ f8 #14127) +#14132 := (<= #14131 0::Int) +#14174 := (or #14132 #14143) +#4481 := (not #4478) +#1444 := (* -1::Int #174) +#5904 := (+ #99 #1444) +#7789 := (<= #5904 0::Int) +#27725 := (or #6064 #2350) +#25038 := (= #14765 #25033) +#23328 := (or #6820 #25038) +#23329 := [quant-inst #14765 #24383]: #23328 +#28975 := [unit-resolution #23329 #4196]: #25038 +#29053 := [symm #28975]: #29042 +#27689 := [monotonicity #29053]: #27694 +#27709 := [symm #27689]: #27697 +#6109 := (not #6064) +#10065 := [hypothesis]: #6109 +#23165 := (or #14143 #6064) +#11105 := (or #2266 #6064) +#7527 := (f13 f14 ?v0!15) +#7748 := (>= #7527 0::Int) #101 := (f13 f14 #12) -#4273 := (pattern #101) -#1736 := (>= #101 0::Int) -#4274 := (forall (vars (?v0 S3)) (:pat #4273) #1736) -#4493 := (or #2276 #4490) -#4496 := (not #4493) -#203 := (f24 f10) -#204 := (= #203 0::Int) -#1490 := (not #204) -#4499 := (or #1490 #4496) -#4502 := (not #4499) -#4505 := (or #1490 #4502) -#4508 := (not #4505) -#793 := (= #101 #189) -#814 := (or #793 #813) -#4421 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4420) #814) -#4426 := (not #4421) -#4511 := (or #4426 #4508) -#4514 := (not #4511) +#4264 := (pattern #101) +#1727 := (>= #101 0::Int) +#4265 := (forall (vars (?v0 S3)) (:pat #4264) #1727) +#4484 := (or #2267 #4481) +#4487 := (not #4484) +#202 := (f24 f10) +#203 := (= #202 0::Int) +#1481 := (not #203) +#4490 := (or #1481 #4487) +#4493 := (not #4490) +#4496 := (or #1481 #4493) +#4499 := (not #4496) +#784 := (= #101 #188) +#805 := (or #784 #804) +#4412 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4411) #805) +#4417 := (not #4412) +#4502 := (or #4417 #4499) +#4505 := (not #4502) decl ?v0!14 :: S3 -#2248 := ?v0!14 -#2253 := (f13 f14 ?v0!14) -#2252 := (f24 ?v0!14) -#2858 := (= #2252 #2253) -#2249 := (f3 f23 ?v0!14) -#2250 := (= f1 #2249) -#2251 := (not #2250) -#2864 := (or #2251 #2858) -#2869 := (not #2864) -#4517 := (or #2869 #4514) -#4520 := (not #4517) -#1478 := (* -1::Int #189) -#1479 := (+ #101 #1478) -#1477 := (>= #1479 0::Int) -#4412 := (forall (vars (?v0 S3)) (:pat #4273 #4394) #1477) -#4417 := (not #4412) -#4523 := (or #4417 #4520) -#4526 := (not #4523) +#2239 := ?v0!14 +#2244 := (f13 f14 ?v0!14) +#2243 := (f24 ?v0!14) +#2849 := (= #2243 #2244) +#2240 := (f3 f23 ?v0!14) +#2241 := (= f1 #2240) +#2242 := (not #2241) +#2855 := (or #2242 #2849) +#2860 := (not #2855) +#4508 := (or #2860 #4505) +#4511 := (not #4508) +#1469 := (* -1::Int #188) +#1470 := (+ #101 #1469) +#1468 := (>= #1470 0::Int) +#4403 := (forall (vars (?v0 S3)) (:pat #4264 #4385) #1468) +#4408 := (not #4403) +#4514 := (or #4408 #4511) +#4517 := (not #4514) decl ?v0!13 :: S3 -#2230 := ?v0!13 -#2233 := (f13 f14 ?v0!13) -#2848 := (* -1::Int #2233) -#2231 := (f24 ?v0!13) -#2849 := (+ #2231 #2848) -#2850 := (<= #2849 0::Int) -#2855 := (not #2850) -#4529 := (or #2855 #4526) -#4532 := (not #4529) -#183 := (f5 f22 #12) -#4395 := (pattern #183) -#184 := (f9 #183) -#1621 := (+ #184 #1478) -#1622 := (+ #174 #1621) -#1623 := (= #1622 0::Int) -#1447 := (* -1::Int #184) -#1454 := (+ #1453 #1447) -#1455 := (+ #101 #1454) -#1456 := (<= #1455 0::Int) -#1448 := (+ f8 #1447) -#1449 := (<= #1448 0::Int) -#3417 := (or #1449 #1456 #1623) -#4404 := (forall (vars (?v0 S3)) (:pat #4395 #4273 #4394) #3417) -#4409 := (not #4404) -#3397 := (or #1449 #1456) -#3398 := (not #3397) -#3401 := (or #793 #3398) -#4396 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4395) #3401) -#4401 := (not #4396) +#2221 := ?v0!13 +#2224 := (f13 f14 ?v0!13) +#2839 := (* -1::Int #2224) +#2222 := (f24 ?v0!13) +#2840 := (+ #2222 #2839) +#2841 := (<= #2840 0::Int) +#2846 := (not #2841) +#4520 := (or #2846 #4517) +#4523 := (not #4520) +#182 := (f5 f22 #12) +#4386 := (pattern #182) +#183 := (f9 #182) +#1612 := (+ #183 #1469) +#1613 := (+ #174 #1612) +#1614 := (= #1613 0::Int) +#1438 := (* -1::Int #183) +#1445 := (+ #1444 #1438) +#1446 := (+ #101 #1445) +#1447 := (<= #1446 0::Int) +#1439 := (+ f8 #1438) +#1440 := (<= #1439 0::Int) +#3408 := (or #1440 #1447 #1614) +#4395 := (forall (vars (?v0 S3)) (:pat #4386 #4264 #4385) #3408) +#4400 := (not #4395) +#3388 := (or #1440 #1447) +#3389 := (not #3388) +#3392 := (or #784 #3389) +#4387 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4386) #3392) +#4392 := (not #4387) decl ?v0!12 :: S3 -#2206 := ?v0!12 -#2212 := (f3 f15 ?v0!12) -#2213 := (= f1 #2212) -#2207 := (f13 f14 ?v0!12) -#2208 := (* -1::Int #2207) -#2209 := (+ f8 #2208) -#2210 := (<= #2209 0::Int) -#1653 := (+ f8 #1453) -#1654 := (<= #1653 0::Int) +#2197 := ?v0!12 +#2203 := (f3 f15 ?v0!12) +#2204 := (= f1 #2203) +#2198 := (f13 f14 ?v0!12) +#2199 := (* -1::Int #2198) +#2200 := (+ f8 #2199) +#2201 := (<= #2200 0::Int) +#1644 := (+ f8 #1444) +#1645 := (<= #1644 0::Int) #105 := (f3 f15 #12) -#4315 := (pattern #105) -#1636 := (+ #101 #1453) -#1635 := (>= #1636 0::Int) -#533 := (= f1 #105) -#1642 := (or #533 #1635) -#4386 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #1642) -#4391 := (not #4386) +#4306 := (pattern #105) +#1627 := (+ #101 #1444) +#1626 := (>= #1627 0::Int) +#532 := (= f1 #105) +#1633 := (or #532 #1626) +#4377 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #1633) +#4382 := (not #4377) +#171 := (f3 f15 f22) +#753 := (= f1 #171) decl f4 :: (-> S2 S3 S1 S2) -#773 := (f4 f15 f22 f1) -#776 := (= f23 #773) -#995 := (not #776) -#171 := (f3 f15 f22) -#754 := (= f1 #171) -#4535 := (or #754 #995 #4391 #1654 #2210 #2213 #4401 #4409 #4532) -#4538 := (not #4535) +#180 := (f4 f15 f22 f1) +#181 := (= f23 #180) +#986 := (not #181) +#4526 := (or #986 #753 #4382 #1645 #2201 #2204 #4392 #4400 #4523) +#4529 := (not #4526) decl ?v0!11 :: S3 -#2140 := ?v0!11 +#2131 := ?v0!11 decl ?v1!10 :: S3 -#2139 := ?v1!10 -#2145 := (f5 ?v1!10 ?v0!11) -#2146 := (f9 #2145) -#2153 := (* -1::Int #2146) +#2130 := ?v1!10 +#2136 := (f5 ?v1!10 ?v0!11) +#2137 := (f9 #2136) +#2144 := (* -1::Int #2137) decl f19 :: S5 #137 := f19 -#2143 := (f13 f19 ?v1!10) -#2149 := (* -1::Int #2143) -#2805 := (+ #2149 #2153) -#2141 := (f13 f19 ?v0!11) -#2806 := (+ #2141 #2805) -#2807 := (<= #2806 0::Int) -#2154 := (+ f8 #2153) -#2155 := (<= #2154 0::Int) -#2150 := (+ f8 #2149) -#2151 := (<= #2150 0::Int) -#3361 := (or #2151 #2155 #2807) -#3366 := (not #3361) +#2134 := (f13 f19 ?v1!10) +#2140 := (* -1::Int #2134) +#2796 := (+ #2140 #2144) +#2132 := (f13 f19 ?v0!11) +#2797 := (+ #2132 #2796) +#2798 := (<= #2797 0::Int) +#2145 := (+ f8 #2144) +#2146 := (<= #2145 0::Int) +#2141 := (+ f8 #2140) +#2142 := (<= #2141 0::Int) +#3352 := (or #2142 #2146 #2798) +#3357 := (not #3352) #145 := (f13 f19 #23) -#1355 := (* -1::Int #145) +#1346 := (* -1::Int #145) #142 := (f13 f19 #12) -#1356 := (+ #142 #1355) -#1362 := (+ #82 #1356) -#1385 := (>= #1362 0::Int) -#1342 := (* -1::Int #142) -#1343 := (+ f8 #1342) -#1344 := (<= #1343 0::Int) -#3329 := (or #1235 #1344 #1385) -#4348 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3329) -#4353 := (not #4348) +#1347 := (+ #142 #1346) +#1353 := (+ #82 #1347) +#1376 := (>= #1353 0::Int) +#1333 := (* -1::Int #142) +#1334 := (+ f8 #1333) +#1335 := (<= #1334 0::Int) +#3320 := (or #1226 #1335 #1376) +#4339 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3320) +#4344 := (not #4339) #157 := (f13 f19 f10) #158 := (= #157 0::Int) -#4356 := (or #158 #4353) -#4359 := (not #4356) -#4362 := (or #4359 #3366) -#4365 := (not #4362) -#4324 := (pattern #142) +#4347 := (or #158 #4344) +#4350 := (not #4347) +#4353 := (or #4350 #3357) +#4356 := (not #4353) +#4315 := (pattern #142) decl ?v1!9 :: (-> S3 S3) -#2116 := (?v1!9 #12) -#2119 := (f5 #2116 #12) -#2120 := (f9 #2119) -#2775 := (* -1::Int #2120) -#2117 := (f13 f19 #2116) -#2758 := (* -1::Int #2117) -#2776 := (+ #2758 #2775) -#2777 := (+ #142 #2776) -#2778 := (= #2777 0::Int) -#3299 := (not #2778) -#2759 := (+ #142 #2758) -#2760 := (<= #2759 0::Int) -#3300 := (or #2760 #3299) -#3301 := (not #3300) +#2107 := (?v1!9 #12) +#2110 := (f5 #2107 #12) +#2111 := (f9 #2110) +#2766 := (* -1::Int #2111) +#2108 := (f13 f19 #2107) +#2749 := (* -1::Int #2108) +#2767 := (+ #2749 #2766) +#2768 := (+ #142 #2767) +#2769 := (= #2768 0::Int) +#3290 := (not #2769) +#2750 := (+ #142 #2749) +#2751 := (<= #2750 0::Int) +#3291 := (or #2751 #3290) +#3292 := (not #3291) #57 := (= #12 f10) -#3307 := (or #57 #1344 #3301) -#4340 := (forall (vars (?v0 S3)) (:pat #4324) #3307) -#4345 := (not #4340) -#4368 := (or #4345 #4365) -#4371 := (not #4368) +#3298 := (or #57 #1335 #3292) +#4331 := (forall (vars (?v0 S3)) (:pat #4315) #3298) +#4336 := (not #4331) +#4359 := (or #4336 #4356) +#4362 := (not #4359) decl ?v0!8 :: S3 -#2076 := ?v0!8 -#2080 := (f5 #12 ?v0!8) -#4325 := (pattern #2080) -#2081 := (f9 #2080) -#2077 := (f13 f19 ?v0!8) -#2078 := (* -1::Int #2077) -#2728 := (+ #2078 #2081) -#2729 := (+ #142 #2728) -#2732 := (= #2729 0::Int) -#3263 := (not #2732) -#2079 := (+ #142 #2078) -#2084 := (>= #2079 0::Int) -#3264 := (or #2084 #3263) -#4326 := (forall (vars (?v1 S3)) (:pat #4324 #4325) #3264) -#4331 := (not #4326) -#2704 := (= f10 ?v0!8) -#2088 := (+ f8 #2078) -#2089 := (<= #2088 0::Int) -#4334 := (or #2089 #2704 #4331) -#4337 := (not #4334) -#4374 := (or #4337 #4371) -#4377 := (not #4374) -#1297 := (* -1::Int #101) -#1298 := (+ f8 #1297) -#1299 := (<= #1298 0::Int) -#3249 := (or #533 #1299) -#4316 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #3249) -#4321 := (not #4316) -#624 := (= f14 f19) -#715 := (not #624) +#2067 := ?v0!8 +#2071 := (f5 #12 ?v0!8) +#4316 := (pattern #2071) +#2072 := (f9 #2071) +#2068 := (f13 f19 ?v0!8) +#2069 := (* -1::Int #2068) +#2719 := (+ #2069 #2072) +#2720 := (+ #142 #2719) +#2723 := (= #2720 0::Int) +#3254 := (not #2723) +#2070 := (+ #142 #2069) +#2075 := (>= #2070 0::Int) +#3255 := (or #2075 #3254) +#4317 := (forall (vars (?v1 S3)) (:pat #4315 #4316) #3255) +#4322 := (not #4317) +#2695 := (= f10 ?v0!8) +#2079 := (+ f8 #2069) +#2080 := (<= #2079 0::Int) +#4325 := (or #2080 #2695 #4322) +#4328 := (not #4325) +#4365 := (or #4328 #4362) +#4368 := (not #4365) +#1288 := (* -1::Int #101) +#1289 := (+ f8 #1288) +#1290 := (<= #1289 0::Int) +#3240 := (or #532 #1290) +#4307 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #3240) +#4312 := (not #4307) +#623 := (= f14 f19) +#714 := (not #623) decl f16 :: S2 #132 := f16 -#621 := (= f15 f16) -#733 := (not #621) +#620 := (= f15 f16) +#732 := (not #620) decl f21 :: S5 #140 := f21 decl f20 :: S5 #139 := f20 #141 := (= f20 f21) -#706 := (not #141) +#705 := (not #141) decl f18 :: S3 #135 := f18 decl f17 :: S3 #134 := f17 #136 := (= f17 f18) -#724 := (not #136) -#4380 := (or #724 #706 #733 #715 #4321 #4377) -#4383 := (not #4380) -#4541 := (or #4383 #4538) -#4544 := (not #4541) -#2039 := (?v1!7 #12) -#2040 := (f13 f14 #2039) -#2663 := (* -1::Int #2040) -#2678 := (+ #101 #2663) -#2679 := (<= #2678 0::Int) -#2044 := (f5 #2039 #12) -#2045 := (f9 #2044) -#2664 := (* -1::Int #2045) -#2665 := (+ #2663 #2664) -#2666 := (+ #101 #2665) -#2667 := (= #2666 0::Int) -#3233 := (not #2667) -#2048 := (f3 f15 #2039) -#2049 := (= f1 #2048) -#3232 := (not #2049) -#3234 := (or #3232 #3233 #2679) -#3235 := (not #3234) -#3241 := (or #57 #1299 #3235) -#4307 := (forall (vars (?v0 S3)) (:pat #4273) #3241) -#4312 := (not #4307) +#723 := (not #136) +#4371 := (or #723 #705 #732 #714 #4312 #4368) +#4374 := (not #4371) +#4532 := (or #4374 #4529) +#4535 := (not #4532) +#2030 := (?v1!7 #12) +#2031 := (f13 f14 #2030) +#2654 := (* -1::Int #2031) +#2669 := (+ #101 #2654) +#2670 := (<= #2669 0::Int) +#2035 := (f5 #2030 #12) +#2036 := (f9 #2035) +#2655 := (* -1::Int #2036) +#2656 := (+ #2654 #2655) +#2657 := (+ #101 #2656) +#2658 := (= #2657 0::Int) +#3224 := (not #2658) +#2039 := (f3 f15 #2030) +#2040 := (= f1 #2039) +#3223 := (not #2040) +#3225 := (or #3223 #3224 #2670) +#3226 := (not #3225) +#3232 := (or #57 #1290 #3226) +#4298 := (forall (vars (?v0 S3)) (:pat #4264) #3232) +#4303 := (not #4298) decl f11 :: (-> S3 Int) #58 := (f11 #12) -#4218 := (pattern #58) +#4209 := (pattern #58) decl ?v1!6 :: (-> S3 S3) -#2011 := (?v1!6 #12) -#2015 := (f11 #2011) -#2622 := (* -1::Int #2015) -#2012 := (f5 #2011 #12) -#2013 := (f9 #2012) -#2639 := (* -1::Int #2013) -#2640 := (+ #2639 #2622) -#2641 := (+ #58 #2640) -#2642 := (= #2641 0::Int) -#3205 := (not #2642) -#2623 := (+ #58 #2622) -#2624 := (<= #2623 0::Int) +#2002 := (?v1!6 #12) +#2006 := (f11 #2002) +#2613 := (* -1::Int #2006) +#2003 := (f5 #2002 #12) +#2004 := (f9 #2003) +#2630 := (* -1::Int #2004) +#2631 := (+ #2630 #2613) +#2632 := (+ #58 #2631) +#2633 := (= #2632 0::Int) +#3196 := (not #2633) +#2614 := (+ #58 #2613) +#2615 := (<= #2614 0::Int) decl f12 :: (-> S3 S1) -#2021 := (f12 #2011) -#2022 := (= f1 #2021) -#3204 := (not #2022) -#3206 := (or #3204 #2624 #3205) -#3207 := (not #3206) -#1259 := (* -1::Int #58) -#1260 := (+ f8 #1259) -#1261 := (<= #1260 0::Int) -#3213 := (or #57 #1261 #3207) -#4299 := (forall (vars (?v0 S3)) (:pat #4218) #3213) -#4304 := (not #4299) +#2012 := (f12 #2002) +#2013 := (= f1 #2012) +#3195 := (not #2013) +#3197 := (or #3195 #2615 #3196) +#3198 := (not #3197) +#1250 := (* -1::Int #58) +#1251 := (+ f8 #1250) +#1252 := (<= #1251 0::Int) +#3204 := (or #57 #1252 #3198) +#4290 := (forall (vars (?v0 S3)) (:pat #4209) #3204) +#4295 := (not #4290) #108 := (f3 f15 #23) -#4290 := (pattern #105 #108) +#4281 := (pattern #105 #108) #111 := (f13 f14 #23) -#1311 := (* -1::Int #111) -#1312 := (+ #101 #1311) -#1315 := (>= #1312 0::Int) -#539 := (= f1 #108) -#3170 := (not #539) -#3185 := (or #533 #3170 #1315) -#4291 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4290) #3185) -#4296 := (not #4291) -#1313 := (+ #82 #1312) -#1708 := (>= #1313 0::Int) -#536 := (not #533) -#3162 := (or #536 #1235 #1708) -#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3162) +#1302 := (* -1::Int #111) +#1303 := (+ #101 #1302) +#1306 := (>= #1303 0::Int) +#538 := (= f1 #108) +#3161 := (not #538) +#3176 := (or #532 #3161 #1306) +#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4281) #3176) #4287 := (not #4282) -#4279 := (not #4274) +#1304 := (+ #82 #1303) +#1699 := (>= #1304 0::Int) +#535 := (not #532) +#3153 := (or #535 #1226 #1699) +#4273 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3153) +#4278 := (not #4273) +#4270 := (not #4265) #100 := (= #99 0::Int) -#1747 := (not #100) -#4547 := (or #1747 #4279 #4287 #4296 #4304 #4312 #4544) -#4550 := (not #4547) +#1738 := (not #100) +#4538 := (or #1738 #4270 #4278 #4287 #4295 #4303 #4535) +#4541 := (not #4538) decl ?v0!5 :: S3 -#1967 := ?v0!5 -#1968 := (f5 #12 ?v0!5) -#4258 := (pattern #1968) +#1958 := ?v0!5 +#1959 := (f5 #12 ?v0!5) +#4249 := (pattern #1959) #66 := (f12 #12) -#4225 := (pattern #66) -#1970 := (f11 ?v0!5) -#1971 := (* -1::Int #1970) -#1969 := (f9 #1968) -#2590 := (+ #1969 #1971) -#2591 := (+ #58 #2590) -#2594 := (= #2591 0::Int) -#3123 := (not #2594) -#1975 := (+ #58 #1971) -#1976 := (>= #1975 0::Int) -#454 := (= f1 #66) -#457 := (not #454) -#3124 := (or #457 #1976 #3123) -#4259 := (forall (vars (?v1 S3)) (:pat #4225 #4218 #4258) #3124) -#4264 := (not #4259) -#2566 := (= f10 ?v0!5) -#1980 := (+ f8 #1971) -#1981 := (<= #1980 0::Int) -#4267 := (or #1981 #2566 #4264) -#4270 := (not #4267) -#4553 := (or #4270 #4550) -#4556 := (not #4553) -#77 := (f11 #23) -#1211 := (* -1::Int #77) -#1232 := (+ #1211 #82) -#1233 := (+ #58 #1232) -#1230 := (>= #1233 0::Int) -#3115 := (or #457 #1230 #1235) -#4250 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3115) +#4216 := (pattern #66) +#1961 := (f11 ?v0!5) +#1962 := (* -1::Int #1961) +#1960 := (f9 #1959) +#2581 := (+ #1960 #1962) +#2582 := (+ #58 #2581) +#2585 := (= #2582 0::Int) +#3114 := (not #2585) +#1966 := (+ #58 #1962) +#1967 := (>= #1966 0::Int) +#453 := (= f1 #66) +#456 := (not #453) +#3115 := (or #456 #1967 #3114) +#4250 := (forall (vars (?v1 S3)) (:pat #4216 #4209 #4249) #3115) #4255 := (not #4250) -#4559 := (or #4255 #4556) -#4562 := (not #4559) +#2557 := (= f10 ?v0!5) +#1971 := (+ f8 #1962) +#1972 := (<= #1971 0::Int) +#4258 := (or #1972 #2557 #4255) +#4261 := (not #4258) +#4544 := (or #4261 #4541) +#4547 := (not #4544) +#77 := (f11 #23) +#1202 := (* -1::Int #77) +#1223 := (+ #1202 #82) +#1224 := (+ #58 #1223) +#1221 := (>= #1224 0::Int) +#3106 := (or #456 #1221 #1226) +#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3106) +#4246 := (not #4241) +#4550 := (or #4246 #4547) +#4553 := (not #4550) decl ?v1!3 :: S3 -#1936 := ?v1!3 -#1951 := (f11 ?v1!3) +#1927 := ?v1!3 +#1942 := (f11 ?v1!3) decl ?v0!4 :: S3 -#1937 := ?v0!4 -#1948 := (f11 ?v0!4) -#1949 := (* -1::Int #1948) -#2547 := (+ #1949 #1951) -#1938 := (f5 ?v1!3 ?v0!4) -#1939 := (f9 #1938) -#2548 := (+ #1939 #2547) -#2551 := (>= #2548 0::Int) -#1944 := (f12 ?v1!3) -#1945 := (= f1 #1944) -#3078 := (not #1945) +#1928 := ?v0!4 +#1939 := (f11 ?v0!4) #1940 := (* -1::Int #1939) -#1941 := (+ f8 #1940) -#1942 := (<= #1941 0::Int) -#3093 := (or #1942 #3078 #2551) -#5222 := [hypothesis]: #1945 -#4226 := (forall (vars (?v0 S3)) (:pat #4225) #457) -#460 := (forall (vars (?v0 S3)) #457) -#4229 := (iff #460 #4226) -#4227 := (iff #457 #457) -#4228 := [refl]: #4227 -#4230 := [quant-intro #4228]: #4229 -#1858 := (~ #460 #460) -#1888 := (~ #457 #457) -#1889 := [refl]: #1888 -#1859 := [nnf-pos #1889]: #1858 +#2538 := (+ #1940 #1942) +#1929 := (f5 ?v1!3 ?v0!4) +#1930 := (f9 #1929) +#2539 := (+ #1930 #2538) +#2542 := (>= #2539 0::Int) +#1935 := (f12 ?v1!3) +#1936 := (= f1 #1935) +#3069 := (not #1936) +#1931 := (* -1::Int #1930) +#1932 := (+ f8 #1931) +#1933 := (<= #1932 0::Int) +#3084 := (or #1933 #3069 #2542) +#5213 := [hypothesis]: #1936 +#4217 := (forall (vars (?v0 S3)) (:pat #4216) #456) +#459 := (forall (vars (?v0 S3)) #456) +#4220 := (iff #459 #4217) +#4218 := (iff #456 #456) +#4219 := [refl]: #4218 +#4221 := [quant-intro #4219]: #4220 +#1849 := (~ #459 #459) +#1879 := (~ #456 #456) +#1880 := [refl]: #1879 +#1850 := [nnf-pos #1880]: #1849 #59 := (= #58 0::Int) #62 := (not #57) -#1805 := (or #62 #59) -#1808 := (forall (vars (?v0 S3)) #1805) -#1811 := (not #1808) -#1739 := (forall (vars (?v0 S3)) #1736) -#1742 := (not #1739) -#542 := (and #536 #539) -#548 := (not #542) -#1725 := (or #548 #1315) -#1730 := (forall (vars (?v0 S3) (?v1 S3)) #1725) +#1796 := (or #62 #59) +#1799 := (forall (vars (?v0 S3)) #1796) +#1802 := (not #1799) +#1730 := (forall (vars (?v0 S3)) #1727) #1733 := (not #1730) -#1236 := (not #1235) -#1700 := (and #533 #1236) -#1705 := (not #1700) -#1711 := (or #1705 #1708) -#1714 := (forall (vars (?v0 S3) (?v1 S3)) #1711) -#1717 := (not #1714) -#1647 := (forall (vars (?v0 S3)) #1642) -#1650 := (not #1647) -#1457 := (not #1456) -#1450 := (not #1449) -#1460 := (and #1450 #1457) -#1618 := (not #1460) -#1626 := (or #1618 #1623) -#1629 := (forall (vars (?v0 S3)) #1626) -#1632 := (not #1629) -#1556 := (= #1534 0::Int) -#1559 := (not #1502) -#1568 := (and #807 #1559 #1556) -#1573 := (exists (vars (?v1 S3)) #1568) -#1545 := (+ f8 #1478) -#1546 := (<= #1545 0::Int) -#1547 := (not #1546) -#1550 := (and #62 #1547) -#1553 := (not #1550) -#1576 := (or #1553 #1573) -#1579 := (forall (vars (?v0 S3)) #1576) -#1524 := (and #807 #1236) -#1529 := (not #1524) -#1536 := (or #1529 #1532) -#1539 := (forall (vars (?v0 S3) (?v1 S3)) #1536) -#1542 := (not #1539) -#1582 := (or #1542 #1579) -#1585 := (and #1539 #1582) -#830 := (and #813 #827) -#836 := (not #830) -#1510 := (or #836 #1502) -#1515 := (forall (vars (?v0 S3) (?v1 S3)) #1510) -#1518 := (not #1515) -#1588 := (or #1518 #1585) -#1591 := (and #1515 #1588) -#1496 := (forall (vars (?v0 S3)) #1493) -#1499 := (not #1496) -#1594 := (or #1499 #1591) -#1597 := (and #1496 #1594) -#1600 := (or #1490 #1597) -#1603 := (and #204 #1600) -#819 := (forall (vars (?v0 S3)) #814) -#953 := (not #819) -#1606 := (or #953 #1603) -#1609 := (and #819 #1606) -#1482 := (forall (vars (?v0 S3)) #1477) -#1485 := (not #1482) -#1612 := (or #1485 #1609) -#1615 := (and #1482 #1612) -#1466 := (or #793 #1460) -#1471 := (forall (vars (?v0 S3)) #1466) -#1474 := (not #1471) -#1300 := (not #1299) -#1419 := (and #536 #1300) -#1424 := (exists (vars (?v0 S3)) #1419) -#1665 := (not #1424) -#1689 := (or #754 #995 #1665 #1474 #1615 #1632 #1650 #1654) -#1345 := (not #1344) -#1379 := (and #1236 #1345) -#1382 := (not #1379) -#1388 := (or #1382 #1385) -#1391 := (forall (vars (?v0 S3) (?v1 S3)) #1388) -#1394 := (not #1391) -#1402 := (or #158 #1394) -#1407 := (and #1391 #1402) -#1360 := (= #1362 0::Int) -#1354 := (>= #1356 0::Int) -#1357 := (not #1354) -#1364 := (and #1357 #1360) -#1367 := (exists (vars (?v1 S3)) #1364) -#1348 := (and #62 #1345) -#1351 := (not #1348) -#1370 := (or #1351 #1367) -#1373 := (forall (vars (?v0 S3)) #1370) -#1376 := (not #1373) -#1410 := (or #1376 #1407) -#1413 := (and #1373 #1410) -#1442 := (or #724 #706 #733 #715 #1413 #1424) -#1694 := (and #1442 #1689) -#1316 := (not #1315) -#1309 := (= #1313 0::Int) -#1325 := (and #533 #1309 #1316) -#1330 := (exists (vars (?v1 S3)) #1325) -#1303 := (and #62 #1300) -#1306 := (not #1303) -#1333 := (or #1306 #1330) -#1336 := (forall (vars (?v0 S3)) #1333) -#1339 := (not #1336) -#1271 := (= #1233 0::Int) -#1212 := (+ #58 #1211) -#1210 := (>= #1212 0::Int) -#1274 := (not #1210) -#1283 := (and #454 #1274 #1271) -#1288 := (exists (vars (?v1 S3)) #1283) -#1262 := (not #1261) -#1265 := (and #62 #1262) -#1268 := (not #1265) -#1291 := (or #1268 #1288) -#1294 := (forall (vars (?v0 S3)) #1291) -#1750 := (not #1294) -#1771 := (or #1747 #1750 #1339 #1694 #1717 #1733 #1742) -#1776 := (and #1294 #1771) -#1242 := (and #454 #1236) -#1247 := (not #1242) -#1250 := (or #1230 #1247) -#1253 := (forall (vars (?v0 S3) (?v1 S3)) #1250) -#1256 := (not #1253) -#1779 := (or #1256 #1776) -#1782 := (and #1253 #1779) +#541 := (and #535 #538) +#547 := (not #541) +#1716 := (or #547 #1306) +#1721 := (forall (vars (?v0 S3) (?v1 S3)) #1716) +#1724 := (not #1721) +#1227 := (not #1226) +#1691 := (and #532 #1227) +#1696 := (not #1691) +#1702 := (or #1696 #1699) +#1705 := (forall (vars (?v0 S3) (?v1 S3)) #1702) +#1708 := (not #1705) +#1638 := (forall (vars (?v0 S3)) #1633) +#1641 := (not #1638) +#1448 := (not #1447) +#1441 := (not #1440) +#1451 := (and #1441 #1448) +#1609 := (not #1451) +#1617 := (or #1609 #1614) +#1620 := (forall (vars (?v0 S3)) #1617) +#1623 := (not #1620) +#1547 := (= #1525 0::Int) +#1550 := (not #1493) +#1559 := (and #798 #1550 #1547) +#1564 := (exists (vars (?v1 S3)) #1559) +#1536 := (+ f8 #1469) +#1537 := (<= #1536 0::Int) +#1538 := (not #1537) +#1541 := (and #62 #1538) +#1544 := (not #1541) +#1567 := (or #1544 #1564) +#1570 := (forall (vars (?v0 S3)) #1567) +#1515 := (and #798 #1227) +#1520 := (not #1515) +#1527 := (or #1520 #1523) +#1530 := (forall (vars (?v0 S3) (?v1 S3)) #1527) +#1533 := (not #1530) +#1573 := (or #1533 #1570) +#1576 := (and #1530 #1573) +#821 := (and #804 #818) +#827 := (not #821) +#1501 := (or #827 #1493) +#1506 := (forall (vars (?v0 S3) (?v1 S3)) #1501) +#1509 := (not #1506) +#1579 := (or #1509 #1576) +#1582 := (and #1506 #1579) +#1487 := (forall (vars (?v0 S3)) #1484) +#1490 := (not #1487) +#1585 := (or #1490 #1582) +#1588 := (and #1487 #1585) +#1591 := (or #1481 #1588) +#1594 := (and #203 #1591) +#810 := (forall (vars (?v0 S3)) #805) +#944 := (not #810) +#1597 := (or #944 #1594) +#1600 := (and #810 #1597) +#1473 := (forall (vars (?v0 S3)) #1468) +#1476 := (not #1473) +#1603 := (or #1476 #1600) +#1606 := (and #1473 #1603) +#1457 := (or #784 #1451) +#1462 := (forall (vars (?v0 S3)) #1457) +#1465 := (not #1462) +#1291 := (not #1290) +#1410 := (and #535 #1291) +#1415 := (exists (vars (?v0 S3)) #1410) +#1656 := (not #1415) +#1680 := (or #986 #753 #1656 #1465 #1606 #1623 #1641 #1645) +#1336 := (not #1335) +#1370 := (and #1227 #1336) +#1373 := (not #1370) +#1379 := (or #1373 #1376) +#1382 := (forall (vars (?v0 S3) (?v1 S3)) #1379) +#1385 := (not #1382) +#1393 := (or #158 #1385) +#1398 := (and #1382 #1393) +#1351 := (= #1353 0::Int) +#1345 := (>= #1347 0::Int) +#1348 := (not #1345) +#1355 := (and #1348 #1351) +#1358 := (exists (vars (?v1 S3)) #1355) +#1339 := (and #62 #1336) +#1342 := (not #1339) +#1361 := (or #1342 #1358) +#1364 := (forall (vars (?v0 S3)) #1361) +#1367 := (not #1364) +#1401 := (or #1367 #1398) +#1404 := (and #1364 #1401) +#1433 := (or #723 #705 #732 #714 #1404 #1415) +#1685 := (and #1433 #1680) +#1307 := (not #1306) +#1300 := (= #1304 0::Int) +#1316 := (and #532 #1300 #1307) +#1321 := (exists (vars (?v1 S3)) #1316) +#1294 := (and #62 #1291) +#1297 := (not #1294) +#1324 := (or #1297 #1321) +#1327 := (forall (vars (?v0 S3)) #1324) +#1330 := (not #1327) +#1262 := (= #1224 0::Int) +#1203 := (+ #58 #1202) +#1201 := (>= #1203 0::Int) +#1265 := (not #1201) +#1274 := (and #453 #1265 #1262) +#1279 := (exists (vars (?v1 S3)) #1274) +#1253 := (not #1252) +#1256 := (and #62 #1253) +#1259 := (not #1256) +#1282 := (or #1259 #1279) +#1285 := (forall (vars (?v0 S3)) #1282) +#1741 := (not #1285) +#1762 := (or #1738 #1741 #1330 #1685 #1708 #1724 #1733) +#1767 := (and #1285 #1762) +#1233 := (and #453 #1227) +#1238 := (not #1233) +#1241 := (or #1221 #1238) +#1244 := (forall (vars (?v0 S3) (?v1 S3)) #1241) +#1247 := (not #1244) +#1770 := (or #1247 #1767) +#1773 := (and #1244 #1770) #74 := (f12 #23) -#466 := (= f1 #74) -#469 := (and #457 #466) -#475 := (not #469) -#1217 := (or #475 #1210) -#1222 := (forall (vars (?v0 S3) (?v1 S3)) #1217) -#1225 := (not #1222) -#1785 := (or #1225 #1782) -#1788 := (and #1222 #1785) -#1201 := (>= #58 0::Int) -#1202 := (forall (vars (?v0 S3)) #1201) -#1205 := (not #1202) -#1791 := (or #1205 #1788) -#1794 := (and #1202 #1791) +#465 := (= f1 #74) +#468 := (and #456 #465) +#474 := (not #468) +#1208 := (or #474 #1201) +#1213 := (forall (vars (?v0 S3) (?v1 S3)) #1208) +#1216 := (not #1213) +#1776 := (or #1216 #1773) +#1779 := (and #1213 #1776) +#1192 := (>= #58 0::Int) +#1193 := (forall (vars (?v0 S3)) #1192) +#1196 := (not #1193) +#1782 := (or #1196 #1779) +#1785 := (and #1193 #1782) #70 := (f11 f10) #71 := (= #70 0::Int) -#1196 := (not #71) -#1797 := (or #1196 #1794) -#1800 := (and #71 #1797) -#1160 := (not #460) -#440 := (= f8 #58) -#446 := (or #57 #440) -#451 := (forall (vars (?v0 S3)) #446) -#1169 := (not #451) -#1823 := (or #1169 #1160 #1800 #1811) -#1828 := (not #1823) +#1187 := (not #71) +#1788 := (or #1187 #1785) +#1791 := (and #71 #1788) +#1151 := (not #459) +#439 := (= f8 #58) +#445 := (or #57 #439) +#450 := (forall (vars (?v0 S3)) #445) +#1160 := (not #450) +#1814 := (or #1160 #1151 #1791 #1802) +#1819 := (not #1814) #1 := true -#216 := (+ #189 #82) -#223 := (= #211 #216) -#200 := (= #199 f1) -#224 := (and #200 #223) -#222 := (< #189 #211) -#225 := (and #222 #224) -#226 := (exists (vars (?v1 S3)) #225) -#220 := (< #189 f8) -#221 := (and #62 #220) -#227 := (implies #221 #226) -#228 := (forall (vars (?v0 S3)) #227) -#229 := (and #228 true) -#217 := (<= #211 #216) +#215 := (+ #188 #82) +#222 := (= #210 #215) +#199 := (= #198 f1) +#223 := (and #199 #222) +#221 := (< #188 #210) +#224 := (and #221 #223) +#225 := (exists (vars (?v1 S3)) #224) +#219 := (< #188 f8) +#220 := (and #62 #219) +#226 := (implies #220 #225) +#227 := (forall (vars (?v0 S3)) #226) +#228 := (and #227 true) +#216 := (<= #210 #215) #83 := (< #82 f8) -#215 := (and #200 #83) -#218 := (implies #215 #217) -#219 := (forall (vars (?v0 S3) (?v1 S3)) #218) -#230 := (implies #219 #229) -#231 := (and #219 #230) -#212 := (<= #211 #189) -#209 := (= #208 f1) -#207 := (not #200) -#210 := (and #207 #209) -#213 := (implies #210 #212) -#214 := (forall (vars (?v0 S3) (?v1 S3)) #213) -#232 := (implies #214 #231) -#233 := (and #214 #232) -#205 := (<= 0::Int #189) -#206 := (forall (vars (?v0 S3)) #205) -#234 := (implies #206 #233) -#235 := (and #206 #234) -#236 := (implies #204 #235) -#237 := (and #204 #236) -#194 := (= #189 #101) -#201 := (implies #200 #194) -#202 := (forall (vars (?v0 S3)) #201) -#238 := (implies #202 #237) -#239 := (and #202 #238) -#197 := (<= #189 #101) -#198 := (forall (vars (?v0 S3)) #197) -#240 := (implies #198 #239) -#241 := (and #198 #240) -#186 := (+ #174 #184) -#187 := (< #186 #101) -#185 := (< #184 f8) -#188 := (and #185 #187) -#193 := (not #188) -#195 := (implies #193 #194) -#196 := (forall (vars (?v0 S3)) #195) -#242 := (implies #196 #241) -#190 := (= #189 #186) -#191 := (implies #188 #190) -#192 := (forall (vars (?v0 S3)) #191) -#243 := (implies #192 #242) -decl f2 :: S1 -#5 := f2 -#180 := (ite true f1 f2) -#181 := (f4 f15 f22 #180) -#182 := (= f23 #181) -#244 := (implies #182 #243) +#214 := (and #199 #83) +#217 := (implies #214 #216) +#218 := (forall (vars (?v0 S3) (?v1 S3)) #217) +#229 := (implies #218 #228) +#230 := (and #218 #229) +#211 := (<= #210 #188) +#208 := (= #207 f1) +#206 := (not #199) +#209 := (and #206 #208) +#212 := (implies #209 #211) +#213 := (forall (vars (?v0 S3) (?v1 S3)) #212) +#231 := (implies #213 #230) +#232 := (and #213 #231) +#204 := (<= 0::Int #188) +#205 := (forall (vars (?v0 S3)) #204) +#233 := (implies #205 #232) +#234 := (and #205 #233) +#235 := (implies #203 #234) +#236 := (and #203 #235) +#193 := (= #188 #101) +#200 := (implies #199 #193) +#201 := (forall (vars (?v0 S3)) #200) +#237 := (implies #201 #236) +#238 := (and #201 #237) +#196 := (<= #188 #101) +#197 := (forall (vars (?v0 S3)) #196) +#239 := (implies #197 #238) +#240 := (and #197 #239) +#185 := (+ #174 #183) +#186 := (< #185 #101) +#184 := (< #183 f8) +#187 := (and #184 #186) +#192 := (not #187) +#194 := (implies #192 #193) +#195 := (forall (vars (?v0 S3)) #194) +#241 := (implies #195 #240) +#189 := (= #188 #185) +#190 := (implies #187 #189) +#191 := (forall (vars (?v0 S3)) #190) +#242 := (implies #191 #241) +#243 := (implies #181 #242) #176 := (<= #174 #101) #106 := (= #105 f1) #107 := (not #106) #177 := (implies #107 #176) #178 := (forall (vars (?v0 S3)) #177) -#245 := (implies #178 #244) +#244 := (implies #178 #243) #175 := (< #174 f8) -#246 := (implies #175 #245) +#245 := (implies #175 #244) #172 := (= #171 f1) #173 := (not #172) -#247 := (implies #173 #246) +#246 := (implies #173 #245) #120 := (< #101 f8) #129 := (and #107 #120) #130 := (exists (vars (?v0 S3)) #129) -#248 := (implies #130 #247) -#249 := (implies true #248) +#247 := (implies #130 #246) +#248 := (implies true #247) #159 := (and #158 true) #147 := (+ #142 #82) #154 := (<= #145 #147) @@ -913,7 +908,7 @@ #131 := (not #130) #168 := (implies #131 #167) #169 := (implies true #168) -#250 := (and #169 #249) +#249 := (and #169 #248) #116 := (+ #101 #82) #123 := (= #111 #116) #124 := (and #106 #123) @@ -923,23 +918,23 @@ #121 := (and #62 #120) #127 := (implies #121 #126) #128 := (forall (vars (?v0 S3)) #127) -#251 := (implies #128 #250) +#250 := (implies #128 #249) #117 := (<= #111 #116) #115 := (and #106 #83) #118 := (implies #115 #117) #119 := (forall (vars (?v0 S3) (?v1 S3)) #118) -#252 := (implies #119 #251) +#251 := (implies #119 #250) #112 := (<= #111 #101) #109 := (= #108 f1) #110 := (and #107 #109) #113 := (implies #110 #112) #114 := (forall (vars (?v0 S3) (?v1 S3)) #113) -#253 := (implies #114 #252) +#252 := (implies #114 #251) #102 := (<= 0::Int #101) #103 := (forall (vars (?v0 S3)) #102) -#254 := (implies #103 #253) -#255 := (implies #100 #254) -#256 := (implies true #255) +#253 := (implies #103 #252) +#254 := (implies #100 #253) +#255 := (implies true #254) #85 := (+ #58 #82) #92 := (= #77 #85) #67 := (= #66 f1) @@ -951,3880 +946,3874 @@ #90 := (and #62 #89) #96 := (implies #90 #95) #97 := (forall (vars (?v0 S3)) #96) -#257 := (implies #97 #256) -#258 := (and #97 #257) +#256 := (implies #97 #255) +#257 := (and #97 #256) #86 := (<= #77 #85) #84 := (and #67 #83) #87 := (implies #84 #86) #88 := (forall (vars (?v0 S3) (?v1 S3)) #87) -#259 := (implies #88 #258) -#260 := (and #88 #259) +#258 := (implies #88 #257) +#259 := (and #88 #258) #78 := (<= #77 #58) #75 := (= #74 f1) #68 := (not #67) #76 := (and #68 #75) #79 := (implies #76 #78) #80 := (forall (vars (?v0 S3) (?v1 S3)) #79) -#261 := (implies #80 #260) -#262 := (and #80 #261) +#260 := (implies #80 #259) +#261 := (and #80 #260) #72 := (<= 0::Int #58) #73 := (forall (vars (?v0 S3)) #72) -#263 := (implies #73 #262) -#264 := (and #73 #263) -#265 := (implies #71 #264) -#266 := (and #71 #265) +#262 := (implies #73 #261) +#263 := (and #73 #262) +#264 := (implies #71 #263) +#265 := (and #71 #264) #69 := (forall (vars (?v0 S3)) #68) -#267 := (implies #69 #266) +#266 := (implies #69 #265) #63 := (= #58 f8) #64 := (implies #62 #63) #65 := (forall (vars (?v0 S3)) #64) -#268 := (implies #65 #267) +#267 := (implies #65 #266) #60 := (implies #57 #59) #61 := (forall (vars (?v0 S3)) #60) -#269 := (implies #61 #268) -#270 := (implies true #269) -#271 := (not #270) -#1831 := (iff #271 #1828) -#853 := (+ #82 #189) -#871 := (= #211 #853) -#874 := (and #807 #871) -#877 := (and #222 #874) -#880 := (exists (vars (?v1 S3)) #877) -#886 := (not #221) -#887 := (or #886 #880) -#892 := (forall (vars (?v0 S3)) #887) -#856 := (<= #211 #853) -#848 := (and #83 #807) -#862 := (not #848) -#863 := (or #862 #856) -#868 := (forall (vars (?v0 S3) (?v1 S3)) #863) -#905 := (not #868) -#906 := (or #905 #892) -#911 := (and #868 #906) -#837 := (or #212 #836) -#842 := (forall (vars (?v0 S3) (?v1 S3)) #837) -#917 := (not #842) -#918 := (or #917 #911) -#923 := (and #842 #918) -#929 := (not #206) -#930 := (or #929 #923) -#935 := (and #206 #930) -#822 := (= 0::Int #203) -#941 := (not #822) -#942 := (or #941 #935) -#947 := (and #822 #942) -#954 := (or #953 #947) -#959 := (and #819 #954) -#965 := (not #198) -#966 := (or #965 #959) -#971 := (and #198 #966) -#799 := (or #188 #793) -#804 := (forall (vars (?v0 S3)) #799) -#977 := (not #804) -#978 := (or #977 #971) -#779 := (= #186 #189) -#785 := (or #193 #779) -#790 := (forall (vars (?v0 S3)) #785) -#986 := (not #790) +#268 := (implies #61 #267) +#269 := (implies true #268) +#270 := (not #269) +#1822 := (iff #270 #1819) +#844 := (+ #82 #188) +#862 := (= #210 #844) +#865 := (and #798 #862) +#868 := (and #221 #865) +#871 := (exists (vars (?v1 S3)) #868) +#877 := (not #220) +#878 := (or #877 #871) +#883 := (forall (vars (?v0 S3)) #878) +#847 := (<= #210 #844) +#839 := (and #83 #798) +#853 := (not #839) +#854 := (or #853 #847) +#859 := (forall (vars (?v0 S3) (?v1 S3)) #854) +#896 := (not #859) +#897 := (or #896 #883) +#902 := (and #859 #897) +#828 := (or #211 #827) +#833 := (forall (vars (?v0 S3) (?v1 S3)) #828) +#908 := (not #833) +#909 := (or #908 #902) +#914 := (and #833 #909) +#920 := (not #205) +#921 := (or #920 #914) +#926 := (and #205 #921) +#813 := (= 0::Int #202) +#932 := (not #813) +#933 := (or #932 #926) +#938 := (and #813 #933) +#945 := (or #944 #938) +#950 := (and #810 #945) +#956 := (not #197) +#957 := (or #956 #950) +#962 := (and #197 #957) +#790 := (or #187 #784) +#795 := (forall (vars (?v0 S3)) #790) +#968 := (not #795) +#969 := (or #968 #962) +#770 := (= #185 #188) +#776 := (or #192 #770) +#781 := (forall (vars (?v0 S3)) #776) +#977 := (not #781) +#978 := (or #977 #969) #987 := (or #986 #978) +#762 := (or #176 #532) +#767 := (forall (vars (?v0 S3)) #762) +#995 := (not #767) #996 := (or #995 #987) -#763 := (or #176 #533) -#768 := (forall (vars (?v0 S3)) #763) -#1004 := (not #768) +#1004 := (not #175) #1005 := (or #1004 #996) -#1013 := (not #175) -#1014 := (or #1013 #1005) -#1022 := (or #754 #1014) -#610 := (and #120 #536) -#615 := (exists (vars (?v0 S3)) #610) -#618 := (not #615) -#1030 := (or #618 #1022) -#669 := (= 0::Int #157) -#627 := (+ #82 #142) -#654 := (<= #145 #627) -#651 := (and #83 #143) -#660 := (not #651) -#661 := (or #660 #654) -#666 := (forall (vars (?v0 S3) (?v1 S3)) #661) -#682 := (not #666) -#683 := (or #682 #669) -#688 := (and #666 #683) -#630 := (= #145 #627) -#633 := (and #146 #630) -#636 := (exists (vars (?v1 S3)) #633) -#642 := (not #144) -#643 := (or #642 #636) -#648 := (forall (vars (?v0 S3)) #643) -#694 := (not #648) -#695 := (or #694 #688) -#700 := (and #648 #695) -#707 := (or #706 #700) -#716 := (or #715 #707) -#725 := (or #724 #716) -#734 := (or #733 #725) -#742 := (or #615 #734) -#1042 := (and #742 #1030) -#565 := (+ #82 #101) -#583 := (= #111 #565) -#586 := (and #533 #583) -#589 := (and #122 #586) -#592 := (exists (vars (?v1 S3)) #589) -#598 := (not #121) -#599 := (or #598 #592) -#604 := (forall (vars (?v0 S3)) #599) -#1048 := (not #604) -#1049 := (or #1048 #1042) -#568 := (<= #111 #565) -#560 := (and #83 #533) -#574 := (not #560) -#575 := (or #574 #568) -#580 := (forall (vars (?v0 S3) (?v1 S3)) #575) -#1057 := (not #580) +#1013 := (or #753 #1005) +#609 := (and #120 #535) +#614 := (exists (vars (?v0 S3)) #609) +#617 := (not #614) +#1021 := (or #617 #1013) +#668 := (= 0::Int #157) +#626 := (+ #82 #142) +#653 := (<= #145 #626) +#650 := (and #83 #143) +#659 := (not #650) +#660 := (or #659 #653) +#665 := (forall (vars (?v0 S3) (?v1 S3)) #660) +#681 := (not #665) +#682 := (or #681 #668) +#687 := (and #665 #682) +#629 := (= #145 #626) +#632 := (and #146 #629) +#635 := (exists (vars (?v1 S3)) #632) +#641 := (not #144) +#642 := (or #641 #635) +#647 := (forall (vars (?v0 S3)) #642) +#693 := (not #647) +#694 := (or #693 #687) +#699 := (and #647 #694) +#706 := (or #705 #699) +#715 := (or #714 #706) +#724 := (or #723 #715) +#733 := (or #732 #724) +#741 := (or #614 #733) +#1033 := (and #741 #1021) +#564 := (+ #82 #101) +#582 := (= #111 #564) +#585 := (and #532 #582) +#588 := (and #122 #585) +#591 := (exists (vars (?v1 S3)) #588) +#597 := (not #121) +#598 := (or #597 #591) +#603 := (forall (vars (?v0 S3)) #598) +#1039 := (not #603) +#1040 := (or #1039 #1033) +#567 := (<= #111 #564) +#559 := (and #83 #532) +#573 := (not #559) +#574 := (or #573 #567) +#579 := (forall (vars (?v0 S3) (?v1 S3)) #574) +#1048 := (not #579) +#1049 := (or #1048 #1040) +#548 := (or #112 #547) +#553 := (forall (vars (?v0 S3) (?v1 S3)) #548) +#1057 := (not #553) #1058 := (or #1057 #1049) -#549 := (or #112 #548) -#554 := (forall (vars (?v0 S3) (?v1 S3)) #549) -#1066 := (not #554) +#1066 := (not #103) #1067 := (or #1066 #1058) -#1075 := (not #103) +#529 := (= 0::Int #99) +#1075 := (not #529) #1076 := (or #1075 #1067) -#530 := (= 0::Int #99) -#1084 := (not #530) -#1085 := (or #1084 #1076) -#507 := (and #92 #454) -#512 := (and #91 #507) -#515 := (exists (vars (?v1 S3)) #512) -#521 := (not #90) -#522 := (or #521 #515) -#527 := (forall (vars (?v0 S3)) #522) -#1100 := (not #527) -#1101 := (or #1100 #1085) -#1106 := (and #527 #1101) -#487 := (and #83 #454) -#495 := (not #487) -#496 := (or #86 #495) -#501 := (forall (vars (?v0 S3) (?v1 S3)) #496) -#1112 := (not #501) -#1113 := (or #1112 #1106) -#1118 := (and #501 #1113) -#476 := (or #78 #475) -#481 := (forall (vars (?v0 S3) (?v1 S3)) #476) -#1124 := (not #481) -#1125 := (or #1124 #1118) -#1130 := (and #481 #1125) -#1136 := (not #73) -#1137 := (or #1136 #1130) -#1142 := (and #73 #1137) -#463 := (= 0::Int #70) -#1148 := (not #463) -#1149 := (or #1148 #1142) -#1154 := (and #463 #1149) -#1161 := (or #1160 #1154) +#506 := (and #92 #453) +#511 := (and #91 #506) +#514 := (exists (vars (?v1 S3)) #511) +#520 := (not #90) +#521 := (or #520 #514) +#526 := (forall (vars (?v0 S3)) #521) +#1091 := (not #526) +#1092 := (or #1091 #1076) +#1097 := (and #526 #1092) +#486 := (and #83 #453) +#494 := (not #486) +#495 := (or #86 #494) +#500 := (forall (vars (?v0 S3) (?v1 S3)) #495) +#1103 := (not #500) +#1104 := (or #1103 #1097) +#1109 := (and #500 #1104) +#475 := (or #78 #474) +#480 := (forall (vars (?v0 S3) (?v1 S3)) #475) +#1115 := (not #480) +#1116 := (or #1115 #1109) +#1121 := (and #480 #1116) +#1127 := (not #73) +#1128 := (or #1127 #1121) +#1133 := (and #73 #1128) +#462 := (= 0::Int #70) +#1139 := (not #462) +#1140 := (or #1139 #1133) +#1145 := (and #462 #1140) +#1152 := (or #1151 #1145) +#1161 := (or #1160 #1152) +#425 := (= 0::Int #58) +#431 := (or #62 #425) +#436 := (forall (vars (?v0 S3)) #431) +#1169 := (not #436) #1170 := (or #1169 #1161) -#426 := (= 0::Int #58) -#432 := (or #62 #426) -#437 := (forall (vars (?v0 S3)) #432) -#1178 := (not #437) -#1179 := (or #1178 #1170) -#1191 := (not #1179) -#1829 := (iff #1191 #1828) -#1826 := (iff #1179 #1823) -#1814 := (or #1160 #1800) -#1817 := (or #1169 #1814) -#1820 := (or #1811 #1817) -#1824 := (iff #1820 #1823) -#1825 := [rewrite]: #1824 -#1821 := (iff #1179 #1820) -#1818 := (iff #1170 #1817) -#1815 := (iff #1161 #1814) -#1801 := (iff #1154 #1800) -#1798 := (iff #1149 #1797) -#1795 := (iff #1142 #1794) -#1792 := (iff #1137 #1791) -#1789 := (iff #1130 #1788) -#1786 := (iff #1125 #1785) -#1783 := (iff #1118 #1782) -#1780 := (iff #1113 #1779) -#1777 := (iff #1106 #1776) -#1774 := (iff #1101 #1771) -#1753 := (or #1339 #1694) -#1756 := (or #1717 #1753) -#1759 := (or #1733 #1756) -#1762 := (or #1742 #1759) -#1765 := (or #1747 #1762) -#1768 := (or #1750 #1765) -#1772 := (iff #1768 #1771) -#1773 := [rewrite]: #1772 -#1769 := (iff #1101 #1768) -#1766 := (iff #1085 #1765) -#1763 := (iff #1076 #1762) -#1760 := (iff #1067 #1759) -#1757 := (iff #1058 #1756) -#1754 := (iff #1049 #1753) -#1695 := (iff #1042 #1694) -#1692 := (iff #1030 #1689) -#1668 := (or #1474 #1615) -#1671 := (or #1632 #1668) -#1674 := (or #995 #1671) -#1677 := (or #1650 #1674) -#1680 := (or #1654 #1677) -#1683 := (or #754 #1680) -#1686 := (or #1665 #1683) -#1690 := (iff #1686 #1689) -#1691 := [rewrite]: #1690 -#1687 := (iff #1030 #1686) -#1684 := (iff #1022 #1683) -#1681 := (iff #1014 #1680) -#1678 := (iff #1005 #1677) -#1675 := (iff #996 #1674) -#1672 := (iff #987 #1671) -#1669 := (iff #978 #1668) -#1616 := (iff #971 #1615) -#1613 := (iff #966 #1612) -#1610 := (iff #959 #1609) -#1607 := (iff #954 #1606) -#1604 := (iff #947 #1603) -#1601 := (iff #942 #1600) -#1598 := (iff #935 #1597) -#1595 := (iff #930 #1594) -#1592 := (iff #923 #1591) -#1589 := (iff #918 #1588) -#1586 := (iff #911 #1585) -#1583 := (iff #906 #1582) -#1580 := (iff #892 #1579) -#1577 := (iff #887 #1576) -#1574 := (iff #880 #1573) -#1571 := (iff #877 #1568) -#1562 := (and #807 #1556) -#1565 := (and #1559 #1562) -#1569 := (iff #1565 #1568) -#1570 := [rewrite]: #1569 -#1566 := (iff #877 #1565) -#1563 := (iff #874 #1562) -#1557 := (iff #871 #1556) -#1558 := [rewrite]: #1557 -#1564 := [monotonicity #1558]: #1563 -#1560 := (iff #222 #1559) +#1182 := (not #1170) +#1820 := (iff #1182 #1819) +#1817 := (iff #1170 #1814) +#1805 := (or #1151 #1791) +#1808 := (or #1160 #1805) +#1811 := (or #1802 #1808) +#1815 := (iff #1811 #1814) +#1816 := [rewrite]: #1815 +#1812 := (iff #1170 #1811) +#1809 := (iff #1161 #1808) +#1806 := (iff #1152 #1805) +#1792 := (iff #1145 #1791) +#1789 := (iff #1140 #1788) +#1786 := (iff #1133 #1785) +#1783 := (iff #1128 #1782) +#1780 := (iff #1121 #1779) +#1777 := (iff #1116 #1776) +#1774 := (iff #1109 #1773) +#1771 := (iff #1104 #1770) +#1768 := (iff #1097 #1767) +#1765 := (iff #1092 #1762) +#1744 := (or #1330 #1685) +#1747 := (or #1708 #1744) +#1750 := (or #1724 #1747) +#1753 := (or #1733 #1750) +#1756 := (or #1738 #1753) +#1759 := (or #1741 #1756) +#1763 := (iff #1759 #1762) +#1764 := [rewrite]: #1763 +#1760 := (iff #1092 #1759) +#1757 := (iff #1076 #1756) +#1754 := (iff #1067 #1753) +#1751 := (iff #1058 #1750) +#1748 := (iff #1049 #1747) +#1745 := (iff #1040 #1744) +#1686 := (iff #1033 #1685) +#1683 := (iff #1021 #1680) +#1659 := (or #1465 #1606) +#1662 := (or #1623 #1659) +#1665 := (or #986 #1662) +#1668 := (or #1641 #1665) +#1671 := (or #1645 #1668) +#1674 := (or #753 #1671) +#1677 := (or #1656 #1674) +#1681 := (iff #1677 #1680) +#1682 := [rewrite]: #1681 +#1678 := (iff #1021 #1677) +#1675 := (iff #1013 #1674) +#1672 := (iff #1005 #1671) +#1669 := (iff #996 #1668) +#1666 := (iff #987 #1665) +#1663 := (iff #978 #1662) +#1660 := (iff #969 #1659) +#1607 := (iff #962 #1606) +#1604 := (iff #957 #1603) +#1601 := (iff #950 #1600) +#1598 := (iff #945 #1597) +#1595 := (iff #938 #1594) +#1592 := (iff #933 #1591) +#1589 := (iff #926 #1588) +#1586 := (iff #921 #1585) +#1583 := (iff #914 #1582) +#1580 := (iff #909 #1579) +#1577 := (iff #902 #1576) +#1574 := (iff #897 #1573) +#1571 := (iff #883 #1570) +#1568 := (iff #878 #1567) +#1565 := (iff #871 #1564) +#1562 := (iff #868 #1559) +#1553 := (and #798 #1547) +#1556 := (and #1550 #1553) +#1560 := (iff #1556 #1559) #1561 := [rewrite]: #1560 -#1567 := [monotonicity #1561 #1564]: #1566 -#1572 := [trans #1567 #1570]: #1571 -#1575 := [quant-intro #1572]: #1574 -#1554 := (iff #886 #1553) -#1551 := (iff #221 #1550) -#1548 := (iff #220 #1547) +#1557 := (iff #868 #1556) +#1554 := (iff #865 #1553) +#1548 := (iff #862 #1547) #1549 := [rewrite]: #1548 -#1552 := [monotonicity #1549]: #1551 -#1555 := [monotonicity #1552]: #1554 -#1578 := [monotonicity #1555 #1575]: #1577 -#1581 := [quant-intro #1578]: #1580 -#1543 := (iff #905 #1542) -#1540 := (iff #868 #1539) -#1537 := (iff #863 #1536) -#1533 := (iff #856 #1532) -#1535 := [rewrite]: #1533 -#1530 := (iff #862 #1529) -#1527 := (iff #848 #1524) -#1521 := (and #1236 #807) -#1525 := (iff #1521 #1524) -#1526 := [rewrite]: #1525 -#1522 := (iff #848 #1521) -#1237 := (iff #83 #1236) -#1238 := [rewrite]: #1237 -#1523 := [monotonicity #1238]: #1522 -#1528 := [trans #1523 #1526]: #1527 -#1531 := [monotonicity #1528]: #1530 -#1538 := [monotonicity #1531 #1535]: #1537 -#1541 := [quant-intro #1538]: #1540 -#1544 := [monotonicity #1541]: #1543 -#1584 := [monotonicity #1544 #1581]: #1583 -#1587 := [monotonicity #1541 #1584]: #1586 -#1519 := (iff #917 #1518) -#1516 := (iff #842 #1515) -#1513 := (iff #837 #1510) -#1507 := (or #1502 #836) -#1511 := (iff #1507 #1510) -#1512 := [rewrite]: #1511 -#1508 := (iff #837 #1507) -#1505 := (iff #212 #1502) -#1506 := [rewrite]: #1505 -#1509 := [monotonicity #1506]: #1508 -#1514 := [trans #1509 #1512]: #1513 -#1517 := [quant-intro #1514]: #1516 -#1520 := [monotonicity #1517]: #1519 -#1590 := [monotonicity #1520 #1587]: #1589 -#1593 := [monotonicity #1517 #1590]: #1592 -#1500 := (iff #929 #1499) -#1497 := (iff #206 #1496) -#1494 := (iff #205 #1493) -#1495 := [rewrite]: #1494 -#1498 := [quant-intro #1495]: #1497 -#1501 := [monotonicity #1498]: #1500 -#1596 := [monotonicity #1501 #1593]: #1595 -#1599 := [monotonicity #1498 #1596]: #1598 -#1491 := (iff #941 #1490) -#1488 := (iff #822 #204) -#1489 := [rewrite]: #1488 +#1555 := [monotonicity #1549]: #1554 +#1551 := (iff #221 #1550) +#1552 := [rewrite]: #1551 +#1558 := [monotonicity #1552 #1555]: #1557 +#1563 := [trans #1558 #1561]: #1562 +#1566 := [quant-intro #1563]: #1565 +#1545 := (iff #877 #1544) +#1542 := (iff #220 #1541) +#1539 := (iff #219 #1538) +#1540 := [rewrite]: #1539 +#1543 := [monotonicity #1540]: #1542 +#1546 := [monotonicity #1543]: #1545 +#1569 := [monotonicity #1546 #1566]: #1568 +#1572 := [quant-intro #1569]: #1571 +#1534 := (iff #896 #1533) +#1531 := (iff #859 #1530) +#1528 := (iff #854 #1527) +#1524 := (iff #847 #1523) +#1526 := [rewrite]: #1524 +#1521 := (iff #853 #1520) +#1518 := (iff #839 #1515) +#1512 := (and #1227 #798) +#1516 := (iff #1512 #1515) +#1517 := [rewrite]: #1516 +#1513 := (iff #839 #1512) +#1228 := (iff #83 #1227) +#1229 := [rewrite]: #1228 +#1514 := [monotonicity #1229]: #1513 +#1519 := [trans #1514 #1517]: #1518 +#1522 := [monotonicity #1519]: #1521 +#1529 := [monotonicity #1522 #1526]: #1528 +#1532 := [quant-intro #1529]: #1531 +#1535 := [monotonicity #1532]: #1534 +#1575 := [monotonicity #1535 #1572]: #1574 +#1578 := [monotonicity #1532 #1575]: #1577 +#1510 := (iff #908 #1509) +#1507 := (iff #833 #1506) +#1504 := (iff #828 #1501) +#1498 := (or #1493 #827) +#1502 := (iff #1498 #1501) +#1503 := [rewrite]: #1502 +#1499 := (iff #828 #1498) +#1496 := (iff #211 #1493) +#1497 := [rewrite]: #1496 +#1500 := [monotonicity #1497]: #1499 +#1505 := [trans #1500 #1503]: #1504 +#1508 := [quant-intro #1505]: #1507 +#1511 := [monotonicity #1508]: #1510 +#1581 := [monotonicity #1511 #1578]: #1580 +#1584 := [monotonicity #1508 #1581]: #1583 +#1491 := (iff #920 #1490) +#1488 := (iff #205 #1487) +#1485 := (iff #204 #1484) +#1486 := [rewrite]: #1485 +#1489 := [quant-intro #1486]: #1488 #1492 := [monotonicity #1489]: #1491 -#1602 := [monotonicity #1492 #1599]: #1601 -#1605 := [monotonicity #1489 #1602]: #1604 -#1608 := [monotonicity #1605]: #1607 -#1611 := [monotonicity #1608]: #1610 -#1486 := (iff #965 #1485) -#1483 := (iff #198 #1482) -#1480 := (iff #197 #1477) -#1481 := [rewrite]: #1480 -#1484 := [quant-intro #1481]: #1483 -#1487 := [monotonicity #1484]: #1486 -#1614 := [monotonicity #1487 #1611]: #1613 -#1617 := [monotonicity #1484 #1614]: #1616 -#1475 := (iff #977 #1474) -#1472 := (iff #804 #1471) -#1469 := (iff #799 #1466) -#1463 := (or #1460 #793) -#1467 := (iff #1463 #1466) -#1468 := [rewrite]: #1467 -#1464 := (iff #799 #1463) -#1461 := (iff #188 #1460) -#1458 := (iff #187 #1457) +#1587 := [monotonicity #1492 #1584]: #1586 +#1590 := [monotonicity #1489 #1587]: #1589 +#1482 := (iff #932 #1481) +#1479 := (iff #813 #203) +#1480 := [rewrite]: #1479 +#1483 := [monotonicity #1480]: #1482 +#1593 := [monotonicity #1483 #1590]: #1592 +#1596 := [monotonicity #1480 #1593]: #1595 +#1599 := [monotonicity #1596]: #1598 +#1602 := [monotonicity #1599]: #1601 +#1477 := (iff #956 #1476) +#1474 := (iff #197 #1473) +#1471 := (iff #196 #1468) +#1472 := [rewrite]: #1471 +#1475 := [quant-intro #1472]: #1474 +#1478 := [monotonicity #1475]: #1477 +#1605 := [monotonicity #1478 #1602]: #1604 +#1608 := [monotonicity #1475 #1605]: #1607 +#1466 := (iff #968 #1465) +#1463 := (iff #795 #1462) +#1460 := (iff #790 #1457) +#1454 := (or #1451 #784) +#1458 := (iff #1454 #1457) #1459 := [rewrite]: #1458 -#1451 := (iff #185 #1450) -#1452 := [rewrite]: #1451 -#1462 := [monotonicity #1452 #1459]: #1461 -#1465 := [monotonicity #1462]: #1464 -#1470 := [trans #1465 #1468]: #1469 -#1473 := [quant-intro #1470]: #1472 -#1476 := [monotonicity #1473]: #1475 -#1670 := [monotonicity #1476 #1617]: #1669 -#1633 := (iff #986 #1632) -#1630 := (iff #790 #1629) -#1627 := (iff #785 #1626) -#1624 := (iff #779 #1623) -#1625 := [rewrite]: #1624 -#1619 := (iff #193 #1618) -#1620 := [monotonicity #1462]: #1619 -#1628 := [monotonicity #1620 #1625]: #1627 -#1631 := [quant-intro #1628]: #1630 -#1634 := [monotonicity #1631]: #1633 -#1673 := [monotonicity #1634 #1670]: #1672 +#1455 := (iff #790 #1454) +#1452 := (iff #187 #1451) +#1449 := (iff #186 #1448) +#1450 := [rewrite]: #1449 +#1442 := (iff #184 #1441) +#1443 := [rewrite]: #1442 +#1453 := [monotonicity #1443 #1450]: #1452 +#1456 := [monotonicity #1453]: #1455 +#1461 := [trans #1456 #1459]: #1460 +#1464 := [quant-intro #1461]: #1463 +#1467 := [monotonicity #1464]: #1466 +#1661 := [monotonicity #1467 #1608]: #1660 +#1624 := (iff #977 #1623) +#1621 := (iff #781 #1620) +#1618 := (iff #776 #1617) +#1615 := (iff #770 #1614) +#1616 := [rewrite]: #1615 +#1610 := (iff #192 #1609) +#1611 := [monotonicity #1453]: #1610 +#1619 := [monotonicity #1611 #1616]: #1618 +#1622 := [quant-intro #1619]: #1621 +#1625 := [monotonicity #1622]: #1624 +#1664 := [monotonicity #1625 #1661]: #1663 +#1667 := [monotonicity #1664]: #1666 +#1642 := (iff #995 #1641) +#1639 := (iff #767 #1638) +#1636 := (iff #762 #1633) +#1630 := (or #1626 #532) +#1634 := (iff #1630 #1633) +#1635 := [rewrite]: #1634 +#1631 := (iff #762 #1630) +#1628 := (iff #176 #1626) +#1629 := [rewrite]: #1628 +#1632 := [monotonicity #1629]: #1631 +#1637 := [trans #1632 #1635]: #1636 +#1640 := [quant-intro #1637]: #1639 +#1643 := [monotonicity #1640]: #1642 +#1670 := [monotonicity #1643 #1667]: #1669 +#1654 := (iff #1004 #1645) +#1646 := (not #1645) +#1649 := (not #1646) +#1652 := (iff #1649 #1645) +#1653 := [rewrite]: #1652 +#1650 := (iff #1004 #1649) +#1647 := (iff #175 #1646) +#1648 := [rewrite]: #1647 +#1651 := [monotonicity #1648]: #1650 +#1655 := [trans #1651 #1653]: #1654 +#1673 := [monotonicity #1655 #1670]: #1672 #1676 := [monotonicity #1673]: #1675 -#1651 := (iff #1004 #1650) -#1648 := (iff #768 #1647) -#1645 := (iff #763 #1642) -#1639 := (or #1635 #533) -#1643 := (iff #1639 #1642) -#1644 := [rewrite]: #1643 -#1640 := (iff #763 #1639) -#1637 := (iff #176 #1635) -#1638 := [rewrite]: #1637 -#1641 := [monotonicity #1638]: #1640 -#1646 := [trans #1641 #1644]: #1645 -#1649 := [quant-intro #1646]: #1648 -#1652 := [monotonicity #1649]: #1651 -#1679 := [monotonicity #1652 #1676]: #1678 -#1663 := (iff #1013 #1654) -#1655 := (not #1654) -#1658 := (not #1655) -#1661 := (iff #1658 #1654) -#1662 := [rewrite]: #1661 -#1659 := (iff #1013 #1658) -#1656 := (iff #175 #1655) -#1657 := [rewrite]: #1656 -#1660 := [monotonicity #1657]: #1659 -#1664 := [trans #1660 #1662]: #1663 -#1682 := [monotonicity #1664 #1679]: #1681 -#1685 := [monotonicity #1682]: #1684 -#1666 := (iff #618 #1665) -#1425 := (iff #615 #1424) -#1422 := (iff #610 #1419) -#1416 := (and #1300 #536) -#1420 := (iff #1416 #1419) -#1421 := [rewrite]: #1420 -#1417 := (iff #610 #1416) -#1301 := (iff #120 #1300) -#1302 := [rewrite]: #1301 -#1418 := [monotonicity #1302]: #1417 -#1423 := [trans #1418 #1421]: #1422 -#1426 := [quant-intro #1423]: #1425 -#1667 := [monotonicity #1426]: #1666 -#1688 := [monotonicity #1667 #1685]: #1687 -#1693 := [trans #1688 #1691]: #1692 -#1445 := (iff #742 #1442) -#1427 := (or #706 #1413) -#1430 := (or #715 #1427) -#1433 := (or #724 #1430) -#1436 := (or #733 #1433) -#1439 := (or #1424 #1436) -#1443 := (iff #1439 #1442) -#1444 := [rewrite]: #1443 -#1440 := (iff #742 #1439) -#1437 := (iff #734 #1436) -#1434 := (iff #725 #1433) -#1431 := (iff #716 #1430) -#1428 := (iff #707 #1427) -#1414 := (iff #700 #1413) -#1411 := (iff #695 #1410) -#1408 := (iff #688 #1407) -#1405 := (iff #683 #1402) -#1399 := (or #1394 #158) -#1403 := (iff #1399 #1402) -#1404 := [rewrite]: #1403 -#1400 := (iff #683 #1399) -#1397 := (iff #669 #158) -#1398 := [rewrite]: #1397 -#1395 := (iff #682 #1394) -#1392 := (iff #666 #1391) -#1389 := (iff #661 #1388) -#1386 := (iff #654 #1385) -#1387 := [rewrite]: #1386 -#1383 := (iff #660 #1382) -#1380 := (iff #651 #1379) -#1346 := (iff #143 #1345) -#1347 := [rewrite]: #1346 -#1381 := [monotonicity #1238 #1347]: #1380 -#1384 := [monotonicity #1381]: #1383 -#1390 := [monotonicity #1384 #1387]: #1389 -#1393 := [quant-intro #1390]: #1392 -#1396 := [monotonicity #1393]: #1395 -#1401 := [monotonicity #1396 #1398]: #1400 -#1406 := [trans #1401 #1404]: #1405 -#1409 := [monotonicity #1393 #1406]: #1408 -#1377 := (iff #694 #1376) -#1374 := (iff #648 #1373) -#1371 := (iff #643 #1370) -#1368 := (iff #636 #1367) -#1365 := (iff #633 #1364) -#1361 := (iff #630 #1360) -#1363 := [rewrite]: #1361 -#1358 := (iff #146 #1357) -#1359 := [rewrite]: #1358 -#1366 := [monotonicity #1359 #1363]: #1365 -#1369 := [quant-intro #1366]: #1368 -#1352 := (iff #642 #1351) -#1349 := (iff #144 #1348) -#1350 := [monotonicity #1347]: #1349 -#1353 := [monotonicity #1350]: #1352 -#1372 := [monotonicity #1353 #1369]: #1371 -#1375 := [quant-intro #1372]: #1374 -#1378 := [monotonicity #1375]: #1377 -#1412 := [monotonicity #1378 #1409]: #1411 -#1415 := [monotonicity #1375 #1412]: #1414 -#1429 := [monotonicity #1415]: #1428 -#1432 := [monotonicity #1429]: #1431 -#1435 := [monotonicity #1432]: #1434 -#1438 := [monotonicity #1435]: #1437 -#1441 := [monotonicity #1426 #1438]: #1440 -#1446 := [trans #1441 #1444]: #1445 -#1696 := [monotonicity #1446 #1693]: #1695 -#1340 := (iff #1048 #1339) -#1337 := (iff #604 #1336) -#1334 := (iff #599 #1333) -#1331 := (iff #592 #1330) -#1328 := (iff #589 #1325) -#1319 := (and #533 #1309) -#1322 := (and #1316 #1319) -#1326 := (iff #1322 #1325) -#1327 := [rewrite]: #1326 -#1323 := (iff #589 #1322) -#1320 := (iff #586 #1319) -#1310 := (iff #583 #1309) -#1314 := [rewrite]: #1310 -#1321 := [monotonicity #1314]: #1320 -#1317 := (iff #122 #1316) +#1657 := (iff #617 #1656) +#1416 := (iff #614 #1415) +#1413 := (iff #609 #1410) +#1407 := (and #1291 #535) +#1411 := (iff #1407 #1410) +#1412 := [rewrite]: #1411 +#1408 := (iff #609 #1407) +#1292 := (iff #120 #1291) +#1293 := [rewrite]: #1292 +#1409 := [monotonicity #1293]: #1408 +#1414 := [trans #1409 #1412]: #1413 +#1417 := [quant-intro #1414]: #1416 +#1658 := [monotonicity #1417]: #1657 +#1679 := [monotonicity #1658 #1676]: #1678 +#1684 := [trans #1679 #1682]: #1683 +#1436 := (iff #741 #1433) +#1418 := (or #705 #1404) +#1421 := (or #714 #1418) +#1424 := (or #723 #1421) +#1427 := (or #732 #1424) +#1430 := (or #1415 #1427) +#1434 := (iff #1430 #1433) +#1435 := [rewrite]: #1434 +#1431 := (iff #741 #1430) +#1428 := (iff #733 #1427) +#1425 := (iff #724 #1424) +#1422 := (iff #715 #1421) +#1419 := (iff #706 #1418) +#1405 := (iff #699 #1404) +#1402 := (iff #694 #1401) +#1399 := (iff #687 #1398) +#1396 := (iff #682 #1393) +#1390 := (or #1385 #158) +#1394 := (iff #1390 #1393) +#1395 := [rewrite]: #1394 +#1391 := (iff #682 #1390) +#1388 := (iff #668 #158) +#1389 := [rewrite]: #1388 +#1386 := (iff #681 #1385) +#1383 := (iff #665 #1382) +#1380 := (iff #660 #1379) +#1377 := (iff #653 #1376) +#1378 := [rewrite]: #1377 +#1374 := (iff #659 #1373) +#1371 := (iff #650 #1370) +#1337 := (iff #143 #1336) +#1338 := [rewrite]: #1337 +#1372 := [monotonicity #1229 #1338]: #1371 +#1375 := [monotonicity #1372]: #1374 +#1381 := [monotonicity #1375 #1378]: #1380 +#1384 := [quant-intro #1381]: #1383 +#1387 := [monotonicity #1384]: #1386 +#1392 := [monotonicity #1387 #1389]: #1391 +#1397 := [trans #1392 #1395]: #1396 +#1400 := [monotonicity #1384 #1397]: #1399 +#1368 := (iff #693 #1367) +#1365 := (iff #647 #1364) +#1362 := (iff #642 #1361) +#1359 := (iff #635 #1358) +#1356 := (iff #632 #1355) +#1352 := (iff #629 #1351) +#1354 := [rewrite]: #1352 +#1349 := (iff #146 #1348) +#1350 := [rewrite]: #1349 +#1357 := [monotonicity #1350 #1354]: #1356 +#1360 := [quant-intro #1357]: #1359 +#1343 := (iff #641 #1342) +#1340 := (iff #144 #1339) +#1341 := [monotonicity #1338]: #1340 +#1344 := [monotonicity #1341]: #1343 +#1363 := [monotonicity #1344 #1360]: #1362 +#1366 := [quant-intro #1363]: #1365 +#1369 := [monotonicity #1366]: #1368 +#1403 := [monotonicity #1369 #1400]: #1402 +#1406 := [monotonicity #1366 #1403]: #1405 +#1420 := [monotonicity #1406]: #1419 +#1423 := [monotonicity #1420]: #1422 +#1426 := [monotonicity #1423]: #1425 +#1429 := [monotonicity #1426]: #1428 +#1432 := [monotonicity #1417 #1429]: #1431 +#1437 := [trans #1432 #1435]: #1436 +#1687 := [monotonicity #1437 #1684]: #1686 +#1331 := (iff #1039 #1330) +#1328 := (iff #603 #1327) +#1325 := (iff #598 #1324) +#1322 := (iff #591 #1321) +#1319 := (iff #588 #1316) +#1310 := (and #532 #1300) +#1313 := (and #1307 #1310) +#1317 := (iff #1313 #1316) #1318 := [rewrite]: #1317 -#1324 := [monotonicity #1318 #1321]: #1323 -#1329 := [trans #1324 #1327]: #1328 -#1332 := [quant-intro #1329]: #1331 -#1307 := (iff #598 #1306) -#1304 := (iff #121 #1303) -#1305 := [monotonicity #1302]: #1304 -#1308 := [monotonicity #1305]: #1307 -#1335 := [monotonicity #1308 #1332]: #1334 -#1338 := [quant-intro #1335]: #1337 -#1341 := [monotonicity #1338]: #1340 -#1755 := [monotonicity #1341 #1696]: #1754 -#1718 := (iff #1057 #1717) -#1715 := (iff #580 #1714) -#1712 := (iff #575 #1711) -#1709 := (iff #568 #1708) -#1710 := [rewrite]: #1709 -#1706 := (iff #574 #1705) -#1703 := (iff #560 #1700) -#1697 := (and #1236 #533) -#1701 := (iff #1697 #1700) -#1702 := [rewrite]: #1701 -#1698 := (iff #560 #1697) -#1699 := [monotonicity #1238]: #1698 -#1704 := [trans #1699 #1702]: #1703 -#1707 := [monotonicity #1704]: #1706 -#1713 := [monotonicity #1707 #1710]: #1712 -#1716 := [quant-intro #1713]: #1715 -#1719 := [monotonicity #1716]: #1718 -#1758 := [monotonicity #1719 #1755]: #1757 +#1314 := (iff #588 #1313) +#1311 := (iff #585 #1310) +#1301 := (iff #582 #1300) +#1305 := [rewrite]: #1301 +#1312 := [monotonicity #1305]: #1311 +#1308 := (iff #122 #1307) +#1309 := [rewrite]: #1308 +#1315 := [monotonicity #1309 #1312]: #1314 +#1320 := [trans #1315 #1318]: #1319 +#1323 := [quant-intro #1320]: #1322 +#1298 := (iff #597 #1297) +#1295 := (iff #121 #1294) +#1296 := [monotonicity #1293]: #1295 +#1299 := [monotonicity #1296]: #1298 +#1326 := [monotonicity #1299 #1323]: #1325 +#1329 := [quant-intro #1326]: #1328 +#1332 := [monotonicity #1329]: #1331 +#1746 := [monotonicity #1332 #1687]: #1745 +#1709 := (iff #1048 #1708) +#1706 := (iff #579 #1705) +#1703 := (iff #574 #1702) +#1700 := (iff #567 #1699) +#1701 := [rewrite]: #1700 +#1697 := (iff #573 #1696) +#1694 := (iff #559 #1691) +#1688 := (and #1227 #532) +#1692 := (iff #1688 #1691) +#1693 := [rewrite]: #1692 +#1689 := (iff #559 #1688) +#1690 := [monotonicity #1229]: #1689 +#1695 := [trans #1690 #1693]: #1694 +#1698 := [monotonicity #1695]: #1697 +#1704 := [monotonicity #1698 #1701]: #1703 +#1707 := [quant-intro #1704]: #1706 +#1710 := [monotonicity #1707]: #1709 +#1749 := [monotonicity #1710 #1746]: #1748 +#1725 := (iff #1057 #1724) +#1722 := (iff #553 #1721) +#1719 := (iff #548 #1716) +#1713 := (or #1306 #547) +#1717 := (iff #1713 #1716) +#1718 := [rewrite]: #1717 +#1714 := (iff #548 #1713) +#1711 := (iff #112 #1306) +#1712 := [rewrite]: #1711 +#1715 := [monotonicity #1712]: #1714 +#1720 := [trans #1715 #1718]: #1719 +#1723 := [quant-intro #1720]: #1722 +#1726 := [monotonicity #1723]: #1725 +#1752 := [monotonicity #1726 #1749]: #1751 #1734 := (iff #1066 #1733) -#1731 := (iff #554 #1730) -#1728 := (iff #549 #1725) -#1722 := (or #1315 #548) -#1726 := (iff #1722 #1725) -#1727 := [rewrite]: #1726 -#1723 := (iff #549 #1722) -#1720 := (iff #112 #1315) -#1721 := [rewrite]: #1720 -#1724 := [monotonicity #1721]: #1723 -#1729 := [trans #1724 #1727]: #1728 +#1731 := (iff #103 #1730) +#1728 := (iff #102 #1727) +#1729 := [rewrite]: #1728 #1732 := [quant-intro #1729]: #1731 #1735 := [monotonicity #1732]: #1734 -#1761 := [monotonicity #1735 #1758]: #1760 -#1743 := (iff #1075 #1742) -#1740 := (iff #103 #1739) -#1737 := (iff #102 #1736) -#1738 := [rewrite]: #1737 -#1741 := [quant-intro #1738]: #1740 -#1744 := [monotonicity #1741]: #1743 -#1764 := [monotonicity #1744 #1761]: #1763 -#1748 := (iff #1084 #1747) -#1745 := (iff #530 #100) -#1746 := [rewrite]: #1745 -#1749 := [monotonicity #1746]: #1748 -#1767 := [monotonicity #1749 #1764]: #1766 -#1751 := (iff #1100 #1750) -#1295 := (iff #527 #1294) -#1292 := (iff #522 #1291) -#1289 := (iff #515 #1288) -#1286 := (iff #512 #1283) -#1277 := (and #1271 #454) -#1280 := (and #1274 #1277) -#1284 := (iff #1280 #1283) -#1285 := [rewrite]: #1284 -#1281 := (iff #512 #1280) -#1278 := (iff #507 #1277) -#1272 := (iff #92 #1271) -#1273 := [rewrite]: #1272 -#1279 := [monotonicity #1273]: #1278 -#1275 := (iff #91 #1274) +#1755 := [monotonicity #1735 #1752]: #1754 +#1739 := (iff #1075 #1738) +#1736 := (iff #529 #100) +#1737 := [rewrite]: #1736 +#1740 := [monotonicity #1737]: #1739 +#1758 := [monotonicity #1740 #1755]: #1757 +#1742 := (iff #1091 #1741) +#1286 := (iff #526 #1285) +#1283 := (iff #521 #1282) +#1280 := (iff #514 #1279) +#1277 := (iff #511 #1274) +#1268 := (and #1262 #453) +#1271 := (and #1265 #1268) +#1275 := (iff #1271 #1274) #1276 := [rewrite]: #1275 -#1282 := [monotonicity #1276 #1279]: #1281 -#1287 := [trans #1282 #1285]: #1286 -#1290 := [quant-intro #1287]: #1289 -#1269 := (iff #521 #1268) -#1266 := (iff #90 #1265) -#1263 := (iff #89 #1262) +#1272 := (iff #511 #1271) +#1269 := (iff #506 #1268) +#1263 := (iff #92 #1262) #1264 := [rewrite]: #1263 -#1267 := [monotonicity #1264]: #1266 -#1270 := [monotonicity #1267]: #1269 -#1293 := [monotonicity #1270 #1290]: #1292 -#1296 := [quant-intro #1293]: #1295 -#1752 := [monotonicity #1296]: #1751 -#1770 := [monotonicity #1752 #1767]: #1769 -#1775 := [trans #1770 #1773]: #1774 -#1778 := [monotonicity #1296 #1775]: #1777 -#1257 := (iff #1112 #1256) -#1254 := (iff #501 #1253) -#1251 := (iff #496 #1250) -#1248 := (iff #495 #1247) -#1245 := (iff #487 #1242) -#1239 := (and #1236 #454) -#1243 := (iff #1239 #1242) -#1244 := [rewrite]: #1243 -#1240 := (iff #487 #1239) -#1241 := [monotonicity #1238]: #1240 -#1246 := [trans #1241 #1244]: #1245 +#1270 := [monotonicity #1264]: #1269 +#1266 := (iff #91 #1265) +#1267 := [rewrite]: #1266 +#1273 := [monotonicity #1267 #1270]: #1272 +#1278 := [trans #1273 #1276]: #1277 +#1281 := [quant-intro #1278]: #1280 +#1260 := (iff #520 #1259) +#1257 := (iff #90 #1256) +#1254 := (iff #89 #1253) +#1255 := [rewrite]: #1254 +#1258 := [monotonicity #1255]: #1257 +#1261 := [monotonicity #1258]: #1260 +#1284 := [monotonicity #1261 #1281]: #1283 +#1287 := [quant-intro #1284]: #1286 +#1743 := [monotonicity #1287]: #1742 +#1761 := [monotonicity #1743 #1758]: #1760 +#1766 := [trans #1761 #1764]: #1765 +#1769 := [monotonicity #1287 #1766]: #1768 +#1248 := (iff #1103 #1247) +#1245 := (iff #500 #1244) +#1242 := (iff #495 #1241) +#1239 := (iff #494 #1238) +#1236 := (iff #486 #1233) +#1230 := (and #1227 #453) +#1234 := (iff #1230 #1233) +#1235 := [rewrite]: #1234 +#1231 := (iff #486 #1230) +#1232 := [monotonicity #1229]: #1231 +#1237 := [trans #1232 #1235]: #1236 +#1240 := [monotonicity #1237]: #1239 +#1220 := (iff #86 #1221) +#1219 := [rewrite]: #1220 +#1243 := [monotonicity #1219 #1240]: #1242 +#1246 := [quant-intro #1243]: #1245 #1249 := [monotonicity #1246]: #1248 -#1229 := (iff #86 #1230) -#1228 := [rewrite]: #1229 -#1252 := [monotonicity #1228 #1249]: #1251 -#1255 := [quant-intro #1252]: #1254 -#1258 := [monotonicity #1255]: #1257 -#1781 := [monotonicity #1258 #1778]: #1780 -#1784 := [monotonicity #1255 #1781]: #1783 -#1226 := (iff #1124 #1225) -#1223 := (iff #481 #1222) -#1220 := (iff #476 #1217) -#1214 := (or #1210 #475) -#1218 := (iff #1214 #1217) -#1219 := [rewrite]: #1218 -#1215 := (iff #476 #1214) -#1209 := (iff #78 #1210) -#1213 := [rewrite]: #1209 -#1216 := [monotonicity #1213]: #1215 -#1221 := [trans #1216 #1219]: #1220 -#1224 := [quant-intro #1221]: #1223 -#1227 := [monotonicity #1224]: #1226 -#1787 := [monotonicity #1227 #1784]: #1786 -#1790 := [monotonicity #1224 #1787]: #1789 -#1206 := (iff #1136 #1205) -#1203 := (iff #73 #1202) -#1199 := (iff #72 #1201) -#1200 := [rewrite]: #1199 -#1204 := [quant-intro #1200]: #1203 +#1772 := [monotonicity #1249 #1769]: #1771 +#1775 := [monotonicity #1246 #1772]: #1774 +#1217 := (iff #1115 #1216) +#1214 := (iff #480 #1213) +#1211 := (iff #475 #1208) +#1205 := (or #1201 #474) +#1209 := (iff #1205 #1208) +#1210 := [rewrite]: #1209 +#1206 := (iff #475 #1205) +#1200 := (iff #78 #1201) +#1204 := [rewrite]: #1200 #1207 := [monotonicity #1204]: #1206 -#1793 := [monotonicity #1207 #1790]: #1792 -#1796 := [monotonicity #1204 #1793]: #1795 -#1197 := (iff #1148 #1196) -#1194 := (iff #463 #71) -#1195 := [rewrite]: #1194 +#1212 := [trans #1207 #1210]: #1211 +#1215 := [quant-intro #1212]: #1214 +#1218 := [monotonicity #1215]: #1217 +#1778 := [monotonicity #1218 #1775]: #1777 +#1781 := [monotonicity #1215 #1778]: #1780 +#1197 := (iff #1127 #1196) +#1194 := (iff #73 #1193) +#1190 := (iff #72 #1192) +#1191 := [rewrite]: #1190 +#1195 := [quant-intro #1191]: #1194 #1198 := [monotonicity #1195]: #1197 -#1799 := [monotonicity #1198 #1796]: #1798 -#1802 := [monotonicity #1195 #1799]: #1801 -#1816 := [monotonicity #1802]: #1815 -#1819 := [monotonicity #1816]: #1818 -#1812 := (iff #1178 #1811) -#1809 := (iff #437 #1808) -#1806 := (iff #432 #1805) -#1803 := (iff #426 #59) -#1804 := [rewrite]: #1803 -#1807 := [monotonicity #1804]: #1806 -#1810 := [quant-intro #1807]: #1809 -#1813 := [monotonicity #1810]: #1812 -#1822 := [monotonicity #1813 #1819]: #1821 -#1827 := [trans #1822 #1825]: #1826 -#1830 := [monotonicity #1827]: #1829 -#1192 := (iff #271 #1191) -#1189 := (iff #270 #1179) -#1184 := (implies true #1179) -#1187 := (iff #1184 #1179) -#1188 := [rewrite]: #1187 -#1185 := (iff #270 #1184) -#1182 := (iff #269 #1179) -#1175 := (implies #437 #1170) -#1180 := (iff #1175 #1179) -#1181 := [rewrite]: #1180 +#1784 := [monotonicity #1198 #1781]: #1783 +#1787 := [monotonicity #1195 #1784]: #1786 +#1188 := (iff #1139 #1187) +#1185 := (iff #462 #71) +#1186 := [rewrite]: #1185 +#1189 := [monotonicity #1186]: #1188 +#1790 := [monotonicity #1189 #1787]: #1789 +#1793 := [monotonicity #1186 #1790]: #1792 +#1807 := [monotonicity #1793]: #1806 +#1810 := [monotonicity #1807]: #1809 +#1803 := (iff #1169 #1802) +#1800 := (iff #436 #1799) +#1797 := (iff #431 #1796) +#1794 := (iff #425 #59) +#1795 := [rewrite]: #1794 +#1798 := [monotonicity #1795]: #1797 +#1801 := [quant-intro #1798]: #1800 +#1804 := [monotonicity #1801]: #1803 +#1813 := [monotonicity #1804 #1810]: #1812 +#1818 := [trans #1813 #1816]: #1817 +#1821 := [monotonicity #1818]: #1820 +#1183 := (iff #270 #1182) +#1180 := (iff #269 #1170) +#1175 := (implies true #1170) +#1178 := (iff #1175 #1170) +#1179 := [rewrite]: #1178 #1176 := (iff #269 #1175) #1173 := (iff #268 #1170) -#1166 := (implies #451 #1161) +#1166 := (implies #436 #1161) #1171 := (iff #1166 #1170) #1172 := [rewrite]: #1171 #1167 := (iff #268 #1166) #1164 := (iff #267 #1161) -#1157 := (implies #460 #1154) +#1157 := (implies #450 #1152) #1162 := (iff #1157 #1161) #1163 := [rewrite]: #1162 #1158 := (iff #267 #1157) -#1155 := (iff #266 #1154) -#1152 := (iff #265 #1149) -#1145 := (implies #463 #1142) -#1150 := (iff #1145 #1149) -#1151 := [rewrite]: #1150 +#1155 := (iff #266 #1152) +#1148 := (implies #459 #1145) +#1153 := (iff #1148 #1152) +#1154 := [rewrite]: #1153 +#1149 := (iff #266 #1148) #1146 := (iff #265 #1145) -#1143 := (iff #264 #1142) -#1140 := (iff #263 #1137) -#1133 := (implies #73 #1130) -#1138 := (iff #1133 #1137) -#1139 := [rewrite]: #1138 +#1143 := (iff #264 #1140) +#1136 := (implies #462 #1133) +#1141 := (iff #1136 #1140) +#1142 := [rewrite]: #1141 +#1137 := (iff #264 #1136) #1134 := (iff #263 #1133) -#1131 := (iff #262 #1130) -#1128 := (iff #261 #1125) -#1121 := (implies #481 #1118) -#1126 := (iff #1121 #1125) -#1127 := [rewrite]: #1126 +#1131 := (iff #262 #1128) +#1124 := (implies #73 #1121) +#1129 := (iff #1124 #1128) +#1130 := [rewrite]: #1129 +#1125 := (iff #262 #1124) #1122 := (iff #261 #1121) -#1119 := (iff #260 #1118) -#1116 := (iff #259 #1113) -#1109 := (implies #501 #1106) -#1114 := (iff #1109 #1113) -#1115 := [rewrite]: #1114 +#1119 := (iff #260 #1116) +#1112 := (implies #480 #1109) +#1117 := (iff #1112 #1116) +#1118 := [rewrite]: #1117 +#1113 := (iff #260 #1112) #1110 := (iff #259 #1109) -#1107 := (iff #258 #1106) -#1104 := (iff #257 #1101) -#1097 := (implies #527 #1085) -#1102 := (iff #1097 #1101) -#1103 := [rewrite]: #1102 +#1107 := (iff #258 #1104) +#1100 := (implies #500 #1097) +#1105 := (iff #1100 #1104) +#1106 := [rewrite]: #1105 +#1101 := (iff #258 #1100) #1098 := (iff #257 #1097) -#1095 := (iff #256 #1085) -#1090 := (implies true #1085) -#1093 := (iff #1090 #1085) +#1095 := (iff #256 #1092) +#1088 := (implies #526 #1076) +#1093 := (iff #1088 #1092) #1094 := [rewrite]: #1093 -#1091 := (iff #256 #1090) -#1088 := (iff #255 #1085) -#1081 := (implies #530 #1076) -#1086 := (iff #1081 #1085) -#1087 := [rewrite]: #1086 +#1089 := (iff #256 #1088) +#1086 := (iff #255 #1076) +#1081 := (implies true #1076) +#1084 := (iff #1081 #1076) +#1085 := [rewrite]: #1084 #1082 := (iff #255 #1081) #1079 := (iff #254 #1076) -#1072 := (implies #103 #1067) +#1072 := (implies #529 #1067) #1077 := (iff #1072 #1076) #1078 := [rewrite]: #1077 #1073 := (iff #254 #1072) #1070 := (iff #253 #1067) -#1063 := (implies #554 #1058) +#1063 := (implies #103 #1058) #1068 := (iff #1063 #1067) #1069 := [rewrite]: #1068 #1064 := (iff #253 #1063) #1061 := (iff #252 #1058) -#1054 := (implies #580 #1049) +#1054 := (implies #553 #1049) #1059 := (iff #1054 #1058) #1060 := [rewrite]: #1059 #1055 := (iff #252 #1054) #1052 := (iff #251 #1049) -#1045 := (implies #604 #1042) +#1045 := (implies #579 #1040) #1050 := (iff #1045 #1049) #1051 := [rewrite]: #1050 #1046 := (iff #251 #1045) -#1043 := (iff #250 #1042) -#1040 := (iff #249 #1030) -#1035 := (implies true #1030) -#1038 := (iff #1035 #1030) -#1039 := [rewrite]: #1038 -#1036 := (iff #249 #1035) -#1033 := (iff #248 #1030) -#1027 := (implies #615 #1022) -#1031 := (iff #1027 #1030) -#1032 := [rewrite]: #1031 -#1028 := (iff #248 #1027) -#1025 := (iff #247 #1022) -#757 := (not #754) -#1019 := (implies #757 #1014) -#1023 := (iff #1019 #1022) -#1024 := [rewrite]: #1023 -#1020 := (iff #247 #1019) -#1017 := (iff #246 #1014) -#1010 := (implies #175 #1005) -#1015 := (iff #1010 #1014) -#1016 := [rewrite]: #1015 +#1043 := (iff #250 #1040) +#1036 := (implies #603 #1033) +#1041 := (iff #1036 #1040) +#1042 := [rewrite]: #1041 +#1037 := (iff #250 #1036) +#1034 := (iff #249 #1033) +#1031 := (iff #248 #1021) +#1026 := (implies true #1021) +#1029 := (iff #1026 #1021) +#1030 := [rewrite]: #1029 +#1027 := (iff #248 #1026) +#1024 := (iff #247 #1021) +#1018 := (implies #614 #1013) +#1022 := (iff #1018 #1021) +#1023 := [rewrite]: #1022 +#1019 := (iff #247 #1018) +#1016 := (iff #246 #1013) +#756 := (not #753) +#1010 := (implies #756 #1005) +#1014 := (iff #1010 #1013) +#1015 := [rewrite]: #1014 #1011 := (iff #246 #1010) #1008 := (iff #245 #1005) -#1001 := (implies #768 #996) +#1001 := (implies #175 #996) #1006 := (iff #1001 #1005) #1007 := [rewrite]: #1006 #1002 := (iff #245 #1001) #999 := (iff #244 #996) -#992 := (implies #776 #987) +#992 := (implies #767 #987) #997 := (iff #992 #996) #998 := [rewrite]: #997 #993 := (iff #244 #992) #990 := (iff #243 #987) -#983 := (implies #790 #978) +#983 := (implies #181 #978) #988 := (iff #983 #987) #989 := [rewrite]: #988 #984 := (iff #243 #983) #981 := (iff #242 #978) -#974 := (implies #804 #971) +#974 := (implies #781 #969) #979 := (iff #974 #978) #980 := [rewrite]: #979 #975 := (iff #242 #974) -#972 := (iff #241 #971) -#969 := (iff #240 #966) -#962 := (implies #198 #959) -#967 := (iff #962 #966) -#968 := [rewrite]: #967 +#972 := (iff #241 #969) +#965 := (implies #795 #962) +#970 := (iff #965 #969) +#971 := [rewrite]: #970 +#966 := (iff #241 #965) #963 := (iff #240 #962) -#960 := (iff #239 #959) -#957 := (iff #238 #954) -#950 := (implies #819 #947) -#955 := (iff #950 #954) -#956 := [rewrite]: #955 +#960 := (iff #239 #957) +#953 := (implies #197 #950) +#958 := (iff #953 #957) +#959 := [rewrite]: #958 +#954 := (iff #239 #953) #951 := (iff #238 #950) -#948 := (iff #237 #947) -#945 := (iff #236 #942) -#938 := (implies #822 #935) -#943 := (iff #938 #942) -#944 := [rewrite]: #943 +#948 := (iff #237 #945) +#941 := (implies #810 #938) +#946 := (iff #941 #945) +#947 := [rewrite]: #946 +#942 := (iff #237 #941) #939 := (iff #236 #938) -#936 := (iff #235 #935) -#933 := (iff #234 #930) -#926 := (implies #206 #923) -#931 := (iff #926 #930) -#932 := [rewrite]: #931 +#936 := (iff #235 #933) +#929 := (implies #813 #926) +#934 := (iff #929 #933) +#935 := [rewrite]: #934 +#930 := (iff #235 #929) #927 := (iff #234 #926) -#924 := (iff #233 #923) -#921 := (iff #232 #918) -#914 := (implies #842 #911) -#919 := (iff #914 #918) -#920 := [rewrite]: #919 +#924 := (iff #233 #921) +#917 := (implies #205 #914) +#922 := (iff #917 #921) +#923 := [rewrite]: #922 +#918 := (iff #233 #917) #915 := (iff #232 #914) -#912 := (iff #231 #911) -#909 := (iff #230 #906) -#902 := (implies #868 #892) -#907 := (iff #902 #906) -#908 := [rewrite]: #907 +#912 := (iff #231 #909) +#905 := (implies #833 #902) +#910 := (iff #905 #909) +#911 := [rewrite]: #910 +#906 := (iff #231 #905) #903 := (iff #230 #902) -#900 := (iff #229 #892) -#895 := (and #892 true) -#898 := (iff #895 #892) +#900 := (iff #229 #897) +#893 := (implies #859 #883) +#898 := (iff #893 #897) #899 := [rewrite]: #898 -#896 := (iff #229 #895) -#893 := (iff #228 #892) -#890 := (iff #227 #887) -#883 := (implies #221 #880) -#888 := (iff #883 #887) -#889 := [rewrite]: #888 +#894 := (iff #229 #893) +#891 := (iff #228 #883) +#886 := (and #883 true) +#889 := (iff #886 #883) +#890 := [rewrite]: #889 +#887 := (iff #228 #886) #884 := (iff #227 #883) -#881 := (iff #226 #880) -#878 := (iff #225 #877) -#875 := (iff #224 #874) -#872 := (iff #223 #871) -#854 := (= #216 #853) -#855 := [rewrite]: #854 -#873 := [monotonicity #855]: #872 -#808 := (iff #200 #807) -#809 := [rewrite]: #808 -#876 := [monotonicity #809 #873]: #875 -#879 := [monotonicity #876]: #878 -#882 := [quant-intro #879]: #881 -#885 := [monotonicity #882]: #884 -#891 := [trans #885 #889]: #890 -#894 := [quant-intro #891]: #893 -#897 := [monotonicity #894]: #896 -#901 := [trans #897 #899]: #900 -#869 := (iff #219 #868) -#866 := (iff #218 #863) -#859 := (implies #848 #856) -#864 := (iff #859 #863) -#865 := [rewrite]: #864 +#881 := (iff #226 #878) +#874 := (implies #220 #871) +#879 := (iff #874 #878) +#880 := [rewrite]: #879 +#875 := (iff #226 #874) +#872 := (iff #225 #871) +#869 := (iff #224 #868) +#866 := (iff #223 #865) +#863 := (iff #222 #862) +#845 := (= #215 #844) +#846 := [rewrite]: #845 +#864 := [monotonicity #846]: #863 +#799 := (iff #199 #798) +#800 := [rewrite]: #799 +#867 := [monotonicity #800 #864]: #866 +#870 := [monotonicity #867]: #869 +#873 := [quant-intro #870]: #872 +#876 := [monotonicity #873]: #875 +#882 := [trans #876 #880]: #881 +#885 := [quant-intro #882]: #884 +#888 := [monotonicity #885]: #887 +#892 := [trans #888 #890]: #891 #860 := (iff #218 #859) -#857 := (iff #217 #856) -#858 := [monotonicity #855]: #857 -#851 := (iff #215 #848) -#845 := (and #807 #83) -#849 := (iff #845 #848) -#850 := [rewrite]: #849 -#846 := (iff #215 #845) -#847 := [monotonicity #809]: #846 -#852 := [trans #847 #850]: #851 -#861 := [monotonicity #852 #858]: #860 -#867 := [trans #861 #865]: #866 -#870 := [quant-intro #867]: #869 -#904 := [monotonicity #870 #901]: #903 -#910 := [trans #904 #908]: #909 -#913 := [monotonicity #870 #910]: #912 -#843 := (iff #214 #842) -#840 := (iff #213 #837) -#833 := (implies #830 #212) -#838 := (iff #833 #837) -#839 := [rewrite]: #838 +#857 := (iff #217 #854) +#850 := (implies #839 #847) +#855 := (iff #850 #854) +#856 := [rewrite]: #855 +#851 := (iff #217 #850) +#848 := (iff #216 #847) +#849 := [monotonicity #846]: #848 +#842 := (iff #214 #839) +#836 := (and #798 #83) +#840 := (iff #836 #839) +#841 := [rewrite]: #840 +#837 := (iff #214 #836) +#838 := [monotonicity #800]: #837 +#843 := [trans #838 #841]: #842 +#852 := [monotonicity #843 #849]: #851 +#858 := [trans #852 #856]: #857 +#861 := [quant-intro #858]: #860 +#895 := [monotonicity #861 #892]: #894 +#901 := [trans #895 #899]: #900 +#904 := [monotonicity #861 #901]: #903 #834 := (iff #213 #833) -#831 := (iff #210 #830) -#828 := (iff #209 #827) -#829 := [rewrite]: #828 -#825 := (iff #207 #813) -#826 := [monotonicity #809]: #825 -#832 := [monotonicity #826 #829]: #831 -#835 := [monotonicity #832]: #834 -#841 := [trans #835 #839]: #840 -#844 := [quant-intro #841]: #843 -#916 := [monotonicity #844 #913]: #915 -#922 := [trans #916 #920]: #921 -#925 := [monotonicity #844 #922]: #924 +#831 := (iff #212 #828) +#824 := (implies #821 #211) +#829 := (iff #824 #828) +#830 := [rewrite]: #829 +#825 := (iff #212 #824) +#822 := (iff #209 #821) +#819 := (iff #208 #818) +#820 := [rewrite]: #819 +#816 := (iff #206 #804) +#817 := [monotonicity #800]: #816 +#823 := [monotonicity #817 #820]: #822 +#826 := [monotonicity #823]: #825 +#832 := [trans #826 #830]: #831 +#835 := [quant-intro #832]: #834 +#907 := [monotonicity #835 #904]: #906 +#913 := [trans #907 #911]: #912 +#916 := [monotonicity #835 #913]: #915 +#919 := [monotonicity #916]: #918 +#925 := [trans #919 #923]: #924 #928 := [monotonicity #925]: #927 -#934 := [trans #928 #932]: #933 -#937 := [monotonicity #934]: #936 -#823 := (iff #204 #822) -#824 := [rewrite]: #823 -#940 := [monotonicity #824 #937]: #939 -#946 := [trans #940 #944]: #945 -#949 := [monotonicity #824 #946]: #948 -#820 := (iff #202 #819) -#817 := (iff #201 #814) -#810 := (implies #807 #793) -#815 := (iff #810 #814) -#816 := [rewrite]: #815 +#814 := (iff #203 #813) +#815 := [rewrite]: #814 +#931 := [monotonicity #815 #928]: #930 +#937 := [trans #931 #935]: #936 +#940 := [monotonicity #815 #937]: #939 #811 := (iff #201 #810) -#794 := (iff #194 #793) -#795 := [rewrite]: #794 -#812 := [monotonicity #809 #795]: #811 -#818 := [trans #812 #816]: #817 -#821 := [quant-intro #818]: #820 -#952 := [monotonicity #821 #949]: #951 -#958 := [trans #952 #956]: #957 -#961 := [monotonicity #821 #958]: #960 +#808 := (iff #200 #805) +#801 := (implies #798 #784) +#806 := (iff #801 #805) +#807 := [rewrite]: #806 +#802 := (iff #200 #801) +#785 := (iff #193 #784) +#786 := [rewrite]: #785 +#803 := [monotonicity #800 #786]: #802 +#809 := [trans #803 #807]: #808 +#812 := [quant-intro #809]: #811 +#943 := [monotonicity #812 #940]: #942 +#949 := [trans #943 #947]: #948 +#952 := [monotonicity #812 #949]: #951 +#955 := [monotonicity #952]: #954 +#961 := [trans #955 #959]: #960 #964 := [monotonicity #961]: #963 -#970 := [trans #964 #968]: #969 -#973 := [monotonicity #970]: #972 -#805 := (iff #196 #804) -#802 := (iff #195 #799) -#796 := (implies #193 #793) -#800 := (iff #796 #799) -#801 := [rewrite]: #800 -#797 := (iff #195 #796) -#798 := [monotonicity #795]: #797 -#803 := [trans #798 #801]: #802 -#806 := [quant-intro #803]: #805 -#976 := [monotonicity #806 #973]: #975 -#982 := [trans #976 #980]: #981 -#791 := (iff #192 #790) -#788 := (iff #191 #785) -#782 := (implies #188 #779) -#786 := (iff #782 #785) -#787 := [rewrite]: #786 -#783 := (iff #191 #782) -#780 := (iff #190 #779) -#781 := [rewrite]: #780 -#784 := [monotonicity #781]: #783 -#789 := [trans #784 #787]: #788 -#792 := [quant-intro #789]: #791 -#985 := [monotonicity #792 #982]: #984 -#991 := [trans #985 #989]: #990 -#777 := (iff #182 #776) -#774 := (= #181 #773) -#771 := (= #180 f1) +#796 := (iff #195 #795) +#793 := (iff #194 #790) +#787 := (implies #192 #784) +#791 := (iff #787 #790) +#792 := [rewrite]: #791 +#788 := (iff #194 #787) +#789 := [monotonicity #786]: #788 +#794 := [trans #789 #792]: #793 +#797 := [quant-intro #794]: #796 +#967 := [monotonicity #797 #964]: #966 +#973 := [trans #967 #971]: #972 +#782 := (iff #191 #781) +#779 := (iff #190 #776) +#773 := (implies #187 #770) +#777 := (iff #773 #776) +#778 := [rewrite]: #777 +#774 := (iff #190 #773) +#771 := (iff #189 #770) #772 := [rewrite]: #771 #775 := [monotonicity #772]: #774 -#778 := [monotonicity #775]: #777 -#994 := [monotonicity #778 #991]: #993 +#780 := [trans #775 #778]: #779 +#783 := [quant-intro #780]: #782 +#976 := [monotonicity #783 #973]: #975 +#982 := [trans #976 #980]: #981 +#985 := [monotonicity #982]: #984 +#991 := [trans #985 #989]: #990 +#768 := (iff #178 #767) +#765 := (iff #177 #762) +#759 := (implies #535 #176) +#763 := (iff #759 #762) +#764 := [rewrite]: #763 +#760 := (iff #177 #759) +#536 := (iff #107 #535) +#533 := (iff #106 #532) +#534 := [rewrite]: #533 +#537 := [monotonicity #534]: #536 +#761 := [monotonicity #537]: #760 +#766 := [trans #761 #764]: #765 +#769 := [quant-intro #766]: #768 +#994 := [monotonicity #769 #991]: #993 #1000 := [trans #994 #998]: #999 -#769 := (iff #178 #768) -#766 := (iff #177 #763) -#760 := (implies #536 #176) -#764 := (iff #760 #763) -#765 := [rewrite]: #764 -#761 := (iff #177 #760) -#537 := (iff #107 #536) -#534 := (iff #106 #533) -#535 := [rewrite]: #534 -#538 := [monotonicity #535]: #537 -#762 := [monotonicity #538]: #761 -#767 := [trans #762 #765]: #766 -#770 := [quant-intro #767]: #769 -#1003 := [monotonicity #770 #1000]: #1002 +#1003 := [monotonicity #1000]: #1002 #1009 := [trans #1003 #1007]: #1008 -#1012 := [monotonicity #1009]: #1011 -#1018 := [trans #1012 #1016]: #1017 -#758 := (iff #173 #757) -#755 := (iff #172 #754) -#756 := [rewrite]: #755 -#759 := [monotonicity #756]: #758 -#1021 := [monotonicity #759 #1018]: #1020 -#1026 := [trans #1021 #1024]: #1025 -#616 := (iff #130 #615) -#613 := (iff #129 #610) -#607 := (and #536 #120) -#611 := (iff #607 #610) -#612 := [rewrite]: #611 -#608 := (iff #129 #607) -#609 := [monotonicity #538]: #608 -#614 := [trans #609 #612]: #613 -#617 := [quant-intro #614]: #616 -#1029 := [monotonicity #617 #1026]: #1028 -#1034 := [trans #1029 #1032]: #1033 -#1037 := [monotonicity #1034]: #1036 -#1041 := [trans #1037 #1039]: #1040 -#752 := (iff #169 #742) -#747 := (implies true #742) -#750 := (iff #747 #742) -#751 := [rewrite]: #750 -#748 := (iff #169 #747) -#745 := (iff #168 #742) -#739 := (implies #618 #734) -#743 := (iff #739 #742) -#744 := [rewrite]: #743 -#740 := (iff #168 #739) -#737 := (iff #167 #734) -#730 := (implies #621 #725) -#735 := (iff #730 #734) -#736 := [rewrite]: #735 -#731 := (iff #167 #730) -#728 := (iff #166 #725) -#721 := (implies #136 #716) -#726 := (iff #721 #725) -#727 := [rewrite]: #726 -#722 := (iff #166 #721) -#719 := (iff #165 #716) -#712 := (implies #624 #707) -#717 := (iff #712 #716) -#718 := [rewrite]: #717 -#713 := (iff #165 #712) -#710 := (iff #164 #707) -#703 := (implies #141 #700) -#708 := (iff #703 #707) -#709 := [rewrite]: #708 -#704 := (iff #164 #703) -#701 := (iff #163 #700) -#698 := (iff #162 #695) -#691 := (implies #648 #688) -#696 := (iff #691 #695) -#697 := [rewrite]: #696 -#692 := (iff #162 #691) -#689 := (iff #161 #688) -#686 := (iff #160 #683) -#679 := (implies #666 #669) -#684 := (iff #679 #683) -#685 := [rewrite]: #684 -#680 := (iff #160 #679) -#677 := (iff #159 #669) -#672 := (and #669 true) -#675 := (iff #672 #669) -#676 := [rewrite]: #675 -#673 := (iff #159 #672) -#670 := (iff #158 #669) -#671 := [rewrite]: #670 -#674 := [monotonicity #671]: #673 -#678 := [trans #674 #676]: #677 -#667 := (iff #156 #666) -#664 := (iff #155 #661) -#657 := (implies #651 #654) -#662 := (iff #657 #661) -#663 := [rewrite]: #662 -#658 := (iff #155 #657) -#655 := (iff #154 #654) -#628 := (= #147 #627) -#629 := [rewrite]: #628 -#656 := [monotonicity #629]: #655 -#652 := (iff #153 #651) -#653 := [rewrite]: #652 -#659 := [monotonicity #653 #656]: #658 -#665 := [trans #659 #663]: #664 -#668 := [quant-intro #665]: #667 -#681 := [monotonicity #668 #678]: #680 -#687 := [trans #681 #685]: #686 -#690 := [monotonicity #668 #687]: #689 -#649 := (iff #152 #648) -#646 := (iff #151 #643) -#639 := (implies #144 #636) -#644 := (iff #639 #643) -#645 := [rewrite]: #644 -#640 := (iff #151 #639) -#637 := (iff #150 #636) -#634 := (iff #149 #633) -#631 := (iff #148 #630) -#632 := [monotonicity #629]: #631 -#635 := [monotonicity #632]: #634 -#638 := [quant-intro #635]: #637 -#641 := [monotonicity #638]: #640 -#647 := [trans #641 #645]: #646 -#650 := [quant-intro #647]: #649 -#693 := [monotonicity #650 #690]: #692 -#699 := [trans #693 #697]: #698 -#702 := [monotonicity #650 #699]: #701 -#705 := [monotonicity #702]: #704 -#711 := [trans #705 #709]: #710 -#625 := (iff #138 #624) -#626 := [rewrite]: #625 -#714 := [monotonicity #626 #711]: #713 -#720 := [trans #714 #718]: #719 -#723 := [monotonicity #720]: #722 -#729 := [trans #723 #727]: #728 -#622 := (iff #133 #621) -#623 := [rewrite]: #622 -#732 := [monotonicity #623 #729]: #731 -#738 := [trans #732 #736]: #737 -#619 := (iff #131 #618) -#620 := [monotonicity #617]: #619 -#741 := [monotonicity #620 #738]: #740 -#746 := [trans #741 #744]: #745 -#749 := [monotonicity #746]: #748 -#753 := [trans #749 #751]: #752 -#1044 := [monotonicity #753 #1041]: #1043 -#605 := (iff #128 #604) -#602 := (iff #127 #599) -#595 := (implies #121 #592) -#600 := (iff #595 #599) -#601 := [rewrite]: #600 -#596 := (iff #127 #595) -#593 := (iff #126 #592) -#590 := (iff #125 #589) -#587 := (iff #124 #586) -#584 := (iff #123 #583) -#566 := (= #116 #565) -#567 := [rewrite]: #566 -#585 := [monotonicity #567]: #584 -#588 := [monotonicity #535 #585]: #587 -#591 := [monotonicity #588]: #590 -#594 := [quant-intro #591]: #593 -#597 := [monotonicity #594]: #596 -#603 := [trans #597 #601]: #602 -#606 := [quant-intro #603]: #605 -#1047 := [monotonicity #606 #1044]: #1046 +#757 := (iff #173 #756) +#754 := (iff #172 #753) +#755 := [rewrite]: #754 +#758 := [monotonicity #755]: #757 +#1012 := [monotonicity #758 #1009]: #1011 +#1017 := [trans #1012 #1015]: #1016 +#615 := (iff #130 #614) +#612 := (iff #129 #609) +#606 := (and #535 #120) +#610 := (iff #606 #609) +#611 := [rewrite]: #610 +#607 := (iff #129 #606) +#608 := [monotonicity #537]: #607 +#613 := [trans #608 #611]: #612 +#616 := [quant-intro #613]: #615 +#1020 := [monotonicity #616 #1017]: #1019 +#1025 := [trans #1020 #1023]: #1024 +#1028 := [monotonicity #1025]: #1027 +#1032 := [trans #1028 #1030]: #1031 +#751 := (iff #169 #741) +#746 := (implies true #741) +#749 := (iff #746 #741) +#750 := [rewrite]: #749 +#747 := (iff #169 #746) +#744 := (iff #168 #741) +#738 := (implies #617 #733) +#742 := (iff #738 #741) +#743 := [rewrite]: #742 +#739 := (iff #168 #738) +#736 := (iff #167 #733) +#729 := (implies #620 #724) +#734 := (iff #729 #733) +#735 := [rewrite]: #734 +#730 := (iff #167 #729) +#727 := (iff #166 #724) +#720 := (implies #136 #715) +#725 := (iff #720 #724) +#726 := [rewrite]: #725 +#721 := (iff #166 #720) +#718 := (iff #165 #715) +#711 := (implies #623 #706) +#716 := (iff #711 #715) +#717 := [rewrite]: #716 +#712 := (iff #165 #711) +#709 := (iff #164 #706) +#702 := (implies #141 #699) +#707 := (iff #702 #706) +#708 := [rewrite]: #707 +#703 := (iff #164 #702) +#700 := (iff #163 #699) +#697 := (iff #162 #694) +#690 := (implies #647 #687) +#695 := (iff #690 #694) +#696 := [rewrite]: #695 +#691 := (iff #162 #690) +#688 := (iff #161 #687) +#685 := (iff #160 #682) +#678 := (implies #665 #668) +#683 := (iff #678 #682) +#684 := [rewrite]: #683 +#679 := (iff #160 #678) +#676 := (iff #159 #668) +#671 := (and #668 true) +#674 := (iff #671 #668) +#675 := [rewrite]: #674 +#672 := (iff #159 #671) +#669 := (iff #158 #668) +#670 := [rewrite]: #669 +#673 := [monotonicity #670]: #672 +#677 := [trans #673 #675]: #676 +#666 := (iff #156 #665) +#663 := (iff #155 #660) +#656 := (implies #650 #653) +#661 := (iff #656 #660) +#662 := [rewrite]: #661 +#657 := (iff #155 #656) +#654 := (iff #154 #653) +#627 := (= #147 #626) +#628 := [rewrite]: #627 +#655 := [monotonicity #628]: #654 +#651 := (iff #153 #650) +#652 := [rewrite]: #651 +#658 := [monotonicity #652 #655]: #657 +#664 := [trans #658 #662]: #663 +#667 := [quant-intro #664]: #666 +#680 := [monotonicity #667 #677]: #679 +#686 := [trans #680 #684]: #685 +#689 := [monotonicity #667 #686]: #688 +#648 := (iff #152 #647) +#645 := (iff #151 #642) +#638 := (implies #144 #635) +#643 := (iff #638 #642) +#644 := [rewrite]: #643 +#639 := (iff #151 #638) +#636 := (iff #150 #635) +#633 := (iff #149 #632) +#630 := (iff #148 #629) +#631 := [monotonicity #628]: #630 +#634 := [monotonicity #631]: #633 +#637 := [quant-intro #634]: #636 +#640 := [monotonicity #637]: #639 +#646 := [trans #640 #644]: #645 +#649 := [quant-intro #646]: #648 +#692 := [monotonicity #649 #689]: #691 +#698 := [trans #692 #696]: #697 +#701 := [monotonicity #649 #698]: #700 +#704 := [monotonicity #701]: #703 +#710 := [trans #704 #708]: #709 +#624 := (iff #138 #623) +#625 := [rewrite]: #624 +#713 := [monotonicity #625 #710]: #712 +#719 := [trans #713 #717]: #718 +#722 := [monotonicity #719]: #721 +#728 := [trans #722 #726]: #727 +#621 := (iff #133 #620) +#622 := [rewrite]: #621 +#731 := [monotonicity #622 #728]: #730 +#737 := [trans #731 #735]: #736 +#618 := (iff #131 #617) +#619 := [monotonicity #616]: #618 +#740 := [monotonicity #619 #737]: #739 +#745 := [trans #740 #743]: #744 +#748 := [monotonicity #745]: #747 +#752 := [trans #748 #750]: #751 +#1035 := [monotonicity #752 #1032]: #1034 +#604 := (iff #128 #603) +#601 := (iff #127 #598) +#594 := (implies #121 #591) +#599 := (iff #594 #598) +#600 := [rewrite]: #599 +#595 := (iff #127 #594) +#592 := (iff #126 #591) +#589 := (iff #125 #588) +#586 := (iff #124 #585) +#583 := (iff #123 #582) +#565 := (= #116 #564) +#566 := [rewrite]: #565 +#584 := [monotonicity #566]: #583 +#587 := [monotonicity #534 #584]: #586 +#590 := [monotonicity #587]: #589 +#593 := [quant-intro #590]: #592 +#596 := [monotonicity #593]: #595 +#602 := [trans #596 #600]: #601 +#605 := [quant-intro #602]: #604 +#1038 := [monotonicity #605 #1035]: #1037 +#1044 := [trans #1038 #1042]: #1043 +#580 := (iff #119 #579) +#577 := (iff #118 #574) +#570 := (implies #559 #567) +#575 := (iff #570 #574) +#576 := [rewrite]: #575 +#571 := (iff #118 #570) +#568 := (iff #117 #567) +#569 := [monotonicity #566]: #568 +#562 := (iff #115 #559) +#556 := (and #532 #83) +#560 := (iff #556 #559) +#561 := [rewrite]: #560 +#557 := (iff #115 #556) +#558 := [monotonicity #534]: #557 +#563 := [trans #558 #561]: #562 +#572 := [monotonicity #563 #569]: #571 +#578 := [trans #572 #576]: #577 +#581 := [quant-intro #578]: #580 +#1047 := [monotonicity #581 #1044]: #1046 #1053 := [trans #1047 #1051]: #1052 -#581 := (iff #119 #580) -#578 := (iff #118 #575) -#571 := (implies #560 #568) -#576 := (iff #571 #575) -#577 := [rewrite]: #576 -#572 := (iff #118 #571) -#569 := (iff #117 #568) -#570 := [monotonicity #567]: #569 -#563 := (iff #115 #560) -#557 := (and #533 #83) -#561 := (iff #557 #560) -#562 := [rewrite]: #561 -#558 := (iff #115 #557) -#559 := [monotonicity #535]: #558 -#564 := [trans #559 #562]: #563 -#573 := [monotonicity #564 #570]: #572 -#579 := [trans #573 #577]: #578 -#582 := [quant-intro #579]: #581 -#1056 := [monotonicity #582 #1053]: #1055 +#554 := (iff #114 #553) +#551 := (iff #113 #548) +#544 := (implies #541 #112) +#549 := (iff #544 #548) +#550 := [rewrite]: #549 +#545 := (iff #113 #544) +#542 := (iff #110 #541) +#539 := (iff #109 #538) +#540 := [rewrite]: #539 +#543 := [monotonicity #537 #540]: #542 +#546 := [monotonicity #543]: #545 +#552 := [trans #546 #550]: #551 +#555 := [quant-intro #552]: #554 +#1056 := [monotonicity #555 #1053]: #1055 #1062 := [trans #1056 #1060]: #1061 -#555 := (iff #114 #554) -#552 := (iff #113 #549) -#545 := (implies #542 #112) -#550 := (iff #545 #549) -#551 := [rewrite]: #550 -#546 := (iff #113 #545) -#543 := (iff #110 #542) -#540 := (iff #109 #539) -#541 := [rewrite]: #540 -#544 := [monotonicity #538 #541]: #543 -#547 := [monotonicity #544]: #546 -#553 := [trans #547 #551]: #552 -#556 := [quant-intro #553]: #555 -#1065 := [monotonicity #556 #1062]: #1064 +#1065 := [monotonicity #1062]: #1064 #1071 := [trans #1065 #1069]: #1070 -#1074 := [monotonicity #1071]: #1073 +#530 := (iff #100 #529) +#531 := [rewrite]: #530 +#1074 := [monotonicity #531 #1071]: #1073 #1080 := [trans #1074 #1078]: #1079 -#531 := (iff #100 #530) -#532 := [rewrite]: #531 -#1083 := [monotonicity #532 #1080]: #1082 -#1089 := [trans #1083 #1087]: #1088 -#1092 := [monotonicity #1089]: #1091 -#1096 := [trans #1092 #1094]: #1095 -#528 := (iff #97 #527) -#525 := (iff #96 #522) -#518 := (implies #90 #515) -#523 := (iff #518 #522) -#524 := [rewrite]: #523 -#519 := (iff #96 #518) -#516 := (iff #95 #515) -#513 := (iff #94 #512) -#510 := (iff #93 #507) -#504 := (and #454 #92) -#508 := (iff #504 #507) -#509 := [rewrite]: #508 -#505 := (iff #93 #504) -#455 := (iff #67 #454) -#456 := [rewrite]: #455 -#506 := [monotonicity #456]: #505 -#511 := [trans #506 #509]: #510 -#514 := [monotonicity #511]: #513 -#517 := [quant-intro #514]: #516 -#520 := [monotonicity #517]: #519 -#526 := [trans #520 #524]: #525 -#529 := [quant-intro #526]: #528 -#1099 := [monotonicity #529 #1096]: #1098 -#1105 := [trans #1099 #1103]: #1104 -#1108 := [monotonicity #529 #1105]: #1107 -#502 := (iff #88 #501) -#499 := (iff #87 #496) -#492 := (implies #487 #86) -#497 := (iff #492 #496) -#498 := [rewrite]: #497 -#493 := (iff #87 #492) -#490 := (iff #84 #487) -#484 := (and #454 #83) -#488 := (iff #484 #487) -#489 := [rewrite]: #488 -#485 := (iff #84 #484) -#486 := [monotonicity #456]: #485 -#491 := [trans #486 #489]: #490 -#494 := [monotonicity #491]: #493 -#500 := [trans #494 #498]: #499 -#503 := [quant-intro #500]: #502 -#1111 := [monotonicity #503 #1108]: #1110 -#1117 := [trans #1111 #1115]: #1116 -#1120 := [monotonicity #503 #1117]: #1119 -#482 := (iff #80 #481) -#479 := (iff #79 #476) -#472 := (implies #469 #78) -#477 := (iff #472 #476) -#478 := [rewrite]: #477 -#473 := (iff #79 #472) -#470 := (iff #76 #469) -#467 := (iff #75 #466) -#468 := [rewrite]: #467 -#458 := (iff #68 #457) -#459 := [monotonicity #456]: #458 -#471 := [monotonicity #459 #468]: #470 -#474 := [monotonicity #471]: #473 -#480 := [trans #474 #478]: #479 -#483 := [quant-intro #480]: #482 -#1123 := [monotonicity #483 #1120]: #1122 -#1129 := [trans #1123 #1127]: #1128 -#1132 := [monotonicity #483 #1129]: #1131 +#1083 := [monotonicity #1080]: #1082 +#1087 := [trans #1083 #1085]: #1086 +#527 := (iff #97 #526) +#524 := (iff #96 #521) +#517 := (implies #90 #514) +#522 := (iff #517 #521) +#523 := [rewrite]: #522 +#518 := (iff #96 #517) +#515 := (iff #95 #514) +#512 := (iff #94 #511) +#509 := (iff #93 #506) +#503 := (and #453 #92) +#507 := (iff #503 #506) +#508 := [rewrite]: #507 +#504 := (iff #93 #503) +#454 := (iff #67 #453) +#455 := [rewrite]: #454 +#505 := [monotonicity #455]: #504 +#510 := [trans #505 #508]: #509 +#513 := [monotonicity #510]: #512 +#516 := [quant-intro #513]: #515 +#519 := [monotonicity #516]: #518 +#525 := [trans #519 #523]: #524 +#528 := [quant-intro #525]: #527 +#1090 := [monotonicity #528 #1087]: #1089 +#1096 := [trans #1090 #1094]: #1095 +#1099 := [monotonicity #528 #1096]: #1098 +#501 := (iff #88 #500) +#498 := (iff #87 #495) +#491 := (implies #486 #86) +#496 := (iff #491 #495) +#497 := [rewrite]: #496 +#492 := (iff #87 #491) +#489 := (iff #84 #486) +#483 := (and #453 #83) +#487 := (iff #483 #486) +#488 := [rewrite]: #487 +#484 := (iff #84 #483) +#485 := [monotonicity #455]: #484 +#490 := [trans #485 #488]: #489 +#493 := [monotonicity #490]: #492 +#499 := [trans #493 #497]: #498 +#502 := [quant-intro #499]: #501 +#1102 := [monotonicity #502 #1099]: #1101 +#1108 := [trans #1102 #1106]: #1107 +#1111 := [monotonicity #502 #1108]: #1110 +#481 := (iff #80 #480) +#478 := (iff #79 #475) +#471 := (implies #468 #78) +#476 := (iff #471 #475) +#477 := [rewrite]: #476 +#472 := (iff #79 #471) +#469 := (iff #76 #468) +#466 := (iff #75 #465) +#467 := [rewrite]: #466 +#457 := (iff #68 #456) +#458 := [monotonicity #455]: #457 +#470 := [monotonicity #458 #467]: #469 +#473 := [monotonicity #470]: #472 +#479 := [trans #473 #477]: #478 +#482 := [quant-intro #479]: #481 +#1114 := [monotonicity #482 #1111]: #1113 +#1120 := [trans #1114 #1118]: #1119 +#1123 := [monotonicity #482 #1120]: #1122 +#1126 := [monotonicity #1123]: #1125 +#1132 := [trans #1126 #1130]: #1131 #1135 := [monotonicity #1132]: #1134 -#1141 := [trans #1135 #1139]: #1140 -#1144 := [monotonicity #1141]: #1143 -#464 := (iff #71 #463) -#465 := [rewrite]: #464 -#1147 := [monotonicity #465 #1144]: #1146 -#1153 := [trans #1147 #1151]: #1152 -#1156 := [monotonicity #465 #1153]: #1155 -#461 := (iff #69 #460) -#462 := [quant-intro #459]: #461 -#1159 := [monotonicity #462 #1156]: #1158 +#463 := (iff #71 #462) +#464 := [rewrite]: #463 +#1138 := [monotonicity #464 #1135]: #1137 +#1144 := [trans #1138 #1142]: #1143 +#1147 := [monotonicity #464 #1144]: #1146 +#460 := (iff #69 #459) +#461 := [quant-intro #458]: #460 +#1150 := [monotonicity #461 #1147]: #1149 +#1156 := [trans #1150 #1154]: #1155 +#451 := (iff #65 #450) +#448 := (iff #64 #445) +#442 := (implies #62 #439) +#446 := (iff #442 #445) +#447 := [rewrite]: #446 +#443 := (iff #64 #442) +#440 := (iff #63 #439) +#441 := [rewrite]: #440 +#444 := [monotonicity #441]: #443 +#449 := [trans #444 #447]: #448 +#452 := [quant-intro #449]: #451 +#1159 := [monotonicity #452 #1156]: #1158 #1165 := [trans #1159 #1163]: #1164 -#452 := (iff #65 #451) -#449 := (iff #64 #446) -#443 := (implies #62 #440) -#447 := (iff #443 #446) -#448 := [rewrite]: #447 -#444 := (iff #64 #443) -#441 := (iff #63 #440) -#442 := [rewrite]: #441 -#445 := [monotonicity #442]: #444 -#450 := [trans #445 #448]: #449 -#453 := [quant-intro #450]: #452 -#1168 := [monotonicity #453 #1165]: #1167 +#437 := (iff #61 #436) +#434 := (iff #60 #431) +#428 := (implies #57 #425) +#432 := (iff #428 #431) +#433 := [rewrite]: #432 +#429 := (iff #60 #428) +#426 := (iff #59 #425) +#427 := [rewrite]: #426 +#430 := [monotonicity #427]: #429 +#435 := [trans #430 #433]: #434 +#438 := [quant-intro #435]: #437 +#1168 := [monotonicity #438 #1165]: #1167 #1174 := [trans #1168 #1172]: #1173 -#438 := (iff #61 #437) -#435 := (iff #60 #432) -#429 := (implies #57 #426) -#433 := (iff #429 #432) -#434 := [rewrite]: #433 -#430 := (iff #60 #429) -#427 := (iff #59 #426) -#428 := [rewrite]: #427 -#431 := [monotonicity #428]: #430 -#436 := [trans #431 #434]: #435 -#439 := [quant-intro #436]: #438 -#1177 := [monotonicity #439 #1174]: #1176 -#1183 := [trans #1177 #1181]: #1182 -#1186 := [monotonicity #1183]: #1185 -#1190 := [trans #1186 #1188]: #1189 -#1193 := [monotonicity #1190]: #1192 -#1832 := [trans #1193 #1830]: #1831 -#425 := [asserted]: #271 -#1833 := [mp #425 #1832]: #1828 -#1835 := [not-or-elim #1833]: #460 -#1890 := [mp~ #1835 #1859]: #460 -#4231 := [mp #1890 #4230]: #4226 -#5529 := (not #4226) -#5530 := (or #5529 #3078) -#5525 := [quant-inst #1936]: #5530 -#5337 := [unit-resolution #5525 #4231 #5222]: false -#5345 := [lemma #5337]: #3078 -#3845 := (or #3093 #1945) -#3849 := [def-axiom]: #3845 -#6495 := [unit-resolution #3849 #5345]: #3093 -#3098 := (not #3093) -#4565 := (or #3098 #4562) -#4568 := (not #4565) -#4240 := (pattern #66 #74) -#2519 := (not #466) -#3070 := (or #454 #2519 #1210) -#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3070) -#4246 := (not #4241) -#4571 := (or #4246 #4568) -#4574 := (not #4571) +#1177 := [monotonicity #1174]: #1176 +#1181 := [trans #1177 #1179]: #1180 +#1184 := [monotonicity #1181]: #1183 +#1823 := [trans #1184 #1821]: #1822 +#424 := [asserted]: #270 +#1824 := [mp #424 #1823]: #1819 +#1826 := [not-or-elim #1824]: #459 +#1881 := [mp~ #1826 #1850]: #459 +#4222 := [mp #1881 #4221]: #4217 +#5520 := (not #4217) +#5521 := (or #5520 #3069) +#5516 := [quant-inst #1927]: #5521 +#5328 := [unit-resolution #5516 #4222 #5213]: false +#5336 := [lemma #5328]: #3069 +#3836 := (or #3084 #1936) +#3840 := [def-axiom]: #3836 +#6486 := [unit-resolution #3840 #5336]: #3084 +#3089 := (not #3084) +#4556 := (or #3089 #4553) +#4559 := (not #4556) +#4231 := (pattern #66 #74) +#2510 := (not #465) +#3061 := (or #453 #2510 #1201) +#4232 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4231) #3061) +#4237 := (not #4232) +#4562 := (or #4237 #4559) +#4565 := (not #4562) decl ?v1!1 :: S3 -#1909 := ?v1!1 -#1913 := (f11 ?v1!1) -#2534 := (* -1::Int #1913) +#1900 := ?v1!1 +#1904 := (f11 ?v1!1) +#2525 := (* -1::Int #1904) decl ?v0!2 :: S3 -#1910 := ?v0!2 -#1911 := (f11 ?v0!2) -#2535 := (+ #1911 #2534) -#2536 := (<= #2535 0::Int) -#1918 := (f12 ?v1!1) -#1919 := (= f1 #1918) -#1916 := (f12 ?v0!2) -#1917 := (= f1 #1916) -#2054 := (not #1917) -#2026 := (or #2054 #1919 #2536) -#1928 := (not #2026) -#4577 := (or #1928 #4574) -#4580 := (not #4577) -#4232 := (forall (vars (?v0 S3)) (:pat #4218) #1201) -#4237 := (not #4232) -#4583 := (or #4237 #4580) -#4586 := (not #4583) +#1901 := ?v0!2 +#1902 := (f11 ?v0!2) +#2526 := (+ #1902 #2525) +#2527 := (<= #2526 0::Int) +#1909 := (f12 ?v1!1) +#1910 := (= f1 #1909) +#1907 := (f12 ?v0!2) +#1908 := (= f1 #1907) +#2210 := (not #1908) +#2119 := (or #2210 #1910 #2527) +#2018 := (not #2119) +#4568 := (or #2018 #4565) +#4571 := (not #4568) +#4223 := (forall (vars (?v0 S3)) (:pat #4209) #1192) +#4228 := (not #4223) +#4574 := (or #4228 #4571) +#4577 := (not #4574) decl ?v0!0 :: S3 -#1894 := ?v0!0 -#1895 := (f11 ?v0!0) -#1896 := (>= #1895 0::Int) -#1897 := (not #1896) -#4589 := (or #1897 #4586) -#4592 := (not #4589) -#4595 := (or #1196 #4592) -#4598 := (not #4595) -#4605 := (forall (vars (?v0 S3)) (:pat #4218) #1805) -#4608 := (iff #1808 #4605) -#4606 := (iff #1805 #1805) -#4607 := [refl]: #4606 -#4609 := [quant-intro #4607]: #4608 -#1958 := (~ #1808 #1808) -#1900 := (~ #1805 #1805) -#1901 := [refl]: #1900 -#1959 := [nnf-pos #1901]: #1958 -#1838 := [not-or-elim #1833]: #1808 -#2053 := [mp~ #1838 #1959]: #1808 -#4610 := [mp #2053 #4609]: #4605 -#5324 := [hypothesis]: #1196 -#4784 := (not #4605) -#5260 := (or #4784 #71) -#5144 := (= f10 f10) -#5145 := (not #5144) -#5147 := (or #5145 #71) -#5228 := (or #4784 #5147) -#5262 := (iff #5228 #5260) -#5264 := (iff #5260 #5260) -#5259 := [rewrite]: #5264 -#5233 := (iff #5147 #71) -#5201 := (or false #71) -#5229 := (iff #5201 #71) -#5232 := [rewrite]: #5229 -#5202 := (iff #5147 #5201) -#5199 := (iff #5145 false) -#5196 := (not true) -#5193 := (iff #5196 false) -#5194 := [rewrite]: #5193 -#5197 := (iff #5145 #5196) -#5148 := (iff #5144 true) -#5195 := [rewrite]: #5148 -#5198 := [monotonicity #5195]: #5197 -#5200 := [trans #5198 #5194]: #5199 -#5203 := [monotonicity #5200]: #5202 -#5234 := [trans #5203 #5232]: #5233 -#5263 := [monotonicity #5234]: #5262 -#5269 := [trans #5263 #5259]: #5262 -#5261 := [quant-inst #56]: #5228 -#5295 := [mp #5261 #5269]: #5260 -#5325 := [unit-resolution #5295 #5324 #4610]: false -#5320 := [lemma #5325]: #71 -#4601 := (or #1196 #4598) -#3528 := (forall (vars (?v1 S3)) #3517) -#3535 := (not #3528) -#3513 := (forall (vars (?v0 S3) (?v1 S3)) #3508) -#3534 := (not #3513) -#3536 := (or #2359 #2926 #3534 #3535) -#3537 := (not #3536) -#3542 := (or #3491 #3537) -#3549 := (not #3542) -#3468 := (forall (vars (?v0 S3) (?v1 S3)) #3463) -#3548 := (not #3468) -#3550 := (or #3548 #3549) -#3551 := (not #3550) -#3556 := (or #3445 #3551) -#3562 := (not #3556) -#3563 := (or #1499 #3562) -#3564 := (not #3563) -#3569 := (or #2276 #3564) -#3575 := (not #3569) -#3576 := (or #1490 #3575) -#3577 := (not #3576) -#3582 := (or #1490 #3577) -#3588 := (not #3582) -#3589 := (or #953 #3588) -#3590 := (not #3589) -#3595 := (or #2869 #3590) -#3601 := (not #3595) -#3602 := (or #1485 #3601) -#3603 := (not #3602) -#3608 := (or #2855 #3603) -#3616 := (not #3608) -#3422 := (forall (vars (?v0 S3)) #3417) -#3615 := (not #3422) -#3404 := (forall (vars (?v0 S3)) #3401) -#3614 := (not #3404) -#3617 := (or #754 #995 #1650 #1654 #2210 #2213 #3614 #3615 #3616) -#3618 := (not #3617) -#3334 := (forall (vars (?v0 S3) (?v1 S3)) #3329) -#3340 := (not #3334) -#3341 := (or #158 #3340) -#3342 := (not #3341) -#3369 := (or #3342 #3366) -#3376 := (not #3369) -#3312 := (forall (vars (?v0 S3)) #3307) -#3375 := (not #3312) -#3377 := (or #3375 #3376) -#3378 := (not #3377) -#3275 := (forall (vars (?v1 S3)) #3264) -#3281 := (not #3275) -#3282 := (or #2089 #2704 #3281) -#3283 := (not #3282) -#3383 := (or #3283 #3378) -#3390 := (not #3383) -#3260 := (forall (vars (?v0 S3)) #3249) -#3389 := (not #3260) -#3391 := (or #724 #706 #733 #715 #3389 #3390) -#3392 := (not #3391) -#3623 := (or #3392 #3618) -#3633 := (not #3623) -#3246 := (forall (vars (?v0 S3)) #3241) -#3632 := (not #3246) -#3218 := (forall (vars (?v0 S3)) #3213) -#3631 := (not #3218) -#3190 := (forall (vars (?v0 S3) (?v1 S3)) #3185) -#3630 := (not #3190) -#3167 := (forall (vars (?v0 S3) (?v1 S3)) #3162) -#3629 := (not #3167) -#3634 := (or #1747 #1742 #3629 #3630 #3631 #3632 #3633) -#3635 := (not #3634) -#3135 := (forall (vars (?v1 S3)) #3124) -#3141 := (not #3135) -#3142 := (or #1981 #2566 #3141) -#3143 := (not #3142) -#3640 := (or #3143 #3635) -#3647 := (not #3640) -#3120 := (forall (vars (?v0 S3) (?v1 S3)) #3115) -#3646 := (not #3120) -#3648 := (or #3646 #3647) -#3649 := (not #3648) -#3654 := (or #3098 #3649) -#3661 := (not #3654) -#3075 := (forall (vars (?v0 S3) (?v1 S3)) #3070) -#3660 := (not #3075) -#3662 := (or #3660 #3661) -#3663 := (not #3662) -#3668 := (or #1928 #3663) -#3674 := (not #3668) -#3675 := (or #1205 #3674) -#3676 := (not #3675) -#3681 := (or #1897 #3676) -#3687 := (not #3681) -#3688 := (or #1196 #3687) -#3689 := (not #3688) -#3694 := (or #1196 #3689) -#4602 := (iff #3694 #4601) -#4599 := (iff #3689 #4598) -#4596 := (iff #3688 #4595) -#4593 := (iff #3687 #4592) -#4590 := (iff #3681 #4589) -#4587 := (iff #3676 #4586) -#4584 := (iff #3675 #4583) -#4581 := (iff #3674 #4580) -#4578 := (iff #3668 #4577) -#4575 := (iff #3663 #4574) -#4572 := (iff #3662 #4571) -#4569 := (iff #3661 #4568) +#1885 := ?v0!0 +#1886 := (f11 ?v0!0) +#1887 := (>= #1886 0::Int) +#1888 := (not #1887) +#4580 := (or #1888 #4577) +#4583 := (not #4580) +#4586 := (or #1187 #4583) +#4589 := (not #4586) +#4596 := (forall (vars (?v0 S3)) (:pat #4209) #1796) +#4599 := (iff #1799 #4596) +#4597 := (iff #1796 #1796) +#4598 := [refl]: #4597 +#4600 := [quant-intro #4598]: #4599 +#2044 := (~ #1799 #1799) +#1891 := (~ #1796 #1796) +#1892 := [refl]: #1891 +#2045 := [nnf-pos #1892]: #2044 +#1829 := [not-or-elim #1824]: #1799 +#2209 := [mp~ #1829 #2045]: #1799 +#4601 := [mp #2209 #4600]: #4596 +#5315 := [hypothesis]: #1187 +#4775 := (not #4596) +#5251 := (or #4775 #71) +#5135 := (= f10 f10) +#5136 := (not #5135) +#5138 := (or #5136 #71) +#5219 := (or #4775 #5138) +#5253 := (iff #5219 #5251) +#5255 := (iff #5251 #5251) +#5250 := [rewrite]: #5255 +#5224 := (iff #5138 #71) +#5192 := (or false #71) +#5220 := (iff #5192 #71) +#5223 := [rewrite]: #5220 +#5193 := (iff #5138 #5192) +#5190 := (iff #5136 false) +#5187 := (not true) +#5184 := (iff #5187 false) +#5185 := [rewrite]: #5184 +#5188 := (iff #5136 #5187) +#5139 := (iff #5135 true) +#5186 := [rewrite]: #5139 +#5189 := [monotonicity #5186]: #5188 +#5191 := [trans #5189 #5185]: #5190 +#5194 := [monotonicity #5191]: #5193 +#5225 := [trans #5194 #5223]: #5224 +#5254 := [monotonicity #5225]: #5253 +#5260 := [trans #5254 #5250]: #5253 +#5252 := [quant-inst #56]: #5219 +#5286 := [mp #5252 #5260]: #5251 +#5316 := [unit-resolution #5286 #5315 #4601]: false +#5311 := [lemma #5316]: #71 +#4592 := (or #1187 #4589) +#3519 := (forall (vars (?v1 S3)) #3508) +#3526 := (not #3519) +#3504 := (forall (vars (?v0 S3) (?v1 S3)) #3499) +#3525 := (not #3504) +#3527 := (or #2350 #2917 #3525 #3526) +#3528 := (not #3527) +#3533 := (or #3482 #3528) +#3540 := (not #3533) +#3459 := (forall (vars (?v0 S3) (?v1 S3)) #3454) +#3539 := (not #3459) +#3541 := (or #3539 #3540) +#3542 := (not #3541) +#3547 := (or #3436 #3542) +#3553 := (not #3547) +#3554 := (or #1490 #3553) +#3555 := (not #3554) +#3560 := (or #2267 #3555) +#3566 := (not #3560) +#3567 := (or #1481 #3566) +#3568 := (not #3567) +#3573 := (or #1481 #3568) +#3579 := (not #3573) +#3580 := (or #944 #3579) +#3581 := (not #3580) +#3586 := (or #2860 #3581) +#3592 := (not #3586) +#3593 := (or #1476 #3592) +#3594 := (not #3593) +#3599 := (or #2846 #3594) +#3607 := (not #3599) +#3413 := (forall (vars (?v0 S3)) #3408) +#3606 := (not #3413) +#3395 := (forall (vars (?v0 S3)) #3392) +#3605 := (not #3395) +#3608 := (or #986 #753 #1641 #1645 #2201 #2204 #3605 #3606 #3607) +#3609 := (not #3608) +#3325 := (forall (vars (?v0 S3) (?v1 S3)) #3320) +#3331 := (not #3325) +#3332 := (or #158 #3331) +#3333 := (not #3332) +#3360 := (or #3333 #3357) +#3367 := (not #3360) +#3303 := (forall (vars (?v0 S3)) #3298) +#3366 := (not #3303) +#3368 := (or #3366 #3367) +#3369 := (not #3368) +#3266 := (forall (vars (?v1 S3)) #3255) +#3272 := (not #3266) +#3273 := (or #2080 #2695 #3272) +#3274 := (not #3273) +#3374 := (or #3274 #3369) +#3381 := (not #3374) +#3251 := (forall (vars (?v0 S3)) #3240) +#3380 := (not #3251) +#3382 := (or #723 #705 #732 #714 #3380 #3381) +#3383 := (not #3382) +#3614 := (or #3383 #3609) +#3624 := (not #3614) +#3237 := (forall (vars (?v0 S3)) #3232) +#3623 := (not #3237) +#3209 := (forall (vars (?v0 S3)) #3204) +#3622 := (not #3209) +#3181 := (forall (vars (?v0 S3) (?v1 S3)) #3176) +#3621 := (not #3181) +#3158 := (forall (vars (?v0 S3) (?v1 S3)) #3153) +#3620 := (not #3158) +#3625 := (or #1738 #1733 #3620 #3621 #3622 #3623 #3624) +#3626 := (not #3625) +#3126 := (forall (vars (?v1 S3)) #3115) +#3132 := (not #3126) +#3133 := (or #1972 #2557 #3132) +#3134 := (not #3133) +#3631 := (or #3134 #3626) +#3638 := (not #3631) +#3111 := (forall (vars (?v0 S3) (?v1 S3)) #3106) +#3637 := (not #3111) +#3639 := (or #3637 #3638) +#3640 := (not #3639) +#3645 := (or #3089 #3640) +#3652 := (not #3645) +#3066 := (forall (vars (?v0 S3) (?v1 S3)) #3061) +#3651 := (not #3066) +#3653 := (or #3651 #3652) +#3654 := (not #3653) +#3659 := (or #2018 #3654) +#3665 := (not #3659) +#3666 := (or #1196 #3665) +#3667 := (not #3666) +#3672 := (or #1888 #3667) +#3678 := (not #3672) +#3679 := (or #1187 #3678) +#3680 := (not #3679) +#3685 := (or #1187 #3680) +#4593 := (iff #3685 #4592) +#4590 := (iff #3680 #4589) +#4587 := (iff #3679 #4586) +#4584 := (iff #3678 #4583) +#4581 := (iff #3672 #4580) +#4578 := (iff #3667 #4577) +#4575 := (iff #3666 #4574) +#4572 := (iff #3665 #4571) +#4569 := (iff #3659 #4568) #4566 := (iff #3654 #4565) -#4563 := (iff #3649 #4562) -#4560 := (iff #3648 #4559) -#4557 := (iff #3647 #4556) +#4563 := (iff #3653 #4562) +#4560 := (iff #3652 #4559) +#4557 := (iff #3645 #4556) #4554 := (iff #3640 #4553) -#4551 := (iff #3635 #4550) -#4548 := (iff #3634 #4547) -#4545 := (iff #3633 #4544) -#4542 := (iff #3623 #4541) -#4539 := (iff #3618 #4538) -#4536 := (iff #3617 #4535) -#4533 := (iff #3616 #4532) -#4530 := (iff #3608 #4529) -#4527 := (iff #3603 #4526) -#4524 := (iff #3602 #4523) -#4521 := (iff #3601 #4520) -#4518 := (iff #3595 #4517) -#4515 := (iff #3590 #4514) -#4512 := (iff #3589 #4511) -#4509 := (iff #3588 #4508) -#4506 := (iff #3582 #4505) -#4503 := (iff #3577 #4502) -#4500 := (iff #3576 #4499) -#4497 := (iff #3575 #4496) -#4494 := (iff #3569 #4493) -#4491 := (iff #3564 #4490) -#4488 := (iff #3563 #4487) -#4485 := (iff #3562 #4484) -#4482 := (iff #3556 #4481) -#4479 := (iff #3551 #4478) -#4476 := (iff #3550 #4475) -#4473 := (iff #3549 #4472) +#4551 := (iff #3639 #4550) +#4548 := (iff #3638 #4547) +#4545 := (iff #3631 #4544) +#4542 := (iff #3626 #4541) +#4539 := (iff #3625 #4538) +#4536 := (iff #3624 #4535) +#4533 := (iff #3614 #4532) +#4530 := (iff #3609 #4529) +#4527 := (iff #3608 #4526) +#4524 := (iff #3607 #4523) +#4521 := (iff #3599 #4520) +#4518 := (iff #3594 #4517) +#4515 := (iff #3593 #4514) +#4512 := (iff #3592 #4511) +#4509 := (iff #3586 #4508) +#4506 := (iff #3581 #4505) +#4503 := (iff #3580 #4502) +#4500 := (iff #3579 #4499) +#4497 := (iff #3573 #4496) +#4494 := (iff #3568 #4493) +#4491 := (iff #3567 #4490) +#4488 := (iff #3566 #4487) +#4485 := (iff #3560 #4484) +#4482 := (iff #3555 #4481) +#4479 := (iff #3554 #4478) +#4476 := (iff #3553 #4475) +#4473 := (iff #3547 #4472) #4470 := (iff #3542 #4469) -#4467 := (iff #3537 #4466) -#4464 := (iff #3536 #4463) -#4461 := (iff #3535 #4460) -#4458 := (iff #3528 #4455) -#4456 := (iff #3517 #3517) -#4457 := [refl]: #4456 -#4459 := [quant-intro #4457]: #4458 -#4462 := [monotonicity #4459]: #4461 -#4452 := (iff #3534 #4451) -#4449 := (iff #3513 #4446) +#4467 := (iff #3541 #4466) +#4464 := (iff #3540 #4463) +#4461 := (iff #3533 #4460) +#4458 := (iff #3528 #4457) +#4455 := (iff #3527 #4454) +#4452 := (iff #3526 #4451) +#4449 := (iff #3519 #4446) #4447 := (iff #3508 #3508) #4448 := [refl]: #4447 #4450 := [quant-intro #4448]: #4449 #4453 := [monotonicity #4450]: #4452 -#4465 := [monotonicity #4453 #4462]: #4464 -#4468 := [monotonicity #4465]: #4467 -#4471 := [monotonicity #4468]: #4470 -#4474 := [monotonicity #4471]: #4473 -#4444 := (iff #3548 #4443) -#4441 := (iff #3468 #4438) -#4439 := (iff #3463 #3463) -#4440 := [refl]: #4439 -#4442 := [quant-intro #4440]: #4441 -#4445 := [monotonicity #4442]: #4444 -#4477 := [monotonicity #4445 #4474]: #4476 -#4480 := [monotonicity #4477]: #4479 -#4483 := [monotonicity #4480]: #4482 -#4486 := [monotonicity #4483]: #4485 -#4435 := (iff #1499 #4434) -#4432 := (iff #1496 #4429) -#4430 := (iff #1493 #1493) +#4443 := (iff #3525 #4442) +#4440 := (iff #3504 #4437) +#4438 := (iff #3499 #3499) +#4439 := [refl]: #4438 +#4441 := [quant-intro #4439]: #4440 +#4444 := [monotonicity #4441]: #4443 +#4456 := [monotonicity #4444 #4453]: #4455 +#4459 := [monotonicity #4456]: #4458 +#4462 := [monotonicity #4459]: #4461 +#4465 := [monotonicity #4462]: #4464 +#4435 := (iff #3539 #4434) +#4432 := (iff #3459 #4429) +#4430 := (iff #3454 #3454) #4431 := [refl]: #4430 #4433 := [quant-intro #4431]: #4432 #4436 := [monotonicity #4433]: #4435 -#4489 := [monotonicity #4436 #4486]: #4488 +#4468 := [monotonicity #4436 #4465]: #4467 +#4471 := [monotonicity #4468]: #4470 +#4474 := [monotonicity #4471]: #4473 +#4477 := [monotonicity #4474]: #4476 +#4426 := (iff #1490 #4425) +#4423 := (iff #1487 #4420) +#4421 := (iff #1484 #1484) +#4422 := [refl]: #4421 +#4424 := [quant-intro #4422]: #4423 +#4427 := [monotonicity #4424]: #4426 +#4480 := [monotonicity #4427 #4477]: #4479 +#4483 := [monotonicity #4480]: #4482 +#4486 := [monotonicity #4483]: #4485 +#4489 := [monotonicity #4486]: #4488 #4492 := [monotonicity #4489]: #4491 #4495 := [monotonicity #4492]: #4494 #4498 := [monotonicity #4495]: #4497 #4501 := [monotonicity #4498]: #4500 -#4504 := [monotonicity #4501]: #4503 -#4507 := [monotonicity #4504]: #4506 -#4510 := [monotonicity #4507]: #4509 -#4427 := (iff #953 #4426) -#4424 := (iff #819 #4421) -#4422 := (iff #814 #814) -#4423 := [refl]: #4422 -#4425 := [quant-intro #4423]: #4424 -#4428 := [monotonicity #4425]: #4427 -#4513 := [monotonicity #4428 #4510]: #4512 -#4516 := [monotonicity #4513]: #4515 -#4519 := [monotonicity #4516]: #4518 -#4522 := [monotonicity #4519]: #4521 -#4418 := (iff #1485 #4417) -#4415 := (iff #1482 #4412) -#4413 := (iff #1477 #1477) +#4418 := (iff #944 #4417) +#4415 := (iff #810 #4412) +#4413 := (iff #805 #805) #4414 := [refl]: #4413 #4416 := [quant-intro #4414]: #4415 #4419 := [monotonicity #4416]: #4418 -#4525 := [monotonicity #4419 #4522]: #4524 -#4528 := [monotonicity #4525]: #4527 +#4504 := [monotonicity #4419 #4501]: #4503 +#4507 := [monotonicity #4504]: #4506 +#4510 := [monotonicity #4507]: #4509 +#4513 := [monotonicity #4510]: #4512 +#4409 := (iff #1476 #4408) +#4406 := (iff #1473 #4403) +#4404 := (iff #1468 #1468) +#4405 := [refl]: #4404 +#4407 := [quant-intro #4405]: #4406 +#4410 := [monotonicity #4407]: #4409 +#4516 := [monotonicity #4410 #4513]: #4515 +#4519 := [monotonicity #4516]: #4518 +#4522 := [monotonicity #4519]: #4521 +#4525 := [monotonicity #4522]: #4524 +#4401 := (iff #3606 #4400) +#4398 := (iff #3413 #4395) +#4396 := (iff #3408 #3408) +#4397 := [refl]: #4396 +#4399 := [quant-intro #4397]: #4398 +#4402 := [monotonicity #4399]: #4401 +#4393 := (iff #3605 #4392) +#4390 := (iff #3395 #4387) +#4388 := (iff #3392 #3392) +#4389 := [refl]: #4388 +#4391 := [quant-intro #4389]: #4390 +#4394 := [monotonicity #4391]: #4393 +#4383 := (iff #1641 #4382) +#4380 := (iff #1638 #4377) +#4378 := (iff #1633 #1633) +#4379 := [refl]: #4378 +#4381 := [quant-intro #4379]: #4380 +#4384 := [monotonicity #4381]: #4383 +#4528 := [monotonicity #4384 #4394 #4402 #4525]: #4527 #4531 := [monotonicity #4528]: #4530 -#4534 := [monotonicity #4531]: #4533 -#4410 := (iff #3615 #4409) -#4407 := (iff #3422 #4404) -#4405 := (iff #3417 #3417) -#4406 := [refl]: #4405 -#4408 := [quant-intro #4406]: #4407 -#4411 := [monotonicity #4408]: #4410 -#4402 := (iff #3614 #4401) -#4399 := (iff #3404 #4396) -#4397 := (iff #3401 #3401) -#4398 := [refl]: #4397 -#4400 := [quant-intro #4398]: #4399 -#4403 := [monotonicity #4400]: #4402 -#4392 := (iff #1650 #4391) -#4389 := (iff #1647 #4386) -#4387 := (iff #1642 #1642) -#4388 := [refl]: #4387 -#4390 := [quant-intro #4388]: #4389 -#4393 := [monotonicity #4390]: #4392 -#4537 := [monotonicity #4393 #4403 #4411 #4534]: #4536 -#4540 := [monotonicity #4537]: #4539 -#4384 := (iff #3392 #4383) -#4381 := (iff #3391 #4380) -#4378 := (iff #3390 #4377) #4375 := (iff #3383 #4374) -#4372 := (iff #3378 #4371) -#4369 := (iff #3377 #4368) -#4366 := (iff #3376 #4365) +#4372 := (iff #3382 #4371) +#4369 := (iff #3381 #4368) +#4366 := (iff #3374 #4365) #4363 := (iff #3369 #4362) -#4360 := (iff #3342 #4359) -#4357 := (iff #3341 #4356) -#4354 := (iff #3340 #4353) -#4351 := (iff #3334 #4348) -#4349 := (iff #3329 #3329) -#4350 := [refl]: #4349 -#4352 := [quant-intro #4350]: #4351 +#4360 := (iff #3368 #4359) +#4357 := (iff #3367 #4356) +#4354 := (iff #3360 #4353) +#4351 := (iff #3333 #4350) +#4348 := (iff #3332 #4347) +#4345 := (iff #3331 #4344) +#4342 := (iff #3325 #4339) +#4340 := (iff #3320 #3320) +#4341 := [refl]: #4340 +#4343 := [quant-intro #4341]: #4342 +#4346 := [monotonicity #4343]: #4345 +#4349 := [monotonicity #4346]: #4348 +#4352 := [monotonicity #4349]: #4351 #4355 := [monotonicity #4352]: #4354 #4358 := [monotonicity #4355]: #4357 -#4361 := [monotonicity #4358]: #4360 +#4337 := (iff #3366 #4336) +#4334 := (iff #3303 #4331) +#4332 := (iff #3298 #3298) +#4333 := [refl]: #4332 +#4335 := [quant-intro #4333]: #4334 +#4338 := [monotonicity #4335]: #4337 +#4361 := [monotonicity #4338 #4358]: #4360 #4364 := [monotonicity #4361]: #4363 -#4367 := [monotonicity #4364]: #4366 -#4346 := (iff #3375 #4345) -#4343 := (iff #3312 #4340) -#4341 := (iff #3307 #3307) -#4342 := [refl]: #4341 -#4344 := [quant-intro #4342]: #4343 -#4347 := [monotonicity #4344]: #4346 -#4370 := [monotonicity #4347 #4367]: #4369 -#4373 := [monotonicity #4370]: #4372 -#4338 := (iff #3283 #4337) -#4335 := (iff #3282 #4334) -#4332 := (iff #3281 #4331) -#4329 := (iff #3275 #4326) -#4327 := (iff #3264 #3264) -#4328 := [refl]: #4327 -#4330 := [quant-intro #4328]: #4329 -#4333 := [monotonicity #4330]: #4332 -#4336 := [monotonicity #4333]: #4335 -#4339 := [monotonicity #4336]: #4338 -#4376 := [monotonicity #4339 #4373]: #4375 -#4379 := [monotonicity #4376]: #4378 -#4322 := (iff #3389 #4321) -#4319 := (iff #3260 #4316) -#4317 := (iff #3249 #3249) -#4318 := [refl]: #4317 -#4320 := [quant-intro #4318]: #4319 -#4323 := [monotonicity #4320]: #4322 -#4382 := [monotonicity #4323 #4379]: #4381 -#4385 := [monotonicity #4382]: #4384 -#4543 := [monotonicity #4385 #4540]: #4542 -#4546 := [monotonicity #4543]: #4545 -#4313 := (iff #3632 #4312) -#4310 := (iff #3246 #4307) -#4308 := (iff #3241 #3241) +#4329 := (iff #3274 #4328) +#4326 := (iff #3273 #4325) +#4323 := (iff #3272 #4322) +#4320 := (iff #3266 #4317) +#4318 := (iff #3255 #3255) +#4319 := [refl]: #4318 +#4321 := [quant-intro #4319]: #4320 +#4324 := [monotonicity #4321]: #4323 +#4327 := [monotonicity #4324]: #4326 +#4330 := [monotonicity #4327]: #4329 +#4367 := [monotonicity #4330 #4364]: #4366 +#4370 := [monotonicity #4367]: #4369 +#4313 := (iff #3380 #4312) +#4310 := (iff #3251 #4307) +#4308 := (iff #3240 #3240) #4309 := [refl]: #4308 #4311 := [quant-intro #4309]: #4310 #4314 := [monotonicity #4311]: #4313 -#4305 := (iff #3631 #4304) -#4302 := (iff #3218 #4299) -#4300 := (iff #3213 #3213) -#4301 := [refl]: #4300 -#4303 := [quant-intro #4301]: #4302 -#4306 := [monotonicity #4303]: #4305 -#4297 := (iff #3630 #4296) -#4294 := (iff #3190 #4291) -#4292 := (iff #3185 #3185) -#4293 := [refl]: #4292 -#4295 := [quant-intro #4293]: #4294 -#4298 := [monotonicity #4295]: #4297 -#4288 := (iff #3629 #4287) -#4285 := (iff #3167 #4282) -#4283 := (iff #3162 #3162) +#4373 := [monotonicity #4314 #4370]: #4372 +#4376 := [monotonicity #4373]: #4375 +#4534 := [monotonicity #4376 #4531]: #4533 +#4537 := [monotonicity #4534]: #4536 +#4304 := (iff #3623 #4303) +#4301 := (iff #3237 #4298) +#4299 := (iff #3232 #3232) +#4300 := [refl]: #4299 +#4302 := [quant-intro #4300]: #4301 +#4305 := [monotonicity #4302]: #4304 +#4296 := (iff #3622 #4295) +#4293 := (iff #3209 #4290) +#4291 := (iff #3204 #3204) +#4292 := [refl]: #4291 +#4294 := [quant-intro #4292]: #4293 +#4297 := [monotonicity #4294]: #4296 +#4288 := (iff #3621 #4287) +#4285 := (iff #3181 #4282) +#4283 := (iff #3176 #3176) #4284 := [refl]: #4283 #4286 := [quant-intro #4284]: #4285 #4289 := [monotonicity #4286]: #4288 -#4280 := (iff #1742 #4279) -#4277 := (iff #1739 #4274) -#4275 := (iff #1736 #1736) -#4276 := [refl]: #4275 -#4278 := [quant-intro #4276]: #4277 -#4281 := [monotonicity #4278]: #4280 -#4549 := [monotonicity #4281 #4289 #4298 #4306 #4314 #4546]: #4548 -#4552 := [monotonicity #4549]: #4551 -#4271 := (iff #3143 #4270) -#4268 := (iff #3142 #4267) -#4265 := (iff #3141 #4264) -#4262 := (iff #3135 #4259) -#4260 := (iff #3124 #3124) -#4261 := [refl]: #4260 -#4263 := [quant-intro #4261]: #4262 -#4266 := [monotonicity #4263]: #4265 -#4269 := [monotonicity #4266]: #4268 +#4279 := (iff #3620 #4278) +#4276 := (iff #3158 #4273) +#4274 := (iff #3153 #3153) +#4275 := [refl]: #4274 +#4277 := [quant-intro #4275]: #4276 +#4280 := [monotonicity #4277]: #4279 +#4271 := (iff #1733 #4270) +#4268 := (iff #1730 #4265) +#4266 := (iff #1727 #1727) +#4267 := [refl]: #4266 +#4269 := [quant-intro #4267]: #4268 #4272 := [monotonicity #4269]: #4271 -#4555 := [monotonicity #4272 #4552]: #4554 -#4558 := [monotonicity #4555]: #4557 -#4256 := (iff #3646 #4255) -#4253 := (iff #3120 #4250) +#4540 := [monotonicity #4272 #4280 #4289 #4297 #4305 #4537]: #4539 +#4543 := [monotonicity #4540]: #4542 +#4262 := (iff #3134 #4261) +#4259 := (iff #3133 #4258) +#4256 := (iff #3132 #4255) +#4253 := (iff #3126 #4250) #4251 := (iff #3115 #3115) #4252 := [refl]: #4251 #4254 := [quant-intro #4252]: #4253 #4257 := [monotonicity #4254]: #4256 -#4561 := [monotonicity #4257 #4558]: #4560 -#4564 := [monotonicity #4561]: #4563 -#4567 := [monotonicity #4564]: #4566 -#4570 := [monotonicity #4567]: #4569 -#4247 := (iff #3660 #4246) -#4244 := (iff #3075 #4241) -#4242 := (iff #3070 #3070) +#4260 := [monotonicity #4257]: #4259 +#4263 := [monotonicity #4260]: #4262 +#4546 := [monotonicity #4263 #4543]: #4545 +#4549 := [monotonicity #4546]: #4548 +#4247 := (iff #3637 #4246) +#4244 := (iff #3111 #4241) +#4242 := (iff #3106 #3106) #4243 := [refl]: #4242 #4245 := [quant-intro #4243]: #4244 #4248 := [monotonicity #4245]: #4247 -#4573 := [monotonicity #4248 #4570]: #4572 -#4576 := [monotonicity #4573]: #4575 -#4579 := [monotonicity #4576]: #4578 -#4582 := [monotonicity #4579]: #4581 -#4238 := (iff #1205 #4237) -#4235 := (iff #1202 #4232) -#4233 := (iff #1201 #1201) +#4552 := [monotonicity #4248 #4549]: #4551 +#4555 := [monotonicity #4552]: #4554 +#4558 := [monotonicity #4555]: #4557 +#4561 := [monotonicity #4558]: #4560 +#4238 := (iff #3651 #4237) +#4235 := (iff #3066 #4232) +#4233 := (iff #3061 #3061) #4234 := [refl]: #4233 #4236 := [quant-intro #4234]: #4235 #4239 := [monotonicity #4236]: #4238 -#4585 := [monotonicity #4239 #4582]: #4584 +#4564 := [monotonicity #4239 #4561]: #4563 +#4567 := [monotonicity #4564]: #4566 +#4570 := [monotonicity #4567]: #4569 +#4573 := [monotonicity #4570]: #4572 +#4229 := (iff #1196 #4228) +#4226 := (iff #1193 #4223) +#4224 := (iff #1192 #1192) +#4225 := [refl]: #4224 +#4227 := [quant-intro #4225]: #4226 +#4230 := [monotonicity #4227]: #4229 +#4576 := [monotonicity #4230 #4573]: #4575 +#4579 := [monotonicity #4576]: #4578 +#4582 := [monotonicity #4579]: #4581 +#4585 := [monotonicity #4582]: #4584 #4588 := [monotonicity #4585]: #4587 #4591 := [monotonicity #4588]: #4590 #4594 := [monotonicity #4591]: #4593 -#4597 := [monotonicity #4594]: #4596 -#4600 := [monotonicity #4597]: #4599 -#4603 := [monotonicity #4600]: #4602 -#2355 := (not #2354) -#2957 := (and #807 #2355 #2954) -#2960 := (not #2957) -#2963 := (forall (vars (?v1 S3)) #2960) -#2929 := (not #2926) -#2972 := (and #1539 #2360 #2929 #2963) -#2328 := (not #2327) -#2899 := (and #2328 #2330) -#2902 := (not #2899) -#2920 := (or #2902 #2915) -#2923 := (not #2920) -#2977 := (or #2923 #2972) -#2980 := (and #1515 #2977) -#2299 := (not #2298) -#2874 := (and #2296 #2299) -#2877 := (not #2874) -#2893 := (or #2877 #2888) -#2896 := (not #2893) -#2983 := (or #2896 #2980) -#2986 := (and #1496 #2983) -#2989 := (or #2276 #2986) -#2992 := (and #204 #2989) -#2995 := (or #1490 #2992) -#2998 := (and #819 #2995) -#3001 := (or #2869 #2998) -#3004 := (and #1482 #3001) -#3007 := (or #2855 #3004) -#2214 := (not #2213) -#2211 := (not #2210) -#3013 := (and #757 #776 #1471 #1629 #1647 #1655 #2211 #2214 #3007) -#2156 := (not #2155) -#2152 := (not #2151) -#2792 := (and #2152 #2156) -#2795 := (not #2792) -#2812 := (or #2795 #2807) -#2815 := (not #2812) -#2165 := (not #158) -#2175 := (and #2165 #1391) -#2821 := (or #2175 #2815) -#2765 := (not #2760) -#2783 := (and #2765 #2778) -#2786 := (or #1351 #2783) -#2789 := (forall (vars (?v0 S3)) #2786) -#2826 := (and #2789 #2821) -#2085 := (not #2084) -#2735 := (and #2085 #2732) -#2738 := (not #2735) -#2741 := (forall (vars (?v1 S3)) #2738) -#2707 := (not #2704) -#2090 := (not #2089) -#2747 := (and #2090 #2707 #2741) -#2829 := (or #2747 #2826) -#2191 := (not #1419) -#2194 := (forall (vars (?v0 S3)) #2191) -#2835 := (and #136 #141 #621 #624 #2194 #2829) -#3018 := (or #2835 #3013) -#2684 := (not #2679) -#2687 := (and #2049 #2667 #2684) -#2690 := (or #1306 #2687) -#2693 := (forall (vars (?v0 S3)) #2690) -#2629 := (not #2624) -#2647 := (and #2022 #2629 #2642) -#2650 := (or #1268 #2647) -#2653 := (forall (vars (?v0 S3)) #2650) -#3024 := (and #100 #1714 #1730 #1739 #2653 #2693 #3018) -#1977 := (not #1976) -#2597 := (and #454 #1977 #2594) -#2600 := (not #2597) -#2603 := (forall (vars (?v1 S3)) #2600) -#2569 := (not #2566) -#1982 := (not #1981) -#2609 := (and #1982 #2569 #2603) -#3029 := (or #2609 #3024) -#3032 := (and #1253 #3029) -#1943 := (not #1942) -#2554 := (and #1943 #1945) -#2557 := (not #2554) -#2560 := (or #2551 #2557) -#2563 := (not #2560) -#3035 := (or #2563 #3032) -#3038 := (and #1222 #3035) -#1920 := (not #1919) -#2522 := (and #1917 #1920) -#2525 := (not #2522) -#2541 := (or #2525 #2536) -#2544 := (not #2541) -#3041 := (or #2544 #3038) -#3044 := (and #1202 #3041) -#3047 := (or #1897 #3044) -#3050 := (and #71 #3047) -#3053 := (or #1196 #3050) -#3695 := (iff #3053 #3694) -#3692 := (iff #3050 #3689) -#3684 := (and #71 #3681) -#3690 := (iff #3684 #3689) -#3691 := [rewrite]: #3690 -#3685 := (iff #3050 #3684) -#3682 := (iff #3047 #3681) -#3679 := (iff #3044 #3676) -#3671 := (and #1202 #3668) -#3677 := (iff #3671 #3676) -#3678 := [rewrite]: #3677 -#3672 := (iff #3044 #3671) -#3669 := (iff #3041 #3668) -#3666 := (iff #3038 #3663) -#3657 := (and #3075 #3654) -#3664 := (iff #3657 #3663) -#3665 := [rewrite]: #3664 -#3658 := (iff #3038 #3657) -#3655 := (iff #3035 #3654) -#3652 := (iff #3032 #3649) -#3643 := (and #3120 #3640) -#3650 := (iff #3643 #3649) -#3651 := [rewrite]: #3650 -#3644 := (iff #3032 #3643) -#3641 := (iff #3029 #3640) -#3638 := (iff #3024 #3635) -#3626 := (and #100 #3167 #3190 #1739 #3218 #3246 #3623) -#3636 := (iff #3626 #3635) -#3637 := [rewrite]: #3636 -#3627 := (iff #3024 #3626) -#3624 := (iff #3018 #3623) -#3621 := (iff #3013 #3618) -#3611 := (and #757 #776 #3404 #3422 #1647 #1655 #2211 #2214 #3608) -#3619 := (iff #3611 #3618) -#3620 := [rewrite]: #3619 -#3612 := (iff #3013 #3611) -#3609 := (iff #3007 #3608) -#3606 := (iff #3004 #3603) -#3598 := (and #1482 #3595) -#3604 := (iff #3598 #3603) -#3605 := [rewrite]: #3604 -#3599 := (iff #3004 #3598) -#3596 := (iff #3001 #3595) -#3593 := (iff #2998 #3590) -#3585 := (and #819 #3582) -#3591 := (iff #3585 #3590) -#3592 := [rewrite]: #3591 -#3586 := (iff #2998 #3585) -#3583 := (iff #2995 #3582) -#3580 := (iff #2992 #3577) -#3572 := (and #204 #3569) -#3578 := (iff #3572 #3577) -#3579 := [rewrite]: #3578 -#3573 := (iff #2992 #3572) -#3570 := (iff #2989 #3569) -#3567 := (iff #2986 #3564) -#3559 := (and #1496 #3556) -#3565 := (iff #3559 #3564) -#3566 := [rewrite]: #3565 -#3560 := (iff #2986 #3559) -#3557 := (iff #2983 #3556) -#3554 := (iff #2980 #3551) -#3545 := (and #3468 #3542) -#3552 := (iff #3545 #3551) -#3553 := [rewrite]: #3552 -#3546 := (iff #2980 #3545) -#3543 := (iff #2977 #3542) -#3540 := (iff #2972 #3537) -#3531 := (and #3513 #2360 #2929 #3528) -#3538 := (iff #3531 #3537) -#3539 := [rewrite]: #3538 -#3532 := (iff #2972 #3531) -#3529 := (iff #2963 #3528) -#3526 := (iff #2960 #3517) -#3518 := (not #3517) -#3521 := (not #3518) -#3524 := (iff #3521 #3517) -#3525 := [rewrite]: #3524 -#3522 := (iff #2960 #3521) -#3519 := (iff #2957 #3518) -#3520 := [rewrite]: #3519 -#3523 := [monotonicity #3520]: #3522 -#3527 := [trans #3523 #3525]: #3526 -#3530 := [quant-intro #3527]: #3529 -#3514 := (iff #1539 #3513) -#3511 := (iff #1536 #3508) -#3494 := (or #813 #1235) -#3505 := (or #3494 #1532) -#3509 := (iff #3505 #3508) -#3510 := [rewrite]: #3509 -#3506 := (iff #1536 #3505) -#3503 := (iff #1529 #3494) -#3495 := (not #3494) -#3498 := (not #3495) -#3501 := (iff #3498 #3494) -#3502 := [rewrite]: #3501 -#3499 := (iff #1529 #3498) -#3496 := (iff #1524 #3495) -#3497 := [rewrite]: #3496 -#3500 := [monotonicity #3497]: #3499 -#3504 := [trans #3500 #3502]: #3503 -#3507 := [monotonicity #3504]: #3506 -#3512 := [trans #3507 #3510]: #3511 -#3515 := [quant-intro #3512]: #3514 -#3533 := [monotonicity #3515 #3530]: #3532 -#3541 := [trans #3533 #3539]: #3540 -#3492 := (iff #2923 #3491) -#3489 := (iff #2920 #3486) -#3472 := (or #2327 #3471) -#3483 := (or #3472 #2915) -#3487 := (iff #3483 #3486) +#2346 := (not #2345) +#2948 := (and #798 #2346 #2945) +#2951 := (not #2948) +#2954 := (forall (vars (?v1 S3)) #2951) +#2920 := (not #2917) +#2963 := (and #1530 #2351 #2920 #2954) +#2319 := (not #2318) +#2890 := (and #2319 #2321) +#2893 := (not #2890) +#2911 := (or #2893 #2906) +#2914 := (not #2911) +#2968 := (or #2914 #2963) +#2971 := (and #1506 #2968) +#2290 := (not #2289) +#2865 := (and #2287 #2290) +#2868 := (not #2865) +#2884 := (or #2868 #2879) +#2887 := (not #2884) +#2974 := (or #2887 #2971) +#2977 := (and #1487 #2974) +#2980 := (or #2267 #2977) +#2983 := (and #203 #2980) +#2986 := (or #1481 #2983) +#2989 := (and #810 #2986) +#2992 := (or #2860 #2989) +#2995 := (and #1473 #2992) +#2998 := (or #2846 #2995) +#2205 := (not #2204) +#2202 := (not #2201) +#3004 := (and #181 #756 #1462 #1620 #1638 #1646 #2202 #2205 #2998) +#2147 := (not #2146) +#2143 := (not #2142) +#2783 := (and #2143 #2147) +#2786 := (not #2783) +#2803 := (or #2786 #2798) +#2806 := (not #2803) +#2156 := (not #158) +#2166 := (and #2156 #1382) +#2812 := (or #2166 #2806) +#2756 := (not #2751) +#2774 := (and #2756 #2769) +#2777 := (or #1342 #2774) +#2780 := (forall (vars (?v0 S3)) #2777) +#2817 := (and #2780 #2812) +#2076 := (not #2075) +#2726 := (and #2076 #2723) +#2729 := (not #2726) +#2732 := (forall (vars (?v1 S3)) #2729) +#2698 := (not #2695) +#2081 := (not #2080) +#2738 := (and #2081 #2698 #2732) +#2820 := (or #2738 #2817) +#2182 := (not #1410) +#2185 := (forall (vars (?v0 S3)) #2182) +#2826 := (and #136 #141 #620 #623 #2185 #2820) +#3009 := (or #2826 #3004) +#2675 := (not #2670) +#2678 := (and #2040 #2658 #2675) +#2681 := (or #1297 #2678) +#2684 := (forall (vars (?v0 S3)) #2681) +#2620 := (not #2615) +#2638 := (and #2013 #2620 #2633) +#2641 := (or #1259 #2638) +#2644 := (forall (vars (?v0 S3)) #2641) +#3015 := (and #100 #1705 #1721 #1730 #2644 #2684 #3009) +#1968 := (not #1967) +#2588 := (and #453 #1968 #2585) +#2591 := (not #2588) +#2594 := (forall (vars (?v1 S3)) #2591) +#2560 := (not #2557) +#1973 := (not #1972) +#2600 := (and #1973 #2560 #2594) +#3020 := (or #2600 #3015) +#3023 := (and #1244 #3020) +#1934 := (not #1933) +#2545 := (and #1934 #1936) +#2548 := (not #2545) +#2551 := (or #2542 #2548) +#2554 := (not #2551) +#3026 := (or #2554 #3023) +#3029 := (and #1213 #3026) +#1911 := (not #1910) +#2513 := (and #1908 #1911) +#2516 := (not #2513) +#2532 := (or #2516 #2527) +#2535 := (not #2532) +#3032 := (or #2535 #3029) +#3035 := (and #1193 #3032) +#3038 := (or #1888 #3035) +#3041 := (and #71 #3038) +#3044 := (or #1187 #3041) +#3686 := (iff #3044 #3685) +#3683 := (iff #3041 #3680) +#3675 := (and #71 #3672) +#3681 := (iff #3675 #3680) +#3682 := [rewrite]: #3681 +#3676 := (iff #3041 #3675) +#3673 := (iff #3038 #3672) +#3670 := (iff #3035 #3667) +#3662 := (and #1193 #3659) +#3668 := (iff #3662 #3667) +#3669 := [rewrite]: #3668 +#3663 := (iff #3035 #3662) +#3660 := (iff #3032 #3659) +#3657 := (iff #3029 #3654) +#3648 := (and #3066 #3645) +#3655 := (iff #3648 #3654) +#3656 := [rewrite]: #3655 +#3649 := (iff #3029 #3648) +#3646 := (iff #3026 #3645) +#3643 := (iff #3023 #3640) +#3634 := (and #3111 #3631) +#3641 := (iff #3634 #3640) +#3642 := [rewrite]: #3641 +#3635 := (iff #3023 #3634) +#3632 := (iff #3020 #3631) +#3629 := (iff #3015 #3626) +#3617 := (and #100 #3158 #3181 #1730 #3209 #3237 #3614) +#3627 := (iff #3617 #3626) +#3628 := [rewrite]: #3627 +#3618 := (iff #3015 #3617) +#3615 := (iff #3009 #3614) +#3612 := (iff #3004 #3609) +#3602 := (and #181 #756 #3395 #3413 #1638 #1646 #2202 #2205 #3599) +#3610 := (iff #3602 #3609) +#3611 := [rewrite]: #3610 +#3603 := (iff #3004 #3602) +#3600 := (iff #2998 #3599) +#3597 := (iff #2995 #3594) +#3589 := (and #1473 #3586) +#3595 := (iff #3589 #3594) +#3596 := [rewrite]: #3595 +#3590 := (iff #2995 #3589) +#3587 := (iff #2992 #3586) +#3584 := (iff #2989 #3581) +#3576 := (and #810 #3573) +#3582 := (iff #3576 #3581) +#3583 := [rewrite]: #3582 +#3577 := (iff #2989 #3576) +#3574 := (iff #2986 #3573) +#3571 := (iff #2983 #3568) +#3563 := (and #203 #3560) +#3569 := (iff #3563 #3568) +#3570 := [rewrite]: #3569 +#3564 := (iff #2983 #3563) +#3561 := (iff #2980 #3560) +#3558 := (iff #2977 #3555) +#3550 := (and #1487 #3547) +#3556 := (iff #3550 #3555) +#3557 := [rewrite]: #3556 +#3551 := (iff #2977 #3550) +#3548 := (iff #2974 #3547) +#3545 := (iff #2971 #3542) +#3536 := (and #3459 #3533) +#3543 := (iff #3536 #3542) +#3544 := [rewrite]: #3543 +#3537 := (iff #2971 #3536) +#3534 := (iff #2968 #3533) +#3531 := (iff #2963 #3528) +#3522 := (and #3504 #2351 #2920 #3519) +#3529 := (iff #3522 #3528) +#3530 := [rewrite]: #3529 +#3523 := (iff #2963 #3522) +#3520 := (iff #2954 #3519) +#3517 := (iff #2951 #3508) +#3509 := (not #3508) +#3512 := (not #3509) +#3515 := (iff #3512 #3508) +#3516 := [rewrite]: #3515 +#3513 := (iff #2951 #3512) +#3510 := (iff #2948 #3509) +#3511 := [rewrite]: #3510 +#3514 := [monotonicity #3511]: #3513 +#3518 := [trans #3514 #3516]: #3517 +#3521 := [quant-intro #3518]: #3520 +#3505 := (iff #1530 #3504) +#3502 := (iff #1527 #3499) +#3485 := (or #804 #1226) +#3496 := (or #3485 #1523) +#3500 := (iff #3496 #3499) +#3501 := [rewrite]: #3500 +#3497 := (iff #1527 #3496) +#3494 := (iff #1520 #3485) +#3486 := (not #3485) +#3489 := (not #3486) +#3492 := (iff #3489 #3485) +#3493 := [rewrite]: #3492 +#3490 := (iff #1520 #3489) +#3487 := (iff #1515 #3486) #3488 := [rewrite]: #3487 -#3484 := (iff #2920 #3483) -#3481 := (iff #2902 #3472) -#3473 := (not #3472) -#3476 := (not #3473) -#3479 := (iff #3476 #3472) -#3480 := [rewrite]: #3479 -#3477 := (iff #2902 #3476) -#3474 := (iff #2899 #3473) -#3475 := [rewrite]: #3474 -#3478 := [monotonicity #3475]: #3477 -#3482 := [trans #3478 #3480]: #3481 -#3485 := [monotonicity #3482]: #3484 -#3490 := [trans #3485 #3488]: #3489 -#3493 := [monotonicity #3490]: #3492 -#3544 := [monotonicity #3493 #3541]: #3543 -#3469 := (iff #1515 #3468) -#3466 := (iff #1510 #3463) -#3449 := (or #807 #3448) -#3460 := (or #3449 #1502) -#3464 := (iff #3460 #3463) -#3465 := [rewrite]: #3464 -#3461 := (iff #1510 #3460) -#3458 := (iff #836 #3449) -#3450 := (not #3449) -#3453 := (not #3450) -#3456 := (iff #3453 #3449) -#3457 := [rewrite]: #3456 -#3454 := (iff #836 #3453) -#3451 := (iff #830 #3450) -#3452 := [rewrite]: #3451 -#3455 := [monotonicity #3452]: #3454 -#3459 := [trans #3455 #3457]: #3458 -#3462 := [monotonicity #3459]: #3461 -#3467 := [trans #3462 #3465]: #3466 -#3470 := [quant-intro #3467]: #3469 -#3547 := [monotonicity #3470 #3544]: #3546 -#3555 := [trans #3547 #3553]: #3554 -#3446 := (iff #2896 #3445) -#3443 := (iff #2893 #3440) -#3426 := (or #3425 #2298) -#3437 := (or #3426 #2888) -#3441 := (iff #3437 #3440) -#3442 := [rewrite]: #3441 -#3438 := (iff #2893 #3437) -#3435 := (iff #2877 #3426) -#3427 := (not #3426) -#3430 := (not #3427) -#3433 := (iff #3430 #3426) -#3434 := [rewrite]: #3433 -#3431 := (iff #2877 #3430) -#3428 := (iff #2874 #3427) -#3429 := [rewrite]: #3428 -#3432 := [monotonicity #3429]: #3431 -#3436 := [trans #3432 #3434]: #3435 -#3439 := [monotonicity #3436]: #3438 -#3444 := [trans #3439 #3442]: #3443 -#3447 := [monotonicity #3444]: #3446 -#3558 := [monotonicity #3447 #3555]: #3557 -#3561 := [monotonicity #3558]: #3560 -#3568 := [trans #3561 #3566]: #3567 -#3571 := [monotonicity #3568]: #3570 -#3574 := [monotonicity #3571]: #3573 -#3581 := [trans #3574 #3579]: #3580 -#3584 := [monotonicity #3581]: #3583 -#3587 := [monotonicity #3584]: #3586 -#3594 := [trans #3587 #3592]: #3593 -#3597 := [monotonicity #3594]: #3596 -#3600 := [monotonicity #3597]: #3599 -#3607 := [trans #3600 #3605]: #3606 -#3610 := [monotonicity #3607]: #3609 -#3423 := (iff #1629 #3422) -#3420 := (iff #1626 #3417) -#3414 := (or #3397 #1623) -#3418 := (iff #3414 #3417) -#3419 := [rewrite]: #3418 -#3415 := (iff #1626 #3414) -#3412 := (iff #1618 #3397) -#3407 := (not #3398) -#3410 := (iff #3407 #3397) -#3411 := [rewrite]: #3410 -#3408 := (iff #1618 #3407) -#3399 := (iff #1460 #3398) -#3400 := [rewrite]: #3399 -#3409 := [monotonicity #3400]: #3408 -#3413 := [trans #3409 #3411]: #3412 -#3416 := [monotonicity #3413]: #3415 -#3421 := [trans #3416 #3419]: #3420 -#3424 := [quant-intro #3421]: #3423 -#3405 := (iff #1471 #3404) -#3402 := (iff #1466 #3401) -#3403 := [monotonicity #3400]: #3402 -#3406 := [quant-intro #3403]: #3405 -#3613 := [monotonicity #3406 #3424 #3610]: #3612 -#3622 := [trans #3613 #3620]: #3621 -#3395 := (iff #2835 #3392) -#3386 := (and #136 #141 #621 #624 #3260 #3383) -#3393 := (iff #3386 #3392) -#3394 := [rewrite]: #3393 -#3387 := (iff #2835 #3386) -#3384 := (iff #2829 #3383) -#3381 := (iff #2826 #3378) -#3372 := (and #3312 #3369) -#3379 := (iff #3372 #3378) -#3380 := [rewrite]: #3379 -#3373 := (iff #2826 #3372) -#3370 := (iff #2821 #3369) -#3367 := (iff #2815 #3366) -#3364 := (iff #2812 #3361) -#3347 := (or #2151 #2155) -#3358 := (or #3347 #2807) -#3362 := (iff #3358 #3361) -#3363 := [rewrite]: #3362 -#3359 := (iff #2812 #3358) -#3356 := (iff #2795 #3347) -#3348 := (not #3347) -#3351 := (not #3348) -#3354 := (iff #3351 #3347) -#3355 := [rewrite]: #3354 -#3352 := (iff #2795 #3351) -#3349 := (iff #2792 #3348) -#3350 := [rewrite]: #3349 -#3353 := [monotonicity #3350]: #3352 -#3357 := [trans #3353 #3355]: #3356 -#3360 := [monotonicity #3357]: #3359 -#3365 := [trans #3360 #3363]: #3364 -#3368 := [monotonicity #3365]: #3367 -#3345 := (iff #2175 #3342) -#3337 := (and #2165 #3334) -#3343 := (iff #3337 #3342) -#3344 := [rewrite]: #3343 -#3338 := (iff #2175 #3337) -#3335 := (iff #1391 #3334) -#3332 := (iff #1388 #3329) -#3315 := (or #1235 #1344) -#3326 := (or #3315 #1385) -#3330 := (iff #3326 #3329) -#3331 := [rewrite]: #3330 -#3327 := (iff #1388 #3326) -#3324 := (iff #1382 #3315) -#3316 := (not #3315) -#3319 := (not #3316) -#3322 := (iff #3319 #3315) -#3323 := [rewrite]: #3322 -#3320 := (iff #1382 #3319) -#3317 := (iff #1379 #3316) -#3318 := [rewrite]: #3317 -#3321 := [monotonicity #3318]: #3320 -#3325 := [trans #3321 #3323]: #3324 -#3328 := [monotonicity #3325]: #3327 -#3333 := [trans #3328 #3331]: #3332 -#3336 := [quant-intro #3333]: #3335 -#3339 := [monotonicity #3336]: #3338 -#3346 := [trans #3339 #3344]: #3345 -#3371 := [monotonicity #3346 #3368]: #3370 -#3313 := (iff #2789 #3312) -#3310 := (iff #2786 #3307) -#3288 := (or #57 #1344) -#3304 := (or #3288 #3301) -#3308 := (iff #3304 #3307) +#3491 := [monotonicity #3488]: #3490 +#3495 := [trans #3491 #3493]: #3494 +#3498 := [monotonicity #3495]: #3497 +#3503 := [trans #3498 #3501]: #3502 +#3506 := [quant-intro #3503]: #3505 +#3524 := [monotonicity #3506 #3521]: #3523 +#3532 := [trans #3524 #3530]: #3531 +#3483 := (iff #2914 #3482) +#3480 := (iff #2911 #3477) +#3463 := (or #2318 #3462) +#3474 := (or #3463 #2906) +#3478 := (iff #3474 #3477) +#3479 := [rewrite]: #3478 +#3475 := (iff #2911 #3474) +#3472 := (iff #2893 #3463) +#3464 := (not #3463) +#3467 := (not #3464) +#3470 := (iff #3467 #3463) +#3471 := [rewrite]: #3470 +#3468 := (iff #2893 #3467) +#3465 := (iff #2890 #3464) +#3466 := [rewrite]: #3465 +#3469 := [monotonicity #3466]: #3468 +#3473 := [trans #3469 #3471]: #3472 +#3476 := [monotonicity #3473]: #3475 +#3481 := [trans #3476 #3479]: #3480 +#3484 := [monotonicity #3481]: #3483 +#3535 := [monotonicity #3484 #3532]: #3534 +#3460 := (iff #1506 #3459) +#3457 := (iff #1501 #3454) +#3440 := (or #798 #3439) +#3451 := (or #3440 #1493) +#3455 := (iff #3451 #3454) +#3456 := [rewrite]: #3455 +#3452 := (iff #1501 #3451) +#3449 := (iff #827 #3440) +#3441 := (not #3440) +#3444 := (not #3441) +#3447 := (iff #3444 #3440) +#3448 := [rewrite]: #3447 +#3445 := (iff #827 #3444) +#3442 := (iff #821 #3441) +#3443 := [rewrite]: #3442 +#3446 := [monotonicity #3443]: #3445 +#3450 := [trans #3446 #3448]: #3449 +#3453 := [monotonicity #3450]: #3452 +#3458 := [trans #3453 #3456]: #3457 +#3461 := [quant-intro #3458]: #3460 +#3538 := [monotonicity #3461 #3535]: #3537 +#3546 := [trans #3538 #3544]: #3545 +#3437 := (iff #2887 #3436) +#3434 := (iff #2884 #3431) +#3417 := (or #3416 #2289) +#3428 := (or #3417 #2879) +#3432 := (iff #3428 #3431) +#3433 := [rewrite]: #3432 +#3429 := (iff #2884 #3428) +#3426 := (iff #2868 #3417) +#3418 := (not #3417) +#3421 := (not #3418) +#3424 := (iff #3421 #3417) +#3425 := [rewrite]: #3424 +#3422 := (iff #2868 #3421) +#3419 := (iff #2865 #3418) +#3420 := [rewrite]: #3419 +#3423 := [monotonicity #3420]: #3422 +#3427 := [trans #3423 #3425]: #3426 +#3430 := [monotonicity #3427]: #3429 +#3435 := [trans #3430 #3433]: #3434 +#3438 := [monotonicity #3435]: #3437 +#3549 := [monotonicity #3438 #3546]: #3548 +#3552 := [monotonicity #3549]: #3551 +#3559 := [trans #3552 #3557]: #3558 +#3562 := [monotonicity #3559]: #3561 +#3565 := [monotonicity #3562]: #3564 +#3572 := [trans #3565 #3570]: #3571 +#3575 := [monotonicity #3572]: #3574 +#3578 := [monotonicity #3575]: #3577 +#3585 := [trans #3578 #3583]: #3584 +#3588 := [monotonicity #3585]: #3587 +#3591 := [monotonicity #3588]: #3590 +#3598 := [trans #3591 #3596]: #3597 +#3601 := [monotonicity #3598]: #3600 +#3414 := (iff #1620 #3413) +#3411 := (iff #1617 #3408) +#3405 := (or #3388 #1614) +#3409 := (iff #3405 #3408) +#3410 := [rewrite]: #3409 +#3406 := (iff #1617 #3405) +#3403 := (iff #1609 #3388) +#3398 := (not #3389) +#3401 := (iff #3398 #3388) +#3402 := [rewrite]: #3401 +#3399 := (iff #1609 #3398) +#3390 := (iff #1451 #3389) +#3391 := [rewrite]: #3390 +#3400 := [monotonicity #3391]: #3399 +#3404 := [trans #3400 #3402]: #3403 +#3407 := [monotonicity #3404]: #3406 +#3412 := [trans #3407 #3410]: #3411 +#3415 := [quant-intro #3412]: #3414 +#3396 := (iff #1462 #3395) +#3393 := (iff #1457 #3392) +#3394 := [monotonicity #3391]: #3393 +#3397 := [quant-intro #3394]: #3396 +#3604 := [monotonicity #3397 #3415 #3601]: #3603 +#3613 := [trans #3604 #3611]: #3612 +#3386 := (iff #2826 #3383) +#3377 := (and #136 #141 #620 #623 #3251 #3374) +#3384 := (iff #3377 #3383) +#3385 := [rewrite]: #3384 +#3378 := (iff #2826 #3377) +#3375 := (iff #2820 #3374) +#3372 := (iff #2817 #3369) +#3363 := (and #3303 #3360) +#3370 := (iff #3363 #3369) +#3371 := [rewrite]: #3370 +#3364 := (iff #2817 #3363) +#3361 := (iff #2812 #3360) +#3358 := (iff #2806 #3357) +#3355 := (iff #2803 #3352) +#3338 := (or #2142 #2146) +#3349 := (or #3338 #2798) +#3353 := (iff #3349 #3352) +#3354 := [rewrite]: #3353 +#3350 := (iff #2803 #3349) +#3347 := (iff #2786 #3338) +#3339 := (not #3338) +#3342 := (not #3339) +#3345 := (iff #3342 #3338) +#3346 := [rewrite]: #3345 +#3343 := (iff #2786 #3342) +#3340 := (iff #2783 #3339) +#3341 := [rewrite]: #3340 +#3344 := [monotonicity #3341]: #3343 +#3348 := [trans #3344 #3346]: #3347 +#3351 := [monotonicity #3348]: #3350 +#3356 := [trans #3351 #3354]: #3355 +#3359 := [monotonicity #3356]: #3358 +#3336 := (iff #2166 #3333) +#3328 := (and #2156 #3325) +#3334 := (iff #3328 #3333) +#3335 := [rewrite]: #3334 +#3329 := (iff #2166 #3328) +#3326 := (iff #1382 #3325) +#3323 := (iff #1379 #3320) +#3306 := (or #1226 #1335) +#3317 := (or #3306 #1376) +#3321 := (iff #3317 #3320) +#3322 := [rewrite]: #3321 +#3318 := (iff #1379 #3317) +#3315 := (iff #1373 #3306) +#3307 := (not #3306) +#3310 := (not #3307) +#3313 := (iff #3310 #3306) +#3314 := [rewrite]: #3313 +#3311 := (iff #1373 #3310) +#3308 := (iff #1370 #3307) #3309 := [rewrite]: #3308 -#3305 := (iff #2786 #3304) -#3302 := (iff #2783 #3301) -#3303 := [rewrite]: #3302 -#3297 := (iff #1351 #3288) -#3289 := (not #3288) -#3292 := (not #3289) -#3295 := (iff #3292 #3288) -#3296 := [rewrite]: #3295 -#3293 := (iff #1351 #3292) -#3290 := (iff #1348 #3289) -#3291 := [rewrite]: #3290 -#3294 := [monotonicity #3291]: #3293 -#3298 := [trans #3294 #3296]: #3297 -#3306 := [monotonicity #3298 #3303]: #3305 -#3311 := [trans #3306 #3309]: #3310 -#3314 := [quant-intro #3311]: #3313 -#3374 := [monotonicity #3314 #3371]: #3373 -#3382 := [trans #3374 #3380]: #3381 -#3286 := (iff #2747 #3283) -#3278 := (and #2090 #2707 #3275) -#3284 := (iff #3278 #3283) -#3285 := [rewrite]: #3284 -#3279 := (iff #2747 #3278) -#3276 := (iff #2741 #3275) -#3273 := (iff #2738 #3264) -#3265 := (not #3264) -#3268 := (not #3265) -#3271 := (iff #3268 #3264) -#3272 := [rewrite]: #3271 -#3269 := (iff #2738 #3268) -#3266 := (iff #2735 #3265) -#3267 := [rewrite]: #3266 -#3270 := [monotonicity #3267]: #3269 -#3274 := [trans #3270 #3272]: #3273 -#3277 := [quant-intro #3274]: #3276 -#3280 := [monotonicity #3277]: #3279 -#3287 := [trans #3280 #3285]: #3286 -#3385 := [monotonicity #3287 #3382]: #3384 -#3261 := (iff #2194 #3260) -#3258 := (iff #2191 #3249) -#3250 := (not #3249) -#3253 := (not #3250) -#3256 := (iff #3253 #3249) -#3257 := [rewrite]: #3256 -#3254 := (iff #2191 #3253) -#3251 := (iff #1419 #3250) -#3252 := [rewrite]: #3251 -#3255 := [monotonicity #3252]: #3254 -#3259 := [trans #3255 #3257]: #3258 -#3262 := [quant-intro #3259]: #3261 -#3388 := [monotonicity #3262 #3385]: #3387 -#3396 := [trans #3388 #3394]: #3395 -#3625 := [monotonicity #3396 #3622]: #3624 -#3247 := (iff #2693 #3246) -#3244 := (iff #2690 #3241) -#3221 := (or #57 #1299) -#3238 := (or #3221 #3235) -#3242 := (iff #3238 #3241) +#3312 := [monotonicity #3309]: #3311 +#3316 := [trans #3312 #3314]: #3315 +#3319 := [monotonicity #3316]: #3318 +#3324 := [trans #3319 #3322]: #3323 +#3327 := [quant-intro #3324]: #3326 +#3330 := [monotonicity #3327]: #3329 +#3337 := [trans #3330 #3335]: #3336 +#3362 := [monotonicity #3337 #3359]: #3361 +#3304 := (iff #2780 #3303) +#3301 := (iff #2777 #3298) +#3279 := (or #57 #1335) +#3295 := (or #3279 #3292) +#3299 := (iff #3295 #3298) +#3300 := [rewrite]: #3299 +#3296 := (iff #2777 #3295) +#3293 := (iff #2774 #3292) +#3294 := [rewrite]: #3293 +#3288 := (iff #1342 #3279) +#3280 := (not #3279) +#3283 := (not #3280) +#3286 := (iff #3283 #3279) +#3287 := [rewrite]: #3286 +#3284 := (iff #1342 #3283) +#3281 := (iff #1339 #3280) +#3282 := [rewrite]: #3281 +#3285 := [monotonicity #3282]: #3284 +#3289 := [trans #3285 #3287]: #3288 +#3297 := [monotonicity #3289 #3294]: #3296 +#3302 := [trans #3297 #3300]: #3301 +#3305 := [quant-intro #3302]: #3304 +#3365 := [monotonicity #3305 #3362]: #3364 +#3373 := [trans #3365 #3371]: #3372 +#3277 := (iff #2738 #3274) +#3269 := (and #2081 #2698 #3266) +#3275 := (iff #3269 #3274) +#3276 := [rewrite]: #3275 +#3270 := (iff #2738 #3269) +#3267 := (iff #2732 #3266) +#3264 := (iff #2729 #3255) +#3256 := (not #3255) +#3259 := (not #3256) +#3262 := (iff #3259 #3255) +#3263 := [rewrite]: #3262 +#3260 := (iff #2729 #3259) +#3257 := (iff #2726 #3256) +#3258 := [rewrite]: #3257 +#3261 := [monotonicity #3258]: #3260 +#3265 := [trans #3261 #3263]: #3264 +#3268 := [quant-intro #3265]: #3267 +#3271 := [monotonicity #3268]: #3270 +#3278 := [trans #3271 #3276]: #3277 +#3376 := [monotonicity #3278 #3373]: #3375 +#3252 := (iff #2185 #3251) +#3249 := (iff #2182 #3240) +#3241 := (not #3240) +#3244 := (not #3241) +#3247 := (iff #3244 #3240) +#3248 := [rewrite]: #3247 +#3245 := (iff #2182 #3244) +#3242 := (iff #1410 #3241) #3243 := [rewrite]: #3242 -#3239 := (iff #2690 #3238) -#3236 := (iff #2687 #3235) -#3237 := [rewrite]: #3236 -#3230 := (iff #1306 #3221) -#3222 := (not #3221) -#3225 := (not #3222) -#3228 := (iff #3225 #3221) -#3229 := [rewrite]: #3228 -#3226 := (iff #1306 #3225) -#3223 := (iff #1303 #3222) -#3224 := [rewrite]: #3223 -#3227 := [monotonicity #3224]: #3226 -#3231 := [trans #3227 #3229]: #3230 -#3240 := [monotonicity #3231 #3237]: #3239 -#3245 := [trans #3240 #3243]: #3244 -#3248 := [quant-intro #3245]: #3247 -#3219 := (iff #2653 #3218) -#3216 := (iff #2650 #3213) -#3193 := (or #57 #1261) -#3210 := (or #3193 #3207) -#3214 := (iff #3210 #3213) +#3246 := [monotonicity #3243]: #3245 +#3250 := [trans #3246 #3248]: #3249 +#3253 := [quant-intro #3250]: #3252 +#3379 := [monotonicity #3253 #3376]: #3378 +#3387 := [trans #3379 #3385]: #3386 +#3616 := [monotonicity #3387 #3613]: #3615 +#3238 := (iff #2684 #3237) +#3235 := (iff #2681 #3232) +#3212 := (or #57 #1290) +#3229 := (or #3212 #3226) +#3233 := (iff #3229 #3232) +#3234 := [rewrite]: #3233 +#3230 := (iff #2681 #3229) +#3227 := (iff #2678 #3226) +#3228 := [rewrite]: #3227 +#3221 := (iff #1297 #3212) +#3213 := (not #3212) +#3216 := (not #3213) +#3219 := (iff #3216 #3212) +#3220 := [rewrite]: #3219 +#3217 := (iff #1297 #3216) +#3214 := (iff #1294 #3213) #3215 := [rewrite]: #3214 -#3211 := (iff #2650 #3210) -#3208 := (iff #2647 #3207) -#3209 := [rewrite]: #3208 -#3202 := (iff #1268 #3193) -#3194 := (not #3193) -#3197 := (not #3194) -#3200 := (iff #3197 #3193) -#3201 := [rewrite]: #3200 -#3198 := (iff #1268 #3197) -#3195 := (iff #1265 #3194) -#3196 := [rewrite]: #3195 -#3199 := [monotonicity #3196]: #3198 -#3203 := [trans #3199 #3201]: #3202 -#3212 := [monotonicity #3203 #3209]: #3211 -#3217 := [trans #3212 #3215]: #3216 -#3220 := [quant-intro #3217]: #3219 -#3191 := (iff #1730 #3190) -#3188 := (iff #1725 #3185) -#3171 := (or #533 #3170) -#3182 := (or #3171 #1315) -#3186 := (iff #3182 #3185) +#3218 := [monotonicity #3215]: #3217 +#3222 := [trans #3218 #3220]: #3221 +#3231 := [monotonicity #3222 #3228]: #3230 +#3236 := [trans #3231 #3234]: #3235 +#3239 := [quant-intro #3236]: #3238 +#3210 := (iff #2644 #3209) +#3207 := (iff #2641 #3204) +#3184 := (or #57 #1252) +#3201 := (or #3184 #3198) +#3205 := (iff #3201 #3204) +#3206 := [rewrite]: #3205 +#3202 := (iff #2641 #3201) +#3199 := (iff #2638 #3198) +#3200 := [rewrite]: #3199 +#3193 := (iff #1259 #3184) +#3185 := (not #3184) +#3188 := (not #3185) +#3191 := (iff #3188 #3184) +#3192 := [rewrite]: #3191 +#3189 := (iff #1259 #3188) +#3186 := (iff #1256 #3185) #3187 := [rewrite]: #3186 -#3183 := (iff #1725 #3182) -#3180 := (iff #548 #3171) -#3172 := (not #3171) -#3175 := (not #3172) -#3178 := (iff #3175 #3171) -#3179 := [rewrite]: #3178 -#3176 := (iff #548 #3175) -#3173 := (iff #542 #3172) -#3174 := [rewrite]: #3173 -#3177 := [monotonicity #3174]: #3176 -#3181 := [trans #3177 #3179]: #3180 -#3184 := [monotonicity #3181]: #3183 -#3189 := [trans #3184 #3187]: #3188 -#3192 := [quant-intro #3189]: #3191 -#3168 := (iff #1714 #3167) -#3165 := (iff #1711 #3162) -#3148 := (or #536 #1235) -#3159 := (or #3148 #1708) -#3163 := (iff #3159 #3162) -#3164 := [rewrite]: #3163 -#3160 := (iff #1711 #3159) -#3157 := (iff #1705 #3148) -#3149 := (not #3148) -#3152 := (not #3149) -#3155 := (iff #3152 #3148) -#3156 := [rewrite]: #3155 -#3153 := (iff #1705 #3152) -#3150 := (iff #1700 #3149) -#3151 := [rewrite]: #3150 -#3154 := [monotonicity #3151]: #3153 -#3158 := [trans #3154 #3156]: #3157 -#3161 := [monotonicity #3158]: #3160 -#3166 := [trans #3161 #3164]: #3165 -#3169 := [quant-intro #3166]: #3168 -#3628 := [monotonicity #3169 #3192 #3220 #3248 #3625]: #3627 -#3639 := [trans #3628 #3637]: #3638 -#3146 := (iff #2609 #3143) -#3138 := (and #1982 #2569 #3135) -#3144 := (iff #3138 #3143) -#3145 := [rewrite]: #3144 -#3139 := (iff #2609 #3138) -#3136 := (iff #2603 #3135) -#3133 := (iff #2600 #3124) -#3125 := (not #3124) -#3128 := (not #3125) -#3131 := (iff #3128 #3124) -#3132 := [rewrite]: #3131 -#3129 := (iff #2600 #3128) -#3126 := (iff #2597 #3125) -#3127 := [rewrite]: #3126 -#3130 := [monotonicity #3127]: #3129 -#3134 := [trans #3130 #3132]: #3133 -#3137 := [quant-intro #3134]: #3136 -#3140 := [monotonicity #3137]: #3139 -#3147 := [trans #3140 #3145]: #3146 -#3642 := [monotonicity #3147 #3639]: #3641 -#3121 := (iff #1253 #3120) -#3118 := (iff #1250 #3115) -#3101 := (or #457 #1235) -#3112 := (or #1230 #3101) -#3116 := (iff #3112 #3115) -#3117 := [rewrite]: #3116 -#3113 := (iff #1250 #3112) -#3110 := (iff #1247 #3101) -#3102 := (not #3101) -#3105 := (not #3102) -#3108 := (iff #3105 #3101) -#3109 := [rewrite]: #3108 -#3106 := (iff #1247 #3105) -#3103 := (iff #1242 #3102) -#3104 := [rewrite]: #3103 -#3107 := [monotonicity #3104]: #3106 -#3111 := [trans #3107 #3109]: #3110 -#3114 := [monotonicity #3111]: #3113 -#3119 := [trans #3114 #3117]: #3118 -#3122 := [quant-intro #3119]: #3121 -#3645 := [monotonicity #3122 #3642]: #3644 -#3653 := [trans #3645 #3651]: #3652 -#3099 := (iff #2563 #3098) -#3096 := (iff #2560 #3093) -#3079 := (or #1942 #3078) -#3090 := (or #2551 #3079) -#3094 := (iff #3090 #3093) +#3190 := [monotonicity #3187]: #3189 +#3194 := [trans #3190 #3192]: #3193 +#3203 := [monotonicity #3194 #3200]: #3202 +#3208 := [trans #3203 #3206]: #3207 +#3211 := [quant-intro #3208]: #3210 +#3182 := (iff #1721 #3181) +#3179 := (iff #1716 #3176) +#3162 := (or #532 #3161) +#3173 := (or #3162 #1306) +#3177 := (iff #3173 #3176) +#3178 := [rewrite]: #3177 +#3174 := (iff #1716 #3173) +#3171 := (iff #547 #3162) +#3163 := (not #3162) +#3166 := (not #3163) +#3169 := (iff #3166 #3162) +#3170 := [rewrite]: #3169 +#3167 := (iff #547 #3166) +#3164 := (iff #541 #3163) +#3165 := [rewrite]: #3164 +#3168 := [monotonicity #3165]: #3167 +#3172 := [trans #3168 #3170]: #3171 +#3175 := [monotonicity #3172]: #3174 +#3180 := [trans #3175 #3178]: #3179 +#3183 := [quant-intro #3180]: #3182 +#3159 := (iff #1705 #3158) +#3156 := (iff #1702 #3153) +#3139 := (or #535 #1226) +#3150 := (or #3139 #1699) +#3154 := (iff #3150 #3153) +#3155 := [rewrite]: #3154 +#3151 := (iff #1702 #3150) +#3148 := (iff #1696 #3139) +#3140 := (not #3139) +#3143 := (not #3140) +#3146 := (iff #3143 #3139) +#3147 := [rewrite]: #3146 +#3144 := (iff #1696 #3143) +#3141 := (iff #1691 #3140) +#3142 := [rewrite]: #3141 +#3145 := [monotonicity #3142]: #3144 +#3149 := [trans #3145 #3147]: #3148 +#3152 := [monotonicity #3149]: #3151 +#3157 := [trans #3152 #3155]: #3156 +#3160 := [quant-intro #3157]: #3159 +#3619 := [monotonicity #3160 #3183 #3211 #3239 #3616]: #3618 +#3630 := [trans #3619 #3628]: #3629 +#3137 := (iff #2600 #3134) +#3129 := (and #1973 #2560 #3126) +#3135 := (iff #3129 #3134) +#3136 := [rewrite]: #3135 +#3130 := (iff #2600 #3129) +#3127 := (iff #2594 #3126) +#3124 := (iff #2591 #3115) +#3116 := (not #3115) +#3119 := (not #3116) +#3122 := (iff #3119 #3115) +#3123 := [rewrite]: #3122 +#3120 := (iff #2591 #3119) +#3117 := (iff #2588 #3116) +#3118 := [rewrite]: #3117 +#3121 := [monotonicity #3118]: #3120 +#3125 := [trans #3121 #3123]: #3124 +#3128 := [quant-intro #3125]: #3127 +#3131 := [monotonicity #3128]: #3130 +#3138 := [trans #3131 #3136]: #3137 +#3633 := [monotonicity #3138 #3630]: #3632 +#3112 := (iff #1244 #3111) +#3109 := (iff #1241 #3106) +#3092 := (or #456 #1226) +#3103 := (or #1221 #3092) +#3107 := (iff #3103 #3106) +#3108 := [rewrite]: #3107 +#3104 := (iff #1241 #3103) +#3101 := (iff #1238 #3092) +#3093 := (not #3092) +#3096 := (not #3093) +#3099 := (iff #3096 #3092) +#3100 := [rewrite]: #3099 +#3097 := (iff #1238 #3096) +#3094 := (iff #1233 #3093) #3095 := [rewrite]: #3094 -#3091 := (iff #2560 #3090) -#3088 := (iff #2557 #3079) -#3080 := (not #3079) -#3083 := (not #3080) -#3086 := (iff #3083 #3079) -#3087 := [rewrite]: #3086 -#3084 := (iff #2557 #3083) -#3081 := (iff #2554 #3080) -#3082 := [rewrite]: #3081 -#3085 := [monotonicity #3082]: #3084 -#3089 := [trans #3085 #3087]: #3088 -#3092 := [monotonicity #3089]: #3091 -#3097 := [trans #3092 #3095]: #3096 -#3100 := [monotonicity #3097]: #3099 -#3656 := [monotonicity #3100 #3653]: #3655 -#3076 := (iff #1222 #3075) -#3073 := (iff #1217 #3070) -#3056 := (or #454 #2519) -#3067 := (or #3056 #1210) -#3071 := (iff #3067 #3070) -#3072 := [rewrite]: #3071 -#3068 := (iff #1217 #3067) -#3065 := (iff #475 #3056) -#3057 := (not #3056) -#3060 := (not #3057) -#3063 := (iff #3060 #3056) -#3064 := [rewrite]: #3063 -#3061 := (iff #475 #3060) -#3058 := (iff #469 #3057) -#3059 := [rewrite]: #3058 -#3062 := [monotonicity #3059]: #3061 -#3066 := [trans #3062 #3064]: #3065 -#3069 := [monotonicity #3066]: #3068 -#3074 := [trans #3069 #3072]: #3073 -#3077 := [quant-intro #3074]: #3076 -#3659 := [monotonicity #3077 #3656]: #3658 -#3667 := [trans #3659 #3665]: #3666 -#2218 := (iff #2544 #1928) -#2280 := (iff #2541 #2026) -#2239 := (or #2054 #1919) -#2338 := (or #2239 #2536) -#2027 := (iff #2338 #2026) -#2279 := [rewrite]: #2027 -#2306 := (iff #2541 #2338) -#2260 := (iff #2525 #2239) -#1864 := (not #2239) -#2128 := (not #1864) -#2164 := (iff #2128 #2239) -#2259 := [rewrite]: #2164 -#2129 := (iff #2525 #2128) -#1865 := (iff #2522 #1864) -#2240 := [rewrite]: #1865 -#2163 := [monotonicity #2240]: #2129 -#2337 := [trans #2163 #2259]: #2260 -#2307 := [monotonicity #2337]: #2306 -#1927 := [trans #2307 #2279]: #2280 -#2219 := [monotonicity #1927]: #2218 -#3670 := [monotonicity #2219 #3667]: #3669 -#3673 := [monotonicity #3670]: #3672 -#3680 := [trans #3673 #3678]: #3679 -#3683 := [monotonicity #3680]: #3682 -#3686 := [monotonicity #3683]: #3685 -#3693 := [trans #3686 #3691]: #3692 -#3696 := [monotonicity #3693]: #3695 -#2352 := (+ #2351 #2349) -#2353 := (= #2352 0::Int) -#2356 := (and #807 #2355 #2353) -#2373 := (not #2356) -#2376 := (forall (vars (?v1 S3)) #2373) -#2361 := (= ?v0!20 f10) -#2362 := (not #2361) -#2363 := (and #2362 #2360) -#2364 := (not #2363) -#2370 := (not #2364) -#2380 := (and #2370 #2376) -#2385 := (and #1539 #2380) -#2318 := (* -1::Int #2317) -#2320 := (+ #2319 #2318) -#2323 := (+ #2322 #2320) -#2324 := (>= #2323 0::Int) -#2331 := (and #2330 #2328) -#2332 := (not #2331) -#2333 := (or #2332 #2324) -#2334 := (not #2333) -#2389 := (or #2334 #2385) -#2393 := (and #1515 #2389) -#2291 := (* -1::Int #2290) -#2293 := (+ #2292 #2291) -#2294 := (>= #2293 0::Int) -#2300 := (and #2299 #2296) -#2301 := (not #2300) -#2302 := (or #2301 #2294) -#2303 := (not #2302) -#2397 := (or #2303 #2393) -#2401 := (and #1496 #2397) -#2405 := (or #2276 #2401) -#2270 := (not #1490) -#2409 := (and #2270 #2405) -#2413 := (or #1490 #2409) -#2417 := (and #819 #2413) -#2254 := (= #2253 #2252) -#2255 := (or #2254 #2251) -#2256 := (not #2255) -#2421 := (or #2256 #2417) -#2425 := (and #1482 #2421) -#2232 := (* -1::Int #2231) -#2234 := (+ #2233 #2232) -#2235 := (>= #2234 0::Int) -#2236 := (not #2235) -#2429 := (or #2236 #2425) -#2215 := (and #2214 #2211) -#2203 := (not #995) -#2449 := (and #757 #2203 #2215 #1471 #2429 #1629 #1647 #1655) -#2142 := (* -1::Int #2141) -#2144 := (+ #2143 #2142) -#2147 := (+ #2146 #2144) -#2148 := (>= #2147 0::Int) -#2157 := (and #2156 #2152) -#2158 := (not #2157) -#2159 := (or #2158 #2148) -#2160 := (not #2159) -#2179 := (or #2160 #2175) -#2118 := (+ #2117 #1342) -#2121 := (+ #2120 #2118) -#2122 := (= #2121 0::Int) -#2123 := (>= #2118 0::Int) -#2124 := (not #2123) -#2125 := (and #2124 #2122) -#2130 := (or #1351 #2125) -#2133 := (forall (vars (?v0 S3)) #2130) -#2183 := (and #2133 #2179) -#2082 := (+ #2081 #2079) -#2083 := (= #2082 0::Int) -#2086 := (and #2085 #2083) -#2102 := (not #2086) -#2105 := (forall (vars (?v1 S3)) #2102) -#2091 := (= ?v0!8 f10) -#2092 := (not #2091) -#2093 := (and #2092 #2090) -#2094 := (not #2093) -#2099 := (not #2094) -#2109 := (and #2099 #2105) -#2187 := (or #2109 #2183) -#2073 := (not #715) -#2070 := (not #733) -#2067 := (not #706) -#2064 := (not #724) -#2197 := (and #2064 #2067 #2070 #2073 #2187 #2194) -#2453 := (or #2197 #2449) -#2041 := (+ #2040 #1297) -#2042 := (>= #2041 0::Int) -#2043 := (not #2042) -#2046 := (+ #2045 #2041) -#2047 := (= #2046 0::Int) -#2050 := (and #2049 #2047 #2043) -#2055 := (or #1306 #2050) -#2058 := (forall (vars (?v0 S3)) #2055) -#2014 := (+ #1259 #2013) -#2016 := (+ #2015 #2014) -#2017 := (= #2016 0::Int) -#2018 := (+ #2015 #1259) -#2019 := (>= #2018 0::Int) -#2020 := (not #2019) -#2023 := (and #2022 #2020 #2017) -#2028 := (or #1268 #2023) -#2031 := (forall (vars (?v0 S3)) #2028) -#2006 := (not #1747) -#2478 := (and #2006 #2031 #2058 #2453 #1714 #1730 #1739) -#1972 := (+ #1971 #1969) -#1973 := (+ #58 #1972) -#1974 := (= #1973 0::Int) -#1978 := (and #454 #1977 #1974) -#1994 := (not #1978) -#1997 := (forall (vars (?v1 S3)) #1994) -#1983 := (= ?v0!5 f10) -#1984 := (not #1983) -#1985 := (and #1984 #1982) -#1986 := (not #1985) -#1991 := (not #1986) -#2001 := (and #1991 #1997) -#2482 := (or #2001 #2478) -#2486 := (and #1253 #2482) -#1946 := (and #1945 #1943) -#1947 := (not #1946) -#1950 := (+ #1949 #1939) -#1952 := (+ #1951 #1950) -#1953 := (>= #1952 0::Int) -#1954 := (or #1953 #1947) -#1955 := (not #1954) -#2490 := (or #1955 #2486) -#2494 := (and #1222 #2490) -#1912 := (* -1::Int #1911) -#1914 := (+ #1913 #1912) -#1915 := (>= #1914 0::Int) -#1921 := (and #1920 #1917) -#1922 := (not #1921) -#1923 := (or #1922 #1915) -#1924 := (not #1923) -#2498 := (or #1924 #2494) -#2502 := (and #1202 #2498) -#2506 := (or #1897 #2502) -#1860 := (not #1196) -#2510 := (and #1860 #2506) -#2514 := (or #1196 #2510) -#3054 := (iff #2514 #3053) -#3051 := (iff #2510 #3050) -#3048 := (iff #2506 #3047) -#3045 := (iff #2502 #3044) -#3042 := (iff #2498 #3041) -#3039 := (iff #2494 #3038) -#3036 := (iff #2490 #3035) -#3033 := (iff #2486 #3032) -#3030 := (iff #2482 #3029) -#3027 := (iff #2478 #3024) -#3021 := (and #100 #2653 #2693 #3018 #1714 #1730 #1739) -#3025 := (iff #3021 #3024) -#3026 := [rewrite]: #3025 -#3022 := (iff #2478 #3021) -#3019 := (iff #2453 #3018) -#3016 := (iff #2449 #3013) -#3010 := (and #757 #776 #2215 #1471 #3007 #1629 #1647 #1655) -#3014 := (iff #3010 #3013) -#3015 := [rewrite]: #3014 -#3011 := (iff #2449 #3010) -#3008 := (iff #2429 #3007) -#3005 := (iff #2425 #3004) -#3002 := (iff #2421 #3001) -#2999 := (iff #2417 #2998) -#2996 := (iff #2413 #2995) -#2993 := (iff #2409 #2992) -#2990 := (iff #2405 #2989) -#2987 := (iff #2401 #2986) -#2984 := (iff #2397 #2983) -#2981 := (iff #2393 #2980) -#2978 := (iff #2389 #2977) -#2975 := (iff #2385 #2972) -#2935 := (and #2360 #2929) -#2966 := (and #2935 #2963) -#2969 := (and #1539 #2966) -#2973 := (iff #2969 #2972) -#2974 := [rewrite]: #2973 -#2970 := (iff #2385 #2969) -#2967 := (iff #2380 #2966) -#2964 := (iff #2376 #2963) -#2961 := (iff #2373 #2960) -#2958 := (iff #2356 #2957) -#2955 := (iff #2353 #2954) -#2952 := (= #2352 #2951) -#2953 := [rewrite]: #2952 -#2956 := [monotonicity #2953]: #2955 -#2959 := [monotonicity #2956]: #2958 +#3098 := [monotonicity #3095]: #3097 +#3102 := [trans #3098 #3100]: #3101 +#3105 := [monotonicity #3102]: #3104 +#3110 := [trans #3105 #3108]: #3109 +#3113 := [quant-intro #3110]: #3112 +#3636 := [monotonicity #3113 #3633]: #3635 +#3644 := [trans #3636 #3642]: #3643 +#3090 := (iff #2554 #3089) +#3087 := (iff #2551 #3084) +#3070 := (or #1933 #3069) +#3081 := (or #2542 #3070) +#3085 := (iff #3081 #3084) +#3086 := [rewrite]: #3085 +#3082 := (iff #2551 #3081) +#3079 := (iff #2548 #3070) +#3071 := (not #3070) +#3074 := (not #3071) +#3077 := (iff #3074 #3070) +#3078 := [rewrite]: #3077 +#3075 := (iff #2548 #3074) +#3072 := (iff #2545 #3071) +#3073 := [rewrite]: #3072 +#3076 := [monotonicity #3073]: #3075 +#3080 := [trans #3076 #3078]: #3079 +#3083 := [monotonicity #3080]: #3082 +#3088 := [trans #3083 #3086]: #3087 +#3091 := [monotonicity #3088]: #3090 +#3647 := [monotonicity #3091 #3644]: #3646 +#3067 := (iff #1213 #3066) +#3064 := (iff #1208 #3061) +#3047 := (or #453 #2510) +#3058 := (or #3047 #1201) +#3062 := (iff #3058 #3061) +#3063 := [rewrite]: #3062 +#3059 := (iff #1208 #3058) +#3056 := (iff #474 #3047) +#3048 := (not #3047) +#3051 := (not #3048) +#3054 := (iff #3051 #3047) +#3055 := [rewrite]: #3054 +#3052 := (iff #474 #3051) +#3049 := (iff #468 #3048) +#3050 := [rewrite]: #3049 +#3053 := [monotonicity #3050]: #3052 +#3057 := [trans #3053 #3055]: #3056 +#3060 := [monotonicity #3057]: #3059 +#3065 := [trans #3060 #3063]: #3064 +#3068 := [quant-intro #3065]: #3067 +#3650 := [monotonicity #3068 #3647]: #3649 +#3658 := [trans #3650 #3656]: #3657 +#2250 := (iff #2535 #2018) +#2329 := (iff #2532 #2119) +#2297 := (or #2210 #1910) +#2231 := (or #2297 #2527) +#2120 := (iff #2231 #2119) +#2328 := [rewrite]: #2120 +#1918 := (iff #2532 #2231) +#2271 := (iff #2516 #2297) +#1855 := (not #2297) +#2154 := (not #1855) +#1950 := (iff #2154 #2297) +#2270 := [rewrite]: #1950 +#2155 := (iff #2516 #2154) +#1856 := (iff #2513 #1855) +#2298 := [rewrite]: #1856 +#1949 := [monotonicity #2298]: #2155 +#2230 := [trans #1949 #2270]: #2271 +#1919 := [monotonicity #2230]: #1918 +#2017 := [trans #1919 #2328]: #2329 +#2251 := [monotonicity #2017]: #2250 +#3661 := [monotonicity #2251 #3658]: #3660 +#3664 := [monotonicity #3661]: #3663 +#3671 := [trans #3664 #3669]: #3670 +#3674 := [monotonicity #3671]: #3673 +#3677 := [monotonicity #3674]: #3676 +#3684 := [trans #3677 #3682]: #3683 +#3687 := [monotonicity #3684]: #3686 +#2343 := (+ #2342 #2340) +#2344 := (= #2343 0::Int) +#2347 := (and #798 #2346 #2344) +#2364 := (not #2347) +#2367 := (forall (vars (?v1 S3)) #2364) +#2352 := (= ?v0!20 f10) +#2353 := (not #2352) +#2354 := (and #2353 #2351) +#2355 := (not #2354) +#2361 := (not #2355) +#2371 := (and #2361 #2367) +#2376 := (and #1530 #2371) +#2309 := (* -1::Int #2308) +#2311 := (+ #2310 #2309) +#2314 := (+ #2313 #2311) +#2315 := (>= #2314 0::Int) +#2322 := (and #2321 #2319) +#2323 := (not #2322) +#2324 := (or #2323 #2315) +#2325 := (not #2324) +#2380 := (or #2325 #2376) +#2384 := (and #1506 #2380) +#2282 := (* -1::Int #2281) +#2284 := (+ #2283 #2282) +#2285 := (>= #2284 0::Int) +#2291 := (and #2290 #2287) +#2292 := (not #2291) +#2293 := (or #2292 #2285) +#2294 := (not #2293) +#2388 := (or #2294 #2384) +#2392 := (and #1487 #2388) +#2396 := (or #2267 #2392) +#2261 := (not #1481) +#2400 := (and #2261 #2396) +#2404 := (or #1481 #2400) +#2408 := (and #810 #2404) +#2245 := (= #2244 #2243) +#2246 := (or #2245 #2242) +#2247 := (not #2246) +#2412 := (or #2247 #2408) +#2416 := (and #1473 #2412) +#2223 := (* -1::Int #2222) +#2225 := (+ #2224 #2223) +#2226 := (>= #2225 0::Int) +#2227 := (not #2226) +#2420 := (or #2227 #2416) +#2206 := (and #2205 #2202) +#2192 := (not #986) +#2440 := (and #2192 #756 #2206 #1462 #2420 #1620 #1638 #1646) +#2133 := (* -1::Int #2132) +#2135 := (+ #2134 #2133) +#2138 := (+ #2137 #2135) +#2139 := (>= #2138 0::Int) +#2148 := (and #2147 #2143) +#2149 := (not #2148) +#2150 := (or #2149 #2139) +#2151 := (not #2150) +#2170 := (or #2151 #2166) +#2109 := (+ #2108 #1333) +#2112 := (+ #2111 #2109) +#2113 := (= #2112 0::Int) +#2114 := (>= #2109 0::Int) +#2115 := (not #2114) +#2116 := (and #2115 #2113) +#2121 := (or #1342 #2116) +#2124 := (forall (vars (?v0 S3)) #2121) +#2174 := (and #2124 #2170) +#2073 := (+ #2072 #2070) +#2074 := (= #2073 0::Int) +#2077 := (and #2076 #2074) +#2093 := (not #2077) +#2096 := (forall (vars (?v1 S3)) #2093) +#2082 := (= ?v0!8 f10) +#2083 := (not #2082) +#2084 := (and #2083 #2081) +#2085 := (not #2084) +#2090 := (not #2085) +#2100 := (and #2090 #2096) +#2178 := (or #2100 #2174) +#2064 := (not #714) +#2061 := (not #732) +#2058 := (not #705) +#2055 := (not #723) +#2188 := (and #2055 #2058 #2061 #2064 #2178 #2185) +#2444 := (or #2188 #2440) +#2032 := (+ #2031 #1288) +#2033 := (>= #2032 0::Int) +#2034 := (not #2033) +#2037 := (+ #2036 #2032) +#2038 := (= #2037 0::Int) +#2041 := (and #2040 #2038 #2034) +#2046 := (or #1297 #2041) +#2049 := (forall (vars (?v0 S3)) #2046) +#2005 := (+ #1250 #2004) +#2007 := (+ #2006 #2005) +#2008 := (= #2007 0::Int) +#2009 := (+ #2006 #1250) +#2010 := (>= #2009 0::Int) +#2011 := (not #2010) +#2014 := (and #2013 #2011 #2008) +#2019 := (or #1259 #2014) +#2022 := (forall (vars (?v0 S3)) #2019) +#1997 := (not #1738) +#2469 := (and #1997 #2022 #2049 #2444 #1705 #1721 #1730) +#1963 := (+ #1962 #1960) +#1964 := (+ #58 #1963) +#1965 := (= #1964 0::Int) +#1969 := (and #453 #1968 #1965) +#1985 := (not #1969) +#1988 := (forall (vars (?v1 S3)) #1985) +#1974 := (= ?v0!5 f10) +#1975 := (not #1974) +#1976 := (and #1975 #1973) +#1977 := (not #1976) +#1982 := (not #1977) +#1992 := (and #1982 #1988) +#2473 := (or #1992 #2469) +#2477 := (and #1244 #2473) +#1937 := (and #1936 #1934) +#1938 := (not #1937) +#1941 := (+ #1940 #1930) +#1943 := (+ #1942 #1941) +#1944 := (>= #1943 0::Int) +#1945 := (or #1944 #1938) +#1946 := (not #1945) +#2481 := (or #1946 #2477) +#2485 := (and #1213 #2481) +#1903 := (* -1::Int #1902) +#1905 := (+ #1904 #1903) +#1906 := (>= #1905 0::Int) +#1912 := (and #1911 #1908) +#1913 := (not #1912) +#1914 := (or #1913 #1906) +#1915 := (not #1914) +#2489 := (or #1915 #2485) +#2493 := (and #1193 #2489) +#2497 := (or #1888 #2493) +#1851 := (not #1187) +#2501 := (and #1851 #2497) +#2505 := (or #1187 #2501) +#3045 := (iff #2505 #3044) +#3042 := (iff #2501 #3041) +#3039 := (iff #2497 #3038) +#3036 := (iff #2493 #3035) +#3033 := (iff #2489 #3032) +#3030 := (iff #2485 #3029) +#3027 := (iff #2481 #3026) +#3024 := (iff #2477 #3023) +#3021 := (iff #2473 #3020) +#3018 := (iff #2469 #3015) +#3012 := (and #100 #2644 #2684 #3009 #1705 #1721 #1730) +#3016 := (iff #3012 #3015) +#3017 := [rewrite]: #3016 +#3013 := (iff #2469 #3012) +#3010 := (iff #2444 #3009) +#3007 := (iff #2440 #3004) +#3001 := (and #181 #756 #2206 #1462 #2998 #1620 #1638 #1646) +#3005 := (iff #3001 #3004) +#3006 := [rewrite]: #3005 +#3002 := (iff #2440 #3001) +#2999 := (iff #2420 #2998) +#2996 := (iff #2416 #2995) +#2993 := (iff #2412 #2992) +#2990 := (iff #2408 #2989) +#2987 := (iff #2404 #2986) +#2984 := (iff #2400 #2983) +#2981 := (iff #2396 #2980) +#2978 := (iff #2392 #2977) +#2975 := (iff #2388 #2974) +#2972 := (iff #2384 #2971) +#2969 := (iff #2380 #2968) +#2966 := (iff #2376 #2963) +#2926 := (and #2351 #2920) +#2957 := (and #2926 #2954) +#2960 := (and #1530 #2957) +#2964 := (iff #2960 #2963) +#2965 := [rewrite]: #2964 +#2961 := (iff #2376 #2960) +#2958 := (iff #2371 #2957) +#2955 := (iff #2367 #2954) +#2952 := (iff #2364 #2951) +#2949 := (iff #2347 #2948) +#2946 := (iff #2344 #2945) +#2943 := (= #2343 #2942) +#2944 := [rewrite]: #2943 +#2947 := [monotonicity #2944]: #2946 +#2950 := [monotonicity #2947]: #2949 +#2953 := [monotonicity #2950]: #2952 +#2956 := [quant-intro #2953]: #2955 +#2939 := (iff #2361 #2926) +#2931 := (not #2926) +#2934 := (not #2931) +#2937 := (iff #2934 #2926) +#2938 := [rewrite]: #2937 +#2935 := (iff #2361 #2934) +#2932 := (iff #2355 #2931) +#2929 := (iff #2354 #2926) +#2923 := (and #2920 #2351) +#2927 := (iff #2923 #2926) +#2928 := [rewrite]: #2927 +#2924 := (iff #2354 #2923) +#2921 := (iff #2353 #2920) +#2918 := (iff #2352 #2917) +#2919 := [rewrite]: #2918 +#2922 := [monotonicity #2919]: #2921 +#2925 := [monotonicity #2922]: #2924 +#2930 := [trans #2925 #2928]: #2929 +#2933 := [monotonicity #2930]: #2932 +#2936 := [monotonicity #2933]: #2935 +#2940 := [trans #2936 #2938]: #2939 +#2959 := [monotonicity #2940 #2956]: #2958 #2962 := [monotonicity #2959]: #2961 -#2965 := [quant-intro #2962]: #2964 -#2948 := (iff #2370 #2935) -#2940 := (not #2935) -#2943 := (not #2940) -#2946 := (iff #2943 #2935) -#2947 := [rewrite]: #2946 -#2944 := (iff #2370 #2943) -#2941 := (iff #2364 #2940) -#2938 := (iff #2363 #2935) -#2932 := (and #2929 #2360) -#2936 := (iff #2932 #2935) -#2937 := [rewrite]: #2936 -#2933 := (iff #2363 #2932) -#2930 := (iff #2362 #2929) -#2927 := (iff #2361 #2926) -#2928 := [rewrite]: #2927 -#2931 := [monotonicity #2928]: #2930 -#2934 := [monotonicity #2931]: #2933 -#2939 := [trans #2934 #2937]: #2938 -#2942 := [monotonicity #2939]: #2941 -#2945 := [monotonicity #2942]: #2944 -#2949 := [trans #2945 #2947]: #2948 -#2968 := [monotonicity #2949 #2965]: #2967 -#2971 := [monotonicity #2968]: #2970 -#2976 := [trans #2971 #2974]: #2975 -#2924 := (iff #2334 #2923) -#2921 := (iff #2333 #2920) -#2918 := (iff #2324 #2915) -#2905 := (+ #2319 #2322) -#2906 := (+ #2318 #2905) -#2909 := (>= #2906 0::Int) -#2916 := (iff #2909 #2915) -#2917 := [rewrite]: #2916 -#2910 := (iff #2324 #2909) -#2907 := (= #2323 #2906) +#2967 := [trans #2962 #2965]: #2966 +#2915 := (iff #2325 #2914) +#2912 := (iff #2324 #2911) +#2909 := (iff #2315 #2906) +#2896 := (+ #2310 #2313) +#2897 := (+ #2309 #2896) +#2900 := (>= #2897 0::Int) +#2907 := (iff #2900 #2906) #2908 := [rewrite]: #2907 -#2911 := [monotonicity #2908]: #2910 -#2919 := [trans #2911 #2917]: #2918 -#2903 := (iff #2332 #2902) -#2900 := (iff #2331 #2899) -#2901 := [rewrite]: #2900 -#2904 := [monotonicity #2901]: #2903 -#2922 := [monotonicity #2904 #2919]: #2921 -#2925 := [monotonicity #2922]: #2924 -#2979 := [monotonicity #2925 #2976]: #2978 +#2901 := (iff #2315 #2900) +#2898 := (= #2314 #2897) +#2899 := [rewrite]: #2898 +#2902 := [monotonicity #2899]: #2901 +#2910 := [trans #2902 #2908]: #2909 +#2894 := (iff #2323 #2893) +#2891 := (iff #2322 #2890) +#2892 := [rewrite]: #2891 +#2895 := [monotonicity #2892]: #2894 +#2913 := [monotonicity #2895 #2910]: #2912 +#2916 := [monotonicity #2913]: #2915 +#2970 := [monotonicity #2916 #2967]: #2969 +#2973 := [monotonicity #2970]: #2972 +#2888 := (iff #2294 #2887) +#2885 := (iff #2293 #2884) +#2882 := (iff #2285 #2879) +#2871 := (+ #2282 #2283) +#2874 := (>= #2871 0::Int) +#2880 := (iff #2874 #2879) +#2881 := [rewrite]: #2880 +#2875 := (iff #2285 #2874) +#2872 := (= #2284 #2871) +#2873 := [rewrite]: #2872 +#2876 := [monotonicity #2873]: #2875 +#2883 := [trans #2876 #2881]: #2882 +#2869 := (iff #2292 #2868) +#2866 := (iff #2291 #2865) +#2867 := [rewrite]: #2866 +#2870 := [monotonicity #2867]: #2869 +#2886 := [monotonicity #2870 #2883]: #2885 +#2889 := [monotonicity #2886]: #2888 +#2976 := [monotonicity #2889 #2973]: #2975 +#2979 := [monotonicity #2976]: #2978 #2982 := [monotonicity #2979]: #2981 -#2897 := (iff #2303 #2896) -#2894 := (iff #2302 #2893) -#2891 := (iff #2294 #2888) -#2880 := (+ #2291 #2292) -#2883 := (>= #2880 0::Int) -#2889 := (iff #2883 #2888) -#2890 := [rewrite]: #2889 -#2884 := (iff #2294 #2883) -#2881 := (= #2293 #2880) -#2882 := [rewrite]: #2881 -#2885 := [monotonicity #2882]: #2884 -#2892 := [trans #2885 #2890]: #2891 -#2878 := (iff #2301 #2877) -#2875 := (iff #2300 #2874) -#2876 := [rewrite]: #2875 -#2879 := [monotonicity #2876]: #2878 -#2895 := [monotonicity #2879 #2892]: #2894 -#2898 := [monotonicity #2895]: #2897 -#2985 := [monotonicity #2898 #2982]: #2984 +#2863 := (iff #2261 #203) +#2864 := [rewrite]: #2863 +#2985 := [monotonicity #2864 #2982]: #2984 #2988 := [monotonicity #2985]: #2987 #2991 := [monotonicity #2988]: #2990 -#2872 := (iff #2270 #204) -#2873 := [rewrite]: #2872 -#2994 := [monotonicity #2873 #2991]: #2993 +#2861 := (iff #2247 #2860) +#2858 := (iff #2246 #2855) +#2852 := (or #2849 #2242) +#2856 := (iff #2852 #2855) +#2857 := [rewrite]: #2856 +#2853 := (iff #2246 #2852) +#2850 := (iff #2245 #2849) +#2851 := [rewrite]: #2850 +#2854 := [monotonicity #2851]: #2853 +#2859 := [trans #2854 #2857]: #2858 +#2862 := [monotonicity #2859]: #2861 +#2994 := [monotonicity #2862 #2991]: #2993 #2997 := [monotonicity #2994]: #2996 -#3000 := [monotonicity #2997]: #2999 -#2870 := (iff #2256 #2869) -#2867 := (iff #2255 #2864) -#2861 := (or #2858 #2251) -#2865 := (iff #2861 #2864) -#2866 := [rewrite]: #2865 -#2862 := (iff #2255 #2861) -#2859 := (iff #2254 #2858) -#2860 := [rewrite]: #2859 -#2863 := [monotonicity #2860]: #2862 -#2868 := [trans #2863 #2866]: #2867 -#2871 := [monotonicity #2868]: #2870 -#3003 := [monotonicity #2871 #3000]: #3002 -#3006 := [monotonicity #3003]: #3005 -#2856 := (iff #2236 #2855) -#2853 := (iff #2235 #2850) -#2842 := (+ #2232 #2233) -#2845 := (>= #2842 0::Int) -#2851 := (iff #2845 #2850) -#2852 := [rewrite]: #2851 -#2846 := (iff #2235 #2845) -#2843 := (= #2234 #2842) -#2844 := [rewrite]: #2843 -#2847 := [monotonicity #2844]: #2846 -#2854 := [trans #2847 #2852]: #2853 -#2857 := [monotonicity #2854]: #2856 -#3009 := [monotonicity #2857 #3006]: #3008 -#2840 := (iff #2203 #776) -#2841 := [rewrite]: #2840 -#3012 := [monotonicity #2841 #3009]: #3011 -#3017 := [trans #3012 #3015]: #3016 -#2838 := (iff #2197 #2835) -#2832 := (and #136 #141 #621 #624 #2829 #2194) -#2836 := (iff #2832 #2835) -#2837 := [rewrite]: #2836 -#2833 := (iff #2197 #2832) -#2830 := (iff #2187 #2829) -#2827 := (iff #2183 #2826) -#2824 := (iff #2179 #2821) -#2818 := (or #2815 #2175) -#2822 := (iff #2818 #2821) -#2823 := [rewrite]: #2822 -#2819 := (iff #2179 #2818) -#2816 := (iff #2160 #2815) -#2813 := (iff #2159 #2812) -#2810 := (iff #2148 #2807) -#2798 := (+ #2143 #2146) -#2799 := (+ #2142 #2798) -#2802 := (>= #2799 0::Int) -#2808 := (iff #2802 #2807) -#2809 := [rewrite]: #2808 -#2803 := (iff #2148 #2802) -#2800 := (= #2147 #2799) -#2801 := [rewrite]: #2800 -#2804 := [monotonicity #2801]: #2803 -#2811 := [trans #2804 #2809]: #2810 -#2796 := (iff #2158 #2795) -#2793 := (iff #2157 #2792) -#2794 := [rewrite]: #2793 -#2797 := [monotonicity #2794]: #2796 -#2814 := [monotonicity #2797 #2811]: #2813 -#2817 := [monotonicity #2814]: #2816 -#2820 := [monotonicity #2817]: #2819 -#2825 := [trans #2820 #2823]: #2824 -#2790 := (iff #2133 #2789) -#2787 := (iff #2130 #2786) -#2784 := (iff #2125 #2783) -#2781 := (iff #2122 #2778) -#2768 := (+ #2117 #2120) -#2769 := (+ #1342 #2768) -#2772 := (= #2769 0::Int) -#2779 := (iff #2772 #2778) -#2780 := [rewrite]: #2779 -#2773 := (iff #2122 #2772) -#2770 := (= #2121 #2769) +#2847 := (iff #2227 #2846) +#2844 := (iff #2226 #2841) +#2833 := (+ #2223 #2224) +#2836 := (>= #2833 0::Int) +#2842 := (iff #2836 #2841) +#2843 := [rewrite]: #2842 +#2837 := (iff #2226 #2836) +#2834 := (= #2225 #2833) +#2835 := [rewrite]: #2834 +#2838 := [monotonicity #2835]: #2837 +#2845 := [trans #2838 #2843]: #2844 +#2848 := [monotonicity #2845]: #2847 +#3000 := [monotonicity #2848 #2997]: #2999 +#2831 := (iff #2192 #181) +#2832 := [rewrite]: #2831 +#3003 := [monotonicity #2832 #3000]: #3002 +#3008 := [trans #3003 #3006]: #3007 +#2829 := (iff #2188 #2826) +#2823 := (and #136 #141 #620 #623 #2820 #2185) +#2827 := (iff #2823 #2826) +#2828 := [rewrite]: #2827 +#2824 := (iff #2188 #2823) +#2821 := (iff #2178 #2820) +#2818 := (iff #2174 #2817) +#2815 := (iff #2170 #2812) +#2809 := (or #2806 #2166) +#2813 := (iff #2809 #2812) +#2814 := [rewrite]: #2813 +#2810 := (iff #2170 #2809) +#2807 := (iff #2151 #2806) +#2804 := (iff #2150 #2803) +#2801 := (iff #2139 #2798) +#2789 := (+ #2134 #2137) +#2790 := (+ #2133 #2789) +#2793 := (>= #2790 0::Int) +#2799 := (iff #2793 #2798) +#2800 := [rewrite]: #2799 +#2794 := (iff #2139 #2793) +#2791 := (= #2138 #2790) +#2792 := [rewrite]: #2791 +#2795 := [monotonicity #2792]: #2794 +#2802 := [trans #2795 #2800]: #2801 +#2787 := (iff #2149 #2786) +#2784 := (iff #2148 #2783) +#2785 := [rewrite]: #2784 +#2788 := [monotonicity #2785]: #2787 +#2805 := [monotonicity #2788 #2802]: #2804 +#2808 := [monotonicity #2805]: #2807 +#2811 := [monotonicity #2808]: #2810 +#2816 := [trans #2811 #2814]: #2815 +#2781 := (iff #2124 #2780) +#2778 := (iff #2121 #2777) +#2775 := (iff #2116 #2774) +#2772 := (iff #2113 #2769) +#2759 := (+ #2108 #2111) +#2760 := (+ #1333 #2759) +#2763 := (= #2760 0::Int) +#2770 := (iff #2763 #2769) #2771 := [rewrite]: #2770 -#2774 := [monotonicity #2771]: #2773 -#2782 := [trans #2774 #2780]: #2781 -#2766 := (iff #2124 #2765) -#2763 := (iff #2123 #2760) -#2752 := (+ #1342 #2117) -#2755 := (>= #2752 0::Int) -#2761 := (iff #2755 #2760) +#2764 := (iff #2113 #2763) +#2761 := (= #2112 #2760) #2762 := [rewrite]: #2761 -#2756 := (iff #2123 #2755) -#2753 := (= #2118 #2752) -#2754 := [rewrite]: #2753 -#2757 := [monotonicity #2754]: #2756 -#2764 := [trans #2757 #2762]: #2763 -#2767 := [monotonicity #2764]: #2766 -#2785 := [monotonicity #2767 #2782]: #2784 -#2788 := [monotonicity #2785]: #2787 -#2791 := [quant-intro #2788]: #2790 -#2828 := [monotonicity #2791 #2825]: #2827 -#2750 := (iff #2109 #2747) -#2713 := (and #2090 #2707) -#2744 := (and #2713 #2741) -#2748 := (iff #2744 #2747) -#2749 := [rewrite]: #2748 -#2745 := (iff #2109 #2744) -#2742 := (iff #2105 #2741) -#2739 := (iff #2102 #2738) -#2736 := (iff #2086 #2735) -#2733 := (iff #2083 #2732) -#2730 := (= #2082 #2729) -#2731 := [rewrite]: #2730 -#2734 := [monotonicity #2731]: #2733 -#2737 := [monotonicity #2734]: #2736 -#2740 := [monotonicity #2737]: #2739 -#2743 := [quant-intro #2740]: #2742 -#2726 := (iff #2099 #2713) -#2718 := (not #2713) -#2721 := (not #2718) -#2724 := (iff #2721 #2713) -#2725 := [rewrite]: #2724 -#2722 := (iff #2099 #2721) -#2719 := (iff #2094 #2718) -#2716 := (iff #2093 #2713) -#2710 := (and #2707 #2090) -#2714 := (iff #2710 #2713) -#2715 := [rewrite]: #2714 -#2711 := (iff #2093 #2710) -#2708 := (iff #2092 #2707) -#2705 := (iff #2091 #2704) +#2765 := [monotonicity #2762]: #2764 +#2773 := [trans #2765 #2771]: #2772 +#2757 := (iff #2115 #2756) +#2754 := (iff #2114 #2751) +#2743 := (+ #1333 #2108) +#2746 := (>= #2743 0::Int) +#2752 := (iff #2746 #2751) +#2753 := [rewrite]: #2752 +#2747 := (iff #2114 #2746) +#2744 := (= #2109 #2743) +#2745 := [rewrite]: #2744 +#2748 := [monotonicity #2745]: #2747 +#2755 := [trans #2748 #2753]: #2754 +#2758 := [monotonicity #2755]: #2757 +#2776 := [monotonicity #2758 #2773]: #2775 +#2779 := [monotonicity #2776]: #2778 +#2782 := [quant-intro #2779]: #2781 +#2819 := [monotonicity #2782 #2816]: #2818 +#2741 := (iff #2100 #2738) +#2704 := (and #2081 #2698) +#2735 := (and #2704 #2732) +#2739 := (iff #2735 #2738) +#2740 := [rewrite]: #2739 +#2736 := (iff #2100 #2735) +#2733 := (iff #2096 #2732) +#2730 := (iff #2093 #2729) +#2727 := (iff #2077 #2726) +#2724 := (iff #2074 #2723) +#2721 := (= #2073 #2720) +#2722 := [rewrite]: #2721 +#2725 := [monotonicity #2722]: #2724 +#2728 := [monotonicity #2725]: #2727 +#2731 := [monotonicity #2728]: #2730 +#2734 := [quant-intro #2731]: #2733 +#2717 := (iff #2090 #2704) +#2709 := (not #2704) +#2712 := (not #2709) +#2715 := (iff #2712 #2704) +#2716 := [rewrite]: #2715 +#2713 := (iff #2090 #2712) +#2710 := (iff #2085 #2709) +#2707 := (iff #2084 #2704) +#2701 := (and #2698 #2081) +#2705 := (iff #2701 #2704) #2706 := [rewrite]: #2705 -#2709 := [monotonicity #2706]: #2708 -#2712 := [monotonicity #2709]: #2711 -#2717 := [trans #2712 #2715]: #2716 -#2720 := [monotonicity #2717]: #2719 -#2723 := [monotonicity #2720]: #2722 -#2727 := [trans #2723 #2725]: #2726 -#2746 := [monotonicity #2727 #2743]: #2745 -#2751 := [trans #2746 #2749]: #2750 -#2831 := [monotonicity #2751 #2828]: #2830 -#2702 := (iff #2073 #624) -#2703 := [rewrite]: #2702 -#2700 := (iff #2070 #621) -#2701 := [rewrite]: #2700 -#2698 := (iff #2067 #141) -#2699 := [rewrite]: #2698 -#2696 := (iff #2064 #136) +#2702 := (iff #2084 #2701) +#2699 := (iff #2083 #2698) +#2696 := (iff #2082 #2695) #2697 := [rewrite]: #2696 -#2834 := [monotonicity #2697 #2699 #2701 #2703 #2831]: #2833 -#2839 := [trans #2834 #2837]: #2838 -#3020 := [monotonicity #2839 #3017]: #3019 -#2694 := (iff #2058 #2693) -#2691 := (iff #2055 #2690) -#2688 := (iff #2050 #2687) -#2685 := (iff #2043 #2684) -#2682 := (iff #2042 #2679) -#2672 := (+ #1297 #2040) -#2675 := (>= #2672 0::Int) -#2680 := (iff #2675 #2679) -#2681 := [rewrite]: #2680 -#2676 := (iff #2042 #2675) -#2673 := (= #2041 #2672) -#2674 := [rewrite]: #2673 +#2700 := [monotonicity #2697]: #2699 +#2703 := [monotonicity #2700]: #2702 +#2708 := [trans #2703 #2706]: #2707 +#2711 := [monotonicity #2708]: #2710 +#2714 := [monotonicity #2711]: #2713 +#2718 := [trans #2714 #2716]: #2717 +#2737 := [monotonicity #2718 #2734]: #2736 +#2742 := [trans #2737 #2740]: #2741 +#2822 := [monotonicity #2742 #2819]: #2821 +#2693 := (iff #2064 #623) +#2694 := [rewrite]: #2693 +#2691 := (iff #2061 #620) +#2692 := [rewrite]: #2691 +#2689 := (iff #2058 #141) +#2690 := [rewrite]: #2689 +#2687 := (iff #2055 #136) +#2688 := [rewrite]: #2687 +#2825 := [monotonicity #2688 #2690 #2692 #2694 #2822]: #2824 +#2830 := [trans #2825 #2828]: #2829 +#3011 := [monotonicity #2830 #3008]: #3010 +#2685 := (iff #2049 #2684) +#2682 := (iff #2046 #2681) +#2679 := (iff #2041 #2678) +#2676 := (iff #2034 #2675) +#2673 := (iff #2033 #2670) +#2663 := (+ #1288 #2031) +#2666 := (>= #2663 0::Int) +#2671 := (iff #2666 #2670) +#2672 := [rewrite]: #2671 +#2667 := (iff #2033 #2666) +#2664 := (= #2032 #2663) +#2665 := [rewrite]: #2664 +#2668 := [monotonicity #2665]: #2667 +#2674 := [trans #2668 #2672]: #2673 #2677 := [monotonicity #2674]: #2676 -#2683 := [trans #2677 #2681]: #2682 -#2686 := [monotonicity #2683]: #2685 -#2670 := (iff #2047 #2667) -#2656 := (+ #2040 #2045) -#2657 := (+ #1297 #2656) -#2660 := (= #2657 0::Int) -#2668 := (iff #2660 #2667) -#2669 := [rewrite]: #2668 -#2661 := (iff #2047 #2660) -#2658 := (= #2046 #2657) -#2659 := [rewrite]: #2658 -#2662 := [monotonicity #2659]: #2661 -#2671 := [trans #2662 #2669]: #2670 -#2689 := [monotonicity #2671 #2686]: #2688 -#2692 := [monotonicity #2689]: #2691 -#2695 := [quant-intro #2692]: #2694 -#2654 := (iff #2031 #2653) -#2651 := (iff #2028 #2650) -#2648 := (iff #2023 #2647) -#2645 := (iff #2017 #2642) -#2632 := (+ #2013 #2015) -#2633 := (+ #1259 #2632) -#2636 := (= #2633 0::Int) -#2643 := (iff #2636 #2642) -#2644 := [rewrite]: #2643 -#2637 := (iff #2017 #2636) -#2634 := (= #2016 #2633) +#2661 := (iff #2038 #2658) +#2647 := (+ #2031 #2036) +#2648 := (+ #1288 #2647) +#2651 := (= #2648 0::Int) +#2659 := (iff #2651 #2658) +#2660 := [rewrite]: #2659 +#2652 := (iff #2038 #2651) +#2649 := (= #2037 #2648) +#2650 := [rewrite]: #2649 +#2653 := [monotonicity #2650]: #2652 +#2662 := [trans #2653 #2660]: #2661 +#2680 := [monotonicity #2662 #2677]: #2679 +#2683 := [monotonicity #2680]: #2682 +#2686 := [quant-intro #2683]: #2685 +#2645 := (iff #2022 #2644) +#2642 := (iff #2019 #2641) +#2639 := (iff #2014 #2638) +#2636 := (iff #2008 #2633) +#2623 := (+ #2004 #2006) +#2624 := (+ #1250 #2623) +#2627 := (= #2624 0::Int) +#2634 := (iff #2627 #2633) #2635 := [rewrite]: #2634 -#2638 := [monotonicity #2635]: #2637 -#2646 := [trans #2638 #2644]: #2645 -#2630 := (iff #2020 #2629) -#2627 := (iff #2019 #2624) -#2616 := (+ #1259 #2015) -#2619 := (>= #2616 0::Int) -#2625 := (iff #2619 #2624) +#2628 := (iff #2008 #2627) +#2625 := (= #2007 #2624) #2626 := [rewrite]: #2625 -#2620 := (iff #2019 #2619) -#2617 := (= #2018 #2616) -#2618 := [rewrite]: #2617 -#2621 := [monotonicity #2618]: #2620 -#2628 := [trans #2621 #2626]: #2627 -#2631 := [monotonicity #2628]: #2630 -#2649 := [monotonicity #2631 #2646]: #2648 -#2652 := [monotonicity #2649]: #2651 -#2655 := [quant-intro #2652]: #2654 -#2614 := (iff #2006 #100) -#2615 := [rewrite]: #2614 -#3023 := [monotonicity #2615 #2655 #2695 #3020]: #3022 -#3028 := [trans #3023 #3026]: #3027 -#2612 := (iff #2001 #2609) -#2575 := (and #1982 #2569) -#2606 := (and #2575 #2603) -#2610 := (iff #2606 #2609) -#2611 := [rewrite]: #2610 -#2607 := (iff #2001 #2606) -#2604 := (iff #1997 #2603) -#2601 := (iff #1994 #2600) -#2598 := (iff #1978 #2597) -#2595 := (iff #1974 #2594) -#2592 := (= #1973 #2591) -#2593 := [rewrite]: #2592 -#2596 := [monotonicity #2593]: #2595 -#2599 := [monotonicity #2596]: #2598 -#2602 := [monotonicity #2599]: #2601 -#2605 := [quant-intro #2602]: #2604 -#2588 := (iff #1991 #2575) -#2580 := (not #2575) -#2583 := (not #2580) -#2586 := (iff #2583 #2575) -#2587 := [rewrite]: #2586 -#2584 := (iff #1991 #2583) -#2581 := (iff #1986 #2580) -#2578 := (iff #1985 #2575) -#2572 := (and #2569 #1982) -#2576 := (iff #2572 #2575) -#2577 := [rewrite]: #2576 -#2573 := (iff #1985 #2572) -#2570 := (iff #1984 #2569) -#2567 := (iff #1983 #2566) +#2629 := [monotonicity #2626]: #2628 +#2637 := [trans #2629 #2635]: #2636 +#2621 := (iff #2011 #2620) +#2618 := (iff #2010 #2615) +#2607 := (+ #1250 #2006) +#2610 := (>= #2607 0::Int) +#2616 := (iff #2610 #2615) +#2617 := [rewrite]: #2616 +#2611 := (iff #2010 #2610) +#2608 := (= #2009 #2607) +#2609 := [rewrite]: #2608 +#2612 := [monotonicity #2609]: #2611 +#2619 := [trans #2612 #2617]: #2618 +#2622 := [monotonicity #2619]: #2621 +#2640 := [monotonicity #2622 #2637]: #2639 +#2643 := [monotonicity #2640]: #2642 +#2646 := [quant-intro #2643]: #2645 +#2605 := (iff #1997 #100) +#2606 := [rewrite]: #2605 +#3014 := [monotonicity #2606 #2646 #2686 #3011]: #3013 +#3019 := [trans #3014 #3017]: #3018 +#2603 := (iff #1992 #2600) +#2566 := (and #1973 #2560) +#2597 := (and #2566 #2594) +#2601 := (iff #2597 #2600) +#2602 := [rewrite]: #2601 +#2598 := (iff #1992 #2597) +#2595 := (iff #1988 #2594) +#2592 := (iff #1985 #2591) +#2589 := (iff #1969 #2588) +#2586 := (iff #1965 #2585) +#2583 := (= #1964 #2582) +#2584 := [rewrite]: #2583 +#2587 := [monotonicity #2584]: #2586 +#2590 := [monotonicity #2587]: #2589 +#2593 := [monotonicity #2590]: #2592 +#2596 := [quant-intro #2593]: #2595 +#2579 := (iff #1982 #2566) +#2571 := (not #2566) +#2574 := (not #2571) +#2577 := (iff #2574 #2566) +#2578 := [rewrite]: #2577 +#2575 := (iff #1982 #2574) +#2572 := (iff #1977 #2571) +#2569 := (iff #1976 #2566) +#2563 := (and #2560 #1973) +#2567 := (iff #2563 #2566) #2568 := [rewrite]: #2567 -#2571 := [monotonicity #2568]: #2570 -#2574 := [monotonicity #2571]: #2573 -#2579 := [trans #2574 #2577]: #2578 -#2582 := [monotonicity #2579]: #2581 -#2585 := [monotonicity #2582]: #2584 -#2589 := [trans #2585 #2587]: #2588 -#2608 := [monotonicity #2589 #2605]: #2607 -#2613 := [trans #2608 #2611]: #2612 -#3031 := [monotonicity #2613 #3028]: #3030 -#3034 := [monotonicity #3031]: #3033 -#2564 := (iff #1955 #2563) -#2561 := (iff #1954 #2560) -#2558 := (iff #1947 #2557) +#2564 := (iff #1976 #2563) +#2561 := (iff #1975 #2560) +#2558 := (iff #1974 #2557) +#2559 := [rewrite]: #2558 +#2562 := [monotonicity #2559]: #2561 +#2565 := [monotonicity #2562]: #2564 +#2570 := [trans #2565 #2568]: #2569 +#2573 := [monotonicity #2570]: #2572 +#2576 := [monotonicity #2573]: #2575 +#2580 := [trans #2576 #2578]: #2579 +#2599 := [monotonicity #2580 #2596]: #2598 +#2604 := [trans #2599 #2602]: #2603 +#3022 := [monotonicity #2604 #3019]: #3021 +#3025 := [monotonicity #3022]: #3024 #2555 := (iff #1946 #2554) -#2556 := [rewrite]: #2555 -#2559 := [monotonicity #2556]: #2558 -#2552 := (iff #1953 #2551) -#2549 := (= #1952 #2548) -#2550 := [rewrite]: #2549 -#2553 := [monotonicity #2550]: #2552 -#2562 := [monotonicity #2553 #2559]: #2561 -#2565 := [monotonicity #2562]: #2564 -#3037 := [monotonicity #2565 #3034]: #3036 +#2552 := (iff #1945 #2551) +#2549 := (iff #1938 #2548) +#2546 := (iff #1937 #2545) +#2547 := [rewrite]: #2546 +#2550 := [monotonicity #2547]: #2549 +#2543 := (iff #1944 #2542) +#2540 := (= #1943 #2539) +#2541 := [rewrite]: #2540 +#2544 := [monotonicity #2541]: #2543 +#2553 := [monotonicity #2544 #2550]: #2552 +#2556 := [monotonicity #2553]: #2555 +#3028 := [monotonicity #2556 #3025]: #3027 +#3031 := [monotonicity #3028]: #3030 +#2536 := (iff #1915 #2535) +#2533 := (iff #1914 #2532) +#2530 := (iff #1906 #2527) +#2519 := (+ #1903 #1904) +#2522 := (>= #2519 0::Int) +#2528 := (iff #2522 #2527) +#2529 := [rewrite]: #2528 +#2523 := (iff #1906 #2522) +#2520 := (= #1905 #2519) +#2521 := [rewrite]: #2520 +#2524 := [monotonicity #2521]: #2523 +#2531 := [trans #2524 #2529]: #2530 +#2517 := (iff #1913 #2516) +#2514 := (iff #1912 #2513) +#2515 := [rewrite]: #2514 +#2518 := [monotonicity #2515]: #2517 +#2534 := [monotonicity #2518 #2531]: #2533 +#2537 := [monotonicity #2534]: #2536 +#3034 := [monotonicity #2537 #3031]: #3033 +#3037 := [monotonicity #3034]: #3036 #3040 := [monotonicity #3037]: #3039 -#2545 := (iff #1924 #2544) -#2542 := (iff #1923 #2541) -#2539 := (iff #1915 #2536) -#2528 := (+ #1912 #1913) -#2531 := (>= #2528 0::Int) -#2537 := (iff #2531 #2536) -#2538 := [rewrite]: #2537 -#2532 := (iff #1915 #2531) -#2529 := (= #1914 #2528) -#2530 := [rewrite]: #2529 -#2533 := [monotonicity #2530]: #2532 -#2540 := [trans #2533 #2538]: #2539 -#2526 := (iff #1922 #2525) -#2523 := (iff #1921 #2522) -#2524 := [rewrite]: #2523 -#2527 := [monotonicity #2524]: #2526 -#2543 := [monotonicity #2527 #2540]: #2542 -#2546 := [monotonicity #2543]: #2545 -#3043 := [monotonicity #2546 #3040]: #3042 +#2511 := (iff #1851 #71) +#2512 := [rewrite]: #2511 +#3043 := [monotonicity #2512 #3040]: #3042 #3046 := [monotonicity #3043]: #3045 -#3049 := [monotonicity #3046]: #3048 -#2520 := (iff #1860 #71) -#2521 := [rewrite]: #2520 -#3052 := [monotonicity #2521 #3049]: #3051 -#3055 := [monotonicity #3052]: #3054 -#1836 := (not #1800) -#2515 := (~ #1836 #2514) -#2511 := (not #1797) -#2512 := (~ #2511 #2510) -#2507 := (not #1794) -#2508 := (~ #2507 #2506) -#2503 := (not #1791) -#2504 := (~ #2503 #2502) -#2499 := (not #1788) -#2500 := (~ #2499 #2498) -#2495 := (not #1785) -#2496 := (~ #2495 #2494) -#2491 := (not #1782) -#2492 := (~ #2491 #2490) -#2487 := (not #1779) -#2488 := (~ #2487 #2486) -#2483 := (not #1776) -#2484 := (~ #2483 #2482) -#2479 := (not #1771) -#2480 := (~ #2479 #2478) -#2475 := (not #1742) -#2476 := (~ #2475 #1739) -#2473 := (~ #1739 #1739) -#2471 := (~ #1736 #1736) -#2472 := [refl]: #2471 -#2474 := [nnf-pos #2472]: #2473 -#2477 := [nnf-neg #2474]: #2476 -#2468 := (not #1733) -#2469 := (~ #2468 #1730) -#2466 := (~ #1730 #1730) -#2464 := (~ #1725 #1725) -#2465 := [refl]: #2464 -#2467 := [nnf-pos #2465]: #2466 -#2470 := [nnf-neg #2467]: #2469 -#2461 := (not #1717) -#2462 := (~ #2461 #1714) -#2459 := (~ #1714 #1714) -#2457 := (~ #1711 #1711) -#2458 := [refl]: #2457 -#2460 := [nnf-pos #2458]: #2459 -#2463 := [nnf-neg #2460]: #2462 -#2454 := (not #1694) -#2455 := (~ #2454 #2453) -#2450 := (not #1689) -#2451 := (~ #2450 #2449) -#2447 := (~ #1655 #1655) -#2448 := [refl]: #2447 -#2444 := (not #1650) -#2445 := (~ #2444 #1647) -#2442 := (~ #1647 #1647) -#2440 := (~ #1642 #1642) -#2441 := [refl]: #2440 -#2443 := [nnf-pos #2441]: #2442 -#2446 := [nnf-neg #2443]: #2445 -#2437 := (not #1632) -#2438 := (~ #2437 #1629) -#2435 := (~ #1629 #1629) -#2433 := (~ #1626 #1626) -#2434 := [refl]: #2433 -#2436 := [nnf-pos #2434]: #2435 -#2439 := [nnf-neg #2436]: #2438 -#2430 := (not #1615) -#2431 := (~ #2430 #2429) -#2426 := (not #1612) -#2427 := (~ #2426 #2425) -#2422 := (not #1609) -#2423 := (~ #2422 #2421) -#2418 := (not #1606) -#2419 := (~ #2418 #2417) -#2414 := (not #1603) -#2415 := (~ #2414 #2413) -#2410 := (not #1600) -#2411 := (~ #2410 #2409) -#2406 := (not #1597) -#2407 := (~ #2406 #2405) -#2402 := (not #1594) -#2403 := (~ #2402 #2401) -#2398 := (not #1591) -#2399 := (~ #2398 #2397) -#2394 := (not #1588) -#2395 := (~ #2394 #2393) -#2390 := (not #1585) -#2391 := (~ #2390 #2389) -#2386 := (not #1582) -#2387 := (~ #2386 #2385) -#2367 := (not #1579) -#2383 := (~ #2367 #2380) -#2357 := (exists (vars (?v1 S3)) #2356) -#2365 := (or #2364 #2357) -#2366 := (not #2365) -#2381 := (~ #2366 #2380) -#2377 := (not #2357) +#1827 := (not #1791) +#2506 := (~ #1827 #2505) +#2502 := (not #1788) +#2503 := (~ #2502 #2501) +#2498 := (not #1785) +#2499 := (~ #2498 #2497) +#2494 := (not #1782) +#2495 := (~ #2494 #2493) +#2490 := (not #1779) +#2491 := (~ #2490 #2489) +#2486 := (not #1776) +#2487 := (~ #2486 #2485) +#2482 := (not #1773) +#2483 := (~ #2482 #2481) +#2478 := (not #1770) +#2479 := (~ #2478 #2477) +#2474 := (not #1767) +#2475 := (~ #2474 #2473) +#2470 := (not #1762) +#2471 := (~ #2470 #2469) +#2466 := (not #1733) +#2467 := (~ #2466 #1730) +#2464 := (~ #1730 #1730) +#2462 := (~ #1727 #1727) +#2463 := [refl]: #2462 +#2465 := [nnf-pos #2463]: #2464 +#2468 := [nnf-neg #2465]: #2467 +#2459 := (not #1724) +#2460 := (~ #2459 #1721) +#2457 := (~ #1721 #1721) +#2455 := (~ #1716 #1716) +#2456 := [refl]: #2455 +#2458 := [nnf-pos #2456]: #2457 +#2461 := [nnf-neg #2458]: #2460 +#2452 := (not #1708) +#2453 := (~ #2452 #1705) +#2450 := (~ #1705 #1705) +#2448 := (~ #1702 #1702) +#2449 := [refl]: #2448 +#2451 := [nnf-pos #2449]: #2450 +#2454 := [nnf-neg #2451]: #2453 +#2445 := (not #1685) +#2446 := (~ #2445 #2444) +#2441 := (not #1680) +#2442 := (~ #2441 #2440) +#2438 := (~ #1646 #1646) +#2439 := [refl]: #2438 +#2435 := (not #1641) +#2436 := (~ #2435 #1638) +#2433 := (~ #1638 #1638) +#2431 := (~ #1633 #1633) +#2432 := [refl]: #2431 +#2434 := [nnf-pos #2432]: #2433 +#2437 := [nnf-neg #2434]: #2436 +#2428 := (not #1623) +#2429 := (~ #2428 #1620) +#2426 := (~ #1620 #1620) +#2424 := (~ #1617 #1617) +#2425 := [refl]: #2424 +#2427 := [nnf-pos #2425]: #2426 +#2430 := [nnf-neg #2427]: #2429 +#2421 := (not #1606) +#2422 := (~ #2421 #2420) +#2417 := (not #1603) +#2418 := (~ #2417 #2416) +#2413 := (not #1600) +#2414 := (~ #2413 #2412) +#2409 := (not #1597) +#2410 := (~ #2409 #2408) +#2405 := (not #1594) +#2406 := (~ #2405 #2404) +#2401 := (not #1591) +#2402 := (~ #2401 #2400) +#2397 := (not #1588) +#2398 := (~ #2397 #2396) +#2393 := (not #1585) +#2394 := (~ #2393 #2392) +#2389 := (not #1582) +#2390 := (~ #2389 #2388) +#2385 := (not #1579) +#2386 := (~ #2385 #2384) +#2381 := (not #1576) +#2382 := (~ #2381 #2380) +#2377 := (not #1573) #2378 := (~ #2377 #2376) -#2374 := (~ #2373 #2373) -#2375 := [refl]: #2374 -#2379 := [nnf-neg #2375]: #2378 -#2371 := (~ #2370 #2370) -#2372 := [refl]: #2371 -#2382 := [nnf-neg #2372 #2379]: #2381 -#2368 := (~ #2367 #2366) -#2369 := [sk]: #2368 -#2384 := [trans #2369 #2382]: #2383 -#2343 := (not #1542) -#2344 := (~ #2343 #1539) -#2341 := (~ #1539 #1539) -#2339 := (~ #1536 #1536) -#2340 := [refl]: #2339 -#2342 := [nnf-pos #2340]: #2341 -#2345 := [nnf-neg #2342]: #2344 -#2388 := [nnf-neg #2345 #2384]: #2387 -#2335 := (~ #1542 #2334) -#2336 := [sk]: #2335 -#2392 := [nnf-neg #2336 #2388]: #2391 -#2312 := (not #1518) -#2313 := (~ #2312 #1515) -#2310 := (~ #1515 #1515) -#2308 := (~ #1510 #1510) -#2309 := [refl]: #2308 -#2311 := [nnf-pos #2309]: #2310 -#2314 := [nnf-neg #2311]: #2313 -#2396 := [nnf-neg #2314 #2392]: #2395 -#2304 := (~ #1518 #2303) -#2305 := [sk]: #2304 -#2400 := [nnf-neg #2305 #2396]: #2399 -#2285 := (not #1499) -#2286 := (~ #2285 #1496) -#2283 := (~ #1496 #1496) -#2281 := (~ #1493 #1493) -#2282 := [refl]: #2281 -#2284 := [nnf-pos #2282]: #2283 -#2287 := [nnf-neg #2284]: #2286 -#2404 := [nnf-neg #2287 #2400]: #2403 -#2277 := (~ #1499 #2276) -#2278 := [sk]: #2277 -#2408 := [nnf-neg #2278 #2404]: #2407 -#2271 := (~ #2270 #2270) -#2272 := [refl]: #2271 -#2412 := [nnf-neg #2272 #2408]: #2411 -#2268 := (~ #1490 #1490) -#2269 := [refl]: #2268 -#2416 := [nnf-neg #2269 #2412]: #2415 -#2265 := (not #953) -#2266 := (~ #2265 #819) -#2263 := (~ #819 #819) -#2261 := (~ #814 #814) -#2262 := [refl]: #2261 -#2264 := [nnf-pos #2262]: #2263 -#2267 := [nnf-neg #2264]: #2266 -#2420 := [nnf-neg #2267 #2416]: #2419 -#2257 := (~ #953 #2256) -#2258 := [sk]: #2257 -#2424 := [nnf-neg #2258 #2420]: #2423 -#2245 := (not #1485) -#2246 := (~ #2245 #1482) -#2243 := (~ #1482 #1482) -#2241 := (~ #1477 #1477) -#2242 := [refl]: #2241 -#2244 := [nnf-pos #2242]: #2243 -#2247 := [nnf-neg #2244]: #2246 -#2428 := [nnf-neg #2247 #2424]: #2427 -#2237 := (~ #1485 #2236) -#2238 := [sk]: #2237 -#2432 := [nnf-neg #2238 #2428]: #2431 -#2227 := (not #1474) -#2228 := (~ #2227 #1471) -#2225 := (~ #1471 #1471) -#2223 := (~ #1466 #1466) -#2224 := [refl]: #2223 -#2226 := [nnf-pos #2224]: #2225 -#2229 := [nnf-neg #2226]: #2228 -#2220 := (not #1665) -#2221 := (~ #2220 #2215) -#2216 := (~ #1424 #2215) -#2217 := [sk]: #2216 -#2222 := [nnf-neg #2217]: #2221 -#2204 := (~ #2203 #2203) -#2205 := [refl]: #2204 -#2201 := (~ #757 #757) -#2202 := [refl]: #2201 -#2452 := [nnf-neg #2202 #2205 #2222 #2229 #2432 #2439 #2446 #2448]: #2451 -#2198 := (not #1442) -#2199 := (~ #2198 #2197) -#2195 := (~ #1665 #2194) -#2192 := (~ #2191 #2191) -#2193 := [refl]: #2192 -#2196 := [nnf-neg #2193]: #2195 -#2188 := (not #1413) -#2189 := (~ #2188 #2187) -#2184 := (not #1410) -#2185 := (~ #2184 #2183) -#2180 := (not #1407) -#2181 := (~ #2180 #2179) -#2176 := (not #1402) -#2177 := (~ #2176 #2175) -#2172 := (not #1394) -#2173 := (~ #2172 #1391) -#2170 := (~ #1391 #1391) -#2168 := (~ #1388 #1388) -#2169 := [refl]: #2168 -#2171 := [nnf-pos #2169]: #2170 -#2174 := [nnf-neg #2171]: #2173 -#2166 := (~ #2165 #2165) -#2167 := [refl]: #2166 -#2178 := [nnf-neg #2167 #2174]: #2177 -#2161 := (~ #1394 #2160) -#2162 := [sk]: #2161 -#2182 := [nnf-neg #2162 #2178]: #2181 -#2136 := (not #1376) -#2137 := (~ #2136 #2133) -#2134 := (~ #1373 #2133) -#2131 := (~ #1370 #2130) -#2126 := (~ #1367 #2125) -#2127 := [sk]: #2126 -#2114 := (~ #1351 #1351) -#2115 := [refl]: #2114 -#2132 := [monotonicity #2115 #2127]: #2131 -#2135 := [nnf-pos #2132]: #2134 -#2138 := [nnf-neg #2135]: #2137 -#2186 := [nnf-neg #2138 #2182]: #2185 -#2112 := (~ #1376 #2109) -#2087 := (exists (vars (?v1 S3)) #2086) -#2095 := (or #2094 #2087) -#2096 := (not #2095) -#2110 := (~ #2096 #2109) -#2106 := (not #2087) -#2107 := (~ #2106 #2105) -#2103 := (~ #2102 #2102) -#2104 := [refl]: #2103 -#2108 := [nnf-neg #2104]: #2107 -#2100 := (~ #2099 #2099) -#2101 := [refl]: #2100 -#2111 := [nnf-neg #2101 #2108]: #2110 -#2097 := (~ #1376 #2096) -#2098 := [sk]: #2097 -#2113 := [trans #2098 #2111]: #2112 -#2190 := [nnf-neg #2113 #2186]: #2189 -#2074 := (~ #2073 #2073) -#2075 := [refl]: #2074 -#2071 := (~ #2070 #2070) -#2072 := [refl]: #2071 -#2068 := (~ #2067 #2067) -#2069 := [refl]: #2068 +#2358 := (not #1570) +#2374 := (~ #2358 #2371) +#2348 := (exists (vars (?v1 S3)) #2347) +#2356 := (or #2355 #2348) +#2357 := (not #2356) +#2372 := (~ #2357 #2371) +#2368 := (not #2348) +#2369 := (~ #2368 #2367) +#2365 := (~ #2364 #2364) +#2366 := [refl]: #2365 +#2370 := [nnf-neg #2366]: #2369 +#2362 := (~ #2361 #2361) +#2363 := [refl]: #2362 +#2373 := [nnf-neg #2363 #2370]: #2372 +#2359 := (~ #2358 #2357) +#2360 := [sk]: #2359 +#2375 := [trans #2360 #2373]: #2374 +#2334 := (not #1533) +#2335 := (~ #2334 #1530) +#2332 := (~ #1530 #1530) +#2330 := (~ #1527 #1527) +#2331 := [refl]: #2330 +#2333 := [nnf-pos #2331]: #2332 +#2336 := [nnf-neg #2333]: #2335 +#2379 := [nnf-neg #2336 #2375]: #2378 +#2326 := (~ #1533 #2325) +#2327 := [sk]: #2326 +#2383 := [nnf-neg #2327 #2379]: #2382 +#2303 := (not #1509) +#2304 := (~ #2303 #1506) +#2301 := (~ #1506 #1506) +#2299 := (~ #1501 #1501) +#2300 := [refl]: #2299 +#2302 := [nnf-pos #2300]: #2301 +#2305 := [nnf-neg #2302]: #2304 +#2387 := [nnf-neg #2305 #2383]: #2386 +#2295 := (~ #1509 #2294) +#2296 := [sk]: #2295 +#2391 := [nnf-neg #2296 #2387]: #2390 +#2276 := (not #1490) +#2277 := (~ #2276 #1487) +#2274 := (~ #1487 #1487) +#2272 := (~ #1484 #1484) +#2273 := [refl]: #2272 +#2275 := [nnf-pos #2273]: #2274 +#2278 := [nnf-neg #2275]: #2277 +#2395 := [nnf-neg #2278 #2391]: #2394 +#2268 := (~ #1490 #2267) +#2269 := [sk]: #2268 +#2399 := [nnf-neg #2269 #2395]: #2398 +#2262 := (~ #2261 #2261) +#2263 := [refl]: #2262 +#2403 := [nnf-neg #2263 #2399]: #2402 +#2259 := (~ #1481 #1481) +#2260 := [refl]: #2259 +#2407 := [nnf-neg #2260 #2403]: #2406 +#2256 := (not #944) +#2257 := (~ #2256 #810) +#2254 := (~ #810 #810) +#2252 := (~ #805 #805) +#2253 := [refl]: #2252 +#2255 := [nnf-pos #2253]: #2254 +#2258 := [nnf-neg #2255]: #2257 +#2411 := [nnf-neg #2258 #2407]: #2410 +#2248 := (~ #944 #2247) +#2249 := [sk]: #2248 +#2415 := [nnf-neg #2249 #2411]: #2414 +#2236 := (not #1476) +#2237 := (~ #2236 #1473) +#2234 := (~ #1473 #1473) +#2232 := (~ #1468 #1468) +#2233 := [refl]: #2232 +#2235 := [nnf-pos #2233]: #2234 +#2238 := [nnf-neg #2235]: #2237 +#2419 := [nnf-neg #2238 #2415]: #2418 +#2228 := (~ #1476 #2227) +#2229 := [sk]: #2228 +#2423 := [nnf-neg #2229 #2419]: #2422 +#2218 := (not #1465) +#2219 := (~ #2218 #1462) +#2216 := (~ #1462 #1462) +#2214 := (~ #1457 #1457) +#2215 := [refl]: #2214 +#2217 := [nnf-pos #2215]: #2216 +#2220 := [nnf-neg #2217]: #2219 +#2211 := (not #1656) +#2212 := (~ #2211 #2206) +#2207 := (~ #1415 #2206) +#2208 := [sk]: #2207 +#2213 := [nnf-neg #2208]: #2212 +#2195 := (~ #756 #756) +#2196 := [refl]: #2195 +#2193 := (~ #2192 #2192) +#2194 := [refl]: #2193 +#2443 := [nnf-neg #2194 #2196 #2213 #2220 #2423 #2430 #2437 #2439]: #2442 +#2189 := (not #1433) +#2190 := (~ #2189 #2188) +#2186 := (~ #1656 #2185) +#2183 := (~ #2182 #2182) +#2184 := [refl]: #2183 +#2187 := [nnf-neg #2184]: #2186 +#2179 := (not #1404) +#2180 := (~ #2179 #2178) +#2175 := (not #1401) +#2176 := (~ #2175 #2174) +#2171 := (not #1398) +#2172 := (~ #2171 #2170) +#2167 := (not #1393) +#2168 := (~ #2167 #2166) +#2163 := (not #1385) +#2164 := (~ #2163 #1382) +#2161 := (~ #1382 #1382) +#2159 := (~ #1379 #1379) +#2160 := [refl]: #2159 +#2162 := [nnf-pos #2160]: #2161 +#2165 := [nnf-neg #2162]: #2164 +#2157 := (~ #2156 #2156) +#2158 := [refl]: #2157 +#2169 := [nnf-neg #2158 #2165]: #2168 +#2152 := (~ #1385 #2151) +#2153 := [sk]: #2152 +#2173 := [nnf-neg #2153 #2169]: #2172 +#2127 := (not #1367) +#2128 := (~ #2127 #2124) +#2125 := (~ #1364 #2124) +#2122 := (~ #1361 #2121) +#2117 := (~ #1358 #2116) +#2118 := [sk]: #2117 +#2105 := (~ #1342 #1342) +#2106 := [refl]: #2105 +#2123 := [monotonicity #2106 #2118]: #2122 +#2126 := [nnf-pos #2123]: #2125 +#2129 := [nnf-neg #2126]: #2128 +#2177 := [nnf-neg #2129 #2173]: #2176 +#2103 := (~ #1367 #2100) +#2078 := (exists (vars (?v1 S3)) #2077) +#2086 := (or #2085 #2078) +#2087 := (not #2086) +#2101 := (~ #2087 #2100) +#2097 := (not #2078) +#2098 := (~ #2097 #2096) +#2094 := (~ #2093 #2093) +#2095 := [refl]: #2094 +#2099 := [nnf-neg #2095]: #2098 +#2091 := (~ #2090 #2090) +#2092 := [refl]: #2091 +#2102 := [nnf-neg #2092 #2099]: #2101 +#2088 := (~ #1367 #2087) +#2089 := [sk]: #2088 +#2104 := [trans #2089 #2102]: #2103 +#2181 := [nnf-neg #2104 #2177]: #2180 #2065 := (~ #2064 #2064) #2066 := [refl]: #2065 -#2200 := [nnf-neg #2066 #2069 #2072 #2075 #2190 #2196]: #2199 -#2456 := [nnf-neg #2200 #2452]: #2455 -#2061 := (not #1339) -#2062 := (~ #2061 #2058) -#2059 := (~ #1336 #2058) -#2056 := (~ #1333 #2055) -#2051 := (~ #1330 #2050) -#2052 := [sk]: #2051 -#2037 := (~ #1306 #1306) -#2038 := [refl]: #2037 -#2057 := [monotonicity #2038 #2052]: #2056 -#2060 := [nnf-pos #2057]: #2059 -#2063 := [nnf-neg #2060]: #2062 -#2034 := (not #1750) -#2035 := (~ #2034 #2031) -#2032 := (~ #1294 #2031) -#2029 := (~ #1291 #2028) -#2024 := (~ #1288 #2023) -#2025 := [sk]: #2024 -#2009 := (~ #1268 #1268) -#2010 := [refl]: #2009 -#2030 := [monotonicity #2010 #2025]: #2029 -#2033 := [nnf-pos #2030]: #2032 -#2036 := [nnf-neg #2033]: #2035 -#2007 := (~ #2006 #2006) -#2008 := [refl]: #2007 -#2481 := [nnf-neg #2008 #2036 #2063 #2456 #2463 #2470 #2477]: #2480 -#2004 := (~ #1750 #2001) -#1979 := (exists (vars (?v1 S3)) #1978) -#1987 := (or #1986 #1979) -#1988 := (not #1987) -#2002 := (~ #1988 #2001) -#1998 := (not #1979) -#1999 := (~ #1998 #1997) -#1995 := (~ #1994 #1994) -#1996 := [refl]: #1995 -#2000 := [nnf-neg #1996]: #1999 -#1992 := (~ #1991 #1991) -#1993 := [refl]: #1992 -#2003 := [nnf-neg #1993 #2000]: #2002 -#1989 := (~ #1750 #1988) -#1990 := [sk]: #1989 -#2005 := [trans #1990 #2003]: #2004 -#2485 := [nnf-neg #2005 #2481]: #2484 -#1964 := (not #1256) -#1965 := (~ #1964 #1253) -#1962 := (~ #1253 #1253) -#1960 := (~ #1250 #1250) -#1961 := [refl]: #1960 -#1963 := [nnf-pos #1961]: #1962 -#1966 := [nnf-neg #1963]: #1965 -#2489 := [nnf-neg #1966 #2485]: #2488 -#1956 := (~ #1256 #1955) -#1957 := [sk]: #1956 -#2493 := [nnf-neg #1957 #2489]: #2492 -#1933 := (not #1225) -#1934 := (~ #1933 #1222) -#1931 := (~ #1222 #1222) -#1929 := (~ #1217 #1217) -#1930 := [refl]: #1929 -#1932 := [nnf-pos #1930]: #1931 -#1935 := [nnf-neg #1932]: #1934 -#2497 := [nnf-neg #1935 #2493]: #2496 -#1925 := (~ #1225 #1924) -#1926 := [sk]: #1925 -#2501 := [nnf-neg #1926 #2497]: #2500 -#1906 := (not #1205) -#1907 := (~ #1906 #1202) -#1904 := (~ #1202 #1202) -#1902 := (~ #1201 #1201) -#1903 := [refl]: #1902 -#1905 := [nnf-pos #1903]: #1904 -#1908 := [nnf-neg #1905]: #1907 -#2505 := [nnf-neg #1908 #2501]: #2504 -#1898 := (~ #1205 #1897) -#1899 := [sk]: #1898 -#2509 := [nnf-neg #1899 #2505]: #2508 -#1861 := (~ #1860 #1860) -#1893 := [refl]: #1861 -#2513 := [nnf-neg #1893 #2509]: #2512 -#1891 := (~ #1196 #1196) -#1892 := [refl]: #1891 -#2516 := [nnf-neg #1892 #2513]: #2515 -#1837 := [not-or-elim #1833]: #1836 -#2517 := [mp~ #1837 #2516]: #2514 -#2518 := [mp #2517 #3055]: #3053 -#3697 := [mp #2518 #3696]: #3694 -#4604 := [mp #3697 #4603]: #4601 -#6496 := [unit-resolution #4604 #5320]: #4598 -#3943 := (or #4595 #4589) -#3944 := [def-axiom]: #3943 -#6497 := [unit-resolution #3944 #6496]: #4589 -#6498 := (or #4592 #4586) -#5107 := [hypothesis]: #1897 -#5106 := (<= #1895 0::Int) -#4721 := (or #5106 #1896) -#5139 := [th-lemma arith farkas 1 1]: #4721 -#5140 := [unit-resolution #5139 #5107]: #5106 -#5099 := (not #5106) -#5114 := (or #5099 #1896) -#355 := (<= f8 0::Int) -#356 := (not #355) +#2062 := (~ #2061 #2061) +#2063 := [refl]: #2062 +#2059 := (~ #2058 #2058) +#2060 := [refl]: #2059 +#2056 := (~ #2055 #2055) +#2057 := [refl]: #2056 +#2191 := [nnf-neg #2057 #2060 #2063 #2066 #2181 #2187]: #2190 +#2447 := [nnf-neg #2191 #2443]: #2446 +#2052 := (not #1330) +#2053 := (~ #2052 #2049) +#2050 := (~ #1327 #2049) +#2047 := (~ #1324 #2046) +#2042 := (~ #1321 #2041) +#2043 := [sk]: #2042 +#2028 := (~ #1297 #1297) +#2029 := [refl]: #2028 +#2048 := [monotonicity #2029 #2043]: #2047 +#2051 := [nnf-pos #2048]: #2050 +#2054 := [nnf-neg #2051]: #2053 +#2025 := (not #1741) +#2026 := (~ #2025 #2022) +#2023 := (~ #1285 #2022) +#2020 := (~ #1282 #2019) +#2015 := (~ #1279 #2014) +#2016 := [sk]: #2015 +#2000 := (~ #1259 #1259) +#2001 := [refl]: #2000 +#2021 := [monotonicity #2001 #2016]: #2020 +#2024 := [nnf-pos #2021]: #2023 +#2027 := [nnf-neg #2024]: #2026 +#1998 := (~ #1997 #1997) +#1999 := [refl]: #1998 +#2472 := [nnf-neg #1999 #2027 #2054 #2447 #2454 #2461 #2468]: #2471 +#1995 := (~ #1741 #1992) +#1970 := (exists (vars (?v1 S3)) #1969) +#1978 := (or #1977 #1970) +#1979 := (not #1978) +#1993 := (~ #1979 #1992) +#1989 := (not #1970) +#1990 := (~ #1989 #1988) +#1986 := (~ #1985 #1985) +#1987 := [refl]: #1986 +#1991 := [nnf-neg #1987]: #1990 +#1983 := (~ #1982 #1982) +#1984 := [refl]: #1983 +#1994 := [nnf-neg #1984 #1991]: #1993 +#1980 := (~ #1741 #1979) +#1981 := [sk]: #1980 +#1996 := [trans #1981 #1994]: #1995 +#2476 := [nnf-neg #1996 #2472]: #2475 +#1955 := (not #1247) +#1956 := (~ #1955 #1244) +#1953 := (~ #1244 #1244) +#1951 := (~ #1241 #1241) +#1952 := [refl]: #1951 +#1954 := [nnf-pos #1952]: #1953 +#1957 := [nnf-neg #1954]: #1956 +#2480 := [nnf-neg #1957 #2476]: #2479 +#1947 := (~ #1247 #1946) +#1948 := [sk]: #1947 +#2484 := [nnf-neg #1948 #2480]: #2483 +#1924 := (not #1216) +#1925 := (~ #1924 #1213) +#1922 := (~ #1213 #1213) +#1920 := (~ #1208 #1208) +#1921 := [refl]: #1920 +#1923 := [nnf-pos #1921]: #1922 +#1926 := [nnf-neg #1923]: #1925 +#2488 := [nnf-neg #1926 #2484]: #2487 +#1916 := (~ #1216 #1915) +#1917 := [sk]: #1916 +#2492 := [nnf-neg #1917 #2488]: #2491 +#1897 := (not #1196) +#1898 := (~ #1897 #1193) +#1895 := (~ #1193 #1193) +#1893 := (~ #1192 #1192) +#1894 := [refl]: #1893 +#1896 := [nnf-pos #1894]: #1895 +#1899 := [nnf-neg #1896]: #1898 +#2496 := [nnf-neg #1899 #2492]: #2495 +#1889 := (~ #1196 #1888) +#1890 := [sk]: #1889 +#2500 := [nnf-neg #1890 #2496]: #2499 +#1852 := (~ #1851 #1851) +#1884 := [refl]: #1852 +#2504 := [nnf-neg #1884 #2500]: #2503 +#1882 := (~ #1187 #1187) +#1883 := [refl]: #1882 +#2507 := [nnf-neg #1883 #2504]: #2506 +#1828 := [not-or-elim #1824]: #1827 +#2508 := [mp~ #1828 #2507]: #2505 +#2509 := [mp #2508 #3046]: #3044 +#3688 := [mp #2509 #3687]: #3685 +#4595 := [mp #3688 #4594]: #4592 +#6487 := [unit-resolution #4595 #5311]: #4589 +#3934 := (or #4586 #4580) +#3935 := [def-axiom]: #3934 +#6488 := [unit-resolution #3935 #6487]: #4580 +#6489 := (or #4583 #4577) +#5098 := [hypothesis]: #1888 +#5097 := (<= #1886 0::Int) +#4712 := (or #5097 #1887) +#5130 := [th-lemma arith farkas 1 1]: #4712 +#5131 := [unit-resolution #5130 #5098]: #5097 +#5090 := (not #5097) +#5105 := (or #5090 #1887) +#354 := (<= f8 0::Int) +#355 := (not #354) #46 := (< 0::Int f8) -#357 := (iff #46 #356) -#358 := [rewrite]: #357 -#351 := [asserted]: #46 -#359 := [mp #351 #358]: #356 -#4718 := (* -1::Int #1895) -#4719 := (+ f8 #4718) -#4720 := (<= #4719 0::Int) -#3933 := (= f8 #1895) -#3912 := (= f10 ?v0!0) -#4911 := (not #3912) -#4908 := (= #1895 0::Int) -#5108 := (not #4908) -#5109 := (or #5108 #1896) -#5110 := [th-lemma arith triangle-eq]: #5109 -#5090 := [unit-resolution #5110 #5107]: #5108 -#4917 := (or #4784 #4911 #4908) -#3932 := (= ?v0!0 f10) -#4909 := (not #3932) -#4910 := (or #4909 #4908) -#4648 := (or #4784 #4910) -#5103 := (iff #4648 #4917) -#4715 := (or #4911 #4908) -#4934 := (or #4784 #4715) -#4980 := (iff #4934 #4917) -#5102 := [rewrite]: #4980 -#4978 := (iff #4648 #4934) -#4716 := (iff #4910 #4715) -#4914 := (iff #4909 #4911) -#3914 := (iff #3932 #3912) -#3915 := [rewrite]: #3914 -#4915 := [monotonicity #3915]: #4914 -#4783 := [monotonicity #4915]: #4716 -#4979 := [monotonicity #4783]: #4978 -#5104 := [trans #4979 #5102]: #5103 -#4931 := [quant-inst #1894]: #4648 -#5105 := [mp #4931 #5104]: #4917 -#5091 := [unit-resolution #5105 #4610 #5090]: #4911 -#3927 := (or #3912 #3933) -#4219 := (forall (vars (?v0 S3)) (:pat #4218) #446) -#4222 := (iff #451 #4219) -#4220 := (iff #446 #446) -#4221 := [refl]: #4220 -#4223 := [quant-intro #4221]: #4222 -#1856 := (~ #451 #451) -#1885 := (~ #446 #446) -#1886 := [refl]: #1885 -#1857 := [nnf-pos #1886]: #1856 -#1834 := [not-or-elim #1833]: #451 -#1887 := [mp~ #1834 #1857]: #451 -#4224 := [mp #1887 #4223]: #4219 -#3923 := (not #4219) -#3916 := (or #3923 #3912 #3933) -#3922 := (or #3932 #3933) -#3924 := (or #3923 #3922) -#4662 := (iff #3924 #3916) -#3909 := (or #3923 #3927) -#4646 := (iff #3909 #3916) -#4661 := [rewrite]: #4646 -#4644 := (iff #3924 #3909) -#3918 := (iff #3922 #3927) -#3919 := [monotonicity #3915]: #3918 -#4645 := [monotonicity #3919]: #4644 -#4643 := [trans #4645 #4661]: #4662 -#3907 := [quant-inst #1894]: #3924 -#4717 := [mp #3907 #4643]: #3916 -#5092 := [unit-resolution #4717 #4224]: #3927 -#5093 := [unit-resolution #5092 #5091]: #3933 -#5094 := (not #3933) -#5089 := (or #5094 #4720) -#5095 := [th-lemma arith triangle-eq]: #5089 -#5096 := [unit-resolution #5095 #5093]: #4720 -#5097 := [hypothesis]: #5106 -#5098 := [th-lemma arith farkas 1 -1 1 #5097 #5096 #359]: false -#5115 := [lemma #5098]: #5114 -#5141 := [unit-resolution #5115 #5140 #5107]: false -#5142 := [lemma #5141]: #1896 -#3938 := (or #4592 #1897 #4586) -#3939 := [def-axiom]: #3938 -#6499 := [unit-resolution #3939 #5142]: #6498 -#6500 := [unit-resolution #6499 #6497]: #4586 -#3962 := (or #4583 #4577) -#3963 := [def-axiom]: #3962 -#6501 := [unit-resolution #3963 #6500]: #4577 -#5817 := [hypothesis]: #1917 -#5330 := (or #5529 #2054) -#5335 := [quant-inst #1910]: #5330 -#5818 := [unit-resolution #5335 #4231 #5817]: false -#5819 := [lemma #5818]: #2054 -#3755 := (or #2026 #1917) -#3842 := [def-axiom]: #3755 -#6502 := [unit-resolution #3842 #5819]: #2026 -#3956 := (or #4580 #1928 #4574) -#3958 := [def-axiom]: #3956 -#6503 := [unit-resolution #3958 #6502 #6501]: #4574 -#3983 := (or #4571 #4565) -#3984 := [def-axiom]: #3983 -#6504 := [unit-resolution #3984 #6503]: #4565 -#3979 := (or #4568 #3098 #4562) -#3980 := [def-axiom]: #3979 -#6505 := [unit-resolution #3980 #6504 #6495]: #4562 -#3993 := (or #4559 #4553) -#4014 := [def-axiom]: #3993 -#6506 := [unit-resolution #4014 #6505]: #4553 -#5790 := (= f8 #1970) -#5854 := (not #5790) -#5852 := [hypothesis]: #4270 -#4159 := (or #4267 #1982) -#3833 := [def-axiom]: #4159 -#5853 := [unit-resolution #3833 #5852]: #1982 -#5855 := (or #5854 #1981) -#5856 := [th-lemma arith triangle-eq]: #5855 -#5857 := [unit-resolution #5856 #5853]: #5854 -#3834 := (or #4267 #2569) -#4166 := [def-axiom]: #3834 -#5858 := [unit-resolution #4166 #5852]: #2569 -#5810 := (or #3923 #2566 #5790) -#5791 := (or #1983 #5790) -#5805 := (or #3923 #5791) -#5669 := (iff #5805 #5810) -#5807 := (or #2566 #5790) -#5812 := (or #3923 #5807) -#5815 := (iff #5812 #5810) -#5668 := [rewrite]: #5815 -#5813 := (iff #5805 #5812) -#5808 := (iff #5791 #5807) -#5809 := [monotonicity #2568]: #5808 -#5814 := [monotonicity #5809]: #5813 -#5670 := [trans #5814 #5668]: #5669 -#5811 := [quant-inst #1967]: #5805 -#5475 := [mp #5811 #5670]: #5810 -#5859 := [unit-resolution #5475 #4224 #5858 #5857]: false -#5860 := [lemma #5859]: #4267 -#4001 := (or #4556 #4270 #4550) -#4002 := [def-axiom]: #4001 -#6507 := [unit-resolution #4002 #5860 #6506]: #4550 -#4034 := (or #4547 #4274) -#4030 := [def-axiom]: #4034 -#7121 := [unit-resolution #4030 #6507]: #4274 -#9553 := (or #4279 #7757) -#9554 := [quant-inst #2273]: #9553 -#9580 := [unit-resolution #9554 #7121]: #7757 -#7570 := (* -1::Int #7536) -#7571 := (+ #2274 #7570) -#9581 := (>= #7571 0::Int) -#7539 := (= #2274 #7536) -#10087 := [hypothesis]: #2276 -#11985 := (or #7539 #2275 #6073) -#9988 := (f5 #7211 ?v0!15) -#9989 := (f9 #9988) -#9990 := (* -1::Int #9989) -#7586 := (f5 f22 ?v0!15) -#7587 := (f9 #7586) -#10058 := (+ #7587 #9990) -#10062 := (>= #10058 0::Int) -#10057 := (= #7587 #9989) -#10065 := (= #9989 #7587) -#10063 := (= #9988 #7586) -#10064 := [monotonicity #7790]: #10063 -#10066 := [monotonicity #10064]: #10065 -#10067 := [symm #10066]: #10057 -#10068 := (not #10057) -#10069 := (or #10068 #10062) -#10070 := [th-lemma arith triangle-eq]: #10069 -#10071 := [unit-resolution #10070 #10067]: #10062 -#7968 := (f5 #6069 #7211) -#8217 := (f6 #7968) -#9081 := (f13 f14 #8217) -#9082 := (* -1::Int #9081) -#9455 := (+ #6070 #9082) -#9457 := (>= #9455 0::Int) -#9861 := (= #6070 #9081) -#8218 := (= #6069 #8217) -#8389 := (or #6829 #8218) -#8390 := [quant-inst #6069 #7211]: #8389 -#9280 := [unit-resolution #8390 #4205]: #8218 -#11947 := [monotonicity #9280]: #9861 -#11945 := (not #9861) -#11948 := (or #11945 #9457) -#11949 := [th-lemma arith triangle-eq]: #11948 -#11950 := [unit-resolution #11949 #11947]: #9457 -#10866 := (+ #99 #9082) -#10878 := (<= #10866 0::Int) -#10875 := (= #99 #9081) -#11956 := (= #9081 #99) -#10697 := (= #8217 f10) -#7317 := (= #6069 f10) -#7319 := (= f10 #6069) -#7298 := (?v1!7 #6069) -#7310 := (f3 f15 #7298) -#7311 := (= f1 #7310) -#7312 := (not #7311) -#7303 := (f5 #7298 #6069) -#7304 := (f9 #7303) -#7305 := (* -1::Int #7304) -#7299 := (f13 f14 #7298) -#7300 := (* -1::Int #7299) -#7306 := (+ #7300 #7305) -#7307 := (+ #6070 #7306) -#7308 := (= #7307 0::Int) -#7309 := (not #7308) -#7301 := (+ #6070 #7300) -#7302 := (<= #7301 0::Int) -#7322 := (or #7302 #7309 #7312) -#9607 := (or #2275 #6073 #7302) -#8251 := (not #7302) -#10072 := [hypothesis]: #8251 -#10110 := (or #7539 #2275 #6073 #7302) -#9125 := (>= #7299 0::Int) -#9128 := (or #4279 #9125) -#9299 := [quant-inst #7298]: #9128 -#10073 := [unit-resolution #9299 #7121]: #9125 -#7561 := (* -1::Int #2274) -#7612 := (+ #7561 #7587) -#7613 := (+ #174 #7612) -#9497 := (<= #7613 0::Int) -#7616 := (= #7613 0::Int) -#7591 := (* -1::Int #7587) -#7595 := (+ f8 #7591) -#7596 := (<= #7595 0::Int) -#9510 := (not #7596) -#7605 := (+ #7570 #7587) -#7606 := (+ #174 #7605) -#7607 := (>= #7606 0::Int) -#7638 := (or #7596 #7607) -#7641 := (not #7638) -#10075 := (not #7539) -#10076 := [hypothesis]: #10075 -#7644 := (or #7539 #7641) -#5788 := (or #4547 #4538) -#4722 := (?v1!7 ?v0!8) -#4998 := (f13 f19 #4722) -#5011 := (* -1::Int #4998) -#4723 := (f13 f14 #4722) -#5231 := (+ #4723 #5011) -#5236 := (>= #5231 0::Int) -#5230 := (= #4723 #4998) -#5720 := (= #4998 #4723) -#5715 := [hypothesis]: #4535 -#5716 := [hypothesis]: #4550 -#4023 := (or #4547 #4541) -#3991 := [def-axiom]: #4023 -#5717 := [unit-resolution #3991 #5716]: #4541 -#4028 := (or #4544 #4383 #4538) -#4029 := [def-axiom]: #4028 -#5718 := [unit-resolution #4029 #5717 #5715]: #4383 -#4134 := (or #4380 #624) -#4135 := [def-axiom]: #4134 -#5719 := [unit-resolution #4135 #5718]: #624 -#5714 := [symm #5719]: #138 -#5721 := [monotonicity #5714]: #5720 -#5722 := [symm #5721]: #5230 -#5723 := (not #5230) -#5724 := (or #5723 #5236) -#5737 := [th-lemma arith triangle-eq]: #5724 -#5738 := [unit-resolution #5737 #5722]: #5236 -#4705 := (* -1::Int #4723) -#4655 := (f13 f14 ?v0!8) -#4706 := (+ #4655 #4705) -#4707 := (<= #4706 0::Int) -#4888 := (not #4707) -#4714 := (f3 f15 #4722) -#4785 := (= f1 #4714) -#4786 := (not #4785) -#4708 := (f5 #4722 ?v0!8) -#4709 := (f9 #4708) -#4704 := (* -1::Int #4709) -#4790 := (+ #4704 #4705) -#4791 := (+ #4655 #4790) -#4773 := (= #4791 0::Int) -#4776 := (not #4773) -#4781 := (or #4707 #4776 #4786) -#4855 := (not #4781) -#4656 := (* -1::Int #4655) -#4657 := (+ f8 #4656) -#4637 := (<= #4657 0::Int) -#4993 := (not #4637) -#4136 := (or #4380 #4374) -#4133 := [def-axiom]: #4136 -#5739 := [unit-resolution #4133 #5718]: #4374 -#4032 := (or #4547 #100) -#4033 := [def-axiom]: #4032 -#5740 := [unit-resolution #4033 #5716]: #100 -#5741 := (= #157 #99) -#5736 := [monotonicity #5714]: #5741 -#5742 := [trans #5736 #5740]: #158 -#4146 := (or #4356 #2165) -#3809 := [def-axiom]: #4146 -#5743 := [unit-resolution #3809 #5742]: #4356 -#4035 := (or #4547 #4282) -#4015 := [def-axiom]: #4035 -#5744 := [unit-resolution #4015 #5716]: #4282 -#3850 := (or #4380 #4316) -#4132 := [def-axiom]: #3850 -#5745 := [unit-resolution #4132 #5718]: #4316 -#4976 := (or #3361 #4321 #4287 #715) -#4949 := [hypothesis]: #3366 -#4149 := (or #3361 #2152) -#4150 := [def-axiom]: #4149 -#4950 := [unit-resolution #4150 #4949]: #2152 -#4724 := (f13 f14 ?v1!10) -#4725 := (* -1::Int #4724) -#4726 := (+ f8 #4725) -#4727 := (<= #4726 0::Int) -#4728 := (f3 f15 ?v1!10) -#4729 := (= f1 #4728) -#4800 := (not #4729) -#3837 := (f13 f14 ?v0!11) -#3838 := (* -1::Int #3837) -#4802 := (+ #3838 #4724) -#4803 := (+ #2146 #4802) -#4806 := (>= #4803 0::Int) -#4959 := (not #4806) -#4933 := (+ #2143 #4725) -#4935 := (>= #4933 0::Int) -#4932 := (= #2143 #4724) -#4937 := (= #4724 #2143) -#4936 := [hypothesis]: #624 -#4938 := [monotonicity #4936]: #4937 -#4939 := [symm #4938]: #4932 -#4940 := (not #4932) -#4941 := (or #4940 #4935) -#4942 := [th-lemma arith triangle-eq]: #4941 -#4943 := [unit-resolution #4942 #4939]: #4935 -#4147 := (not #2807) -#4153 := (or #3361 #4147) -#3791 := [def-axiom]: #4153 -#4944 := [unit-resolution #3791 #4949]: #4147 -#4926 := (+ #2141 #3838) -#4930 := (<= #4926 0::Int) -#4925 := (= #2141 #3837) -#4947 := (= #3837 #2141) -#4948 := [monotonicity #4936]: #4947 -#4951 := [symm #4948]: #4925 -#4952 := (not #4925) -#4953 := (or #4952 #4930) -#4964 := [th-lemma arith triangle-eq]: #4953 -#4965 := [unit-resolution #4964 #4951]: #4930 -#4961 := (not #4935) -#4960 := (not #4930) -#4962 := (or #4959 #4960 #2807 #4961) -#4954 := [hypothesis]: #4935 -#4955 := [hypothesis]: #4147 -#4956 := [hypothesis]: #4930 -#4957 := [hypothesis]: #4806 -#4958 := [th-lemma arith farkas 1 -1 1 1 #4957 #4956 #4955 #4954]: false -#4963 := [lemma #4958]: #4962 -#4966 := [unit-resolution #4963 #4965 #4944 #4943]: #4959 -#4969 := (or #4800 #4806) -#4151 := (or #3361 #2156) -#4152 := [def-axiom]: #4151 -#4967 := [unit-resolution #4152 #4949]: #2156 -#4968 := [hypothesis]: #4282 -#4817 := (or #4287 #2155 #4800 #4806) -#4795 := (+ #4724 #3838) -#4796 := (+ #2146 #4795) -#4799 := (>= #4796 0::Int) -#4801 := (or #4800 #2155 #4799) -#4818 := (or #4287 #4801) -#4825 := (iff #4818 #4817) -#4812 := (or #2155 #4800 #4806) -#4820 := (or #4287 #4812) -#4823 := (iff #4820 #4817) -#4824 := [rewrite]: #4823 -#4821 := (iff #4818 #4820) -#4815 := (iff #4801 #4812) -#4809 := (or #4800 #2155 #4806) -#4813 := (iff #4809 #4812) -#4814 := [rewrite]: #4813 -#4810 := (iff #4801 #4809) -#4807 := (iff #4799 #4806) -#4804 := (= #4796 #4803) +#356 := (iff #46 #355) +#357 := [rewrite]: #356 +#350 := [asserted]: #46 +#358 := [mp #350 #357]: #355 +#4709 := (* -1::Int #1886) +#4710 := (+ f8 #4709) +#4711 := (<= #4710 0::Int) +#3924 := (= f8 #1886) +#3903 := (= f10 ?v0!0) +#4902 := (not #3903) +#4899 := (= #1886 0::Int) +#5099 := (not #4899) +#5100 := (or #5099 #1887) +#5101 := [th-lemma arith triangle-eq]: #5100 +#5081 := [unit-resolution #5101 #5098]: #5099 +#4908 := (or #4775 #4902 #4899) +#3923 := (= ?v0!0 f10) +#4900 := (not #3923) +#4901 := (or #4900 #4899) +#4639 := (or #4775 #4901) +#5094 := (iff #4639 #4908) +#4706 := (or #4902 #4899) +#4925 := (or #4775 #4706) +#4971 := (iff #4925 #4908) +#5093 := [rewrite]: #4971 +#4969 := (iff #4639 #4925) +#4707 := (iff #4901 #4706) +#4905 := (iff #4900 #4902) +#3905 := (iff #3923 #3903) +#3906 := [rewrite]: #3905 +#4906 := [monotonicity #3906]: #4905 +#4774 := [monotonicity #4906]: #4707 +#4970 := [monotonicity #4774]: #4969 +#5095 := [trans #4970 #5093]: #5094 +#4922 := [quant-inst #1885]: #4639 +#5096 := [mp #4922 #5095]: #4908 +#5082 := [unit-resolution #5096 #4601 #5081]: #4902 +#3918 := (or #3903 #3924) +#4210 := (forall (vars (?v0 S3)) (:pat #4209) #445) +#4213 := (iff #450 #4210) +#4211 := (iff #445 #445) +#4212 := [refl]: #4211 +#4214 := [quant-intro #4212]: #4213 +#1847 := (~ #450 #450) +#1876 := (~ #445 #445) +#1877 := [refl]: #1876 +#1848 := [nnf-pos #1877]: #1847 +#1825 := [not-or-elim #1824]: #450 +#1878 := [mp~ #1825 #1848]: #450 +#4215 := [mp #1878 #4214]: #4210 +#3914 := (not #4210) +#3907 := (or #3914 #3903 #3924) +#3913 := (or #3923 #3924) +#3915 := (or #3914 #3913) +#4653 := (iff #3915 #3907) +#3900 := (or #3914 #3918) +#4637 := (iff #3900 #3907) +#4652 := [rewrite]: #4637 +#4635 := (iff #3915 #3900) +#3909 := (iff #3913 #3918) +#3910 := [monotonicity #3906]: #3909 +#4636 := [monotonicity #3910]: #4635 +#4634 := [trans #4636 #4652]: #4653 +#3898 := [quant-inst #1885]: #3915 +#4708 := [mp #3898 #4634]: #3907 +#5083 := [unit-resolution #4708 #4215]: #3918 +#5084 := [unit-resolution #5083 #5082]: #3924 +#5085 := (not #3924) +#5080 := (or #5085 #4711) +#5086 := [th-lemma arith triangle-eq]: #5080 +#5087 := [unit-resolution #5086 #5084]: #4711 +#5088 := [hypothesis]: #5097 +#5089 := [th-lemma arith farkas 1 -1 1 #5088 #5087 #358]: false +#5106 := [lemma #5089]: #5105 +#5132 := [unit-resolution #5106 #5131 #5098]: false +#5133 := [lemma #5132]: #1887 +#3929 := (or #4583 #1888 #4577) +#3930 := [def-axiom]: #3929 +#6490 := [unit-resolution #3930 #5133]: #6489 +#6491 := [unit-resolution #6490 #6488]: #4577 +#3953 := (or #4574 #4568) +#3954 := [def-axiom]: #3953 +#6492 := [unit-resolution #3954 #6491]: #4568 +#5808 := [hypothesis]: #1908 +#5321 := (or #5520 #2210) +#5326 := [quant-inst #1901]: #5321 +#5809 := [unit-resolution #5326 #4222 #5808]: false +#5810 := [lemma #5809]: #2210 +#3746 := (or #2119 #1908) +#3833 := [def-axiom]: #3746 +#6493 := [unit-resolution #3833 #5810]: #2119 +#3947 := (or #4571 #2018 #4565) +#3949 := [def-axiom]: #3947 +#6494 := [unit-resolution #3949 #6493 #6492]: #4565 +#3974 := (or #4562 #4556) +#3975 := [def-axiom]: #3974 +#6495 := [unit-resolution #3975 #6494]: #4556 +#3970 := (or #4559 #3089 #4553) +#3971 := [def-axiom]: #3970 +#6496 := [unit-resolution #3971 #6495 #6486]: #4553 +#3984 := (or #4550 #4544) +#4005 := [def-axiom]: #3984 +#6497 := [unit-resolution #4005 #6496]: #4544 +#5781 := (= f8 #1961) +#5845 := (not #5781) +#5843 := [hypothesis]: #4261 +#4150 := (or #4258 #1973) +#3824 := [def-axiom]: #4150 +#5844 := [unit-resolution #3824 #5843]: #1973 +#5846 := (or #5845 #1972) +#5847 := [th-lemma arith triangle-eq]: #5846 +#5848 := [unit-resolution #5847 #5844]: #5845 +#3825 := (or #4258 #2560) +#4157 := [def-axiom]: #3825 +#5849 := [unit-resolution #4157 #5843]: #2560 +#5801 := (or #3914 #2557 #5781) +#5782 := (or #1974 #5781) +#5796 := (or #3914 #5782) +#5660 := (iff #5796 #5801) +#5798 := (or #2557 #5781) +#5803 := (or #3914 #5798) +#5806 := (iff #5803 #5801) +#5659 := [rewrite]: #5806 +#5804 := (iff #5796 #5803) +#5799 := (iff #5782 #5798) +#5800 := [monotonicity #2559]: #5799 +#5805 := [monotonicity #5800]: #5804 +#5661 := [trans #5805 #5659]: #5660 +#5802 := [quant-inst #1958]: #5796 +#5466 := [mp #5802 #5661]: #5801 +#5850 := [unit-resolution #5466 #4215 #5849 #5848]: false +#5851 := [lemma #5850]: #4258 +#3992 := (or #4547 #4261 #4541) +#3993 := [def-axiom]: #3992 +#6498 := [unit-resolution #3993 #5851 #6497]: #4541 +#4025 := (or #4538 #4265) +#4021 := [def-axiom]: #4025 +#7112 := [unit-resolution #4021 #6498]: #4265 +#9544 := (or #4270 #7748) +#9545 := [quant-inst #2264]: #9544 +#9571 := [unit-resolution #9545 #7112]: #7748 +#7561 := (* -1::Int #7527) +#7562 := (+ #2265 #7561) +#9572 := (>= #7562 0::Int) +#7530 := (= #2265 #7527) +#10078 := [hypothesis]: #2267 +#11976 := (or #7530 #2266 #6064) +#9979 := (f5 #7202 ?v0!15) +#9980 := (f9 #9979) +#9981 := (* -1::Int #9980) +#7577 := (f5 f22 ?v0!15) +#7578 := (f9 #7577) +#10049 := (+ #7578 #9981) +#10053 := (>= #10049 0::Int) +#10048 := (= #7578 #9980) +#10056 := (= #9980 #7578) +#10054 := (= #9979 #7577) +#10055 := [monotonicity #7781]: #10054 +#10057 := [monotonicity #10055]: #10056 +#10058 := [symm #10057]: #10048 +#10059 := (not #10048) +#10060 := (or #10059 #10053) +#10061 := [th-lemma arith triangle-eq]: #10060 +#10062 := [unit-resolution #10061 #10058]: #10053 +#7959 := (f5 #6060 #7202) +#8208 := (f6 #7959) +#9072 := (f13 f14 #8208) +#9073 := (* -1::Int #9072) +#9446 := (+ #6061 #9073) +#9448 := (>= #9446 0::Int) +#9852 := (= #6061 #9072) +#8209 := (= #6060 #8208) +#8380 := (or #6820 #8209) +#8381 := [quant-inst #6060 #7202]: #8380 +#9271 := [unit-resolution #8381 #4196]: #8209 +#11938 := [monotonicity #9271]: #9852 +#11936 := (not #9852) +#11939 := (or #11936 #9448) +#11940 := [th-lemma arith triangle-eq]: #11939 +#11941 := [unit-resolution #11940 #11938]: #9448 +#10857 := (+ #99 #9073) +#10869 := (<= #10857 0::Int) +#10866 := (= #99 #9072) +#11947 := (= #9072 #99) +#10688 := (= #8208 f10) +#7308 := (= #6060 f10) +#7310 := (= f10 #6060) +#7289 := (?v1!7 #6060) +#7301 := (f3 f15 #7289) +#7302 := (= f1 #7301) +#7303 := (not #7302) +#7294 := (f5 #7289 #6060) +#7295 := (f9 #7294) +#7296 := (* -1::Int #7295) +#7290 := (f13 f14 #7289) +#7291 := (* -1::Int #7290) +#7297 := (+ #7291 #7296) +#7298 := (+ #6061 #7297) +#7299 := (= #7298 0::Int) +#7300 := (not #7299) +#7292 := (+ #6061 #7291) +#7293 := (<= #7292 0::Int) +#7313 := (or #7293 #7300 #7303) +#9598 := (or #2266 #6064 #7293) +#8242 := (not #7293) +#10063 := [hypothesis]: #8242 +#10101 := (or #7530 #2266 #6064 #7293) +#9116 := (>= #7290 0::Int) +#9119 := (or #4270 #9116) +#9290 := [quant-inst #7289]: #9119 +#10064 := [unit-resolution #9290 #7112]: #9116 +#7552 := (* -1::Int #2265) +#7603 := (+ #7552 #7578) +#7604 := (+ #174 #7603) +#9488 := (<= #7604 0::Int) +#7607 := (= #7604 0::Int) +#7582 := (* -1::Int #7578) +#7586 := (+ f8 #7582) +#7587 := (<= #7586 0::Int) +#9501 := (not #7587) +#7596 := (+ #7561 #7578) +#7597 := (+ #174 #7596) +#7598 := (>= #7597 0::Int) +#7629 := (or #7587 #7598) +#7632 := (not #7629) +#10066 := (not #7530) +#10067 := [hypothesis]: #10066 +#7635 := (or #7530 #7632) +#5779 := (or #4538 #4529) +#4713 := (?v1!7 ?v0!8) +#4989 := (f13 f19 #4713) +#5002 := (* -1::Int #4989) +#4714 := (f13 f14 #4713) +#5222 := (+ #4714 #5002) +#5227 := (>= #5222 0::Int) +#5221 := (= #4714 #4989) +#5711 := (= #4989 #4714) +#5706 := [hypothesis]: #4526 +#5707 := [hypothesis]: #4541 +#4014 := (or #4538 #4532) +#3982 := [def-axiom]: #4014 +#5708 := [unit-resolution #3982 #5707]: #4532 +#4019 := (or #4535 #4374 #4529) +#4020 := [def-axiom]: #4019 +#5709 := [unit-resolution #4020 #5708 #5706]: #4374 +#4125 := (or #4371 #623) +#4126 := [def-axiom]: #4125 +#5710 := [unit-resolution #4126 #5709]: #623 +#5705 := [symm #5710]: #138 +#5712 := [monotonicity #5705]: #5711 +#5713 := [symm #5712]: #5221 +#5714 := (not #5221) +#5715 := (or #5714 #5227) +#5728 := [th-lemma arith triangle-eq]: #5715 +#5729 := [unit-resolution #5728 #5713]: #5227 +#4696 := (* -1::Int #4714) +#4646 := (f13 f14 ?v0!8) +#4697 := (+ #4646 #4696) +#4698 := (<= #4697 0::Int) +#4879 := (not #4698) +#4705 := (f3 f15 #4713) +#4776 := (= f1 #4705) +#4777 := (not #4776) +#4699 := (f5 #4713 ?v0!8) +#4700 := (f9 #4699) +#4695 := (* -1::Int #4700) +#4781 := (+ #4695 #4696) +#4782 := (+ #4646 #4781) +#4764 := (= #4782 0::Int) +#4767 := (not #4764) +#4772 := (or #4698 #4767 #4777) +#4846 := (not #4772) +#4647 := (* -1::Int #4646) +#4648 := (+ f8 #4647) +#4628 := (<= #4648 0::Int) +#4984 := (not #4628) +#4127 := (or #4371 #4365) +#4124 := [def-axiom]: #4127 +#5730 := [unit-resolution #4124 #5709]: #4365 +#4023 := (or #4538 #100) +#4024 := [def-axiom]: #4023 +#5731 := [unit-resolution #4024 #5707]: #100 +#5732 := (= #157 #99) +#5727 := [monotonicity #5705]: #5732 +#5733 := [trans #5727 #5731]: #158 +#4137 := (or #4347 #2156) +#3800 := [def-axiom]: #4137 +#5734 := [unit-resolution #3800 #5733]: #4347 +#4026 := (or #4538 #4273) +#4006 := [def-axiom]: #4026 +#5735 := [unit-resolution #4006 #5707]: #4273 +#3841 := (or #4371 #4307) +#4123 := [def-axiom]: #3841 +#5736 := [unit-resolution #4123 #5709]: #4307 +#4967 := (or #3352 #4312 #4278 #714) +#4940 := [hypothesis]: #3357 +#4140 := (or #3352 #2143) +#4141 := [def-axiom]: #4140 +#4941 := [unit-resolution #4141 #4940]: #2143 +#4715 := (f13 f14 ?v1!10) +#4716 := (* -1::Int #4715) +#4717 := (+ f8 #4716) +#4718 := (<= #4717 0::Int) +#4719 := (f3 f15 ?v1!10) +#4720 := (= f1 #4719) +#4791 := (not #4720) +#3828 := (f13 f14 ?v0!11) +#3829 := (* -1::Int #3828) +#4793 := (+ #3829 #4715) +#4794 := (+ #2137 #4793) +#4797 := (>= #4794 0::Int) +#4950 := (not #4797) +#4924 := (+ #2134 #4716) +#4926 := (>= #4924 0::Int) +#4923 := (= #2134 #4715) +#4928 := (= #4715 #2134) +#4927 := [hypothesis]: #623 +#4929 := [monotonicity #4927]: #4928 +#4930 := [symm #4929]: #4923 +#4931 := (not #4923) +#4932 := (or #4931 #4926) +#4933 := [th-lemma arith triangle-eq]: #4932 +#4934 := [unit-resolution #4933 #4930]: #4926 +#4138 := (not #2798) +#4144 := (or #3352 #4138) +#3782 := [def-axiom]: #4144 +#4935 := [unit-resolution #3782 #4940]: #4138 +#4917 := (+ #2132 #3829) +#4921 := (<= #4917 0::Int) +#4916 := (= #2132 #3828) +#4938 := (= #3828 #2132) +#4939 := [monotonicity #4927]: #4938 +#4942 := [symm #4939]: #4916 +#4943 := (not #4916) +#4944 := (or #4943 #4921) +#4955 := [th-lemma arith triangle-eq]: #4944 +#4956 := [unit-resolution #4955 #4942]: #4921 +#4952 := (not #4926) +#4951 := (not #4921) +#4953 := (or #4950 #4951 #2798 #4952) +#4945 := [hypothesis]: #4926 +#4946 := [hypothesis]: #4138 +#4947 := [hypothesis]: #4921 +#4948 := [hypothesis]: #4797 +#4949 := [th-lemma arith farkas 1 -1 1 1 #4948 #4947 #4946 #4945]: false +#4954 := [lemma #4949]: #4953 +#4957 := [unit-resolution #4954 #4956 #4935 #4934]: #4950 +#4960 := (or #4791 #4797) +#4142 := (or #3352 #2147) +#4143 := [def-axiom]: #4142 +#4958 := [unit-resolution #4143 #4940]: #2147 +#4959 := [hypothesis]: #4273 +#4808 := (or #4278 #2146 #4791 #4797) +#4786 := (+ #4715 #3829) +#4787 := (+ #2137 #4786) +#4790 := (>= #4787 0::Int) +#4792 := (or #4791 #2146 #4790) +#4809 := (or #4278 #4792) +#4816 := (iff #4809 #4808) +#4803 := (or #2146 #4791 #4797) +#4811 := (or #4278 #4803) +#4814 := (iff #4811 #4808) +#4815 := [rewrite]: #4814 +#4812 := (iff #4809 #4811) +#4806 := (iff #4792 #4803) +#4800 := (or #4791 #2146 #4797) +#4804 := (iff #4800 #4803) #4805 := [rewrite]: #4804 -#4808 := [monotonicity #4805]: #4807 -#4811 := [monotonicity #4808]: #4810 -#4816 := [trans #4811 #4814]: #4815 -#4822 := [monotonicity #4816]: #4821 -#4826 := [trans #4822 #4824]: #4825 -#4819 := [quant-inst #2140 #2139]: #4818 -#4827 := [mp #4819 #4826]: #4817 -#4970 := [unit-resolution #4827 #4968 #4967]: #4969 -#4971 := [unit-resolution #4970 #4966]: #4800 -#4731 := (or #4727 #4729) -#4972 := [hypothesis]: #4316 -#4734 := (or #4321 #4727 #4729) -#4730 := (or #4729 #4727) -#4735 := (or #4321 #4730) -#4742 := (iff #4735 #4734) -#4737 := (or #4321 #4731) -#4740 := (iff #4737 #4734) -#4741 := [rewrite]: #4740 -#4738 := (iff #4735 #4737) -#4732 := (iff #4730 #4731) -#4733 := [rewrite]: #4732 -#4739 := [monotonicity #4733]: #4738 -#4743 := [trans #4739 #4741]: #4742 -#4736 := [quant-inst #2139]: #4735 -#4744 := [mp #4736 #4743]: #4734 -#4973 := [unit-resolution #4744 #4972]: #4731 -#4974 := [unit-resolution #4973 #4971]: #4727 -#4975 := [th-lemma arith farkas 1 -1 1 #4943 #4974 #4950]: false -#4977 := [lemma #4975]: #4976 -#5746 := [unit-resolution #4977 #5745 #5744 #5719]: #3361 -#4158 := (or #4365 #4359 #3366) -#4144 := [def-axiom]: #4158 -#5747 := [unit-resolution #4144 #5746 #5743]: #4365 -#3868 := (or #4368 #4362) -#3869 := [def-axiom]: #3868 -#5748 := [unit-resolution #3869 #5747]: #4368 -#4138 := (or #4377 #4337 #4371) -#4142 := [def-axiom]: #4138 -#5749 := [unit-resolution #4142 #5748 #5739]: #4337 -#4170 := (or #4334 #2090) -#4160 := [def-axiom]: #4170 -#5750 := [unit-resolution #4160 #5749]: #2090 -#4986 := (+ #2077 #4656) -#4988 := (>= #4986 0::Int) -#4985 := (= #2077 #4655) -#5413 := (= #4655 #2077) -#5751 := [monotonicity #5719]: #5413 -#5752 := [symm #5751]: #4985 -#5416 := (not #4985) -#5421 := (or #5416 #4988) -#5422 := [th-lemma arith triangle-eq]: #5421 -#5753 := [unit-resolution #5422 #5752]: #4988 -#4994 := (not #4988) -#4995 := (or #4993 #4994 #2089) -#4989 := [hypothesis]: #2090 -#4990 := [hypothesis]: #4637 -#4991 := [hypothesis]: #4988 -#4992 := [th-lemma arith farkas 1 -1 1 #4991 #4990 #4989]: false -#4996 := [lemma #4992]: #4995 -#5754 := [unit-resolution #4996 #5753 #5750]: #4993 -#5764 := (or #4637 #4855) -#3820 := (or #4334 #2707) -#3825 := [def-axiom]: #3820 -#5762 := [unit-resolution #3825 #5749]: #2707 -#4022 := (or #4547 #4307) -#4017 := [def-axiom]: #4022 -#5763 := [unit-resolution #4017 #5716]: #4307 -#4860 := (or #4312 #2704 #4637 #4855) -#4710 := (+ #4705 #4704) -#4711 := (+ #4655 #4710) -#4712 := (= #4711 0::Int) -#4713 := (not #4712) -#4787 := (or #4786 #4713 #4707) -#4788 := (not #4787) -#4789 := (or #2091 #4637 #4788) -#4861 := (or #4312 #4789) -#4884 := (iff #4861 #4860) -#4858 := (or #2704 #4637 #4855) -#4863 := (or #4312 #4858) -#4882 := (iff #4863 #4860) -#4883 := [rewrite]: #4882 -#4879 := (iff #4861 #4863) -#4853 := (iff #4789 #4858) -#4856 := (iff #4788 #4855) -#4798 := (iff #4787 #4781) -#4778 := (or #4786 #4776 #4707) -#4782 := (iff #4778 #4781) -#4797 := [rewrite]: #4782 -#4779 := (iff #4787 #4778) -#4777 := (iff #4713 #4776) -#4774 := (iff #4712 #4773) -#4792 := (= #4711 #4791) -#4793 := [rewrite]: #4792 -#4775 := [monotonicity #4793]: #4774 -#4772 := [monotonicity #4775]: #4777 -#4780 := [monotonicity #4772]: #4779 -#4854 := [trans #4780 #4797]: #4798 -#4857 := [monotonicity #4854]: #4856 -#4859 := [monotonicity #2706 #4857]: #4853 -#4881 := [monotonicity #4859]: #4879 -#4885 := [trans #4881 #4883]: #4884 -#4862 := [quant-inst #2076]: #4861 -#4880 := [mp #4862 #4885]: #4860 -#5765 := [unit-resolution #4880 #5763 #5762]: #5764 -#5766 := [unit-resolution #5765 #5754]: #4855 -#4889 := (or #4781 #4888) -#4890 := [def-axiom]: #4889 -#5767 := [unit-resolution #4890 #5766]: #4888 -#5012 := (+ #2077 #5011) -#5013 := (<= #5012 0::Int) -#5025 := (+ #4704 #5011) -#5026 := (+ #2077 #5025) -#5027 := (= #5026 0::Int) -#5049 := (<= #5026 0::Int) -#5235 := (<= #5231 0::Int) -#5768 := (or #5723 #5235) +#4801 := (iff #4792 #4800) +#4798 := (iff #4790 #4797) +#4795 := (= #4787 #4794) +#4796 := [rewrite]: #4795 +#4799 := [monotonicity #4796]: #4798 +#4802 := [monotonicity #4799]: #4801 +#4807 := [trans #4802 #4805]: #4806 +#4813 := [monotonicity #4807]: #4812 +#4817 := [trans #4813 #4815]: #4816 +#4810 := [quant-inst #2131 #2130]: #4809 +#4818 := [mp #4810 #4817]: #4808 +#4961 := [unit-resolution #4818 #4959 #4958]: #4960 +#4962 := [unit-resolution #4961 #4957]: #4791 +#4722 := (or #4718 #4720) +#4963 := [hypothesis]: #4307 +#4725 := (or #4312 #4718 #4720) +#4721 := (or #4720 #4718) +#4726 := (or #4312 #4721) +#4733 := (iff #4726 #4725) +#4728 := (or #4312 #4722) +#4731 := (iff #4728 #4725) +#4732 := [rewrite]: #4731 +#4729 := (iff #4726 #4728) +#4723 := (iff #4721 #4722) +#4724 := [rewrite]: #4723 +#4730 := [monotonicity #4724]: #4729 +#4734 := [trans #4730 #4732]: #4733 +#4727 := [quant-inst #2130]: #4726 +#4735 := [mp #4727 #4734]: #4725 +#4964 := [unit-resolution #4735 #4963]: #4722 +#4965 := [unit-resolution #4964 #4962]: #4718 +#4966 := [th-lemma arith farkas 1 -1 1 #4934 #4965 #4941]: false +#4968 := [lemma #4966]: #4967 +#5737 := [unit-resolution #4968 #5736 #5735 #5710]: #3352 +#4149 := (or #4356 #4350 #3357) +#4135 := [def-axiom]: #4149 +#5738 := [unit-resolution #4135 #5737 #5734]: #4356 +#3859 := (or #4359 #4353) +#3860 := [def-axiom]: #3859 +#5739 := [unit-resolution #3860 #5738]: #4359 +#4129 := (or #4368 #4328 #4362) +#4133 := [def-axiom]: #4129 +#5740 := [unit-resolution #4133 #5739 #5730]: #4328 +#4161 := (or #4325 #2081) +#4151 := [def-axiom]: #4161 +#5741 := [unit-resolution #4151 #5740]: #2081 +#4977 := (+ #2068 #4647) +#4979 := (>= #4977 0::Int) +#4976 := (= #2068 #4646) +#5404 := (= #4646 #2068) +#5742 := [monotonicity #5710]: #5404 +#5743 := [symm #5742]: #4976 +#5407 := (not #4976) +#5412 := (or #5407 #4979) +#5413 := [th-lemma arith triangle-eq]: #5412 +#5744 := [unit-resolution #5413 #5743]: #4979 +#4985 := (not #4979) +#4986 := (or #4984 #4985 #2080) +#4980 := [hypothesis]: #2081 +#4981 := [hypothesis]: #4628 +#4982 := [hypothesis]: #4979 +#4983 := [th-lemma arith farkas 1 -1 1 #4982 #4981 #4980]: false +#4987 := [lemma #4983]: #4986 +#5745 := [unit-resolution #4987 #5744 #5741]: #4984 +#5755 := (or #4628 #4846) +#3811 := (or #4325 #2698) +#3816 := [def-axiom]: #3811 +#5753 := [unit-resolution #3816 #5740]: #2698 +#4013 := (or #4538 #4298) +#4008 := [def-axiom]: #4013 +#5754 := [unit-resolution #4008 #5707]: #4298 +#4851 := (or #4303 #2695 #4628 #4846) +#4701 := (+ #4696 #4695) +#4702 := (+ #4646 #4701) +#4703 := (= #4702 0::Int) +#4704 := (not #4703) +#4778 := (or #4777 #4704 #4698) +#4779 := (not #4778) +#4780 := (or #2082 #4628 #4779) +#4852 := (or #4303 #4780) +#4875 := (iff #4852 #4851) +#4849 := (or #2695 #4628 #4846) +#4854 := (or #4303 #4849) +#4873 := (iff #4854 #4851) +#4874 := [rewrite]: #4873 +#4870 := (iff #4852 #4854) +#4844 := (iff #4780 #4849) +#4847 := (iff #4779 #4846) +#4789 := (iff #4778 #4772) +#4769 := (or #4777 #4767 #4698) +#4773 := (iff #4769 #4772) +#4788 := [rewrite]: #4773 +#4770 := (iff #4778 #4769) +#4768 := (iff #4704 #4767) +#4765 := (iff #4703 #4764) +#4783 := (= #4702 #4782) +#4784 := [rewrite]: #4783 +#4766 := [monotonicity #4784]: #4765 +#4763 := [monotonicity #4766]: #4768 +#4771 := [monotonicity #4763]: #4770 +#4845 := [trans #4771 #4788]: #4789 +#4848 := [monotonicity #4845]: #4847 +#4850 := [monotonicity #2697 #4848]: #4844 +#4872 := [monotonicity #4850]: #4870 +#4876 := [trans #4872 #4874]: #4875 +#4853 := [quant-inst #2067]: #4852 +#4871 := [mp #4853 #4876]: #4851 +#5756 := [unit-resolution #4871 #5754 #5753]: #5755 +#5757 := [unit-resolution #5756 #5745]: #4846 +#4880 := (or #4772 #4879) +#4881 := [def-axiom]: #4880 +#5758 := [unit-resolution #4881 #5757]: #4879 +#5003 := (+ #2068 #5002) +#5004 := (<= #5003 0::Int) +#5016 := (+ #4695 #5002) +#5017 := (+ #2068 #5016) +#5018 := (= #5017 0::Int) +#5040 := (<= #5017 0::Int) +#5226 := (<= #5222 0::Int) +#5759 := (or #5714 #5226) +#5760 := [th-lemma arith triangle-eq]: #5759 +#5761 := [unit-resolution #5760 #5713]: #5226 +#4877 := (<= #4782 0::Int) +#4896 := (or #4772 #4764) +#4898 := [def-axiom]: #4896 +#5762 := [unit-resolution #4898 #5757]: #4764 +#5763 := (or #4767 #4877) +#5764 := [th-lemma arith triangle-eq]: #5763 +#5765 := [unit-resolution #5764 #5762]: #4877 +#4978 := (<= #4977 0::Int) +#5408 := (or #5407 #4978) +#5409 := [th-lemma arith triangle-eq]: #5408 +#5766 := [unit-resolution #5409 #5743]: #4978 +#5350 := (not #5226) +#5349 := (not #4877) +#5348 := (not #4978) +#5351 := (or #5040 #5348 #5349 #5350) +#5342 := [hypothesis]: #5226 +#5343 := [hypothesis]: #4877 +#5344 := [hypothesis]: #4978 +#5345 := (not #5040) +#5346 := [hypothesis]: #5345 +#5347 := [th-lemma arith farkas -1 1 1 1 #5346 #5344 #5343 #5342]: false +#5352 := [lemma #5347]: #5351 +#5767 := [unit-resolution #5352 #5766 #5765 #5761]: #5040 +#5041 := (>= #5017 0::Int) +#4878 := (>= #4782 0::Int) +#5768 := (or #4767 #4878) #5769 := [th-lemma arith triangle-eq]: #5768 -#5770 := [unit-resolution #5769 #5722]: #5235 -#4886 := (<= #4791 0::Int) -#4905 := (or #4781 #4773) -#4907 := [def-axiom]: #4905 -#5771 := [unit-resolution #4907 #5766]: #4773 -#5772 := (or #4776 #4886) +#5770 := [unit-resolution #5769 #5762]: #4878 +#5750 := (not #5227) +#5390 := (not #4878) +#5751 := (or #5041 #4985 #5390 #5750) +#5746 := [hypothesis]: #5227 +#5386 := [hypothesis]: #4878 +#5747 := (not #5041) +#5748 := [hypothesis]: #5747 +#5749 := [th-lemma arith farkas -1 1 1 1 #5748 #4982 #5386 #5746]: false +#5752 := [lemma #5749]: #5751 +#5771 := [unit-resolution #5752 #5744 #5770 #5729]: #5041 +#5772 := (or #5018 #5345 #5747) #5773 := [th-lemma arith triangle-eq]: #5772 -#5774 := [unit-resolution #5773 #5771]: #4886 -#4987 := (<= #4986 0::Int) -#5417 := (or #5416 #4987) -#5418 := [th-lemma arith triangle-eq]: #5417 -#5775 := [unit-resolution #5418 #5752]: #4987 -#5359 := (not #5235) -#5358 := (not #4886) -#5357 := (not #4987) -#5360 := (or #5049 #5357 #5358 #5359) -#5351 := [hypothesis]: #5235 -#5352 := [hypothesis]: #4886 -#5353 := [hypothesis]: #4987 -#5354 := (not #5049) -#5355 := [hypothesis]: #5354 -#5356 := [th-lemma arith farkas -1 1 1 1 #5355 #5353 #5352 #5351]: false -#5361 := [lemma #5356]: #5360 -#5776 := [unit-resolution #5361 #5775 #5774 #5770]: #5049 -#5050 := (>= #5026 0::Int) -#4887 := (>= #4791 0::Int) -#5777 := (or #4776 #4887) -#5778 := [th-lemma arith triangle-eq]: #5777 -#5779 := [unit-resolution #5778 #5771]: #4887 -#5759 := (not #5236) -#5399 := (not #4887) -#5760 := (or #5050 #4994 #5399 #5759) -#5755 := [hypothesis]: #5236 -#5395 := [hypothesis]: #4887 -#5756 := (not #5050) -#5757 := [hypothesis]: #5756 -#5758 := [th-lemma arith farkas -1 1 1 1 #5757 #4991 #5395 #5755]: false -#5761 := [lemma #5758]: #5760 -#5780 := [unit-resolution #5761 #5753 #5779 #5738]: #5050 -#5781 := (or #5027 #5354 #5756) -#5782 := [th-lemma arith triangle-eq]: #5781 -#5783 := [unit-resolution #5782 #5780 #5776]: #5027 -#5032 := (not #5027) -#5035 := (or #5013 #5032) -#4161 := (or #4334 #4326) -#3821 := [def-axiom]: #4161 -#5784 := [unit-resolution #3821 #5749]: #4326 -#5038 := (or #4331 #5013 #5032) -#4997 := (+ #2078 #4709) -#4999 := (+ #4998 #4997) -#5000 := (= #4999 0::Int) -#5001 := (not #5000) -#5002 := (+ #4998 #2078) -#5003 := (>= #5002 0::Int) -#5004 := (or #5003 #5001) -#5039 := (or #4331 #5004) -#5046 := (iff #5039 #5038) -#5041 := (or #4331 #5035) -#5044 := (iff #5041 #5038) -#5045 := [rewrite]: #5044 -#5042 := (iff #5039 #5041) -#5036 := (iff #5004 #5035) -#5033 := (iff #5001 #5032) -#5030 := (iff #5000 #5027) -#5018 := (+ #4709 #4998) -#5019 := (+ #2078 #5018) -#5022 := (= #5019 0::Int) -#5028 := (iff #5022 #5027) -#5029 := [rewrite]: #5028 -#5023 := (iff #5000 #5022) -#5020 := (= #4999 #5019) -#5021 := [rewrite]: #5020 -#5024 := [monotonicity #5021]: #5023 -#5031 := [trans #5024 #5029]: #5030 -#5034 := [monotonicity #5031]: #5033 -#5016 := (iff #5003 #5013) -#5005 := (+ #2078 #4998) -#5008 := (>= #5005 0::Int) -#5014 := (iff #5008 #5013) -#5015 := [rewrite]: #5014 -#5009 := (iff #5003 #5008) -#5006 := (= #5002 #5005) -#5007 := [rewrite]: #5006 -#5010 := [monotonicity #5007]: #5009 -#5017 := [trans #5010 #5015]: #5016 -#5037 := [monotonicity #5017 #5034]: #5036 -#5043 := [monotonicity #5037]: #5042 -#5047 := [trans #5043 #5045]: #5046 -#5040 := [quant-inst #4722]: #5039 -#5048 := [mp #5040 #5047]: #5038 -#5785 := [unit-resolution #5048 #5784]: #5035 -#5786 := [unit-resolution #5785 #5783]: #5013 -#5787 := [th-lemma arith farkas 1 -1 1 1 #5753 #5786 #5767 #5738]: false -#5789 := [lemma #5787]: #5788 -#6508 := [unit-resolution #5789 #6507]: #4538 -#4044 := (or #4535 #4396) -#4039 := [def-axiom]: #4044 -#6509 := [unit-resolution #4039 #6508]: #4396 -#9499 := (or #4401 #7539 #7641) -#7592 := (+ #1453 #7591) -#7593 := (+ #7536 #7592) -#7594 := (<= #7593 0::Int) -#7635 := (or #7596 #7594) -#7636 := (not #7635) -#7537 := (= #7536 #2274) -#7637 := (or #7537 #7636) -#9500 := (or #4401 #7637) -#9507 := (iff #9500 #9499) -#9502 := (or #4401 #7644) -#9505 := (iff #9502 #9499) -#9506 := [rewrite]: #9505 -#9503 := (iff #9500 #9502) -#7645 := (iff #7637 #7644) -#7642 := (iff #7636 #7641) -#7639 := (iff #7635 #7638) -#7610 := (iff #7594 #7607) -#7598 := (+ #7536 #7591) -#7599 := (+ #1453 #7598) -#7602 := (<= #7599 0::Int) -#7608 := (iff #7602 #7607) -#7609 := [rewrite]: #7608 -#7603 := (iff #7594 #7602) -#7600 := (= #7593 #7599) -#7601 := [rewrite]: #7600 -#7604 := [monotonicity #7601]: #7603 -#7611 := [trans #7604 #7609]: #7610 -#7640 := [monotonicity #7611]: #7639 -#7643 := [monotonicity #7640]: #7642 -#7540 := (iff #7537 #7539) -#7541 := [rewrite]: #7540 -#7646 := [monotonicity #7541 #7643]: #7645 -#9504 := [monotonicity #7646]: #9503 -#9508 := [trans #9504 #9506]: #9507 -#9501 := [quant-inst #2273]: #9500 -#9509 := [mp #9501 #9508]: #9499 -#10077 := [unit-resolution #9509 #6509]: #7644 -#10078 := [unit-resolution #10077 #10076]: #7641 -#9511 := (or #7638 #9510) -#9512 := [def-axiom]: #9511 -#10079 := [unit-resolution #9512 #10078]: #9510 -#9513 := (not #7607) -#9514 := (or #7638 #9513) -#9515 := [def-axiom]: #9514 -#10080 := [unit-resolution #9515 #10078]: #9513 -#7619 := (or #7596 #7607 #7616) -#4045 := (or #4535 #4404) -#4018 := [def-axiom]: #4045 -#6513 := [unit-resolution #4018 #6508]: #4404 -#9486 := (or #4409 #7596 #7607 #7616) -#7588 := (+ #7587 #7561) -#7589 := (+ #174 #7588) -#7590 := (= #7589 0::Int) -#7597 := (or #7596 #7594 #7590) -#9487 := (or #4409 #7597) -#9494 := (iff #9487 #9486) -#9489 := (or #4409 #7619) -#9492 := (iff #9489 #9486) -#9493 := [rewrite]: #9492 -#9490 := (iff #9487 #9489) -#7620 := (iff #7597 #7619) -#7617 := (iff #7590 #7616) -#7614 := (= #7589 #7613) -#7615 := [rewrite]: #7614 -#7618 := [monotonicity #7615]: #7617 -#7621 := [monotonicity #7611 #7618]: #7620 -#9491 := [monotonicity #7621]: #9490 -#9495 := [trans #9491 #9493]: #9494 -#9488 := [quant-inst #2273]: #9487 -#9496 := [mp #9488 #9495]: #9486 -#10081 := [unit-resolution #9496 #6513]: #7619 -#10082 := [unit-resolution #10081 #10080 #10079]: #7616 -#10083 := (not #7616) -#10084 := (or #10083 #9497) -#10085 := [th-lemma arith triangle-eq]: #10084 -#10086 := [unit-resolution #10085 #10082]: #9497 -#10050 := (>= #9989 0::Int) -#10025 := (<= #9989 0::Int) -#10026 := (not #10025) -#9949 := (= ?v0!15 #7211) -#9968 := (not #9949) -#7668 := (f3 f15 ?v0!15) -#7669 := (= f1 #7668) -#5891 := (f3 #773 f22) -#5892 := (= f1 #5891) -#9952 := (ite #9949 #5892 #7669) -#9967 := (not #9952) -#8442 := (f4 f15 #7211 #5891) -#9946 := (f3 #8442 ?v0!15) -#9947 := (= f1 #9946) -#9955 := (iff #9947 #9952) +#5774 := [unit-resolution #5773 #5771 #5767]: #5018 +#5023 := (not #5018) +#5026 := (or #5004 #5023) +#4152 := (or #4325 #4317) +#3812 := [def-axiom]: #4152 +#5775 := [unit-resolution #3812 #5740]: #4317 +#5029 := (or #4322 #5004 #5023) +#4988 := (+ #2069 #4700) +#4990 := (+ #4989 #4988) +#4991 := (= #4990 0::Int) +#4992 := (not #4991) +#4993 := (+ #4989 #2069) +#4994 := (>= #4993 0::Int) +#4995 := (or #4994 #4992) +#5030 := (or #4322 #4995) +#5037 := (iff #5030 #5029) +#5032 := (or #4322 #5026) +#5035 := (iff #5032 #5029) +#5036 := [rewrite]: #5035 +#5033 := (iff #5030 #5032) +#5027 := (iff #4995 #5026) +#5024 := (iff #4992 #5023) +#5021 := (iff #4991 #5018) +#5009 := (+ #4700 #4989) +#5010 := (+ #2069 #5009) +#5013 := (= #5010 0::Int) +#5019 := (iff #5013 #5018) +#5020 := [rewrite]: #5019 +#5014 := (iff #4991 #5013) +#5011 := (= #4990 #5010) +#5012 := [rewrite]: #5011 +#5015 := [monotonicity #5012]: #5014 +#5022 := [trans #5015 #5020]: #5021 +#5025 := [monotonicity #5022]: #5024 +#5007 := (iff #4994 #5004) +#4996 := (+ #2069 #4989) +#4999 := (>= #4996 0::Int) +#5005 := (iff #4999 #5004) +#5006 := [rewrite]: #5005 +#5000 := (iff #4994 #4999) +#4997 := (= #4993 #4996) +#4998 := [rewrite]: #4997 +#5001 := [monotonicity #4998]: #5000 +#5008 := [trans #5001 #5006]: #5007 +#5028 := [monotonicity #5008 #5025]: #5027 +#5034 := [monotonicity #5028]: #5033 +#5038 := [trans #5034 #5036]: #5037 +#5031 := [quant-inst #4713]: #5030 +#5039 := [mp #5031 #5038]: #5029 +#5776 := [unit-resolution #5039 #5775]: #5026 +#5777 := [unit-resolution #5776 #5774]: #5004 +#5778 := [th-lemma arith farkas 1 -1 1 1 #5744 #5777 #5758 #5729]: false +#5780 := [lemma #5778]: #5779 +#6499 := [unit-resolution #5780 #6498]: #4529 +#4035 := (or #4526 #4387) +#4030 := [def-axiom]: #4035 +#6500 := [unit-resolution #4030 #6499]: #4387 +#9490 := (or #4392 #7530 #7632) +#7583 := (+ #1444 #7582) +#7584 := (+ #7527 #7583) +#7585 := (<= #7584 0::Int) +#7626 := (or #7587 #7585) +#7627 := (not #7626) +#7528 := (= #7527 #2265) +#7628 := (or #7528 #7627) +#9491 := (or #4392 #7628) +#9498 := (iff #9491 #9490) +#9493 := (or #4392 #7635) +#9496 := (iff #9493 #9490) +#9497 := [rewrite]: #9496 +#9494 := (iff #9491 #9493) +#7636 := (iff #7628 #7635) +#7633 := (iff #7627 #7632) +#7630 := (iff #7626 #7629) +#7601 := (iff #7585 #7598) +#7589 := (+ #7527 #7582) +#7590 := (+ #1444 #7589) +#7593 := (<= #7590 0::Int) +#7599 := (iff #7593 #7598) +#7600 := [rewrite]: #7599 +#7594 := (iff #7585 #7593) +#7591 := (= #7584 #7590) +#7592 := [rewrite]: #7591 +#7595 := [monotonicity #7592]: #7594 +#7602 := [trans #7595 #7600]: #7601 +#7631 := [monotonicity #7602]: #7630 +#7634 := [monotonicity #7631]: #7633 +#7531 := (iff #7528 #7530) +#7532 := [rewrite]: #7531 +#7637 := [monotonicity #7532 #7634]: #7636 +#9495 := [monotonicity #7637]: #9494 +#9499 := [trans #9495 #9497]: #9498 +#9492 := [quant-inst #2264]: #9491 +#9500 := [mp #9492 #9499]: #9490 +#10068 := [unit-resolution #9500 #6500]: #7635 +#10069 := [unit-resolution #10068 #10067]: #7632 +#9502 := (or #7629 #9501) +#9503 := [def-axiom]: #9502 +#10070 := [unit-resolution #9503 #10069]: #9501 +#9504 := (not #7598) +#9505 := (or #7629 #9504) +#9506 := [def-axiom]: #9505 +#10071 := [unit-resolution #9506 #10069]: #9504 +#7610 := (or #7587 #7598 #7607) +#4036 := (or #4526 #4395) +#4009 := [def-axiom]: #4036 +#6504 := [unit-resolution #4009 #6499]: #4395 +#9477 := (or #4400 #7587 #7598 #7607) +#7579 := (+ #7578 #7552) +#7580 := (+ #174 #7579) +#7581 := (= #7580 0::Int) +#7588 := (or #7587 #7585 #7581) +#9478 := (or #4400 #7588) +#9485 := (iff #9478 #9477) +#9480 := (or #4400 #7610) +#9483 := (iff #9480 #9477) +#9484 := [rewrite]: #9483 +#9481 := (iff #9478 #9480) +#7611 := (iff #7588 #7610) +#7608 := (iff #7581 #7607) +#7605 := (= #7580 #7604) +#7606 := [rewrite]: #7605 +#7609 := [monotonicity #7606]: #7608 +#7612 := [monotonicity #7602 #7609]: #7611 +#9482 := [monotonicity #7612]: #9481 +#9486 := [trans #9482 #9484]: #9485 +#9479 := [quant-inst #2264]: #9478 +#9487 := [mp #9479 #9486]: #9477 +#10072 := [unit-resolution #9487 #6504]: #7610 +#10073 := [unit-resolution #10072 #10071 #10070]: #7607 +#10074 := (not #7607) +#10075 := (or #10074 #9488) +#10076 := [th-lemma arith triangle-eq]: #10075 +#10077 := [unit-resolution #10076 #10073]: #9488 +#10041 := (>= #9980 0::Int) +#10016 := (<= #9980 0::Int) +#10017 := (not #10016) +#9940 := (= ?v0!15 #7202) +#9959 := (not #9940) +#7659 := (f3 f15 ?v0!15) +#7660 := (= f1 #7659) +#5882 := (f3 #180 f22) +#5883 := (= f1 #5882) +#9943 := (ite #9940 #5883 #7660) +#9958 := (not #9943) +#8433 := (f4 f15 #7202 #5882) +#9937 := (f3 #8433 ?v0!15) +#9938 := (= f1 #9937) +#9946 := (iff #9938 #9943) #10 := (:var 1 S1) #9 := (:var 2 S3) #8 := (:var 3 S2) #11 := (f4 #8 #9 #10) #13 := (f3 #11 #12) -#4171 := (pattern #13) +#4162 := (pattern #13) #17 := (f3 #8 #12) -#301 := (= f1 #17) -#298 := (= f1 #10) -#295 := (= #9 #12) -#304 := (ite #295 #298 #301) -#292 := (= f1 #13) -#307 := (iff #292 #304) -#4172 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4171) #307) -#310 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #307) -#4175 := (iff #310 #4172) -#4173 := (iff #307 #307) -#4174 := [refl]: #4173 -#4176 := [quant-intro #4174]: #4175 -#1868 := (~ #310 #310) -#1866 := (~ #307 #307) -#1867 := [refl]: #1866 -#1869 := [nnf-pos #1867]: #1868 +#300 := (= f1 #17) +#297 := (= f1 #10) +#294 := (= #9 #12) +#303 := (ite #294 #297 #300) +#291 := (= f1 #13) +#306 := (iff #291 #303) +#4163 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4162) #306) +#309 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #306) +#4166 := (iff #309 #4163) +#4164 := (iff #306 #306) +#4165 := [refl]: #4164 +#4167 := [quant-intro #4165]: #4166 +#1859 := (~ #309 #309) +#1857 := (~ #306 #306) +#1858 := [refl]: #1857 +#1860 := [nnf-pos #1858]: #1859 #18 := (= #17 f1) #16 := (= #10 f1) #15 := (= #12 #9) @@ -4832,2365 +4821,2365 @@ #14 := (= #13 f1) #20 := (iff #14 #19) #21 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #20) -#311 := (iff #21 #310) -#308 := (iff #20 #307) -#305 := (iff #19 #304) -#302 := (iff #18 #301) -#303 := [rewrite]: #302 -#299 := (iff #16 #298) -#300 := [rewrite]: #299 -#296 := (iff #15 #295) -#297 := [rewrite]: #296 -#306 := [monotonicity #297 #300 #303]: #305 -#293 := (iff #14 #292) -#294 := [rewrite]: #293 -#309 := [monotonicity #294 #306]: #308 -#312 := [quant-intro #309]: #311 -#291 := [asserted]: #21 -#315 := [mp #291 #312]: #310 -#1840 := [mp~ #315 #1869]: #310 -#4177 := [mp #1840 #4176]: #4172 -#6290 := (not #4172) -#9958 := (or #6290 #9955) -#9944 := (= #7211 ?v0!15) -#9945 := (ite #9944 #5892 #7669) -#9948 := (iff #9947 #9945) -#9959 := (or #6290 #9948) -#9961 := (iff #9959 #9958) -#9963 := (iff #9958 #9958) -#9964 := [rewrite]: #9963 -#9956 := (iff #9948 #9955) -#9953 := (iff #9945 #9952) -#9950 := (iff #9944 #9949) -#9951 := [rewrite]: #9950 -#9954 := [monotonicity #9951]: #9953 -#9957 := [monotonicity #9954]: #9956 -#9962 := [monotonicity #9957]: #9961 -#9965 := [trans #9962 #9964]: #9961 -#9960 := [quant-inst #104 #7211 #5891 #2273]: #9959 -#9966 := [mp #9960 #9965]: #9958 -#10088 := [unit-resolution #9966 #4177]: #9955 -#9981 := (not #9947) -#7533 := (f3 f23 ?v0!15) -#7534 := (= f1 #7533) -#7535 := (not #7534) -#10097 := (iff #7535 #9981) -#10095 := (iff #7534 #9947) -#10093 := (iff #9947 #7534) -#10091 := (= #9946 #7533) -#9285 := (= #8442 f23) -#7004 := (= #773 f23) -#4053 := (or #4535 #776) -#4048 := [def-axiom]: #4053 -#6998 := [unit-resolution #4048 #6508]: #776 -#7005 := [symm #6998]: #7004 -#9283 := (= #8442 #773) -#7000 := (= #5891 f1) +#310 := (iff #21 #309) +#307 := (iff #20 #306) +#304 := (iff #19 #303) +#301 := (iff #18 #300) +#302 := [rewrite]: #301 +#298 := (iff #16 #297) +#299 := [rewrite]: #298 +#295 := (iff #15 #294) +#296 := [rewrite]: #295 +#305 := [monotonicity #296 #299 #302]: #304 +#292 := (iff #14 #291) +#293 := [rewrite]: #292 +#308 := [monotonicity #293 #305]: #307 +#311 := [quant-intro #308]: #310 +#290 := [asserted]: #21 +#314 := [mp #290 #311]: #309 +#1831 := [mp~ #314 #1860]: #309 +#4168 := [mp #1831 #4167]: #4163 +#6281 := (not #4163) +#9949 := (or #6281 #9946) +#9935 := (= #7202 ?v0!15) +#9936 := (ite #9935 #5883 #7660) +#9939 := (iff #9938 #9936) +#9950 := (or #6281 #9939) +#9952 := (iff #9950 #9949) +#9954 := (iff #9949 #9949) +#9955 := [rewrite]: #9954 +#9947 := (iff #9939 #9946) +#9944 := (iff #9936 #9943) +#9941 := (iff #9935 #9940) +#9942 := [rewrite]: #9941 +#9945 := [monotonicity #9942]: #9944 +#9948 := [monotonicity #9945]: #9947 +#9953 := [monotonicity #9948]: #9952 +#9956 := [trans #9953 #9955]: #9952 +#9951 := [quant-inst #104 #7202 #5882 #2264]: #9950 +#9957 := [mp #9951 #9956]: #9949 +#10079 := [unit-resolution #9957 #4168]: #9946 +#9972 := (not #9938) +#7524 := (f3 f23 ?v0!15) +#7525 := (= f1 #7524) +#7526 := (not #7525) +#10088 := (iff #7526 #9972) +#10086 := (iff #7525 #9938) +#10084 := (iff #9938 #7525) +#10082 := (= #9937 #7524) +#9276 := (= #8433 f23) +#6995 := (= #180 f23) +#4042 := (or #4526 #181) +#4043 := [def-axiom]: #4042 +#6989 := [unit-resolution #4043 #6499]: #181 +#6996 := [symm #6989]: #6995 +#9274 := (= #8433 #180) +#6991 := (= #5882 f1) #24 := (:var 0 S1) #22 := (:var 2 S2) #25 := (f4 #22 #23 #24) -#4178 := (pattern #25) -#318 := (= f1 #24) +#4169 := (pattern #25) +#317 := (= f1 #24) #26 := (f3 #25 #23) -#314 := (= f1 #26) -#321 := (iff #314 #318) -#4179 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4178) #321) -#324 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #321) -#4182 := (iff #324 #4179) -#4180 := (iff #321 #321) -#4181 := [refl]: #4180 -#4183 := [quant-intro #4181]: #4182 -#1842 := (~ #324 #324) -#1841 := (~ #321 #321) -#1870 := [refl]: #1841 -#1843 := [nnf-pos #1870]: #1842 +#313 := (= f1 #26) +#320 := (iff #313 #317) +#4170 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4169) #320) +#323 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #320) +#4173 := (iff #323 #4170) +#4171 := (iff #320 #320) +#4172 := [refl]: #4171 +#4174 := [quant-intro #4172]: #4173 +#1833 := (~ #323 #323) +#1832 := (~ #320 #320) +#1861 := [refl]: #1832 +#1834 := [nnf-pos #1861]: #1833 #28 := (= #24 f1) #27 := (= #26 f1) #29 := (iff #27 #28) #30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #29) -#325 := (iff #30 #324) -#322 := (iff #29 #321) -#319 := (iff #28 #318) -#320 := [rewrite]: #319 -#316 := (iff #27 #314) -#317 := [rewrite]: #316 -#323 := [monotonicity #317 #320]: #322 -#326 := [quant-intro #323]: #325 -#313 := [asserted]: #30 -#329 := [mp #313 #326]: #324 -#1871 := [mp~ #329 #1843]: #324 -#4184 := [mp #1871 #4183]: #4179 -#5903 := (not #4179) -#5904 := (or #5903 #5892) -#5890 := (= f1 f1) -#5893 := (iff #5892 #5890) -#5905 := (or #5903 #5893) -#5907 := (iff #5905 #5904) -#5909 := (iff #5904 #5904) -#5910 := [rewrite]: #5909 -#5901 := (iff #5893 #5892) -#5896 := (iff #5892 true) -#5899 := (iff #5896 #5892) -#5900 := [rewrite]: #5899 -#5897 := (iff #5893 #5896) -#5894 := (iff #5890 true) -#5895 := [rewrite]: #5894 -#5898 := [monotonicity #5895]: #5897 -#5902 := [trans #5898 #5900]: #5901 -#5908 := [monotonicity #5902]: #5907 -#5911 := [trans #5908 #5910]: #5907 -#5906 := [quant-inst #104 #170 #4]: #5905 -#5912 := [mp #5906 #5911]: #5904 -#6999 := [unit-resolution #5912 #4184]: #5892 -#7001 := [symm #6999]: #7000 -#9284 := [monotonicity #7790 #7001]: #9283 -#9286 := [trans #9284 #7005]: #9285 -#10092 := [monotonicity #9286]: #10091 -#10094 := [monotonicity #10092]: #10093 -#10096 := [symm #10094]: #10095 -#10098 := [monotonicity #10096]: #10097 -#7545 := (or #7535 #7539) -#4019 := (or #4535 #4529) -#4020 := [def-axiom]: #4019 -#7096 := [unit-resolution #4020 #6508]: #4529 -#6311 := (f5 f22 ?v0!13) -#6312 := (f9 #6311) -#6337 := (+ #2232 #6312) -#6338 := (+ #174 #6337) -#6359 := (>= #6338 0::Int) -#6341 := (= #6338 0::Int) -#6316 := (* -1::Int #6312) -#6320 := (+ f8 #6316) -#6321 := (<= #6320 0::Int) -#6388 := (not #6321) -#6330 := (+ #2848 #6312) -#6331 := (+ #174 #6330) -#6332 := (>= #6331 0::Int) -#6367 := (or #6321 #6332) -#6370 := (not #6367) -#6364 := (= #2231 #2233) -#6489 := (not #6364) -#6488 := [hypothesis]: #2855 -#6492 := (or #6489 #2850) -#6493 := [th-lemma arith triangle-eq]: #6492 -#6494 := [unit-resolution #6493 #6488]: #6489 -#6376 := (or #4401 #6364 #6370) -#6317 := (+ #1453 #6316) -#6318 := (+ #2233 #6317) -#6319 := (<= #6318 0::Int) -#6360 := (or #6321 #6319) -#6361 := (not #6360) -#6362 := (= #2233 #2231) -#6363 := (or #6362 #6361) -#6377 := (or #4401 #6363) -#6384 := (iff #6377 #6376) -#6373 := (or #6364 #6370) -#6379 := (or #4401 #6373) -#6382 := (iff #6379 #6376) -#6383 := [rewrite]: #6382 -#6380 := (iff #6377 #6379) -#6374 := (iff #6363 #6373) -#6371 := (iff #6361 #6370) -#6368 := (iff #6360 #6367) -#6335 := (iff #6319 #6332) -#6323 := (+ #2233 #6316) -#6324 := (+ #1453 #6323) -#6327 := (<= #6324 0::Int) -#6333 := (iff #6327 #6332) -#6334 := [rewrite]: #6333 -#6328 := (iff #6319 #6327) -#6325 := (= #6318 #6324) -#6326 := [rewrite]: #6325 -#6329 := [monotonicity #6326]: #6328 -#6336 := [trans #6329 #6334]: #6335 -#6369 := [monotonicity #6336]: #6368 -#6372 := [monotonicity #6369]: #6371 -#6365 := (iff #6362 #6364) -#6366 := [rewrite]: #6365 -#6375 := [monotonicity #6366 #6372]: #6374 -#6381 := [monotonicity #6375]: #6380 -#6385 := [trans #6381 #6383]: #6384 -#6378 := [quant-inst #2230]: #6377 -#6386 := [mp #6378 #6385]: #6376 -#6510 := [unit-resolution #6386 #6509 #6494]: #6370 -#6389 := (or #6367 #6388) -#6390 := [def-axiom]: #6389 -#6511 := [unit-resolution #6390 #6510]: #6388 -#6391 := (not #6332) -#6392 := (or #6367 #6391) -#6393 := [def-axiom]: #6392 -#6512 := [unit-resolution #6393 #6510]: #6391 -#6344 := (or #6321 #6332 #6341) -#6347 := (or #4409 #6321 #6332 #6341) -#6313 := (+ #6312 #2232) -#6314 := (+ #174 #6313) -#6315 := (= #6314 0::Int) -#6322 := (or #6321 #6319 #6315) -#6348 := (or #4409 #6322) -#6355 := (iff #6348 #6347) -#6350 := (or #4409 #6344) -#6353 := (iff #6350 #6347) -#6354 := [rewrite]: #6353 -#6351 := (iff #6348 #6350) -#6345 := (iff #6322 #6344) -#6342 := (iff #6315 #6341) -#6339 := (= #6314 #6338) -#6340 := [rewrite]: #6339 -#6343 := [monotonicity #6340]: #6342 -#6346 := [monotonicity #6336 #6343]: #6345 -#6352 := [monotonicity #6346]: #6351 -#6356 := [trans #6352 #6354]: #6355 -#6349 := [quant-inst #2230]: #6348 -#6357 := [mp #6349 #6356]: #6347 -#6514 := [unit-resolution #6357 #6513]: #6344 -#6515 := [unit-resolution #6514 #6512 #6511]: #6341 -#6516 := (not #6341) -#6517 := (or #6516 #6359) -#6518 := [th-lemma arith triangle-eq]: #6517 -#6519 := [unit-resolution #6518 #6515]: #6359 -#6387 := (>= #2849 0::Int) -#6520 := (or #6387 #2850) -#6521 := [th-lemma arith farkas 1 1]: #6520 -#6522 := [unit-resolution #6521 #6488]: #6387 -#6523 := [th-lemma arith farkas 1 -1 1 #6522 #6512 #6519]: false -#6524 := [lemma #6523]: #2850 -#4049 := (or #4532 #2855 #4526) -#4050 := [def-axiom]: #4049 -#7097 := [unit-resolution #4050 #6524 #7096]: #4526 -#4064 := (or #4523 #4517) -#4065 := [def-axiom]: #4064 -#7098 := [unit-resolution #4065 #7097]: #4517 -#6879 := (= #174 #2253) -#6696 := (= f22 ?v0!14) -#6526 := (f3 f15 ?v0!14) -#6527 := (= f1 #6526) -#6697 := (ite #6696 #5892 #6527) -#6269 := (f4 f15 f22 #5891) -#6700 := (f3 #6269 ?v0!14) -#6701 := (= f1 #6700) -#6703 := (iff #6697 #6701) -#6706 := (or #6290 #6703) -#6702 := (iff #6701 #6697) -#6707 := (or #6290 #6702) -#6709 := (iff #6707 #6706) -#6711 := (iff #6706 #6706) -#6712 := [rewrite]: #6711 -#6704 := (iff #6702 #6703) -#6705 := [rewrite]: #6704 -#6710 := [monotonicity #6705]: #6709 -#6713 := [trans #6710 #6712]: #6709 -#6708 := [quant-inst #104 #170 #5891 #2248]: #6707 -#6714 := [mp #6708 #6713]: #6706 -#6996 := [unit-resolution #6714 #4177]: #6703 -#7012 := (= #2249 #6700) -#7008 := (= #6700 #2249) -#7006 := (= #6269 f23) -#7002 := (= #6269 #773) -#7003 := [monotonicity #7001]: #7002 -#7007 := [trans #7003 #7005]: #7006 -#7009 := [monotonicity #7007]: #7008 -#7013 := [symm #7009]: #7012 -#6994 := [hypothesis]: #2869 -#4127 := (or #2864 #2250) -#4128 := [def-axiom]: #4127 -#6997 := [unit-resolution #4128 #6994]: #2250 -#7014 := [trans #6997 #7013]: #6701 -#6727 := (not #6701) -#6726 := (not #6703) -#6728 := (or #6726 #6697 #6727) -#6729 := [def-axiom]: #6728 -#7015 := [unit-resolution #6729 #7014 #6996]: #6697 -#6555 := (f5 f22 ?v0!14) -#6556 := (f9 #6555) -#6486 := (* -1::Int #2253) -#6573 := (+ #6486 #6556) -#6574 := (+ #174 #6573) -#6575 := (>= #6574 0::Int) -#6603 := (not #6575) -#6557 := (* -1::Int #6556) -#6561 := (+ f8 #6557) -#6562 := (<= #6561 0::Int) -#6580 := (or #6562 #6575) -#6583 := (not #6580) -#4123 := (not #2858) -#4124 := (or #2864 #4123) -#4129 := [def-axiom]: #4124 -#6995 := [unit-resolution #4129 #6994]: #4123 -#6589 := (or #4401 #2858 #6583) -#6558 := (+ #1453 #6557) -#6559 := (+ #2253 #6558) -#6560 := (<= #6559 0::Int) -#6563 := (or #6562 #6560) -#6564 := (not #6563) -#6565 := (or #2254 #6564) -#6590 := (or #4401 #6565) -#6597 := (iff #6590 #6589) -#6586 := (or #2858 #6583) -#6592 := (or #4401 #6586) -#6595 := (iff #6592 #6589) -#6596 := [rewrite]: #6595 -#6593 := (iff #6590 #6592) -#6587 := (iff #6565 #6586) -#6584 := (iff #6564 #6583) -#6581 := (iff #6563 #6580) -#6578 := (iff #6560 #6575) -#6566 := (+ #2253 #6557) -#6567 := (+ #1453 #6566) -#6570 := (<= #6567 0::Int) -#6576 := (iff #6570 #6575) -#6577 := [rewrite]: #6576 -#6571 := (iff #6560 #6570) -#6568 := (= #6559 #6567) -#6569 := [rewrite]: #6568 -#6572 := [monotonicity #6569]: #6571 -#6579 := [trans #6572 #6577]: #6578 -#6582 := [monotonicity #6579]: #6581 -#6585 := [monotonicity #6582]: #6584 -#6588 := [monotonicity #2860 #6585]: #6587 -#6594 := [monotonicity #6588]: #6593 -#6598 := [trans #6594 #6596]: #6597 -#6591 := [quant-inst #2248]: #6590 -#6599 := [mp #6591 #6598]: #6589 -#7016 := [unit-resolution #6599 #6509 #6995]: #6583 -#6604 := (or #6580 #6603) -#6605 := [def-axiom]: #6604 -#7017 := [unit-resolution #6605 #7016]: #6603 -#6715 := (not #6697) -#6941 := (or #6696 #6575 #6715) -#6822 := (f6 #6555) -#6832 := (f13 f14 #6822) -#6847 := (* -1::Int #6832) -#6887 := (+ #174 #6847) -#6889 := (>= #6887 0::Int) -#6886 := (= #174 #6832) -#6893 := (= #6832 #174) -#6891 := (= #6822 f22) -#6823 := (= f22 #6822) -#6830 := (or #6829 #6823) -#6831 := [quant-inst #170 #2248]: #6830 -#6890 := [unit-resolution #6831 #4205]: #6823 -#6892 := [symm #6890]: #6891 -#6894 := [monotonicity #6892]: #6893 -#6895 := [symm #6894]: #6886 -#6896 := (not #6886) -#6897 := (or #6896 #6889) -#6898 := [th-lemma arith triangle-eq]: #6897 -#6899 := [unit-resolution #6898 #6895]: #6889 -#6900 := [hypothesis]: #6603 -#6819 := (>= #6556 0::Int) -#6773 := (<= #6556 0::Int) -#6774 := (not #6773) -#6716 := (not #6696) -#6901 := [hypothesis]: #6716 -#6779 := (or #6696 #6774) +#324 := (iff #30 #323) +#321 := (iff #29 #320) +#318 := (iff #28 #317) +#319 := [rewrite]: #318 +#315 := (iff #27 #313) +#316 := [rewrite]: #315 +#322 := [monotonicity #316 #319]: #321 +#325 := [quant-intro #322]: #324 +#312 := [asserted]: #30 +#328 := [mp #312 #325]: #323 +#1862 := [mp~ #328 #1834]: #323 +#4175 := [mp #1862 #4174]: #4170 +#5894 := (not #4170) +#5895 := (or #5894 #5883) +#5881 := (= f1 f1) +#5884 := (iff #5883 #5881) +#5896 := (or #5894 #5884) +#5898 := (iff #5896 #5895) +#5900 := (iff #5895 #5895) +#5901 := [rewrite]: #5900 +#5892 := (iff #5884 #5883) +#5887 := (iff #5883 true) +#5890 := (iff #5887 #5883) +#5891 := [rewrite]: #5890 +#5888 := (iff #5884 #5887) +#5885 := (iff #5881 true) +#5886 := [rewrite]: #5885 +#5889 := [monotonicity #5886]: #5888 +#5893 := [trans #5889 #5891]: #5892 +#5899 := [monotonicity #5893]: #5898 +#5902 := [trans #5899 #5901]: #5898 +#5897 := [quant-inst #104 #170 #4]: #5896 +#5903 := [mp #5897 #5902]: #5895 +#6990 := [unit-resolution #5903 #4175]: #5883 +#6992 := [symm #6990]: #6991 +#9275 := [monotonicity #7781 #6992]: #9274 +#9277 := [trans #9275 #6996]: #9276 +#10083 := [monotonicity #9277]: #10082 +#10085 := [monotonicity #10083]: #10084 +#10087 := [symm #10085]: #10086 +#10089 := [monotonicity #10087]: #10088 +#7536 := (or #7526 #7530) +#4010 := (or #4526 #4520) +#4011 := [def-axiom]: #4010 +#7087 := [unit-resolution #4011 #6499]: #4520 +#6302 := (f5 f22 ?v0!13) +#6303 := (f9 #6302) +#6328 := (+ #2223 #6303) +#6329 := (+ #174 #6328) +#6350 := (>= #6329 0::Int) +#6332 := (= #6329 0::Int) +#6307 := (* -1::Int #6303) +#6311 := (+ f8 #6307) +#6312 := (<= #6311 0::Int) +#6379 := (not #6312) +#6321 := (+ #2839 #6303) +#6322 := (+ #174 #6321) +#6323 := (>= #6322 0::Int) +#6358 := (or #6312 #6323) +#6361 := (not #6358) +#6355 := (= #2222 #2224) +#6480 := (not #6355) +#6479 := [hypothesis]: #2846 +#6483 := (or #6480 #2841) +#6484 := [th-lemma arith triangle-eq]: #6483 +#6485 := [unit-resolution #6484 #6479]: #6480 +#6367 := (or #4392 #6355 #6361) +#6308 := (+ #1444 #6307) +#6309 := (+ #2224 #6308) +#6310 := (<= #6309 0::Int) +#6351 := (or #6312 #6310) +#6352 := (not #6351) +#6353 := (= #2224 #2222) +#6354 := (or #6353 #6352) +#6368 := (or #4392 #6354) +#6375 := (iff #6368 #6367) +#6364 := (or #6355 #6361) +#6370 := (or #4392 #6364) +#6373 := (iff #6370 #6367) +#6374 := [rewrite]: #6373 +#6371 := (iff #6368 #6370) +#6365 := (iff #6354 #6364) +#6362 := (iff #6352 #6361) +#6359 := (iff #6351 #6358) +#6326 := (iff #6310 #6323) +#6314 := (+ #2224 #6307) +#6315 := (+ #1444 #6314) +#6318 := (<= #6315 0::Int) +#6324 := (iff #6318 #6323) +#6325 := [rewrite]: #6324 +#6319 := (iff #6310 #6318) +#6316 := (= #6309 #6315) +#6317 := [rewrite]: #6316 +#6320 := [monotonicity #6317]: #6319 +#6327 := [trans #6320 #6325]: #6326 +#6360 := [monotonicity #6327]: #6359 +#6363 := [monotonicity #6360]: #6362 +#6356 := (iff #6353 #6355) +#6357 := [rewrite]: #6356 +#6366 := [monotonicity #6357 #6363]: #6365 +#6372 := [monotonicity #6366]: #6371 +#6376 := [trans #6372 #6374]: #6375 +#6369 := [quant-inst #2221]: #6368 +#6377 := [mp #6369 #6376]: #6367 +#6501 := [unit-resolution #6377 #6500 #6485]: #6361 +#6380 := (or #6358 #6379) +#6381 := [def-axiom]: #6380 +#6502 := [unit-resolution #6381 #6501]: #6379 +#6382 := (not #6323) +#6383 := (or #6358 #6382) +#6384 := [def-axiom]: #6383 +#6503 := [unit-resolution #6384 #6501]: #6382 +#6335 := (or #6312 #6323 #6332) +#6338 := (or #4400 #6312 #6323 #6332) +#6304 := (+ #6303 #2223) +#6305 := (+ #174 #6304) +#6306 := (= #6305 0::Int) +#6313 := (or #6312 #6310 #6306) +#6339 := (or #4400 #6313) +#6346 := (iff #6339 #6338) +#6341 := (or #4400 #6335) +#6344 := (iff #6341 #6338) +#6345 := [rewrite]: #6344 +#6342 := (iff #6339 #6341) +#6336 := (iff #6313 #6335) +#6333 := (iff #6306 #6332) +#6330 := (= #6305 #6329) +#6331 := [rewrite]: #6330 +#6334 := [monotonicity #6331]: #6333 +#6337 := [monotonicity #6327 #6334]: #6336 +#6343 := [monotonicity #6337]: #6342 +#6347 := [trans #6343 #6345]: #6346 +#6340 := [quant-inst #2221]: #6339 +#6348 := [mp #6340 #6347]: #6338 +#6505 := [unit-resolution #6348 #6504]: #6335 +#6506 := [unit-resolution #6505 #6503 #6502]: #6332 +#6507 := (not #6332) +#6508 := (or #6507 #6350) +#6509 := [th-lemma arith triangle-eq]: #6508 +#6510 := [unit-resolution #6509 #6506]: #6350 +#6378 := (>= #2840 0::Int) +#6511 := (or #6378 #2841) +#6512 := [th-lemma arith farkas 1 1]: #6511 +#6513 := [unit-resolution #6512 #6479]: #6378 +#6514 := [th-lemma arith farkas 1 -1 1 #6513 #6503 #6510]: false +#6515 := [lemma #6514]: #2841 +#4040 := (or #4523 #2846 #4517) +#4041 := [def-axiom]: #4040 +#7088 := [unit-resolution #4041 #6515 #7087]: #4517 +#4055 := (or #4514 #4508) +#4056 := [def-axiom]: #4055 +#7089 := [unit-resolution #4056 #7088]: #4508 +#6870 := (= #174 #2244) +#6687 := (= f22 ?v0!14) +#6517 := (f3 f15 ?v0!14) +#6518 := (= f1 #6517) +#6688 := (ite #6687 #5883 #6518) +#6260 := (f4 f15 f22 #5882) +#6691 := (f3 #6260 ?v0!14) +#6692 := (= f1 #6691) +#6694 := (iff #6688 #6692) +#6697 := (or #6281 #6694) +#6693 := (iff #6692 #6688) +#6698 := (or #6281 #6693) +#6700 := (iff #6698 #6697) +#6702 := (iff #6697 #6697) +#6703 := [rewrite]: #6702 +#6695 := (iff #6693 #6694) +#6696 := [rewrite]: #6695 +#6701 := [monotonicity #6696]: #6700 +#6704 := [trans #6701 #6703]: #6700 +#6699 := [quant-inst #104 #170 #5882 #2239]: #6698 +#6705 := [mp #6699 #6704]: #6697 +#6987 := [unit-resolution #6705 #4168]: #6694 +#7003 := (= #2240 #6691) +#6999 := (= #6691 #2240) +#6997 := (= #6260 f23) +#6993 := (= #6260 #180) +#6994 := [monotonicity #6992]: #6993 +#6998 := [trans #6994 #6996]: #6997 +#7000 := [monotonicity #6998]: #6999 +#7004 := [symm #7000]: #7003 +#6985 := [hypothesis]: #2860 +#4118 := (or #2855 #2241) +#4119 := [def-axiom]: #4118 +#6988 := [unit-resolution #4119 #6985]: #2241 +#7005 := [trans #6988 #7004]: #6692 +#6718 := (not #6692) +#6717 := (not #6694) +#6719 := (or #6717 #6688 #6718) +#6720 := [def-axiom]: #6719 +#7006 := [unit-resolution #6720 #7005 #6987]: #6688 +#6546 := (f5 f22 ?v0!14) +#6547 := (f9 #6546) +#6477 := (* -1::Int #2244) +#6564 := (+ #6477 #6547) +#6565 := (+ #174 #6564) +#6566 := (>= #6565 0::Int) +#6594 := (not #6566) +#6548 := (* -1::Int #6547) +#6552 := (+ f8 #6548) +#6553 := (<= #6552 0::Int) +#6571 := (or #6553 #6566) +#6574 := (not #6571) +#4114 := (not #2849) +#4115 := (or #2855 #4114) +#4120 := [def-axiom]: #4115 +#6986 := [unit-resolution #4120 #6985]: #4114 +#6580 := (or #4392 #2849 #6574) +#6549 := (+ #1444 #6548) +#6550 := (+ #2244 #6549) +#6551 := (<= #6550 0::Int) +#6554 := (or #6553 #6551) +#6555 := (not #6554) +#6556 := (or #2245 #6555) +#6581 := (or #4392 #6556) +#6588 := (iff #6581 #6580) +#6577 := (or #2849 #6574) +#6583 := (or #4392 #6577) +#6586 := (iff #6583 #6580) +#6587 := [rewrite]: #6586 +#6584 := (iff #6581 #6583) +#6578 := (iff #6556 #6577) +#6575 := (iff #6555 #6574) +#6572 := (iff #6554 #6571) +#6569 := (iff #6551 #6566) +#6557 := (+ #2244 #6548) +#6558 := (+ #1444 #6557) +#6561 := (<= #6558 0::Int) +#6567 := (iff #6561 #6566) +#6568 := [rewrite]: #6567 +#6562 := (iff #6551 #6561) +#6559 := (= #6550 #6558) +#6560 := [rewrite]: #6559 +#6563 := [monotonicity #6560]: #6562 +#6570 := [trans #6563 #6568]: #6569 +#6573 := [monotonicity #6570]: #6572 +#6576 := [monotonicity #6573]: #6575 +#6579 := [monotonicity #2851 #6576]: #6578 +#6585 := [monotonicity #6579]: #6584 +#6589 := [trans #6585 #6587]: #6588 +#6582 := [quant-inst #2239]: #6581 +#6590 := [mp #6582 #6589]: #6580 +#7007 := [unit-resolution #6590 #6500 #6986]: #6574 +#6595 := (or #6571 #6594) +#6596 := [def-axiom]: #6595 +#7008 := [unit-resolution #6596 #7007]: #6594 +#6706 := (not #6688) +#6932 := (or #6687 #6566 #6706) +#6813 := (f6 #6546) +#6823 := (f13 f14 #6813) +#6838 := (* -1::Int #6823) +#6878 := (+ #174 #6838) +#6880 := (>= #6878 0::Int) +#6877 := (= #174 #6823) +#6884 := (= #6823 #174) +#6882 := (= #6813 f22) +#6814 := (= f22 #6813) +#6821 := (or #6820 #6814) +#6822 := [quant-inst #170 #2239]: #6821 +#6881 := [unit-resolution #6822 #4196]: #6814 +#6883 := [symm #6881]: #6882 +#6885 := [monotonicity #6883]: #6884 +#6886 := [symm #6885]: #6877 +#6887 := (not #6877) +#6888 := (or #6887 #6880) +#6889 := [th-lemma arith triangle-eq]: #6888 +#6890 := [unit-resolution #6889 #6886]: #6880 +#6891 := [hypothesis]: #6594 +#6810 := (>= #6547 0::Int) +#6764 := (<= #6547 0::Int) +#6765 := (not #6764) +#6707 := (not #6687) +#6892 := [hypothesis]: #6707 +#6770 := (or #6687 #6765) #48 := (f9 #37) -#407 := (<= #48 0::Int) -#408 := (not #407) -#354 := (= #12 #23) -#414 := (or #354 #408) -#4212 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #414) -#419 := (forall (vars (?v0 S3) (?v1 S3)) #414) -#4215 := (iff #419 #4212) -#4213 := (iff #414 #414) -#4214 := [refl]: #4213 -#4216 := [quant-intro #4214]: #4215 -#1854 := (~ #419 #419) -#1853 := (~ #414 #414) -#1883 := [refl]: #1853 -#1855 := [nnf-pos #1883]: #1854 +#406 := (<= #48 0::Int) +#407 := (not #406) +#353 := (= #12 #23) +#413 := (or #353 #407) +#4203 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #413) +#418 := (forall (vars (?v0 S3) (?v1 S3)) #413) +#4206 := (iff #418 #4203) +#4204 := (iff #413 #413) +#4205 := [refl]: #4204 +#4207 := [quant-intro #4205]: #4206 +#1845 := (~ #418 #418) +#1844 := (~ #413 #413) +#1874 := [refl]: #1844 +#1846 := [nnf-pos #1874]: #1845 #53 := (< 0::Int #48) #47 := (= #23 #12) #52 := (not #47) #54 := (implies #52 #53) #55 := (forall (vars (?v0 S3) (?v1 S3)) #54) -#422 := (iff #55 #419) -#399 := (or #53 #354) -#404 := (forall (vars (?v0 S3) (?v1 S3)) #399) -#420 := (iff #404 #419) -#417 := (iff #399 #414) -#411 := (or #408 #354) -#415 := (iff #411 #414) -#416 := [rewrite]: #415 -#412 := (iff #399 #411) -#409 := (iff #53 #408) -#410 := [rewrite]: #409 -#413 := [monotonicity #410]: #412 -#418 := [trans #413 #416]: #417 -#421 := [quant-intro #418]: #420 -#405 := (iff #55 #404) -#402 := (iff #54 #399) -#368 := (not #354) -#396 := (implies #368 #53) -#400 := (iff #396 #399) -#401 := [rewrite]: #400 -#397 := (iff #54 #396) -#394 := (iff #52 #368) -#360 := (iff #47 #354) -#361 := [rewrite]: #360 -#395 := [monotonicity #361]: #394 -#398 := [monotonicity #395]: #397 -#403 := [trans #398 #401]: #402 -#406 := [quant-intro #403]: #405 -#423 := [trans #406 #421]: #422 -#393 := [asserted]: #55 -#424 := [mp #393 #423]: #419 -#1884 := [mp~ #424 #1855]: #419 -#4217 := [mp #1884 #4216]: #4212 -#6782 := (not #4212) -#6783 := (or #6782 #6696 #6774) -#6775 := (= ?v0!14 f22) -#6776 := (or #6775 #6774) -#6784 := (or #6782 #6776) -#6791 := (iff #6784 #6783) -#6786 := (or #6782 #6779) -#6789 := (iff #6786 #6783) -#6790 := [rewrite]: #6789 -#6787 := (iff #6784 #6786) -#6780 := (iff #6776 #6779) -#6777 := (iff #6775 #6696) -#6778 := [rewrite]: #6777 -#6781 := [monotonicity #6778]: #6780 -#6788 := [monotonicity #6781]: #6787 -#6792 := [trans #6788 #6790]: #6791 -#6785 := [quant-inst #170 #2248]: #6784 -#6793 := [mp #6785 #6792]: #6783 -#6902 := [unit-resolution #6793 #4217]: #6779 -#6903 := [unit-resolution #6902 #6901]: #6774 -#6904 := (or #6819 #6773) -#6905 := [th-lemma arith farkas 1 1]: #6904 -#6906 := [unit-resolution #6905 #6903]: #6819 -#6820 := (f7 #6555) -#6827 := (f13 f14 #6820) -#6828 := (* -1::Int #6827) -#6877 := (+ #2253 #6828) -#6884 := (<= #6877 0::Int) -#6876 := (= #2253 #6827) -#6910 := (= #6827 #2253) -#6908 := (= #6820 ?v0!14) -#6821 := (= ?v0!14 #6820) -#6825 := (or #6824 #6821) -#6826 := [quant-inst #170 #2248]: #6825 -#6907 := [unit-resolution #6826 #4199]: #6821 -#6909 := [symm #6907]: #6908 -#6911 := [monotonicity #6909]: #6910 -#6912 := [symm #6911]: #6876 -#6913 := (not #6876) -#6914 := (or #6913 #6884) -#6915 := [th-lemma arith triangle-eq]: #6914 -#6916 := [unit-resolution #6915 #6912]: #6884 -#6848 := (+ #6827 #6847) -#6849 := (<= #6848 0::Int) -#6835 := (f3 f15 #6820) -#6836 := (= f1 #6835) -#6923 := (= #6526 #6835) -#6919 := (= #6835 #6526) -#6920 := [monotonicity #6909]: #6919 -#6924 := [symm #6920]: #6923 -#6917 := [hypothesis]: #6697 -#6719 := (or #6715 #6696 #6527) -#6720 := [def-axiom]: #6719 -#6918 := [unit-resolution #6720 #6901 #6917]: #6527 -#6925 := [trans #6918 #6924]: #6836 -#6838 := (f3 f15 #6822) -#6839 := (= f1 #6838) -#6933 := (not #6839) -#6934 := (iff #757 #6933) -#6931 := (iff #754 #6839) -#6929 := (iff #6839 #754) -#6927 := (= #6838 #171) -#6928 := [monotonicity #6892]: #6927 -#6930 := [monotonicity #6928]: #6929 -#6932 := [symm #6930]: #6931 -#6935 := [monotonicity #6932]: #6934 -#4051 := (or #4535 #757) -#4052 := [def-axiom]: #4051 -#6926 := [unit-resolution #4052 #6508]: #757 -#6936 := [mp #6926 #6935]: #6933 -#6837 := (not #6836) -#6857 := (or #6837 #6839 #6849) -#3961 := (or #4547 #4291) -#4016 := [def-axiom]: #3961 -#6937 := [unit-resolution #4016 #6507]: #4291 -#6862 := (or #4296 #6837 #6839 #6849) -#6833 := (+ #6832 #6828) -#6834 := (>= #6833 0::Int) -#6840 := (or #6839 #6837 #6834) -#6863 := (or #4296 #6840) -#6870 := (iff #6863 #6862) -#6865 := (or #4296 #6857) -#6868 := (iff #6865 #6862) -#6869 := [rewrite]: #6868 -#6866 := (iff #6863 #6865) -#6860 := (iff #6840 #6857) -#6854 := (or #6839 #6837 #6849) -#6858 := (iff #6854 #6857) -#6859 := [rewrite]: #6858 -#6855 := (iff #6840 #6854) -#6852 := (iff #6834 #6849) -#6841 := (+ #6828 #6832) -#6844 := (>= #6841 0::Int) -#6850 := (iff #6844 #6849) -#6851 := [rewrite]: #6850 -#6845 := (iff #6834 #6844) -#6842 := (= #6833 #6841) -#6843 := [rewrite]: #6842 -#6846 := [monotonicity #6843]: #6845 -#6853 := [trans #6846 #6851]: #6852 -#6856 := [monotonicity #6853]: #6855 -#6861 := [trans #6856 #6859]: #6860 -#6867 := [monotonicity #6861]: #6866 -#6871 := [trans #6867 #6869]: #6870 -#6864 := [quant-inst #6820 #6822]: #6863 -#6872 := [mp #6864 #6871]: #6862 -#6938 := [unit-resolution #6872 #6937]: #6857 -#6939 := [unit-resolution #6938 #6936 #6925]: #6849 -#6940 := [th-lemma arith farkas 1 1 1 -1 1 #6939 #6916 #6906 #6900 #6899]: false -#6942 := [lemma #6940]: #6941 -#7018 := [unit-resolution #6942 #7017 #7015]: #6696 -#7042 := [monotonicity #7018]: #6879 -#7040 := (= #2252 #174) -#7038 := (= #174 #2252) -#6795 := (= #6556 0::Int) -#6802 := (or #6716 #6795) +#421 := (iff #55 #418) +#398 := (or #53 #353) +#403 := (forall (vars (?v0 S3) (?v1 S3)) #398) +#419 := (iff #403 #418) +#416 := (iff #398 #413) +#410 := (or #407 #353) +#414 := (iff #410 #413) +#415 := [rewrite]: #414 +#411 := (iff #398 #410) +#408 := (iff #53 #407) +#409 := [rewrite]: #408 +#412 := [monotonicity #409]: #411 +#417 := [trans #412 #415]: #416 +#420 := [quant-intro #417]: #419 +#404 := (iff #55 #403) +#401 := (iff #54 #398) +#367 := (not #353) +#395 := (implies #367 #53) +#399 := (iff #395 #398) +#400 := [rewrite]: #399 +#396 := (iff #54 #395) +#393 := (iff #52 #367) +#359 := (iff #47 #353) +#360 := [rewrite]: #359 +#394 := [monotonicity #360]: #393 +#397 := [monotonicity #394]: #396 +#402 := [trans #397 #400]: #401 +#405 := [quant-intro #402]: #404 +#422 := [trans #405 #420]: #421 +#392 := [asserted]: #55 +#423 := [mp #392 #422]: #418 +#1875 := [mp~ #423 #1846]: #418 +#4208 := [mp #1875 #4207]: #4203 +#6773 := (not #4203) +#6774 := (or #6773 #6687 #6765) +#6766 := (= ?v0!14 f22) +#6767 := (or #6766 #6765) +#6775 := (or #6773 #6767) +#6782 := (iff #6775 #6774) +#6777 := (or #6773 #6770) +#6780 := (iff #6777 #6774) +#6781 := [rewrite]: #6780 +#6778 := (iff #6775 #6777) +#6771 := (iff #6767 #6770) +#6768 := (iff #6766 #6687) +#6769 := [rewrite]: #6768 +#6772 := [monotonicity #6769]: #6771 +#6779 := [monotonicity #6772]: #6778 +#6783 := [trans #6779 #6781]: #6782 +#6776 := [quant-inst #170 #2239]: #6775 +#6784 := [mp #6776 #6783]: #6774 +#6893 := [unit-resolution #6784 #4208]: #6770 +#6894 := [unit-resolution #6893 #6892]: #6765 +#6895 := (or #6810 #6764) +#6896 := [th-lemma arith farkas 1 1]: #6895 +#6897 := [unit-resolution #6896 #6894]: #6810 +#6811 := (f7 #6546) +#6818 := (f13 f14 #6811) +#6819 := (* -1::Int #6818) +#6868 := (+ #2244 #6819) +#6875 := (<= #6868 0::Int) +#6867 := (= #2244 #6818) +#6901 := (= #6818 #2244) +#6899 := (= #6811 ?v0!14) +#6812 := (= ?v0!14 #6811) +#6816 := (or #6815 #6812) +#6817 := [quant-inst #170 #2239]: #6816 +#6898 := [unit-resolution #6817 #4190]: #6812 +#6900 := [symm #6898]: #6899 +#6902 := [monotonicity #6900]: #6901 +#6903 := [symm #6902]: #6867 +#6904 := (not #6867) +#6905 := (or #6904 #6875) +#6906 := [th-lemma arith triangle-eq]: #6905 +#6907 := [unit-resolution #6906 #6903]: #6875 +#6839 := (+ #6818 #6838) +#6840 := (<= #6839 0::Int) +#6826 := (f3 f15 #6811) +#6827 := (= f1 #6826) +#6914 := (= #6517 #6826) +#6910 := (= #6826 #6517) +#6911 := [monotonicity #6900]: #6910 +#6915 := [symm #6911]: #6914 +#6908 := [hypothesis]: #6688 +#6710 := (or #6706 #6687 #6518) +#6711 := [def-axiom]: #6710 +#6909 := [unit-resolution #6711 #6892 #6908]: #6518 +#6916 := [trans #6909 #6915]: #6827 +#6829 := (f3 f15 #6813) +#6830 := (= f1 #6829) +#6924 := (not #6830) +#6925 := (iff #756 #6924) +#6922 := (iff #753 #6830) +#6920 := (iff #6830 #753) +#6918 := (= #6829 #171) +#6919 := [monotonicity #6883]: #6918 +#6921 := [monotonicity #6919]: #6920 +#6923 := [symm #6921]: #6922 +#6926 := [monotonicity #6923]: #6925 +#4044 := (or #4526 #756) +#4039 := [def-axiom]: #4044 +#6917 := [unit-resolution #4039 #6499]: #756 +#6927 := [mp #6917 #6926]: #6924 +#6828 := (not #6827) +#6848 := (or #6828 #6830 #6840) +#3952 := (or #4538 #4282) +#4007 := [def-axiom]: #3952 +#6928 := [unit-resolution #4007 #6498]: #4282 +#6853 := (or #4287 #6828 #6830 #6840) +#6824 := (+ #6823 #6819) +#6825 := (>= #6824 0::Int) +#6831 := (or #6830 #6828 #6825) +#6854 := (or #4287 #6831) +#6861 := (iff #6854 #6853) +#6856 := (or #4287 #6848) +#6859 := (iff #6856 #6853) +#6860 := [rewrite]: #6859 +#6857 := (iff #6854 #6856) +#6851 := (iff #6831 #6848) +#6845 := (or #6830 #6828 #6840) +#6849 := (iff #6845 #6848) +#6850 := [rewrite]: #6849 +#6846 := (iff #6831 #6845) +#6843 := (iff #6825 #6840) +#6832 := (+ #6819 #6823) +#6835 := (>= #6832 0::Int) +#6841 := (iff #6835 #6840) +#6842 := [rewrite]: #6841 +#6836 := (iff #6825 #6835) +#6833 := (= #6824 #6832) +#6834 := [rewrite]: #6833 +#6837 := [monotonicity #6834]: #6836 +#6844 := [trans #6837 #6842]: #6843 +#6847 := [monotonicity #6844]: #6846 +#6852 := [trans #6847 #6850]: #6851 +#6858 := [monotonicity #6852]: #6857 +#6862 := [trans #6858 #6860]: #6861 +#6855 := [quant-inst #6811 #6813]: #6854 +#6863 := [mp #6855 #6862]: #6853 +#6929 := [unit-resolution #6863 #6928]: #6848 +#6930 := [unit-resolution #6929 #6927 #6916]: #6840 +#6931 := [th-lemma arith farkas 1 1 1 -1 1 #6930 #6907 #6897 #6891 #6890]: false +#6933 := [lemma #6931]: #6932 +#7009 := [unit-resolution #6933 #7008 #7006]: #6687 +#7033 := [monotonicity #7009]: #6870 +#7031 := (= #2243 #174) +#7029 := (= #174 #2243) +#6786 := (= #6547 0::Int) +#6793 := (or #6707 #6786) #49 := (= #48 0::Int) -#382 := (or #49 #368) -#4206 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #382) -#387 := (forall (vars (?v0 S3) (?v1 S3)) #382) -#4209 := (iff #387 #4206) -#4207 := (iff #382 #382) -#4208 := [refl]: #4207 -#4210 := [quant-intro #4208]: #4209 -#1850 := (~ #387 #387) -#1881 := (~ #382 #382) -#1882 := [refl]: #1881 -#1851 := [nnf-pos #1882]: #1850 +#381 := (or #49 #367) +#4197 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #381) +#386 := (forall (vars (?v0 S3) (?v1 S3)) #381) +#4200 := (iff #386 #4197) +#4198 := (iff #381 #381) +#4199 := [refl]: #4198 +#4201 := [quant-intro #4199]: #4200 +#1841 := (~ #386 #386) +#1872 := (~ #381 #381) +#1873 := [refl]: #1872 +#1842 := [nnf-pos #1873]: #1841 #50 := (implies #47 #49) #51 := (forall (vars (?v0 S3) (?v1 S3)) #50) -#390 := (iff #51 #387) -#362 := (= 0::Int #48) -#369 := (or #368 #362) -#374 := (forall (vars (?v0 S3) (?v1 S3)) #369) -#388 := (iff #374 #387) -#385 := (iff #369 #382) -#379 := (or #368 #49) -#383 := (iff #379 #382) -#384 := [rewrite]: #383 -#380 := (iff #369 #379) -#377 := (iff #362 #49) -#378 := [rewrite]: #377 -#381 := [monotonicity #378]: #380 -#386 := [trans #381 #384]: #385 -#389 := [quant-intro #386]: #388 -#375 := (iff #51 #374) -#372 := (iff #50 #369) -#365 := (implies #354 #362) -#370 := (iff #365 #369) -#371 := [rewrite]: #370 -#366 := (iff #50 #365) -#363 := (iff #49 #362) -#364 := [rewrite]: #363 -#367 := [monotonicity #361 #364]: #366 -#373 := [trans #367 #371]: #372 -#376 := [quant-intro #373]: #375 -#391 := [trans #376 #389]: #390 -#352 := [asserted]: #51 -#392 := [mp #352 #391]: #387 -#1852 := [mp~ #392 #1851]: #387 -#4211 := [mp #1852 #4210]: #4206 -#6807 := (not #4206) -#6808 := (or #6807 #6716 #6795) -#6794 := (not #6775) -#6796 := (or #6795 #6794) -#6809 := (or #6807 #6796) -#6816 := (iff #6809 #6808) -#6811 := (or #6807 #6802) -#6814 := (iff #6811 #6808) -#6815 := [rewrite]: #6814 -#6812 := (iff #6809 #6811) -#6805 := (iff #6796 #6802) -#6799 := (or #6795 #6716) -#6803 := (iff #6799 #6802) -#6804 := [rewrite]: #6803 -#6800 := (iff #6796 #6799) -#6797 := (iff #6794 #6716) -#6798 := [monotonicity #6778]: #6797 -#6801 := [monotonicity #6798]: #6800 -#6806 := [trans #6801 #6804]: #6805 -#6813 := [monotonicity #6806]: #6812 -#6817 := [trans #6813 #6815]: #6816 -#6810 := [quant-inst #170 #2248]: #6809 -#6818 := [mp #6810 #6817]: #6808 -#7019 := [unit-resolution #6818 #4211]: #6802 -#7020 := [unit-resolution #7019 #7018]: #6795 -#7021 := (not #6795) -#7022 := (or #7021 #6773) -#7023 := [th-lemma arith triangle-eq]: #7022 -#7024 := [unit-resolution #7023 #7020]: #6773 -#7025 := (or #7021 #6819) -#7026 := [th-lemma arith triangle-eq]: #7025 -#7027 := [unit-resolution #7026 #7020]: #6819 -#6424 := (* -1::Int #2252) -#6612 := (+ #6424 #6556) -#6613 := (+ #174 #6612) -#6633 := (<= #6613 0::Int) -#6616 := (= #6613 0::Int) -#6600 := (not #6562) -#6601 := (or #6580 #6600) -#6602 := [def-axiom]: #6601 -#7028 := [unit-resolution #6602 #7016]: #6600 -#6619 := (or #6562 #6575 #6616) -#6622 := (or #4409 #6562 #6575 #6616) -#6608 := (+ #6556 #6424) -#6609 := (+ #174 #6608) -#6610 := (= #6609 0::Int) -#6611 := (or #6562 #6560 #6610) -#6623 := (or #4409 #6611) -#6630 := (iff #6623 #6622) -#6625 := (or #4409 #6619) -#6628 := (iff #6625 #6622) -#6629 := [rewrite]: #6628 -#6626 := (iff #6623 #6625) -#6620 := (iff #6611 #6619) -#6617 := (iff #6610 #6616) -#6614 := (= #6609 #6613) -#6615 := [rewrite]: #6614 -#6618 := [monotonicity #6615]: #6617 -#6621 := [monotonicity #6579 #6618]: #6620 -#6627 := [monotonicity #6621]: #6626 -#6631 := [trans #6627 #6629]: #6630 -#6624 := [quant-inst #2248]: #6623 -#6632 := [mp #6624 #6631]: #6622 -#7029 := [unit-resolution #6632 #6513]: #6619 -#7030 := [unit-resolution #7029 #7017 #7028]: #6616 -#7031 := (not #6616) -#7032 := (or #7031 #6633) -#7033 := [th-lemma arith triangle-eq]: #7032 -#7034 := [unit-resolution #7033 #7030]: #6633 -#6634 := (>= #6613 0::Int) -#7035 := (or #7031 #6634) -#7036 := [th-lemma arith triangle-eq]: #7035 -#7037 := [unit-resolution #7036 #7030]: #6634 -#7039 := [th-lemma arith eq-propagate 1 1 -1 -1 #7037 #7034 #7027 #7024]: #7038 -#7041 := [symm #7039]: #7040 -#7043 := [trans #7041 #7042]: #2858 -#7044 := [unit-resolution #6995 #7043]: false -#7045 := [lemma #7044]: #2864 -#4060 := (or #4520 #2869 #4514) -#4061 := [def-axiom]: #4060 -#7099 := [unit-resolution #4061 #7045 #7098]: #4514 -#4070 := (or #4511 #4421) -#4072 := [def-axiom]: #4070 -#7100 := [unit-resolution #4072 #7099]: #4421 -#9466 := (or #4426 #7535 #7539) -#7538 := (or #7537 #7535) -#9467 := (or #4426 #7538) -#9474 := (iff #9467 #9466) -#9469 := (or #4426 #7545) -#9472 := (iff #9469 #9466) -#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) -#9980 := [def-axiom]: #9979 -#10100 := [unit-resolution #9980 #10099 #10088]: #9967 -#10101 := (or #9952 #9968) -#6304 := (not #5892) -#9973 := (or #9952 #9968 #6304) -#9974 := [def-axiom]: #9973 -#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 -#9608 := [lemma #9590]: #9607 -#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) -#7314 := (not #7313) -#7318 := (or #7317 #7316 #7314) -#9448 := (or #4312 #7318) -#9461 := (iff #9448 #9211) -#7331 := (or #7316 #7319 #7325) -#9454 := (or #4312 #7331) -#9459 := (iff #9454 #9211) -#9460 := [rewrite]: #9459 -#9456 := (iff #9448 #9454) -#7334 := (iff #7318 #7331) -#7328 := (or #7319 #7316 #7325) -#7332 := (iff #7328 #7331) -#7333 := [rewrite]: #7332 -#7329 := (iff #7318 #7328) -#7326 := (iff #7314 #7325) -#7323 := (iff #7313 #7322) +#389 := (iff #51 #386) +#361 := (= 0::Int #48) +#368 := (or #367 #361) +#373 := (forall (vars (?v0 S3) (?v1 S3)) #368) +#387 := (iff #373 #386) +#384 := (iff #368 #381) +#378 := (or #367 #49) +#382 := (iff #378 #381) +#383 := [rewrite]: #382 +#379 := (iff #368 #378) +#376 := (iff #361 #49) +#377 := [rewrite]: #376 +#380 := [monotonicity #377]: #379 +#385 := [trans #380 #383]: #384 +#388 := [quant-intro #385]: #387 +#374 := (iff #51 #373) +#371 := (iff #50 #368) +#364 := (implies #353 #361) +#369 := (iff #364 #368) +#370 := [rewrite]: #369 +#365 := (iff #50 #364) +#362 := (iff #49 #361) +#363 := [rewrite]: #362 +#366 := [monotonicity #360 #363]: #365 +#372 := [trans #366 #370]: #371 +#375 := [quant-intro #372]: #374 +#390 := [trans #375 #388]: #389 +#351 := [asserted]: #51 +#391 := [mp #351 #390]: #386 +#1843 := [mp~ #391 #1842]: #386 +#4202 := [mp #1843 #4201]: #4197 +#6798 := (not #4197) +#6799 := (or #6798 #6707 #6786) +#6785 := (not #6766) +#6787 := (or #6786 #6785) +#6800 := (or #6798 #6787) +#6807 := (iff #6800 #6799) +#6802 := (or #6798 #6793) +#6805 := (iff #6802 #6799) +#6806 := [rewrite]: #6805 +#6803 := (iff #6800 #6802) +#6796 := (iff #6787 #6793) +#6790 := (or #6786 #6707) +#6794 := (iff #6790 #6793) +#6795 := [rewrite]: #6794 +#6791 := (iff #6787 #6790) +#6788 := (iff #6785 #6707) +#6789 := [monotonicity #6769]: #6788 +#6792 := [monotonicity #6789]: #6791 +#6797 := [trans #6792 #6795]: #6796 +#6804 := [monotonicity #6797]: #6803 +#6808 := [trans #6804 #6806]: #6807 +#6801 := [quant-inst #170 #2239]: #6800 +#6809 := [mp #6801 #6808]: #6799 +#7010 := [unit-resolution #6809 #4202]: #6793 +#7011 := [unit-resolution #7010 #7009]: #6786 +#7012 := (not #6786) +#7013 := (or #7012 #6764) +#7014 := [th-lemma arith triangle-eq]: #7013 +#7015 := [unit-resolution #7014 #7011]: #6764 +#7016 := (or #7012 #6810) +#7017 := [th-lemma arith triangle-eq]: #7016 +#7018 := [unit-resolution #7017 #7011]: #6810 +#6415 := (* -1::Int #2243) +#6603 := (+ #6415 #6547) +#6604 := (+ #174 #6603) +#6624 := (<= #6604 0::Int) +#6607 := (= #6604 0::Int) +#6591 := (not #6553) +#6592 := (or #6571 #6591) +#6593 := [def-axiom]: #6592 +#7019 := [unit-resolution #6593 #7007]: #6591 +#6610 := (or #6553 #6566 #6607) +#6613 := (or #4400 #6553 #6566 #6607) +#6599 := (+ #6547 #6415) +#6600 := (+ #174 #6599) +#6601 := (= #6600 0::Int) +#6602 := (or #6553 #6551 #6601) +#6614 := (or #4400 #6602) +#6621 := (iff #6614 #6613) +#6616 := (or #4400 #6610) +#6619 := (iff #6616 #6613) +#6620 := [rewrite]: #6619 +#6617 := (iff #6614 #6616) +#6611 := (iff #6602 #6610) +#6608 := (iff #6601 #6607) +#6605 := (= #6600 #6604) +#6606 := [rewrite]: #6605 +#6609 := [monotonicity #6606]: #6608 +#6612 := [monotonicity #6570 #6609]: #6611 +#6618 := [monotonicity #6612]: #6617 +#6622 := [trans #6618 #6620]: #6621 +#6615 := [quant-inst #2239]: #6614 +#6623 := [mp #6615 #6622]: #6613 +#7020 := [unit-resolution #6623 #6504]: #6610 +#7021 := [unit-resolution #7020 #7008 #7019]: #6607 +#7022 := (not #6607) +#7023 := (or #7022 #6624) +#7024 := [th-lemma arith triangle-eq]: #7023 +#7025 := [unit-resolution #7024 #7021]: #6624 +#6625 := (>= #6604 0::Int) +#7026 := (or #7022 #6625) +#7027 := [th-lemma arith triangle-eq]: #7026 +#7028 := [unit-resolution #7027 #7021]: #6625 +#7030 := [th-lemma arith eq-propagate 1 1 -1 -1 #7028 #7025 #7018 #7015]: #7029 +#7032 := [symm #7030]: #7031 +#7034 := [trans #7032 #7033]: #2849 +#7035 := [unit-resolution #6986 #7034]: false +#7036 := [lemma #7035]: #2855 +#4051 := (or #4511 #2860 #4505) +#4052 := [def-axiom]: #4051 +#7090 := [unit-resolution #4052 #7036 #7089]: #4505 +#4061 := (or #4502 #4412) +#4063 := [def-axiom]: #4061 +#7091 := [unit-resolution #4063 #7090]: #4412 +#9457 := (or #4417 #7526 #7530) +#7529 := (or #7528 #7526) +#9458 := (or #4417 #7529) +#9465 := (iff #9458 #9457) +#9460 := (or #4417 #7536) +#9463 := (iff #9460 #9457) +#9464 := [rewrite]: #9463 +#9461 := (iff #9458 #9460) +#7539 := (iff #7529 #7536) +#7533 := (or #7530 #7526) +#7537 := (iff #7533 #7536) +#7538 := [rewrite]: #7537 +#7534 := (iff #7529 #7533) +#7535 := [monotonicity #7532]: #7534 +#7540 := [trans #7535 #7538]: #7539 +#9462 := [monotonicity #7540]: #9461 +#9466 := [trans #9462 #9464]: #9465 +#9459 := [quant-inst #2264]: #9458 +#9467 := [mp #9459 #9466]: #9457 +#10080 := [unit-resolution #9467 #7091]: #7536 +#10081 := [unit-resolution #10080 #10067]: #7526 +#10090 := [mp #10081 #10089]: #9972 +#9969 := (not #9946) +#9970 := (or #9969 #9938 #9958) +#9971 := [def-axiom]: #9970 +#10091 := [unit-resolution #9971 #10090 #10079]: #9958 +#10092 := (or #9943 #9959) +#6295 := (not #5883) +#9964 := (or #9943 #9959 #6295) +#9965 := [def-axiom]: #9964 +#10093 := [unit-resolution #9965 #6990]: #10092 +#10094 := [unit-resolution #10093 #10091]: #9959 +#10018 := (or #9940 #10017) +#10021 := (or #6773 #9940 #10017) +#10022 := (or #6773 #10018) +#10024 := (iff #10022 #10021) +#10025 := [rewrite]: #10024 +#10023 := [quant-inst #7202 #2264]: #10022 +#10026 := [mp #10023 #10025]: #10021 +#10095 := [unit-resolution #10026 #4208]: #10018 +#10096 := [unit-resolution #10095 #10094]: #10017 +#10097 := (or #10041 #10016) +#10098 := [th-lemma arith farkas 1 1]: #10097 +#10099 := [unit-resolution #10098 #10096]: #10041 +#10100 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #10064 #10063 #10062]: false +#10102 := [lemma #10100]: #10101 +#9577 := [unit-resolution #10102 #10078 #10065 #10063]: #7530 +#9578 := (or #10066 #9572) +#9579 := [th-lemma arith triangle-eq]: #9578 +#9580 := [unit-resolution #9579 #9577]: #9572 +#9581 := [th-lemma arith farkas -1 1 1 #10078 #9580 #9571]: false +#9599 := [lemma #9581]: #9598 +#11943 := [unit-resolution #9599 #10078 #10065]: #7293 +#9470 := (or #7313 #8242) +#9468 := [def-axiom]: #9470 +#11944 := [unit-resolution #9468 #11943]: #7313 +#7316 := (not #7313) +#12694 := (or #7310 #7316) +#7306 := (+ f8 #6062) +#7307 := (<= #7306 0::Int) +#12688 := (not #7307) +#12691 := (or #12688 #6064) +#4027 := (or #4526 #1646) +#4028 := [def-axiom]: #4027 +#7821 := [unit-resolution #4028 #6499]: #1646 +#12689 := (or #12688 #1645 #6064) +#12690 := [th-lemma arith assign-bounds 1 1]: #12689 +#12692 := [unit-resolution #12690 #7821]: #12691 +#12693 := [unit-resolution #12692 #10065]: #12688 +#12656 := [unit-resolution #4008 #6498]: #4298 +#9202 := (or #4303 #7307 #7310 #7316) +#7304 := (or #7303 #7300 #7293) +#7305 := (not #7304) +#7309 := (or #7308 #7307 #7305) +#9439 := (or #4303 #7309) +#9452 := (iff #9439 #9202) +#7322 := (or #7307 #7310 #7316) +#9445 := (or #4303 #7322) +#9450 := (iff #9445 #9202) +#9451 := [rewrite]: #9450 +#9447 := (iff #9439 #9445) +#7325 := (iff #7309 #7322) +#7319 := (or #7310 #7307 #7316) +#7323 := (iff #7319 #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) -#9282 := [symm #9280]: #9281 -#11955 := [trans #9282 #11954]: #10697 -#11957 := [monotonicity #11955]: #11956 -#11958 := [symm #11957]: #10875 -#11944 := (not #10875) -#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) -#6990 := [th-lemma arith triangle-eq]: #6989 -#6991 := [unit-resolution #6990 #7123]: #3917 -#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 -#11918 := [hypothesis]: #7539 -#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 -#11112 := [lemma #11113]: #11114 -#23130 := [unit-resolution #11112 #10074]: #2275 -#4073 := (or #4511 #4505) -#4074 := [def-axiom]: #4073 -#12708 := [unit-resolution #4074 #7099]: #4505 -#5932 := (= #99 #203) -#12712 := (iff #5932 #204) -#12711 := [commutativity]: #1488 -#12709 := (iff #5932 #822) -#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) -#6731 := (or #6290 #6717) -#6733 := (iff #6731 #6730) -#6735 := (iff #6730 #6730) -#6763 := [rewrite]: #6735 -#6724 := (iff #6717 #6723) -#6721 := (iff #6683 #6718) -#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) -#6545 := (not #6476) -#7109 := (iff #6545 #6983) -#7107 := (iff #6476 #6699) -#7105 := (iff #6699 #6476) -#7103 := (= #6698 #6358) -#7104 := [monotonicity #7007]: #7103 -#7106 := [monotonicity #7104]: #7105 -#7108 := [symm #7106]: #7107 -#7110 := [monotonicity #7108]: #7109 -#7092 := (not #5932) -#7095 := [hypothesis]: #7092 -#6546 := (or #5932 #6545) -#6549 := (or #4426 #5932 #6545) -#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) -#6987 := (or #6986 #6699 #6766) -#6988 := [def-axiom]: #6987 -#7112 := [unit-resolution #6988 #7111 #7091]: #6766 -#7113 := (or #6718 #6767) -#6771 := (or #6718 #6767 #6304) -#6772 := [def-axiom]: #6771 -#7114 := [unit-resolution #6772 #6999]: #7113 -#7115 := [unit-resolution #7114 #7112]: #6767 -#7061 := (or #6088 #7060) -#7064 := (or #6782 #6088 #7060) -#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) -#5937 := (not #5934) -#5940 := (or #5932 #5937) -#5943 := (or #4401 #5932 #5937) -#5930 := (or #5929 #5927) -#5931 := (not #5930) -#5933 := (or #5932 #5931) -#5944 := (or #4401 #5933) -#5951 := (iff #5944 #5943) -#5946 := (or #4401 #5940) -#5949 := (iff #5946 #5943) -#5950 := [rewrite]: #5949 -#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 -#7127 := [th-lemma arith farkas 1 1 1 1 #7126 #7122 #7120 #7117]: false -#7128 := [lemma #7127]: #5932 -#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) -#10288 := [hypothesis]: #3445 -#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 +#7320 := (iff #7309 #7319) +#7317 := (iff #7305 #7316) +#7314 := (iff #7304 #7313) +#7315 := [rewrite]: #7314 +#7318 := [monotonicity #7315]: #7317 +#7311 := (iff #7308 #7310) +#7312 := [rewrite]: #7311 +#7321 := [monotonicity #7312 #7318]: #7320 +#7326 := [trans #7321 #7324]: #7325 +#9449 := [monotonicity #7326]: #9447 +#9453 := [trans #9449 #9451]: #9452 +#9444 := [quant-inst #6060]: #9439 +#9469 := [mp #9444 #9453]: #9202 +#12695 := [unit-resolution #9469 #12656 #12693]: #12694 +#11942 := [unit-resolution #12695 #11944]: #7310 +#11945 := [symm #11942]: #7308 +#9272 := (= #8208 #6060) +#9273 := [symm #9271]: #9272 +#11946 := [trans #9273 #11945]: #10688 +#11948 := [monotonicity #11946]: #11947 +#11949 := [symm #11948]: #10866 +#11935 := (not #10866) +#11950 := (or #11935 #10869) +#11951 := [th-lemma arith triangle-eq]: #11950 +#11952 := [unit-resolution #11951 #11949]: #10869 +#3908 := (>= #99 0::Int) +#7114 := [unit-resolution #4024 #6498]: #100 +#6980 := (or #1738 #3908) +#6981 := [th-lemma arith triangle-eq]: #6980 +#6982 := [unit-resolution #6981 #7114]: #3908 +#11972 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #6982 #11952 #11941 #10062]: false +#11977 := [lemma #11972]: #11976 +#11100 := [unit-resolution #11977 #10078 #10065]: #7530 +#11954 := (not #9572) +#11908 := [hypothesis]: #11954 +#11909 := [hypothesis]: #7530 +#11910 := [unit-resolution #9579 #11909 #11908]: false +#11911 := [lemma #11910]: #9578 +#11101 := [unit-resolution #11911 #11100]: #9572 +#11104 := [th-lemma arith farkas -1 1 1 #10078 #11101 #9571]: false +#11103 := [lemma #11104]: #11105 +#23121 := [unit-resolution #11103 #10065]: #2266 +#4064 := (or #4502 #4496) +#4065 := [def-axiom]: #4064 +#12699 := [unit-resolution #4065 #7090]: #4496 +#5923 := (= #99 #202) +#12703 := (iff #5923 #203) +#12702 := [commutativity]: #1479 +#12700 := (iff #5923 #813) +#12701 := [monotonicity #7114]: #12700 +#12704 := [trans #12701 #12702]: #12703 +#5907 := (f5 f22 f10) +#5908 := (f9 #5907) +#7050 := (<= #5908 0::Int) +#7051 := (not #7050) +#6758 := (not #6079) +#3925 := (f3 f15 f10) +#3928 := (= f1 #3925) +#6709 := (ite #6079 #5883 #3928) +#6757 := (not #6709) +#6689 := (f3 #6260 f10) +#6690 := (= f1 #6689) +#6714 := (iff #6690 #6709) +#6721 := (or #6281 #6714) +#6674 := (ite #6077 #5883 #3928) +#6708 := (iff #6690 #6674) +#6722 := (or #6281 #6708) +#6724 := (iff #6722 #6721) +#6726 := (iff #6721 #6721) +#6754 := [rewrite]: #6726 +#6715 := (iff #6708 #6714) +#6712 := (iff #6674 #6709) +#6080 := (iff #6077 #6079) +#6081 := [rewrite]: #6080 +#6713 := [monotonicity #6081]: #6712 +#6716 := [monotonicity #6713]: #6715 +#6725 := [monotonicity #6716]: #6724 +#6755 := [trans #6725 #6754]: #6724 +#6723 := [quant-inst #104 #170 #5882 #56]: #6722 +#6756 := [mp #6723 #6755]: #6721 +#7082 := [unit-resolution #6756 #4168]: #6714 +#6974 := (not #6690) +#6349 := (f3 f23 f10) +#6467 := (= f1 #6349) +#6536 := (not #6467) +#7100 := (iff #6536 #6974) +#7098 := (iff #6467 #6690) +#7096 := (iff #6690 #6467) +#7094 := (= #6689 #6349) +#7095 := [monotonicity #6998]: #7094 +#7097 := [monotonicity #7095]: #7096 +#7099 := [symm #7097]: #7098 +#7101 := [monotonicity #7099]: #7100 +#7083 := (not #5923) +#7086 := [hypothesis]: #7083 +#6537 := (or #5923 #6536) +#6540 := (or #4417 #5923 #6536) +#6535 := (or #4417 #6537) +#6542 := (iff #6535 #6540) +#6543 := [rewrite]: #6542 +#6541 := [quant-inst #56]: #6535 +#6544 := [mp #6541 #6543]: #6540 +#7092 := [unit-resolution #6544 #7091]: #6537 +#7093 := [unit-resolution #7092 #7086]: #6536 +#7102 := [mp #7093 #7101]: #6974 +#6977 := (not #6714) +#6978 := (or #6977 #6690 #6757) +#6979 := [def-axiom]: #6978 +#7103 := [unit-resolution #6979 #7102 #7082]: #6757 +#7104 := (or #6709 #6758) +#6762 := (or #6709 #6758 #6295) +#6763 := [def-axiom]: #6762 +#7105 := [unit-resolution #6763 #6990]: #7104 +#7106 := [unit-resolution #7105 #7103]: #6758 +#7052 := (or #6079 #7051) +#7055 := (or #6773 #6079 #7051) +#7056 := (or #6773 #7052) +#7058 := (iff #7056 #7055) +#7059 := [rewrite]: #7058 +#7057 := [quant-inst #170 #56]: #7056 +#7060 := [mp #7057 #7059]: #7055 +#7107 := [unit-resolution #7060 #4208]: #7052 +#7108 := [unit-resolution #7107 #7106]: #7051 +#5915 := (* -1::Int #5908) +#5916 := (+ #1444 #5915) +#5917 := (+ #99 #5916) +#5918 := (<= #5917 0::Int) +#5945 := (not #5918) +#5919 := (+ f8 #5915) +#5920 := (<= #5919 0::Int) +#5925 := (or #5918 #5920) +#5928 := (not #5925) +#5931 := (or #5923 #5928) +#5934 := (or #4392 #5923 #5928) +#5921 := (or #5920 #5918) +#5922 := (not #5921) +#5924 := (or #5923 #5922) +#5935 := (or #4392 #5924) +#5942 := (iff #5935 #5934) +#5937 := (or #4392 #5931) +#5940 := (iff #5937 #5934) +#5941 := [rewrite]: #5940 +#5938 := (iff #5935 #5937) +#5932 := (iff #5924 #5931) +#5929 := (iff #5922 #5928) +#5926 := (iff #5921 #5925) +#5927 := [rewrite]: #5926 +#5930 := [monotonicity #5927]: #5929 +#5933 := [monotonicity #5930]: #5932 +#5939 := [monotonicity #5933]: #5938 +#5943 := [trans #5939 #5941]: #5942 +#5936 := [quant-inst #56]: #5935 +#5944 := [mp #5936 #5943]: #5934 +#7109 := [unit-resolution #5944 #6500]: #5931 +#7110 := [unit-resolution #7109 #7086]: #5928 +#5946 := (or #5925 #5945) +#5947 := [def-axiom]: #5946 +#7111 := [unit-resolution #5947 #7110]: #5945 +#6118 := (>= #174 0::Int) +#6121 := (or #4270 #6118) +#6122 := [quant-inst #170]: #6121 +#7113 := [unit-resolution #6122 #7112]: #6118 +#3911 := (<= #99 0::Int) +#7115 := (or #1738 #3911) +#7116 := [th-lemma arith triangle-eq]: #7115 +#7117 := [unit-resolution #7116 #7114]: #3911 +#7118 := [th-lemma arith farkas 1 1 1 1 #7117 #7113 #7111 #7108]: false +#7119 := [lemma #7118]: #5923 +#12705 := [mp #7119 #12704]: #203 +#4074 := (or #4499 #1481 #4493) +#4060 := [def-axiom]: #4074 +#12706 := [unit-resolution #4060 #12705 #12699]: #4493 +#4083 := (or #4490 #4484) +#4067 := [def-axiom]: #4083 +#12707 := [unit-resolution #4067 #12706]: #4484 +#4080 := (or #4487 #2267 #4481) +#4081 := [def-axiom]: #4080 +#12708 := [unit-resolution #4081 #12707]: #4484 +#23122 := [unit-resolution #12708 #23121]: #4481 +#4075 := (or #4478 #4472) +#4077 := [def-axiom]: #4075 +#23130 := [unit-resolution #4077 #23122]: #4472 +#12711 := (or #4475 #4469) +#10279 := [hypothesis]: #3436 +#3964 := (or #3431 #2290) +#3965 := [def-axiom]: #3964 +#9749 := [unit-resolution #3965 #10279]: #2290 +#10370 := (or #3431 #2289) +#10555 := (f5 #7202 ?v1!16) +#10556 := (f9 #10555) +#10573 := (* -1::Int #10556) +#8682 := (f5 f22 ?v1!16) +#8683 := (f9 #8682) +#10576 := (+ #8683 #10573) +#10578 := (>= #10576 0::Int) +#10572 := (= #8683 #10556) +#10583 := (= #10556 #8683) +#10581 := (= #10555 #8682) +#10582 := [monotonicity #7781]: #10581 +#10584 := [monotonicity #10582]: #10583 +#10585 := [symm #10584]: #10572 +#10586 := (not #10572) +#10587 := (or #10586 #10578) +#10588 := [th-lemma arith triangle-eq]: #10587 +#10589 := [unit-resolution #10588 #10585]: #10578 +#5998 := (f24 f22) +#6039 := (* -1::Int #5998) +#6408 := (+ #174 #6039) +#6409 := (>= #6408 0::Int) +#4053 := (or #4514 #4403) +#4054 := [def-axiom]: #4053 +#8184 := [unit-resolution #4054 #7088]: #4403 +#6413 := (or #4408 #6409) +#6414 := [quant-inst #170]: #6413 +#8185 := [unit-resolution #6414 #8184]: #6409 +#4107 := (not #2879) +#4108 := (or #3431 #4107) +#4109 := [def-axiom]: #4108 +#10282 := [unit-resolution #4109 #10279]: #4107 +#10214 := (+ #2281 #6039) +#10215 := (<= #10214 0::Int) +#10203 := (= #2281 #5998) +#10471 := (= ?v0!17 f22) +#8508 := (= ?v0!17 #7202) +#8501 := (f3 f15 ?v0!17) +#8502 := (= f1 #8501) +#8511 := (ite #8508 #5883 #8502) +#8505 := (f3 #8433 ?v0!17) +#8506 := (= f1 #8505) +#8514 := (iff #8506 #8511) +#9702 := (or #6281 #8514) +#8503 := (= #7202 ?v0!17) +#8504 := (ite #8503 #5883 #8502) +#8507 := (iff #8506 #8504) +#9697 := (or #6281 #8507) +#9704 := (iff #9697 #9702) +#9706 := (iff #9702 #9702) +#9707 := [rewrite]: #9706 +#8515 := (iff #8507 #8514) +#8512 := (iff #8504 #8511) +#8509 := (iff #8503 #8508) +#8510 := [rewrite]: #8509 +#8513 := [monotonicity #8510]: #8512 +#8516 := [monotonicity #8513]: #8515 +#9705 := [monotonicity #8516]: #9704 +#9713 := [trans #9705 #9707]: #9704 +#9703 := [quant-inst #104 #7202 #5882 #2280]: #9697 +#9714 := [mp #9703 #9713]: #9702 +#10283 := [unit-resolution #9714 #4168]: #8514 +#10312 := (= #2286 #8505) +#10285 := (= #8505 #2286) +#10222 := [monotonicity #9277]: #10285 +#10313 := [symm #10222]: #10312 +#4122 := (or #3431 #2287) +#3963 := [def-axiom]: #4122 +#10284 := [unit-resolution #3963 #10279]: #2287 +#10314 := [trans #10284 #10313]: #8506 +#9723 := (not #8506) +#9726 := (not #8514) +#9729 := (or #9726 #9723 #8511) +#9730 := [def-axiom]: #9729 +#10315 := [unit-resolution #9730 #10314 #10283]: #8511 +#9722 := (not #8502) +#8476 := (f13 f14 ?v0!17) +#8558 := (* -1::Int #8476) +#7504 := (f13 f14 #7202) +#10477 := (+ #7504 #8558) +#10478 := (>= #10477 0::Int) +#10603 := (not #10478) +#8437 := (= ?v1!16 #7202) +#9607 := (not #8437) +#8429 := (f3 f15 ?v1!16) +#8430 := (= f1 #8429) +#8440 := (ite #8437 #5883 #8430) +#9606 := (not #8440) +#8434 := (f3 #8433 ?v1!16) +#8435 := (= f1 #8434) +#8443 := (iff #8435 #8440) +#9575 := (or #6281 #8443) +#8431 := (= #7202 ?v1!16) +#8432 := (ite #8431 #5883 #8430) +#8436 := (iff #8435 #8432) +#9576 := (or #6281 #8436) +#9601 := (iff #9576 #9575) +#9597 := (iff #9575 #9575) +#9603 := [rewrite]: #9597 +#8444 := (iff #8436 #8443) +#8441 := (iff #8432 #8440) +#8438 := (iff #8431 #8437) +#8439 := [rewrite]: #8438 +#8442 := [monotonicity #8439]: #8441 +#8445 := [monotonicity #8442]: #8444 +#9602 := [monotonicity #8445]: #9601 +#9604 := [trans #9602 #9603]: #9601 +#9600 := [quant-inst #104 #7202 #5882 #2279]: #9576 +#9605 := [mp #9600 #9604]: #9575 +#10316 := [unit-resolution #9605 #4168]: #8443 +#9639 := (not #8435) +#10324 := (iff #2290 #9639) +#10322 := (iff #2289 #8435) +#10320 := (iff #8435 #2289) +#10318 := (= #8434 #2288) +#10319 := [monotonicity #9277]: #10318 +#10321 := [monotonicity #10319]: #10320 +#10323 := [symm #10321]: #10322 +#10325 := [monotonicity #10323]: #10324 +#10317 := [hypothesis]: #2290 +#10326 := [mp #10317 #10325]: #9639 +#9631 := (not #8443) +#9632 := (or #9631 #8435 #9606) +#9638 := [def-axiom]: #9632 +#10327 := [unit-resolution #9638 #10326 #10316]: #9606 +#10328 := (or #8440 #9607) +#9627 := (or #8440 #9607 #6295) +#9622 := [def-axiom]: #9627 +#10329 := [unit-resolution #9622 #6990]: #10328 +#10330 := [unit-resolution #10329 #10327]: #9607 +#8655 := (f13 f14 ?v1!16) +#8666 := (* -1::Int #8655) +#8914 := (+ #174 #8666) +#8915 := (<= #8914 0::Int) +#9628 := (not #8430) +#9629 := (or #8440 #8437 #9628) +#9630 := [def-axiom]: #9629 +#10299 := [unit-resolution #9630 #10330 #10327]: #9628 +#8920 := (or #8430 #8915) +#4045 := (or #4526 #4377) +#4031 := [def-axiom]: #4045 +#10304 := [unit-resolution #4031 #6499]: #4377 +#9975 := (or #4382 #8430 #8915) +#8903 := (+ #8655 #1444) +#8904 := (>= #8903 0::Int) +#8907 := (or #8430 #8904) +#9976 := (or #4382 #8907) +#10011 := (iff #9976 #9975) +#10007 := (or #4382 #8920) +#10010 := (iff #10007 #9975) +#10005 := [rewrite]: #10010 +#10008 := (iff #9976 #10007) +#8921 := (iff #8907 #8920) +#8918 := (iff #8904 #8915) +#8908 := (+ #1444 #8655) +#8911 := (>= #8908 0::Int) +#8916 := (iff #8911 #8915) +#8917 := [rewrite]: #8916 +#8912 := (iff #8904 #8911) +#8909 := (= #8903 #8908) +#8910 := [rewrite]: #8909 +#8913 := [monotonicity #8910]: #8912 +#8919 := [trans #8913 #8917]: #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) +#10009 := [monotonicity #8922]: #10008 +#10012 := [trans #10009 #10005]: #10011 +#10006 := [quant-inst #2279]: #9976 +#10013 := [mp #10006 #10012]: #9975 +#10298 := [unit-resolution #10013 #10304]: #8920 +#10305 := [unit-resolution #10298 #10299]: #8915 +#10577 := (not #8915) +#10624 := (or #10603 #10577 #2879 #8437) +#8708 := (+ #2877 #8683) +#8709 := (+ #174 #8708) +#8712 := (= #8709 0::Int) +#10609 := (not #8712) +#9826 := (<= #8709 0::Int) +#10602 := (not #9826) +#10590 := [hypothesis]: #9607 +#10592 := [hypothesis]: #4107 +#10579 := [hypothesis]: #10478 +#10604 := (or #10602 #2879 #10603 #8437) +#10580 := [hypothesis]: #9826 +#10557 := (<= #10556 0::Int) +#10558 := (not #10557) +#10562 := (or #6773 #8437 #10558) +#10559 := (or #8437 #10558) +#10563 := (or #6773 #10559) +#10565 := (iff #10563 #10562) +#10566 := [rewrite]: #10565 +#10564 := [quant-inst #7202 #2279]: #10563 +#10567 := [mp #10564 #10566]: #10562 +#10591 := [unit-resolution #10567 #4208 #10590]: #10558 +#8559 := (+ #2281 #8558) +#8560 := (<= #8559 0::Int) +#9739 := (or #4408 #8560) +#8548 := (+ #8476 #2282) +#8549 := (>= #8548 0::Int) +#9742 := (or #4408 #8549) +#9757 := (iff #9742 #9739) +#9759 := (iff #9739 #9739) +#9760 := [rewrite]: #9759 +#8563 := (iff #8549 #8560) +#8552 := (+ #2282 #8476) +#8555 := (>= #8552 0::Int) +#8561 := (iff #8555 #8560) +#8562 := [rewrite]: #8561 +#8556 := (iff #8549 #8555) +#8553 := (= #8548 #8552) +#8554 := [rewrite]: #8553 +#8557 := [monotonicity #8554]: #8556 +#8564 := [trans #8557 #8562]: #8563 +#9758 := [monotonicity #8564]: #9757 +#9761 := [trans #9758 #9760]: #9757 +#9756 := [quant-inst #2280]: #9742 +#9762 := [mp #9756 #9761]: #9739 +#10593 := [unit-resolution #9762 #8184]: #8560 +#7520 := (* -1::Int #7504) +#8414 := (+ #174 #7520) +#8420 := (>= #8414 0::Int) +#7327 := (= #174 #7504) +#10594 := (= #7504 #174) +#10595 := [monotonicity #7781]: #10594 +#10596 := [symm #10595]: #7327 +#10597 := (not #7327) +#10598 := (or #10597 #8420) +#10599 := [th-lemma arith triangle-eq]: #10598 +#10600 := [unit-resolution #10599 #10596]: #8420 +#10601 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10600 #10593 #10592 #10591 #10589 #10580 #10579]: false +#10605 := [lemma #10601]: #10604 +#10608 := [unit-resolution #10605 #10579 #10592 #10590]: #10602 +#10610 := (or #10609 #9826) +#10611 := [th-lemma arith triangle-eq]: #10610 +#10612 := [unit-resolution #10611 #10608]: #10609 +#8687 := (* -1::Int #8683) +#8691 := (+ f8 #8687) +#8692 := (<= #8691 0::Int) +#9840 := (not #8692) +#8701 := (+ #8666 #8683) +#8702 := (+ #174 #8701) +#8703 := (>= #8702 0::Int) +#8738 := (or #8692 #8703) +#8741 := (not #8738) +#8735 := (= #2283 #8655) +#10614 := (not #8735) +#8667 := (+ #2283 #8666) +#9839 := (>= #8667 0::Int) +#10575 := (not #9839) +#10570 := [hypothesis]: #8915 +#10606 := (or #10575 #2879 #10577 #10603) +#10571 := [hypothesis]: #9839 +#10574 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10600 #10593 #10592 #10571 #10570 #10579]: false +#10607 := [lemma #10574]: #10606 +#10613 := [unit-resolution #10607 #10579 #10570 #10592]: #10575 +#10615 := (or #10614 #9839) +#10616 := [th-lemma arith triangle-eq]: #10615 +#10617 := [unit-resolution #10616 #10613]: #10614 +#8744 := (or #8735 #8741) +#9828 := (or #4392 #8735 #8741) +#8688 := (+ #1444 #8687) +#8689 := (+ #8655 #8688) +#8690 := (<= #8689 0::Int) +#8731 := (or #8692 #8690) +#8732 := (not #8731) +#8733 := (= #8655 #2283) +#8734 := (or #8733 #8732) +#9829 := (or #4392 #8734) +#9836 := (iff #9829 #9828) +#9830 := (or #4392 #8744) +#9833 := (iff #9830 #9828) +#9834 := [rewrite]: #9833 +#9831 := (iff #9829 #9830) +#8745 := (iff #8734 #8744) +#8742 := (iff #8732 #8741) +#8739 := (iff #8731 #8738) +#8706 := (iff #8690 #8703) +#8694 := (+ #8655 #8687) +#8695 := (+ #1444 #8694) +#8698 := (<= #8695 0::Int) +#8704 := (iff #8698 #8703) +#8705 := [rewrite]: #8704 +#8699 := (iff #8690 #8698) +#8696 := (= #8689 #8695) +#8697 := [rewrite]: #8696 +#8700 := [monotonicity #8697]: #8699 +#8707 := [trans #8700 #8705]: #8706 +#8740 := [monotonicity #8707]: #8739 +#8743 := [monotonicity #8740]: #8742 +#8736 := (iff #8733 #8735) +#8737 := [rewrite]: #8736 +#8746 := [monotonicity #8737 #8743]: #8745 +#9832 := [monotonicity #8746]: #9831 +#9837 := [trans #9832 #9834]: #9836 +#9808 := [quant-inst #2279]: #9829 +#9838 := [mp #9808 #9837]: #9828 +#10618 := [unit-resolution #9838 #6500]: #8744 +#10619 := [unit-resolution #10618 #10617]: #8741 +#9835 := (or #8738 #9840) +#9841 := [def-axiom]: #9835 +#10620 := [unit-resolution #9841 #10619]: #9840 +#9842 := (not #8703) +#9843 := (or #8738 #9842) +#9844 := [def-axiom]: #9843 +#10621 := [unit-resolution #9844 #10619]: #9842 +#8715 := (or #8692 #8703 #8712) +#9814 := (or #4400 #8692 #8703 #8712) +#8684 := (+ #8683 #2877) +#8685 := (+ #174 #8684) +#8686 := (= #8685 0::Int) +#8693 := (or #8692 #8690 #8686) +#9815 := (or #4400 #8693) +#9821 := (iff #9815 #9814) +#9817 := (or #4400 #8715) +#9819 := (iff #9817 #9814) +#9820 := [rewrite]: #9819 +#9812 := (iff #9815 #9817) +#8716 := (iff #8693 #8715) +#8713 := (iff #8686 #8712) +#8710 := (= #8685 #8709) +#8711 := [rewrite]: #8710 +#8714 := [monotonicity #8711]: #8713 +#8717 := [monotonicity #8707 #8714]: #8716 +#9818 := [monotonicity #8717]: #9812 +#9822 := [trans #9818 #9820]: #9821 +#9816 := [quant-inst #2279]: #9815 +#9825 := [mp #9816 #9822]: #9814 +#10622 := [unit-resolution #9825 #6504]: #8715 +#10623 := [unit-resolution #10622 #10621 #10620 #10612]: false +#10625 := [lemma #10623]: #10624 +#10306 := [unit-resolution #10625 #10305 #10282 #10330]: #10603 +#10301 := (or #9722 #10478) +#10286 := [hypothesis]: #10603 +#10288 := [hypothesis]: #8502 +#7506 := (f3 f15 #7202) +#7507 := (= f1 #7506) +#10294 := (not #7507) +#10295 := (iff #756 #10294) +#10287 := (iff #753 #7507) +#10291 := (iff #7507 #753) +#10289 := (= #7506 #171) +#10290 := [monotonicity #7781]: #10289 +#10292 := [monotonicity #10290]: #10291 +#10293 := [symm #10292]: #10287 +#10296 := [monotonicity #10293]: #10295 +#10297 := [mp #6917 #10296]: #10294 +#10224 := (or #4287 #7507 #9722 #10478) +#10485 := (or #7507 #9722 #10478) +#10230 := (or #4287 #10485) +#10232 := (iff #10230 #10224) +#10233 := [rewrite]: #10232 +#10231 := [quant-inst #2280 #7202]: #10230 +#10234 := [mp #10231 #10233]: #10224 +#10300 := [unit-resolution #10234 #6928 #10297 #10288 #10286]: false +#10302 := [lemma #10300]: #10301 +#10307 := [unit-resolution #10302 #10306]: #9722 +#9715 := (not #8511) +#9718 := (or #9715 #8508 #8502) +#9719 := [def-axiom]: #9718 +#10308 := [unit-resolution #9719 #10307 #10315]: #8508 +#10309 := [trans #10308 #7781]: #10471 +#10310 := [monotonicity #10309]: #10203 +#10337 := (not #10203) +#10338 := (or #10337 #10215) +#10336 := [th-lemma arith triangle-eq]: #10338 +#10339 := [unit-resolution #10336 #10310]: #10215 +#10341 := (not #6409) +#10340 := (not #10215) +#10346 := (or #10575 #10340 #2879 #10577 #10341) +#10347 := [th-lemma arith assign-bounds -1 1 -1 1]: #10346 +#10345 := [unit-resolution #10347 #10282 #8185 #10305 #10339]: #10575 +#10348 := [unit-resolution #10616 #10345]: #10614 +#10349 := [unit-resolution #10618 #10348]: #8741 +#10174 := (or #8738 #8712) +#10170 := [hypothesis]: #10609 +#10171 := [hypothesis]: #8741 +#10172 := [unit-resolution #9841 #10171]: #9840 +#10167 := [unit-resolution #9844 #10171]: #9842 +#10173 := [unit-resolution #10622 #10167 #10172 #10170]: false +#10175 := [lemma #10173]: #10174 +#10350 := [unit-resolution #10175 #10349]: #8712 +#10367 := [unit-resolution #10611 #10350]: #9826 +#10368 := [unit-resolution #10567 #4208 #10330]: #10558 +#10369 := [th-lemma arith farkas 1 1 1 1 1 1 #10368 #10367 #10339 #10282 #8185 #10589]: false +#10371 := [lemma #10369]: #10370 +#9750 := [unit-resolution #10371 #9749 #10279]: false +#9751 := [lemma #9750]: #3431 +#4097 := (or #4475 #3436 #4469) +#4084 := [def-axiom]: #4097 +#12712 := [unit-resolution #4084 #9751]: #12711 +#23123 := [unit-resolution #12712 #23130]: #4469 +#3991 := (or #4466 #4460) +#3999 := [def-axiom]: #3991 +#23124 := [unit-resolution #3999 #23123]: #4460 +#23125 := (or #4463 #4457) +#14662 := (f5 f22 ?v0!19) +#14663 := (f9 #14662) +#14458 := (f13 f14 ?v0!19) +#14594 := (* -1::Int #14458) +#14710 := (+ #14594 #14663) +#14711 := (+ #174 #14710) +#14712 := (>= #14711 0::Int) +#14951 := (not #14712) +#14666 := (* -1::Int #14663) +#15450 := (+ #2313 #14666) +#15451 := (>= #15450 0::Int) +#15449 := (= #2313 #14663) +#15659 := (= #2312 #14662) +#15686 := (= ?v1!18 f22) +#13656 := (= ?v1!18 #7202) +#13649 := (f3 f15 ?v1!18) +#13650 := (= f1 #13649) +#13793 := (not #13650) +#13789 := (f13 f14 ?v1!18) +#14914 := (+ #13789 #14594) +#14915 := (+ #2313 #14914) +#14910 := (>= #14915 0::Int) +#15610 := (not #14910) +#14595 := (+ #2308 #14594) +#14596 := (<= #14595 0::Int) +#14809 := (or #4408 #14596) +#14561 := (+ #14458 #2309) +#14588 := (>= #14561 0::Int) +#14810 := (or #4408 #14588) +#14812 := (iff #14810 #14809) +#14814 := (iff #14809 #14809) +#14815 := [rewrite]: #14814 +#14613 := (iff #14588 #14596) +#14589 := (+ #2309 #14458) +#14592 := (>= #14589 0::Int) +#14597 := (iff #14592 #14596) +#14612 := [rewrite]: #14597 +#14587 := (iff #14588 #14592) +#14590 := (= #14561 #14589) +#14591 := [rewrite]: #14590 +#14593 := [monotonicity #14591]: #14587 +#14614 := [trans #14593 #14612]: #14613 +#14813 := [monotonicity #14614]: #14812 +#14763 := [trans #14813 #14815]: #14812 +#14811 := [quant-inst #2307]: #14810 +#14882 := [mp #14811 #14763]: #14809 +#15599 := [unit-resolution #14882 #8184]: #14596 +#4113 := (not #2906) +#15600 := [hypothesis]: #3482 +#3942 := (or #3477 #4113) +#3944 := [def-axiom]: #3942 +#15598 := [unit-resolution #3944 #15600]: #4113 +#13806 := (* -1::Int #13789) +#13807 := (+ #2310 #13806) +#13535 := (>= #13807 0::Int) +#13875 := (= #2310 #13789) +#4112 := (or #3477 #2321) +#4106 := [def-axiom]: #4112 +#15601 := [unit-resolution #4106 #15600]: #2321 +#13767 := (or #4417 #3462 #13875) +#13873 := (= #13789 #2310) +#13743 := (or #13873 #3462) +#13768 := (or #4417 #13743) +#13790 := (iff #13768 #13767) +#13741 := (or #3462 #13875) +#13782 := (or #4417 #13741) +#13792 := (iff #13782 #13767) +#13784 := [rewrite]: #13792 +#13787 := (iff #13768 #13782) +#13749 := (iff #13743 #13741) +#13744 := (or #13875 #3462) +#13747 := (iff #13744 #13741) +#13748 := [rewrite]: #13747 +#13745 := (iff #13743 #13744) +#13876 := (iff #13873 #13875) +#13877 := [rewrite]: #13876 +#13746 := [monotonicity #13877]: #13745 +#13750 := [trans #13746 #13748]: #13749 +#13791 := [monotonicity #13750]: #13787 +#13794 := [trans #13791 #13784]: #13790 +#13786 := [quant-inst #2306]: #13768 +#13795 := [mp #13786 #13794]: #13767 +#15606 := [unit-resolution #13795 #7091 #15601]: #13875 +#15607 := (not #13875) +#15608 := (or #15607 #13535) +#15592 := [th-lemma arith triangle-eq]: #15608 +#15609 := [unit-resolution #15592 #15606]: #13535 +#15605 := (not #14596) +#15602 := (not #13535) +#15611 := (or #15610 #15602 #15605 #2906) +#15613 := [th-lemma arith assign-bounds 1 -1 1]: #15611 +#15614 := [unit-resolution #15613 #15609 #15598 #15599]: #15610 +#15619 := (or #13793 #14910) +#4105 := (or #3477 #2319) +#4111 := [def-axiom]: #4105 +#15617 := [unit-resolution #4111 #15600]: #2319 +#15618 := [unit-resolution #4006 #6498]: #4273 +#13302 := (or #4278 #2318 #13793 #14910) +#14916 := (or #13793 #2318 #14910) +#13531 := (or #4278 #14916) +#15117 := (iff #13531 #13302) +#14917 := (or #2318 #13793 #14910) +#13537 := (or #4278 #14917) +#15115 := (iff #13537 #13302) +#15116 := [rewrite]: #15115 +#13639 := (iff #13531 #13537) +#14918 := (iff #14916 #14917) +#14919 := [rewrite]: #14918 +#15114 := [monotonicity #14919]: #13639 +#15118 := [trans #15114 #15116]: #15117 +#13534 := [quant-inst #2307 #2306]: #13531 +#15119 := [mp #13534 #15118]: #13302 +#15612 := [unit-resolution #15119 #15618 #15617]: #15619 +#15620 := [unit-resolution #15612 #15614]: #13793 +#13659 := (ite #13656 #5883 #13650) +#13653 := (f3 #8433 ?v1!18) +#13654 := (= f1 #13653) +#13662 := (iff #13654 #13659) +#15003 := (or #6281 #13662) +#13651 := (= #7202 ?v1!18) +#13652 := (ite #13651 #5883 #13650) +#13655 := (iff #13654 #13652) +#15008 := (or #6281 #13655) +#14881 := (iff #15008 #15003) +#15034 := (iff #15003 #15003) +#15035 := [rewrite]: #15034 +#13663 := (iff #13655 #13662) +#13660 := (iff #13652 #13659) +#13657 := (iff #13651 #13656) +#13658 := [rewrite]: #13657 +#13661 := [monotonicity #13658]: #13660 +#13664 := [monotonicity #13661]: #13663 +#15010 := [monotonicity #13664]: #14881 +#15051 := [trans #15010 #15035]: #14881 +#15009 := [quant-inst #104 #7202 #5882 #2306]: #15008 +#14880 := [mp #15009 #15051]: #15003 +#15621 := [unit-resolution #14880 #4168]: #13662 +#15681 := (= #2320 #13653) +#15615 := (= #13653 #2320) +#15616 := [monotonicity #9277]: #15615 +#15683 := [symm #15616]: #15681 +#15684 := [trans #15601 #15683]: #13654 +#13228 := (not #13654) +#12821 := (not #13662) +#12779 := (or #12821 #13228 #13659) +#13241 := [def-axiom]: #12779 +#15685 := [unit-resolution #13241 #15684 #15621]: #13659 +#15052 := (not #13659) +#15050 := (or #15052 #13656 #13650) +#15058 := [def-axiom]: #15050 +#15679 := [unit-resolution #15058 #15685 #15620]: #13656 +#15658 := [trans #15679 #7781]: #15686 +#15657 := [monotonicity #15658]: #15659 +#15661 := [monotonicity #15657]: #15449 +#15663 := (not #15449) +#15664 := (or #15663 #15451) +#15665 := [th-lemma arith triangle-eq]: #15664 +#15660 := [unit-resolution #15665 #15661]: #15451 +#15229 := (+ #2310 #6039) +#15231 := (>= #15229 0::Int) +#15441 := (= #2310 #5998) +#15752 := [monotonicity #15658]: #15441 +#15662 := (not #15441) +#15758 := (or #15662 #15231) +#15759 := [th-lemma arith triangle-eq]: #15758 +#15760 := [unit-resolution #15759 #15752]: #15231 +#6665 := (<= #6408 0::Int) +#5999 := (= #174 #5998) +#6538 := (f3 f23 f22) +#6539 := (= f1 #6538) +#8175 := (= #5882 #6538) +#8173 := (= #6538 #5882) +#8174 := [monotonicity #6989]: #8173 +#8176 := [symm #8174]: #8175 +#8177 := [trans #6990 #8176]: #6539 +#6545 := (not #6539) +#6597 := (or #5999 #6545) +#6678 := (or #4417 #5999 #6545) +#6679 := (or #4417 #6597) +#6681 := (iff #6679 #6678) +#6682 := [rewrite]: #6681 +#6680 := [quant-inst #170]: #6679 +#6683 := [mp #6680 #6682]: #6678 +#8178 := [unit-resolution #6683 #7091]: #6597 +#8179 := [unit-resolution #8178 #8177]: #5999 +#8180 := (not #5999) +#8181 := (or #8180 #6665) +#8182 := [th-lemma arith triangle-eq]: #8181 +#8183 := [unit-resolution #8182 #8179]: #6665 +#16330 := (not #15451) +#12643 := (not #6665) +#15761 := (not #15231) +#15757 := (or #14951 #15605 #2906 #15761 #12643 #16330) +#15765 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15757 +#15766 := [unit-resolution #15765 #15599 #8183 #15760 #15598 #15660]: #14951 +#14670 := (+ f8 #14666) +#14722 := (<= #14670 0::Int) +#15005 := (not #14722) +#16331 := (or #15005 #16330 #2318) +#16327 := [hypothesis]: #2319 +#16322 := [hypothesis]: #14722 +#16328 := [hypothesis]: #15451 +#16329 := [th-lemma arith farkas 1 -1 1 #16328 #16322 #16327]: false +#16332 := [lemma #16329]: #16331 +#15767 := [unit-resolution #16332 #15660 #15617]: #15005 +#14716 := (+ #2309 #14663) +#14717 := (+ #174 #14716) +#14734 := (= #14717 0::Int) +#15802 := (not #14734) +#14848 := (>= #14717 0::Int) +#15763 := (not #14848) +#15784 := (or #15763 #2906 #15761 #12643 #16330) +#15796 := [th-lemma arith assign-bounds 1 1 -1 1]: #15784 +#15797 := [unit-resolution #15796 #15760 #8183 #15598 #15660]: #15763 +#15803 := (or #15802 #14848) +#15804 := [th-lemma arith triangle-eq]: #15803 +#15838 := [unit-resolution #15804 #15797]: #15802 +#14759 := (or #14712 #14722 #14734) +#14883 := (or #4400 #14712 #14722 #14734) +#14664 := (+ #14663 #2309) +#14665 := (+ #174 #14664) +#14660 := (= #14665 0::Int) +#14667 := (+ #1444 #14666) +#14668 := (+ #14458 #14667) +#14669 := (<= #14668 0::Int) +#14723 := (or #14722 #14669 #14660) +#14884 := (or #4400 #14723) +#14851 := (iff #14884 #14883) +#14886 := (or #4400 #14759) +#14849 := (iff #14886 #14883) +#14850 := [rewrite]: #14849 +#14912 := (iff #14884 #14886) +#14761 := (iff #14723 #14759) +#14756 := (or #14722 #14712 #14734) +#14754 := (iff #14756 #14759) +#14760 := [rewrite]: #14754 +#14757 := (iff #14723 #14756) +#14735 := (iff #14660 #14734) +#14718 := (= #14665 #14717) +#14719 := [rewrite]: #14718 +#14755 := [monotonicity #14719]: #14735 +#14709 := (iff #14669 #14712) +#14724 := (+ #14458 #14666) +#14725 := (+ #1444 #14724) +#14728 := (<= #14725 0::Int) +#14713 := (iff #14728 #14712) +#14714 := [rewrite]: #14713 +#14729 := (iff #14669 #14728) +#14726 := (= #14668 #14725) +#14727 := [rewrite]: #14726 +#14730 := [monotonicity #14727]: #14729 +#14715 := [trans #14730 #14714]: #14709 +#14758 := [monotonicity #14715 #14755]: #14757 +#14762 := [trans #14758 #14760]: #14761 +#14913 := [monotonicity #14762]: #14912 +#14911 := [trans #14913 #14850]: #14851 +#14885 := [quant-inst #2307]: #14884 +#14852 := [mp #14885 #14911]: #14883 +#15836 := [unit-resolution #14852 #6504]: #14759 +#15837 := [unit-resolution #15836 #15838 #15767 #15766]: false +#15833 := [lemma #15837]: #3477 +#3980 := (or #4463 #3482 #4457) +#3995 := [def-axiom]: #3980 +#23140 := [unit-resolution #3995 #15833]: #23125 +#23141 := [unit-resolution #23140 #23124]: #4457 +#4099 := (or #4454 #2351) +#4101 := [def-axiom]: #4099 +#23142 := [unit-resolution #4101 #23141]: #2351 +#23143 := (= #9072 #6061) +#23144 := [monotonicity #9273]: #23143 +#23146 := [symm #23144]: #9852 +#23147 := [unit-resolution #11940 #23146]: #9448 +#9809 := (<= #9446 0::Int) +#23139 := (or #11936 #9809) +#23145 := [th-lemma arith triangle-eq]: #23139 +#23148 := [unit-resolution #23145 #23146]: #9809 +#23149 := (not #9809) +#23155 := (or #10869 #23149) +#7349 := (>= #6061 0::Int) +#7287 := (not #7349) +#7288 := [hypothesis]: #7287 +#7969 := (or #4270 #7349) +#7970 := [quant-inst #6060]: #7969 +#7475 := [unit-resolution #7970 #7112 #7288]: false +#7479 := [lemma #7475]: #7349 +#7044 := (not #3911) +#23150 := (or #10869 #7044 #7287 #23149) +#23152 := [th-lemma arith assign-bounds -1 1 -1]: #23150 +#23156 := [unit-resolution #23152 #7479 #7117]: #23155 +#23154 := [unit-resolution #23156 #23148]: #10869 +#3986 := (or #4454 #4446) +#3987 := [def-axiom]: #3986 +#23157 := [unit-resolution #3987 #23141]: #4446 +#24096 := (or #14174 #4451) +#8769 := (f24 #7202) +#9535 := (* -1::Int #8769) +#14029 := (+ #2338 #9535) +#14217 := (<= #14029 0::Int) +#10155 := (f3 f23 #7202) +#10156 := (= f1 #10155) +#11801 := (= #5882 #10155) +#11794 := (= #10155 #5882) +#11800 := [monotonicity #6989 #7781]: #11794 +#11802 := [symm #11800]: #11801 +#11803 := [trans #6990 #11802]: #10156 +#14203 := (f9 #14202) +#14229 := (* -1::Int #14203) +#14230 := (+ #9535 #14229) +#14231 := (+ #2338 #14230) +#14232 := (= #14231 0::Int) +#15147 := (>= #14231 0::Int) +#14148 := (+ #2339 #14123) +#14149 := (+ #174 #14148) +#14418 := (<= #14149 0::Int) +#14152 := (= #14149 0::Int) +#14177 := (not #14174) +#21302 := [hypothesis]: #14177 +#21307 := (or #14174 #14152) +#21296 := (not #14152) +#21297 := [hypothesis]: #21296 +#12463 := (not #14132) +#12470 := (or #14174 #12463) +#12471 := [def-axiom]: #12470 +#21303 := [unit-resolution #12471 #21302]: #12463 +#12460 := (not #14143) +#12469 := (or #14174 #12460) +#12472 := [def-axiom]: #12469 +#21304 := [unit-resolution #12472 #21302]: #12460 +#14155 := (or #14132 #14143 #14152) +#12402 := (or #4400 #14132 #14143 #14152) +#14124 := (+ #14123 #2339) +#14125 := (+ #174 #14124) +#14126 := (= #14125 0::Int) +#14128 := (+ #1444 #14127) +#14129 := (+ #14065 #14128) +#14130 := (<= #14129 0::Int) +#14133 := (or #14132 #14130 #14126) +#12426 := (or #4400 #14133) +#12431 := (iff #12426 #12402) +#12399 := (or #4400 #14155) +#12430 := (iff #12399 #12402) +#12425 := [rewrite]: #12430 +#12428 := (iff #12426 #12399) +#14156 := (iff #14133 #14155) +#14153 := (iff #14126 #14152) +#14150 := (= #14125 #14149) +#14151 := [rewrite]: #14150 +#14154 := [monotonicity #14151]: #14153 +#14146 := (iff #14130 #14143) +#14134 := (+ #14065 #14127) +#14135 := (+ #1444 #14134) +#14138 := (<= #14135 0::Int) +#14144 := (iff #14138 #14143) +#14145 := [rewrite]: #14144 +#14139 := (iff #14130 #14138) +#14136 := (= #14129 #14135) +#14137 := [rewrite]: #14136 +#14140 := [monotonicity #14137]: #14139 +#14147 := [trans #14140 #14145]: #14146 +#14157 := [monotonicity #14147 #14154]: #14156 +#12429 := [monotonicity #14157]: #12428 +#12433 := [trans #12429 #12425]: #12431 +#12427 := [quant-inst #2337]: #12426 +#12434 := [mp #12427 #12433]: #12402 +#21305 := [unit-resolution #12434 #6504]: #14155 +#21306 := [unit-resolution #21305 #21304 #21303 #21297]: false +#21308 := [lemma #21306]: #21307 +#24013 := [unit-resolution #21308 #21302]: #14152 +#24014 := (or #21296 #14418) +#24015 := [th-lemma arith triangle-eq]: #24014 +#24016 := [unit-resolution #24015 #24013]: #14418 +#17675 := (not #14418) +#24037 := (or #15147 #17675) +#9536 := (+ #5998 #9535) +#7436 := (>= #9536 0::Int) +#9534 := (= #5998 #8769) +#11865 := (= #8769 #5998) +#11866 := [monotonicity #7781]: #11865 +#11867 := [symm #11866]: #9534 +#11868 := (not #9534) +#24011 := (or #11868 #7436) +#24017 := [th-lemma arith triangle-eq]: #24011 +#24018 := [unit-resolution #24017 #11867]: #7436 +#13344 := (+ #14123 #14229) +#13577 := (>= #13344 0::Int) +#7914 := (= #14123 #14203) +#24021 := (= #14203 #14123) +#24028 := [monotonicity #24020]: #24021 +#24029 := [symm #24028]: #7914 +#24027 := (not #7914) +#24030 := (or #24027 #13577) +#24031 := [th-lemma arith triangle-eq]: #24030 +#24032 := [unit-resolution #24031 #24029]: #13577 +#24035 := (not #13577) +#24034 := (not #7436) +#24033 := (or #15147 #24034 #10341 #24035 #17675) +#24036 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24033 +#24038 := [unit-resolution #24036 #24032 #24018 #8185]: #24037 +#24026 := [unit-resolution #24038 #24016]: #15147 +#15125 := (<= #14231 0::Int) +#14419 := (>= #14149 0::Int) +#24039 := (or #21296 #14419) #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) +#24041 := [unit-resolution #24040 #24013]: #14419 +#24045 := (not #14419) +#24049 := (or #15125 #24045) +#9537 := (<= #9536 0::Int) +#11869 := (or #11868 #9537) +#11870 := [th-lemma arith triangle-eq]: #11869 +#11871 := [unit-resolution #11870 #11867]: #9537 +#13345 := (<= #13344 0::Int) +#24042 := (or #24027 #13345) +#24025 := [th-lemma arith triangle-eq]: #24042 +#24043 := [unit-resolution #24025 #24029]: #13345 +#24044 := (not #13345) +#12642 := (not #9537) +#24046 := (or #15125 #12642 #12643 #24044 #24045) +#24047 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24046 +#24050 := [unit-resolution #24047 #24043 #11871 #8183]: #24049 +#24051 := [unit-resolution #24050 #24041]: #15125 +#24053 := (not #15147) +#24052 := (not #15125) +#24048 := (or #14232 #24052 #24053) +#24054 := [th-lemma arith triangle-eq]: #24048 +#24055 := [unit-resolution #24054 #24051 #24026]: #14232 +#14237 := (not #14232) +#10168 := (not #10156) +#14240 := (or #10168 #14217 #14237) +#24056 := [hypothesis]: #4446 +#12768 := (or #4451 #10168 #14217 #14237) +#14204 := (+ #2339 #14203) +#14205 := (+ #8769 #14204) +#14206 := (= #14205 0::Int) +#14207 := (not #14206) +#14208 := (+ #8769 #2339) +#14209 := (>= #14208 0::Int) +#14210 := (or #10168 #14209 #14207) +#12775 := (or #4451 #14210) +#12828 := (iff #12775 #12768) +#12839 := (or #4451 #14240) +#12862 := (iff #12839 #12768) +#12868 := [rewrite]: #12862 +#12866 := (iff #12775 #12839) +#14241 := (iff #14210 #14240) +#14238 := (iff #14207 #14237) +#14235 := (iff #14206 #14232) +#14222 := (+ #8769 #14203) +#14223 := (+ #2339 #14222) +#14226 := (= #14223 0::Int) +#14233 := (iff #14226 #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 -#12482 := (or #14186 #14141 #14152) -#12483 := [def-axiom]: #12482 -#23160 := [unit-resolution #12483 #23147 #23167]: #14141 -#14189 := (or #14085 #14186) -#12444 := (or #4401 #14085 #14186) -#14180 := (or #14141 #14139) -#14181 := (not #14180) -#14182 := (or #14081 #14181) -#12463 := (or #4401 #14182) -#12468 := (iff #12463 #12444) -#12441 := (or #4401 #14189) -#12467 := (iff #12441 #12444) -#12462 := [rewrite]: #12467 -#12465 := (iff #12463 #12441) -#14190 := (iff #14182 #14189) -#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 -#12471 := [mp #12464 #12470]: #12444 -#23168 := [unit-resolution #12471 #6509]: #14189 -#23146 := [unit-resolution #23168 #23167]: #14085 -#23169 := [unit-resolution #24712 #23146]: #19567 -#23170 := [unit-resolution #24083 #23147 #24041 #23169 #24027 #8194]: #24061 -#23162 := (or #15134 #15156) -#23171 := [th-lemma arith farkas 1 1]: #23162 -#23172 := [unit-resolution #23171 #23170]: #15156 -#23173 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24052 #23172 #11880 #8192 #23160 #10074 #23163 #23156 #6991 #23151]: false -#23175 := [lemma #23173]: #23174 -#27691 := [unit-resolution #23175 #10074]: #14152 -#27696 := [unit-resolution #12481 #27691]: #14183 -#27708 := [unit-resolution #12471 #6509 #27696]: #14085 -#27709 := [unit-resolution #24710 #27708]: #19567 -#21437 := (or #21435 #21436 #2359) -#21430 := [hypothesis]: #19567 -#21431 := [hypothesis]: #14792 -#21434 := [th-lemma arith farkas -1 1 1 #21431 #21430 #19783]: false -#21438 := [lemma #21434]: #21437 -#27710 := [unit-resolution #21438 #27709 #19783]: #21435 -#4111 := (or #4463 #2929) -#4109 := [def-axiom]: #4111 -#27711 := [unit-resolution #4109 #23150]: #2929 -#24435 := (or #4312 #2926 #14792 #14797) -#14789 := (or #14788 #14785 #14778) -#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) -#21658 := (+ #2347 #21657) -#17955 := (<= #21658 0::Int) -#29064 := (not #17955) -#18266 := (>= #21658 0::Int) -#21447 := (+ #14775 #21446) -#21448 := (>= #21447 0::Int) -#25332 := (or #4417 #21448) -#25339 := [quant-inst #14774]: #25332 -#28969 := [unit-resolution #25339 #8193]: #21448 -#28961 := [hypothesis]: #15536 -#28966 := (not #21448) -#28967 := (or #18266 #28964 #21436 #28966) -#28963 := [th-lemma arith assign-bounds -1 -1 -1]: #28967 -#28962 := [unit-resolution #28963 #28961 #21430 #28969]: #18266 -#21659 := (= #21658 0::Int) -#21664 := (not #21659) -#21644 := (+ #2347 #21446) -#21645 := (<= #21644 0::Int) -#28965 := (not #21645) -#28968 := [hypothesis]: #24448 -#28985 := (or #28965 #14778 #21436 #28966) -#28999 := [th-lemma arith assign-bounds -1 -1 -1]: #28985 -#29042 := [unit-resolution #28999 #28968 #21430 #28969]: #28965 -#21429 := (f3 f23 #14774) -#21409 := (= f1 #21429) -#25158 := (f3 f23 #25042) -#25147 := (= f1 #25158) -#29043 := (iff #25147 #21409) -#29046 := (iff #21409 #25147) -#29045 := (= #21429 #25158) -#29000 := [monotonicity #28984]: #29045 -#29041 := [monotonicity #29000]: #29046 -#29049 := [symm #29041]: #29043 -#30426 := (= #7211 #25042) -#30420 := (ite #30426 #5892 #26214) -#30488 := [hypothesis]: #26214 -#30492 := (or #30420 #26242) -#30464 := (not #30420) -#30484 := [hypothesis]: #30464 -#30465 := (not #30426) -#30485 := (or #30420 #30465) -#30470 := (or #30420 #30465 #6304) -#30471 := [def-axiom]: #30470 -#30486 := [unit-resolution #30471 #6999]: #30485 -#30487 := [unit-resolution #30486 #30484]: #30465 -#30489 := (or #30420 #30426) -#30472 := (or #30420 #30426 #26242) -#30473 := [def-axiom]: #30472 -#30490 := [unit-resolution #30473 #30488]: #30489 -#30491 := [unit-resolution #30490 #30487 #30484]: false -#30493 := [lemma #30491]: #30492 -#28983 := [unit-resolution #30493 #30488]: #30420 -#30259 := (or #25147 #30464) -#30449 := (f3 #8442 #25042) -#30254 := (= #30449 #25158) -#30250 := (= #25158 #30449) -#18324 := (= f23 #8442) -#18225 := (= #773 #8442) -#18326 := [symm #9284]: #18225 -#18323 := [trans #6998 #18326]: #18324 -#30251 := [monotonicity #18323]: #30250 -#30256 := [symm #30251]: #30254 -#30450 := (= f1 #30449) -#30452 := (iff #30420 #30450) -#30194 := (or #6290 #30452) -#30451 := (iff #30450 #30420) -#30192 := (or #6290 #30451) -#30199 := (iff #30192 #30194) -#30201 := (iff #30194 #30194) -#30190 := [rewrite]: #30201 -#30453 := (iff #30451 #30452) -#30454 := [rewrite]: #30453 -#30200 := [monotonicity #30454]: #30199 -#30202 := [trans #30200 #30190]: #30199 -#30198 := [quant-inst #104 #7211 #5891 #25042]: #30192 -#30203 := [mp #30198 #30202]: #30194 -#30246 := [unit-resolution #30203 #4177]: #30452 -#30204 := (not #30452) -#30248 := (or #30204 #30450) -#30247 := [hypothesis]: #30420 -#30209 := (or #30204 #30464 #30450) -#30210 := [def-axiom]: #30209 -#30249 := [unit-resolution #30210 #30247]: #30248 -#30240 := [unit-resolution #30249 #30246]: #30450 -#30257 := [trans #30240 #30256]: #25147 -#25159 := (not #25147) -#30241 := [hypothesis]: #25159 -#30258 := [unit-resolution #30241 #30257]: false -#30260 := [lemma #30258]: #30259 -#29044 := [unit-resolution #30260 #28983]: #25147 -#29050 := [mp #29044 #29049]: #21409 -#21415 := (not #21409) -#21667 := (or #21415 #21645 #21664) -#16840 := (or #4460 #21415 #21645 #21664) -#21631 := (+ #2348 #14780) -#21632 := (+ #21416 #21631) -#21633 := (= #21632 0::Int) -#21634 := (not #21633) -#21635 := (+ #21416 #2348) -#21636 := (>= #21635 0::Int) -#21637 := (or #21415 #21636 #21634) -#16841 := (or #4460 #21637) -#16874 := (iff #16841 #16840) -#16854 := (or #4460 #21667) -#16857 := (iff #16854 #16840) -#16852 := [rewrite]: #16857 -#16855 := (iff #16841 #16854) -#21668 := (iff #21637 #21667) -#21665 := (iff #21634 #21664) -#21662 := (iff #21633 #21659) -#21650 := (+ #14780 #21416) -#21651 := (+ #2348 #21650) -#21654 := (= #21651 0::Int) -#21660 := (iff #21654 #21659) -#21661 := [rewrite]: #21660 -#21655 := (iff #21633 #21654) -#21652 := (= #21632 #21651) -#21653 := [rewrite]: #21652 -#21656 := [monotonicity #21653]: #21655 -#21663 := [trans #21656 #21661]: #21662 -#21666 := [monotonicity #21663]: #21665 -#21648 := (iff #21636 #21645) -#21638 := (+ #2348 #21416) -#21641 := (>= #21638 0::Int) -#21646 := (iff #21641 #21645) -#21647 := [rewrite]: #21646 -#21642 := (iff #21636 #21641) -#21639 := (= #21635 #21638) -#21640 := [rewrite]: #21639 -#21643 := [monotonicity #21640]: #21642 -#21649 := [trans #21643 #21647]: #21648 -#21669 := [monotonicity #21649 #21666]: #21668 -#16862 := [monotonicity #21669]: #16855 -#16859 := [trans #16862 #16852]: #16874 -#16853 := [quant-inst #14774]: #16841 -#16903 := [mp #16853 #16859]: #16840 -#29061 := [unit-resolution #16903 #24065]: #21667 -#29059 := [unit-resolution #29061 #29050 #29042]: #21664 -#29048 := (not #18266) -#29060 := (or #21659 #29064 #29048) -#29063 := [th-lemma arith triangle-eq]: #29060 -#29071 := [unit-resolution #29063 #29059 #28962]: #29064 -#25329 := (<= #21447 0::Int) -#21417 := (= #14775 #21416) -#26209 := (f13 f14 #25042) -#25148 := (f24 #25042) -#26948 := (= #25148 #26209) -#29155 := (iff #26948 #21417) -#29077 := (= #21416 #14775) -#29069 := (iff #29077 #21417) -#29154 := [commutativity]: #29069 -#29080 := (iff #26948 #29077) -#29078 := (= #26209 #14775) -#29047 := [monotonicity #29062]: #29078 -#29073 := (= #25148 #21416) -#24500 := (= #21416 #25148) -#29079 := [monotonicity #28984]: #24500 -#29070 := [symm #29079]: #29073 -#29082 := [monotonicity #29070 #29047]: #29080 -#29153 := [trans #29082 #29154]: #29155 -#26988 := (or #25159 #26948) -#26991 := (or #4426 #25159 #26948) -#26982 := (= #26209 #25148) -#27001 := (or #26982 #25159) -#27008 := (or #4426 #27001) -#27013 := (iff #27008 #26991) -#27010 := (or #4426 #26988) -#26966 := (iff #27010 #26991) -#27012 := [rewrite]: #26966 -#27003 := (iff #27008 #27010) -#27004 := (iff #27001 #26988) -#26981 := (or #26948 #25159) -#26989 := (iff #26981 #26988) -#26990 := [rewrite]: #26989 -#26987 := (iff #27001 #26981) -#26985 := (iff #26982 #26948) -#26947 := [rewrite]: #26985 -#26986 := [monotonicity #26947]: #26987 -#27007 := [trans #26986 #26990]: #27004 -#27011 := [monotonicity #27007]: #27003 -#26965 := [trans #27011 #27012]: #27013 -#27009 := [quant-inst #25042]: #27008 -#27015 := [mp #27009 #26965]: #26991 -#29072 := [unit-resolution #27015 #7100]: #26988 -#29068 := [unit-resolution #29072 #29044]: #26948 -#29156 := [mp #29068 #29153]: #21417 -#29157 := (not #21417) -#29158 := (or #29157 #25329) -#29118 := [th-lemma arith triangle-eq]: #29158 -#29151 := [unit-resolution #29118 #29156]: #25329 -#14117 := (<= #14116 0::Int) -#13521 := (or #4417 #14117) -#14107 := (+ #14074 #2348) -#14108 := (>= #14107 0::Int) -#13551 := (or #4417 #14108) -#13518 := (iff #13551 #13521) -#13567 := (iff #13521 #13521) -#13575 := [rewrite]: #13567 -#14120 := (iff #14108 #14117) -#14109 := (+ #2348 #14074) -#14112 := (>= #14109 0::Int) -#14118 := (iff #14112 #14117) -#14119 := [rewrite]: #14118 -#14113 := (iff #14108 #14112) -#14110 := (= #14107 #14109) -#14111 := [rewrite]: #14110 -#14114 := [monotonicity #14111]: #14113 -#14121 := [trans #14114 #14119]: #14120 -#13570 := [monotonicity #14121]: #13518 -#13578 := [trans #13570 #13575]: #13518 -#13561 := [quant-inst #2346]: #13551 -#13576 := [mp #13561 #13578]: #13521 -#29110 := [unit-resolution #13576 #8193]: #14117 -#29159 := [hypothesis]: #15512 -#29109 := [th-lemma arith farkas -1 -1 -1 1 #29159 #29110 #29151 #29071]: false -#29113 := [lemma #29109]: #29112 -#27702 := [unit-resolution #29113 #27701 #23166 #27699 #27709 #27717]: #26242 -#27720 := [unit-resolution #27702 #27719]: false -#27735 := [lemma #27720]: #27734 -#26718 := [unit-resolution #27735 #19783]: #6073 -#6119 := (or #6091 #6118) -#6120 := [def-axiom]: #6119 -#26719 := [unit-resolution #6120 #26718]: #6091 -#6094 := (not #6091) -#12666 := (or #6088 #6094) -#6105 := (or #4312 #1654 #6088 #6094) -#6084 := (or #6083 #6080 #6073) -#6085 := (not #6084) -#6087 := (or #6086 #1654 #6085) -#6106 := (or #4312 #6087) -#6113 := (iff #6106 #6105) -#6100 := (or #1654 #6088 #6094) -#6108 := (or #4312 #6100) -#6111 := (iff #6108 #6105) -#6112 := [rewrite]: #6111 -#6109 := (iff #6106 #6108) -#6103 := (iff #6087 #6100) -#6097 := (or #6088 #1654 #6094) -#6101 := (iff #6097 #6100) -#6102 := [rewrite]: #6101 -#6098 := (iff #6087 #6097) -#6095 := (iff #6085 #6094) -#6092 := (iff #6084 #6091) +#14227 := (iff #14206 #14226) +#14224 := (= #14205 #14223) +#14225 := [rewrite]: #14224 +#14228 := [monotonicity #14225]: #14227 +#14236 := [trans #14228 #14234]: #14235 +#14239 := [monotonicity #14236]: #14238 +#14220 := (iff #14209 #14217) +#14211 := (+ #2339 #8769) +#14214 := (>= #14211 0::Int) +#14218 := (iff #14214 #14217) +#14219 := [rewrite]: #14218 +#14215 := (iff #14209 #14214) +#14212 := (= #14208 #14211) +#14213 := [rewrite]: #14212 +#14216 := [monotonicity #14213]: #14215 +#14221 := [trans #14216 #14219]: #14220 +#14242 := [monotonicity #14221 #14239]: #14241 +#12867 := [monotonicity #14242]: #12866 +#12894 := [trans #12867 #12868]: #12828 +#12832 := [quant-inst #7202]: #12775 +#12895 := [mp #12832 #12894]: #12768 +#24057 := [unit-resolution #12895 #24056]: #14240 +#24058 := [unit-resolution #24057 #24055 #11803]: #14217 +#12478 := (f5 f10 ?v0!20) +#17146 := (f7 #12478) +#22307 := (f5 #7202 #17146) +#22316 := (f9 #22307) +#22319 := (* -1::Int #22316) +#22448 := (+ #14123 #22319) +#17182 := (>= #22448 0::Int) +#17168 := (= #14123 #22316) +#24059 := (= #22316 #14123) +#24063 := (= #22307 #14122) +#24061 := (= #17146 ?v0!20) +#17147 := (= ?v0!20 #17146) +#17170 := (or #6815 #17147) +#17171 := [quant-inst #56 #2337]: #17170 +#24060 := [unit-resolution #17171 #4190]: #17147 +#24062 := [symm #24060]: #24061 +#24064 := [monotonicity #7781 #24062]: #24063 +#24065 := [monotonicity #24064]: #24059 +#24066 := [symm #24065]: #17168 +#24067 := (not #17168) +#24068 := (or #24067 #17182) +#24069 := [th-lemma arith triangle-eq]: #24068 +#24071 := [unit-resolution #24069 #24066]: #17182 +#22375 := (<= #22316 0::Int) +#22355 := (not #22375) +#22358 := (= #7202 #17146) +#22388 := (not #22358) +#20545 := (f3 f15 #17146) +#20562 := (= f1 #20545) +#23972 := (ite #22358 #5883 #20562) +#23992 := (not #23972) +#23973 := (f3 #8433 #17146) +#23978 := (= f1 #23973) +#23980 := (iff #23972 #23978) +#23984 := (or #6281 #23980) +#23979 := (iff #23978 #23972) +#23985 := (or #6281 #23979) +#23987 := (iff #23985 #23984) +#23983 := (iff #23984 #23984) +#23989 := [rewrite]: #23983 +#23981 := (iff #23979 #23980) +#23982 := [rewrite]: #23981 +#23988 := [monotonicity #23982]: #23987 +#23990 := [trans #23988 #23989]: #23987 +#23986 := [quant-inst #104 #7202 #5882 #17146]: #23985 +#23991 := [mp #23986 #23990]: #23984 +#24072 := [unit-resolution #23991 #4168]: #23980 +#24004 := (not #23978) +#10237 := (f3 f23 ?v0!20) +#10238 := (= f1 #10237) +#10239 := (not #10238) +#24085 := (iff #10239 #24004) +#24083 := (iff #10238 #23978) +#24080 := (iff #23978 #10238) +#24078 := (= #23973 #10237) +#24079 := [monotonicity #9277 #24062]: #24078 +#24082 := [monotonicity #24079]: #24080 +#24084 := [symm #24082]: #24083 +#24086 := [monotonicity #24084]: #24085 +#24699 := (not #14076) +#21427 := (not #19558) +#24073 := (or #14143 #21427 #24035 #24052 #24034 #10341) +#24074 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24073 +#24075 := [unit-resolution #24074 #24051 #24032 #21304 #24018 #8185]: #21427 +#24700 := (or #24699 #19558) +#24687 := [hypothesis]: #21427 +#24688 := [hypothesis]: #14076 +#24701 := [th-lemma arith triangle-eq]: #24700 +#24702 := [unit-resolution #24701 #24688 #24687]: false +#24703 := [lemma #24702]: #24700 +#24070 := [unit-resolution #24703 #24075]: #24699 +#14082 := (or #10239 #14076) +#12325 := (or #4417 #10239 #14076) +#14072 := (= #14065 #2338) +#14075 := (or #14072 #10239) +#12365 := (or #4417 #14075) +#12373 := (iff #12365 #12325) +#12368 := (or #4417 #14082) +#12370 := (iff #12368 #12325) +#12372 := [rewrite]: #12370 +#12369 := (iff #12365 #12368) +#14085 := (iff #14075 #14082) +#14079 := (or #14076 #10239) +#14083 := (iff #14079 #14082) +#14084 := [rewrite]: #14083 +#14080 := (iff #14075 #14079) +#14077 := (iff #14072 #14076) +#14078 := [rewrite]: #14077 +#14081 := [monotonicity #14078]: #14080 +#14086 := [trans #14081 #14084]: #14085 +#12364 := [monotonicity #14086]: #12369 +#12374 := [trans #12364 #12372]: #12373 +#12367 := [quant-inst #2337]: #12365 +#12393 := [mp #12367 #12374]: #12325 +#24076 := [unit-resolution #12393 #7091]: #14082 +#24077 := [unit-resolution #24076 #24070]: #10239 +#24081 := [mp #24077 #24086]: #24004 +#24003 := (not #23980) +#24006 := (or #24003 #23992 #23978) +#24007 := [def-axiom]: #24006 +#24087 := [unit-resolution #24007 #24081 #24072]: #23992 +#24088 := (or #23972 #22388) +#23999 := (or #23972 #22388 #6295) +#24000 := [def-axiom]: #23999 +#24089 := [unit-resolution #24000 #6990]: #24088 +#24090 := [unit-resolution #24089 #24087]: #22388 +#22360 := (or #22358 #22355) +#23949 := (or #6773 #22358 #22355) +#22356 := (= #17146 #7202) +#22357 := (or #22356 #22355) +#23950 := (or #6773 #22357) +#23957 := (iff #23950 #23949) +#23952 := (or #6773 #22360) +#23955 := (iff #23952 #23949) +#23956 := [rewrite]: #23955 +#23953 := (iff #23950 #23952) +#22361 := (iff #22357 #22360) +#22359 := (iff #22356 #22358) +#22354 := [rewrite]: #22359 +#22362 := [monotonicity #22354]: #22361 +#23954 := [monotonicity #22362]: #23953 +#23958 := [trans #23954 #23956]: #23957 +#23951 := [quant-inst #7202 #17146]: #23950 +#23959 := [mp #23951 #23958]: #23949 +#24091 := [unit-resolution #23959 #4208]: #22360 +#24094 := [unit-resolution #24091 #24090]: #22355 +#24095 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24018 #8185 #24094 #24071 #24016 #24058]: false +#24097 := [lemma #24095]: #24096 +#23158 := [unit-resolution #24097 #23157]: #14174 +#23138 := [hypothesis]: #12460 +#12473 := (or #14177 #14132 #14143) +#12474 := [def-axiom]: #12473 +#23151 := [unit-resolution #12474 #23138 #23158]: #14132 +#14180 := (or #14076 #14177) +#12435 := (or #4392 #14076 #14177) +#14171 := (or #14132 #14130) +#14172 := (not #14171) +#14173 := (or #14072 #14172) +#12454 := (or #4392 #14173) +#12459 := (iff #12454 #12435) +#12432 := (or #4392 #14180) +#12458 := (iff #12432 #12435) +#12453 := [rewrite]: #12458 +#12456 := (iff #12454 #12432) +#14181 := (iff #14173 #14180) +#14178 := (iff #14172 #14177) +#14175 := (iff #14171 #14174) +#14176 := [monotonicity #14147]: #14175 +#14179 := [monotonicity #14176]: #14178 +#14182 := [monotonicity #14078 #14179]: #14181 +#12457 := [monotonicity #14182]: #12456 +#12461 := [trans #12457 #12453]: #12459 +#12455 := [quant-inst #2337]: #12454 +#12462 := [mp #12455 #12461]: #12435 +#23159 := [unit-resolution #12462 #6500]: #14180 +#23137 := [unit-resolution #23159 #23158]: #14076 +#23160 := [unit-resolution #24703 #23137]: #19558 +#23161 := [unit-resolution #24074 #23138 #24032 #23160 #24018 #8185]: #24052 +#23153 := (or #15125 #15147) +#23162 := [th-lemma arith farkas 1 1]: #23153 +#23163 := [unit-resolution #23162 #23161]: #15147 +#23164 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24043 #23163 #11871 #8183 #23151 #10065 #23154 #23147 #6982 #23142]: false +#23166 := [lemma #23164]: #23165 +#27682 := [unit-resolution #23166 #10065]: #14143 +#27687 := [unit-resolution #12472 #27682]: #14174 +#27699 := [unit-resolution #12462 #6500 #27687]: #14076 +#27700 := [unit-resolution #24701 #27699]: #19558 +#21428 := (or #21426 #21427 #2350) +#21421 := [hypothesis]: #19558 +#21422 := [hypothesis]: #14783 +#21425 := [th-lemma arith farkas -1 1 1 #21422 #21421 #19774]: false +#21429 := [lemma #21425]: #21428 +#27701 := [unit-resolution #21429 #27700 #19774]: #21426 +#4102 := (or #4454 #2920) +#4100 := [def-axiom]: #4102 +#27702 := [unit-resolution #4100 #23141]: #2920 +#24426 := (or #4303 #2917 #14783 #14788) +#14780 := (or #14779 #14776 #14769) +#14781 := (not #14780) +#14784 := (or #2352 #14783 #14781) +#24435 := (or #4303 #14784) +#24441 := (iff #24435 #24426) +#14791 := (or #2917 #14783 #14788) +#24432 := (or #4303 #14791) +#24440 := (iff #24432 #24426) +#24436 := [rewrite]: #24440 +#24431 := (iff #24435 #24432) +#14792 := (iff #14784 #14791) +#14789 := (iff #14781 #14788) +#14786 := (iff #14780 #14785) +#14787 := [rewrite]: #14786 +#14790 := [monotonicity #14787]: #14789 +#14793 := [monotonicity #2919 #14790]: #14792 +#24438 := [monotonicity #14793]: #24431 +#24430 := [trans #24438 #24436]: #24441 +#24437 := [quant-inst #2337]: #24435 +#24453 := [mp #24437 #24430]: #24426 +#27704 := [unit-resolution #24453 #12656 #27702 #27701]: #14788 +#24457 := (or #14785 #14778) +#24443 := [def-axiom]: #24457 +#27669 := [unit-resolution #24443 #27704]: #14778 +#27710 := [trans #27669 #27709]: #26205 +#26233 := (not #26205) +#15527 := (>= #14774 0::Int) +#24455 := (or #14785 #14775) +#24456 := [def-axiom]: #24455 +#27706 := [unit-resolution #24456 #27704]: #14775 +#27707 := (or #14776 #15527) +#27705 := [th-lemma arith triangle-eq]: #27707 +#27708 := [unit-resolution #27705 #27706]: #15527 +#24439 := (not #14769) +#24454 := (or #14785 #24439) +#24433 := [def-axiom]: #24454 +#27690 := [unit-resolution #24433 #27704]: #24439 +#15503 := (<= #14774 0::Int) +#27688 := (or #14776 #15503) +#27691 := [th-lemma arith triangle-eq]: #27688 +#27692 := [unit-resolution #27691 #27706]: #15503 +#28955 := (not #15527) +#29072 := (not #15503) +#29103 := (or #26233 #29072 #4451 #14769 #21427 #28955) +#21407 := (f24 #14765) +#21437 := (* -1::Int #21407) +#21648 := (+ #14772 #21437) +#21649 := (+ #2338 #21648) +#17946 := (<= #21649 0::Int) +#29055 := (not #17946) +#18257 := (>= #21649 0::Int) +#21438 := (+ #14766 #21437) +#21439 := (>= #21438 0::Int) +#25323 := (or #4408 #21439) +#25330 := [quant-inst #14765]: #25323 +#28960 := [unit-resolution #25330 #8184]: #21439 +#28952 := [hypothesis]: #15527 +#28957 := (not #21439) +#28958 := (or #18257 #28955 #21427 #28957) +#28954 := [th-lemma arith assign-bounds -1 -1 -1]: #28958 +#28953 := [unit-resolution #28954 #28952 #21421 #28960]: #18257 +#21650 := (= #21649 0::Int) +#21655 := (not #21650) +#21635 := (+ #2338 #21437) +#21636 := (<= #21635 0::Int) +#28956 := (not #21636) +#28959 := [hypothesis]: #24439 +#28976 := (or #28956 #14769 #21427 #28957) +#28990 := [th-lemma arith assign-bounds -1 -1 -1]: #28976 +#29033 := [unit-resolution #28990 #28959 #21421 #28960]: #28956 +#21420 := (f3 f23 #14765) +#21400 := (= f1 #21420) +#25149 := (f3 f23 #25033) +#25138 := (= f1 #25149) +#29034 := (iff #25138 #21400) +#29037 := (iff #21400 #25138) +#29036 := (= #21420 #25149) +#28991 := [monotonicity #28975]: #29036 +#29032 := [monotonicity #28991]: #29037 +#29040 := [symm #29032]: #29034 +#30417 := (= #7202 #25033) +#30411 := (ite #30417 #5883 #26205) +#30479 := [hypothesis]: #26205 +#30483 := (or #30411 #26233) +#30455 := (not #30411) +#30475 := [hypothesis]: #30455 +#30456 := (not #30417) +#30476 := (or #30411 #30456) +#30461 := (or #30411 #30456 #6295) +#30462 := [def-axiom]: #30461 +#30477 := [unit-resolution #30462 #6990]: #30476 +#30478 := [unit-resolution #30477 #30475]: #30456 +#30480 := (or #30411 #30417) +#30463 := (or #30411 #30417 #26233) +#30464 := [def-axiom]: #30463 +#30481 := [unit-resolution #30464 #30479]: #30480 +#30482 := [unit-resolution #30481 #30478 #30475]: false +#30484 := [lemma #30482]: #30483 +#28974 := [unit-resolution #30484 #30479]: #30411 +#30250 := (or #25138 #30455) +#30440 := (f3 #8433 #25033) +#30245 := (= #30440 #25149) +#30241 := (= #25149 #30440) +#18315 := (= f23 #8433) +#18216 := (= #180 #8433) +#18317 := [symm #9275]: #18216 +#18314 := [trans #6989 #18317]: #18315 +#30242 := [monotonicity #18314]: #30241 +#30247 := [symm #30242]: #30245 +#30441 := (= f1 #30440) +#30443 := (iff #30411 #30441) +#30185 := (or #6281 #30443) +#30442 := (iff #30441 #30411) +#30183 := (or #6281 #30442) +#30190 := (iff #30183 #30185) +#30192 := (iff #30185 #30185) +#30181 := [rewrite]: #30192 +#30444 := (iff #30442 #30443) +#30445 := [rewrite]: #30444 +#30191 := [monotonicity #30445]: #30190 +#30193 := [trans #30191 #30181]: #30190 +#30189 := [quant-inst #104 #7202 #5882 #25033]: #30183 +#30194 := [mp #30189 #30193]: #30185 +#30237 := [unit-resolution #30194 #4168]: #30443 +#30195 := (not #30443) +#30239 := (or #30195 #30441) +#30238 := [hypothesis]: #30411 +#30200 := (or #30195 #30455 #30441) +#30201 := [def-axiom]: #30200 +#30240 := [unit-resolution #30201 #30238]: #30239 +#30231 := [unit-resolution #30240 #30237]: #30441 +#30248 := [trans #30231 #30247]: #25138 +#25150 := (not #25138) +#30232 := [hypothesis]: #25150 +#30249 := [unit-resolution #30232 #30248]: false +#30251 := [lemma #30249]: #30250 +#29035 := [unit-resolution #30251 #28974]: #25138 +#29041 := [mp #29035 #29040]: #21400 +#21406 := (not #21400) +#21658 := (or #21406 #21636 #21655) +#16831 := (or #4451 #21406 #21636 #21655) +#21622 := (+ #2339 #14771) +#21623 := (+ #21407 #21622) +#21624 := (= #21623 0::Int) +#21625 := (not #21624) +#21626 := (+ #21407 #2339) +#21627 := (>= #21626 0::Int) +#21628 := (or #21406 #21627 #21625) +#16832 := (or #4451 #21628) +#16865 := (iff #16832 #16831) +#16845 := (or #4451 #21658) +#16848 := (iff #16845 #16831) +#16843 := [rewrite]: #16848 +#16846 := (iff #16832 #16845) +#21659 := (iff #21628 #21658) +#21656 := (iff #21625 #21655) +#21653 := (iff #21624 #21650) +#21641 := (+ #14771 #21407) +#21642 := (+ #2339 #21641) +#21645 := (= #21642 0::Int) +#21651 := (iff #21645 #21650) +#21652 := [rewrite]: #21651 +#21646 := (iff #21624 #21645) +#21643 := (= #21623 #21642) +#21644 := [rewrite]: #21643 +#21647 := [monotonicity #21644]: #21646 +#21654 := [trans #21647 #21652]: #21653 +#21657 := [monotonicity #21654]: #21656 +#21639 := (iff #21627 #21636) +#21629 := (+ #2339 #21407) +#21632 := (>= #21629 0::Int) +#21637 := (iff #21632 #21636) +#21638 := [rewrite]: #21637 +#21633 := (iff #21627 #21632) +#21630 := (= #21626 #21629) +#21631 := [rewrite]: #21630 +#21634 := [monotonicity #21631]: #21633 +#21640 := [trans #21634 #21638]: #21639 +#21660 := [monotonicity #21640 #21657]: #21659 +#16853 := [monotonicity #21660]: #16846 +#16850 := [trans #16853 #16843]: #16865 +#16844 := [quant-inst #14765]: #16832 +#16894 := [mp #16844 #16850]: #16831 +#29052 := [unit-resolution #16894 #24056]: #21658 +#29050 := [unit-resolution #29052 #29041 #29033]: #21655 +#29039 := (not #18257) +#29051 := (or #21650 #29055 #29039) +#29054 := [th-lemma arith triangle-eq]: #29051 +#29062 := [unit-resolution #29054 #29050 #28953]: #29055 +#25320 := (<= #21438 0::Int) +#21408 := (= #14766 #21407) +#26200 := (f13 f14 #25033) +#25139 := (f24 #25033) +#26939 := (= #25139 #26200) +#29146 := (iff #26939 #21408) +#29068 := (= #21407 #14766) +#29060 := (iff #29068 #21408) +#29145 := [commutativity]: #29060 +#29071 := (iff #26939 #29068) +#29069 := (= #26200 #14766) +#29038 := [monotonicity #29053]: #29069 +#29064 := (= #25139 #21407) +#24491 := (= #21407 #25139) +#29070 := [monotonicity #28975]: #24491 +#29061 := [symm #29070]: #29064 +#29073 := [monotonicity #29061 #29038]: #29071 +#29144 := [trans #29073 #29145]: #29146 +#26979 := (or #25150 #26939) +#26982 := (or #4417 #25150 #26939) +#26973 := (= #26200 #25139) +#26992 := (or #26973 #25150) +#26999 := (or #4417 #26992) +#27004 := (iff #26999 #26982) +#27001 := (or #4417 #26979) +#26957 := (iff #27001 #26982) +#27003 := [rewrite]: #26957 +#26994 := (iff #26999 #27001) +#26995 := (iff #26992 #26979) +#26972 := (or #26939 #25150) +#26980 := (iff #26972 #26979) +#26981 := [rewrite]: #26980 +#26978 := (iff #26992 #26972) +#26976 := (iff #26973 #26939) +#26938 := [rewrite]: #26976 +#26977 := [monotonicity #26938]: #26978 +#26998 := [trans #26977 #26981]: #26995 +#27002 := [monotonicity #26998]: #26994 +#26956 := [trans #27002 #27003]: #27004 +#27000 := [quant-inst #25033]: #26999 +#27006 := [mp #27000 #26956]: #26982 +#29063 := [unit-resolution #27006 #7091]: #26979 +#29059 := [unit-resolution #29063 #29035]: #26939 +#29147 := [mp #29059 #29144]: #21408 +#29148 := (not #21408) +#29149 := (or #29148 #25320) +#29109 := [th-lemma arith triangle-eq]: #29149 +#29142 := [unit-resolution #29109 #29147]: #25320 +#14108 := (<= #14107 0::Int) +#13512 := (or #4408 #14108) +#14098 := (+ #14065 #2339) +#14099 := (>= #14098 0::Int) +#13542 := (or #4408 #14099) +#13509 := (iff #13542 #13512) +#13558 := (iff #13512 #13512) +#13566 := [rewrite]: #13558 +#14111 := (iff #14099 #14108) +#14100 := (+ #2339 #14065) +#14103 := (>= #14100 0::Int) +#14109 := (iff #14103 #14108) +#14110 := [rewrite]: #14109 +#14104 := (iff #14099 #14103) +#14101 := (= #14098 #14100) +#14102 := [rewrite]: #14101 +#14105 := [monotonicity #14102]: #14104 +#14112 := [trans #14105 #14110]: #14111 +#13561 := [monotonicity #14112]: #13509 +#13569 := [trans #13561 #13566]: #13509 +#13552 := [quant-inst #2337]: #13542 +#13567 := [mp #13552 #13569]: #13512 +#29101 := [unit-resolution #13567 #8184]: #14108 +#29150 := [hypothesis]: #15503 +#29100 := [th-lemma arith farkas -1 -1 -1 1 #29150 #29101 #29142 #29062]: false +#29104 := [lemma #29100]: #29103 +#27693 := [unit-resolution #29104 #27692 #23157 #27690 #27700 #27708]: #26233 +#27711 := [unit-resolution #27693 #27710]: false +#27726 := [lemma #27711]: #27725 +#26709 := [unit-resolution #27726 #19774]: #6064 +#6110 := (or #6082 #6109) +#6111 := [def-axiom]: #6110 +#26710 := [unit-resolution #6111 #26709]: #6082 +#6085 := (not #6082) +#12657 := (or #6079 #6085) +#6096 := (or #4303 #1645 #6079 #6085) +#6075 := (or #6074 #6071 #6064) +#6076 := (not #6075) +#6078 := (or #6077 #1645 #6076) +#6097 := (or #4303 #6078) +#6104 := (iff #6097 #6096) +#6091 := (or #1645 #6079 #6085) +#6099 := (or #4303 #6091) +#6102 := (iff #6099 #6096) +#6103 := [rewrite]: #6102 +#6100 := (iff #6097 #6099) +#6094 := (iff #6078 #6091) +#6088 := (or #6079 #1645 #6085) +#6092 := (iff #6088 #6091) #6093 := [rewrite]: #6092 -#6096 := [monotonicity #6093]: #6095 -#6099 := [monotonicity #6090 #6096]: #6098 -#6104 := [trans #6099 #6102]: #6103 -#6110 := [monotonicity #6104]: #6109 -#6114 := [trans #6110 #6112]: #6113 -#6107 := [quant-inst #170]: #6106 -#6115 := [mp #6107 #6114]: #6105 -#12667 := [unit-resolution #6115 #12665 #7830]: #12666 -#26765 := [unit-resolution #12667 #26719]: #6088 -#26766 := [symm #26765]: #6086 -#26762 := [monotonicity #26766]: #7825 -#26769 := [symm #26762]: #7797 -#7792 := (not #7797) -#7822 := (or #7792 #7798) -#7828 := [th-lemma arith triangle-eq]: #7822 -#26764 := [unit-resolution #7828 #26769]: #7798 -#9969 := (not #7798) -#8364 := (or #2275 #9969) -#9900 := (not #9497) -#9582 := [hypothesis]: #7798 -#9654 := (or #9900 #2275 #9969) -#10028 := (= #9989 0::Int) -#9975 := (not #10028) -#9785 := (not #10050) -#9583 := [hypothesis]: #9497 -#6992 := (not #3917) -#9899 := (not #10062) -#9972 := (or #9785 #9899 #2275 #9900 #6992 #9969) -#9892 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9972 -#9898 := [unit-resolution #9892 #9583 #6991 #10071 #10087 #9582]: #9785 -#9859 := (or #9975 #10050) -#9971 := [th-lemma arith triangle-eq]: #9859 -#9653 := [unit-resolution #9971 #9898]: #9975 -#9970 := (or #10025 #9899 #2275 #9900 #6992 #9969) -#10041 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9970 -#10042 := [unit-resolution #10041 #9583 #6991 #10087 #10071 #9582]: #10025 -#9863 := [unit-resolution #10035 #4217 #10042]: #9949 -#9528 := (or #6807 #9968 #10028) -#10029 := (or #10028 #9968) -#9547 := (or #6807 #10029) -#9801 := (iff #9547 #9528) -#10036 := (or #9968 #10028) -#9498 := (or #6807 #10036) -#9535 := (iff #9498 #9528) -#9800 := [rewrite]: #9535 -#9537 := (iff #9547 #9498) -#10037 := (iff #10029 #10036) -#10038 := [rewrite]: #10037 -#9541 := [monotonicity #10038]: #9537 -#9802 := [trans #9541 #9800]: #9801 -#9539 := [quant-inst #7211 #2273]: #9547 -#9761 := [mp #9539 #9802]: #9528 -#9862 := [unit-resolution #9761 #4211 #9863 #9653]: false -#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 +#6089 := (iff #6078 #6088) +#6086 := (iff #6076 #6085) +#6083 := (iff #6075 #6082) +#6084 := [rewrite]: #6083 +#6087 := [monotonicity #6084]: #6086 +#6090 := [monotonicity #6081 #6087]: #6089 +#6095 := [trans #6090 #6093]: #6094 +#6101 := [monotonicity #6095]: #6100 +#6105 := [trans #6101 #6103]: #6104 +#6098 := [quant-inst #170]: #6097 +#6106 := [mp #6098 #6105]: #6096 +#12658 := [unit-resolution #6106 #12656 #7821]: #12657 +#26756 := [unit-resolution #12658 #26710]: #6079 +#26757 := [symm #26756]: #6077 +#26753 := [monotonicity #26757]: #7816 +#26760 := [symm #26753]: #7788 +#7783 := (not #7788) +#7813 := (or #7783 #7789) +#7819 := [th-lemma arith triangle-eq]: #7813 +#26755 := [unit-resolution #7819 #26760]: #7789 +#9960 := (not #7789) +#8355 := (or #2266 #9960) +#9891 := (not #9488) +#9573 := [hypothesis]: #7789 +#9645 := (or #9891 #2266 #9960) +#10019 := (= #9980 0::Int) +#9966 := (not #10019) +#9776 := (not #10041) +#9574 := [hypothesis]: #9488 +#6983 := (not #3908) +#9890 := (not #10053) +#9963 := (or #9776 #9890 #2266 #9891 #6983 #9960) +#9883 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9963 +#9889 := [unit-resolution #9883 #9574 #6982 #10062 #10078 #9573]: #9776 +#9850 := (or #9966 #10041) +#9962 := [th-lemma arith triangle-eq]: #9850 +#9644 := [unit-resolution #9962 #9889]: #9966 +#9961 := (or #10016 #9890 #2266 #9891 #6983 #9960) +#10032 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9961 +#10033 := [unit-resolution #10032 #9574 #6982 #10078 #10062 #9573]: #10016 +#9854 := [unit-resolution #10026 #4208 #10033]: #9940 +#9519 := (or #6798 #9959 #10019) +#10020 := (or #10019 #9959) +#9538 := (or #6798 #10020) +#9792 := (iff #9538 #9519) +#10027 := (or #9959 #10019) +#9489 := (or #6798 #10027) +#9526 := (iff #9489 #9519) +#9791 := [rewrite]: #9526 +#9528 := (iff #9538 #9489) +#10028 := (iff #10020 #10027) +#10029 := [rewrite]: #10028 +#9532 := [monotonicity #10029]: #9528 +#9793 := [trans #9532 #9791]: #9792 +#9530 := [quant-inst #7202 #2264]: #9538 +#9752 := [mp #9530 #9793]: #9519 +#9853 := [unit-resolution #9752 #4202 #9854 #9644]: false +#10133 := [lemma #9853]: #9645 +#9525 := [unit-resolution #10133 #10078 #9573]: #9891 +#9529 := [unit-resolution #10076 #9525]: #10074 +#8418 := (or #7629 #7607) +#9089 := [hypothesis]: #10074 +#8415 := [hypothesis]: #7632 +#8417 := [unit-resolution #9503 #8415]: #9501 +#8457 := [unit-resolution #9506 #8415]: #9504 +#8458 := [unit-resolution #10072 #8457 #8417 #9089]: false +#9334 := [lemma #8458]: #8418 +#9748 := [unit-resolution #9334 #9529]: #7629 +#9790 := [unit-resolution #10068 #9748]: #7530 +#9746 := [unit-resolution #11911 #9790]: #9572 +#9888 := [th-lemma arith farkas 1 -1 1 #9571 #10078 #9746]: false +#8313 := [lemma #9888]: #8355 +#26761 := [unit-resolution #8313 #26755]: #2266 +#26759 := [unit-resolution #12708 #26761]: #4481 +#26762 := [unit-resolution #4077 #26759]: #4472 +#26758 := [unit-resolution #12712 #26762]: #4469 +#26763 := [unit-resolution #3999 #26758]: #4460 +#26771 := [unit-resolution #23140 #26763]: #4457 +#26773 := [unit-resolution #3987 #26771]: #4446 +#26770 := [unit-resolution #24097 #26773]: #14174 +#26774 := [unit-resolution #12462 #6500 #26770]: #14076 +#26772 := [unit-resolution #24701 #26774]: #19558 +#26788 := [unit-resolution #21429 #26772 #19774]: #21426 +#26791 := [unit-resolution #4100 #26771]: #2920 +#26783 := [unit-resolution #24453 #12656 #26791 #26788]: #14788 +#26766 := [unit-resolution #24443 #26783]: #14778 +#26825 := [trans #26766 #26819]: #26205 +#26789 := [unit-resolution #24456 #26783]: #14775 +#26784 := [unit-resolution #27691 #26789]: #15503 +#26782 := [unit-resolution #24433 #26783]: #24439 +#26785 := [unit-resolution #27705 #26789]: #15527 +#26781 := [unit-resolution #29104 #26785 #26773 #26782 #26772 #26784]: #26233 +#26820 := [unit-resolution #26781 #26825]: false +#26821 := [lemma #26820]: #2350 +#8220 := [unit-resolution #4101 #26821]: #4454 +#8224 := [unit-resolution #23140 #8220]: #4463 +#8310 := [unit-resolution #3999 #8224]: #4466 +#8229 := [unit-resolution #12712 #8310]: #4475 +#8233 := [unit-resolution #4077 #8229]: #4478 +#8239 := [unit-resolution #12708 #8233]: #2267 +#8333 := [unit-resolution #11103 #8239]: #6064 +#8358 := [unit-resolution #6111 #8333]: #6082 +#8276 := [unit-resolution #12658 #8358]: #6079 +#8416 := [symm #8276]: #6077 +#8345 := [monotonicity #8416]: #7816 +#8349 := [symm #8345]: #7788 +#8351 := [unit-resolution #8313 #8239]: #9960 +[unit-resolution #7819 #8351 #8349]: false unsat diff -r 679118e35378 -r a4d1b5eef12e src/HOL/Boogie/Examples/VCC_Max.certs --- a/src/HOL/Boogie/Examples/VCC_Max.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/Boogie/Examples/VCC_Max.certs Sun Dec 19 18:55:21 2010 +0100 @@ -1,1510 +1,758 @@ -d334e94512e2be06e90930c75ed763964895b7de 7803 0 +3b08169b1d21e7df09081614598ecffbfc739ade 7774 0 #2 := false -decl f121 :: (-> S19 S20 Int) +#161 := 0::Int +decl f122 :: (-> S19 S20 Int) decl f77 :: (-> S20 Int S18 S20) decl f19 :: S18 #50 := f19 decl ?v0!14 :: Int -#18614 := ?v0!14 +#18578 := ?v0!14 decl f54 :: (-> S18 Int S20) -decl f298 :: Int -#3041 := f298 -#3042 := (f54 f19 f298) -#18619 := (f77 #3042 ?v0!14 f19) -decl f297 :: S19 -#3039 := f297 -#18620 := (f121 f297 #18619) -decl f309 :: Int -#3139 := f309 -#3257 := (f77 #3042 f309 f19) -#3266 := (f121 f297 #3257) -#30591 := (= #3266 #18620) -#30624 := (not #30591) -#161 := 0::Int +decl f299 :: Int +#3041 := f299 +#3042 := (f54 f19 f299) +#18583 := (f77 #3042 ?v0!14 f19) +decl f298 :: S19 +#3039 := f298 +#18584 := (f122 f298 #18583) #4203 := -1::Int -#18941 := (* -1::Int #18620) -#30619 := (+ #3266 #18941) -#30621 := (>= #30619 0::Int) -#30631 := (not #30621) +#18905 := (* -1::Int #18584) +decl f310 :: Int +#3139 := f310 +#3257 := (f77 #3042 f310 f19) +#3266 := (f122 f298 #3257) +#30336 := (+ #3266 #18905) +#30338 := (>= #30336 0::Int) +#30332 := (= #3266 #18584) +#29868 := (= f310 ?v0!14) +decl f308 :: Int +#3131 := f308 +#29822 := (+ f308 #18905) +#29823 := (>= #29822 0::Int) +#30220 := (not #29823) +decl f316 :: Int +#3275 := f316 +#13534 := (* -1::Int f316) +#24551 := (+ f308 #13534) +#24552 := (<= #24551 0::Int) +#30447 := (+ #3266 #13534) +#30448 := (<= #30447 0::Int) +#30446 := (= #3266 f316) decl f315 :: Int -#3275 := f315 -#13570 := (* -1::Int f315) -#30344 := (+ #3266 #13570) -#30172 := (<= #30344 0::Int) -#30343 := (= #3266 f315) -decl f314 :: Int -#3268 := f314 -#12601 := (= f314 f315) -#18942 := (+ f315 #18941) -#18943 := (>= #18942 0::Int) -#18928 := (* -1::Int ?v0!14) -decl f317 :: Int -#3285 := f317 -#18929 := (+ f317 #18928) -#18930 := (<= #18929 0::Int) -#18616 := (>= ?v0!14 0::Int) -#22396 := (not #18616) -#7632 := 4294967295::Int -#18615 := (<= ?v0!14 4294967295::Int) -#22395 := (not #18615) -#22411 := (or #22395 #22396 #18930 #18943) -#22416 := (not #22411) +#3268 := f315 +#12565 := (= f315 f316) +#18906 := (+ f316 #18905) +#18907 := (>= #18906 0::Int) +#18892 := (* -1::Int ?v0!14) +decl f318 :: Int +#3285 := f318 +#18893 := (+ f318 #18892) +#18894 := (<= #18893 0::Int) +#18580 := (>= ?v0!14 0::Int) +#22360 := (not #18580) +#7596 := 4294967295::Int +#18579 := (<= ?v0!14 4294967295::Int) +#22359 := (not #18579) +#22375 := (or #22359 #22360 #18894 #18907) +#22380 := (not #22375) #202 := (:var 0 Int) #3123 := (f77 #3042 #202 f19) -#23363 := (pattern #3123) -#15219 := (<= #202 4294967295::Int) -#19613 := (not #15219) -#3124 := (f121 f297 #3123) -#13571 := (+ #3124 #13570) -#13572 := (<= #13571 0::Int) -#13551 := (* -1::Int f317) -#13559 := (+ #202 #13551) -#13558 := (>= #13559 0::Int) +#23327 := (pattern #3123) +#15183 := (<= #202 4294967295::Int) +#19577 := (not #15183) +#3124 := (f122 f298 #3123) +#13535 := (+ #3124 #13534) +#13536 := (<= #13535 0::Int) +#13515 := (* -1::Int f318) +#13523 := (+ #202 #13515) +#13522 := (>= #13523 0::Int) #4202 := (>= #202 0::Int) -#5124 := (not #4202) -#22377 := (or #5124 #13558 #13572 #19613) -#23380 := (forall (vars (?v0 Int)) (:pat #23363) #22377) -#23385 := (not #23380) -decl f316 :: Int -#3277 := f316 -#13592 := (* -1::Int f316) -decl f296 :: Int -#3036 := f296 -#13593 := (+ f296 #13592) -#13594 := (<= #13593 0::Int) -#3298 := (f77 #3042 f316 f19) -#3299 := (f121 f297 #3298) -#12643 := (= f315 #3299) -#22362 := (not #12643) -#22363 := (or #22362 #13594) -#22364 := (not #22363) -#23388 := (or #22364 #23385) -#23391 := (not #23388) -#23394 := (or #23391 #22416) -#23397 := (not #23394) -#13552 := (+ f296 #13551) -#13550 := (>= #13552 0::Int) -#13555 := (not #13550) -#23400 := (or #13555 #23397) -#23403 := (not #23400) -#23406 := (or #13555 #23403) -#23409 := (not #23406) -#15899 := 4294967294::Int -#15900 := (<= f309 4294967294::Int) -#18597 := (not #15900) -#13619 := (+ f309 #13551) -#13618 := (= #13619 -1::Int) -#13622 := (not #13618) +#5104 := (not #4202) +#22341 := (or #5104 #13522 #13536 #19577) +#23344 := (forall (vars (?v0 Int)) (:pat #23327) #22341) +#23349 := (not #23344) +decl f317 :: Int +#3277 := f317 +#13556 := (* -1::Int f317) +decl f297 :: Int +#3036 := f297 +#13557 := (+ f297 #13556) +#13558 := (<= #13557 0::Int) +#3298 := (f77 #3042 f317 f19) +#3299 := (f122 f298 #3298) +#12607 := (= f316 #3299) +#22326 := (not #12607) +#22327 := (or #22326 #13558) +#22328 := (not #22327) +#23352 := (or #22328 #23349) +#23355 := (not #23352) +#23358 := (or #23355 #22380) +#23361 := (not #23358) +#13516 := (+ f297 #13515) +#13514 := (>= #13516 0::Int) +#13519 := (not #13514) +#23364 := (or #13519 #23361) +#23367 := (not #23364) +#23370 := (or #13519 #23367) +#23373 := (not #23370) +#15863 := 4294967294::Int +#15864 := (<= f310 4294967294::Int) +#18561 := (not #15864) +#13583 := (+ f310 #13515) +#13582 := (= #13583 -1::Int) +#13586 := (not #13582) #935 := 2::Int -#13542 := (>= f317 2::Int) -#22439 := (not #13542) -#13534 := (>= f309 -1::Int) -#18594 := (not #13534) -#13525 := (>= f316 0::Int) -#22438 := (not #13525) -decl f301 :: (-> S19 S17 S17 Int S18 S1) +#13506 := (>= f318 2::Int) +#22403 := (not #13506) +#13498 := (>= f310 -1::Int) +#18558 := (not #13498) +#13489 := (>= f317 0::Int) +#22402 := (not #13489) +decl f302 :: (-> S19 S17 S17 Int S18 S1) decl f16 :: S18 #46 := f16 -decl f284 :: S17 -#3012 := f284 -decl f280 :: S17 -#3008 := f280 -#3287 := (f301 f297 f280 f284 f317 f16) +decl f285 :: S17 +#3012 := f285 +decl f281 :: S17 +#3008 := f281 +#3287 := (f302 f298 f281 f285 f318 f16) decl f1 :: S1 #4 := f1 -#12622 := (= f1 #3287) -#12692 := (not #12622) -#23412 := (or #12692 #22438 #18594 #22439 #13622 #18597 #23409) -#23415 := (not #23412) -#23418 := (or #18594 #18597 #23415) -#23421 := (not #23418) +#12586 := (= f1 #3287) +#12656 := (not #12586) +#23376 := (or #12656 #22402 #18558 #22403 #13586 #18561 #23373) +#23379 := (not #23376) +#23382 := (or #18558 #18561 #23379) +#23385 := (not #23382) #42 := 1::Int -#13516 := (>= f309 1::Int) -#13656 := (not #13516) -#12604 := (= f309 f316) -#12731 := (not #12604) -#12740 := (not #12601) -decl f286 :: S17 -#3014 := f286 -decl f281 :: S17 -#3009 := f281 -#3272 := (f301 f297 f281 f286 f309 f16) -#12596 := (= f1 #3272) -#12758 := (not #12596) -decl f288 :: S17 -#3016 := f288 +#13480 := (>= f310 1::Int) +#13620 := (not #13480) +#12568 := (= f310 f317) +#12695 := (not #12568) +#12704 := (not #12565) +decl f287 :: S17 +#3014 := f287 decl f282 :: S17 -#3010 := f282 -#3270 := (f301 f297 f282 f288 f314 f19) -#12593 := (= f1 #3270) -#12767 := (not #12593) -#12590 := (= #3266 f314) -#12776 := (not #12590) +#3009 := f282 +#3272 := (f302 f298 f282 f287 f310 f16) +#12560 := (= f1 #3272) +#12722 := (not #12560) +decl f289 :: S17 +#3016 := f289 +decl f283 :: S17 +#3010 := f283 +#3270 := (f302 f298 f283 f289 f315 f19) +#12557 := (= f1 #3270) +#12731 := (not #12557) +#12554 := (= #3266 f315) +#12740 := (not #12554) decl f79 :: (-> S19 S20 S1) -#3263 := (f79 f297 #3257) -#12584 := (= f1 #3263) -#18565 := (not #12584) +#3263 := (f79 f298 #3257) +#12548 := (= f1 #3263) +#18529 := (not #12548) decl f59 :: (-> S20 S18 S1) #3258 := (f59 #3257 f19) -#12575 := (= f1 #3258) -#18556 := (not #12575) -#23424 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #23421) -#23427 := (not #23424) -decl f36 :: (-> S19 S20 S20) -decl f146 :: (-> S29 S20) -decl f69 :: (-> S28 S20 S29) -decl f70 :: (-> S19 S28) -#3220 := (f70 f297) -#27834 := (f69 #3220 #3257) -#28494 := (f146 #27834) -#28497 := (f36 f297 #28494) -decl f37 :: S20 -#116 := f37 -#28498 := (= f37 #28497) -decl f221 :: (-> S19 S20 S1) -#28495 := (f221 f297 #28494) -#28496 := (= f1 #28495) -#28554 := (or #28496 #28498) -#28557 := (not #28554) -decl f147 :: (-> S29 S1) -#28507 := (f147 #27834) -#28508 := (= f1 #28507) -#28509 := (not #28508) -decl f38 :: (-> S19 S20 S1) -#28504 := (f38 f297 #28494) -#28505 := (= f1 #28504) -#28506 := (not #28505) -#28548 := (or #28506 #28509) -#28551 := (not #28548) -decl f23 :: (-> S18 S23) -decl f24 :: (-> S20 S18) -#28202 := (f24 #3257) -#28512 := (f23 #28202) -decl f25 :: S23 -#67 := f25 -#28530 := (= f25 #28512) -#28545 := (not #28530) -#28501 := (f24 #28494) -#28502 := (f23 #28501) -#28503 := (= f25 #28502) -#28563 := (or #28503 #28545 #28551 #28557) -#28568 := (not #28563) -#28519 := (f36 f297 #3257) -#28520 := (= f37 #28519) -#28517 := (f221 f297 #3257) -#28518 := (= f1 #28517) -#28533 := (or #28518 #28520) -#28536 := (not #28533) -#28539 := (or #28530 #28536) -#28542 := (not #28539) -#28571 := (or #28542 #28568) -#28574 := (not #28571) +#12539 := (= f1 #3258) +#18520 := (not #12539) +#23388 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #23385) +#23391 := (not #23388) +#13673 := (* -1::Int #3266) +#13674 := (+ f308 #13673) +#13672 := (>= #13674 0::Int) +#13671 := (not #13672) +decl f309 :: Int +#3135 := f309 +#13477 := (>= f309 0::Int) +#22443 := (not #13477) +#12806 := (= f309 f317) +#12812 := (not #12806) +#12803 := (= f308 f316) +#12821 := (not #12803) +#23418 := (or #12821 #12812 #22443 #13620 #22402 #13671 #23385) +#23421 := (not #23418) +#28423 := [hypothesis]: #23421 +#24557 := (or #23418 #12803) +#24558 := [def-axiom]: #24557 +#28430 := [unit-resolution #24558 #28423]: #12803 +#29525 := (or #12821 #24552) +#29591 := [th-lemma arith triangle-eq]: #29525 +#29590 := [unit-resolution #29591 #28430]: #24552 +#24448 := (not #18907) +#29594 := (or #23418 #22328) +#13941 := (* -1::Int f309) +#13942 := (+ f297 #13941) +#13943 := (<= #13942 0::Int) +#13944 := (not #13943) +decl ?v0!15 :: Int +#18702 := ?v0!15 +#18707 := (f77 #3042 ?v0!15 f19) +#18708 := (f122 f298 #18707) +#19053 := (* -1::Int #18708) +decl f314 :: Int +#3166 := f314 +#19054 := (+ f314 #19053) +#19055 := (>= #19054 0::Int) +#19040 := (* -1::Int ?v0!15) +#19041 := (+ f297 #19040) +#19042 := (<= #19041 0::Int) +#18704 := (>= ?v0!15 0::Int) +#22537 := (not #18704) +#18703 := (<= ?v0!15 4294967295::Int) +#22536 := (not #18703) +#22552 := (or #22536 #22537 #19042 #19055) +#22557 := (not #22552) +#13406 := (* -1::Int f297) +#13794 := (+ #202 #13406) +#13793 := (>= #13794 0::Int) +#3173 := (= #3124 f314) +#22510 := (not #3173) +#22511 := (or #22510 #5104 #13793 #19577) +#23468 := (forall (vars (?v0 Int)) (:pat #23327) #22511) +#23473 := (not #23468) +#13805 := (* -1::Int f314) +#13806 := (+ #3124 #13805) +#13807 := (<= #13806 0::Int) +#22502 := (or #5104 #13793 #13807 #19577) +#23460 := (forall (vars (?v0 Int)) (:pat #23327) #22502) +#23465 := (not #23460) +#23476 := (or #23465 #23473) +#23479 := (not #23476) +#23482 := (or #23479 #22557) +#23485 := (not #23482) +#13501 := (* -1::Int f310) +#13764 := (+ f297 #13501) +#13765 := (<= #13764 0::Int) +#13766 := (not #13765) +#12242 := (= f308 f314) +#12277 := (not #12242) +decl f313 :: Int +#3164 := f313 +#12239 := (= f309 f313) +#12286 := (not #12239) +decl f312 :: Int +#3162 := f312 +#12236 := (= f310 f312) +#12295 := (not #12236) +decl f311 :: Int +#3160 := f311 +#12233 := (= f308 f311) +#12304 := (not #12233) +#23488 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #23485) +#23491 := (not #23488) +#23394 := (or #18520 #18529 #23391) +#23397 := (not #23394) decl f35 :: (-> S19 S20 S1) -#3260 := (f35 f297 #3257) -#12578 := (= f1 #3260) -#18559 := (not #12578) -#28577 := (or #18559 #28574) -#28580 := (not #28577) -#28583 := (iff #12584 #28580) -#29899 := (not #28583) -#30296 := [hypothesis]: #29899 -#62 := (:var 0 S20) -#86 := (:var 1 S19) -#2438 := (f79 #86 #62) -#2439 := (pattern #2438) -#324 := (f70 #86) -#2441 := (f69 #324 #62) -#2445 := (f146 #2441) -#2456 := (f221 #86 #2445) -#10696 := (= f1 #2456) -#2454 := (f36 #86 #2445) -#10693 := (= f37 #2454) -#10699 := (or #10693 #10696) -#22070 := (not #10699) -#2450 := (f24 #2445) -#2451 := (f23 #2450) -#10687 := (= f25 #2451) -#2446 := (f38 #86 #2445) -#10678 := (= f1 #2446) -#10681 := (not #10678) -#2442 := (f147 #2441) -#10672 := (= f1 #2442) -#10675 := (not #10672) -#10684 := (or #10675 #10681) -#22069 := (not #10684) -#65 := (f24 #62) -#66 := (f23 #65) -#68 := (= #66 f25) -#91 := (not #68) -#22071 := (or #91 #22069 #10687 #22070) -#22072 := (not #22071) -#2462 := (f221 #86 #62) -#10711 := (= f1 #2462) -#182 := (f36 #86 #62) -#3761 := (= f37 #182) -#10714 := (or #3761 #10711) -#22064 := (not #10714) -#22065 := (or #68 #22064) -#22066 := (not #22065) -#22075 := (or #22066 #22072) -#22081 := (not #22075) -#186 := (f35 #86 #62) -#3767 := (= f1 #186) -#11297 := (not #3767) -#22082 := (or #11297 #22081) -#22083 := (not #22082) -#10668 := (= f1 #2438) -#22088 := (iff #10668 #22083) -#22091 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22088) -#10690 := (not #10687) -#10732 := (and #68 #10684 #10690 #10699) -#10717 := (and #91 #10714) -#10738 := (or #10717 #10732) -#10743 := (and #3767 #10738) -#10746 := (iff #10668 #10743) -#10749 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10746) -#22092 := (iff #10749 #22091) -#22089 := (iff #10746 #22088) -#22086 := (iff #10743 #22083) -#22078 := (and #3767 #22075) -#22084 := (iff #22078 #22083) -#22085 := [rewrite]: #22084 -#22079 := (iff #10743 #22078) -#22076 := (iff #10738 #22075) -#22073 := (iff #10732 #22072) -#22074 := [rewrite]: #22073 -#22067 := (iff #10717 #22066) -#22068 := [rewrite]: #22067 -#22077 := [monotonicity #22068 #22074]: #22076 -#22080 := [monotonicity #22077]: #22079 -#22087 := [trans #22080 #22085]: #22086 -#22090 := [monotonicity #22087]: #22089 -#22093 := [quant-intro #22090]: #22092 -#18014 := (~ #10749 #10749) -#18012 := (~ #10746 #10746) -#18013 := [refl]: #18012 -#18015 := [nnf-pos #18013]: #18014 -#2463 := (= #2462 f1) -#183 := (= #182 f37) -#2464 := (or #183 #2463) -#2465 := (and #91 #2464) -#2457 := (= #2456 f1) -#2455 := (= #2454 f37) -#2458 := (or #2455 #2457) -#2452 := (= #2451 f25) -#2453 := (not #2452) -#2459 := (and #2453 #2458) -#2447 := (= #2446 f1) -#2448 := (not #2447) -#2443 := (= #2442 f1) -#2444 := (not #2443) -#2449 := (or #2444 #2448) -#2460 := (and #2449 #2459) -#2461 := (and #68 #2460) -#2466 := (or #2461 #2465) -#187 := (= #186 f1) -#2467 := (and #187 #2466) -#2440 := (= #2438 f1) -#2468 := (iff #2440 #2467) -#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468) -#10752 := (iff #2469 #10749) -#10702 := (and #10690 #10699) -#10705 := (and #10684 #10702) -#10708 := (and #68 #10705) -#10720 := (or #10708 #10717) -#10723 := (and #3767 #10720) -#10726 := (iff #10668 #10723) -#10729 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10726) -#10750 := (iff #10729 #10749) -#10747 := (iff #10726 #10746) -#10744 := (iff #10723 #10743) -#10741 := (iff #10720 #10738) -#10735 := (or #10732 #10717) -#10739 := (iff #10735 #10738) -#10740 := [rewrite]: #10739 -#10736 := (iff #10720 #10735) -#10733 := (iff #10708 #10732) -#10734 := [rewrite]: #10733 -#10737 := [monotonicity #10734]: #10736 -#10742 := [trans #10737 #10740]: #10741 -#10745 := [monotonicity #10742]: #10744 -#10748 := [monotonicity #10745]: #10747 -#10751 := [quant-intro #10748]: #10750 -#10730 := (iff #2469 #10729) -#10727 := (iff #2468 #10726) -#10724 := (iff #2467 #10723) -#10721 := (iff #2466 #10720) -#10718 := (iff #2465 #10717) -#10715 := (iff #2464 #10714) -#10712 := (iff #2463 #10711) -#10713 := [rewrite]: #10712 -#3762 := (iff #183 #3761) -#3763 := [rewrite]: #3762 -#10716 := [monotonicity #3763 #10713]: #10715 -#10719 := [monotonicity #10716]: #10718 -#10709 := (iff #2461 #10708) -#10706 := (iff #2460 #10705) -#10703 := (iff #2459 #10702) -#10700 := (iff #2458 #10699) -#10697 := (iff #2457 #10696) -#10698 := [rewrite]: #10697 -#10694 := (iff #2455 #10693) -#10695 := [rewrite]: #10694 -#10701 := [monotonicity #10695 #10698]: #10700 -#10691 := (iff #2453 #10690) -#10688 := (iff #2452 #10687) -#10689 := [rewrite]: #10688 -#10692 := [monotonicity #10689]: #10691 -#10704 := [monotonicity #10692 #10701]: #10703 -#10685 := (iff #2449 #10684) -#10682 := (iff #2448 #10681) -#10679 := (iff #2447 #10678) -#10680 := [rewrite]: #10679 -#10683 := [monotonicity #10680]: #10682 -#10676 := (iff #2444 #10675) -#10673 := (iff #2443 #10672) -#10674 := [rewrite]: #10673 -#10677 := [monotonicity #10674]: #10676 -#10686 := [monotonicity #10677 #10683]: #10685 -#10707 := [monotonicity #10686 #10704]: #10706 -#10710 := [monotonicity #10707]: #10709 -#10722 := [monotonicity #10710 #10719]: #10721 -#3768 := (iff #187 #3767) -#3769 := [rewrite]: #3768 -#10725 := [monotonicity #3769 #10722]: #10724 -#10670 := (iff #2440 #10668) -#10671 := [rewrite]: #10670 -#10728 := [monotonicity #10671 #10725]: #10727 -#10731 := [quant-intro #10728]: #10730 -#10753 := [trans #10731 #10751]: #10752 -#10667 := [asserted]: #2469 -#10754 := [mp #10667 #10753]: #10749 -#18016 := [mp~ #10754 #18015]: #10749 -#22094 := [mp #18016 #22093]: #22091 -#28423 := (not #22091) -#29896 := (or #28423 #28583) -#28499 := (or #28498 #28496) -#28500 := (not #28499) -#28510 := (or #28509 #28506) -#28511 := (not #28510) -#28513 := (= #28512 f25) -#28514 := (not #28513) -#28515 := (or #28514 #28511 #28503 #28500) -#28516 := (not #28515) -#28521 := (or #28520 #28518) -#28522 := (not #28521) -#28523 := (or #28513 #28522) -#28524 := (not #28523) -#28525 := (or #28524 #28516) -#28526 := (not #28525) -#28527 := (or #18559 #28526) -#28528 := (not #28527) -#28529 := (iff #12584 #28528) -#29897 := (or #28423 #28529) -#29946 := (iff #29897 #29896) -#29888 := (iff #29896 #29896) -#29891 := [rewrite]: #29888 -#28584 := (iff #28529 #28583) -#28581 := (iff #28528 #28580) -#28578 := (iff #28527 #28577) -#28575 := (iff #28526 #28574) -#28572 := (iff #28525 #28571) -#28569 := (iff #28516 #28568) -#28566 := (iff #28515 #28563) -#28560 := (or #28545 #28551 #28503 #28557) -#28564 := (iff #28560 #28563) -#28565 := [rewrite]: #28564 -#28561 := (iff #28515 #28560) -#28558 := (iff #28500 #28557) -#28555 := (iff #28499 #28554) -#28556 := [rewrite]: #28555 -#28559 := [monotonicity #28556]: #28558 -#28552 := (iff #28511 #28551) -#28549 := (iff #28510 #28548) -#28550 := [rewrite]: #28549 -#28553 := [monotonicity #28550]: #28552 -#28546 := (iff #28514 #28545) -#28531 := (iff #28513 #28530) -#28532 := [rewrite]: #28531 -#28547 := [monotonicity #28532]: #28546 -#28562 := [monotonicity #28547 #28553 #28559]: #28561 -#28567 := [trans #28562 #28565]: #28566 -#28570 := [monotonicity #28567]: #28569 -#28543 := (iff #28524 #28542) -#28540 := (iff #28523 #28539) -#28537 := (iff #28522 #28536) -#28534 := (iff #28521 #28533) -#28535 := [rewrite]: #28534 -#28538 := [monotonicity #28535]: #28537 -#28541 := [monotonicity #28532 #28538]: #28540 -#28544 := [monotonicity #28541]: #28543 -#28573 := [monotonicity #28544 #28570]: #28572 -#28576 := [monotonicity #28573]: #28575 -#28579 := [monotonicity #28576]: #28578 -#28582 := [monotonicity #28579]: #28581 -#28585 := [monotonicity #28582]: #28584 -#29935 := [monotonicity #28585]: #29946 -#29933 := [trans #29935 #29891]: #29946 -#29945 := [quant-inst #3039 #3257]: #29897 -#29889 := [mp #29945 #29933]: #29896 -#30214 := [unit-resolution #29889 #22094 #30296]: false -#30215 := [lemma #30214]: #28583 -#30322 := (or #29899 #12584) -#30167 := [hypothesis]: #28563 -decl f127 :: (-> S20 Int) -#3043 := (f127 #3042) -decl f135 :: (-> S18 Int S18) -#3040 := (f135 f19 f296) -#3044 := (f54 #3040 #3043) -#3047 := (f36 f297 #3044) -#30199 := (= #3047 #28497) -#30193 := (= #28497 #3047) -#30284 := (= #28494 #3044) -decl f154 :: (-> S18 Int) -#24998 := (f154 #3040) -decl f155 :: (-> S18 S18) -#24996 := (f155 #3040) -#27144 := (f135 #24996 #24998) -#27145 := (f54 #27144 #3043) -#28787 := (= #27145 #3044) -#28807 := (= #27144 #3040) -#28805 := (= #24998 f296) -#24999 := (= f296 #24998) -#369 := (:var 1 S18) -#1401 := (f135 #369 #202) -#1638 := (pattern #1401) -#1649 := (f154 #1401) -#8444 := (= #202 #1649) -#8447 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8444) -#17390 := (~ #8447 #8447) -#17388 := (~ #8444 #8444) -#17389 := [refl]: #17388 -#17391 := [nnf-pos #17389]: #17390 -#1650 := (= #1649 #202) -#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650) -#8448 := (iff #1651 #8447) -#8445 := (iff #1650 #8444) -#8446 := [rewrite]: #8445 -#8449 := [quant-intro #8446]: #8448 -#8443 := [asserted]: #1651 -#8452 := [mp #8443 #8449]: #8447 -#17392 := [mp~ #8452 #17391]: #8447 -#25005 := (not #8447) -#25006 := (or #25005 #24999) -#25007 := [quant-inst #50 #3036]: #25006 -#28406 := [unit-resolution #25007 #17392]: #24999 -#28806 := [symm #28406]: #28805 -#28385 := (= #24996 f19) -#24997 := (= f19 #24996) -#1652 := (f155 #1401) -#8451 := (= #369 #1652) -#8455 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8451) -#17395 := (~ #8455 #8455) -#17393 := (~ #8451 #8451) -#17394 := [refl]: #17393 -#17396 := [nnf-pos #17394]: #17395 -#1653 := (= #1652 #369) -#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653) -#8456 := (iff #1654 #8455) -#8453 := (iff #1653 #8451) -#8454 := [rewrite]: #8453 -#8457 := [quant-intro #8454]: #8456 -#8450 := [asserted]: #1654 -#8460 := [mp #8450 #8457]: #8455 -#17397 := [mp~ #8460 #17396]: #8455 -#25000 := (not #8455) -#25001 := (or #25000 #24997) -#25002 := [quant-inst #50 #3036]: #25001 -#28384 := [unit-resolution #25002 #17397]: #24997 -#28386 := [symm #28384]: #28385 -#28808 := [monotonicity #28386 #28806]: #28807 -#28789 := [monotonicity #28808]: #28787 -#30282 := (= #28494 #27145) -decl f136 :: (-> S20 S20 Int) -decl f39 :: (-> Int S20) -decl f40 :: (-> S20 Int) -#3076 := (f40 #3042) -#24833 := (f39 #3076) -#27122 := (f24 #24833) -#29367 := (f77 #24833 f309 #27122) -#29368 := (f136 #29367 #24833) -#29431 := (f77 #27145 #29368 #24996) -#29452 := (f69 #3220 #29431) -#29458 := (f146 #29452) -#30280 := (= #29458 #27145) -#29459 := (= #27145 #29458) -#29460 := (not #29459) -#29456 := (f147 #29452) -#29457 := (= f1 #29456) -decl f78 :: (-> S29 S1) -#29453 := (f78 #29452) -#29454 := (= f1 #29453) -#29455 := (not #29454) -#29449 := (f35 f297 #29431) -#29450 := (= f1 #29449) -#29451 := (not #29450) -#29481 := (or #29451 #29455 #29457 #29460) -#29484 := (not #29481) -#29474 := (* -1::Int #29368) -#29475 := (+ #24998 #29474) -#29476 := (<= #29475 0::Int) -#30241 := (not #29476) -#29583 := (+ f309 #29474) -#29585 := (>= #29583 0::Int) -#29369 := (= f309 #29368) -#55 := (:var 1 S20) -#1433 := (f24 #55) -#1434 := (f77 #55 #202 #1433) -#1435 := (pattern #1434) -#1436 := (f136 #1434 #55) -#7824 := (= #202 #1436) -#7828 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7824) -#17105 := (~ #7828 #7828) -#17103 := (~ #7824 #7824) -#17104 := [refl]: #17103 -#17106 := [nnf-pos #17104]: #17105 -#1437 := (= #1436 #202) -#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437) -#7829 := (iff #1438 #7828) -#7826 := (iff #1437 #7824) -#7827 := [rewrite]: #7826 -#7830 := [quant-intro #7827]: #7829 -#7823 := [asserted]: #1438 -#7833 := [mp #7823 #7830]: #7828 -#17107 := [mp~ #7833 #17106]: #7828 -#27129 := (not #7828) -#29432 := (or #27129 #29369) -#29448 := [quant-inst #24833 #3139]: #29432 -#29674 := [unit-resolution #29448 #17107]: #29369 -#29675 := (not #29369) -#30235 := (or #29675 #29585) -#30236 := [th-lemma arith triangle-eq]: #30235 -#30237 := [unit-resolution #30236 #29674]: #29585 -#13537 := (* -1::Int f309) -#13800 := (+ f296 #13537) -#13801 := (<= #13800 0::Int) -#13802 := (not #13801) -#13709 := (* -1::Int #3266) -decl f307 :: Int -#3131 := f307 -#13710 := (+ f307 #13709) -#13708 := (>= #13710 0::Int) -#13707 := (not #13708) -decl f308 :: Int -#3135 := f308 -#13513 := (>= f308 0::Int) -#22479 := (not #13513) -#12842 := (= f308 f316) -#12848 := (not #12842) -#12839 := (= f307 f315) -#12857 := (not #12839) -#23454 := (or #12857 #12848 #22479 #13656 #22438 #13707 #23421) +#3260 := (f35 f298 #3257) +#12542 := (= f1 #3260) +#18523 := (not #12542) +#23400 := (or #18520 #18523 #23397) +#23403 := (not #23400) +#23406 := (or #18520 #18523 #23403) +#23409 := (not #23406) +#23412 := (or #22443 #13620 #13672 #23409) +#23415 := (not #23412) +#23424 := (or #23415 #23421) +#23427 := (not #23424) +#23430 := (or #18520 #18529 #22443 #13620 #23427) +#23433 := (not #23430) +#23436 := (or #18520 #18529 #23433) +#23439 := (not #23436) +#23442 := (or #18520 #18523 #23439) +#23445 := (not #23442) +#23448 := (or #18520 #18523 #23445) +#23451 := (not #23448) +#23454 := (or #22443 #13620 #13765 #23451) #23457 := (not #23454) -#23430 := (or #18556 #18565 #23427) -#23433 := (not #23430) -#23436 := (or #18556 #18559 #23433) -#23439 := (not #23436) -#23442 := (or #18556 #18559 #23439) -#23445 := (not #23442) -#23448 := (or #22479 #13656 #13708 #23445) -#23451 := (not #23448) -#23460 := (or #23451 #23457) -#23463 := (not #23460) -#23466 := (or #18556 #18565 #22479 #13656 #23463) -#23469 := (not #23466) -#23472 := (or #18556 #18565 #23469) -#23475 := (not #23472) -#23478 := (or #18556 #18559 #23475) -#23481 := (not #23478) -#23484 := (or #18556 #18559 #23481) -#23487 := (not #23484) -#23490 := (or #22479 #13656 #13801 #23487) -#23493 := (not #23490) -decl ?v0!15 :: Int -#18738 := ?v0!15 -#18743 := (f77 #3042 ?v0!15 f19) -#18744 := (f121 f297 #18743) -#19089 := (* -1::Int #18744) -decl f313 :: Int -#3166 := f313 -#19090 := (+ f313 #19089) -#19091 := (>= #19090 0::Int) -#19076 := (* -1::Int ?v0!15) -#19077 := (+ f296 #19076) -#19078 := (<= #19077 0::Int) -#18740 := (>= ?v0!15 0::Int) -#22573 := (not #18740) -#18739 := (<= ?v0!15 4294967295::Int) -#22572 := (not #18739) -#22588 := (or #22572 #22573 #19078 #19091) -#22593 := (not #22588) -#13442 := (* -1::Int f296) -#13830 := (+ #202 #13442) -#13829 := (>= #13830 0::Int) -#3173 := (= #3124 f313) -#22546 := (not #3173) -#22547 := (or #22546 #5124 #13829 #19613) -#23504 := (forall (vars (?v0 Int)) (:pat #23363) #22547) -#23509 := (not #23504) -#13841 := (* -1::Int f313) -#13842 := (+ #3124 #13841) -#13843 := (<= #13842 0::Int) -#22538 := (or #5124 #13829 #13843 #19613) -#23496 := (forall (vars (?v0 Int)) (:pat #23363) #22538) -#23501 := (not #23496) -#23512 := (or #23501 #23509) -#23515 := (not #23512) -#23518 := (or #23515 #22593) -#23521 := (not #23518) -#12278 := (= f307 f313) -#12313 := (not #12278) -decl f312 :: Int -#3164 := f312 -#12275 := (= f308 f312) -#12322 := (not #12275) -decl f311 :: Int -#3162 := f311 -#12272 := (= f309 f311) -#12331 := (not #12272) -decl f310 :: Int -#3160 := f310 -#12269 := (= f307 f310) -#12340 := (not #12269) -#23524 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #23521) -#23527 := (not #23524) -#23530 := (or #23493 #23527) -#23533 := (not #23530) -#14006 := (* -1::Int f307) -#14007 := (+ #3124 #14006) -#14008 := (<= #14007 0::Int) -#13995 := (+ #202 #13537) -#13994 := (>= #13995 0::Int) -#22354 := (or #5124 #13994 #14008 #19613) -#23372 := (forall (vars (?v0 Int)) (:pat #23363) #22354) -#23377 := (not #23372) +#23494 := (or #23457 #23491) +#23497 := (not #23494) +#13970 := (* -1::Int f308) +#13971 := (+ #3124 #13970) +#13972 := (<= #13971 0::Int) +#13959 := (+ #202 #13501) +#13958 := (>= #13959 0::Int) +#22318 := (or #5104 #13958 #13972 #19577) +#23336 := (forall (vars (?v0 Int)) (:pat #23327) #22318) +#23341 := (not #23336) #1374 := 255::Int -#15885 := (<= f307 255::Int) -#22623 := (not #15885) -#15868 := (<= f308 4294967295::Int) -#22622 := (not #15868) -#15851 := (<= f309 4294967295::Int) -#22621 := (not #15851) -#14056 := (>= f307 0::Int) -#22619 := (not #14056) -#14034 := (>= f309 0::Int) -#22618 := (not #14034) -#14028 := (>= #13800 0::Int) -#14031 := (not #14028) -#13977 := (* -1::Int f308) -#13978 := (+ f296 #13977) -#13979 := (<= #13978 0::Int) -#13508 := (<= f296 0::Int) -decl f302 :: (-> S19 S17 S17 S20 S18 S1) +#15849 := (<= f308 255::Int) +#22587 := (not #15849) +#15832 := (<= f309 4294967295::Int) +#22586 := (not #15832) +#15815 := (<= f310 4294967295::Int) +#22585 := (not #15815) +#14020 := (>= f308 0::Int) +#22583 := (not #14020) +#13998 := (>= f310 0::Int) +#22582 := (not #13998) +#13992 := (>= #13764 0::Int) +#13995 := (not #13992) +#13472 := (<= f297 0::Int) +decl f303 :: (-> S19 S17 S17 S20 S18 S1) decl f18 :: (-> S18 S18) #51 := (f18 f19) +decl f292 :: S17 +#3019 := f292 +decl f284 :: S17 +#3011 := f284 +#3250 := (f303 f298 f284 f292 #3042 #51) +#12522 := (= f1 #3250) +#22581 := (not #12522) +decl f40 :: (-> S20 Int) +#3076 := (f40 #3042) +#3248 := (f302 f298 f284 f292 #3076 #51) +#12519 := (= f1 #3248) +#22580 := (not #12519) decl f291 :: S17 -#3019 := f291 -decl f283 :: S17 -#3011 := f283 -#3250 := (f302 f297 f283 f291 #3042 #51) -#12558 := (= f1 #3250) -#22617 := (not #12558) -#3248 := (f301 f297 f283 f291 #3076 #51) -#12555 := (= f1 #3248) -#22616 := (not #12555) -decl f290 :: S17 -#3018 := f290 -#3246 := (f301 f297 f283 f290 f296 f16) -#12552 := (= f1 #3246) -#13033 := (not #12552) -#3244 := (f301 f297 f283 f288 f307 f19) -#12549 := (= f1 #3244) -#13042 := (not #12549) -#3242 := (f301 f297 f283 f286 f308 f16) -#12546 := (= f1 #3242) -#13051 := (not #12546) -#3240 := (f301 f297 f283 f284 f309 f16) -#12543 := (= f1 #3240) -#13060 := (not #12543) -decl f189 :: (-> S19 S19 S1) -#3232 := (f189 f297 f297) -#12515 := (= f1 #3232) -#13974 := (not #12515) -decl f213 :: (-> S17 S19 S1) -#3157 := (f213 f283 f297) -#12258 := (= f1 #3157) -#15299 := (not #12258) -#3152 := (f77 #3042 f308 f19) -#3153 := (f121 f297 #3152) -#12250 := (= f307 #3153) -#22615 := (not #12250) +#3018 := f291 +#3246 := (f302 f298 f284 f291 f297 f16) +#12516 := (= f1 #3246) +#12997 := (not #12516) +#3244 := (f302 f298 f284 f289 f308 f19) +#12513 := (= f1 #3244) +#13006 := (not #12513) +#3242 := (f302 f298 f284 f287 f309 f16) +#12510 := (= f1 #3242) +#13015 := (not #12510) +#3240 := (f302 f298 f284 f285 f310 f16) +#12507 := (= f1 #3240) +#13024 := (not #12507) +decl f190 :: (-> S19 S19 S1) +#3232 := (f190 f298 f298) +#12479 := (= f1 #3232) +#13938 := (not #12479) +decl f214 :: (-> S17 S19 S1) +#3157 := (f214 f284 f298) +#12222 := (= f1 #3157) +#15263 := (not #12222) +#3152 := (f77 #3042 f309 f19) +#3153 := (f122 f298 #3152) +#12214 := (= f308 #3153) +#22579 := (not #12214) #3098 := (f77 #3042 0::Int f19) -#3108 := (f121 f297 #3098) -decl f306 :: Int -#3107 := f306 -#3109 := (= f306 #3108) -#13267 := (not #3109) -#23536 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #23377 #23533) -#23539 := (not #23536) -#23542 := (or #13267 #13508 #23539) -#23545 := (not #23542) -#13488 := (* -1::Int #3124) -#13489 := (+ f306 #13488) -#13487 := (>= #13489 0::Int) -#13475 := (>= #202 1::Int) -#22343 := (or #5124 #13475 #13487 #19613) -#23364 := (forall (vars (?v0 Int)) (:pat #23363) #22343) -#23369 := (not #23364) -#23548 := (or #23369 #23545) -#23551 := (not #23548) +#3108 := (f122 f298 #3098) +decl f307 :: Int +#3107 := f307 +#3109 := (= f307 #3108) +#13231 := (not #3109) +#23500 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #23341 #23497) +#23503 := (not #23500) +#23506 := (or #13231 #13472 #23503) +#23509 := (not #23506) +#13452 := (* -1::Int #3124) +#13453 := (+ f307 #13452) +#13451 := (>= #13453 0::Int) +#13439 := (>= #202 1::Int) +#22307 := (or #5104 #13439 #13451 #19577) +#23328 := (forall (vars (?v0 Int)) (:pat #23327) #22307) +#23333 := (not #23328) +#23512 := (or #23333 #23509) +#23515 := (not #23512) decl ?v0!13 :: Int -#18477 := ?v0!13 -#18487 := (>= ?v0!13 1::Int) -#18482 := (f77 #3042 ?v0!13 f19) -#18483 := (f121 f297 #18482) -#18484 := (* -1::Int #18483) -#18485 := (+ f306 #18484) -#18486 := (>= #18485 0::Int) -#18479 := (>= ?v0!13 0::Int) -#22317 := (not #18479) -#18478 := (<= ?v0!13 4294967295::Int) -#22316 := (not #18478) -#22332 := (or #22316 #22317 #18486 #18487) -#22337 := (not #22332) -#23554 := (or #22337 #23551) +#18441 := ?v0!13 +#18451 := (>= ?v0!13 1::Int) +#18446 := (f77 #3042 ?v0!13 f19) +#18447 := (f122 f298 #18446) +#18448 := (* -1::Int #18447) +#18449 := (+ f307 #18448) +#18450 := (>= #18449 0::Int) +#18443 := (>= ?v0!13 0::Int) +#22281 := (not #18443) +#18442 := (<= ?v0!13 4294967295::Int) +#22280 := (not #18442) +#22296 := (or #22280 #22281 #18450 #18451) +#22301 := (not #22296) +#23518 := (or #22301 #23515) +#23521 := (not #23518) +#13433 := (>= f297 1::Int) +#13436 := (not #13433) +#23524 := (or #13436 #23521) +#23527 := (not #23524) +#23530 := (or #13436 #23527) +#23533 := (not #23530) +decl f286 :: S17 +#3013 := f286 +#3114 := (f302 f298 f286 f285 1::Int f16) +#12165 := (= f1 #3114) +#13204 := (not #12165) +decl f288 :: S17 +#3015 := f288 +#3112 := (f302 f298 f288 f287 0::Int f16) +#12162 := (= f1 #3112) +#13213 := (not #12162) +decl f290 :: S17 +#3017 := f290 +#3110 := (f302 f298 f290 f289 f307 f19) +#12159 := (= f1 #3110) +#13222 := (not #12159) +#3104 := (f79 f298 #3098) +#12153 := (= f1 #3104) +#18418 := (not #12153) +#3099 := (f59 #3098 f19) +#12144 := (= f1 #3099) +#18409 := (not #12144) +#23536 := (or #13231 #18409 #18418 #13222 #13213 #13204 #23533) +#23539 := (not #23536) +#23542 := (or #18409 #18418 #23539) +#23545 := (not #23542) +#3101 := (f35 f298 #3098) +#12147 := (= f1 #3101) +#18412 := (not #12147) +#23548 := (or #18409 #18412 #23545) +#23551 := (not #23548) +#23554 := (or #18409 #18412 #23551) #23557 := (not #23554) -#13469 := (>= f296 1::Int) -#13472 := (not #13469) -#23560 := (or #13472 #23557) +decl f212 :: (-> S19 S20 S20 S31 S1) +decl f306 :: S31 +#3095 := f306 +decl f128 :: (-> S20 Int) +#3043 := (f128 #3042) +decl f136 :: (-> S18 Int S18) +#3040 := (f136 f19 f297) +#3044 := (f54 #3040 #3043) +#3096 := (f212 f298 #3044 #3044 f306) +#12141 := (= f1 #3096) +#13264 := (not #12141) +#23560 := (or #13264 #23557) #23563 := (not #23560) -#23566 := (or #13472 #23563) -#23569 := (not #23566) -decl f285 :: S17 -#3013 := f285 -#3114 := (f301 f297 f285 f284 1::Int f16) -#12201 := (= f1 #3114) -#13240 := (not #12201) -decl f287 :: S17 -#3015 := f287 -#3112 := (f301 f297 f287 f286 0::Int f16) -#12198 := (= f1 #3112) -#13249 := (not #12198) -decl f289 :: S17 -#3017 := f289 -#3110 := (f301 f297 f289 f288 f306 f19) -#12195 := (= f1 #3110) -#13258 := (not #12195) -#3104 := (f79 f297 #3098) -#12189 := (= f1 #3104) -#18454 := (not #12189) -#3099 := (f59 #3098 f19) -#12180 := (= f1 #3099) -#18445 := (not #12180) -#23572 := (or #13267 #18445 #18454 #13258 #13249 #13240 #23569) -#23575 := (not #23572) -#27039 := (f24 #3098) -#27040 := (= #24996 #27039) -#27013 := (f59 #3098 #24996) -#27014 := (= f1 #27013) -#27042 := (iff #27014 #27040) -#275 := (:var 0 S18) -#2729 := (f59 #55 #275) -#2730 := (pattern #2729) -#11369 := (= f1 #2729) -#9220 := (= #275 #1433) -#11390 := (iff #9220 #11369) -#23294 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11390) -#11395 := (forall (vars (?v0 S20) (?v1 S18)) #11390) -#23297 := (iff #11395 #23294) -#23295 := (iff #11390 #11390) -#23296 := [refl]: #23295 -#23298 := [quant-intro #23296]: #23297 -#18287 := (~ #11395 #11395) -#18285 := (~ #11390 #11390) -#18286 := [refl]: #18285 -#18288 := [nnf-pos #18286]: #18287 -#1939 := (= #1433 #275) -#2731 := (= #2729 f1) -#2736 := (iff #2731 #1939) -#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736) -#11396 := (iff #2737 #11395) -#11393 := (iff #2736 #11390) -#11386 := (iff #11369 #9220) -#11391 := (iff #11386 #11390) -#11392 := [rewrite]: #11391 -#11388 := (iff #2736 #11386) -#9221 := (iff #1939 #9220) -#9222 := [rewrite]: #9221 -#11371 := (iff #2731 #11369) -#11372 := [rewrite]: #11371 -#11389 := [monotonicity #11372 #9222]: #11388 -#11394 := [trans #11389 #11392]: #11393 -#11397 := [quant-intro #11394]: #11396 -#11385 := [asserted]: #2737 -#11400 := [mp #11385 #11397]: #11395 -#18289 := [mp~ #11400 #18288]: #11395 -#23299 := [mp #18289 #23298]: #23294 -#26210 := (not #23294) -#27513 := (or #26210 #27042) -#27041 := (iff #27040 #27014) -#27551 := (or #26210 #27041) -#27552 := (iff #27551 #27513) -#27592 := (iff #27513 #27513) -#27593 := [rewrite]: #27592 -#27043 := (iff #27041 #27042) -#27044 := [rewrite]: #27043 -#27594 := [monotonicity #27044]: #27552 -#27595 := [trans #27594 #27593]: #27552 -#27546 := [quant-inst #3098 #24996]: #27551 -#27596 := [mp #27546 #27595]: #27513 -#27640 := [unit-resolution #27596 #23299]: #27042 -#25112 := (f24 #3042) -#27668 := (= #25112 #27039) -#27682 := (= #27039 #25112) -#27680 := (= #3098 #3042) -#27070 := (f127 #24833) -#27086 := (f54 #24996 #27070) -#27410 := (= #27086 #3042) -#27367 := (= #27070 f298) -#28390 := (= #3043 f298) -#25116 := (= f298 #3043) +decl f23 :: (-> S18 S23) +decl f24 :: (-> S20 S18) +#24844 := (f128 #3044) +#26146 := (f54 #3040 #24844) +#26550 := (f24 #26146) +#26792 := (f23 #26550) +decl f25 :: S23 +#67 := f25 +#26795 := (= f25 #26792) +#26915 := (not #26795) +#3053 := (f23 #3040) +#12079 := (= f25 #3053) +#12082 := (not #12079) +#26897 := (iff #12082 #26915) +#26913 := (iff #12079 #26795) +#26911 := (iff #26795 #12079) +#26909 := (= #26792 #3053) +#26875 := (= #26550 #3040) +#25081 := (f24 #3044) +#28877 := (= #25081 #3040) +#25084 := (= #3040 #25081) +#369 := (:var 1 S18) #2761 := (f54 #369 #202) -#23300 := (pattern #2761) -#2762 := (f127 #2761) -#11445 := (= #202 #2762) -#23301 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11445) -#11449 := (forall (vars (?v0 S18) (?v1 Int)) #11445) -#23304 := (iff #11449 #23301) -#23302 := (iff #11445 #11445) -#23303 := [refl]: #23302 -#23305 := [quant-intro #23303]: #23304 -#18302 := (~ #11449 #11449) -#18300 := (~ #11445 #11445) -#18301 := [refl]: #18300 -#18303 := [nnf-pos #18301]: #18302 -#2763 := (= #2762 #202) -#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763) -#11450 := (iff #2764 #11449) -#11447 := (iff #2763 #11445) -#11448 := [rewrite]: #11447 -#11451 := [quant-intro #11448]: #11450 -#11444 := [asserted]: #2764 -#11454 := [mp #11444 #11451]: #11449 -#18304 := [mp~ #11454 #18303]: #11449 -#23306 := [mp #18304 #23305]: #23301 -#25070 := (not #23301) -#25121 := (or #25070 #25116) -#25122 := [quant-inst #50 #3041]: #25121 -#28389 := [unit-resolution #25122 #23306]: #25116 -#28391 := [symm #28389]: #28390 -#27143 := (= #27070 #3043) -#27141 := (= #24833 #3042) -#24834 := (= #3042 #24833) -#132 := (f40 #62) -#23211 := (pattern #132) -#133 := (f39 #132) -#3682 := (= #62 #133) -#23212 := (forall (vars (?v0 S20)) (:pat #23211) #3682) -#3685 := (forall (vars (?v0 S20)) #3682) -#23213 := (iff #3685 #23212) -#23215 := (iff #23212 #23212) -#23216 := [rewrite]: #23215 -#23214 := [rewrite]: #23213 -#23217 := [trans #23214 #23216]: #23213 -#16342 := (~ #3685 #3685) -#16332 := (~ #3682 #3682) -#16333 := [refl]: #16332 -#16398 := [nnf-pos #16333]: #16342 -#134 := (= #133 #62) -#135 := (forall (vars (?v0 S20)) #134) -#3686 := (iff #135 #3685) -#3683 := (iff #134 #3682) -#3684 := [rewrite]: #3683 -#3687 := [quant-intro #3684]: #3686 -#3681 := [asserted]: #135 -#3690 := [mp #3681 #3687]: #3685 -#16399 := [mp~ #3690 #16398]: #3685 -#23218 := [mp #16399 #23217]: #23212 -#24837 := (not #23212) -#24838 := (or #24837 #24834) -#24839 := [quant-inst #3042]: #24838 -#27140 := [unit-resolution #24839 #23218]: #24834 -#27142 := [symm #27140]: #27141 -#27275 := [monotonicity #27142]: #27143 -#27368 := [trans #27275 #28391]: #27367 -#27414 := [monotonicity #28386 #27368]: #27410 -#27415 := (= #3098 #27086) -#27064 := (f77 #24833 0::Int #24996) -#27089 := (= #27064 #27086) -#27092 := (not #27089) -decl f149 :: (-> S20 S20 S1) -#27065 := (f149 #27064 #24833) -#27066 := (= f1 #27065) -#27067 := (not #27066) -#27098 := (or #27067 #27092) -#27103 := (not #27098) -#28651 := [hypothesis]: #27098 -#289 := (:var 1 Int) -#60 := (:var 2 S20) -#1622 := (f77 #60 #289 #275) -#1623 := (pattern #1622) -#1624 := (f149 #1622 #60) -#8390 := (= f1 #1624) -#21232 := (not #8390) -decl f150 :: (-> S18 Int) -#1627 := (f150 #275) -#1628 := (* #289 #1627) -#1626 := (f127 #60) -#1629 := (+ #1626 #1628) -#1630 := (f54 #275 #1629) -#1631 := (= #1622 #1630) -#21231 := (not #1631) -#21233 := (or #21231 #21232) -#21234 := (not #21233) -#21237 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21234) -#8396 := (and #1631 #8390) -#8401 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8396) -#21238 := (iff #8401 #21237) -#21235 := (iff #8396 #21234) -#21236 := [rewrite]: #21235 -#21239 := [quant-intro #21236]: #21238 -#17365 := (~ #8401 #8401) -#17363 := (~ #8396 #8396) -#17364 := [refl]: #17363 -#17366 := [nnf-pos #17364]: #17365 -#1625 := (= #1624 f1) -#1632 := (and #1625 #1631) -#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632) -#8402 := (iff #1633 #8401) -#8399 := (iff #1632 #8396) -#8393 := (and #8390 #1631) -#8397 := (iff #8393 #8396) -#8398 := [rewrite]: #8397 -#8394 := (iff #1632 #8393) -#8391 := (iff #1625 #8390) -#8392 := [rewrite]: #8391 -#8395 := [monotonicity #8392]: #8394 -#8400 := [trans #8395 #8398]: #8399 -#8403 := [quant-intro #8400]: #8402 -#8389 := [asserted]: #1633 -#8406 := [mp #8389 #8403]: #8401 -#17367 := [mp~ #8406 #17366]: #8401 -#21240 := [mp #17367 #21239]: #21237 -#27721 := (not #21237) -#27728 := (or #27721 #27103) -#27068 := (f150 #24996) -#27069 := (* 0::Int #27068) -#27071 := (+ #27070 #27069) -#27072 := (f54 #24996 #27071) -#27073 := (= #27064 #27072) -#27074 := (not #27073) -#27075 := (or #27074 #27067) -#27076 := (not #27075) -#27729 := (or #27721 #27076) -#27730 := (iff #27729 #27728) -#27736 := (iff #27728 #27728) -#27737 := [rewrite]: #27736 -#27104 := (iff #27076 #27103) -#27101 := (iff #27075 #27098) -#27095 := (or #27092 #27067) -#27099 := (iff #27095 #27098) -#27100 := [rewrite]: #27099 -#27096 := (iff #27075 #27095) -#27093 := (iff #27074 #27092) -#27090 := (iff #27073 #27089) -#27087 := (= #27072 #27086) -#27084 := (= #27071 #27070) -#27079 := (+ #27070 0::Int) -#27082 := (= #27079 #27070) -#27083 := [rewrite]: #27082 -#27080 := (= #27071 #27079) -#27077 := (= #27069 0::Int) -#27078 := [rewrite]: #27077 -#27081 := [monotonicity #27078]: #27080 -#27085 := [trans #27081 #27083]: #27084 -#27088 := [monotonicity #27085]: #27087 -#27091 := [monotonicity #27088]: #27090 -#27094 := [monotonicity #27091]: #27093 -#27097 := [monotonicity #27094]: #27096 -#27102 := [trans #27097 #27100]: #27101 -#27105 := [monotonicity #27102]: #27104 -#27731 := [monotonicity #27105]: #27730 -#27745 := [trans #27731 #27737]: #27730 -#27727 := [quant-inst #24833 #161 #24996]: #27729 -#27746 := [mp #27727 #27745]: #27728 -#28652 := [unit-resolution #27746 #21240 #28651]: false -#28653 := [lemma #28652]: #27103 -#27748 := (or #27098 #27089) -#27749 := [def-axiom]: #27748 -#27673 := [unit-resolution #27749 #28653]: #27089 -#27371 := (= #3098 #27064) -#27409 := [monotonicity #27140 #28384]: #27371 -#27674 := [trans #27409 #27673]: #27415 -#27675 := [trans #27674 #27414]: #27680 -#27676 := [monotonicity #27675]: #27682 -#27669 := [symm #27676]: #27668 -#27670 := (= #24996 #25112) -#25113 := (= f19 #25112) +#23264 := (pattern #2761) #2765 := (f24 #2761) -#11453 := (= #369 #2765) -#23307 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11453) -#11457 := (forall (vars (?v0 S18) (?v1 Int)) #11453) -#23310 := (iff #11457 #23307) -#23308 := (iff #11453 #11453) -#23309 := [refl]: #23308 -#23311 := [quant-intro #23309]: #23310 -#18307 := (~ #11457 #11457) -#18305 := (~ #11453 #11453) -#18306 := [refl]: #18305 -#18308 := [nnf-pos #18306]: #18307 +#11417 := (= #369 #2765) +#23271 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11417) +#11421 := (forall (vars (?v0 S18) (?v1 Int)) #11417) +#23274 := (iff #11421 #23271) +#23272 := (iff #11417 #11417) +#23273 := [refl]: #23272 +#23275 := [quant-intro #23273]: #23274 +#18271 := (~ #11421 #11421) +#18269 := (~ #11417 #11417) +#18270 := [refl]: #18269 +#18272 := [nnf-pos #18270]: #18271 #2766 := (= #2765 #369) #2767 := (forall (vars (?v0 S18) (?v1 Int)) #2766) -#11458 := (iff #2767 #11457) -#11455 := (iff #2766 #11453) -#11456 := [rewrite]: #11455 -#11459 := [quant-intro #11456]: #11458 -#11452 := [asserted]: #2767 -#11462 := [mp #11452 #11459]: #11457 -#18309 := [mp~ #11462 #18308]: #11457 -#23312 := [mp #18309 #23311]: #23307 -#25064 := (not #23307) -#25118 := (or #25064 #25113) -#25119 := [quant-inst #50 #3041]: #25118 -#27139 := [unit-resolution #25119 #23312]: #25113 -#27671 := [trans #28386 #27139]: #27670 -#27672 := [trans #27671 #27669]: #27040 -#27021 := (not #27014) -#27677 := (iff #18445 #27021) -#27722 := (iff #12180 #27014) -#27750 := (iff #27014 #12180) -#27744 := (= #27013 #3099) -#27747 := [monotonicity #28386]: #27744 -#27751 := [monotonicity #27747]: #27750 -#27723 := [symm #27751]: #27722 -#27724 := [monotonicity #27723]: #27677 -#27667 := [hypothesis]: #18445 -#27725 := [mp #27667 #27724]: #27021 -#27604 := (not #27040) -#27597 := (not #27042) -#27605 := (or #27597 #27014 #27604) -#27603 := [def-axiom]: #27605 -#27726 := [unit-resolution #27603 #27725 #27672 #27640]: false -#27642 := [lemma #27726]: #12180 -#28945 := (or #27098 #12189) -#26985 := (f69 #3220 #3098) -#27775 := (f146 #26985) -#27778 := (f36 f297 #27775) -#27786 := (= f37 #27778) -#27776 := (f221 f297 #27775) -#27777 := (= f1 #27776) -#28363 := (or #27777 #27786) -#28365 := (not #28363) -#28146 := (f147 #26985) -#28147 := (= f1 #28146) -#28148 := (not #28147) -#28100 := (f38 f297 #27775) -#28093 := (= f1 #28100) -#28145 := (not #28093) -#28326 := (or #28145 #28148) -#28340 := (not #28326) -#27920 := (f23 #27039) -#28266 := (= f25 #27920) -#28322 := (not #28266) -#28095 := (f24 #27775) -#28096 := (f23 #28095) -#28097 := (= f25 #28096) -#28345 := (or #28097 #28322 #28340 #28365) -#28437 := (not #28345) -#28209 := (f221 f297 #3098) -#28207 := (= f1 #28209) -#28196 := (f36 f297 #3098) -#28197 := (= f37 #28196) -#28195 := (or #28197 #28207) -#28275 := (not #28195) -#28271 := (or #28275 #28266) -#28273 := (not #28271) -#28440 := (or #28273 #28437) -#28443 := (not #28440) -#3101 := (f35 f297 #3098) -#12183 := (= f1 #3101) -#18448 := (not #12183) -#28446 := (or #18448 #28443) -#28377 := (not #28446) -#28367 := (iff #12189 #28377) -#28434 := (or #28423 #28367) -#27787 := (or #27786 #27777) -#28094 := (not #27787) -#27921 := (or #28148 #28145) -#27919 := (not #27921) -#27931 := (= #27920 f25) -#27965 := (not #27931) -#27966 := (or #27965 #27919 #28097 #28094) -#28208 := (not #27966) -#28276 := (or #27931 #28275) -#28274 := (not #28276) -#28277 := (or #28274 #28208) -#28278 := (not #28277) -#28279 := (or #18448 #28278) -#28264 := (not #28279) -#28265 := (iff #12189 #28264) -#28435 := (or #28423 #28265) -#28448 := (iff #28435 #28434) -#28450 := (iff #28434 #28434) -#28451 := [rewrite]: #28450 -#28348 := (iff #28265 #28367) -#28378 := (iff #28264 #28377) -#28368 := (iff #28279 #28446) -#28444 := (iff #28278 #28443) -#28441 := (iff #28277 #28440) -#28438 := (iff #28208 #28437) -#28360 := (iff #27966 #28345) -#28341 := (or #28322 #28340 #28097 #28365) -#28346 := (iff #28341 #28345) -#28347 := [rewrite]: #28346 -#28343 := (iff #27966 #28341) -#28339 := (iff #28094 #28365) -#28364 := (iff #27787 #28363) -#28359 := [rewrite]: #28364 -#28342 := [monotonicity #28359]: #28339 -#28361 := (iff #27919 #28340) -#28331 := (iff #27921 #28326) -#28332 := [rewrite]: #28331 -#28362 := [monotonicity #28332]: #28361 -#28281 := (iff #27965 #28322) -#28267 := (iff #27931 #28266) -#28268 := [rewrite]: #28267 -#28325 := [monotonicity #28268]: #28281 -#28344 := [monotonicity #28325 #28362 #28342]: #28343 -#28436 := [trans #28344 #28347]: #28360 -#28439 := [monotonicity #28436]: #28438 -#28320 := (iff #28274 #28273) -#28284 := (iff #28276 #28271) -#28263 := (or #28266 #28275) -#28272 := (iff #28263 #28271) -#28283 := [rewrite]: #28272 -#28269 := (iff #28276 #28263) -#28270 := [monotonicity #28268]: #28269 -#28282 := [trans #28270 #28283]: #28284 -#28321 := [monotonicity #28282]: #28320 -#28442 := [monotonicity #28321 #28439]: #28441 -#28445 := [monotonicity #28442]: #28444 -#28369 := [monotonicity #28445]: #28368 -#28213 := [monotonicity #28369]: #28378 -#28349 := [monotonicity #28213]: #28348 -#28449 := [monotonicity #28349]: #28448 -#28456 := [trans #28449 #28451]: #28448 -#28447 := [quant-inst #3039 #3098]: #28435 -#28457 := [mp #28447 #28456]: #28434 -#28776 := [unit-resolution #28457 #22094]: #28367 -#28625 := (not #28367) -#28779 := (or #28625 #28446) -#28778 := [hypothesis]: #18454 -#28626 := (or #28625 #12189 #28446) -#28627 := [def-axiom]: #28626 -#28777 := [unit-resolution #28627 #28778]: #28779 -#28780 := [unit-resolution #28777 #28776]: #28446 -#28816 := (or #28377 #28443) -decl f26 :: (-> S20 S21 S1) -decl f27 :: (-> S19 S20 S21) -#24880 := (f127 #3044) -#26182 := (f54 #3040 #24880) -#26775 := (f27 f297 #26182) -#27233 := (f26 #27145 #26775) -#27234 := (= f1 #27233) -#26776 := (f26 #26182 #26775) -#28795 := (= #26776 #27233) -#28792 := (= #27233 #26776) -#28790 := (= #27145 #26182) -#26189 := (= #3044 #26182) +#11422 := (iff #2767 #11421) +#11419 := (iff #2766 #11417) +#11420 := [rewrite]: #11419 +#11423 := [quant-intro #11420]: #11422 +#11416 := [asserted]: #2767 +#11426 := [mp #11416 #11423]: #11421 +#18273 := [mp~ #11426 #18272]: #11421 +#23276 := [mp #18273 #23275]: #23271 +#25028 := (not #23271) +#25089 := (or #25028 #25084) +#25090 := [quant-inst #3040 #3043]: #25089 +#28876 := [unit-resolution #25090 #23276]: #25084 +#28878 := [symm #28876]: #28877 +#26873 := (= #26550 #25081) +#26866 := (= #26146 #3044) +#26153 := (= #3044 #26146) #3049 := (f59 #3044 #3040) -#12109 := (= f1 #3049) +#12073 := (= f1 #3049) decl f34 :: (-> S18 S1) #3056 := (f34 #3040) -#12121 := (= f1 #3056) -#3053 := (f23 #3040) -#12115 := (= f25 #3053) -#12118 := (not #12115) -#3051 := (f35 f297 #3044) -#12112 := (= f1 #3051) -#12106 := (= f37 #3047) -#3045 := (f38 f297 #3044) -#12102 := (= f1 #3045) -#14228 := (and #12102 #12106 #12109 #12112 #12118 #12121) -decl f293 :: Int -#3024 := f293 -#14284 := (* -1::Int f293) -decl f89 :: Int -#472 := f89 -#14285 := (+ f89 #14284) -#14283 := (>= #14285 0::Int) -#14281 := (>= f293 0::Int) -#14288 := (and #14281 #14283) -#14291 := (not #14288) +#12085 := (= f1 #3056) +#3051 := (f35 f298 #3044) +#12076 := (= f1 #3051) +decl f36 :: (-> S19 S20 S20) +#3047 := (f36 f298 #3044) +decl f37 :: S20 +#116 := f37 +#12070 := (= f37 #3047) +decl f38 :: (-> S19 S20 S1) +#3045 := (f38 f298 #3044) +#12066 := (= f1 #3045) +#14192 := (and #12066 #12070 #12073 #12076 #12082 #12085) decl f294 :: Int -#3028 := f294 -#14270 := (* -1::Int f294) -decl f87 :: Int -#452 := f87 -#14271 := (+ f87 #14270) -#14269 := (>= #14271 0::Int) -#14267 := (>= f294 0::Int) -#14274 := (and #14267 #14269) -#14277 := (not #14274) +#3024 := f294 +#14248 := (* -1::Int f294) +decl f90 :: Int +#472 := f90 +#14249 := (+ f90 #14248) +#14247 := (>= #14249 0::Int) +#14245 := (>= f294 0::Int) +#14252 := (and #14245 #14247) +#14255 := (not #14252) decl f295 :: Int -#3032 := f295 -#14256 := (* -1::Int f295) -#14257 := (+ f87 #14256) -#14255 := (>= #14257 0::Int) -#14253 := (>= f295 0::Int) -#14260 := (and #14253 #14255) -#14263 := (not #14260) +#3028 := f295 +#14234 := (* -1::Int f295) +decl f88 :: Int +#452 := f88 +#14235 := (+ f88 #14234) +#14233 := (>= #14235 0::Int) +#14231 := (>= f295 0::Int) +#14238 := (and #14231 #14233) +#14241 := (not #14238) +decl f296 :: Int +#3032 := f296 +#14220 := (* -1::Int f296) +#14221 := (+ f88 #14220) +#14219 := (>= #14221 0::Int) +#14217 := (>= f296 0::Int) +#14224 := (and #14217 #14219) +#14227 := (not #14224) #1085 := 1099511627776::Int -#14241 := (>= f296 1099511627776::Int) -#14231 := (not #14228) -decl f299 :: (-> S34 Int) +#14205 := (>= f297 1099511627776::Int) +#14195 := (not #14192) +decl f300 :: (-> S34 Int) #3070 := (:var 0 S34) -#3071 := (f299 #3070) +#3071 := (f300 #3070) #3072 := (pattern #3071) -decl f300 :: Int -#3073 := f300 -#14218 := (* -1::Int f300) -#14219 := (+ #3071 #14218) -#14217 := (>= #14219 0::Int) -#14216 := (not #14217) -#14222 := (forall (vars (?v0 S34)) (:pat #3072) #14216) -#14225 := (not #14222) -#13509 := (not #13508) -#14072 := (and #3109 #13509) -#14077 := (not #14072) -#14060 := (+ f89 #14006) -#14059 := (>= #14060 0::Int) -#14063 := (and #14056 #14059) -#14066 := (not #14063) -#14047 := (+ f87 #13977) -#14046 := (>= #14047 0::Int) -#14050 := (and #13513 #14046) -#14053 := (not #14050) -#13538 := (+ f87 #13537) -#14037 := (>= #13538 0::Int) -#14040 := (and #14034 #14037) -#14043 := (not #14040) -#4514 := (* -1::Int f87) -#4515 := (+ #202 #4514) -#4516 := (<= #4515 0::Int) -#4523 := (and #4202 #4516) -#5738 := (not #4523) -#14017 := (or #5738 #13994 #14008) -#14022 := (forall (vars (?v0 Int)) #14017) -#14025 := (not #14022) -#13980 := (not #13979) -#13986 := (and #12250 #13980) -#13991 := (not #13986) -#13831 := (not #13829) -#13869 := (and #3173 #4202 #4516 #13831) -#13874 := (exists (vars (?v0 Int)) #13869) -#13852 := (or #5738 #13829 #13843) -#13857 := (forall (vars (?v0 Int)) #13852) -#13877 := (not #13857) -#13883 := (or #13877 #13874) -#13888 := (and #13857 #13883) -#13518 := (and #13513 #13516) -#13521 := (not #13518) -decl f227 :: S1 -#2541 := f227 -#10960 := (= f1 f227) -#12374 := (not #10960) -#13915 := (or #12374 #12340 #12331 #12322 #12313 #13521 #13888) -#13920 := (and #10960 #13915) -#13945 := (or #13521 #13802 #13920) -#13536 := (>= #13538 1::Int) -#13625 := (and #13534 #13536) -#13628 := (not #13625) -#13595 := (not #13594) -#13601 := (and #12643 #13595) -#13581 := (or #5738 #13558 #13572) -#13586 := (forall (vars (?v0 Int)) #13581) -#13589 := (not #13586) -#13606 := (or #13589 #13601) -#13609 := (and #13586 #13606) -#13612 := (or #13555 #13609) -#13615 := (and #13550 #13612) -#13544 := (and #13525 #13542) -#13547 := (not #13544) -#13643 := (or #12692 #13547 #13615 #13622 #13628) -#13651 := (and #13534 #13536 #13643) -#13527 := (and #13516 #13525) -#13530 := (not #13527) -#13762 := (or #12857 #12848 #13521 #13530 #13651 #13707) -#12587 := (and #12575 #12584) -#12785 := (not #12587) -#13683 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #13651) -#13691 := (and #12575 #12584 #13683) -#12581 := (and #12575 #12578) -#12797 := (not #12581) -#13696 := (or #12797 #13691) -#13702 := (and #12575 #12578 #13696) -#13732 := (or #13521 #13702 #13708) -#13767 := (and #13732 #13762) -#13776 := (or #12785 #13521 #13767) -#13784 := (and #12575 #12584 #13776) -#13789 := (or #12797 #13784) -#13795 := (and #12575 #12578 #13789) -#13824 := (or #13521 #13795 #13801) -#13950 := (and #13824 #13945) -#12561 := (and #12555 #12558) -#13024 := (not #12561) +decl f301 :: Int +#3073 := f301 +#14182 := (* -1::Int f301) +#14183 := (+ #3071 #14182) +#14181 := (>= #14183 0::Int) +#14180 := (not #14181) +#14186 := (forall (vars (?v0 S34)) (:pat #3072) #14180) +#14189 := (not #14186) +#13473 := (not #13472) +#14036 := (and #3109 #13473) +#14041 := (not #14036) +#14024 := (+ f90 #13970) +#14023 := (>= #14024 0::Int) +#14027 := (and #14020 #14023) +#14030 := (not #14027) +#14011 := (+ f88 #13941) +#14010 := (>= #14011 0::Int) +#14014 := (and #13477 #14010) +#14017 := (not #14014) +#13502 := (+ f88 #13501) +#14001 := (>= #13502 0::Int) +#14004 := (and #13998 #14001) +#14007 := (not #14004) +#4494 := (* -1::Int f88) +#4495 := (+ #202 #4494) +#4496 := (<= #4495 0::Int) +#4503 := (and #4202 #4496) +#5712 := (not #4503) +#13981 := (or #5712 #13958 #13972) +#13986 := (forall (vars (?v0 Int)) #13981) +#13989 := (not #13986) +#13950 := (and #12214 #13944) +#13955 := (not #13950) +#13795 := (not #13793) +#13833 := (and #3173 #4202 #4496 #13795) +#13838 := (exists (vars (?v0 Int)) #13833) +#13816 := (or #5712 #13793 #13807) +#13821 := (forall (vars (?v0 Int)) #13816) +#13841 := (not #13821) +#13847 := (or #13841 #13838) +#13852 := (and #13821 #13847) +#13482 := (and #13477 #13480) +#13485 := (not #13482) +decl f228 :: S1 +#2541 := f228 +#10924 := (= f1 f228) +#12338 := (not #10924) +#13879 := (or #12338 #12304 #12295 #12286 #12277 #13485 #13852) +#13884 := (and #10924 #13879) +#13909 := (or #13485 #13766 #13884) +#13500 := (>= #13502 1::Int) +#13589 := (and #13498 #13500) +#13592 := (not #13589) +#13559 := (not #13558) +#13565 := (and #12607 #13559) +#13545 := (or #5712 #13522 #13536) +#13550 := (forall (vars (?v0 Int)) #13545) +#13553 := (not #13550) +#13570 := (or #13553 #13565) +#13573 := (and #13550 #13570) +#13576 := (or #13519 #13573) +#13579 := (and #13514 #13576) +#13508 := (and #13489 #13506) +#13511 := (not #13508) +#13607 := (or #12656 #13511 #13579 #13586 #13592) +#13615 := (and #13498 #13500 #13607) +#13491 := (and #13480 #13489) +#13494 := (not #13491) +#13726 := (or #12821 #12812 #13485 #13494 #13615 #13671) +#12551 := (and #12539 #12548) +#12749 := (not #12551) +#13647 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #13615) +#13655 := (and #12539 #12548 #13647) +#12545 := (and #12539 #12542) +#12761 := (not #12545) +#13660 := (or #12761 #13655) +#13666 := (and #12539 #12542 #13660) +#13696 := (or #13485 #13666 #13672) +#13731 := (and #13696 #13726) +#13740 := (or #12749 #13485 #13731) +#13748 := (and #12539 #12548 #13740) +#13753 := (or #12761 #13748) +#13759 := (and #12539 #12542 #13753) +#13788 := (or #13485 #13759 #13765) +#13914 := (and #13788 #13909) +#12525 := (and #12519 #12522) +#12988 := (not #12525) decl f66 :: (-> S19 S1) -#3067 := (f66 f297) -#12145 := (= f1 #3067) -#12264 := (and #12145 #12258) -#12402 := (not #12264) -#14143 := (or #12402 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13950 #13991 #14025 #14031 #14043 #14053 #14066 #14077) -#14151 := (and #3109 #13509 #14143) -#13497 := (or #5738 #13475 #13487) -#13502 := (forall (vars (?v0 Int)) #13497) -#13505 := (not #13502) -#14156 := (or #13505 #14151) -#14159 := (and #13502 #14156) -#14162 := (or #13472 #14159) -#14165 := (and #13469 #14162) -#12192 := (and #12180 #12189) -#13276 := (not #12192) -#14186 := (or #13267 #13276 #13258 #13249 #13240 #14165) -#14194 := (and #12180 #12189 #14186) -#12186 := (and #12180 #12183) -#13288 := (not #12186) -#14199 := (or #13288 #14194) -#14205 := (and #12180 #12183 #14199) -decl f211 :: (-> S19 S20 S20 S31 S1) -decl f305 :: S31 -#3095 := f305 -#3096 := (f211 f297 #3044 #3044 f305) -#12177 := (= f1 #3096) -#13300 := (not #12177) -#14210 := (or #13300 #14205) -#14213 := (and #12177 #14210) -#13443 := (+ f87 #13442) -#13441 := (>= #13443 0::Int) -#13439 := (>= f296 0::Int) -#13446 := (and #13439 #13441) -#13449 := (not #13446) -decl f304 :: (-> Int S20 S1) -decl f303 :: Int -#3084 := f303 -#3087 := (f304 f303 #62) +#3067 := (f66 f298) +#12109 := (= f1 #3067) +#12228 := (and #12109 #12222) +#12366 := (not #12228) +#14107 := (or #12366 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13914 #13955 #13989 #13995 #14007 #14017 #14030 #14041) +#14115 := (and #3109 #13473 #14107) +#13461 := (or #5712 #13439 #13451) +#13466 := (forall (vars (?v0 Int)) #13461) +#13469 := (not #13466) +#14120 := (or #13469 #14115) +#14123 := (and #13466 #14120) +#14126 := (or #13436 #14123) +#14129 := (and #13433 #14126) +#12156 := (and #12144 #12153) +#13240 := (not #12156) +#14150 := (or #13231 #13240 #13222 #13213 #13204 #14129) +#14158 := (and #12144 #12153 #14150) +#12150 := (and #12144 #12147) +#13252 := (not #12150) +#14163 := (or #13252 #14158) +#14169 := (and #12144 #12147 #14163) +#14174 := (or #13264 #14169) +#14177 := (and #12141 #14174) +#13407 := (+ f88 #13406) +#13405 := (>= #13407 0::Int) +#13403 := (>= f297 0::Int) +#13410 := (and #13403 #13405) +#13413 := (not #13410) +decl f305 :: (-> Int S20 S1) +#62 := (:var 0 S20) +decl f304 :: Int +#3084 := f304 +#3087 := (f305 f304 #62) #3088 := (pattern #3087) -#12163 := (= f1 #3087) -#12169 := (not #12163) -#12174 := (forall (vars (?v0 S20)) (:pat #3088) #12169) -#13321 := (not #12174) -decl f292 :: S17 -#3020 := f292 -#3082 := (f301 f297 f292 f290 f296 f16) -#12160 := (= f1 #3082) -#13339 := (not #12160) -#3079 := (f302 f297 f292 f291 #3042 #51) -#12154 := (= f1 #3079) -#3077 := (f301 f297 f292 f291 #3076 #51) -#12151 := (= f1 #3077) -#12157 := (and #12151 #12154) -#13348 := (not #12157) -#3065 := (f213 f292 f297) -#12142 := (= f1 #3065) -#12148 := (and #12142 #12145) -#13366 := (not #12148) -decl f214 :: (-> S19 S1) -#3063 := (f214 f297) -#12139 := (= f1 #3063) -#13375 := (not #12139) -decl f184 :: (-> S19 Int) -#3085 := (f184 f297) -#3086 := (= f303 #3085) -#13330 := (not #3086) -#14336 := (or #13330 #13375 #13366 #13348 #13339 #13321 #13449 #13508 #14213 #14225 #14231 #14241 #14263 #14277 #14291) -#14341 := (not #14336) +#12127 := (= f1 #3087) +#12133 := (not #12127) +#12138 := (forall (vars (?v0 S20)) (:pat #3088) #12133) +#13285 := (not #12138) +decl f293 :: S17 +#3020 := f293 +#3082 := (f302 f298 f293 f291 f297 f16) +#12124 := (= f1 #3082) +#13303 := (not #12124) +#3079 := (f303 f298 f293 f292 #3042 #51) +#12118 := (= f1 #3079) +#3077 := (f302 f298 f293 f292 #3076 #51) +#12115 := (= f1 #3077) +#12121 := (and #12115 #12118) +#13312 := (not #12121) +#3065 := (f214 f293 f298) +#12106 := (= f1 #3065) +#12112 := (and #12106 #12109) +#13330 := (not #12112) +decl f215 :: (-> S19 S1) +#3063 := (f215 f298) +#12103 := (= f1 #3063) +#13339 := (not #12103) +decl f185 :: (-> S19 Int) +#3085 := (f185 f298) +#3086 := (= f304 #3085) +#13294 := (not #3086) +#14300 := (or #13294 #13339 #13330 #13312 #13303 #13285 #13413 #13472 #14177 #14189 #14195 #14205 #14227 #14241 #14255) +#14305 := (not #14300) #1 := true -#3168 := (< #202 f296) +#3168 := (< #202 f297) #3174 := (and #3168 #3173) -#454 := (<= #202 f87) +#454 := (<= #202 f88) #3175 := (and #454 #3174) #327 := (<= 0::Int #202) #3176 := (and #327 #3175) #3177 := (exists (vars (?v0 Int)) #3176) #3178 := (and #3177 true) -#3169 := (<= #3124 f313) +#3169 := (<= #3124 f314) #3170 := (implies #3168 #3169) #455 := (and #327 #454) #3171 := (implies #455 #3170) #3172 := (forall (vars (?v0 Int)) #3171) #3179 := (implies #3172 #3178) #3180 := (and #3172 #3179) -#3167 := (= f313 f307) +#3167 := (= f314 f308) #3181 := (implies #3167 #3180) -#3165 := (= f312 f308) +#3165 := (= f313 f309) #3182 := (implies #3165 #3181) -#3163 := (= f311 f309) +#3163 := (= f312 f310) #3183 := (implies #3163 #3182) -#3161 := (= f310 f307) +#3161 := (= f311 f308) #3184 := (implies #3161 #3183) -#3136 := (<= 0::Int f308) -#3143 := (<= 1::Int f309) +#3136 := (<= 0::Int f309) +#3143 := (<= 1::Int f310) #3144 := (and #3143 #3136) #3185 := (implies #3144 #3184) #3186 := (implies #3144 #3185) #3187 := (implies #3144 #3186) -#2542 := (= f227 f1) +#2542 := (= f228 f1) #3188 := (implies #2542 #3187) #3189 := (and #2542 #3188) #3190 := (implies #3144 #3189) #3191 := (implies #3144 #3190) #3348 := (implies #3144 #3191) #3349 := (implies #3144 #3348) -#3347 := (<= f296 f309) +#3347 := (<= f297 f310) #3350 := (implies #3347 #3349) #3351 := (implies #3144 #3350) -#3300 := (= #3299 f315) -#3297 := (< f316 f296) +#3300 := (= #3299 f316) +#3297 := (< f317 f297) #3301 := (and #3297 #3300) #3302 := (and #3301 true) -#3293 := (<= #3124 f315) -#3292 := (< #202 f317) +#3293 := (<= #3124 f316) +#3292 := (< #202 f318) #3294 := (implies #3292 #3293) #3295 := (implies #455 #3294) #3296 := (forall (vars (?v0 Int)) #3295) #3303 := (implies #3296 #3302) #3304 := (and #3296 #3303) -#3291 := (<= f317 f296) +#3291 := (<= f318 f297) #3305 := (implies #3291 #3304) #3306 := (and #3291 #3305) -#3279 := (<= 0::Int f316) -#3289 := (<= 2::Int f317) +#3279 := (<= 0::Int f317) +#3289 := (<= 2::Int f318) #3290 := (and #3289 #3279) #3307 := (implies #3290 #3306) #3288 := (= #3287 f1) #3308 := (implies #3288 #3307) -#3281 := (+ f309 1::Int) -#3286 := (= f317 #3281) +#3281 := (+ f310 1::Int) +#3286 := (= f318 #3281) #3309 := (implies #3286 #3308) -#3283 := (<= #3281 f87) +#3283 := (<= #3281 f88) #3282 := (<= 0::Int #3281) #3284 := (and #3282 #3283) #3310 := (implies #3284 #3309) #3311 := (and #3284 #3310) #3280 := (and #3143 #3279) #3312 := (implies #3280 #3311) -#3329 := (= f316 f308) +#3329 := (= f317 f309) #3330 := (implies #3329 #3312) -#3328 := (= f315 f307) +#3328 := (= f316 f308) #3331 := (implies #3328 #3330) #3332 := (implies #3144 #3331) #3333 := (implies #3144 #3332) #3334 := (implies #3144 #3333) -#3327 := (<= #3266 f307) +#3327 := (<= #3266 f308) #3335 := (implies #3327 #3334) #3336 := (implies #3144 #3335) -#3278 := (= f316 f309) +#3278 := (= f317 f310) #3313 := (implies #3278 #3312) -#3276 := (= f315 f314) +#3276 := (= f316 f315) #3314 := (implies #3276 #3313) #3274 := (and #3143 #3143) #3315 := (implies #3274 #3314) @@ -1512,7 +760,7 @@ #3316 := (implies #3273 #3315) #3271 := (= #3270 f1) #3317 := (implies #3271 #3316) -#3269 := (= f314 #3266) +#3269 := (= f315 #3266) #3318 := (implies #3269 #3317) #3264 := (= #3263 f1) #3259 := (= #3258 f1) @@ -1525,7 +773,7 @@ #3322 := (and #3262 #3321) #3323 := (implies #3144 #3322) #3324 := (implies #3144 #3323) -#3267 := (< f307 #3266) +#3267 := (< f308 #3266) #3325 := (implies #3267 #3324) #3326 := (implies #3144 #3325) #3337 := (and #3326 #3336) @@ -1536,14 +784,16 @@ #3342 := (and #3262 #3341) #3343 := (implies #3144 #3342) #3344 := (implies #3144 #3343) -#3256 := (< f309 f296) +#3256 := (< f310 f297) #3345 := (implies #3256 #3344) #3346 := (implies #3144 #3345) #3352 := (and #3346 #3351) #3353 := (implies #3144 #3352) decl f52 :: (-> S19 S27) -#3197 := (f52 f297) +#3197 := (f52 f298) #3254 := (= #3197 #3197) +decl f70 :: (-> S19 S28) +#3220 := (f70 f298) #3253 := (= #3220 #3220) #3255 := (and #3253 #3254) #3354 := (implies #3255 #3353) @@ -1564,8 +814,8 @@ #3159 := (and #3158 #3068) #3360 := (implies #3159 #3359) #3233 := (= #3232 f1) -decl f183 :: (-> S19 S20 Int) -#3228 := (f183 f297 #62) +decl f184 :: (-> S19 S20 Int) +#3228 := (f184 f298 #62) #3229 := (pattern #3228) #3230 := (<= #3228 #3228) #3231 := (forall (vars (?v0 S20)) (:pat #3229) #3230) @@ -1573,9 +823,10 @@ #3227 := (<= #3085 #3085) #3235 := (and #3227 #3234) #3361 := (implies #3235 #3360) +decl f69 :: (-> S28 S20 S29) #3221 := (f69 #3220 #62) #3222 := (pattern #3221) -#3210 := (f79 f297 #62) +#3210 := (f79 f298 #62) #3211 := (= #3210 f1) #3223 := (= #3221 #3221) #3224 := (and #3223 #3211) @@ -1592,7 +843,7 @@ #3237 := (and #3219 #3236) decl f30 :: (-> S24 S20 Int) decl f31 :: (-> S19 S24) -#3207 := (f31 f297) +#3207 := (f31 f298) #3208 := (f30 #3207 #62) #3209 := (pattern #3208) #3212 := (= #3208 #3208) @@ -1600,12 +851,12 @@ #3214 := (implies #3211 #3213) #3215 := (forall (vars (?v0 S20)) (:pat #3209) #3214) #3238 := (and #3215 #3237) -decl f272 :: S23 -#2903 := f272 -#3200 := (f36 f297 #62) +decl f273 :: S23 +#2903 := f273 +#3200 := (f36 f298 #62) #3201 := (f24 #3200) #3202 := (f23 #3201) -#3203 := (= #3202 f272) +#3203 := (= #3202 f273) #3204 := (not #3203) #3205 := (implies #3204 #3204) #3206 := (forall (vars (?v0 S20)) (:pat #3199) #3205) @@ -1622,43 +873,43 @@ #3196 := (implies #3144 #3195) #3366 := (and #3196 #3365) #3367 := (implies #3144 #3366) -#3154 := (= #3153 f307) -#3151 := (< f308 f296) +#3154 := (= #3153 f308) +#3151 := (< f309 f297) #3155 := (and #3151 #3154) #3368 := (implies #3155 #3367) -#3147 := (<= #3124 f307) -#3146 := (< #202 f309) +#3147 := (<= #3124 f308) +#3146 := (< #202 f310) #3148 := (implies #3146 #3147) #3149 := (implies #455 #3148) #3150 := (forall (vars (?v0 Int)) #3149) #3369 := (implies #3150 #3368) -#3145 := (<= f309 f296) +#3145 := (<= f310 f297) #3370 := (implies #3145 #3369) #3371 := (implies #3144 #3370) -#3141 := (<= f309 f87) -#3140 := (<= 0::Int f309) +#3141 := (<= f310 f88) +#3140 := (<= 0::Int f310) #3142 := (and #3140 #3141) #3372 := (implies #3142 #3371) -#3137 := (<= f308 f87) +#3137 := (<= f309 f88) #3138 := (and #3136 #3137) #3373 := (implies #3138 #3372) -#3133 := (<= f307 f89) -#3132 := (<= 0::Int f307) +#3133 := (<= f308 f90) +#3132 := (<= 0::Int f308) #3134 := (and #3132 #3133) #3374 := (implies #3134 #3373) -#3129 := (= #3108 f306) -#3038 := (< 0::Int f296) +#3129 := (= #3108 f307) +#3038 := (< 0::Int f297) #3130 := (and #3038 #3129) #3375 := (implies #3130 #3374) #3376 := (and #3130 #3375) -#3125 := (<= #3124 f306) +#3125 := (<= #3124 f307) #3122 := (< #202 1::Int) #3126 := (implies #3122 #3125) #3127 := (implies #455 #3126) #3128 := (forall (vars (?v0 Int)) #3127) #3377 := (implies #3128 #3376) #3378 := (and #3128 #3377) -#3121 := (<= 1::Int f296) +#3121 := (<= 1::Int f297) #3379 := (implies #3121 #3378) #3380 := (and #3121 #3379) #3117 := (<= 0::Int 0::Int) @@ -1686,8 +937,8 @@ #3097 := (= #3096 f1) #3390 := (implies #3097 #3389) #3391 := (and #3097 #3390) -#3093 := (<= f296 f87) -#3092 := (<= 0::Int f296) +#3093 := (<= f297 f88) +#3092 := (<= 0::Int f297) #3094 := (and #3092 #3093) #3392 := (implies #3094 #3391) #3089 := (= #3087 f1) @@ -1701,7 +952,7 @@ #3078 := (= #3077 f1) #3081 := (and #3078 #3080) #3396 := (implies #3081 #3395) -#3074 := (< #3071 f300) +#3074 := (< #3071 f301) #3075 := (forall (vars (?v0 S34)) (:pat #3072) #3074) #3397 := (implies #3075 #3396) #3066 := (= #3065 f1) @@ -1723,2278 +974,2252 @@ #3062 := (and #3046 #3061) #3400 := (implies #3062 #3399) #3401 := (implies #3038 #3400) -#3037 := (< f296 1099511627776::Int) +#3037 := (< f297 1099511627776::Int) #3402 := (implies #3037 #3401) -#3034 := (<= f295 f87) -#3033 := (<= 0::Int f295) +#3034 := (<= f296 f88) +#3033 := (<= 0::Int f296) #3035 := (and #3033 #3034) #3403 := (implies #3035 #3402) -#3030 := (<= f294 f87) -#3029 := (<= 0::Int f294) +#3030 := (<= f295 f88) +#3029 := (<= 0::Int f295) #3031 := (and #3029 #3030) #3404 := (implies #3031 #3403) -#3026 := (<= f293 f89) -#3025 := (<= 0::Int f293) +#3026 := (<= f294 f90) +#3025 := (<= 0::Int f294) #3027 := (and #3025 #3026) #3405 := (implies #3027 #3404) #3406 := (not #3405) -#14344 := (iff #3406 #14341) -#12281 := (not #3168) -#12282 := (or #12281 #3169) -#5729 := (not #455) -#12288 := (or #5729 #12282) -#12293 := (forall (vars (?v0 Int)) #12288) -#12301 := (not #12293) -#12302 := (or #3177 #12301) -#12307 := (and #12293 #12302) -#12314 := (or #12313 #12307) -#12323 := (or #12322 #12314) -#12332 := (or #12331 #12323) -#12341 := (or #12340 #12332) -#12232 := (and #3136 #3143) -#12349 := (not #12232) -#12350 := (or #12349 #12341) -#12358 := (or #12349 #12350) -#12366 := (or #12349 #12358) -#12375 := (or #12374 #12366) -#12380 := (and #10960 #12375) -#12386 := (or #12349 #12380) -#12394 := (or #12349 #12386) -#12973 := (or #12349 #12394) -#12981 := (or #12349 #12973) -#12989 := (not #3347) -#12990 := (or #12989 #12981) -#12998 := (or #12349 #12990) -#12646 := (and #3297 #12643) -#12628 := (not #3292) -#12629 := (or #12628 #3293) -#12635 := (or #5729 #12629) -#12640 := (forall (vars (?v0 Int)) #12635) -#12659 := (not #12640) -#12660 := (or #12659 #12646) -#12665 := (and #12640 #12660) -#12671 := (not #3291) -#12672 := (or #12671 #12665) -#12677 := (and #3291 #12672) -#12625 := (and #3279 #3289) -#12683 := (not #12625) -#12684 := (or #12683 #12677) -#12693 := (or #12692 #12684) -#12607 := (+ 1::Int f309) -#12619 := (= f317 #12607) -#12701 := (not #12619) -#12702 := (or #12701 #12693) -#12613 := (<= #12607 f87) -#12610 := (<= 0::Int #12607) -#12616 := (and #12610 #12613) -#12710 := (not #12616) -#12711 := (or #12710 #12702) -#12716 := (and #12616 #12711) -#12722 := (not #3280) -#12723 := (or #12722 #12716) -#12849 := (or #12723 #12848) -#12858 := (or #12857 #12849) -#12866 := (or #12349 #12858) -#12874 := (or #12349 #12866) -#12882 := (or #12349 #12874) -#12890 := (not #3327) -#12891 := (or #12890 #12882) -#12899 := (or #12349 #12891) +#14308 := (iff #3406 #14305) +#12245 := (not #3168) +#12246 := (or #12245 #3169) +#5703 := (not #455) +#12252 := (or #5703 #12246) +#12257 := (forall (vars (?v0 Int)) #12252) +#12265 := (not #12257) +#12266 := (or #3177 #12265) +#12271 := (and #12257 #12266) +#12278 := (or #12277 #12271) +#12287 := (or #12286 #12278) +#12296 := (or #12295 #12287) +#12305 := (or #12304 #12296) +#12196 := (and #3136 #3143) +#12313 := (not #12196) +#12314 := (or #12313 #12305) +#12322 := (or #12313 #12314) +#12330 := (or #12313 #12322) +#12339 := (or #12338 #12330) +#12344 := (and #10924 #12339) +#12350 := (or #12313 #12344) +#12358 := (or #12313 #12350) +#12937 := (or #12313 #12358) +#12945 := (or #12313 #12937) +#12953 := (not #3347) +#12954 := (or #12953 #12945) +#12962 := (or #12313 #12954) +#12610 := (and #3297 #12607) +#12592 := (not #3292) +#12593 := (or #12592 #3293) +#12599 := (or #5703 #12593) +#12604 := (forall (vars (?v0 Int)) #12599) +#12623 := (not #12604) +#12624 := (or #12623 #12610) +#12629 := (and #12604 #12624) +#12635 := (not #3291) +#12636 := (or #12635 #12629) +#12641 := (and #3291 #12636) +#12589 := (and #3279 #3289) +#12647 := (not #12589) +#12648 := (or #12647 #12641) +#12657 := (or #12656 #12648) +#12571 := (+ 1::Int f310) +#12583 := (= f318 #12571) +#12665 := (not #12583) +#12666 := (or #12665 #12657) +#12577 := (<= #12571 f88) +#12574 := (<= 0::Int #12571) +#12580 := (and #12574 #12577) +#12674 := (not #12580) +#12675 := (or #12674 #12666) +#12680 := (and #12580 #12675) +#12686 := (not #3280) +#12687 := (or #12686 #12680) +#12813 := (or #12687 #12812) +#12822 := (or #12821 #12813) +#12830 := (or #12313 #12822) +#12838 := (or #12313 #12830) +#12846 := (or #12313 #12838) +#12854 := (not #3327) +#12855 := (or #12854 #12846) +#12863 := (or #12313 #12855) +#12696 := (or #12695 #12687) +#12705 := (or #12704 #12696) +#12713 := (not #3143) +#12714 := (or #12713 #12705) +#12723 := (or #12722 #12714) #12732 := (or #12731 #12723) #12741 := (or #12740 #12732) -#12749 := (not #3143) #12750 := (or #12749 #12741) -#12759 := (or #12758 #12750) -#12768 := (or #12767 #12759) -#12777 := (or #12776 #12768) -#12786 := (or #12785 #12777) -#12791 := (and #12587 #12786) -#12798 := (or #12797 #12791) -#12803 := (and #12581 #12798) -#12809 := (or #12349 #12803) -#12817 := (or #12349 #12809) -#12825 := (not #3267) -#12826 := (or #12825 #12817) -#12834 := (or #12349 #12826) -#12904 := (and #12834 #12899) -#12910 := (or #12349 #12904) -#12918 := (or #12785 #12910) -#12923 := (and #12587 #12918) -#12929 := (or #12797 #12923) -#12934 := (and #12581 #12929) -#12940 := (or #12349 #12934) -#12948 := (or #12349 #12940) -#12956 := (not #3256) -#12957 := (or #12956 #12948) -#12965 := (or #12349 #12957) -#13003 := (and #12965 #12998) -#13009 := (or #12349 #13003) -#13025 := (or #13024 #13009) -#13034 := (or #13033 #13025) -#13043 := (or #13042 #13034) -#13052 := (or #13051 #13043) -#13061 := (or #13060 #13052) -#13069 := (or #12402 #13061) -#12518 := (and #3231 #12515) -#12521 := (and #3227 #12518) -#13077 := (not #12521) -#13078 := (or #13077 #13069) -#13086 := (or #13077 #13078) -#13094 := (or #12349 #13086) -#13102 := (or #12349 #13094) -#13110 := (or #12349 #13102) -#13125 := (or #12349 #13110) -#12253 := (and #3151 #12250) -#13133 := (not #12253) -#13134 := (or #13133 #13125) -#12235 := (not #3146) -#12236 := (or #12235 #3147) -#12242 := (or #5729 #12236) -#12247 := (forall (vars (?v0 Int)) #12242) -#13142 := (not #12247) -#13143 := (or #13142 #13134) -#13151 := (not #3145) -#13152 := (or #13151 #13143) -#13160 := (or #12349 #13152) -#13168 := (not #3142) -#13169 := (or #13168 #13160) -#13177 := (not #3138) -#13178 := (or #13177 #13169) -#13186 := (not #3134) -#13187 := (or #13186 #13178) -#12229 := (and #3038 #3109) -#13195 := (not #12229) -#13196 := (or #13195 #13187) -#13201 := (and #12229 #13196) -#12212 := (not #3122) -#12213 := (or #12212 #3125) -#12219 := (or #5729 #12213) -#12224 := (forall (vars (?v0 Int)) #12219) -#13207 := (not #12224) -#13208 := (or #13207 #13201) -#13213 := (and #12224 #13208) -#13219 := (not #3121) -#13220 := (or #13219 #13213) -#13225 := (and #3121 #13220) -#12206 := (and #3116 #3117) -#12209 := (and #3116 #12206) -#13231 := (not #12209) -#13232 := (or #13231 #13225) +#12755 := (and #12551 #12750) +#12762 := (or #12761 #12755) +#12767 := (and #12545 #12762) +#12773 := (or #12313 #12767) +#12781 := (or #12313 #12773) +#12789 := (not #3267) +#12790 := (or #12789 #12781) +#12798 := (or #12313 #12790) +#12868 := (and #12798 #12863) +#12874 := (or #12313 #12868) +#12882 := (or #12749 #12874) +#12887 := (and #12551 #12882) +#12893 := (or #12761 #12887) +#12898 := (and #12545 #12893) +#12904 := (or #12313 #12898) +#12912 := (or #12313 #12904) +#12920 := (not #3256) +#12921 := (or #12920 #12912) +#12929 := (or #12313 #12921) +#12967 := (and #12929 #12962) +#12973 := (or #12313 #12967) +#12989 := (or #12988 #12973) +#12998 := (or #12997 #12989) +#13007 := (or #13006 #12998) +#13016 := (or #13015 #13007) +#13025 := (or #13024 #13016) +#13033 := (or #12366 #13025) +#12482 := (and #3231 #12479) +#12485 := (and #3227 #12482) +#13041 := (not #12485) +#13042 := (or #13041 #13033) +#13050 := (or #13041 #13042) +#13058 := (or #12313 #13050) +#13066 := (or #12313 #13058) +#13074 := (or #12313 #13066) +#13089 := (or #12313 #13074) +#12217 := (and #3151 #12214) +#13097 := (not #12217) +#13098 := (or #13097 #13089) +#12199 := (not #3146) +#12200 := (or #12199 #3147) +#12206 := (or #5703 #12200) +#12211 := (forall (vars (?v0 Int)) #12206) +#13106 := (not #12211) +#13107 := (or #13106 #13098) +#13115 := (not #3145) +#13116 := (or #13115 #13107) +#13124 := (or #12313 #13116) +#13132 := (not #3142) +#13133 := (or #13132 #13124) +#13141 := (not #3138) +#13142 := (or #13141 #13133) +#13150 := (not #3134) +#13151 := (or #13150 #13142) +#12193 := (and #3038 #3109) +#13159 := (not #12193) +#13160 := (or #13159 #13151) +#13165 := (and #12193 #13160) +#12176 := (not #3122) +#12177 := (or #12176 #3125) +#12183 := (or #5703 #12177) +#12188 := (forall (vars (?v0 Int)) #12183) +#13171 := (not #12188) +#13172 := (or #13171 #13165) +#13177 := (and #12188 #13172) +#13183 := (not #3121) +#13184 := (or #13183 #13177) +#13189 := (and #3121 #13184) +#12170 := (and #3116 #3117) +#12173 := (and #3116 #12170) +#13195 := (not #12173) +#13196 := (or #13195 #13189) +#13205 := (or #13204 #13196) +#13214 := (or #13213 #13205) +#13223 := (or #13222 #13214) +#13232 := (or #13231 #13223) #13241 := (or #13240 #13232) -#13250 := (or #13249 #13241) -#13259 := (or #13258 #13250) -#13268 := (or #13267 #13259) -#13277 := (or #13276 #13268) -#13282 := (and #12192 #13277) -#13289 := (or #13288 #13282) -#13294 := (and #12186 #13289) -#13301 := (or #13300 #13294) -#13306 := (and #12177 #13301) -#13312 := (not #3094) -#13313 := (or #13312 #13306) +#13246 := (and #12156 #13241) +#13253 := (or #13252 #13246) +#13258 := (and #12150 #13253) +#13265 := (or #13264 #13258) +#13270 := (and #12141 #13265) +#13276 := (not #3094) +#13277 := (or #13276 #13270) +#13286 := (or #13285 #13277) +#13295 := (or #13294 #13286) +#13304 := (or #13303 #13295) +#13313 := (or #13312 #13304) +#13321 := (not 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+#13877 := (iff #12339 #13876) +#13874 := (iff #12330 #13873) +#13871 := (iff #12322 #13870) +#13868 := (iff #12314 #13867) +#13865 := (iff #12305 #13864) +#13862 := (iff #12296 #13861) +#13859 := (iff #12287 #13858) +#13856 := (iff #12278 #13855) +#13853 := (iff #12271 #13852) +#13850 := (iff #12266 #13847) +#13844 := (or #13838 #13841) +#13848 := (iff #13844 #13847) +#13849 := [rewrite]: #13848 +#13845 := (iff #12266 #13844) +#13842 := (iff #12265 #13841) +#13822 := (iff #12257 #13821) +#13819 := (iff #12252 #13816) +#13810 := (or #13793 #13807) +#13813 := (or #5712 #13810) +#13817 := (iff #13813 #13816) +#13818 := [rewrite]: #13817 +#13814 := (iff #12252 #13813) +#13811 := (iff #12246 #13810) +#13808 := (iff #3169 #13807) +#13809 := [rewrite]: #13808 +#13803 := (iff #12245 #13793) +#13798 := (not #13795) +#13801 := (iff #13798 #13793) +#13802 := [rewrite]: #13801 +#13799 := (iff #12245 #13798) +#13796 := (iff #3168 #13795) +#13797 := [rewrite]: #13796 +#13800 := [monotonicity #13797]: #13799 +#13804 := [trans #13800 #13802]: #13803 +#13812 := [monotonicity #13804 #13809]: #13811 +#5713 := (iff #5703 #5712) +#4504 := (iff #455 #4503) +#4497 := (iff #454 #4496) +#4498 := [rewrite]: #4497 #4200 := (iff #327 #4202) #4201 := [rewrite]: #4200 -#4525 := [monotonicity #4201 #4518]: #4524 -#5740 := [monotonicity #4525]: #5739 -#13851 := [monotonicity #5740 #13848]: #13850 -#13856 := [trans #13851 #13854]: #13855 -#13859 := [quant-intro #13856]: #13858 -#13879 := [monotonicity #13859]: #13878 -#13875 := (iff #3177 #13874) -#13872 := (iff #3176 #13869) -#13860 := (and #13831 #3173) -#13863 := (and #4516 #13860) -#13866 := (and #4202 #13863) -#13870 := (iff #13866 #13869) -#13871 := [rewrite]: #13870 -#13867 := (iff #3176 #13866) -#13864 := (iff #3175 #13863) -#13861 := (iff #3174 #13860) -#13862 := [monotonicity #13833]: #13861 -#13865 := [monotonicity #4518 #13862]: #13864 -#13868 := [monotonicity #4201 #13865]: #13867 -#13873 := [trans #13868 #13871]: #13872 -#13876 := [quant-intro #13873]: #13875 -#13882 := [monotonicity #13876 #13879]: #13881 -#13887 := [trans #13882 #13885]: #13886 -#13890 := [monotonicity #13859 #13887]: #13889 -#13893 := [monotonicity #13890]: #13892 -#13896 := [monotonicity #13893]: #13895 -#13899 := [monotonicity #13896]: #13898 -#13902 := [monotonicity #13899]: #13901 -#13522 := (iff #12349 #13521) -#13519 := (iff #12232 #13518) -#13515 := (iff #3143 #13516) -#13517 := [rewrite]: #13515 -#13512 := (iff #3136 #13513) -#13514 := [rewrite]: #13512 -#13520 := [monotonicity #13514 #13517]: #13519 -#13523 := [monotonicity #13520]: #13522 -#13905 := [monotonicity #13523 #13902]: #13904 -#13908 := [monotonicity #13523 #13905]: #13907 -#13911 := [monotonicity #13523 #13908]: #13910 -#13914 := [monotonicity #13911]: #13913 -#13919 := [trans #13914 #13917]: #13918 -#13922 := [monotonicity #13919]: #13921 -#13929 := [monotonicity #13523 #13922]: #13928 -#13932 := [monotonicity #13523 #13929]: #13931 -#13935 := [monotonicity #13523 #13932]: #13934 -#13938 := [monotonicity #13523 #13935]: #13937 -#13925 := (iff #12989 #13802) -#13923 := (iff #3347 #13801) -#13924 := [rewrite]: #13923 -#13926 := [monotonicity #13924]: #13925 -#13941 := [monotonicity #13926 #13938]: #13940 -#13944 := [monotonicity #13523 #13941]: #13943 -#13949 := [trans #13944 #13947]: #13948 -#13827 := (iff #12965 #13824) -#13812 := (or #13521 #13795) -#13815 := (or #13521 #13812) -#13818 := (or #13801 #13815) -#13821 := (or #13521 #13818) -#13825 := (iff #13821 #13824) -#13826 := [rewrite]: #13825 -#13822 := (iff #12965 #13821) -#13819 := (iff #12957 #13818) -#13816 := (iff #12948 #13815) -#13813 := (iff #12940 #13812) -#13798 := (iff #12934 #13795) -#13792 := (and #12581 #13789) -#13796 := (iff #13792 #13795) -#13797 := [rewrite]: #13796 -#13793 := (iff #12934 #13792) -#13790 := (iff #12929 #13789) -#13787 := (iff #12923 #13784) -#13781 := (and #12587 #13776) -#13785 := (iff #13781 #13784) -#13786 := [rewrite]: #13785 -#13782 := (iff #12923 #13781) -#13779 := (iff #12918 #13776) -#13770 := (or #13521 #13767) -#13773 := (or #12785 #13770) -#13777 := (iff #13773 #13776) -#13778 := [rewrite]: #13777 -#13774 := (iff #12918 #13773) -#13771 := (iff #12910 #13770) -#13768 := (iff #12904 #13767) -#13765 := (iff #12899 #13762) -#13659 := (or #13530 #13651) -#13741 := (or #13659 #12848) -#13744 := (or #12857 #13741) -#13747 := (or #13521 #13744) -#13750 := (or #13521 #13747) -#13753 := (or #13521 #13750) -#13756 := (or #13707 #13753) -#13759 := (or #13521 #13756) -#13763 := (iff #13759 #13762) -#13764 := [rewrite]: #13763 -#13760 := (iff #12899 #13759) -#13757 := (iff #12891 #13756) -#13754 := (iff #12882 #13753) -#13751 := (iff #12874 #13750) -#13748 := (iff #12866 #13747) -#13745 := (iff #12858 #13744) -#13742 := (iff #12849 #13741) -#13660 := (iff #12723 #13659) -#13654 := (iff #12716 #13651) -#13648 := (and #13625 #13643) -#13652 := (iff #13648 #13651) -#13653 := [rewrite]: #13652 -#13649 := (iff #12716 #13648) -#13646 := (iff #12711 #13643) -#13631 := (or #13547 #13615) -#13634 := (or #12692 #13631) -#13637 := (or #13622 #13634) -#13640 := (or #13628 #13637) -#13644 := (iff #13640 #13643) -#13645 := [rewrite]: #13644 -#13641 := (iff #12711 #13640) -#13638 := (iff #12702 #13637) -#13635 := (iff #12693 #13634) -#13632 := (iff #12684 #13631) -#13616 := (iff #12677 #13615) -#13613 := (iff #12672 #13612) -#13610 := (iff #12665 #13609) -#13607 := (iff #12660 #13606) -#13604 := (iff #12646 #13601) -#13598 := (and #13595 #12643) -#13602 := (iff #13598 #13601) -#13603 := [rewrite]: #13602 -#13599 := (iff #12646 #13598) -#13596 := (iff #3297 #13595) -#13597 := [rewrite]: #13596 -#13600 := [monotonicity #13597]: #13599 -#13605 := [trans #13600 #13603]: #13604 -#13590 := (iff #12659 #13589) -#13587 := (iff #12640 #13586) -#13584 := (iff #12635 #13581) -#13575 := (or #13558 #13572) -#13578 := (or #5738 #13575) -#13582 := (iff #13578 #13581) -#13583 := [rewrite]: #13582 -#13579 := (iff #12635 #13578) -#13576 := (iff #12629 #13575) -#13573 := (iff #3293 #13572) -#13574 := [rewrite]: #13573 -#13568 := (iff #12628 #13558) -#13560 := (not #13558) -#13563 := (not #13560) -#13566 := (iff #13563 #13558) +#4505 := [monotonicity #4201 #4498]: #4504 +#5714 := [monotonicity #4505]: #5713 +#13815 := [monotonicity #5714 #13812]: #13814 +#13820 := [trans #13815 #13818]: #13819 +#13823 := [quant-intro #13820]: #13822 +#13843 := [monotonicity #13823]: #13842 +#13839 := (iff #3177 #13838) +#13836 := (iff #3176 #13833) +#13824 := (and #13795 #3173) +#13827 := (and #4496 #13824) +#13830 := (and #4202 #13827) +#13834 := (iff #13830 #13833) +#13835 := [rewrite]: #13834 +#13831 := (iff #3176 #13830) +#13828 := (iff #3175 #13827) +#13825 := (iff #3174 #13824) +#13826 := [monotonicity #13797]: #13825 +#13829 := [monotonicity #4498 #13826]: #13828 +#13832 := [monotonicity #4201 #13829]: #13831 +#13837 := [trans #13832 #13835]: #13836 +#13840 := [quant-intro #13837]: #13839 +#13846 := [monotonicity #13840 #13843]: #13845 +#13851 := [trans #13846 #13849]: #13850 +#13854 := [monotonicity #13823 #13851]: #13853 +#13857 := [monotonicity #13854]: #13856 +#13860 := [monotonicity #13857]: #13859 +#13863 := [monotonicity #13860]: #13862 +#13866 := [monotonicity #13863]: #13865 +#13486 := (iff #12313 #13485) +#13483 := (iff #12196 #13482) +#13479 := (iff #3143 #13480) +#13481 := [rewrite]: #13479 +#13476 := (iff #3136 #13477) +#13478 := [rewrite]: #13476 +#13484 := [monotonicity #13478 #13481]: #13483 +#13487 := [monotonicity #13484]: #13486 +#13869 := [monotonicity #13487 #13866]: #13868 +#13872 := [monotonicity #13487 #13869]: #13871 +#13875 := [monotonicity #13487 #13872]: #13874 +#13878 := [monotonicity #13875]: #13877 +#13883 := [trans #13878 #13881]: #13882 +#13886 := [monotonicity #13883]: #13885 +#13893 := [monotonicity #13487 #13886]: #13892 +#13896 := [monotonicity #13487 #13893]: #13895 +#13899 := [monotonicity #13487 #13896]: #13898 +#13902 := [monotonicity #13487 #13899]: #13901 +#13889 := (iff #12953 #13766) +#13887 := (iff #3347 #13765) +#13888 := [rewrite]: #13887 +#13890 := [monotonicity #13888]: #13889 +#13905 := [monotonicity #13890 #13902]: #13904 +#13908 := [monotonicity #13487 #13905]: #13907 +#13913 := [trans #13908 #13911]: #13912 +#13791 := (iff #12929 #13788) +#13776 := (or #13485 #13759) +#13779 := (or #13485 #13776) +#13782 := (or #13765 #13779) +#13785 := (or #13485 #13782) +#13789 := (iff #13785 #13788) +#13790 := [rewrite]: #13789 +#13786 := (iff #12929 #13785) +#13783 := (iff #12921 #13782) +#13780 := (iff #12912 #13779) +#13777 := (iff #12904 #13776) +#13762 := (iff #12898 #13759) +#13756 := (and #12545 #13753) +#13760 := (iff #13756 #13759) +#13761 := [rewrite]: #13760 +#13757 := (iff #12898 #13756) +#13754 := (iff #12893 #13753) +#13751 := (iff #12887 #13748) +#13745 := (and #12551 #13740) +#13749 := (iff #13745 #13748) +#13750 := [rewrite]: #13749 +#13746 := (iff #12887 #13745) +#13743 := (iff #12882 #13740) +#13734 := (or #13485 #13731) +#13737 := (or #12749 #13734) +#13741 := (iff #13737 #13740) +#13742 := [rewrite]: #13741 +#13738 := (iff #12882 #13737) +#13735 := (iff #12874 #13734) +#13732 := (iff #12868 #13731) +#13729 := (iff #12863 #13726) +#13623 := (or #13494 #13615) +#13705 := (or #13623 #12812) +#13708 := (or #12821 #13705) +#13711 := (or #13485 #13708) +#13714 := (or #13485 #13711) +#13717 := (or #13485 #13714) +#13720 := (or #13671 #13717) +#13723 := (or #13485 #13720) +#13727 := (iff #13723 #13726) +#13728 := [rewrite]: #13727 +#13724 := (iff #12863 #13723) +#13721 := (iff #12855 #13720) +#13718 := (iff #12846 #13717) +#13715 := (iff #12838 #13714) +#13712 := (iff #12830 #13711) +#13709 := (iff #12822 #13708) +#13706 := (iff #12813 #13705) +#13624 := (iff #12687 #13623) +#13618 := (iff #12680 #13615) +#13612 := (and #13589 #13607) +#13616 := (iff #13612 #13615) +#13617 := [rewrite]: #13616 +#13613 := (iff #12680 #13612) +#13610 := (iff #12675 #13607) +#13595 := (or #13511 #13579) +#13598 := (or #12656 #13595) +#13601 := (or #13586 #13598) +#13604 := (or #13592 #13601) +#13608 := (iff #13604 #13607) +#13609 := [rewrite]: #13608 +#13605 := (iff #12675 #13604) +#13602 := (iff #12666 #13601) +#13599 := (iff #12657 #13598) +#13596 := (iff #12648 #13595) +#13580 := (iff #12641 #13579) +#13577 := (iff #12636 #13576) +#13574 := (iff #12629 #13573) +#13571 := (iff #12624 #13570) +#13568 := (iff #12610 #13565) +#13562 := (and #13559 #12607) +#13566 := (iff #13562 #13565) #13567 := [rewrite]: #13566 -#13564 := (iff #12628 #13563) -#13561 := (iff #3292 #13560) -#13562 := [rewrite]: #13561 -#13565 := [monotonicity #13562]: #13564 -#13569 := [trans #13565 #13567]: #13568 -#13577 := [monotonicity #13569 #13574]: #13576 -#13580 := [monotonicity #5740 #13577]: #13579 -#13585 := [trans #13580 #13583]: #13584 -#13588 := [quant-intro #13585]: #13587 -#13591 := [monotonicity #13588]: #13590 -#13608 := [monotonicity #13591 #13605]: #13607 -#13611 := [monotonicity #13588 #13608]: #13610 -#13556 := (iff #12671 #13555) -#13553 := (iff #3291 #13550) -#13554 := [rewrite]: #13553 -#13557 := [monotonicity #13554]: #13556 -#13614 := [monotonicity #13557 #13611]: #13613 -#13617 := [monotonicity #13554 #13614]: #13616 -#13548 := (iff #12683 #13547) -#13545 := (iff #12625 #13544) -#13541 := (iff #3289 #13542) -#13543 := [rewrite]: #13541 -#13524 := (iff #3279 #13525) -#13526 := [rewrite]: #13524 -#13546 := [monotonicity #13526 #13543]: #13545 -#13549 := [monotonicity #13546]: #13548 -#13633 := [monotonicity #13549 #13617]: #13632 -#13636 := [monotonicity #13633]: #13635 -#13623 := (iff #12701 #13622) -#13620 := (iff #12619 #13618) -#13621 := [rewrite]: #13620 -#13624 := [monotonicity #13621]: #13623 -#13639 := [monotonicity #13624 #13636]: #13638 -#13629 := (iff #12710 #13628) -#13626 := (iff #12616 #13625) -#13539 := (iff #12613 #13536) -#13540 := [rewrite]: #13539 -#13533 := (iff #12610 #13534) -#13535 := [rewrite]: #13533 -#13627 := [monotonicity #13535 #13540]: #13626 -#13630 := [monotonicity #13627]: #13629 -#13642 := [monotonicity #13630 #13639]: #13641 -#13647 := [trans #13642 #13645]: #13646 -#13650 := [monotonicity #13627 #13647]: #13649 -#13655 := [trans #13650 #13653]: #13654 -#13531 := (iff #12722 #13530) -#13528 := (iff #3280 #13527) -#13529 := [monotonicity #13517 #13526]: #13528 -#13532 := [monotonicity #13529]: #13531 -#13661 := [monotonicity #13532 #13655]: #13660 -#13743 := [monotonicity #13661]: #13742 -#13746 := [monotonicity #13743]: #13745 -#13749 := [monotonicity #13523 #13746]: #13748 -#13752 := [monotonicity #13523 #13749]: #13751 -#13755 := [monotonicity #13523 #13752]: #13754 -#13739 := (iff #12890 #13707) -#13737 := (iff #3327 #13708) -#13738 := [rewrite]: #13737 -#13740 := [monotonicity #13738]: #13739 -#13758 := [monotonicity #13740 #13755]: #13757 -#13761 := [monotonicity #13523 #13758]: #13760 -#13766 := [trans #13761 #13764]: #13765 -#13735 := (iff #12834 #13732) -#13720 := (or #13521 #13702) -#13723 := (or #13521 #13720) -#13726 := (or #13708 #13723) -#13729 := (or #13521 #13726) -#13733 := (iff #13729 #13732) -#13734 := [rewrite]: #13733 -#13730 := (iff #12834 #13729) -#13727 := (iff #12826 #13726) -#13724 := (iff #12817 #13723) -#13721 := (iff #12809 #13720) -#13705 := (iff #12803 #13702) -#13699 := (and #12581 #13696) -#13703 := (iff #13699 #13702) -#13704 := [rewrite]: #13703 -#13700 := (iff #12803 #13699) -#13697 := (iff #12798 #13696) -#13694 := (iff #12791 #13691) -#13688 := (and #12587 #13683) -#13692 := (iff #13688 #13691) -#13693 := [rewrite]: #13692 -#13689 := (iff #12791 #13688) -#13686 := (iff #12786 #13683) -#13662 := (or #12731 #13659) -#13665 := (or #12740 #13662) -#13668 := (or #13656 #13665) -#13671 := (or #12758 #13668) -#13674 := (or #12767 #13671) -#13677 := (or #12776 #13674) -#13680 := (or #12785 #13677) -#13684 := (iff #13680 #13683) -#13685 := [rewrite]: #13684 -#13681 := (iff #12786 #13680) -#13678 := (iff #12777 #13677) -#13675 := (iff #12768 #13674) -#13672 := (iff #12759 #13671) -#13669 := (iff #12750 #13668) -#13666 := (iff #12741 #13665) -#13663 := (iff #12732 #13662) -#13664 := [monotonicity #13661]: #13663 -#13667 := [monotonicity #13664]: #13666 -#13657 := (iff #12749 #13656) -#13658 := [monotonicity #13517]: #13657 -#13670 := [monotonicity #13658 #13667]: #13669 -#13673 := [monotonicity #13670]: #13672 -#13676 := [monotonicity #13673]: #13675 +#13563 := (iff #12610 #13562) +#13560 := (iff #3297 #13559) +#13561 := [rewrite]: #13560 +#13564 := [monotonicity #13561]: #13563 +#13569 := [trans #13564 #13567]: #13568 +#13554 := (iff #12623 #13553) +#13551 := (iff #12604 #13550) +#13548 := (iff #12599 #13545) +#13539 := (or #13522 #13536) +#13542 := (or #5712 #13539) +#13546 := (iff #13542 #13545) +#13547 := [rewrite]: #13546 +#13543 := (iff #12599 #13542) +#13540 := (iff #12593 #13539) +#13537 := (iff #3293 #13536) +#13538 := [rewrite]: #13537 +#13532 := (iff #12592 #13522) +#13524 := (not #13522) +#13527 := (not #13524) +#13530 := (iff #13527 #13522) +#13531 := [rewrite]: #13530 +#13528 := (iff #12592 #13527) +#13525 := (iff #3292 #13524) +#13526 := [rewrite]: #13525 +#13529 := [monotonicity #13526]: #13528 +#13533 := [trans #13529 #13531]: #13532 +#13541 := [monotonicity #13533 #13538]: #13540 +#13544 := [monotonicity #5714 #13541]: #13543 +#13549 := [trans #13544 #13547]: #13548 +#13552 := [quant-intro #13549]: #13551 +#13555 := [monotonicity #13552]: #13554 +#13572 := [monotonicity #13555 #13569]: #13571 +#13575 := [monotonicity #13552 #13572]: #13574 +#13520 := (iff #12635 #13519) +#13517 := (iff #3291 #13514) +#13518 := [rewrite]: #13517 +#13521 := [monotonicity #13518]: #13520 +#13578 := [monotonicity #13521 #13575]: #13577 +#13581 := [monotonicity #13518 #13578]: #13580 +#13512 := (iff #12647 #13511) +#13509 := (iff #12589 #13508) +#13505 := (iff #3289 #13506) +#13507 := [rewrite]: #13505 +#13488 := (iff #3279 #13489) +#13490 := [rewrite]: #13488 +#13510 := [monotonicity #13490 #13507]: #13509 +#13513 := [monotonicity #13510]: #13512 +#13597 := [monotonicity #13513 #13581]: #13596 +#13600 := [monotonicity #13597]: #13599 +#13587 := (iff #12665 #13586) +#13584 := (iff #12583 #13582) +#13585 := [rewrite]: #13584 +#13588 := [monotonicity #13585]: #13587 +#13603 := [monotonicity #13588 #13600]: #13602 +#13593 := (iff #12674 #13592) +#13590 := (iff #12580 #13589) +#13503 := (iff #12577 #13500) +#13504 := [rewrite]: #13503 +#13497 := (iff #12574 #13498) +#13499 := [rewrite]: #13497 +#13591 := [monotonicity #13499 #13504]: #13590 +#13594 := [monotonicity #13591]: #13593 +#13606 := [monotonicity #13594 #13603]: #13605 +#13611 := [trans #13606 #13609]: #13610 +#13614 := [monotonicity #13591 #13611]: #13613 +#13619 := [trans #13614 #13617]: #13618 +#13495 := (iff #12686 #13494) +#13492 := (iff #3280 #13491) +#13493 := [monotonicity #13481 #13490]: #13492 +#13496 := [monotonicity #13493]: #13495 +#13625 := [monotonicity #13496 #13619]: #13624 +#13707 := [monotonicity #13625]: #13706 +#13710 := [monotonicity #13707]: #13709 +#13713 := [monotonicity #13487 #13710]: #13712 +#13716 := [monotonicity #13487 #13713]: #13715 +#13719 := [monotonicity #13487 #13716]: #13718 +#13703 := (iff #12854 #13671) +#13701 := (iff #3327 #13672) +#13702 := [rewrite]: #13701 +#13704 := [monotonicity #13702]: #13703 +#13722 := [monotonicity #13704 #13719]: #13721 +#13725 := [monotonicity #13487 #13722]: #13724 +#13730 := [trans #13725 #13728]: #13729 +#13699 := (iff #12798 #13696) +#13684 := (or #13485 #13666) +#13687 := (or #13485 #13684) +#13690 := (or #13672 #13687) +#13693 := (or #13485 #13690) +#13697 := (iff #13693 #13696) +#13698 := [rewrite]: #13697 +#13694 := (iff #12798 #13693) +#13691 := (iff #12790 #13690) +#13688 := (iff #12781 #13687) +#13685 := (iff #12773 #13684) +#13669 := (iff #12767 #13666) +#13663 := (and #12545 #13660) +#13667 := (iff #13663 #13666) +#13668 := [rewrite]: #13667 +#13664 := (iff #12767 #13663) +#13661 := (iff #12762 #13660) +#13658 := (iff #12755 #13655) +#13652 := (and #12551 #13647) +#13656 := (iff #13652 #13655) +#13657 := [rewrite]: #13656 +#13653 := (iff #12755 #13652) +#13650 := (iff #12750 #13647) +#13626 := (or #12695 #13623) +#13629 := (or #12704 #13626) +#13632 := (or #13620 #13629) +#13635 := (or #12722 #13632) +#13638 := (or #12731 #13635) +#13641 := (or #12740 #13638) +#13644 := (or #12749 #13641) +#13648 := (iff #13644 #13647) +#13649 := [rewrite]: #13648 +#13645 := (iff #12750 #13644) +#13642 := (iff #12741 #13641) +#13639 := (iff #12732 #13638) +#13636 := (iff #12723 #13635) +#13633 := (iff #12714 #13632) +#13630 := (iff #12705 #13629) +#13627 := (iff #12696 #13626) +#13628 := [monotonicity #13625]: #13627 +#13631 := [monotonicity #13628]: #13630 +#13621 := (iff #12713 #13620) +#13622 := [monotonicity #13481]: #13621 +#13634 := [monotonicity #13622 #13631]: #13633 +#13637 := [monotonicity #13634]: #13636 +#13640 := [monotonicity #13637]: #13639 +#13643 := [monotonicity #13640]: #13642 +#13646 := [monotonicity #13643]: #13645 +#13651 := [trans #13646 #13649]: #13650 +#13654 := [monotonicity #13651]: #13653 +#13659 := [trans #13654 #13657]: #13658 +#13662 := [monotonicity #13659]: #13661 +#13665 := [monotonicity #13662]: #13664 +#13670 := [trans #13665 #13668]: #13669 +#13686 := [monotonicity #13487 #13670]: #13685 +#13689 := [monotonicity #13487 #13686]: #13688 +#13682 := (iff #12789 #13672) +#13677 := (not #13671) +#13680 := (iff #13677 #13672) +#13681 := [rewrite]: #13680 +#13678 := (iff #12789 #13677) +#13675 := (iff #3267 #13671) +#13676 := [rewrite]: #13675 #13679 := [monotonicity #13676]: #13678 -#13682 := [monotonicity #13679]: #13681 -#13687 := [trans #13682 #13685]: #13686 -#13690 := [monotonicity #13687]: #13689 -#13695 := [trans #13690 #13693]: #13694 -#13698 := [monotonicity #13695]: #13697 -#13701 := [monotonicity #13698]: #13700 -#13706 := [trans #13701 #13704]: #13705 -#13722 := [monotonicity #13523 #13706]: #13721 -#13725 := [monotonicity #13523 #13722]: #13724 -#13718 := (iff #12825 #13708) -#13713 := (not #13707) -#13716 := (iff #13713 #13708) -#13717 := [rewrite]: #13716 -#13714 := (iff #12825 #13713) -#13711 := (iff #3267 #13707) -#13712 := [rewrite]: #13711 -#13715 := [monotonicity #13712]: #13714 -#13719 := [trans #13715 #13717]: #13718 -#13728 := [monotonicity #13719 #13725]: #13727 -#13731 := [monotonicity #13523 #13728]: #13730 -#13736 := [trans #13731 #13734]: #13735 -#13769 := [monotonicity #13736 #13766]: #13768 -#13772 := [monotonicity #13523 #13769]: #13771 -#13775 := [monotonicity #13772]: #13774 -#13780 := [trans #13775 #13778]: #13779 -#13783 := [monotonicity #13780]: #13782 -#13788 := [trans #13783 #13786]: #13787 -#13791 := [monotonicity #13788]: #13790 -#13794 := [monotonicity #13791]: #13793 -#13799 := [trans #13794 #13797]: #13798 -#13814 := [monotonicity #13523 #13799]: #13813 -#13817 := [monotonicity #13523 #13814]: #13816 -#13810 := (iff #12956 #13801) -#13805 := (not #13802) -#13808 := (iff #13805 #13801) -#13809 := [rewrite]: #13808 -#13806 := (iff #12956 #13805) -#13803 := (iff #3256 #13802) -#13804 := [rewrite]: #13803 -#13807 := [monotonicity #13804]: #13806 -#13811 := [trans #13807 #13809]: #13810 -#13820 := [monotonicity #13811 #13817]: #13819 -#13823 := [monotonicity #13523 #13820]: #13822 -#13828 := [trans #13823 #13826]: #13827 -#13952 := [monotonicity #13828 #13949]: #13951 -#14082 := [monotonicity #13523 #13952]: #14081 -#14085 := [monotonicity #14082]: #14084 -#14088 := [monotonicity #14085]: #14087 -#14091 := [monotonicity #14088]: #14090 -#14094 := [monotonicity #14091]: #14093 -#14097 := [monotonicity #14094]: #14096 -#14100 := [monotonicity #14097]: #14099 -#13975 := (iff #13077 #13974) -#13972 := (iff #12521 #12515) -#13964 := (and true #12515) -#13967 := (and true #13964) -#13970 := (iff #13967 #12515) -#13971 := [rewrite]: #13970 -#13968 := (iff #12521 #13967) -#13965 := (iff #12518 #13964) -#13960 := (iff #3231 true) -#13955 := (forall (vars (?v0 S20)) (:pat #3229) true) -#13958 := (iff #13955 true) -#13959 := [elim-unused]: #13958 -#13956 := (iff #3231 #13955) -#13953 := (iff #3230 true) -#13954 := [rewrite]: #13953 -#13957 := [quant-intro #13954]: #13956 -#13961 := [trans #13957 #13959]: #13960 -#13966 := [monotonicity #13961]: #13965 -#13962 := (iff #3227 true) -#13963 := [rewrite]: #13962 -#13969 := [monotonicity #13963 #13966]: #13968 -#13973 := [trans #13969 #13971]: #13972 -#13976 := [monotonicity #13973]: #13975 -#14103 := [monotonicity #13976 #14100]: #14102 -#14106 := [monotonicity #13976 #14103]: #14105 -#14109 := [monotonicity #13523 #14106]: #14108 -#14112 := [monotonicity #13523 #14109]: #14111 -#14115 := [monotonicity #13523 #14112]: #14114 -#14118 := [monotonicity #13523 #14115]: #14117 -#13992 := (iff #13133 #13991) -#13989 := (iff #12253 #13986) -#13983 := (and #13980 #12250) -#13987 := (iff #13983 #13986) -#13988 := [rewrite]: #13987 -#13984 := (iff #12253 #13983) -#13981 := (iff #3151 #13980) -#13982 := [rewrite]: #13981 -#13985 := [monotonicity #13982]: #13984 -#13990 := [trans #13985 #13988]: #13989 -#13993 := [monotonicity #13990]: #13992 -#14121 := [monotonicity #13993 #14118]: #14120 -#14026 := (iff #13142 #14025) -#14023 := (iff #12247 #14022) -#14020 := (iff #12242 #14017) -#14011 := (or #13994 #14008) -#14014 := (or #5738 #14011) -#14018 := (iff #14014 #14017) -#14019 := [rewrite]: #14018 -#14015 := (iff #12242 #14014) -#14012 := (iff #12236 #14011) -#14009 := (iff #3147 #14008) -#14010 := [rewrite]: #14009 -#14004 := (iff #12235 #13994) -#13996 := (not #13994) -#13999 := (not #13996) -#14002 := (iff #13999 #13994) +#13683 := [trans #13679 #13681]: #13682 +#13692 := [monotonicity #13683 #13689]: #13691 +#13695 := [monotonicity #13487 #13692]: #13694 +#13700 := [trans #13695 #13698]: #13699 +#13733 := [monotonicity #13700 #13730]: #13732 +#13736 := [monotonicity #13487 #13733]: #13735 +#13739 := [monotonicity #13736]: #13738 +#13744 := [trans #13739 #13742]: #13743 +#13747 := [monotonicity #13744]: #13746 +#13752 := [trans #13747 #13750]: #13751 +#13755 := [monotonicity #13752]: #13754 +#13758 := [monotonicity #13755]: #13757 +#13763 := [trans #13758 #13761]: #13762 +#13778 := [monotonicity #13487 #13763]: #13777 +#13781 := [monotonicity #13487 #13778]: #13780 +#13774 := (iff #12920 #13765) +#13769 := (not #13766) +#13772 := (iff #13769 #13765) +#13773 := [rewrite]: #13772 +#13770 := (iff #12920 #13769) +#13767 := (iff #3256 #13766) +#13768 := [rewrite]: #13767 +#13771 := [monotonicity #13768]: #13770 +#13775 := [trans #13771 #13773]: #13774 +#13784 := [monotonicity #13775 #13781]: #13783 +#13787 := [monotonicity #13487 #13784]: #13786 +#13792 := [trans #13787 #13790]: #13791 +#13916 := [monotonicity #13792 #13913]: #13915 +#14046 := [monotonicity #13487 #13916]: #14045 +#14049 := [monotonicity #14046]: #14048 +#14052 := [monotonicity #14049]: #14051 +#14055 := [monotonicity #14052]: #14054 +#14058 := [monotonicity #14055]: #14057 +#14061 := [monotonicity #14058]: #14060 +#14064 := [monotonicity #14061]: #14063 +#13939 := (iff #13041 #13938) +#13936 := (iff #12485 #12479) +#13928 := (and true #12479) +#13931 := (and true #13928) +#13934 := (iff #13931 #12479) +#13935 := [rewrite]: #13934 +#13932 := (iff #12485 #13931) +#13929 := (iff #12482 #13928) +#13924 := (iff #3231 true) +#13919 := (forall (vars (?v0 S20)) (:pat #3229) true) +#13922 := (iff #13919 true) +#13923 := [elim-unused]: #13922 +#13920 := (iff #3231 #13919) +#13917 := (iff #3230 true) +#13918 := [rewrite]: #13917 +#13921 := [quant-intro #13918]: #13920 +#13925 := [trans #13921 #13923]: #13924 +#13930 := [monotonicity #13925]: #13929 +#13926 := (iff #3227 true) +#13927 := [rewrite]: #13926 +#13933 := [monotonicity #13927 #13930]: #13932 +#13937 := [trans #13933 #13935]: #13936 +#13940 := [monotonicity #13937]: #13939 +#14067 := [monotonicity #13940 #14064]: #14066 +#14070 := [monotonicity #13940 #14067]: #14069 +#14073 := [monotonicity #13487 #14070]: #14072 +#14076 := [monotonicity #13487 #14073]: #14075 +#14079 := [monotonicity #13487 #14076]: #14078 +#14082 := [monotonicity #13487 #14079]: #14081 +#13956 := (iff #13097 #13955) +#13953 := (iff #12217 #13950) +#13947 := (and #13944 #12214) +#13951 := (iff #13947 #13950) +#13952 := [rewrite]: #13951 +#13948 := (iff #12217 #13947) +#13945 := (iff #3151 #13944) +#13946 := [rewrite]: #13945 +#13949 := [monotonicity #13946]: #13948 +#13954 := [trans #13949 #13952]: #13953 +#13957 := [monotonicity #13954]: #13956 +#14085 := [monotonicity #13957 #14082]: #14084 +#13990 := (iff #13106 #13989) +#13987 := (iff #12211 #13986) +#13984 := (iff #12206 #13981) +#13975 := (or #13958 #13972) +#13978 := (or #5712 #13975) +#13982 := (iff #13978 #13981) +#13983 := [rewrite]: #13982 +#13979 := (iff #12206 #13978) +#13976 := (iff #12200 #13975) +#13973 := (iff #3147 #13972) +#13974 := [rewrite]: #13973 +#13968 := (iff #12199 #13958) +#13960 := (not #13958) +#13963 := (not #13960) +#13966 := (iff #13963 #13958) +#13967 := [rewrite]: #13966 +#13964 := (iff #12199 #13963) +#13961 := (iff #3146 #13960) +#13962 := [rewrite]: #13961 +#13965 := [monotonicity #13962]: #13964 +#13969 := [trans #13965 #13967]: #13968 +#13977 := [monotonicity #13969 #13974]: #13976 +#13980 := [monotonicity #5714 #13977]: #13979 +#13985 := [trans #13980 #13983]: #13984 +#13988 := [quant-intro #13985]: #13987 +#13991 := [monotonicity #13988]: #13990 +#14088 := [monotonicity #13991 #14085]: #14087 +#13996 := (iff #13115 #13995) +#13993 := (iff #3145 #13992) +#13994 := [rewrite]: #13993 +#13997 := [monotonicity #13994]: #13996 +#14091 := [monotonicity #13997 #14088]: #14090 +#14094 := [monotonicity #13487 #14091]: #14093 +#14008 := (iff #13132 #14007) +#14005 := (iff #3142 #14004) +#14002 := (iff #3141 #14001) #14003 := [rewrite]: #14002 -#14000 := (iff #12235 #13999) -#13997 := (iff #3146 #13996) -#13998 := [rewrite]: #13997 -#14001 := [monotonicity #13998]: #14000 -#14005 := [trans #14001 #14003]: #14004 -#14013 := [monotonicity #14005 #14010]: #14012 -#14016 := [monotonicity #5740 #14013]: #14015 -#14021 := [trans #14016 #14019]: #14020 -#14024 := [quant-intro #14021]: #14023 -#14027 := [monotonicity #14024]: #14026 -#14124 := [monotonicity #14027 #14121]: #14123 -#14032 := (iff #13151 #14031) -#14029 := (iff #3145 #14028) -#14030 := [rewrite]: #14029 -#14033 := [monotonicity #14030]: #14032 -#14127 := [monotonicity #14033 #14124]: #14126 -#14130 := [monotonicity #13523 #14127]: #14129 -#14044 := (iff #13168 #14043) -#14041 := (iff #3142 #14040) -#14038 := (iff #3141 #14037) -#14039 := [rewrite]: #14038 -#14035 := (iff #3140 #14034) -#14036 := [rewrite]: #14035 -#14042 := [monotonicity #14036 #14039]: #14041 -#14045 := [monotonicity #14042]: #14044 -#14133 := [monotonicity #14045 #14130]: #14132 -#14054 := (iff #13177 #14053) -#14051 := (iff #3138 #14050) -#14048 := (iff #3137 #14046) -#14049 := [rewrite]: #14048 -#14052 := [monotonicity #13514 #14049]: #14051 -#14055 := [monotonicity #14052]: #14054 -#14136 := [monotonicity #14055 #14133]: #14135 -#14067 := (iff #13186 #14066) -#14064 := (iff #3134 #14063) -#14061 := (iff #3133 #14059) -#14062 := [rewrite]: #14061 -#14057 := (iff #3132 #14056) -#14058 := [rewrite]: #14057 -#14065 := [monotonicity #14058 #14062]: #14064 -#14068 := [monotonicity #14065]: #14067 -#14139 := [monotonicity #14068 #14136]: #14138 -#14078 := (iff #13195 #14077) -#14075 := (iff #12229 #14072) -#14073 := (iff #14069 #14072) -#14074 := [rewrite]: #14073 -#14070 := (iff #12229 #14069) -#13510 := (iff #3038 #13509) -#13511 := [rewrite]: #13510 -#14071 := [monotonicity #13511]: #14070 -#14076 := [trans #14071 #14074]: #14075 -#14079 := [monotonicity #14076]: #14078 -#14142 := [monotonicity #14079 #14139]: #14141 -#14147 := [trans #14142 #14145]: #14146 -#14150 := [monotonicity #14071 #14147]: #14149 -#14155 := [trans #14150 #14153]: #14154 -#13506 := (iff #13207 #13505) -#13503 := (iff #12224 #13502) -#13500 := (iff #12219 #13497) -#13491 := (or #13475 #13487) -#13494 := (or #5738 #13491) -#13498 := (iff #13494 #13497) -#13499 := [rewrite]: #13498 -#13495 := (iff #12219 #13494) -#13492 := (iff #12213 #13491) -#13486 := (iff #3125 #13487) -#13490 := [rewrite]: #13486 -#13484 := (iff #12212 #13475) -#13476 := (not #13475) -#13479 := (not #13476) -#13482 := (iff #13479 #13475) -#13483 := [rewrite]: #13482 -#13480 := (iff #12212 #13479) -#13477 := (iff #3122 #13476) -#13478 := [rewrite]: #13477 -#13481 := [monotonicity #13478]: #13480 -#13485 := [trans #13481 #13483]: #13484 -#13493 := [monotonicity #13485 #13490]: #13492 -#13496 := [monotonicity #5740 #13493]: #13495 -#13501 := [trans #13496 #13499]: #13500 -#13504 := [quant-intro #13501]: #13503 -#13507 := [monotonicity #13504]: #13506 -#14158 := [monotonicity #13507 #14155]: #14157 -#14161 := [monotonicity #13504 #14158]: #14160 -#13473 := (iff #13219 #13472) -#13470 := (iff #3121 #13469) -#13471 := [rewrite]: #13470 -#13474 := [monotonicity #13471]: #13473 -#14164 := [monotonicity #13474 #14161]: #14163 -#14167 := [monotonicity #13471 #14164]: #14166 -#13467 := (iff #13231 false) -#12256 := (iff #3156 false) -#12257 := [rewrite]: #12256 -#13465 := (iff #13231 #3156) -#13463 := (iff #12209 true) -#12568 := (and true true) -#13458 := (and true #12568) -#13461 := (iff #13458 true) -#13462 := [rewrite]: #13461 -#13459 := (iff #12209 #13458) -#13456 := (iff #12206 #12568) -#13454 := (iff #3117 true) -#13455 := [rewrite]: #13454 -#13452 := (iff #3116 true) -#13453 := [rewrite]: #13452 -#13457 := [monotonicity #13453 #13455]: #13456 -#13460 := [monotonicity #13453 #13457]: #13459 -#13464 := [trans #13460 #13462]: #13463 -#13466 := [monotonicity #13464]: #13465 -#13468 := [trans #13466 #12257]: #13467 -#14170 := [monotonicity #13468 #14167]: #14169 -#14173 := [monotonicity #14170]: #14172 +#13999 := (iff #3140 #13998) +#14000 := [rewrite]: #13999 +#14006 := [monotonicity #14000 #14003]: #14005 +#14009 := [monotonicity #14006]: #14008 +#14097 := [monotonicity #14009 #14094]: #14096 +#14018 := (iff #13141 #14017) +#14015 := (iff #3138 #14014) +#14012 := (iff #3137 #14010) +#14013 := [rewrite]: #14012 +#14016 := [monotonicity #13478 #14013]: #14015 +#14019 := [monotonicity #14016]: #14018 +#14100 := [monotonicity #14019 #14097]: #14099 +#14031 := (iff #13150 #14030) +#14028 := (iff #3134 #14027) +#14025 := (iff #3133 #14023) +#14026 := [rewrite]: #14025 +#14021 := (iff #3132 #14020) +#14022 := [rewrite]: #14021 +#14029 := [monotonicity #14022 #14026]: #14028 +#14032 := [monotonicity #14029]: #14031 +#14103 := [monotonicity #14032 #14100]: #14102 +#14042 := (iff #13159 #14041) +#14039 := (iff #12193 #14036) +#14037 := (iff #14033 #14036) +#14038 := [rewrite]: #14037 +#14034 := (iff #12193 #14033) +#13474 := (iff #3038 #13473) +#13475 := [rewrite]: #13474 +#14035 := [monotonicity #13475]: #14034 +#14040 := [trans #14035 #14038]: #14039 +#14043 := [monotonicity #14040]: #14042 +#14106 := [monotonicity #14043 #14103]: #14105 +#14111 := [trans #14106 #14109]: #14110 +#14114 := [monotonicity #14035 #14111]: #14113 +#14119 := [trans #14114 #14117]: #14118 +#13470 := (iff #13171 #13469) +#13467 := (iff #12188 #13466) +#13464 := (iff #12183 #13461) +#13455 := (or #13439 #13451) +#13458 := (or #5712 #13455) +#13462 := (iff #13458 #13461) +#13463 := [rewrite]: #13462 +#13459 := (iff #12183 #13458) +#13456 := (iff #12177 #13455) +#13450 := (iff #3125 #13451) +#13454 := [rewrite]: #13450 +#13448 := (iff #12176 #13439) +#13440 := (not #13439) +#13443 := (not #13440) +#13446 := (iff #13443 #13439) +#13447 := [rewrite]: #13446 +#13444 := (iff #12176 #13443) +#13441 := (iff #3122 #13440) +#13442 := [rewrite]: #13441 +#13445 := [monotonicity #13442]: #13444 +#13449 := [trans #13445 #13447]: #13448 +#13457 := [monotonicity #13449 #13454]: #13456 +#13460 := [monotonicity #5714 #13457]: #13459 +#13465 := [trans #13460 #13463]: #13464 +#13468 := [quant-intro #13465]: #13467 +#13471 := [monotonicity #13468]: #13470 +#14122 := [monotonicity #13471 #14119]: #14121 +#14125 := [monotonicity #13468 #14122]: #14124 +#13437 := (iff #13183 #13436) +#13434 := (iff #3121 #13433) +#13435 := [rewrite]: #13434 +#13438 := [monotonicity #13435]: #13437 +#14128 := [monotonicity #13438 #14125]: #14127 +#14131 := [monotonicity #13435 #14128]: #14130 +#13431 := (iff #13195 false) +#12220 := (iff #3156 false) +#12221 := [rewrite]: #12220 +#13429 := (iff #13195 #3156) +#13427 := (iff #12173 true) +#12532 := (and true true) +#13422 := (and true #12532) +#13425 := (iff #13422 true) +#13426 := [rewrite]: #13425 +#13423 := (iff #12173 #13422) +#13420 := (iff #12170 #12532) +#13418 := (iff #3117 true) +#13419 := [rewrite]: #13418 +#13416 := (iff #3116 true) +#13417 := [rewrite]: #13416 +#13421 := [monotonicity #13417 #13419]: #13420 +#13424 := [monotonicity #13417 #13421]: #13423 +#13428 := [trans #13424 #13426]: #13427 +#13430 := [monotonicity #13428]: #13429 +#13432 := [trans #13430 #12221]: #13431 +#14134 := [monotonicity #13432 #14131]: #14133 +#14137 := [monotonicity #14134]: #14136 +#14140 := [monotonicity #14137]: #14139 +#14143 := [monotonicity #14140]: #14142 +#14146 := [monotonicity #14143]: #14145 +#14149 := [monotonicity #14146]: #14148 +#14154 := [trans #14149 #14152]: #14153 +#14157 := [monotonicity #14154]: #14156 +#14162 := [trans #14157 #14160]: #14161 +#14165 := [monotonicity #14162]: #14164 +#14168 := [monotonicity #14165]: #14167 +#14173 := [trans #14168 #14171]: #14172 #14176 := [monotonicity #14173]: #14175 #14179 := [monotonicity #14176]: #14178 -#14182 := [monotonicity #14179]: #14181 -#14185 := [monotonicity #14182]: #14184 -#14190 := [trans #14185 #14188]: #14189 -#14193 := [monotonicity #14190]: #14192 -#14198 := [trans #14193 #14196]: #14197 -#14201 := [monotonicity #14198]: #14200 -#14204 := [monotonicity #14201]: #14203 -#14209 := [trans #14204 #14207]: #14208 -#14212 := [monotonicity #14209]: #14211 -#14215 := [monotonicity #14212]: #14214 -#13450 := (iff #13312 #13449) -#13447 := (iff #3094 #13446) -#13444 := (iff #3093 #13441) -#13445 := [rewrite]: #13444 -#13438 := (iff #3092 #13439) -#13440 := [rewrite]: #13438 -#13448 := [monotonicity #13440 #13445]: #13447 -#13451 := [monotonicity #13448]: #13450 -#14296 := [monotonicity #13451 #14215]: #14295 -#14299 := [monotonicity #14296]: #14298 -#14302 := [monotonicity #14299]: #14301 -#14305 := [monotonicity #14302]: #14304 -#14308 := [monotonicity #14305]: #14307 -#14226 := (iff #13357 #14225) -#14223 := (iff #3075 #14222) -#14220 := (iff #3074 #14216) -#14221 := [rewrite]: #14220 -#14224 := [quant-intro #14221]: #14223 -#14227 := [monotonicity #14224]: #14226 -#14311 := [monotonicity #14227 #14308]: #14310 -#14314 := [monotonicity #14311]: #14313 -#14317 := [monotonicity #14314]: #14316 -#14232 := (iff #13384 #14231) -#14229 := (iff #12136 #14228) -#14230 := [rewrite]: #14229 -#14233 := [monotonicity #14230]: #14232 -#14320 := [monotonicity #14233 #14317]: #14319 -#14239 := (iff #13393 #13508) -#14234 := (not #13509) -#14237 := (iff #14234 #13508) -#14238 := [rewrite]: #14237 -#14235 := (iff #13393 #14234) -#14236 := [monotonicity #13511]: #14235 -#14240 := [trans #14236 #14238]: #14239 -#14323 := [monotonicity #14240 #14320]: #14322 -#14250 := (iff #13402 #14241) -#14242 := (not #14241) -#14245 := (not #14242) -#14248 := (iff #14245 #14241) -#14249 := [rewrite]: #14248 -#14246 := (iff #13402 #14245) -#14243 := (iff #3037 #14242) -#14244 := [rewrite]: #14243 -#14247 := [monotonicity #14244]: #14246 -#14251 := [trans #14247 #14249]: #14250 -#14326 := [monotonicity #14251 #14323]: #14325 -#14264 := (iff #13411 #14263) -#14261 := (iff #3035 #14260) -#14258 := (iff #3034 #14255) -#14259 := [rewrite]: #14258 -#14252 := (iff #3033 #14253) -#14254 := [rewrite]: #14252 -#14262 := [monotonicity #14254 #14259]: #14261 -#14265 := [monotonicity #14262]: #14264 -#14329 := [monotonicity #14265 #14326]: #14328 -#14278 := (iff #13420 #14277) -#14275 := (iff #3031 #14274) -#14272 := (iff #3030 #14269) -#14273 := [rewrite]: #14272 -#14266 := (iff #3029 #14267) -#14268 := [rewrite]: #14266 -#14276 := [monotonicity #14268 #14273]: #14275 -#14279 := [monotonicity #14276]: #14278 -#14332 := [monotonicity #14279 #14329]: #14331 -#14292 := (iff #13429 #14291) -#14289 := (iff #3027 #14288) -#14286 := (iff #3026 #14283) -#14287 := [rewrite]: #14286 -#14280 := (iff #3025 #14281) -#14282 := [rewrite]: #14280 -#14290 := [monotonicity #14282 #14287]: #14289 -#14293 := [monotonicity #14290]: #14292 -#14335 := [monotonicity #14293 #14332]: #14334 -#14340 := [trans #14335 #14338]: #14339 -#14343 := [monotonicity #14340]: #14342 -#13436 := (iff #3406 #13435) -#13433 := (iff #3405 #13430) -#13426 := (implies #3027 #13421) -#13431 := (iff #13426 #13430) -#13432 := [rewrite]: #13431 -#13427 := (iff #3405 #13426) -#13424 := (iff #3404 #13421) -#13417 := (implies #3031 #13412) -#13422 := (iff #13417 #13421) -#13423 := [rewrite]: #13422 -#13418 := (iff #3404 #13417) -#13415 := (iff #3403 #13412) -#13408 := (implies #3035 #13403) -#13413 := (iff #13408 #13412) -#13414 := [rewrite]: #13413 -#13409 := (iff #3403 #13408) -#13406 := (iff #3402 #13403) -#13399 := (implies #3037 #13394) -#13404 := (iff #13399 #13403) -#13405 := [rewrite]: #13404 -#13400 := (iff #3402 #13399) -#13397 := (iff #3401 #13394) -#13390 := (implies #3038 #13385) +#13414 := (iff #13276 #13413) +#13411 := (iff #3094 #13410) +#13408 := (iff #3093 #13405) +#13409 := [rewrite]: #13408 +#13402 := (iff #3092 #13403) +#13404 := [rewrite]: #13402 +#13412 := [monotonicity #13404 #13409]: #13411 +#13415 := [monotonicity #13412]: #13414 +#14260 := [monotonicity #13415 #14179]: #14259 +#14263 := [monotonicity #14260]: #14262 +#14266 := [monotonicity #14263]: #14265 +#14269 := [monotonicity #14266]: #14268 +#14272 := [monotonicity #14269]: #14271 +#14190 := (iff #13321 #14189) +#14187 := (iff #3075 #14186) +#14184 := (iff #3074 #14180) +#14185 := [rewrite]: #14184 +#14188 := [quant-intro #14185]: #14187 +#14191 := [monotonicity #14188]: #14190 +#14275 := [monotonicity #14191 #14272]: #14274 +#14278 := [monotonicity #14275]: #14277 +#14281 := [monotonicity #14278]: #14280 +#14196 := (iff #13348 #14195) +#14193 := (iff #12100 #14192) +#14194 := [rewrite]: #14193 +#14197 := [monotonicity #14194]: #14196 +#14284 := [monotonicity #14197 #14281]: #14283 +#14203 := (iff #13357 #13472) +#14198 := (not #13473) +#14201 := (iff #14198 #13472) +#14202 := [rewrite]: #14201 +#14199 := (iff #13357 #14198) +#14200 := [monotonicity #13475]: #14199 +#14204 := [trans #14200 #14202]: #14203 +#14287 := [monotonicity #14204 #14284]: #14286 +#14214 := (iff #13366 #14205) +#14206 := (not #14205) +#14209 := (not #14206) +#14212 := (iff #14209 #14205) +#14213 := [rewrite]: #14212 +#14210 := (iff #13366 #14209) +#14207 := (iff #3037 #14206) +#14208 := [rewrite]: #14207 +#14211 := [monotonicity #14208]: #14210 +#14215 := [trans #14211 #14213]: #14214 +#14290 := [monotonicity #14215 #14287]: #14289 +#14228 := (iff #13375 #14227) +#14225 := (iff #3035 #14224) +#14222 := (iff #3034 #14219) +#14223 := [rewrite]: #14222 +#14216 := (iff #3033 #14217) +#14218 := [rewrite]: #14216 +#14226 := [monotonicity #14218 #14223]: #14225 +#14229 := [monotonicity #14226]: #14228 +#14293 := [monotonicity #14229 #14290]: #14292 +#14242 := (iff #13384 #14241) +#14239 := (iff #3031 #14238) +#14236 := (iff #3030 #14233) +#14237 := [rewrite]: #14236 +#14230 := (iff #3029 #14231) +#14232 := [rewrite]: #14230 +#14240 := [monotonicity #14232 #14237]: #14239 +#14243 := [monotonicity #14240]: #14242 +#14296 := [monotonicity #14243 #14293]: #14295 +#14256 := (iff #13393 #14255) +#14253 := (iff #3027 #14252) +#14250 := (iff #3026 #14247) +#14251 := [rewrite]: #14250 +#14244 := (iff #3025 #14245) +#14246 := [rewrite]: #14244 +#14254 := [monotonicity #14246 #14251]: #14253 +#14257 := [monotonicity #14254]: #14256 +#14299 := [monotonicity #14257 #14296]: #14298 +#14304 := [trans #14299 #14302]: #14303 +#14307 := [monotonicity #14304]: #14306 +#13400 := (iff #3406 #13399) +#13397 := (iff #3405 #13394) +#13390 := (implies #3027 #13385) #13395 := (iff #13390 #13394) #13396 := [rewrite]: #13395 -#13391 := (iff #3401 #13390) -#13388 := (iff #3400 #13385) -#13381 := (implies #12136 #13376) +#13391 := (iff #3405 #13390) +#13388 := (iff #3404 #13385) +#13381 := (implies #3031 #13376) #13386 := (iff #13381 #13385) #13387 := [rewrite]: #13386 -#13382 := (iff #3400 #13381) -#13379 := (iff #3399 #13376) -#13372 := (implies #12139 #13367) +#13382 := (iff #3404 #13381) +#13379 := (iff #3403 #13376) +#13372 := (implies #3035 #13367) #13377 := (iff #13372 #13376) #13378 := [rewrite]: #13377 -#13373 := (iff #3399 #13372) -#13370 := (iff #3398 #13367) -#13363 := (implies #12148 #13358) +#13373 := (iff #3403 #13372) +#13370 := (iff #3402 #13367) +#13363 := (implies #3037 #13358) #13368 := (iff #13363 #13367) #13369 := [rewrite]: #13368 -#13364 := (iff #3398 #13363) -#13361 := (iff #3397 #13358) -#13354 := (implies #3075 #13349) +#13364 := (iff #3402 #13363) +#13361 := (iff #3401 #13358) +#13354 := (implies #3038 #13349) #13359 := (iff #13354 #13358) #13360 := [rewrite]: #13359 -#13355 := (iff #3397 #13354) -#13352 := (iff #3396 #13349) -#13345 := (implies #12157 #13340) +#13355 := (iff #3401 #13354) +#13352 := (iff #3400 #13349) +#13345 := (implies #12100 #13340) #13350 := (iff #13345 #13349) #13351 := [rewrite]: #13350 -#13346 := (iff #3396 #13345) -#13343 := (iff #3395 #13340) -#13336 := (implies #12160 #13331) +#13346 := (iff #3400 #13345) +#13343 := (iff #3399 #13340) +#13336 := (implies #12103 #13331) #13341 := (iff #13336 #13340) #13342 := [rewrite]: #13341 -#13337 := (iff #3395 #13336) -#13334 := (iff #3394 #13331) -#13327 := (implies #3086 #13322) +#13337 := (iff #3399 #13336) +#13334 := (iff #3398 #13331) +#13327 := (implies #12112 #13322) #13332 := (iff #13327 #13331) #13333 := [rewrite]: #13332 -#13328 := (iff #3394 #13327) -#13325 := (iff #3393 #13322) -#13318 := (implies #12174 #13313) +#13328 := (iff #3398 #13327) +#13325 := (iff #3397 #13322) +#13318 := (implies #3075 #13313) #13323 := (iff #13318 #13322) #13324 := [rewrite]: #13323 -#13319 := (iff #3393 #13318) -#13316 := (iff #3392 #13313) -#13309 := (implies #3094 #13306) +#13319 := (iff #3397 #13318) +#13316 := (iff #3396 #13313) +#13309 := (implies #12121 #13304) #13314 := (iff #13309 #13313) #13315 := [rewrite]: #13314 -#13310 := (iff #3392 #13309) -#13307 := (iff #3391 #13306) -#13304 := (iff #3390 #13301) -#13297 := (implies #12177 #13294) -#13302 := (iff #13297 #13301) -#13303 := [rewrite]: #13302 -#13298 := (iff #3390 #13297) -#13295 := (iff #3389 #13294) -#13292 := (iff #3388 #13289) -#13285 := (implies #12186 #13282) -#13290 := (iff #13285 #13289) -#13291 := [rewrite]: #13290 -#13286 := (iff #3388 #13285) -#13283 := (iff #3387 #13282) -#13280 := (iff #3386 #13277) -#13273 := (implies #12192 #13268) +#13310 := (iff #3396 #13309) +#13307 := (iff #3395 #13304) +#13300 := (implies #12124 #13295) +#13305 := (iff #13300 #13304) +#13306 := [rewrite]: #13305 +#13301 := (iff #3395 #13300) +#13298 := (iff #3394 #13295) +#13291 := (implies #3086 #13286) +#13296 := (iff #13291 #13295) +#13297 := [rewrite]: #13296 +#13292 := (iff #3394 #13291) +#13289 := (iff #3393 #13286) +#13282 := (implies #12138 #13277) +#13287 := (iff #13282 #13286) +#13288 := [rewrite]: #13287 +#13283 := (iff #3393 #13282) +#13280 := (iff #3392 #13277) +#13273 := (implies #3094 #13270) #13278 := (iff #13273 #13277) #13279 := [rewrite]: #13278 -#13274 := (iff #3386 #13273) -#13271 := (iff #3385 #13268) -#13264 := (implies #3109 #13259) -#13269 := (iff #13264 #13268) -#13270 := [rewrite]: #13269 -#13265 := (iff #3385 #13264) -#13262 := (iff #3384 #13259) -#13255 := (implies #12195 #13250) -#13260 := (iff #13255 #13259) -#13261 := [rewrite]: #13260 -#13256 := (iff #3384 #13255) -#13253 := (iff #3383 #13250) -#13246 := (implies #12198 #13241) -#13251 := (iff #13246 #13250) -#13252 := [rewrite]: #13251 -#13247 := (iff #3383 #13246) -#13244 := (iff #3382 #13241) -#13237 := (implies #12201 #13232) +#13274 := (iff #3392 #13273) +#13271 := (iff #3391 #13270) +#13268 := (iff #3390 #13265) +#13261 := (implies #12141 #13258) +#13266 := (iff #13261 #13265) +#13267 := [rewrite]: #13266 +#13262 := (iff #3390 #13261) +#13259 := (iff #3389 #13258) +#13256 := (iff #3388 #13253) +#13249 := (implies #12150 #13246) +#13254 := (iff #13249 #13253) +#13255 := [rewrite]: #13254 +#13250 := (iff #3388 #13249) +#13247 := (iff #3387 #13246) +#13244 := (iff #3386 #13241) +#13237 := (implies #12156 #13232) #13242 := (iff #13237 #13241) #13243 := [rewrite]: #13242 -#13238 := (iff #3382 #13237) -#13235 := (iff #3381 #13232) -#13228 := (implies #12209 #13225) +#13238 := (iff #3386 #13237) +#13235 := (iff #3385 #13232) +#13228 := (implies #3109 #13223) #13233 := (iff #13228 #13232) #13234 := [rewrite]: #13233 -#13229 := (iff #3381 #13228) -#13226 := (iff #3380 #13225) -#13223 := (iff #3379 #13220) -#13216 := (implies #3121 #13213) -#13221 := (iff #13216 #13220) -#13222 := [rewrite]: #13221 -#13217 := (iff #3379 #13216) -#13214 := (iff #3378 #13213) -#13211 := (iff #3377 #13208) -#13204 := (implies #12224 #13201) -#13209 := (iff #13204 #13208) -#13210 := [rewrite]: #13209 -#13205 := (iff #3377 #13204) -#13202 := (iff #3376 #13201) -#13199 := (iff #3375 #13196) -#13192 := (implies #12229 #13187) +#13229 := (iff #3385 #13228) +#13226 := (iff #3384 #13223) +#13219 := (implies #12159 #13214) +#13224 := (iff #13219 #13223) +#13225 := [rewrite]: #13224 +#13220 := (iff #3384 #13219) +#13217 := (iff #3383 #13214) +#13210 := (implies #12162 #13205) +#13215 := (iff #13210 #13214) +#13216 := [rewrite]: #13215 +#13211 := (iff #3383 #13210) +#13208 := (iff #3382 #13205) +#13201 := (implies #12165 #13196) +#13206 := (iff #13201 #13205) +#13207 := [rewrite]: #13206 +#13202 := (iff #3382 #13201) +#13199 := (iff #3381 #13196) +#13192 := (implies #12173 #13189) #13197 := (iff #13192 #13196) #13198 := [rewrite]: #13197 -#13193 := (iff #3375 #13192) -#13190 := (iff #3374 #13187) -#13183 := (implies #3134 #13178) -#13188 := (iff #13183 #13187) -#13189 := [rewrite]: #13188 -#13184 := (iff #3374 #13183) -#13181 := (iff #3373 #13178) -#13174 := (implies #3138 #13169) -#13179 := (iff #13174 #13178) -#13180 := [rewrite]: #13179 -#13175 := (iff #3373 #13174) -#13172 := (iff #3372 #13169) -#13165 := (implies #3142 #13160) -#13170 := (iff #13165 #13169) -#13171 := [rewrite]: #13170 -#13166 := (iff #3372 #13165) -#13163 := (iff #3371 #13160) -#13157 := (implies #12232 #13152) -#13161 := (iff #13157 #13160) +#13193 := (iff #3381 #13192) +#13190 := (iff #3380 #13189) +#13187 := (iff #3379 #13184) +#13180 := (implies #3121 #13177) +#13185 := (iff #13180 #13184) +#13186 := [rewrite]: #13185 +#13181 := (iff #3379 #13180) +#13178 := (iff #3378 #13177) +#13175 := (iff #3377 #13172) +#13168 := (implies #12188 #13165) +#13173 := (iff #13168 #13172) +#13174 := [rewrite]: #13173 +#13169 := (iff #3377 #13168) +#13166 := (iff #3376 #13165) +#13163 := (iff #3375 #13160) +#13156 := (implies #12193 #13151) +#13161 := (iff #13156 #13160) #13162 := [rewrite]: #13161 -#13158 := (iff #3371 #13157) -#13155 := (iff #3370 #13152) -#13148 := (implies #3145 #13143) -#13153 := (iff #13148 #13152) -#13154 := [rewrite]: #13153 -#13149 := (iff #3370 #13148) -#13146 := (iff #3369 #13143) -#13139 := (implies #12247 #13134) -#13144 := (iff #13139 #13143) -#13145 := [rewrite]: #13144 -#13140 := (iff #3369 #13139) -#13137 := (iff #3368 #13134) -#13130 := (implies #12253 #13125) -#13135 := (iff #13130 #13134) -#13136 := [rewrite]: #13135 -#13131 := (iff #3368 #13130) -#13128 := (iff #3367 #13125) -#13122 := (implies #12232 #13110) -#13126 := (iff #13122 #13125) -#13127 := [rewrite]: #13126 -#13123 := (iff #3367 #13122) -#13120 := (iff #3366 #13110) -#13115 := (and true #13110) -#13118 := (iff #13115 #13110) -#13119 := [rewrite]: #13118 -#13116 := (iff #3366 #13115) -#13113 := (iff #3365 #13110) -#13107 := (implies #12232 #13102) -#13111 := (iff #13107 #13110) -#13112 := [rewrite]: #13111 -#13108 := (iff #3365 #13107) -#13105 := (iff #3364 #13102) -#13099 := (implies #12232 #13094) -#13103 := (iff #13099 #13102) -#13104 := [rewrite]: #13103 -#13100 := (iff #3364 #13099) -#13097 := (iff #3363 #13094) -#13091 := (implies #12232 #13086) -#13095 := (iff #13091 #13094) -#13096 := [rewrite]: #13095 -#13092 := (iff #3363 #13091) -#13089 := (iff #3362 #13086) -#13083 := (implies #12521 #13078) -#13087 := (iff #13083 #13086) -#13088 := [rewrite]: #13087 -#13084 := (iff #3362 #13083) -#13081 := (iff #3361 #13078) -#13074 := (implies #12521 #13069) -#13079 := (iff #13074 #13078) -#13080 := [rewrite]: #13079 -#13075 := (iff #3361 #13074) -#13072 := (iff #3360 #13069) -#13066 := (implies #12264 #13061) -#13070 := (iff #13066 #13069) -#13071 := [rewrite]: #13070 -#13067 := (iff #3360 #13066) -#13064 := (iff #3359 #13061) -#13057 := (implies #12543 #13052) -#13062 := (iff #13057 #13061) -#13063 := [rewrite]: #13062 -#13058 := (iff #3359 #13057) -#13055 := (iff #3358 #13052) -#13048 := (implies #12546 #13043) -#13053 := (iff #13048 #13052) -#13054 := [rewrite]: #13053 -#13049 := (iff #3358 #13048) -#13046 := (iff #3357 #13043) -#13039 := (implies #12549 #13034) -#13044 := (iff #13039 #13043) -#13045 := [rewrite]: #13044 -#13040 := (iff #3357 #13039) -#13037 := (iff #3356 #13034) -#13030 := (implies #12552 #13025) -#13035 := (iff #13030 #13034) -#13036 := [rewrite]: #13035 -#13031 := (iff #3356 #13030) -#13028 := (iff #3355 #13025) -#13021 := (implies #12561 #13009) +#13157 := (iff #3375 #13156) +#13154 := (iff #3374 #13151) +#13147 := (implies #3134 #13142) +#13152 := (iff #13147 #13151) +#13153 := [rewrite]: #13152 +#13148 := (iff #3374 #13147) +#13145 := (iff #3373 #13142) +#13138 := (implies #3138 #13133) +#13143 := (iff #13138 #13142) +#13144 := [rewrite]: #13143 +#13139 := (iff #3373 #13138) +#13136 := (iff #3372 #13133) +#13129 := (implies #3142 #13124) +#13134 := (iff #13129 #13133) +#13135 := [rewrite]: #13134 +#13130 := (iff #3372 #13129) +#13127 := (iff #3371 #13124) +#13121 := (implies #12196 #13116) +#13125 := (iff #13121 #13124) +#13126 := [rewrite]: #13125 +#13122 := (iff #3371 #13121) +#13119 := (iff #3370 #13116) +#13112 := (implies #3145 #13107) +#13117 := (iff #13112 #13116) +#13118 := [rewrite]: #13117 +#13113 := (iff #3370 #13112) +#13110 := (iff #3369 #13107) +#13103 := (implies #12211 #13098) +#13108 := (iff #13103 #13107) +#13109 := [rewrite]: #13108 +#13104 := (iff #3369 #13103) +#13101 := (iff #3368 #13098) +#13094 := (implies #12217 #13089) +#13099 := (iff #13094 #13098) +#13100 := [rewrite]: #13099 +#13095 := (iff #3368 #13094) +#13092 := (iff #3367 #13089) +#13086 := (implies #12196 #13074) +#13090 := (iff #13086 #13089) +#13091 := [rewrite]: #13090 +#13087 := (iff #3367 #13086) +#13084 := (iff #3366 #13074) +#13079 := (and true #13074) +#13082 := (iff #13079 #13074) +#13083 := [rewrite]: #13082 +#13080 := (iff #3366 #13079) +#13077 := (iff #3365 #13074) +#13071 := (implies #12196 #13066) +#13075 := (iff #13071 #13074) +#13076 := [rewrite]: #13075 +#13072 := (iff #3365 #13071) +#13069 := (iff #3364 #13066) +#13063 := (implies #12196 #13058) +#13067 := (iff #13063 #13066) +#13068 := [rewrite]: #13067 +#13064 := (iff #3364 #13063) +#13061 := (iff #3363 #13058) +#13055 := (implies #12196 #13050) +#13059 := (iff #13055 #13058) +#13060 := [rewrite]: #13059 +#13056 := (iff #3363 #13055) +#13053 := (iff #3362 #13050) +#13047 := (implies #12485 #13042) +#13051 := (iff #13047 #13050) +#13052 := [rewrite]: #13051 +#13048 := (iff #3362 #13047) +#13045 := (iff #3361 #13042) +#13038 := (implies #12485 #13033) +#13043 := (iff #13038 #13042) +#13044 := [rewrite]: #13043 +#13039 := (iff #3361 #13038) +#13036 := (iff #3360 #13033) +#13030 := (implies #12228 #13025) +#13034 := (iff #13030 #13033) +#13035 := [rewrite]: #13034 +#13031 := (iff #3360 #13030) +#13028 := (iff #3359 #13025) +#13021 := (implies #12507 #13016) #13026 := (iff #13021 #13025) #13027 := [rewrite]: #13026 -#13022 := (iff #3355 #13021) -#13019 := (iff #3354 #13009) -#13014 := (implies true #13009) -#13017 := (iff #13014 #13009) +#13022 := (iff #3359 #13021) +#13019 := (iff #3358 #13016) +#13012 := (implies #12510 #13007) +#13017 := (iff #13012 #13016) #13018 := [rewrite]: #13017 -#13015 := (iff #3354 #13014) -#13012 := (iff #3353 #13009) -#13006 := (implies #12232 #13003) -#13010 := (iff #13006 #13009) -#13011 := [rewrite]: #13010 -#13007 := (iff #3353 #13006) -#13004 := (iff #3352 #13003) -#13001 := (iff #3351 #12998) -#12995 := (implies #12232 #12990) -#12999 := (iff #12995 #12998) +#13013 := (iff #3358 #13012) +#13010 := (iff #3357 #13007) +#13003 := (implies #12513 #12998) +#13008 := (iff #13003 #13007) +#13009 := [rewrite]: #13008 +#13004 := (iff #3357 #13003) +#13001 := (iff #3356 #12998) +#12994 := (implies #12516 #12989) +#12999 := (iff #12994 #12998) #13000 := [rewrite]: #12999 -#12996 := (iff #3351 #12995) -#12993 := (iff #3350 #12990) -#12986 := (implies #3347 #12981) -#12991 := (iff #12986 #12990) -#12992 := [rewrite]: #12991 -#12987 := (iff #3350 #12986) -#12984 := (iff #3349 #12981) -#12978 := (implies #12232 #12973) -#12982 := (iff #12978 #12981) -#12983 := [rewrite]: #12982 -#12979 := (iff #3349 #12978) -#12976 := (iff #3348 #12973) -#12970 := (implies #12232 #12394) +#12995 := (iff #3356 #12994) +#12992 := (iff #3355 #12989) +#12985 := (implies #12525 #12973) +#12990 := (iff #12985 #12989) +#12991 := [rewrite]: #12990 +#12986 := (iff #3355 #12985) +#12983 := (iff #3354 #12973) +#12978 := (implies true #12973) +#12981 := (iff #12978 #12973) +#12982 := [rewrite]: #12981 +#12979 := (iff #3354 #12978) +#12976 := (iff #3353 #12973) +#12970 := (implies #12196 #12967) #12974 := (iff #12970 #12973) #12975 := [rewrite]: #12974 -#12971 := (iff #3348 #12970) -#12397 := (iff #3191 #12394) -#12391 := (implies #12232 #12386) -#12395 := (iff #12391 #12394) -#12396 := [rewrite]: #12395 -#12392 := (iff #3191 #12391) -#12389 := (iff #3190 #12386) -#12383 := (implies #12232 #12380) -#12387 := (iff #12383 #12386) -#12388 := [rewrite]: #12387 -#12384 := (iff #3190 #12383) -#12381 := (iff #3189 #12380) -#12378 := (iff #3188 #12375) -#12371 := (implies #10960 #12366) -#12376 := (iff #12371 #12375) -#12377 := [rewrite]: #12376 -#12372 := (iff #3188 #12371) -#12369 := (iff #3187 #12366) -#12363 := (implies #12232 #12358) -#12367 := (iff #12363 #12366) -#12368 := [rewrite]: #12367 -#12364 := (iff #3187 #12363) -#12361 := (iff #3186 #12358) -#12355 := (implies #12232 #12350) +#12971 := (iff #3353 #12970) +#12968 := (iff #3352 #12967) +#12965 := (iff #3351 #12962) +#12959 := (implies #12196 #12954) +#12963 := (iff #12959 #12962) +#12964 := [rewrite]: #12963 +#12960 := (iff #3351 #12959) +#12957 := (iff #3350 #12954) +#12950 := (implies #3347 #12945) +#12955 := (iff #12950 #12954) +#12956 := [rewrite]: #12955 +#12951 := (iff #3350 #12950) +#12948 := (iff #3349 #12945) +#12942 := (implies #12196 #12937) +#12946 := (iff #12942 #12945) +#12947 := [rewrite]: #12946 +#12943 := (iff #3349 #12942) +#12940 := (iff #3348 #12937) +#12934 := (implies #12196 #12358) +#12938 := (iff #12934 #12937) +#12939 := [rewrite]: #12938 +#12935 := (iff #3348 #12934) +#12361 := (iff #3191 #12358) +#12355 := (implies #12196 #12350) #12359 := (iff #12355 #12358) #12360 := [rewrite]: #12359 -#12356 := (iff #3186 #12355) -#12353 := (iff #3185 #12350) -#12346 := (implies #12232 #12341) -#12351 := (iff #12346 #12350) +#12356 := (iff #3191 #12355) +#12353 := (iff #3190 #12350) +#12347 := (implies #12196 #12344) +#12351 := (iff #12347 #12350) #12352 := [rewrite]: #12351 -#12347 := (iff #3185 #12346) -#12344 := (iff #3184 #12341) -#12337 := (implies #12269 #12332) -#12342 := (iff #12337 #12341) -#12343 := [rewrite]: #12342 -#12338 := (iff #3184 #12337) -#12335 := (iff #3183 #12332) -#12328 := (implies #12272 #12323) -#12333 := (iff #12328 #12332) -#12334 := [rewrite]: #12333 -#12329 := (iff #3183 #12328) -#12326 := (iff #3182 #12323) -#12319 := (implies #12275 #12314) -#12324 := (iff #12319 #12323) -#12325 := [rewrite]: #12324 -#12320 := (iff #3182 #12319) -#12317 := (iff #3181 #12314) -#12310 := (implies #12278 #12307) +#12348 := (iff #3190 #12347) +#12345 := (iff #3189 #12344) +#12342 := (iff #3188 #12339) +#12335 := (implies #10924 #12330) +#12340 := (iff #12335 #12339) +#12341 := [rewrite]: #12340 +#12336 := (iff #3188 #12335) +#12333 := (iff #3187 #12330) +#12327 := (implies #12196 #12322) +#12331 := (iff #12327 #12330) +#12332 := [rewrite]: #12331 +#12328 := (iff #3187 #12327) +#12325 := (iff #3186 #12322) +#12319 := (implies #12196 #12314) +#12323 := (iff #12319 #12322) +#12324 := [rewrite]: #12323 +#12320 := (iff #3186 #12319) +#12317 := (iff #3185 #12314) +#12310 := (implies #12196 #12305) #12315 := (iff #12310 #12314) #12316 := [rewrite]: #12315 -#12311 := (iff #3181 #12310) -#12308 := (iff #3180 #12307) -#12305 := (iff #3179 #12302) -#12298 := (implies #12293 #3177) -#12303 := (iff #12298 #12302) -#12304 := [rewrite]: #12303 -#12299 := (iff #3179 #12298) -#12296 := (iff #3178 #3177) -#12297 := [rewrite]: #12296 -#12294 := (iff #3172 #12293) -#12291 := (iff #3171 #12288) -#12285 := (implies #455 #12282) -#12289 := (iff #12285 #12288) -#12290 := [rewrite]: #12289 -#12286 := (iff #3171 #12285) -#12283 := (iff #3170 #12282) -#12284 := [rewrite]: #12283 -#12287 := [monotonicity #12284]: #12286 -#12292 := [trans #12287 #12290]: #12291 -#12295 := [quant-intro #12292]: #12294 -#12300 := [monotonicity #12295 #12297]: #12299 -#12306 := [trans #12300 #12304]: #12305 -#12309 := [monotonicity #12295 #12306]: #12308 -#12279 := (iff #3167 #12278) +#12311 := (iff #3185 #12310) +#12308 := (iff #3184 #12305) +#12301 := (implies #12233 #12296) +#12306 := (iff #12301 #12305) +#12307 := [rewrite]: #12306 +#12302 := (iff #3184 #12301) +#12299 := (iff #3183 #12296) +#12292 := (implies #12236 #12287) +#12297 := (iff #12292 #12296) +#12298 := [rewrite]: #12297 +#12293 := (iff #3183 #12292) +#12290 := (iff #3182 #12287) +#12283 := (implies #12239 #12278) +#12288 := (iff #12283 #12287) +#12289 := [rewrite]: #12288 +#12284 := (iff #3182 #12283) +#12281 := (iff #3181 #12278) +#12274 := (implies #12242 #12271) +#12279 := (iff #12274 #12278) #12280 := [rewrite]: #12279 -#12312 := [monotonicity #12280 #12309]: #12311 +#12275 := (iff #3181 #12274) +#12272 := (iff #3180 #12271) +#12269 := (iff #3179 #12266) +#12262 := (implies #12257 #3177) +#12267 := (iff #12262 #12266) +#12268 := [rewrite]: #12267 +#12263 := (iff #3179 #12262) +#12260 := (iff #3178 #3177) +#12261 := [rewrite]: #12260 +#12258 := (iff #3172 #12257) +#12255 := (iff #3171 #12252) +#12249 := (implies #455 #12246) +#12253 := (iff #12249 #12252) +#12254 := [rewrite]: #12253 +#12250 := (iff #3171 #12249) +#12247 := (iff #3170 #12246) +#12248 := [rewrite]: #12247 +#12251 := [monotonicity #12248]: #12250 +#12256 := [trans #12251 #12254]: #12255 +#12259 := [quant-intro #12256]: #12258 +#12264 := [monotonicity #12259 #12261]: #12263 +#12270 := [trans #12264 #12268]: #12269 +#12273 := [monotonicity #12259 #12270]: #12272 +#12243 := (iff #3167 #12242) +#12244 := [rewrite]: #12243 +#12276 := [monotonicity #12244 #12273]: #12275 +#12282 := [trans #12276 #12280]: #12281 +#12240 := (iff #3165 #12239) +#12241 := [rewrite]: #12240 +#12285 := [monotonicity #12241 #12282]: #12284 +#12291 := [trans #12285 #12289]: #12290 +#12237 := (iff #3163 #12236) +#12238 := [rewrite]: #12237 +#12294 := [monotonicity #12238 #12291]: #12293 +#12300 := [trans #12294 #12298]: #12299 +#12234 := (iff #3161 #12233) +#12235 := [rewrite]: #12234 +#12303 := [monotonicity #12235 #12300]: #12302 +#12309 := [trans #12303 #12307]: #12308 +#12197 := (iff #3144 #12196) +#12198 := [rewrite]: #12197 +#12312 := [monotonicity #12198 #12309]: #12311 #12318 := [trans #12312 #12316]: #12317 -#12276 := (iff #3165 #12275) -#12277 := [rewrite]: #12276 -#12321 := [monotonicity #12277 #12318]: #12320 -#12327 := [trans #12321 #12325]: #12326 -#12273 := (iff #3163 #12272) -#12274 := [rewrite]: #12273 -#12330 := [monotonicity #12274 #12327]: #12329 -#12336 := [trans #12330 #12334]: #12335 -#12270 := (iff #3161 #12269) -#12271 := [rewrite]: #12270 -#12339 := [monotonicity #12271 #12336]: #12338 -#12345 := [trans #12339 #12343]: #12344 -#12233 := (iff #3144 #12232) -#12234 := [rewrite]: #12233 -#12348 := [monotonicity #12234 #12345]: #12347 -#12354 := [trans #12348 #12352]: #12353 -#12357 := [monotonicity #12234 #12354]: #12356 +#12321 := [monotonicity #12198 #12318]: #12320 +#12326 := [trans #12321 #12324]: #12325 +#12329 := [monotonicity #12198 #12326]: #12328 +#12334 := [trans #12329 #12332]: #12333 +#10926 := (iff #2542 #10924) +#10927 := [rewrite]: #10926 +#12337 := [monotonicity #10927 #12334]: #12336 +#12343 := [trans #12337 #12341]: #12342 +#12346 := [monotonicity #10927 #12343]: #12345 +#12349 := [monotonicity #12198 #12346]: #12348 +#12354 := [trans #12349 #12352]: #12353 +#12357 := [monotonicity #12198 #12354]: #12356 #12362 := [trans #12357 #12360]: #12361 -#12365 := [monotonicity #12234 #12362]: #12364 -#12370 := [trans #12365 #12368]: #12369 -#10962 := (iff #2542 #10960) -#10963 := [rewrite]: #10962 -#12373 := [monotonicity #10963 #12370]: #12372 -#12379 := [trans #12373 #12377]: #12378 -#12382 := [monotonicity #10963 #12379]: #12381 -#12385 := [monotonicity #12234 #12382]: #12384 -#12390 := [trans #12385 #12388]: #12389 -#12393 := [monotonicity #12234 #12390]: #12392 -#12398 := [trans #12393 #12396]: #12397 -#12972 := [monotonicity #12234 #12398]: #12971 -#12977 := [trans #12972 #12975]: #12976 -#12980 := [monotonicity #12234 #12977]: #12979 -#12985 := [trans #12980 #12983]: #12984 -#12988 := [monotonicity #12985]: #12987 -#12994 := [trans #12988 #12992]: #12993 -#12997 := [monotonicity #12234 #12994]: #12996 -#13002 := [trans #12997 #13000]: #13001 -#12968 := (iff #3346 #12965) -#12962 := (implies #12232 #12957) -#12966 := (iff #12962 #12965) -#12967 := [rewrite]: #12966 -#12963 := (iff #3346 #12962) -#12960 := (iff #3345 #12957) -#12953 := (implies #3256 #12948) -#12958 := (iff #12953 #12957) -#12959 := [rewrite]: #12958 -#12954 := (iff #3345 #12953) -#12951 := (iff #3344 #12948) -#12945 := (implies #12232 #12940) -#12949 := (iff #12945 #12948) -#12950 := [rewrite]: #12949 -#12946 := (iff #3344 #12945) -#12943 := (iff #3343 #12940) -#12937 := (implies #12232 #12934) -#12941 := (iff #12937 #12940) -#12942 := [rewrite]: #12941 -#12938 := (iff #3343 #12937) -#12935 := (iff #3342 #12934) -#12932 := (iff #3341 #12929) -#12926 := (implies #12581 #12923) +#12936 := [monotonicity #12198 #12362]: #12935 +#12941 := [trans #12936 #12939]: #12940 +#12944 := [monotonicity #12198 #12941]: #12943 +#12949 := [trans #12944 #12947]: #12948 +#12952 := [monotonicity #12949]: #12951 +#12958 := [trans #12952 #12956]: #12957 +#12961 := [monotonicity #12198 #12958]: #12960 +#12966 := [trans #12961 #12964]: #12965 +#12932 := (iff #3346 #12929) +#12926 := (implies #12196 #12921) #12930 := (iff #12926 #12929) #12931 := [rewrite]: #12930 -#12927 := (iff #3341 #12926) -#12924 := (iff #3340 #12923) -#12921 := (iff #3339 #12918) -#12915 := (implies #12587 #12910) -#12919 := (iff #12915 #12918) -#12920 := [rewrite]: #12919 -#12916 := (iff #3339 #12915) -#12913 := (iff #3338 #12910) -#12907 := (implies #12232 #12904) -#12911 := (iff #12907 #12910) -#12912 := [rewrite]: #12911 -#12908 := (iff #3338 #12907) -#12905 := (iff #3337 #12904) -#12902 := (iff #3336 #12899) -#12896 := (implies #12232 #12891) -#12900 := (iff #12896 #12899) -#12901 := [rewrite]: #12900 -#12897 := (iff #3336 #12896) -#12894 := (iff #3335 #12891) -#12887 := (implies #3327 #12882) -#12892 := (iff #12887 #12891) -#12893 := [rewrite]: #12892 -#12888 := (iff #3335 #12887) -#12885 := (iff #3334 #12882) -#12879 := (implies #12232 #12874) +#12927 := (iff #3346 #12926) +#12924 := (iff #3345 #12921) +#12917 := (implies #3256 #12912) +#12922 := (iff #12917 #12921) +#12923 := [rewrite]: #12922 +#12918 := (iff #3345 #12917) +#12915 := (iff #3344 #12912) +#12909 := (implies #12196 #12904) +#12913 := (iff #12909 #12912) +#12914 := [rewrite]: #12913 +#12910 := (iff #3344 #12909) +#12907 := (iff #3343 #12904) +#12901 := (implies #12196 #12898) +#12905 := (iff #12901 #12904) +#12906 := [rewrite]: #12905 +#12902 := (iff #3343 #12901) +#12899 := (iff #3342 #12898) +#12896 := (iff #3341 #12893) +#12890 := (implies #12545 #12887) +#12894 := (iff #12890 #12893) +#12895 := [rewrite]: #12894 +#12891 := (iff #3341 #12890) +#12888 := (iff #3340 #12887) +#12885 := (iff #3339 #12882) +#12879 := (implies #12551 #12874) #12883 := (iff #12879 #12882) #12884 := [rewrite]: #12883 -#12880 := (iff #3334 #12879) -#12877 := (iff #3333 #12874) -#12871 := (implies #12232 #12866) +#12880 := (iff #3339 #12879) +#12877 := (iff #3338 #12874) +#12871 := (implies #12196 #12868) #12875 := (iff #12871 #12874) #12876 := [rewrite]: #12875 -#12872 := (iff #3333 #12871) -#12869 := (iff #3332 #12866) -#12863 := (implies #12232 #12858) -#12867 := (iff #12863 #12866) -#12868 := [rewrite]: #12867 -#12864 := (iff #3332 #12863) -#12861 := (iff #3331 #12858) -#12854 := (implies #12839 #12849) -#12859 := (iff #12854 #12858) -#12860 := [rewrite]: #12859 -#12855 := (iff #3331 #12854) -#12852 := (iff #3330 #12849) -#12845 := (implies #12842 #12723) -#12850 := (iff #12845 #12849) -#12851 := [rewrite]: #12850 -#12846 := (iff #3330 #12845) -#12726 := (iff #3312 #12723) -#12719 := (implies #3280 #12716) +#12872 := (iff #3338 #12871) +#12869 := (iff #3337 #12868) +#12866 := (iff #3336 #12863) +#12860 := (implies #12196 #12855) +#12864 := (iff #12860 #12863) +#12865 := [rewrite]: #12864 +#12861 := (iff #3336 #12860) +#12858 := (iff #3335 #12855) +#12851 := (implies #3327 #12846) +#12856 := (iff #12851 #12855) +#12857 := [rewrite]: #12856 +#12852 := (iff #3335 #12851) +#12849 := (iff #3334 #12846) +#12843 := (implies #12196 #12838) +#12847 := (iff #12843 #12846) +#12848 := [rewrite]: #12847 +#12844 := (iff #3334 #12843) +#12841 := (iff #3333 #12838) +#12835 := (implies #12196 #12830) +#12839 := (iff #12835 #12838) +#12840 := [rewrite]: #12839 +#12836 := (iff #3333 #12835) +#12833 := (iff #3332 #12830) +#12827 := (implies #12196 #12822) +#12831 := (iff #12827 #12830) +#12832 := [rewrite]: #12831 +#12828 := (iff #3332 #12827) +#12825 := (iff #3331 #12822) +#12818 := (implies #12803 #12813) +#12823 := (iff #12818 #12822) +#12824 := [rewrite]: #12823 +#12819 := (iff #3331 #12818) +#12816 := (iff #3330 #12813) +#12809 := (implies #12806 #12687) +#12814 := (iff #12809 #12813) +#12815 := [rewrite]: #12814 +#12810 := (iff #3330 #12809) +#12690 := (iff #3312 #12687) +#12683 := (implies #3280 #12680) +#12688 := (iff #12683 #12687) +#12689 := [rewrite]: #12688 +#12684 := (iff #3312 #12683) +#12681 := (iff #3311 #12680) +#12678 := (iff #3310 #12675) +#12671 := (implies #12580 #12666) +#12676 := (iff #12671 #12675) +#12677 := [rewrite]: #12676 +#12672 := (iff #3310 #12671) +#12669 := (iff #3309 #12666) +#12662 := (implies #12583 #12657) +#12667 := (iff #12662 #12666) +#12668 := [rewrite]: #12667 +#12663 := (iff #3309 #12662) +#12660 := (iff #3308 #12657) +#12653 := (implies #12586 #12648) +#12658 := (iff #12653 #12657) +#12659 := [rewrite]: #12658 +#12654 := (iff #3308 #12653) +#12651 := (iff #3307 #12648) +#12644 := (implies #12589 #12641) +#12649 := (iff #12644 #12648) +#12650 := [rewrite]: #12649 +#12645 := (iff #3307 #12644) +#12642 := (iff #3306 #12641) +#12639 := (iff #3305 #12636) +#12632 := (implies #3291 #12629) +#12637 := (iff #12632 #12636) +#12638 := [rewrite]: #12637 +#12633 := (iff #3305 #12632) +#12630 := (iff #3304 #12629) +#12627 := (iff #3303 #12624) +#12620 := (implies #12604 #12610) +#12625 := (iff #12620 #12624) +#12626 := [rewrite]: #12625 +#12621 := (iff #3303 #12620) +#12618 := (iff #3302 #12610) +#12613 := (and #12610 true) +#12616 := (iff #12613 #12610) +#12617 := [rewrite]: #12616 +#12614 := (iff #3302 #12613) +#12611 := (iff #3301 #12610) +#12608 := (iff #3300 #12607) +#12609 := [rewrite]: #12608 +#12612 := [monotonicity #12609]: #12611 +#12615 := [monotonicity #12612]: #12614 +#12619 := [trans #12615 #12617]: #12618 +#12605 := (iff #3296 #12604) +#12602 := (iff #3295 #12599) +#12596 := (implies #455 #12593) +#12600 := (iff #12596 #12599) +#12601 := [rewrite]: #12600 +#12597 := (iff #3295 #12596) +#12594 := (iff #3294 #12593) +#12595 := [rewrite]: #12594 +#12598 := [monotonicity #12595]: #12597 +#12603 := [trans #12598 #12601]: #12602 +#12606 := [quant-intro #12603]: #12605 +#12622 := [monotonicity #12606 #12619]: #12621 +#12628 := [trans #12622 #12626]: #12627 +#12631 := [monotonicity #12606 #12628]: #12630 +#12634 := [monotonicity #12631]: #12633 +#12640 := [trans #12634 #12638]: #12639 +#12643 := [monotonicity #12640]: #12642 +#12590 := (iff #3290 #12589) +#12591 := [rewrite]: #12590 +#12646 := [monotonicity #12591 #12643]: #12645 +#12652 := [trans #12646 #12650]: #12651 +#12587 := (iff #3288 #12586) +#12588 := [rewrite]: #12587 +#12655 := [monotonicity #12588 #12652]: #12654 +#12661 := [trans #12655 #12659]: #12660 +#12584 := (iff #3286 #12583) +#12572 := (= #3281 #12571) +#12573 := [rewrite]: #12572 +#12585 := [monotonicity #12573]: #12584 +#12664 := [monotonicity #12585 #12661]: #12663 +#12670 := [trans #12664 #12668]: #12669 +#12581 := (iff #3284 #12580) +#12578 := (iff #3283 #12577) +#12579 := [monotonicity #12573]: #12578 +#12575 := (iff #3282 #12574) +#12576 := [monotonicity #12573]: #12575 +#12582 := [monotonicity #12576 #12579]: #12581 +#12673 := [monotonicity #12582 #12670]: #12672 +#12679 := [trans #12673 #12677]: #12678 +#12682 := [monotonicity #12582 #12679]: #12681 +#12685 := [monotonicity #12682]: #12684 +#12691 := [trans #12685 #12689]: #12690 +#12807 := (iff #3329 #12806) +#12808 := [rewrite]: #12807 +#12811 := [monotonicity #12808 #12691]: #12810 +#12817 := [trans #12811 #12815]: #12816 +#12804 := (iff #3328 #12803) +#12805 := [rewrite]: #12804 +#12820 := [monotonicity #12805 #12817]: #12819 +#12826 := [trans #12820 #12824]: #12825 +#12829 := [monotonicity #12198 #12826]: #12828 +#12834 := [trans #12829 #12832]: #12833 +#12837 := [monotonicity #12198 #12834]: #12836 +#12842 := [trans #12837 #12840]: #12841 +#12845 := [monotonicity #12198 #12842]: #12844 +#12850 := [trans #12845 #12848]: #12849 +#12853 := [monotonicity #12850]: #12852 +#12859 := [trans #12853 #12857]: #12858 +#12862 := [monotonicity #12198 #12859]: #12861 +#12867 := [trans #12862 #12865]: #12866 +#12801 := (iff #3326 #12798) +#12795 := (implies #12196 #12790) +#12799 := (iff #12795 #12798) +#12800 := [rewrite]: #12799 +#12796 := (iff #3326 #12795) +#12793 := (iff #3325 #12790) +#12786 := (implies #3267 #12781) +#12791 := (iff #12786 #12790) +#12792 := [rewrite]: #12791 +#12787 := (iff #3325 #12786) +#12784 := (iff #3324 #12781) +#12778 := (implies #12196 #12773) +#12782 := (iff #12778 #12781) +#12783 := [rewrite]: #12782 +#12779 := (iff #3324 #12778) +#12776 := (iff #3323 #12773) +#12770 := (implies #12196 #12767) +#12774 := (iff #12770 #12773) +#12775 := [rewrite]: #12774 +#12771 := (iff #3323 #12770) +#12768 := (iff #3322 #12767) +#12765 := (iff #3321 #12762) +#12758 := (implies #12545 #12755) +#12763 := (iff #12758 #12762) +#12764 := [rewrite]: #12763 +#12759 := (iff #3321 #12758) +#12756 := (iff #3320 #12755) +#12753 := (iff #3319 #12750) +#12746 := (implies #12551 #12741) +#12751 := (iff #12746 #12750) +#12752 := [rewrite]: #12751 +#12747 := (iff #3319 #12746) +#12744 := (iff #3318 #12741) +#12737 := (implies #12554 #12732) +#12742 := (iff #12737 #12741) +#12743 := [rewrite]: #12742 +#12738 := (iff #3318 #12737) +#12735 := (iff #3317 #12732) +#12728 := (implies #12557 #12723) +#12733 := (iff #12728 #12732) +#12734 := [rewrite]: #12733 +#12729 := (iff #3317 #12728) +#12726 := (iff #3316 #12723) +#12719 := (implies #12560 #12714) #12724 := (iff #12719 #12723) #12725 := [rewrite]: #12724 -#12720 := (iff #3312 #12719) -#12717 := (iff #3311 #12716) -#12714 := (iff #3310 #12711) -#12707 := (implies #12616 #12702) -#12712 := (iff #12707 #12711) -#12713 := [rewrite]: #12712 -#12708 := (iff #3310 #12707) -#12705 := (iff #3309 #12702) -#12698 := (implies #12619 #12693) -#12703 := (iff #12698 #12702) -#12704 := [rewrite]: #12703 -#12699 := (iff #3309 #12698) -#12696 := (iff #3308 #12693) -#12689 := (implies #12622 #12684) -#12694 := (iff #12689 #12693) -#12695 := [rewrite]: #12694 -#12690 := (iff #3308 #12689) -#12687 := (iff #3307 #12684) -#12680 := (implies #12625 #12677) -#12685 := (iff #12680 #12684) -#12686 := [rewrite]: #12685 -#12681 := (iff #3307 #12680) -#12678 := (iff #3306 #12677) -#12675 := (iff #3305 #12672) -#12668 := (implies #3291 #12665) -#12673 := (iff #12668 #12672) -#12674 := [rewrite]: #12673 -#12669 := (iff #3305 #12668) -#12666 := (iff #3304 #12665) -#12663 := (iff #3303 #12660) -#12656 := (implies #12640 #12646) -#12661 := (iff #12656 #12660) -#12662 := [rewrite]: #12661 -#12657 := (iff #3303 #12656) -#12654 := (iff #3302 #12646) -#12649 := (and #12646 true) -#12652 := (iff #12649 #12646) -#12653 := [rewrite]: #12652 -#12650 := (iff #3302 #12649) -#12647 := (iff #3301 #12646) -#12644 := (iff #3300 #12643) -#12645 := [rewrite]: #12644 -#12648 := [monotonicity #12645]: #12647 -#12651 := [monotonicity #12648]: #12650 -#12655 := [trans #12651 #12653]: #12654 -#12641 := (iff #3296 #12640) -#12638 := (iff #3295 #12635) -#12632 := (implies #455 #12629) -#12636 := (iff #12632 #12635) -#12637 := [rewrite]: #12636 -#12633 := (iff #3295 #12632) -#12630 := (iff #3294 #12629) -#12631 := [rewrite]: #12630 -#12634 := [monotonicity #12631]: #12633 -#12639 := [trans #12634 #12637]: #12638 -#12642 := [quant-intro #12639]: #12641 -#12658 := [monotonicity #12642 #12655]: #12657 -#12664 := [trans #12658 #12662]: #12663 -#12667 := [monotonicity #12642 #12664]: #12666 -#12670 := [monotonicity #12667]: #12669 -#12676 := [trans #12670 #12674]: #12675 -#12679 := [monotonicity #12676]: #12678 -#12626 := (iff #3290 #12625) -#12627 := [rewrite]: #12626 -#12682 := [monotonicity #12627 #12679]: #12681 -#12688 := [trans #12682 #12686]: #12687 -#12623 := (iff #3288 #12622) -#12624 := [rewrite]: #12623 -#12691 := [monotonicity #12624 #12688]: #12690 -#12697 := [trans #12691 #12695]: #12696 -#12620 := (iff #3286 #12619) -#12608 := (= #3281 #12607) -#12609 := [rewrite]: #12608 -#12621 := [monotonicity #12609]: #12620 -#12700 := [monotonicity #12621 #12697]: #12699 -#12706 := [trans #12700 #12704]: #12705 -#12617 := (iff #3284 #12616) -#12614 := (iff #3283 #12613) -#12615 := [monotonicity #12609]: #12614 -#12611 := (iff #3282 #12610) -#12612 := [monotonicity #12609]: #12611 -#12618 := [monotonicity #12612 #12615]: #12617 -#12709 := [monotonicity #12618 #12706]: #12708 -#12715 := [trans #12709 #12713]: #12714 -#12718 := [monotonicity #12618 #12715]: #12717 -#12721 := [monotonicity #12718]: #12720 +#12720 := (iff #3316 #12719) +#12717 := (iff #3315 #12714) +#12710 := (implies #3143 #12705) +#12715 := (iff #12710 #12714) +#12716 := [rewrite]: #12715 +#12711 := (iff #3315 #12710) +#12708 := (iff #3314 #12705) +#12701 := (implies #12565 #12696) +#12706 := (iff #12701 #12705) +#12707 := [rewrite]: #12706 +#12702 := (iff #3314 #12701) +#12699 := (iff #3313 #12696) +#12692 := (implies #12568 #12687) +#12697 := (iff #12692 #12696) +#12698 := [rewrite]: #12697 +#12693 := (iff #3313 #12692) +#12569 := (iff #3278 #12568) +#12570 := [rewrite]: #12569 +#12694 := [monotonicity #12570 #12691]: #12693 +#12700 := [trans #12694 #12698]: #12699 +#12566 := (iff #3276 #12565) +#12567 := [rewrite]: #12566 +#12703 := [monotonicity #12567 #12700]: #12702 +#12709 := [trans #12703 #12707]: #12708 +#12563 := (iff #3274 #3143) +#12564 := [rewrite]: #12563 +#12712 := [monotonicity #12564 #12709]: #12711 +#12718 := [trans #12712 #12716]: #12717 +#12561 := (iff #3273 #12560) +#12562 := [rewrite]: #12561 +#12721 := [monotonicity #12562 #12718]: #12720 #12727 := [trans #12721 #12725]: #12726 -#12843 := (iff #3329 #12842) -#12844 := [rewrite]: #12843 -#12847 := [monotonicity #12844 #12727]: #12846 -#12853 := [trans #12847 #12851]: #12852 -#12840 := (iff #3328 #12839) -#12841 := [rewrite]: #12840 -#12856 := [monotonicity #12841 #12853]: #12855 -#12862 := [trans #12856 #12860]: #12861 -#12865 := [monotonicity #12234 #12862]: #12864 -#12870 := [trans #12865 #12868]: #12869 -#12873 := [monotonicity #12234 #12870]: #12872 +#12558 := (iff #3271 #12557) +#12559 := [rewrite]: #12558 +#12730 := [monotonicity #12559 #12727]: #12729 +#12736 := [trans #12730 #12734]: #12735 +#12555 := (iff #3269 #12554) +#12556 := [rewrite]: #12555 +#12739 := [monotonicity #12556 #12736]: #12738 +#12745 := [trans #12739 #12743]: #12744 +#12552 := (iff #3265 #12551) +#12549 := (iff #3264 #12548) +#12550 := [rewrite]: #12549 +#12540 := (iff #3259 #12539) +#12541 := [rewrite]: #12540 +#12553 := [monotonicity #12541 #12550]: #12552 +#12748 := [monotonicity #12553 #12745]: #12747 +#12754 := [trans #12748 #12752]: #12753 +#12757 := [monotonicity #12553 #12754]: #12756 +#12546 := (iff #3262 #12545) +#12543 := (iff #3261 #12542) +#12544 := [rewrite]: #12543 +#12547 := [monotonicity #12541 #12544]: #12546 +#12760 := [monotonicity #12547 #12757]: #12759 +#12766 := [trans #12760 #12764]: #12765 +#12769 := [monotonicity #12547 #12766]: #12768 +#12772 := [monotonicity #12198 #12769]: #12771 +#12777 := [trans #12772 #12775]: #12776 +#12780 := [monotonicity #12198 #12777]: #12779 +#12785 := [trans #12780 #12783]: #12784 +#12788 := [monotonicity #12785]: #12787 +#12794 := [trans #12788 #12792]: #12793 +#12797 := [monotonicity #12198 #12794]: #12796 +#12802 := [trans #12797 #12800]: #12801 +#12870 := [monotonicity #12802 #12867]: #12869 +#12873 := [monotonicity #12198 #12870]: #12872 #12878 := [trans #12873 #12876]: #12877 -#12881 := [monotonicity #12234 #12878]: #12880 +#12881 := [monotonicity #12553 #12878]: #12880 #12886 := [trans #12881 #12884]: #12885 -#12889 := [monotonicity #12886]: #12888 -#12895 := [trans #12889 #12893]: #12894 -#12898 := [monotonicity #12234 #12895]: #12897 -#12903 := [trans #12898 #12901]: #12902 -#12837 := (iff #3326 #12834) -#12831 := (implies #12232 #12826) -#12835 := (iff #12831 #12834) -#12836 := [rewrite]: #12835 -#12832 := (iff #3326 #12831) -#12829 := (iff #3325 #12826) -#12822 := (implies #3267 #12817) -#12827 := (iff #12822 #12826) -#12828 := [rewrite]: #12827 -#12823 := (iff #3325 #12822) -#12820 := (iff #3324 #12817) -#12814 := (implies #12232 #12809) -#12818 := (iff #12814 #12817) -#12819 := [rewrite]: #12818 -#12815 := (iff #3324 #12814) -#12812 := (iff #3323 #12809) -#12806 := (implies #12232 #12803) -#12810 := (iff #12806 #12809) -#12811 := [rewrite]: #12810 -#12807 := (iff #3323 #12806) -#12804 := (iff #3322 #12803) -#12801 := (iff #3321 #12798) -#12794 := (implies #12581 #12791) -#12799 := (iff #12794 #12798) -#12800 := [rewrite]: #12799 -#12795 := (iff #3321 #12794) -#12792 := (iff #3320 #12791) -#12789 := (iff #3319 #12786) -#12782 := (implies #12587 #12777) -#12787 := (iff #12782 #12786) -#12788 := [rewrite]: #12787 -#12783 := (iff #3319 #12782) -#12780 := (iff #3318 #12777) -#12773 := (implies #12590 #12768) -#12778 := (iff #12773 #12777) -#12779 := [rewrite]: #12778 -#12774 := (iff #3318 #12773) -#12771 := (iff #3317 #12768) -#12764 := (implies #12593 #12759) -#12769 := (iff #12764 #12768) -#12770 := [rewrite]: #12769 -#12765 := (iff #3317 #12764) -#12762 := (iff #3316 #12759) -#12755 := (implies #12596 #12750) -#12760 := (iff #12755 #12759) -#12761 := [rewrite]: #12760 -#12756 := (iff #3316 #12755) -#12753 := (iff #3315 #12750) -#12746 := (implies #3143 #12741) -#12751 := (iff #12746 #12750) -#12752 := [rewrite]: #12751 -#12747 := (iff #3315 #12746) -#12744 := (iff #3314 #12741) -#12737 := (implies #12601 #12732) -#12742 := (iff #12737 #12741) -#12743 := [rewrite]: #12742 -#12738 := (iff #3314 #12737) -#12735 := (iff #3313 #12732) -#12728 := (implies #12604 #12723) -#12733 := (iff #12728 #12732) -#12734 := [rewrite]: #12733 -#12729 := (iff #3313 #12728) -#12605 := (iff #3278 #12604) -#12606 := [rewrite]: #12605 -#12730 := [monotonicity #12606 #12727]: #12729 -#12736 := [trans #12730 #12734]: #12735 -#12602 := (iff #3276 #12601) -#12603 := [rewrite]: #12602 -#12739 := [monotonicity #12603 #12736]: #12738 -#12745 := [trans #12739 #12743]: #12744 -#12599 := (iff #3274 #3143) -#12600 := [rewrite]: #12599 -#12748 := [monotonicity #12600 #12745]: #12747 -#12754 := [trans #12748 #12752]: #12753 -#12597 := (iff #3273 #12596) -#12598 := [rewrite]: #12597 -#12757 := [monotonicity #12598 #12754]: #12756 -#12763 := [trans #12757 #12761]: #12762 -#12594 := (iff #3271 #12593) -#12595 := [rewrite]: #12594 -#12766 := [monotonicity #12595 #12763]: #12765 -#12772 := [trans #12766 #12770]: #12771 -#12591 := (iff #3269 #12590) -#12592 := [rewrite]: #12591 -#12775 := [monotonicity #12592 #12772]: #12774 -#12781 := [trans #12775 #12779]: #12780 -#12588 := (iff #3265 #12587) -#12585 := (iff #3264 #12584) -#12586 := [rewrite]: #12585 -#12576 := (iff #3259 #12575) -#12577 := [rewrite]: #12576 -#12589 := [monotonicity #12577 #12586]: #12588 -#12784 := [monotonicity #12589 #12781]: #12783 -#12790 := [trans #12784 #12788]: #12789 -#12793 := [monotonicity #12589 #12790]: #12792 -#12582 := (iff #3262 #12581) -#12579 := (iff #3261 #12578) -#12580 := [rewrite]: #12579 -#12583 := [monotonicity #12577 #12580]: #12582 -#12796 := [monotonicity #12583 #12793]: #12795 -#12802 := [trans #12796 #12800]: #12801 -#12805 := [monotonicity #12583 #12802]: #12804 -#12808 := [monotonicity #12234 #12805]: #12807 -#12813 := [trans #12808 #12811]: #12812 -#12816 := [monotonicity #12234 #12813]: #12815 -#12821 := [trans #12816 #12819]: #12820 -#12824 := [monotonicity #12821]: #12823 -#12830 := [trans #12824 #12828]: #12829 -#12833 := [monotonicity #12234 #12830]: #12832 -#12838 := [trans #12833 #12836]: #12837 -#12906 := [monotonicity #12838 #12903]: #12905 -#12909 := [monotonicity #12234 #12906]: #12908 -#12914 := [trans #12909 #12912]: #12913 -#12917 := [monotonicity #12589 #12914]: #12916 -#12922 := [trans #12917 #12920]: #12921 -#12925 := [monotonicity #12589 #12922]: #12924 -#12928 := [monotonicity #12583 #12925]: #12927 +#12889 := [monotonicity #12553 #12886]: #12888 +#12892 := [monotonicity #12547 #12889]: #12891 +#12897 := [trans #12892 #12895]: #12896 +#12900 := [monotonicity #12547 #12897]: #12899 +#12903 := [monotonicity #12198 #12900]: #12902 +#12908 := [trans #12903 #12906]: #12907 +#12911 := [monotonicity #12198 #12908]: #12910 +#12916 := [trans #12911 #12914]: #12915 +#12919 := [monotonicity #12916]: #12918 +#12925 := [trans #12919 #12923]: #12924 +#12928 := [monotonicity #12198 #12925]: #12927 #12933 := [trans #12928 #12931]: #12932 -#12936 := [monotonicity #12583 #12933]: #12935 -#12939 := [monotonicity #12234 #12936]: #12938 -#12944 := [trans #12939 #12942]: #12943 -#12947 := [monotonicity #12234 #12944]: #12946 -#12952 := [trans #12947 #12950]: #12951 -#12955 := [monotonicity #12952]: #12954 -#12961 := [trans #12955 #12959]: #12960 -#12964 := [monotonicity #12234 #12961]: #12963 -#12969 := [trans #12964 #12967]: #12968 -#13005 := [monotonicity #12969 #13002]: #13004 -#13008 := [monotonicity #12234 #13005]: #13007 -#13013 := [trans #13008 #13011]: #13012 -#12573 := (iff #3255 true) -#12571 := (iff #12568 true) -#12572 := [rewrite]: #12571 -#12569 := (iff #3255 #12568) -#12566 := (iff #3254 true) -#12567 := [rewrite]: #12566 -#12564 := (iff #3253 true) -#12565 := [rewrite]: #12564 -#12570 := [monotonicity #12565 #12567]: #12569 -#12574 := [trans #12570 #12572]: #12573 -#13016 := [monotonicity #12574 #13013]: #13015 -#13020 := [trans #13016 #13018]: #13019 -#12562 := (iff #3252 #12561) -#12559 := (iff #3251 #12558) -#12560 := [rewrite]: #12559 -#12556 := (iff #3249 #12555) -#12557 := [rewrite]: #12556 -#12563 := [monotonicity #12557 #12560]: #12562 -#13023 := [monotonicity #12563 #13020]: #13022 +#12969 := [monotonicity #12933 #12966]: #12968 +#12972 := [monotonicity #12198 #12969]: #12971 +#12977 := [trans #12972 #12975]: #12976 +#12537 := (iff #3255 true) +#12535 := (iff #12532 true) +#12536 := [rewrite]: #12535 +#12533 := (iff #3255 #12532) +#12530 := (iff #3254 true) +#12531 := [rewrite]: #12530 +#12528 := (iff #3253 true) +#12529 := [rewrite]: #12528 +#12534 := [monotonicity #12529 #12531]: #12533 +#12538 := [trans #12534 #12536]: #12537 +#12980 := [monotonicity #12538 #12977]: #12979 +#12984 := [trans #12980 #12982]: #12983 +#12526 := (iff #3252 #12525) +#12523 := (iff #3251 #12522) +#12524 := [rewrite]: #12523 +#12520 := (iff #3249 #12519) +#12521 := [rewrite]: #12520 +#12527 := [monotonicity #12521 #12524]: #12526 +#12987 := [monotonicity #12527 #12984]: #12986 +#12993 := [trans #12987 #12991]: #12992 +#12517 := (iff #3247 #12516) +#12518 := [rewrite]: #12517 +#12996 := [monotonicity #12518 #12993]: #12995 +#13002 := [trans #12996 #13000]: #13001 +#12514 := (iff #3245 #12513) +#12515 := [rewrite]: #12514 +#13005 := [monotonicity #12515 #13002]: #13004 +#13011 := [trans #13005 #13009]: #13010 +#12511 := (iff #3243 #12510) +#12512 := [rewrite]: #12511 +#13014 := [monotonicity #12512 #13011]: #13013 +#13020 := [trans #13014 #13018]: #13019 +#12508 := (iff #3241 #12507) +#12509 := [rewrite]: #12508 +#13023 := [monotonicity #12509 #13020]: #13022 #13029 := [trans #13023 #13027]: #13028 -#12553 := (iff #3247 #12552) -#12554 := [rewrite]: #12553 -#13032 := [monotonicity #12554 #13029]: #13031 -#13038 := [trans #13032 #13036]: #13037 -#12550 := (iff #3245 #12549) -#12551 := [rewrite]: #12550 -#13041 := [monotonicity #12551 #13038]: #13040 -#13047 := [trans #13041 #13045]: #13046 -#12547 := (iff #3243 #12546) -#12548 := [rewrite]: #12547 -#13050 := [monotonicity #12548 #13047]: #13049 -#13056 := [trans #13050 #13054]: #13055 -#12544 := (iff #3241 #12543) -#12545 := [rewrite]: #12544 -#13059 := [monotonicity #12545 #13056]: #13058 -#13065 := [trans #13059 #13063]: #13064 -#12267 := (iff #3159 #12264) -#12261 := (and #12258 #12145) -#12265 := (iff #12261 #12264) -#12266 := [rewrite]: #12265 -#12262 := (iff #3159 #12261) -#12146 := (iff #3068 #12145) -#12147 := [rewrite]: #12146 -#12259 := (iff #3158 #12258) -#12260 := [rewrite]: #12259 -#12263 := [monotonicity #12260 #12147]: #12262 -#12268 := [trans #12263 #12266]: #12267 -#13068 := [monotonicity #12268 #13065]: #13067 -#13073 := [trans #13068 #13071]: #13072 -#12522 := (iff #3235 #12521) -#12519 := (iff #3234 #12518) -#12516 := (iff #3233 #12515) -#12517 := [rewrite]: #12516 -#12520 := [monotonicity #12517]: #12519 -#12523 := [monotonicity #12520]: #12522 -#13076 := [monotonicity #12523 #13073]: #13075 -#13082 := [trans #13076 #13080]: #13081 -#12541 := (iff #3239 #12521) -#12524 := (and true #12521) -#12527 := (iff #12524 #12521) -#12528 := [rewrite]: #12527 -#12539 := (iff #3239 #12524) -#12537 := (iff #3238 #12521) -#12535 := (iff #3238 #12524) -#12533 := (iff #3237 #12521) -#12531 := (iff #3237 #12524) -#12529 := (iff #3236 #12521) -#12525 := (iff #3236 #12524) -#12513 := (iff #3226 true) -#12508 := (forall (vars (?v0 S20)) (:pat #3222) true) -#12511 := (iff #12508 true) -#12512 := [elim-unused]: #12511 -#12509 := (iff #3226 #12508) -#12506 := (iff #3225 true) -#12458 := (= f1 #3210) -#12470 := (implies #12458 #12458) -#12473 := (iff #12470 true) -#12474 := [rewrite]: #12473 -#12504 := (iff #3225 #12470) -#12502 := (iff #3224 #12458) -#12463 := (and true #12458) -#12466 := (iff #12463 #12458) -#12467 := [rewrite]: #12466 -#12500 := (iff #3224 #12463) -#12459 := (iff #3211 #12458) -#12460 := [rewrite]: #12459 -#12498 := (iff #3223 true) -#12499 := [rewrite]: #12498 -#12501 := [monotonicity #12499 #12460]: #12500 -#12503 := [trans #12501 #12467]: #12502 -#12505 := [monotonicity #12460 #12503]: #12504 -#12507 := [trans #12505 #12474]: #12506 -#12510 := [quant-intro #12507]: #12509 -#12514 := [trans #12510 #12512]: #12513 -#12526 := [monotonicity #12514 #12523]: #12525 -#12530 := [trans #12526 #12528]: #12529 -#12496 := (iff #3219 true) -#12451 := (forall (vars (?v0 S20)) (:pat #3199) true) -#12454 := (iff #12451 true) -#12455 := [elim-unused]: #12454 -#12494 := (iff #3219 #12451) -#12492 := (iff #3218 true) -#12490 := (iff #3218 #12470) -#12488 := (iff #3217 #12458) -#12486 := (iff #3217 #12463) -#12484 := (iff #3216 true) -#12485 := [rewrite]: #12484 -#12487 := [monotonicity #12485 #12460]: #12486 -#12489 := [trans #12487 #12467]: #12488 -#12491 := [monotonicity #12460 #12489]: #12490 -#12493 := [trans #12491 #12474]: #12492 -#12495 := [quant-intro #12493]: #12494 -#12497 := [trans #12495 #12455]: #12496 -#12532 := [monotonicity #12497 #12530]: #12531 -#12534 := [trans #12532 #12528]: #12533 -#12482 := (iff #3215 true) -#12477 := (forall (vars (?v0 S20)) (:pat #3209) true) -#12480 := (iff #12477 true) -#12481 := [elim-unused]: #12480 -#12478 := (iff #3215 #12477) -#12475 := (iff #3214 true) -#12471 := (iff #3214 #12470) -#12468 := (iff #3213 #12458) -#12464 := (iff #3213 #12463) -#12461 := (iff #3212 true) -#12462 := [rewrite]: #12461 -#12465 := [monotonicity #12462 #12460]: #12464 -#12469 := [trans #12465 #12467]: #12468 -#12472 := [monotonicity #12460 #12469]: #12471 -#12476 := [trans #12472 #12474]: #12475 -#12479 := [quant-intro #12476]: #12478 -#12483 := [trans #12479 #12481]: #12482 -#12536 := [monotonicity #12483 #12534]: #12535 -#12538 := [trans #12536 #12528]: #12537 -#12456 := (iff #3206 true) -#12452 := (iff #3206 #12451) -#12449 := (iff #3205 true) -#12438 := (= f272 #3202) -#12441 := (not #12438) -#12444 := (implies #12441 #12441) -#12447 := (iff #12444 true) -#12448 := [rewrite]: #12447 -#12445 := (iff #3205 #12444) -#12442 := (iff #3204 #12441) -#12439 := (iff #3203 #12438) -#12440 := [rewrite]: #12439 -#12443 := [monotonicity #12440]: #12442 -#12446 := [monotonicity #12443 #12443]: #12445 -#12450 := [trans #12446 #12448]: #12449 -#12453 := [quant-intro #12450]: #12452 -#12457 := [trans #12453 #12455]: #12456 -#12540 := [monotonicity #12457 #12538]: #12539 -#12542 := [trans #12540 #12528]: #12541 -#13085 := [monotonicity #12542 #13082]: #13084 -#13090 := [trans #13085 #13088]: #13089 -#13093 := [monotonicity #12234 #13090]: #13092 -#13098 := [trans #13093 #13096]: #13097 -#13101 := [monotonicity #12234 #13098]: #13100 -#13106 := [trans #13101 #13104]: #13105 -#13109 := [monotonicity #12234 #13106]: #13108 -#13114 := [trans #13109 #13112]: #13113 -#12436 := (iff #3196 true) -#12431 := (implies #12232 true) -#12434 := (iff #12431 true) -#12435 := [rewrite]: #12434 -#12432 := (iff #3196 #12431) -#12429 := (iff #3195 true) -#12403 := (or #12402 #12394) -#12411 := (or #12349 #12403) -#12419 := (or #12349 #12411) -#12424 := (implies false #12419) -#12427 := (iff #12424 true) -#12428 := [rewrite]: #12427 -#12425 := (iff #3195 #12424) -#12422 := (iff #3194 #12419) -#12416 := (implies #12232 #12411) -#12420 := (iff #12416 #12419) -#12421 := [rewrite]: #12420 -#12417 := (iff #3194 #12416) -#12414 := (iff #3193 #12411) -#12408 := (implies #12232 #12403) -#12412 := (iff #12408 #12411) -#12413 := [rewrite]: #12412 -#12409 := (iff #3193 #12408) -#12406 := (iff #3192 #12403) -#12399 := (implies #12264 #12394) -#12404 := (iff #12399 #12403) -#12405 := [rewrite]: #12404 -#12400 := (iff #3192 #12399) -#12401 := [monotonicity #12268 #12398]: #12400 -#12407 := [trans #12401 #12405]: #12406 -#12410 := [monotonicity #12234 #12407]: #12409 -#12415 := [trans #12410 #12413]: #12414 -#12418 := [monotonicity #12234 #12415]: #12417 -#12423 := [trans #12418 #12421]: #12422 -#12426 := [monotonicity #12257 #12423]: #12425 -#12430 := [trans #12426 #12428]: #12429 -#12433 := [monotonicity #12234 #12430]: #12432 -#12437 := [trans #12433 #12435]: #12436 -#13117 := [monotonicity #12437 #13114]: #13116 -#13121 := [trans #13117 #13119]: #13120 -#13124 := [monotonicity #12234 #13121]: #13123 -#13129 := [trans #13124 #13127]: #13128 -#12254 := (iff #3155 #12253) -#12251 := (iff #3154 #12250) -#12252 := [rewrite]: #12251 -#12255 := [monotonicity #12252]: #12254 -#13132 := [monotonicity #12255 #13129]: #13131 -#13138 := [trans #13132 #13136]: #13137 -#12248 := (iff #3150 #12247) -#12245 := (iff #3149 #12242) -#12239 := (implies #455 #12236) -#12243 := (iff #12239 #12242) -#12244 := [rewrite]: #12243 -#12240 := (iff #3149 #12239) -#12237 := (iff #3148 #12236) -#12238 := [rewrite]: #12237 -#12241 := [monotonicity #12238]: #12240 -#12246 := [trans #12241 #12244]: #12245 -#12249 := [quant-intro #12246]: #12248 -#13141 := [monotonicity #12249 #13138]: #13140 -#13147 := [trans #13141 #13145]: #13146 -#13150 := [monotonicity #13147]: #13149 -#13156 := [trans #13150 #13154]: #13155 -#13159 := [monotonicity #12234 #13156]: #13158 -#13164 := [trans #13159 #13162]: #13163 -#13167 := [monotonicity #13164]: #13166 -#13173 := [trans #13167 #13171]: #13172 -#13176 := [monotonicity #13173]: #13175 -#13182 := [trans #13176 #13180]: #13181 -#13185 := [monotonicity #13182]: #13184 -#13191 := [trans #13185 #13189]: #13190 -#12230 := (iff #3130 #12229) -#12227 := (iff #3129 #3109) -#12228 := [rewrite]: #12227 -#12231 := [monotonicity #12228]: #12230 -#13194 := [monotonicity #12231 #13191]: #13193 +#12231 := (iff #3159 #12228) +#12225 := (and #12222 #12109) +#12229 := (iff #12225 #12228) +#12230 := [rewrite]: #12229 +#12226 := (iff #3159 #12225) +#12110 := (iff #3068 #12109) +#12111 := [rewrite]: #12110 +#12223 := (iff #3158 #12222) +#12224 := [rewrite]: #12223 +#12227 := [monotonicity #12224 #12111]: #12226 +#12232 := [trans #12227 #12230]: #12231 +#13032 := [monotonicity #12232 #13029]: #13031 +#13037 := [trans #13032 #13035]: #13036 +#12486 := (iff #3235 #12485) +#12483 := (iff #3234 #12482) +#12480 := (iff #3233 #12479) +#12481 := [rewrite]: #12480 +#12484 := [monotonicity #12481]: #12483 +#12487 := [monotonicity #12484]: #12486 +#13040 := [monotonicity #12487 #13037]: #13039 +#13046 := [trans #13040 #13044]: #13045 +#12505 := (iff #3239 #12485) +#12488 := (and true #12485) +#12491 := (iff #12488 #12485) +#12492 := [rewrite]: #12491 +#12503 := (iff #3239 #12488) +#12501 := (iff #3238 #12485) +#12499 := (iff #3238 #12488) +#12497 := (iff #3237 #12485) +#12495 := (iff #3237 #12488) +#12493 := (iff #3236 #12485) +#12489 := (iff #3236 #12488) +#12477 := (iff #3226 true) +#12472 := (forall (vars (?v0 S20)) (:pat #3222) true) +#12475 := (iff #12472 true) +#12476 := [elim-unused]: #12475 +#12473 := (iff #3226 #12472) +#12470 := (iff #3225 true) +#12422 := (= f1 #3210) +#12434 := (implies #12422 #12422) +#12437 := (iff #12434 true) +#12438 := [rewrite]: #12437 +#12468 := (iff #3225 #12434) +#12466 := (iff #3224 #12422) +#12427 := (and true #12422) +#12430 := (iff #12427 #12422) +#12431 := [rewrite]: #12430 +#12464 := (iff #3224 #12427) +#12423 := (iff #3211 #12422) +#12424 := [rewrite]: #12423 +#12462 := (iff #3223 true) +#12463 := [rewrite]: #12462 +#12465 := [monotonicity #12463 #12424]: #12464 +#12467 := [trans #12465 #12431]: #12466 +#12469 := [monotonicity #12424 #12467]: #12468 +#12471 := [trans #12469 #12438]: #12470 +#12474 := [quant-intro #12471]: #12473 +#12478 := [trans #12474 #12476]: #12477 +#12490 := [monotonicity #12478 #12487]: #12489 +#12494 := [trans #12490 #12492]: #12493 +#12460 := (iff #3219 true) +#12415 := (forall (vars (?v0 S20)) (:pat #3199) true) +#12418 := (iff #12415 true) +#12419 := [elim-unused]: #12418 +#12458 := (iff #3219 #12415) +#12456 := (iff #3218 true) +#12454 := (iff #3218 #12434) +#12452 := (iff #3217 #12422) +#12450 := (iff #3217 #12427) +#12448 := (iff #3216 true) +#12449 := [rewrite]: #12448 +#12451 := [monotonicity #12449 #12424]: #12450 +#12453 := [trans #12451 #12431]: #12452 +#12455 := [monotonicity #12424 #12453]: #12454 +#12457 := [trans #12455 #12438]: #12456 +#12459 := [quant-intro #12457]: #12458 +#12461 := [trans #12459 #12419]: #12460 +#12496 := [monotonicity #12461 #12494]: #12495 +#12498 := [trans #12496 #12492]: #12497 +#12446 := (iff #3215 true) +#12441 := (forall (vars (?v0 S20)) (:pat #3209) true) +#12444 := (iff #12441 true) +#12445 := [elim-unused]: #12444 +#12442 := (iff #3215 #12441) +#12439 := (iff #3214 true) +#12435 := (iff #3214 #12434) +#12432 := (iff #3213 #12422) +#12428 := (iff #3213 #12427) +#12425 := (iff #3212 true) +#12426 := [rewrite]: #12425 +#12429 := [monotonicity #12426 #12424]: #12428 +#12433 := [trans #12429 #12431]: #12432 +#12436 := [monotonicity #12424 #12433]: #12435 +#12440 := [trans #12436 #12438]: #12439 +#12443 := [quant-intro #12440]: #12442 +#12447 := [trans #12443 #12445]: #12446 +#12500 := [monotonicity #12447 #12498]: #12499 +#12502 := [trans #12500 #12492]: #12501 +#12420 := (iff #3206 true) +#12416 := (iff #3206 #12415) +#12413 := (iff #3205 true) +#12402 := (= f273 #3202) +#12405 := (not #12402) +#12408 := (implies #12405 #12405) +#12411 := (iff #12408 true) +#12412 := [rewrite]: #12411 +#12409 := (iff #3205 #12408) +#12406 := (iff #3204 #12405) +#12403 := (iff #3203 #12402) +#12404 := [rewrite]: #12403 +#12407 := [monotonicity #12404]: #12406 +#12410 := [monotonicity #12407 #12407]: #12409 +#12414 := [trans #12410 #12412]: #12413 +#12417 := [quant-intro #12414]: #12416 +#12421 := [trans #12417 #12419]: #12420 +#12504 := [monotonicity #12421 #12502]: #12503 +#12506 := [trans #12504 #12492]: #12505 +#13049 := [monotonicity #12506 #13046]: #13048 +#13054 := [trans #13049 #13052]: #13053 +#13057 := [monotonicity #12198 #13054]: #13056 +#13062 := [trans #13057 #13060]: #13061 +#13065 := [monotonicity #12198 #13062]: #13064 +#13070 := [trans #13065 #13068]: #13069 +#13073 := [monotonicity #12198 #13070]: #13072 +#13078 := [trans #13073 #13076]: #13077 +#12400 := (iff #3196 true) +#12395 := (implies #12196 true) +#12398 := (iff #12395 true) +#12399 := [rewrite]: #12398 +#12396 := (iff #3196 #12395) +#12393 := (iff #3195 true) +#12367 := (or #12366 #12358) +#12375 := (or #12313 #12367) +#12383 := (or #12313 #12375) +#12388 := (implies false #12383) +#12391 := (iff #12388 true) +#12392 := [rewrite]: #12391 +#12389 := (iff #3195 #12388) +#12386 := (iff #3194 #12383) +#12380 := (implies #12196 #12375) +#12384 := (iff #12380 #12383) +#12385 := [rewrite]: #12384 +#12381 := (iff #3194 #12380) +#12378 := (iff #3193 #12375) +#12372 := (implies #12196 #12367) +#12376 := (iff #12372 #12375) +#12377 := [rewrite]: #12376 +#12373 := (iff #3193 #12372) +#12370 := (iff #3192 #12367) +#12363 := (implies #12228 #12358) +#12368 := (iff #12363 #12367) +#12369 := [rewrite]: #12368 +#12364 := (iff #3192 #12363) +#12365 := [monotonicity #12232 #12362]: #12364 +#12371 := [trans #12365 #12369]: #12370 +#12374 := [monotonicity #12198 #12371]: #12373 +#12379 := [trans #12374 #12377]: #12378 +#12382 := [monotonicity #12198 #12379]: #12381 +#12387 := [trans #12382 #12385]: #12386 +#12390 := [monotonicity #12221 #12387]: #12389 +#12394 := [trans #12390 #12392]: #12393 +#12397 := [monotonicity #12198 #12394]: #12396 +#12401 := [trans #12397 #12399]: #12400 +#13081 := [monotonicity #12401 #13078]: #13080 +#13085 := [trans #13081 #13083]: #13084 +#13088 := [monotonicity #12198 #13085]: #13087 +#13093 := [trans #13088 #13091]: #13092 +#12218 := (iff #3155 #12217) +#12215 := (iff #3154 #12214) +#12216 := [rewrite]: #12215 +#12219 := [monotonicity #12216]: #12218 +#13096 := [monotonicity #12219 #13093]: #13095 +#13102 := [trans #13096 #13100]: #13101 +#12212 := (iff #3150 #12211) +#12209 := (iff #3149 #12206) +#12203 := (implies #455 #12200) +#12207 := (iff #12203 #12206) +#12208 := [rewrite]: #12207 +#12204 := (iff #3149 #12203) +#12201 := (iff #3148 #12200) +#12202 := [rewrite]: #12201 +#12205 := [monotonicity #12202]: #12204 +#12210 := [trans #12205 #12208]: #12209 +#12213 := [quant-intro #12210]: #12212 +#13105 := [monotonicity #12213 #13102]: #13104 +#13111 := [trans #13105 #13109]: #13110 +#13114 := [monotonicity #13111]: #13113 +#13120 := [trans #13114 #13118]: #13119 +#13123 := [monotonicity #12198 #13120]: #13122 +#13128 := [trans #13123 #13126]: #13127 +#13131 := [monotonicity #13128]: #13130 +#13137 := [trans #13131 #13135]: #13136 +#13140 := [monotonicity #13137]: #13139 +#13146 := [trans #13140 #13144]: #13145 +#13149 := [monotonicity #13146]: #13148 +#13155 := [trans #13149 #13153]: #13154 +#12194 := (iff #3130 #12193) +#12191 := (iff #3129 #3109) +#12192 := [rewrite]: #12191 +#12195 := [monotonicity #12192]: #12194 +#13158 := [monotonicity #12195 #13155]: #13157 +#13164 := [trans #13158 #13162]: #13163 +#13167 := [monotonicity #12195 #13164]: #13166 +#12189 := (iff #3128 #12188) +#12186 := (iff #3127 #12183) +#12180 := (implies #455 #12177) +#12184 := (iff #12180 #12183) +#12185 := [rewrite]: #12184 +#12181 := (iff #3127 #12180) +#12178 := (iff #3126 #12177) +#12179 := [rewrite]: #12178 +#12182 := [monotonicity #12179]: #12181 +#12187 := [trans #12182 #12185]: #12186 +#12190 := [quant-intro #12187]: #12189 +#13170 := [monotonicity #12190 #13167]: #13169 +#13176 := [trans #13170 #13174]: #13175 +#13179 := [monotonicity #12190 #13176]: #13178 +#13182 := [monotonicity #13179]: #13181 +#13188 := [trans #13182 #13186]: #13187 +#13191 := [monotonicity #13188]: #13190 +#12174 := (iff #3120 #12173) +#12171 := (iff #3119 #12170) +#12168 := (iff #3118 #3117) +#12169 := [rewrite]: #12168 +#12172 := [monotonicity #12169]: #12171 +#12175 := [monotonicity #12172]: #12174 +#13194 := [monotonicity #12175 #13191]: #13193 #13200 := [trans #13194 #13198]: #13199 -#13203 := [monotonicity #12231 #13200]: #13202 -#12225 := (iff #3128 #12224) -#12222 := (iff #3127 #12219) -#12216 := (implies #455 #12213) -#12220 := (iff #12216 #12219) -#12221 := [rewrite]: #12220 -#12217 := (iff #3127 #12216) -#12214 := (iff #3126 #12213) -#12215 := [rewrite]: #12214 -#12218 := [monotonicity #12215]: #12217 -#12223 := [trans #12218 #12221]: #12222 -#12226 := [quant-intro #12223]: #12225 -#13206 := [monotonicity #12226 #13203]: #13205 -#13212 := [trans #13206 #13210]: #13211 -#13215 := [monotonicity #12226 #13212]: #13214 -#13218 := [monotonicity #13215]: #13217 -#13224 := [trans #13218 #13222]: #13223 -#13227 := [monotonicity #13224]: #13226 -#12210 := (iff #3120 #12209) -#12207 := (iff #3119 #12206) -#12204 := (iff #3118 #3117) -#12205 := [rewrite]: #12204 -#12208 := [monotonicity #12205]: #12207 -#12211 := [monotonicity #12208]: #12210 -#13230 := [monotonicity #12211 #13227]: #13229 +#12166 := (iff #3115 #12165) +#12167 := [rewrite]: #12166 +#13203 := [monotonicity #12167 #13200]: #13202 +#13209 := [trans #13203 #13207]: #13208 +#12163 := (iff #3113 #12162) +#12164 := [rewrite]: #12163 +#13212 := [monotonicity #12164 #13209]: #13211 +#13218 := [trans #13212 #13216]: #13217 +#12160 := (iff #3111 #12159) +#12161 := [rewrite]: #12160 +#13221 := [monotonicity #12161 #13218]: #13220 +#13227 := [trans #13221 #13225]: #13226 +#13230 := [monotonicity #13227]: #13229 #13236 := [trans #13230 #13234]: #13235 -#12202 := (iff #3115 #12201) -#12203 := [rewrite]: #12202 -#13239 := [monotonicity #12203 #13236]: #13238 +#12157 := (iff #3106 #12156) +#12154 := (iff #3105 #12153) +#12155 := [rewrite]: #12154 +#12145 := (iff #3100 #12144) +#12146 := [rewrite]: #12145 +#12158 := [monotonicity #12146 #12155]: #12157 +#13239 := [monotonicity #12158 #13236]: #13238 #13245 := [trans #13239 #13243]: #13244 -#12199 := (iff #3113 #12198) -#12200 := [rewrite]: #12199 -#13248 := [monotonicity #12200 #13245]: #13247 -#13254 := [trans #13248 #13252]: #13253 -#12196 := (iff #3111 #12195) -#12197 := [rewrite]: #12196 -#13257 := [monotonicity #12197 #13254]: #13256 -#13263 := [trans #13257 #13261]: #13262 -#13266 := [monotonicity #13263]: #13265 -#13272 := [trans #13266 #13270]: #13271 -#12193 := (iff #3106 #12192) -#12190 := (iff #3105 #12189) -#12191 := [rewrite]: #12190 -#12181 := (iff #3100 #12180) -#12182 := [rewrite]: #12181 -#12194 := [monotonicity #12182 #12191]: #12193 -#13275 := [monotonicity #12194 #13272]: #13274 +#13248 := [monotonicity #12158 #13245]: #13247 +#12151 := (iff #3103 #12150) +#12148 := (iff #3102 #12147) +#12149 := [rewrite]: #12148 +#12152 := [monotonicity #12146 #12149]: #12151 +#13251 := [monotonicity #12152 #13248]: #13250 +#13257 := [trans #13251 #13255]: #13256 +#13260 := [monotonicity #12152 #13257]: #13259 +#12142 := (iff #3097 #12141) +#12143 := [rewrite]: #12142 +#13263 := [monotonicity #12143 #13260]: #13262 +#13269 := [trans #13263 #13267]: #13268 +#13272 := [monotonicity #12143 #13269]: #13271 +#13275 := [monotonicity #13272]: #13274 #13281 := [trans #13275 #13279]: #13280 -#13284 := [monotonicity #12194 #13281]: #13283 -#12187 := (iff #3103 #12186) -#12184 := (iff #3102 #12183) -#12185 := [rewrite]: #12184 -#12188 := [monotonicity #12182 #12185]: #12187 -#13287 := [monotonicity #12188 #13284]: #13286 -#13293 := [trans #13287 #13291]: #13292 -#13296 := [monotonicity #12188 #13293]: #13295 -#12178 := (iff #3097 #12177) -#12179 := [rewrite]: #12178 -#13299 := [monotonicity #12179 #13296]: #13298 -#13305 := [trans #13299 #13303]: #13304 -#13308 := [monotonicity #12179 #13305]: #13307 -#13311 := [monotonicity #13308]: #13310 +#12139 := (iff #3091 #12138) +#12136 := (iff #3090 #12133) +#12130 := (iff #12127 false) +#12134 := (iff #12130 #12133) +#12135 := [rewrite]: #12134 +#12131 := (iff #3090 #12130) +#12128 := (iff #3089 #12127) +#12129 := [rewrite]: #12128 +#12132 := [monotonicity #12129]: #12131 +#12137 := [trans #12132 #12135]: #12136 +#12140 := [quant-intro #12137]: #12139 +#13284 := [monotonicity #12140 #13281]: #13283 +#13290 := [trans #13284 #13288]: #13289 +#13293 := [monotonicity #13290]: #13292 +#13299 := [trans #13293 #13297]: #13298 +#12125 := (iff #3083 #12124) +#12126 := [rewrite]: #12125 +#13302 := [monotonicity #12126 #13299]: #13301 +#13308 := [trans #13302 #13306]: #13307 +#12122 := (iff #3081 #12121) +#12119 := (iff #3080 #12118) +#12120 := [rewrite]: #12119 +#12116 := (iff #3078 #12115) +#12117 := [rewrite]: #12116 +#12123 := [monotonicity #12117 #12120]: #12122 +#13311 := [monotonicity #12123 #13308]: #13310 #13317 := [trans #13311 #13315]: #13316 -#12175 := (iff #3091 #12174) -#12172 := (iff #3090 #12169) -#12166 := (iff #12163 false) -#12170 := (iff #12166 #12169) -#12171 := [rewrite]: #12170 -#12167 := (iff #3090 #12166) -#12164 := (iff #3089 #12163) -#12165 := [rewrite]: #12164 -#12168 := [monotonicity #12165]: #12167 -#12173 := [trans #12168 #12171]: #12172 -#12176 := [quant-intro #12173]: #12175 -#13320 := [monotonicity #12176 #13317]: #13319 +#13320 := [monotonicity #13317]: #13319 #13326 := [trans #13320 #13324]: #13325 -#13329 := [monotonicity #13326]: #13328 +#12113 := (iff #3069 #12112) +#12107 := (iff #3066 #12106) +#12108 := [rewrite]: #12107 +#12114 := [monotonicity #12108 #12111]: #12113 +#13329 := [monotonicity #12114 #13326]: #13328 #13335 := [trans #13329 #13333]: #13334 -#12161 := (iff #3083 #12160) -#12162 := [rewrite]: #12161 -#13338 := [monotonicity #12162 #13335]: #13337 +#12104 := (iff #3064 #12103) +#12105 := [rewrite]: #12104 +#13338 := [monotonicity #12105 #13335]: #13337 #13344 := [trans #13338 #13342]: #13343 -#12158 := (iff #3081 #12157) -#12155 := (iff #3080 #12154) -#12156 := [rewrite]: #12155 -#12152 := (iff #3078 #12151) -#12153 := [rewrite]: #12152 -#12159 := [monotonicity #12153 #12156]: #12158 -#13347 := [monotonicity #12159 #13344]: #13346 +#12101 := (iff #3062 #12100) +#12098 := (iff #3061 #12097) +#12095 := (iff #3060 #12094) +#12092 := (iff #3059 #12091) +#12089 := (iff #3058 #12088) +#12086 := (iff #3057 #12085) +#12087 := [rewrite]: #12086 +#12083 := (iff #3055 #12082) +#12080 := (iff #3054 #12079) +#12081 := [rewrite]: #12080 +#12084 := [monotonicity #12081]: #12083 +#12090 := [monotonicity #12084 #12087]: #12089 +#12077 := (iff #3052 #12076) +#12078 := [rewrite]: #12077 +#12093 := [monotonicity #12078 #12090]: #12092 +#12074 := (iff #3050 #12073) +#12075 := [rewrite]: #12074 +#12096 := [monotonicity #12075 #12093]: #12095 +#12071 := (iff #3048 #12070) +#12072 := [rewrite]: #12071 +#12099 := [monotonicity #12072 #12096]: #12098 +#12068 := (iff #3046 #12066) +#12069 := [rewrite]: #12068 +#12102 := [monotonicity #12069 #12099]: #12101 +#13347 := [monotonicity #12102 #13344]: #13346 #13353 := [trans #13347 #13351]: #13352 #13356 := [monotonicity #13353]: #13355 #13362 := [trans #13356 #13360]: #13361 -#12149 := (iff #3069 #12148) -#12143 := (iff #3066 #12142) -#12144 := [rewrite]: #12143 -#12150 := [monotonicity #12144 #12147]: #12149 -#13365 := [monotonicity #12150 #13362]: #13364 +#13365 := [monotonicity #13362]: #13364 #13371 := [trans #13365 #13369]: #13370 -#12140 := (iff #3064 #12139) -#12141 := [rewrite]: #12140 -#13374 := [monotonicity #12141 #13371]: #13373 +#13374 := [monotonicity #13371]: #13373 #13380 := [trans #13374 #13378]: #13379 -#12137 := (iff #3062 #12136) -#12134 := (iff #3061 #12133) -#12131 := (iff #3060 #12130) -#12128 := (iff #3059 #12127) -#12125 := (iff #3058 #12124) -#12122 := (iff #3057 #12121) -#12123 := [rewrite]: #12122 -#12119 := (iff #3055 #12118) -#12116 := (iff #3054 #12115) -#12117 := [rewrite]: #12116 -#12120 := [monotonicity #12117]: #12119 -#12126 := [monotonicity #12120 #12123]: #12125 -#12113 := (iff #3052 #12112) -#12114 := [rewrite]: #12113 -#12129 := [monotonicity #12114 #12126]: #12128 -#12110 := (iff #3050 #12109) -#12111 := [rewrite]: #12110 -#12132 := [monotonicity #12111 #12129]: #12131 -#12107 := (iff #3048 #12106) -#12108 := [rewrite]: #12107 -#12135 := [monotonicity #12108 #12132]: #12134 -#12104 := (iff #3046 #12102) -#12105 := [rewrite]: #12104 -#12138 := [monotonicity #12105 #12135]: #12137 -#13383 := [monotonicity #12138 #13380]: #13382 +#13383 := [monotonicity #13380]: #13382 #13389 := [trans #13383 #13387]: #13388 #13392 := [monotonicity #13389]: #13391 #13398 := [trans #13392 #13396]: #13397 #13401 := [monotonicity #13398]: #13400 -#13407 := [trans #13401 #13405]: #13406 -#13410 := [monotonicity #13407]: #13409 -#13416 := [trans #13410 #13414]: #13415 -#13419 := [monotonicity #13416]: #13418 -#13425 := [trans #13419 #13423]: #13424 -#13428 := [monotonicity #13425]: #13427 -#13434 := [trans #13428 #13432]: #13433 -#13437 := [monotonicity #13434]: #13436 -#14345 := [trans #13437 #14343]: #14344 -#12101 := [asserted]: #3406 -#14346 := [mp #12101 #14345]: #14341 -#14364 := [not-or-elim #14346]: #14228 -#14367 := [and-elim #14364]: #12109 -#11376 := (not #11369) -#1302 := (f127 #55) +#14309 := [trans #13401 #14307]: #14308 +#12065 := [asserted]: #3406 +#14310 := [mp #12065 #14309]: #14305 +#14328 := [not-or-elim #14310]: #14192 +#14331 := [and-elim #14328]: #12073 +#275 := (:var 0 S18) +#55 := (:var 1 S20) +#2729 := (f59 #55 #275) +#2730 := (pattern #2729) +#11333 := (= f1 #2729) +#11340 := (not #11333) +#1302 := (f128 #55) #2732 := (f54 #275 #1302) #2733 := (= #55 #2732) -#11377 := (or #2733 #11376) -#11382 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11377) -#18282 := (~ #11382 #11382) -#18280 := (~ #11377 #11377) -#18281 := [refl]: #18280 -#18283 := [nnf-pos #18281]: #18282 +#11341 := (or #2733 #11340) +#11346 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11341) +#18246 := (~ #11346 #11346) +#18244 := (~ #11341 #11341) +#18245 := [refl]: #18244 +#18247 := [nnf-pos #18245]: #18246 +#2731 := (= #2729 f1) #2734 := (implies #2731 #2733) #2735 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #2734) -#11383 := (iff #2735 #11382) -#11380 := (iff #2734 #11377) -#11373 := (implies #11369 #2733) -#11378 := (iff #11373 #11377) -#11379 := [rewrite]: #11378 -#11374 := (iff #2734 #11373) -#11375 := [monotonicity #11372]: #11374 -#11381 := [trans #11375 #11379]: #11380 -#11384 := [quant-intro #11381]: #11383 -#11368 := [asserted]: #2735 -#11387 := [mp #11368 #11384]: #11382 -#18284 := [mp~ #11387 #18283]: #11382 -#26181 := (not #12109) -#26194 := (not #11382) -#26195 := (or #26194 #26181 #26189) -#26190 := (or #26189 #26181) -#26196 := (or #26194 #26190) -#26203 := (iff #26196 #26195) -#26191 := (or #26181 #26189) -#26198 := (or #26194 #26191) -#26201 := (iff #26198 #26195) -#26202 := [rewrite]: #26201 -#26199 := (iff #26196 #26198) -#26192 := (iff #26190 #26191) -#26193 := [rewrite]: #26192 -#26200 := [monotonicity #26193]: #26199 -#26204 := [trans #26200 #26202]: #26203 -#26197 := [quant-inst #3044 #3040]: #26196 -#26205 := [mp #26197 #26204]: #26195 -#28848 := [unit-resolution #26205 #18284 #14367]: #26189 -#28791 := [trans #28789 #28848]: #28790 -#28793 := [monotonicity #28791]: #28792 -#28796 := [symm #28793]: #28795 -#26777 := (= f1 #26776) -decl f64 :: (-> S19 S20 S21) -#26765 := (f64 f297 #26182) -#26766 := (f26 #62 #26765) -#26772 := (pattern #26766) -decl f208 :: (-> S18 S1) -#26586 := (f24 #26182) -#26769 := (f208 #26586) -#26770 := (= f1 #26769) -#26767 := (= f1 #26766) -#26768 := (not #26767) -decl f158 :: (-> S20 S21 S1) -decl f203 :: (-> S22 S21) -decl f22 :: (-> S19 S20 S22) -#26761 := (f22 f297 #26182) -#26762 := (f203 #26761) -#26763 := (f158 #62 #26762) -#26764 := (= f1 #26763) -#26782 := (or #26764 #26768 #26770) -#26785 := (forall (vars (?v3 S20)) (:pat #26772) #26782) -#26788 := (not #26785) -#26778 := (not #26777) -#26626 := (f38 f297 #26182) -#26627 := (= f1 #26626) -#26649 := (not #26627) -#26791 := (or #26649 #26778 #26788) -#26794 := (not #26791) -decl f207 :: (-> S19 S20 S20 S1) -#26714 := (f207 f297 #26182 #26182) -#26715 := (= f1 #26714) -#26716 := (f211 f297 #26182 #26182 f305) -#26717 := (= f1 #26716) -#26719 := (iff #26715 #26717) +#11347 := (iff #2735 #11346) +#11344 := (iff #2734 #11341) +#11337 := (implies #11333 #2733) +#11342 := (iff #11337 #11341) +#11343 := [rewrite]: #11342 +#11338 := (iff #2734 #11337) +#11335 := (iff #2731 #11333) +#11336 := [rewrite]: #11335 +#11339 := [monotonicity #11336]: #11338 +#11345 := [trans #11339 #11343]: #11344 +#11348 := [quant-intro #11345]: #11347 +#11332 := [asserted]: #2735 +#11351 := [mp #11332 #11348]: #11346 +#18248 := [mp~ #11351 #18247]: #11346 +#26145 := (not #12073) +#26158 := (not #11346) +#26159 := (or #26158 #26145 #26153) +#26154 := (or #26153 #26145) +#26160 := (or #26158 #26154) +#26167 := (iff #26160 #26159) +#26155 := (or #26145 #26153) +#26162 := (or #26158 #26155) +#26165 := (iff #26162 #26159) +#26166 := [rewrite]: #26165 +#26163 := (iff #26160 #26162) +#26156 := (iff #26154 #26155) +#26157 := [rewrite]: #26156 +#26164 := [monotonicity #26157]: #26163 +#26168 := [trans #26164 #26166]: #26167 +#26161 := [quant-inst #3044 #3040]: #26160 +#26169 := [mp #26161 #26168]: #26159 +#28875 := [unit-resolution #26169 #18248 #14331]: #26153 +#26872 := [symm #28875]: #26866 +#26874 := [monotonicity #26872]: #26873 +#26876 := [trans #26874 #28878]: #26875 +#26910 := [monotonicity #26876]: #26909 +#26912 := [monotonicity #26910]: #26911 +#26914 := [symm #26912]: #26913 +#26899 := [monotonicity #26914]: #26897 +#14333 := [and-elim #14328]: #12082 +#26900 := [mp #14333 #26899]: #26915 +decl f208 :: (-> S19 S20 S20 S1) +#26678 := (f208 f298 #26146 #26146) +#26679 := (= f1 #26678) +#26700 := (not #26679) +#26680 := (f212 f298 #26146 #26146 f306) +#26681 := (= f1 #26680) +#26683 := (iff #26679 #26681) #2299 := (:var 0 S31) +#60 := (:var 2 S20) #53 := (:var 3 S19) -#2311 := (f211 #53 #60 #55 #2299) +#2311 := (f212 #53 #60 #55 #2299) #2312 := (pattern #2311) -#2314 := (f207 #53 #60 #55) -#10318 := (= f1 #2314) -#10314 := (= f1 #2311) -#10321 := (iff #10314 #10318) -#10324 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10321) -#17924 := (~ #10324 #10324) -#17922 := (~ #10321 #10321) -#17923 := [refl]: #17922 -#17925 := [nnf-pos #17923]: #17924 +#2314 := (f208 #53 #60 #55) +#10282 := (= f1 #2314) +#10278 := (= f1 #2311) +#10285 := (iff #10278 #10282) +#10288 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10285) +#17888 := (~ #10288 #10288) +#17886 := (~ #10285 #10285) +#17887 := [refl]: #17886 +#17889 := [nnf-pos #17887]: #17888 #2315 := (= #2314 f1) #2313 := (= #2311 f1) #2316 := (iff #2313 #2315) #2317 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #2316) -#10325 := (iff #2317 #10324) -#10322 := (iff #2316 #10321) -#10319 := (iff #2315 #10318) -#10320 := [rewrite]: #10319 -#10316 := (iff #2313 #10314) -#10317 := [rewrite]: #10316 -#10323 := [monotonicity #10317 #10320]: #10322 -#10326 := [quant-intro #10323]: #10325 -#10313 := [asserted]: #2317 -#10329 := [mp #10313 #10326]: #10324 -#17926 := [mp~ #10329 #17925]: #10324 -#26731 := (not #10324) -#26749 := (or #26731 #26719) -#26718 := (iff #26717 #26715) -#26734 := (or #26731 #26718) -#26738 := (iff #26734 #26749) -#26739 := (iff #26749 #26749) -#26740 := [rewrite]: #26739 -#26720 := (iff #26718 #26719) -#26721 := [rewrite]: #26720 -#26735 := [monotonicity #26721]: #26738 -#26741 := [trans #26735 #26740]: #26738 -#26737 := [quant-inst #3039 #26182 #26182 #3095]: #26734 -#26742 := [mp #26737 #26741]: #26749 -#26937 := [unit-resolution #26742 #17926]: #26719 -#28782 := (= #3096 #26716) -#26939 := (= #26716 #3096) -#26934 := (= #26182 #3044) -#26940 := [symm #28848]: #26934 -#26966 := [monotonicity #26940 #26940]: #26939 -#28799 := [symm #26966]: #28782 -#26828 := (f23 #26586) -#26831 := (= f25 #26828) -#26933 := (not #26831) -#26947 := (iff #12118 #26933) -#26950 := (iff #12115 #26831) -#26948 := (iff #26831 #12115) -#26960 := (= #26828 #3053) -#26943 := (= #26586 #3040) -#25117 := (f24 #3044) -#28850 := (= #25117 #3040) -#25120 := (= #3040 #25117) -#25125 := (or #25064 #25120) -#25126 := [quant-inst #3040 #3043]: #25125 -#28849 := [unit-resolution #25126 #23312]: #25120 -#28851 := [symm #28849]: #28850 -#26941 := (= #26586 #25117) -#26942 := [monotonicity #26940]: #26941 -#26944 := [trans #26942 #28851]: #26943 -#26946 := [monotonicity #26944]: #26960 -#26949 := [monotonicity #26946]: #26948 -#26951 := [symm #26949]: #26950 -#26935 := [monotonicity #26951]: #26947 -#14369 := [and-elim #14364]: #12118 -#26936 := [mp #14369 #26935]: #26933 -#26736 := (not #26715) -#26733 := (not #26717) -#26958 := (iff #13300 #26733) -#26969 := (iff #12177 #26717) -#26967 := (iff #26717 #12177) -#26968 := [monotonicity #26966]: #26967 -#26957 := [symm #26968]: #26969 -#26959 := [monotonicity #26957]: #26958 -#26938 := [hypothesis]: #13300 -#26972 := [mp #26938 #26959]: #26733 -#26722 := (not #26719) -#26753 := (or #26722 #26736 #26717) -#26754 := [def-axiom]: #26753 -#26974 := [unit-resolution #26754 #26972 #26937]: #26736 -#26820 := (f35 f297 #26182) -#26821 := (= f1 #26820) -#26965 := (= #3051 #26820) -#26975 := (= #26820 #3051) -#26963 := [monotonicity #26940]: #26975 -#26961 := [symm #26963]: #26965 -#14368 := [and-elim #14364]: #12112 -#26973 := [trans #14368 #26961]: #26821 -#26823 := (f59 #26182 #26586) -#26824 := (= f1 #26823) -#26978 := (= #3049 #26823) -#26976 := (= #26823 #3049) -#26962 := [monotonicity #26940 #26944]: #26976 -#26979 := [symm #26962]: #26978 -#26980 := [trans #14367 #26979]: #26824 -#26825 := (not #26824) -#26822 := (not #26821) -#27030 := (or #26715 #26822 #26825 #26831) -#26598 := (f36 f297 #26182) -#26826 := (= f37 #26598) -#26989 := (= #3047 #26598) -#26981 := (= #26598 #3047) -#26987 := [monotonicity #26940]: #26981 -#27001 := [symm #26987]: #26989 -#14366 := [and-elim #14364]: #12106 -#27002 := [trans #14366 #27001]: #26826 -#27008 := (= #3045 #26626) -#27003 := (= #26626 #3045) -#27004 := [monotonicity #26940]: #27003 -#27009 := [symm #27004]: #27008 -#14365 := [and-elim #14364]: #12102 -#27010 := [trans #14365 #27009]: #26627 -#26587 := (f34 #26586) -#26594 := (= f1 #26587) -#27019 := (= #3056 #26587) -#26996 := (= #26587 #3056) -#26997 := [monotonicity #26944]: #26996 -#27020 := [symm #26997]: #27019 -#14370 := [and-elim #14364]: #12121 -#27029 := [trans #14370 #27020]: #26594 -#14349 := [not-or-elim #14346]: #12148 -#14351 := [and-elim #14349]: #12145 -#2270 := (f207 #86 #62 #62) +#10289 := (iff #2317 #10288) +#10286 := (iff #2316 #10285) +#10283 := (iff #2315 #10282) +#10284 := [rewrite]: #10283 +#10280 := (iff #2313 #10278) +#10281 := [rewrite]: #10280 +#10287 := [monotonicity #10281 #10284]: #10286 +#10290 := [quant-intro #10287]: #10289 +#10277 := [asserted]: #2317 +#10293 := [mp #10277 #10290]: #10288 +#17890 := [mp~ #10293 #17889]: #10288 +#26698 := (not #10288) +#26699 := (or #26698 #26683) +#26682 := (iff #26681 #26679) +#26701 := (or #26698 #26682) +#26703 := (iff #26701 #26699) +#26705 := (iff #26699 #26699) +#26706 := [rewrite]: #26705 +#26684 := (iff #26682 #26683) +#26685 := [rewrite]: #26684 +#26704 := [monotonicity #26685]: #26703 +#26686 := [trans #26704 #26706]: #26703 +#26702 := [quant-inst #3039 #26146 #26146 #3095]: #26701 +#26688 := [mp #26702 #26686]: #26699 +#26901 := [unit-resolution #26688 #17890]: #26683 +#26697 := (not #26681) +#26908 := (iff #13264 #26697) +#26906 := (iff #12141 #26681) +#26904 := (iff #26681 #12141) +#26903 := (= #26680 #3096) +#26898 := [monotonicity #26872 #26872]: #26903 +#26905 := [monotonicity #26898]: #26904 +#26907 := [symm #26905]: #26906 +#26924 := [monotonicity #26907]: #26908 +#26902 := [hypothesis]: #13264 +#26925 := [mp #26902 #26924]: #26697 +#26689 := (not #26683) +#26691 := (or #26689 #26700 #26681) +#26692 := [def-axiom]: #26691 +#26926 := [unit-resolution #26692 #26925 #26901]: #26700 +#26784 := (f35 f298 #26146) +#26785 := (= f1 #26784) +#26930 := (= #3051 #26784) +#26927 := (= #26784 #3051) +#26928 := [monotonicity #26872]: #26927 +#26931 := [symm #26928]: #26930 +#14332 := [and-elim #14328]: #12076 +#26932 := [trans #14332 #26931]: #26785 +#26787 := (f59 #26146 #26550) +#26788 := (= f1 #26787) +#26923 := (= #3049 #26787) +#26933 := (= #26787 #3049) +#26921 := [monotonicity #26872 #26876]: #26933 +#26936 := [symm #26921]: #26923 +#26938 := [trans #14331 #26936]: #26788 +#26789 := (not #26788) +#26786 := (not #26785) +#26972 := (or #26679 #26786 #26789 #26795) +#26562 := (f36 f298 #26146) +#26790 := (= f37 #26562) +#26941 := (= #3047 #26562) +#26939 := (= #26562 #3047) +#26937 := [monotonicity #26872]: #26939 +#26942 := [symm #26937]: #26941 +#14330 := [and-elim #14328]: #12070 +#26943 := [trans #14330 #26942]: #26790 +#26590 := (f38 f298 #26146) +#26591 := (= f1 #26590) +#26952 := (= #3045 #26590) +#26944 := (= #26590 #3045) +#26945 := [monotonicity #26872]: #26944 +#26953 := [symm #26945]: #26952 +#14329 := [and-elim #14328]: #12066 +#26965 := [trans #14329 #26953]: #26591 +#26551 := (f34 #26550) +#26558 := (= f1 #26551) +#26969 := (= #3056 #26551) +#26966 := (= #26551 #3056) +#26967 := [monotonicity #26876]: #26966 +#26970 := [symm #26967]: #26969 +#14334 := [and-elim #14328]: #12085 +#26971 := [trans #14334 #26970]: #26558 +#14313 := [not-or-elim #14310]: #12112 +#14315 := [and-elim #14313]: #12109 +#86 := (:var 1 S19) +#2270 := (f208 #86 #62 #62) #2271 := (pattern #2270) -#10190 := (= f1 #2270) +#10154 := (= f1 #2270) #269 := (f66 #86) #4055 := (= f1 #269) -#19481 := (not #4055) +#19445 := (not #4055) +#186 := (f35 #86 #62) +#3767 := (= f1 #186) +#11261 := (not #3767) +#65 := (f24 #62) #184 := (f59 #62 #65) #3764 := (= f1 #184) -#19355 := (not #3764) -#19354 := (not #3761) +#19319 := (not #3764) +#182 := (f36 #86 #62) +#3761 := (= f37 #182) +#19318 := (not #3761) #175 := (f38 #86 #62) #3746 := (= f1 #175) -#10910 := (not #3746) +#10874 := (not #3746) #110 := (f34 #65) #3595 := (= f1 #110) -#10969 := (not #3595) -#21914 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481 #10190) -#21919 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21914) -#10205 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055) -#10208 := (not #10205) -#10214 := (or #10190 #10208) -#10219 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10214) -#21920 := (iff #10219 #21919) -#21917 := (iff #10214 #21914) -#21900 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481) -#21911 := (or #10190 #21900) -#21915 := (iff #21911 #21914) -#21916 := [rewrite]: #21915 -#21912 := (iff #10214 #21911) -#21909 := (iff #10208 #21900) -#21901 := (not #21900) -#21904 := (not #21901) -#21907 := (iff #21904 #21900) -#21908 := [rewrite]: #21907 -#21905 := (iff #10208 #21904) -#21902 := (iff #10205 #21901) -#21903 := [rewrite]: #21902 -#21906 := [monotonicity #21903]: #21905 -#21910 := [trans #21906 #21908]: #21909 -#21913 := [monotonicity #21910]: #21912 -#21918 := [trans #21913 #21916]: #21917 -#21921 := [quant-intro #21918]: #21920 -#17892 := (~ #10219 #10219) -#17890 := (~ #10214 #10214) -#17891 := [refl]: #17890 -#17893 := [nnf-pos #17891]: #17892 +#10933 := (not #3595) +#66 := (f23 #65) +#68 := (= #66 f25) +#21878 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445 #10154) +#21883 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21878) +#91 := (not #68) +#10169 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055) +#10172 := (not #10169) +#10178 := (or #10154 #10172) +#10183 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10178) +#21884 := (iff #10183 #21883) +#21881 := (iff #10178 #21878) +#21864 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445) +#21875 := (or #10154 #21864) +#21879 := (iff #21875 #21878) +#21880 := [rewrite]: #21879 +#21876 := (iff #10178 #21875) +#21873 := (iff #10172 #21864) +#21865 := (not #21864) +#21868 := (not #21865) +#21871 := (iff #21868 #21864) +#21872 := [rewrite]: #21871 +#21869 := (iff #10172 #21868) +#21866 := (iff #10169 #21865) +#21867 := [rewrite]: #21866 +#21870 := [monotonicity #21867]: #21869 +#21874 := [trans #21870 #21872]: #21873 +#21877 := [monotonicity #21874]: #21876 +#21882 := [trans #21877 #21880]: #21881 +#21885 := [quant-intro #21882]: #21884 +#17856 := (~ #10183 #10183) +#17854 := (~ #10178 #10178) +#17855 := [refl]: #17854 +#17857 := [nnf-pos #17855]: #17856 #2278 := (= #2270 f1) #111 := (= #110 f1) #2272 := (and #91 #111) +#187 := (= #186 f1) #2273 := (and #187 #2272) #185 := (= #184 f1) #2274 := (and #185 #2273) +#183 := (= #182 f37) #2275 := (and #183 #2274) #176 := (= #175 f1) #2276 := (and #176 #2275) @@ -4002,186 +3227,2200 @@ #2277 := (and #271 #2276) #2279 := (implies #2277 #2278) #2280 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #2279) -#10222 := (iff #2280 #10219) -#10171 := (and #91 #3595) -#10175 := (and #3767 #10171) -#10178 := (and #3764 #10175) -#10181 := (and #3761 #10178) -#10184 := (and #3746 #10181) -#10187 := (and #4055 #10184) -#10196 := (not #10187) -#10197 := (or #10196 #10190) -#10202 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10197) -#10220 := (iff #10202 #10219) -#10217 := (iff #10197 #10214) -#10211 := (or #10208 #10190) -#10215 := (iff #10211 #10214) -#10216 := [rewrite]: #10215 -#10212 := (iff #10197 #10211) -#10209 := (iff #10196 #10208) -#10206 := (iff #10187 #10205) -#10207 := [rewrite]: #10206 -#10210 := [monotonicity #10207]: #10209 -#10213 := [monotonicity #10210]: #10212 -#10218 := [trans #10213 #10216]: #10217 -#10221 := [quant-intro #10218]: #10220 -#10203 := (iff #2280 #10202) -#10200 := (iff #2279 #10197) -#10193 := (implies #10187 #10190) -#10198 := (iff #10193 #10197) -#10199 := [rewrite]: #10198 -#10194 := (iff #2279 #10193) -#10191 := (iff #2278 #10190) -#10192 := [rewrite]: #10191 -#10188 := (iff #2277 #10187) -#10185 := (iff #2276 #10184) -#10182 := (iff #2275 #10181) -#10179 := (iff #2274 #10178) -#10176 := (iff #2273 #10175) -#10173 := (iff #2272 #10171) +#10186 := (iff #2280 #10183) +#10135 := (and #91 #3595) +#10139 := (and #3767 #10135) +#10142 := (and #3764 #10139) +#10145 := (and #3761 #10142) +#10148 := (and #3746 #10145) +#10151 := (and #4055 #10148) +#10160 := (not #10151) +#10161 := (or #10160 #10154) +#10166 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10161) +#10184 := (iff #10166 #10183) +#10181 := (iff #10161 #10178) +#10175 := (or #10172 #10154) +#10179 := (iff #10175 #10178) +#10180 := [rewrite]: #10179 +#10176 := (iff #10161 #10175) +#10173 := (iff #10160 #10172) +#10170 := (iff #10151 #10169) +#10171 := [rewrite]: #10170 +#10174 := [monotonicity #10171]: #10173 +#10177 := [monotonicity #10174]: #10176 +#10182 := [trans #10177 #10180]: #10181 +#10185 := [quant-intro #10182]: #10184 +#10167 := (iff #2280 #10166) +#10164 := (iff #2279 #10161) +#10157 := (implies #10151 #10154) +#10162 := (iff #10157 #10161) +#10163 := [rewrite]: #10162 +#10158 := (iff #2279 #10157) +#10155 := (iff #2278 #10154) +#10156 := [rewrite]: #10155 +#10152 := (iff #2277 #10151) +#10149 := (iff #2276 #10148) +#10146 := (iff #2275 #10145) +#10143 := (iff #2274 #10142) +#10140 := (iff #2273 #10139) +#10137 := (iff #2272 #10135) #3596 := (iff #111 #3595) #3597 := [rewrite]: #3596 -#10174 := [monotonicity #3597]: #10173 -#10177 := [monotonicity #3769 #10174]: #10176 +#10138 := [monotonicity #3597]: #10137 +#3768 := (iff #187 #3767) +#3769 := [rewrite]: #3768 +#10141 := [monotonicity #3769 #10138]: #10140 #3765 := (iff #185 #3764) #3766 := [rewrite]: #3765 -#10180 := [monotonicity #3766 #10177]: #10179 -#10183 := [monotonicity #3763 #10180]: #10182 +#10144 := [monotonicity #3766 #10141]: #10143 +#3762 := (iff #183 #3761) +#3763 := [rewrite]: #3762 +#10147 := [monotonicity #3763 #10144]: #10146 #3748 := (iff #176 #3746) #3749 := [rewrite]: #3748 -#10186 := [monotonicity #3749 #10183]: #10185 +#10150 := [monotonicity #3749 #10147]: #10149 #4057 := (iff #271 #4055) #4058 := [rewrite]: #4057 -#10189 := [monotonicity #4058 #10186]: #10188 -#10195 := [monotonicity #10189 #10192]: #10194 -#10201 := [trans #10195 #10199]: #10200 -#10204 := [quant-intro #10201]: #10203 -#10223 := [trans #10204 #10221]: #10222 -#10170 := [asserted]: #2280 -#10224 := [mp #10170 #10223]: #10219 -#17894 := [mp~ #10224 #17893]: #10219 -#21922 := [mp #17894 #21921]: #21919 -#26827 := (not #26826) -#26595 := (not #26594) -#24846 := (not #12145) -#26800 := (not #21919) -#26802 := (or #26800 #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831) -#26829 := (= #26828 f25) -#26830 := (or #26829 #26595 #26649 #26827 #26825 #26822 #24846 #26715) -#26803 := (or #26800 #26830) -#26843 := (iff #26803 #26802) -#26837 := (or #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831) -#26805 := (or #26800 #26837) -#26847 := (iff #26805 #26802) -#26848 := [rewrite]: #26847 -#26844 := (iff #26803 #26805) -#26840 := (iff #26830 #26837) -#26834 := (or #26831 #26595 #26649 #26827 #26825 #26822 #24846 #26715) -#26838 := (iff #26834 #26837) -#26839 := [rewrite]: #26838 -#26835 := (iff #26830 #26834) -#26832 := (iff #26829 #26831) -#26833 := [rewrite]: #26832 -#26836 := [monotonicity #26833]: #26835 -#26841 := [trans #26836 #26839]: #26840 -#26846 := [monotonicity #26841]: #26844 -#26849 := [trans #26846 #26848]: #26843 -#26804 := [quant-inst #3039 #26182]: #26803 -#26845 := [mp #26804 #26849]: #26802 -#27031 := [unit-resolution #26845 #21922 #14351 #27029 #27010 #27002]: #27030 -#27032 := [unit-resolution #27031 #26980 #26973 #26974 #26936]: false -#27033 := [lemma #27032]: #12177 -#28800 := [trans #27033 #28799]: #26717 -#26724 := (or #26722 #26715 #26733) -#26751 := [def-axiom]: #26724 -#28801 := [unit-resolution #26751 #28800 #26937]: #26715 -#26797 := (or #26736 #26794) +#10153 := [monotonicity #4058 #10150]: #10152 +#10159 := [monotonicity #10153 #10156]: #10158 +#10165 := [trans #10159 #10163]: #10164 +#10168 := [quant-intro #10165]: #10167 +#10187 := [trans #10168 #10185]: #10186 +#10134 := [asserted]: #2280 +#10188 := [mp #10134 #10187]: #10183 +#17858 := [mp~ #10188 #17857]: #10183 +#21886 := [mp #17858 #21885]: #21883 +#26791 := (not #26790) +#26613 := (not #26591) +#26559 := (not #26558) +#24810 := (not #12109) +#26766 := (not #21883) +#26767 := (or #26766 #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795) +#26793 := (= #26792 f25) +#26794 := (or #26793 #26559 #26613 #26791 #26789 #26786 #24810 #26679) +#26768 := (or #26766 #26794) +#26774 := (iff #26768 #26767) +#26801 := (or #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795) +#26770 := (or #26766 #26801) +#26772 := (iff #26770 #26767) +#26773 := [rewrite]: #26772 +#26765 := (iff #26768 #26770) +#26804 := (iff #26794 #26801) +#26798 := (or #26795 #26559 #26613 #26791 #26789 #26786 #24810 #26679) +#26802 := (iff #26798 #26801) +#26803 := [rewrite]: #26802 +#26799 := (iff #26794 #26798) +#26796 := (iff #26793 #26795) +#26797 := [rewrite]: #26796 +#26800 := [monotonicity #26797]: #26799 +#26805 := [trans #26800 #26803]: #26804 +#26771 := [monotonicity #26805]: #26765 +#26775 := [trans #26771 #26773]: #26774 +#26769 := [quant-inst #3039 #26146]: #26768 +#26806 := [mp #26769 #26775]: #26767 +#26973 := [unit-resolution #26806 #21886 #14315 #26971 #26965 #26943]: #26972 +#26974 := [unit-resolution #26973 #26938 #26932 #26926 #26900]: false +#26960 := [lemma #26974]: #12141 +#23566 := (or #13264 #23563) +#22522 := (forall (vars (?v0 Int)) #22511) +#22529 := (not #22522) +#22507 := (forall (vars (?v0 Int)) #22502) +#22528 := (not #22507) +#22530 := (or #22528 #22529) +#22531 := (not #22530) +#22560 := (or #22531 #22557) +#22566 := (not #22560) +#22567 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #22566) +#22568 := (not #22567) +#22346 := (forall (vars (?v0 Int)) #22341) +#22352 := (not #22346) +#22353 := (or #22328 #22352) +#22354 := (not #22353) +#22383 := (or #22354 #22380) +#22389 := (not #22383) +#22390 := (or #13519 #22389) +#22391 := (not #22390) +#22396 := (or #13519 #22391) +#22404 := (not #22396) +#22405 := (or #12656 #22402 #18558 #22403 #13586 #18561 #22404) +#22406 := (not #22405) +#22411 := (or #18558 #18561 #22406) +#22417 := (not #22411) +#22454 := (or #12821 #12812 #22443 #13620 #22402 #13671 #22417) +#22455 := (not #22454) +#22418 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #22417) +#22419 := (not #22418) +#22424 := (or #18520 #18529 #22419) +#22430 := (not #22424) +#22431 := (or #18520 #18523 #22430) +#22432 := (not #22431) +#22437 := (or #18520 #18523 #22432) +#22444 := (not #22437) +#22445 := (or #22443 #13620 #13672 #22444) +#22446 := (not #22445) +#22460 := (or #22446 #22455) +#22466 := (not #22460) +#22467 := (or #18520 #18529 #22443 #13620 #22466) +#22468 := (not #22467) +#22473 := (or #18520 #18529 #22468) +#22479 := (not #22473) +#22480 := (or #18520 #18523 #22479) +#22481 := (not #22480) +#22486 := (or #18520 #18523 #22481) +#22492 := (not #22486) +#22493 := (or #22443 #13620 #13765 #22492) +#22494 := (not #22493) +#22573 := (or #22494 #22568) +#22588 := (not #22573) +#22323 := (forall (vars (?v0 Int)) #22318) +#22584 := (not #22323) +#22589 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #22584 #22588) +#22590 := (not #22589) +#22595 := (or #13231 #13472 #22590) +#22602 := (not #22595) +#22312 := (forall (vars (?v0 Int)) #22307) +#22601 := (not #22312) +#22603 := (or #22601 #22602) +#22604 := (not #22603) +#22609 := (or #22301 #22604) +#22615 := (not #22609) +#22616 := (or #13436 #22615) +#22617 := (not #22616) +#22622 := (or #13436 #22617) +#22628 := (not #22622) +#22629 := (or #13231 #18409 #18418 #13222 #13213 #13204 #22628) +#22630 := (not #22629) +#22635 := (or #18409 #18418 #22630) +#22641 := (not #22635) +#22642 := (or #18409 #18412 #22641) +#22643 := (not #22642) +#22648 := (or #18409 #18412 #22643) +#22654 := (not #22648) +#22655 := (or #13264 #22654) +#22656 := (not #22655) +#22661 := (or #13264 #22656) +#23567 := (iff #22661 #23566) +#23564 := (iff #22656 #23563) +#23561 := (iff #22655 #23560) +#23558 := (iff #22654 #23557) +#23555 := (iff #22648 #23554) +#23552 := (iff #22643 #23551) +#23549 := (iff #22642 #23548) +#23546 := (iff #22641 #23545) +#23543 := (iff #22635 #23542) +#23540 := (iff #22630 #23539) +#23537 := (iff #22629 #23536) +#23534 := (iff #22628 #23533) +#23531 := (iff #22622 #23530) +#23528 := (iff #22617 #23527) +#23525 := (iff #22616 #23524) +#23522 := (iff #22615 #23521) +#23519 := (iff #22609 #23518) +#23516 := (iff #22604 #23515) +#23513 := (iff #22603 #23512) +#23510 := (iff #22602 #23509) +#23507 := (iff #22595 #23506) +#23504 := (iff #22590 #23503) +#23501 := (iff #22589 #23500) +#23498 := (iff #22588 #23497) +#23495 := (iff #22573 #23494) +#23492 := (iff #22568 #23491) +#23489 := (iff #22567 #23488) +#23486 := (iff #22566 #23485) +#23483 := (iff #22560 #23482) +#23480 := (iff #22531 #23479) +#23477 := (iff #22530 #23476) +#23474 := (iff #22529 #23473) +#23471 := (iff #22522 #23468) +#23469 := (iff #22511 #22511) +#23470 := [refl]: #23469 +#23472 := [quant-intro #23470]: #23471 +#23475 := [monotonicity #23472]: #23474 +#23466 := (iff #22528 #23465) +#23463 := (iff #22507 #23460) +#23461 := (iff #22502 #22502) +#23462 := [refl]: #23461 +#23464 := [quant-intro #23462]: #23463 +#23467 := [monotonicity #23464]: #23466 +#23478 := [monotonicity #23467 #23475]: #23477 +#23481 := [monotonicity #23478]: #23480 +#23484 := [monotonicity #23481]: #23483 +#23487 := [monotonicity #23484]: #23486 +#23490 := [monotonicity #23487]: #23489 +#23493 := [monotonicity #23490]: #23492 +#23458 := (iff #22494 #23457) +#23455 := (iff #22493 #23454) +#23452 := (iff #22492 #23451) +#23449 := (iff #22486 #23448) +#23446 := (iff #22481 #23445) +#23443 := (iff #22480 #23442) +#23440 := (iff #22479 #23439) +#23437 := (iff #22473 #23436) +#23434 := (iff #22468 #23433) +#23431 := (iff #22467 #23430) +#23428 := (iff #22466 #23427) +#23425 := (iff #22460 #23424) +#23422 := (iff #22455 #23421) +#23419 := (iff #22454 #23418) +#23386 := (iff #22417 #23385) +#23383 := (iff #22411 #23382) +#23380 := (iff #22406 #23379) +#23377 := (iff #22405 #23376) +#23374 := (iff #22404 #23373) +#23371 := (iff #22396 #23370) +#23368 := (iff #22391 #23367) +#23365 := (iff #22390 #23364) +#23362 := (iff #22389 #23361) +#23359 := (iff #22383 #23358) +#23356 := (iff #22354 #23355) +#23353 := (iff #22353 #23352) +#23350 := (iff #22352 #23349) +#23347 := (iff #22346 #23344) +#23345 := (iff #22341 #22341) +#23346 := [refl]: #23345 +#23348 := [quant-intro #23346]: #23347 +#23351 := [monotonicity #23348]: #23350 +#23354 := [monotonicity #23351]: #23353 +#23357 := [monotonicity #23354]: #23356 +#23360 := [monotonicity #23357]: #23359 +#23363 := [monotonicity #23360]: #23362 +#23366 := [monotonicity #23363]: #23365 +#23369 := [monotonicity #23366]: #23368 +#23372 := [monotonicity #23369]: #23371 +#23375 := [monotonicity #23372]: #23374 +#23378 := [monotonicity #23375]: #23377 +#23381 := [monotonicity #23378]: #23380 +#23384 := [monotonicity #23381]: #23383 +#23387 := [monotonicity #23384]: #23386 +#23420 := [monotonicity #23387]: #23419 +#23423 := [monotonicity #23420]: #23422 +#23416 := (iff #22446 #23415) +#23413 := (iff #22445 #23412) +#23410 := (iff #22444 #23409) +#23407 := (iff #22437 #23406) +#23404 := (iff #22432 #23403) +#23401 := (iff #22431 #23400) +#23398 := (iff #22430 #23397) +#23395 := (iff #22424 #23394) +#23392 := (iff #22419 #23391) +#23389 := (iff #22418 #23388) +#23390 := [monotonicity #23387]: #23389 +#23393 := [monotonicity #23390]: #23392 +#23396 := [monotonicity #23393]: #23395 +#23399 := [monotonicity #23396]: #23398 +#23402 := [monotonicity #23399]: #23401 +#23405 := [monotonicity #23402]: #23404 +#23408 := [monotonicity #23405]: #23407 +#23411 := [monotonicity #23408]: #23410 +#23414 := [monotonicity #23411]: #23413 +#23417 := [monotonicity #23414]: #23416 +#23426 := [monotonicity #23417 #23423]: #23425 +#23429 := [monotonicity #23426]: #23428 +#23432 := [monotonicity #23429]: #23431 +#23435 := [monotonicity #23432]: #23434 +#23438 := [monotonicity #23435]: #23437 +#23441 := [monotonicity #23438]: #23440 +#23444 := [monotonicity #23441]: #23443 +#23447 := [monotonicity #23444]: #23446 +#23450 := [monotonicity #23447]: #23449 +#23453 := [monotonicity #23450]: #23452 +#23456 := [monotonicity #23453]: #23455 +#23459 := [monotonicity #23456]: #23458 +#23496 := [monotonicity #23459 #23493]: #23495 +#23499 := [monotonicity #23496]: #23498 +#23342 := (iff #22584 #23341) +#23339 := (iff #22323 #23336) +#23337 := (iff #22318 #22318) +#23338 := [refl]: #23337 +#23340 := [quant-intro #23338]: #23339 +#23343 := [monotonicity #23340]: #23342 +#23502 := [monotonicity #23343 #23499]: #23501 +#23505 := [monotonicity #23502]: #23504 +#23508 := [monotonicity #23505]: #23507 +#23511 := [monotonicity #23508]: #23510 +#23334 := (iff #22601 #23333) +#23331 := (iff #22312 #23328) +#23329 := (iff #22307 #22307) +#23330 := [refl]: #23329 +#23332 := [quant-intro #23330]: #23331 +#23335 := [monotonicity #23332]: #23334 +#23514 := [monotonicity #23335 #23511]: #23513 +#23517 := [monotonicity #23514]: #23516 +#23520 := [monotonicity #23517]: #23519 +#23523 := [monotonicity #23520]: #23522 +#23526 := [monotonicity #23523]: #23525 +#23529 := [monotonicity #23526]: #23528 +#23532 := [monotonicity #23529]: #23531 +#23535 := [monotonicity #23532]: #23534 +#23538 := [monotonicity #23535]: #23537 +#23541 := [monotonicity #23538]: #23540 +#23544 := [monotonicity #23541]: #23543 +#23547 := [monotonicity #23544]: #23546 +#23550 := [monotonicity #23547]: #23549 +#23553 := [monotonicity #23550]: #23552 +#23556 := [monotonicity #23553]: #23555 +#23559 := [monotonicity #23556]: #23558 +#23562 := [monotonicity #23559]: #23561 +#23565 := [monotonicity #23562]: #23564 +#23568 := [monotonicity #23565]: #23567 +#19060 := (and #18703 #18704) +#19063 := (not #19060) +#19066 := (or #19042 #19055 #19063) +#19069 := (not #19066) +#15985 := (and #3173 #4202 #13795 #15183) +#18726 := (not #15985) +#18729 := (forall (vars (?v0 Int)) #18726) +#14426 := (and #4202 #15183) +#14425 := (not #14426) +#15971 := (or #13793 #13807 #14425) +#15976 := (forall (vars (?v0 Int)) #15971) +#18733 := (and #15976 #18729) +#19075 := (or #18733 #19069) +#19083 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #19075) +#18912 := (and #18579 #18580) +#18915 := (not #18912) +#18918 := (or #18894 #18907 #18915) +#18921 := (not #18918) +#15872 := (or #13522 #13536 #14425) +#15877 := (forall (vars (?v0 Int)) #15872) +#18595 := (not #13565) +#18605 := (and #18595 #15877) +#18927 := (or #18605 #18921) +#18932 := (and #13514 #18927) +#18935 := (or #13519 #18932) +#18943 := (and #12586 #13489 #13498 #13506 #13582 #15864 #18935) +#18948 := (or #18558 #18561 #18943) +#18988 := (and #12803 #12806 #13477 #13480 #13489 #13672 #18948) +#18954 := (and #12539 #12548 #12554 #12557 #12560 #12565 #12568 #13480 #13489 #18948) +#18959 := (or #18520 #18529 #18954) +#18965 := (and #12539 #12542 #18959) +#18970 := (or #18520 #18523 #18965) +#18976 := (and #13477 #13480 #13671 #18970) +#18993 := (or #18976 #18988) +#18999 := (and #12539 #12548 #13477 #13480 #18993) +#19004 := (or #18520 #18529 #18999) +#19010 := (and #12539 #12542 #19004) +#19015 := (or #18520 #18523 #19010) +#19021 := (and #13477 #13480 #13766 #19015) +#19088 := (or #19021 #19083) +#15798 := (or #13958 #13972 #14425) +#15803 := (forall (vars (?v0 Int)) #15798) +#19094 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #15803 #15815 #15832 #15849 #19088) +#19099 := (or #13231 #13472 #19094) +#15784 := (or #13439 #13451 #14425) +#15789 := (forall (vars (?v0 Int)) #15784) +#19102 := (and #15789 #19099) +#18815 := (and #18442 #18443) +#18818 := (not #18815) +#18824 := (or #18450 #18451 #18818) +#18829 := (not #18824) +#19105 := (or #18829 #19102) +#19108 := (and #13433 #19105) +#19111 := (or #13436 #19108) +#19117 := (and #3109 #12144 #12153 #12159 #12162 #12165 #19111) +#19122 := (or #18409 #18418 #19117) +#19128 := (and #12144 #12147 #19122) +#19133 := (or #18409 #18412 #19128) +#19136 := (and #12141 #19133) +#19139 := (or #13264 #19136) +#22662 := (iff #19139 #22661) +#22659 := (iff #19136 #22656) +#22651 := (and #12141 #22648) +#22657 := (iff #22651 #22656) +#22658 := [rewrite]: #22657 +#22652 := (iff #19136 #22651) +#22649 := (iff #19133 #22648) +#22646 := (iff #19128 #22643) +#22638 := (and #12144 #12147 #22635) +#22644 := (iff #22638 #22643) +#22645 := [rewrite]: #22644 +#22639 := (iff #19128 #22638) +#22636 := (iff #19122 #22635) +#22633 := (iff #19117 #22630) +#22625 := (and #3109 #12144 #12153 #12159 #12162 #12165 #22622) +#22631 := (iff #22625 #22630) +#22632 := [rewrite]: #22631 +#22626 := (iff #19117 #22625) +#22623 := (iff #19111 #22622) +#22620 := (iff #19108 #22617) +#22612 := (and #13433 #22609) +#22618 := (iff #22612 #22617) +#22619 := [rewrite]: #22618 +#22613 := (iff #19108 #22612) +#22610 := (iff #19105 #22609) +#22607 := (iff #19102 #22604) +#22598 := (and #22312 #22595) +#22605 := (iff #22598 #22604) +#22606 := [rewrite]: #22605 +#22599 := (iff #19102 #22598) +#22596 := (iff #19099 #22595) +#22593 := (iff #19094 #22590) +#22576 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #22323 #15815 #15832 #15849 #22573) +#22591 := (iff #22576 #22590) +#22592 := [rewrite]: #22591 +#22577 := (iff #19094 #22576) +#22574 := (iff #19088 #22573) +#22571 := (iff #19083 #22568) +#22563 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #22560) +#22569 := (iff #22563 #22568) +#22570 := [rewrite]: #22569 +#22564 := (iff #19083 #22563) +#22561 := (iff #19075 #22560) +#22558 := (iff #19069 #22557) +#22555 := (iff #19066 #22552) +#22538 := (or #22536 #22537) +#22549 := (or #19042 #19055 #22538) +#22553 := (iff #22549 #22552) +#22554 := [rewrite]: #22553 +#22550 := (iff #19066 #22549) +#22547 := (iff #19063 #22538) +#22539 := (not #22538) +#22542 := (not #22539) +#22545 := (iff #22542 #22538) +#22546 := [rewrite]: #22545 +#22543 := (iff #19063 #22542) +#22540 := (iff #19060 #22539) +#22541 := [rewrite]: #22540 +#22544 := [monotonicity #22541]: #22543 +#22548 := [trans #22544 #22546]: #22547 +#22551 := [monotonicity #22548]: #22550 +#22556 := [trans #22551 #22554]: #22555 +#22559 := [monotonicity #22556]: #22558 +#22534 := (iff #18733 #22531) +#22525 := (and #22507 #22522) +#22532 := (iff #22525 #22531) +#22533 := [rewrite]: #22532 +#22526 := (iff #18733 #22525) +#22523 := (iff #18729 #22522) +#22520 := (iff #18726 #22511) +#22512 := (not #22511) +#22515 := (not #22512) +#22518 := (iff #22515 #22511) +#22519 := [rewrite]: #22518 +#22516 := (iff #18726 #22515) +#22513 := (iff #15985 #22512) +#22514 := [rewrite]: #22513 +#22517 := [monotonicity #22514]: #22516 +#22521 := [trans #22517 #22519]: #22520 +#22524 := [quant-intro #22521]: #22523 +#22508 := (iff #15976 #22507) +#22505 := (iff #15971 #22502) +#20215 := (or #5104 #19577) +#22499 := (or #13793 #13807 #20215) +#22503 := (iff #22499 #22502) +#22504 := [rewrite]: #22503 +#22500 := (iff #15971 #22499) +#20224 := (iff #14425 #20215) +#20216 := (not #20215) +#20219 := (not #20216) +#20222 := (iff #20219 #20215) +#20223 := [rewrite]: #20222 +#20220 := (iff #14425 #20219) +#20217 := (iff #14426 #20216) +#20218 := [rewrite]: #20217 +#20221 := [monotonicity #20218]: #20220 +#20225 := [trans #20221 #20223]: #20224 +#22501 := [monotonicity #20225]: #22500 +#22506 := [trans #22501 #22504]: #22505 +#22509 := [quant-intro #22506]: #22508 +#22527 := [monotonicity #22509 #22524]: #22526 +#22535 := [trans #22527 #22533]: #22534 +#22562 := [monotonicity #22535 #22559]: #22561 +#22565 := [monotonicity #22562]: #22564 +#22572 := [trans #22565 #22570]: #22571 +#22497 := (iff #19021 #22494) +#22489 := (and #13477 #13480 #13766 #22486) +#22495 := (iff #22489 #22494) +#22496 := [rewrite]: #22495 +#22490 := (iff #19021 #22489) +#22487 := (iff #19015 #22486) +#22484 := (iff #19010 #22481) +#22476 := (and #12539 #12542 #22473) +#22482 := (iff #22476 #22481) +#22483 := [rewrite]: #22482 +#22477 := (iff #19010 #22476) +#22474 := (iff #19004 #22473) +#22471 := (iff #18999 #22468) +#22463 := (and #12539 #12548 #13477 #13480 #22460) +#22469 := (iff #22463 #22468) +#22470 := [rewrite]: #22469 +#22464 := (iff #18999 #22463) +#22461 := (iff #18993 #22460) +#22458 := (iff #18988 #22455) +#22451 := (and #12803 #12806 #13477 #13480 #13489 #13672 #22411) +#22456 := (iff #22451 #22455) +#22457 := [rewrite]: #22456 +#22452 := (iff #18988 #22451) +#22412 := (iff #18948 #22411) +#22409 := (iff #18943 #22406) +#22399 := (and #12586 #13489 #13498 #13506 #13582 #15864 #22396) +#22407 := (iff #22399 #22406) +#22408 := [rewrite]: #22407 +#22400 := (iff #18943 #22399) +#22397 := (iff #18935 #22396) +#22394 := (iff #18932 #22391) +#22386 := (and #13514 #22383) +#22392 := (iff #22386 #22391) +#22393 := [rewrite]: #22392 +#22387 := (iff #18932 #22386) +#22384 := (iff #18927 #22383) +#22381 := (iff #18921 #22380) +#22378 := (iff #18918 #22375) +#22361 := (or #22359 #22360) +#22372 := (or #18894 #18907 #22361) +#22376 := (iff #22372 #22375) +#22377 := [rewrite]: #22376 +#22373 := (iff #18918 #22372) +#22370 := (iff #18915 #22361) +#22362 := (not #22361) +#22365 := (not #22362) +#22368 := (iff #22365 #22361) +#22369 := [rewrite]: #22368 +#22366 := (iff #18915 #22365) +#22363 := (iff #18912 #22362) +#22364 := [rewrite]: #22363 +#22367 := [monotonicity #22364]: #22366 +#22371 := [trans #22367 #22369]: #22370 +#22374 := [monotonicity #22371]: #22373 +#22379 := [trans #22374 #22377]: #22378 +#22382 := [monotonicity #22379]: #22381 +#22357 := (iff #18605 #22354) +#22349 := (and #22327 #22346) +#22355 := (iff #22349 #22354) +#22356 := [rewrite]: #22355 +#22350 := (iff #18605 #22349) +#22347 := (iff #15877 #22346) +#22344 := (iff #15872 #22341) +#22338 := (or #13522 #13536 #20215) +#22342 := (iff #22338 #22341) +#22343 := [rewrite]: #22342 +#22339 := (iff #15872 #22338) +#22340 := [monotonicity #20225]: #22339 +#22345 := [trans #22340 #22343]: #22344 +#22348 := [quant-intro #22345]: #22347 +#22336 := (iff #18595 #22327) +#22331 := (not #22328) +#22334 := (iff #22331 #22327) +#22335 := [rewrite]: #22334 +#22332 := (iff #18595 #22331) +#22329 := (iff #13565 #22328) +#22330 := [rewrite]: #22329 +#22333 := [monotonicity #22330]: #22332 +#22337 := [trans #22333 #22335]: #22336 +#22351 := [monotonicity #22337 #22348]: #22350 +#22358 := [trans #22351 #22356]: #22357 +#22385 := [monotonicity #22358 #22382]: #22384 +#22388 := [monotonicity #22385]: #22387 +#22395 := [trans #22388 #22393]: #22394 +#22398 := [monotonicity #22395]: #22397 +#22401 := [monotonicity #22398]: #22400 +#22410 := [trans #22401 #22408]: #22409 +#22413 := [monotonicity #22410]: #22412 +#22453 := [monotonicity #22413]: #22452 +#22459 := [trans #22453 #22457]: #22458 +#22449 := (iff #18976 #22446) +#22440 := (and #13477 #13480 #13671 #22437) +#22447 := (iff #22440 #22446) +#22448 := [rewrite]: #22447 +#22441 := (iff #18976 #22440) +#22438 := (iff #18970 #22437) +#22435 := (iff #18965 #22432) +#22427 := (and #12539 #12542 #22424) +#22433 := (iff #22427 #22432) +#22434 := [rewrite]: #22433 +#22428 := (iff #18965 #22427) +#22425 := (iff #18959 #22424) +#22422 := (iff #18954 #22419) +#22414 := (and #12539 #12548 #12554 #12557 #12560 #12565 #12568 #13480 #13489 #22411) +#22420 := (iff #22414 #22419) +#22421 := [rewrite]: #22420 +#22415 := (iff #18954 #22414) +#22416 := [monotonicity #22413]: #22415 +#22423 := [trans #22416 #22421]: #22422 +#22426 := [monotonicity #22423]: #22425 +#22429 := [monotonicity #22426]: #22428 +#22436 := [trans #22429 #22434]: #22435 +#22439 := [monotonicity #22436]: #22438 +#22442 := [monotonicity #22439]: #22441 +#22450 := [trans #22442 #22448]: #22449 +#22462 := [monotonicity #22450 #22459]: #22461 +#22465 := [monotonicity #22462]: #22464 +#22472 := [trans #22465 #22470]: #22471 +#22475 := [monotonicity #22472]: #22474 +#22478 := [monotonicity #22475]: #22477 +#22485 := [trans #22478 #22483]: #22484 +#22488 := [monotonicity #22485]: #22487 +#22491 := [monotonicity #22488]: #22490 +#22498 := [trans #22491 #22496]: #22497 +#22575 := [monotonicity #22498 #22572]: #22574 +#22324 := (iff #15803 #22323) +#22321 := (iff #15798 #22318) +#22315 := (or #13958 #13972 #20215) +#22319 := (iff #22315 #22318) +#22320 := [rewrite]: #22319 +#22316 := (iff #15798 #22315) +#22317 := [monotonicity #20225]: #22316 +#22322 := [trans #22317 #22320]: #22321 +#22325 := [quant-intro #22322]: #22324 +#22578 := [monotonicity #22325 #22575]: #22577 +#22594 := [trans #22578 #22592]: #22593 +#22597 := [monotonicity #22594]: #22596 +#22313 := (iff #15789 #22312) +#22310 := (iff #15784 #22307) +#22304 := (or #13439 #13451 #20215) +#22308 := (iff #22304 #22307) +#22309 := [rewrite]: #22308 +#22305 := (iff #15784 #22304) +#22306 := [monotonicity #20225]: #22305 +#22311 := [trans #22306 #22309]: #22310 +#22314 := [quant-intro #22311]: #22313 +#22600 := [monotonicity #22314 #22597]: #22599 +#22608 := [trans #22600 #22606]: #22607 +#22302 := (iff #18829 #22301) +#22299 := (iff #18824 #22296) +#22282 := (or #22280 #22281) +#22293 := (or #18450 #18451 #22282) +#22297 := (iff #22293 #22296) +#22298 := [rewrite]: #22297 +#22294 := (iff #18824 #22293) +#22291 := (iff #18818 #22282) +#22283 := (not #22282) +#22286 := (not #22283) +#22289 := (iff #22286 #22282) +#22290 := [rewrite]: #22289 +#22287 := (iff #18818 #22286) +#22284 := (iff #18815 #22283) +#22285 := [rewrite]: #22284 +#22288 := [monotonicity #22285]: #22287 +#22292 := [trans #22288 #22290]: #22291 +#22295 := [monotonicity #22292]: #22294 +#22300 := [trans #22295 #22298]: #22299 +#22303 := [monotonicity #22300]: #22302 +#22611 := [monotonicity #22303 #22608]: #22610 +#22614 := [monotonicity #22611]: #22613 +#22621 := [trans #22614 #22619]: #22620 +#22624 := [monotonicity #22621]: #22623 +#22627 := [monotonicity #22624]: #22626 +#22634 := [trans #22627 #22632]: #22633 +#22637 := [monotonicity #22634]: #22636 +#22640 := [monotonicity #22637]: #22639 +#22647 := [trans #22640 #22645]: #22646 +#22650 := [monotonicity #22647]: #22649 +#22653 := [monotonicity #22650]: #22652 +#22660 := [trans #22653 #22658]: #22659 +#22663 := [monotonicity #22660]: #22662 +#18705 := (and #18704 #18703) +#18706 := (not #18705) +#18709 := (+ #18708 #13805) +#18710 := (<= #18709 0::Int) +#18711 := (+ ?v0!15 #13406) +#18712 := (>= #18711 0::Int) +#18713 := (or #18712 #18710 #18706) +#18714 := (not #18713) +#18737 := (or #18714 #18733) +#18490 := (not #13485) +#18697 := (not #12277) +#18694 := (not #12286) +#18691 := (not #12295) +#18688 := (not #12304) +#18741 := (and #18688 #18691 #18694 #18697 #18490 #13769 #18737) +#15900 := (and #13498 #15864) +#15903 := (not #15900) +#18621 := (not #15903) +#18581 := (and #18580 #18579) +#18582 := (not #18581) +#18585 := (+ #18584 #13534) +#18586 := (<= #18585 0::Int) +#18587 := (+ ?v0!14 #13515) +#18588 := (>= #18587 0::Int) +#18589 := (or #18588 #18586 #18582) +#18590 := (not #18589) +#18609 := (or #18590 #18605) +#18575 := (not #13519) +#18613 := (and #18575 #18609) +#18617 := (or #13519 #18613) +#18570 := (not #13586) +#18567 := (not #13511) +#18564 := (not #12656) +#18624 := (and #18564 #18567 #18570 #18617 #18621) +#18628 := (or #18558 #18561 #18624) +#18555 := (not #13494) +#18655 := (not #12812) +#18652 := (not #12821) +#18660 := (and #18652 #18655 #18490 #18555 #13677 #18628) +#18552 := (not #13620) +#18549 := (not #12695) +#18546 := (not #12704) +#18543 := (not #12722) +#18540 := (not #12731) +#18537 := (not #12740) +#18532 := (not #12749) +#18632 := (and #18532 #18537 #18540 #18543 #18546 #18549 #18552 #18555 #18628) +#18636 := (or #18520 #18529 #18632) +#18526 := (not #12761) +#18640 := (and #18526 #18636) +#18644 := (or #18520 #18523 #18640) +#18648 := (and #18490 #13671 #18644) +#18664 := (or #18648 #18660) +#18668 := (and #18532 #18490 #18664) +#18672 := (or #18520 #18529 #18668) +#18676 := (and #18526 #18672) +#18680 := (or #18520 #18523 #18676) +#18684 := (and #18490 #13766 #18680) +#18745 := (or #18684 #18741) +#15854 := (and #14020 #15849) +#15857 := (not #15854) +#18515 := (not #15857) +#15837 := (and #13477 #15832) +#15840 := (not #15837) +#18512 := (not #15840) +#15820 := (and #13998 #15815) +#15823 := (not #15820) +#18509 := (not #15823) +#18499 := (not #14041) +#18496 := (not #13995) +#18493 := (not #13955) +#18487 := (not #12988) +#18484 := (not #12997) +#18481 := (not #13006) +#18478 := (not #13015) +#18475 := (not #13024) +#18472 := (not #13938) +#18469 := (not #15263) +#18749 := (and #18469 #18472 #18475 #18478 #18481 #18484 #18487 #18490 #18493 #18496 #18499 #15803 #18509 #18512 #18515 #18745) +#18753 := (or #13231 #14198 #18749) +#18757 := (and #15789 #18753) +#18444 := (and #18443 #18442) +#18445 := (not #18444) +#18452 := (or #18451 #18450 #18445) +#18453 := (not #18452) +#18761 := (or #18453 #18757) +#18438 := (not #13436) +#18765 := (and #18438 #18761) +#18769 := (or #13436 #18765) +#18433 := (not #13204) +#18430 := (not #13213) +#18427 := (not #13222) +#18424 := (not #13240) +#18421 := (not #13231) +#18773 := (and #18421 #18424 #18427 #18430 #18433 #18769) +#18777 := (or #18409 #18418 #18773) +#18415 := (not #13252) +#18781 := (and #18415 #18777) +#18785 := (or #18409 #18412 #18781) +#18406 := (not #13264) +#18789 := (and #18406 #18785) +#18793 := (or #13264 #18789) +#19140 := (iff #18793 #19139) +#19137 := (iff #18789 #19136) +#19134 := (iff #18785 #19133) +#19131 := (iff #18781 #19128) +#19125 := (and #12150 #19122) +#19129 := (iff #19125 #19128) +#19130 := [rewrite]: #19129 +#19126 := (iff #18781 #19125) +#19123 := (iff #18777 #19122) +#19120 := (iff #18773 #19117) +#19114 := (and #3109 #12156 #12159 #12162 #12165 #19111) +#19118 := (iff #19114 #19117) +#19119 := [rewrite]: #19118 +#19115 := (iff #18773 #19114) +#19112 := (iff #18769 #19111) +#19109 := (iff #18765 #19108) +#19106 := (iff #18761 #19105) +#19103 := (iff #18757 #19102) +#19100 := (iff #18753 #19099) +#19097 := (iff #18749 #19094) +#19091 := (and #12222 #12479 #12507 #12510 #12513 #12516 #12525 #13482 #13950 #13992 #14036 #15803 #15820 #15837 #15854 #19088) +#19095 := (iff #19091 #19094) +#19096 := [rewrite]: #19095 +#19092 := (iff #18749 #19091) +#19089 := (iff #18745 #19088) +#19086 := (iff #18741 #19083) +#19080 := (and #12233 #12236 #12239 #12242 #13482 #13765 #19075) +#19084 := (iff #19080 #19083) +#19085 := [rewrite]: #19084 +#19081 := (iff #18741 #19080) +#19078 := (iff #18737 #19075) +#19072 := (or #19069 #18733) +#19076 := (iff #19072 #19075) +#19077 := [rewrite]: #19076 +#19073 := (iff #18737 #19072) +#19070 := (iff #18714 #19069) +#19067 := (iff #18713 #19066) +#19064 := (iff #18706 #19063) +#19061 := (iff #18705 #19060) +#19062 := [rewrite]: #19061 +#19065 := [monotonicity #19062]: #19064 +#19058 := (iff #18710 #19055) +#19047 := (+ #13805 #18708) +#19050 := (<= #19047 0::Int) +#19056 := (iff #19050 #19055) +#19057 := [rewrite]: #19056 +#19051 := (iff #18710 #19050) +#19048 := (= #18709 #19047) +#19049 := [rewrite]: #19048 +#19052 := [monotonicity #19049]: #19051 +#19059 := [trans #19052 #19057]: #19058 +#19045 := (iff #18712 #19042) +#19034 := (+ #13406 ?v0!15) +#19037 := (>= #19034 0::Int) +#19043 := (iff #19037 #19042) +#19044 := [rewrite]: #19043 +#19038 := (iff #18712 #19037) +#19035 := (= #18711 #19034) +#19036 := [rewrite]: #19035 +#19039 := [monotonicity #19036]: #19038 +#19046 := [trans #19039 #19044]: #19045 +#19068 := [monotonicity #19046 #19059 #19065]: #19067 +#19071 := [monotonicity #19068]: #19070 +#19074 := [monotonicity #19071]: #19073 +#19079 := [trans #19074 #19077]: #19078 +#18846 := (iff #18490 #13482) +#18847 := [rewrite]: #18846 +#19032 := (iff #18697 #12242) +#19033 := [rewrite]: #19032 +#19030 := (iff #18694 #12239) +#19031 := [rewrite]: #19030 +#19028 := (iff #18691 #12236) +#19029 := [rewrite]: #19028 +#19026 := (iff #18688 #12233) +#19027 := [rewrite]: #19026 +#19082 := [monotonicity #19027 #19029 #19031 #19033 #18847 #13773 #19079]: #19081 +#19087 := [trans #19082 #19085]: #19086 +#19024 := (iff #18684 #19021) +#19018 := (and #13482 #13766 #19015) +#19022 := (iff #19018 #19021) +#19023 := [rewrite]: #19022 +#19019 := (iff #18684 #19018) +#19016 := (iff #18680 #19015) +#19013 := (iff #18676 #19010) +#19007 := (and #12545 #19004) +#19011 := (iff #19007 #19010) +#19012 := [rewrite]: #19011 +#19008 := (iff #18676 #19007) +#19005 := (iff #18672 #19004) +#19002 := (iff #18668 #18999) +#18996 := (and #12551 #13482 #18993) +#19000 := (iff #18996 #18999) +#19001 := [rewrite]: #19000 +#18997 := (iff #18668 #18996) +#18994 := (iff #18664 #18993) +#18991 := (iff #18660 #18988) +#18985 := (and #12803 #12806 #13482 #13491 #13672 #18948) +#18989 := (iff #18985 #18988) +#18990 := [rewrite]: #18989 +#18986 := (iff #18660 #18985) +#18949 := (iff #18628 #18948) +#18946 := (iff #18624 #18943) +#18940 := (and #12586 #13508 #13582 #18935 #15900) +#18944 := (iff #18940 #18943) +#18945 := [rewrite]: #18944 +#18941 := (iff #18624 #18940) +#18938 := (iff #18621 #15900) +#18939 := [rewrite]: #18938 +#18936 := (iff #18617 #18935) +#18933 := (iff #18613 #18932) +#18930 := (iff #18609 #18927) +#18924 := (or #18921 #18605) +#18928 := (iff #18924 #18927) +#18929 := [rewrite]: #18928 +#18925 := (iff #18609 #18924) +#18922 := (iff #18590 #18921) +#18919 := (iff #18589 #18918) +#18916 := (iff #18582 #18915) +#18913 := (iff #18581 #18912) +#18914 := [rewrite]: #18913 +#18917 := [monotonicity #18914]: #18916 +#18910 := (iff #18586 #18907) +#18899 := (+ #13534 #18584) +#18902 := (<= #18899 0::Int) +#18908 := (iff #18902 #18907) +#18909 := [rewrite]: #18908 +#18903 := (iff #18586 #18902) +#18900 := (= #18585 #18899) +#18901 := [rewrite]: #18900 +#18904 := [monotonicity #18901]: #18903 +#18911 := [trans #18904 #18909]: #18910 +#18897 := (iff #18588 #18894) +#18886 := (+ #13515 ?v0!14) +#18889 := (>= #18886 0::Int) +#18895 := (iff #18889 #18894) +#18896 := [rewrite]: #18895 +#18890 := (iff #18588 #18889) +#18887 := (= #18587 #18886) +#18888 := [rewrite]: #18887 +#18891 := [monotonicity #18888]: #18890 +#18898 := [trans #18891 #18896]: #18897 +#18920 := [monotonicity #18898 #18911 #18917]: #18919 +#18923 := [monotonicity #18920]: #18922 +#18926 := [monotonicity #18923]: #18925 +#18931 := [trans #18926 #18929]: #18930 +#18884 := (iff #18575 #13514) +#18885 := [rewrite]: #18884 +#18934 := [monotonicity #18885 #18931]: #18933 +#18937 := [monotonicity #18934]: #18936 +#18882 := (iff #18570 #13582) +#18883 := [rewrite]: #18882 +#18880 := (iff #18567 #13508) +#18881 := [rewrite]: #18880 +#18878 := (iff #18564 #12586) +#18879 := [rewrite]: #18878 +#18942 := [monotonicity #18879 #18881 #18883 #18937 #18939]: #18941 +#18947 := [trans #18942 #18945]: #18946 +#18950 := [monotonicity #18947]: #18949 +#18876 := (iff #18555 #13491) +#18877 := [rewrite]: #18876 +#18983 := (iff #18655 #12806) +#18984 := [rewrite]: #18983 +#18981 := (iff #18652 #12803) +#18982 := [rewrite]: #18981 +#18987 := [monotonicity #18982 #18984 #18847 #18877 #13681 #18950]: #18986 +#18992 := [trans #18987 #18990]: #18991 +#18979 := (iff #18648 #18976) +#18973 := (and #13482 #13671 #18970) +#18977 := (iff #18973 #18976) +#18978 := [rewrite]: #18977 +#18974 := (iff #18648 #18973) +#18971 := (iff #18644 #18970) +#18968 := (iff #18640 #18965) +#18962 := (and #12545 #18959) +#18966 := (iff #18962 #18965) +#18967 := [rewrite]: #18966 +#18963 := (iff #18640 #18962) +#18960 := (iff #18636 #18959) +#18957 := (iff #18632 #18954) +#18951 := (and #12551 #12554 #12557 #12560 #12565 #12568 #13480 #13491 #18948) +#18955 := (iff #18951 #18954) +#18956 := [rewrite]: #18955 +#18952 := (iff #18632 #18951) +#18874 := (iff #18552 #13480) +#18875 := [rewrite]: #18874 +#18872 := (iff #18549 #12568) +#18873 := [rewrite]: #18872 +#18870 := (iff #18546 #12565) +#18871 := [rewrite]: #18870 +#18868 := (iff #18543 #12560) +#18869 := [rewrite]: #18868 +#18866 := (iff #18540 #12557) +#18867 := [rewrite]: #18866 +#18864 := (iff #18537 #12554) +#18865 := [rewrite]: #18864 +#18862 := (iff #18532 #12551) +#18863 := [rewrite]: #18862 +#18953 := [monotonicity #18863 #18865 #18867 #18869 #18871 #18873 #18875 #18877 #18950]: #18952 +#18958 := [trans #18953 #18956]: #18957 +#18961 := [monotonicity #18958]: #18960 +#18860 := (iff #18526 #12545) +#18861 := [rewrite]: #18860 +#18964 := [monotonicity #18861 #18961]: #18963 +#18969 := [trans #18964 #18967]: #18968 +#18972 := [monotonicity #18969]: #18971 +#18975 := [monotonicity #18847 #18972]: #18974 +#18980 := [trans #18975 #18978]: #18979 +#18995 := [monotonicity #18980 #18992]: #18994 +#18998 := [monotonicity #18863 #18847 #18995]: #18997 +#19003 := [trans #18998 #19001]: #19002 +#19006 := [monotonicity #19003]: #19005 +#19009 := [monotonicity #18861 #19006]: #19008 +#19014 := [trans #19009 #19012]: #19013 +#19017 := [monotonicity #19014]: #19016 +#19020 := [monotonicity #18847 #19017]: #19019 +#19025 := [trans #19020 #19023]: #19024 +#19090 := [monotonicity #19025 #19087]: #19089 +#18858 := (iff #18515 #15854) +#18859 := [rewrite]: #18858 +#18856 := (iff #18512 #15837) +#18857 := [rewrite]: #18856 +#18854 := (iff #18509 #15820) +#18855 := [rewrite]: #18854 +#18852 := (iff #18499 #14036) +#18853 := [rewrite]: #18852 +#18850 := (iff #18496 #13992) +#18851 := [rewrite]: #18850 +#18848 := (iff #18493 #13950) +#18849 := [rewrite]: #18848 +#18844 := (iff #18487 #12525) +#18845 := [rewrite]: #18844 +#18842 := (iff #18484 #12516) +#18843 := [rewrite]: #18842 +#18840 := (iff #18481 #12513) +#18841 := [rewrite]: #18840 +#18838 := (iff #18478 #12510) +#18839 := [rewrite]: #18838 +#18836 := (iff #18475 #12507) +#18837 := [rewrite]: #18836 +#18834 := (iff #18472 #12479) +#18835 := [rewrite]: #18834 +#18832 := (iff #18469 #12222) +#18833 := [rewrite]: #18832 +#19093 := [monotonicity #18833 #18835 #18837 #18839 #18841 #18843 #18845 #18847 #18849 #18851 #18853 #18855 #18857 #18859 #19090]: #19092 +#19098 := [trans #19093 #19096]: #19097 +#19101 := [monotonicity #14202 #19098]: #19100 +#19104 := [monotonicity #19101]: #19103 +#18830 := (iff #18453 #18829) +#18827 := (iff #18452 #18824) +#18821 := (or #18451 #18450 #18818) +#18825 := (iff #18821 #18824) +#18826 := [rewrite]: #18825 +#18822 := (iff #18452 #18821) +#18819 := (iff #18445 #18818) +#18816 := (iff #18444 #18815) +#18817 := [rewrite]: #18816 +#18820 := [monotonicity #18817]: #18819 +#18823 := [monotonicity #18820]: #18822 +#18828 := [trans #18823 #18826]: #18827 +#18831 := [monotonicity #18828]: #18830 +#19107 := [monotonicity #18831 #19104]: #19106 +#18813 := (iff #18438 #13433) +#18814 := [rewrite]: #18813 +#19110 := [monotonicity #18814 #19107]: #19109 +#19113 := [monotonicity #19110]: #19112 +#18811 := (iff #18433 #12165) +#18812 := [rewrite]: #18811 +#18809 := (iff #18430 #12162) +#18810 := [rewrite]: #18809 +#18807 := (iff #18427 #12159) +#18808 := [rewrite]: #18807 +#18805 := (iff #18424 #12156) +#18806 := [rewrite]: #18805 +#18803 := (iff #18421 #3109) +#18804 := [rewrite]: #18803 +#19116 := [monotonicity #18804 #18806 #18808 #18810 #18812 #19113]: #19115 +#19121 := [trans #19116 #19119]: #19120 +#19124 := [monotonicity #19121]: #19123 +#18801 := (iff #18415 #12150) +#18802 := [rewrite]: #18801 +#19127 := [monotonicity #18802 #19124]: #19126 +#19132 := [trans #19127 #19130]: #19131 +#19135 := [monotonicity #19132]: #19134 +#18799 := (iff #18406 #12141) +#18800 := [rewrite]: #18799 +#19138 := [monotonicity #18800 #19135]: #19137 +#19141 := [monotonicity #19138]: #19140 +#15990 := (exists (vars (?v0 Int)) #15985) +#15979 := (not #15976) +#15993 := (or #15979 #15990) +#15996 := (and #15976 #15993) +#15999 := (or #12304 #12295 #12286 #12277 #13485 #13766 #15996) +#15880 := (not #15877) +#15886 := (or #13565 #15880) +#15891 := (and #15877 #15886) +#15894 := (or #13519 #15891) +#15897 := (and #13514 #15894) +#15909 := (or #12656 #13511 #13586 #15897 #15903) +#15914 := (and #13498 #15864 #15909) +#15940 := (or #12821 #12812 #13485 #13494 #13671 #15914) +#15917 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #15914) +#15920 := (and #12539 #12548 #15917) +#15923 := (or #12761 #15920) +#15926 := (and #12539 #12542 #15923) +#15932 := (or #13485 #13672 #15926) +#15945 := (and #15932 #15940) +#15948 := (or #12749 #13485 #15945) +#15951 := (and #12539 #12548 #15948) +#15954 := (or #12761 #15951) +#15957 := (and #12539 #12542 #15954) +#15963 := (or #13485 #13765 #15957) +#16002 := (and #15963 #15999) +#15806 := (not #15803) +#16008 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13995 #14041 #15806 #15823 #15840 #15857 #16002) +#16013 := (and #3109 #13473 #16008) +#15792 := (not #15789) +#16016 := (or #15792 #16013) +#16019 := (and #15789 #16016) +#16022 := (or #13436 #16019) +#16025 := (and #13433 #16022) +#16028 := (or #13231 #13240 #13222 #13213 #13204 #16025) +#16031 := (and #12144 #12153 #16028) +#16034 := (or #13252 #16031) +#16037 := (and #12144 #12147 #16034) +#16040 := (or #13264 #16037) +#16043 := (and #12141 #16040) +#16046 := (not #16043) +#18794 := (~ #16046 #18793) +#18790 := (not #16040) +#18791 := (~ #18790 #18789) +#18786 := (not #16037) +#18787 := (~ #18786 #18785) +#18782 := (not #16034) +#18783 := (~ #18782 #18781) +#18778 := (not #16031) +#18779 := (~ #18778 #18777) +#18774 := (not #16028) +#18775 := (~ #18774 #18773) +#18770 := (not #16025) +#18771 := (~ #18770 #18769) +#18766 := (not #16022) +#18767 := (~ #18766 #18765) +#18762 := (not #16019) +#18763 := (~ #18762 #18761) +#18758 := (not #16016) +#18759 := (~ #18758 #18757) +#18754 := (not #16013) +#18755 := (~ #18754 #18753) +#18750 := (not #16008) +#18751 := (~ #18750 #18749) +#18746 := (not #16002) +#18747 := (~ #18746 #18745) +#18742 := (not #15999) +#18743 := (~ #18742 #18741) +#18738 := (not #15996) +#18739 := (~ #18738 #18737) +#18734 := (not #15993) +#18735 := (~ #18734 #18733) +#18730 := (not #15990) +#18731 := (~ #18730 #18729) +#18727 := (~ #18726 #18726) +#18728 := [refl]: #18727 +#18732 := [nnf-neg #18728]: #18731 +#18723 := (not #15979) +#18724 := (~ #18723 #15976) +#18721 := (~ #15976 #15976) +#18719 := (~ #15971 #15971) +#18720 := [refl]: #18719 +#18722 := [nnf-pos #18720]: #18721 +#18725 := [nnf-neg #18722]: #18724 +#18736 := [nnf-neg #18725 #18732]: #18735 +#18715 := (~ #15979 #18714) +#18716 := [sk]: #18715 +#18740 := [nnf-neg #18716 #18736]: #18739 +#18700 := (~ #13769 #13769) +#18701 := [refl]: #18700 +#18491 := (~ #18490 #18490) +#18492 := [refl]: #18491 +#18698 := (~ #18697 #18697) +#18699 := [refl]: #18698 +#18695 := (~ #18694 #18694) +#18696 := [refl]: #18695 +#18692 := (~ #18691 #18691) +#18693 := [refl]: #18692 +#18689 := (~ #18688 #18688) +#18690 := [refl]: #18689 +#18744 := [nnf-neg #18690 #18693 #18696 #18699 #18492 #18701 #18740]: #18743 +#18685 := (not #15963) +#18686 := (~ #18685 #18684) +#18681 := (not #15957) +#18682 := (~ #18681 #18680) +#18677 := (not #15954) +#18678 := (~ #18677 #18676) +#18673 := (not #15951) +#18674 := (~ #18673 #18672) +#18669 := (not #15948) +#18670 := (~ #18669 #18668) +#18665 := (not #15945) +#18666 := (~ #18665 #18664) +#18661 := (not #15940) +#18662 := (~ #18661 #18660) +#18629 := (not #15914) +#18630 := (~ #18629 #18628) +#18625 := (not #15909) +#18626 := (~ #18625 #18624) +#18622 := (~ #18621 #18621) +#18623 := [refl]: #18622 +#18618 := (not #15897) +#18619 := (~ #18618 #18617) +#18614 := (not #15894) +#18615 := (~ #18614 #18613) +#18610 := (not #15891) +#18611 := (~ #18610 #18609) +#18606 := (not #15886) +#18607 := (~ #18606 #18605) +#18602 := (not #15880) +#18603 := (~ #18602 #15877) +#18600 := (~ #15877 #15877) +#18598 := (~ #15872 #15872) +#18599 := [refl]: #18598 +#18601 := [nnf-pos #18599]: #18600 +#18604 := [nnf-neg #18601]: #18603 +#18596 := (~ #18595 #18595) +#18597 := [refl]: #18596 +#18608 := [nnf-neg #18597 #18604]: #18607 +#18591 := (~ #15880 #18590) +#18592 := [sk]: #18591 +#18612 := [nnf-neg #18592 #18608]: #18611 +#18576 := (~ #18575 #18575) +#18577 := [refl]: #18576 +#18616 := [nnf-neg #18577 #18612]: #18615 +#18573 := (~ #13519 #13519) +#18574 := [refl]: #18573 +#18620 := [nnf-neg #18574 #18616]: #18619 +#18571 := (~ #18570 #18570) +#18572 := [refl]: #18571 +#18568 := (~ #18567 #18567) +#18569 := [refl]: #18568 +#18565 := (~ #18564 #18564) +#18566 := [refl]: #18565 +#18627 := [nnf-neg #18566 #18569 #18572 #18620 #18623]: #18626 +#18562 := (~ #18561 #18561) +#18563 := [refl]: #18562 +#18559 := (~ #18558 #18558) +#18560 := [refl]: #18559 +#18631 := [nnf-neg #18560 #18563 #18627]: #18630 +#18658 := (~ #13677 #13677) +#18659 := [refl]: #18658 +#18556 := (~ #18555 #18555) +#18557 := [refl]: #18556 +#18656 := (~ #18655 #18655) +#18657 := [refl]: #18656 +#18653 := (~ #18652 #18652) +#18654 := [refl]: #18653 +#18663 := [nnf-neg #18654 #18657 #18492 #18557 #18659 #18631]: #18662 +#18649 := (not #15932) +#18650 := (~ #18649 #18648) +#18645 := (not #15926) +#18646 := (~ #18645 #18644) +#18641 := (not #15923) +#18642 := (~ #18641 #18640) +#18637 := (not #15920) +#18638 := (~ #18637 #18636) +#18633 := (not #15917) +#18634 := (~ #18633 #18632) +#18553 := (~ #18552 #18552) +#18554 := [refl]: #18553 +#18550 := (~ #18549 #18549) +#18551 := [refl]: #18550 +#18547 := (~ #18546 #18546) +#18548 := [refl]: #18547 +#18544 := (~ #18543 #18543) +#18545 := [refl]: #18544 +#18541 := (~ #18540 #18540) +#18542 := [refl]: #18541 +#18538 := (~ #18537 #18537) +#18539 := [refl]: #18538 +#18533 := (~ #18532 #18532) +#18534 := [refl]: #18533 +#18635 := [nnf-neg #18534 #18539 #18542 #18545 #18548 #18551 #18554 #18557 #18631]: #18634 +#18530 := (~ #18529 #18529) +#18531 := [refl]: #18530 +#18521 := (~ #18520 #18520) +#18522 := [refl]: #18521 +#18639 := [nnf-neg #18522 #18531 #18635]: #18638 +#18527 := (~ #18526 #18526) +#18528 := [refl]: #18527 +#18643 := [nnf-neg #18528 #18639]: #18642 +#18524 := (~ #18523 #18523) +#18525 := [refl]: #18524 +#18647 := [nnf-neg #18522 #18525 #18643]: #18646 +#18535 := (~ #13671 #13671) +#18536 := [refl]: #18535 +#18651 := [nnf-neg #18492 #18536 #18647]: #18650 +#18667 := [nnf-neg #18651 #18663]: #18666 +#18671 := [nnf-neg #18534 #18492 #18667]: #18670 +#18675 := [nnf-neg #18522 #18531 #18671]: #18674 +#18679 := [nnf-neg #18528 #18675]: #18678 +#18683 := [nnf-neg #18522 #18525 #18679]: #18682 +#18518 := (~ #13766 #13766) +#18519 := [refl]: #18518 +#18687 := [nnf-neg #18492 #18519 #18683]: #18686 +#18748 := [nnf-neg #18687 #18744]: #18747 +#18516 := (~ #18515 #18515) +#18517 := [refl]: #18516 +#18513 := (~ #18512 #18512) +#18514 := [refl]: #18513 +#18510 := (~ #18509 #18509) +#18511 := [refl]: #18510 +#18506 := (not #15806) +#18507 := (~ #18506 #15803) +#18504 := (~ #15803 #15803) +#18502 := (~ #15798 #15798) +#18503 := [refl]: #18502 +#18505 := [nnf-pos #18503]: #18504 +#18508 := [nnf-neg #18505]: #18507 +#18500 := (~ #18499 #18499) +#18501 := [refl]: #18500 +#18497 := (~ #18496 #18496) +#18498 := [refl]: #18497 +#18494 := (~ #18493 #18493) +#18495 := [refl]: #18494 +#18488 := (~ #18487 #18487) +#18489 := [refl]: #18488 +#18485 := (~ #18484 #18484) +#18486 := [refl]: #18485 +#18482 := (~ #18481 #18481) +#18483 := [refl]: #18482 +#18479 := (~ #18478 #18478) +#18480 := [refl]: #18479 +#18476 := (~ #18475 #18475) +#18477 := [refl]: #18476 +#18473 := (~ #18472 #18472) +#18474 := [refl]: #18473 +#18470 := (~ #18469 #18469) +#18471 := [refl]: #18470 +#18752 := [nnf-neg #18471 #18474 #18477 #18480 #18483 #18486 #18489 #18492 #18495 #18498 #18501 #18508 #18511 #18514 #18517 #18748]: #18751 +#18467 := (~ #14198 #14198) +#18468 := [refl]: #18467 +#18465 := (~ #13231 #13231) +#18466 := [refl]: #18465 +#18756 := [nnf-neg #18466 #18468 #18752]: #18755 +#18462 := (not #15792) +#18463 := (~ #18462 #15789) +#18460 := (~ #15789 #15789) +#18458 := (~ #15784 #15784) +#18459 := [refl]: #18458 +#18461 := [nnf-pos #18459]: #18460 +#18464 := [nnf-neg #18461]: #18463 +#18760 := [nnf-neg #18464 #18756]: #18759 +#18454 := (~ #15792 #18453) +#18455 := [sk]: #18454 +#18764 := [nnf-neg #18455 #18760]: #18763 +#18439 := (~ #18438 #18438) +#18440 := [refl]: #18439 +#18768 := [nnf-neg #18440 #18764]: #18767 +#18436 := (~ #13436 #13436) +#18437 := [refl]: #18436 +#18772 := [nnf-neg #18437 #18768]: #18771 +#18434 := (~ #18433 #18433) +#18435 := [refl]: #18434 +#18431 := (~ #18430 #18430) +#18432 := [refl]: #18431 +#18428 := (~ #18427 #18427) +#18429 := [refl]: #18428 +#18425 := (~ #18424 #18424) +#18426 := [refl]: #18425 +#18422 := (~ #18421 #18421) +#18423 := [refl]: #18422 +#18776 := [nnf-neg #18423 #18426 #18429 #18432 #18435 #18772]: #18775 +#18419 := (~ #18418 #18418) +#18420 := [refl]: #18419 +#18410 := (~ #18409 #18409) +#18411 := [refl]: #18410 +#18780 := [nnf-neg #18411 #18420 #18776]: #18779 +#18416 := (~ #18415 #18415) +#18417 := [refl]: #18416 +#18784 := [nnf-neg #18417 #18780]: #18783 +#18413 := (~ #18412 #18412) +#18414 := [refl]: #18413 +#18788 := [nnf-neg #18411 #18414 #18784]: #18787 +#18407 := (~ #18406 #18406) +#18408 := [refl]: #18407 +#18792 := [nnf-neg #18408 #18788]: #18791 +#18404 := (~ #13264 #13264) +#18405 := [refl]: #18404 +#18795 := [nnf-neg #18405 #18792]: #18794 +#15288 := (or #12304 #12295 #12286 #12277 #13485 #13766 #13852) +#15293 := (and #13788 #15288) +#15299 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13989 #13995 #14007 #14017 #14030 #14041 #15293) +#15304 := (and #3109 #13473 #15299) +#15307 := (or #13469 #15304) +#15310 := (and #13466 #15307) +#15313 := (or #13436 #15310) +#15316 := (and #13433 #15313) +#15319 := (or #13231 #13240 #13222 #13213 #13204 #15316) +#15322 := (and #12144 #12153 #15319) +#15325 := (or #13252 #15322) +#15328 := (and #12144 #12147 #15325) +#15331 := (or #13264 #15328) +#15334 := (and #12141 #15331) +#15337 := (not #15334) +#16047 := (iff #15337 #16046) +#16044 := (iff #15334 #16043) +#16041 := (iff #15331 #16040) +#16038 := (iff #15328 #16037) +#16035 := (iff #15325 #16034) +#16032 := (iff #15322 #16031) +#16029 := (iff #15319 #16028) +#16026 := (iff #15316 #16025) +#16023 := (iff #15313 #16022) +#16020 := (iff #15310 #16019) +#16017 := (iff #15307 #16016) +#16014 := (iff #15304 #16013) +#16011 := (iff #15299 #16008) +#16005 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #15806 #13995 #15823 #15840 #15857 #14041 #16002) +#16009 := (iff #16005 #16008) +#16010 := [rewrite]: #16009 +#16006 := (iff #15299 #16005) +#16003 := (iff #15293 #16002) +#16000 := (iff #15288 #15999) +#15997 := (iff #13852 #15996) +#15994 := (iff #13847 #15993) +#15991 := (iff #13838 #15990) +#15988 := (iff #13833 #15985) +#15982 := (and #3173 #4202 #15183 #13795) +#15986 := (iff #15982 #15985) +#15987 := [rewrite]: #15986 +#15983 := (iff #13833 #15982) +#15178 := (iff #4496 #15183) +#15199 := -4294967295::Int +#15191 := (+ -4294967295::Int #202) +#15184 := (<= #15191 0::Int) +#15180 := (iff #15184 #15183) +#15181 := [rewrite]: #15180 +#15185 := (iff #4496 #15184) +#15186 := (= #4495 #15191) +#15192 := (+ #202 -4294967295::Int) +#15188 := (= #15192 #15191) +#15189 := [rewrite]: #15188 +#15193 := (= #4495 #15192) +#15194 := (= #4494 -4294967295::Int) +#15200 := (* -1::Int 4294967295::Int) +#15196 := (= #15200 -4294967295::Int) +#15197 := [rewrite]: #15196 +#15201 := (= #4494 #15200) +#7601 := (= f88 4294967295::Int) +#990 := 65536::Int +#1365 := (* 65536::Int 65536::Int) +#1370 := (- #1365 1::Int) +#1371 := (= f88 #1370) +#7602 := (iff #1371 #7601) +#7599 := (= #1370 4294967295::Int) +#1053 := 4294967296::Int +#7592 := (- 4294967296::Int 1::Int) +#7597 := (= #7592 4294967295::Int) +#7598 := [rewrite]: #7597 +#7594 := (= #1370 #7592) +#7563 := (= #1365 4294967296::Int) +#7564 := [rewrite]: #7563 +#7595 := [monotonicity #7564]: #7594 +#7600 := [trans #7595 #7598]: #7599 +#7603 := [monotonicity #7600]: #7602 +#7591 := [asserted]: #1371 +#7606 := [mp #7591 #7603]: #7601 +#15198 := [monotonicity #7606]: #15201 +#15195 := [trans #15198 #15197]: #15194 +#15190 := [monotonicity #15195]: #15193 +#15187 := [trans #15190 #15189]: #15186 +#15182 := [monotonicity #15187]: #15185 +#15179 := [trans #15182 #15181]: #15178 +#15984 := [monotonicity #15179]: #15983 +#15989 := [trans #15984 #15987]: #15988 +#15992 := [quant-intro #15989]: #15991 +#15980 := (iff #13841 #15979) +#15977 := (iff #13821 #15976) +#15974 := (iff #13816 #15971) +#15968 := (or #14425 #13793 #13807) +#15972 := (iff #15968 #15971) +#15973 := [rewrite]: #15972 +#15969 := (iff #13816 #15968) +#14422 := (iff #5712 #14425) +#14427 := (iff #4503 #14426) +#14424 := [monotonicity #15179]: #14427 +#14423 := [monotonicity #14424]: #14422 +#15970 := [monotonicity #14423]: #15969 +#15975 := [trans #15970 #15973]: #15974 +#15978 := [quant-intro #15975]: #15977 +#15981 := [monotonicity #15978]: #15980 +#15995 := [monotonicity #15981 #15992]: #15994 +#15998 := [monotonicity #15978 #15995]: #15997 +#16001 := [monotonicity #15998]: #16000 +#15966 := (iff #13788 #15963) +#15960 := (or #13485 #15957 #13765) +#15964 := (iff #15960 #15963) +#15965 := [rewrite]: #15964 +#15961 := (iff #13788 #15960) +#15958 := (iff #13759 #15957) +#15955 := (iff #13753 #15954) +#15952 := (iff #13748 #15951) +#15949 := (iff #13740 #15948) +#15946 := (iff #13731 #15945) +#15943 := (iff #13726 #15940) +#15937 := (or #12821 #12812 #13485 #13494 #15914 #13671) +#15941 := (iff #15937 #15940) +#15942 := [rewrite]: #15941 +#15938 := (iff #13726 #15937) +#15915 := (iff #13615 #15914) +#15912 := (iff #13607 #15909) +#15906 := (or #12656 #13511 #15897 #13586 #15903) +#15910 := (iff #15906 #15909) +#15911 := [rewrite]: #15910 +#15907 := (iff #13607 #15906) +#15904 := (iff #13592 #15903) +#15901 := (iff #13589 #15900) +#15867 := (iff #13500 #15864) +#15809 := (+ 4294967295::Int #13501) +#15860 := (>= #15809 1::Int) +#15865 := (iff #15860 #15864) +#15866 := [rewrite]: #15865 +#15861 := (iff #13500 #15860) +#15810 := (= #13502 #15809) +#15811 := [monotonicity #7606]: #15810 +#15862 := [monotonicity #15811]: #15861 +#15868 := [trans #15862 #15866]: #15867 +#15902 := [monotonicity #15868]: #15901 +#15905 := [monotonicity #15902]: #15904 +#15898 := (iff #13579 #15897) +#15895 := (iff #13576 #15894) +#15892 := (iff #13573 #15891) +#15889 := (iff #13570 #15886) +#15883 := (or #15880 #13565) +#15887 := (iff #15883 #15886) +#15888 := [rewrite]: #15887 +#15884 := (iff #13570 #15883) +#15881 := (iff #13553 #15880) +#15878 := (iff #13550 #15877) +#15875 := (iff #13545 #15872) +#15869 := (or #14425 #13522 #13536) +#15873 := (iff #15869 #15872) +#15874 := [rewrite]: #15873 +#15870 := (iff #13545 #15869) +#15871 := [monotonicity #14423]: #15870 +#15876 := [trans #15871 #15874]: #15875 +#15879 := [quant-intro #15876]: #15878 +#15882 := [monotonicity #15879]: #15881 +#15885 := [monotonicity #15882]: #15884 +#15890 := [trans #15885 #15888]: #15889 +#15893 := [monotonicity #15879 #15890]: #15892 +#15896 := [monotonicity #15893]: #15895 +#15899 := [monotonicity #15896]: #15898 +#15908 := [monotonicity #15899 #15905]: #15907 +#15913 := [trans #15908 #15911]: #15912 +#15916 := [monotonicity #15868 #15913]: #15915 +#15939 := [monotonicity #15916]: #15938 +#15944 := [trans #15939 #15942]: #15943 +#15935 := (iff #13696 #15932) +#15929 := (or #13485 #15926 #13672) +#15933 := (iff #15929 #15932) +#15934 := [rewrite]: #15933 +#15930 := (iff #13696 #15929) +#15927 := (iff #13666 #15926) +#15924 := (iff #13660 #15923) +#15921 := (iff #13655 #15920) +#15918 := (iff #13647 #15917) +#15919 := [monotonicity #15916]: #15918 +#15922 := [monotonicity #15919]: #15921 +#15925 := [monotonicity #15922]: #15924 +#15928 := [monotonicity #15925]: #15927 +#15931 := [monotonicity #15928]: #15930 +#15936 := [trans #15931 #15934]: #15935 +#15947 := [monotonicity #15936 #15944]: #15946 +#15950 := [monotonicity #15947]: #15949 +#15953 := [monotonicity #15950]: #15952 +#15956 := [monotonicity #15953]: #15955 +#15959 := [monotonicity #15956]: #15958 +#15962 := [monotonicity #15959]: #15961 +#15967 := [trans #15962 #15965]: #15966 +#16004 := [monotonicity #15967 #16001]: #16003 +#15858 := (iff #14030 #15857) +#15855 := (iff #14027 #15854) +#15852 := (iff #14023 #15849) +#15843 := (+ 255::Int #13970) +#15846 := (>= #15843 0::Int) +#15850 := (iff #15846 #15849) +#15851 := [rewrite]: #15850 +#15847 := (iff #14023 #15846) +#15844 := (= #14024 #15843) +#1375 := (= f90 255::Int) +#7605 := [asserted]: #1375 +#15845 := [monotonicity #7605]: #15844 +#15848 := [monotonicity #15845]: #15847 +#15853 := [trans #15848 #15851]: #15852 +#15856 := [monotonicity #15853]: #15855 +#15859 := [monotonicity #15856]: #15858 +#15841 := (iff #14017 #15840) +#15838 := (iff #14014 #15837) +#15835 := (iff #14010 #15832) +#15826 := (+ 4294967295::Int #13941) +#15829 := (>= #15826 0::Int) +#15833 := (iff #15829 #15832) +#15834 := [rewrite]: #15833 +#15830 := (iff #14010 #15829) +#15827 := (= #14011 #15826) +#15828 := [monotonicity #7606]: #15827 +#15831 := [monotonicity #15828]: #15830 +#15836 := [trans #15831 #15834]: #15835 +#15839 := [monotonicity #15836]: #15838 +#15842 := [monotonicity #15839]: #15841 +#15824 := (iff #14007 #15823) +#15821 := (iff #14004 #15820) +#15818 := (iff #14001 #15815) +#15812 := (>= #15809 0::Int) +#15816 := (iff #15812 #15815) +#15817 := [rewrite]: #15816 +#15813 := (iff #14001 #15812) +#15814 := [monotonicity #15811]: #15813 +#15819 := [trans #15814 #15817]: #15818 +#15822 := [monotonicity #15819]: #15821 +#15825 := [monotonicity #15822]: #15824 +#15807 := (iff #13989 #15806) +#15804 := (iff #13986 #15803) +#15801 := (iff #13981 #15798) +#15795 := (or #14425 #13958 #13972) +#15799 := (iff #15795 #15798) +#15800 := [rewrite]: #15799 +#15796 := (iff #13981 #15795) +#15797 := [monotonicity #14423]: #15796 +#15802 := [trans #15797 #15800]: #15801 +#15805 := [quant-intro #15802]: #15804 +#15808 := [monotonicity #15805]: #15807 +#16007 := [monotonicity #15808 #15825 #15842 #15859 #16004]: #16006 +#16012 := [trans #16007 #16010]: #16011 +#16015 := [monotonicity #16012]: #16014 +#15793 := (iff #13469 #15792) +#15790 := (iff #13466 #15789) +#15787 := (iff #13461 #15784) +#15781 := (or #14425 #13439 #13451) +#15785 := (iff #15781 #15784) +#15786 := [rewrite]: #15785 +#15782 := (iff #13461 #15781) +#15783 := [monotonicity #14423]: #15782 +#15788 := [trans #15783 #15786]: #15787 +#15791 := [quant-intro #15788]: #15790 +#15794 := [monotonicity #15791]: #15793 +#16018 := [monotonicity #15794 #16015]: #16017 +#16021 := [monotonicity #15791 #16018]: #16020 +#16024 := [monotonicity #16021]: #16023 +#16027 := [monotonicity #16024]: #16026 +#16030 := [monotonicity #16027]: #16029 +#16033 := [monotonicity #16030]: #16032 +#16036 := [monotonicity #16033]: #16035 +#16039 := [monotonicity #16036]: #16038 +#16042 := [monotonicity #16039]: #16041 +#16045 := [monotonicity #16042]: #16044 +#16048 := [monotonicity #16045]: #16047 +#14325 := (not #14177) +#15338 := (iff #14325 #15337) +#15335 := (iff #14177 #15334) +#15332 := (iff #14174 #15331) +#15329 := (iff #14169 #15328) +#15326 := (iff #14163 #15325) +#15323 := (iff #14158 #15322) +#15320 := (iff #14150 #15319) +#15317 := (iff #14129 #15316) +#15314 := (iff #14126 #15313) +#15311 := (iff #14123 #15310) +#15308 := (iff #14120 #15307) +#15305 := (iff #14115 #15304) +#15302 := (iff #14107 #15299) +#15296 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #15293 #13955 #13989 #13995 #14007 #14017 #14030 #14041) +#15300 := (iff #15296 #15299) +#15301 := [rewrite]: #15300 +#15297 := (iff #14107 #15296) +#15294 := (iff #13914 #15293) +#15291 := (iff #13909 #15288) +#15273 := (or #12304 #12295 #12286 #12277 #13485 #13852) +#15285 := (or #13485 #13766 #15273) +#15289 := (iff #15285 #15288) +#15290 := [rewrite]: #15289 +#15286 := (iff #13909 #15285) +#15283 := (iff #13884 #15273) +#15278 := (and true #15273) +#15281 := (iff #15278 #15273) +#15282 := [rewrite]: #15281 +#15279 := (iff #13884 #15278) +#15276 := (iff #13879 #15273) +#15270 := (or false #12304 #12295 #12286 #12277 #13485 #13852) +#15274 := (iff #15270 #15273) +#15275 := [rewrite]: #15274 +#15271 := (iff #13879 #15270) +#15268 := (iff #12338 false) +#15266 := (iff #12338 #3156) +#15004 := (iff #10924 true) +#10923 := [asserted]: #2542 +#10930 := [mp #10923 #10927]: #10924 +#15005 := [iff-true #10930]: #15004 +#15267 := [monotonicity #15005]: #15266 +#15269 := [trans #15267 #12221]: #15268 +#15272 := [monotonicity #15269]: #15271 +#15277 := [trans #15272 #15275]: #15276 +#15280 := [monotonicity #15005 #15277]: #15279 +#15284 := [trans #15280 #15282]: #15283 +#15287 := [monotonicity #15284]: #15286 +#15292 := [trans #15287 #15290]: #15291 +#15295 := [monotonicity #15292]: #15294 +#15264 := (iff #12366 #15263) +#15261 := (iff #12228 #12222) +#15256 := (and true #12222) +#15259 := (iff #15256 #12222) +#15260 := [rewrite]: #15259 +#15257 := (iff #12228 #15256) +#15240 := (iff #12109 true) +#15241 := [iff-true #14315]: #15240 +#15258 := [monotonicity #15241]: #15257 +#15262 := [trans #15258 #15260]: #15261 +#15265 := [monotonicity #15262]: #15264 +#15298 := [monotonicity #15265 #15295]: #15297 +#15303 := [trans #15298 #15301]: #15302 +#15306 := [monotonicity #15303]: #15305 +#15309 := [monotonicity #15306]: #15308 +#15312 := [monotonicity #15309]: #15311 +#15315 := [monotonicity #15312]: #15314 +#15318 := [monotonicity #15315]: #15317 +#15321 := [monotonicity #15318]: #15320 +#15324 := [monotonicity #15321]: #15323 +#15327 := [monotonicity #15324]: #15326 +#15330 := [monotonicity #15327]: #15329 +#15333 := [monotonicity #15330]: #15332 +#15336 := [monotonicity #15333]: #15335 +#15339 := [monotonicity #15336]: #15338 +#14326 := [not-or-elim #14310]: #14325 +#15340 := [mp #14326 #15339]: #15337 +#16049 := [mp #15340 #16048]: #16046 +#18796 := [mp~ #16049 #18795]: #18793 +#18797 := [mp #18796 #19141]: #19139 +#22664 := [mp #18797 #22663]: #22661 +#23569 := [mp #22664 #23568]: #23566 +#29167 := [unit-resolution #23569 #26960]: #23563 +#24793 := (or #23560 #23554) +#24794 := [def-axiom]: #24793 +#29168 := [unit-resolution #24794 #29167]: #23554 +#27003 := (f24 #3098) +decl f156 :: (-> S18 S18) +#24960 := (f156 #3040) +#27004 := (= #24960 #27003) +decl f39 :: (-> Int S20) +#24797 := (f39 #3076) +#27034 := (f128 #24797) +decl f81 :: (-> Int Int Int) +decl f151 :: (-> S18 Int) +#27032 := (f151 #24960) +#27033 := (f81 0::Int #27032) +#27041 := (+ #27033 #27034) +#27044 := (f54 #24960 #27041) +#27233 := (f24 #27044) +#27604 := (= #27233 #27003) +#27600 := (= #27003 #27233) +#27572 := (= #3098 #27044) +#27028 := (f77 #24797 0::Int #24960) +#27047 := (= #27028 #27044) +#27050 := (not #27047) +decl f150 :: (-> S20 S20 S1) +#27029 := (f150 #27028 #24797) +#27030 := (= f1 #27029) +#27031 := (not #27030) +#27056 := (or #27031 #27050) +#27061 := (not #27056) +#289 := (:var 1 Int) +#1622 := (f77 #60 #289 #275) +#1623 := (pattern #1622) +#1624 := (f150 #1622 #60) +#8354 := (= f1 #1624) +#21196 := (not #8354) +#1627 := (f151 #275) +#1628 := (f81 #289 #1627) +#1626 := (f128 #60) +#1629 := (+ #1626 #1628) +#1630 := (f54 #275 #1629) +#1631 := (= #1622 #1630) +#21195 := (not #1631) +#21197 := (or #21195 #21196) +#21198 := (not #21197) +#21201 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21198) +#8360 := (and #1631 #8354) +#8365 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8360) +#21202 := (iff #8365 #21201) +#21199 := (iff #8360 #21198) +#21200 := [rewrite]: #21199 +#21203 := [quant-intro #21200]: #21202 +#17329 := (~ #8365 #8365) +#17327 := (~ #8360 #8360) +#17328 := [refl]: #17327 +#17330 := [nnf-pos #17328]: #17329 +#1625 := (= #1624 f1) +#1632 := (and #1625 #1631) +#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632) +#8366 := (iff #1633 #8365) +#8363 := (iff #1632 #8360) +#8357 := (and #8354 #1631) +#8361 := (iff #8357 #8360) +#8362 := [rewrite]: #8361 +#8358 := (iff #1632 #8357) +#8355 := (iff #1625 #8354) +#8356 := [rewrite]: #8355 +#8359 := [monotonicity #8356]: #8358 +#8364 := [trans #8359 #8362]: #8363 +#8367 := [quant-intro #8364]: #8366 +#8353 := [asserted]: #1633 +#8370 := [mp #8353 #8367]: #8365 +#17331 := [mp~ #8370 #17330]: #8365 +#21204 := [mp #17331 #21203]: #21201 +#27451 := (not #21201) +#27452 := (or #27451 #27061) +#27035 := (+ #27034 #27033) +#27036 := (f54 #24960 #27035) +#27037 := (= #27028 #27036) +#27038 := (not #27037) +#27039 := (or #27038 #27031) +#27040 := (not #27039) +#27453 := (or #27451 #27040) +#27449 := (iff #27453 #27452) +#27456 := (iff #27452 #27452) +#27457 := [rewrite]: #27456 +#27062 := (iff #27040 #27061) +#27059 := (iff #27039 #27056) +#27053 := (or #27050 #27031) +#27057 := (iff #27053 #27056) +#27058 := [rewrite]: #27057 +#27054 := (iff #27039 #27053) +#27051 := (iff #27038 #27050) +#27048 := (iff #27037 #27047) +#27045 := (= #27036 #27044) +#27042 := (= #27035 #27041) +#27043 := [rewrite]: #27042 +#27046 := [monotonicity #27043]: #27045 +#27049 := [monotonicity #27046]: #27048 +#27052 := [monotonicity #27049]: #27051 +#27055 := [monotonicity #27052]: #27054 +#27060 := [trans #27055 #27058]: #27059 +#27063 := [monotonicity #27060]: #27062 +#27455 := [monotonicity #27063]: #27449 +#27458 := [trans #27455 #27457]: #27449 +#27454 := [quant-inst #24797 #161 #24960]: #27453 +#27459 := [mp #27454 #27458]: #27452 +#27562 := [unit-resolution #27459 #21204]: #27061 +#27468 := (or #27056 #27047) +#27466 := [def-axiom]: #27468 +#27568 := [unit-resolution #27466 #27562]: #27047 +#27570 := (= #3098 #27028) +#24961 := (= f19 #24960) +#1401 := (f136 #369 #202) +#1638 := (pattern #1401) +#1652 := (f156 #1401) +#8415 := (= #369 #1652) +#8419 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8415) +#17359 := (~ #8419 #8419) +#17357 := (~ #8415 #8415) +#17358 := [refl]: #17357 +#17360 := [nnf-pos #17358]: #17359 +#1653 := (= #1652 #369) +#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653) +#8420 := (iff #1654 #8419) +#8417 := (iff #1653 #8415) +#8418 := [rewrite]: #8417 +#8421 := [quant-intro #8418]: #8420 +#8414 := [asserted]: #1654 +#8424 := [mp #8414 #8421]: #8419 +#17361 := [mp~ #8424 #17360]: #8419 +#24964 := (not #8419) +#24965 := (or #24964 #24961) +#24966 := [quant-inst #50 #3036]: #24965 +#28486 := [unit-resolution #24966 #17361]: #24961 +#24798 := (= #3042 #24797) +#132 := (f40 #62) +#23175 := (pattern #132) +#133 := (f39 #132) +#3682 := (= #62 #133) +#23176 := (forall (vars (?v0 S20)) (:pat #23175) #3682) +#3685 := (forall (vars (?v0 S20)) #3682) +#23177 := (iff #3685 #23176) +#23179 := (iff #23176 #23176) +#23180 := [rewrite]: #23179 +#23178 := [rewrite]: #23177 +#23181 := [trans #23178 #23180]: #23177 +#16306 := (~ #3685 #3685) +#16296 := (~ #3682 #3682) +#16297 := [refl]: #16296 +#16362 := [nnf-pos #16297]: #16306 +#134 := (= #133 #62) +#135 := (forall (vars (?v0 S20)) #134) +#3686 := (iff #135 #3685) +#3683 := (iff #134 #3682) +#3684 := [rewrite]: #3683 +#3687 := [quant-intro #3684]: #3686 +#3681 := [asserted]: #135 +#3690 := [mp #3681 #3687]: #3685 +#16363 := [mp~ #3690 #16362]: #3685 +#23182 := [mp #16363 #23181]: #23176 +#24801 := (not #23176) +#24802 := (or #24801 #24798) +#24803 := [quant-inst #3042]: #24802 +#27569 := [unit-resolution #24803 #23182]: #24798 +#27571 := [monotonicity #27569 #28486]: #27570 +#27599 := [trans #27571 #27568]: #27572 +#27601 := [monotonicity #27599]: #27600 +#27591 := [symm #27601]: #27604 +#27234 := (= #24960 #27233) +#27497 := (or #25028 #27234) +#27503 := [quant-inst #24960 #27041]: #27497 +#27567 := [unit-resolution #27503 #23276]: #27234 +#27592 := [trans #27567 #27591]: #27004 +#27413 := (not #27004) +#26977 := (f59 #3098 #24960) +#26978 := (= f1 #26977) +#27006 := (iff #26978 #27004) +#1433 := (f24 #55) +#9184 := (= #275 #1433) +#11354 := (iff #9184 #11333) +#23258 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11354) +#11359 := (forall (vars (?v0 S20) (?v1 S18)) #11354) +#23261 := (iff #11359 #23258) +#23259 := (iff #11354 #11354) +#23260 := [refl]: #23259 +#23262 := [quant-intro #23260]: #23261 +#18251 := (~ #11359 #11359) +#18249 := (~ #11354 #11354) +#18250 := [refl]: #18249 +#18252 := [nnf-pos #18250]: #18251 +#1939 := (= #1433 #275) +#2736 := (iff #2731 #1939) +#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736) +#11360 := (iff #2737 #11359) +#11357 := (iff #2736 #11354) +#11350 := (iff #11333 #9184) +#11355 := (iff #11350 #11354) +#11356 := [rewrite]: #11355 +#11352 := (iff #2736 #11350) +#9185 := (iff #1939 #9184) +#9186 := [rewrite]: #9185 +#11353 := [monotonicity #11336 #9186]: #11352 +#11358 := [trans #11353 #11356]: #11357 +#11361 := [quant-intro #11358]: #11360 +#11349 := [asserted]: #2737 +#11364 := [mp #11349 #11361]: #11359 +#18253 := [mp~ #11364 #18252]: #11359 +#23263 := [mp #18253 #23262]: #23258 +#26174 := (not #23258) +#27419 := (or #26174 #27006) +#27005 := (iff #27004 #26978) +#27420 := (or #26174 #27005) +#27407 := (iff #27420 #27419) +#27409 := (iff #27419 #27419) +#27410 := [rewrite]: #27409 +#27007 := (iff #27005 #27006) +#27008 := [rewrite]: #27007 +#27408 := [monotonicity #27008]: #27407 +#27411 := [trans #27408 #27410]: #27407 +#27405 := [quant-inst #3098 #24960]: #27420 +#27406 := [mp #27405 #27411]: #27419 +#27530 := [unit-resolution #27406 #23263]: #27006 +#26985 := (not #26978) +#27563 := (iff #18409 #26985) +#27535 := (iff #12144 #26978) +#27533 := (iff #26978 #12144) +#27526 := (= #26977 #3099) +#28487 := (= #24960 f19) +#28488 := [symm #28486]: #28487 +#27532 := [monotonicity #28488]: #27526 +#27534 := [monotonicity #27532]: #27533 +#27536 := [symm #27534]: #27535 +#27564 := [monotonicity #27536]: #27563 +#27531 := [hypothesis]: #18409 +#27565 := [mp #27531 #27564]: #26985 +#27412 := (not #27006) +#27414 := (or #27412 #26978 #27413) +#27415 := [def-axiom]: #27414 +#27566 := [unit-resolution #27415 #27565 #27530]: #27413 +#27590 := [unit-resolution #27566 #27592]: false +#27593 := [lemma #27590]: #12144 +#27181 := (f54 #24960 #3043) +#27182 := (f77 #27181 0::Int #24960) +#27186 := (f35 f298 #27182) +#27187 := (= f1 #27186) +#27188 := (not #27187) +#28139 := (iff #18412 #27188) +#28109 := (iff #12147 #27187) +#28136 := (iff #27187 #12147) +#28133 := (= #27186 #3101) +#27752 := (= #27182 #3098) +#28494 := (= #27181 #3042) +#28492 := (= #3043 f299) +#25080 := (= f299 #3043) +#2762 := (f128 #2761) +#11409 := (= #202 #2762) +#23265 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11409) +#11413 := (forall (vars (?v0 S18) (?v1 Int)) #11409) +#23268 := (iff #11413 #23265) +#23266 := (iff #11409 #11409) +#23267 := [refl]: #23266 +#23269 := [quant-intro #23267]: #23268 +#18266 := (~ #11413 #11413) +#18264 := (~ #11409 #11409) +#18265 := [refl]: #18264 +#18267 := [nnf-pos #18265]: #18266 +#2763 := (= #2762 #202) +#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763) +#11414 := (iff #2764 #11413) +#11411 := (iff #2763 #11409) +#11412 := [rewrite]: #11411 +#11415 := [quant-intro #11412]: #11414 +#11408 := [asserted]: #2764 +#11418 := [mp #11408 #11415]: #11413 +#18268 := [mp~ #11418 #18267]: #11413 +#23270 := [mp #18268 #23269]: #23265 +#25034 := (not #23265) +#25085 := (or #25034 #25080) +#25086 := [quant-inst #50 #3041]: #25085 +#28491 := [unit-resolution #25086 #23270]: #25080 +#28493 := [symm #28491]: #28492 +#28495 := [monotonicity #28488 #28493]: #28494 +#28135 := [monotonicity #28495 #28488]: #27752 +#27928 := [monotonicity #28135]: #28133 +#28137 := [monotonicity #27928]: #28136 +#28138 := [symm #28137]: #28109 +#28111 := [monotonicity #28138]: #28139 +#27751 := [hypothesis]: #18412 +#28112 := [mp #27751 #28111]: #27188 +decl f148 :: (-> S29 S1) +#27183 := (f69 #3220 #27182) +#27184 := (f148 #27183) +#27185 := (= f1 #27184) +#27198 := (or #27185 #27188) +#27201 := (not #27198) +decl f33 :: (-> S18 S1) +#27194 := (f33 #24960) +#27195 := (= f1 #27194) +#2848 := (f33 f19) +#28526 := (= #2848 #27194) +#28523 := (= #27194 #2848) +#28524 := [monotonicity #28488]: #28523 +#28527 := [symm #28524]: #28526 +#11588 := (= f1 #2848) +#2849 := (= #2848 f1) +#11590 := (iff #2849 #11588) +#11591 := [rewrite]: #11590 +#11587 := [asserted]: #2849 +#11594 := [mp #11587 #11591]: #11588 +#28528 := [trans #11594 #28527]: #27195 +#27196 := (not #27195) +#28357 := (or #27196 #27201) +decl f26 :: (-> S20 S21 S1) +decl f27 :: (-> S19 S20 S21) +#26739 := (f27 f298 #26146) +decl f155 :: (-> S18 Int) +#24962 := (f155 #3040) +#27102 := (f136 #24960 #24962) +#27103 := (f54 #27102 #3043) +#27191 := (f26 #27103 #26739) +#27192 := (= f1 #27191) +#26740 := (f26 #26146 #26739) +#28128 := (= #26740 #27191) +#28366 := (= #27191 #26740) +#28055 := (= #27103 #26146) +#28363 := (= #27103 #3044) +#28152 := (= #27102 #3040) +#28151 := (= #24962 f297) +#24963 := (= f297 #24962) +#1649 := (f155 #1401) +#8408 := (= #202 #1649) +#8411 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8408) +#17354 := (~ #8411 #8411) +#17352 := (~ #8408 #8408) +#17353 := [refl]: #17352 +#17355 := [nnf-pos #17353]: #17354 +#1650 := (= #1649 #202) +#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650) +#8412 := (iff #1651 #8411) +#8409 := (iff #1650 #8408) +#8410 := [rewrite]: #8409 +#8413 := [quant-intro #8410]: #8412 +#8407 := [asserted]: #1651 +#8416 := [mp #8407 #8413]: #8411 +#17356 := [mp~ #8416 #17355]: #8411 +#24969 := (not #8411) +#24970 := (or #24969 #24963) +#24971 := [quant-inst #50 #3036]: #24970 +#28508 := [unit-resolution #24971 #17356]: #24963 +#27929 := [symm #28508]: #28151 +#28153 := [monotonicity #28488 #27929]: #28152 +#28364 := [monotonicity #28153]: #28363 +#28365 := [trans #28364 #28875]: #28055 +#28367 := [monotonicity #28365]: #28366 +#28129 := [symm #28367]: #28128 +#26741 := (= f1 #26740) +decl f64 :: (-> S19 S20 S21) +#26729 := (f64 f298 #26146) +#26730 := (f26 #62 #26729) +#26736 := (pattern #26730) +decl f209 :: (-> S18 S1) +#26733 := (f209 #26550) +#26734 := (= f1 #26733) +#26731 := (= f1 #26730) +#26732 := (not #26731) +decl f159 :: (-> S20 S21 S1) +decl f204 :: (-> S22 S21) +decl f22 :: (-> S19 S20 S22) +#26725 := (f22 f298 #26146) +#26726 := (f204 #26725) +#26727 := (f159 #62 #26726) +#26728 := (= f1 #26727) +#26746 := (or #26728 #26732 #26734) +#26749 := (forall (vars (?v3 S20)) (:pat #26736) #26746) +#26752 := (not #26749) +#26742 := (not #26741) +#26755 := (or #26613 #26742 #26752) +#26758 := (not #26755) +#28107 := (= #3096 #26680) +#28113 := [symm #26898]: #28107 +#28131 := [trans #26960 #28113]: #26681 +#26687 := (or #26689 #26679 #26697) +#26690 := [def-axiom]: #26687 +#28108 := [unit-resolution #26690 #28131 #26901]: #26679 +#26761 := (or #26700 #26758) #54 := (:var 2 S19) -#2218 := (f207 #54 #55 #62) +#2218 := (f208 #54 #55 #62) #2281 := (pattern #2218) #2282 := (f64 #53 #60) #2283 := (f26 #62 #2282) #2284 := (pattern #2283) #2210 := (f22 #53 #55) -#2290 := (f203 #2210) -#2291 := (f158 #62 #2290) -#10238 := (= f1 #2291) -#10232 := (= f1 #2283) -#21923 := (not #10232) +#2290 := (f204 #2210) +#2291 := (f159 #62 #2290) +#10202 := (= f1 #2291) +#10196 := (= f1 #2283) +#21887 := (not #10196) #1425 := (f24 #60) -#2285 := (f208 #1425) -#10226 := (= f1 #2285) -#21938 := (or #10226 #21923 #10238) -#21943 := (forall (vars (?v3 S20)) (:pat #2284) #21938) -#21949 := (not #21943) +#2285 := (f209 #1425) +#10190 := (= f1 #2285) +#21902 := (or #10190 #21887 #10202) +#21907 := (forall (vars (?v3 S20)) (:pat #2284) #21902) +#21913 := (not #21907) #2197 := (f27 #54 #62) #2198 := (f26 #55 #2197) -#9926 := (= f1 #2198) -#21758 := (not #9926) +#9890 := (= f1 #2198) +#21722 := (not #9890) #221 := (f38 #54 #55) #3873 := (= f1 #221) -#10576 := (not #3873) -#21950 := (or #10576 #21758 #21949) -#21951 := (not #21950) -#9974 := (= f1 #2218) -#10262 := (not #9974) -#21956 := (or #10262 #21951) -#21959 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21956) -#10229 := (not #10226) -#10235 := (and #10229 #10232) -#10244 := (not #10235) -#10245 := (or #10244 #10238) -#10250 := (forall (vars (?v3 S20)) (:pat #2284) #10245) -#10271 := (and #3873 #9926 #10250) -#10274 := (or #10262 #10271) -#10277 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10274) -#21960 := (iff #10277 #21959) -#21957 := (iff #10274 #21956) -#21954 := (iff #10271 #21951) -#21946 := (and #3873 #9926 #21943) -#21952 := (iff #21946 #21951) -#21953 := [rewrite]: #21952 -#21947 := (iff #10271 #21946) -#21944 := (iff #10250 #21943) -#21941 := (iff #10245 #21938) -#21924 := (or #10226 #21923) -#21935 := (or #21924 #10238) -#21939 := (iff #21935 #21938) -#21940 := [rewrite]: #21939 -#21936 := (iff #10245 #21935) -#21933 := (iff #10244 #21924) -#21925 := (not #21924) -#21928 := (not #21925) -#21931 := (iff #21928 #21924) -#21932 := [rewrite]: #21931 -#21929 := (iff #10244 #21928) -#21926 := (iff #10235 #21925) -#21927 := [rewrite]: #21926 -#21930 := [monotonicity #21927]: #21929 -#21934 := [trans #21930 #21932]: #21933 -#21937 := [monotonicity #21934]: #21936 -#21942 := [trans #21937 #21940]: #21941 -#21945 := [quant-intro #21942]: #21944 -#21948 := [monotonicity #21945]: #21947 -#21955 := [trans #21948 #21953]: #21954 -#21958 := [monotonicity #21955]: #21957 -#21961 := [quant-intro #21958]: #21960 -#17909 := (~ #10277 #10277) -#17907 := (~ #10274 #10274) -#17905 := (~ #10271 #10271) -#17903 := (~ #10250 #10250) -#17901 := (~ #10245 #10245) -#17902 := [refl]: #17901 -#17904 := [nnf-pos #17902]: #17903 -#17899 := (~ #9926 #9926) -#17900 := [refl]: #17899 -#17897 := (~ #3873 #3873) -#17898 := [refl]: #17897 -#17906 := [monotonicity #17898 #17900 #17904]: #17905 -#17895 := (~ #10262 #10262) -#17896 := [refl]: #17895 -#17908 := [monotonicity #17896 #17906]: #17907 -#17910 := [nnf-pos #17908]: #17909 +#10540 := (not #3873) +#21914 := (or #10540 #21722 #21913) +#21915 := (not #21914) +#9938 := (= f1 #2218) +#10226 := (not #9938) +#21920 := (or #10226 #21915) +#21923 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21920) +#10193 := (not #10190) +#10199 := (and #10193 #10196) +#10208 := (not #10199) +#10209 := (or #10208 #10202) +#10214 := (forall (vars (?v3 S20)) (:pat #2284) #10209) +#10235 := (and #3873 #9890 #10214) +#10238 := (or #10226 #10235) +#10241 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10238) +#21924 := (iff #10241 #21923) +#21921 := (iff #10238 #21920) +#21918 := (iff #10235 #21915) +#21910 := (and #3873 #9890 #21907) +#21916 := (iff #21910 #21915) +#21917 := [rewrite]: #21916 +#21911 := (iff #10235 #21910) +#21908 := (iff #10214 #21907) +#21905 := (iff #10209 #21902) +#21888 := (or #10190 #21887) +#21899 := (or #21888 #10202) +#21903 := (iff #21899 #21902) +#21904 := [rewrite]: #21903 +#21900 := (iff #10209 #21899) +#21897 := (iff #10208 #21888) +#21889 := (not #21888) +#21892 := (not #21889) +#21895 := (iff #21892 #21888) +#21896 := [rewrite]: #21895 +#21893 := (iff #10208 #21892) +#21890 := (iff #10199 #21889) +#21891 := [rewrite]: #21890 +#21894 := [monotonicity #21891]: #21893 +#21898 := [trans #21894 #21896]: #21897 +#21901 := [monotonicity #21898]: #21900 +#21906 := [trans #21901 #21904]: #21905 +#21909 := [quant-intro #21906]: #21908 +#21912 := [monotonicity #21909]: #21911 +#21919 := [trans #21912 #21917]: #21918 +#21922 := [monotonicity #21919]: #21921 +#21925 := [quant-intro #21922]: #21924 +#17873 := (~ #10241 #10241) +#17871 := (~ #10238 #10238) +#17869 := (~ #10235 #10235) +#17867 := (~ #10214 #10214) +#17865 := (~ #10209 #10209) +#17866 := [refl]: #17865 +#17868 := [nnf-pos #17866]: #17867 +#17863 := (~ #9890 #9890) +#17864 := [refl]: #17863 +#17861 := (~ #3873 #3873) +#17862 := [refl]: #17861 +#17870 := [monotonicity #17862 #17864 #17868]: #17869 +#17859 := (~ #10226 #10226) +#17860 := [refl]: #17859 +#17872 := [monotonicity #17860 #17870]: #17871 +#17874 := [nnf-pos #17872]: #17873 #2292 := (= #2291 f1) #2288 := (= #2283 f1) #2286 := (= #2285 f1) @@ -4196,154 +5435,110 @@ #2219 := (= #2218 f1) #2297 := (implies #2219 #2296) #2298 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #2297) -#10280 := (iff #2298 #10277) -#10253 := (and #3873 #10250) -#10256 := (and #9926 #10253) -#10263 := (or #10262 #10256) -#10268 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10263) -#10278 := (iff #10268 #10277) -#10275 := (iff #10263 #10274) -#10272 := (iff #10256 #10271) -#10273 := [rewrite]: #10272 -#10276 := [monotonicity #10273]: #10275 -#10279 := [quant-intro #10276]: #10278 -#10269 := (iff #2298 #10268) -#10266 := (iff #2297 #10263) -#10259 := (implies #9974 #10256) -#10264 := (iff #10259 #10263) -#10265 := [rewrite]: #10264 -#10260 := (iff #2297 #10259) -#10257 := (iff #2296 #10256) -#10254 := (iff #2295 #10253) -#10251 := (iff #2294 #10250) -#10248 := (iff #2293 #10245) -#10241 := (implies #10235 #10238) -#10246 := (iff #10241 #10245) -#10247 := [rewrite]: #10246 -#10242 := (iff #2293 #10241) -#10239 := (iff #2292 #10238) -#10240 := [rewrite]: #10239 -#10236 := (iff #2289 #10235) -#10233 := (iff #2288 #10232) -#10234 := [rewrite]: #10233 -#10230 := (iff #2287 #10229) -#10227 := (iff #2286 #10226) -#10228 := [rewrite]: #10227 -#10231 := [monotonicity #10228]: #10230 -#10237 := [monotonicity #10231 #10234]: #10236 -#10243 := [monotonicity #10237 #10240]: #10242 -#10249 := [trans #10243 #10247]: #10248 -#10252 := [quant-intro #10249]: #10251 +#10244 := (iff #2298 #10241) +#10217 := (and #3873 #10214) +#10220 := (and #9890 #10217) +#10227 := (or #10226 #10220) +#10232 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10227) +#10242 := (iff #10232 #10241) +#10239 := (iff #10227 #10238) +#10236 := (iff #10220 #10235) +#10237 := [rewrite]: #10236 +#10240 := [monotonicity #10237]: #10239 +#10243 := [quant-intro #10240]: #10242 +#10233 := (iff #2298 #10232) +#10230 := (iff #2297 #10227) +#10223 := (implies #9938 #10220) +#10228 := (iff #10223 #10227) +#10229 := [rewrite]: #10228 +#10224 := (iff #2297 #10223) +#10221 := (iff #2296 #10220) +#10218 := (iff #2295 #10217) +#10215 := (iff #2294 #10214) +#10212 := (iff #2293 #10209) +#10205 := (implies #10199 #10202) +#10210 := (iff #10205 #10209) +#10211 := [rewrite]: #10210 +#10206 := (iff #2293 #10205) +#10203 := (iff #2292 #10202) +#10204 := [rewrite]: #10203 +#10200 := (iff #2289 #10199) +#10197 := (iff #2288 #10196) +#10198 := [rewrite]: #10197 +#10194 := (iff #2287 #10193) +#10191 := (iff #2286 #10190) +#10192 := [rewrite]: #10191 +#10195 := [monotonicity #10192]: #10194 +#10201 := [monotonicity #10195 #10198]: #10200 +#10207 := [monotonicity #10201 #10204]: #10206 +#10213 := [trans #10207 #10211]: #10212 +#10216 := [quant-intro #10213]: #10215 #3874 := (iff #225 #3873) #3875 := [rewrite]: #3874 -#10255 := [monotonicity #3875 #10252]: #10254 -#9927 := (iff #2203 #9926) -#9928 := [rewrite]: #9927 -#10258 := [monotonicity #9928 #10255]: #10257 -#9975 := (iff #2219 #9974) -#9976 := [rewrite]: #9975 -#10261 := [monotonicity #9976 #10258]: #10260 -#10267 := [trans #10261 #10265]: #10266 -#10270 := [quant-intro #10267]: #10269 -#10281 := [trans #10270 #10279]: #10280 -#10225 := [asserted]: #2298 -#10282 := [mp #10225 #10281]: #10277 -#17911 := [mp~ #10282 #17910]: #10277 -#21962 := [mp #17911 #21961]: #21959 -#26806 := (not #21959) -#26801 := (or #26806 #26736 #26794) -#26771 := (or #26770 #26768 #26764) -#26773 := (forall (vars (?v3 S20)) (:pat #26772) #26771) -#26774 := (not #26773) -#26779 := (or #26649 #26778 #26774) -#26780 := (not #26779) -#26781 := (or #26736 #26780) -#26758 := (or #26806 #26781) -#26852 := (iff #26758 #26801) -#26808 := (or #26806 #26797) -#26811 := (iff #26808 #26801) -#26850 := [rewrite]: #26811 -#26809 := (iff #26758 #26808) -#26798 := (iff #26781 #26797) -#26795 := (iff #26780 #26794) -#26792 := (iff #26779 #26791) -#26789 := (iff #26774 #26788) -#26786 := (iff #26773 #26785) -#26783 := (iff #26771 #26782) -#26784 := [rewrite]: #26783 -#26787 := [quant-intro #26784]: #26786 -#26790 := [monotonicity #26787]: #26789 -#26793 := [monotonicity #26790]: #26792 -#26796 := [monotonicity #26793]: #26795 -#26799 := [monotonicity #26796]: #26798 -#26810 := [monotonicity #26799]: #26809 -#26853 := [trans #26810 #26850]: #26852 -#26807 := [quant-inst #3039 #26182 #26182]: #26758 -#26858 := [mp #26807 #26853]: #26801 -#28802 := [unit-resolution #26858 #21962]: #26797 -#28803 := [unit-resolution #28802 #28801]: #26794 -#26851 := (or #26791 #26777) -#26863 := [def-axiom]: #26851 -#28804 := [unit-resolution #26863 #28803]: #26777 -#28797 := [trans #28804 #28796]: #27234 -#27235 := (not #27234) -#27547 := (or #12183 #27235) -#27223 := (f54 #24996 #3043) -#27224 := (f77 #27223 0::Int #24996) -#27228 := (f35 f297 #27224) -#27229 := (= f1 #27228) -#27230 := (not #27229) -#27503 := (iff #18448 #27230) -#27491 := (iff #12183 #27229) -#27489 := (iff #27229 #12183) -#27487 := (= #27228 #3101) -#27486 := (= #27224 #3098) -#28392 := (= #27223 #3042) -#28393 := [monotonicity #28386 #28391]: #28392 -#27481 := [monotonicity #28393 #28386]: #27486 -#27488 := [monotonicity #27481]: #27487 -#27490 := [monotonicity #27488]: #27489 -#27502 := [symm #27490]: #27491 -#27511 := [monotonicity #27502]: #27503 -#27485 := [hypothesis]: #18448 -#27512 := [mp #27485 #27511]: #27230 -#27225 := (f69 #3220 #27224) -#27226 := (f147 #27225) -#27227 := (= f1 #27226) -#27240 := (or #27227 #27230) -#27243 := (not #27240) -decl f33 :: (-> S18 S1) -#27236 := (f33 #24996) -#27237 := (= f1 #27236) -#2848 := (f33 f19) -#28424 := (= #2848 #27236) -#28421 := (= #27236 #2848) -#28422 := [monotonicity #28386]: #28421 -#28425 := [symm #28422]: #28424 -#11624 := (= f1 #2848) -#2849 := (= #2848 f1) -#11626 := (iff #2849 #11624) -#11627 := [rewrite]: #11626 -#11623 := [asserted]: #2849 -#11630 := [mp #11623 #11627]: #11624 -#28426 := [trans #11630 #28425]: #27237 -#27238 := (not #27237) -#27517 := (or #27238 #27243) -#28427 := [hypothesis]: #27234 -#27181 := (<= #24998 0::Int) -#27514 := (not #27181) -#14360 := [not-or-elim #14346]: #13509 -#27164 := (* -1::Int #24998) -#27273 := (+ f296 #27164) -#27274 := (<= #27273 0::Int) -#28407 := (not #24999) -#28408 := (or #28407 #27274) -#28409 := [th-lemma arith triangle-eq]: #28408 -#28410 := [unit-resolution #28409 #28406]: #27274 -#28416 := (not #27274) -#27515 := (or #27514 #13508 #28416) -#27510 := [th-lemma arith assign-bounds -1 1]: #27515 -#27516 := [unit-resolution #27510 #28410 #14360]: #27514 +#10219 := [monotonicity #3875 #10216]: #10218 +#9891 := (iff #2203 #9890) +#9892 := [rewrite]: #9891 +#10222 := [monotonicity #9892 #10219]: #10221 +#9939 := (iff #2219 #9938) +#9940 := [rewrite]: #9939 +#10225 := [monotonicity #9940 #10222]: #10224 +#10231 := [trans #10225 #10229]: #10230 +#10234 := [quant-intro #10231]: #10233 +#10245 := [trans #10234 #10243]: #10244 +#10189 := [asserted]: #2298 +#10246 := [mp #10189 #10245]: #10241 +#17875 := [mp~ #10246 #17874]: #10241 +#21926 := [mp #17875 #21925]: #21923 +#26714 := (not #21923) +#26720 := (or #26714 #26700 #26758) +#26735 := (or #26734 #26732 #26728) +#26737 := (forall (vars (?v3 S20)) (:pat #26736) #26735) +#26738 := (not #26737) +#26743 := (or #26613 #26742 #26738) +#26744 := (not #26743) +#26745 := (or #26700 #26744) +#26716 := (or #26714 #26745) +#26810 := (iff #26716 #26720) +#26722 := (or #26714 #26761) +#26776 := (iff #26722 #26720) +#26808 := [rewrite]: #26776 +#26723 := (iff #26716 #26722) +#26762 := (iff #26745 #26761) +#26759 := (iff #26744 #26758) +#26756 := (iff #26743 #26755) +#26753 := (iff #26738 #26752) +#26750 := (iff #26737 #26749) +#26747 := (iff #26735 #26746) +#26748 := [rewrite]: #26747 +#26751 := [quant-intro #26748]: #26750 +#26754 := [monotonicity #26751]: #26753 +#26757 := [monotonicity #26754]: #26756 +#26760 := [monotonicity #26757]: #26759 +#26763 := [monotonicity #26760]: #26762 +#26724 := [monotonicity #26763]: #26723 +#26811 := [trans #26724 #26808]: #26810 +#26721 := [quant-inst #3039 #26146 #26146]: #26716 +#26812 := [mp #26721 #26811]: #26720 +#28140 := [unit-resolution #26812 #21926]: #26761 +#28132 := [unit-resolution #28140 #28108]: #26758 +#26809 := (or #26755 #26741) +#26814 := [def-axiom]: #26809 +#28150 := [unit-resolution #26814 #28132]: #26741 +#28130 := [trans #28150 #28129]: #27192 +#27139 := (<= #24962 0::Int) +#28353 := (not #27139) +#14324 := [not-or-elim #14310]: #13473 +#27122 := (* -1::Int #24962) +#27258 := (+ f297 #27122) +#27259 := (<= #27258 0::Int) +#28509 := (not #24963) +#28510 := (or #28509 #27259) +#28511 := [th-lemma arith triangle-eq]: #28510 +#28512 := [unit-resolution #28511 #28508]: #27259 +#28518 := (not #27259) +#28354 := (or #28353 #13472 #28518) +#28355 := [th-lemma arith assign-bounds -1 1]: #28354 +#28356 := [unit-resolution #28355 #28512 #14324]: #28353 #279 := (f33 #275) #805 := (:var 4 Int) #2121 := (f54 #275 #805) @@ -4353,67 +5548,67 @@ #1408 := (:var 3 S20) #2119 := (f27 #1416 #1408) #310 := (:var 2 Int) -#2117 := (f135 #275 #310) +#2117 := (f136 #275 #310) #2118 := (f54 #2117 #805) #2120 := (f26 #2118 #2119) #2139 := (pattern #2120 #2138 #279) #1590 := (f70 #1416) #2136 := (f69 #1590 #2122) #2137 := (pattern #2120 #2136 #279) -#2142 := (f147 #2136) -#9734 := (= f1 #2142) +#2142 := (f148 #2136) +#9698 := (= f1 #2142) #2140 := (f35 #1416 #2122) -#9731 := (= f1 #2140) -#21668 := (not #9731) -#21669 := (or #21668 #9734) -#21670 := (not #21669) -#9675 := (= f1 #2120) -#21644 := (not #9675) +#9695 := (= f1 #2140) +#21632 := (not #9695) +#21633 := (or #21632 #9698) +#21634 := (not #21633) +#9639 := (= f1 #2120) +#21608 := (not #9639) #2125 := (f66 #1416) -#9672 := (= f1 #2125) -#21643 := (not #9672) +#9636 := (= f1 #2125) +#21607 := (not #9636) #4206 := (* -1::Int #310) -#6270 := (+ #289 #4206) -#6867 := (>= #6270 0::Int) -#4468 := (>= #289 0::Int) -#19581 := (not #4468) +#6244 := (+ #289 #4206) +#6841 := (>= #6244 0::Int) +#4448 := (>= #289 0::Int) +#19545 := (not #4448) #4084 := (= f1 #279) -#10461 := (not #4084) -#21676 := (or #10461 #19581 #6867 #21643 #21644 #21670) -#21681 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21676) -#9737 := (not #9734) -#9740 := (and #9731 #9737) -#7934 := (not #6867) -#9713 := (and #4084 #4468 #7934 #9672 #9675) -#9718 := (not #9713) -#9754 := (or #9718 #9740) -#9757 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9754) -#21682 := (iff #9757 #21681) -#21679 := (iff #9754 #21676) -#21645 := (or #10461 #19581 #6867 #21643 #21644) -#21673 := (or #21645 #21670) -#21677 := (iff #21673 #21676) -#21678 := [rewrite]: #21677 -#21674 := (iff #9754 #21673) -#21671 := (iff #9740 #21670) -#21672 := [rewrite]: #21671 -#21654 := (iff #9718 #21645) -#21646 := (not #21645) -#21649 := (not #21646) -#21652 := (iff #21649 #21645) -#21653 := [rewrite]: #21652 -#21650 := (iff #9718 #21649) -#21647 := (iff #9713 #21646) -#21648 := [rewrite]: #21647 -#21651 := [monotonicity #21648]: #21650 -#21655 := [trans #21651 #21653]: #21654 -#21675 := [monotonicity #21655 #21672]: #21674 -#21680 := [trans #21675 #21678]: #21679 -#21683 := [quant-intro #21680]: #21682 -#17775 := (~ #9757 #9757) -#17773 := (~ #9754 #9754) -#17774 := [refl]: #17773 -#17776 := [nnf-pos #17774]: #17775 +#10425 := (not #4084) +#21640 := (or #10425 #19545 #6841 #21607 #21608 #21634) +#21645 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21640) +#9701 := (not #9698) +#9704 := (and #9695 #9701) +#7898 := (not #6841) +#9677 := (and #4084 #4448 #7898 #9636 #9639) +#9682 := (not #9677) +#9718 := (or #9682 #9704) +#9721 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9718) +#21646 := (iff #9721 #21645) +#21643 := (iff #9718 #21640) +#21609 := (or #10425 #19545 #6841 #21607 #21608) +#21637 := (or #21609 #21634) +#21641 := (iff #21637 #21640) +#21642 := [rewrite]: #21641 +#21638 := (iff #9718 #21637) +#21635 := (iff #9704 #21634) +#21636 := [rewrite]: #21635 +#21618 := (iff #9682 #21609) +#21610 := (not #21609) +#21613 := (not #21610) +#21616 := (iff #21613 #21609) +#21617 := [rewrite]: #21616 +#21614 := (iff #9682 #21613) +#21611 := (iff #9677 #21610) +#21612 := [rewrite]: #21611 +#21615 := [monotonicity #21612]: #21614 +#21619 := [trans #21615 #21617]: #21618 +#21639 := [monotonicity #21619 #21636]: #21638 +#21644 := [trans #21639 #21642]: #21643 +#21647 := [quant-intro #21644]: #21646 +#17739 := (~ #9721 #9721) +#17737 := (~ #9718 #9718) +#17738 := [refl]: #17737 +#17740 := [nnf-pos #17738]: #17739 #2143 := (= #2142 f1) #2144 := (not #2143) #2141 := (= #2140 f1) @@ -4429,242 +5624,476 @@ #2130 := (and #2126 #2129) #2146 := (implies #2130 #2145) #2147 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #2146) -#9760 := (iff #2147 #9757) -#9681 := (and #1478 #9675) -#9686 := (and #4084 #9681) -#9689 := (and #9672 #9686) -#9695 := (not #9689) -#9746 := (or #9695 #9740) -#9751 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9746) -#9758 := (iff #9751 #9757) -#9755 := (iff #9746 #9754) -#9719 := (iff #9695 #9718) -#9716 := (iff #9689 #9713) -#7937 := (and #4468 #7934) -#9704 := (and #7937 #9675) -#9707 := (and #4084 #9704) -#9710 := (and #9672 #9707) -#9714 := (iff #9710 #9713) -#9715 := [rewrite]: #9714 -#9711 := (iff #9689 #9710) -#9708 := (iff #9686 #9707) -#9705 := (iff #9681 #9704) -#7938 := (iff #1478 #7937) -#7935 := (iff #1477 #7934) -#7936 := [rewrite]: #7935 -#4467 := (iff #440 #4468) -#4469 := [rewrite]: #4467 -#7939 := [monotonicity #4469 #7936]: #7938 -#9706 := [monotonicity #7939]: #9705 -#9709 := [monotonicity #9706]: #9708 -#9712 := [monotonicity #9709]: #9711 -#9717 := [trans #9712 #9715]: #9716 -#9720 := [monotonicity #9717]: #9719 -#9756 := [monotonicity #9720]: #9755 -#9759 := [quant-intro #9756]: #9758 -#9752 := (iff #2147 #9751) -#9749 := (iff #2146 #9746) -#9743 := (implies #9689 #9740) -#9747 := (iff #9743 #9746) -#9748 := [rewrite]: #9747 -#9744 := (iff #2146 #9743) -#9741 := (iff #2145 #9740) -#9738 := (iff #2144 #9737) -#9735 := (iff #2143 #9734) -#9736 := [rewrite]: #9735 -#9739 := [monotonicity #9736]: #9738 -#9732 := (iff #2141 #9731) -#9733 := [rewrite]: #9732 -#9742 := [monotonicity #9733 #9739]: #9741 -#9690 := (iff #2130 #9689) -#9687 := (iff #2129 #9686) -#9684 := (iff #2128 #9681) -#9678 := (and #9675 #1478) -#9682 := (iff #9678 #9681) -#9683 := [rewrite]: #9682 -#9679 := (iff #2128 #9678) -#9676 := (iff #2127 #9675) -#9677 := [rewrite]: #9676 -#9680 := [monotonicity #9677]: #9679 -#9685 := [trans #9680 #9683]: #9684 +#9724 := (iff #2147 #9721) +#9645 := (and #1478 #9639) +#9650 := (and #4084 #9645) +#9653 := (and #9636 #9650) +#9659 := (not #9653) +#9710 := (or #9659 #9704) +#9715 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9710) +#9722 := (iff #9715 #9721) +#9719 := (iff #9710 #9718) +#9683 := (iff #9659 #9682) +#9680 := (iff #9653 #9677) +#7901 := (and #4448 #7898) +#9668 := (and #7901 #9639) +#9671 := (and #4084 #9668) +#9674 := (and #9636 #9671) +#9678 := (iff #9674 #9677) +#9679 := [rewrite]: #9678 +#9675 := (iff #9653 #9674) +#9672 := (iff #9650 #9671) +#9669 := (iff #9645 #9668) +#7902 := (iff #1478 #7901) +#7899 := (iff #1477 #7898) +#7900 := [rewrite]: #7899 +#4447 := (iff #440 #4448) +#4449 := [rewrite]: #4447 +#7903 := [monotonicity #4449 #7900]: #7902 +#9670 := [monotonicity #7903]: #9669 +#9673 := [monotonicity #9670]: #9672 +#9676 := [monotonicity #9673]: #9675 +#9681 := [trans #9676 #9679]: #9680 +#9684 := [monotonicity #9681]: #9683 +#9720 := [monotonicity #9684]: #9719 +#9723 := [quant-intro #9720]: #9722 +#9716 := (iff #2147 #9715) +#9713 := (iff #2146 #9710) +#9707 := (implies #9653 #9704) +#9711 := (iff #9707 #9710) +#9712 := [rewrite]: #9711 +#9708 := (iff #2146 #9707) +#9705 := (iff #2145 #9704) +#9702 := (iff #2144 #9701) +#9699 := (iff #2143 #9698) +#9700 := [rewrite]: #9699 +#9703 := [monotonicity #9700]: #9702 +#9696 := (iff #2141 #9695) +#9697 := [rewrite]: #9696 +#9706 := [monotonicity #9697 #9703]: #9705 +#9654 := (iff #2130 #9653) +#9651 := (iff #2129 #9650) +#9648 := (iff #2128 #9645) +#9642 := (and #9639 #1478) +#9646 := (iff #9642 #9645) +#9647 := [rewrite]: #9646 +#9643 := (iff #2128 #9642) +#9640 := (iff #2127 #9639) +#9641 := [rewrite]: #9640 +#9644 := [monotonicity #9641]: #9643 +#9649 := [trans #9644 #9647]: #9648 #4085 := (iff #280 #4084) #4086 := [rewrite]: #4085 -#9688 := [monotonicity #4086 #9685]: #9687 -#9673 := (iff #2126 #9672) -#9674 := [rewrite]: #9673 -#9691 := [monotonicity #9674 #9688]: #9690 -#9745 := [monotonicity #9691 #9742]: #9744 -#9750 := [trans #9745 #9748]: #9749 -#9753 := [quant-intro #9750]: #9752 -#9761 := [trans #9753 #9759]: #9760 -#9730 := [asserted]: #2147 -#9762 := [mp #9730 #9761]: #9757 -#17777 := [mp~ #9762 #17776]: #9757 -#21684 := [mp #17777 #21683]: #21681 -#27254 := (not #21681) -#27453 := (or #27254 #24846 #27181 #27235 #27238 #27243) -#27231 := (or #27230 #27227) -#27232 := (not #27231) -#27165 := (+ 0::Int #27164) -#27166 := (>= #27165 0::Int) -#27167 := (>= 0::Int 0::Int) -#27168 := (not #27167) -#27239 := (or #27238 #27168 #27166 #24846 #27235 #27232) -#27454 := (or #27254 #27239) -#27466 := (iff #27454 #27453) -#27249 := (or #24846 #27181 #27235 #27238 #27243) -#27459 := (or #27254 #27249) -#27464 := (iff #27459 #27453) -#27465 := [rewrite]: #27464 -#27460 := (iff #27454 #27459) -#27252 := (iff #27239 #27249) -#27246 := (or #27238 false #27181 #24846 #27235 #27243) -#27250 := (iff #27246 #27249) -#27251 := [rewrite]: #27250 -#27247 := (iff #27239 #27246) -#27244 := (iff #27232 #27243) -#27241 := (iff #27231 #27240) -#27242 := [rewrite]: #27241 -#27245 := [monotonicity #27242]: #27244 -#27184 := (iff #27166 #27181) -#27178 := (>= #27164 0::Int) -#27182 := (iff #27178 #27181) -#27183 := [rewrite]: #27182 -#27179 := (iff #27166 #27178) -#27176 := (= #27165 #27164) -#27177 := [rewrite]: #27176 -#27180 := [monotonicity #27177]: #27179 -#27185 := [trans #27180 #27183]: #27184 -#27174 := (iff #27168 false) -#27172 := (iff #27168 #3156) -#27170 := (iff #27167 true) -#27171 := [rewrite]: #27170 -#27173 := [monotonicity #27171]: #27172 -#27175 := [trans #27173 #12257]: #27174 -#27248 := [monotonicity #27175 #27185 #27245]: #27247 -#27253 := [trans #27248 #27251]: #27252 -#27461 := [monotonicity #27253]: #27460 -#27492 := [trans #27461 #27465]: #27466 -#27455 := [quant-inst #3039 #3043 #26182 #24998 #161 #24996]: #27454 -#27493 := [mp #27455 #27492]: #27453 -#27518 := [unit-resolution #27493 #21684 #14351 #27516 #28427]: #27517 -#27519 := [unit-resolution #27518 #28426]: #27243 -#27497 := (or #27240 #27229) -#27482 := [def-axiom]: #27497 -#27520 := [unit-resolution #27482 #27519 #27512]: false -#27548 := [lemma #27520]: #27547 -#28798 := [unit-resolution #27548 #28797]: #12183 -#28623 := (or #28377 #18448 #28443) -#28624 := [def-axiom]: #28623 -#28817 := [unit-resolution #28624 #28798]: #28816 -#28818 := [unit-resolution #28817 #28780]: #28443 -#28615 := (or #28440 #28345) -#28616 := [def-axiom]: #28615 -#28819 := [unit-resolution #28616 #28818]: #28345 -#28592 := (not #27227) -#28835 := (iff #28592 #28148) -#28832 := (iff #27227 #28147) -#28814 := (= #27226 #28146) -#28824 := (= #27225 #26985) -#28825 := [monotonicity #27481]: #28824 -#28815 := [monotonicity #28825]: #28814 -#28834 := [monotonicity #28815]: #28832 -#28833 := [monotonicity #28834]: #28835 -#28821 := [unit-resolution #27493 #21684 #14351 #27516 #28797]: #27517 -#28822 := [unit-resolution #28821 #28426]: #27243 -#28593 := (or #27240 #28592) -#28594 := [def-axiom]: #28593 -#28823 := [unit-resolution #28594 #28822]: #28592 -#28836 := [mp #28823 #28833]: #28148 -#28478 := (or #28326 #28147) -#28484 := [def-axiom]: #28478 -#28837 := [unit-resolution #28484 #28836]: #28326 -#25501 := (f23 f19) -#28366 := (= #25501 #27920) -#27753 := (= #27920 #25501) -#27686 := (= #27039 f19) -#27684 := (= #25112 f19) -#27685 := [symm #27139]: #27684 -#27369 := [hypothesis]: #27103 -#27370 := [unit-resolution #27749 #27369]: #27089 -#27416 := [trans #27409 #27370]: #27415 -#27681 := [trans #27416 #27414]: #27680 -#27683 := [monotonicity #27681]: #27682 -#27687 := [trans #27683 #27685]: #27686 -#27754 := [monotonicity #27687]: #27753 -#28467 := [symm #27754]: #28366 -#25502 := (= f25 #25501) -#25509 := (iff #11624 #25502) -#2363 := (pattern #279) -#2902 := (f23 #275) -#11803 := (= f25 #2902) -#11807 := (iff #4084 #11803) -#11810 := (forall (vars (?v0 S18)) (:pat #2363) #11807) -#18402 := (~ #11810 #11810) -#18400 := (~ #11807 #11807) -#18401 := [refl]: #18400 -#18403 := [nnf-pos #18401]: #18402 -#2915 := (= #2902 f25) -#2916 := (iff #280 #2915) -#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916) -#11811 := (iff #2917 #11810) -#11808 := (iff #2916 #11807) -#11805 := (iff #2915 #11803) -#11806 := [rewrite]: #11805 -#11809 := [monotonicity #4086 #11806]: #11808 -#11812 := [quant-intro #11809]: #11811 -#11802 := [asserted]: #2917 -#11815 := [mp #11802 #11812]: #11810 -#18404 := [mp~ #11815 #18403]: #11810 -#25168 := (not #11810) -#25512 := (or #25168 #25509) -#25513 := [quant-inst #50]: #25512 -#28838 := [unit-resolution #25513 #18404]: #25509 -#25514 := (not #25509) -#28839 := (or #25514 #25502) -#25518 := (not #11624) -#25519 := (or #25514 #25518 #25502) -#25520 := [def-axiom]: #25519 -#28840 := [unit-resolution #25520 #11630]: #28839 -#28841 := [unit-resolution #28840 #28838]: #25502 -#28468 := [trans #28841 #28467]: #28266 -#28602 := (not #28097) -#28934 := (iff #12118 #28602) -#28932 := (iff #12115 #28097) -#28930 := (iff #28097 #12115) -#28928 := (= #28096 #3053) -#28926 := (= #28095 #3040) -#28924 := (= #28095 #25117) -#28922 := (= #27775 #3044) -#28920 := (= #27775 #27145) -#27146 := (f77 #27145 0::Int #24996) -#27150 := (f69 #3220 #27146) -#27156 := (f146 #27150) -#28918 := (= #27156 #27145) -#27157 := (= #27145 #27156) -#27158 := (not #27157) -#27154 := (f147 #27150) -#27155 := (= f1 #27154) -#27151 := (f78 #27150) -#27152 := (= f1 #27151) -#27153 := (not #27152) -#27147 := (f35 f297 #27146) -#27148 := (= f1 #27147) -#27149 := (not #27148) -#27186 := (or #27149 #27153 #27155 #27158) -#27189 := (not #27186) -#27161 := (f35 f297 #27145) -#27162 := (= f1 #27161) -#28492 := (= #3051 #27161) -#28489 := (= #27161 #3051) -#28490 := [monotonicity #28789]: #28489 -#28872 := [symm #28490]: #28492 -#28873 := [trans #14368 #28872]: #27162 -#27163 := (not #27162) -#28859 := (or #27163 #27189) +#9652 := [monotonicity #4086 #9649]: #9651 +#9637 := (iff #2126 #9636) +#9638 := [rewrite]: #9637 +#9655 := [monotonicity #9638 #9652]: #9654 +#9709 := [monotonicity #9655 #9706]: #9708 +#9714 := [trans #9709 #9712]: #9713 +#9717 := [quant-intro #9714]: #9716 +#9725 := [trans #9717 #9723]: #9724 +#9694 := [asserted]: #2147 +#9726 := [mp #9694 #9725]: #9721 +#17741 := [mp~ #9726 #17740]: #9721 +#21648 := [mp #17741 #21647]: #21645 +#27193 := (not #27192) +#27212 := (not #21645) +#27669 := (or #27212 #24810 #27139 #27193 #27196 #27201) +#27189 := (or #27188 #27185) +#27190 := (not #27189) +#27123 := (+ 0::Int #27122) +#27124 := (>= #27123 0::Int) +#27125 := (>= 0::Int 0::Int) +#27126 := (not #27125) +#27197 := (or #27196 #27126 #27124 #24810 #27193 #27190) +#27664 := (or #27212 #27197) +#27712 := (iff #27664 #27669) +#27207 := (or #24810 #27139 #27193 #27196 #27201) +#27671 := (or #27212 #27207) +#27674 := (iff #27671 #27669) +#27711 := [rewrite]: #27674 +#27672 := (iff #27664 #27671) +#27210 := (iff #27197 #27207) +#27204 := (or #27196 false #27139 #24810 #27193 #27201) +#27208 := (iff #27204 #27207) +#27209 := [rewrite]: #27208 +#27205 := (iff #27197 #27204) +#27202 := (iff #27190 #27201) +#27199 := (iff #27189 #27198) +#27200 := [rewrite]: #27199 +#27203 := [monotonicity #27200]: #27202 +#27142 := (iff #27124 #27139) +#27136 := (>= #27122 0::Int) +#27140 := (iff #27136 #27139) +#27141 := [rewrite]: #27140 +#27137 := (iff #27124 #27136) +#27134 := (= #27123 #27122) +#27135 := [rewrite]: #27134 +#27138 := [monotonicity #27135]: #27137 +#27143 := [trans #27138 #27141]: #27142 +#27132 := (iff #27126 false) +#27130 := (iff #27126 #3156) +#27128 := (iff #27125 true) +#27129 := [rewrite]: #27128 +#27131 := [monotonicity #27129]: #27130 +#27133 := [trans #27131 #12221]: #27132 +#27206 := [monotonicity #27133 #27143 #27203]: #27205 +#27211 := [trans #27206 #27209]: #27210 +#27673 := [monotonicity #27211]: #27672 +#27713 := [trans #27673 #27711]: #27712 +#27670 := [quant-inst #3039 #3043 #26146 #24962 #161 #24960]: #27664 +#27714 := [mp #27670 #27713]: #27669 +#28373 := [unit-resolution #27714 #21648 #14315 #28356 #28130]: #28357 +#28352 := [unit-resolution #28373 #28528]: #27201 +#27717 := (or #27198 #27187) +#27718 := [def-axiom]: #27717 +#28371 := [unit-resolution #27718 #28352 #28112]: false +#28372 := [lemma #28371]: #12147 +#24789 := (or #23557 #18409 #18412 #23551) +#24790 := [def-axiom]: #24789 +#29169 := [unit-resolution #24790 #28372 #27593 #29168]: #23551 +#24779 := (or #23548 #23542) +#24780 := [def-axiom]: #24779 +#29170 := [unit-resolution #24780 #29169]: #23542 +decl f147 :: (-> S29 S20) +#28602 := (f69 #3220 #27044) +#28603 := (f147 #28602) +#28607 := (f36 f298 #28603) +#28608 := (= f37 #28607) +decl f222 :: (-> S19 S20 S1) +#28605 := (f222 f298 #28603) +#28606 := (= f1 #28605) +#28756 := (or #28606 #28608) +#28740 := (not #28756) +#28634 := (f148 #28602) +#28635 := (= f1 #28634) +#28636 := (not #28635) +#28631 := (f38 f298 #28603) +#28632 := (= f1 #28631) +#28633 := (not #28632) +#28750 := (or #28633 #28636) +#28753 := (not #28750) +#28639 := (f23 #27233) +#28647 := (= f25 #28639) +#28726 := (not #28647) +#28619 := (f24 #28603) +#28629 := (f23 #28619) +#28630 := (= f25 #28629) +#28745 := (or #28630 #28726 #28753 #28740) +#28793 := (not #28745) +#28624 := (f36 f298 #27044) +#28625 := (= f37 #28624) +#28623 := (f222 f298 #27044) +#28616 := (= f1 #28623) +#28595 := (or #28616 #28625) +#28597 := (not #28595) +#28706 := (or #28597 #28647) +#28704 := (not #28706) +#28796 := (or #28704 #28793) +#28779 := (not #28796) +#28643 := (f35 f298 #27044) +#28644 := (= f1 #28643) +#27803 := (= #3101 #28643) +#27432 := (= #28643 #3101) +#27430 := (= #27044 #3098) +#27425 := (= #27028 #3098) +#27426 := [symm #27571]: #27425 +#27382 := (= #27044 #27028) +#27383 := [symm #27568]: #27382 +#27431 := [trans #27383 #27426]: #27430 +#27742 := [monotonicity #27431]: #27432 +#28586 := [symm #27742]: #27803 +#28587 := [trans #28372 #28586]: #28644 +#28649 := (not #28644) +#28782 := (or #28649 #28779) +#28784 := (not #28782) +#28652 := (f79 f298 #27044) +#28648 := (= f1 #28652) +#28787 := (iff #28648 #28784) +#2438 := (f79 #86 #62) +#2439 := (pattern #2438) +#324 := (f70 #86) +#2441 := (f69 #324 #62) +#2445 := (f147 #2441) +#2456 := (f222 #86 #2445) +#10660 := (= f1 #2456) +#2454 := (f36 #86 #2445) +#10657 := (= f37 #2454) +#10663 := (or #10657 #10660) +#22034 := (not #10663) +#2450 := (f24 #2445) +#2451 := (f23 #2450) +#10651 := (= f25 #2451) +#2446 := (f38 #86 #2445) +#10642 := (= f1 #2446) +#10645 := (not #10642) +#2442 := (f148 #2441) +#10636 := (= f1 #2442) +#10639 := (not #10636) +#10648 := (or #10639 #10645) +#22033 := (not #10648) +#22035 := (or #91 #22033 #10651 #22034) +#22036 := (not #22035) +#2462 := (f222 #86 #62) +#10675 := (= f1 #2462) +#10678 := (or #3761 #10675) +#22028 := (not #10678) +#22029 := (or #68 #22028) +#22030 := (not #22029) +#22039 := (or #22030 #22036) +#22045 := (not #22039) +#22046 := (or #11261 #22045) +#22047 := (not #22046) +#10632 := (= f1 #2438) +#22052 := (iff #10632 #22047) +#22055 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22052) +#10654 := (not #10651) +#10696 := (and #68 #10648 #10654 #10663) +#10681 := (and #91 #10678) +#10702 := (or #10681 #10696) +#10707 := (and #3767 #10702) +#10710 := (iff #10632 #10707) +#10713 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10710) +#22056 := (iff #10713 #22055) +#22053 := (iff #10710 #22052) +#22050 := (iff #10707 #22047) +#22042 := (and #3767 #22039) +#22048 := (iff #22042 #22047) +#22049 := [rewrite]: #22048 +#22043 := (iff #10707 #22042) +#22040 := (iff #10702 #22039) +#22037 := (iff #10696 #22036) +#22038 := [rewrite]: #22037 +#22031 := (iff #10681 #22030) +#22032 := [rewrite]: #22031 +#22041 := [monotonicity #22032 #22038]: #22040 +#22044 := [monotonicity #22041]: #22043 +#22051 := [trans #22044 #22049]: #22050 +#22054 := [monotonicity #22051]: #22053 +#22057 := [quant-intro #22054]: #22056 +#17978 := (~ #10713 #10713) +#17976 := (~ #10710 #10710) +#17977 := [refl]: #17976 +#17979 := [nnf-pos #17977]: #17978 +#2463 := (= #2462 f1) +#2464 := (or #183 #2463) +#2465 := (and #91 #2464) +#2457 := (= #2456 f1) +#2455 := (= #2454 f37) +#2458 := (or #2455 #2457) +#2452 := (= #2451 f25) +#2453 := (not #2452) +#2459 := (and #2453 #2458) +#2447 := (= #2446 f1) +#2448 := (not #2447) +#2443 := (= #2442 f1) +#2444 := (not #2443) +#2449 := (or #2444 #2448) +#2460 := (and #2449 #2459) +#2461 := (and #68 #2460) +#2466 := (or #2461 #2465) +#2467 := (and #187 #2466) +#2440 := (= #2438 f1) +#2468 := (iff #2440 #2467) +#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468) +#10716 := (iff #2469 #10713) +#10666 := (and #10654 #10663) +#10669 := (and #10648 #10666) +#10672 := (and #68 #10669) +#10684 := (or #10672 #10681) +#10687 := (and #3767 #10684) +#10690 := (iff #10632 #10687) +#10693 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10690) +#10714 := (iff #10693 #10713) +#10711 := (iff #10690 #10710) +#10708 := (iff #10687 #10707) +#10705 := (iff #10684 #10702) +#10699 := (or #10696 #10681) +#10703 := (iff #10699 #10702) +#10704 := [rewrite]: #10703 +#10700 := (iff #10684 #10699) +#10697 := (iff #10672 #10696) +#10698 := [rewrite]: #10697 +#10701 := [monotonicity #10698]: #10700 +#10706 := [trans #10701 #10704]: #10705 +#10709 := [monotonicity #10706]: #10708 +#10712 := [monotonicity #10709]: #10711 +#10715 := [quant-intro #10712]: #10714 +#10694 := (iff #2469 #10693) +#10691 := (iff #2468 #10690) +#10688 := (iff #2467 #10687) +#10685 := (iff #2466 #10684) +#10682 := (iff #2465 #10681) +#10679 := (iff #2464 #10678) +#10676 := (iff #2463 #10675) +#10677 := [rewrite]: #10676 +#10680 := [monotonicity #3763 #10677]: #10679 +#10683 := [monotonicity #10680]: #10682 +#10673 := (iff #2461 #10672) +#10670 := (iff #2460 #10669) +#10667 := (iff #2459 #10666) +#10664 := (iff #2458 #10663) +#10661 := (iff #2457 #10660) +#10662 := [rewrite]: #10661 +#10658 := (iff #2455 #10657) +#10659 := [rewrite]: #10658 +#10665 := [monotonicity #10659 #10662]: #10664 +#10655 := (iff #2453 #10654) +#10652 := (iff #2452 #10651) +#10653 := [rewrite]: #10652 +#10656 := [monotonicity #10653]: #10655 +#10668 := [monotonicity #10656 #10665]: #10667 +#10649 := (iff #2449 #10648) +#10646 := (iff #2448 #10645) +#10643 := (iff #2447 #10642) +#10644 := [rewrite]: #10643 +#10647 := [monotonicity #10644]: #10646 +#10640 := (iff #2444 #10639) +#10637 := (iff #2443 #10636) +#10638 := [rewrite]: #10637 +#10641 := [monotonicity #10638]: #10640 +#10650 := [monotonicity #10641 #10647]: #10649 +#10671 := [monotonicity #10650 #10668]: #10670 +#10674 := [monotonicity #10671]: #10673 +#10686 := [monotonicity #10674 #10683]: #10685 +#10689 := [monotonicity #3769 #10686]: #10688 +#10634 := (iff #2440 #10632) +#10635 := [rewrite]: #10634 +#10692 := [monotonicity #10635 #10689]: #10691 +#10695 := [quant-intro #10692]: #10694 +#10717 := [trans #10695 #10715]: #10716 +#10631 := [asserted]: #2469 +#10718 := [mp #10631 #10717]: #10713 +#17980 := [mp~ #10718 #17979]: #10713 +#22058 := [mp #17980 #22057]: #22055 +#28805 := (not #22055) +#28806 := (or #28805 #28787) +#28609 := (or #28608 #28606) +#28618 := (not #28609) +#28637 := (or #28636 #28633) +#28638 := (not #28637) +#28617 := (= #28639 f25) +#28620 := (not #28617) +#28621 := (or #28620 #28638 #28630 #28618) +#28622 := (not #28621) +#28626 := (or #28625 #28616) +#28627 := (not #28626) +#28628 := (or #28617 #28627) +#28640 := (not #28628) +#28641 := (or #28640 #28622) +#28642 := (not #28641) +#28650 := (or #28649 #28642) +#28651 := (not #28650) +#28653 := (iff #28648 #28651) +#28804 := (or #28805 #28653) +#28808 := (iff #28804 #28806) +#28826 := (iff #28806 #28806) +#28827 := [rewrite]: #28826 +#28788 := (iff #28653 #28787) +#28785 := (iff #28651 #28784) +#28783 := (iff #28650 #28782) +#28780 := (iff #28642 #28779) +#28797 := (iff #28641 #28796) +#28794 := (iff #28622 #28793) +#28791 := (iff #28621 #28745) +#28742 := (or #28726 #28753 #28630 #28740) +#28746 := (iff #28742 #28745) +#28747 := [rewrite]: #28746 +#28743 := (iff #28621 #28742) +#28741 := (iff #28618 #28740) +#28757 := (iff #28609 #28756) +#28758 := [rewrite]: #28757 +#28739 := [monotonicity #28758]: #28741 +#28754 := (iff #28638 #28753) +#28751 := (iff #28637 #28750) +#28752 := [rewrite]: #28751 +#28755 := [monotonicity #28752]: #28754 +#28748 := (iff #28620 #28726) +#28654 := (iff #28617 #28647) +#28593 := [rewrite]: #28654 +#28749 := [monotonicity #28593]: #28748 +#28744 := [monotonicity #28749 #28755 #28739]: #28743 +#28792 := [trans #28744 #28747]: #28791 +#28795 := [monotonicity #28792]: #28794 +#28724 := (iff #28640 #28704) +#28711 := (iff #28628 #28706) +#28479 := (or #28647 #28597) +#28707 := (iff #28479 #28706) +#28710 := [rewrite]: #28707 +#28480 := (iff #28628 #28479) +#28598 := (iff #28627 #28597) +#28596 := (iff #28626 #28595) +#28594 := [rewrite]: #28596 +#28468 := [monotonicity #28594]: #28598 +#28469 := [monotonicity #28593 #28468]: #28480 +#28703 := [trans #28469 #28710]: #28711 +#28725 := [monotonicity #28703]: #28724 +#28777 := [monotonicity #28725 #28795]: #28797 +#28781 := [monotonicity #28777]: #28780 +#28778 := [monotonicity #28781]: #28783 +#28786 := [monotonicity #28778]: #28785 +#28803 := [monotonicity #28786]: #28788 +#28809 := [monotonicity #28803]: #28808 +#28828 := [trans #28809 #28827]: #28808 +#28807 := [quant-inst #3039 #27044]: #28804 +#28829 := [mp #28807 #28828]: #28806 +#28588 := [unit-resolution #28829 #22058]: #28787 +#27354 := (not #28648) +#28886 := (iff #18418 #27354) +#28899 := (iff #12153 #28648) +#28789 := (iff #28648 #12153) +#28590 := (= #28652 #3104) +#28591 := [monotonicity #27431]: #28590 +#28790 := [monotonicity #28591]: #28789 +#28900 := [symm #28790]: #28899 +#28887 := [monotonicity #28900]: #28886 +#28589 := [hypothesis]: #18418 +#28906 := [mp #28589 #28887]: #27354 +#27264 := (not #28787) +#27352 := (or #27264 #28648 #28782) +#27353 := [def-axiom]: #27352 +#28907 := [unit-resolution #27353 #28906 #28588]: #28782 +#27262 := (or #28784 #28649 #28779) +#27263 := [def-axiom]: #27262 +#28908 := [unit-resolution #27263 #28907 #28587]: #28779 +#28841 := (not #28630) +#29014 := (iff #12082 #28841) +#29012 := (iff #12079 #28630) +#29010 := (iff #28630 #12079) +#29008 := (= #28629 #3053) +#29006 := (= #28619 #3040) +#29004 := (= #28619 #25081) +#29002 := (= #28603 #3044) +#29000 := (= #28603 #27103) +#27104 := (f77 #27103 0::Int #24960) +#27108 := (f69 #3220 #27104) +#27114 := (f147 #27108) +#28998 := (= #27114 #27103) +#27115 := (= #27103 #27114) +#27116 := (not #27115) +#27112 := (f148 #27108) +#27113 := (= f1 #27112) +decl f78 :: (-> S29 S1) +#27109 := (f78 #27108) +#27110 := (= f1 #27109) +#27111 := (not #27110) +#27105 := (f35 f298 #27104) +#27106 := (= f1 #27105) +#27107 := (not #27106) +#27144 := (or #27107 #27111 #27113 #27116) +#27147 := (not #27144) +#27119 := (f35 f298 #27103) +#27120 := (= f1 #27119) +#28912 := (= #3051 #27119) +#28909 := (= #27119 #3051) +#28910 := [monotonicity #28364]: #28909 +#28913 := [symm #28910]: #28912 +#28914 := [trans #14332 #28913]: #27120 +#27121 := (not #27120) +#28915 := (or #27121 #27147) #319 := (:var 3 Int) #353 := (:var 2 S18) -#1513 := (f135 #353 #289) +#1513 := (f136 #353 #289) #1514 := (f54 #1513 #319) #1510 := (f54 #353 #319) #1511 := (f77 #1510 #202 #353) @@ -4677,60 +6106,60 @@ #1515 := (pattern #1512 #1514) #1521 := (f77 #1514 #202 #353) #1530 := (f35 #74 #1521) -#8095 := (= f1 #1530) -#21008 := (not #8095) +#8059 := (= f1 #1530) +#20972 := (not #8059) #1522 := (f69 #1516 #1521) #1528 := (f78 #1522) -#8092 := (= f1 #1528) -#21007 := (not #8092) -#1525 := (f147 #1522) -#8086 := (= f1 #1525) -#1523 := (f146 #1522) -#8083 := (= #1514 #1523) -#21006 := (not #8083) -#21009 := (or #21006 #8086 #21007 #21008) -#21010 := (not #21009) +#8056 := (= f1 #1528) +#20971 := (not #8056) +#1525 := (f148 #1522) +#8050 := (= f1 #1525) +#1523 := (f147 #1522) +#8047 := (= #1514 #1523) +#20970 := (not #8047) +#20973 := (or #20970 #8050 #20971 #20972) +#20974 := (not #20973) #1519 := (f35 #74 #1514) -#8080 := (= f1 #1519) -#8118 := (not #8080) -#5395 := (* -1::Int #289) -#6275 := (+ #202 #5395) -#6276 := (>= #6275 0::Int) -#21016 := (or #5124 #6276 #8118 #21010) -#21021 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #21016) -#8089 := (not #8086) -#8127 := (and #8083 #8089 #8092 #8095) -#7779 := (not #6276) -#7782 := (and #4202 #7779) -#7785 := (not #7782) -#8136 := (or #7785 #8118 #8127) -#8141 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8136) -#21022 := (iff #8141 #21021) -#21019 := (iff #8136 #21016) -#20891 := (or #5124 #6276) -#21013 := (or #20891 #8118 #21010) -#21017 := (iff #21013 #21016) -#21018 := [rewrite]: #21017 -#21014 := (iff #8136 #21013) -#21011 := (iff #8127 #21010) -#21012 := [rewrite]: #21011 -#20900 := (iff #7785 #20891) -#20892 := (not #20891) -#20895 := (not #20892) -#20898 := (iff #20895 #20891) -#20899 := [rewrite]: #20898 -#20896 := (iff #7785 #20895) -#20893 := (iff #7782 #20892) -#20894 := [rewrite]: #20893 -#20897 := [monotonicity #20894]: #20896 -#20901 := [trans #20897 #20899]: #20900 -#21015 := [monotonicity #20901 #21012]: #21014 -#21020 := [trans #21015 #21018]: #21019 -#21023 := [quant-intro #21020]: #21022 -#17140 := (~ #8141 #8141) -#17138 := (~ #8136 #8136) -#17139 := [refl]: #17138 -#17141 := [nnf-pos #17139]: #17140 +#8044 := (= f1 #1519) +#8082 := (not #8044) +#5372 := (* -1::Int #289) +#6249 := (+ #202 #5372) +#6250 := (>= #6249 0::Int) +#20980 := (or #5104 #6250 #8082 #20974) +#20985 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #20980) +#8053 := (not #8050) +#8091 := (and #8047 #8053 #8056 #8059) +#7743 := (not #6250) +#7746 := (and #4202 #7743) +#7749 := (not #7746) +#8100 := (or #7749 #8082 #8091) +#8105 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8100) +#20986 := (iff #8105 #20985) +#20983 := (iff #8100 #20980) +#20855 := (or #5104 #6250) +#20977 := (or #20855 #8082 #20974) +#20981 := (iff #20977 #20980) +#20982 := [rewrite]: #20981 +#20978 := (iff #8100 #20977) +#20975 := (iff #8091 #20974) +#20976 := [rewrite]: #20975 +#20864 := (iff #7749 #20855) +#20856 := (not #20855) +#20859 := (not #20856) +#20862 := (iff #20859 #20855) +#20863 := [rewrite]: #20862 +#20860 := (iff #7749 #20859) +#20857 := (iff #7746 #20856) +#20858 := [rewrite]: #20857 +#20861 := [monotonicity #20858]: #20860 +#20865 := [trans #20861 #20863]: #20864 +#20979 := [monotonicity #20865 #20976]: #20978 +#20984 := [trans #20979 #20982]: #20983 +#20987 := [quant-intro #20984]: #20986 +#17104 := (~ #8105 #8105) +#17102 := (~ #8100 #8100) +#17103 := [refl]: #17102 +#17105 := [nnf-pos #17103]: #17104 #1531 := (= #1530 f1) #1529 := (= #1528 f1) #1532 := (and #1529 #1531) @@ -4745,3060 +6174,1602 @@ #1520 := (= #1519 f1) #1536 := (implies #1520 #1535) #1537 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #1536) -#8144 := (iff #1537 #8141) -#8098 := (and #8092 #8095) -#8101 := (and #8089 #8098) -#8104 := (and #8083 #8101) -#7749 := (not #1415) -#8110 := (or #7749 #8104) -#8119 := (or #8118 #8110) -#8124 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8119) -#8142 := (iff #8124 #8141) -#8139 := (iff #8119 #8136) -#8130 := (or #7785 #8127) -#8133 := (or #8118 #8130) -#8137 := (iff #8133 #8136) -#8138 := [rewrite]: #8137 -#8134 := (iff #8119 #8133) -#8131 := (iff #8110 #8130) -#8128 := (iff #8104 #8127) -#8129 := [rewrite]: #8128 -#7786 := (iff #7749 #7785) -#7783 := (iff #1415 #7782) -#7780 := (iff #1414 #7779) -#7781 := [rewrite]: #7780 -#7784 := [monotonicity #4201 #7781]: #7783 -#7787 := [monotonicity #7784]: #7786 -#8132 := [monotonicity #7787 #8129]: #8131 -#8135 := [monotonicity #8132]: #8134 -#8140 := [trans #8135 #8138]: #8139 -#8143 := [quant-intro #8140]: #8142 -#8125 := (iff #1537 #8124) -#8122 := (iff #1536 #8119) -#8115 := (implies #8080 #8110) -#8120 := (iff #8115 #8119) -#8121 := [rewrite]: #8120 -#8116 := (iff #1536 #8115) -#8113 := (iff #1535 #8110) -#8107 := (implies #1415 #8104) -#8111 := (iff #8107 #8110) -#8112 := [rewrite]: #8111 -#8108 := (iff #1535 #8107) -#8105 := (iff #1534 #8104) -#8102 := (iff #1533 #8101) -#8099 := (iff #1532 #8098) -#8096 := (iff #1531 #8095) -#8097 := [rewrite]: #8096 -#8093 := (iff #1529 #8092) -#8094 := [rewrite]: #8093 -#8100 := [monotonicity #8094 #8097]: #8099 -#8090 := (iff #1527 #8089) -#8087 := (iff #1526 #8086) -#8088 := [rewrite]: #8087 -#8091 := [monotonicity #8088]: #8090 -#8103 := [monotonicity #8091 #8100]: #8102 -#8084 := (iff #1524 #8083) +#8108 := (iff #1537 #8105) +#8062 := (and #8056 #8059) +#8065 := (and #8053 #8062) +#8068 := (and #8047 #8065) +#7713 := (not #1415) +#8074 := (or #7713 #8068) +#8083 := (or #8082 #8074) +#8088 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8083) +#8106 := (iff #8088 #8105) +#8103 := (iff #8083 #8100) +#8094 := (or #7749 #8091) +#8097 := (or #8082 #8094) +#8101 := (iff #8097 #8100) +#8102 := [rewrite]: #8101 +#8098 := (iff #8083 #8097) +#8095 := (iff #8074 #8094) +#8092 := (iff #8068 #8091) +#8093 := [rewrite]: #8092 +#7750 := (iff #7713 #7749) +#7747 := (iff #1415 #7746) +#7744 := (iff #1414 #7743) +#7745 := [rewrite]: #7744 +#7748 := [monotonicity #4201 #7745]: #7747 +#7751 := [monotonicity #7748]: #7750 +#8096 := [monotonicity #7751 #8093]: #8095 +#8099 := [monotonicity #8096]: #8098 +#8104 := [trans #8099 #8102]: #8103 +#8107 := [quant-intro #8104]: #8106 +#8089 := (iff #1537 #8088) +#8086 := (iff #1536 #8083) +#8079 := (implies #8044 #8074) +#8084 := (iff #8079 #8083) #8085 := [rewrite]: #8084 -#8106 := [monotonicity #8085 #8103]: #8105 -#8109 := [monotonicity #8106]: #8108 -#8114 := [trans #8109 #8112]: #8113 -#8081 := (iff #1520 #8080) -#8082 := [rewrite]: #8081 -#8117 := [monotonicity #8082 #8114]: #8116 -#8123 := [trans #8117 #8121]: #8122 -#8126 := [quant-intro #8123]: #8125 -#8145 := [trans #8126 #8143]: #8144 -#8079 := [asserted]: #1537 -#8146 := [mp #8079 #8145]: #8141 -#17142 := [mp~ #8146 #17141]: #8141 -#21024 := [mp #17142 #21023]: #21021 -#28639 := (not #21021) -#28640 := (or #28639 #27163 #27181 #27189) -#27159 := (or #27158 #27155 #27153 #27149) -#27160 := (not #27159) -#27169 := (or #27168 #27166 #27163 #27160) -#28641 := (or #28639 #27169) -#28648 := (iff #28641 #28640) -#27195 := (or #27163 #27181 #27189) -#28643 := (or #28639 #27195) -#28646 := (iff #28643 #28640) -#28647 := [rewrite]: #28646 -#28644 := (iff #28641 #28643) -#27198 := (iff #27169 #27195) -#27192 := (or false #27181 #27163 #27189) -#27196 := (iff #27192 #27195) -#27197 := [rewrite]: #27196 -#27193 := (iff #27169 #27192) -#27190 := (iff #27160 #27189) -#27187 := (iff #27159 #27186) -#27188 := [rewrite]: #27187 -#27191 := [monotonicity #27188]: #27190 -#27194 := [monotonicity #27175 #27185 #27191]: #27193 -#27199 := [trans #27194 #27197]: #27198 -#28645 := [monotonicity #27199]: #28644 -#28649 := [trans #28645 #28647]: #28648 -#28642 := [quant-inst #3039 #3043 #24996 #24998 #161]: #28641 -#28650 := [mp #28642 #28649]: #28640 -#28860 := [unit-resolution #28650 #21024 #27516]: #28859 -#28879 := [unit-resolution #28860 #28873]: #27189 -#28589 := (or #27186 #27157) -#28587 := [def-axiom]: #28589 -#28880 := [unit-resolution #28587 #28879]: #27157 -#28919 := [symm #28880]: #28918 -#28916 := (= #27775 #27156) -#28914 := (= #26985 #27150) -#28912 := (= #27150 #26985) -#28910 := (= #27146 #3098) -#28900 := (= #27064 #3098) -#28901 := [symm #27409]: #28900 -#28908 := (= #27146 #27064) -#28898 := (= #27086 #27064) -#28899 := [symm #27370]: #28898 -#28906 := (= #27146 #27086) -#28896 := (= #3042 #27086) -#28897 := [symm #27414]: #28896 -#28904 := (= #27146 #3042) -#27318 := (f127 #26182) -#27332 := (f54 #24996 #27318) -#28894 := (= #27332 #3042) -#28888 := (= #27318 f298) -#28886 := (= #27318 #3043) -#28884 := (= #24880 #3043) -#25123 := (= #3043 #24880) -#25128 := (or #25070 #25123) -#25129 := [quant-inst #3040 #3043]: #25128 -#28881 := [unit-resolution #25129 #23306]: #25123 -#28885 := [symm #28881]: #28884 -#28882 := (= #27318 #24880) -#28883 := [monotonicity #26940]: #28882 -#28887 := [trans #28883 #28885]: #28886 -#28889 := [trans #28887 #28391]: #28888 -#28895 := [monotonicity #28386 #28889]: #28894 -#28902 := (= #27146 #27332) -#27314 := (f77 #26182 0::Int #24996) -#27335 := (= #27314 #27332) -#27338 := (not #27335) -#27315 := (f149 #27314 #26182) -#27316 := (= f1 #27315) -#27317 := (not #27316) -#27344 := (or #27317 #27338) -#27349 := (not #27344) -#28722 := (or #27721 #27349) -#27319 := (+ #27318 #27069) -#27320 := (f54 #24996 #27319) -#27321 := (= #27314 #27320) -#27322 := (not #27321) -#27323 := (or #27322 #27317) -#27324 := (not #27323) -#28764 := (or #27721 #27324) -#28766 := (iff #28764 #28722) -#28768 := (iff #28722 #28722) -#28769 := [rewrite]: #28768 -#27350 := (iff #27324 #27349) -#27347 := (iff #27323 #27344) -#27341 := (or #27338 #27317) -#27345 := (iff #27341 #27344) -#27346 := [rewrite]: #27345 -#27342 := (iff #27323 #27341) -#27339 := (iff #27322 #27338) -#27336 := (iff #27321 #27335) -#27333 := (= #27320 #27332) -#27330 := (= #27319 #27318) -#27325 := (+ #27318 0::Int) -#27328 := (= #27325 #27318) -#27329 := [rewrite]: #27328 -#27326 := (= #27319 #27325) -#27327 := [monotonicity #27078]: #27326 -#27331 := [trans #27327 #27329]: #27330 -#27334 := [monotonicity #27331]: #27333 -#27337 := [monotonicity #27334]: #27336 -#27340 := [monotonicity #27337]: #27339 -#27343 := [monotonicity #27340]: #27342 -#27348 := [trans #27343 #27346]: #27347 -#27351 := [monotonicity #27348]: #27350 -#28767 := [monotonicity #27351]: #28766 -#28770 := [trans #28767 #28769]: #28766 -#28765 := [quant-inst #26182 #161 #24996]: #28764 -#28752 := [mp #28765 #28770]: #28722 -#28890 := [unit-resolution #28752 #21240]: #27349 -#28756 := (or #27344 #27335) -#28757 := [def-axiom]: #28756 -#28891 := [unit-resolution #28757 #28890]: #27335 -#28892 := (= #27146 #27314) -#28893 := [monotonicity #28791]: #28892 -#28903 := [trans #28893 #28891]: #28902 -#28905 := [trans #28903 #28895]: #28904 -#28907 := [trans #28905 #28897]: #28906 -#28909 := [trans #28907 #28899]: #28908 -#28911 := [trans #28909 #28901]: #28910 -#28913 := [monotonicity #28911]: #28912 -#28915 := [symm #28913]: #28914 -#28917 := [monotonicity #28915]: #28916 -#28921 := [trans #28917 #28919]: #28920 -#28923 := [trans #28921 #28789]: #28922 -#28925 := [monotonicity #28923]: #28924 -#28927 := [trans #28925 #28851]: #28926 -#28929 := [monotonicity #28927]: #28928 -#28931 := [monotonicity #28929]: #28930 -#28933 := [symm #28931]: #28932 -#28935 := [monotonicity #28933]: #28934 -#28936 := [mp #14369 #28935]: #28602 -#28940 := (= #3047 #27778) -#28937 := (= #27778 #3047) -#28938 := [monotonicity #28923]: #28937 -#28941 := [symm #28938]: #28940 -#28942 := [trans #14366 #28941]: #27786 -#28597 := (not #27786) -#28598 := (or #28363 #28597) -#28599 := [def-axiom]: #28598 -#28943 := [unit-resolution #28599 #28942]: #28363 -#28611 := (or #28437 #28097 #28322 #28340 #28365) -#28612 := [def-axiom]: #28611 -#28944 := [unit-resolution #28612 #28943 #28936 #28468 #28837 #28819]: false -#28946 := [lemma #28944]: #28945 -#29128 := [unit-resolution #28946 #28653]: #12189 -#23578 := (or #18445 #18454 #23575) -#23581 := (not #23578) -#23584 := (or #18445 #18448 #23581) -#23587 := (not #23584) -#23590 := (or #18445 #18448 #23587) -#23593 := (not #23590) -#23596 := (or #13300 #23593) -#23599 := (not #23596) -#23602 := (or #13300 #23599) -#22558 := (forall (vars (?v0 Int)) #22547) -#22565 := (not #22558) -#22543 := (forall (vars (?v0 Int)) #22538) -#22564 := (not #22543) -#22566 := (or #22564 #22565) -#22567 := (not #22566) -#22596 := (or #22567 #22593) -#22602 := (not #22596) -#22603 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #22602) -#22604 := (not #22603) -#22382 := (forall (vars (?v0 Int)) #22377) -#22388 := (not #22382) -#22389 := (or #22364 #22388) -#22390 := (not #22389) -#22419 := (or #22390 #22416) -#22425 := (not #22419) -#22426 := (or #13555 #22425) -#22427 := (not #22426) -#22432 := (or #13555 #22427) -#22440 := (not #22432) -#22441 := (or #12692 #22438 #18594 #22439 #13622 #18597 #22440) -#22442 := (not #22441) -#22447 := (or #18594 #18597 #22442) -#22453 := (not #22447) -#22490 := (or #12857 #12848 #22479 #13656 #22438 #13707 #22453) -#22491 := (not #22490) -#22454 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #22453) -#22455 := (not #22454) -#22460 := (or #18556 #18565 #22455) -#22466 := (not #22460) -#22467 := (or #18556 #18559 #22466) -#22468 := (not #22467) -#22473 := (or #18556 #18559 #22468) -#22480 := (not #22473) -#22481 := (or #22479 #13656 #13708 #22480) -#22482 := (not #22481) -#22496 := (or #22482 #22491) -#22502 := (not #22496) -#22503 := (or #18556 #18565 #22479 #13656 #22502) -#22504 := (not #22503) -#22509 := (or #18556 #18565 #22504) -#22515 := (not #22509) -#22516 := (or #18556 #18559 #22515) -#22517 := (not #22516) -#22522 := (or #18556 #18559 #22517) -#22528 := (not #22522) -#22529 := (or #22479 #13656 #13801 #22528) -#22530 := (not #22529) -#22609 := (or #22530 #22604) -#22624 := (not #22609) -#22359 := (forall (vars (?v0 Int)) #22354) -#22620 := (not #22359) -#22625 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #22620 #22624) -#22626 := (not #22625) -#22631 := (or #13267 #13508 #22626) -#22638 := (not #22631) -#22348 := (forall (vars (?v0 Int)) #22343) -#22637 := (not #22348) -#22639 := (or #22637 #22638) -#22640 := (not #22639) -#22645 := (or #22337 #22640) -#22651 := (not #22645) -#22652 := (or #13472 #22651) -#22653 := (not #22652) -#22658 := (or #13472 #22653) -#22664 := (not #22658) -#22665 := (or #13267 #18445 #18454 #13258 #13249 #13240 #22664) -#22666 := (not #22665) -#22671 := (or #18445 #18454 #22666) -#22677 := (not #22671) -#22678 := (or #18445 #18448 #22677) -#22679 := (not #22678) -#22684 := (or #18445 #18448 #22679) -#22690 := (not #22684) -#22691 := (or #13300 #22690) -#22692 := (not #22691) -#22697 := (or #13300 #22692) -#23603 := (iff #22697 #23602) -#23600 := (iff #22692 #23599) -#23597 := (iff #22691 #23596) -#23594 := (iff #22690 #23593) -#23591 := (iff #22684 #23590) -#23588 := (iff #22679 #23587) -#23585 := (iff #22678 #23584) -#23582 := (iff #22677 #23581) -#23579 := (iff #22671 #23578) -#23576 := (iff #22666 #23575) -#23573 := (iff #22665 #23572) -#23570 := (iff #22664 #23569) -#23567 := (iff #22658 #23566) -#23564 := (iff #22653 #23563) -#23561 := (iff #22652 #23560) -#23558 := (iff #22651 #23557) -#23555 := (iff #22645 #23554) -#23552 := (iff #22640 #23551) -#23549 := (iff #22639 #23548) -#23546 := (iff #22638 #23545) -#23543 := (iff #22631 #23542) -#23540 := (iff #22626 #23539) -#23537 := (iff #22625 #23536) -#23534 := (iff #22624 #23533) -#23531 := (iff #22609 #23530) -#23528 := (iff #22604 #23527) -#23525 := (iff #22603 #23524) -#23522 := (iff #22602 #23521) -#23519 := (iff #22596 #23518) -#23516 := (iff #22567 #23515) -#23513 := (iff #22566 #23512) -#23510 := (iff #22565 #23509) -#23507 := (iff #22558 #23504) -#23505 := (iff #22547 #22547) -#23506 := [refl]: #23505 -#23508 := [quant-intro #23506]: #23507 -#23511 := [monotonicity #23508]: #23510 -#23502 := (iff #22564 #23501) -#23499 := (iff #22543 #23496) -#23497 := (iff #22538 #22538) -#23498 := [refl]: #23497 -#23500 := [quant-intro #23498]: #23499 -#23503 := [monotonicity #23500]: #23502 -#23514 := [monotonicity #23503 #23511]: #23513 -#23517 := [monotonicity #23514]: #23516 -#23520 := [monotonicity #23517]: #23519 -#23523 := [monotonicity #23520]: #23522 -#23526 := [monotonicity #23523]: #23525 -#23529 := [monotonicity #23526]: #23528 -#23494 := (iff #22530 #23493) -#23491 := (iff #22529 #23490) -#23488 := (iff #22528 #23487) -#23485 := (iff #22522 #23484) -#23482 := (iff #22517 #23481) -#23479 := (iff #22516 #23478) -#23476 := (iff #22515 #23475) -#23473 := (iff #22509 #23472) -#23470 := (iff #22504 #23469) -#23467 := (iff #22503 #23466) -#23464 := (iff #22502 #23463) -#23461 := (iff #22496 #23460) -#23458 := (iff #22491 #23457) -#23455 := (iff #22490 #23454) -#23422 := (iff #22453 #23421) -#23419 := (iff #22447 #23418) -#23416 := (iff #22442 #23415) -#23413 := (iff #22441 #23412) -#23410 := (iff #22440 #23409) -#23407 := (iff #22432 #23406) -#23404 := (iff #22427 #23403) -#23401 := (iff #22426 #23400) -#23398 := (iff #22425 #23397) -#23395 := (iff #22419 #23394) -#23392 := (iff #22390 #23391) -#23389 := (iff #22389 #23388) -#23386 := (iff #22388 #23385) -#23383 := (iff #22382 #23380) -#23381 := (iff #22377 #22377) -#23382 := [refl]: #23381 -#23384 := [quant-intro #23382]: #23383 -#23387 := [monotonicity #23384]: #23386 -#23390 := [monotonicity #23387]: #23389 -#23393 := [monotonicity #23390]: #23392 -#23396 := [monotonicity #23393]: #23395 -#23399 := [monotonicity #23396]: #23398 -#23402 := [monotonicity #23399]: #23401 -#23405 := [monotonicity #23402]: #23404 -#23408 := [monotonicity #23405]: #23407 -#23411 := [monotonicity #23408]: #23410 -#23414 := [monotonicity #23411]: #23413 -#23417 := [monotonicity #23414]: #23416 -#23420 := [monotonicity #23417]: #23419 -#23423 := [monotonicity #23420]: #23422 -#23456 := [monotonicity #23423]: #23455 -#23459 := [monotonicity #23456]: #23458 -#23452 := (iff #22482 #23451) -#23449 := (iff #22481 #23448) -#23446 := (iff #22480 #23445) -#23443 := (iff #22473 #23442) -#23440 := (iff #22468 #23439) -#23437 := (iff #22467 #23436) -#23434 := (iff #22466 #23433) -#23431 := (iff #22460 #23430) -#23428 := (iff #22455 #23427) -#23425 := (iff #22454 #23424) -#23426 := [monotonicity #23423]: #23425 -#23429 := [monotonicity #23426]: #23428 -#23432 := [monotonicity #23429]: #23431 -#23435 := [monotonicity #23432]: #23434 -#23438 := [monotonicity #23435]: #23437 -#23441 := [monotonicity #23438]: #23440 -#23444 := [monotonicity #23441]: #23443 -#23447 := [monotonicity #23444]: #23446 -#23450 := [monotonicity #23447]: #23449 -#23453 := [monotonicity #23450]: #23452 -#23462 := [monotonicity #23453 #23459]: #23461 -#23465 := [monotonicity #23462]: #23464 -#23468 := [monotonicity #23465]: #23467 -#23471 := [monotonicity #23468]: #23470 -#23474 := [monotonicity #23471]: #23473 -#23477 := [monotonicity #23474]: #23476 -#23480 := [monotonicity #23477]: #23479 -#23483 := [monotonicity #23480]: #23482 -#23486 := [monotonicity #23483]: #23485 -#23489 := [monotonicity #23486]: #23488 -#23492 := [monotonicity #23489]: #23491 -#23495 := [monotonicity #23492]: #23494 -#23532 := [monotonicity #23495 #23529]: #23531 -#23535 := [monotonicity #23532]: #23534 -#23378 := (iff #22620 #23377) -#23375 := (iff #22359 #23372) -#23373 := (iff #22354 #22354) -#23374 := [refl]: #23373 -#23376 := [quant-intro #23374]: #23375 -#23379 := [monotonicity #23376]: #23378 -#23538 := [monotonicity #23379 #23535]: #23537 -#23541 := [monotonicity #23538]: #23540 -#23544 := [monotonicity #23541]: #23543 -#23547 := [monotonicity #23544]: #23546 -#23370 := (iff #22637 #23369) -#23367 := (iff #22348 #23364) -#23365 := (iff #22343 #22343) -#23366 := [refl]: #23365 -#23368 := [quant-intro #23366]: #23367 -#23371 := [monotonicity #23368]: #23370 -#23550 := [monotonicity #23371 #23547]: #23549 -#23553 := [monotonicity #23550]: #23552 -#23556 := [monotonicity #23553]: #23555 -#23559 := [monotonicity #23556]: #23558 -#23562 := [monotonicity #23559]: #23561 -#23565 := [monotonicity #23562]: #23564 -#23568 := [monotonicity #23565]: #23567 -#23571 := [monotonicity #23568]: #23570 -#23574 := [monotonicity #23571]: #23573 -#23577 := [monotonicity #23574]: #23576 -#23580 := [monotonicity #23577]: #23579 -#23583 := [monotonicity #23580]: #23582 -#23586 := [monotonicity #23583]: #23585 -#23589 := [monotonicity #23586]: #23588 -#23592 := [monotonicity #23589]: #23591 -#23595 := [monotonicity #23592]: #23594 -#23598 := [monotonicity #23595]: #23597 -#23601 := [monotonicity #23598]: #23600 -#23604 := [monotonicity #23601]: #23603 -#19096 := (and #18739 #18740) -#19099 := (not #19096) -#19102 := (or #19078 #19091 #19099) -#19105 := (not #19102) -#16021 := (and #3173 #4202 #13831 #15219) -#18762 := (not #16021) -#18765 := (forall (vars (?v0 Int)) #18762) -#14462 := (and #4202 #15219) -#14461 := (not #14462) -#16007 := (or #13829 #13843 #14461) -#16012 := (forall (vars (?v0 Int)) #16007) -#18769 := (and #16012 #18765) -#19111 := (or #18769 #19105) -#19119 := (and #12269 #12272 #12275 #12278 #13513 #13516 #13801 #19111) -#18948 := (and #18615 #18616) -#18951 := (not #18948) -#18954 := (or #18930 #18943 #18951) -#18957 := (not #18954) -#15908 := (or #13558 #13572 #14461) -#15913 := (forall (vars (?v0 Int)) #15908) -#18631 := (not #13601) -#18641 := (and #18631 #15913) -#18963 := (or #18641 #18957) -#18968 := (and #13550 #18963) -#18971 := (or #13555 #18968) -#18979 := (and #12622 #13525 #13534 #13542 #13618 #15900 #18971) -#18984 := (or #18594 #18597 #18979) -#19024 := (and #12839 #12842 #13513 #13516 #13525 #13708 #18984) -#18990 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #18984) -#18995 := (or #18556 #18565 #18990) -#19001 := (and #12575 #12578 #18995) -#19006 := (or #18556 #18559 #19001) -#19012 := (and #13513 #13516 #13707 #19006) -#19029 := (or #19012 #19024) -#19035 := (and #12575 #12584 #13513 #13516 #19029) -#19040 := (or #18556 #18565 #19035) -#19046 := (and #12575 #12578 #19040) -#19051 := (or #18556 #18559 #19046) -#19057 := (and #13513 #13516 #13802 #19051) -#19124 := (or #19057 #19119) -#15834 := (or #13994 #14008 #14461) -#15839 := (forall (vars (?v0 Int)) #15834) -#19130 := (and #3109 #12250 #12258 #12515 #12543 #12546 #12549 #12552 #12555 #12558 #13509 #13513 #13516 #13980 #14028 #14034 #14056 #15839 #15851 #15868 #15885 #19124) -#19135 := (or #13267 #13508 #19130) -#15820 := (or #13475 #13487 #14461) -#15825 := (forall (vars (?v0 Int)) #15820) -#19138 := (and #15825 #19135) -#18851 := (and #18478 #18479) -#18854 := (not #18851) -#18860 := (or #18486 #18487 #18854) -#18865 := (not #18860) -#19141 := (or #18865 #19138) -#19144 := (and #13469 #19141) -#19147 := (or #13472 #19144) -#19153 := (and #3109 #12180 #12189 #12195 #12198 #12201 #19147) -#19158 := (or #18445 #18454 #19153) -#19164 := (and #12180 #12183 #19158) -#19169 := (or #18445 #18448 #19164) -#19172 := (and #12177 #19169) -#19175 := (or #13300 #19172) -#22698 := (iff #19175 #22697) -#22695 := (iff #19172 #22692) -#22687 := (and #12177 #22684) -#22693 := (iff #22687 #22692) -#22694 := [rewrite]: #22693 -#22688 := (iff #19172 #22687) -#22685 := (iff #19169 #22684) -#22682 := (iff #19164 #22679) -#22674 := (and #12180 #12183 #22671) -#22680 := (iff #22674 #22679) -#22681 := [rewrite]: #22680 -#22675 := (iff #19164 #22674) -#22672 := (iff #19158 #22671) -#22669 := (iff #19153 #22666) -#22661 := (and #3109 #12180 #12189 #12195 #12198 #12201 #22658) -#22667 := (iff #22661 #22666) -#22668 := [rewrite]: #22667 -#22662 := (iff #19153 #22661) -#22659 := (iff #19147 #22658) -#22656 := (iff #19144 #22653) -#22648 := (and #13469 #22645) -#22654 := (iff #22648 #22653) -#22655 := [rewrite]: #22654 -#22649 := (iff #19144 #22648) -#22646 := (iff #19141 #22645) -#22643 := (iff #19138 #22640) -#22634 := (and #22348 #22631) -#22641 := (iff #22634 #22640) -#22642 := [rewrite]: #22641 -#22635 := (iff #19138 #22634) -#22632 := (iff #19135 #22631) -#22629 := (iff #19130 #22626) -#22612 := (and #3109 #12250 #12258 #12515 #12543 #12546 #12549 #12552 #12555 #12558 #13509 #13513 #13516 #13980 #14028 #14034 #14056 #22359 #15851 #15868 #15885 #22609) -#22627 := (iff #22612 #22626) -#22628 := [rewrite]: #22627 -#22613 := (iff #19130 #22612) -#22610 := (iff #19124 #22609) -#22607 := (iff #19119 #22604) -#22599 := (and #12269 #12272 #12275 #12278 #13513 #13516 #13801 #22596) -#22605 := (iff #22599 #22604) -#22606 := [rewrite]: #22605 -#22600 := (iff #19119 #22599) -#22597 := (iff #19111 #22596) -#22594 := (iff #19105 #22593) -#22591 := (iff #19102 #22588) -#22574 := (or #22572 #22573) -#22585 := (or #19078 #19091 #22574) -#22589 := (iff #22585 #22588) -#22590 := [rewrite]: #22589 -#22586 := (iff #19102 #22585) -#22583 := (iff #19099 #22574) -#22575 := (not #22574) -#22578 := (not #22575) -#22581 := (iff #22578 #22574) -#22582 := [rewrite]: #22581 -#22579 := (iff #19099 #22578) -#22576 := (iff #19096 #22575) -#22577 := [rewrite]: #22576 -#22580 := [monotonicity #22577]: #22579 -#22584 := [trans #22580 #22582]: #22583 -#22587 := [monotonicity #22584]: #22586 -#22592 := [trans #22587 #22590]: #22591 -#22595 := [monotonicity #22592]: #22594 -#22570 := (iff #18769 #22567) -#22561 := (and #22543 #22558) -#22568 := (iff #22561 #22567) -#22569 := [rewrite]: #22568 -#22562 := (iff #18769 #22561) -#22559 := (iff #18765 #22558) -#22556 := (iff #18762 #22547) -#22548 := (not #22547) -#22551 := (not #22548) -#22554 := (iff #22551 #22547) -#22555 := [rewrite]: #22554 -#22552 := (iff #18762 #22551) -#22549 := (iff #16021 #22548) -#22550 := [rewrite]: #22549 -#22553 := [monotonicity #22550]: #22552 -#22557 := [trans #22553 #22555]: #22556 -#22560 := [quant-intro #22557]: #22559 -#22544 := (iff #16012 #22543) -#22541 := (iff #16007 #22538) -#20251 := (or #5124 #19613) -#22535 := (or #13829 #13843 #20251) -#22539 := (iff #22535 #22538) -#22540 := [rewrite]: #22539 -#22536 := (iff #16007 #22535) -#20260 := (iff #14461 #20251) -#20252 := (not #20251) -#20255 := (not #20252) -#20258 := (iff #20255 #20251) -#20259 := [rewrite]: #20258 -#20256 := (iff #14461 #20255) -#20253 := (iff #14462 #20252) -#20254 := [rewrite]: #20253 -#20257 := [monotonicity #20254]: #20256 -#20261 := [trans #20257 #20259]: #20260 -#22537 := [monotonicity #20261]: #22536 -#22542 := [trans #22537 #22540]: #22541 -#22545 := [quant-intro #22542]: #22544 -#22563 := [monotonicity #22545 #22560]: #22562 -#22571 := [trans #22563 #22569]: #22570 -#22598 := [monotonicity #22571 #22595]: #22597 -#22601 := [monotonicity #22598]: #22600 -#22608 := [trans #22601 #22606]: #22607 -#22533 := (iff #19057 #22530) -#22525 := (and #13513 #13516 #13802 #22522) -#22531 := (iff #22525 #22530) -#22532 := [rewrite]: #22531 -#22526 := (iff #19057 #22525) -#22523 := (iff #19051 #22522) -#22520 := (iff #19046 #22517) -#22512 := (and #12575 #12578 #22509) -#22518 := (iff #22512 #22517) -#22519 := [rewrite]: #22518 -#22513 := (iff #19046 #22512) -#22510 := (iff #19040 #22509) -#22507 := (iff #19035 #22504) -#22499 := (and #12575 #12584 #13513 #13516 #22496) -#22505 := (iff #22499 #22504) -#22506 := [rewrite]: #22505 -#22500 := (iff #19035 #22499) -#22497 := (iff #19029 #22496) -#22494 := (iff #19024 #22491) -#22487 := (and #12839 #12842 #13513 #13516 #13525 #13708 #22447) -#22492 := (iff #22487 #22491) -#22493 := [rewrite]: #22492 -#22488 := (iff #19024 #22487) -#22448 := (iff #18984 #22447) -#22445 := (iff #18979 #22442) -#22435 := (and #12622 #13525 #13534 #13542 #13618 #15900 #22432) -#22443 := (iff #22435 #22442) -#22444 := [rewrite]: #22443 -#22436 := (iff #18979 #22435) -#22433 := (iff #18971 #22432) -#22430 := (iff #18968 #22427) -#22422 := (and #13550 #22419) -#22428 := (iff #22422 #22427) -#22429 := [rewrite]: #22428 -#22423 := (iff #18968 #22422) -#22420 := (iff #18963 #22419) -#22417 := (iff #18957 #22416) -#22414 := (iff #18954 #22411) -#22397 := (or #22395 #22396) -#22408 := (or #18930 #18943 #22397) -#22412 := (iff #22408 #22411) -#22413 := [rewrite]: #22412 -#22409 := (iff #18954 #22408) -#22406 := (iff #18951 #22397) -#22398 := (not #22397) -#22401 := (not #22398) -#22404 := (iff #22401 #22397) -#22405 := [rewrite]: #22404 -#22402 := (iff #18951 #22401) -#22399 := (iff #18948 #22398) -#22400 := [rewrite]: #22399 -#22403 := [monotonicity #22400]: #22402 -#22407 := [trans #22403 #22405]: #22406 -#22410 := [monotonicity #22407]: #22409 -#22415 := [trans #22410 #22413]: #22414 -#22418 := [monotonicity #22415]: #22417 -#22393 := (iff #18641 #22390) -#22385 := (and #22363 #22382) -#22391 := (iff #22385 #22390) -#22392 := [rewrite]: #22391 -#22386 := (iff #18641 #22385) -#22383 := (iff #15913 #22382) -#22380 := (iff #15908 #22377) -#22374 := (or #13558 #13572 #20251) -#22378 := (iff #22374 #22377) -#22379 := [rewrite]: #22378 -#22375 := (iff #15908 #22374) -#22376 := [monotonicity #20261]: #22375 -#22381 := [trans #22376 #22379]: #22380 -#22384 := [quant-intro #22381]: #22383 -#22372 := (iff #18631 #22363) -#22367 := (not #22364) -#22370 := (iff #22367 #22363) -#22371 := [rewrite]: #22370 -#22368 := (iff #18631 #22367) -#22365 := (iff #13601 #22364) -#22366 := [rewrite]: #22365 -#22369 := [monotonicity #22366]: #22368 -#22373 := [trans #22369 #22371]: #22372 -#22387 := [monotonicity #22373 #22384]: #22386 -#22394 := [trans #22387 #22392]: #22393 -#22421 := [monotonicity #22394 #22418]: #22420 -#22424 := [monotonicity #22421]: #22423 -#22431 := [trans #22424 #22429]: #22430 -#22434 := [monotonicity #22431]: #22433 -#22437 := [monotonicity #22434]: #22436 -#22446 := [trans #22437 #22444]: #22445 -#22449 := [monotonicity #22446]: #22448 -#22489 := [monotonicity #22449]: #22488 -#22495 := [trans #22489 #22493]: #22494 -#22485 := (iff #19012 #22482) -#22476 := (and #13513 #13516 #13707 #22473) -#22483 := (iff #22476 #22482) -#22484 := [rewrite]: #22483 -#22477 := (iff #19012 #22476) -#22474 := (iff #19006 #22473) -#22471 := (iff #19001 #22468) -#22463 := (and #12575 #12578 #22460) -#22469 := (iff #22463 #22468) -#22470 := [rewrite]: #22469 -#22464 := (iff #19001 #22463) -#22461 := (iff #18995 #22460) -#22458 := (iff #18990 #22455) -#22450 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #22447) -#22456 := (iff #22450 #22455) -#22457 := [rewrite]: #22456 -#22451 := (iff #18990 #22450) -#22452 := [monotonicity #22449]: #22451 -#22459 := [trans #22452 #22457]: #22458 -#22462 := [monotonicity #22459]: #22461 -#22465 := [monotonicity #22462]: #22464 -#22472 := [trans #22465 #22470]: #22471 -#22475 := [monotonicity #22472]: #22474 -#22478 := [monotonicity #22475]: #22477 -#22486 := [trans #22478 #22484]: #22485 -#22498 := [monotonicity #22486 #22495]: #22497 -#22501 := [monotonicity #22498]: #22500 -#22508 := [trans #22501 #22506]: #22507 -#22511 := [monotonicity #22508]: #22510 -#22514 := [monotonicity #22511]: #22513 -#22521 := [trans #22514 #22519]: #22520 -#22524 := [monotonicity #22521]: #22523 -#22527 := [monotonicity #22524]: #22526 -#22534 := [trans #22527 #22532]: #22533 -#22611 := [monotonicity #22534 #22608]: #22610 -#22360 := (iff #15839 #22359) -#22357 := (iff #15834 #22354) -#22351 := (or #13994 #14008 #20251) -#22355 := (iff #22351 #22354) -#22356 := [rewrite]: #22355 -#22352 := (iff #15834 #22351) -#22353 := [monotonicity #20261]: #22352 -#22358 := [trans #22353 #22356]: #22357 -#22361 := [quant-intro #22358]: #22360 -#22614 := [monotonicity #22361 #22611]: #22613 -#22630 := [trans #22614 #22628]: #22629 -#22633 := [monotonicity #22630]: #22632 -#22349 := (iff #15825 #22348) -#22346 := (iff #15820 #22343) -#22340 := (or #13475 #13487 #20251) -#22344 := (iff #22340 #22343) -#22345 := [rewrite]: #22344 -#22341 := (iff #15820 #22340) -#22342 := [monotonicity #20261]: #22341 -#22347 := [trans #22342 #22345]: #22346 -#22350 := [quant-intro #22347]: #22349 -#22636 := [monotonicity #22350 #22633]: #22635 -#22644 := [trans #22636 #22642]: #22643 -#22338 := (iff #18865 #22337) -#22335 := (iff #18860 #22332) -#22318 := (or #22316 #22317) -#22329 := (or #18486 #18487 #22318) -#22333 := (iff #22329 #22332) -#22334 := [rewrite]: #22333 -#22330 := (iff #18860 #22329) -#22327 := (iff #18854 #22318) -#22319 := (not #22318) -#22322 := (not #22319) -#22325 := (iff #22322 #22318) -#22326 := [rewrite]: #22325 -#22323 := (iff #18854 #22322) -#22320 := (iff #18851 #22319) -#22321 := [rewrite]: #22320 -#22324 := [monotonicity #22321]: #22323 -#22328 := [trans #22324 #22326]: #22327 -#22331 := [monotonicity #22328]: #22330 -#22336 := [trans #22331 #22334]: #22335 -#22339 := [monotonicity #22336]: #22338 -#22647 := [monotonicity #22339 #22644]: #22646 -#22650 := [monotonicity #22647]: #22649 -#22657 := [trans #22650 #22655]: #22656 -#22660 := [monotonicity #22657]: #22659 -#22663 := [monotonicity #22660]: #22662 -#22670 := [trans #22663 #22668]: #22669 -#22673 := [monotonicity #22670]: #22672 -#22676 := [monotonicity #22673]: #22675 -#22683 := [trans #22676 #22681]: #22682 -#22686 := [monotonicity #22683]: #22685 -#22689 := [monotonicity #22686]: #22688 -#22696 := [trans #22689 #22694]: #22695 -#22699 := [monotonicity #22696]: #22698 -#18741 := (and #18740 #18739) -#18742 := (not #18741) -#18745 := (+ #18744 #13841) -#18746 := (<= #18745 0::Int) -#18747 := (+ ?v0!15 #13442) -#18748 := (>= #18747 0::Int) -#18749 := (or #18748 #18746 #18742) -#18750 := (not #18749) -#18773 := (or #18750 #18769) -#18526 := (not #13521) -#18733 := (not #12313) -#18730 := (not #12322) -#18727 := (not #12331) -#18724 := (not #12340) -#18777 := (and #18724 #18727 #18730 #18733 #18526 #13805 #18773) -#15936 := (and #13534 #15900) -#15939 := (not #15936) -#18657 := (not #15939) -#18617 := (and #18616 #18615) -#18618 := (not #18617) -#18621 := (+ #18620 #13570) -#18622 := (<= #18621 0::Int) -#18623 := (+ ?v0!14 #13551) -#18624 := (>= #18623 0::Int) -#18625 := (or #18624 #18622 #18618) -#18626 := (not #18625) -#18645 := (or #18626 #18641) -#18611 := (not #13555) -#18649 := (and #18611 #18645) -#18653 := (or #13555 #18649) -#18606 := (not #13622) -#18603 := (not #13547) -#18600 := (not #12692) -#18660 := (and #18600 #18603 #18606 #18653 #18657) -#18664 := (or #18594 #18597 #18660) -#18591 := (not #13530) -#18691 := (not #12848) -#18688 := (not #12857) -#18696 := (and #18688 #18691 #18526 #18591 #13713 #18664) -#18588 := (not #13656) -#18585 := (not #12731) -#18582 := (not #12740) -#18579 := (not #12758) -#18576 := (not #12767) -#18573 := (not #12776) -#18568 := (not #12785) -#18668 := (and #18568 #18573 #18576 #18579 #18582 #18585 #18588 #18591 #18664) -#18672 := (or #18556 #18565 #18668) -#18562 := (not #12797) -#18676 := (and #18562 #18672) -#18680 := (or #18556 #18559 #18676) -#18684 := (and #18526 #13707 #18680) -#18700 := (or #18684 #18696) -#18704 := (and #18568 #18526 #18700) -#18708 := (or #18556 #18565 #18704) -#18712 := (and #18562 #18708) -#18716 := (or #18556 #18559 #18712) -#18720 := (and #18526 #13802 #18716) -#18781 := (or #18720 #18777) -#15890 := (and #14056 #15885) -#15893 := (not #15890) -#18551 := (not #15893) -#15873 := (and #13513 #15868) -#15876 := (not #15873) -#18548 := (not #15876) -#15856 := (and #14034 #15851) -#15859 := (not #15856) -#18545 := (not #15859) -#18535 := (not #14077) -#18532 := (not #14031) -#18529 := (not #13991) -#18523 := (not #13024) -#18520 := (not #13033) -#18517 := (not #13042) -#18514 := (not #13051) -#18511 := (not #13060) -#18508 := (not #13974) -#18505 := (not #15299) -#18785 := (and #18505 #18508 #18511 #18514 #18517 #18520 #18523 #18526 #18529 #18532 #18535 #15839 #18545 #18548 #18551 #18781) -#18789 := (or #13267 #14234 #18785) -#18793 := (and #15825 #18789) -#18480 := (and #18479 #18478) -#18481 := (not #18480) -#18488 := (or #18487 #18486 #18481) -#18489 := (not #18488) -#18797 := (or #18489 #18793) -#18474 := (not #13472) -#18801 := (and #18474 #18797) -#18805 := (or #13472 #18801) -#18469 := (not #13240) -#18466 := (not #13249) -#18463 := (not #13258) -#18460 := (not #13276) -#18457 := (not #13267) -#18809 := (and #18457 #18460 #18463 #18466 #18469 #18805) -#18813 := (or #18445 #18454 #18809) -#18451 := (not #13288) -#18817 := (and #18451 #18813) -#18821 := (or #18445 #18448 #18817) -#18442 := (not #13300) -#18825 := (and #18442 #18821) -#18829 := (or #13300 #18825) -#19176 := (iff #18829 #19175) -#19173 := (iff #18825 #19172) -#19170 := (iff #18821 #19169) -#19167 := (iff #18817 #19164) -#19161 := (and #12186 #19158) -#19165 := (iff #19161 #19164) -#19166 := [rewrite]: #19165 -#19162 := (iff #18817 #19161) -#19159 := (iff #18813 #19158) -#19156 := (iff #18809 #19153) -#19150 := (and #3109 #12192 #12195 #12198 #12201 #19147) -#19154 := (iff #19150 #19153) -#19155 := [rewrite]: #19154 -#19151 := (iff #18809 #19150) -#19148 := (iff #18805 #19147) -#19145 := (iff #18801 #19144) -#19142 := (iff #18797 #19141) -#19139 := (iff #18793 #19138) -#19136 := (iff #18789 #19135) -#19133 := (iff #18785 #19130) -#19127 := (and #12258 #12515 #12543 #12546 #12549 #12552 #12561 #13518 #13986 #14028 #14072 #15839 #15856 #15873 #15890 #19124) -#19131 := (iff #19127 #19130) -#19132 := [rewrite]: #19131 -#19128 := (iff #18785 #19127) -#19125 := (iff #18781 #19124) -#19122 := (iff #18777 #19119) -#19116 := (and #12269 #12272 #12275 #12278 #13518 #13801 #19111) -#19120 := (iff #19116 #19119) -#19121 := [rewrite]: #19120 -#19117 := (iff #18777 #19116) -#19114 := (iff #18773 #19111) -#19108 := (or #19105 #18769) -#19112 := (iff #19108 #19111) -#19113 := [rewrite]: #19112 -#19109 := (iff #18773 #19108) -#19106 := (iff #18750 #19105) -#19103 := (iff #18749 #19102) -#19100 := (iff #18742 #19099) -#19097 := (iff #18741 #19096) -#19098 := [rewrite]: #19097 -#19101 := [monotonicity #19098]: #19100 -#19094 := (iff #18746 #19091) -#19083 := (+ #13841 #18744) -#19086 := (<= #19083 0::Int) -#19092 := (iff #19086 #19091) -#19093 := [rewrite]: #19092 -#19087 := (iff #18746 #19086) -#19084 := (= #18745 #19083) -#19085 := [rewrite]: #19084 -#19088 := [monotonicity #19085]: #19087 -#19095 := [trans #19088 #19093]: #19094 -#19081 := (iff #18748 #19078) -#19070 := (+ #13442 ?v0!15) -#19073 := (>= #19070 0::Int) -#19079 := (iff #19073 #19078) -#19080 := [rewrite]: #19079 -#19074 := (iff #18748 #19073) -#19071 := (= #18747 #19070) -#19072 := [rewrite]: #19071 -#19075 := [monotonicity #19072]: #19074 -#19082 := [trans #19075 #19080]: #19081 -#19104 := [monotonicity #19082 #19095 #19101]: #19103 -#19107 := [monotonicity #19104]: #19106 -#19110 := [monotonicity #19107]: #19109 -#19115 := [trans #19110 #19113]: #19114 -#18882 := (iff #18526 #13518) -#18883 := [rewrite]: #18882 -#19068 := (iff #18733 #12278) -#19069 := [rewrite]: #19068 -#19066 := (iff #18730 #12275) -#19067 := [rewrite]: #19066 -#19064 := (iff #18727 #12272) -#19065 := [rewrite]: #19064 -#19062 := (iff #18724 #12269) -#19063 := [rewrite]: #19062 -#19118 := [monotonicity #19063 #19065 #19067 #19069 #18883 #13809 #19115]: #19117 -#19123 := [trans #19118 #19121]: #19122 -#19060 := (iff #18720 #19057) -#19054 := (and #13518 #13802 #19051) -#19058 := (iff #19054 #19057) -#19059 := [rewrite]: #19058 -#19055 := (iff #18720 #19054) -#19052 := (iff #18716 #19051) -#19049 := (iff #18712 #19046) -#19043 := (and #12581 #19040) -#19047 := (iff #19043 #19046) -#19048 := [rewrite]: #19047 -#19044 := (iff #18712 #19043) -#19041 := (iff #18708 #19040) -#19038 := (iff #18704 #19035) -#19032 := (and #12587 #13518 #19029) -#19036 := (iff #19032 #19035) -#19037 := [rewrite]: #19036 -#19033 := (iff #18704 #19032) -#19030 := (iff #18700 #19029) -#19027 := (iff #18696 #19024) -#19021 := (and #12839 #12842 #13518 #13527 #13708 #18984) -#19025 := (iff #19021 #19024) -#19026 := [rewrite]: #19025 -#19022 := (iff #18696 #19021) -#18985 := (iff #18664 #18984) -#18982 := (iff #18660 #18979) -#18976 := (and #12622 #13544 #13618 #18971 #15936) -#18980 := (iff #18976 #18979) -#18981 := [rewrite]: #18980 -#18977 := (iff #18660 #18976) -#18974 := (iff #18657 #15936) -#18975 := [rewrite]: #18974 -#18972 := (iff #18653 #18971) -#18969 := (iff #18649 #18968) -#18966 := (iff #18645 #18963) -#18960 := (or #18957 #18641) -#18964 := (iff #18960 #18963) -#18965 := [rewrite]: #18964 -#18961 := (iff #18645 #18960) -#18958 := (iff #18626 #18957) -#18955 := (iff #18625 #18954) -#18952 := (iff #18618 #18951) -#18949 := (iff #18617 #18948) -#18950 := [rewrite]: #18949 -#18953 := [monotonicity #18950]: #18952 -#18946 := (iff #18622 #18943) -#18935 := (+ #13570 #18620) -#18938 := (<= #18935 0::Int) -#18944 := (iff #18938 #18943) -#18945 := [rewrite]: #18944 -#18939 := (iff #18622 #18938) -#18936 := (= #18621 #18935) -#18937 := [rewrite]: #18936 -#18940 := [monotonicity #18937]: #18939 -#18947 := [trans #18940 #18945]: #18946 -#18933 := (iff #18624 #18930) -#18922 := (+ #13551 ?v0!14) -#18925 := (>= #18922 0::Int) -#18931 := (iff #18925 #18930) -#18932 := [rewrite]: #18931 -#18926 := (iff #18624 #18925) -#18923 := (= #18623 #18922) -#18924 := [rewrite]: #18923 -#18927 := [monotonicity #18924]: #18926 -#18934 := [trans #18927 #18932]: #18933 -#18956 := [monotonicity #18934 #18947 #18953]: #18955 -#18959 := [monotonicity #18956]: #18958 -#18962 := [monotonicity #18959]: #18961 -#18967 := [trans #18962 #18965]: #18966 -#18920 := (iff #18611 #13550) -#18921 := [rewrite]: #18920 -#18970 := [monotonicity #18921 #18967]: #18969 -#18973 := [monotonicity #18970]: #18972 -#18918 := (iff #18606 #13618) -#18919 := [rewrite]: #18918 -#18916 := (iff #18603 #13544) -#18917 := [rewrite]: #18916 -#18914 := (iff #18600 #12622) -#18915 := [rewrite]: #18914 -#18978 := [monotonicity #18915 #18917 #18919 #18973 #18975]: #18977 -#18983 := [trans #18978 #18981]: #18982 -#18986 := [monotonicity #18983]: #18985 -#18912 := (iff #18591 #13527) -#18913 := [rewrite]: #18912 -#19019 := (iff #18691 #12842) -#19020 := [rewrite]: #19019 -#19017 := (iff #18688 #12839) -#19018 := [rewrite]: #19017 -#19023 := [monotonicity #19018 #19020 #18883 #18913 #13717 #18986]: #19022 -#19028 := [trans #19023 #19026]: #19027 -#19015 := (iff #18684 #19012) -#19009 := (and #13518 #13707 #19006) -#19013 := (iff #19009 #19012) -#19014 := [rewrite]: #19013 -#19010 := (iff #18684 #19009) -#19007 := (iff #18680 #19006) -#19004 := (iff #18676 #19001) -#18998 := (and #12581 #18995) -#19002 := (iff #18998 #19001) -#19003 := [rewrite]: #19002 -#18999 := (iff #18676 #18998) -#18996 := (iff #18672 #18995) -#18993 := (iff #18668 #18990) -#18987 := (and #12587 #12590 #12593 #12596 #12601 #12604 #13516 #13527 #18984) -#18991 := (iff #18987 #18990) -#18992 := [rewrite]: #18991 -#18988 := (iff #18668 #18987) -#18910 := (iff #18588 #13516) -#18911 := [rewrite]: #18910 -#18908 := (iff #18585 #12604) -#18909 := [rewrite]: #18908 -#18906 := (iff #18582 #12601) -#18907 := [rewrite]: #18906 -#18904 := (iff #18579 #12596) -#18905 := [rewrite]: #18904 -#18902 := (iff #18576 #12593) -#18903 := [rewrite]: #18902 -#18900 := (iff #18573 #12590) -#18901 := [rewrite]: #18900 -#18898 := (iff #18568 #12587) -#18899 := [rewrite]: #18898 -#18989 := [monotonicity #18899 #18901 #18903 #18905 #18907 #18909 #18911 #18913 #18986]: #18988 -#18994 := [trans #18989 #18992]: #18993 -#18997 := [monotonicity #18994]: #18996 -#18896 := (iff #18562 #12581) -#18897 := [rewrite]: #18896 -#19000 := [monotonicity #18897 #18997]: #18999 -#19005 := [trans #19000 #19003]: #19004 -#19008 := [monotonicity #19005]: #19007 -#19011 := [monotonicity #18883 #19008]: #19010 -#19016 := [trans #19011 #19014]: #19015 -#19031 := [monotonicity #19016 #19028]: #19030 -#19034 := [monotonicity #18899 #18883 #19031]: #19033 -#19039 := [trans #19034 #19037]: #19038 -#19042 := [monotonicity #19039]: #19041 -#19045 := [monotonicity #18897 #19042]: #19044 -#19050 := [trans #19045 #19048]: #19049 -#19053 := [monotonicity #19050]: #19052 -#19056 := [monotonicity #18883 #19053]: #19055 -#19061 := [trans #19056 #19059]: #19060 -#19126 := [monotonicity #19061 #19123]: #19125 -#18894 := (iff #18551 #15890) -#18895 := [rewrite]: #18894 -#18892 := (iff #18548 #15873) -#18893 := [rewrite]: #18892 -#18890 := (iff #18545 #15856) -#18891 := [rewrite]: #18890 -#18888 := (iff #18535 #14072) -#18889 := [rewrite]: #18888 -#18886 := (iff #18532 #14028) -#18887 := [rewrite]: #18886 -#18884 := (iff #18529 #13986) -#18885 := [rewrite]: #18884 -#18880 := (iff #18523 #12561) -#18881 := [rewrite]: #18880 -#18878 := (iff #18520 #12552) -#18879 := [rewrite]: #18878 -#18876 := (iff #18517 #12549) -#18877 := [rewrite]: #18876 -#18874 := (iff #18514 #12546) -#18875 := [rewrite]: #18874 -#18872 := (iff #18511 #12543) -#18873 := [rewrite]: #18872 -#18870 := (iff #18508 #12515) -#18871 := [rewrite]: #18870 -#18868 := (iff #18505 #12258) -#18869 := [rewrite]: #18868 -#19129 := [monotonicity #18869 #18871 #18873 #18875 #18877 #18879 #18881 #18883 #18885 #18887 #18889 #18891 #18893 #18895 #19126]: #19128 -#19134 := [trans #19129 #19132]: #19133 -#19137 := [monotonicity #14238 #19134]: #19136 -#19140 := [monotonicity #19137]: #19139 -#18866 := (iff #18489 #18865) -#18863 := (iff #18488 #18860) -#18857 := (or #18487 #18486 #18854) -#18861 := (iff #18857 #18860) -#18862 := [rewrite]: #18861 -#18858 := (iff #18488 #18857) -#18855 := (iff #18481 #18854) -#18852 := (iff #18480 #18851) -#18853 := [rewrite]: #18852 -#18856 := [monotonicity #18853]: #18855 -#18859 := [monotonicity #18856]: #18858 -#18864 := [trans #18859 #18862]: #18863 -#18867 := [monotonicity #18864]: #18866 -#19143 := [monotonicity #18867 #19140]: #19142 -#18849 := (iff #18474 #13469) -#18850 := [rewrite]: #18849 -#19146 := [monotonicity #18850 #19143]: #19145 -#19149 := [monotonicity #19146]: #19148 -#18847 := (iff #18469 #12201) -#18848 := [rewrite]: #18847 -#18845 := (iff #18466 #12198) -#18846 := [rewrite]: #18845 -#18843 := (iff #18463 #12195) -#18844 := [rewrite]: #18843 -#18841 := (iff #18460 #12192) -#18842 := [rewrite]: #18841 -#18839 := (iff #18457 #3109) -#18840 := [rewrite]: #18839 -#19152 := [monotonicity #18840 #18842 #18844 #18846 #18848 #19149]: #19151 -#19157 := [trans #19152 #19155]: #19156 -#19160 := [monotonicity #19157]: #19159 -#18837 := (iff #18451 #12186) -#18838 := [rewrite]: #18837 -#19163 := [monotonicity #18838 #19160]: #19162 -#19168 := [trans #19163 #19166]: #19167 -#19171 := [monotonicity #19168]: #19170 -#18835 := (iff #18442 #12177) -#18836 := [rewrite]: #18835 -#19174 := [monotonicity #18836 #19171]: #19173 -#19177 := [monotonicity #19174]: #19176 -#16026 := (exists (vars (?v0 Int)) #16021) -#16015 := (not #16012) -#16029 := (or #16015 #16026) -#16032 := (and #16012 #16029) -#16035 := (or #12340 #12331 #12322 #12313 #13521 #13802 #16032) -#15916 := (not #15913) -#15922 := (or #13601 #15916) -#15927 := (and #15913 #15922) -#15930 := (or #13555 #15927) -#15933 := (and #13550 #15930) -#15945 := (or #12692 #13547 #13622 #15933 #15939) -#15950 := (and #13534 #15900 #15945) -#15976 := (or #12857 #12848 #13521 #13530 #13707 #15950) -#15953 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #15950) -#15956 := (and #12575 #12584 #15953) -#15959 := (or #12797 #15956) -#15962 := (and #12575 #12578 #15959) -#15968 := (or #13521 #13708 #15962) -#15981 := (and #15968 #15976) -#15984 := (or #12785 #13521 #15981) -#15987 := (and #12575 #12584 #15984) -#15990 := (or #12797 #15987) -#15993 := (and #12575 #12578 #15990) -#15999 := (or #13521 #13801 #15993) -#16038 := (and #15999 #16035) -#15842 := (not #15839) -#16044 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14031 #14077 #15842 #15859 #15876 #15893 #16038) -#16049 := (and #3109 #13509 #16044) -#15828 := (not #15825) -#16052 := (or #15828 #16049) -#16055 := (and #15825 #16052) -#16058 := (or #13472 #16055) -#16061 := (and #13469 #16058) -#16064 := (or #13267 #13276 #13258 #13249 #13240 #16061) -#16067 := (and #12180 #12189 #16064) -#16070 := (or #13288 #16067) -#16073 := (and #12180 #12183 #16070) -#16076 := (or #13300 #16073) -#16079 := (and #12177 #16076) -#16082 := (not #16079) -#18830 := (~ #16082 #18829) -#18826 := (not #16076) -#18827 := (~ #18826 #18825) -#18822 := (not #16073) -#18823 := (~ #18822 #18821) -#18818 := (not #16070) -#18819 := (~ #18818 #18817) -#18814 := (not #16067) -#18815 := (~ #18814 #18813) -#18810 := (not #16064) -#18811 := (~ #18810 #18809) -#18806 := (not #16061) -#18807 := (~ #18806 #18805) -#18802 := (not #16058) -#18803 := (~ #18802 #18801) -#18798 := (not #16055) -#18799 := (~ #18798 #18797) -#18794 := (not #16052) -#18795 := (~ #18794 #18793) -#18790 := (not #16049) -#18791 := (~ #18790 #18789) -#18786 := (not #16044) -#18787 := (~ #18786 #18785) -#18782 := (not #16038) -#18783 := (~ #18782 #18781) -#18778 := (not #16035) -#18779 := (~ #18778 #18777) -#18774 := (not #16032) -#18775 := (~ #18774 #18773) -#18770 := (not #16029) -#18771 := (~ #18770 #18769) -#18766 := (not #16026) -#18767 := (~ #18766 #18765) -#18763 := (~ #18762 #18762) -#18764 := [refl]: #18763 -#18768 := [nnf-neg #18764]: #18767 -#18759 := (not #16015) -#18760 := (~ #18759 #16012) -#18757 := (~ #16012 #16012) -#18755 := (~ #16007 #16007) -#18756 := [refl]: #18755 -#18758 := [nnf-pos #18756]: #18757 -#18761 := [nnf-neg #18758]: #18760 -#18772 := [nnf-neg #18761 #18768]: #18771 -#18751 := (~ #16015 #18750) -#18752 := [sk]: #18751 -#18776 := [nnf-neg #18752 #18772]: #18775 -#18736 := (~ #13805 #13805) -#18737 := [refl]: #18736 -#18527 := (~ #18526 #18526) -#18528 := [refl]: #18527 -#18734 := (~ #18733 #18733) -#18735 := [refl]: #18734 -#18731 := (~ #18730 #18730) -#18732 := [refl]: #18731 -#18728 := (~ #18727 #18727) -#18729 := [refl]: #18728 -#18725 := (~ #18724 #18724) -#18726 := [refl]: #18725 -#18780 := [nnf-neg #18726 #18729 #18732 #18735 #18528 #18737 #18776]: #18779 -#18721 := (not #15999) -#18722 := (~ #18721 #18720) -#18717 := (not #15993) -#18718 := (~ #18717 #18716) -#18713 := (not #15990) -#18714 := (~ #18713 #18712) -#18709 := (not #15987) -#18710 := (~ #18709 #18708) -#18705 := (not #15984) -#18706 := (~ #18705 #18704) -#18701 := (not #15981) -#18702 := (~ #18701 #18700) -#18697 := (not #15976) -#18698 := (~ #18697 #18696) -#18665 := (not #15950) -#18666 := (~ #18665 #18664) -#18661 := (not #15945) -#18662 := (~ #18661 #18660) -#18658 := (~ #18657 #18657) -#18659 := [refl]: #18658 -#18654 := (not #15933) -#18655 := (~ #18654 #18653) -#18650 := (not #15930) -#18651 := (~ #18650 #18649) -#18646 := (not #15927) -#18647 := (~ #18646 #18645) -#18642 := (not #15922) -#18643 := (~ #18642 #18641) -#18638 := (not #15916) -#18639 := (~ #18638 #15913) -#18636 := (~ #15913 #15913) -#18634 := (~ #15908 #15908) -#18635 := [refl]: #18634 -#18637 := [nnf-pos #18635]: #18636 -#18640 := [nnf-neg #18637]: #18639 -#18632 := (~ #18631 #18631) -#18633 := [refl]: #18632 -#18644 := [nnf-neg #18633 #18640]: #18643 -#18627 := (~ #15916 #18626) -#18628 := [sk]: #18627 -#18648 := [nnf-neg #18628 #18644]: #18647 -#18612 := (~ #18611 #18611) -#18613 := [refl]: #18612 -#18652 := [nnf-neg #18613 #18648]: #18651 -#18609 := (~ #13555 #13555) -#18610 := [refl]: #18609 -#18656 := [nnf-neg #18610 #18652]: #18655 -#18607 := (~ #18606 #18606) -#18608 := [refl]: #18607 -#18604 := (~ #18603 #18603) -#18605 := [refl]: #18604 -#18601 := (~ #18600 #18600) -#18602 := [refl]: #18601 -#18663 := [nnf-neg #18602 #18605 #18608 #18656 #18659]: #18662 -#18598 := (~ #18597 #18597) -#18599 := [refl]: #18598 -#18595 := (~ #18594 #18594) -#18596 := [refl]: #18595 -#18667 := [nnf-neg #18596 #18599 #18663]: #18666 -#18694 := (~ #13713 #13713) -#18695 := [refl]: #18694 -#18592 := (~ #18591 #18591) -#18593 := [refl]: #18592 -#18692 := (~ #18691 #18691) -#18693 := [refl]: #18692 -#18689 := (~ #18688 #18688) -#18690 := [refl]: #18689 -#18699 := [nnf-neg #18690 #18693 #18528 #18593 #18695 #18667]: #18698 -#18685 := (not #15968) -#18686 := (~ #18685 #18684) -#18681 := (not #15962) -#18682 := (~ #18681 #18680) -#18677 := (not #15959) -#18678 := (~ #18677 #18676) -#18673 := (not #15956) -#18674 := (~ #18673 #18672) -#18669 := (not #15953) -#18670 := (~ #18669 #18668) -#18589 := (~ #18588 #18588) -#18590 := [refl]: #18589 -#18586 := (~ #18585 #18585) -#18587 := [refl]: #18586 -#18583 := (~ #18582 #18582) -#18584 := [refl]: #18583 -#18580 := (~ #18579 #18579) -#18581 := [refl]: #18580 -#18577 := (~ #18576 #18576) -#18578 := [refl]: #18577 -#18574 := (~ #18573 #18573) -#18575 := [refl]: #18574 -#18569 := (~ #18568 #18568) -#18570 := [refl]: #18569 -#18671 := [nnf-neg #18570 #18575 #18578 #18581 #18584 #18587 #18590 #18593 #18667]: #18670 -#18566 := (~ #18565 #18565) -#18567 := [refl]: #18566 -#18557 := (~ #18556 #18556) -#18558 := [refl]: #18557 -#18675 := [nnf-neg #18558 #18567 #18671]: #18674 -#18563 := (~ #18562 #18562) -#18564 := [refl]: #18563 -#18679 := [nnf-neg #18564 #18675]: #18678 -#18560 := (~ #18559 #18559) -#18561 := [refl]: #18560 -#18683 := [nnf-neg #18558 #18561 #18679]: #18682 -#18571 := (~ #13707 #13707) -#18572 := [refl]: #18571 -#18687 := [nnf-neg #18528 #18572 #18683]: #18686 -#18703 := [nnf-neg #18687 #18699]: #18702 -#18707 := [nnf-neg #18570 #18528 #18703]: #18706 -#18711 := [nnf-neg #18558 #18567 #18707]: #18710 -#18715 := [nnf-neg #18564 #18711]: #18714 -#18719 := [nnf-neg #18558 #18561 #18715]: #18718 -#18554 := (~ #13802 #13802) -#18555 := [refl]: #18554 -#18723 := [nnf-neg #18528 #18555 #18719]: #18722 -#18784 := [nnf-neg #18723 #18780]: #18783 -#18552 := (~ #18551 #18551) -#18553 := [refl]: #18552 -#18549 := (~ #18548 #18548) -#18550 := [refl]: #18549 -#18546 := (~ #18545 #18545) -#18547 := [refl]: #18546 -#18542 := (not #15842) -#18543 := (~ #18542 #15839) -#18540 := (~ #15839 #15839) -#18538 := (~ #15834 #15834) -#18539 := [refl]: #18538 -#18541 := [nnf-pos #18539]: #18540 -#18544 := [nnf-neg #18541]: #18543 -#18536 := (~ #18535 #18535) -#18537 := [refl]: #18536 -#18533 := (~ #18532 #18532) -#18534 := [refl]: #18533 -#18530 := (~ #18529 #18529) -#18531 := [refl]: #18530 -#18524 := (~ #18523 #18523) -#18525 := [refl]: #18524 -#18521 := (~ #18520 #18520) -#18522 := [refl]: #18521 -#18518 := (~ #18517 #18517) -#18519 := [refl]: #18518 -#18515 := (~ #18514 #18514) -#18516 := [refl]: #18515 -#18512 := (~ #18511 #18511) -#18513 := [refl]: #18512 -#18509 := (~ #18508 #18508) -#18510 := [refl]: #18509 -#18506 := (~ #18505 #18505) -#18507 := [refl]: #18506 -#18788 := [nnf-neg #18507 #18510 #18513 #18516 #18519 #18522 #18525 #18528 #18531 #18534 #18537 #18544 #18547 #18550 #18553 #18784]: #18787 -#18503 := (~ #14234 #14234) -#18504 := [refl]: #18503 -#18501 := (~ #13267 #13267) -#18502 := [refl]: #18501 -#18792 := [nnf-neg #18502 #18504 #18788]: #18791 -#18498 := (not #15828) -#18499 := (~ #18498 #15825) -#18496 := (~ #15825 #15825) -#18494 := (~ #15820 #15820) -#18495 := [refl]: #18494 -#18497 := [nnf-pos #18495]: #18496 -#18500 := [nnf-neg #18497]: #18499 -#18796 := [nnf-neg #18500 #18792]: #18795 -#18490 := (~ #15828 #18489) -#18491 := [sk]: #18490 -#18800 := [nnf-neg #18491 #18796]: #18799 -#18475 := (~ #18474 #18474) -#18476 := [refl]: #18475 -#18804 := [nnf-neg #18476 #18800]: #18803 -#18472 := (~ #13472 #13472) -#18473 := [refl]: #18472 -#18808 := [nnf-neg #18473 #18804]: #18807 -#18470 := (~ #18469 #18469) -#18471 := [refl]: #18470 -#18467 := (~ #18466 #18466) -#18468 := [refl]: #18467 -#18464 := (~ #18463 #18463) -#18465 := [refl]: #18464 -#18461 := (~ #18460 #18460) -#18462 := [refl]: #18461 -#18458 := (~ #18457 #18457) -#18459 := [refl]: #18458 -#18812 := [nnf-neg #18459 #18462 #18465 #18468 #18471 #18808]: #18811 -#18455 := (~ #18454 #18454) -#18456 := [refl]: #18455 -#18446 := (~ #18445 #18445) -#18447 := [refl]: #18446 -#18816 := [nnf-neg #18447 #18456 #18812]: #18815 -#18452 := (~ #18451 #18451) -#18453 := [refl]: #18452 -#18820 := [nnf-neg #18453 #18816]: #18819 -#18449 := (~ #18448 #18448) -#18450 := [refl]: #18449 -#18824 := [nnf-neg #18447 #18450 #18820]: #18823 -#18443 := (~ #18442 #18442) -#18444 := [refl]: #18443 -#18828 := [nnf-neg #18444 #18824]: #18827 -#18440 := (~ #13300 #13300) -#18441 := [refl]: #18440 -#18831 := [nnf-neg #18441 #18828]: #18830 -#15324 := (or #12340 #12331 #12322 #12313 #13521 #13802 #13888) -#15329 := (and #13824 #15324) -#15335 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14025 #14031 #14043 #14053 #14066 #14077 #15329) -#15340 := (and #3109 #13509 #15335) -#15343 := (or #13505 #15340) -#15346 := (and #13502 #15343) -#15349 := (or #13472 #15346) -#15352 := (and #13469 #15349) -#15355 := (or #13267 #13276 #13258 #13249 #13240 #15352) -#15358 := (and #12180 #12189 #15355) -#15361 := (or #13288 #15358) -#15364 := (and #12180 #12183 #15361) -#15367 := (or #13300 #15364) -#15370 := (and #12177 #15367) -#15373 := (not #15370) -#16083 := (iff #15373 #16082) -#16080 := (iff #15370 #16079) -#16077 := (iff #15367 #16076) -#16074 := (iff #15364 #16073) -#16071 := (iff #15361 #16070) -#16068 := (iff #15358 #16067) -#16065 := (iff #15355 #16064) -#16062 := (iff #15352 #16061) -#16059 := (iff #15349 #16058) -#16056 := (iff #15346 #16055) -#16053 := (iff #15343 #16052) -#16050 := (iff #15340 #16049) -#16047 := (iff #15335 #16044) -#16041 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #15842 #14031 #15859 #15876 #15893 #14077 #16038) -#16045 := (iff #16041 #16044) -#16046 := [rewrite]: #16045 -#16042 := (iff #15335 #16041) -#16039 := (iff #15329 #16038) -#16036 := (iff #15324 #16035) -#16033 := (iff #13888 #16032) -#16030 := (iff #13883 #16029) -#16027 := (iff #13874 #16026) -#16024 := (iff #13869 #16021) -#16018 := (and #3173 #4202 #15219 #13831) -#16022 := (iff #16018 #16021) -#16023 := [rewrite]: #16022 -#16019 := (iff #13869 #16018) -#15214 := (iff #4516 #15219) -#15235 := -4294967295::Int -#15227 := (+ -4294967295::Int #202) -#15220 := (<= #15227 0::Int) -#15216 := (iff #15220 #15219) -#15217 := [rewrite]: #15216 -#15221 := (iff #4516 #15220) -#15222 := (= #4515 #15227) -#15228 := (+ #202 -4294967295::Int) -#15224 := (= #15228 #15227) -#15225 := [rewrite]: #15224 -#15229 := (= #4515 #15228) -#15230 := (= #4514 -4294967295::Int) -#15236 := (* -1::Int 4294967295::Int) -#15232 := (= #15236 -4294967295::Int) -#15233 := [rewrite]: #15232 -#15237 := (= #4514 #15236) -#7637 := (= f87 4294967295::Int) -#990 := 65536::Int -#1365 := (* 65536::Int 65536::Int) -#1370 := (- #1365 1::Int) -#1371 := (= f87 #1370) -#7638 := (iff #1371 #7637) -#7635 := (= #1370 4294967295::Int) -#1053 := 4294967296::Int -#7628 := (- 4294967296::Int 1::Int) -#7633 := (= #7628 4294967295::Int) -#7634 := [rewrite]: #7633 -#7630 := (= #1370 #7628) -#7599 := (= #1365 4294967296::Int) -#7600 := [rewrite]: #7599 -#7631 := [monotonicity #7600]: #7630 -#7636 := [trans #7631 #7634]: #7635 -#7639 := [monotonicity #7636]: #7638 -#7627 := [asserted]: #1371 -#7642 := [mp #7627 #7639]: #7637 -#15234 := [monotonicity #7642]: #15237 -#15231 := [trans #15234 #15233]: #15230 -#15226 := [monotonicity #15231]: #15229 -#15223 := [trans #15226 #15225]: #15222 -#15218 := [monotonicity #15223]: #15221 -#15215 := [trans #15218 #15217]: #15214 -#16020 := [monotonicity #15215]: #16019 -#16025 := [trans #16020 #16023]: #16024 -#16028 := [quant-intro #16025]: #16027 -#16016 := (iff #13877 #16015) -#16013 := (iff #13857 #16012) -#16010 := (iff #13852 #16007) -#16004 := (or #14461 #13829 #13843) -#16008 := (iff #16004 #16007) -#16009 := [rewrite]: #16008 -#16005 := (iff #13852 #16004) -#14458 := (iff #5738 #14461) -#14463 := (iff #4523 #14462) -#14460 := [monotonicity #15215]: #14463 -#14459 := [monotonicity #14460]: #14458 -#16006 := [monotonicity #14459]: #16005 -#16011 := [trans #16006 #16009]: #16010 -#16014 := [quant-intro #16011]: #16013 -#16017 := [monotonicity #16014]: #16016 -#16031 := [monotonicity #16017 #16028]: #16030 -#16034 := [monotonicity #16014 #16031]: #16033 -#16037 := [monotonicity #16034]: #16036 -#16002 := (iff #13824 #15999) -#15996 := (or #13521 #15993 #13801) -#16000 := (iff #15996 #15999) -#16001 := [rewrite]: #16000 -#15997 := (iff #13824 #15996) -#15994 := (iff #13795 #15993) -#15991 := (iff #13789 #15990) -#15988 := (iff #13784 #15987) -#15985 := (iff #13776 #15984) -#15982 := (iff #13767 #15981) -#15979 := (iff #13762 #15976) -#15973 := (or #12857 #12848 #13521 #13530 #15950 #13707) -#15977 := (iff #15973 #15976) -#15978 := [rewrite]: #15977 -#15974 := (iff #13762 #15973) -#15951 := (iff #13651 #15950) -#15948 := (iff #13643 #15945) -#15942 := (or #12692 #13547 #15933 #13622 #15939) -#15946 := (iff #15942 #15945) -#15947 := [rewrite]: #15946 -#15943 := (iff #13643 #15942) -#15940 := (iff #13628 #15939) -#15937 := (iff #13625 #15936) -#15903 := (iff #13536 #15900) -#15845 := (+ 4294967295::Int #13537) -#15896 := (>= #15845 1::Int) -#15901 := (iff #15896 #15900) -#15902 := [rewrite]: #15901 -#15897 := (iff #13536 #15896) -#15846 := (= #13538 #15845) -#15847 := [monotonicity #7642]: #15846 -#15898 := [monotonicity #15847]: #15897 -#15904 := [trans #15898 #15902]: #15903 -#15938 := [monotonicity #15904]: #15937 -#15941 := [monotonicity #15938]: #15940 -#15934 := (iff #13615 #15933) -#15931 := (iff #13612 #15930) -#15928 := (iff #13609 #15927) -#15925 := (iff #13606 #15922) -#15919 := (or #15916 #13601) -#15923 := (iff #15919 #15922) -#15924 := [rewrite]: #15923 -#15920 := (iff #13606 #15919) -#15917 := (iff #13589 #15916) -#15914 := (iff #13586 #15913) -#15911 := (iff #13581 #15908) -#15905 := (or #14461 #13558 #13572) -#15909 := (iff #15905 #15908) -#15910 := [rewrite]: #15909 -#15906 := (iff #13581 #15905) -#15907 := [monotonicity #14459]: #15906 -#15912 := [trans #15907 #15910]: #15911 -#15915 := [quant-intro #15912]: #15914 -#15918 := [monotonicity #15915]: #15917 -#15921 := [monotonicity #15918]: #15920 -#15926 := [trans #15921 #15924]: #15925 -#15929 := [monotonicity #15915 #15926]: #15928 -#15932 := [monotonicity #15929]: #15931 -#15935 := [monotonicity #15932]: #15934 -#15944 := [monotonicity #15935 #15941]: #15943 -#15949 := [trans #15944 #15947]: #15948 -#15952 := [monotonicity #15904 #15949]: #15951 -#15975 := [monotonicity #15952]: #15974 -#15980 := [trans #15975 #15978]: #15979 -#15971 := (iff #13732 #15968) -#15965 := (or #13521 #15962 #13708) -#15969 := (iff #15965 #15968) -#15970 := [rewrite]: #15969 -#15966 := (iff #13732 #15965) -#15963 := (iff #13702 #15962) -#15960 := (iff #13696 #15959) -#15957 := (iff #13691 #15956) -#15954 := (iff #13683 #15953) -#15955 := [monotonicity #15952]: #15954 -#15958 := [monotonicity #15955]: #15957 -#15961 := [monotonicity #15958]: #15960 -#15964 := [monotonicity #15961]: #15963 -#15967 := [monotonicity #15964]: #15966 -#15972 := [trans #15967 #15970]: #15971 -#15983 := [monotonicity #15972 #15980]: #15982 -#15986 := [monotonicity #15983]: #15985 -#15989 := [monotonicity #15986]: #15988 -#15992 := [monotonicity #15989]: #15991 -#15995 := [monotonicity #15992]: #15994 -#15998 := [monotonicity #15995]: #15997 -#16003 := [trans #15998 #16001]: #16002 -#16040 := [monotonicity #16003 #16037]: #16039 -#15894 := (iff #14066 #15893) -#15891 := (iff #14063 #15890) -#15888 := (iff #14059 #15885) -#15879 := (+ 255::Int #14006) -#15882 := (>= #15879 0::Int) -#15886 := (iff #15882 #15885) -#15887 := [rewrite]: #15886 -#15883 := (iff #14059 #15882) -#15880 := (= #14060 #15879) -#1375 := (= f89 255::Int) -#7641 := [asserted]: #1375 -#15881 := [monotonicity #7641]: #15880 -#15884 := [monotonicity #15881]: #15883 -#15889 := [trans #15884 #15887]: #15888 -#15892 := [monotonicity #15889]: #15891 -#15895 := [monotonicity #15892]: #15894 -#15877 := (iff #14053 #15876) -#15874 := (iff #14050 #15873) -#15871 := (iff #14046 #15868) -#15862 := (+ 4294967295::Int #13977) -#15865 := (>= #15862 0::Int) -#15869 := (iff #15865 #15868) -#15870 := [rewrite]: #15869 -#15866 := (iff #14046 #15865) -#15863 := (= #14047 #15862) -#15864 := [monotonicity #7642]: #15863 -#15867 := [monotonicity #15864]: #15866 -#15872 := [trans #15867 #15870]: #15871 -#15875 := [monotonicity #15872]: #15874 -#15878 := [monotonicity #15875]: #15877 -#15860 := (iff #14043 #15859) -#15857 := (iff #14040 #15856) -#15854 := (iff #14037 #15851) -#15848 := (>= #15845 0::Int) -#15852 := (iff #15848 #15851) -#15853 := [rewrite]: #15852 -#15849 := (iff #14037 #15848) -#15850 := [monotonicity #15847]: #15849 -#15855 := [trans #15850 #15853]: #15854 -#15858 := [monotonicity #15855]: #15857 -#15861 := [monotonicity #15858]: #15860 -#15843 := (iff #14025 #15842) -#15840 := (iff #14022 #15839) -#15837 := (iff #14017 #15834) -#15831 := (or #14461 #13994 #14008) -#15835 := (iff #15831 #15834) -#15836 := [rewrite]: #15835 -#15832 := (iff #14017 #15831) -#15833 := [monotonicity #14459]: #15832 -#15838 := [trans #15833 #15836]: #15837 -#15841 := [quant-intro #15838]: #15840 -#15844 := [monotonicity #15841]: #15843 -#16043 := [monotonicity #15844 #15861 #15878 #15895 #16040]: #16042 -#16048 := [trans #16043 #16046]: #16047 -#16051 := [monotonicity #16048]: #16050 -#15829 := (iff #13505 #15828) -#15826 := (iff #13502 #15825) -#15823 := (iff #13497 #15820) -#15817 := (or #14461 #13475 #13487) -#15821 := (iff #15817 #15820) -#15822 := [rewrite]: #15821 -#15818 := (iff #13497 #15817) -#15819 := [monotonicity #14459]: #15818 -#15824 := [trans #15819 #15822]: #15823 -#15827 := [quant-intro #15824]: #15826 -#15830 := [monotonicity #15827]: #15829 -#16054 := [monotonicity #15830 #16051]: #16053 -#16057 := [monotonicity #15827 #16054]: #16056 -#16060 := [monotonicity #16057]: #16059 -#16063 := [monotonicity #16060]: #16062 -#16066 := [monotonicity #16063]: #16065 -#16069 := [monotonicity #16066]: #16068 -#16072 := [monotonicity #16069]: #16071 -#16075 := [monotonicity #16072]: #16074 -#16078 := [monotonicity #16075]: #16077 -#16081 := [monotonicity #16078]: #16080 -#16084 := [monotonicity #16081]: #16083 -#14361 := (not #14213) -#15374 := (iff #14361 #15373) -#15371 := (iff #14213 #15370) -#15368 := (iff #14210 #15367) -#15365 := (iff #14205 #15364) -#15362 := (iff #14199 #15361) -#15359 := (iff #14194 #15358) -#15356 := (iff #14186 #15355) -#15353 := (iff #14165 #15352) -#15350 := (iff #14162 #15349) -#15347 := (iff #14159 #15346) -#15344 := (iff #14156 #15343) -#15341 := (iff #14151 #15340) -#15338 := (iff #14143 #15335) -#15332 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #15329 #13991 #14025 #14031 #14043 #14053 #14066 #14077) -#15336 := (iff #15332 #15335) -#15337 := [rewrite]: #15336 -#15333 := (iff #14143 #15332) -#15330 := (iff #13950 #15329) -#15327 := (iff #13945 #15324) -#15309 := (or #12340 #12331 #12322 #12313 #13521 #13888) -#15321 := (or #13521 #13802 #15309) -#15325 := (iff #15321 #15324) -#15326 := [rewrite]: #15325 -#15322 := (iff #13945 #15321) -#15319 := (iff #13920 #15309) -#15314 := (and true #15309) -#15317 := (iff #15314 #15309) -#15318 := [rewrite]: #15317 -#15315 := (iff #13920 #15314) -#15312 := (iff #13915 #15309) -#15306 := (or false #12340 #12331 #12322 #12313 #13521 #13888) -#15310 := (iff #15306 #15309) -#15311 := [rewrite]: #15310 -#15307 := (iff #13915 #15306) -#15304 := (iff #12374 false) -#15302 := (iff #12374 #3156) -#15040 := (iff #10960 true) -#10959 := [asserted]: #2542 -#10966 := [mp #10959 #10963]: #10960 -#15041 := [iff-true #10966]: #15040 -#15303 := [monotonicity #15041]: #15302 -#15305 := [trans #15303 #12257]: #15304 -#15308 := [monotonicity #15305]: #15307 -#15313 := [trans #15308 #15311]: #15312 -#15316 := [monotonicity #15041 #15313]: #15315 -#15320 := [trans #15316 #15318]: #15319 -#15323 := [monotonicity #15320]: #15322 -#15328 := [trans #15323 #15326]: #15327 -#15331 := [monotonicity #15328]: #15330 -#15300 := (iff #12402 #15299) -#15297 := (iff #12264 #12258) -#15292 := (and true #12258) -#15295 := (iff #15292 #12258) -#15296 := [rewrite]: #15295 -#15293 := (iff #12264 #15292) -#15276 := (iff #12145 true) -#15277 := [iff-true #14351]: #15276 -#15294 := [monotonicity #15277]: #15293 -#15298 := [trans #15294 #15296]: #15297 -#15301 := [monotonicity #15298]: #15300 -#15334 := [monotonicity #15301 #15331]: #15333 -#15339 := [trans #15334 #15337]: #15338 -#15342 := [monotonicity #15339]: #15341 -#15345 := [monotonicity #15342]: #15344 -#15348 := [monotonicity #15345]: #15347 -#15351 := [monotonicity #15348]: #15350 -#15354 := [monotonicity #15351]: #15353 -#15357 := [monotonicity #15354]: #15356 -#15360 := [monotonicity #15357]: #15359 -#15363 := [monotonicity #15360]: #15362 -#15366 := [monotonicity #15363]: #15365 -#15369 := [monotonicity #15366]: #15368 -#15372 := [monotonicity #15369]: #15371 -#15375 := [monotonicity #15372]: #15374 -#14362 := [not-or-elim #14346]: #14361 -#15376 := [mp #14362 #15375]: #15373 -#16085 := [mp #15376 #16084]: #16082 -#18832 := [mp~ #16085 #18831]: #18829 -#18833 := [mp #18832 #19177]: #19175 -#22700 := [mp #18833 #22699]: #22697 -#23605 := [mp #22700 #23604]: #23602 -#29129 := [unit-resolution #23605 #27033]: #23599 -#24829 := (or #23596 #23590) -#24830 := [def-axiom]: #24829 -#29130 := [unit-resolution #24830 #29129]: #23590 -#24825 := (or #23593 #18445 #18448 #23587) -#24826 := [def-axiom]: #24825 -#29134 := [unit-resolution #24826 #27642 #28798 #29130]: #23587 -#24815 := (or #23584 #23578) -#24816 := [def-axiom]: #24815 -#29135 := [unit-resolution #24816 #29134]: #23578 -#24809 := (or #23581 #18445 #18454 #23575) -#24810 := [def-axiom]: #24809 -#29136 := [unit-resolution #24810 #29135 #29128 #27642]: #23575 -#24787 := (or #23572 #3109) -#24788 := [def-axiom]: #24787 -#29137 := [unit-resolution #24788 #29136]: #3109 -#24799 := (or #23572 #23566) -#24800 := [def-axiom]: #24799 -#29663 := [unit-resolution #24800 #29136]: #23566 -#29664 := (or #23569 #23563) -#27310 := [hypothesis]: #13472 -#27311 := [th-lemma arith farkas 1 1 #14360 #27310]: false -#27312 := [lemma #27311]: #13469 -#24785 := (or #23569 #13472 #23563) -#24786 := [def-axiom]: #24785 -#29665 := [unit-resolution #24786 #27312]: #29664 -#29666 := [unit-resolution #29665 #29663]: #23563 -#24777 := (or #23560 #23554) -#24778 := [def-axiom]: #24777 -#29667 := [unit-resolution #24778 #29666]: #23554 -#27615 := (* -1::Int #3108) -#27616 := (+ f306 #27615) -#27617 := (>= #27616 0::Int) -#29138 := (or #13267 #27617) -#29139 := [th-lemma arith triangle-eq]: #29138 -#29140 := [unit-resolution #29139 #29137]: #27617 -#24455 := (not #18486) -#29141 := [hypothesis]: #22337 -#24456 := (or #22332 #24455) -#24457 := [def-axiom]: #24456 -#29142 := [unit-resolution #24457 #29141]: #24455 -#29102 := (+ #3108 #18484) -#29104 := (>= #29102 0::Int) -#29101 := (= #3108 #18483) -#29149 := (= #18483 #3108) -#29147 := (= #18482 #3098) -#29145 := (= ?v0!13 0::Int) -#24458 := (not #18487) -#24459 := (or #22332 #24458) -#24460 := [def-axiom]: #24459 -#29143 := [unit-resolution #24460 #29141]: #24458 -#24453 := (or #22332 #18479) -#24454 := [def-axiom]: #24453 -#29144 := [unit-resolution #24454 #29141]: #18479 -#29146 := [th-lemma arith eq-propagate 0 0 #29144 #29143]: #29145 -#29148 := [monotonicity #29146]: #29147 -#29150 := [monotonicity #29148]: #29149 -#29151 := [symm #29150]: #29101 -#29152 := (not #29101) -#29153 := (or #29152 #29104) -#29154 := [th-lemma arith triangle-eq]: #29153 -#29155 := [unit-resolution #29154 #29151]: #29104 -#29156 := [th-lemma arith farkas 1 -1 1 #29155 #29142 #29140]: false -#29157 := [lemma #29156]: #22332 -#24773 := (or #23557 #22337 #23551) +#8080 := (iff #1536 #8079) +#8077 := (iff #1535 #8074) +#8071 := (implies #1415 #8068) +#8075 := (iff #8071 #8074) +#8076 := [rewrite]: #8075 +#8072 := (iff #1535 #8071) +#8069 := (iff #1534 #8068) +#8066 := (iff #1533 #8065) +#8063 := (iff #1532 #8062) +#8060 := (iff #1531 #8059) +#8061 := [rewrite]: #8060 +#8057 := (iff #1529 #8056) +#8058 := [rewrite]: #8057 +#8064 := [monotonicity #8058 #8061]: #8063 +#8054 := (iff #1527 #8053) +#8051 := (iff #1526 #8050) +#8052 := [rewrite]: #8051 +#8055 := [monotonicity #8052]: #8054 +#8067 := [monotonicity #8055 #8064]: #8066 +#8048 := (iff #1524 #8047) +#8049 := [rewrite]: #8048 +#8070 := [monotonicity #8049 #8067]: #8069 +#8073 := [monotonicity #8070]: #8072 +#8078 := [trans #8073 #8076]: #8077 +#8045 := (iff #1520 #8044) +#8046 := [rewrite]: #8045 +#8081 := [monotonicity #8046 #8078]: #8080 +#8087 := [trans #8081 #8085]: #8086 +#8090 := [quant-intro #8087]: #8089 +#8109 := [trans #8090 #8107]: #8108 +#8043 := [asserted]: #1537 +#8110 := [mp #8043 #8109]: #8105 +#17106 := [mp~ #8110 #17105]: #8105 +#20988 := [mp #17106 #20987]: #20985 +#27726 := (not #20985) +#27734 := (or #27726 #27121 #27139 #27147) +#27117 := (or #27116 #27113 #27111 #27107) +#27118 := (not #27117) +#27127 := (or #27126 #27124 #27121 #27118) +#27725 := (or #27726 #27127) +#28114 := (iff #27725 #27734) +#27153 := (or #27121 #27139 #27147) +#27733 := (or #27726 #27153) +#27738 := (iff #27733 #27734) +#27739 := [rewrite]: #27738 +#27736 := (iff #27725 #27733) +#27156 := (iff #27127 #27153) +#27150 := (or false #27139 #27121 #27147) +#27154 := (iff #27150 #27153) +#27155 := [rewrite]: #27154 +#27151 := (iff #27127 #27150) +#27148 := (iff #27118 #27147) +#27145 := (iff #27117 #27144) +#27146 := [rewrite]: #27145 +#27149 := [monotonicity #27146]: #27148 +#27152 := [monotonicity #27133 #27143 #27149]: #27151 +#27157 := [trans #27152 #27155]: #27156 +#27737 := [monotonicity #27157]: #27736 +#28134 := [trans #27737 #27739]: #28114 +#27735 := [quant-inst #3039 #3043 #24960 #24962 #161]: #27725 +#27527 := [mp #27735 #28134]: #27734 +#28916 := [unit-resolution #27527 #20988 #28356]: #28915 +#28917 := [unit-resolution #28916 #28914]: #27147 +#28369 := (or #27144 #27115) +#28110 := [def-axiom]: #28369 +#28918 := [unit-resolution #28110 #28917]: #27115 +#28999 := [symm #28918]: #28998 +#28996 := (= #28603 #27114) +#28994 := (= #28602 #27108) +#26949 := (f69 #3220 #3098) +#28992 := (= #26949 #27108) +#28990 := (= #27108 #26949) +#28986 := (= #27104 #3098) +#26957 := (f128 #3098) +#26986 := (f54 #24960 #26957) +#28980 := (= #26986 #3098) +#26987 := (= #3098 #26986) +#28920 := (= #3099 #26977) +#28921 := [symm #27532]: #28920 +#28922 := [trans #27593 #28921]: #26978 +#26989 := (or #26985 #26987) +#27469 := (or #26158 #26985 #26987) +#26988 := (or #26987 #26985) +#27470 := (or #26158 #26988) +#27635 := (iff #27470 #27469) +#27506 := (or #26158 #26989) +#27519 := (iff #27506 #27469) +#27632 := [rewrite]: #27519 +#27507 := (iff #27470 #27506) +#26990 := (iff #26988 #26989) +#26991 := [rewrite]: #26990 +#27518 := [monotonicity #26991]: #27507 +#27636 := [trans #27518 #27632]: #27635 +#27505 := [quant-inst #3098 #24960]: #27470 +#27637 := [mp #27505 #27636]: #27469 +#28923 := [unit-resolution #27637 #18248]: #26989 +#28924 := [unit-resolution #28923 #28922]: #26987 +#28981 := [symm #28924]: #28980 +#28984 := (= #27104 #26986) +#27307 := (f128 #26146) +#27314 := (+ #27033 #27307) +#27317 := (f54 #24960 #27314) +#28978 := (= #27317 #26986) +#28972 := (= #27314 #26957) +#28970 := (= #26957 #27314) +#28573 := (* -1::Int #27307) +#28580 := (+ #24844 #28573) +#28581 := (<= #28580 0::Int) +#28579 := (= #24844 #27307) +#28925 := (= #27307 #24844) +#28926 := [monotonicity #26872]: #28925 +#28927 := [symm #28926]: #28579 +#28928 := (not #28579) +#28929 := (or #28928 #28581) +#28930 := [th-lemma arith triangle-eq]: #28929 +#28931 := [unit-resolution #28930 #28927]: #28581 +#28582 := (>= #28580 0::Int) +#28932 := (or #28928 #28582) +#28933 := [th-lemma arith triangle-eq]: #28932 +#28934 := [unit-resolution #28933 #28927]: #28582 +#27237 := (f128 #27044) +#27241 := (* -1::Int #27237) +#28542 := (+ #26957 #27241) +#28543 := (<= #28542 0::Int) +#28541 := (= #26957 #27237) +#28935 := (= #27237 #26957) +#28936 := [monotonicity #27431]: #28935 +#28937 := [symm #28936]: #28541 +#28938 := (not #28541) +#28939 := (or #28938 #28543) +#28940 := [th-lemma arith triangle-eq]: #28939 +#28941 := [unit-resolution #28940 #28937]: #28543 +#28544 := (>= #28542 0::Int) +#28942 := (or #28938 #28544) +#28943 := [th-lemma arith triangle-eq]: #28942 +#28944 := [unit-resolution #28943 #28937]: #28544 +#27710 := (* -1::Int #27034) +#27716 := (+ #24844 #27710) +#27719 := (<= #27716 0::Int) +#27715 := (= #24844 #27034) +#28952 := (= #3043 #27034) +#28950 := (= #27034 #3043) +#28945 := (= #24797 #3042) +#28946 := [symm #27569]: #28945 +#28951 := [monotonicity #28946]: #28950 +#28953 := [symm #28951]: #28952 +#28948 := (= #24844 #3043) +#25087 := (= #3043 #24844) +#25092 := (or #25034 #25087) +#25093 := [quant-inst #3040 #3043]: #25092 +#28947 := [unit-resolution #25093 #23270]: #25087 +#28949 := [symm #28947]: #28948 +#28954 := [trans #28949 #28953]: #27715 +#28955 := (not #27715) +#28956 := (or #28955 #27719) +#28957 := [th-lemma arith triangle-eq]: #28956 +#28958 := [unit-resolution #28957 #28954]: #27719 +#27720 := (>= #27716 0::Int) +#28959 := (or #28955 #27720) +#28960 := [th-lemma arith triangle-eq]: #28959 +#28961 := [unit-resolution #28960 #28954]: #27720 +#27242 := (+ #27034 #27241) +#27243 := (+ #27033 #27242) +#28409 := (<= #27243 0::Int) +#27244 := (= #27243 0::Int) +#28127 := (or #25034 #27244) +#27238 := (= #27041 #27237) +#28359 := (or #25034 #27238) +#28461 := (iff #28359 #28127) +#28464 := (iff #28127 #28127) +#28465 := [rewrite]: #28464 +#27245 := (iff #27238 #27244) +#27246 := [rewrite]: #27245 +#28358 := [monotonicity #27246]: #28461 +#28466 := [trans #28358 #28465]: #28461 +#28463 := [quant-inst #24960 #27041]: #28359 +#28467 := [mp #28463 #28466]: #28127 +#28962 := [unit-resolution #28467 #23270]: #27244 +#28963 := (not #27244) +#28964 := (or #28963 #28409) +#28965 := [th-lemma arith triangle-eq]: #28964 +#28966 := [unit-resolution #28965 #28962]: #28409 +#28540 := (>= #27243 0::Int) +#28967 := (or #28963 #28540) +#28968 := [th-lemma arith triangle-eq]: #28967 +#28969 := [unit-resolution #28968 #28962]: #28540 +#28971 := [th-lemma arith eq-propagate -1 -1 -1 -1 1 1 1 1 #28969 #28966 #28961 #28958 #28944 #28941 #28934 #28931]: #28970 +#28973 := [symm #28971]: #28972 +#28979 := [monotonicity #28973]: #28978 +#28982 := (= #27104 #27317) +#27303 := (f77 #26146 0::Int #24960) +#27320 := (= #27303 #27317) +#27323 := (not #27320) +#27304 := (f150 #27303 #26146) +#27305 := (= f1 #27304) +#27306 := (not #27305) +#27329 := (or #27306 #27323) +#27334 := (not #27329) +#28552 := (or #27451 #27334) +#27308 := (+ #27307 #27033) +#27309 := (f54 #24960 #27308) +#27310 := (= #27303 #27309) +#27311 := (not #27310) +#27312 := (or #27311 #27306) +#27313 := (not #27312) +#28553 := (or #27451 #27313) +#28555 := (iff #28553 #28552) +#28568 := (iff #28552 #28552) +#28569 := [rewrite]: #28568 +#27335 := (iff #27313 #27334) +#27332 := (iff #27312 #27329) +#27326 := (or #27323 #27306) +#27330 := (iff #27326 #27329) +#27331 := [rewrite]: #27330 +#27327 := (iff #27312 #27326) +#27324 := (iff #27311 #27323) +#27321 := (iff #27310 #27320) +#27318 := (= #27309 #27317) +#27315 := (= #27308 #27314) +#27316 := [rewrite]: #27315 +#27319 := [monotonicity #27316]: #27318 +#27322 := [monotonicity #27319]: #27321 +#27325 := [monotonicity #27322]: #27324 +#27328 := [monotonicity #27325]: #27327 +#27333 := [trans #27328 #27331]: #27332 +#27336 := [monotonicity #27333]: #27335 +#28556 := [monotonicity #27336]: #28555 +#28570 := [trans #28556 #28569]: #28555 +#28554 := [quant-inst #26146 #161 #24960]: #28553 +#28571 := [mp #28554 #28570]: #28552 +#28974 := [unit-resolution #28571 #21204]: #27334 +#28576 := (or #27329 #27320) +#28577 := [def-axiom]: #28576 +#28975 := [unit-resolution #28577 #28974]: #27320 +#28976 := (= #27104 #27303) +#28977 := [monotonicity #28365]: #28976 +#28983 := [trans #28977 #28975]: #28982 +#28985 := [trans #28983 #28979]: #28984 +#28987 := [trans #28985 #28981]: #28986 +#28991 := [monotonicity #28987]: #28990 +#28993 := [symm #28991]: #28992 +#28988 := (= #28602 #26949) +#28989 := [monotonicity #27431]: #28988 +#28995 := [trans #28989 #28993]: #28994 +#28997 := [monotonicity #28995]: #28996 +#29001 := [trans #28997 #28999]: #29000 +#29003 := [trans #29001 #28364]: #29002 +#29005 := [monotonicity #29003]: #29004 +#29007 := [trans #29005 #28878]: #29006 +#29009 := [monotonicity #29007]: #29008 +#29011 := [monotonicity #29009]: #29010 +#29013 := [symm #29011]: #29012 +#29015 := [monotonicity #29013]: #29014 +#29016 := [mp #14333 #29015]: #28841 +#29020 := (= #3047 #28607) +#29017 := (= #28607 #3047) +#29018 := [monotonicity #29003]: #29017 +#29021 := [symm #29018]: #29020 +#29022 := [trans #14330 #29021]: #28608 +#28848 := (not #28608) +#28849 := (or #28756 #28848) +#28850 := [def-axiom]: #28849 +#29023 := [unit-resolution #28850 #29022]: #28756 +#25465 := (f23 f19) +#29036 := (= #25465 #28639) +#29032 := (= #28639 #25465) +#29030 := (= #27233 f19) +#29028 := (= #27233 #24960) +#29029 := [symm #27567]: #29028 +#29031 := [trans #29029 #28488]: #29030 +#29033 := [monotonicity #29031]: #29032 +#29037 := [symm #29033]: #29036 +#25466 := (= f25 #25465) +#25473 := (iff #11588 #25466) +#2363 := (pattern #279) +#2902 := (f23 #275) +#11767 := (= f25 #2902) +#11771 := (iff #4084 #11767) +#11774 := (forall (vars (?v0 S18)) (:pat #2363) #11771) +#18366 := (~ #11774 #11774) +#18364 := (~ #11771 #11771) +#18365 := [refl]: #18364 +#18367 := [nnf-pos #18365]: #18366 +#2915 := (= #2902 f25) +#2916 := (iff #280 #2915) +#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916) +#11775 := (iff #2917 #11774) +#11772 := (iff #2916 #11771) +#11769 := (iff #2915 #11767) +#11770 := [rewrite]: #11769 +#11773 := [monotonicity #4086 #11770]: #11772 +#11776 := [quant-intro #11773]: #11775 +#11766 := [asserted]: #2917 +#11779 := [mp #11766 #11776]: #11774 +#18368 := [mp~ #11779 #18367]: #11774 +#25132 := (not #11774) +#25476 := (or #25132 #25473) +#25477 := [quant-inst #50]: #25476 +#29024 := [unit-resolution #25477 #18368]: #25473 +#25478 := (not #25473) +#29025 := (or #25478 #25466) +#25482 := (not #11588) +#25483 := (or #25478 #25482 #25466) +#25484 := [def-axiom]: #25483 +#29026 := [unit-resolution #25484 #11594]: #29025 +#29027 := [unit-resolution #29026 #29024]: #25466 +#29038 := [trans #29027 #29037]: #28647 +#28125 := (not #27185) +#29056 := (iff #28125 #28636) +#29054 := (iff #27185 #28635) +#29052 := (iff #28635 #27185) +#29050 := (= #28634 #27184) +#29048 := (= #28602 #27183) +#29046 := (= #26949 #27183) +#29044 := (= #27183 #26949) +#29045 := [monotonicity #28135]: #29044 +#29047 := [symm #29045]: #29046 +#29049 := [trans #28989 #29047]: #29048 +#29051 := [monotonicity #29049]: #29050 +#29053 := [monotonicity #29051]: #29052 +#29055 := [symm #29053]: #29054 +#29057 := [monotonicity #29055]: #29056 +#28141 := (or #27198 #28125) +#28142 := [def-axiom]: #28141 +#29043 := [unit-resolution #28142 #28352]: #28125 +#29058 := [mp #29043 #29057]: #28636 +#28824 := (or #28750 #28635) +#28825 := [def-axiom]: #28824 +#29059 := [unit-resolution #28825 #29058]: #28750 +#28866 := (or #28793 #28630 #28726 #28753 #28740) +#28867 := [def-axiom]: #28866 +#29060 := [unit-resolution #28867 #29059 #29038 #29023 #29016]: #28793 +#27098 := (or #28796 #28745) +#27099 := [def-axiom]: #27098 +#29061 := [unit-resolution #27099 #29060 #28908]: false +#29062 := [lemma #29061]: #12153 +#24773 := (or #23545 #18409 #18418 #23539) #24774 := [def-axiom]: #24773 -#29668 := [unit-resolution #24774 #29157 #29667]: #23551 -#24765 := (or #23548 #23542) -#24766 := [def-axiom]: #24765 -#29669 := [unit-resolution #24766 #29668]: #23542 -#29670 := (or #23545 #13267 #23539) -#24761 := (or #23545 #13267 #13508 #23539) -#24762 := [def-axiom]: #24761 -#29671 := [unit-resolution #24762 #14360]: #29670 -#29672 := [unit-resolution #29671 #29669 #29137]: #23539 -#24751 := (or #23536 #23530) +#29171 := [unit-resolution #24774 #29062 #27593 #29170]: #23539 +#24751 := (or #23536 #3109) #24752 := [def-axiom]: #24751 -#30100 := [unit-resolution #24752 #29672]: #23530 -#24749 := (or #23536 #23372) +#29172 := [unit-resolution #24752 #29171]: #3109 +#29126 := (+ #3108 #18448) +#29128 := (>= #29126 0::Int) +#29125 := (= #3108 #18447) +#29159 := (= #18447 #3108) +#29157 := (= #18446 #3098) +#29155 := (= ?v0!13 0::Int) +#24422 := (not #18451) +#29152 := [hypothesis]: #22301 +#24423 := (or #22296 #24422) +#24424 := [def-axiom]: #24423 +#29153 := [unit-resolution #24424 #29152]: #24422 +#24417 := (or #22296 #18443) +#24418 := [def-axiom]: #24417 +#29154 := [unit-resolution #24418 #29152]: #18443 +#29156 := [th-lemma arith eq-propagate 0 0 #29154 #29153]: #29155 +#29158 := [monotonicity #29156]: #29157 +#29160 := [monotonicity #29158]: #29159 +#29161 := [symm #29160]: #29125 +#29162 := (not #29125) +#29163 := (or #29162 #29128) +#29164 := [th-lemma arith triangle-eq]: #29163 +#29165 := [unit-resolution #29164 #29161]: #29128 +#24419 := (not #18450) +#24420 := (or #22296 #24419) +#24421 := [def-axiom]: #24420 +#29166 := [unit-resolution #24421 #29152]: #24419 +#27612 := (* -1::Int #3108) +#27613 := (+ f307 #27612) +#27614 := (>= #27613 0::Int) +#29173 := (or #13231 #27614) +#29174 := [th-lemma arith triangle-eq]: #29173 +#29175 := [unit-resolution #29174 #29172]: #27614 +#29176 := [th-lemma arith farkas 1 -1 1 #29175 #29166 #29165]: false +#29177 := [lemma #29176]: #22296 +#24763 := (or #23536 #23530) +#24764 := [def-axiom]: #24763 +#29735 := [unit-resolution #24764 #29171]: #23530 +#29073 := [hypothesis]: #13436 +#29074 := [th-lemma arith farkas 1 1 #14324 #29073]: false +#29075 := [lemma #29074]: #13433 +#24749 := (or #23533 #13436 #23527) #24750 := [def-axiom]: #24749 -#30095 := [unit-resolution #24750 #29672]: #23372 -#24711 := (or #23536 #12250) -#24712 := [def-axiom]: #24711 -#30101 := [unit-resolution #24712 #29672]: #12250 -#24745 := (or #23536 #15868) -#24746 := [def-axiom]: #24745 -#30102 := [unit-resolution #24746 #29672]: #15868 -#24735 := (or #23536 #13980) -#24736 := [def-axiom]: #24735 -#30103 := [unit-resolution #24736 #29672]: #13980 -#27607 := (f24 #27086) -#27608 := (f77 #27086 f308 #27607) -#27609 := (f136 #27608 #27086) -#27690 := (>= #27609 0::Int) -#24731 := (or #23536 #13513) -#24732 := [def-axiom]: #24731 -#30104 := [unit-resolution #24732 #29672]: #13513 -#27706 := (* -1::Int #27609) -#27779 := (+ f308 #27706) -#27780 := (<= #27779 0::Int) -#27610 := (= f308 #27609) -#29180 := (f77 #24833 f308 #27122) -#29181 := (f136 #29180 #24833) -#30129 := (= #29181 #27609) -#30127 := (= #27609 #29181) -#30105 := (= #27086 #24833) -#30109 := [trans #27414 #27140]: #30105 -#30124 := (= #27608 #29180) -#30122 := (= #3152 #29180) -#30120 := (= #29180 #3152) -#30112 := (= #27122 f19) -#30110 := (= #27122 #25112) -#30111 := [monotonicity #27142]: #30110 -#30113 := [trans #30111 #27685]: #30112 -#30121 := [monotonicity #27142 #30113]: #30120 -#30123 := [symm #30121]: #30122 -#30118 := (= #27608 #3152) -#30116 := (= #27607 f19) -#30114 := (= #27607 #25112) -#30115 := [monotonicity #27414]: #30114 -#30117 := [trans #30115 #27685]: #30116 -#30119 := [monotonicity #27414 #30117]: #30118 -#30125 := [trans #30119 #30123]: #30124 -#30128 := [monotonicity #30125 #30109]: #30127 -#30130 := [symm #30128]: #30129 -#29182 := (= f308 #29181) -#29185 := (or #27129 #29182) -#29186 := [quant-inst #24833 #3135]: #29185 -#30126 := [unit-resolution #29186 #17107]: #29182 -#30131 := [trans #30126 #30130]: #27610 -#28118 := (not #27610) -#30132 := (or #28118 #27780) -#30133 := [th-lemma arith triangle-eq]: #30132 -#30134 := [unit-resolution #30133 #30131]: #27780 -#30135 := (not #27780) -#30136 := (or #27690 #22479 #30135) -#30137 := [th-lemma arith assign-bounds -1 1]: #30136 -#30138 := [unit-resolution #30137 #30134 #30104]: #27690 -#27691 := (not #27690) -#28143 := (or #23524 #27691 #13979 #22622 #22615 #23377) -#27988 := (f77 #3042 #27609 f19) -#27989 := (f121 f297 #27988) -#27992 := (= f313 #27989) -#28098 := (= #3153 #27989) -#28111 := (= #27989 #3153) -#28105 := (= #27988 #3152) -#28103 := (= #27609 f308) -#27613 := (or #27129 #27610) -#27614 := [quant-inst #27086 #3135]: #27613 -#28102 := [unit-resolution #27614 #17107]: #27610 -#28104 := [symm #28102]: #28103 -#28106 := [monotonicity #28104]: #28105 -#28112 := [monotonicity #28106]: #28111 -#28113 := [symm #28112]: #28098 -#28114 := (= f313 #3153) -#28107 := [hypothesis]: #12250 -#28108 := [hypothesis]: #23527 -#24691 := (or #23524 #12278) -#24692 := [def-axiom]: #24691 -#28109 := [unit-resolution #24692 #28108]: #12278 -#28110 := [symm #28109]: #3167 -#28115 := [trans #28110 #28107]: #28114 -#28116 := [trans #28115 #28113]: #27992 -#27973 := (<= #27609 4294967295::Int) -#28117 := [hypothesis]: #15868 -#27781 := (>= #27779 0::Int) -#28119 := (or #28118 #27781) -#28120 := [th-lemma arith triangle-eq]: #28119 -#28121 := [unit-resolution #28120 #28102]: #27781 -#28122 := (not #27781) -#28123 := (or #27973 #22622 #28122) -#28124 := [th-lemma arith assign-bounds -1 1]: #28123 -#28125 := [unit-resolution #28124 #28121 #28117]: #27973 -#28015 := (+ f296 #27706) -#28016 := (<= #28015 0::Int) -#28127 := (not #28016) -#28126 := [hypothesis]: #13980 -#28128 := (or #28127 #13979 #28122) -#28129 := [th-lemma arith assign-bounds -1 -1]: #28128 -#28130 := [unit-resolution #28129 #28121 #28126]: #28127 -#27995 := (not #27992) -#27974 := (not #27973) -#28140 := (or #27974 #27995 #28016) -#28131 := [hypothesis]: #27690 -#24699 := (or #23524 #23518) +#29738 := [unit-resolution #24750 #29075 #29735]: #23527 +#24741 := (or #23524 #23518) +#24742 := [def-axiom]: #24741 +#29739 := [unit-resolution #24742 #29738]: #23518 +#24737 := (or #23521 #22301 #23515) +#24738 := [def-axiom]: #24737 +#29740 := [unit-resolution #24738 #29739 #29177]: #23515 +#24729 := (or #23512 #23506) +#24730 := [def-axiom]: #24729 +#29741 := [unit-resolution #24730 #29740]: #23506 +#29742 := (or #23509 #13231 #23503) +#24725 := (or #23509 #13231 #13472 #23503) +#24726 := [def-axiom]: #24725 +#29743 := [unit-resolution #24726 #14324]: #29742 +#29744 := [unit-resolution #29743 #29741 #29172]: #23503 +#24699 := (or #23500 #13944) #24700 := [def-axiom]: #24699 -#28132 := [unit-resolution #24700 #28108]: #23518 -#24697 := (or #23524 #13801) -#24698 := [def-axiom]: #24697 -#28133 := [unit-resolution #24698 #28108]: #13801 -#28039 := [hypothesis]: #23372 -#27785 := (+ f307 #13841) -#27788 := (<= #27785 0::Int) -#28134 := (or #12313 #27788) -#28135 := [th-lemma arith triangle-eq]: #28134 -#28136 := [unit-resolution #28135 #28109]: #27788 -#28044 := (not #27788) -#28045 := (or #22588 #28044 #23377 #13802) -#28032 := [hypothesis]: #27788 -#24674 := (not #19091) -#28033 := [hypothesis]: #22593 -#24675 := (or #22588 #24674) +#29749 := [unit-resolution #24700 #29744]: #13944 +#24675 := (or #23500 #12214) #24676 := [def-axiom]: #24675 -#28034 := [unit-resolution #24676 #28033]: #24674 -#27868 := (+ f307 #19089) -#27869 := (>= #27868 0::Int) -#27856 := (+ f309 #19076) -#27857 := (<= #27856 0::Int) -#28029 := (not #27857) -#28023 := [hypothesis]: #13801 -#24671 := (not #19078) -#24672 := (or #22588 #24671) -#24673 := [def-axiom]: #24672 -#28035 := [unit-resolution #24673 #28033]: #24671 -#28030 := (or #28029 #19078 #13802) -#28024 := [hypothesis]: #27857 -#28027 := [hypothesis]: #24671 -#28028 := [th-lemma arith farkas -1 1 1 #28027 #28024 #28023]: false -#28031 := [lemma #28028]: #28030 -#28036 := [unit-resolution #28031 #28035 #28023]: #28029 -#28040 := (or #27857 #27869) -#24669 := (or #22588 #18740) -#24670 := [def-axiom]: #24669 -#28037 := [unit-resolution #24670 #28033]: #18740 -#24667 := (or #22588 #18739) -#24668 := [def-axiom]: #24667 -#28038 := [unit-resolution #24668 #28033]: #18739 -#27882 := (or #23377 #22572 #22573 #27857 #27869) -#27845 := (+ #18744 #14006) -#27846 := (<= #27845 0::Int) -#27847 := (+ ?v0!15 #13537) -#27848 := (>= #27847 0::Int) -#27849 := (or #22573 #27848 #27846 #22572) -#27883 := (or #23377 #27849) -#27890 := (iff #27883 #27882) -#27877 := (or #22572 #22573 #27857 #27869) -#27885 := (or #23377 #27877) -#27888 := (iff #27885 #27882) -#27889 := [rewrite]: #27888 -#27886 := (iff #27883 #27885) -#27880 := (iff #27849 #27877) -#27874 := (or #22573 #27857 #27869 #22572) -#27878 := (iff #27874 #27877) -#27879 := [rewrite]: #27878 -#27875 := (iff #27849 #27874) -#27872 := (iff #27846 #27869) -#27862 := (+ #14006 #18744) -#27865 := (<= #27862 0::Int) -#27870 := (iff #27865 #27869) -#27871 := [rewrite]: #27870 -#27866 := (iff #27846 #27865) -#27863 := (= #27845 #27862) -#27864 := [rewrite]: #27863 -#27867 := [monotonicity #27864]: #27866 -#27873 := [trans #27867 #27871]: #27872 -#27860 := (iff #27848 #27857) -#27850 := (+ #13537 ?v0!15) -#27853 := (>= #27850 0::Int) -#27858 := (iff #27853 #27857) -#27859 := [rewrite]: #27858 -#27854 := (iff #27848 #27853) -#27851 := (= #27847 #27850) -#27852 := [rewrite]: #27851 -#27855 := [monotonicity #27852]: #27854 -#27861 := [trans #27855 #27859]: #27860 -#27876 := [monotonicity #27861 #27873]: #27875 -#27881 := [trans #27876 #27879]: #27880 -#27887 := [monotonicity #27881]: #27886 -#27891 := [trans #27887 #27889]: #27890 -#27884 := [quant-inst #18738]: #27883 -#27892 := [mp #27884 #27891]: #27882 -#28041 := [unit-resolution #27892 #28039 #28038 #28037]: #28040 -#28042 := [unit-resolution #28041 #28036]: #27869 -#28043 := [th-lemma arith farkas -1 1 1 #28042 #28034 #28032]: false -#28046 := [lemma #28043]: #28045 -#28137 := [unit-resolution #28046 #28136 #28039 #28133]: #22588 -#24683 := (or #23521 #23515 #22593) -#24684 := [def-axiom]: #24683 -#28138 := [unit-resolution #24684 #28137 #28132]: #23515 -#24663 := (or #23512 #23504) +#29747 := [unit-resolution #24676 #29744]: #12214 +#28447 := (or #23418 #22328 #13943 #22579) +#28422 := [hypothesis]: #22327 +#28434 := (= #3153 #3299) +#28432 := (= #3299 #3153) +#28428 := (= #3298 #3152) +#24559 := (or #23418 #12806) +#24560 := [def-axiom]: #24559 +#28426 := [unit-resolution #24560 #28423]: #12806 +#28427 := [symm #28426]: #3329 +#28429 := [monotonicity #28427]: #28428 +#28433 := [monotonicity #28429]: #28432 +#28435 := [symm #28433]: #28434 +#28436 := (= f316 #3153) +#28062 := [hypothesis]: #12214 +#28431 := [symm #28430]: #3328 +#28437 := [trans #28431 #28062]: #28436 +#28438 := [trans #28437 #28435]: #12607 +#28081 := [hypothesis]: #13944 +#24554 := (+ f309 #13556) +#24556 := (>= #24554 0::Int) +#28439 := (or #12812 #24556) +#28440 := [th-lemma arith triangle-eq]: #28439 +#28441 := [unit-resolution #28440 #28426]: #24556 +#28442 := (not #24556) +#28443 := (or #13559 #13943 #28442) +#28444 := [th-lemma arith assign-bounds -1 -1]: #28443 +#28445 := [unit-resolution #28444 #28441 #28081]: #13559 +#24433 := (or #22328 #22326 #13558) +#24434 := [def-axiom]: #24433 +#28446 := [unit-resolution #24434 #28445 #28438 #28422]: false +#28448 := [lemma #28446]: #28447 +#29589 := [unit-resolution #28448 #29747 #29749]: #29594 +#29595 := [unit-resolution #29589 #28423]: #22328 +#24435 := (or #23352 #22327) +#24436 := [def-axiom]: #24435 +#29718 := [unit-resolution #24436 #29595]: #23352 +#24569 := (or #23418 #23382) +#24570 := [def-axiom]: #24569 +#29771 := [unit-resolution #24570 #28423]: #23382 +#29795 := (or #23385 #23379) +#24715 := (or #23500 #23494) +#24716 := [def-axiom]: #24715 +#29745 := [unit-resolution #24716 #29744]: #23494 +#24713 := (or #23500 #23336) +#24714 := [def-axiom]: #24713 +#29746 := [unit-resolution #24714 #29744]: #23336 +#24709 := (or #23500 #15832) +#24710 := [def-axiom]: #24709 +#29748 := [unit-resolution #24710 #29744]: #15832 +decl f137 :: (-> S20 S20 Int) +#27080 := (f24 #24797) +#27605 := (f77 #24797 f309 #27080) +#27606 := (f137 #27605 #24797) +#27679 := (>= #27606 0::Int) +#24695 := (or #23500 #13477) +#24696 := [def-axiom]: #24695 +#29750 := [unit-resolution #24696 #29744]: #13477 +#27695 := (* -1::Int #27606) +#27744 := (+ f309 #27695) +#27745 := (<= #27744 0::Int) +#27607 := (= f309 #27606) +#1434 := (f77 #55 #202 #1433) +#1435 := (pattern #1434) +#1436 := (f137 #1434 #55) +#7788 := (= #202 #1436) +#7792 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7788) +#17069 := (~ #7792 #7792) +#17067 := (~ #7788 #7788) +#17068 := [refl]: #17067 +#17070 := [nnf-pos #17068]: #17069 +#1437 := (= #1436 #202) +#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437) +#7793 := (iff #1438 #7792) +#7790 := (iff #1437 #7788) +#7791 := [rewrite]: #7790 +#7794 := [quant-intro #7791]: #7793 +#7787 := [asserted]: #1438 +#7797 := [mp #7787 #7794]: #7792 +#17071 := [mp~ #7797 #17070]: #7792 +#27087 := (not #7792) +#27610 := (or #27087 #27607) +#27611 := [quant-inst #24797 #3135]: #27610 +#28057 := [unit-resolution #27611 #17071]: #27607 +#28073 := (not #27607) +#29751 := (or #28073 #27745) +#29752 := [th-lemma arith triangle-eq]: #29751 +#29753 := [unit-resolution #29752 #28057]: #27745 +#29754 := (not #27745) +#29755 := (or #27679 #22443 #29754) +#29756 := [th-lemma arith assign-bounds -1 1]: #29755 +#29757 := [unit-resolution #29756 #29753 #29750]: #27679 +#27680 := (not #27679) +#28098 := (or #23488 #27680 #13943 #22586 #22579 #23341) +#27951 := (f77 #3042 #27606 f19) +#27952 := (f122 f298 #27951) +#27955 := (= f314 #27952) +#28053 := (= #3153 #27952) +#28066 := (= #27952 #3153) +#28060 := (= #27951 #3152) +#28058 := (= #27606 f309) +#28059 := [symm #28057]: #28058 +#28061 := [monotonicity #28059]: #28060 +#28067 := [monotonicity #28061]: #28066 +#28068 := [symm #28067]: #28053 +#28069 := (= f314 #3153) +#28063 := [hypothesis]: #23491 +#24655 := (or #23488 #12242) +#24656 := [def-axiom]: #24655 +#28064 := [unit-resolution #24656 #28063]: #12242 +#28065 := [symm #28064]: #3167 +#28070 := [trans #28065 #28062]: #28069 +#28071 := [trans #28070 #28068]: #27955 +#27936 := (<= #27606 4294967295::Int) +#28072 := [hypothesis]: #15832 +#27746 := (>= #27744 0::Int) +#28074 := (or #28073 #27746) +#28075 := [th-lemma arith triangle-eq]: #28074 +#28076 := [unit-resolution #28075 #28057]: #27746 +#28077 := (not #27746) +#28078 := (or #27936 #22586 #28077) +#28079 := [th-lemma arith assign-bounds -1 1]: #28078 +#28080 := [unit-resolution #28079 #28076 #28072]: #27936 +#27993 := (+ f297 #27695) +#27994 := (<= #27993 0::Int) +#28082 := (not #27994) +#28083 := (or #28082 #13943 #28077) +#28084 := [th-lemma arith assign-bounds -1 -1]: #28083 +#28085 := [unit-resolution #28084 #28076 #28081]: #28082 +#27958 := (not #27955) +#27937 := (not #27936) +#28095 := (or #27937 #27958 #27994) +#28086 := [hypothesis]: #27679 +#24663 := (or #23488 #23482) #24664 := [def-axiom]: #24663 -#28139 := [unit-resolution #24664 #28138]: #23504 -#28052 := (or #23509 #27691 #27974 #27995 #28016) -#27979 := (+ #27609 #13442) -#27980 := (>= #27979 0::Int) -#27987 := (= #27989 f313) -#27990 := (not #27987) -#27991 := (or #27990 #27691 #27980 #27974) -#28053 := (or #23509 #27991) -#28060 := (iff #28053 #28052) -#28047 := (or #27691 #27974 #27995 #28016) -#28055 := (or #23509 #28047) -#28058 := (iff #28055 #28052) -#28059 := [rewrite]: #28058 -#28056 := (iff #28053 #28055) -#28050 := (iff #27991 #28047) -#27996 := (or #27995 #27691 #28016 #27974) -#28048 := (iff #27996 #28047) -#28049 := [rewrite]: #28048 -#27997 := (iff #27991 #27996) -#28026 := (iff #27980 #28016) -#28010 := (+ #13442 #27609) -#28007 := (>= #28010 0::Int) -#28017 := (iff #28007 #28016) -#28025 := [rewrite]: #28017 -#28013 := (iff #27980 #28007) -#28011 := (= #27979 #28010) -#28012 := [rewrite]: #28011 -#28014 := [monotonicity #28012]: #28013 -#27928 := [trans #28014 #28025]: #28026 -#28008 := (iff #27990 #27995) -#27993 := (iff #27987 #27992) -#27994 := [rewrite]: #27993 -#28009 := [monotonicity #27994]: #28008 -#28020 := [monotonicity #28009 #27928]: #27997 -#28051 := [trans #28020 #28049]: #28050 -#28057 := [monotonicity #28051]: #28056 -#28061 := [trans #28057 #28059]: #28060 -#28054 := [quant-inst #27609]: #28053 -#28062 := [mp #28054 #28061]: #28052 -#28141 := [unit-resolution #28062 #28139 #28131]: #28140 -#28142 := [unit-resolution #28141 #28130 #28125 #28116]: false -#28144 := [lemma #28142]: #28143 -#30139 := [unit-resolution #28144 #30138 #30103 #30102 #30101 #30095]: #23524 -#24707 := (or #23533 #23493 #23527) -#24708 := [def-axiom]: #24707 -#30140 := [unit-resolution #24708 #30139 #30100]: #23493 -#24655 := (or #23490 #13802) -#24656 := [def-axiom]: #24655 -#30141 := [unit-resolution #24656 #30140]: #13802 -#30242 := (not #29585) -#30243 := (or #30241 #28416 #30242 #13801) -#30244 := [th-lemma arith assign-bounds 1 -1 -1]: #30243 -#30245 := [unit-resolution #30244 #28410 #30141 #30237]: #30241 -#29465 := (>= #29368 0::Int) -#24733 := (or #23536 #13516) -#24734 := [def-axiom]: #24733 -#29673 := [unit-resolution #24734 #29672]: #13516 -#29584 := (<= #29583 0::Int) -#29676 := (or #29675 #29584) -#29677 := [th-lemma arith triangle-eq]: #29676 -#29678 := [unit-resolution #29677 #29674]: #29584 -#29466 := (not #29465) -#29679 := [hypothesis]: #29466 -#29680 := [th-lemma arith farkas 1 1 1 #29679 #29678 #29673]: false -#29681 := [lemma #29680]: #29465 -#30247 := (or #29466 #29476 #29484) -#29495 := (or #28639 #27163 #29466 #29476 #29484) -#29461 := (or #29460 #29457 #29455 #29451) -#29462 := (not #29461) -#29463 := (+ #29368 #27164) -#29464 := (>= #29463 0::Int) -#29467 := (or #29466 #29464 #27163 #29462) -#29496 := (or #28639 #29467) -#29503 := (iff #29496 #29495) -#29490 := (or #27163 #29466 #29476 #29484) -#29498 := (or #28639 #29490) -#29501 := (iff #29498 #29495) -#29502 := [rewrite]: #29501 -#29499 := (iff #29496 #29498) -#29493 := (iff #29467 #29490) -#29487 := (or #29466 #29476 #27163 #29484) -#29491 := (iff #29487 #29490) -#29492 := [rewrite]: #29491 -#29488 := (iff #29467 #29487) -#29485 := (iff #29462 #29484) -#29482 := (iff #29461 #29481) +#28087 := [unit-resolution #24664 #28063]: #23482 +#27749 := (+ f308 #13805) +#27750 := (<= #27749 0::Int) +#28088 := (or #12277 #27750) +#28089 := [th-lemma arith triangle-eq]: #28088 +#28090 := [unit-resolution #28089 #28064]: #27750 +#27982 := [hypothesis]: #23336 +#24661 := (or #23488 #13765) +#24662 := [def-axiom]: #24661 +#28091 := [unit-resolution #24662 #28063]: #13765 +#27973 := (not #27750) +#27988 := (or #22552 #13766 #23341 #27973) +#27976 := [hypothesis]: #13765 +#27820 := (+ f310 #19040) +#27821 := (<= #27820 0::Int) +#27832 := (+ f308 #19053) +#27833 := (>= #27832 0::Int) +#27972 := (not #27833) +#27966 := [hypothesis]: #27750 +#24638 := (not #19055) +#27977 := [hypothesis]: #22557 +#24639 := (or #22552 #24638) +#24640 := [def-axiom]: #24639 +#27978 := [unit-resolution #24640 #27977]: #24638 +#27974 := (or #27972 #19055 #27973) +#27967 := [hypothesis]: #24638 +#27970 := [hypothesis]: #27833 +#27971 := [th-lemma arith farkas -1 1 1 #27970 #27967 #27966]: false +#27975 := [lemma #27971]: #27974 +#27979 := [unit-resolution #27975 #27978 #27966]: #27972 +#27983 := (or #27821 #27833) +#24633 := (or #22552 #18704) +#24634 := [def-axiom]: #24633 +#27980 := [unit-resolution #24634 #27977]: #18704 +#24631 := (or #22552 #18703) +#24632 := [def-axiom]: #24631 +#27981 := [unit-resolution #24632 #27977]: #18703 +#27846 := (or #23341 #22536 #22537 #27821 #27833) +#27809 := (+ #18708 #13970) +#27810 := (<= #27809 0::Int) +#27811 := (+ ?v0!15 #13501) +#27812 := (>= #27811 0::Int) +#27813 := (or #22537 #27812 #27810 #22536) +#27847 := (or #23341 #27813) +#27854 := (iff #27847 #27846) +#27841 := (or #22536 #22537 #27821 #27833) +#27849 := (or #23341 #27841) +#27852 := (iff #27849 #27846) +#27853 := [rewrite]: #27852 +#27850 := (iff #27847 #27849) +#27844 := (iff #27813 #27841) +#27838 := (or #22537 #27821 #27833 #22536) +#27842 := (iff #27838 #27841) +#27843 := [rewrite]: #27842 +#27839 := (iff #27813 #27838) +#27836 := (iff #27810 #27833) +#27826 := (+ #13970 #18708) +#27829 := (<= #27826 0::Int) +#27834 := (iff #27829 #27833) +#27835 := [rewrite]: #27834 +#27830 := (iff #27810 #27829) +#27827 := (= #27809 #27826) +#27828 := [rewrite]: #27827 +#27831 := [monotonicity #27828]: #27830 +#27837 := [trans #27831 #27835]: #27836 +#27824 := (iff #27812 #27821) +#27814 := (+ #13501 ?v0!15) +#27817 := (>= #27814 0::Int) +#27822 := (iff #27817 #27821) +#27823 := [rewrite]: #27822 +#27818 := (iff #27812 #27817) +#27815 := (= #27811 #27814) +#27816 := [rewrite]: #27815 +#27819 := [monotonicity #27816]: #27818 +#27825 := [trans #27819 #27823]: #27824 +#27840 := [monotonicity #27825 #27837]: #27839 +#27845 := [trans #27840 #27843]: #27844 +#27851 := [monotonicity #27845]: #27850 +#27855 := [trans #27851 #27853]: #27854 +#27848 := [quant-inst #18702]: #27847 +#27856 := [mp #27848 #27855]: #27846 +#27984 := [unit-resolution #27856 #27982 #27981 #27980]: #27983 +#27985 := [unit-resolution #27984 #27979]: #27821 +#24635 := (not #19042) +#24636 := (or #22552 #24635) +#24637 := [def-axiom]: #24636 +#27986 := [unit-resolution #24637 #27977]: #24635 +#27987 := [th-lemma arith farkas -1 1 1 #27986 #27985 #27976]: false +#27989 := [lemma #27987]: #27988 +#28092 := [unit-resolution #27989 #28091 #27982 #28090]: #22552 +#24647 := (or #23485 #23479 #22557) +#24648 := [def-axiom]: #24647 +#28093 := [unit-resolution #24648 #28092 #28087]: #23479 +#24627 := (or #23476 #23468) +#24628 := [def-axiom]: #24627 +#28094 := [unit-resolution #24628 #28093]: #23468 +#28007 := (or #23473 #27680 #27937 #27958 #27994) +#27942 := (+ #27606 #13406) +#27943 := (>= #27942 0::Int) +#27950 := (= #27952 f314) +#27953 := (not #27950) +#27954 := (or #27953 #27680 #27943 #27937) +#28008 := (or #23473 #27954) +#28015 := (iff #28008 #28007) +#28002 := (or #27680 #27937 #27958 #27994) +#28010 := (or #23473 #28002) +#28013 := (iff #28010 #28007) +#28014 := [rewrite]: #28013 +#28011 := (iff #28008 #28010) +#28005 := (iff #27954 #28002) +#27999 := (or #27958 #27680 #27994 #27937) +#28003 := (iff #27999 #28002) +#28004 := [rewrite]: #28003 +#28000 := (iff #27954 #27999) +#27997 := (iff #27943 #27994) +#27959 := (+ #13406 #27606) +#27990 := (>= #27959 0::Int) +#27995 := (iff #27990 #27994) +#27996 := [rewrite]: #27995 +#27991 := (iff #27943 #27990) +#27960 := (= #27942 #27959) +#27963 := [rewrite]: #27960 +#27992 := [monotonicity #27963]: #27991 +#27998 := [trans #27992 #27996]: #27997 +#27968 := (iff #27953 #27958) +#27956 := (iff #27950 #27955) +#27957 := [rewrite]: #27956 +#27969 := [monotonicity #27957]: #27968 +#28001 := [monotonicity #27969 #27998]: #28000 +#28006 := [trans #28001 #28004]: #28005 +#28012 := [monotonicity #28006]: #28011 +#28016 := [trans #28012 #28014]: #28015 +#28009 := [quant-inst #27606]: #28008 +#28017 := [mp #28009 #28016]: #28007 +#28096 := [unit-resolution #28017 #28094 #28086]: #28095 +#28097 := [unit-resolution #28096 #28085 #28080 #28071]: false +#28099 := [lemma #28097]: #28098 +#29758 := [unit-resolution #28099 #29757 #29749 #29748 #29747 #29746]: #23488 +#24671 := (or #23497 #23457 #23491) +#24672 := [def-axiom]: #24671 +#29759 := [unit-resolution #24672 #29758 #29745]: #23457 +#24619 := (or #23454 #13766) +#24620 := [def-axiom]: #24619 +#29760 := [unit-resolution #24620 #29759]: #13766 +#28712 := (or #15864 #13765) +#15775 := (<= f297 4294967295::Int) +#15778 := (iff #13405 #15775) +#15769 := (+ 4294967295::Int #13406) +#15772 := (>= #15769 0::Int) +#15776 := (iff #15772 #15775) +#15777 := [rewrite]: #15776 +#15773 := (iff #13405 #15772) +#15770 := (= #13407 #15769) +#15771 := [monotonicity #7606]: #15770 +#15774 := [monotonicity #15771]: #15773 +#15779 := [trans #15774 #15777]: #15778 +#14321 := [not-or-elim #14310]: #13410 +#14323 := [and-elim #14321]: #13405 +#15780 := [mp #14323 #15779]: #15775 +#28513 := [hypothesis]: #13766 +#28701 := [hypothesis]: #18561 +#28702 := [th-lemma arith farkas -1 -1 1 #28701 #28513 #15780]: false +#28713 := [lemma #28702]: #28712 +#29775 := [unit-resolution #28713 #29760]: #15864 +#24697 := (or #23500 #13480) +#24698 := [def-axiom]: #24697 +#29674 := [unit-resolution #24698 #29744]: #13480 +#29789 := (or #13620 #13498) +#29781 := [th-lemma arith farkas 1 1]: #29789 +#29770 := [unit-resolution #29781 #29674]: #13498 +#24493 := (or #23385 #18558 #18561 #23379) +#24494 := [def-axiom]: #24493 +#29796 := [unit-resolution #24494 #29770 #29775]: #29795 +#29797 := [unit-resolution #29796 #29771]: #23379 +#24483 := (or #23376 #23370) +#24484 := [def-axiom]: #24483 +#29798 := [unit-resolution #24484 #29797]: #23370 +#24428 := (>= #13583 -1::Int) +#24479 := (or #23376 #13582) +#24480 := [def-axiom]: #24479 +#29788 := [unit-resolution #24480 #29797]: #13582 +#29593 := (or #13586 #24428) +#29608 := [th-lemma arith triangle-eq]: #29593 +#29883 := [unit-resolution #29608 #29788]: #24428 +#29763 := (not #24428) +#29764 := (or #13514 #29763) +#29734 := [hypothesis]: #24428 +#29761 := [hypothesis]: #13519 +#29762 := [th-lemma arith farkas -1 1 1 #29761 #29760 #29734]: false +#29765 := [lemma #29762]: #29764 +#29611 := [unit-resolution #29765 #29883]: #13514 +#24469 := (or #23373 #13519 #23367) +#24470 := [def-axiom]: #24469 +#29612 := [unit-resolution #24470 #29611 #29798]: #23367 +#24461 := (or #23364 #23358) +#24462 := [def-axiom]: #24461 +#29610 := [unit-resolution #24462 #29612]: #23358 +#24457 := (or #23361 #23355 #22380) +#24458 := [def-axiom]: #24457 +#29766 := [unit-resolution #24458 #29610 #29718]: #22380 +#24449 := (or #22375 #24448) +#24450 := [def-axiom]: #24449 +#29724 := [unit-resolution #24450 #29766]: #24448 +#30349 := (not #24552) +#29599 := (or #30220 #18907 #30349) +#29597 := [th-lemma arith assign-bounds -1 -1]: #29599 +#29598 := [unit-resolution #29597 #29724 #29590]: #30220 +#24443 := (or #22375 #18580) +#24444 := [def-axiom]: #24443 +#29609 := [unit-resolution #24444 #29766]: #18580 +#24441 := (or #22375 #18579) +#24442 := [def-axiom]: #24441 +#29607 := [unit-resolution #24442 #29766]: #18579 +#29528 := (not #29868) +#30337 := (not #30332) +#30348 := (not #30338) +#24567 := (or #23418 #13672) +#24568 := [def-axiom]: #24567 +#29677 := [unit-resolution #24568 #28423]: #13672 +#30350 := (or #30348 #18907 #30349 #13671) +#30343 := [hypothesis]: #13672 +#30344 := [hypothesis]: #24552 +#30345 := [hypothesis]: #24448 +#30346 := [hypothesis]: #30338 +#30347 := [th-lemma arith farkas 1 -1 -1 1 #30346 #30345 #30344 #30343]: false +#30351 := [lemma #30347]: #30350 +#29874 := [unit-resolution #30351 #29724 #29590 #29677]: #30348 +#30339 := (or #30337 #30338) +#30340 := [th-lemma arith triangle-eq]: #30339 +#29875 := [unit-resolution #30340 #29874]: #30337 +#29596 := (or #29528 #30332) +#30115 := (= #18584 #3266) +#30117 := (= #18583 #3257) +#30119 := (= ?v0!14 f310) +#29952 := [hypothesis]: #29868 +#30116 := [symm #29952]: #30119 +#30118 := [monotonicity #30116]: #30117 +#30110 := [monotonicity #30118]: #30115 +#30120 := [symm #30110]: #30332 +#29943 := [hypothesis]: #30337 +#30077 := [unit-resolution #29943 #30120]: false +#30080 := [lemma #30077]: #29596 +#29873 := [unit-resolution #30080 #29875]: #29528 +#29810 := (+ f310 #18892) +#29634 := (>= #29810 0::Int) +#24445 := (not #18894) +#24446 := (or #22375 #24445) +#24447 := [def-axiom]: #24446 +#29887 := [unit-resolution #24447 #29766]: #24445 +#29882 := (or #29634 #18894 #29763) +#29717 := [th-lemma arith assign-bounds 1 1]: #29882 +#29618 := [unit-resolution #29717 #29887 #29883]: #29634 +#30414 := (not #29634) +#30418 := (or #30414 #29868 #22359 #22360 #29823) +#30217 := [hypothesis]: #29528 +#30226 := [hypothesis]: #29634 +#29811 := (<= #29810 0::Int) +#30221 := [hypothesis]: #30220 +#30222 := [hypothesis]: #18580 +#30238 := [hypothesis]: #18579 +#29699 := (or #23341 #22359 #22360 #29811 #29823) +#29799 := (+ #18584 #13970) +#29800 := (<= #29799 0::Int) +#29801 := (+ ?v0!14 #13501) +#29802 := (>= #29801 0::Int) +#29803 := (or #22360 #29802 #29800 #22359) +#29936 := (or #23341 #29803) +#30174 := (iff #29936 #29699) +#29831 := (or #22359 #22360 #29811 #29823) +#29867 := (or #23341 #29831) +#30176 := (iff #29867 #29699) +#30172 := [rewrite]: #30176 +#30161 := (iff #29936 #29867) +#29834 := (iff #29803 #29831) +#29828 := (or #22360 #29811 #29823 #22359) +#29832 := (iff #29828 #29831) +#29833 := [rewrite]: #29832 +#29829 := (iff #29803 #29828) +#29826 := (iff #29800 #29823) +#29816 := (+ #13970 #18584) +#29819 := (<= #29816 0::Int) +#29824 := (iff #29819 #29823) +#29825 := [rewrite]: #29824 +#29820 := (iff #29800 #29819) +#29817 := (= #29799 #29816) +#29818 := [rewrite]: #29817 +#29821 := [monotonicity #29818]: #29820 +#29827 := [trans #29821 #29825]: #29826 +#29814 := (iff #29802 #29811) +#29804 := (+ #13501 ?v0!14) +#29807 := (>= #29804 0::Int) +#29812 := (iff #29807 #29811) +#29813 := [rewrite]: #29812 +#29808 := (iff #29802 #29807) +#29805 := (= #29801 #29804) +#29806 := [rewrite]: #29805 +#29809 := [monotonicity #29806]: #29808 +#29815 := [trans #29809 #29813]: #29814 +#29830 := [monotonicity #29815 #29827]: #29829 +#29835 := [trans #29830 #29833]: #29834 +#30170 := [monotonicity #29835]: #30161 +#30177 := [trans #30170 #30172]: #30174 +#29870 := [quant-inst #18578]: #29936 +#30173 := [mp #29870 #30177]: #29699 +#30239 := [unit-resolution #30173 #29746 #30238 #30222 #30221]: #29811 +#30413 := (not #29811) +#30415 := (or #29868 #30413 #30414) +#30416 := [th-lemma arith triangle-eq]: #30415 +#30417 := [unit-resolution #30416 #30239 #30226 #30217]: false +#30419 := [lemma #30417]: #30418 +#29716 := [unit-resolution #30419 #29618 #29873 #29607 #29609 #29598]: false +#29631 := [lemma #29716]: #23418 +#27798 := (f69 #3220 #3257) +#28223 := (f147 #27798) +#28228 := (f36 f298 #28223) +#28229 := (= f37 #28228) +#28224 := (f222 f298 #28223) +#28227 := (= f1 #28224) +#28285 := (or #28227 #28229) +#28288 := (not #28285) +#28238 := (f148 #27798) +#28239 := (= f1 #28238) +#28240 := (not #28239) +#28235 := (f38 f298 #28223) +#28236 := (= f1 #28235) +#28237 := (not #28236) +#28279 := (or #28237 #28240) +#28282 := (not #28279) +#28118 := (f24 #3257) +#28243 := (f23 #28118) +#28261 := (= f25 #28243) +#28276 := (not #28261) +#28232 := (f24 #28223) +#28233 := (f23 #28232) +#28234 := (= f25 #28233) +#28294 := (or #28234 #28276 #28282 #28288) +#28299 := (not #28294) +#28250 := (f36 f298 #3257) +#28251 := (= f37 #28250) +#28248 := (f222 f298 #3257) +#28249 := (= f1 #28248) +#28264 := (or #28249 #28251) +#28267 := (not #28264) +#28270 := (or #28261 #28267) +#28273 := (not #28270) +#28302 := (or #28273 #28299) +#28305 := (not #28302) +#28308 := (or #18523 #28305) +#28311 := (not #28308) +#28314 := (iff #12548 #28311) +#30431 := (not #28314) +#30440 := [hypothesis]: #30431 +#29632 := (or #28805 #28314) +#28230 := (or #28229 #28227) +#28231 := (not #28230) +#28241 := (or #28240 #28237) +#28242 := (not #28241) +#28244 := (= #28243 f25) +#28245 := (not #28244) +#28246 := (or #28245 #28242 #28234 #28231) +#28247 := (not #28246) +#28252 := (or #28251 #28249) +#28253 := (not #28252) +#28254 := (or #28244 #28253) +#28255 := (not #28254) +#28256 := (or #28255 #28247) +#28257 := (not #28256) +#28258 := (or #18523 #28257) +#28259 := (not #28258) +#28260 := (iff #12548 #28259) +#29633 := (or #28805 #28260) +#29715 := (iff #29633 #29632) +#30083 := (iff #29632 #29632) +#30081 := [rewrite]: #30083 +#28315 := (iff #28260 #28314) +#28312 := (iff #28259 #28311) +#28309 := (iff #28258 #28308) +#28306 := (iff #28257 #28305) +#28303 := (iff #28256 #28302) +#28300 := (iff #28247 #28299) +#28297 := (iff #28246 #28294) +#28291 := (or #28276 #28282 #28234 #28288) +#28295 := (iff #28291 #28294) +#28296 := [rewrite]: #28295 +#28292 := (iff #28246 #28291) +#28289 := (iff #28231 #28288) +#28286 := (iff #28230 #28285) +#28287 := [rewrite]: #28286 +#28290 := [monotonicity #28287]: #28289 +#28283 := (iff #28242 #28282) +#28280 := (iff #28241 #28279) +#28281 := [rewrite]: #28280 +#28284 := [monotonicity #28281]: #28283 +#28277 := (iff #28245 #28276) +#28262 := (iff #28244 #28261) +#28263 := [rewrite]: #28262 +#28278 := [monotonicity #28263]: #28277 +#28293 := [monotonicity #28278 #28284 #28290]: #28292 +#28298 := [trans #28293 #28296]: #28297 +#28301 := [monotonicity #28298]: #28300 +#28274 := (iff #28255 #28273) +#28271 := (iff #28254 #28270) +#28268 := (iff #28253 #28267) +#28265 := (iff #28252 #28264) +#28266 := [rewrite]: #28265 +#28269 := [monotonicity #28266]: #28268 +#28272 := [monotonicity #28263 #28269]: #28271 +#28275 := [monotonicity #28272]: #28274 +#28304 := [monotonicity #28275 #28301]: #28303 +#28307 := [monotonicity #28304]: #28306 +#28310 := [monotonicity #28307]: #28309 +#28313 := [monotonicity #28310]: #28312 +#28316 := [monotonicity #28313]: #28315 +#30082 := [monotonicity #28316]: #29715 +#30079 := [trans #30082 #30081]: #29715 +#29714 := [quant-inst #3039 #3257]: #29633 +#29698 := [mp #29714 #30079]: #29632 +#30441 := [unit-resolution #29698 #22058 #30440]: false +#30442 := [lemma #30441]: #28314 +#30489 := (or #30431 #12548) +#29869 := [hypothesis]: #28294 +#29937 := (= #3047 #28228) +#29960 := (= #28228 #3047) +#30333 := (= #28223 #3044) +#30330 := (= #28223 #27103) +#28220 := (f77 #24797 f310 #27080) +#28221 := (f137 #28220 #24797) +#28154 := (f77 #27103 #28221 #24960) +#28159 := (f69 #3220 #28154) +#28219 := (f147 #28159) +#30328 := (= #28219 #27103) +#28206 := (= #27103 #28219) +#28217 := (f148 #28159) +#28218 := (= f1 #28217) +#28214 := (f78 #28159) +#28215 := (= f1 #28214) +#28216 := (not #28215) +#28207 := (not #28206) +#28149 := (f35 f298 #28154) +#28157 := (= f1 #28149) +#28158 := (not #28157) +#28338 := (or #28158 #28207 #28216 #28218) +#28341 := (not #28338) +#28211 := (>= #28221 0::Int) +#24703 := (or #23500 #13998) +#24704 := [def-axiom]: #24703 +#30247 := [unit-resolution #24704 #29744]: #13998 +#28331 := (* -1::Int #28221) +#28472 := (+ f310 #28331) +#28473 := (<= #28472 0::Int) +#28222 := (= f310 #28221) +#28155 := (or #27087 #28222) +#28156 := [quant-inst #24797 #3139]: #28155 +#28478 := [unit-resolution #28156 #17071]: #28222 +#28481 := (not #28222) +#28482 := (or #28481 #28473) +#28483 := [th-lemma arith triangle-eq]: #28482 +#28484 := [unit-resolution #28483 #28478]: #28473 +#30252 := (not #28473) +#30253 := (or #28211 #22582 #30252) +#30282 := [th-lemma arith assign-bounds 1 1]: #30253 +#30283 := [unit-resolution #30282 #28484 #30247]: #28211 +#28212 := (not #28211) +#30281 := (or #28212 #28341) +#28332 := (+ #24962 #28331) +#28333 := (<= #28332 0::Int) +#28517 := (not #28333) +#28474 := (>= #28472 0::Int) +#28514 := (or #28481 #28474) +#28515 := [th-lemma arith triangle-eq]: #28514 +#28516 := [unit-resolution #28515 #28478]: #28474 +#28519 := (not #28474) +#30285 := (or #28517 #28519 #13765) +#28520 := (or #28517 #28518 #28519 #13765) +#28521 := [th-lemma arith assign-bounds 1 -1 -1]: #28520 +#30258 := [unit-resolution #28521 #28512]: #30285 +#30286 := [unit-resolution #30258 #28516 #29760]: #28517 +#29476 := (or #27726 #27121 #28212 #28333 #28341) +#28205 := (or #28207 #28218 #28216 #28158) +#28208 := (not #28205) +#28209 := (+ #28221 #27122) +#28210 := (>= #28209 0::Int) +#28213 := (or #28212 #28210 #27121 #28208) +#29477 := (or #27726 #28213) +#29484 := (iff #29477 #29476) +#28347 := (or #27121 #28212 #28333 #28341) +#29479 := (or #27726 #28347) +#29482 := (iff #29479 #29476) #29483 := [rewrite]: #29482 -#29486 := [monotonicity #29483]: #29485 -#29479 := (iff #29464 #29476) -#29468 := (+ #27164 #29368) -#29471 := (>= #29468 0::Int) -#29477 := (iff #29471 #29476) -#29478 := [rewrite]: #29477 -#29472 := (iff #29464 #29471) -#29469 := (= #29463 #29468) -#29470 := [rewrite]: #29469 -#29473 := [monotonicity #29470]: #29472 -#29480 := [trans #29473 #29478]: #29479 -#29489 := [monotonicity #29480 #29486]: #29488 -#29494 := [trans #29489 #29492]: #29493 -#29500 := [monotonicity #29494]: #29499 -#29504 := [trans #29500 #29502]: #29503 -#29497 := [quant-inst #3039 #3043 #24996 #24998 #29368]: #29496 -#29505 := [mp #29497 #29504]: #29495 -#30248 := [unit-resolution #29505 #21024 #28873]: #30247 -#30249 := [unit-resolution #30248 #29681 #30245]: #29484 -#29513 := (or #29481 #29459) -#29514 := [def-axiom]: #29513 -#30250 := [unit-resolution #29514 #30249]: #29459 -#30281 := [symm #30250]: #30280 -#30278 := (= #28494 #29458) -#30276 := (= #27834 #29452) -#30274 := (= #29452 #27834) -#30272 := (= #29431 #3257) -#28088 := (f127 #3257) -#28199 := (f54 #24996 #28088) -#30266 := (= #28199 #3257) -#28200 := (= #3257 #28199) -#28205 := (f59 #3257 #24996) -#28206 := (= f1 #28205) -#30252 := (= #3258 #28205) -#29418 := (= #28205 #3258) -#29419 := [monotonicity #28386]: #29418 -#30253 := [symm #29419]: #30252 -#28203 := (= #24996 #28202) -#28182 := (* f309 #27068) -#29340 := (+ #27070 #28182) -#29341 := (f54 #24996 #29340) -#29371 := (f24 #29341) -#29443 := (= #29371 #28202) -#29439 := (= #28202 #29371) -#29437 := (= #3257 #29341) -#29336 := (f77 #24833 f309 #24996) -#29342 := (= #29336 #29341) -#29343 := (not #29342) -#29337 := (f149 #29336 #24833) -#29338 := (= f1 #29337) -#29339 := (not #29338) -#29346 := (or #29339 #29343) -#29349 := (not #29346) -#29352 := (or #27721 #29349) -#29344 := (or #29343 #29339) -#29345 := (not #29344) -#29353 := (or #27721 #29345) -#29355 := (iff #29353 #29352) -#29357 := (iff #29352 #29352) -#29358 := [rewrite]: #29357 -#29350 := (iff #29345 #29349) -#29347 := (iff #29344 #29346) -#29348 := [rewrite]: #29347 -#29351 := [monotonicity #29348]: #29350 -#29356 := [monotonicity #29351]: #29355 -#29359 := [trans #29356 #29358]: #29355 -#29354 := [quant-inst #24833 #3139 #24996]: #29353 -#29360 := [mp #29354 #29359]: #29352 -#29429 := [unit-resolution #29360 #21240]: #29349 -#29363 := (or #29346 #29342) -#29364 := [def-axiom]: #29363 -#29430 := [unit-resolution #29364 #29429]: #29342 -#29435 := (= #3257 #29336) -#29433 := (= #29336 #3257) -#29434 := [monotonicity #27142 #28386]: #29433 -#29436 := [symm #29434]: #29435 -#29438 := [trans #29436 #29430]: #29437 -#29440 := [monotonicity #29438]: #29439 -#29444 := [symm #29440]: #29443 -#29374 := (= #24996 #29371) -#29379 := (or #25064 #29374) -#29380 := [quant-inst #24996 #29340]: #29379 -#29428 := [unit-resolution #29380 #23312]: #29374 -#29445 := [trans #29428 #29444]: #28203 -#29320 := (not #28203) -#28280 := (iff #28203 #28206) -#29315 := (or #26210 #28280) -#29316 := [quant-inst #3257 #24996]: #29315 -#29416 := [unit-resolution #29316 #23299]: #28280 -#28198 := (not #28206) -#29424 := (iff #18556 #28198) -#29422 := (iff #12575 #28206) -#29420 := (iff #28206 #12575) -#29421 := [monotonicity #29419]: #29420 -#29423 := [symm #29421]: #29422 -#29425 := [monotonicity #29423]: #29424 -#29417 := [hypothesis]: #18556 -#29426 := [mp #29417 #29425]: #28198 -#29317 := (not #28280) -#29321 := (or #29317 #29320 #28206) -#29322 := [def-axiom]: #29321 -#29427 := [unit-resolution #29322 #29426 #29416]: #29320 -#29446 := [unit-resolution #29427 #29445]: false -#29447 := [lemma #29446]: #12575 -#30254 := [trans #29447 #30253]: #28206 -#28201 := (or #28200 #28198) -#29376 := (or #26194 #28200 #28198) -#29388 := (or #26194 #28201) -#29387 := (iff #29388 #29376) -#29390 := [rewrite]: #29387 -#29389 := [quant-inst #3257 #24996]: #29388 -#29391 := [mp #29389 #29390]: #29376 -#30255 := [unit-resolution #29391 #18284]: #28201 -#30256 := [unit-resolution #30255 #30254]: #28200 -#30267 := [symm #30256]: #30266 -#30270 := (= #29431 #28199) -#29648 := (* #27068 #29368) -#29651 := (+ #27318 #29648) -#29654 := (f54 #24996 #29651) -#30264 := (= #29654 #28199) -#30258 := (= #29651 #28088) -#30229 := (= #28088 #29651) -#30230 := (* -1::Int #29651) -#30231 := (+ #28088 #30230) -#30232 := (<= #30231 0::Int) -#29206 := (* -1::Int #27070) -#29207 := (+ #24880 #29206) -#29209 := (>= #29207 0::Int) -#29205 := (= #24880 #27070) -#30031 := (= #3043 #27070) -#29986 := [symm #27275]: #30031 -#29987 := [trans #28885 #29986]: #29205 -#30032 := (not #29205) -#30000 := (or #30032 #29209) -#29997 := [th-lemma arith triangle-eq]: #30000 -#29984 := [unit-resolution #29997 #29987]: #29209 -#29700 := (* -1::Int #27318) -#29701 := (+ #24880 #29700) -#29702 := (<= #29701 0::Int) -#29699 := (= #24880 #27318) -#29989 := [symm #28883]: #29699 -#29990 := (not #29699) -#29991 := (or #29990 #29702) -#29992 := [th-lemma arith triangle-eq]: #29991 -#29993 := [unit-resolution #29992 #29989]: #29702 -#29377 := (f127 #29341) -#29381 := (* -1::Int #29377) -#29587 := (+ #28088 #29381) -#29588 := (<= #29587 0::Int) -#29586 := (= #28088 #29377) -#30043 := (= #29377 #28088) -#30035 := (= #29341 #3257) -#30026 := (= #29341 #29336) -#30034 := [symm #29430]: #30026 -#30042 := [trans #30034 #29434]: #30035 -#30041 := [monotonicity #30042]: #30043 -#30033 := [symm #30041]: #29586 -#30044 := (not #29586) -#30045 := (or #30044 #29588) -#30046 := [th-lemma arith triangle-eq]: #30045 -#30049 := [unit-resolution #30046 #30033]: #29588 -#29382 := (+ #28182 #29381) -#29383 := (+ #27070 #29382) -#29571 := (>= #29383 0::Int) -#29384 := (= #29383 0::Int) -#29559 := (or #25070 #29384) -#29378 := (= #29340 #29377) -#29560 := (or #25070 #29378) -#29564 := (iff #29560 #29559) -#29566 := (iff #29559 #29559) -#29567 := [rewrite]: #29566 -#29385 := (iff #29378 #29384) -#29386 := [rewrite]: #29385 -#29565 := [monotonicity #29386]: #29564 -#29568 := [trans #29565 #29567]: #29564 -#29563 := [quant-inst #24996 #29340]: #29560 -#29569 := [mp #29563 #29568]: #29559 -#30050 := [unit-resolution #29569 #23306]: #29384 -#30055 := (not #29384) -#30058 := (or #30055 #29571) -#30057 := [th-lemma arith triangle-eq]: #30058 -#30059 := [unit-resolution #30057 #30050]: #29571 -#29212 := (>= #27068 1::Int) -#29210 := (= #27068 1::Int) -#2998 := (f150 f19) -#2999 := (= #2998 1::Int) -#12057 := [asserted]: #2999 -#30060 := (= #27068 #2998) -#30080 := [monotonicity #28386]: #30060 -#30081 := [trans #30080 #12057]: #29210 -#30082 := (not #29210) -#30098 := (or #30082 #29212) -#30099 := [th-lemma arith triangle-eq]: #30098 -#30056 := [unit-resolution #30099 #30081]: #29212 -#29211 := (<= #27068 1::Int) -#30145 := (or #30082 #29211) -#30146 := [th-lemma arith triangle-eq]: #30145 -#30147 := [unit-resolution #30146 #30081]: #29211 -#30028 := (not #29584) -#30027 := (not #29702) -#29999 := (not #29211) -#29754 := (not #29212) -#29998 := (not #29209) -#29995 := (not #29571) -#29994 := (not #29588) -#30029 := (or #30232 #29994 #29995 #29998 #29754 #29999 #29754 #29999 #30027 #30028) -#30030 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30029 -#30025 := [unit-resolution #30030 #30147 #30056 #30059 #29678 #30049 #29993 #29984]: #30232 -#30233 := (>= #30231 0::Int) -#29208 := (<= #29207 0::Int) -#30152 := (or #30032 #29208) -#30153 := [th-lemma arith triangle-eq]: #30152 -#30154 := [unit-resolution #30153 #29987]: #29208 -#29703 := (>= #29701 0::Int) -#30155 := (or #29990 #29703) -#30156 := [th-lemma arith triangle-eq]: #30155 -#30157 := [unit-resolution #30156 #29989]: #29703 -#29589 := (>= #29587 0::Int) -#30150 := (or #30044 #29589) -#30151 := [th-lemma arith triangle-eq]: #30150 -#30148 := [unit-resolution #30151 #30033]: #29589 -#29570 := (<= #29383 0::Int) -#30149 := (or #30055 #29570) -#30158 := [th-lemma arith triangle-eq]: #30149 -#30159 := [unit-resolution #30158 #30050]: #29570 -#30162 := (not #29703) -#30161 := (not #29208) -#29784 := (not #29570) -#30160 := (not #29589) -#30163 := (or #30233 #30160 #29784 #30161 #29754 #29999 #29754 #29999 #30162 #30242) -#30164 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30163 -#30165 := [unit-resolution #30164 #30147 #30056 #30159 #30237 #30148 #30157 #30154]: #30233 -#30169 := (not #30233) -#30168 := (not #30232) -#30178 := (or #30229 #30168 #30169) -#30179 := [th-lemma arith triangle-eq]: #30178 -#30180 := [unit-resolution #30179 #30165 #30025]: #30229 -#30177 := [symm #30180]: #30258 -#30186 := [monotonicity #30177]: #30264 -#30268 := (= #29431 #29654) -#29637 := (f77 #26182 #29368 #24996) -#29657 := (= #29637 #29654) -#29592 := (not #29657) -#29638 := (f149 #29637 #26182) -#29639 := (= f1 #29638) -#29640 := (not #29639) -#29597 := (or #29640 #29592) -#29660 := (not #29597) -#29684 := (or #27721 #29660) -#29641 := (* #29368 #27068) -#29642 := (+ #27318 #29641) -#29643 := (f54 #24996 #29642) -#29644 := (= #29637 #29643) -#29645 := (not #29644) -#29646 := (or #29645 #29640) -#29647 := (not #29646) -#29685 := (or #27721 #29647) -#29687 := (iff #29685 #29684) -#29689 := (iff #29684 #29684) -#29690 := [rewrite]: #29689 -#29682 := (iff #29647 #29660) -#29661 := (iff #29646 #29597) -#29594 := (or #29592 #29640) -#29598 := (iff #29594 #29597) -#29599 := [rewrite]: #29598 -#29595 := (iff #29646 #29594) -#29593 := (iff #29645 #29592) -#29658 := (iff #29644 #29657) -#29655 := (= #29643 #29654) -#29652 := (= #29642 #29651) -#29649 := (= #29641 #29648) -#29650 := [rewrite]: #29649 -#29653 := [monotonicity #29650]: #29652 -#29656 := [monotonicity #29653]: #29655 -#29659 := [monotonicity #29656]: #29658 -#29591 := [monotonicity #29659]: #29593 -#29596 := [monotonicity #29591]: #29595 -#29662 := [trans #29596 #29599]: #29661 -#29683 := [monotonicity #29662]: #29682 -#29688 := [monotonicity #29683]: #29687 -#29691 := [trans #29688 #29690]: #29687 -#29686 := [quant-inst #26182 #29368 #24996]: #29685 -#29692 := [mp #29686 #29691]: #29684 -#30260 := [unit-resolution #29692 #21240]: #29660 -#29695 := (or #29597 #29657) -#29696 := [def-axiom]: #29695 -#30261 := [unit-resolution #29696 #30260]: #29657 -#30262 := (= #29431 #29637) -#30263 := [monotonicity #28791]: #30262 -#30269 := [trans #30263 #30261]: #30268 -#30187 := [trans #30269 #30186]: #30270 -#30188 := [trans #30187 #30267]: #30272 -#30189 := [monotonicity #30188]: #30274 -#30190 := [symm #30189]: #30276 -#30185 := [monotonicity #30190]: #30278 -#30191 := [trans #30185 #30281]: #30282 -#30192 := [trans #30191 #28789]: #30284 -#30194 := [monotonicity #30192]: #30193 -#30200 := [symm #30194]: #30199 -#30198 := [trans #14366 #30200]: #28498 -#29947 := (not #28498) -#29948 := (or #28554 #29947) -#29934 := [def-axiom]: #29948 -#30201 := [unit-resolution #29934 #30198]: #28554 -#30210 := (= #25501 #28512) -#30212 := (= #28512 #25501) -#30205 := (= #28202 f19) -#30203 := (= #28202 #24996) -#29392 := (or #29317 #28203 #28198) -#29393 := [def-axiom]: #29392 -#30202 := [unit-resolution #29393 #30254 #29416]: #28203 -#30204 := [symm #30202]: #30203 -#30211 := [trans #30204 #28386]: #30205 -#30213 := [monotonicity #30211]: #30212 -#30216 := [symm #30213]: #30210 -#30217 := [trans #28841 #30216]: #28530 -#29890 := (not #28503) -#30239 := (iff #12118 #29890) -#30251 := (iff #12115 #28503) -#30224 := (iff #28503 #12115) -#30222 := (= #28502 #3053) -#30220 := (= #28501 #3040) -#30218 := (= #28501 #25117) -#30219 := [monotonicity #30192]: #30218 -#30221 := [trans #30219 #28851]: #30220 -#30223 := [monotonicity #30221]: #30222 -#30288 := [monotonicity #30223]: #30224 -#30246 := [symm #30288]: #30251 -#30240 := [monotonicity #30246]: #30239 -#30238 := [mp #14369 #30240]: #29890 -#29517 := (f77 #27223 #29368 #24996) -#29518 := (f69 #3220 #29517) -#29519 := (f147 #29518) -#29520 := (= f1 #29519) -#29552 := (not #29520) -#30315 := (iff #29552 #28509) -#30313 := (iff #29520 #28508) -#30311 := (iff #28508 #29520) -#30309 := (= #28507 #29519) -#30307 := (= #27834 #29518) -#30305 := (= #29518 #27834) -#30303 := (= #29517 #3257) -#30301 := (= #29368 f309) -#30302 := [symm #29674]: #30301 -#30304 := [monotonicity #28393 #30302 #28386]: #30303 -#30306 := [monotonicity #30304]: #30305 -#30308 := [symm #30306]: #30307 -#30310 := [monotonicity #30308]: #30309 -#30312 := [monotonicity #30310]: #30311 -#30314 := [symm #30312]: #30313 -#30316 := [monotonicity #30314]: #30315 -#29521 := (f35 f297 #29517) -#29522 := (= f1 #29521) -#29523 := (not #29522) -#29527 := (or #29520 #29523) -#29530 := (not #29527) -#30297 := (or #29466 #29476 #29530) -#29541 := (or #27254 #24846 #27235 #27238 #29466 #29476 #29530) -#29524 := (or #29523 #29520) -#29525 := (not #29524) -#29526 := (or #27238 #29466 #29464 #24846 #27235 #29525) -#29542 := (or #27254 #29526) -#29549 := (iff #29542 #29541) -#29536 := (or #24846 #27235 #27238 #29466 #29476 #29530) -#29544 := (or #27254 #29536) -#29547 := (iff #29544 #29541) -#29548 := [rewrite]: #29547 -#29545 := (iff #29542 #29544) -#29539 := (iff #29526 #29536) -#29533 := (or #27238 #29466 #29476 #24846 #27235 #29530) -#29537 := (iff #29533 #29536) -#29538 := [rewrite]: #29537 -#29534 := (iff #29526 #29533) -#29531 := (iff #29525 #29530) -#29528 := (iff #29524 #29527) -#29529 := [rewrite]: #29528 -#29532 := [monotonicity #29529]: #29531 -#29535 := [monotonicity #29480 #29532]: #29534 -#29540 := [trans #29535 #29538]: #29539 -#29546 := [monotonicity #29540]: #29545 -#29550 := [trans #29546 #29548]: #29549 -#29543 := [quant-inst #3039 #3043 #26182 #24998 #29368 #24996]: #29542 -#29551 := [mp #29543 #29550]: #29541 -#30298 := [unit-resolution #29551 #21684 #14351 #28797 #28426]: #30297 -#30299 := [unit-resolution #30298 #29681 #30245]: #29530 -#29553 := (or #29527 #29552) -#29554 := [def-axiom]: #29553 -#30300 := [unit-resolution #29554 #30299]: #29552 -#30317 := [mp #30300 #30316]: #28509 -#29772 := (or #28548 #28508) -#29773 := [def-axiom]: #29772 -#30318 := [unit-resolution #29773 #30317]: #28548 -#29907 := (or #28568 #28503 #28545 #28551 #28557) -#29965 := [def-axiom]: #29907 -#30319 := [unit-resolution #29965 #30318 #30238 #30217 #30201 #30167]: false -#30320 := [lemma #30319]: #28568 -#29805 := (or #28571 #28563) -#29738 := [def-axiom]: #29805 -#30175 := [unit-resolution #29738 #30320]: #28571 -#28432 := (or #12578 #13656 #27235 #13801) -#28375 := [hypothesis]: #13516 -#28210 := (f77 #27086 f309 #27607) -#28211 := (f136 #28210 #27086) -#28242 := (* -1::Int #28211) -#28370 := (+ f309 #28242) -#28371 := (<= #28370 0::Int) -#28212 := (= f309 #28211) -#28215 := (or #27129 #28212) -#28216 := [quant-inst #27086 #3139]: #28215 -#28376 := [unit-resolution #28216 #17107]: #28212 -#28379 := (not #28212) -#28380 := (or #28379 #28371) -#28381 := [th-lemma arith triangle-eq]: #28380 -#28382 := [unit-resolution #28381 #28376]: #28371 -#28233 := (>= #28211 0::Int) -#28234 := (not #28233) -#28285 := (f77 #27223 #28211 #24996) -#28289 := (f35 f297 #28285) -#28290 := (= f1 #28289) -#28291 := (not #28290) -#28286 := (f69 #3220 #28285) -#28287 := (f147 #28286) -#28288 := (= f1 #28287) -#28295 := (or #28288 #28291) -#28402 := (iff #18559 #28291) -#28400 := (iff #12578 #28290) -#28398 := (iff #28290 #12578) -#28396 := (= #28289 #3260) -#28394 := (= #28285 #3257) -#28387 := (= #28211 f309) -#28388 := [symm #28376]: #28387 -#28395 := [monotonicity #28393 #28388 #28386]: #28394 -#28397 := [monotonicity #28395]: #28396 -#28399 := [monotonicity #28397]: #28398 -#28401 := [symm #28399]: #28400 -#28403 := [monotonicity #28401]: #28402 -#28383 := [hypothesis]: #18559 -#28404 := [mp #28383 #28403]: #28291 -#28323 := (or #28295 #28290) -#28324 := [def-axiom]: #28323 -#28405 := [unit-resolution #28324 #28404]: #28295 -#28243 := (+ #24998 #28242) -#28244 := (<= #28243 0::Int) -#28415 := (not #28244) -#28411 := [hypothesis]: #13802 -#28372 := (>= #28370 0::Int) -#28412 := (or #28379 #28372) -#28413 := [th-lemma arith triangle-eq]: #28412 -#28414 := [unit-resolution #28413 #28376]: #28372 -#28417 := (not #28372) -#28418 := (or #28415 #28416 #28417 #13801) -#28419 := [th-lemma arith assign-bounds 1 -1 -1]: #28418 -#28420 := [unit-resolution #28419 #28414 #28411 #28410]: #28415 -#28298 := (not #28295) -#28428 := (or #28234 #28244 #28298) -#28309 := (or #27254 #24846 #27235 #27238 #28234 #28244 #28298) -#28292 := (or #28291 #28288) -#28293 := (not #28292) -#28231 := (+ #28211 #27164) -#28232 := (>= #28231 0::Int) -#28294 := (or #27238 #28234 #28232 #24846 #27235 #28293) -#28310 := (or #27254 #28294) -#28317 := (iff #28310 #28309) -#28304 := (or #24846 #27235 #27238 #28234 #28244 #28298) -#28312 := (or #27254 #28304) -#28315 := (iff #28312 #28309) -#28316 := [rewrite]: #28315 -#28313 := (iff #28310 #28312) -#28307 := (iff #28294 #28304) -#28301 := (or #27238 #28234 #28244 #24846 #27235 #28298) -#28305 := (iff #28301 #28304) -#28306 := [rewrite]: #28305 -#28302 := (iff #28294 #28301) -#28299 := (iff #28293 #28298) -#28296 := (iff #28292 #28295) -#28297 := [rewrite]: #28296 -#28300 := [monotonicity #28297]: #28299 -#28247 := (iff #28232 #28244) -#28236 := (+ #27164 #28211) -#28239 := (>= #28236 0::Int) -#28245 := (iff #28239 #28244) -#28246 := [rewrite]: #28245 -#28240 := (iff #28232 #28239) -#28237 := (= #28231 #28236) -#28238 := [rewrite]: #28237 -#28241 := [monotonicity #28238]: #28240 -#28248 := [trans #28241 #28246]: #28247 -#28303 := [monotonicity #28248 #28300]: #28302 -#28308 := [trans #28303 #28306]: #28307 -#28314 := [monotonicity #28308]: #28313 -#28318 := [trans #28314 #28316]: #28317 -#28311 := [quant-inst #3039 #3043 #26182 #24998 #28211 #24996]: #28310 -#28319 := [mp #28311 #28318]: #28309 -#28429 := [unit-resolution #28319 #21684 #14351 #28427 #28426]: #28428 -#28430 := [unit-resolution #28429 #28420 #28405]: #28234 -#28431 := [th-lemma arith farkas 1 1 1 #28430 #28382 #28375]: false -#28433 := [lemma #28431]: #28432 -#30142 := [unit-resolution #28433 #30141 #28797 #29673]: #12578 -#30170 := (or #28580 #18559 #28574) -#30171 := [def-axiom]: #30170 -#30321 := [unit-resolution #30171 #30142 #30175]: #28580 -#29900 := (or #29899 #12584 #28577) -#29898 := [def-axiom]: #29900 -#30323 := [unit-resolution #29898 #30321]: #30322 -#30324 := [unit-resolution #30323 #30215]: #12584 -#30424 := (+ f309 #18928) -#30620 := (>= #30424 0::Int) -#30702 := (not #30620) -#30595 := (= f309 ?v0!14) -#30648 := (not #30595) -#30651 := [hypothesis]: #23457 -#24603 := (or #23454 #13708) +#29480 := (iff #29477 #29479) +#28350 := (iff #28213 #28347) +#28344 := (or #28212 #28333 #27121 #28341) +#28348 := (iff #28344 #28347) +#28349 := [rewrite]: #28348 +#28345 := (iff #28213 #28344) +#28342 := (iff #28208 #28341) +#28339 := (iff #28205 #28338) +#28340 := [rewrite]: #28339 +#28343 := [monotonicity #28340]: #28342 +#28336 := (iff #28210 #28333) +#28225 := (+ #27122 #28221) +#28328 := (>= #28225 0::Int) +#28334 := (iff #28328 #28333) +#28335 := [rewrite]: #28334 +#28329 := (iff #28210 #28328) +#28226 := (= #28209 #28225) +#28327 := [rewrite]: #28226 +#28330 := [monotonicity #28327]: #28329 +#28337 := [trans #28330 #28335]: #28336 +#28346 := [monotonicity #28337 #28343]: #28345 +#28351 := [trans #28346 #28349]: #28350 +#29481 := [monotonicity #28351]: #29480 +#29485 := [trans #29481 #29483]: #29484 +#29478 := [quant-inst #3039 #3043 #24960 #24962 #28221]: #29477 +#29486 := [mp #29478 #29485]: #29476 +#30287 := [unit-resolution #29486 #20988 #30286 #28914]: #30281 +#30288 := [unit-resolution #30287 #30283]: #28341 +#29489 := (or #28338 #28206) +#29490 := [def-axiom]: #29489 +#30257 := [unit-resolution #29490 #30288]: #28206 +#30329 := [symm #30257]: #30328 +#30326 := (= #28223 #28219) +#30324 := (= #27798 #28159) +#29979 := (= #28159 #27798) +#29970 := (= #28154 #3257) +#27807 := (f128 #3257) +#28101 := (f54 #24960 #27807) +#30319 := (= #28101 #3257) +#28102 := (= #3257 #28101) +#28047 := (f59 #3257 #24960) +#28042 := (= f1 #28047) +#30290 := (= #3258 #28047) +#29430 := (= #28047 #3258) +#29431 := [monotonicity #28488]: #29430 +#30291 := [symm #29431]: #30290 +#28119 := (= #24960 #28118) +#28192 := (f81 f310 #27032) +#28193 := (+ #27034 #28192) +#28194 := (f54 #24960 #28193) +#28449 := (f24 #28194) +#29455 := (= #28449 #28118) +#29451 := (= #28118 #28449) +#29449 := (= #3257 #28194) +#28188 := (f77 #24797 f310 #24960) +#28195 := (= #28188 #28194) +#28196 := (not #28195) +#28189 := (f150 #28188 #24797) +#28190 := (= f1 #28189) +#28191 := (not #28190) +#28199 := (or #28191 #28196) +#28202 := (not #28199) +#29398 := (or #27451 #28202) +#28197 := (or #28196 #28191) +#28198 := (not #28197) +#29399 := (or #27451 #28198) +#29401 := (iff #29399 #29398) +#29403 := (iff #29398 #29398) +#29404 := [rewrite]: #29403 +#28203 := (iff #28198 #28202) +#28200 := (iff #28197 #28199) +#28201 := [rewrite]: #28200 +#28204 := [monotonicity #28201]: #28203 +#29402 := [monotonicity #28204]: #29401 +#29405 := [trans #29402 #29404]: #29401 +#29400 := [quant-inst #24797 #3139 #24960]: #29399 +#29406 := [mp #29400 #29405]: #29398 +#29441 := [unit-resolution #29406 #21204]: #28202 +#29409 := (or #28199 #28195) +#29410 := [def-axiom]: #29409 +#29442 := [unit-resolution #29410 #29441]: #28195 +#29447 := (= #3257 #28188) +#29445 := (= #28188 #3257) +#29446 := [monotonicity #28946 #28488]: #29445 +#29448 := [symm #29446]: #29447 +#29450 := [trans #29448 #29442]: #29449 +#29452 := [monotonicity #29450]: #29451 +#29456 := [symm #29452]: #29455 +#28450 := (= #24960 #28449) +#29417 := (or #25028 #28450) +#29418 := [quant-inst #24960 #28193]: #29417 +#29440 := [unit-resolution #29418 #23276]: #28450 +#29457 := [trans #29440 #29456]: #28119 +#29378 := (not #28119) +#28121 := (iff #28042 #28119) +#29368 := (or #26174 #28121) +#28120 := (iff #28119 #28042) +#29369 := (or #26174 #28120) +#29371 := (iff #29369 #29368) +#29373 := (iff #29368 #29368) +#29374 := [rewrite]: #29373 +#28122 := (iff #28120 #28121) +#28123 := [rewrite]: #28122 +#29372 := [monotonicity #28123]: #29371 +#29375 := [trans #29372 #29374]: #29371 +#29370 := [quant-inst #3257 #24960]: #29369 +#29376 := [mp #29370 #29375]: #29368 +#29428 := [unit-resolution #29376 #23263]: #28121 +#28100 := (not #28042) +#29436 := (iff #18520 #28100) +#29434 := (iff #12539 #28042) +#29432 := (iff #28042 #12539) +#29433 := [monotonicity #29431]: #29432 +#29435 := [symm #29433]: #29434 +#29437 := [monotonicity #29435]: #29436 +#29429 := [hypothesis]: #18520 +#29438 := [mp #29429 #29437]: #28100 +#29377 := (not #28121) +#29379 := (or #29377 #28042 #29378) +#29380 := [def-axiom]: #29379 +#29439 := [unit-resolution #29380 #29438 #29428]: #29378 +#29458 := [unit-resolution #29439 #29457]: false +#29459 := [lemma #29458]: #12539 +#30299 := [trans #29459 #30291]: #28042 +#28104 := (or #28100 #28102) +#29381 := (or #26158 #28100 #28102) +#28103 := (or #28102 #28100) +#29382 := (or #26158 #28103) +#29424 := (iff #29382 #29381) +#29413 := (or #26158 #28104) +#29422 := (iff #29413 #29381) +#29423 := [rewrite]: #29422 +#29420 := (iff #29382 #29413) +#28105 := (iff #28103 #28104) +#28106 := [rewrite]: #28105 +#29421 := [monotonicity #28106]: #29420 +#29425 := [trans #29421 #29423]: #29424 +#29419 := [quant-inst #3257 #24960]: #29382 +#29426 := [mp #29419 #29425]: #29381 +#30300 := [unit-resolution #29426 #18248]: #28104 +#30303 := [unit-resolution #30300 #30299]: #28102 +#30298 := [symm #30303]: #30319 +#30322 := (= #28154 #28101) +#29661 := (f81 #28221 #27032) +#29662 := (+ #27307 #29661) +#29663 := (f54 #24960 #29662) +#30312 := (= #29663 #28101) +#30302 := (= #29662 #27807) +#30237 := (= #27807 #29662) +#30243 := (* -1::Int #29662) +#30244 := (+ #27807 #30243) +#30190 := (<= #30244 0::Int) +#29586 := (* -1::Int #29661) +#29526 := (+ #28192 #29586) +#29527 := (<= #29526 0::Int) +#29585 := (= #28192 #29661) +#30240 := (= #29661 #28192) +#28489 := (= #28221 f310) +#28490 := [symm #28478]: #28489 +#30230 := [monotonicity #28490]: #30240 +#30355 := [symm #30230]: #29585 +#30289 := (not #29585) +#30284 := (or #30289 #29527) +#30363 := [th-lemma arith triangle-eq]: #30284 +#30364 := [unit-resolution #30363 #30355]: #29527 +#28451 := (f128 #28194) +#28455 := (* -1::Int #28451) +#29517 := (+ #27807 #28455) +#29518 := (<= #29517 0::Int) +#29516 := (= #27807 #28451) +#30369 := (= #28451 #27807) +#30367 := (= #28194 #3257) +#30365 := (= #28194 #28188) +#30366 := [symm #29442]: #30365 +#30368 := [trans #30366 #29446]: #30367 +#30370 := [monotonicity #30368]: #30369 +#30371 := [symm #30370]: #29516 +#30372 := (not #29516) +#30373 := (or #30372 #29518) +#30374 := [th-lemma arith triangle-eq]: #30373 +#30375 := [unit-resolution #30374 #30371]: #29518 +#28456 := (+ #28192 #28455) +#28457 := (+ #27034 #28456) +#29515 := (>= #28457 0::Int) +#28458 := (= #28457 0::Int) +#29503 := (or #25034 #28458) +#28452 := (= #28193 #28451) +#29504 := (or #25034 #28452) +#29508 := (iff #29504 #29503) +#29510 := (iff #29503 #29503) +#29511 := [rewrite]: #29510 +#28459 := (iff #28452 #28458) +#28460 := [rewrite]: #28459 +#29509 := [monotonicity #28460]: #29508 +#29512 := [trans #29509 #29511]: #29508 +#29507 := [quant-inst #24960 #28193]: #29504 +#29513 := [mp #29507 #29512]: #29503 +#30376 := [unit-resolution #29513 #23270]: #28458 +#30377 := (not #28458) +#30378 := (or #30377 #29515) +#30379 := [th-lemma arith triangle-eq]: #30378 +#30380 := [unit-resolution #30379 #30376]: #29515 +#30385 := (not #29527) +#30384 := (not #28581) +#30383 := (not #27720) +#30382 := (not #29515) +#30381 := (not #29518) +#30386 := (or #30190 #30381 #30382 #30383 #30384 #30385) +#30387 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30386 +#30388 := [unit-resolution #30387 #28931 #30380 #30375 #30364 #28961]: #30190 +#30245 := (>= #30244 0::Int) +#29637 := (>= #29526 0::Int) +#30389 := (or #30289 #29637) +#30390 := [th-lemma arith triangle-eq]: #30389 +#30391 := [unit-resolution #30390 #30355]: #29637 +#29519 := (>= #29517 0::Int) +#30392 := (or #30372 #29519) +#30393 := [th-lemma arith triangle-eq]: #30392 +#30394 := [unit-resolution #30393 #30371]: #29519 +#29514 := (<= #28457 0::Int) +#30395 := (or #30377 #29514) +#30396 := [th-lemma arith triangle-eq]: #30395 +#30397 := [unit-resolution #30396 #30376]: #29514 +#30402 := (not #29637) +#30401 := (not #28582) +#30400 := (not #27719) +#30399 := (not #29514) +#30398 := (not #29519) +#30403 := (or #30245 #30398 #30399 #30400 #30401 #30402) +#30404 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30403 +#30405 := [unit-resolution #30404 #28934 #30397 #30394 #30391 #28958]: #30245 +#30407 := (not #30245) +#30406 := (not #30190) +#30408 := (or #30237 #30406 #30407) +#30409 := [th-lemma arith triangle-eq]: #30408 +#30410 := [unit-resolution #30409 #30405 #30388]: #30237 +#29871 := [symm #30410]: #30302 +#29864 := [monotonicity #29871]: #30312 +#30320 := (= #28154 #29663) +#29657 := (f77 #26146 #28221 #24960) +#29664 := (= #29657 #29663) +#29665 := (not #29664) +#29658 := (f150 #29657 #26146) +#29659 := (= f1 #29658) +#29660 := (not #29659) +#29668 := (or #29660 #29665) +#29671 := (not #29668) +#29559 := (or #27451 #29671) +#29666 := (or #29665 #29660) +#29667 := (not #29666) +#29560 := (or #27451 #29667) +#29562 := (iff #29560 #29559) +#29564 := (iff #29559 #29559) +#29578 := [rewrite]: #29564 +#29672 := (iff #29667 #29671) +#29669 := (iff #29666 #29668) +#29670 := [rewrite]: #29669 +#29673 := [monotonicity #29670]: #29672 +#29563 := [monotonicity #29673]: #29562 +#29579 := [trans #29563 #29578]: #29562 +#29561 := [quant-inst #26146 #28221 #24960]: #29560 +#29577 := [mp #29561 #29579]: #29559 +#30315 := [unit-resolution #29577 #21204]: #29671 +#29581 := (or #29668 #29664) +#29582 := [def-axiom]: #29581 +#30316 := [unit-resolution #29582 #30315]: #29664 +#30301 := (= #28154 #29657) +#30317 := [monotonicity #28365]: #30301 +#30321 := [trans #30317 #30316]: #30320 +#29872 := [trans #30321 #29864]: #30322 +#29955 := [trans #29872 #30298]: #29970 +#29956 := [monotonicity #29955]: #29979 +#29957 := [symm #29956]: #30324 +#29958 := [monotonicity #29957]: #30326 +#29959 := [trans #29958 #30329]: #30330 +#29954 := [trans #29959 #28364]: #30333 +#29934 := [monotonicity #29954]: #29960 +#29935 := [symm #29934]: #29937 +#29944 := [trans #14330 #29935]: #28229 +#29725 := (not #28229) +#29773 := (or #28285 #29725) +#29774 := [def-axiom]: #29773 +#29951 := [unit-resolution #29774 #29944]: #28285 +#29706 := (= #25465 #28243) +#29679 := (= #28243 #25465) +#29938 := (= #28118 f19) +#29839 := (= #28118 #24960) +#29427 := (or #29377 #28100 #28119) +#29453 := [def-axiom]: #29427 +#29953 := [unit-resolution #29453 #30299 #29428]: #28119 +#29681 := [symm #29953]: #29839 +#29682 := [trans #29681 #28488]: #29938 +#29680 := [monotonicity #29682]: #29679 +#30114 := [symm #29680]: #29706 +#29708 := [trans #29027 #30114]: #28261 +#29794 := (not #28234) +#29837 := (iff #12082 #29794) +#30112 := (iff #12079 #28234) +#29876 := (iff #28234 #12079) +#29843 := (= #28233 #3053) +#29844 := (= #28232 #3040) +#29842 := (= #28232 #25081) +#29707 := [monotonicity #29954]: #29842 +#29845 := [trans #29707 #28878]: #29844 +#29846 := [monotonicity #29845]: #29843 +#29836 := [monotonicity #29846]: #29876 +#30113 := [symm #29836]: #30112 +#29838 := [monotonicity #30113]: #29837 +#30111 := [mp #14333 #29838]: #29794 +#28374 := (f77 #27181 #28221 #24960) +#28375 := (f69 #3220 #28374) +#28376 := (f148 #28375) +#28377 := (= f1 #28376) +#29498 := (not #28377) +#30162 := (iff #29498 #28240) +#30093 := (iff #28377 #28239) +#30146 := (iff #28239 #28377) +#30141 := (= #28238 #28376) +#30156 := (= #27798 #28375) +#30096 := (= #28375 #27798) +#28496 := (= #28374 #3257) +#28497 := [monotonicity #28495 #28490 #28488]: #28496 +#30097 := [monotonicity #28497]: #30096 +#30142 := [symm #30097]: #30156 +#29981 := [monotonicity #30142]: #30141 +#30140 := [monotonicity #29981]: #30146 +#30157 := [symm #30140]: #30093 +#30171 := [monotonicity #30157]: #30162 +#28378 := (f35 f298 #28374) +#28379 := (= f1 #28378) +#28380 := (not #28379) +#28384 := (or #28377 #28380) +#28317 := (not #28384) +#30144 := (or #28212 #28317) +#28415 := (or #27212 #24810 #27193 #27196 #28212 #28333 #28317) +#28381 := (or #28380 #28377) +#28382 := (not #28381) +#28383 := (or #27196 #28212 #28210 #24810 #27193 #28382) +#28416 := (or #27212 #28383) +#28407 := (iff #28416 #28415) +#28323 := (or #24810 #27193 #27196 #28212 #28333 #28317) +#28418 := (or #27212 #28323) +#28405 := (iff #28418 #28415) +#28406 := [rewrite]: #28405 +#28419 := (iff #28416 #28418) +#28326 := (iff #28383 #28323) +#28318 := (or #27196 #28212 #28333 #24810 #27193 #28317) +#28324 := (iff #28318 #28323) +#28325 := [rewrite]: #28324 +#28321 := (iff #28383 #28318) +#28319 := (iff #28382 #28317) +#28385 := (iff #28381 #28384) +#28386 := [rewrite]: #28385 +#28320 := [monotonicity #28386]: #28319 +#28322 := [monotonicity #28337 #28320]: #28321 +#28414 := [trans #28322 #28325]: #28326 +#28404 := [monotonicity #28414]: #28419 +#28408 := [trans #28404 #28406]: #28407 +#28417 := [quant-inst #3039 #3043 #26146 #24962 #28221 #24960]: #28416 +#28403 := [mp #28417 #28408]: #28415 +#30145 := [unit-resolution #28403 #21648 #14315 #28130 #30286 #28528]: #30144 +#30138 := [unit-resolution #30145 #30283]: #28317 +#29499 := (or #28384 #29498) +#29500 := [def-axiom]: #29499 +#30095 := [unit-resolution #29500 #30138]: #29498 +#30137 := [mp #30095 #30171]: #28240 +#29767 := (or #28279 #28239) +#29768 := [def-axiom]: #29767 +#30094 := [unit-resolution #29768 #30137]: #28279 +#29524 := (or #28299 #28234 #28276 #28282 #28288) +#29592 := [def-axiom]: #29524 +#30092 := [unit-resolution #29592 #30094 #30111 #29708 #29951 #29869]: false +#30175 := [lemma #30092]: #28299 +#30421 := (or #28302 #28294) +#30422 := [def-axiom]: #30421 +#30484 := [unit-resolution #30422 #30175]: #28302 +#28534 := (or #12542 #13620 #27193 #13765) +#28477 := [hypothesis]: #13480 +#28504 := (iff #18523 #28380) +#28502 := (iff #12542 #28379) +#28500 := (iff #28379 #12542) +#28498 := (= #28378 #3260) +#28499 := [monotonicity #28497]: #28498 +#28501 := [monotonicity #28499]: #28500 +#28503 := [symm #28501]: #28502 +#28505 := [monotonicity #28503]: #28504 +#28485 := [hypothesis]: #18523 +#28506 := [mp #28485 #28505]: #28380 +#28412 := (or #28384 #28379) +#28413 := [def-axiom]: #28412 +#28507 := [unit-resolution #28413 #28506]: #28384 +#28522 := [unit-resolution #28521 #28516 #28513 #28512]: #28517 +#28530 := (or #28212 #28333 #28317) +#28529 := [hypothesis]: #27192 +#28531 := [unit-resolution #28403 #21648 #14315 #28529 #28528]: #28530 +#28532 := [unit-resolution #28531 #28522 #28507]: #28212 +#28533 := [th-lemma arith farkas 1 1 1 #28532 #28484 #28477]: false +#28535 := [lemma #28533]: #28534 +#29600 := [unit-resolution #28535 #29760 #28130 #29674]: #12542 +#30429 := (or #28311 #18523 #28305) +#30430 := [def-axiom]: #30429 +#30488 := [unit-resolution #30430 #29600 #30484]: #28311 +#30432 := (or #30431 #12548 #28308) +#30433 := [def-axiom]: #30432 +#30490 := [unit-resolution #30433 #30488]: #30489 +#30491 := [unit-resolution #30490 #30442]: #12548 +#29604 := (or #18529 #23421 #23391) +#27935 := [hypothesis]: #23418 +#27930 := [hypothesis]: #12548 +#29655 := (or #23406 #18529 #23421) +#24621 := (or #23454 #23448) +#24622 := [def-axiom]: #24621 +#29654 := [unit-resolution #24622 #29759]: #23448 +#27883 := (or #23406 #18520 #18529 #23421 #23451) +#27931 := [hypothesis]: #12539 +#27894 := [hypothesis]: #23448 +#27932 := [hypothesis]: #23409 +#24535 := (or #23406 #12542) +#24536 := [def-axiom]: #24535 +#27927 := [unit-resolution #24536 #27932]: #12542 +#24613 := (or #23451 #18520 #18523 #23445) +#24614 := [def-axiom]: #24613 +#27933 := [unit-resolution #24614 #27927 #27894 #27931]: #23445 +#24603 := (or #23442 #23436) #24604 := [def-axiom]: #24603 -#30652 := [unit-resolution #24604 #30651]: #13708 -#24587 := (+ f307 #13570) -#24588 := (<= #24587 0::Int) -#24593 := (or #23454 #12839) -#24594 := [def-axiom]: #24593 -#30653 := [unit-resolution #24594 #30651]: #12839 -#30654 := (or #12857 #24588) -#30655 := [th-lemma arith triangle-eq]: #30654 -#30656 := [unit-resolution #30655 #30653]: #24588 -#24484 := (not #18943) -#30195 := [hypothesis]: #23421 -#24605 := (or #23454 #23418) -#24606 := [def-axiom]: #24605 -#30176 := [unit-resolution #24606 #30195]: #23454 -#24549 := (or #23424 #23418) -#24550 := [def-axiom]: #24549 -#30325 := [unit-resolution #24550 #30195]: #23424 -#30326 := (or #23433 #18565 #23427) -#24559 := (or #23433 #18556 #18565 #23427) -#24560 := [def-axiom]: #24559 -#30327 := [unit-resolution #24560 #29447]: #30326 -#30328 := [unit-resolution #30327 #30325 #30324]: #23433 -#29801 := (or #23430 #23457) -#29776 := [hypothesis]: #23454 -#29777 := [hypothesis]: #23433 -#24555 := (or #23430 #12584) -#24556 := [def-axiom]: #24555 -#29775 := [unit-resolution #24556 #29777]: #12584 -#29789 := (or #18565 #23469) -#24657 := (or #23490 #23484) -#24658 := [def-axiom]: #24657 -#29786 := [unit-resolution #24658 #30140]: #23484 -#27971 := (or #23472 #23487 #18559) -#27967 := [hypothesis]: #12578 -#27968 := [hypothesis]: #23484 -#27930 := [hypothesis]: #23475 -#24627 := (or #23472 #12575) -#24628 := [def-axiom]: #24627 -#27969 := [unit-resolution #24628 #27930]: #12575 -#24639 := (or #23478 #23472) -#24640 := [def-axiom]: #24639 -#27964 := [unit-resolution #24640 #27930]: #23478 -#24649 := (or #23487 #18556 #18559 #23481) -#24650 := [def-axiom]: #24649 -#27970 := [unit-resolution #24650 #27964 #27969 #27968 #27967]: false -#27972 := [lemma #27970]: #27971 -#29787 := [unit-resolution #27972 #30142 #29786]: #23472 -#24633 := (or #23475 #18556 #18565 #23469) -#24634 := [def-axiom]: #24633 -#29788 := [unit-resolution #24634 #29787]: #23472 -#29790 := [unit-resolution #29788 #29447]: #29789 -#29791 := [unit-resolution #29790 #29775]: #23469 -#24623 := (or #23466 #23460) -#24624 := [def-axiom]: #24623 -#29792 := [unit-resolution #24624 #29791]: #23460 -#24565 := (or #23436 #23430) -#24566 := [def-axiom]: #24565 -#29793 := [unit-resolution #24566 #29777]: #23436 -#29796 := (or #23445 #23439) -#29794 := (or #23445 #18556 #23439) -#24575 := (or #23445 #18556 #18559 #23439) -#24576 := [def-axiom]: #24575 -#29795 := [unit-resolution #24576 #30142]: #29794 -#29797 := [unit-resolution #29795 #29447]: #29796 -#29798 := [unit-resolution #29797 #29793]: #23445 -#24583 := (or #23448 #23442) -#24584 := [def-axiom]: #24583 -#29799 := [unit-resolution #24584 #29798]: #23448 -#24613 := (or #23463 #23451 #23457) -#24614 := [def-axiom]: #24613 -#29800 := [unit-resolution #24614 #29799 #29792 #29776]: false -#29802 := [lemma #29800]: #29801 -#30329 := [unit-resolution #29802 #30328 #30176]: false -#30330 := [lemma #30329]: #23418 -#30607 := (or #23421 #23415) -#15811 := (<= f296 4294967295::Int) -#15814 := (iff #13441 #15811) -#15805 := (+ 4294967295::Int #13442) -#15808 := (>= #15805 0::Int) -#15812 := (iff #15808 #15811) -#15813 := [rewrite]: #15812 -#15809 := (iff #13441 #15808) -#15806 := (= #13443 #15805) -#15807 := [monotonicity #7642]: #15806 -#15810 := [monotonicity #15807]: #15809 -#15815 := [trans #15810 #15813]: #15814 -#14357 := [not-or-elim #14346]: #13446 -#14359 := [and-elim #14357]: #13441 -#15816 := [mp #14359 #15815]: #15811 -#29996 := [hypothesis]: #18597 -#29985 := [th-lemma arith farkas -1 -1 1 #30141 #29996 #15816]: false -#29988 := [lemma #29985]: #15900 -#30605 := (or #23421 #18597 #23415) -#30602 := (or #13656 #13534) -#30603 := [th-lemma arith farkas 1 1]: #30602 -#30604 := [unit-resolution #30603 #29673]: #13534 -#24529 := (or #23421 #18594 #18597 #23415) +#27934 := [unit-resolution #24604 #27933]: #23436 +#24547 := (or #23412 #23406) +#24548 := [def-axiom]: #24547 +#28043 := [unit-resolution #24548 #27932]: #23412 +#24577 := (or #23427 #23415 #23421) +#24578 := [def-axiom]: #24577 +#28044 := [unit-resolution #24578 #28043 #27935]: #23427 +#24587 := (or #23430 #23424) +#24588 := [def-axiom]: #24587 +#27884 := [unit-resolution #24588 #28044]: #23430 +#24597 := (or #23439 #18520 #18529 #23433) +#24598 := [def-axiom]: #24597 +#27885 := [unit-resolution #24598 #27884 #27934 #27931 #27930]: false +#27895 := [lemma #27885]: #27883 +#29684 := [unit-resolution #27895 #29459 #29654]: #29655 +#29685 := [unit-resolution #29684 #27930 #27935]: #23406 +#29686 := [hypothesis]: #23388 +#29687 := (or #23397 #18529 #23391) +#24523 := (or #23397 #18520 #18529 #23391) +#24524 := [def-axiom]: #24523 +#29688 := [unit-resolution #24524 #29459]: #29687 +#29675 := [unit-resolution #29688 #27930 #29686]: #23397 +#24529 := (or #23400 #23394) #24530 := [def-axiom]: #24529 -#30606 := [unit-resolution #24530 #30604]: #30605 -#30608 := [unit-resolution #30606 #29988]: #30607 -#30609 := [unit-resolution #30608 #30330]: #23415 -#24519 := (or #23412 #23406) -#24520 := [def-axiom]: #24519 -#30660 := [unit-resolution #24520 #30609]: #23406 -#24464 := (>= #13619 -1::Int) -#24515 := (or #23412 #13618) -#24516 := [def-axiom]: #24515 -#30610 := [unit-resolution #24516 #30609]: #13618 -#30611 := (or #13622 #24464) -#30612 := [th-lemma arith triangle-eq]: #30611 -#30613 := [unit-resolution #30612 #30610]: #24464 -#29780 := (not #24464) -#29781 := (or #29780 #13550) -#29774 := [hypothesis]: #24464 -#29778 := [hypothesis]: #13555 -#29779 := [th-lemma arith farkas -1 1 1 #29778 #30141 #29774]: false -#29782 := [lemma #29779]: #29781 -#30661 := [unit-resolution #29782 #30613]: #13550 -#24505 := (or #23409 #13555 #23403) +#29676 := [unit-resolution #24530 #29675]: #23400 +#29601 := (or #23409 #23403) +#24539 := (or #23409 #18520 #18523 #23403) +#24540 := [def-axiom]: #24539 +#29602 := [unit-resolution #24540 #29600 #29459]: #29601 +#29603 := [unit-resolution #29602 #29676 #29685]: false +#29605 := [lemma #29603]: #29604 +#30492 := [unit-resolution #29605 #30491 #29631]: #23391 +#24505 := (or #23388 #12565) #24506 := [def-axiom]: #24505 -#30662 := [unit-resolution #24506 #30661 #30660]: #23403 -#24497 := (or #23400 #23394) -#24498 := [def-axiom]: #24497 -#30663 := [unit-resolution #24498 #30662]: #23394 -#24590 := (+ f308 #13592) -#24592 := (>= #24590 0::Int) -#24595 := (or #23454 #12842) -#24596 := [def-axiom]: #24595 -#30664 := [unit-resolution #24596 #30651]: #12842 -#30665 := (or #12848 #24592) -#30666 := [th-lemma arith triangle-eq]: #30665 -#30667 := [unit-resolution #30666 #30664]: #24592 -#30668 := (not #24592) -#30671 := (or #13595 #30668) -#30669 := (or #13595 #13979 #30668) -#30670 := [th-lemma arith assign-bounds -1 -1]: #30669 -#30672 := [unit-resolution #30670 #30103]: #30671 -#30673 := [unit-resolution #30672 #30667]: #13595 -#30680 := (= #3153 #3299) -#30678 := (= #3299 #3153) -#30675 := (= #3298 #3152) -#30674 := [symm #30664]: #3329 -#30676 := [monotonicity #30674]: #30675 -#30679 := [monotonicity #30676]: #30678 -#30681 := [symm #30679]: #30680 -#30682 := (= f315 #3153) -#30677 := [symm #30653]: #3328 -#30683 := [trans #30677 #30101]: #30682 -#30684 := [trans #30683 #30681]: #12643 -#24469 := (or #22364 #22362 #13594) -#24470 := [def-axiom]: #24469 -#30685 := [unit-resolution #24470 #30684 #30673]: #22364 -#24471 := (or #23388 #22363) -#24472 := [def-axiom]: #24471 -#30686 := [unit-resolution #24472 #30685]: #23388 -#24493 := (or #23397 #23391 #22416) -#24494 := [def-axiom]: #24493 -#30687 := [unit-resolution #24494 #30686 #30663]: #22416 -#24485 := (or #22411 #24484) -#24486 := [def-axiom]: #24485 -#30688 := [unit-resolution #24486 #30687]: #24484 -#30632 := (not #24588) -#30633 := (or #30631 #18943 #30632 #13707) -#30626 := [hypothesis]: #13708 -#30627 := [hypothesis]: #24588 -#30628 := [hypothesis]: #24484 -#30629 := [hypothesis]: #30621 -#30630 := [th-lemma arith farkas 1 -1 -1 1 #30629 #30628 #30627 #30626]: false -#30634 := [lemma #30630]: #30633 -#30689 := [unit-resolution #30634 #30688 #30656 #30652]: #30631 -#30625 := (or #30624 #30621) -#30635 := [th-lemma arith triangle-eq]: #30625 -#30690 := [unit-resolution #30635 #30689]: #30624 -#30649 := (or #30648 #30591) -#30644 := (= #18620 #3266) -#30642 := (= #18619 #3257) -#30640 := (= ?v0!14 f309) -#30639 := [hypothesis]: #30595 -#30641 := [symm #30639]: #30640 -#30643 := [monotonicity #30641]: #30642 -#30645 := [monotonicity #30643]: #30644 -#30646 := [symm #30645]: #30591 -#30638 := [hypothesis]: #30624 -#30647 := [unit-resolution #30638 #30646]: false -#30650 := [lemma #30647]: #30649 -#30691 := [unit-resolution #30650 #30690]: #30648 -#30705 := (or #30595 #30702) -#30425 := (<= #30424 0::Int) -#30436 := (+ f307 #18941) -#30437 := (>= #30436 0::Int) -#30692 := (not #30437) -#30693 := (or #30692 #18943 #30632) -#30694 := [th-lemma arith assign-bounds -1 -1]: #30693 -#30695 := [unit-resolution #30694 #30656 #30688]: #30692 -#30698 := (or #30425 #30437) -#24479 := (or #22411 #18616) -#24480 := [def-axiom]: #24479 -#30696 := [unit-resolution #24480 #30687]: #18616 -#24477 := (or #22411 #18615) -#24478 := [def-axiom]: #24477 -#30697 := [unit-resolution #24478 #30687]: #18615 -#30450 := (or #23377 #22395 #22396 #30425 #30437) -#30413 := (+ #18620 #14006) -#30414 := (<= #30413 0::Int) -#30415 := (+ ?v0!14 #13537) -#30416 := (>= #30415 0::Int) -#30417 := (or #22396 #30416 #30414 #22395) -#30451 := (or #23377 #30417) -#30458 := (iff #30451 #30450) -#30445 := (or #22395 #22396 #30425 #30437) -#30453 := (or #23377 #30445) -#30456 := (iff #30453 #30450) -#30457 := [rewrite]: #30456 -#30454 := (iff #30451 #30453) -#30448 := (iff #30417 #30445) -#30442 := (or #22396 #30425 #30437 #22395) -#30446 := (iff #30442 #30445) -#30447 := [rewrite]: #30446 -#30443 := (iff #30417 #30442) -#30440 := (iff #30414 #30437) -#30430 := (+ #14006 #18620) -#30433 := (<= #30430 0::Int) -#30438 := (iff #30433 #30437) -#30439 := [rewrite]: #30438 -#30434 := (iff #30414 #30433) -#30431 := (= #30413 #30430) -#30432 := [rewrite]: #30431 -#30435 := [monotonicity #30432]: #30434 -#30441 := [trans #30435 #30439]: #30440 -#30428 := (iff #30416 #30425) -#30418 := (+ #13537 ?v0!14) -#30421 := (>= #30418 0::Int) -#30426 := (iff #30421 #30425) -#30427 := [rewrite]: #30426 -#30422 := (iff #30416 #30421) -#30419 := (= #30415 #30418) -#30420 := [rewrite]: #30419 -#30423 := [monotonicity #30420]: #30422 -#30429 := [trans #30423 #30427]: #30428 -#30444 := [monotonicity #30429 #30441]: #30443 -#30449 := [trans #30444 #30447]: #30448 -#30455 := [monotonicity #30449]: #30454 -#30459 := [trans #30455 #30457]: #30458 -#30452 := [quant-inst #18614]: #30451 -#30460 := [mp #30452 #30459]: #30450 -#30699 := [unit-resolution #30460 #30095 #30697 #30696]: #30698 -#30700 := [unit-resolution #30699 #30695]: #30425 -#30701 := (not #30425) -#30703 := (or #30595 #30701 #30702) -#30704 := [th-lemma arith triangle-eq]: #30703 -#30706 := [unit-resolution #30704 #30700]: #30705 -#30707 := [unit-resolution #30706 #30691]: #30702 -#24481 := (not #18930) -#24482 := (or #22411 #24481) -#24483 := [def-axiom]: #24482 -#30708 := [unit-resolution #24483 #30687]: #24481 -#30709 := [th-lemma arith farkas -1 -1 1 #30708 #30613 #30707]: false -#30710 := [lemma #30709]: #23454 -#26725 := [unit-resolution #29802 #30710]: #23430 -#26728 := [unit-resolution #30327 #26725 #30324]: #23427 -#24541 := (or #23424 #12601) -#24542 := [def-axiom]: #24541 -#30556 := [unit-resolution #24542 #26728]: #12601 -#24535 := (or #23424 #12590) -#24536 := [def-axiom]: #24535 -#30557 := [unit-resolution #24536 #26728]: #12590 -#30555 := [trans #30557 #30556]: #30343 -#30558 := (not #30343) -#30559 := (or #30558 #30172) -#30560 := [th-lemma arith triangle-eq]: #30559 -#30561 := [unit-resolution #30560 #30555]: #30172 -#30340 := (+ f309 #13592) -#30342 := (>= #30340 0::Int) -#24543 := (or #23424 #12604) -#24544 := [def-axiom]: #24543 -#26729 := [unit-resolution #24544 #26728]: #12604 -#26730 := (or #12731 #30342) -#30377 := [th-lemma arith triangle-eq]: #26730 -#30378 := [unit-resolution #30377 #26729]: #30342 -#30379 := [hypothesis]: #13594 -#30374 := [th-lemma arith farkas -1 1 1 #30379 #30378 #30141]: false -#30380 := [lemma #30374]: #13595 -#30585 := (or #22364 #13594) -#30575 := (= #3266 #3299) -#30577 := (= #3299 #3266) -#30563 := (= #3298 #3257) -#30562 := [symm #26729]: #3278 -#30576 := [monotonicity #30562]: #30563 -#30578 := [monotonicity #30576]: #30577 -#30581 := [symm #30578]: #30575 -#30582 := (= f315 #3266) -#30580 := [symm #30557]: #3269 -#30579 := [symm #30556]: #3276 -#30583 := [trans #30579 #30580]: #30582 -#30584 := [trans #30583 #30581]: #12643 -#30593 := [unit-resolution #24470 #30584]: #30585 -#30594 := [unit-resolution #30593 #30380]: #22364 -#30496 := [unit-resolution #24472 #30594]: #23388 -#30564 := [unit-resolution #24494 #30663]: #23394 -#30565 := [unit-resolution #30564 #30496]: #22416 -#30592 := [unit-resolution #24486 #30565]: #24484 -#30658 := (not #30172) -#30659 := (or #30631 #18943 #30658) -#30657 := [th-lemma arith assign-bounds -1 -1]: #30659 -#30711 := [unit-resolution #30657 #30592 #30561]: #30631 -#30712 := [unit-resolution #30635 #30711]: #30624 -#30713 := [unit-resolution #24483 #30565]: #24481 -#30714 := (or #30620 #18930 #29780) -#30715 := [th-lemma arith assign-bounds -1 -1]: #30714 -#30716 := [unit-resolution #30715 #30713 #30613]: #30620 -#30724 := (or #30692 #18943) -#30717 := [unit-resolution #29790 #30324]: #23469 -#30718 := [unit-resolution #24624 #30717]: #23460 -#30719 := [unit-resolution #24614 #30710 #30718]: #23451 -#24581 := (or #23448 #13707) -#24582 := [def-axiom]: #24581 -#30720 := [unit-resolution #24582 #30719]: #13707 -#30721 := (or #24588 #30658 #13708) -#30722 := [th-lemma arith assign-bounds 1 1]: #30721 -#30723 := [unit-resolution #30722 #30720 #30561]: #24588 -#30725 := [unit-resolution #30694 #30723]: #30724 -#30726 := [unit-resolution #30725 #30592]: #30692 -#30727 := [unit-resolution #24480 #30565]: #18616 -#30728 := [unit-resolution #24478 #30565]: #18615 -#30729 := [unit-resolution #30460 #30095 #30728 #30727 #30726]: #30425 -#30730 := [unit-resolution #30704 #30729 #30716]: #30595 -[unit-resolution #30650 #30730 #30712]: false +#30493 := [unit-resolution #24506 #30492]: #12565 +#24499 := (or #23388 #12554) +#24500 := [def-axiom]: #24499 +#30494 := [unit-resolution #24500 #30492]: #12554 +#30495 := [trans #30494 #30493]: #30446 +#30496 := (not #30446) +#30497 := (or #30496 #30448) +#30498 := [th-lemma arith triangle-eq]: #30497 +#30499 := [unit-resolution #30498 #30495]: #30448 +#30501 := (or #18529 #23433) +#28051 := (or #23436 #23451 #18523) +#28115 := [hypothesis]: #12542 +#28116 := [hypothesis]: #23439 +#24591 := (or #23436 #12539) +#24592 := [def-axiom]: #24591 +#28050 := [unit-resolution #24592 #28116]: #12539 +#28048 := [unit-resolution #24604 #28116]: #23442 +#28049 := [unit-resolution #24614 #28048 #28050 #27894 #28115]: false +#28052 := [lemma #28049]: #28051 +#30500 := [unit-resolution #28052 #29600 #29654]: #23436 +#30502 := [unit-resolution #24598 #30500 #29459]: #30501 +#30503 := [unit-resolution #30502 #30491]: #23433 +#30504 := [unit-resolution #24588 #30503]: #23424 +#30505 := [unit-resolution #24578 #30504 #29631]: #23415 +#24545 := (or #23412 #13671) +#24546 := [def-axiom]: #24545 +#30506 := [unit-resolution #24546 #30505]: #13671 +#30507 := (not #30448) +#30508 := (or #24552 #30507 #13672) +#30509 := [th-lemma arith assign-bounds 1 1]: #30508 +#30510 := [unit-resolution #30509 #30506 #30499]: #24552 +#24513 := (or #23388 #23382) +#24514 := [def-axiom]: #24513 +#30511 := [unit-resolution #24514 #30492]: #23382 +#30512 := [unit-resolution #29796 #30511]: #23379 +#30513 := [unit-resolution #24484 #30512]: #23370 +#30514 := [unit-resolution #24480 #30512]: #13582 +#30515 := [unit-resolution #29608 #30514]: #24428 +#30516 := [unit-resolution #29765 #30515]: #13514 +#30517 := [unit-resolution #24470 #30516 #30513]: #23367 +#30518 := [unit-resolution #24462 #30517]: #23358 +#30527 := (= #3266 #3299) +#30523 := (= #3299 #3266) +#30521 := (= #3298 #3257) +#24507 := (or #23388 #12568) +#24508 := [def-axiom]: #24507 +#30519 := [unit-resolution #24508 #30492]: #12568 +#30520 := [symm #30519]: #3278 +#30522 := [monotonicity #30520]: #30521 +#30524 := [monotonicity #30522]: #30523 +#30528 := [symm #30524]: #30527 +#30529 := (= f316 #3266) +#30526 := [symm #30494]: #3269 +#30525 := [symm #30493]: #3276 +#30530 := [trans #30525 #30526]: #30529 +#30531 := [trans #30530 #30528]: #12607 +#30443 := (+ f310 #13556) +#30445 := (>= #30443 0::Int) +#30532 := (or #12695 #30445) +#30533 := [th-lemma arith triangle-eq]: #30532 +#30534 := [unit-resolution #30533 #30519]: #30445 +#30535 := (not #30445) +#30536 := (or #13559 #13765 #30535) +#30537 := [th-lemma arith assign-bounds -1 -1]: #30536 +#30538 := [unit-resolution #30537 #29760 #30534]: #13559 +#30539 := [unit-resolution #24434 #30538 #30531]: #22328 +#30540 := [unit-resolution #24436 #30539]: #23352 +#30541 := [unit-resolution #24458 #30540 #30518]: #22380 +#30542 := [unit-resolution #24450 #30541]: #24448 +#30543 := [unit-resolution #29597 #30542 #30510]: #30220 +#30544 := [unit-resolution #24444 #30541]: #18580 +#30545 := [unit-resolution #24442 #30541]: #18579 +#30546 := [unit-resolution #24447 #30541]: #24445 +#30547 := [unit-resolution #29717 #30546 #30515]: #29634 +#30548 := [unit-resolution #30419 #30547 #30545 #30544 #30543]: #29868 +#30549 := [unit-resolution #30080 #30548]: #30332 +#30550 := [unit-resolution #30340 #30549]: #30338 +[th-lemma arith farkas -1 -1 1 #30542 #30499 #30550]: false unsat diff -r 679118e35378 -r a4d1b5eef12e src/HOL/Multivariate_Analysis/Integration.certs --- a/src/HOL/Multivariate_Analysis/Integration.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/Multivariate_Analysis/Integration.certs Sun Dec 19 18:55:21 2010 +0100 @@ -621,18 +621,18 @@ #427 := [unit-resolution #411 #426]: #395 [th-lemma arith farkas 2 1 2 3 1 1 #421 #319 #321 #414 #318 #427]: false unsat -f26ffd00d169b6b4684265a03d23c9e0efe94a58 57 0 +76aef63700c44d6a49155f473f80703718124469 57 0 #2 := false #37 := 0::Real decl f12 :: (-> S5 Real) decl f13 :: (-> S4 S4 S5) decl f14 :: (-> S3 S4) +decl f4 :: S3 +#8 := f4 +#45 := (f14 f4) decl f10 :: S3 #25 := f10 -#45 := (f14 f10) -decl f4 :: S3 -#8 := f4 -#44 := (f14 f4) +#44 := (f14 f10) #46 := (f13 #44 #45) #47 := (f12 #46) #258 := (>= #47 0::Real) @@ -642,11 +642,11 @@ #134 := [asserted]: #50 #266 := (or #49 #260) #48 := (<= #47 0::Real) -#114 := [asserted]: #48 +#133 := [asserted]: #48 #259 := (not #48) #264 := (or #49 #259 #260) #265 := [th-lemma arith triangle-eq]: #264 -#267 := [unit-resolution #265 #114]: #266 +#267 := [unit-resolution #265 #133]: #266 #268 := [unit-resolution #267 #134]: #260 #39 := (:var 0 S4) #38 := (:var 1 S4) @@ -670,8 +670,8 @@ #135 := (iff #42 #136) #137 := [rewrite]: #135 #140 := [quant-intro #137]: #139 -#113 := [asserted]: #43 -#141 := [mp #113 #140]: #138 +#132 := [asserted]: #43 +#141 := [mp #132 #140]: #138 #167 := [mp~ #141 #166]: #138 #257 := [mp #167 #256]: #252 #261 := (not #252) diff -r 679118e35378 -r a4d1b5eef12e src/HOL/SMT_Examples/SMT_Examples.certs --- a/src/HOL/SMT_Examples/SMT_Examples.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples.certs Sun Dec 19 18:55:21 2010 +0100 @@ -146,7 +146,65 @@ #74 := [and-elim #72]: #43 [mp #74 #88]: false unsat -b369848437710a3b368c375ee857c21adc3f6e30 1 0 +bc6de36d6c86b416e91711bb23067cc8250ac153 59 0 +#2 := false +decl f1 :: S1 +#4 := f1 +decl f6 :: S1 +#15 := f6 +#16 := (= f6 f1) +decl f5 :: S1 +#13 := f5 +#14 := (= f5 f1) +#17 := (and #14 #16) +decl f4 :: S1 +#10 := f4 +#11 := (= f4 f1) +decl f3 :: S1 +#8 := f3 +#9 := (= f3 f1) +#12 := (and #9 #11) +#18 := (or #12 #17) +#19 := (implies #18 #18) +#20 := (not #19) +#74 := (iff #20 false) +#1 := true +#69 := (not true) +#72 := (iff #69 false) +#73 := [rewrite]: #72 +#70 := (iff #20 #69) +#67 := (iff #19 true) +#53 := (= f1 f6) +#50 := (= f1 f5) +#56 := (and #50 #53) +#44 := (= f1 f4) +#41 := (= f1 f3) +#47 := (and #41 #44) +#59 := (or #47 #56) +#62 := (implies #59 #59) +#65 := (iff #62 true) +#66 := [rewrite]: #65 +#63 := (iff #19 #62) +#60 := (iff #18 #59) +#57 := (iff #17 #56) +#54 := (iff #16 #53) +#55 := [rewrite]: #54 +#51 := (iff #14 #50) +#52 := [rewrite]: #51 +#58 := [monotonicity #52 #55]: #57 +#48 := (iff #12 #47) +#45 := (iff #11 #44) +#46 := [rewrite]: #45 +#42 := (iff #9 #41) +#43 := [rewrite]: #42 +#49 := [monotonicity #43 #46]: #48 +#61 := [monotonicity #49 #58]: #60 +#64 := [monotonicity #61 #61]: #63 +#68 := [trans #64 #66]: #67 +#71 := [monotonicity #68]: #70 +#75 := [trans #71 #73]: #74 +#40 := [asserted]: #20 +[mp #40 #75]: false unsat e334e079d0f61721e404e4ca140ce40c317189ba 94 0 #2 := false @@ -3973,59 +4031,48 @@ #241 := [unit-resolution #190 #240]: #156 [th-lemma arith farkas -1 -1 1 1 #241 #218 #128 #239]: false unsat -a63737c6fce2a605078af85686032a125631e608 53 0 +c722596cfa285e209992f7087932c1ec15fd226b 42 0 #2 := false decl f3 :: (-> S1 S2) +decl f1 :: S1 +#4 := f1 +#13 := (f3 f1) decl f2 :: S1 #5 := f2 -decl f1 :: S1 -#4 := f1 -#1 := true -#13 := (ite true f1 f2) -#14 := (f3 #13) #9 := 3::Int #8 := 2::Int #10 := (< 2::Int 3::Int) #11 := (ite #10 f1 f2) #12 := (f3 #11) -#15 := (= #12 #14) -#16 := (not #15) -#69 := (iff #16 false) -#39 := (f3 f1) -#42 := (= #12 #39) -#45 := (not #42) -#67 := (iff #45 false) -#62 := (not true) -#65 := (iff #62 false) -#66 := [rewrite]: #65 -#63 := (iff #45 #62) -#60 := (iff #42 true) -#55 := (= #39 #39) -#58 := (iff #55 true) +#14 := (= #12 #13) +#15 := (not #14) +#60 := (iff #15 false) +#1 := true +#55 := (not true) +#58 := (iff #55 false) #59 := [rewrite]: #58 -#56 := (iff #42 #55) -#52 := (= #11 f1) -#37 := (= #13 f1) -#38 := [rewrite]: #37 -#50 := (= #11 #13) -#48 := (iff #10 true) -#49 := [rewrite]: #48 -#51 := [monotonicity #49]: #50 -#53 := [trans #51 #38]: #52 -#54 := [monotonicity #53]: #42 +#56 := (iff #15 #55) +#53 := (iff #14 true) +#48 := (= #13 #13) +#51 := (iff #48 true) +#52 := [rewrite]: #51 +#49 := (iff #14 #48) +#45 := (= #11 f1) +#40 := (ite true f1 f2) +#43 := (= #40 f1) +#44 := [rewrite]: #43 +#41 := (= #11 #40) +#38 := (iff #10 true) +#39 := [rewrite]: #38 +#42 := [monotonicity #39]: #41 +#46 := [trans #42 #44]: #45 +#47 := [monotonicity #46]: #14 +#50 := [monotonicity #47]: #49 +#54 := [trans #50 #52]: #53 #57 := [monotonicity #54]: #56 #61 := [trans #57 #59]: #60 -#64 := [monotonicity #61]: #63 -#68 := [trans #64 #66]: #67 -#46 := (iff #16 #45) -#43 := (iff #15 #42) -#40 := (= #14 #39) -#41 := [monotonicity #38]: #40 -#44 := [monotonicity #41]: #43 -#47 := [monotonicity #44]: #46 -#70 := [trans #47 #68]: #69 -#36 := [asserted]: #16 -[mp #36 #70]: false +#35 := [asserted]: #15 +[mp #35 #61]: false unsat 4d8a8a08b49cb28d987bdc1bcdbb3a144907bf45 54 0 #2 := false @@ -4288,7 +4335,7 @@ #42 := [asserted]: #22 [mp #42 #79]: false unsat -900d439115908f4ef5998166e284e3a309f354ef 104 0 +78003574b5d95d4c28641909502b0f435784ad24 104 0 #2 := false decl f1 :: S1 #4 := f1 @@ -7376,698 +7423,425 @@ #37 := [asserted]: #17 [mp #37 #73]: false unsat -75da1862a2fd162477f9d85292ff8ab2e18559e4 342 0 +f9ae47f5aef750f37ea2d9309845d7cf08946d8c 211 0 #2 := false -#21 := 0::Int +#12 := 0::Int decl f3 :: Int #8 := f3 -#419 := (<= f3 0::Int) -#446 := (>= f3 0::Int) -#753 := (not #446) -#409 := (not #419) -#754 := (or #409 #753) -#715 := (not #754) -#11 := 2::Int -#443 := (mod f3 2::Int) -#113 := -1::Int -#444 := (* -1::Int #443) -decl f4 :: (-> Int Int Int) -#12 := (f4 f3 2::Int) -#445 := (+ #12 #444) -#442 := (= #445 0::Int) -#705 := (not #442) -#717 := (>= #445 0::Int) -#647 := (not #717) -#654 := [hypothesis]: #717 -#689 := (>= #443 0::Int) -#1 := true -#65 := [true-axiom]: true -#665 := (or false #689) -#643 := [th-lemma arith]: #665 -#644 := [unit-resolution #643 #65]: #689 -#95 := (>= #12 0::Int) -#98 := (not #95) -#9 := 1::Int -#13 := (* 2::Int #12) -#14 := (+ #13 1::Int) -#15 := (+ f3 #14) -#10 := (+ f3 1::Int) -#16 := (<= #10 #15) -#17 := (not #16) -#103 := (iff #17 #98) -#77 := (+ f3 #13) -#78 := (+ 1::Int #77) -#68 := (+ 1::Int f3) -#83 := (<= #68 #78) -#86 := (not #83) -#101 := (iff #86 #98) -#93 := (>= #13 0::Int) -#89 := (not #93) -#99 := (iff #89 #98) -#96 := (iff #93 #95) -#97 := [rewrite]: #96 -#100 := [monotonicity #97]: #99 -#90 := (iff #86 #89) -#91 := (iff #83 #93) -#92 := [rewrite]: #91 -#94 := [monotonicity #92]: #90 -#102 := [trans #94 #100]: #101 -#87 := (iff #17 #86) -#84 := (iff #16 #83) -#81 := (= #15 #78) -#71 := (+ 1::Int #13) -#74 := (+ f3 #71) -#79 := (= #74 #78) -#80 := [rewrite]: #79 -#75 := (= #15 #74) -#72 := (= #14 #71) -#73 := [rewrite]: #72 -#76 := [monotonicity #73]: #75 -#82 := [trans #76 #80]: #81 -#69 := (= #10 #68) -#70 := [rewrite]: #69 -#85 := [monotonicity #70 #82]: #84 -#88 := [monotonicity #85]: #87 -#104 := [trans #88 #102]: #103 -#67 := [asserted]: #17 -#105 := [mp #67 #104]: #98 -#646 := [th-lemma arith farkas -1 1 1 #105 #644 #654]: false -#648 := [lemma #646]: #647 -#660 := (or #705 #717) -#661 := [th-lemma arith triangle-eq]: #660 -#662 := [unit-resolution #661 #648]: #705 -#637 := (or #715 #442) -#741 := -2::Int -#439 := (* -1::Int f3) -#465 := (mod #439 -2::Int) -#361 := (+ #12 #465) -#460 := (= #361 0::Int) -#739 := (ite #754 #442 #460) -#763 := (= #12 0::Int) -#764 := (= f3 0::Int) -#450 := (ite #764 #763 #739) -#19 := (:var 0 Int) -#18 := (:var 1 Int) -#39 := (f4 #18 #19) -#775 := (pattern #39) -#117 := (* -1::Int #19) -#114 := (* -1::Int #18) -#172 := (mod #114 #117) -#287 := (+ #39 #172) -#288 := (= #287 0::Int) -#40 := (mod #18 #19) -#284 := (* -1::Int #40) -#285 := (+ #39 #284) -#286 := (= #285 0::Int) -#146 := (>= #18 0::Int) -#139 := (<= #19 0::Int) -#231 := (or #139 #146) -#232 := (not #231) -#135 := (<= #18 0::Int) -#229 := (or #135 #139) -#230 := (not #229) -#235 := (or #230 #232) -#289 := (ite #235 #286 #288) -#283 := (= #39 0::Int) -#22 := (= #18 0::Int) -#290 := (ite #22 #283 #289) -#282 := (= #18 #39) -#23 := (= #19 0::Int) -#291 := (ite #23 #282 #290) -#776 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #775) #291) -#294 := (forall (vars (?v0 Int) (?v1 Int)) #291) -#779 := (iff #294 #776) -#777 := (iff #291 #291) -#778 := [refl]: #777 -#780 := [quant-intro #778]: #779 -#178 := (* -1::Int #172) -#251 := (ite #235 #40 #178) -#254 := (ite #22 0::Int #251) -#257 := (ite #23 #18 #254) -#260 := (= #39 #257) -#263 := (forall (vars (?v0 Int) (?v1 Int)) #260) -#295 := (iff #263 #294) -#292 := (iff #260 #291) -#293 := [rewrite]: #292 -#296 := [quant-intro #293]: #295 -#147 := (not #146) -#140 := (not #139) -#150 := (and #140 #147) +#122 := (<= f3 0::Int) +#135 := (>= f3 0::Int) #136 := (not #135) -#143 := (and #136 #140) -#153 := (or #143 #150) -#198 := (ite #153 #40 #178) -#201 := (ite #22 0::Int #198) -#204 := (ite #23 #18 #201) -#207 := (= #39 #204) -#210 := (forall (vars (?v0 Int) (?v1 Int)) #207) -#264 := (iff #210 #263) -#261 := (iff #207 #260) -#258 := (= #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#236 := (iff #153 #235) -#233 := (iff #150 #232) -#234 := [rewrite]: #233 -#223 := (iff #143 #230) -#224 := [rewrite]: #223 -#237 := [monotonicity #224 #234]: #236 -#253 := [monotonicity #237]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [monotonicity #259]: #261 -#265 := [quant-intro #262]: #264 -#221 := (~ #210 #210) -#220 := (~ #207 #207) -#217 := [refl]: #220 -#222 := [nnf-pos #217]: #221 -#33 := (- #19) -#32 := (- #18) -#41 := (mod #32 #33) -#42 := (- #41) -#26 := (< 0::Int #19) -#28 := (< #18 0::Int) -#29 := (and #28 #26) -#25 := (< 0::Int #18) -#27 := (and #25 #26) -#30 := (or #27 #29) -#43 := (ite #30 #40 #42) -#44 := (ite #22 0::Int #43) -#45 := (ite #23 #18 #44) -#46 := (= #39 #45) -#47 := (forall (vars (?v0 Int) (?v1 Int)) #46) -#213 := (iff #47 #210) -#107 := (and #26 #28) -#110 := (or #27 #107) -#183 := (ite #110 #40 #178) -#186 := (ite #22 0::Int #183) -#189 := (ite #23 #18 #186) -#192 := (= #39 #189) -#195 := (forall (vars (?v0 Int) (?v1 Int)) #192) -#211 := (iff #195 #210) -#208 := (iff #192 #207) -#205 := (= #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#154 := (iff #110 #153) -#151 := (iff #107 #150) -#148 := (iff #28 #147) -#149 := [rewrite]: #148 -#141 := (iff #26 #140) -#142 := [rewrite]: #141 -#152 := [monotonicity #142 #149]: #151 -#144 := (iff #27 #143) -#137 := (iff #25 #136) +#123 := (not #122) +#146 := (or #123 #136) +#195 := (not #146) +#69 := -2::Int +#65 := -1::Int +#66 := (* -1::Int f3) +#72 := (mod #66 -2::Int) +#78 := (* -1::Int #72) +#11 := 2::Int +#21 := (mod f3 2::Int) +#149 := (ite #146 #21 #78) +#193 := (= #21 #149) +#284 := (not #193) +#14 := (= f3 0::Int) +#152 := (ite #14 0::Int #149) +#268 := (* -1::Int #152) +#269 := (+ #21 #268) +#270 := (<= #269 0::Int) +#267 := (= #21 #152) +#192 := (= #149 #152) +#202 := (not #14) +#191 := (= #152 0::Int) +#209 := (not #191) +#175 := (>= #152 0::Int) +#178 := (not #175) +#9 := 1::Int +#23 := (- 2::Int) +#22 := (- f3) +#24 := (mod #22 #23) +#25 := (- #24) +#16 := (< 0::Int 2::Int) +#18 := (< f3 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int f3) +#17 := (and #15 #16) +#20 := (or #17 #19) +#26 := (ite #20 #21 #25) +#27 := (ite #14 0::Int #26) +#13 := (= 2::Int 0::Int) +#28 := (ite #13 f3 #27) +#29 := (* 2::Int #28) +#30 := (+ #29 1::Int) +#31 := (+ f3 #30) +#10 := (+ f3 1::Int) +#32 := (<= #10 #31) +#33 := (not #32) +#183 := (iff #33 #178) +#59 := (and #16 #18) +#62 := (or #17 #59) +#83 := (ite #62 #21 #78) +#86 := (ite #14 0::Int #83) +#96 := (* 2::Int #86) +#110 := (+ f3 #96) +#111 := (+ 1::Int #110) +#54 := (+ 1::Int f3) +#116 := (<= #54 #111) +#119 := (not #116) +#181 := (iff #119 #178) +#155 := (* 2::Int #152) +#168 := (>= #155 0::Int) +#172 := (not #168) +#179 := (iff #172 #178) +#176 := (iff #168 #175) +#177 := [rewrite]: #176 +#180 := [monotonicity #177]: #179 +#173 := (iff #119 #172) +#170 := (iff #116 #168) +#158 := (+ f3 #155) +#161 := (+ 1::Int #158) +#164 := (<= #54 #161) +#167 := (iff #164 #168) +#169 := [rewrite]: #167 +#165 := (iff #116 #164) +#162 := (= #111 #161) +#159 := (= #110 #158) +#156 := (= #96 #155) +#153 := (= #86 #152) +#150 := (= #83 #149) +#147 := (iff #62 #146) +#144 := (iff #59 #136) +#1 := true +#139 := (and true #136) +#142 := (iff #139 #136) +#143 := [rewrite]: #142 +#140 := (iff #59 #139) +#137 := (iff #18 #136) #138 := [rewrite]: #137 -#145 := [monotonicity #138 #142]: #144 -#155 := [monotonicity #145 #152]: #154 -#200 := [monotonicity #155]: #199 -#203 := [monotonicity #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [monotonicity #206]: #208 -#212 := [quant-intro #209]: #211 -#196 := (iff #47 #195) -#193 := (iff #46 #192) -#190 := (= #45 #189) -#187 := (= #44 #186) -#184 := (= #43 #183) -#181 := (= #42 #178) -#175 := (- #172) -#179 := (= #175 #178) -#180 := [rewrite]: #179 -#176 := (= #42 #175) -#173 := (= #41 #172) -#118 := (= #33 #117) -#119 := [rewrite]: #118 -#115 := (= #32 #114) -#116 := [rewrite]: #115 -#174 := [monotonicity #116 #119]: #173 -#177 := [monotonicity #174]: #176 -#182 := [trans #177 #180]: #181 -#111 := (iff #30 #110) -#108 := (iff #29 #107) -#109 := [rewrite]: #108 -#112 := [monotonicity #109]: #111 -#185 := [monotonicity #112 #182]: #184 -#188 := [monotonicity #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [monotonicity #191]: #193 -#197 := [quant-intro #194]: #196 -#214 := [trans #197 #212]: #213 -#171 := [asserted]: #47 -#215 := [mp #171 #214]: #210 -#218 := [mp~ #215 #222]: #210 -#266 := [mp #218 #265]: #263 -#297 := [mp #266 #296]: #294 -#781 := [mp #297 #780]: #776 -#734 := (not #776) -#723 := (or #734 #450) -#355 := (* -1::Int 2::Int) -#440 := (mod #439 #355) -#441 := (+ #12 #440) -#432 := (= #441 0::Int) -#425 := (<= 2::Int 0::Int) -#760 := (or #425 #446) -#762 := (not #760) -#549 := (or #419 #425) -#756 := (not #549) -#430 := (or #756 #762) -#431 := (ite #430 #442 #432) -#765 := (ite #764 #763 #431) -#766 := (= f3 #12) -#761 := (= 2::Int 0::Int) -#767 := (ite #761 #766 #765) -#724 := (or #734 #767) -#720 := (iff #724 #723) -#726 := (iff #723 #723) -#727 := [rewrite]: #726 -#733 := (iff #767 #450) -#453 := (ite false #766 #450) -#447 := (iff #453 #450) -#729 := [rewrite]: #447 -#731 := (iff #767 #453) -#451 := (iff #765 #450) -#736 := (iff #431 #739) -#461 := (iff #432 #460) -#737 := (= #441 #361) -#466 := (= #440 #465) -#742 := (= #355 -2::Int) -#464 := [rewrite]: #742 -#467 := [monotonicity #464]: #466 -#738 := [monotonicity #467]: #737 -#735 := [monotonicity #738]: #461 -#752 := (iff #430 #754) -#393 := (iff #762 #753) -#388 := (iff #760 #446) -#747 := (or false #446) -#744 := (iff #747 #446) -#750 := [rewrite]: #744 -#748 := (iff #760 #747) -#422 := (iff #425 false) -#758 := [rewrite]: #422 -#749 := [monotonicity #758]: #748 -#751 := [trans #749 #750]: #388 -#394 := [monotonicity #751]: #393 -#745 := (iff #756 #409) -#407 := (iff #549 #419) -#418 := (or #419 false) -#743 := (iff #418 #419) -#406 := [rewrite]: #743 -#759 := (iff #549 #418) -#402 := [monotonicity #758]: #759 -#408 := [trans #402 #406]: #407 -#746 := [monotonicity #408]: #745 -#755 := [monotonicity #746 #394]: #752 -#740 := [monotonicity #755 #735]: #736 -#452 := [monotonicity #740]: #451 -#757 := (iff #761 false) -#417 := [rewrite]: #757 -#732 := [monotonicity #417 #452]: #731 -#730 := [trans #732 #729]: #733 -#721 := [monotonicity #730]: #720 -#722 := [trans #721 #727]: #720 -#725 := [quant-inst #8 #11]: #724 -#728 := [mp #725 #722]: #723 -#663 := [unit-resolution #728 #781]: #450 -#593 := (not #764) -#592 := (not #450) -#649 := (or #592 #593) -#698 := (not #763) -#664 := (or #698 #95) -#688 := [th-lemma arith triangle-eq]: #664 -#682 := [unit-resolution #688 #105]: #698 -#552 := (or #592 #593 #763) -#700 := [def-axiom]: #552 -#650 := [unit-resolution #700 #682]: #649 -#645 := [unit-resolution #650 #663]: #593 -#602 := (or #592 #764 #739) -#697 := [def-axiom]: #602 -#651 := [unit-resolution #697 #645 #663]: #739 -#719 := (not #739) -#548 := (or #719 #715 #442) -#550 := [def-axiom]: #548 -#633 := [unit-resolution #550 #651]: #637 -#634 := [unit-resolution #633 #662]: #715 -#570 := (or #754 #419) -#571 := [def-axiom]: #570 -#635 := [unit-resolution #571 #634]: #419 -#713 := (or #754 #446) -#714 := [def-axiom]: #713 -#638 := [unit-resolution #714 #634]: #446 -#639 := (or #764 #409 #753) -#640 := [th-lemma arith triangle-eq]: #639 -#641 := [unit-resolution #640 #645]: #754 -[unit-resolution #641 #638 #635]: false -unsat -3b8dfbe5d2104f714ba2e5d249bcf001c2c84dba 349 0 +#126 := (iff #16 true) +#127 := [rewrite]: #126 +#141 := [monotonicity #127 #138]: #140 +#145 := [trans #141 #143]: #144 +#133 := (iff #17 #123) +#128 := (and #123 true) +#131 := (iff #128 #123) +#132 := [rewrite]: #131 +#129 := (iff #17 #128) +#124 := (iff #15 #123) +#125 := [rewrite]: #124 +#130 := [monotonicity #125 #127]: #129 +#134 := [trans #130 #132]: #133 +#148 := [monotonicity #134 #145]: #147 +#151 := [monotonicity #148]: #150 +#154 := [monotonicity #151]: #153 +#157 := [monotonicity #154]: #156 +#160 := [monotonicity #157]: #159 +#163 := [monotonicity #160]: #162 +#166 := [monotonicity #163]: #165 +#171 := [trans #166 #169]: #170 +#174 := [monotonicity #171]: #173 +#182 := [trans #174 #180]: #181 +#120 := (iff #33 #119) +#117 := (iff #32 #116) +#114 := (= #31 #111) +#102 := (+ 1::Int #96) +#107 := (+ f3 #102) +#112 := (= #107 #111) +#113 := [rewrite]: #112 +#108 := (= #31 #107) +#105 := (= #30 #102) +#99 := (+ #96 1::Int) +#103 := (= #99 #102) +#104 := [rewrite]: #103 +#100 := (= #30 #99) +#97 := (= #29 #96) +#94 := (= #28 #86) +#89 := (ite false f3 #86) +#92 := (= #89 #86) +#93 := [rewrite]: #92 +#90 := (= #28 #89) +#87 := (= #27 #86) +#84 := (= #26 #83) +#81 := (= #25 #78) +#75 := (- #72) +#79 := (= #75 #78) +#80 := [rewrite]: #79 +#76 := (= #25 #75) +#73 := (= #24 #72) +#70 := (= #23 -2::Int) +#71 := [rewrite]: #70 +#67 := (= #22 #66) +#68 := [rewrite]: #67 +#74 := [monotonicity #68 #71]: #73 +#77 := [monotonicity #74]: #76 +#82 := [trans #77 #80]: #81 +#63 := (iff #20 #62) +#60 := (iff #19 #59) +#61 := [rewrite]: #60 +#64 := [monotonicity #61]: #63 +#85 := [monotonicity #64 #82]: #84 +#88 := [monotonicity #85]: #87 +#57 := (iff #13 false) +#58 := [rewrite]: #57 +#91 := [monotonicity #58 #88]: #90 +#95 := [trans #91 #93]: #94 +#98 := [monotonicity #95]: #97 +#101 := [monotonicity #98]: #100 +#106 := [trans #101 #104]: #105 +#109 := [monotonicity #106]: #108 +#115 := [trans #109 #113]: #114 +#55 := (= #10 #54) +#56 := [rewrite]: #55 +#118 := [monotonicity #56 #115]: #117 +#121 := [monotonicity #118]: #120 +#184 := [trans #121 #182]: #183 +#53 := [asserted]: #33 +#185 := [mp #53 #184]: #178 +#208 := [hypothesis]: #191 +#210 := (or #209 #175) +#211 := [th-lemma arith triangle-eq]: #210 +#212 := [unit-resolution #211 #208 #185]: false +#213 := [lemma #212]: #209 +#203 := (or #202 #191) +#204 := [def-axiom]: #203 +#272 := [unit-resolution #204 #213]: #202 +#205 := (or #14 #192) +#206 := [def-axiom]: #205 +#273 := [unit-resolution #206 #272]: #192 +#274 := [hypothesis]: #193 +#275 := [trans #274 #273]: #267 +#276 := (not #267) +#277 := (or #276 #270) +#278 := [th-lemma arith triangle-eq]: #277 +#279 := [unit-resolution #278 #275]: #270 +#239 := (>= #21 0::Int) +#51 := [true-axiom]: true +#280 := (or false #239) +#281 := [th-lemma arith]: #280 +#282 := [unit-resolution #281 #51]: #239 +#283 := [th-lemma arith farkas -1 1 1 #282 #185 #279]: false +#285 := [lemma #283]: #284 +#198 := (or #195 #193) +#199 := [def-axiom]: #198 +#262 := [unit-resolution #199 #285]: #195 +#189 := (or #146 #122) +#190 := [def-axiom]: #189 +#263 := [unit-resolution #190 #262]: #122 +#187 := (or #146 #135) +#188 := [def-axiom]: #187 +#264 := [unit-resolution #188 #262]: #135 +#265 := (or #14 #123 #136) +#266 := [th-lemma arith triangle-eq]: #265 +#237 := [unit-resolution #266 #272]: #146 +[unit-resolution #237 #264 #263]: false +unsat +a9554a5e9a99c006412b9165d7d1ec39d927f284 207 0 #2 := false -#20 := 0::Int +#10 := 0::Int decl f3 :: Int #8 := f3 -#438 := (>= f3 0::Int) -#758 := (<= f3 0::Int) -#404 := (not #758) -#747 := (not #438) -#751 := (or #747 #404) -#714 := (not #751) +#112 := (<= f3 0::Int) +#125 := (>= f3 0::Int) +#126 := (not #125) +#113 := (not #112) +#136 := (or #113 #126) +#184 := (not #136) +#65 := -2::Int +#61 := -1::Int +#62 := (* -1::Int f3) +#68 := (mod #62 -2::Int) +#74 := (* -1::Int #68) #9 := 2::Int -#439 := (mod f3 2::Int) -#108 := -1::Int -#440 := (* -1::Int #439) -decl f4 :: (-> Int Int Int) -#10 := (f4 f3 2::Int) -#368 := (+ #10 #440) -#441 := (= #368 0::Int) -#587 := (not #441) -#544 := (<= #368 0::Int) -#647 := (not #544) -#655 := (>= #439 2::Int) -#656 := (not #655) +#19 := (mod f3 2::Int) +#139 := (ite #136 #19 #74) +#182 := (= #19 #139) +#279 := (not #182) +#251 := (>= #19 2::Int) +#252 := (not #251) #1 := true -#64 := [true-axiom]: true -#643 := (or false #656) -#644 := [th-lemma arith]: #643 -#645 := [unit-resolution #644 #64]: #656 -#646 := [hypothesis]: #544 -#93 := (>= #10 2::Int) -#13 := 3::Int -#14 := (+ f3 3::Int) -#11 := (+ #10 #10) -#12 := (+ f3 #11) -#15 := (< #12 #14) -#16 := (not #15) -#98 := (iff #16 #93) -#73 := (+ 3::Int f3) -#67 := (* 2::Int #10) -#70 := (+ f3 #67) -#76 := (< #70 #73) -#79 := (not #76) -#96 := (iff #79 #93) -#86 := (>= #67 3::Int) -#94 := (iff #86 #93) -#95 := [rewrite]: #94 -#91 := (iff #79 #86) -#84 := (not #86) -#83 := (not #84) -#89 := (iff #83 #86) -#90 := [rewrite]: #89 -#87 := (iff #79 #83) -#85 := (iff #76 #84) -#82 := [rewrite]: #85 -#88 := [monotonicity #82]: #87 -#92 := [trans #88 #90]: #91 -#97 := [trans #92 #95]: #96 -#80 := (iff #16 #79) -#77 := (iff #15 #76) -#74 := (= #14 #73) -#75 := [rewrite]: #74 -#71 := (= #12 #70) -#68 := (= #11 #67) -#69 := [rewrite]: #68 -#72 := [monotonicity #69]: #71 -#78 := [monotonicity #72 #75]: #77 -#81 := [monotonicity #78]: #80 -#99 := [trans #81 #97]: #98 -#66 := [asserted]: #16 -#100 := [mp #66 #99]: #93 -#641 := [th-lemma arith farkas -1 1 1 #100 #646 #645]: false -#633 := [lemma #641]: #647 -#650 := (or #587 #544) -#661 := [th-lemma arith triangle-eq]: #650 -#639 := [unit-resolution #661 #633]: #587 -#611 := (or #714 #441) -#462 := -2::Int -#435 := (* -1::Int f3) -#733 := (mod #435 -2::Int) -#457 := (+ #10 #733) -#732 := (= #457 0::Int) -#447 := (ite #751 #441 #732) -#427 := (= #10 0::Int) -#759 := (= f3 0::Int) -#727 := (ite #759 #427 #447) -#18 := (:var 0 Int) -#17 := (:var 1 Int) -#38 := (f4 #17 #18) -#771 := (pattern #38) -#112 := (* -1::Int #18) -#109 := (* -1::Int #17) -#167 := (mod #109 #112) -#282 := (+ #38 #167) -#283 := (= #282 0::Int) -#39 := (mod #17 #18) -#279 := (* -1::Int #39) -#280 := (+ #38 #279) -#281 := (= #280 0::Int) -#141 := (>= #17 0::Int) -#134 := (<= #18 0::Int) -#226 := (or #134 #141) -#227 := (not #226) -#130 := (<= #17 0::Int) -#224 := (or #130 #134) -#225 := (not #224) -#230 := (or #225 #227) -#284 := (ite #230 #281 #283) -#278 := (= #38 0::Int) -#21 := (= #17 0::Int) -#285 := (ite #21 #278 #284) -#277 := (= #17 #38) -#22 := (= #18 0::Int) -#286 := (ite #22 #277 #285) -#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #286) -#289 := (forall (vars (?v0 Int) (?v1 Int)) #286) -#775 := (iff #289 #772) -#773 := (iff #286 #286) -#774 := [refl]: #773 -#776 := [quant-intro #774]: #775 -#173 := (* -1::Int #167) -#246 := (ite #230 #39 #173) -#249 := (ite #21 0::Int #246) -#252 := (ite #22 #17 #249) -#255 := (= #38 #252) -#258 := (forall (vars (?v0 Int) (?v1 Int)) #255) -#290 := (iff #258 #289) -#287 := (iff #255 #286) -#288 := [rewrite]: #287 -#291 := [quant-intro #288]: #290 -#142 := (not #141) -#135 := (not #134) -#145 := (and #135 #142) -#131 := (not #130) -#138 := (and #131 #135) -#148 := (or #138 #145) -#193 := (ite #148 #39 #173) -#196 := (ite #21 0::Int #193) -#199 := (ite #22 #17 #196) -#202 := (= #38 #199) -#205 := (forall (vars (?v0 Int) (?v1 Int)) #202) -#259 := (iff #205 #258) -#256 := (iff #202 #255) -#253 := (= #199 #252) -#250 := (= #196 #249) -#247 := (= #193 #246) -#231 := (iff #148 #230) -#228 := (iff #145 #227) -#229 := [rewrite]: #228 -#218 := (iff #138 #225) -#219 := [rewrite]: #218 -#232 := [monotonicity #219 #229]: #231 -#248 := [monotonicity #232]: #247 -#251 := [monotonicity #248]: #250 -#254 := [monotonicity #251]: #253 -#257 := [monotonicity #254]: #256 -#260 := [quant-intro #257]: #259 -#216 := (~ #205 #205) -#215 := (~ #202 #202) -#212 := [refl]: #215 -#217 := [nnf-pos #212]: #216 -#32 := (- #18) -#31 := (- #17) -#40 := (mod #31 #32) -#41 := (- #40) -#25 := (< 0::Int #18) -#27 := (< #17 0::Int) -#28 := (and #27 #25) -#24 := (< 0::Int #17) -#26 := (and #24 #25) -#29 := (or #26 #28) -#42 := (ite #29 #39 #41) -#43 := (ite #21 0::Int #42) -#44 := (ite #22 #17 #43) -#45 := (= #38 #44) -#46 := (forall (vars (?v0 Int) (?v1 Int)) #45) -#208 := (iff #46 #205) -#102 := (and #25 #27) -#105 := (or #26 #102) -#178 := (ite #105 #39 #173) -#181 := (ite #21 0::Int #178) -#184 := (ite #22 #17 #181) -#187 := (= #38 #184) -#190 := (forall (vars (?v0 Int) (?v1 Int)) #187) -#206 := (iff #190 #205) -#203 := (iff #187 #202) -#200 := (= #184 #199) -#197 := (= #181 #196) -#194 := (= #178 #193) -#149 := (iff #105 #148) -#146 := (iff #102 #145) -#143 := (iff #27 #142) -#144 := [rewrite]: #143 -#136 := (iff #25 #135) -#137 := [rewrite]: #136 -#147 := [monotonicity #137 #144]: #146 -#139 := (iff #26 #138) -#132 := (iff #24 #131) +#50 := [true-axiom]: true +#267 := (or false #252) +#268 := [th-lemma arith]: #267 +#269 := [unit-resolution #268 #50]: #252 +#12 := (= f3 0::Int) +#142 := (ite #12 0::Int #139) +#263 := (* -1::Int #142) +#264 := (+ #19 #263) +#266 := (>= #264 0::Int) +#262 := (= #19 #142) +#181 := (= #139 #142) +#191 := (not #12) +#180 := (= #142 0::Int) +#204 := (not #180) +#196 := (<= #142 0::Int) +#198 := (not #196) +#167 := (>= #142 2::Int) +#29 := 3::Int +#30 := (+ f3 3::Int) +#21 := (- 2::Int) +#20 := (- f3) +#22 := (mod #20 #21) +#23 := (- #22) +#14 := (< 0::Int 2::Int) +#16 := (< f3 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int f3) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#25 := (ite #12 0::Int #24) +#11 := (= 2::Int 0::Int) +#26 := (ite #11 f3 #25) +#27 := (+ #26 #26) +#28 := (+ f3 #27) +#31 := (< #28 #30) +#32 := (not #31) +#172 := (iff #32 #167) +#103 := (+ 3::Int f3) +#55 := (and #14 #16) +#58 := (or #15 #55) +#79 := (ite #58 #19 #74) +#82 := (ite #12 0::Int #79) +#95 := (* 2::Int #82) +#100 := (+ f3 #95) +#106 := (< #100 #103) +#109 := (not #106) +#170 := (iff #109 #167) +#145 := (* 2::Int #142) +#155 := (>= #145 3::Int) +#168 := (iff #155 #167) +#169 := [rewrite]: #168 +#165 := (iff #109 #155) +#154 := (not #155) +#160 := (not #154) +#163 := (iff #160 #155) +#164 := [rewrite]: #163 +#161 := (iff #109 #160) +#158 := (iff #106 #154) +#148 := (+ f3 #145) +#151 := (< #148 #103) +#156 := (iff #151 #154) +#157 := [rewrite]: #156 +#152 := (iff #106 #151) +#149 := (= #100 #148) +#146 := (= #95 #145) +#143 := (= #82 #142) +#140 := (= #79 #139) +#137 := (iff #58 #136) +#134 := (iff #55 #126) +#129 := (and true #126) +#132 := (iff #129 #126) #133 := [rewrite]: #132 -#140 := [monotonicity #133 #137]: #139 -#150 := [monotonicity #140 #147]: #149 -#195 := [monotonicity #150]: #194 -#198 := [monotonicity #195]: #197 -#201 := [monotonicity #198]: #200 -#204 := [monotonicity #201]: #203 -#207 := [quant-intro #204]: #206 -#191 := (iff #46 #190) -#188 := (iff #45 #187) -#185 := (= #44 #184) -#182 := (= #43 #181) -#179 := (= #42 #178) -#176 := (= #41 #173) -#170 := (- #167) -#174 := (= #170 #173) -#175 := [rewrite]: #174 -#171 := (= #41 #170) -#168 := (= #40 #167) -#113 := (= #32 #112) -#114 := [rewrite]: #113 -#110 := (= #31 #109) -#111 := [rewrite]: #110 -#169 := [monotonicity #111 #114]: #168 -#172 := [monotonicity #169]: #171 -#177 := [trans #172 #175]: #176 -#106 := (iff #29 #105) -#103 := (iff #28 #102) -#104 := [rewrite]: #103 -#107 := [monotonicity #104]: #106 -#180 := [monotonicity #107 #177]: #179 -#183 := [monotonicity #180]: #182 -#186 := [monotonicity #183]: #185 -#189 := [monotonicity #186]: #188 -#192 := [quant-intro #189]: #191 -#209 := [trans #192 #207]: #208 -#166 := [asserted]: #46 -#210 := [mp #166 #209]: #205 -#213 := [mp~ #210 #217]: #205 -#261 := [mp #213 #260]: #258 -#292 := [mp #261 #291]: #289 -#777 := [mp #292 #776]: #772 -#716 := (not #772) -#717 := (or #716 #727) -#350 := (* -1::Int 2::Int) -#436 := (mod #435 #350) -#437 := (+ #10 #436) -#428 := (= #437 0::Int) -#442 := (<= 2::Int 0::Int) -#421 := (or #442 #438) -#756 := (not #421) -#415 := (or #758 #442) -#545 := (not #415) -#752 := (or #545 #756) -#426 := (ite #752 #441 #428) -#760 := (ite #759 #427 #426) -#761 := (= f3 #10) -#762 := (= 2::Int 0::Int) -#757 := (ite #762 #761 #760) -#722 := (or #716 #757) -#718 := (iff #722 #717) -#565 := (iff #717 #717) -#566 := [rewrite]: #565 -#720 := (iff #757 #727) -#725 := (ite false #761 #727) -#730 := (iff #725 #727) -#719 := [rewrite]: #730 -#729 := (iff #757 #725) -#728 := (iff #760 #727) -#448 := (iff #426 #447) -#736 := (iff #428 #732) -#731 := (= #437 #457) -#734 := (= #436 #733) -#463 := (= #350 -2::Int) -#356 := [rewrite]: #463 -#456 := [monotonicity #356]: #734 -#735 := [monotonicity #456]: #731 -#446 := [monotonicity #735]: #736 -#460 := (iff #752 #751) -#390 := (or #404 #747) -#737 := (iff #390 #751) -#738 := [rewrite]: #737 -#750 := (iff #752 #390) -#749 := (iff #756 #747) -#746 := (iff #421 #438) -#742 := (or false #438) -#745 := (iff #742 #438) -#740 := [rewrite]: #745 -#743 := (iff #421 #742) -#413 := (iff #442 false) -#418 := [rewrite]: #413 -#744 := [monotonicity #418]: #743 -#384 := [trans #744 #740]: #746 -#389 := [monotonicity #384]: #749 -#405 := (iff #545 #404) -#402 := (iff #415 #758) -#754 := (or #758 false) -#398 := (iff #754 #758) -#739 := [rewrite]: #398 -#414 := (iff #415 #754) -#755 := [monotonicity #418]: #414 -#403 := [trans #755 #739]: #402 -#741 := [monotonicity #403]: #405 -#748 := [monotonicity #741 #389]: #750 -#461 := [trans #748 #738]: #460 -#449 := [monotonicity #461 #446]: #448 -#443 := [monotonicity #449]: #728 -#763 := (iff #762 false) -#753 := [rewrite]: #763 -#726 := [monotonicity #753 #443]: #729 -#721 := [trans #726 #719]: #720 -#724 := [monotonicity #721]: #718 -#567 := [trans #724 #566]: #718 -#723 := [quant-inst #8 #9]: #722 -#709 := [mp #723 #567]: #717 -#640 := [unit-resolution #709 #777]: #727 -#694 := (not #759) -#693 := (not #727) -#636 := (or #693 #694) -#600 := (not #427) -#710 := (<= #10 0::Int) -#642 := (not #710) -#672 := (not #93) -#673 := (or #642 #672) -#629 := [th-lemma arith farkas 1 1]: #673 -#630 := [unit-resolution #629 #100]: #642 -#631 := (or #600 #710) -#634 := [th-lemma arith triangle-eq]: #631 -#635 := [unit-resolution #634 #630]: #600 -#697 := (or #693 #694 #427) -#582 := [def-axiom]: #697 -#637 := [unit-resolution #582 #635]: #636 -#632 := [unit-resolution #637 #640]: #694 -#597 := (or #693 #759 #447) -#599 := [def-axiom]: #597 -#638 := [unit-resolution #599 #632 #640]: #447 -#701 := (not #447) -#703 := (or #701 #714 #441) -#704 := [def-axiom]: #703 -#612 := [unit-resolution #704 #638]: #611 -#613 := [unit-resolution #612 #639]: #714 -#712 := (or #751 #438) -#706 := [def-axiom]: #712 -#506 := [unit-resolution #706 #613]: #438 -#707 := (or #751 #758) -#713 := [def-axiom]: #707 -#617 := [unit-resolution #713 #613]: #758 -#618 := (or #759 #404 #747) -#619 := [th-lemma arith triangle-eq]: #618 -#624 := [unit-resolution #619 #632]: #390 -[unit-resolution #624 #617 #506]: false +#130 := (iff #55 #129) +#127 := (iff #16 #126) +#128 := [rewrite]: #127 +#116 := (iff #14 true) +#117 := [rewrite]: #116 +#131 := [monotonicity #117 #128]: #130 +#135 := [trans #131 #133]: #134 +#123 := (iff #15 #113) +#118 := (and #113 true) +#121 := (iff #118 #113) +#122 := [rewrite]: #121 +#119 := (iff #15 #118) +#114 := (iff #13 #113) +#115 := [rewrite]: #114 +#120 := [monotonicity #115 #117]: #119 +#124 := [trans #120 #122]: #123 +#138 := [monotonicity #124 #135]: #137 +#141 := [monotonicity #138]: #140 +#144 := [monotonicity #141]: #143 +#147 := [monotonicity #144]: #146 +#150 := [monotonicity #147]: #149 +#153 := [monotonicity #150]: #152 +#159 := [trans #153 #157]: #158 +#162 := [monotonicity #159]: #161 +#166 := [trans #162 #164]: #165 +#171 := [trans #166 #169]: #170 +#110 := (iff #32 #109) +#107 := (iff #31 #106) +#104 := (= #30 #103) +#105 := [rewrite]: #104 +#101 := (= #28 #100) +#98 := (= #27 #95) +#92 := (+ #82 #82) +#96 := (= #92 #95) +#97 := [rewrite]: #96 +#93 := (= #27 #92) +#90 := (= #26 #82) +#85 := (ite false f3 #82) +#88 := (= #85 #82) +#89 := [rewrite]: #88 +#86 := (= #26 #85) +#83 := (= #25 #82) +#80 := (= #24 #79) +#77 := (= #23 #74) +#71 := (- #68) +#75 := (= #71 #74) +#76 := [rewrite]: #75 +#72 := (= #23 #71) +#69 := (= #22 #68) +#66 := (= #21 -2::Int) +#67 := [rewrite]: #66 +#63 := (= #20 #62) +#64 := [rewrite]: #63 +#70 := [monotonicity #64 #67]: #69 +#73 := [monotonicity #70]: #72 +#78 := [trans #73 #76]: #77 +#59 := (iff #18 #58) +#56 := (iff #17 #55) +#57 := [rewrite]: #56 +#60 := [monotonicity #57]: #59 +#81 := [monotonicity #60 #78]: #80 +#84 := [monotonicity #81]: #83 +#53 := (iff #11 false) +#54 := [rewrite]: #53 +#87 := [monotonicity #54 #84]: #86 +#91 := [trans #87 #89]: #90 +#94 := [monotonicity #91 #91]: #93 +#99 := [trans #94 #97]: #98 +#102 := [monotonicity #99]: #101 +#108 := [monotonicity #102 #105]: #107 +#111 := [monotonicity #108]: #110 +#173 := [trans #111 #171]: #172 +#52 := [asserted]: #32 +#174 := [mp #52 #173]: #167 +#199 := (not #167) +#200 := (or #198 #199) +#201 := [th-lemma arith farkas 1 1]: #200 +#202 := [unit-resolution #201 #174]: #198 +#203 := [hypothesis]: #180 +#205 := (or #204 #196) +#206 := [th-lemma arith triangle-eq]: #205 +#207 := [unit-resolution #206 #203 #202]: false +#208 := [lemma #207]: #204 +#192 := (or #191 #180) +#193 := [def-axiom]: #192 +#270 := [unit-resolution #193 #208]: #191 +#194 := (or #12 #181) +#195 := [def-axiom]: #194 +#271 := [unit-resolution #195 #270]: #181 +#272 := [hypothesis]: #182 +#273 := [trans #272 #271]: #262 +#274 := (not #262) +#275 := (or #274 #266) +#276 := [th-lemma arith triangle-eq]: #275 +#277 := [unit-resolution #276 #273]: #266 +#278 := [th-lemma arith farkas -1 -1 1 #174 #277 #269]: false +#280 := [lemma #278]: #279 +#187 := (or #184 #182) +#188 := [def-axiom]: #187 +#257 := [unit-resolution #188 #280]: #184 +#178 := (or #136 #112) +#179 := [def-axiom]: #178 +#258 := [unit-resolution #179 #257]: #112 +#176 := (or #136 #125) +#177 := [def-axiom]: #176 +#259 := [unit-resolution #177 #257]: #125 +#260 := (or #12 #113 #126) +#261 := [th-lemma arith triangle-eq]: #260 +#232 := [unit-resolution #261 #270]: #136 +[unit-resolution #232 #259 #258]: false unsat cfa8a4e8b0964986b89eaf37e6038032e9b8b0d6 101 0 #2 := false @@ -8171,936 +7945,783 @@ #123 := [th-lemma arith triangle-eq]: #122 [unit-resolution #123 #119 #112 #46]: false unsat -742e212b0179422ed718ceb7818522f48622510c 930 0 +cf727a25fbaea6abf5a0d302bf954b4ffa92b324 777 0 #2 := false -#20 := 1::Int -decl f3 :: (-> Int Int Int) -#11 := 2::Int -decl f5 :: Int -#9 := f5 -#22 := (f3 f5 2::Int) -#1103 := (<= #22 1::Int) -#13 := 0::Int -#574 := (mod f5 2::Int) -#108 := -1::Int -#575 := (* -1::Int #574) -#576 := (+ #22 #575) -#954 := (<= #576 0::Int) -#577 := (= #576 0::Int) -decl f4 :: Int -#8 := f4 -#10 := (+ f4 f5) -#461 := (>= #10 0::Int) -#778 := (= #10 0::Int) -#458 := (mod #10 2::Int) -#459 := (* -1::Int #458) -#12 := (f3 #10 2::Int) -#460 := (+ #12 #459) -#457 := (= #460 0::Int) -#715 := (not #457) -#720 := (<= #460 0::Int) -#1107 := [hypothesis]: #457 -#1108 := (or #715 #720) -#1109 := [th-lemma arith triangle-eq]: #1108 -#1110 := [unit-resolution #1109 #1107]: #720 -#722 := (>= #460 0::Int) -#1111 := (or #715 #722) -#1322 := [th-lemma arith triangle-eq]: #1111 -#1323 := [unit-resolution #1322 #1107]: #722 -#1193 := (not #720) -#1239 := (not #722) -#1348 := (or #1239 #1193) -#1112 := (div f5 2::Int) -#476 := -2::Int -#1125 := (* -2::Int #1112) -#1126 := (+ #575 #1125) -#1127 := (+ f5 #1126) -#1124 := (= #1127 0::Int) -#1161 := (not #1124) -#1276 := [hypothesis]: #1161 +#9 := 0::Int +#30 := 4::Int +decl f3 :: Int +#11 := f3 +#546 := (div f3 4::Int) +#208 := -4::Int +#574 := (* -4::Int #546) +#39 := (mod f3 4::Int) +#107 := -1::Int +#573 := (* -1::Int #39) +#575 := (+ #573 #574) +#576 := (+ f3 #575) +#581 := (<= #576 0::Int) +#572 := (= #576 0::Int) #1 := true -#72 := [true-axiom]: true -#1154 := (or false #1124) -#1159 := [th-lemma arith]: #1154 -#1277 := [unit-resolution #1159 #72 #1276]: false -#1278 := [lemma #1277]: #1124 -#1274 := (or #1161 #1239 #1193) -#1134 := (>= #574 0::Int) -#1157 := (or false #1134) -#1158 := [th-lemma arith]: #1157 -#1151 := [unit-resolution #1158 #72]: #1134 -#1224 := (>= #1127 0::Int) -#1246 := [hypothesis]: #1124 -#1247 := (or #1161 #1224) -#1248 := [th-lemma arith triangle-eq]: #1247 -#1249 := [unit-resolution #1248 #1246]: #1224 -#17 := 3::Int -#15 := 4::Int -#16 := (f3 f4 4::Int) -#568 := (>= #16 3::Int) -#18 := (= #16 3::Int) -#75 := [asserted]: #18 -#967 := (not #18) -#993 := (or #967 #568) -#994 := [th-lemma arith triangle-eq]: #993 -#995 := [unit-resolution #994 #75]: #568 -#865 := (div f4 4::Int) -#663 := -4::Int -#881 := (* -4::Int #865) -#696 := (mod f4 4::Int) -#698 := (* -1::Int #696) -#882 := (+ #698 #881) -#883 := (+ f4 #882) -#889 := (>= #883 0::Int) -#880 := (= #883 0::Int) -#971 := (or false #880) -#972 := [th-lemma arith]: #971 -#973 := [unit-resolution #972 #72]: #880 -#974 := (not #880) -#996 := (or #974 #889) -#997 := [th-lemma arith triangle-eq]: #996 -#998 := [unit-resolution #997 #973]: #889 -#560 := (>= #12 0::Int) -#14 := (= #12 0::Int) -#74 := [asserted]: #14 -#622 := (not #14) -#1230 := (or #622 #560) -#1231 := [th-lemma arith triangle-eq]: #1230 -#1232 := [unit-resolution #1231 #74]: #560 -#811 := (div #10 2::Int) -#828 := (* -2::Int #811) -#829 := (+ #459 #828) -#830 := (+ f5 #829) -#831 := (+ f4 #830) -#1106 := (>= #831 0::Int) -#826 := (= #831 0::Int) -#1167 := (or false #826) -#1168 := [th-lemma arith]: #1167 -#1169 := [unit-resolution #1168 #72]: #826 -#1180 := (not #826) -#1233 := (or #1180 #1106) -#1234 := [th-lemma arith triangle-eq]: #1233 -#1235 := [unit-resolution #1234 #1169]: #1106 -#708 := (+ #16 #698) -#600 := (>= #708 0::Int) -#709 := (= #708 0::Int) -#482 := (* -1::Int f4) -#660 := (mod #482 -4::Int) -#648 := (+ #16 #660) -#653 := (= #648 0::Int) -#710 := (>= f4 0::Int) -#669 := (not #710) -#701 := (<= f4 0::Int) -#670 := (not #701) -#659 := (or #670 #669) -#656 := (ite #659 #709 #653) -#689 := (= f4 0::Int) -#590 := (not #689) -#688 := (= #16 0::Int) -#595 := (not #688) -#428 := (= 3::Int 0::Int) -#430 := (iff #428 false) -#419 := [rewrite]: #430 -#425 := [hypothesis]: #688 -#426 := (= 3::Int #16) -#427 := [symm #75]: #426 -#429 := [trans #427 #425]: #428 -#431 := [mp #429 #419]: false -#412 := [lemma #431]: #595 -#1027 := (or #590 #688) -#630 := (ite #689 #688 #656) -#27 := (:var 0 Int) -#26 := (:var 1 Int) -#46 := (f3 #26 #27) -#790 := (pattern #46) -#112 := (* -1::Int #27) -#109 := (* -1::Int #26) -#173 := (mod #109 #112) -#302 := (+ #46 #173) -#303 := (= #302 0::Int) -#47 := (mod #26 #27) -#299 := (* -1::Int #47) -#300 := (+ #46 #299) -#301 := (= #300 0::Int) -#147 := (>= #26 0::Int) -#140 := (<= #27 0::Int) -#246 := (or #140 #147) -#247 := (not #246) -#136 := (<= #26 0::Int) -#242 := (or #136 #140) -#243 := (not #242) -#250 := (or #243 #247) -#304 := (ite #250 #301 #303) -#298 := (= #46 0::Int) -#29 := (= #26 0::Int) -#305 := (ite #29 #298 #304) -#297 := (= #26 #46) -#30 := (= #27 0::Int) -#306 := (ite #30 #297 #305) -#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #306) -#309 := (forall (vars (?v0 Int) (?v1 Int)) #306) -#794 := (iff #309 #791) -#792 := (iff #306 #306) -#793 := [refl]: #792 -#795 := [quant-intro #793]: #794 -#179 := (* -1::Int #173) -#266 := (ite #250 #47 #179) -#269 := (ite #29 0::Int #266) -#272 := (ite #30 #26 #269) -#275 := (= #46 #272) -#278 := (forall (vars (?v0 Int) (?v1 Int)) #275) -#310 := (iff #278 #309) -#307 := (iff #275 #306) -#308 := [rewrite]: #307 -#311 := [quant-intro #308]: #310 -#148 := (not #147) -#141 := (not #140) -#151 := (and #141 #148) -#137 := (not #136) -#144 := (and #137 #141) -#154 := (or #144 #151) -#199 := (ite #154 #47 #179) -#202 := (ite #29 0::Int #199) -#205 := (ite #30 #26 #202) -#208 := (= #46 #205) -#211 := (forall (vars (?v0 Int) (?v1 Int)) #208) -#279 := (iff #211 #278) -#276 := (iff #208 #275) -#273 := (= #205 #272) -#270 := (= #202 #269) -#267 := (= #199 #266) -#251 := (iff #154 #250) -#248 := (iff #151 #247) -#249 := [rewrite]: #248 -#244 := (iff #144 #243) -#245 := [rewrite]: #244 -#252 := [monotonicity #245 #249]: #251 -#268 := [monotonicity #252]: #267 -#271 := [monotonicity #268]: #270 +#93 := [true-axiom]: true +#721 := (or false #572) +#722 := [th-lemma arith]: #721 +#723 := [unit-resolution #722 #93]: #572 +#724 := (not #572) +#725 := (or #724 #581) +#726 := [th-lemma arith triangle-eq]: #725 +#727 := [unit-resolution #726 #723]: #581 +#582 := (>= #576 0::Int) +#728 := (or #724 #582) +#729 := [th-lemma arith triangle-eq]: #728 +#730 := [unit-resolution #729 #723]: #582 +#600 := (>= #39 4::Int) +#601 := (not #600) +#731 := (or false #601) +#732 := [th-lemma arith]: #731 +#733 := [unit-resolution #732 #93]: #601 +#47 := 3::Int +#613 := (>= #39 3::Int) +#872 := (= #39 3::Int) +#108 := (* -1::Int f3) +#211 := (mod #108 -4::Int) +#217 := (* -1::Int #211) +#258 := (>= f3 0::Int) +#259 := (not #258) +#245 := (<= f3 0::Int) +#246 := (not #245) +#269 := (or #246 #259) +#272 := (ite #269 #39 #217) +#32 := (= f3 0::Int) +#275 := (ite #32 0::Int #272) +#282 := (= #275 3::Int) +#41 := (- 4::Int) +#40 := (- f3) +#42 := (mod #40 #41) +#43 := (- #42) +#34 := (< 0::Int 4::Int) +#36 := (< f3 0::Int) +#37 := (and #36 #34) +#33 := (< 0::Int f3) +#35 := (and #33 #34) +#38 := (or #35 #37) +#44 := (ite #38 #39 #43) +#45 := (ite #32 0::Int #44) +#31 := (= 4::Int 0::Int) +#46 := (ite #31 f3 #45) +#48 := (= #46 3::Int) +#286 := (iff #48 #282) +#200 := (and #34 #36) +#203 := (or #35 #200) +#222 := (ite #203 #39 #217) +#197 := (= 0::Int f3) +#225 := (ite #197 0::Int #222) +#238 := (= 3::Int #225) +#284 := (iff #238 #282) +#278 := (= 3::Int #275) +#281 := (iff #278 #282) +#283 := [rewrite]: #281 +#279 := (iff #238 #278) +#276 := (= #225 #275) +#273 := (= #222 #272) +#270 := (iff #203 #269) +#267 := (iff #200 #259) +#262 := (and true #259) +#265 := (iff #262 #259) +#266 := [rewrite]: #265 +#263 := (iff #200 #262) +#260 := (iff #36 #259) +#261 := [rewrite]: #260 +#249 := (iff #34 true) +#250 := [rewrite]: #249 +#264 := [monotonicity #250 #261]: #263 +#268 := [trans #264 #266]: #267 +#256 := (iff #35 #246) +#251 := (and #246 true) +#254 := (iff #251 #246) +#255 := [rewrite]: #254 +#252 := (iff #35 #251) +#247 := (iff #33 #246) +#248 := [rewrite]: #247 +#253 := [monotonicity #248 #250]: #252 +#257 := [trans #253 #255]: #256 +#271 := [monotonicity #257 #268]: #270 #274 := [monotonicity #271]: #273 -#277 := [monotonicity #274]: #276 -#280 := [quant-intro #277]: #279 -#221 := (~ #211 #211) -#223 := (~ #208 #208) -#220 := [refl]: #223 -#224 := [nnf-pos #220]: #221 -#40 := (- #27) -#39 := (- #26) -#48 := (mod #39 #40) -#49 := (- #48) -#33 := (< 0::Int #27) -#35 := (< #26 0::Int) -#36 := (and #35 #33) -#32 := (< 0::Int #26) -#34 := (and #32 #33) -#37 := (or #34 #36) -#50 := (ite #37 #47 #49) -#51 := (ite #29 0::Int #50) -#52 := (ite #30 #26 #51) -#53 := (= #46 #52) -#54 := (forall (vars (?v0 Int) (?v1 Int)) #53) -#214 := (iff #54 #211) -#102 := (and #33 #35) -#105 := (or #34 #102) -#184 := (ite #105 #47 #179) -#93 := (= 0::Int #26) -#187 := (ite #93 0::Int #184) -#96 := (= 0::Int #27) -#190 := (ite #96 #26 #187) -#193 := (= #46 #190) -#196 := (forall (vars (?v0 Int) (?v1 Int)) #193) -#212 := (iff #196 #211) -#209 := (iff #193 #208) -#206 := (= #190 #205) -#203 := (= #187 #202) -#200 := (= #184 #199) -#155 := (iff #105 #154) -#152 := (iff #102 #151) -#149 := (iff #35 #148) -#150 := [rewrite]: #149 -#142 := (iff #33 #141) -#143 := [rewrite]: #142 -#153 := [monotonicity #143 #150]: #152 -#145 := (iff #34 #144) -#138 := (iff #32 #137) -#139 := [rewrite]: #138 -#146 := [monotonicity #139 #143]: #145 -#156 := [monotonicity #146 #153]: #155 -#201 := [monotonicity #156]: #200 -#130 := (iff #93 #29) -#131 := [rewrite]: #130 -#204 := [monotonicity #131 #201]: #203 -#132 := (iff #96 #30) -#133 := [rewrite]: #132 -#207 := [monotonicity #133 #204]: #206 -#210 := [monotonicity #207]: #209 -#213 := [quant-intro #210]: #212 -#197 := (iff #54 #196) -#194 := (iff #53 #193) -#191 := (= #52 #190) -#188 := (= #51 #187) -#185 := (= #50 #184) -#182 := (= #49 #179) -#176 := (- #173) -#180 := (= #176 #179) -#181 := [rewrite]: #180 -#177 := (= #49 #176) -#174 := (= #48 #173) -#113 := (= #40 #112) -#114 := [rewrite]: #113 -#110 := (= #39 #109) -#111 := [rewrite]: #110 -#175 := [monotonicity #111 #114]: #174 -#178 := [monotonicity #175]: #177 -#183 := [trans #178 #181]: #182 -#106 := (iff #37 #105) -#103 := (iff #36 #102) -#104 := [rewrite]: #103 -#107 := [monotonicity #104]: #106 -#186 := [monotonicity #107 #183]: #185 -#94 := (iff #29 #93) -#95 := [rewrite]: #94 -#189 := [monotonicity #95 #186]: #188 -#97 := (iff #30 #96) -#98 := [rewrite]: #97 -#192 := [monotonicity #98 #189]: #191 -#195 := [monotonicity #192]: #194 -#198 := [quant-intro #195]: #197 -#215 := [trans #198 #213]: #214 -#172 := [asserted]: #54 -#216 := [mp #172 #215]: #211 -#225 := [mp~ #216 #224]: #211 -#281 := [mp #225 #280]: #278 -#312 := [mp #281 #311]: #309 -#796 := [mp #312 #795]: #791 -#584 := (not #791) -#641 := (or #584 #630) -#718 := (* -1::Int 4::Int) -#705 := (mod #482 #718) -#707 := (+ #16 #705) -#699 := (= #707 0::Int) -#706 := (<= 4::Int 0::Int) -#711 := (or #706 #710) -#700 := (not #711) -#702 := (or #701 #706) -#703 := (not #702) -#697 := (or #703 #700) -#704 := (ite #697 #709 #699) -#691 := (ite #689 #688 #704) -#692 := (= f4 #16) -#693 := (= 4::Int 0::Int) -#694 := (ite #693 #692 #691) -#644 := (or #584 #694) -#646 := (iff #644 #641) -#647 := (iff #641 #641) -#627 := [rewrite]: #647 -#639 := (iff #694 #630) -#525 := (ite false #692 #630) -#638 := (iff #525 #630) -#643 := [rewrite]: #638 -#636 := (iff #694 #525) -#631 := (iff #691 #630) -#651 := (iff #704 #656) -#654 := (iff #699 #653) -#649 := (= #707 #648) -#666 := (= #705 #660) -#664 := (= #718 -4::Int) -#665 := [rewrite]: #664 -#652 := [monotonicity #665]: #666 -#650 := [monotonicity #652]: #649 -#655 := [monotonicity #650]: #654 -#661 := (iff #697 #659) -#680 := (iff #700 #669) -#678 := (iff #711 #710) -#673 := (or false #710) -#676 := (iff #673 #710) -#677 := [rewrite]: #676 -#674 := (iff #711 #673) -#681 := (iff #706 false) -#682 := [rewrite]: #681 -#675 := [monotonicity #682]: #674 -#679 := [trans #675 #677]: #678 -#658 := [monotonicity #679]: #680 -#671 := (iff #703 #670) -#667 := (iff #702 #701) -#684 := (or #701 false) -#683 := (iff #684 #701) -#687 := [rewrite]: #683 -#685 := (iff #702 #684) -#686 := [monotonicity #682]: #685 -#668 := [trans #686 #687]: #667 -#672 := [monotonicity #668]: #671 -#662 := [monotonicity #672 #658]: #661 -#657 := [monotonicity #662 #655]: #651 -#632 := [monotonicity #657]: #631 -#690 := (iff #693 false) -#695 := [rewrite]: #690 -#637 := [monotonicity #695 #632]: #636 -#640 := [trans #637 #643]: #639 -#642 := [monotonicity #640]: #646 -#573 := [trans #642 #627]: #646 -#645 := [quant-inst #8 #15]: #644 -#628 := [mp #645 #573]: #641 -#1048 := [unit-resolution #628 #796]: #630 -#589 := (not #630) -#591 := (or #589 #590 #688) -#592 := [def-axiom]: #591 -#1047 := [unit-resolution #592 #1048]: #1027 -#1043 := [unit-resolution #1047 #412]: #590 -#957 := (or #689 #656) -#593 := (or #589 #689 #656) -#594 := [def-axiom]: #593 -#964 := [unit-resolution #594 #1048]: #957 -#1033 := [unit-resolution #964 #1043]: #656 -#635 := (not #659) -#860 := [hypothesis]: #635 -#609 := (or #659 #701) -#633 := [def-axiom]: #609 -#861 := [unit-resolution #633 #860]: #701 -#634 := (or #659 #710) -#629 := [def-axiom]: #634 -#862 := [unit-resolution #629 #860]: #710 -#863 := (or #689 #670 #669) -#864 := [th-lemma arith triangle-eq]: #863 -#913 := [unit-resolution #864 #862 #861 #1043]: false -#914 := [lemma #913]: #659 -#611 := (not #656) -#613 := (or #611 #635 #709) -#614 := [def-axiom]: #613 -#1165 := [unit-resolution #614 #914 #1033]: #709 -#605 := (not #709) -#1054 := (or #605 #600) -#1055 := [th-lemma arith triangle-eq]: #1054 -#1236 := [unit-resolution #1055 #1165]: #600 -#1237 := [hypothesis]: #722 -#1170 := (* -1::Int #1112) -#1035 := (* -2::Int #865) -#1171 := (+ #1035 #1170) -#1155 := (* -1::Int #811) -#1172 := (+ #1155 #1171) -#1173 := (+ #698 #1172) -#1174 := (+ #459 #1173) -#1175 := (+ #16 #1174) -#1176 := (+ #12 #1175) -#1177 := (+ f5 #1176) -#1178 := (+ f4 #1177) -#1179 := (>= #1178 2::Int) -#1191 := (not #1179) -#955 := (>= #576 0::Int) -#1184 := [hypothesis]: #720 -#1240 := (or #577 #1239 #1193) -#561 := (<= #16 3::Int) -#968 := (or #967 #561) -#966 := [th-lemma arith triangle-eq]: #968 -#970 := [unit-resolution #966 #75]: #561 -#888 := (<= #883 0::Int) -#975 := (or #974 #888) -#976 := [th-lemma arith triangle-eq]: #975 -#982 := [unit-resolution #976 #973]: #888 -#580 := (<= f5 0::Int) -#556 := (= f5 0::Int) -#1059 := (not #577) -#1146 := [hypothesis]: #1059 -#1222 := (or #556 #577) -#376 := (* -1::Int f5) -#521 := (mod #376 -2::Int) -#523 := (+ #22 #521) -#508 := (= #523 0::Int) -#546 := (not #580) -#578 := (>= f5 0::Int) -#526 := (not #578) -#536 := (or #526 #546) -#511 := (ite #536 #577 #508) -#1066 := (not #556) -#1207 := [hypothesis]: #1066 -#1201 := (or #556 #511) -#555 := (= #22 0::Int) -#514 := (ite #556 #555 #511) -#382 := (or #584 #514) -#370 := (* -1::Int 2::Int) -#570 := (mod #376 #370) -#571 := (+ #22 #570) -#572 := (= #571 0::Int) -#440 := (<= 2::Int 0::Int) -#579 := (or #440 #578) -#562 := (not #579) -#550 := (or #580 #440) -#551 := (not #550) -#552 := (or #551 #562) -#553 := (ite #552 #577 #572) -#557 := (ite #556 #555 #553) -#400 := (= f5 #22) -#781 := (= 2::Int 0::Int) -#558 := (ite #781 #400 #557) -#383 := (or #584 #558) -#371 := (iff #383 #382) -#375 := (iff #382 #382) -#797 := [rewrite]: #375 -#498 := (iff #558 #514) -#517 := (ite false #400 #514) -#495 := (iff #517 #514) -#497 := [rewrite]: #495 -#506 := (iff #558 #517) -#515 := (iff #557 #514) -#512 := (iff #553 #511) -#509 := (iff #572 #508) -#505 := (= #571 #523) -#522 := (= #570 #521) -#750 := (= #370 -2::Int) -#754 := [rewrite]: #750 -#520 := [monotonicity #754]: #522 -#507 := [monotonicity #520]: #505 -#510 := [monotonicity #507]: #509 -#533 := (iff #552 #536) -#531 := (or #546 #526) -#529 := (iff #531 #536) -#532 := [rewrite]: #529 -#535 := (iff #552 #531) -#527 := (iff #562 #526) -#534 := (iff #579 #578) -#540 := (or false #578) -#539 := (iff #540 #578) -#544 := [rewrite]: #539 -#542 := (iff #579 #540) -#758 := (iff #440 false) -#421 := [rewrite]: #758 -#543 := [monotonicity #421]: #542 -#524 := [trans #543 #544]: #534 -#530 := [monotonicity #524]: #527 -#549 := (iff #551 #546) -#547 := (iff #550 #580) -#554 := (or #580 false) -#541 := (iff #554 #580) -#545 := [rewrite]: #541 -#559 := (iff #550 #554) -#538 := [monotonicity #421]: #559 -#548 := [trans #538 #545]: #547 -#537 := [monotonicity #548]: #549 -#528 := [monotonicity #537 #530]: #535 -#519 := [trans #528 #532]: #533 -#513 := [monotonicity #519 #510]: #512 -#516 := [monotonicity #513]: #515 -#782 := (iff #781 false) -#772 := [rewrite]: #782 -#518 := [monotonicity #772 #516]: #506 -#499 := [trans #518 #497]: #498 -#372 := [monotonicity #499]: #371 -#798 := [trans #372 #797]: #371 -#384 := [quant-inst #9 #11]: #383 -#799 := [mp #384 #798]: #382 -#1156 := [unit-resolution #799 #796]: #514 -#1028 := (not #514) -#1034 := (or #1028 #556 #511) -#1070 := [def-axiom]: #1034 -#1202 := [unit-resolution #1070 #1156]: #1201 -#1208 := [unit-resolution #1202 #1207]: #511 -#1205 := (or #578 #577) -#1147 := [hypothesis]: #526 -#388 := (or #536 #578) -#389 := [def-axiom]: #388 -#1148 := [unit-resolution #389 #1147]: #536 -#1149 := (or #1066 #578) -#1150 := [th-lemma arith triangle-eq]: #1149 -#1133 := [unit-resolution #1150 #1147]: #1066 -#1203 := [unit-resolution #1202 #1133]: #511 -#917 := (not #536) -#836 := (not #511) -#1025 := (or #836 #917 #577) -#1026 := [def-axiom]: #1025 -#1204 := [unit-resolution #1026 #1203 #1148 #1146]: false -#1206 := [lemma #1204]: #1205 -#1209 := [unit-resolution #1206 #1146]: #578 -#1217 := (or #556 #546 #526) -#1218 := [th-lemma arith triangle-eq]: #1217 -#1219 := [unit-resolution #1218 #1207 #1209]: #546 -#915 := (or #536 #580) -#916 := [def-axiom]: #915 -#1220 := [unit-resolution #916 #1219]: #536 -#1221 := [unit-resolution #1026 #1220 #1208 #1146]: false -#1223 := [lemma #1221]: #1222 -#1226 := [unit-resolution #1223 #1146]: #556 -#1227 := (or #1066 #580) -#1228 := [th-lemma arith triangle-eq]: #1227 -#1229 := [unit-resolution #1228 #1226]: #580 -#599 := (<= #12 0::Int) -#1186 := (or #622 #599) -#1187 := [th-lemma arith triangle-eq]: #1186 -#1188 := [unit-resolution #1187 #74]: #599 -#1105 := (<= #831 0::Int) -#1181 := (or #1180 #1105) -#1182 := [th-lemma arith triangle-eq]: #1181 -#1183 := [unit-resolution #1182 #1169]: #1105 -#569 := (<= #708 0::Int) -#1050 := (or #605 #569) -#1051 := [th-lemma arith triangle-eq]: #1050 -#1166 := [unit-resolution #1051 #1165]: #569 -#1238 := [th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #1237 #1184 #1236 #1166 #1235 #1183 #1232 #1188 #1209 #1229 #998 #982 #995 #970]: false -#1241 := [lemma #1238]: #1240 -#1250 := [unit-resolution #1241 #1237 #1184]: #577 -#1251 := (or #1059 #955) -#1252 := [th-lemma arith triangle-eq]: #1251 -#1253 := [unit-resolution #1252 #1250]: #955 -#1104 := (>= #22 1::Int) -#1152 := (not #1104) -#1254 := (or #1059 #954) -#1255 := [th-lemma arith triangle-eq]: #1254 -#1256 := [unit-resolution #1255 #1250]: #954 -#1140 := (>= #574 2::Int) -#1141 := (not #1140) -#1257 := (or false #1141) -#1258 := [th-lemma arith]: #1257 -#1259 := [unit-resolution #1258 #72]: #1141 -#1260 := (not #954) -#1261 := (or #1103 #1140 #1260) -#1262 := [th-lemma arith assign-bounds 1 1]: #1261 -#1263 := [unit-resolution #1262 #1259 #1256]: #1103 -#1266 := (not #1103) -#1269 := (or #1266 #1152) -#23 := (= #22 1::Int) -#219 := (not #23) -#19 := (f3 f4 2::Int) -#21 := (= #19 1::Int) -#1097 := (or #635 #21) -#918 := (div f4 2::Int) -#1036 := (* -1::Int #918) -#1037 := (+ #1035 #1036) -#1038 := (+ #698 #1037) -#483 := (mod f4 2::Int) -#484 := (* -1::Int #483) -#1039 := (+ #484 #1038) -#1040 := (+ #16 #1039) -#1041 := (+ f4 #1040) -#1042 := (>= #1041 2::Int) -#1030 := (not #1042) -#1045 := [hypothesis]: #659 -#1049 := [unit-resolution #614 #1045 #1033]: #709 -#1052 := [unit-resolution #1051 #1049]: #569 -#988 := (not #569) -#1031 := (or #1030 #988) -#940 := (>= #483 0::Int) -#1023 := (or false #940) -#1024 := [th-lemma arith]: #1023 -#1021 := [unit-resolution #1024 #72]: #940 -#983 := [hypothesis]: #569 -#931 := (* -2::Int #918) -#932 := (+ #484 #931) -#933 := (+ f4 #932) -#938 := (<= #933 0::Int) -#930 := (= #933 0::Int) -#1011 := (or false #930) -#1010 := [th-lemma arith]: #1011 -#1009 := [unit-resolution #1010 #72]: #930 -#958 := (not #930) -#959 := (or #958 #938) -#965 := [th-lemma arith triangle-eq]: #959 -#963 := [unit-resolution #965 #1009]: #938 -#1022 := [hypothesis]: #1042 -#1029 := [th-lemma arith farkas -1 2 -1 -1 -1 1 #970 #1022 #982 #963 #983 #1021]: false -#1032 := [lemma #1029]: #1031 -#1053 := [unit-resolution #1032 #1052]: #1030 -#1056 := [unit-resolution #1055 #1049]: #600 -#939 := (>= #933 0::Int) -#1064 := (or #958 #939) -#1065 := [th-lemma arith triangle-eq]: #1064 -#1068 := [unit-resolution #1065 #1009]: #939 -#485 := (+ #19 #484) -#385 := (>= #485 0::Int) -#477 := (= #485 0::Int) -#500 := (mod #482 -2::Int) -#504 := (+ #19 #500) -#491 := (= #504 0::Int) -#478 := (ite #659 #477 #491) -#464 := (= #19 0::Int) -#420 := (ite #689 #464 #478) -#411 := (or #584 #420) -#493 := (mod #482 #370) -#492 := (+ #19 #493) -#494 := (= #492 0::Int) -#469 := (or #440 #710) -#470 := (not #469) -#471 := (or #701 #440) -#463 := (not #471) -#472 := (or #463 #470) -#473 := (ite #472 #477 #494) -#474 := (ite #689 #464 #473) -#441 := (= f4 #19) -#443 := (ite #781 #441 #474) -#386 := (or #584 #443) -#391 := (iff #386 #411) -#398 := (iff #411 #411) -#399 := [rewrite]: #398 -#410 := (iff #443 #420) -#413 := (ite false #441 #420) -#406 := (iff #413 #420) -#407 := [rewrite]: #406 -#416 := (iff #443 #413) -#414 := (iff #474 #420) -#488 := (iff #473 #478) -#486 := (iff #494 #491) -#489 := (= #492 #504) -#503 := (= #493 #500) -#496 := [monotonicity #754]: #503 -#490 := [monotonicity #496]: #489 -#487 := [monotonicity #490]: #486 -#501 := (iff #472 #659) -#438 := (iff #470 #669) -#453 := (iff #469 #710) -#452 := (iff #469 #673) -#442 := [monotonicity #421]: #452 -#436 := [trans #442 #677]: #453 +#243 := (iff #197 #32) +#244 := [rewrite]: #243 +#277 := [monotonicity #244 #274]: #276 +#280 := [monotonicity #277]: #279 +#285 := [trans #280 #283]: #284 +#241 := (iff #48 #238) +#235 := (= #225 3::Int) +#239 := (iff #235 #238) +#240 := [rewrite]: #239 +#236 := (iff #48 #235) +#233 := (= #46 #225) +#228 := (ite false f3 #225) +#231 := (= #228 #225) +#232 := [rewrite]: #231 +#229 := (= #46 #228) +#226 := (= #45 #225) +#223 := (= #44 #222) +#220 := (= #43 #217) +#214 := (- #211) +#218 := (= #214 #217) +#219 := [rewrite]: #218 +#215 := (= #43 #214) +#212 := (= #42 #211) +#209 := (= #41 -4::Int) +#210 := [rewrite]: #209 +#206 := (= #40 #108) +#207 := [rewrite]: #206 +#213 := [monotonicity #207 #210]: #212 +#216 := [monotonicity #213]: #215 +#221 := [trans #216 #219]: #220 +#204 := (iff #38 #203) +#201 := (iff #37 #200) +#202 := [rewrite]: #201 +#205 := [monotonicity #202]: #204 +#224 := [monotonicity #205 #221]: #223 +#198 := (iff #32 #197) +#199 := [rewrite]: #198 +#227 := [monotonicity #199 #224]: #226 +#195 := (iff #31 false) +#196 := [rewrite]: #195 +#230 := [monotonicity #196 #227]: #229 +#234 := [trans #230 #232]: #233 +#237 := [monotonicity #234]: #236 +#242 := [trans #237 #240]: #241 +#287 := [trans #242 #285]: #286 +#194 := [asserted]: #48 +#288 := [mp #194 #287]: #282 +#883 := (= #39 #275) +#495 := (= #272 #275) +#509 := (not #32) +#494 := (= #275 0::Int) +#829 := (not #494) +#608 := (= 3::Int 0::Int) +#610 := (iff #608 false) +#827 := [rewrite]: #610 +#606 := [hypothesis]: #494 +#607 := [symm #288]: #278 +#609 := [trans #607 #606]: #608 +#828 := [mp #609 #827]: false +#830 := [lemma #828]: #829 +#510 := (or #509 #494) +#511 := [def-axiom]: #510 +#831 := [unit-resolution #511 #830]: #509 +#512 := (or #32 #495) +#513 := [def-axiom]: #512 +#881 := [unit-resolution #513 #831]: #495 +#496 := (= #39 #272) +#502 := (not #269) +#666 := [hypothesis]: #502 +#498 := (or #269 #245) +#499 := [def-axiom]: #498 +#667 := [unit-resolution #499 #666]: #245 +#500 := (or #269 #258) +#501 := [def-axiom]: #500 +#813 := [unit-resolution #501 #666]: #258 +#814 := (or #32 #246 #259) +#832 := [th-lemma arith triangle-eq]: #814 +#865 := [unit-resolution #832 #813 #667 #831]: false +#866 := [lemma #865]: #269 +#505 := (or #502 #496) +#506 := [def-axiom]: #505 +#882 := [unit-resolution #506 #866]: #496 +#884 := [trans #882 #881]: #883 +#885 := [trans #884 #288]: #872 +#886 := (not #872) +#887 := (or #886 #613) +#888 := [th-lemma arith triangle-eq]: #887 +#889 := [unit-resolution #888 #885]: #613 +#8 := 2::Int +decl f4 :: Int +#12 := f4 +#13 := (+ f3 f4) +#614 := (div #13 2::Int) +#113 := -2::Int +#632 := (* -2::Int #614) +#21 := (mod #13 2::Int) +#631 := (* -1::Int #21) +#633 := (+ #631 #632) +#634 := (+ f4 #633) +#635 := (+ f3 #634) +#639 := (<= #635 0::Int) +#629 := (= #635 0::Int) +#735 := (or false #629) +#736 := [th-lemma arith]: #735 +#737 := [unit-resolution #736 #93]: #629 +#738 := (not #629) +#739 := (or #738 #639) +#740 := [th-lemma arith triangle-eq]: #739 +#741 := [unit-resolution #740 #737]: #639 +#640 := (>= #635 0::Int) +#742 := (or #738 #640) +#743 := [th-lemma arith triangle-eq]: #742 +#744 := [unit-resolution #743 #737]: #640 +#710 := (<= #21 0::Int) +#709 := (= #21 0::Int) +#109 := (* -1::Int f4) +#110 := (+ #108 #109) +#116 := (mod #110 -2::Int) +#122 := (* -1::Int #116) +#163 := (>= #13 0::Int) +#164 := (not #163) +#150 := (<= #13 0::Int) +#151 := (not #150) +#174 := (or #151 #164) +#177 := (ite #174 #21 #122) +#14 := (= #13 0::Int) +#180 := (ite #14 0::Int #177) +#187 := (= #180 0::Int) +#23 := (- 2::Int) +#22 := (- #13) +#24 := (mod #22 #23) +#25 := (- #24) +#16 := (< 0::Int 2::Int) +#18 := (< #13 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #13) +#17 := (and #15 #16) +#20 := (or #17 #19) +#26 := (ite #20 #21 #25) +#27 := (ite #14 0::Int #26) +#10 := (= 2::Int 0::Int) +#28 := (ite #10 #13 #27) +#29 := (= #28 0::Int) +#191 := (iff #29 #187) +#101 := (and #16 #18) +#104 := (or #17 #101) +#127 := (ite #104 #21 #122) +#98 := (= 0::Int #13) +#130 := (ite #98 0::Int #127) +#143 := (= 0::Int #130) +#189 := (iff #143 #187) +#183 := (= 0::Int #180) +#186 := (iff #183 #187) +#188 := [rewrite]: #186 +#184 := (iff #143 #183) +#181 := (= #130 #180) +#178 := (= #127 #177) +#175 := (iff #104 #174) +#172 := (iff #101 #164) +#167 := (and true #164) +#170 := (iff #167 #164) +#171 := [rewrite]: #170 +#168 := (iff #101 #167) +#165 := (iff #18 #164) +#166 := [rewrite]: #165 +#154 := (iff #16 true) +#155 := [rewrite]: #154 +#169 := [monotonicity #155 #166]: #168 +#173 := [trans #169 #171]: #172 +#161 := (iff #17 #151) +#156 := (and #151 true) +#159 := (iff #156 #151) +#160 := [rewrite]: #159 +#157 := (iff #17 #156) +#152 := (iff #15 #151) +#153 := [rewrite]: #152 +#158 := [monotonicity #153 #155]: #157 +#162 := [trans #158 #160]: #161 +#176 := [monotonicity #162 #173]: #175 +#179 := [monotonicity #176]: #178 +#148 := (iff #98 #14) +#149 := [rewrite]: #148 +#182 := [monotonicity #149 #179]: #181 +#185 := [monotonicity #182]: #184 +#190 := [trans #185 #188]: #189 +#146 := (iff #29 #143) +#140 := (= #130 0::Int) +#144 := (iff #140 #143) +#145 := [rewrite]: #144 +#141 := (iff #29 #140) +#138 := (= #28 #130) +#133 := (ite false #13 #130) +#136 := (= #133 #130) +#137 := [rewrite]: #136 +#134 := (= #28 #133) +#131 := (= #27 #130) +#128 := (= #26 #127) +#125 := (= #25 #122) +#119 := (- #116) +#123 := (= #119 #122) +#124 := [rewrite]: #123 +#120 := (= #25 #119) +#117 := (= #24 #116) +#114 := (= #23 -2::Int) +#115 := [rewrite]: #114 +#111 := (= #22 #110) +#112 := [rewrite]: #111 +#118 := [monotonicity #112 #115]: #117 +#121 := [monotonicity #118]: #120 +#126 := [trans #121 #124]: #125 +#105 := (iff #20 #104) +#102 := (iff #19 #101) +#103 := [rewrite]: #102 +#106 := [monotonicity #103]: #105 +#129 := [monotonicity #106 #126]: #128 +#99 := (iff #14 #98) +#100 := [rewrite]: #99 +#132 := [monotonicity #100 #129]: #131 +#96 := (iff #10 false) +#97 := [rewrite]: #96 +#135 := [monotonicity #97 #132]: #134 +#139 := [trans #135 #137]: #138 +#142 := [monotonicity #139]: #141 +#147 := [trans #142 #145]: #146 +#192 := [trans #147 #190]: #191 +#95 := [asserted]: #29 +#193 := [mp #95 #192]: #187 +#757 := (= #21 #180) +#475 := (= #177 #180) +#489 := (not #14) +#423 := (>= f4 0::Int) +#424 := (not #423) +#412 := (<= f4 0::Int) +#413 := (not #412) +#434 := (or #413 #424) +#534 := (not #434) +#58 := 1::Int +#66 := (mod f4 2::Int) +#834 := (>= #66 1::Int) +#837 := (not #834) +#904 := (= #66 1::Int) +#957 := (not #904) +#345 := (mod #109 -2::Int) +#351 := (* -1::Int #345) +#437 := (ite #434 #66 #351) +#60 := (= f4 0::Int) +#440 := (ite #60 0::Int #437) +#447 := (= #440 1::Int) +#468 := (not #447) +#958 := (iff #468 #957) +#955 := (iff #447 #904) +#953 := (iff #904 #447) +#951 := (= #66 #440) +#527 := (= #437 #440) +#541 := (not #60) +#552 := [hypothesis]: #434 +#895 := (or #541 #534) +#558 := [hypothesis]: #60 +#553 := (or #541 #412) +#554 := [th-lemma arith triangle-eq]: #553 +#555 := [unit-resolution #554 #558]: #412 +#559 := (or #541 #423) +#892 := [th-lemma arith triangle-eq]: #559 +#893 := [unit-resolution #892 #558]: #423 +#535 := (or #534 #413 #424) +#536 := [def-axiom]: #535 +#894 := [unit-resolution #536 #893 #555 #552]: false +#896 := [lemma #894]: #895 +#947 := [unit-resolution #896 #552]: #541 +#544 := (or #60 #527) +#545 := [def-axiom]: #544 +#948 := [unit-resolution #545 #947]: #527 +#528 := (= #66 #437) +#537 := (or #534 #528) +#538 := [def-axiom]: #537 +#946 := [unit-resolution #538 #552]: #528 +#952 := [trans #946 #948]: #951 +#954 := [monotonicity #952]: #953 +#956 := [symm #954]: #955 +#959 := [monotonicity #956]: #958 +#299 := (mod #108 -2::Int) +#305 := (* -1::Int #299) +#52 := (mod f3 2::Int) +#396 := (ite #269 #52 #305) +#399 := (ite #32 0::Int #396) +#406 := (= #399 1::Int) +#708 := (>= #52 1::Int) +#669 := (div f3 2::Int) +#683 := (* -2::Int #669) +#682 := (* -1::Int #52) +#684 := (+ #682 #683) +#685 := (+ f3 #684) +#556 := (<= #685 0::Int) +#681 := (= #685 0::Int) +#551 := (or false #681) +#560 := [th-lemma arith]: #551 +#561 := [unit-resolution #560 #93]: #681 +#874 := (not #681) +#875 := (or #874 #556) +#876 := [th-lemma arith triangle-eq]: #875 +#877 := [unit-resolution #876 #561]: #556 +#557 := (>= #685 0::Int) +#878 := (or #874 #557) +#879 := [th-lemma arith triangle-eq]: #878 +#880 := [unit-resolution #879 #561]: #557 +#716 := (not #708) +#717 := [hypothesis]: #716 +#692 := (>= #52 0::Int) +#718 := (or false #692) +#719 := [th-lemma arith]: #718 +#720 := [unit-resolution #719 #93]: #692 +#890 := [th-lemma arith gcd-test 1/4 1/4 1/4 1/4 -1/4 -1/4 -1/4 -1/4 #889 #733 #730 #727 #720 #717 #880 #877]: false +#891 := [lemma #890]: #708 +#938 := (or #406 #716) +#515 := (= #396 #399) +#524 := (or #32 #515) +#525 := [def-axiom]: #524 +#936 := [unit-resolution #525 #831]: #515 +#516 := (= #52 #396) +#518 := (or #502 #516) +#519 := [def-axiom]: #518 +#937 := [unit-resolution #519 #866]: #516 +#785 := (not #516) +#784 := (not #515) +#803 := (or #406 #784 #785 #716) +#690 := (= #52 1::Int) +#707 := (<= #52 1::Int) +#788 := (not #707) +#789 := [hypothesis]: #788 +#698 := (>= #52 2::Int) +#699 := (not #698) +#790 := (or false #699) +#791 := [th-lemma arith]: #790 +#792 := [unit-resolution #791 #93]: #699 +#793 := [th-lemma arith farkas 1 1 #792 #789]: false +#794 := [lemma #793]: #707 +#797 := [hypothesis]: #708 +#798 := (or #690 #788 #716) +#799 := [th-lemma arith triangle-eq]: #798 +#800 := [unit-resolution #799 #797 #794]: #690 +#780 := (= #399 #52) +#778 := (= #396 #52) +#774 := [hypothesis]: #516 +#779 := [symm #774]: #778 +#776 := (= #399 #396) +#775 := [hypothesis]: #515 +#777 := [symm #775]: #776 +#781 := [trans #777 #779]: #780 +#801 := [trans #781 #800]: #406 +#467 := (not #406) +#796 := [hypothesis]: #467 +#802 := [unit-resolution #796 #801]: false +#804 := [lemma #802]: #803 +#939 := [unit-resolution #804 #937 #936]: #938 +#944 := [unit-resolution #939 #891]: #406 +#461 := (or #467 #468) +#451 := (and #406 #447) +#454 := (not #451) +#472 := (iff #454 #461) +#462 := (not #461) +#463 := (not #462) +#470 := (iff #463 #461) +#471 := [rewrite]: #470 +#464 := (iff #454 #463) +#465 := (iff #451 #462) +#466 := [rewrite]: #465 +#469 := [monotonicity #466]: #464 +#473 := [trans #469 #471]: #472 +#67 := (- f4) +#68 := (mod #67 #23) +#69 := (- #68) +#63 := (< f4 0::Int) +#64 := (and #63 #16) +#61 := (< 0::Int f4) +#62 := (and #61 #16) +#65 := (or #62 #64) +#70 := (ite #65 #66 #69) +#71 := (ite #60 0::Int #70) +#72 := (ite #10 f4 #71) +#73 := (= #72 1::Int) +#53 := (mod #40 #23) +#54 := (- #53) +#50 := (and #36 #16) +#49 := (and #33 #16) +#51 := (or #49 #50) +#55 := (ite #51 #52 #54) +#56 := (ite #32 0::Int #55) +#57 := (ite #10 f3 #56) +#59 := (= #57 1::Int) +#74 := (and #59 #73) +#75 := (not #74) +#457 := (iff #75 #454) +#337 := (and #16 #63) +#334 := (and #16 #61) +#340 := (or #334 #337) +#356 := (ite #340 #66 #351) +#331 := (= 0::Int f4) +#359 := (ite #331 0::Int #356) +#372 := (= 1::Int #359) +#293 := (and #16 #36) +#290 := (and #16 #33) +#296 := (or #290 #293) +#310 := (ite #296 #52 #305) +#313 := (ite #197 0::Int #310) +#326 := (= 1::Int #313) +#377 := (and #326 #372) +#380 := (not #377) +#455 := (iff #380 #454) +#452 := (iff #377 #451) +#449 := (iff #372 #447) +#443 := (= 1::Int #440) +#446 := (iff #443 #447) +#448 := [rewrite]: #446 +#444 := (iff #372 #443) +#441 := (= #359 #440) +#438 := (= #356 #437) +#435 := (iff #340 #434) +#432 := (iff #337 #424) +#427 := (and true #424) +#430 := (iff #427 #424) +#431 := [rewrite]: #430 +#428 := (iff #337 #427) +#425 := (iff #63 #424) +#426 := [rewrite]: #425 +#429 := [monotonicity #155 #426]: #428 +#433 := [trans #429 #431]: #432 +#421 := (iff #334 #413) +#416 := (and true #413) +#419 := (iff #416 #413) +#420 := [rewrite]: #419 +#417 := (iff #334 #416) +#414 := (iff #61 #413) +#415 := [rewrite]: #414 +#418 := [monotonicity #155 #415]: #417 +#422 := [trans #418 #420]: #421 +#436 := [monotonicity #422 #433]: #435 #439 := [monotonicity #436]: #438 -#450 := (iff #463 #670) -#448 := (iff #471 #701) -#444 := (iff #471 #684) -#435 := [monotonicity #421]: #444 -#449 := [trans #435 #687]: #448 -#451 := [monotonicity #449]: #450 -#502 := [monotonicity #451 #439]: #501 -#418 := [monotonicity #502 #487]: #488 -#415 := [monotonicity #418]: #414 -#404 := [monotonicity #772 #415]: #416 -#405 := [trans #404 #407]: #410 -#396 := [monotonicity #405]: #391 -#401 := [trans #396 #399]: #391 -#390 := [quant-inst #8 #11]: #386 -#397 := [mp #390 #401]: #411 -#1069 := [unit-resolution #397 #796]: #420 -#379 := (not #420) -#1072 := (or #379 #478) -#373 := (or #379 #689 #478) -#374 := [def-axiom]: #373 -#1073 := [unit-resolution #374 #1043]: #1072 -#1074 := [unit-resolution #1073 #1069]: #478 -#392 := (not #478) -#393 := (or #392 #635 #477) -#394 := [def-axiom]: #393 -#1075 := [unit-resolution #394 #1045 #1074]: #477 -#380 := (not #477) -#1076 := (or #380 #385) -#1077 := [th-lemma arith triangle-eq]: #1076 -#1078 := [unit-resolution #1077 #1075]: #385 -#801 := (>= #19 1::Int) -#1015 := (not #801) -#800 := (<= #19 1::Int) -#946 := (>= #483 2::Int) -#947 := (not #946) -#1079 := (or false #947) -#1080 := [th-lemma arith]: #1079 -#1081 := [unit-resolution #1080 #72]: #947 -#402 := (<= #485 0::Int) -#1082 := (or #380 #402) -#1083 := [th-lemma arith triangle-eq]: #1082 -#1084 := [unit-resolution #1083 #1075]: #402 -#1085 := (not #402) -#1086 := (or #800 #946 #1085) -#1087 := [th-lemma arith assign-bounds 1 1]: #1086 -#1088 := [unit-resolution #1087 #1084 #1081]: #800 -#1090 := (not #800) -#1093 := (or #1090 #1015) -#218 := (not #21) -#1089 := [hypothesis]: #218 -#1091 := (or #21 #1090 #1015) -#1092 := [th-lemma arith triangle-eq]: #1091 -#1094 := [unit-resolution #1092 #1089]: #1093 -#1095 := [unit-resolution #1094 #1088]: #1015 -#1096 := [th-lemma arith farkas -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1 #995 #998 #1095 #1078 #1068 #1056 #1053]: false -#1098 := [lemma #1096]: #1097 -#1264 := [unit-resolution #1098 #914]: #21 -#230 := (or #218 #219) -#24 := (and #21 #23) -#25 := (not #24) -#239 := (iff #25 #230) -#231 := (not #230) -#234 := (not #231) -#237 := (iff #234 #230) -#238 := [rewrite]: #237 -#235 := (iff #25 #234) -#232 := (iff #24 #231) -#233 := [rewrite]: #232 -#236 := [monotonicity #233]: #235 -#240 := [trans #236 #238]: #239 -#76 := [asserted]: #25 -#241 := [mp #76 #240]: #230 -#1265 := [unit-resolution #241 #1264]: #219 -#1267 := (or #23 #1266 #1152) -#1268 := [th-lemma arith triangle-eq]: #1267 -#1270 := [unit-resolution #1268 #1265]: #1269 -#1271 := [unit-resolution #1270 #1263]: #1152 -#1192 := (not #955) -#1194 := (or #1191 #1192 #1193 #1104) -#1153 := [hypothesis]: #1152 -#1132 := (<= #1127 0::Int) -#1160 := [unit-resolution #1159 #72]: #1124 -#1162 := (or #1161 #1132) -#1163 := [th-lemma arith triangle-eq]: #1162 -#1164 := [unit-resolution #1163 #1160]: #1132 -#1185 := [hypothesis]: #1179 -#1189 := [hypothesis]: #955 -#1190 := [th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1 #1189 #1188 #1185 #1184 #1183 #1166 #1164 #982 #970 #1153]: false -#1195 := [lemma #1190]: #1194 -#1272 := [unit-resolution #1195 #1271 #1184 #1253]: #1191 -#1273 := [th-lemma arith farkas -2 1 1 1 1 1 1 1 1 #1272 #1237 #1236 #1235 #1232 #998 #995 #1249 #1151]: false -#1275 := [lemma #1273]: #1274 -#1349 := [unit-resolution #1275 #1278]: #1348 -#1350 := [unit-resolution #1349 #1323 #1110]: false -#1351 := [lemma #1350]: #715 -#1281 := (or #778 #457) -#1225 := [hypothesis]: #715 -#752 := (+ #482 #376) -#751 := (mod #752 -2::Int) -#466 := (+ #12 #751) -#746 := (= #466 0::Int) -#770 := (not #461) -#434 := (<= #10 0::Int) -#764 := (not #434) -#479 := (or #764 #770) -#744 := (ite #479 #457 #746) -#618 := (not #778) -#802 := [hypothesis]: #618 -#1243 := (or #778 #744) -#749 := (ite #778 #14 #744) -#585 := (or #584 #749) -#454 := (* -1::Int #10) -#455 := (mod #454 #370) -#456 := (+ #12 #455) -#447 := (= #456 0::Int) -#775 := (or #440 #461) -#777 := (not #775) -#564 := (or #434 #440) -#771 := (not #564) -#445 := (or #771 #777) -#446 := (ite #445 #457 #447) -#779 := (ite #778 #14 #446) -#780 := (= #10 #12) -#776 := (ite #781 #780 #779) -#586 := (or #584 #776) -#729 := (iff #586 #585) -#731 := (iff #585 #585) -#725 := [rewrite]: #731 -#737 := (iff #776 #749) -#432 := (* -1::Int #12) -#437 := (+ f5 #432) -#773 := (+ f4 #437) -#433 := (= #773 0::Int) -#740 := (ite false #433 #749) -#741 := (iff #740 #749) -#742 := [rewrite]: #741 -#735 := (iff #776 #740) -#738 := (iff #779 #749) -#748 := (iff #446 #744) -#747 := (iff #447 #746) -#467 := (= #456 #466) -#755 := (= #455 #751) -#753 := (= #454 #752) -#475 := [rewrite]: #753 -#465 := [monotonicity #475 #754]: #755 -#468 := [monotonicity #465]: #467 -#462 := [monotonicity #468]: #747 -#480 := (iff #445 #479) -#756 := (iff #777 #770) -#769 := (iff #775 #461) -#403 := (or false #461) -#408 := (iff #403 #461) -#409 := [rewrite]: #408 -#766 := (iff #775 #403) -#768 := [monotonicity #421]: #766 -#767 := [trans #768 #409]: #769 -#757 := [monotonicity #767]: #756 -#759 := (iff #771 #764) -#762 := (iff #564 #434) -#422 := (or #434 false) -#760 := (iff #422 #434) -#761 := [rewrite]: #760 -#423 := (iff #564 #422) -#424 := [monotonicity #421]: #423 -#763 := [trans #424 #761]: #762 -#765 := [monotonicity #763]: #759 -#481 := [monotonicity #765 #757]: #480 -#745 := [monotonicity #481 #462]: #748 -#739 := [monotonicity #745]: #738 -#774 := (iff #780 #433) -#417 := [rewrite]: #774 -#736 := [monotonicity #772 #417 #739]: #735 -#743 := [trans #736 #742]: #737 -#730 := [monotonicity #743]: #729 -#726 := [trans #730 #725]: #729 -#728 := [quant-inst #10 #11]: #586 -#732 := [mp #728 #726]: #585 -#1242 := [unit-resolution #732 #796]: #749 -#616 := (not #749) -#620 := (or #616 #778 #744) -#621 := [def-axiom]: #620 -#1244 := [unit-resolution #621 #1242]: #1243 -#1245 := [unit-resolution #1244 #802]: #744 -#809 := (or #479 #778) -#565 := (not #479) -#803 := [hypothesis]: #565 -#733 := (or #479 #434) -#727 := [def-axiom]: #733 -#804 := [unit-resolution #727 #803]: #434 -#734 := (or #479 #461) -#563 := [def-axiom]: #734 -#805 := [unit-resolution #563 #803]: #461 -#806 := (or #778 #764 #770) -#807 := [th-lemma arith triangle-eq]: #806 -#808 := [unit-resolution #807 #805 #804 #802]: false -#810 := [lemma #808]: #809 -#1279 := [unit-resolution #810 #802]: #479 -#724 := (not #744) -#606 := (or #724 #565 #457) -#607 := [def-axiom]: #606 -#1280 := [unit-resolution #607 #1279 #1245 #1225]: false -#1282 := [lemma #1280]: #1281 -#1352 := [unit-resolution #1282 #1351]: #778 -#1353 := (or #618 #461) -#1354 := [th-lemma arith triangle-eq]: #1353 -#1355 := [unit-resolution #1354 #1352]: #461 -#1356 := (or #618 #434) -#1357 := [th-lemma arith triangle-eq]: #1356 -#1358 := [unit-resolution #1357 #1352]: #434 -#1346 := (or #577 #770 #764) -#1295 := [hypothesis]: #434 -#1327 := (or #526 #764 #701) -#1005 := [hypothesis]: #670 -#1289 := [hypothesis]: #578 -#1291 := [th-lemma arith farkas -1 1 1 #1295 #1289 #1005]: false -#1328 := [lemma #1291]: #1327 -#1342 := [unit-resolution #1328 #1209 #1295]: #701 -#1343 := [unit-resolution #864 #1043]: #659 -#1344 := [unit-resolution #1343 #1342]: #669 -#1290 := [hypothesis]: #461 -#1345 := [th-lemma arith farkas -1 1 1 #1290 #1344 #1229]: false -#1347 := [lemma #1345]: #1346 -#1359 := [unit-resolution #1347 #1358 #1355]: #577 -#1360 := [unit-resolution #1255 #1359]: #954 -#1361 := (or #1103 #1260) -#1302 := [hypothesis]: #1140 -#1308 := [unit-resolution #1258 #72 #1302]: false -#1321 := [lemma #1308]: #1141 -#1362 := [unit-resolution #1262 #1321]: #1361 -#1363 := [unit-resolution #1362 #1360]: #1103 -#1303 := (+ #698 #1171) -#1326 := (+ #575 #1303) -#1335 := (+ #16 #1326) -#1336 := (+ f5 #1335) -#1337 := (+ f4 #1336) -#1338 := (>= #1337 2::Int) -#1329 := (not #1338) -#1330 := (or #1329 #764) -#1294 := [unit-resolution #1163 #1278]: #1132 -#1310 := [hypothesis]: #1338 -#1309 := [th-lemma arith farkas 2 -1 -1 -1 -1 -1 1 #1310 #1295 #1166 #982 #970 #1294 #1151]: false -#1331 := [lemma #1309]: #1330 -#1364 := [unit-resolution #1331 #1358]: #1329 -#1365 := [unit-resolution #1252 #1359]: #955 -#1340 := (or #1192 #1338 #770 #1104) -#1332 := [unit-resolution #1248 #1278]: #1224 -#1325 := [th-lemma arith #1290 #1153 #1189 #1236 #998 #995 #1332]: #1338 -#1324 := [hypothesis]: #1329 -#1339 := [unit-resolution #1324 #1325]: false -#1341 := [lemma #1339]: #1340 -#1366 := [unit-resolution #1341 #1365 #1355 #1364]: #1104 -[unit-resolution #1270 #1366 #1363]: false +#410 := (iff #331 #60) +#411 := [rewrite]: #410 +#442 := [monotonicity #411 #439]: #441 +#445 := [monotonicity #442]: #444 +#450 := [trans #445 #448]: #449 +#408 := (iff #326 #406) +#402 := (= 1::Int #399) +#405 := (iff #402 #406) +#407 := [rewrite]: #405 +#403 := (iff #326 #402) +#400 := (= #313 #399) +#397 := (= #310 #396) +#394 := (iff #296 #269) +#392 := (iff #293 #259) +#390 := (iff #293 #262) +#391 := [monotonicity #155 #261]: #390 +#393 := [trans #391 #266]: #392 +#388 := (iff #290 #246) +#383 := (and true #246) +#386 := (iff #383 #246) +#387 := [rewrite]: #386 +#384 := (iff #290 #383) +#385 := [monotonicity #155 #248]: #384 +#389 := [trans #385 #387]: #388 +#395 := [monotonicity #389 #393]: #394 +#398 := [monotonicity #395]: #397 +#401 := [monotonicity #244 #398]: #400 +#404 := [monotonicity #401]: #403 +#409 := [trans #404 #407]: #408 +#453 := [monotonicity #409 #450]: #452 +#456 := [monotonicity #453]: #455 +#381 := (iff #75 #380) +#378 := (iff #74 #377) +#375 := (iff #73 #372) +#369 := (= #359 1::Int) +#373 := (iff #369 #372) +#374 := [rewrite]: #373 +#370 := (iff #73 #369) +#367 := (= #72 #359) +#362 := (ite false f4 #359) +#365 := (= #362 #359) +#366 := [rewrite]: #365 +#363 := (= #72 #362) +#360 := (= #71 #359) +#357 := (= #70 #356) +#354 := (= #69 #351) +#348 := (- #345) +#352 := (= #348 #351) +#353 := [rewrite]: #352 +#349 := (= #69 #348) +#346 := (= #68 #345) +#343 := (= #67 #109) +#344 := [rewrite]: #343 +#347 := [monotonicity #344 #115]: #346 +#350 := [monotonicity #347]: #349 +#355 := [trans #350 #353]: #354 +#341 := (iff #65 #340) +#338 := (iff #64 #337) +#339 := [rewrite]: #338 +#335 := (iff #62 #334) +#336 := [rewrite]: #335 +#342 := [monotonicity #336 #339]: #341 +#358 := [monotonicity #342 #355]: #357 +#332 := (iff #60 #331) +#333 := [rewrite]: #332 +#361 := [monotonicity #333 #358]: #360 +#364 := [monotonicity #97 #361]: #363 +#368 := [trans #364 #366]: #367 +#371 := [monotonicity #368]: #370 +#376 := [trans #371 #374]: #375 +#329 := (iff #59 #326) +#323 := (= #313 1::Int) +#327 := (iff #323 #326) +#328 := [rewrite]: #327 +#324 := (iff #59 #323) +#321 := (= #57 #313) +#316 := (ite false f3 #313) +#319 := (= #316 #313) +#320 := [rewrite]: #319 +#317 := (= #57 #316) +#314 := (= #56 #313) +#311 := (= #55 #310) +#308 := (= #54 #305) +#302 := (- #299) +#306 := (= #302 #305) +#307 := [rewrite]: #306 +#303 := (= #54 #302) +#300 := (= #53 #299) +#301 := [monotonicity #207 #115]: #300 +#304 := [monotonicity #301]: #303 +#309 := [trans #304 #307]: #308 +#297 := (iff #51 #296) +#294 := (iff #50 #293) +#295 := [rewrite]: #294 +#291 := (iff #49 #290) +#292 := [rewrite]: #291 +#298 := [monotonicity #292 #295]: #297 +#312 := [monotonicity #298 #309]: #311 +#315 := [monotonicity #199 #312]: #314 +#318 := [monotonicity #97 #315]: #317 +#322 := [trans #318 #320]: #321 +#325 := [monotonicity #322]: #324 +#330 := [trans #325 #328]: #329 +#379 := [monotonicity #330 #376]: #378 +#382 := [monotonicity #379]: #381 +#458 := [trans #382 #456]: #457 +#289 := [asserted]: #75 +#459 := [mp #289 #458]: #454 +#474 := [mp #459 #473]: #461 +#945 := [unit-resolution #474 #944]: #468 +#960 := [mp #945 #959]: #957 +#963 := (or #904 #837) +#833 := (<= #66 1::Int) +#858 := (not #833) +#859 := [hypothesis]: #858 +#821 := (>= #66 2::Int) +#822 := (not #821) +#860 := (or false #822) +#861 := [th-lemma arith]: #860 +#862 := [unit-resolution #861 #93]: #822 +#863 := [th-lemma arith farkas 1 1 #862 #859]: false +#864 := [lemma #863]: #833 +#961 := (or #904 #858 #837) +#962 := [th-lemma arith triangle-eq]: #961 +#964 := [unit-resolution #962 #864]: #963 +#965 := [unit-resolution #964 #960]: #837 +#909 := (or #151 #834) +#906 := [hypothesis]: #150 +#838 := [hypothesis]: #837 +#931 := (or #163 #834) +#705 := (div f4 2::Int) +#806 := (* -2::Int #705) +#805 := (* -1::Int #66) +#807 := (+ #805 #806) +#808 := (+ f4 #807) +#897 := (<= #808 0::Int) +#795 := (= #808 0::Int) +#911 := (or false #795) +#913 := [th-lemma arith]: #911 +#914 := [unit-resolution #913 #93]: #795 +#915 := (not #795) +#916 := (or #915 #897) +#917 := [th-lemma arith triangle-eq]: #916 +#918 := [unit-resolution #917 #914]: #897 +#898 := (>= #808 0::Int) +#919 := (or #915 #898) +#920 := [th-lemma arith triangle-eq]: #919 +#921 := [unit-resolution #920 #914]: #898 +#815 := (>= #66 0::Int) +#839 := (or false #815) +#840 := [th-lemma arith]: #839 +#841 := [unit-resolution #840 #93]: #815 +#922 := [hypothesis]: #164 +#751 := (or #489 #163) +#752 := [th-lemma arith triangle-eq]: #751 +#923 := [unit-resolution #752 #922]: #489 +#492 := (or #14 #475) +#493 := [def-axiom]: #492 +#924 := [unit-resolution #493 #923]: #475 +#476 := (= #21 #177) +#480 := (or #174 #163) +#481 := [def-axiom]: #480 +#925 := [unit-resolution #481 #922]: #174 +#482 := (not #174) +#485 := (or #482 #476) +#486 := [def-axiom]: #485 +#926 := [unit-resolution #486 #925]: #476 +#927 := [trans #926 #924]: #757 +#928 := [trans #927 #193]: #709 +#760 := (not #709) +#761 := (or #760 #710) +#762 := [th-lemma arith triangle-eq]: #761 +#929 := [unit-resolution #762 #928]: #710 +#641 := (>= #21 0::Int) +#764 := (or false #641) +#765 := [th-lemma arith]: #764 +#766 := [unit-resolution #765 #93]: #641 +#930 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #766 #929 #744 #741 #889 #733 #730 #727 #841 #838 #921 #918]: false +#932 := [lemma #930]: #931 +#907 := [unit-resolution #932 #838]: #163 +#908 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 1/2 1/2 1/2 1/2 #841 #838 #921 #918 #907 #906 #889 #733 #730 #727]: false +#910 := [lemma #908]: #909 +#966 := [unit-resolution #910 #965]: #151 +#967 := (or #489 #150) +#968 := [th-lemma arith triangle-eq]: #967 +#969 := [unit-resolution #968 #966]: #489 +#970 := [unit-resolution #493 #969]: #475 +#478 := (or #174 #150) +#479 := [def-axiom]: #478 +#971 := [unit-resolution #479 #966]: #174 +#972 := [unit-resolution #486 #971]: #476 +#973 := [trans #972 #970]: #757 +#974 := [trans #973 #193]: #709 +#975 := [unit-resolution #762 #974]: #710 +#976 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 #841 #965 #921 #918 #889 #733 #730 #727 #766 #975 #744 #741]: false +#977 := [lemma #976]: #534 +#532 := (or #434 #423) +#533 := [def-axiom]: #532 +#836 := [unit-resolution #533 #977]: #423 +#845 := (or #434 #258) +#769 := (not #613) +#770 := (or #434 #769 #258) +#734 := [hypothesis]: #613 +#745 := [hypothesis]: #259 +#746 := [hypothesis]: #534 +#530 := (or #434 #412) +#531 := [def-axiom]: #530 +#747 := [unit-resolution #531 #746]: #412 +#748 := (or #164 #258 #413) +#749 := [th-lemma arith assign-bounds -1 -1]: #748 +#750 := [unit-resolution #749 #747 #745]: #164 +#753 := [unit-resolution #752 #750]: #489 +#754 := [unit-resolution #493 #753]: #475 +#755 := [unit-resolution #481 #750]: #174 +#756 := [unit-resolution #486 #755]: #476 +#758 := [trans #756 #754]: #757 +#759 := [trans #758 #193]: #709 +#763 := [unit-resolution #762 #759]: #710 +#767 := [unit-resolution #533 #746]: #423 +#768 := [th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #767 #747 #766 #763 #744 #741 #734 #733 #730 #727]: false +#771 := [lemma #768]: #770 +#846 := [unit-resolution #771 #889]: #845 +#847 := [unit-resolution #846 #977]: #258 +#503 := (or #502 #246 #259) +#504 := [def-axiom]: #503 +#844 := [unit-resolution #504 #866]: #269 +#848 := [unit-resolution #844 #847]: #246 +#849 := (or #151 #424 #245) +#850 := [th-lemma arith assign-bounds -1 -1]: #849 +#851 := [unit-resolution #850 #848 #836]: #151 +#842 := [unit-resolution #968 #851]: #489 +#843 := [unit-resolution #493 #842]: #475 +#852 := [unit-resolution #479 #851]: #174 +#853 := [unit-resolution #486 #852]: #476 +#854 := [trans #853 #843]: #757 +#855 := [trans #854 #193]: #709 +#856 := [unit-resolution #762 #855]: #710 +#857 := [unit-resolution #531 #977]: #412 +[th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #836 #857 #766 #856 #744 #741 #889 #733 #730 #727]: false unsat c04d38458726eb1b2cafd52bd3881d6f8160666f 24 0 #2 := false @@ -10440,288 +10061,318 @@ unsat ERROR: line 11 column 83: invalid pattern. -8f616b17d0807409dc26bfdf9593c5fcd06fb7e7 1 0 -unsat -3eb9cf11ee8774c9212c37c265e7552f3b8f24a9 75 0 -#2 := false -#10 := 1::Int -decl f5 :: Int -#12 := f5 -#16 := (+ f5 1::Int) -decl f3 :: Int -#8 := f3 -#17 := (* f3 #16) -decl f4 :: Int -#9 := f4 -#15 := (* f3 f4) -#18 := (+ #15 #17) -#11 := (+ f4 1::Int) -#13 := (+ #11 f5) -#14 := (* f3 #13) -#19 := (= #14 #18) -#20 := (not #19) -#93 := (iff #20 false) -#1 := true -#88 := (not true) -#91 := (iff #88 false) -#92 := [rewrite]: #91 -#89 := (iff #20 #88) -#86 := (iff #19 true) -#56 := (* f3 f5) -#57 := (+ #15 #56) -#58 := (+ f3 #57) -#81 := (= #58 #58) -#84 := (iff #81 true) -#85 := [rewrite]: #84 -#82 := (iff #19 #81) -#79 := (= #18 #58) -#69 := (+ f3 #56) -#74 := (+ #15 #69) -#77 := (= #74 #58) -#78 := [rewrite]: #77 -#75 := (= #18 #74) -#72 := (= #17 #69) -#63 := (+ 1::Int f5) -#66 := (* f3 #63) -#70 := (= #66 #69) -#71 := [rewrite]: #70 -#67 := (= #17 #66) -#64 := (= #16 #63) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#73 := [trans #68 #71]: #72 -#76 := [monotonicity #73]: #75 -#80 := [trans #76 #78]: #79 -#61 := (= #14 #58) -#47 := (+ f4 f5) -#48 := (+ 1::Int #47) -#53 := (* f3 #48) -#59 := (= #53 #58) -#60 := [rewrite]: #59 -#54 := (= #14 #53) -#51 := (= #13 #48) -#41 := (+ 1::Int f4) -#44 := (+ #41 f5) -#49 := (= #44 #48) -#50 := [rewrite]: #49 -#45 := (= #13 #44) -#42 := (= #11 #41) -#43 := [rewrite]: #42 -#46 := [monotonicity #43]: #45 -#52 := [trans #46 #50]: #51 -#55 := [monotonicity #52]: #54 -#62 := [trans #55 #60]: #61 -#83 := [monotonicity #62 #80]: #82 -#87 := [trans #83 #85]: #86 -#90 := [monotonicity #87]: #89 -#94 := [trans #90 #92]: #93 -#40 := [asserted]: #20 -[mp #40 #94]: false -unsat -741a564e40e4b6610d1d47bdab19a223e004482a 62 0 +8aba3814871680009d1d0267516334493c303e78 175 0 #2 := false -decl f4 :: Real -#10 := f4 -decl f3 :: Real -#8 := f3 -#16 := 2::Real -#17 := (* 2::Real f3) -#18 := (* #17 f4) -#9 := 1::Real -#13 := (- 1::Real f4) -#14 := (* f3 #13) -#11 := (+ 1::Real f4) -#12 := (* f3 #11) -#15 := (- #12 #14) -#19 := (= #15 #18) -#20 := (not #19) -#81 := (iff #20 false) -#1 := true -#76 := (not true) -#79 := (iff #76 false) -#80 := [rewrite]: #79 -#77 := (iff #20 #76) -#74 := (iff #19 true) -#41 := (* f3 f4) -#63 := (* 2::Real #41) -#69 := (= #63 #63) -#72 := (iff #69 true) -#73 := [rewrite]: #72 -#70 := (iff #19 #69) -#67 := (= #18 #63) -#68 := [rewrite]: #67 -#65 := (= #15 #63) -#45 := -1::Real -#53 := (* -1::Real #41) -#54 := (+ f3 #53) -#42 := (+ f3 #41) -#59 := (- #42 #54) -#62 := (= #59 #63) -#64 := [rewrite]: #62 -#60 := (= #15 #59) -#57 := (= #14 #54) -#46 := (* -1::Real f4) -#47 := (+ 1::Real #46) -#50 := (* f3 #47) -#55 := (= #50 #54) -#56 := [rewrite]: #55 -#51 := (= #14 #50) -#48 := (= #13 #47) -#49 := [rewrite]: #48 -#52 := [monotonicity #49]: #51 -#58 := [trans #52 #56]: #57 -#43 := (= #12 #42) -#44 := [rewrite]: #43 -#61 := [monotonicity #44 #58]: #60 -#66 := [trans #61 #64]: #65 -#71 := [monotonicity #66 #68]: #70 -#75 := [trans #71 #73]: #74 -#78 := [monotonicity #75]: #77 -#82 := [trans #78 #80]: #81 -#40 := [asserted]: #20 -[mp #40 #82]: false -unsat -06d1bd5308956fb019ef1c09bf97c6326d872fd6 141 0 -#2 := false -decl f6 :: Int -#13 := f6 -decl f7 :: Int -#17 := f7 -decl f5 :: Int -#12 := f5 -#28 := (+ f5 f7) -#29 := (+ #28 f6) +#8 := 0::Int decl f4 :: Int -#10 := f4 -#9 := 1::Int -#11 := (+ 1::Int f4) -#30 := (* #11 #29) -#25 := (* f7 f4) -#23 := (* #11 f7) -#14 := (+ f5 f6) -#20 := 2::Int -#21 := (* 2::Int #11) -#22 := (* #21 #14) -#24 := (+ #22 #23) -#26 := (+ #24 #25) -decl f3 :: Int -#8 := f3 -#27 := (+ f3 #26) -#31 := (- #27 #30) -#18 := (* f4 f7) -#15 := (* #11 #14) -#16 := (+ f3 #15) -#19 := (+ #16 #18) -#32 := (= #19 #31) -#33 := (not #32) -#157 := (iff #33 false) -#1 := true -#152 := (not true) -#155 := (iff #152 false) -#156 := [rewrite]: #155 -#153 := (iff #33 #152) -#150 := (iff #32 true) -#55 := (* f4 f6) -#54 := (* f4 f5) +#18 := f4 +#138 := (<= f4 0::Int) +#139 := (not #138) +decl f5 :: Int +#20 := f5 +#134 := (<= f5 0::Int) +#135 := (not #134) +decl f3 :: (-> Int Int Int) +#21 := (f3 f4 f5) +#123 := (<= #21 0::Int) +#155 := (or #123 #135 #138) +#160 := (not #155) +#23 := (< 0::Int f5) +#22 := (< 0::Int #21) +#24 := (implies #22 #23) +#19 := (< 0::Int f4) +#25 := (implies #19 #24) +#26 := (not #25) +#163 := (iff #26 #160) +#107 := (not #22) +#108 := (or #107 #23) +#114 := (not #19) +#115 := (or #114 #108) +#120 := (not #115) +#161 := (iff #120 #160) +#158 := (iff #115 #155) +#149 := (or #123 #135) +#152 := (or #138 #149) +#156 := (iff #152 #155) +#157 := [rewrite]: #156 +#153 := (iff #115 #152) +#150 := (iff #108 #149) +#136 := (iff #23 #135) +#137 := [rewrite]: #136 +#132 := (iff #107 #123) +#124 := (not #123) +#127 := (not #124) +#130 := (iff #127 #123) +#131 := [rewrite]: #130 +#128 := (iff #107 #127) +#125 := (iff #22 #124) +#126 := [rewrite]: #125 +#129 := [monotonicity #126]: #128 +#133 := [trans #129 #131]: #132 +#151 := [monotonicity #133 #137]: #150 +#147 := (iff #114 #138) +#142 := (not #139) +#145 := (iff #142 #138) +#146 := [rewrite]: #145 +#143 := (iff #114 #142) +#140 := (iff #19 #139) +#141 := [rewrite]: #140 +#144 := [monotonicity #141]: #143 +#148 := [trans #144 #146]: #147 +#154 := [monotonicity #148 #151]: #153 +#159 := [trans #154 #157]: #158 +#162 := [monotonicity #159]: #161 +#121 := (iff #26 #120) +#118 := (iff #25 #115) +#111 := (implies #19 #108) +#116 := (iff #111 #115) +#117 := [rewrite]: #116 +#112 := (iff #25 #111) +#109 := (iff #24 #108) +#110 := [rewrite]: #109 +#113 := [monotonicity #110]: #112 +#119 := [trans #113 #117]: #118 +#122 := [monotonicity #119]: #121 +#164 := [trans #122 #162]: #163 +#106 := [asserted]: #26 +#165 := [mp #106 #164]: #160 +#168 := [not-or-elim #165]: #139 +#167 := [not-or-elim #165]: #134 +#166 := [not-or-elim #165]: #124 +#10 := (:var 0 Int) +#9 := (:var 1 Int) +#11 := (f3 #9 #10) +#647 := (pattern #11) +#78 := (<= #11 0::Int) +#74 := (<= #10 0::Int) +#75 := (not #74) +#63 := (<= #9 0::Int) +#95 := (or #63 #75 #78) +#648 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #647) #95) +#100 := (forall (vars (?v0 Int) (?v1 Int)) #95) +#651 := (iff #100 #648) +#649 := (iff #95 #95) +#650 := [refl]: #649 +#652 := [quant-intro #650]: #651 +#182 := (~ #100 #100) +#180 := (~ #95 #95) +#181 := [refl]: #180 +#183 := [nnf-pos #181]: #182 +#14 := (< 0::Int #10) +#13 := (< 0::Int #9) +#15 := (implies #13 #14) +#12 := (< 0::Int #11) +#16 := (implies #12 #15) +#17 := (forall (vars (?v0 Int) (?v1 Int)) #16) +#103 := (iff #17 #100) +#47 := (not #13) +#48 := (or #47 #14) +#54 := (not #12) +#55 := (or #54 #48) +#60 := (forall (vars (?v0 Int) (?v1 Int)) #55) +#101 := (iff #60 #100) +#98 := (iff #55 #95) +#89 := (or #63 #75) +#92 := (or #78 #89) +#96 := (iff #92 #95) +#97 := [rewrite]: #96 +#93 := (iff #55 #92) +#90 := (iff #48 #89) +#76 := (iff #14 #75) +#77 := [rewrite]: #76 +#72 := (iff #47 #63) +#64 := (not #63) +#67 := (not #64) +#70 := (iff #67 #63) +#71 := [rewrite]: #70 +#68 := (iff #47 #67) +#65 := (iff #13 #64) +#66 := [rewrite]: #65 +#69 := [monotonicity #66]: #68 +#73 := [trans #69 #71]: #72 +#91 := [monotonicity #73 #77]: #90 +#87 := (iff #54 #78) +#79 := (not #78) +#82 := (not #79) +#85 := (iff #82 #78) +#86 := [rewrite]: #85 +#83 := (iff #54 #82) +#80 := (iff #12 #79) +#81 := [rewrite]: #80 +#84 := [monotonicity #81]: #83 +#88 := [trans #84 #86]: #87 +#94 := [monotonicity #88 #91]: #93 +#99 := [trans #94 #97]: #98 +#102 := [quant-intro #99]: #101 +#61 := (iff #17 #60) +#58 := (iff #16 #55) +#51 := (implies #12 #48) +#56 := (iff #51 #55) +#57 := [rewrite]: #56 +#52 := (iff #16 #51) +#49 := (iff #15 #48) +#50 := [rewrite]: #49 +#53 := [monotonicity #50]: #52 +#59 := [trans #53 #57]: #58 +#62 := [quant-intro #59]: #61 +#104 := [trans #62 #102]: #103 +#46 := [asserted]: #17 +#105 := [mp #46 #104]: #100 +#170 := [mp~ #105 #183]: #100 +#653 := [mp #170 #652]: #648 +#319 := (not #648) +#310 := (or #319 #123 #135 #138) +#232 := (or #138 #135 #123) +#321 := (or #319 #232) +#639 := (iff #321 #310) +#250 := (or #319 #155) +#324 := (iff #250 #310) +#303 := [rewrite]: #324 +#323 := (iff #321 #250) +#317 := (iff #232 #155) +#318 := [rewrite]: #317 +#320 := [monotonicity #318]: #323 +#641 := [trans #320 #303]: #639 +#322 := [quant-inst #18 #20]: #321 +#297 := [mp #322 #641]: #310 +[unit-resolution #297 #653 #166 #167 #168]: false +unsat +0db52837dc3c07a6a4d5ca34a945edf7aeac1fdf 136 0 +#2 := false +#58 := 0::Int +decl f3 :: (-> Int Int Int) +decl f6 :: Int +#22 := f6 +#20 := 1::Int +#80 := (+ 1::Int f6) +decl f4 :: Int +#18 := f4 +#83 := (f3 f4 #80) +decl f5 :: Int +#19 := f5 +#71 := (+ f5 f6) +#72 := (+ 1::Int #71) +#77 := (f3 f4 #72) +#53 := -1::Int +#99 := (* -1::Int #77) +#100 := (+ #99 #83) +#25 := (f3 f4 f5) +#101 := (+ #25 #100) +#97 := (= #101 0::Int) +#98 := (not #97) +#26 := (+ f6 1::Int) +#27 := (f3 f4 #26) +#28 := (+ #25 #27) +#21 := (+ f5 1::Int) +#23 := (+ #21 f6) +#24 := (f3 f4 #23) +#29 := (= #24 #28) +#30 := (not #29) +#104 := (iff #30 #98) +#86 := (+ #25 #83) +#89 := (= #77 #86) +#92 := (not #89) +#102 := (iff #92 #98) +#96 := (iff #89 #97) +#95 := [rewrite]: #96 +#103 := [monotonicity #95]: #102 +#93 := (iff #30 #92) +#90 := (iff #29 #89) +#87 := (= #28 #86) +#84 := (= #27 #83) +#81 := (= #26 #80) +#82 := [rewrite]: #81 +#85 := [monotonicity #82]: #84 +#88 := [monotonicity #85]: #87 +#78 := (= #24 #77) +#75 := (= #23 #72) +#52 := (+ 1::Int f5) +#68 := (+ #52 f6) +#73 := (= #68 #72) +#74 := [rewrite]: #73 +#69 := (= #23 #68) +#66 := (= #21 #52) +#67 := [rewrite]: #66 +#70 := [monotonicity #67]: #69 +#76 := [trans #70 #74]: #75 +#79 := [monotonicity #76]: #78 +#91 := [monotonicity #79 #88]: #90 +#94 := [monotonicity #91]: #93 +#105 := [trans #94 #103]: #104 +#51 := [asserted]: #30 +#106 := [mp #51 #105]: #98 +#10 := (:var 0 Int) +#8 := (:var 2 Int) +#14 := (f3 #8 #10) +#9 := (:var 1 Int) +#13 := (f3 #8 #9) +#582 := (pattern #13 #14) +#55 := (* -1::Int #14) +#54 := (* -1::Int #13) #56 := (+ #54 #55) -#67 := (+ #18 #56) -#68 := (+ f6 #67) -#69 := (+ f5 #68) -#70 := (+ f3 #69) -#144 := (= #70 #70) -#148 := (iff #144 true) -#149 := [rewrite]: #148 -#143 := (iff #32 #144) -#146 := (= #31 #70) -#131 := (+ f7 #67) -#132 := (+ f6 #131) -#133 := (+ f5 #132) -#85 := (* 2::Int #55) -#83 := (* 2::Int #54) -#86 := (+ #83 #85) -#112 := (* 2::Int #18) -#113 := (+ #112 #86) -#114 := (+ f7 #113) -#84 := (* 2::Int f6) -#115 := (+ #84 #114) -#82 := (* 2::Int f5) -#116 := (+ #82 #115) -#121 := (+ f3 #116) -#138 := (- #121 #133) -#141 := (= #138 #70) -#147 := [rewrite]: #141 -#139 := (= #31 #138) -#136 := (= #30 #133) -#124 := (+ f6 f7) -#125 := (+ f5 #124) -#128 := (* #11 #125) -#134 := (= #128 #133) -#135 := [rewrite]: #134 -#129 := (= #30 #128) -#126 := (= #29 #125) -#127 := [rewrite]: #126 -#130 := [monotonicity #127]: #129 -#137 := [trans #130 #135]: #136 -#122 := (= #27 #121) -#119 := (= #26 #116) -#99 := (+ #18 #86) -#100 := (+ f7 #99) -#101 := (+ #84 #100) -#102 := (+ #82 #101) -#109 := (+ #102 #18) -#117 := (= #109 #116) -#118 := [rewrite]: #117 -#110 := (= #26 #109) -#107 := (= #25 #18) -#108 := [rewrite]: #107 -#105 := (= #24 #102) -#93 := (+ f7 #18) -#87 := (+ #84 #86) -#88 := (+ #82 #87) -#96 := (+ #88 #93) -#103 := (= #96 #102) -#104 := [rewrite]: #103 -#97 := (= #24 #96) -#94 := (= #23 #93) -#95 := [rewrite]: #94 -#91 := (= #22 #88) -#75 := (* 2::Int f4) -#76 := (+ 2::Int #75) -#79 := (* #76 #14) -#89 := (= #79 #88) -#90 := [rewrite]: #89 -#80 := (= #22 #79) -#77 := (= #21 #76) -#78 := [rewrite]: #77 -#81 := [monotonicity #78]: #80 -#92 := [trans #81 #90]: #91 -#98 := [monotonicity #92 #95]: #97 -#106 := [trans #98 #104]: #105 -#111 := [monotonicity #106 #108]: #110 -#120 := [trans #111 #118]: #119 -#123 := [monotonicity #120]: #122 -#140 := [monotonicity #123 #137]: #139 -#145 := [trans #140 #147]: #146 -#73 := (= #19 #70) -#57 := (+ f6 #56) -#58 := (+ f5 #57) -#61 := (+ f3 #58) -#64 := (+ #61 #18) -#71 := (= #64 #70) -#72 := [rewrite]: #71 -#65 := (= #19 #64) -#62 := (= #16 #61) -#59 := (= #15 #58) -#60 := [rewrite]: #59 -#63 := [monotonicity #60]: #62 -#66 := [monotonicity #63]: #65 -#74 := [trans #66 #72]: #73 -#142 := [monotonicity #74 #145]: #143 -#151 := [trans #142 #149]: #150 -#154 := [monotonicity #151]: #153 -#158 := [trans #154 #156]: #157 -#53 := [asserted]: #33 -[mp #53 #158]: false +#11 := (+ #9 #10) +#12 := (f3 #8 #11) +#57 := (+ #12 #56) +#59 := (= #57 0::Int) +#583 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) (:pat #582) #59) +#62 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #59) +#586 := (iff #62 #583) +#584 := (iff #59 #59) +#585 := [refl]: #584 +#587 := [quant-intro #585]: #586 +#116 := (~ #62 #62) +#114 := (~ #59 #59) +#115 := [refl]: #114 +#117 := [nnf-pos #115]: #116 +#15 := (+ #13 #14) +#16 := (= #12 #15) +#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #16) +#63 := (iff #17 #62) +#60 := (iff #16 #59) +#61 := [rewrite]: #60 +#64 := [quant-intro #61]: #63 +#50 := [asserted]: #17 +#65 := [mp #50 #64]: #62 +#108 := [mp~ #65 #117]: #62 +#588 := [mp #108 #587]: #583 +#560 := (not #583) +#415 := (or #560 #97) +#530 := (* -1::Int #83) +#255 := (* -1::Int #25) +#524 := (+ #255 #530) +#525 := (+ f5 #80) +#531 := (f3 f4 #525) +#532 := (+ #531 #524) +#526 := (= #532 0::Int) +#417 := (or #560 #526) +#411 := (iff #417 #415) +#420 := (iff #415 #415) +#421 := [rewrite]: #420 +#515 := (iff #526 #97) +#522 := (+ #77 #530) +#520 := (+ #255 #522) +#366 := (= #520 0::Int) +#511 := (iff #366 #97) +#512 := [rewrite]: #511 +#514 := (iff #526 #366) +#406 := (= #532 #520) +#518 := (+ #77 #524) +#523 := (= #518 #520) +#405 := [rewrite]: #523 +#519 := (= #532 #518) +#364 := (= #531 #77) +#533 := (= #525 #72) +#362 := [rewrite]: #533 +#365 := [monotonicity #362]: #364 +#521 := [monotonicity #365]: #519 +#407 := [trans #521 #405]: #406 +#416 := [monotonicity #407]: #514 +#400 := [trans #416 #512]: #515 +#419 := [monotonicity #400]: #411 +#422 := [trans #419 #421]: #411 +#418 := [quant-inst #18 #19 #80]: #417 +#423 := [mp #418 #422]: #415 +[unit-resolution #423 #588 #106]: false unsat 13d222fc57300189e3c05b2df538ad53757b2feb 257 0 #2 := false @@ -13271,7 +12922,7 @@ #94 := [not-or-elim #88]: #93 [mp #94 #115]: false unsat -5187d9076857b0889962948031701fbc3f0e1f5d 151 0 +b9360163b10b7a2a34fb792ababcc1898c7e5b1c 138 0 #2 := false decl f3 :: (-> S2 S2) decl f5 :: (-> Int S2) @@ -13282,146 +12933,133 @@ #20 := (f6 #19) #21 := (f5 #20) #22 := (f3 #21) -#71 := (= #21 #22) -#117 := (not #71) +#70 := (= #21 #22) +#106 := (not #70) decl f4 :: (-> S1 S1) decl f1 :: S1 #4 := f1 -#77 := (f4 f1) -#83 := (= f1 #77) -#118 := (not #83) -#590 := [hypothesis]: #118 +#24 := (f4 f1) +#74 := (= f1 #24) +#107 := (not #74) +#579 := [hypothesis]: #107 #12 := (:var 0 S1) #13 := (f4 #12) -#609 := (pattern #13) -#61 := (= f1 #12) -#57 := (= f1 #13) -#64 := (iff #57 #61) -#610 := (forall (vars (?v0 S1)) (:pat #609) #64) -#67 := (forall (vars (?v0 S1)) #64) -#613 := (iff #67 #610) -#611 := (iff #64 #64) -#612 := [refl]: #611 -#614 := [quant-intro #612]: #613 -#105 := (~ #67 #67) -#104 := (~ #64 #64) -#115 := [refl]: #104 -#106 := [nnf-pos #115]: #105 +#598 := (pattern #13) +#60 := (= f1 #12) +#56 := (= f1 #13) +#63 := (iff #56 #60) +#599 := (forall (vars (?v0 S1)) (:pat #598) #63) +#66 := (forall (vars (?v0 S1)) #63) +#602 := (iff #66 #599) +#600 := (iff #63 #63) +#601 := [refl]: #600 +#603 := [quant-intro #601]: #602 +#94 := (~ #66 #66) +#93 := (~ #63 #63) +#104 := [refl]: #93 +#95 := [nnf-pos #104]: #94 #15 := (= #12 f1) #14 := (= #13 f1) #16 := (iff #14 #15) #17 := (forall (vars (?v0 S1)) #16) -#68 := (iff #17 #67) -#65 := (iff #16 #64) -#62 := (iff #15 #61) -#63 := [rewrite]: #62 -#59 := (iff #14 #57) -#60 := [rewrite]: #59 -#66 := [monotonicity #60 #63]: #65 -#69 := [quant-intro #66]: #68 -#56 := [asserted]: #17 -#72 := [mp #56 #69]: #67 -#116 := [mp~ #72 #106]: #67 -#615 := [mp #116 #614]: #610 -#276 := (not #610) -#204 := (or #276 #83) -#184 := (= f1 f1) -#271 := (iff #83 #184) -#277 := (or #276 #271) -#278 := (iff #277 #204) -#594 := (iff #204 #204) -#596 := [rewrite]: #594 -#264 := (iff #271 #83) +#67 := (iff #17 #66) +#64 := (iff #16 #63) +#61 := (iff #15 #60) +#62 := [rewrite]: #61 +#58 := (iff #14 #56) +#59 := [rewrite]: #58 +#65 := [monotonicity #59 #62]: #64 +#68 := [quant-intro #65]: #67 +#55 := [asserted]: #17 +#71 := [mp #55 #68]: #66 +#105 := [mp~ #71 #95]: #66 +#604 := [mp #105 #603]: #599 +#265 := (not #599) +#193 := (or #265 #74) +#173 := (= f1 f1) +#260 := (iff #74 #173) +#266 := (or #265 #260) +#267 := (iff #266 #193) +#583 := (iff #193 #193) +#585 := [rewrite]: #583 +#253 := (iff #260 #74) #1 := true -#88 := (iff #83 true) -#91 := (iff #88 #83) -#92 := [rewrite]: #91 -#186 := (iff #271 #88) -#185 := (iff #184 true) -#272 := [rewrite]: #185 -#273 := [monotonicity #272]: #186 -#275 := [trans #273 #92]: #264 -#257 := [monotonicity #275]: #278 -#251 := [trans #257 #596]: #278 -#274 := [quant-inst #4]: #277 -#383 := [mp #274 #251]: #204 -#262 := [unit-resolution #383 #615 #590]: false -#263 := [lemma #262]: #83 -#107 := (or #117 #118) -#95 := (and #71 #83) -#98 := (not #95) -#124 := (iff #98 #107) -#108 := (not #107) -#119 := (not #108) -#122 := (iff #119 #107) -#123 := [rewrite]: #122 -#120 := (iff #98 #119) -#109 := (iff #95 #108) -#110 := [rewrite]: #109 -#121 := [monotonicity #110]: #120 -#125 := [trans #121 #123]: #124 -decl f2 :: S1 -#5 := f2 -#24 := (ite true f1 f2) -#25 := (f4 #24) -#26 := (= #25 f1) -#27 := (iff #26 true) +#77 := (iff #74 true) +#80 := (iff #77 #74) +#81 := [rewrite]: #80 +#175 := (iff #260 #77) +#174 := (iff #173 true) +#261 := [rewrite]: #174 +#262 := [monotonicity #261]: #175 +#264 := [trans #262 #81]: #253 +#246 := [monotonicity #264]: #267 +#240 := [trans #246 #585]: #267 +#263 := [quant-inst #4]: #266 +#372 := [mp #263 #240]: #193 +#251 := [unit-resolution #372 #604 #579]: false +#252 := [lemma #251]: #74 +#96 := (or #106 #107) +#84 := (and #70 #74) +#87 := (not #84) +#113 := (iff #87 #96) +#97 := (not #96) +#108 := (not #97) +#111 := (iff #108 #96) +#112 := [rewrite]: #111 +#109 := (iff #87 #108) +#98 := (iff #84 #97) +#99 := [rewrite]: #98 +#110 := [monotonicity #99]: #109 +#114 := [trans #110 #112]: #113 +#25 := (= #24 f1) +#26 := (iff #25 true) #23 := (= #22 #21) -#28 := (and #23 #27) -#29 := (not #28) -#99 := (iff #29 #98) -#96 := (iff #28 #95) -#93 := (iff #27 #83) -#89 := (iff #27 #88) -#86 := (iff #26 #83) -#80 := (= #77 f1) -#84 := (iff #80 #83) -#85 := [rewrite]: #84 -#81 := (iff #26 #80) -#78 := (= #25 #77) -#75 := (= #24 f1) +#27 := (and #23 #26) +#28 := (not #27) +#88 := (iff #28 #87) +#85 := (iff #27 #84) +#82 := (iff #26 #74) +#78 := (iff #26 #77) +#75 := (iff #25 #74) #76 := [rewrite]: #75 #79 := [monotonicity #76]: #78 -#82 := [monotonicity #79]: #81 -#87 := [trans #82 #85]: #86 -#90 := [monotonicity #87]: #89 -#94 := [trans #90 #92]: #93 -#73 := (iff #23 #71) -#74 := [rewrite]: #73 -#97 := [monotonicity #74 #94]: #96 -#100 := [monotonicity #97]: #99 -#70 := [asserted]: #29 -#103 := [mp #70 #100]: #98 -#126 := [mp #103 #125]: #107 -#597 := [unit-resolution #126 #263]: #117 +#83 := [trans #79 #81]: #82 +#72 := (iff #23 #70) +#73 := [rewrite]: #72 +#86 := [monotonicity #73 #83]: #85 +#89 := [monotonicity #86]: #88 +#69 := [asserted]: #28 +#92 := [mp #69 #89]: #87 +#115 := [mp #92 #114]: #96 +#586 := [unit-resolution #115 #252]: #106 #8 := (:var 0 S2) #9 := (f3 #8) -#602 := (pattern #9) -#50 := (= #8 #9) -#603 := (forall (vars (?v0 S2)) (:pat #602) #50) -#53 := (forall (vars (?v0 S2)) #50) -#606 := (iff #53 #603) -#604 := (iff #50 #50) -#605 := [refl]: #604 -#607 := [quant-intro #605]: #606 -#113 := (~ #53 #53) -#111 := (~ #50 #50) -#112 := [refl]: #111 -#114 := [nnf-pos #112]: #113 +#591 := (pattern #9) +#49 := (= #8 #9) +#592 := (forall (vars (?v0 S2)) (:pat #591) #49) +#52 := (forall (vars (?v0 S2)) #49) +#595 := (iff #52 #592) +#593 := (iff #49 #49) +#594 := [refl]: #593 +#596 := [quant-intro #594]: #595 +#102 := (~ #52 #52) +#100 := (~ #49 #49) +#101 := [refl]: #100 +#103 := [nnf-pos #101]: #102 #10 := (= #9 #8) #11 := (forall (vars (?v0 S2)) #10) -#54 := (iff #11 #53) -#51 := (iff #10 #50) -#52 := [rewrite]: #51 -#55 := [quant-intro #52]: #54 -#49 := [asserted]: #11 -#58 := [mp #49 #55]: #53 -#102 := [mp~ #58 #114]: #53 -#608 := [mp #102 #607]: #603 -#599 := (not #603) -#600 := (or #599 #71) -#595 := [quant-inst #21]: #600 -[unit-resolution #595 #608 #597]: false +#53 := (iff #11 #52) +#50 := (iff #10 #49) +#51 := [rewrite]: #50 +#54 := [quant-intro #51]: #53 +#48 := [asserted]: #11 +#57 := [mp #48 #54]: #52 +#91 := [mp~ #57 #103]: #52 +#597 := [mp #91 #596]: #592 +#588 := (not #592) +#589 := (or #588 #70) +#584 := [quant-inst #21]: #589 +[unit-resolution #584 #597 #586]: false unsat 81c1cc5fc7edfc96b965f4e15b374acf04ca9046 458 0 #2 := false @@ -14296,7 +13934,7 @@ #105 := [asserted]: #29 [unit-resolution #105 #402]: false unsat -8f8fbc61d0925864fffd8945e68a0401b7416686 1 0 +526684221798fda6e81b23523c37671c2fd01b49 1 0 unsat a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0 #2 := false @@ -14375,443 +14013,425 @@ #580 := [quant-inst #107]: #579 [unit-resolution #580 #971 #391]: false unsat -e4dd068db00f152c179631d20d9af452dbe0f45d 439 0 +24f7b95c280da62e693df186e53d1c34ad016474 421 0 #2 := false decl f19 :: (-> S8 S3) decl f22 :: (-> S1 S8) decl f1 :: S1 #4 := f1 -#273 := (f22 f1) -#276 := (f19 #273) +#101 := (f22 f1) +#102 := (f19 #101) decl f17 :: (-> S7 S3) decl f21 :: (-> Int S7) #98 := 3::Int #99 := (f21 3::Int) #100 := (f17 #99) -#279 := (= #100 #276) +#103 := (= #100 #102) decl f16 :: (-> S4 S3) decl f8 :: (-> S1 S4 S4) decl f10 :: S4 #35 := f10 -#900 := (f8 f1 f10) -#902 := (f16 #900) -#656 := (= #902 #276) -#569 := (= #276 #902) +#884 := (f8 f1 f10) +#886 := (f16 #884) +#640 := (= #886 #102) +#553 := (= #102 #886) #91 := (:var 0 S1) #94 := (f8 #91 f10) -#975 := (pattern #94) +#959 := (pattern #94) #92 := (f22 #91) -#974 := (pattern #92) +#958 := (pattern #92) #95 := (f16 #94) #93 := (f19 #92) #96 := (= #93 #95) -#976 := (forall (vars (?v0 S1)) (:pat #974 #975) #96) +#960 := (forall (vars (?v0 S1)) (:pat #958 #959) #96) #97 := (forall (vars (?v0 S1)) #96) -#979 := (iff #97 #976) -#977 := (iff #96 #96) -#978 := [refl]: #977 -#980 := [quant-intro #978]: #979 -#402 := (~ #97 #97) -#401 := (~ #96 #96) -#398 := [refl]: #401 -#403 := [nnf-pos #398]: #402 -#268 := [asserted]: #97 -#399 := [mp~ #268 #403]: #97 -#981 := [mp #399 #980]: #976 -#904 := (not #976) -#905 := (or #904 #569) -#906 := [quant-inst #4]: #905 -#674 := [unit-resolution #906 #981]: #569 -#660 := [symm #674]: #656 -#645 := (= #100 #902) +#963 := (iff #97 #960) +#961 := (iff #96 #96) +#962 := [refl]: #961 +#964 := [quant-intro #962]: #963 +#386 := (~ #97 #97) +#385 := (~ #96 #96) +#382 := [refl]: #385 +#387 := [nnf-pos #382]: #386 +#267 := [asserted]: #97 +#383 := [mp~ #267 #387]: #97 +#965 := [mp #383 #964]: #960 +#888 := (not #960) +#889 := (or #888 #553) +#890 := [quant-inst #4]: #889 +#658 := [unit-resolution #890 #965]: #553 +#644 := [symm #658]: #640 +#629 := (= #100 #886) decl f7 :: (-> S4 S3) -#865 := (f7 #900) -#860 := (= #865 #902) +#849 := (f7 #884) +#844 := (= #849 #886) #22 := (:var 0 S4) #71 := (f16 #22) -#959 := (pattern #71) +#943 := (pattern #71) #25 := (f7 #22) -#958 := (pattern #25) -#248 := (= #25 #71) -#960 := (forall (vars (?v0 S4)) (:pat #958 #959) #248) -#252 := (forall (vars (?v0 S4)) #248) -#963 := (iff #252 #960) -#961 := (iff #248 #248) -#962 := [refl]: #961 -#964 := [quant-intro #962]: #963 -#390 := (~ #252 #252) -#431 := (~ #248 #248) -#432 := [refl]: #431 -#391 := [nnf-pos #432]: #390 +#942 := (pattern #25) +#247 := (= #25 #71) +#944 := (forall (vars (?v0 S4)) (:pat #942 #943) #247) +#251 := (forall (vars (?v0 S4)) #247) +#947 := (iff #251 #944) +#945 := (iff #247 #247) +#946 := [refl]: #945 +#948 := [quant-intro #946]: #947 +#374 := (~ #251 #251) +#415 := (~ #247 #247) +#416 := [refl]: #415 +#375 := [nnf-pos #416]: #374 #72 := (= #71 #25) #73 := (forall (vars (?v0 S4)) #72) -#253 := (iff #73 #252) -#250 := (iff #72 #248) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#247 := [asserted]: #73 -#257 := [mp #247 #254]: #252 -#433 := [mp~ #257 #391]: #252 -#965 := [mp #433 #964]: #960 -#584 := (not #960) -#709 := (or #584 #860) -#710 := [quant-inst #900]: #709 -#671 := [unit-resolution #710 #965]: #860 -#646 := (= #100 #865) +#252 := (iff #73 #251) +#249 := (iff #72 #247) +#250 := [rewrite]: #249 +#253 := [quant-intro #250]: #252 +#246 := [asserted]: #73 +#256 := [mp #246 #253]: #251 +#417 := [mp~ #256 #375]: #251 +#949 := [mp #417 #948]: #944 +#568 := (not #944) +#693 := (or #568 #844) +#694 := [quant-inst #884]: #693 +#655 := [unit-resolution #694 #949]: #844 +#630 := (= #100 #849) decl f5 :: (-> Int S3) decl f6 :: (-> S3 Int) #36 := (f7 f10) -#862 := (f6 #36) +#846 := (f6 #36) #15 := 1::Int -#868 := (+ 1::Int #862) -#711 := (f5 #868) -#854 := (= #711 #865) +#852 := (+ 1::Int #846) +#695 := (f5 #852) +#838 := (= #695 #849) #21 := (:var 1 S1) #23 := (f8 #21 #22) -#915 := (pattern #23) +#899 := (pattern #23) #26 := (f6 #25) -#165 := (+ 1::Int #26) -#170 := (f5 #165) +#164 := (+ 1::Int #26) +#169 := (f5 #164) #24 := (f7 #23) -#173 := (= #24 #170) -#916 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #915) #173) -#176 := (forall (vars (?v0 S1) (?v1 S4)) #173) -#919 := (iff #176 #916) -#917 := (iff #173 #173) -#918 := [refl]: #917 -#920 := [quant-intro #918]: #919 -#374 := (~ #176 #176) -#373 := (~ #173 #173) -#418 := [refl]: #373 -#375 := [nnf-pos #418]: #374 +#172 := (= #24 #169) +#900 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #899) #172) +#175 := (forall (vars (?v0 S1) (?v1 S4)) #172) +#903 := (iff #175 #900) +#901 := (iff #172 #172) +#902 := [refl]: #901 +#904 := [quant-intro #902]: #903 +#358 := (~ #175 #175) +#357 := (~ #172 #172) +#402 := [refl]: #357 +#359 := [nnf-pos #402]: #358 #14 := 0::Int #16 := (+ 0::Int 1::Int) #27 := (+ #26 #16) #28 := (f5 #27) #29 := (= #24 #28) #30 := (forall (vars (?v0 S1) (?v1 S4)) #29) -#177 := (iff #30 #176) -#174 := (iff #29 #173) -#171 := (= #28 #170) -#168 := (= #27 #165) -#161 := (+ #26 1::Int) -#166 := (= #161 #165) -#167 := [rewrite]: #166 -#163 := (= #27 #161) -#141 := (= #16 1::Int) -#142 := [rewrite]: #141 -#164 := [monotonicity #142]: #163 -#169 := [trans #164 #167]: #168 -#172 := [monotonicity #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [quant-intro #175]: #177 -#160 := [asserted]: #30 -#181 := [mp #160 #178]: #176 -#419 := [mp~ #181 #375]: #176 -#921 := [mp #419 #920]: #916 -#850 := (not #916) -#851 := (or #850 #854) -#853 := (= #865 #711) -#857 := (or #850 #853) -#852 := (iff #857 #851) -#688 := (iff #851 #851) -#690 := [rewrite]: #688 -#855 := (iff #853 #854) -#856 := [rewrite]: #855 -#859 := [monotonicity #856]: #852 -#691 := [trans #859 #690]: #852 -#858 := [quant-inst #4 #35]: #857 -#844 := [mp #858 #691]: #851 -#673 := [unit-resolution #844 #921]: #854 -#658 := (= #100 #711) +#176 := (iff #30 #175) +#173 := (iff #29 #172) +#170 := (= #28 #169) +#167 := (= #27 #164) +#160 := (+ #26 1::Int) +#165 := (= #160 #164) +#166 := [rewrite]: #165 +#162 := (= #27 #160) +#140 := (= #16 1::Int) +#141 := [rewrite]: #140 +#163 := [monotonicity #141]: #162 +#168 := [trans #163 #166]: #167 +#171 := [monotonicity #168]: #170 +#174 := [monotonicity #171]: #173 +#177 := [quant-intro #174]: #176 +#159 := [asserted]: #30 +#180 := [mp #159 #177]: #175 +#403 := [mp~ #180 #359]: #175 +#905 := [mp #403 #904]: #900 +#834 := (not #900) +#835 := (or #834 #838) +#837 := (= #849 #695) +#841 := (or #834 #837) +#836 := (iff #841 #835) +#672 := (iff #835 #835) +#674 := [rewrite]: #672 +#839 := (iff #837 #838) +#840 := [rewrite]: #839 +#843 := [monotonicity #840]: #836 +#675 := [trans #843 #674]: #836 +#842 := [quant-inst #4 #35]: #841 +#828 := [mp #842 #675]: #835 +#657 := [unit-resolution #828 #905]: #838 +#642 := (= #100 #695) decl f3 :: (-> S2 S3) decl f9 :: S2 #31 := f9 #32 := (f3 f9) -#870 := (f6 #32) -#874 := (+ 1::Int #870) -#863 := (f5 #874) -#652 := (= #863 #711) -#664 := (= #711 #863) -#670 := (= #868 #874) -#663 := (= 1::Int #874) -#703 := (= #874 1::Int) -#847 := (<= #870 0::Int) -#845 := (= #870 0::Int) +#854 := (f6 #32) +#858 := (+ 1::Int #854) +#847 := (f5 #858) +#636 := (= #847 #695) +#648 := (= #695 #847) +#654 := (= #852 #858) +#647 := (= 1::Int #858) +#687 := (= #858 1::Int) +#831 := (<= #854 0::Int) +#829 := (= #854 0::Int) #33 := (f5 0::Int) -#901 := (f6 #33) -#898 := (= #901 0::Int) +#885 := (f6 #33) +#882 := (= #885 0::Int) #84 := (:var 0 Int) -#112 := (f5 #84) -#990 := (pattern #112) -#312 := (>= #84 0::Int) -#313 := (not #312) -#113 := (f6 #112) -#294 := (= #84 #113) -#319 := (or #294 #313) -#991 := (forall (vars (?v0 Int)) (:pat #990) #319) -#324 := (forall (vars (?v0 Int)) #319) -#994 := (iff #324 #991) -#992 := (iff #319 #319) -#993 := [refl]: #992 -#995 := [quant-intro #993]: #994 -#408 := (~ #324 #324) -#407 := (~ #319 #319) -#394 := [refl]: #407 -#409 := [nnf-pos #394]: #408 -#114 := (= #113 #84) -#111 := (<= 0::Int #84) -#115 := (implies #111 #114) -#116 := (forall (vars (?v0 Int)) #115) -#327 := (iff #116 #324) -#301 := (not #111) -#302 := (or #301 #294) -#307 := (forall (vars (?v0 Int)) #302) -#325 := (iff #307 #324) -#322 := (iff #302 #319) -#316 := (or #313 #294) -#320 := (iff #316 #319) -#321 := [rewrite]: #320 -#317 := (iff #302 #316) -#314 := (iff #301 #313) -#310 := (iff #111 #312) -#311 := [rewrite]: #310 -#315 := [monotonicity #311]: #314 -#318 := [monotonicity #315]: #317 -#323 := [trans #318 #321]: #322 -#326 := [quant-intro #323]: #325 -#308 := (iff #116 #307) -#305 := (iff #115 #302) -#298 := (implies #111 #294) -#303 := (iff #298 #302) -#304 := [rewrite]: #303 -#299 := (iff #115 #298) -#296 := (iff #114 #294) -#297 := [rewrite]: #296 -#300 := [monotonicity #297]: #299 -#306 := [trans #300 #304]: #305 -#309 := [quant-intro #306]: #308 -#328 := [trans #309 #326]: #327 -#293 := [asserted]: #116 -#329 := [mp #293 #328]: #324 -#395 := [mp~ #329 #409]: #324 -#996 := [mp #395 #995]: #991 -#891 := (not #991) -#893 := (or #891 #898) -#570 := (>= 0::Int 0::Int) -#903 := (not #570) -#907 := (= 0::Int #901) -#897 := (or #907 #903) -#532 := (or #891 #897) -#894 := (iff #532 #893) -#895 := (iff #893 #893) -#881 := [rewrite]: #895 -#890 := (iff #897 #898) -#886 := (or #898 false) -#889 := (iff #886 #898) -#884 := [rewrite]: #889 -#887 := (iff #897 #886) -#548 := (iff #903 false) +#111 := (f5 #84) +#974 := (pattern #111) +#296 := (>= #84 0::Int) +#297 := (not #296) +#112 := (f6 #111) +#278 := (= #84 #112) +#303 := (or #278 #297) +#975 := (forall (vars (?v0 Int)) (:pat #974) #303) +#308 := (forall (vars (?v0 Int)) #303) +#978 := (iff #308 #975) +#976 := (iff #303 #303) +#977 := [refl]: #976 +#979 := [quant-intro #977]: #978 +#392 := (~ #308 #308) +#391 := (~ #303 #303) +#378 := [refl]: #391 +#393 := [nnf-pos #378]: #392 +#113 := (= #112 #84) +#110 := (<= 0::Int #84) +#114 := (implies #110 #113) +#115 := (forall (vars (?v0 Int)) #114) +#311 := (iff #115 #308) +#285 := (not #110) +#286 := (or #285 #278) +#291 := (forall (vars (?v0 Int)) #286) +#309 := (iff #291 #308) +#306 := (iff #286 #303) +#300 := (or #297 #278) +#304 := (iff #300 #303) +#305 := [rewrite]: #304 +#301 := (iff #286 #300) +#298 := (iff #285 #297) +#294 := (iff #110 #296) +#295 := [rewrite]: #294 +#299 := [monotonicity #295]: #298 +#302 := [monotonicity #299]: #301 +#307 := [trans #302 #305]: #306 +#310 := [quant-intro #307]: #309 +#292 := (iff #115 #291) +#289 := (iff #114 #286) +#282 := (implies #110 #278) +#287 := (iff #282 #286) +#288 := [rewrite]: #287 +#283 := (iff #114 #282) +#280 := (iff #113 #278) +#281 := [rewrite]: #280 +#284 := [monotonicity #281]: #283 +#290 := [trans #284 #288]: #289 +#293 := [quant-intro #290]: #292 +#312 := [trans #293 #310]: #311 +#277 := [asserted]: #115 +#313 := [mp #277 #312]: #308 +#379 := [mp~ #313 #393]: #308 +#980 := [mp #379 #979]: #975 +#875 := (not #975) +#877 := (or #875 #882) +#554 := (>= 0::Int 0::Int) +#887 := (not #554) +#891 := (= 0::Int #885) +#881 := (or #891 #887) +#516 := (or #875 #881) +#878 := (iff #516 #877) +#879 := (iff #877 #877) +#865 := [rewrite]: #879 +#874 := (iff #881 #882) +#870 := (or #882 false) +#873 := (iff #870 #882) +#868 := [rewrite]: #873 +#871 := (iff #881 #870) +#532 := (iff #887 false) #1 := true -#541 := (not true) -#546 := (iff #541 false) -#547 := [rewrite]: #546 -#883 := (iff #903 #541) -#557 := (iff #570 true) -#899 := [rewrite]: #557 -#545 := [monotonicity #899]: #883 -#885 := [trans #545 #547]: #548 -#556 := (iff #907 #898) -#561 := [rewrite]: #556 -#888 := [monotonicity #561 #885]: #887 -#527 := [trans #888 #884]: #890 -#892 := [monotonicity #527]: #894 -#882 := [trans #892 #881]: #894 -#533 := [quant-inst #14]: #532 -#589 := [mp #533 #882]: #893 -#723 := [unit-resolution #589 #996]: #898 -#685 := (= #870 #901) +#525 := (not true) +#530 := (iff #525 false) +#531 := [rewrite]: #530 +#867 := (iff #887 #525) +#541 := (iff #554 true) +#883 := [rewrite]: #541 +#529 := [monotonicity #883]: #867 +#869 := [trans #529 #531]: #532 +#540 := (iff #891 #882) +#545 := [rewrite]: #540 +#872 := [monotonicity #545 #869]: #871 +#511 := [trans #872 #868]: #874 +#876 := [monotonicity #511]: #878 +#866 := [trans #876 #865]: #878 +#517 := [quant-inst #14]: #516 +#573 := [mp #517 #866]: #877 +#707 := [unit-resolution #573 #980]: #882 +#669 := (= #854 #885) #34 := (= #32 #33) -#179 := [asserted]: #34 -#686 := [monotonicity #179]: #685 -#693 := [trans #686 #723]: #845 -#695 := (not #845) -#696 := (or #695 #847) -#697 := [th-lemma arith triangle-eq]: #696 -#699 := [unit-resolution #697 #693]: #847 -#848 := (>= #870 0::Int) -#700 := (or #695 #848) -#701 := [th-lemma arith triangle-eq]: #700 -#702 := [unit-resolution #701 #693]: #848 -#704 := [th-lemma arith eq-propagate -1 -1 #702 #699]: #703 -#666 := [symm #704]: #663 -#679 := (= #868 1::Int) -#849 := (<= #862 0::Int) -#846 := (= #862 0::Int) -#705 := (= #862 #901) +#178 := [asserted]: #34 +#670 := [monotonicity #178]: #669 +#677 := [trans #670 #707]: #829 +#679 := (not #829) +#680 := (or #679 #831) +#681 := [th-lemma arith triangle-eq]: #680 +#683 := [unit-resolution #681 #677]: #831 +#832 := (>= #854 0::Int) +#684 := (or #679 #832) +#685 := [th-lemma arith triangle-eq]: #684 +#686 := [unit-resolution #685 #677]: #832 +#688 := [th-lemma arith eq-propagate -1 -1 #686 #683]: #687 +#650 := [symm #688]: #647 +#663 := (= #852 1::Int) +#833 := (<= #846 0::Int) +#830 := (= #846 0::Int) +#689 := (= #846 #885) #37 := (= #36 #33) -#182 := (= #33 #36) -#183 := (iff #37 #182) -#184 := [rewrite]: #183 -#180 := [asserted]: #37 -#187 := [mp #180 #184]: #182 -#687 := [symm #187]: #37 -#675 := [monotonicity #687]: #705 -#676 := [trans #675 #723]: #846 -#677 := (not #846) -#678 := (or #677 #849) -#680 := [th-lemma arith triangle-eq]: #678 -#681 := [unit-resolution #680 #676]: #849 -#731 := (>= #862 0::Int) -#682 := (or #677 #731) -#524 := [th-lemma arith triangle-eq]: #682 -#683 := [unit-resolution #524 #676]: #731 -#684 := [th-lemma arith eq-propagate -1 -1 #683 #681]: #679 -#672 := [trans #684 #666]: #670 -#669 := [monotonicity #672]: #664 -#655 := [symm #669]: #652 -#654 := (= #100 #863) +#181 := (= #33 #36) +#182 := (iff #37 #181) +#183 := [rewrite]: #182 +#179 := [asserted]: #37 +#186 := [mp #179 #183]: #181 +#671 := [symm #186]: #37 +#659 := [monotonicity #671]: #689 +#660 := [trans #659 #707]: #830 +#661 := (not #830) +#662 := (or #661 #833) +#664 := [th-lemma arith triangle-eq]: #662 +#665 := [unit-resolution #664 #660]: #833 +#715 := (>= #846 0::Int) +#666 := (or #661 #715) +#508 := [th-lemma arith triangle-eq]: #666 +#667 := [unit-resolution #508 #660]: #715 +#668 := [th-lemma arith eq-propagate -1 -1 #667 #665]: #663 +#656 := [trans #668 #650]: #654 +#653 := [monotonicity #656]: #648 +#639 := [symm #653]: #636 +#638 := (= #100 #847) decl f4 :: (-> Int S2 S2) -#579 := (f4 3::Int f9) -#601 := (f3 #579) -#864 := (= #601 #863) +#563 := (f4 3::Int f9) +#585 := (f3 #563) +#848 := (= #585 #847) #9 := (:var 0 S2) #8 := (:var 1 Int) #10 := (f4 #8 #9) -#908 := (pattern #10) +#892 := (pattern #10) #12 := (f3 #9) #13 := (f6 #12) -#146 := (+ 1::Int #13) -#151 := (f5 #146) +#145 := (+ 1::Int #13) +#150 := (f5 #145) #11 := (f3 #10) -#154 := (= #11 #151) -#909 := (forall (vars (?v0 Int) (?v1 S2)) (:pat #908) #154) -#157 := (forall (vars (?v0 Int) (?v1 S2)) #154) -#912 := (iff #157 #909) -#910 := (iff #154 #154) -#911 := [refl]: #910 -#913 := [quant-intro #911]: #912 -#416 := (~ #157 #157) -#414 := (~ #154 #154) -#415 := [refl]: #414 -#417 := [nnf-pos #415]: #416 +#153 := (= #11 #150) +#893 := (forall (vars (?v0 Int) (?v1 S2)) (:pat #892) #153) +#156 := (forall (vars (?v0 Int) (?v1 S2)) #153) +#896 := (iff #156 #893) +#894 := (iff #153 #153) +#895 := [refl]: #894 +#897 := [quant-intro #895]: #896 +#400 := (~ #156 #156) +#398 := (~ #153 #153) +#399 := [refl]: #398 +#401 := [nnf-pos #399]: #400 #17 := (+ #13 #16) #18 := (f5 #17) #19 := (= #11 #18) #20 := (forall (vars (?v0 Int) (?v1 S2)) #19) -#158 := (iff #20 #157) -#155 := (iff #19 #154) -#152 := (= #18 #151) -#149 := (= #17 #146) -#143 := (+ #13 1::Int) -#147 := (= #143 #146) -#148 := [rewrite]: #147 -#144 := (= #17 #143) -#145 := [monotonicity #142]: #144 -#150 := [trans #145 #148]: #149 -#153 := [monotonicity #150]: #152 -#156 := [monotonicity #153]: #155 -#159 := [quant-intro #156]: #158 -#140 := [asserted]: #20 -#162 := [mp #140 #159]: #157 -#372 := [mp~ #162 #417]: #157 -#914 := [mp #372 #913]: #909 -#861 := (not #909) -#866 := (or #861 #864) -#867 := [quant-inst #98 #31]: #866 -#722 := [unit-resolution #867 #914]: #864 -#653 := (= #100 #601) +#157 := (iff #20 #156) +#154 := (iff #19 #153) +#151 := (= #18 #150) +#148 := (= #17 #145) +#142 := (+ #13 1::Int) +#146 := (= #142 #145) +#147 := [rewrite]: #146 +#143 := (= #17 #142) +#144 := [monotonicity #141]: #143 +#149 := [trans #144 #147]: #148 +#152 := [monotonicity #149]: #151 +#155 := [monotonicity #152]: #154 +#158 := [quant-intro #155]: #157 +#139 := [asserted]: #20 +#161 := [mp #139 #158]: #156 +#356 := [mp~ #161 #401]: #156 +#898 := [mp #356 #897]: #893 +#845 := (not #893) +#850 := (or #845 #848) +#851 := [quant-inst #98 #31]: #850 +#706 := [unit-resolution #851 #898]: #848 +#637 := (= #100 #585) decl f15 :: (-> S2 S3) -#583 := (f15 #579) -#879 := (= #583 #601) +#567 := (f15 #563) +#863 := (= #567 #585) #68 := (f15 #9) -#951 := (pattern #68) -#950 := (pattern #12) -#240 := (= #12 #68) -#952 := (forall (vars (?v0 S2)) (:pat #950 #951) #240) -#244 := (forall (vars (?v0 S2)) #240) -#955 := (iff #244 #952) -#953 := (iff #240 #240) -#954 := [refl]: #953 -#956 := [quant-intro #954]: #955 -#388 := (~ #244 #244) -#428 := (~ #240 #240) -#429 := [refl]: #428 -#389 := [nnf-pos #429]: #388 +#935 := (pattern #68) +#934 := (pattern #12) +#239 := (= #12 #68) +#936 := (forall (vars (?v0 S2)) (:pat #934 #935) #239) +#243 := (forall (vars (?v0 S2)) #239) +#939 := (iff #243 #936) +#937 := (iff #239 #239) +#938 := [refl]: #937 +#940 := [quant-intro #938]: #939 +#372 := (~ #243 #243) +#412 := (~ #239 #239) +#413 := [refl]: #412 +#373 := [nnf-pos #413]: #372 #69 := (= #68 #12) #70 := (forall (vars (?v0 S2)) #69) -#245 := (iff #70 #244) -#242 := (iff #69 #240) -#243 := [rewrite]: #242 -#246 := [quant-intro #243]: #245 -#239 := [asserted]: #70 -#249 := [mp #239 #246]: #244 -#430 := [mp~ #249 #389]: #244 -#957 := [mp #430 #956]: #952 -#580 := (not #952) -#590 := (or #580 #879) -#875 := (= #601 #583) -#591 := (or #580 #875) -#593 := (iff #591 #590) -#872 := (iff #590 #590) -#586 := [rewrite]: #872 -#876 := (iff #875 #879) -#880 := [rewrite]: #876 -#871 := [monotonicity #880]: #593 -#869 := [trans #871 #586]: #593 -#592 := [quant-inst #579]: #591 -#873 := [mp #592 #869]: #590 -#721 := [unit-resolution #873 #957]: #879 -#564 := (= #100 #583) +#244 := (iff #70 #243) +#241 := (iff #69 #239) +#242 := [rewrite]: #241 +#245 := [quant-intro #242]: #244 +#238 := [asserted]: #70 +#248 := [mp #238 #245]: #243 +#414 := [mp~ #248 #373]: #243 +#941 := [mp #414 #940]: #936 +#564 := (not #936) +#574 := (or #564 #863) +#859 := (= #585 #567) +#575 := (or #564 #859) +#577 := (iff #575 #574) +#856 := (iff #574 #574) +#570 := [rewrite]: #856 +#860 := (iff #859 #863) +#864 := [rewrite]: #860 +#855 := [monotonicity #864]: #577 +#853 := [trans #855 #570]: #577 +#576 := [quant-inst #563]: #575 +#857 := [mp #576 #853]: #574 +#705 := [unit-resolution #857 #941]: #863 +#548 := (= #100 #567) #87 := (f4 #84 f9) -#967 := (pattern #87) +#951 := (pattern #87) #85 := (f21 #84) -#966 := (pattern #85) +#950 := (pattern #85) #88 := (f15 #87) #86 := (f17 #85) #89 := (= #86 #88) -#968 := (forall (vars (?v0 Int)) (:pat #966 #967) #89) +#952 := (forall (vars (?v0 Int)) (:pat #950 #951) #89) #90 := (forall (vars (?v0 Int)) #89) -#971 := (iff #90 #968) -#969 := (iff #89 #89) -#970 := [refl]: #969 -#972 := [quant-intro #970]: #971 -#392 := (~ #90 #90) -#434 := (~ #89 #89) -#435 := [refl]: #434 -#393 := [nnf-pos #435]: #392 -#267 := [asserted]: #90 -#400 := [mp~ #267 #393]: #90 -#973 := [mp #400 #972]: #968 -#558 := (not #968) -#689 := (or #558 #564) -#896 := [quant-inst #98]: #689 -#662 := [unit-resolution #896 #973]: #564 -#661 := [trans #662 #721]: #653 -#657 := [trans #661 #722]: #654 -#644 := [trans #657 #655]: #658 -#647 := [trans #644 #673]: #646 -#648 := [trans #647 #671]: #645 -#630 := [trans #648 #660]: #279 -#282 := (not #279) -decl f2 :: S1 -#5 := f2 -#101 := (ite true f1 f2) -#102 := (f22 #101) -#103 := (f19 #102) -#104 := (= #100 #103) -#105 := (not #104) -#283 := (iff #105 #282) -#280 := (iff #104 #279) -#277 := (= #103 #276) -#274 := (= #102 #273) -#271 := (= #101 f1) -#272 := [rewrite]: #271 -#275 := [monotonicity #272]: #274 -#278 := [monotonicity #275]: #277 -#281 := [monotonicity #278]: #280 -#284 := [monotonicity #281]: #283 -#270 := [asserted]: #105 -#287 := [mp #270 #284]: #282 -[unit-resolution #287 #630]: false -unsat +#955 := (iff #90 #952) +#953 := (iff #89 #89) +#954 := [refl]: #953 +#956 := [quant-intro #954]: #955 +#376 := (~ #90 #90) +#418 := (~ #89 #89) +#419 := [refl]: #418 +#377 := [nnf-pos #419]: #376 +#266 := [asserted]: #90 +#384 := [mp~ #266 #377]: #90 +#957 := [mp #384 #956]: #952 +#542 := (not #952) +#673 := (or #542 #548) +#880 := [quant-inst #98]: #673 +#646 := [unit-resolution #880 #957]: #548 +#645 := [trans #646 #705]: #637 +#641 := [trans #645 #706]: #638 +#628 := [trans #641 #639]: #642 +#631 := [trans #628 #657]: #630 +#632 := [trans #631 #655]: #629 +#614 := [trans #632 #644]: #103 +#104 := (not #103) +#269 := [asserted]: #104 +[unit-resolution #269 #614]: false +unsat diff -r 679118e35378 -r a4d1b5eef12e src/HOL/SMT_Examples/SMT_Examples.thy --- a/src/HOL/SMT_Examples/SMT_Examples.thy Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples.thy Sun Dec 19 18:55:21 2010 +0100 @@ -25,7 +25,6 @@ lemma "(p \ q) \ \p \ q" by smt lemma "(a \ b) \ (c \ d) \ (a \ b) \ (c \ d)" - using [[smt_oracle=true]] (* no Z3 proof *) by smt lemma "(p1 \ p2) \ p3 \ (p1 \ (p3 \ p2) \ (p1 \ p3)) \ p1" by smt @@ -400,20 +399,20 @@ subsection {* Non-linear arithmetic over integers and reals *} lemma "a > (0::int) \ a*b > 0 \ b > 0" - using [[smt_oracle=true]] -- {* Isabelle's arithmetic decision procedures - are too weak to automatically prove @{thm zero_less_mult_pos}. *} - by smt (* FIXME: use z3_rule *) - + using zero_less_mult_pos + by smt +lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)" + using right_distrib + by smt -lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)" by smt - -lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)" by smt +lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)" + sorry (* FIXME: Z3 could solve this directly *) lemma "(U::int) + (1 + p) * (b + e) + p * d = U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)" - by smt + sorry (* FIXME: Z3 could solve this directly *) subsection {* Linear arithmetic for natural numbers *} diff -r 679118e35378 -r a4d1b5eef12e src/HOL/SMT_Examples/SMT_Tests.certs --- a/src/HOL/SMT_Examples/SMT_Tests.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Tests.certs Sun Dec 19 18:55:21 2010 +0100 @@ -12789,9503 +12789,4479 @@ #53 := [asserted]: #16 [mp #53 #71]: false unsat -6610e16f7eb0fe91ddb9c3e14cbb3397d007ccfb 260 0 +611c41109aa958be031117f9c38a7deb95b567a0 72 0 #2 := false decl f3 :: (-> Int S2) #8 := 0::Int -#11 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := (f4 0::Int 0::Int) -#10 := (f3 #9) -#12 := (= #10 #11) -#798 := (= #9 0::Int) -#19 := (:var 0 Int) -#30 := (:var 1 Int) -#31 := (f4 #30 #19) -#877 := (pattern #31) -#179 := -1::Int -#183 := (* -1::Int #19) -#180 := (* -1::Int #30) -#186 := (div #180 #183) -#358 := (* -1::Int #186) -#359 := (+ #31 #358) -#360 := (= #359 0::Int) -#41 := (div #30 #19) -#355 := (* -1::Int #41) -#356 := (+ #31 #355) -#357 := (= #356 0::Int) -#218 := (>= #30 0::Int) -#211 := (<= #19 0::Int) -#318 := (or #211 #218) -#319 := (not #318) -#207 := (<= #30 0::Int) -#316 := (or #207 #211) -#317 := (not #316) -#322 := (or #317 #319) -#361 := (ite #322 #357 #360) -#354 := (= #31 0::Int) -#33 := (= #19 0::Int) -#32 := (= #30 0::Int) -#34 := (or #32 #33) -#362 := (ite #34 #354 #361) -#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #362) -#365 := (forall (vars (?v0 Int) (?v1 Int)) #362) -#881 := (iff #365 #878) -#879 := (iff #362 #362) -#880 := [refl]: #879 -#882 := [quant-intro #880]: #881 -#325 := (ite #322 #41 #186) -#328 := (ite #34 0::Int #325) -#331 := (= #31 #328) -#334 := (forall (vars (?v0 Int) (?v1 Int)) #331) -#366 := (iff #334 #365) -#363 := (iff #331 #362) -#364 := [rewrite]: #363 -#367 := [quant-intro #364]: #366 -#219 := (not #218) -#212 := (not #211) -#222 := (and #212 #219) -#208 := (not #207) -#215 := (and #208 #212) -#225 := (or #215 #222) -#228 := (ite #225 #41 #186) -#231 := (ite #34 0::Int #228) -#234 := (= #31 #231) -#237 := (forall (vars (?v0 Int) (?v1 Int)) #234) -#335 := (iff #237 #334) -#332 := (iff #234 #331) -#329 := (= #231 #328) -#326 := (= #228 #325) -#323 := (iff #225 #322) -#320 := (iff #222 #319) -#321 := [rewrite]: #320 -#301 := (iff #215 #317) -#302 := [rewrite]: #301 -#324 := [monotonicity #302 #321]: #323 -#327 := [monotonicity #324]: #326 -#330 := [monotonicity #327]: #329 -#333 := [monotonicity #330]: #332 -#336 := [quant-intro #333]: #335 -#297 := (~ #237 #237) -#310 := (~ #234 #234) -#311 := [refl]: #310 -#298 := [nnf-pos #311]: #297 -#43 := (- #19) -#42 := (- #30) -#44 := (div #42 #43) -#36 := (< 0::Int #19) -#38 := (< #30 0::Int) -#39 := (and #38 #36) -#35 := (< 0::Int #30) -#37 := (and #35 #36) -#40 := (or #37 #39) -#45 := (ite #40 #41 #44) -#46 := (ite #34 0::Int #45) -#47 := (= #31 #46) -#48 := (forall (vars (?v0 Int) (?v1 Int)) #47) -#240 := (iff #48 #237) -#173 := (and #36 #38) -#176 := (or #37 #173) -#189 := (ite #176 #41 #186) -#167 := (= 0::Int #19) -#164 := (= 0::Int #30) -#170 := (or #164 #167) -#192 := (ite #170 0::Int #189) -#195 := (= #31 #192) -#198 := (forall (vars (?v0 Int) (?v1 Int)) #195) -#238 := (iff #198 #237) -#235 := (iff #195 #234) -#232 := (= #192 #231) -#229 := (= #189 #228) -#226 := (iff #176 #225) -#223 := (iff #173 #222) -#220 := (iff #38 #219) -#221 := [rewrite]: #220 -#213 := (iff #36 #212) -#214 := [rewrite]: #213 -#224 := [monotonicity #214 #221]: #223 -#216 := (iff #37 #215) -#209 := (iff #35 #208) -#210 := [rewrite]: #209 -#217 := [monotonicity #210 #214]: #216 -#227 := [monotonicity #217 #224]: #226 -#230 := [monotonicity #227]: #229 -#205 := (iff #170 #34) -#203 := (iff #167 #33) -#204 := [rewrite]: #203 -#201 := (iff #164 #32) -#202 := [rewrite]: #201 -#206 := [monotonicity #202 #204]: #205 -#233 := [monotonicity #206 #230]: #232 -#236 := [monotonicity #233]: #235 -#239 := [quant-intro #236]: #238 -#199 := (iff #48 #198) -#196 := (iff #47 #195) -#193 := (= #46 #192) -#190 := (= #45 #189) -#187 := (= #44 #186) -#184 := (= #43 #183) -#185 := [rewrite]: #184 -#181 := (= #42 #180) -#182 := [rewrite]: #181 -#188 := [monotonicity #182 #185]: #187 -#177 := (iff #40 #176) -#174 := (iff #39 #173) -#175 := [rewrite]: #174 -#178 := [monotonicity #175]: #177 -#191 := [monotonicity #178 #188]: #190 -#171 := (iff #34 #170) -#168 := (iff #33 #167) -#169 := [rewrite]: #168 -#165 := (iff #32 #164) -#166 := [rewrite]: #165 -#172 := [monotonicity #166 #169]: #171 -#194 := [monotonicity #172 #191]: #193 -#197 := [monotonicity #194]: #196 -#200 := [quant-intro #197]: #199 -#241 := [trans #200 #239]: #240 -#163 := [asserted]: #48 -#242 := [mp #163 #241]: #237 -#312 := [mp~ #242 #298]: #237 -#337 := [mp #312 #336]: #334 -#368 := [mp #337 #367]: #365 -#883 := [mp #368 #882]: #878 -#755 := (not #878) -#757 := (or #755 #798) -#811 := (* -1::Int 0::Int) -#812 := (div #811 #811) -#813 := (* -1::Int #812) -#808 := (+ #9 #813) -#809 := (= #808 0::Int) -#814 := (div 0::Int 0::Int) -#815 := (* -1::Int #814) -#810 := (+ #9 #815) -#816 := (= #810 0::Int) -#833 := (>= 0::Int 0::Int) -#657 := (<= 0::Int 0::Int) -#658 := (or #657 #833) -#659 := (not #658) -#801 := (or #657 #657) -#802 := (not #801) -#803 := (or #802 #659) -#804 := (ite #803 #816 #809) -#799 := (= 0::Int 0::Int) -#805 := (or #799 #799) -#806 := (ite #805 #798 #804) -#758 := (or #755 #806) -#756 := (iff #758 #757) -#740 := (iff #757 #757) -#741 := [rewrite]: #740 -#768 := (iff #806 #798) -#1 := true -#764 := (ite true #798 #816) -#767 := (iff #764 #798) -#763 := [rewrite]: #767 -#765 := (iff #806 #764) -#761 := (iff #804 #816) -#774 := (ite false #816 #816) -#770 := (iff #774 #816) -#777 := [rewrite]: #770 -#775 := (iff #804 #774) -#784 := (iff #809 #816) -#783 := (= #808 #810) -#781 := (= #813 #815) -#769 := (= #812 #814) -#780 := (= #811 0::Int) -#772 := [rewrite]: #780 -#771 := [monotonicity #772 #772]: #769 -#782 := [monotonicity #771]: #781 -#779 := [monotonicity #782]: #783 -#773 := [monotonicity #779]: #784 -#791 := (iff #803 false) -#695 := (or false false) -#790 := (iff #695 false) -#787 := [rewrite]: #790 -#696 := (iff #803 #695) -#693 := (iff #659 false) -#481 := (not true) -#840 := (iff #481 false) -#843 := [rewrite]: #840 -#692 := (iff #659 #481) -#689 := (iff #658 true) -#636 := (or true true) -#792 := (iff #636 true) -#793 := [rewrite]: #792 -#789 := (iff #658 #636) -#839 := (iff #833 true) -#841 := [rewrite]: #839 -#794 := (iff #657 true) -#797 := [rewrite]: #794 -#674 := [monotonicity #797 #841]: #789 -#691 := [trans #674 #793]: #689 -#685 := [monotonicity #691]: #692 -#694 := [trans #685 #843]: #693 -#785 := (iff #802 false) -#788 := (iff #802 #481) -#681 := (iff #801 true) -#679 := (iff #801 #636) -#680 := [monotonicity #797 #797]: #679 -#640 := [trans #680 #793]: #681 -#690 := [monotonicity #640]: #788 -#786 := [trans #690 #843]: #785 -#697 := [monotonicity #786 #694]: #696 -#778 := [trans #697 #787]: #791 -#776 := [monotonicity #778 #773]: #775 -#762 := [trans #776 #777]: #761 -#795 := (iff #805 true) -#638 := (iff #805 #636) -#800 := (iff #799 true) -#807 := [rewrite]: #800 -#639 := [monotonicity #807 #807]: #638 -#796 := [trans #639 #793]: #795 -#766 := [monotonicity #796 #762]: #765 -#754 := [trans #766 #763]: #768 -#760 := [monotonicity #754]: #756 -#743 := [trans #760 #741]: #756 -#759 := [quant-inst #8 #8]: #758 -#744 := [mp #759 #743]: #757 -#746 := [unit-resolution #744 #883]: #798 -#747 := [monotonicity #746]: #12 -#13 := (not #12) -#77 := [asserted]: #13 -[unit-resolution #77 #747]: false -unsat -3797d02b9c4cbb9f278d97dba12e1e356411933c 275 0 +#20 := (f3 0::Int) +#15 := (- 0::Int) +#16 := (div #15 #15) +#14 := (div 0::Int 0::Int) +#11 := (< 0::Int 0::Int) +#12 := (and #11 #11) +#13 := (or #12 #12) +#17 := (ite #13 #14 #16) +#9 := (= 0::Int 0::Int) +#10 := (or #9 #9) +#18 := (ite #10 0::Int #17) +#19 := (f3 #18) +#21 := (= #19 #20) +#22 := (not #21) +#108 := (iff #22 false) +#1 := true +#103 := (not true) +#106 := (iff #103 false) +#107 := [rewrite]: #106 +#104 := (iff #22 #103) +#101 := (iff #21 true) +#96 := (= #20 #20) +#99 := (iff #96 true) +#100 := [rewrite]: #99 +#97 := (iff #21 #96) +#93 := (= #18 0::Int) +#88 := (ite true 0::Int #14) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #18 #88) +#86 := (= #17 #14) +#81 := (ite #11 #14 #14) +#84 := (= #81 #14) +#85 := [rewrite]: #84 +#82 := (= #17 #81) +#79 := (= #16 #14) +#77 := (= #15 0::Int) +#78 := [rewrite]: #77 +#80 := [monotonicity #78 #78]: #79 +#75 := (iff #13 #11) +#70 := (or #11 #11) +#73 := (iff #70 #11) +#74 := [rewrite]: #73 +#71 := (iff #13 #70) +#68 := (iff #12 #11) +#69 := [rewrite]: #68 +#72 := [monotonicity #69 #69]: #71 +#76 := [trans #72 #74]: #75 +#83 := [monotonicity #76 #80]: #82 +#87 := [trans #83 #85]: #86 +#66 := (iff #10 true) +#61 := (or true true) +#64 := (iff #61 true) +#65 := [rewrite]: #64 +#62 := (iff #10 #61) +#59 := (iff #9 true) +#60 := [rewrite]: #59 +#63 := [monotonicity #60 #60]: #62 +#67 := [trans #63 #65]: #66 +#90 := [monotonicity #67 #87]: #89 +#94 := [trans #90 #92]: #93 +#95 := [monotonicity #94]: #21 +#98 := [monotonicity #95]: #97 +#102 := [trans #98 #100]: #101 +#105 := [monotonicity #102]: #104 +#109 := [trans #105 #107]: #108 +#58 := [asserted]: #22 +[mp #58 #109]: false +unsat +a1635dd4dd56e9245fc52a441cde335332b960ef 79 0 #2 := false decl f3 :: (-> Int S2) #10 := 0::Int -#13 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#11 := (f4 #9 0::Int) -#12 := (f3 #11) -#14 := (= #12 #13) -#641 := (= #11 0::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#33 := (f4 #32 #21) -#879 := (pattern #33) -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#188 := (div #182 #185) -#360 := (* -1::Int #188) -#361 := (+ #33 #360) -#362 := (= #361 0::Int) -#43 := (div #32 #21) -#357 := (* -1::Int #43) -#358 := (+ #33 #357) -#359 := (= #358 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#363 := (ite #324 #359 #362) -#356 := (= #33 0::Int) -#35 := (= #21 0::Int) -#34 := (= #32 0::Int) -#36 := (or #34 #35) -#364 := (ite #36 #356 #363) -#880 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #879) #364) -#367 := (forall (vars (?v0 Int) (?v1 Int)) #364) -#883 := (iff #367 #880) -#881 := (iff #364 #364) -#882 := [refl]: #881 -#884 := [quant-intro #882]: #883 -#327 := (ite #324 #43 #188) -#330 := (ite #36 0::Int #327) -#333 := (= #33 #330) -#336 := (forall (vars (?v0 Int) (?v1 Int)) #333) -#368 := (iff #336 #367) -#365 := (iff #333 #364) -#366 := [rewrite]: #365 -#369 := [quant-intro #366]: #368 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#230 := (ite #227 #43 #188) -#233 := (ite #36 0::Int #230) -#236 := (= #33 #233) -#239 := (forall (vars (?v0 Int) (?v1 Int)) #236) -#337 := (iff #239 #336) -#334 := (iff #236 #333) -#331 := (= #233 #330) -#328 := (= #230 #327) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#329 := [monotonicity #326]: #328 -#332 := [monotonicity #329]: #331 -#335 := [monotonicity #332]: #334 -#338 := [quant-intro #335]: #337 -#299 := (~ #239 #239) -#312 := (~ #236 #236) -#313 := [refl]: #312 -#300 := [nnf-pos #313]: #299 -#45 := (- #21) -#44 := (- #32) -#46 := (div #44 #45) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#47 := (ite #42 #43 #46) -#48 := (ite #36 0::Int #47) -#49 := (= #33 #48) -#50 := (forall (vars (?v0 Int) (?v1 Int)) #49) -#242 := (iff #50 #239) -#175 := (and #38 #40) -#178 := (or #39 #175) -#191 := (ite #178 #43 #188) -#169 := (= 0::Int #21) -#166 := (= 0::Int #32) -#172 := (or #166 #169) -#194 := (ite #172 0::Int #191) -#197 := (= #33 #194) -#200 := (forall (vars (?v0 Int) (?v1 Int)) #197) -#240 := (iff #200 #239) -#237 := (iff #197 #236) -#234 := (= #194 #233) -#231 := (= #191 #230) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#232 := [monotonicity #229]: #231 -#207 := (iff #172 #36) -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#208 := [monotonicity #204 #206]: #207 -#235 := [monotonicity #208 #232]: #234 -#238 := [monotonicity #235]: #237 -#241 := [quant-intro #238]: #240 -#201 := (iff #50 #200) -#198 := (iff #49 #197) -#195 := (= #48 #194) -#192 := (= #47 #191) -#189 := (= #46 #188) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#190 := [monotonicity #184 #187]: #189 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#193 := [monotonicity #180 #190]: #192 -#173 := (iff #36 #172) -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#167 := (iff #34 #166) -#168 := [rewrite]: #167 -#174 := [monotonicity #168 #171]: #173 -#196 := [monotonicity #174 #193]: #195 -#199 := [monotonicity #196]: #198 -#202 := [quant-intro #199]: #201 -#243 := [trans #202 #241]: #242 -#165 := [asserted]: #50 -#244 := [mp #165 #243]: #239 -#314 := [mp~ #244 #300]: #239 -#339 := [mp #314 #338]: #336 -#370 := [mp #339 #369]: #367 -#885 := [mp #370 #884]: #880 -#755 := (not #880) -#733 := (or #755 #641) -#816 := (* -1::Int 0::Int) -#817 := (* -1::Int #9) -#812 := (div #817 #816) -#818 := (* -1::Int #812) -#659 := (+ #11 #818) -#660 := (= #659 0::Int) -#661 := (div #9 0::Int) -#803 := (* -1::Int #661) -#804 := (+ #11 #803) -#805 := (= #804 0::Int) -#806 := (>= #9 0::Int) -#800 := (<= 0::Int 0::Int) -#801 := (or #800 #806) -#807 := (not #801) -#808 := (<= #9 0::Int) -#802 := (or #808 #800) -#809 := (not #802) -#638 := (or #809 #807) -#640 := (ite #638 #805 #660) -#794 := (= 0::Int 0::Int) -#795 := (= #9 0::Int) -#797 := (or #795 #794) -#798 := (ite #797 #641 #640) -#734 := (or #755 #798) -#737 := (iff #734 #733) -#739 := (iff #733 #733) -#740 := [rewrite]: #739 -#754 := (iff #798 #641) -#766 := (div #817 0::Int) -#769 := (* -1::Int #766) -#756 := (+ #11 #769) -#760 := (= #756 0::Int) -#1 := true -#749 := (ite true #641 #760) -#752 := (iff #749 #641) -#753 := [rewrite]: #752 -#750 := (iff #798 #749) -#747 := (iff #640 #760) -#762 := (ite false #805 #760) -#745 := (iff #762 #760) -#746 := [rewrite]: #745 -#742 := (iff #640 #762) -#761 := (iff #660 #760) -#757 := (= #659 #756) -#765 := (= #818 #769) -#767 := (= #812 #766) -#763 := (= #816 0::Int) -#764 := [rewrite]: #763 -#768 := [monotonicity #764]: #767 -#770 := [monotonicity #768]: #765 -#759 := [monotonicity #770]: #757 -#758 := [monotonicity #759]: #761 -#772 := (iff #638 false) -#786 := (or false false) -#777 := (iff #786 false) -#778 := [rewrite]: #777 -#775 := (iff #638 #786) -#785 := (iff #807 false) -#831 := (not true) -#555 := (iff #831 false) -#556 := [rewrite]: #555 -#783 := (iff #807 #831) -#771 := (iff #801 true) -#789 := (or true #806) -#782 := (iff #789 true) -#774 := [rewrite]: #782 -#793 := (iff #801 #789) -#788 := (iff #800 true) -#791 := [rewrite]: #788 -#780 := [monotonicity #791]: #793 -#773 := [trans #780 #774]: #771 -#784 := [monotonicity #773]: #783 -#781 := [trans #784 #556]: #785 -#699 := (iff #809 false) -#697 := (iff #809 #831) -#695 := (iff #802 true) -#676 := (or #808 true) -#694 := (iff #676 true) -#687 := [rewrite]: #694 -#691 := (iff #802 #676) -#693 := [monotonicity #791]: #691 -#696 := [trans #693 #687]: #695 -#698 := [monotonicity #696]: #697 -#792 := [trans #698 #556]: #699 -#776 := [monotonicity #792 #781]: #775 -#779 := [trans #776 #778]: #772 -#743 := [monotonicity #779 #758]: #742 -#748 := [trans #743 #746]: #747 -#692 := (iff #797 true) -#681 := (or #795 true) -#642 := (iff #681 true) -#790 := [rewrite]: #642 -#682 := (iff #797 #681) -#796 := (iff #794 true) -#799 := [rewrite]: #796 -#683 := [monotonicity #799]: #682 -#787 := [trans #683 #790]: #692 -#751 := [monotonicity #787 #748]: #750 -#744 := [trans #751 #753]: #754 -#738 := [monotonicity #744]: #737 -#735 := [trans #738 #740]: #737 -#736 := [quant-inst #9 #10]: #734 -#741 := [mp #736 #735]: #733 -#723 := [unit-resolution #741 #885]: #641 -#724 := [monotonicity #723]: #14 -#15 := (not #14) -#79 := [asserted]: #15 -[unit-resolution #79 #724]: false -unsat -589d59789d263d5382384d3b16ffc9ff725b6206 297 0 +#27 := (f3 0::Int) +#22 := (- 0::Int) +decl f4 :: (-> S2 Int) +decl f5 :: S2 +#8 := f5 +#9 := (f4 f5) +#21 := (- #9) +#23 := (div #21 #22) +#20 := (div #9 0::Int) +#15 := (< 0::Int 0::Int) +#17 := (< #9 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #9) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 0::Int 0::Int) +#11 := (= #9 0::Int) +#13 := (or #11 #12) +#25 := (ite #13 0::Int #24) +#26 := (f3 #25) +#28 := (= #26 #27) +#29 := (not #28) +#113 := (iff #29 false) +#1 := true +#108 := (not true) +#111 := (iff #108 false) +#112 := [rewrite]: #111 +#109 := (iff #29 #108) +#106 := (iff #28 true) +#101 := (= #27 #27) +#104 := (iff #101 true) +#105 := [rewrite]: #104 +#102 := (iff #28 #101) +#98 := (= #25 0::Int) +#81 := -1::Int +#82 := (* -1::Int #9) +#87 := (div #82 0::Int) +#75 := (and #15 #17) +#78 := (or #16 #75) +#90 := (ite #78 #20 #87) +#93 := (ite true 0::Int #90) +#96 := (= #93 0::Int) +#97 := [rewrite]: #96 +#94 := (= #25 #93) +#91 := (= #24 #90) +#88 := (= #23 #87) +#85 := (= #22 0::Int) +#86 := [rewrite]: #85 +#83 := (= #21 #82) +#84 := [rewrite]: #83 +#89 := [monotonicity #84 #86]: #88 +#79 := (iff #19 #78) +#76 := (iff #18 #75) +#77 := [rewrite]: #76 +#80 := [monotonicity #77]: #79 +#92 := [monotonicity #80 #89]: #91 +#73 := (iff #13 true) +#68 := (or #11 true) +#71 := (iff #68 true) +#72 := [rewrite]: #71 +#69 := (iff #13 #68) +#66 := (iff #12 true) +#67 := [rewrite]: #66 +#70 := [monotonicity #67]: #69 +#74 := [trans #70 #72]: #73 +#95 := [monotonicity #74 #92]: #94 +#99 := [trans #95 #97]: #98 +#100 := [monotonicity #99]: #28 +#103 := [monotonicity #100]: #102 +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107]: #109 +#114 := [trans #110 #112]: #113 +#65 := [asserted]: #29 +[mp #65 #114]: false +unsat +e01bd2bd51de7fe522eece30b6126b14fb1617b9 81 0 #2 := false decl f3 :: (-> Int S2) #8 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 1::Int -#10 := (f4 0::Int 1::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#806 := (= #10 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#32 := (f4 #31 #20) -#877 := (pattern #32) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#187 := (div #181 #184) -#359 := (* -1::Int #187) -#360 := (+ #32 #359) -#361 := (= #360 0::Int) -#42 := (div #31 #20) -#356 := (* -1::Int #42) -#357 := (+ #32 #356) -#358 := (= #357 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#362 := (ite #323 #358 #361) -#355 := (= #32 0::Int) -#34 := (= #20 0::Int) -#33 := (= #31 0::Int) -#35 := (or #33 #34) -#363 := (ite #35 #355 #362) -#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363) -#366 := (forall (vars (?v0 Int) (?v1 Int)) #363) -#881 := (iff #366 #878) -#879 := (iff #363 #363) -#880 := [refl]: #879 -#882 := [quant-intro #880]: #881 -#326 := (ite #323 #42 #187) -#329 := (ite #35 0::Int #326) -#332 := (= #32 #329) -#335 := (forall (vars (?v0 Int) (?v1 Int)) #332) -#367 := (iff #335 #366) -#364 := (iff #332 #363) -#365 := [rewrite]: #364 -#368 := [quant-intro #365]: #367 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#229 := (ite #226 #42 #187) -#232 := (ite #35 0::Int #229) -#235 := (= #32 #232) -#238 := (forall (vars (?v0 Int) (?v1 Int)) #235) -#336 := (iff #238 #335) -#333 := (iff #235 #332) -#330 := (= #232 #329) -#327 := (= #229 #326) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#328 := [monotonicity #325]: #327 -#331 := [monotonicity #328]: #330 -#334 := [monotonicity #331]: #333 -#337 := [quant-intro #334]: #336 -#298 := (~ #238 #238) -#311 := (~ #235 #235) -#312 := [refl]: #311 -#299 := [nnf-pos #312]: #298 -#44 := (- #20) -#43 := (- #31) -#45 := (div #43 #44) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#46 := (ite #41 #42 #45) -#47 := (ite #35 0::Int #46) -#48 := (= #32 #47) -#49 := (forall (vars (?v0 Int) (?v1 Int)) #48) -#241 := (iff #49 #238) -#174 := (and #37 #39) -#177 := (or #38 #174) -#190 := (ite #177 #42 #187) -#168 := (= 0::Int #20) -#165 := (= 0::Int #31) -#171 := (or #165 #168) -#193 := (ite #171 0::Int #190) -#196 := (= #32 #193) -#199 := (forall (vars (?v0 Int) (?v1 Int)) #196) -#239 := (iff #199 #238) -#236 := (iff #196 #235) -#233 := (= #193 #232) -#230 := (= #190 #229) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#231 := [monotonicity #228]: #230 -#206 := (iff #171 #35) -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#207 := [monotonicity #203 #205]: #206 -#234 := [monotonicity #207 #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [quant-intro #237]: #239 -#200 := (iff #49 #199) -#197 := (iff #48 #196) -#194 := (= #47 #193) -#191 := (= #46 #190) -#188 := (= #45 #187) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#189 := [monotonicity #183 #186]: #188 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#192 := [monotonicity #179 #189]: #191 -#172 := (iff #35 #171) -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#173 := [monotonicity #167 #170]: #172 -#195 := [monotonicity #173 #192]: #194 -#198 := [monotonicity #195]: #197 -#201 := [quant-intro #198]: #200 -#242 := [trans #201 #240]: #241 -#164 := [asserted]: #49 -#243 := [mp #164 #242]: #238 -#313 := [mp~ #243 #299]: #238 -#338 := [mp #313 #337]: #335 -#369 := [mp #338 #368]: #366 -#883 := [mp #369 #882]: #878 -#724 := (not #878) -#730 := (or #724 #806) -#812 := (* -1::Int 1::Int) -#813 := (* -1::Int 0::Int) -#808 := (div #813 #812) -#809 := (* -1::Int #808) -#814 := (+ #10 #809) -#815 := (= #814 0::Int) -#810 := (div 0::Int 1::Int) -#816 := (* -1::Int #810) -#657 := (+ #10 #816) -#658 := (= #657 0::Int) -#834 := (>= 0::Int 0::Int) -#659 := (<= 1::Int 0::Int) -#801 := (or #659 #834) -#802 := (not #801) -#803 := (<= 0::Int 0::Int) -#804 := (or #803 #659) -#798 := (not #804) -#799 := (or #798 #802) -#805 := (ite #799 #658 #815) -#800 := (= 1::Int 0::Int) -#807 := (= 0::Int 0::Int) -#636 := (or #807 #800) -#638 := (ite #636 #806 #805) -#703 := (or #724 #638) -#705 := (iff #703 #730) -#709 := (iff #730 #730) -#710 := [rewrite]: #709 -#728 := (iff #638 #806) -#1 := true -#721 := (ite true #806 #806) -#726 := (iff #721 #806) -#727 := [rewrite]: #726 -#722 := (iff #638 #721) -#739 := (iff #805 #806) -#735 := (ite false #806 #806) -#738 := (iff #735 #806) -#733 := [rewrite]: #738 -#736 := (iff #805 #735) -#732 := (iff #815 #806) -#753 := (= #814 #10) -#766 := (+ #10 0::Int) -#768 := (= #766 #10) -#754 := [rewrite]: #768 -#752 := (= #814 #766) -#750 := (= #809 0::Int) -#761 := (= #813 0::Int) -#762 := [rewrite]: #761 -#748 := (= #809 #813) -#746 := (= #808 0::Int) -#740 := (div 0::Int -1::Int) -#744 := (= #740 0::Int) -#745 := [rewrite]: #744 -#741 := (= #808 #740) -#756 := (= #812 -1::Int) -#760 := [rewrite]: #756 -#743 := [monotonicity #762 #760]: #741 -#747 := [trans #743 #745]: #746 -#749 := [monotonicity #747]: #748 -#751 := [trans #749 #762]: #750 -#742 := [monotonicity #751]: #752 -#731 := [trans #742 #754]: #753 -#734 := [monotonicity #731]: #732 -#758 := (iff #658 #806) -#755 := (= #657 #10) -#767 := (= #657 #766) -#764 := (= #816 0::Int) -#770 := (= #816 #813) -#775 := (= #810 0::Int) -#776 := [rewrite]: #775 -#777 := [monotonicity #776]: #770 -#765 := [trans #777 #762]: #764 -#763 := [monotonicity #765]: #767 -#757 := [trans #763 #754]: #755 -#759 := [monotonicity #757]: #758 -#773 := (iff #799 false) -#781 := (or false false) -#779 := (iff #781 false) -#784 := [rewrite]: #779 -#782 := (iff #799 #781) -#769 := (iff #802 false) -#482 := (not true) -#843 := (iff #482 false) -#829 := [rewrite]: #843 -#780 := (iff #802 #482) -#791 := (iff #801 true) -#695 := (or false true) -#790 := (iff #695 true) -#787 := [rewrite]: #790 -#696 := (iff #801 #695) -#841 := (iff #834 true) -#481 := [rewrite]: #841 -#785 := (iff #659 false) -#786 := [rewrite]: #785 -#697 := [monotonicity #786 #481]: #696 -#778 := [trans #697 #787]: #791 -#772 := [monotonicity #778]: #780 -#771 := [trans #772 #829]: #769 -#693 := (iff #798 false) -#692 := (iff #798 #482) -#689 := (iff #804 true) -#796 := (or true false) -#679 := (iff #796 true) -#680 := [rewrite]: #679 -#789 := (iff #804 #796) -#788 := (iff #803 true) -#690 := [rewrite]: #788 -#674 := [monotonicity #690 #786]: #789 -#691 := [trans #674 #680]: #689 -#685 := [monotonicity #691]: #692 -#694 := [trans #685 #829]: #693 -#783 := [monotonicity #694 #771]: #782 -#774 := [trans #783 #784]: #773 -#737 := [monotonicity #774 #759 #734]: #736 -#725 := [trans #737 #733]: #739 -#681 := (iff #636 true) -#794 := (iff #636 #796) -#793 := (iff #800 false) -#795 := [rewrite]: #793 -#639 := (iff #807 true) -#792 := [rewrite]: #639 -#797 := [monotonicity #792 #795]: #794 -#640 := [trans #797 #680]: #681 -#723 := [monotonicity #640 #725]: #722 -#729 := [trans #723 #727]: #728 -#598 := [monotonicity #729]: #705 -#711 := [trans #598 #710]: #705 -#704 := [quant-inst #8 #9]: #703 -#716 := [mp #704 #711]: #730 -#713 := [unit-resolution #716 #883]: #806 -#714 := [monotonicity #713]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #714]: false -unsat -009cf27bd16a3881b93b6b7959195f72499a5829 300 0 +#24 := (f3 0::Int) +#10 := 1::Int +#19 := (- 1::Int) +#18 := (- 0::Int) +#20 := (div #18 #19) +#17 := (div 0::Int 1::Int) +#14 := (< 0::Int 1::Int) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#21 := (ite #16 #17 #20) +#11 := (= 1::Int 0::Int) +#9 := (= 0::Int 0::Int) +#12 := (or #9 #11) +#22 := (ite #12 0::Int #21) +#23 := (f3 #22) +#25 := (= #23 #24) +#26 := (not #25) +#117 := (iff #26 false) +#1 := true +#112 := (not true) +#115 := (iff #112 false) +#116 := [rewrite]: #115 +#113 := (iff #26 #112) +#110 := (iff #25 true) +#105 := (= #24 #24) +#108 := (iff #105 true) +#109 := [rewrite]: #108 +#106 := (iff #25 #105) +#102 := (= #22 0::Int) +#97 := (ite true 0::Int 0::Int) +#100 := (= #97 0::Int) +#101 := [rewrite]: #100 +#98 := (= #22 #97) +#95 := (= #21 0::Int) +#90 := (ite #15 0::Int 0::Int) +#93 := (= #90 0::Int) +#94 := [rewrite]: #93 +#91 := (= #21 #90) +#88 := (= #20 0::Int) +#80 := -1::Int +#83 := (div 0::Int -1::Int) +#86 := (= #83 0::Int) +#87 := [rewrite]: #86 +#84 := (= #20 #83) +#81 := (= #19 -1::Int) +#82 := [rewrite]: #81 +#78 := (= #18 0::Int) +#79 := [rewrite]: #78 +#85 := [monotonicity #79 #82]: #84 +#89 := [trans #85 #87]: #88 +#76 := (= #17 0::Int) +#77 := [rewrite]: #76 +#74 := (iff #16 #15) +#75 := [rewrite]: #74 +#92 := [monotonicity #75 #77 #89]: #91 +#96 := [trans #92 #94]: #95 +#72 := (iff #12 true) +#67 := (or true false) +#70 := (iff #67 true) +#71 := [rewrite]: #70 +#68 := (iff #12 #67) +#65 := (iff #11 false) +#66 := [rewrite]: #65 +#63 := (iff #9 true) +#64 := [rewrite]: #63 +#69 := [monotonicity #64 #66]: #68 +#73 := [trans #69 #71]: #72 +#99 := [monotonicity #73 #96]: #98 +#103 := [trans #99 #101]: #102 +#104 := [monotonicity #103]: #25 +#107 := [monotonicity #104]: #106 +#111 := [trans #107 #109]: #110 +#114 := [monotonicity #111]: #113 +#118 := [trans #114 #116]: #117 +#62 := [asserted]: #26 +[mp #62 #118]: false +unsat +4d757130b0dc28fe958cf4c129cd34caadcedd08 82 0 #2 := false decl f3 :: (-> Int S2) #8 := 1::Int -#11 := (f3 1::Int) -decl f4 :: (-> Int Int Int) -#9 := (f4 1::Int 1::Int) -#10 := (f3 #9) -#12 := (= #10 #11) -#759 := (= #9 1::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#32 := (f4 #31 #20) -#877 := (pattern #32) -#19 := 0::Int -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#187 := (div #181 #184) -#359 := (* -1::Int #187) -#360 := (+ #32 #359) -#361 := (= #360 0::Int) -#42 := (div #31 #20) -#356 := (* -1::Int #42) -#357 := (+ #32 #356) -#358 := (= #357 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#362 := (ite #323 #358 #361) -#355 := (= #32 0::Int) -#34 := (= #20 0::Int) -#33 := (= #31 0::Int) -#35 := (or #33 #34) -#363 := (ite #35 #355 #362) -#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363) -#366 := (forall (vars (?v0 Int) (?v1 Int)) #363) -#881 := (iff #366 #878) -#879 := (iff #363 #363) -#880 := [refl]: #879 -#882 := [quant-intro #880]: #881 -#326 := (ite #323 #42 #187) -#329 := (ite #35 0::Int #326) -#332 := (= #32 #329) -#335 := (forall (vars (?v0 Int) (?v1 Int)) #332) -#367 := (iff #335 #366) -#364 := (iff #332 #363) -#365 := [rewrite]: #364 -#368 := [quant-intro #365]: #367 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#229 := (ite #226 #42 #187) -#232 := (ite #35 0::Int #229) -#235 := (= #32 #232) -#238 := (forall (vars (?v0 Int) (?v1 Int)) #235) -#336 := (iff #238 #335) -#333 := (iff #235 #332) -#330 := (= #232 #329) -#327 := (= #229 #326) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#328 := [monotonicity #325]: #327 -#331 := [monotonicity #328]: #330 -#334 := [monotonicity #331]: #333 -#337 := [quant-intro #334]: #336 -#298 := (~ #238 #238) -#311 := (~ #235 #235) -#312 := [refl]: #311 -#299 := [nnf-pos #312]: #298 -#44 := (- #20) -#43 := (- #31) -#45 := (div #43 #44) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#46 := (ite #41 #42 #45) -#47 := (ite #35 0::Int #46) -#48 := (= #32 #47) -#49 := (forall (vars (?v0 Int) (?v1 Int)) #48) -#241 := (iff #49 #238) -#174 := (and #37 #39) -#177 := (or #38 #174) -#190 := (ite #177 #42 #187) -#168 := (= 0::Int #20) -#165 := (= 0::Int #31) -#171 := (or #165 #168) -#193 := (ite #171 0::Int #190) -#196 := (= #32 #193) -#199 := (forall (vars (?v0 Int) (?v1 Int)) #196) -#239 := (iff #199 #238) -#236 := (iff #196 #235) -#233 := (= #193 #232) -#230 := (= #190 #229) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#231 := [monotonicity #228]: #230 -#206 := (iff #171 #35) -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#207 := [monotonicity #203 #205]: #206 -#234 := [monotonicity #207 #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [quant-intro #237]: #239 -#200 := (iff #49 #199) -#197 := (iff #48 #196) -#194 := (= #47 #193) -#191 := (= #46 #190) -#188 := (= #45 #187) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#189 := [monotonicity #183 #186]: #188 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#192 := [monotonicity #179 #189]: #191 -#172 := (iff #35 #171) -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#173 := [monotonicity #167 #170]: #172 -#195 := [monotonicity #173 #192]: #194 -#198 := [monotonicity #195]: #197 -#201 := [quant-intro #198]: #200 -#242 := [trans #201 #240]: #241 -#164 := [asserted]: #49 -#243 := [mp #164 #242]: #238 -#313 := [mp~ #243 #299]: #238 -#338 := [mp #313 #337]: #335 -#369 := [mp #338 #368]: #366 -#883 := [mp #369 #882]: #878 -#705 := (not #878) -#598 := (or #705 #759) -#813 := (* -1::Int 1::Int) -#808 := (div #813 #813) -#809 := (* -1::Int #808) -#814 := (+ #9 #809) -#815 := (= #814 0::Int) -#810 := (div 1::Int 1::Int) -#816 := (* -1::Int #810) -#657 := (+ #9 #816) -#658 := (= #657 0::Int) -#834 := (>= 1::Int 0::Int) -#659 := (<= 1::Int 0::Int) -#801 := (or #659 #834) -#802 := (not #801) -#803 := (or #659 #659) -#804 := (not #803) -#798 := (or #804 #802) -#799 := (ite #798 #658 #815) -#805 := (= #9 0::Int) -#806 := (= 1::Int 0::Int) -#800 := (or #806 #806) -#807 := (ite #800 #805 #799) -#709 := (or #705 #807) -#711 := (iff #709 #598) -#712 := (iff #598 #598) -#713 := [rewrite]: #712 -#703 := (iff #807 #759) -#727 := (ite false #805 #759) -#724 := (iff #727 #759) -#730 := [rewrite]: #724 -#728 := (iff #807 #727) -#723 := (iff #799 #759) -#1 := true -#733 := (ite true #759 #759) -#721 := (iff #733 #759) -#722 := [rewrite]: #721 -#739 := (iff #799 #733) -#737 := (iff #815 #759) -#766 := (+ -1::Int #9) -#755 := (= #766 0::Int) -#756 := (iff #755 #759) -#760 := [rewrite]: #756 -#735 := (iff #815 #755) -#732 := (= #814 #766) -#762 := (+ #9 -1::Int) -#767 := (= #762 #766) -#763 := [rewrite]: #767 -#753 := (= #814 #762) -#752 := (= #809 -1::Int) -#776 := (= #813 -1::Int) -#770 := [rewrite]: #776 -#750 := (= #809 #813) -#748 := (= #808 1::Int) -#743 := (div -1::Int -1::Int) -#746 := (= #743 1::Int) -#747 := [rewrite]: #746 -#744 := (= #808 #743) -#745 := [monotonicity #770 #770]: #744 -#749 := [trans #745 #747]: #748 -#751 := [monotonicity #749]: #750 -#742 := [trans #751 #770]: #752 -#731 := [monotonicity #742]: #753 -#734 := [trans #731 #763]: #732 -#736 := [monotonicity #734]: #735 -#738 := [trans #736 #760]: #737 -#740 := (iff #658 #759) -#757 := (iff #658 #755) -#768 := (= #657 #766) -#764 := (= #657 #762) -#777 := (= #816 -1::Int) -#774 := (= #816 #813) -#784 := (= #810 1::Int) -#773 := [rewrite]: #784 -#775 := [monotonicity #773]: #774 -#761 := [trans #775 #770]: #777 -#765 := [monotonicity #761]: #764 -#754 := [trans #765 #763]: #768 -#758 := [monotonicity #754]: #757 -#741 := [trans #758 #760]: #740 -#783 := (iff #798 true) -#772 := (or true false) -#781 := (iff #772 true) -#782 := [rewrite]: #781 -#769 := (iff #798 #772) -#778 := (iff #802 false) -#482 := (not true) -#843 := (iff #482 false) -#829 := [rewrite]: #843 -#787 := (iff #802 #482) -#697 := (iff #801 true) -#685 := (or false true) -#695 := (iff #685 true) -#696 := [rewrite]: #695 -#693 := (iff #801 #685) -#841 := (iff #834 true) -#481 := [rewrite]: #841 -#679 := (iff #659 false) -#680 := [rewrite]: #679 -#694 := [monotonicity #680 #481]: #693 -#790 := [trans #694 #696]: #697 -#791 := [monotonicity #790]: #787 -#780 := [trans #791 #829]: #778 -#691 := (iff #804 true) -#785 := (not false) -#674 := (iff #785 true) -#689 := [rewrite]: #674 -#786 := (iff #804 #785) -#788 := (iff #803 false) -#639 := (or false false) -#795 := (iff #639 false) -#796 := [rewrite]: #795 -#681 := (iff #803 #639) -#640 := [monotonicity #680 #680]: #681 -#690 := [trans #640 #796]: #788 -#789 := [monotonicity #690]: #786 -#692 := [trans #789 #689]: #691 -#771 := [monotonicity #692 #780]: #769 -#779 := [trans #771 #782]: #783 -#725 := [monotonicity #779 #741 #738]: #739 -#726 := [trans #725 #722]: #723 -#794 := (iff #800 false) -#792 := (iff #800 #639) -#636 := (iff #806 false) -#638 := [rewrite]: #636 -#793 := [monotonicity #638 #638]: #792 -#797 := [trans #793 #796]: #794 -#729 := [monotonicity #797 #726]: #728 -#704 := [trans #729 #730]: #703 -#716 := [monotonicity #704]: #711 -#714 := [trans #716 #713]: #711 -#710 := [quant-inst #8 #8]: #709 -#717 := [mp #710 #714]: #598 -#715 := [unit-resolution #717 #883]: #759 -#720 := [monotonicity #715]: #12 -#13 := (not #12) -#78 := [asserted]: #13 -[unit-resolution #78 #720]: false -unsat -ec9d2fe48d42e5d40fd0739c3491a43f0bf8c69d 311 0 +#23 := (f3 1::Int) +#18 := (- 1::Int) +#19 := (div #18 #18) +#17 := (div 1::Int 1::Int) +#9 := 0::Int +#12 := (< 0::Int 1::Int) +#14 := (< 1::Int 0::Int) +#15 := (and #14 #12) +#13 := (and #12 #12) +#16 := (or #13 #15) +#20 := (ite #16 #17 #19) +#10 := (= 1::Int 0::Int) +#11 := (or #10 #10) +#21 := (ite #11 0::Int #20) +#22 := (f3 #21) +#24 := (= #22 #23) +#25 := (not #24) +#118 := (iff #25 false) +#1 := true +#113 := (not true) +#116 := (iff #113 false) +#117 := [rewrite]: #116 +#114 := (iff #25 #113) +#111 := (iff #24 true) +#106 := (= #23 #23) +#109 := (iff #106 true) +#110 := [rewrite]: #109 +#107 := (iff #24 #106) +#103 := (= #21 1::Int) +#98 := (ite false 0::Int 1::Int) +#101 := (= #98 1::Int) +#102 := [rewrite]: #101 +#99 := (= #21 #98) +#96 := (= #20 1::Int) +#73 := (and #12 #14) +#76 := (or #12 #73) +#91 := (ite #76 1::Int 1::Int) +#94 := (= #91 1::Int) +#95 := [rewrite]: #94 +#92 := (= #20 #91) +#89 := (= #19 1::Int) +#81 := -1::Int +#84 := (div -1::Int -1::Int) +#87 := (= #84 1::Int) +#88 := [rewrite]: #87 +#85 := (= #19 #84) +#82 := (= #18 -1::Int) +#83 := [rewrite]: #82 +#86 := [monotonicity #83 #83]: #85 +#90 := [trans #86 #88]: #89 +#79 := (= #17 1::Int) +#80 := [rewrite]: #79 +#77 := (iff #16 #76) +#74 := (iff #15 #73) +#75 := [rewrite]: #74 +#71 := (iff #13 #12) +#72 := [rewrite]: #71 +#78 := [monotonicity #72 #75]: #77 +#93 := [monotonicity #78 #80 #90]: #92 +#97 := [trans #93 #95]: #96 +#69 := (iff #11 false) +#64 := (or false false) +#67 := (iff #64 false) +#68 := [rewrite]: #67 +#65 := (iff #11 #64) +#62 := (iff #10 false) +#63 := [rewrite]: #62 +#66 := [monotonicity #63 #63]: #65 +#70 := [trans #66 #68]: #69 +#100 := [monotonicity #70 #97]: #99 +#104 := [trans #100 #102]: #103 +#105 := [monotonicity #104]: #24 +#108 := [monotonicity #105]: #107 +#112 := [trans #108 #110]: #111 +#115 := [monotonicity #112]: #114 +#119 := [trans #115 #117]: #118 +#61 := [asserted]: #25 +[mp #61 #119]: false +unsat +5e55bd29247a2ea10048c10929dae98ba0bdec4e 89 0 #2 := false decl f3 :: (-> Int S2) #8 := 3::Int -#12 := (f3 3::Int) -decl f4 :: (-> Int Int Int) -#9 := 1::Int -#10 := (f4 3::Int 1::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#747 := (= #10 3::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#33 := (f4 #32 #21) -#878 := (pattern #33) -#20 := 0::Int -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#188 := (div #182 #185) -#360 := (* -1::Int #188) -#361 := (+ #33 #360) -#362 := (= #361 0::Int) -#43 := (div #32 #21) -#357 := (* -1::Int #43) -#358 := (+ #33 #357) -#359 := (= #358 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#363 := (ite #324 #359 #362) -#356 := (= #33 0::Int) -#35 := (= #21 0::Int) -#34 := (= #32 0::Int) -#36 := (or #34 #35) -#364 := (ite #36 #356 #363) -#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364) -#367 := (forall (vars (?v0 Int) (?v1 Int)) #364) -#882 := (iff #367 #879) -#880 := (iff #364 #364) -#881 := [refl]: #880 -#883 := [quant-intro #881]: #882 -#327 := (ite #324 #43 #188) -#330 := (ite #36 0::Int #327) -#333 := (= #33 #330) -#336 := (forall (vars (?v0 Int) (?v1 Int)) #333) -#368 := (iff #336 #367) -#365 := (iff #333 #364) -#366 := [rewrite]: #365 -#369 := [quant-intro #366]: #368 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#230 := (ite #227 #43 #188) -#233 := (ite #36 0::Int #230) -#236 := (= #33 #233) -#239 := (forall (vars (?v0 Int) (?v1 Int)) #236) -#337 := (iff #239 #336) -#334 := (iff #236 #333) -#331 := (= #233 #330) -#328 := (= #230 #327) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#329 := [monotonicity #326]: #328 -#332 := [monotonicity #329]: #331 -#335 := [monotonicity #332]: #334 -#338 := [quant-intro #335]: #337 -#299 := (~ #239 #239) -#312 := (~ #236 #236) -#313 := [refl]: #312 -#300 := [nnf-pos #313]: #299 -#45 := (- #21) -#44 := (- #32) -#46 := (div #44 #45) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#47 := (ite #42 #43 #46) -#48 := (ite #36 0::Int #47) -#49 := (= #33 #48) -#50 := (forall (vars (?v0 Int) (?v1 Int)) #49) -#242 := (iff #50 #239) -#175 := (and #38 #40) -#178 := (or #39 #175) -#191 := (ite #178 #43 #188) -#169 := (= 0::Int #21) -#166 := (= 0::Int #32) -#172 := (or #166 #169) -#194 := (ite #172 0::Int #191) -#197 := (= #33 #194) -#200 := (forall (vars (?v0 Int) (?v1 Int)) #197) -#240 := (iff #200 #239) -#237 := (iff #197 #236) -#234 := (= #194 #233) -#231 := (= #191 #230) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#232 := [monotonicity #229]: #231 -#207 := (iff #172 #36) -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#208 := [monotonicity #204 #206]: #207 -#235 := [monotonicity #208 #232]: #234 -#238 := [monotonicity #235]: #237 -#241 := [quant-intro #238]: #240 -#201 := (iff #50 #200) -#198 := (iff #49 #197) -#195 := (= #48 #194) -#192 := (= #47 #191) -#189 := (= #46 #188) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#190 := [monotonicity #184 #187]: #189 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#193 := [monotonicity #180 #190]: #192 -#173 := (iff #36 #172) -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#167 := (iff #34 #166) -#168 := [rewrite]: #167 -#174 := [monotonicity #168 #171]: #173 -#196 := [monotonicity #174 #193]: #195 -#199 := [monotonicity #196]: #198 -#202 := [quant-intro #199]: #201 -#243 := [trans #202 #241]: #242 -#165 := [asserted]: #50 -#244 := [mp #165 #243]: #239 -#314 := [mp~ #244 #300]: #239 -#339 := [mp #314 #338]: #336 -#370 := [mp #339 #369]: #367 -#884 := [mp #370 #883]: #879 -#719 := (not #879) -#720 := (or #719 #747) -#814 := (* -1::Int 1::Int) -#809 := (* -1::Int 3::Int) -#810 := (div #809 #814) -#815 := (* -1::Int #810) -#816 := (+ #10 #815) -#811 := (= #816 0::Int) -#817 := (div 3::Int 1::Int) -#658 := (* -1::Int #817) -#659 := (+ #10 #658) -#660 := (= #659 0::Int) -#835 := (>= 3::Int 0::Int) -#802 := (<= 1::Int 0::Int) -#803 := (or #802 #835) -#804 := (not #803) -#805 := (<= 3::Int 0::Int) -#799 := (or #805 #802) -#800 := (not #799) -#806 := (or #800 #804) -#807 := (ite #806 #660 #811) -#801 := (= #10 0::Int) -#808 := (= 1::Int 0::Int) -#637 := (= 3::Int 0::Int) -#639 := (or #637 #808) -#640 := (ite #639 #801 #807) -#716 := (or #719 #640) -#701 := (iff #716 #720) -#702 := (iff #720 #720) -#683 := [rewrite]: #702 -#715 := (iff #640 #747) -#711 := (ite false #801 #747) -#713 := (iff #711 #747) -#714 := [rewrite]: #713 -#712 := (iff #640 #711) -#599 := (iff #807 #747) -#1 := true -#725 := (ite true #747 #747) -#705 := (iff #725 #747) -#706 := [rewrite]: #705 -#731 := (iff #807 #725) -#729 := (iff #811 #747) -#767 := -3::Int -#760 := (+ -3::Int #10) -#744 := (= #760 0::Int) -#748 := (iff #744 #747) -#749 := [rewrite]: #748 -#727 := (iff #811 #744) -#723 := (= #816 #760) -#756 := (+ #10 -3::Int) -#757 := (= #756 #760) -#761 := [rewrite]: #757 -#726 := (= #816 #756) -#734 := (= #815 -3::Int) -#768 := (= #809 -3::Int) -#764 := [rewrite]: #768 -#738 := (= #815 #809) -#736 := (= #810 3::Int) -#743 := (div -3::Int -1::Int) -#733 := (= #743 3::Int) -#735 := [rewrite]: #733 -#754 := (= #810 #743) -#752 := (= #814 -1::Int) -#753 := [rewrite]: #752 -#732 := [monotonicity #764 #753]: #754 -#737 := [trans #732 #735]: #736 -#739 := [monotonicity #737]: #738 -#740 := [trans #739 #764]: #734 -#722 := [monotonicity #740]: #726 -#724 := [trans #722 #761]: #723 -#728 := [monotonicity #724]: #727 -#730 := [trans #728 #749]: #729 -#750 := (iff #660 #747) -#745 := (iff #660 #744) -#741 := (= #659 #760) -#758 := (= #659 #756) -#769 := (= #658 -3::Int) -#765 := (= #658 #809) -#762 := (= #817 3::Int) -#763 := [rewrite]: #762 -#766 := [monotonicity #763]: #765 -#755 := [trans #766 #764]: #769 -#759 := [monotonicity #755]: #758 -#742 := [trans #759 #761]: #741 -#746 := [monotonicity #742]: #745 -#751 := [trans #746 #749]: #750 -#771 := (iff #806 true) -#785 := (or true false) -#776 := (iff #785 true) -#777 := [rewrite]: #776 -#774 := (iff #806 #785) -#784 := (iff #804 false) -#483 := (not true) -#844 := (iff #483 false) -#830 := [rewrite]: #844 -#782 := (iff #804 #483) -#770 := (iff #803 true) -#788 := (or false true) -#781 := (iff #788 true) -#773 := [rewrite]: #781 -#792 := (iff #803 #788) -#842 := (iff #835 true) -#482 := [rewrite]: #842 -#787 := (iff #802 false) -#790 := [rewrite]: #787 -#779 := [monotonicity #790 #482]: #792 -#772 := [trans #779 #773]: #770 -#783 := [monotonicity #772]: #782 -#780 := [trans #783 #830]: #784 -#698 := (iff #800 true) -#686 := (not false) -#696 := (iff #686 true) -#697 := [rewrite]: #696 -#694 := (iff #800 #686) -#692 := (iff #799 false) -#795 := (or false false) -#681 := (iff #795 false) -#682 := [rewrite]: #681 -#675 := (iff #799 #795) -#691 := (iff #805 false) -#786 := [rewrite]: #691 -#690 := [monotonicity #786 #790]: #675 -#693 := [trans #690 #682]: #692 -#695 := [monotonicity #693]: #694 -#791 := [trans #695 #697]: #698 -#775 := [monotonicity #791 #780]: #774 -#778 := [trans #775 #777]: #771 -#704 := [monotonicity #778 #751 #730]: #731 -#710 := [trans #704 #706]: #599 -#641 := (iff #639 false) -#798 := (iff #639 #795) -#796 := (iff #808 false) -#797 := [rewrite]: #796 -#793 := (iff #637 false) -#794 := [rewrite]: #793 -#680 := [monotonicity #794 #797]: #798 -#789 := [trans #680 #682]: #641 -#717 := [monotonicity #789 #710]: #712 -#718 := [trans #717 #714]: #715 -#647 := [monotonicity #718]: #701 -#707 := [trans #647 #683]: #701 -#721 := [quant-inst #8 #9]: #716 -#708 := [mp #721 #707]: #720 -#677 := [unit-resolution #708 #884]: #747 -#684 := [monotonicity #677]: #13 -#14 := (not #13) -#79 := [asserted]: #14 -[unit-resolution #79 #684]: false -unsat -3563b0bf363f404d85eb515efc0ea6c63953194a 378 0 -#2 := false -decl f3 :: (-> Int S2) -decl f4 :: (-> Int Int Int) -#10 := 1::Int -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#11 := (f4 #9 1::Int) -#12 := (f3 #11) -#80 := (= f6 #12) -#451 := (f3 #9) -#669 := (= #451 #12) -#663 := (= #12 #451) -#731 := (= #11 #9) -#845 := (div #9 1::Int) -#660 := (= #845 #9) -#598 := (= #9 #845) -#20 := 0::Int -#188 := -1::Int -#840 := (* -1::Int #845) -#632 := (+ #9 #840) -#638 := (<= #632 0::Int) -#631 := (= #632 0::Int) -#1 := true -#77 := [true-axiom]: true -#588 := (or false #631) -#589 := [th-lemma arith]: #588 -#590 := [unit-resolution #589 #77]: #631 -#591 := (not #631) -#592 := (or #591 #638) -#593 := [th-lemma arith triangle-eq]: #592 -#594 := [unit-resolution #593 #590]: #638 -#481 := (>= #632 0::Int) -#595 := (or #591 #481) -#596 := [th-lemma arith triangle-eq]: #595 -#597 := [unit-resolution #596 #590]: #481 -#587 := [th-lemma arith eq-propagate 1 1 #597 #594]: #598 -#578 := [symm #587]: #660 -#604 := (= #11 #845) -#846 := (+ #11 #840) -#790 := (<= #846 0::Int) -#484 := (= #846 0::Int) -#562 := (= #9 0::Int) -#776 := (not #562) -#715 := (= 0::Int #9) -#654 := [hypothesis]: #562 -#730 := [symm #654]: #715 -#560 := (= #11 0::Int) -#709 := (or #776 #560) -#514 := (* -1::Int #9) -#644 := (div #514 -1::Int) -#800 := (* -1::Int #644) -#804 := (+ #11 #800) -#687 := (= #804 0::Int) -#850 := (<= #9 0::Int) -#830 := (not #850) -#847 := (>= #9 0::Int) -#665 := (not #847) -#812 := (or #665 #830) -#648 := (ite #812 #484 #687) -#793 := (ite #562 #560 #648) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#33 := (f4 #32 #21) -#885 := (pattern #33) -#192 := (* -1::Int #21) -#189 := (* -1::Int #32) -#195 := (div #189 #192) -#367 := (* -1::Int #195) -#368 := (+ #33 #367) -#369 := (= #368 0::Int) -#43 := (div #32 #21) -#364 := (* -1::Int #43) -#365 := (+ #33 #364) -#366 := (= #365 0::Int) -#227 := (>= #32 0::Int) -#220 := (<= #21 0::Int) -#327 := (or #220 #227) -#328 := (not #327) -#216 := (<= #32 0::Int) -#325 := (or #216 #220) -#326 := (not #325) -#331 := (or #326 #328) -#370 := (ite #331 #366 #369) -#363 := (= #33 0::Int) -#35 := (= #21 0::Int) -#34 := (= #32 0::Int) -#36 := (or #34 #35) -#371 := (ite #36 #363 #370) -#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #371) -#374 := (forall (vars (?v0 Int) (?v1 Int)) #371) -#889 := (iff #374 #886) -#887 := (iff #371 #371) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#334 := (ite #331 #43 #195) -#337 := (ite #36 0::Int #334) -#340 := (= #33 #337) -#343 := (forall (vars (?v0 Int) (?v1 Int)) #340) -#375 := (iff #343 #374) -#372 := (iff #340 #371) -#373 := [rewrite]: #372 -#376 := [quant-intro #373]: #375 -#228 := (not #227) -#221 := (not #220) -#231 := (and #221 #228) -#217 := (not #216) -#224 := (and #217 #221) -#234 := (or #224 #231) -#237 := (ite #234 #43 #195) -#240 := (ite #36 0::Int #237) -#243 := (= #33 #240) -#246 := (forall (vars (?v0 Int) (?v1 Int)) #243) -#344 := (iff #246 #343) -#341 := (iff #243 #340) -#338 := (= #240 #337) -#335 := (= #237 #334) -#332 := (iff #234 #331) -#329 := (iff #231 #328) -#330 := [rewrite]: #329 -#310 := (iff #224 #326) -#311 := [rewrite]: #310 -#333 := [monotonicity #311 #330]: #332 -#336 := [monotonicity #333]: #335 -#339 := [monotonicity #336]: #338 -#342 := [monotonicity #339]: #341 -#345 := [quant-intro #342]: #344 -#306 := (~ #246 #246) -#319 := (~ #243 #243) -#320 := [refl]: #319 -#307 := [nnf-pos #320]: #306 -#45 := (- #21) -#44 := (- #32) -#46 := (div #44 #45) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#47 := (ite #42 #43 #46) -#48 := (ite #36 0::Int #47) -#49 := (= #33 #48) -#50 := (forall (vars (?v0 Int) (?v1 Int)) #49) -#249 := (iff #50 #246) -#182 := (and #38 #40) -#185 := (or #39 #182) -#198 := (ite #185 #43 #195) -#176 := (= 0::Int #21) -#173 := (= 0::Int #32) -#179 := (or #173 #176) -#201 := (ite #179 0::Int #198) -#204 := (= #33 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#247 := (iff #207 #246) -#244 := (iff #204 #243) -#241 := (= #201 #240) -#238 := (= #198 #237) -#235 := (iff #185 #234) -#232 := (iff #182 #231) -#229 := (iff #40 #228) -#230 := [rewrite]: #229 -#222 := (iff #38 #221) -#223 := [rewrite]: #222 -#233 := [monotonicity #223 #230]: #232 -#225 := (iff #39 #224) -#218 := (iff #37 #217) -#219 := [rewrite]: #218 -#226 := [monotonicity #219 #223]: #225 -#236 := [monotonicity #226 #233]: #235 -#239 := [monotonicity #236]: #238 -#214 := (iff #179 #36) -#212 := (iff #176 #35) -#213 := [rewrite]: #212 -#210 := (iff #173 #34) -#211 := [rewrite]: #210 -#215 := [monotonicity #211 #213]: #214 -#242 := [monotonicity #215 #239]: #241 -#245 := [monotonicity #242]: #244 -#248 := [quant-intro #245]: #247 -#208 := (iff #50 #207) -#205 := (iff #49 #204) -#202 := (= #48 #201) -#199 := (= #47 #198) -#196 := (= #46 #195) -#193 := (= #45 #192) -#194 := [rewrite]: #193 -#190 := (= #44 #189) -#191 := [rewrite]: #190 -#197 := [monotonicity #191 #194]: #196 -#186 := (iff #42 #185) -#183 := (iff #41 #182) -#184 := [rewrite]: #183 -#187 := [monotonicity #184]: #186 -#200 := [monotonicity #187 #197]: #199 -#180 := (iff #36 #179) -#177 := (iff #35 #176) -#178 := [rewrite]: #177 -#174 := (iff #34 #173) -#175 := [rewrite]: #174 -#181 := [monotonicity #175 #178]: #180 -#203 := [monotonicity #181 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#250 := [trans #209 #248]: #249 -#172 := [asserted]: #50 -#251 := [mp #172 #250]: #246 -#321 := [mp~ #251 #307]: #246 -#346 := [mp #321 #345]: #343 -#377 := [mp #346 #376]: #374 -#891 := [mp #377 #890]: #886 -#682 := (not #886) -#697 := (or #682 #793) -#854 := (* -1::Int 1::Int) -#841 := (div #514 #854) -#842 := (* -1::Int #841) -#843 := (+ #11 #842) -#844 := (= #843 0::Int) -#849 := (<= 1::Int 0::Int) -#489 := (or #849 #847) -#490 := (not #489) -#848 := (or #850 #849) -#851 := (not #848) -#837 := (or #851 #490) -#838 := (ite #837 #484 #844) -#561 := (= 1::Int 0::Int) -#563 := (or #562 #561) -#457 := (ite #563 #560 #838) -#699 := (or #682 #457) -#693 := (iff #699 #697) -#702 := (iff #697 #697) -#703 := [rewrite]: #702 -#794 := (iff #457 #793) -#796 := (iff #838 #648) -#688 := (iff #844 #687) -#802 := (= #843 #804) -#801 := (= #842 #800) -#646 := (= #841 #644) -#808 := (= #854 -1::Int) -#815 := [rewrite]: #808 -#647 := [monotonicity #815]: #646 -#803 := [monotonicity #647]: #801 -#805 := [monotonicity #803]: #802 -#689 := [monotonicity #805]: #688 -#813 := (iff #837 #812) -#809 := (or #830 #665) -#806 := (iff #809 #812) -#807 := [rewrite]: #806 -#810 := (iff #837 #809) -#666 := (iff #490 #665) -#818 := (iff #489 #847) -#821 := (or false #847) -#822 := (iff #821 #847) -#823 := [rewrite]: #822 -#816 := (iff #489 #821) -#547 := (iff #849 false) -#548 := [rewrite]: #547 -#817 := [monotonicity #548]: #816 -#824 := [trans #817 #823]: #818 -#667 := [monotonicity #824]: #666 -#819 := (iff #851 #830) -#829 := (iff #848 #850) -#549 := (or #850 false) -#543 := (iff #549 #850) -#825 := [rewrite]: #543 -#827 := (iff #848 #549) -#828 := [monotonicity #548]: #827 -#826 := [trans #828 #825]: #829 -#820 := [monotonicity #826]: #819 -#811 := [monotonicity #820 #667]: #810 -#814 := [trans #811 #807]: #813 -#698 := [monotonicity #814 #689]: #796 -#836 := (iff #563 #562) -#556 := (or #562 false) -#835 := (iff #556 #562) -#832 := [rewrite]: #835 -#557 := (iff #563 #556) -#833 := (iff #561 false) -#834 := [rewrite]: #833 -#831 := [monotonicity #834]: #557 -#546 := [trans #831 #832]: #836 -#797 := [monotonicity #546 #698]: #794 -#701 := [monotonicity #797]: #693 -#704 := [trans #701 #703]: #693 -#700 := [quant-inst #9 #10]: #699 -#705 := [mp #700 #704]: #697 -#684 := [unit-resolution #705 #891]: #793 -#771 := (not #793) -#762 := (or #771 #776 #560) -#763 := [def-axiom]: #762 -#690 := [unit-resolution #763 #684]: #709 -#714 := [unit-resolution #690 #654]: #560 -#707 := [trans #714 #730]: #731 -#668 := [monotonicity #707]: #663 -#670 := [symm #668]: #669 -#535 := (= f6 #451) -#15 := (:var 0 S2) -#16 := (f5 #15) -#864 := (pattern #16) -#17 := (f3 #16) -#87 := (= #15 #17) -#865 := (forall (vars (?v0 S2)) (:pat #864) #87) -#91 := (forall (vars (?v0 S2)) #87) -#866 := (iff #91 #865) -#868 := (iff #865 #865) -#869 := [rewrite]: #868 -#867 := [rewrite]: #866 -#870 := [trans #867 #869]: #866 -#314 := (~ #91 #91) -#312 := (~ #87 #87) -#313 := [refl]: #312 -#315 := [nnf-pos #313]: #314 -#18 := (= #17 #15) -#19 := (forall (vars (?v0 S2)) #18) -#92 := (iff #19 #91) -#89 := (iff #18 #87) +#27 := (f3 3::Int) +#11 := 1::Int +#22 := (- 1::Int) +#21 := (- 3::Int) +#23 := (div #21 #22) +#20 := (div 3::Int 1::Int) +#9 := 0::Int +#15 := (< 0::Int 1::Int) +#17 := (< 3::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 3::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 1::Int 0::Int) +#10 := (= 3::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (f3 #25) +#28 := (= #26 #27) +#29 := (not #28) +#125 := (iff #29 false) +#1 := true +#120 := (not true) +#123 := (iff #120 false) +#124 := [rewrite]: #123 +#121 := (iff #29 #120) +#118 := (iff #28 true) +#113 := (= #27 #27) +#116 := (iff #113 true) +#117 := [rewrite]: #116 +#114 := (iff #28 #113) +#110 := (= #25 3::Int) +#105 := (ite false 0::Int 3::Int) +#108 := (= #105 3::Int) +#109 := [rewrite]: #108 +#106 := (= #25 #105) +#103 := (= #24 3::Int) +#77 := (and #15 #17) +#80 := (or #16 #77) +#98 := (ite #80 3::Int 3::Int) +#101 := (= #98 3::Int) +#102 := [rewrite]: #101 +#99 := (= #24 #98) +#96 := (= #23 3::Int) +#88 := -1::Int +#85 := -3::Int +#91 := (div -3::Int -1::Int) +#94 := (= #91 3::Int) +#95 := [rewrite]: #94 +#92 := (= #23 #91) +#89 := (= #22 -1::Int) #90 := [rewrite]: #89 -#93 := [quant-intro #90]: #92 -#86 := [asserted]: #19 -#96 := [mp #86 #93]: #91 -#300 := [mp~ #96 #315]: #91 -#871 := [mp #300 #870]: #865 -#528 := (not #865) -#539 := (or #528 #535) -#540 := [quant-inst #8]: #539 -#662 := [unit-resolution #540 #871]: #535 -#671 := [trans #662 #670]: #80 -#83 := (not #80) -#13 := (= #12 f6) -#14 := (not #13) -#84 := (iff #14 #83) -#81 := (iff #13 #80) -#82 := [rewrite]: #81 -#85 := [monotonicity #82]: #84 -#79 := [asserted]: #14 -#88 := [mp #79 #85]: #83 -#672 := [unit-resolution #88 #671]: false -#673 := [lemma #672]: #776 -#706 := (or #562 #484) -#780 := (not #812) -#769 := (not #484) -#710 := [hypothesis]: #769 -#716 := [hypothesis]: #776 -#691 := (or #562 #648) -#765 := (or #771 #562 #648) -#766 := [def-axiom]: #765 -#650 := [unit-resolution #766 #684]: #691 -#681 := [unit-resolution #650 #716]: #648 -#782 := (not #648) -#783 := (or #782 #780 #484) -#784 := [def-axiom]: #783 -#683 := [unit-resolution #784 #681 #710]: #780 -#786 := (or #812 #850) -#788 := [def-axiom]: #786 -#685 := [unit-resolution #788 #683]: #850 -#795 := (or #812 #847) -#799 := [def-axiom]: #795 -#692 := [unit-resolution #799 #683]: #847 -#694 := (or #562 #830 #665) -#695 := [th-lemma arith triangle-eq]: #694 -#696 := [unit-resolution #695 #716 #692 #685]: false -#686 := [lemma #696]: #706 -#610 := [unit-resolution #686 #673]: #484 -#613 := (or #769 #790) -#614 := [th-lemma arith triangle-eq]: #613 -#600 := [unit-resolution #614 #610]: #790 -#791 := (>= #846 0::Int) -#602 := (or #769 #791) -#603 := [th-lemma arith triangle-eq]: #602 -#601 := [unit-resolution #603 #610]: #791 -#586 := [th-lemma arith eq-propagate 1 1 #601 #600]: #604 -#579 := [trans #586 #578]: #731 -#580 := [monotonicity #579]: #663 -#581 := [symm #580]: #669 -#582 := [trans #662 #581]: #80 -[unit-resolution #88 #582]: false -unsat -84bb282eead031ef4ff9718b6ca086d90bb4eefb 298 0 -#2 := false -decl f3 :: (-> Int S2) -#8 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 3::Int -#10 := (f4 0::Int 3::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#806 := (= #10 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#32 := (f4 #31 #20) -#878 := (pattern #32) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#187 := (div #181 #184) -#359 := (* -1::Int #187) -#360 := (+ #32 #359) -#361 := (= #360 0::Int) -#42 := (div #31 #20) -#356 := (* -1::Int #42) -#357 := (+ #32 #356) -#358 := (= #357 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#362 := (ite #323 #358 #361) -#355 := (= #32 0::Int) -#34 := (= #20 0::Int) -#33 := (= #31 0::Int) -#35 := (or #33 #34) -#363 := (ite #35 #355 #362) -#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #363) -#366 := (forall (vars (?v0 Int) (?v1 Int)) #363) -#882 := (iff #366 #879) -#880 := (iff #363 #363) -#881 := [refl]: #880 -#883 := [quant-intro #881]: #882 -#326 := (ite #323 #42 #187) -#329 := (ite #35 0::Int #326) -#332 := (= #32 #329) -#335 := (forall (vars (?v0 Int) (?v1 Int)) #332) -#367 := (iff #335 #366) -#364 := (iff #332 #363) -#365 := [rewrite]: #364 -#368 := [quant-intro #365]: #367 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#229 := (ite #226 #42 #187) -#232 := (ite #35 0::Int #229) -#235 := (= #32 #232) -#238 := (forall (vars (?v0 Int) (?v1 Int)) #235) -#336 := (iff #238 #335) -#333 := (iff #235 #332) -#330 := (= #232 #329) -#327 := (= #229 #326) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#328 := [monotonicity #325]: #327 -#331 := [monotonicity #328]: #330 -#334 := [monotonicity #331]: #333 -#337 := [quant-intro #334]: #336 -#298 := (~ #238 #238) -#311 := (~ #235 #235) -#312 := [refl]: #311 -#299 := [nnf-pos #312]: #298 -#44 := (- #20) -#43 := (- #31) -#45 := (div #43 #44) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#46 := (ite #41 #42 #45) -#47 := (ite #35 0::Int #46) -#48 := (= #32 #47) -#49 := (forall (vars (?v0 Int) (?v1 Int)) #48) -#241 := (iff #49 #238) -#174 := (and #37 #39) -#177 := (or #38 #174) -#190 := (ite #177 #42 #187) -#168 := (= 0::Int #20) -#165 := (= 0::Int #31) -#171 := (or #165 #168) -#193 := (ite #171 0::Int #190) -#196 := (= #32 #193) -#199 := (forall (vars (?v0 Int) (?v1 Int)) #196) -#239 := (iff #199 #238) -#236 := (iff #196 #235) -#233 := (= #193 #232) -#230 := (= #190 #229) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#231 := [monotonicity #228]: #230 -#206 := (iff #171 #35) -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#207 := [monotonicity #203 #205]: #206 -#234 := [monotonicity #207 #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [quant-intro #237]: #239 -#200 := (iff #49 #199) -#197 := (iff #48 #196) -#194 := (= #47 #193) -#191 := (= #46 #190) -#188 := (= #45 #187) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#189 := [monotonicity #183 #186]: #188 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#192 := [monotonicity #179 #189]: #191 -#172 := (iff #35 #171) -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#173 := [monotonicity #167 #170]: #172 -#195 := [monotonicity #173 #192]: #194 -#198 := [monotonicity #195]: #197 -#201 := [quant-intro #198]: #200 -#242 := [trans #201 #240]: #241 -#164 := [asserted]: #49 -#243 := [mp #164 #242]: #238 -#313 := [mp~ #243 #299]: #238 -#338 := [mp #313 #337]: #335 -#369 := [mp #338 #368]: #366 -#884 := [mp #369 #883]: #879 -#725 := (not #879) -#731 := (or #725 #806) -#812 := (* -1::Int 3::Int) -#813 := (* -1::Int 0::Int) -#814 := (div #813 #812) -#809 := (* -1::Int #814) -#810 := (+ #10 #809) -#815 := (= #810 0::Int) -#816 := (div 0::Int 3::Int) -#811 := (* -1::Int #816) -#817 := (+ #10 #811) -#658 := (= #817 0::Int) -#834 := (>= 0::Int 0::Int) -#659 := (<= 3::Int 0::Int) -#660 := (or #659 #834) -#802 := (not #660) -#803 := (<= 0::Int 0::Int) -#804 := (or #803 #659) -#805 := (not #804) -#799 := (or #805 #802) -#800 := (ite #799 #658 #815) -#807 := (= 3::Int 0::Int) -#801 := (= 0::Int 0::Int) -#808 := (or #801 #807) -#637 := (ite #808 #806 #800) -#704 := (or #725 #637) -#706 := (iff #704 #731) -#710 := (iff #731 #731) -#711 := [rewrite]: #710 -#729 := (iff #637 #806) -#1 := true -#722 := (ite true #806 #806) -#727 := (iff #722 #806) -#728 := [rewrite]: #727 -#723 := (iff #637 #722) -#740 := (iff #800 #806) -#736 := (ite false #806 #806) -#739 := (iff #736 #806) -#734 := [rewrite]: #739 -#737 := (iff #800 #736) -#733 := (iff #815 #806) -#754 := (= #810 #10) -#766 := (+ #10 0::Int) -#764 := (= #766 #10) -#769 := [rewrite]: #764 -#753 := (= #810 #766) -#751 := (= #809 0::Int) -#778 := (= #813 0::Int) -#762 := [rewrite]: #778 -#749 := (= #809 #813) -#747 := (= #814 0::Int) -#760 := -3::Int -#741 := (div 0::Int -3::Int) -#745 := (= #741 0::Int) -#746 := [rewrite]: #745 -#742 := (= #814 #741) -#757 := (= #812 -3::Int) -#761 := [rewrite]: #757 -#744 := [monotonicity #762 #761]: #742 -#748 := [trans #744 #746]: #747 -#750 := [monotonicity #748]: #749 -#752 := [trans #750 #762]: #751 -#743 := [monotonicity #752]: #753 -#732 := [trans #743 #769]: #754 -#735 := [monotonicity #732]: #733 -#758 := (iff #658 #806) -#755 := (= #817 #10) -#767 := (= #817 #766) -#763 := (= #811 0::Int) -#777 := (= #811 #813) -#775 := (= #816 0::Int) -#776 := [rewrite]: #775 -#771 := [monotonicity #776]: #777 -#765 := [trans #771 #762]: #763 -#768 := [monotonicity #765]: #767 -#756 := [trans #768 #769]: #755 -#759 := [monotonicity #756]: #758 -#785 := (iff #799 false) -#772 := (or false false) -#784 := (iff #772 false) -#780 := [rewrite]: #784 -#782 := (iff #799 #772) -#773 := (iff #802 false) -#482 := (not true) -#841 := (iff #482 false) -#844 := [rewrite]: #841 -#779 := (iff #802 #482) -#788 := (iff #660 true) -#695 := (or false true) -#698 := (iff #695 true) -#791 := [rewrite]: #698 -#696 := (iff #660 #695) -#840 := (iff #834 true) -#842 := [rewrite]: #840 -#691 := (iff #659 false) -#786 := [rewrite]: #691 -#697 := [monotonicity #786 #842]: #696 -#792 := [trans #697 #791]: #788 -#781 := [monotonicity #792]: #779 -#770 := [trans #781 #844]: #773 -#686 := (iff #805 false) -#692 := (iff #805 #482) -#675 := (iff #804 true) -#796 := (or true false) -#798 := (iff #796 true) -#680 := [rewrite]: #798 -#787 := (iff #804 #796) -#641 := (iff #803 true) -#789 := [rewrite]: #641 -#790 := [monotonicity #789 #786]: #787 -#690 := [trans #790 #680]: #675 -#693 := [monotonicity #690]: #692 -#694 := [trans #693 #844]: #686 -#783 := [monotonicity #694 #770]: #782 -#774 := [trans #783 #780]: #785 -#738 := [monotonicity #774 #759 #735]: #737 -#726 := [trans #738 #734]: #740 -#681 := (iff #808 true) -#797 := (iff #808 #796) -#793 := (iff #807 false) -#794 := [rewrite]: #793 -#639 := (iff #801 true) -#640 := [rewrite]: #639 -#795 := [monotonicity #640 #794]: #797 -#682 := [trans #795 #680]: #681 -#724 := [monotonicity #682 #726]: #723 -#730 := [trans #724 #728]: #729 -#599 := [monotonicity #730]: #706 -#712 := [trans #599 #711]: #706 -#705 := [quant-inst #8 #9]: #704 -#717 := [mp #705 #712]: #731 -#714 := [unit-resolution #717 #884]: #806 -#715 := [monotonicity #714]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #715]: false -unsat -753372d6275197bbef48a8ecc32b53d9fd3d1075 315 0 -#2 := false -decl f3 :: (-> Int S2) -#12 := 0::Int -#13 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 3::Int -#8 := 1::Int -#10 := (f4 1::Int 3::Int) -#11 := (f3 #10) -#14 := (= #11 #13) -#801 := (= #10 0::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#33 := (f4 #32 #21) -#878 := (pattern #33) -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#188 := (div #182 #185) -#360 := (* -1::Int #188) -#361 := (+ #33 #360) -#362 := (= #361 0::Int) -#43 := (div #32 #21) -#357 := (* -1::Int #43) -#358 := (+ #33 #357) -#359 := (= #358 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#363 := (ite #324 #359 #362) -#356 := (= #33 0::Int) -#35 := (= #21 0::Int) -#34 := (= #32 0::Int) -#36 := (or #34 #35) -#364 := (ite #36 #356 #363) -#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364) -#367 := (forall (vars (?v0 Int) (?v1 Int)) #364) -#882 := (iff #367 #879) -#880 := (iff #364 #364) -#881 := [refl]: #880 -#883 := [quant-intro #881]: #882 -#327 := (ite #324 #43 #188) -#330 := (ite #36 0::Int #327) -#333 := (= #33 #330) -#336 := (forall (vars (?v0 Int) (?v1 Int)) #333) -#368 := (iff #336 #367) -#365 := (iff #333 #364) -#366 := [rewrite]: #365 -#369 := [quant-intro #366]: #368 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#230 := (ite #227 #43 #188) -#233 := (ite #36 0::Int #230) -#236 := (= #33 #233) -#239 := (forall (vars (?v0 Int) (?v1 Int)) #236) -#337 := (iff #239 #336) -#334 := (iff #236 #333) -#331 := (= #233 #330) -#328 := (= #230 #327) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#329 := [monotonicity #326]: #328 -#332 := [monotonicity #329]: #331 -#335 := [monotonicity #332]: #334 -#338 := [quant-intro #335]: #337 -#299 := (~ #239 #239) -#312 := (~ #236 #236) -#313 := [refl]: #312 -#300 := [nnf-pos #313]: #299 -#45 := (- #21) -#44 := (- #32) -#46 := (div #44 #45) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#47 := (ite #42 #43 #46) -#48 := (ite #36 0::Int #47) -#49 := (= #33 #48) -#50 := (forall (vars (?v0 Int) (?v1 Int)) #49) -#242 := (iff #50 #239) -#175 := (and #38 #40) -#178 := (or #39 #175) -#191 := (ite #178 #43 #188) -#169 := (= 0::Int #21) -#166 := (= 0::Int #32) -#172 := (or #166 #169) -#194 := (ite #172 0::Int #191) -#197 := (= #33 #194) -#200 := (forall (vars (?v0 Int) (?v1 Int)) #197) -#240 := (iff #200 #239) -#237 := (iff #197 #236) -#234 := (= #194 #233) -#231 := (= #191 #230) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#232 := [monotonicity #229]: #231 -#207 := (iff #172 #36) -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#208 := [monotonicity #204 #206]: #207 -#235 := [monotonicity #208 #232]: #234 -#238 := [monotonicity #235]: #237 -#241 := [quant-intro #238]: #240 -#201 := (iff #50 #200) -#198 := (iff #49 #197) -#195 := (= #48 #194) -#192 := (= #47 #191) -#189 := (= #46 #188) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#190 := [monotonicity #184 #187]: #189 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#193 := [monotonicity #180 #190]: #192 -#173 := (iff #36 #172) -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#167 := (iff #34 #166) -#168 := [rewrite]: #167 -#174 := [monotonicity #168 #171]: #173 -#196 := [monotonicity #174 #193]: #195 -#199 := [monotonicity #196]: #198 -#202 := [quant-intro #199]: #201 -#243 := [trans #202 #241]: #242 -#165 := [asserted]: #50 -#244 := [mp #165 #243]: #239 -#314 := [mp~ #244 #300]: #239 -#339 := [mp #314 #338]: #336 -#370 := [mp #339 #369]: #367 -#884 := [mp #370 #883]: #879 -#702 := (not #879) -#683 := (or #702 #801) -#813 := (* -1::Int 3::Int) -#814 := (* -1::Int 1::Int) -#809 := (div #814 #813) -#810 := (* -1::Int #809) -#815 := (+ #10 #810) -#816 := (= #815 0::Int) -#811 := (div 1::Int 3::Int) -#817 := (* -1::Int #811) -#658 := (+ #10 #817) -#659 := (= #658 0::Int) -#660 := (>= 1::Int 0::Int) -#802 := (<= 3::Int 0::Int) -#803 := (or #802 #660) -#804 := (not #803) -#805 := (<= 1::Int 0::Int) -#799 := (or #805 #802) -#800 := (not #799) -#806 := (or #800 #804) -#807 := (ite #806 #659 #816) -#808 := (= 3::Int 0::Int) -#637 := (= 1::Int 0::Int) -#639 := (or #637 #808) -#640 := (ite #639 #801 #807) -#707 := (or #702 #640) -#703 := (iff #707 #683) -#677 := (iff #683 #683) -#684 := [rewrite]: #677 -#701 := (iff #640 #801) -#718 := (ite false #801 #801) -#716 := (iff #718 #801) -#721 := [rewrite]: #716 -#719 := (iff #640 #718) -#714 := (iff #807 #801) -#731 := (= #10 1::Int) -#1 := true -#710 := (ite true #801 #731) -#717 := (iff #710 #801) -#713 := [rewrite]: #717 -#711 := (iff #807 #710) -#706 := (iff #816 #731) -#722 := (+ -1::Int #10) -#729 := (= #722 0::Int) -#704 := (iff #729 #731) -#705 := [rewrite]: #704 -#730 := (iff #816 #729) -#727 := (= #815 #722) -#734 := (+ #10 -1::Int) -#723 := (= #734 #722) -#724 := [rewrite]: #723 -#740 := (= #815 #734) -#738 := (= #810 -1::Int) -#747 := (= #814 -1::Int) -#748 := [rewrite]: #747 -#736 := (= #810 #814) -#733 := (= #809 1::Int) -#749 := -3::Int -#752 := (div -1::Int -3::Int) -#754 := (= #752 1::Int) -#732 := [rewrite]: #754 -#753 := (= #809 #752) -#750 := (= #813 -3::Int) -#751 := [rewrite]: #750 -#743 := [monotonicity #748 #751]: #753 -#735 := [trans #743 #732]: #733 -#737 := [monotonicity #735]: #736 -#739 := [trans #737 #748]: #738 -#726 := [monotonicity #739]: #740 -#728 := [trans #726 #724]: #727 -#725 := [monotonicity #728]: #730 -#599 := [trans #725 #705]: #706 -#745 := (iff #659 #801) -#742 := (= #658 #10) -#759 := (+ #10 0::Int) -#761 := (= #759 #10) -#741 := [rewrite]: #761 -#760 := (= #658 #759) -#756 := (= #817 0::Int) -#767 := (* -1::Int 0::Int) -#769 := (= #767 0::Int) -#755 := [rewrite]: #769 -#768 := (= #817 #767) -#765 := (= #811 0::Int) -#766 := [rewrite]: #765 -#764 := [monotonicity #766]: #768 -#758 := [trans #764 #755]: #756 -#757 := [monotonicity #758]: #760 -#744 := [trans #757 #741]: #742 -#746 := [monotonicity #744]: #745 -#762 := (iff #806 true) -#775 := (or true false) -#771 := (iff #775 true) -#778 := [rewrite]: #771 -#776 := (iff #806 #775) -#785 := (iff #804 false) -#483 := (not true) -#844 := (iff #483 false) -#830 := [rewrite]: #844 -#784 := (iff #804 #483) -#782 := (iff #803 true) -#779 := (or false true) -#770 := (iff #779 true) -#772 := [rewrite]: #770 -#781 := (iff #803 #779) -#788 := (iff #660 true) -#792 := [rewrite]: #788 -#787 := (iff #802 false) -#790 := [rewrite]: #787 -#773 := [monotonicity #790 #792]: #781 -#783 := [trans #773 #772]: #782 -#780 := [monotonicity #783]: #784 -#774 := [trans #780 #830]: #785 -#698 := (iff #800 true) -#686 := (not false) -#696 := (iff #686 true) -#697 := [rewrite]: #696 -#694 := (iff #800 #686) -#692 := (iff #799 false) -#795 := (or false false) -#681 := (iff #795 false) -#682 := [rewrite]: #681 -#675 := (iff #799 #795) -#691 := (iff #805 false) -#786 := [rewrite]: #691 -#690 := [monotonicity #786 #790]: #675 -#693 := [trans #690 #682]: #692 -#695 := [monotonicity #693]: #694 -#791 := [trans #695 #697]: #698 -#777 := [monotonicity #791 #774]: #776 -#763 := [trans #777 #778]: #762 -#712 := [monotonicity #763 #746 #599]: #711 -#715 := [trans #712 #713]: #714 -#641 := (iff #639 false) -#798 := (iff #639 #795) -#796 := (iff #808 false) -#797 := [rewrite]: #796 -#793 := (iff #637 false) -#794 := [rewrite]: #793 -#680 := [monotonicity #794 #797]: #798 -#789 := [trans #680 #682]: #641 -#720 := [monotonicity #789 #715]: #719 -#647 := [trans #720 #721]: #701 -#709 := [monotonicity #647]: #703 -#643 := [trans #709 #684]: #703 -#708 := [quant-inst #8 #9]: #707 -#674 := [mp #708 #643]: #683 -#678 := [unit-resolution #674 #884]: #801 -#685 := [monotonicity #678]: #14 -#15 := (not #14) -#79 := [asserted]: #15 -[unit-resolution #79 #685]: false -unsat -c4211064b5728b62240cb2d0bc31b06836a1e3c1 305 0 -#2 := false -decl f3 :: (-> Int S2) -#11 := 1::Int -#12 := (f3 1::Int) -decl f4 :: (-> Int Int Int) -#8 := 3::Int -#9 := (f4 3::Int 3::Int) -#10 := (f3 #9) -#13 := (= #10 #12) -#742 := (= #9 1::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#33 := (f4 #32 #21) -#878 := (pattern #33) -#20 := 0::Int -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#188 := (div #182 #185) -#360 := (* -1::Int #188) -#361 := (+ #33 #360) -#362 := (= #361 0::Int) -#43 := (div #32 #21) -#357 := (* -1::Int #43) -#358 := (+ #33 #357) -#359 := (= #358 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#363 := (ite #324 #359 #362) -#356 := (= #33 0::Int) -#35 := (= #21 0::Int) -#34 := (= #32 0::Int) -#36 := (or #34 #35) -#364 := (ite #36 #356 #363) -#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364) -#367 := (forall (vars (?v0 Int) (?v1 Int)) #364) -#882 := (iff #367 #879) -#880 := (iff #364 #364) -#881 := [refl]: #880 -#883 := [quant-intro #881]: #882 -#327 := (ite #324 #43 #188) -#330 := (ite #36 0::Int #327) -#333 := (= #33 #330) -#336 := (forall (vars (?v0 Int) (?v1 Int)) #333) -#368 := (iff #336 #367) -#365 := (iff #333 #364) -#366 := [rewrite]: #365 -#369 := [quant-intro #366]: #368 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#230 := (ite #227 #43 #188) -#233 := (ite #36 0::Int #230) -#236 := (= #33 #233) -#239 := (forall (vars (?v0 Int) (?v1 Int)) #236) -#337 := (iff #239 #336) -#334 := (iff #236 #333) -#331 := (= #233 #330) -#328 := (= #230 #327) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#329 := [monotonicity #326]: #328 -#332 := [monotonicity #329]: #331 -#335 := [monotonicity #332]: #334 -#338 := [quant-intro #335]: #337 -#299 := (~ #239 #239) -#312 := (~ #236 #236) -#313 := [refl]: #312 -#300 := [nnf-pos #313]: #299 -#45 := (- #21) -#44 := (- #32) -#46 := (div #44 #45) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#47 := (ite #42 #43 #46) -#48 := (ite #36 0::Int #47) -#49 := (= #33 #48) -#50 := (forall (vars (?v0 Int) (?v1 Int)) #49) -#242 := (iff #50 #239) -#175 := (and #38 #40) -#178 := (or #39 #175) -#191 := (ite #178 #43 #188) -#169 := (= 0::Int #21) -#166 := (= 0::Int #32) -#172 := (or #166 #169) -#194 := (ite #172 0::Int #191) -#197 := (= #33 #194) -#200 := (forall (vars (?v0 Int) (?v1 Int)) #197) -#240 := (iff #200 #239) -#237 := (iff #197 #236) -#234 := (= #194 #233) -#231 := (= #191 #230) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#232 := [monotonicity #229]: #231 -#207 := (iff #172 #36) -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#208 := [monotonicity #204 #206]: #207 -#235 := [monotonicity #208 #232]: #234 -#238 := [monotonicity #235]: #237 -#241 := [quant-intro #238]: #240 -#201 := (iff #50 #200) -#198 := (iff #49 #197) -#195 := (= #48 #194) -#192 := (= #47 #191) -#189 := (= #46 #188) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#190 := [monotonicity #184 #187]: #189 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#193 := [monotonicity #180 #190]: #192 -#173 := (iff #36 #172) -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#167 := (iff #34 #166) -#168 := [rewrite]: #167 -#174 := [monotonicity #168 #171]: #173 -#196 := [monotonicity #174 #193]: #195 -#199 := [monotonicity #196]: #198 -#202 := [quant-intro #199]: #201 -#243 := [trans #202 #241]: #242 -#165 := [asserted]: #50 -#244 := [mp #165 #243]: #239 -#314 := [mp~ #244 #300]: #239 -#339 := [mp #314 #338]: #336 -#370 := [mp #339 #369]: #367 -#884 := [mp #370 #883]: #879 -#714 := (not #879) -#715 := (or #714 #742) -#814 := (* -1::Int 3::Int) -#809 := (div #814 #814) -#810 := (* -1::Int #809) -#815 := (+ #9 #810) -#816 := (= #815 0::Int) -#811 := (div 3::Int 3::Int) -#817 := (* -1::Int #811) -#658 := (+ #9 #817) -#659 := (= #658 0::Int) -#660 := (>= 3::Int 0::Int) -#802 := (<= 3::Int 0::Int) -#803 := (or #802 #660) -#804 := (not #803) -#805 := (or #802 #802) -#799 := (not #805) -#800 := (or #799 #804) -#806 := (ite #800 #659 #816) -#807 := (= #9 0::Int) -#801 := (= 3::Int 0::Int) -#808 := (or #801 #801) -#637 := (ite #808 #807 #806) -#718 := (or #714 #637) -#720 := (iff #718 #715) -#721 := (iff #715 #715) -#701 := [rewrite]: #721 -#717 := (iff #637 #742) -#706 := (ite false #807 #742) -#711 := (iff #706 #742) -#712 := [rewrite]: #711 -#599 := (iff #637 #706) -#704 := (iff #806 #742) -#1 := true -#728 := (ite true #742 #742) -#725 := (iff #728 #742) -#731 := [rewrite]: #725 -#729 := (iff #806 #728) -#724 := (iff #816 #742) -#755 := (+ -1::Int #9) -#757 := (= #755 0::Int) -#744 := (iff #757 #742) -#745 := [rewrite]: #744 -#722 := (iff #816 #757) -#740 := (= #815 #755) -#768 := (+ #9 -1::Int) -#756 := (= #768 #755) -#758 := [rewrite]: #756 -#739 := (= #815 #768) -#737 := (= #810 -1::Int) -#771 := (* -1::Int 1::Int) -#763 := (= #771 -1::Int) -#765 := [rewrite]: #763 -#735 := (= #810 #771) -#732 := (= #809 1::Int) -#748 := -3::Int -#751 := (div -3::Int -3::Int) -#743 := (= #751 1::Int) -#754 := [rewrite]: #743 -#752 := (= #809 #751) -#749 := (= #814 -3::Int) -#750 := [rewrite]: #749 -#753 := [monotonicity #750 #750]: #752 -#733 := [trans #753 #754]: #732 -#736 := [monotonicity #733]: #735 -#738 := [trans #736 #765]: #737 -#734 := [monotonicity #738]: #739 -#726 := [trans #734 #758]: #740 -#723 := [monotonicity #726]: #722 -#727 := [trans #723 #745]: #724 -#746 := (iff #659 #742) -#761 := (iff #659 #757) -#759 := (= #658 #755) -#764 := (= #658 #768) -#766 := (= #817 -1::Int) -#778 := (= #817 #771) -#776 := (= #811 1::Int) -#777 := [rewrite]: #776 -#762 := [monotonicity #777]: #778 -#767 := [trans #762 #765]: #766 -#769 := [monotonicity #767]: #764 -#760 := [trans #769 #758]: #759 -#741 := [monotonicity #760]: #761 -#747 := [trans #741 #745]: #746 -#774 := (iff #800 true) -#782 := (or true false) -#780 := (iff #782 true) -#785 := [rewrite]: #780 -#783 := (iff #800 #782) -#770 := (iff #804 false) -#483 := (not true) -#844 := (iff #483 false) -#830 := [rewrite]: #844 -#781 := (iff #804 #483) -#792 := (iff #803 true) -#696 := (or false true) -#791 := (iff #696 true) -#788 := [rewrite]: #791 -#697 := (iff #803 #696) -#694 := (iff #660 true) -#695 := [rewrite]: #694 -#681 := (iff #802 false) -#682 := [rewrite]: #681 -#698 := [monotonicity #682 #695]: #697 -#779 := [trans #698 #788]: #792 -#773 := [monotonicity #779]: #781 -#772 := [trans #773 #830]: #770 -#693 := (iff #799 true) -#787 := (not false) -#690 := (iff #787 true) -#692 := [rewrite]: #690 -#790 := (iff #799 #787) -#691 := (iff #805 false) -#793 := (or false false) -#797 := (iff #793 false) -#795 := [rewrite]: #797 -#641 := (iff #805 #793) -#789 := [monotonicity #682 #682]: #641 -#786 := [trans #789 #795]: #691 -#675 := [monotonicity #786]: #790 -#686 := [trans #675 #692]: #693 -#784 := [monotonicity #686 #772]: #783 -#775 := [trans #784 #785]: #774 -#730 := [monotonicity #775 #747 #727]: #729 -#705 := [trans #730 #731]: #704 -#798 := (iff #808 false) -#794 := (iff #808 #793) -#639 := (iff #801 false) -#640 := [rewrite]: #639 -#796 := [monotonicity #640 #640]: #794 -#680 := [trans #796 #795]: #798 -#710 := [monotonicity #680 #705]: #599 -#713 := [trans #710 #712]: #717 -#716 := [monotonicity #713]: #720 -#647 := [trans #716 #701]: #720 -#719 := [quant-inst #8 #8]: #718 -#702 := [mp #719 #647]: #715 -#708 := [unit-resolution #702 #884]: #742 -#703 := [monotonicity #708]: #13 -#14 := (not #13) -#79 := [asserted]: #14 -[unit-resolution #79 #703]: false -unsat -c8c3466ffe36eb7d0f579df3f5c17ffb47bc161f 459 0 -#2 := false -#19 := 0::Int -#10 := 3::Int +#86 := (= #21 -3::Int) +#87 := [rewrite]: #86 +#93 := [monotonicity #87 #90]: #92 +#97 := [trans #93 #95]: #96 +#83 := (= #20 3::Int) +#84 := [rewrite]: #83 +#81 := (iff #19 #80) +#78 := (iff #18 #77) +#79 := [rewrite]: #78 +#82 := [monotonicity #79]: #81 +#100 := [monotonicity #82 #84 #97]: #99 +#104 := [trans #100 #102]: #103 +#75 := (iff #13 false) +#70 := (or false false) +#73 := (iff #70 false) +#74 := [rewrite]: #73 +#71 := (iff #13 #70) +#68 := (iff #12 false) +#69 := [rewrite]: #68 +#66 := (iff #10 false) +#67 := [rewrite]: #66 +#72 := [monotonicity #67 #69]: #71 +#76 := [trans #72 #74]: #75 +#107 := [monotonicity #76 #104]: #106 +#111 := [trans #107 #109]: #110 +#112 := [monotonicity #111]: #28 +#115 := [monotonicity #112]: #114 +#119 := [trans #115 #117]: #118 +#122 := [monotonicity #119]: #121 +#126 := [trans #122 #124]: #125 +#65 := [asserted]: #29 +[mp #65 #126]: false +unsat +541d6fe80b1182e33d84e37f649671b9536f0b45 313 0 +#2 := false +decl f3 :: (-> Int S2) +#81 := -1::Int decl f4 :: (-> S2 Int) decl f5 :: S2 #8 := f5 #9 := (f4 f5) -#807 := (mod #9 3::Int) -#81 := -1::Int -#753 := (* -1::Int #807) -#523 := (div #9 3::Int) -#549 := -3::Int -#751 := (* -3::Int #523) -#754 := (+ #751 #753) -#755 := (+ #9 #754) -#750 := (= #755 0::Int) -#1 := true -#76 := [true-axiom]: true -#719 := (or false #750) -#720 := [th-lemma arith]: #719 -#721 := [unit-resolution #720 #76]: #750 -#759 := (>= #755 0::Int) -#662 := (not #759) -#760 := (>= #807 0::Int) -#664 := (or false #760) -#665 := [th-lemma arith]: #664 -#670 := [unit-resolution #665 #76]: #760 -decl f3 :: (-> Int Int Int) -#11 := (f3 #9 3::Int) -#84 := (* -1::Int #11) -#85 := (+ #9 #84) -#83 := (>= #85 0::Int) -#87 := (not #83) -#12 := (<= #11 #9) -#13 := (not #12) -#88 := (iff #13 #87) -#82 := (iff #12 #83) -#86 := [rewrite]: #82 -#89 := [monotonicity #86]: #88 -#78 := [asserted]: #13 -#90 := [mp #78 #89]: #87 -#858 := (* -1::Int #523) -#860 := (+ #11 #858) -#689 := (<= #860 0::Int) -#517 := (= #860 0::Int) -#539 := (* -1::Int #9) -#829 := (div #539 -3::Int) -#827 := (* -1::Int #829) -#832 := (+ #11 #827) -#823 := (= #832 0::Int) -#861 := (<= #9 0::Int) -#491 := (not #861) -#647 := (>= #9 0::Int) -#565 := (not #647) -#833 := (or #565 #491) -#824 := (ite #833 #517 #823) -#515 := (= #9 0::Int) -#706 := (not #515) -#817 := (<= #11 0::Int) -#865 := (= #11 0::Int) -#740 := [hypothesis]: #515 -#713 := (or #706 #865) -#826 := (ite #515 #865 #824) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#32 := (f3 #31 #20) -#887 := (pattern #32) -#193 := (* -1::Int #20) -#190 := (* -1::Int #31) -#196 := (div #190 #193) -#368 := (* -1::Int #196) -#369 := (+ #32 #368) -#370 := (= #369 0::Int) -#42 := (div #31 #20) -#365 := (* -1::Int #42) -#366 := (+ #32 #365) -#367 := (= #366 0::Int) -#228 := (>= #31 0::Int) -#221 := (<= #20 0::Int) -#328 := (or #221 #228) -#329 := (not #328) -#217 := (<= #31 0::Int) -#326 := (or #217 #221) -#327 := (not #326) -#332 := (or #327 #329) -#371 := (ite #332 #367 #370) -#364 := (= #32 0::Int) -#34 := (= #20 0::Int) -#33 := (= #31 0::Int) -#35 := (or #33 #34) -#372 := (ite #35 #364 #371) -#888 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #887) #372) -#375 := (forall (vars (?v0 Int) (?v1 Int)) #372) -#891 := (iff #375 #888) -#889 := (iff #372 #372) -#890 := [refl]: #889 -#892 := [quant-intro #890]: #891 -#335 := (ite #332 #42 #196) -#338 := (ite #35 0::Int #335) -#341 := (= #32 #338) -#344 := (forall (vars (?v0 Int) (?v1 Int)) #341) -#376 := (iff #344 #375) -#373 := (iff #341 #372) -#374 := [rewrite]: #373 -#377 := [quant-intro #374]: #376 -#229 := (not #228) -#222 := (not #221) -#232 := (and #222 #229) -#218 := (not #217) -#225 := (and #218 #222) -#235 := (or #225 #232) -#238 := (ite #235 #42 #196) -#241 := (ite #35 0::Int #238) -#244 := (= #32 #241) -#247 := (forall (vars (?v0 Int) (?v1 Int)) #244) -#345 := (iff #247 #344) -#342 := (iff #244 #341) -#339 := (= #241 #338) -#336 := (= #238 #335) -#333 := (iff #235 #332) -#330 := (iff #232 #329) -#331 := [rewrite]: #330 -#311 := (iff #225 #327) -#312 := [rewrite]: #311 -#334 := [monotonicity #312 #331]: #333 -#337 := [monotonicity #334]: #336 -#340 := [monotonicity #337]: #339 -#343 := [monotonicity #340]: #342 -#346 := [quant-intro #343]: #345 -#307 := (~ #247 #247) -#320 := (~ #244 #244) -#321 := [refl]: #320 -#308 := [nnf-pos #321]: #307 -#44 := (- #20) -#43 := (- #31) -#45 := (div #43 #44) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#46 := (ite #41 #42 #45) -#47 := (ite #35 0::Int #46) -#48 := (= #32 #47) -#49 := (forall (vars (?v0 Int) (?v1 Int)) #48) -#250 := (iff #49 #247) -#184 := (and #37 #39) -#187 := (or #38 #184) -#199 := (ite #187 #42 #196) -#178 := (= 0::Int #20) -#175 := (= 0::Int #31) -#181 := (or #175 #178) -#202 := (ite #181 0::Int #199) -#205 := (= #32 #202) -#208 := (forall (vars (?v0 Int) (?v1 Int)) #205) -#248 := (iff #208 #247) -#245 := (iff #205 #244) -#242 := (= #202 #241) -#239 := (= #199 #238) -#236 := (iff #187 #235) -#233 := (iff #184 #232) -#230 := (iff #39 #229) -#231 := [rewrite]: #230 -#223 := (iff #37 #222) -#224 := [rewrite]: #223 -#234 := [monotonicity #224 #231]: #233 -#226 := (iff #38 #225) -#219 := (iff #36 #218) -#220 := [rewrite]: #219 -#227 := [monotonicity #220 #224]: #226 -#237 := [monotonicity #227 #234]: #236 -#240 := [monotonicity #237]: #239 -#215 := (iff #181 #35) -#213 := (iff #178 #34) -#214 := [rewrite]: #213 -#211 := (iff #175 #33) -#212 := [rewrite]: #211 -#216 := [monotonicity #212 #214]: #215 -#243 := [monotonicity #216 #240]: #242 -#246 := [monotonicity #243]: #245 -#249 := [quant-intro #246]: #248 -#209 := (iff #49 #208) -#206 := (iff #48 #205) -#203 := (= #47 #202) -#200 := (= #46 #199) -#197 := (= #45 #196) -#194 := (= #44 #193) -#195 := [rewrite]: #194 -#191 := (= #43 #190) -#192 := [rewrite]: #191 -#198 := [monotonicity #192 #195]: #197 -#188 := (iff #41 #187) -#185 := (iff #40 #184) -#186 := [rewrite]: #185 -#189 := [monotonicity #186]: #188 -#201 := [monotonicity #189 #198]: #200 -#182 := (iff #35 #181) -#179 := (iff #34 #178) -#180 := [rewrite]: #179 -#176 := (iff #33 #175) -#177 := [rewrite]: #176 -#183 := [monotonicity #177 #180]: #182 -#204 := [monotonicity #183 #201]: #203 -#207 := [monotonicity #204]: #206 -#210 := [quant-intro #207]: #209 -#251 := [trans #210 #249]: #250 -#174 := [asserted]: #49 -#252 := [mp #174 #251]: #247 -#322 := [mp~ #252 #308]: #247 -#347 := [mp #322 #346]: #344 -#378 := [mp #347 #377]: #375 -#893 := [mp #378 #892]: #888 -#669 := (not #888) -#811 := (or #669 #826) -#538 := (* -1::Int 3::Int) -#470 := (div #539 #538) -#543 := (* -1::Int #470) -#540 := (+ #11 #543) -#544 := (= #540 0::Int) -#854 := (<= 3::Int 0::Int) -#528 := (or #854 #647) -#529 := (not #528) -#862 := (or #861 #854) -#863 := (not #862) -#864 := (or #863 #529) -#859 := (ite #864 #517 #544) -#855 := (= 3::Int 0::Int) -#520 := (or #515 #855) -#856 := (ite #520 #865 #859) -#812 := (or #669 #856) -#814 := (iff #812 #811) -#809 := (iff #811 #811) -#815 := [rewrite]: #809 -#667 := (iff #856 #826) -#825 := (iff #859 #824) -#818 := (iff #544 #823) -#821 := (= #540 #832) -#831 := (= #543 #827) -#830 := (= #470 #829) -#550 := (= #538 -3::Int) -#551 := [rewrite]: #550 -#545 := [monotonicity #551]: #830 -#828 := [monotonicity #545]: #831 -#822 := [monotonicity #828]: #821 -#819 := [monotonicity #822]: #818 -#838 := (iff #864 #833) -#836 := (or #491 #565) -#837 := (iff #836 #833) -#834 := [rewrite]: #837 -#558 := (iff #864 #836) -#458 := (iff #529 #565) -#563 := (iff #528 #647) -#850 := (or false #647) -#840 := (iff #850 #647) -#562 := [rewrite]: #840 -#853 := (iff #528 #850) -#844 := (iff #854 false) -#845 := [rewrite]: #844 -#839 := [monotonicity #845]: #853 -#564 := [trans #839 #562]: #563 -#835 := [monotonicity #564]: #458 -#492 := (iff #863 #491) -#849 := (iff #862 #861) -#846 := (or #861 false) -#848 := (iff #846 #861) -#486 := [rewrite]: #848 -#847 := (iff #862 #846) -#842 := [monotonicity #845]: #847 -#851 := [trans #842 #486]: #849 -#852 := [monotonicity #851]: #492 -#559 := [monotonicity #852 #835]: #558 -#548 := [trans #559 #834]: #838 -#820 := [monotonicity #548 #819]: #825 -#507 := (iff #520 #515) -#500 := (or #515 false) -#505 := (iff #500 #515) -#506 := [rewrite]: #505 -#841 := (iff #520 #500) -#516 := (iff #855 false) -#857 := [rewrite]: #516 -#504 := [monotonicity #857]: #841 -#843 := [trans #504 #506]: #507 -#668 := [monotonicity #843 #820]: #667 -#808 := [monotonicity #668]: #814 -#816 := [trans #808 #815]: #814 -#813 := [quant-inst #9 #10]: #812 -#810 := [mp #813 #816]: #811 -#728 := [unit-resolution #810 #893]: #826 -#705 := (not #826) -#707 := (or #705 #706 #865) -#800 := [def-axiom]: #707 -#714 := [unit-resolution #800 #728]: #713 -#715 := [unit-resolution #714 #740]: #865 -#788 := (not #865) -#608 := (or #788 #817) -#758 := [th-lemma arith triangle-eq]: #608 -#674 := [unit-resolution #758 #715]: #817 -#675 := (or #706 #647) -#676 := [th-lemma arith triangle-eq]: #675 -#677 := [unit-resolution #676 #740]: #647 -#678 := [th-lemma arith farkas -1 1 1 #677 #90 #674]: false -#679 := [lemma #678]: #706 -#729 := (or #515 #824) -#797 := (or #705 #515 #824) -#801 := [def-axiom]: #797 -#725 := [unit-resolution #801 #728]: #729 -#651 := [unit-resolution #725 #679]: #824 -decl f6 :: (-> Int S2) -#452 := (f6 #9) -#791 := (f4 #452) -#792 := (= #791 0::Int) -#696 := (not #792) -#697 := (iff #706 #696) -#687 := (iff #515 #792) -#683 := (iff #792 #515) -#693 := (= #791 #9) -#718 := (= #452 f5) -#537 := (= f5 #452) -#14 := (:var 0 S2) -#15 := (f4 #14) -#866 := (pattern #15) -#16 := (f6 #15) -#80 := (= #14 #16) -#867 := (forall (vars (?v0 S2)) (:pat #866) #80) -#93 := (forall (vars (?v0 S2)) #80) -#868 := (iff #93 #867) -#870 := (iff #867 #867) -#871 := [rewrite]: #870 -#869 := [rewrite]: #868 -#872 := [trans #869 #871]: #868 -#315 := (~ #93 #93) -#313 := (~ #80 #80) -#314 := [refl]: #313 -#316 := [nnf-pos #314]: #315 -#17 := (= #16 #14) -#18 := (forall (vars (?v0 S2)) #17) -#94 := (iff #18 #93) -#91 := (iff #17 #80) -#92 := [rewrite]: #91 -#95 := [quant-intro #92]: #94 -#79 := [asserted]: #18 -#98 := [mp #79 #95]: #93 -#301 := [mp~ #98 #316]: #93 -#873 := [mp #301 #872]: #867 -#530 := (not #867) -#541 := (or #530 #537) -#542 := [quant-inst #8]: #541 -#712 := [unit-resolution #542 #873]: #537 -#686 := [symm #712]: #718 -#652 := [monotonicity #686]: #693 -#685 := [monotonicity #652]: #683 -#694 := [symm #685]: #687 -#698 := [monotonicity #694]: #697 -#653 := [mp #679 #698]: #696 -#789 := (or #647 #792) -#22 := (f6 #20) -#874 := (pattern #22) -#114 := (>= #20 0::Int) -#23 := (f4 #22) -#28 := (= #23 0::Int) -#163 := (or #28 #114) -#881 := (forall (vars (?v0 Int)) (:pat #874) #163) -#168 := (forall (vars (?v0 Int)) #163) -#884 := (iff #168 #881) -#882 := (iff #163 #163) -#883 := [refl]: #882 -#885 := [quant-intro #883]: #884 -#305 := (~ #168 #168) -#317 := (~ #163 #163) -#318 := [refl]: #317 -#306 := [nnf-pos #318]: #305 -#27 := (< #20 0::Int) -#29 := (implies #27 #28) -#30 := (forall (vars (?v0 Int)) #29) -#171 := (iff #30 #168) -#134 := (= 0::Int #23) -#140 := (not #27) -#141 := (or #140 #134) -#146 := (forall (vars (?v0 Int)) #141) -#169 := (iff #146 #168) -#166 := (iff #141 #163) -#160 := (or #114 #28) -#164 := (iff #160 #163) -#165 := [rewrite]: #164 -#161 := (iff #141 #160) -#158 := (iff #134 #28) -#159 := [rewrite]: #158 -#156 := (iff #140 #114) -#116 := (not #114) -#151 := (not #116) -#154 := (iff #151 #114) -#155 := [rewrite]: #154 -#152 := (iff #140 #151) -#149 := (iff #27 #116) -#150 := [rewrite]: #149 -#153 := [monotonicity #150]: #152 -#157 := [trans #153 #155]: #156 -#162 := [monotonicity #157 #159]: #161 -#167 := [trans #162 #165]: #166 -#170 := [quant-intro #167]: #169 -#147 := (iff #30 #146) -#144 := (iff #29 #141) -#137 := (implies #27 #134) -#142 := (iff #137 #141) -#143 := [rewrite]: #142 -#138 := (iff #29 #137) -#135 := (iff #28 #134) -#136 := [rewrite]: #135 -#139 := [monotonicity #136]: #138 -#145 := [trans #139 #143]: #144 -#148 := [quant-intro #145]: #147 -#172 := [trans #148 #170]: #171 -#133 := [asserted]: #30 -#173 := [mp #133 #172]: #168 -#319 := [mp~ #173 #306]: #168 -#886 := [mp #319 #885]: #881 -#784 := (not #881) -#785 := (or #784 #647 #792) -#793 := (or #792 #647) -#786 := (or #784 #793) -#776 := (iff #786 #785) -#787 := (or #784 #789) -#774 := (iff #787 #785) -#775 := [rewrite]: #774 -#771 := (iff #786 #787) -#794 := (iff #793 #789) -#783 := [rewrite]: #794 -#772 := [monotonicity #783]: #771 -#777 := [trans #772 #775]: #776 -#780 := [quant-inst #9]: #786 -#773 := [mp #780 #777]: #785 -#688 := [unit-resolution #773 #886]: #789 -#654 := [unit-resolution #688 #653]: #647 -#655 := (or #515 #491 #565) -#657 := [th-lemma arith triangle-eq]: #655 -#658 := [unit-resolution #657 #654 #679]: #491 -#802 := (or #833 #861) -#803 := [def-axiom]: #802 -#659 := [unit-resolution #803 #658]: #833 -#805 := (not #833) -#700 := (not #824) -#795 := (or #700 #805 #517) -#796 := [def-axiom]: #795 -#660 := [unit-resolution #796 #659 #651]: #517 -#699 := (not #517) -#692 := (or #699 #689) -#716 := [th-lemma arith triangle-eq]: #692 -#661 := [unit-resolution #716 #660]: #689 -#663 := (not #689) -#645 := (not #760) -#633 := (or #662 #565 #645 #663 #83) -#634 := [th-lemma arith assign-bounds 2 1 3 3]: #633 -#635 := [unit-resolution #634 #654 #661 #90 #670]: #662 -#726 := (not #750) -#722 := (or #726 #759) -#723 := [th-lemma arith triangle-eq]: #722 -[unit-resolution #723 #635 #721]: false -unsat -f4adf2827c5540d070c2e622505c61938b50a2ed 636 0 -#2 := false -decl f3 :: (-> Int S2) -decl f4 :: (-> Int Int Int) -#10 := 3::Int -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#11 := (f4 #9 3::Int) -#12 := (f3 #11) -#83 := (= f6 #12) -#14 := 0::Int -#15 := (f3 0::Int) -#932 := (= #15 #12) -#930 := (= #12 #15) -#819 := (= #11 0::Int) -#822 := (= #9 0::Int) -#867 := (f5 #15) -#866 := (= #867 0::Int) -#24 := (:var 0 Int) -#26 := (f3 #24) -#890 := (pattern #26) -#130 := (>= #24 0::Int) -#131 := (not #130) -#27 := (f5 #26) -#112 := (= #24 #27) -#137 := (or #112 #131) -#891 := (forall (vars (?v0 Int)) (:pat #890) #137) -#142 := (forall (vars (?v0 Int)) #137) -#894 := (iff #142 #891) -#892 := (iff #137 #137) -#893 := [refl]: #892 -#895 := [quant-intro #893]: #894 -#319 := (~ #142 #142) -#318 := (~ #137 #137) -#315 := [refl]: #318 -#320 := [nnf-pos #315]: #319 -#28 := (= #27 #24) -#25 := (<= 0::Int #24) -#29 := (implies #25 #28) -#30 := (forall (vars (?v0 Int)) #29) -#145 := (iff #30 #142) -#119 := (not #25) -#120 := (or #119 #112) -#125 := (forall (vars (?v0 Int)) #120) -#143 := (iff #125 #142) -#140 := (iff #120 #137) -#134 := (or #131 #112) -#138 := (iff #134 #137) -#139 := [rewrite]: #138 -#135 := (iff #120 #134) -#132 := (iff #119 #131) -#128 := (iff #25 #130) -#129 := [rewrite]: #128 -#133 := [monotonicity #129]: #132 -#136 := [monotonicity #133]: #135 -#141 := [trans #136 #139]: #140 -#144 := [quant-intro #141]: #143 -#126 := (iff #30 #125) -#123 := (iff #29 #120) -#116 := (implies #25 #112) -#121 := (iff #116 #120) -#122 := [rewrite]: #121 -#117 := (iff #29 #116) -#114 := (iff #28 #112) +#82 := (* -1::Int #9) +#87 := (div #82 -1::Int) +#12 := 1::Int +#21 := (div #9 1::Int) +#10 := 0::Int +#123 := (>= #9 0::Int) +#124 := (not #123) +#110 := (<= #9 0::Int) +#111 := (not #110) +#134 := (or #111 #124) +#137 := (ite #134 #21 #87) +#11 := (= #9 0::Int) +#140 := (ite #11 0::Int #137) +#143 := (f3 #140) +#146 := (= f5 #143) +#725 := (f3 #9) +#688 := (= #725 #143) +#691 := (= #143 #725) +#411 := (= #140 #9) +#602 := (= #9 #140) +#510 := (* -1::Int #21) +#663 := (+ #9 #510) +#668 := (<= #663 0::Int) +#509 := (= #663 0::Int) +#1 := true +#63 := [true-axiom]: true +#653 := (or false #509) +#654 := [th-lemma arith]: #653 +#650 := [unit-resolution #654 #63]: #509 +#655 := (not #509) +#644 := (or #655 #668) +#645 := [th-lemma arith triangle-eq]: #644 +#646 := [unit-resolution #645 #650]: #668 +#550 := (>= #663 0::Int) +#647 := (or #655 #550) +#641 := [th-lemma arith triangle-eq]: #647 +#648 := [unit-resolution #641 #650]: #550 +#643 := (* -1::Int #140) +#640 := (+ #21 #643) +#642 := (<= #640 0::Int) +#651 := (= #21 #140) +#398 := (= #137 #140) +#389 := (not #11) +#409 := (= 0::Int #9) +#695 := [hypothesis]: #11 +#410 := [symm #695]: #409 +#313 := (= #140 0::Int) +#390 := (or #389 #313) +#722 := [def-axiom]: #390 +#699 := [unit-resolution #722 #695]: #313 +#412 := [trans #699 #410]: #411 +#406 := [monotonicity #412]: #691 +#692 := [symm #406]: #688 +#720 := (= f5 #725) +#30 := (:var 0 S2) +#31 := (f4 #30) +#727 := (pattern #31) +#32 := (f3 #31) +#156 := (= #30 #32) +#728 := (forall (vars (?v0 S2)) (:pat #727) #156) +#159 := (forall (vars (?v0 S2)) #156) +#729 := (iff #159 #728) +#731 := (iff #728 #728) +#732 := [rewrite]: #731 +#730 := [rewrite]: #729 +#733 := [trans #730 #732]: #729 +#253 := (~ #159 #159) +#251 := (~ #156 #156) +#252 := [refl]: #251 +#254 := [nnf-pos #252]: #253 +#33 := (= #32 #30) +#34 := (forall (vars (?v0 S2)) #33) +#160 := (iff #34 #159) +#157 := (iff #33 #156) +#158 := [rewrite]: #157 +#161 := [quant-intro #158]: #160 +#155 := [asserted]: #34 +#164 := [mp #155 #161]: #159 +#243 := [mp~ #164 #254]: #159 +#734 := [mp #243 #733]: #728 +#376 := (not #728) +#381 := (or #376 #720) +#717 := [quant-inst #8]: #381 +#690 := [unit-resolution #717 #734]: #720 +#689 := [trans #690 #692]: #146 +#149 := (not #146) +#23 := (- 1::Int) +#22 := (- #9) +#24 := (div #22 #23) +#16 := (< 0::Int 1::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= 1::Int 0::Int) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (f3 #26) +#28 := (= #27 f5) +#29 := (not #28) +#152 := (iff #29 #149) +#75 := (and #16 #18) +#78 := (or #17 #75) +#90 := (ite #78 #21 #87) +#93 := (ite #11 0::Int #90) +#96 := (f3 #93) +#102 := (= f5 #96) +#107 := (not #102) +#150 := (iff #107 #149) +#147 := (iff #102 #146) +#144 := (= #96 #143) +#141 := (= #93 #140) +#138 := (= #90 #137) +#135 := (iff #78 #134) +#132 := (iff #75 #124) +#127 := (and true #124) +#130 := (iff #127 #124) +#131 := [rewrite]: #130 +#128 := (iff #75 #127) +#125 := (iff #18 #124) +#126 := [rewrite]: #125 +#114 := (iff #16 true) #115 := [rewrite]: #114 -#118 := [monotonicity #115]: #117 -#124 := [trans #118 #122]: #123 -#127 := [quant-intro #124]: #126 -#146 := [trans #127 #144]: #145 -#111 := [asserted]: #30 -#147 := [mp #111 #146]: #142 -#316 := [mp~ #147 #320]: #142 -#896 := [mp #316 #895]: #891 -#880 := (not #891) -#565 := (or #880 #866) -#502 := (>= 0::Int 0::Int) -#865 := (not #502) -#507 := (= 0::Int #867) -#508 := (or #507 #865) -#566 := (or #880 #508) -#845 := (iff #566 #565) -#561 := (iff #565 #565) -#843 := [rewrite]: #561 -#854 := (iff #508 #866) -#574 := (or #866 false) -#853 := (iff #574 #866) -#850 := [rewrite]: #853 -#575 := (iff #508 #574) -#851 := (iff #865 false) -#1 := true -#578 := (not true) -#581 := (iff #578 false) -#474 := [rewrite]: #581 -#579 := (iff #865 #578) -#855 := (iff #502 true) -#856 := [rewrite]: #855 -#580 := [monotonicity #856]: #579 -#852 := [trans #580 #474]: #851 -#868 := (iff #507 #866) -#869 := [rewrite]: #868 -#849 := [monotonicity #869 #852]: #575 -#564 := [trans #849 #850]: #854 -#846 := [monotonicity #564]: #845 -#847 := [trans #846 #843]: #845 -#567 := [quant-inst #14]: #566 -#844 := [mp #567 #847]: #565 -#923 := [unit-resolution #844 #896]: #866 -#926 := (= #9 #867) -#16 := (= f6 #15) -#560 := (f3 #9) -#918 := (= #560 #15) -#473 := (= #15 #560) -#471 := (= 0::Int #9) -#544 := (f5 #12) -#626 := (= #544 #9) -#497 := (= #9 #544) -#97 := (not #16) -#570 := [hypothesis]: #97 -#555 := (or #83 #16) -#98 := (iff #83 #97) -#13 := (= #12 f6) -#17 := (iff #13 #16) -#18 := (not #17) -#101 := (iff #18 #98) -#89 := (iff #16 #83) -#94 := (not #89) -#99 := (iff #94 #98) -#100 := [rewrite]: #99 -#95 := (iff #18 #94) -#92 := (iff #17 #89) -#86 := (iff #83 #16) -#90 := (iff #86 #89) -#91 := [rewrite]: #90 -#87 := (iff #17 #86) -#84 := (iff #13 #83) -#85 := [rewrite]: #84 -#88 := [monotonicity #85]: #87 -#93 := [trans #88 #91]: #92 -#96 := [monotonicity #93]: #95 -#102 := [trans #96 #100]: #101 -#82 := [asserted]: #18 -#105 := [mp #82 #102]: #98 -#468 := (not #98) -#553 := (or #83 #16 #468) -#554 := [def-axiom]: #553 -#546 := [unit-resolution #554 #105]: #555 -#562 := [unit-resolution #546 #570]: #83 -#498 := [monotonicity #562]: #497 -#477 := [symm #498]: #626 -#482 := (= 0::Int #544) -#545 := (= #11 #544) -#874 := (>= #11 0::Int) -#557 := (not #83) -#628 := (or #874 #557) -#878 := (= #544 0::Int) -#630 := (iff #878 #822) -#623 := [hypothesis]: #83 -#625 := [symm #623]: #13 -#629 := [monotonicity #625]: #626 -#634 := [monotonicity #629]: #630 -#876 := (not #874) -#647 := [hypothesis]: #876 -#532 := (or #874 #878) -#32 := (= #27 0::Int) -#178 := (or #32 #130) -#897 := (forall (vars (?v0 Int)) (:pat #890) #178) -#183 := (forall (vars (?v0 Int)) #178) -#900 := (iff #183 #897) -#898 := (iff #178 #178) -#899 := [refl]: #898 -#901 := [quant-intro #899]: #900 -#321 := (~ #183 #183) -#333 := (~ #178 #178) -#334 := [refl]: #333 -#322 := [nnf-pos #334]: #321 -#31 := (< #24 0::Int) -#33 := (implies #31 #32) -#34 := (forall (vars (?v0 Int)) #33) -#186 := (iff #34 #183) -#149 := (= 0::Int #27) -#155 := (not #31) -#156 := (or #155 #149) -#161 := (forall (vars (?v0 Int)) #156) -#184 := (iff #161 #183) -#181 := (iff #156 #178) -#175 := (or #130 #32) -#179 := (iff #175 #178) -#180 := [rewrite]: #179 -#176 := (iff #156 #175) -#173 := (iff #149 #32) -#174 := [rewrite]: #173 -#171 := (iff #155 #130) -#166 := (not #131) -#169 := (iff #166 #130) -#170 := [rewrite]: #169 -#167 := (iff #155 #166) -#164 := (iff #31 #131) -#165 := [rewrite]: #164 -#168 := [monotonicity #165]: #167 -#172 := [trans #168 #170]: #171 -#177 := [monotonicity #172 #174]: #176 -#182 := [trans #177 #180]: #181 -#185 := [quant-intro #182]: #184 -#162 := (iff #34 #161) -#159 := (iff #33 #156) -#152 := (implies #31 #149) -#157 := (iff #152 #156) -#158 := [rewrite]: #157 -#153 := (iff #33 #152) -#150 := (iff #32 #149) -#151 := [rewrite]: #150 -#154 := [monotonicity #151]: #153 -#160 := [trans #154 #158]: #159 -#163 := [quant-intro #160]: #162 -#187 := [trans #163 #185]: #186 -#148 := [asserted]: #34 -#188 := [mp #148 #187]: #183 -#335 := [mp~ #188 #322]: #183 -#902 := [mp #335 #901]: #897 -#857 := (not #897) -#520 := (or #857 #874 #878) -#879 := (or #878 #874) -#521 := (or #857 #879) -#863 := (iff #521 #520) -#523 := (or #857 #532) -#861 := (iff #523 #520) -#862 := [rewrite]: #861 -#859 := (iff #521 #523) -#873 := (iff #879 #532) -#516 := [rewrite]: #873 -#860 := [monotonicity #516]: #859 -#858 := [trans #860 #862]: #863 -#522 := [quant-inst #11]: #521 -#864 := [mp #522 #858]: #520 -#643 := [unit-resolution #864 #902]: #532 -#633 := [unit-resolution #643 #647]: #878 -#627 := [mp #633 #634]: #822 -#740 := (not #822) -#746 := (not #819) -#645 := (or #746 #874) -#648 := [th-lemma arith triangle-eq]: #645 -#636 := [unit-resolution #648 #647]: #746 -#641 := (or #740 #819) -#788 := -3::Int -#205 := -1::Int -#842 := (* -1::Int #9) -#792 := (div #842 -3::Int) -#794 := (* -1::Int #792) -#783 := (+ #11 #794) -#782 := (= #783 0::Int) -#828 := (div #9 3::Int) -#829 := (* -1::Int #828) -#830 := (+ #11 #829) -#824 := (= #830 0::Int) -#833 := (<= #9 0::Int) -#723 := (not #833) -#825 := (>= #9 0::Int) -#808 := (not #825) -#801 := (or #808 #723) -#767 := (ite #801 #824 #782) -#771 := (ite #822 #819 #767) -#35 := (:var 1 Int) -#36 := (f4 #35 #24) -#903 := (pattern #36) -#209 := (* -1::Int #24) -#206 := (* -1::Int #35) -#212 := (div #206 #209) -#384 := (* -1::Int #212) -#385 := (+ #36 #384) -#386 := (= #385 0::Int) -#46 := (div #35 #24) -#381 := (* -1::Int #46) -#382 := (+ #36 #381) -#383 := (= #382 0::Int) -#244 := (>= #35 0::Int) -#237 := (<= #24 0::Int) -#344 := (or #237 #244) -#345 := (not #344) -#233 := (<= #35 0::Int) -#342 := (or #233 #237) -#343 := (not #342) -#348 := (or #343 #345) -#387 := (ite #348 #383 #386) -#380 := (= #36 0::Int) -#38 := (= #24 0::Int) -#37 := (= #35 0::Int) -#39 := (or #37 #38) -#388 := (ite #39 #380 #387) -#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #388) -#391 := (forall (vars (?v0 Int) (?v1 Int)) #388) -#907 := (iff #391 #904) -#905 := (iff #388 #388) -#906 := [refl]: #905 -#908 := [quant-intro #906]: #907 -#351 := (ite #348 #46 #212) -#354 := (ite #39 0::Int #351) -#357 := (= #36 #354) -#360 := (forall (vars (?v0 Int) (?v1 Int)) #357) -#392 := (iff #360 #391) -#389 := (iff #357 #388) -#390 := [rewrite]: #389 -#393 := [quant-intro #390]: #392 -#245 := (not #244) -#238 := (not #237) -#248 := (and #238 #245) -#234 := (not #233) -#241 := (and #234 #238) -#251 := (or #241 #248) -#254 := (ite #251 #46 #212) -#257 := (ite #39 0::Int #254) -#260 := (= #36 #257) -#263 := (forall (vars (?v0 Int) (?v1 Int)) #260) -#361 := (iff #263 #360) -#358 := (iff #260 #357) -#355 := (= #257 #354) -#352 := (= #254 #351) -#349 := (iff #251 #348) -#346 := (iff #248 #345) -#347 := [rewrite]: #346 -#327 := (iff #241 #343) -#328 := [rewrite]: #327 -#350 := [monotonicity #328 #347]: #349 -#353 := [monotonicity #350]: #352 -#356 := [monotonicity #353]: #355 -#359 := [monotonicity #356]: #358 -#362 := [quant-intro #359]: #361 -#323 := (~ #263 #263) -#336 := (~ #260 #260) -#337 := [refl]: #336 -#324 := [nnf-pos #337]: #323 -#48 := (- #24) -#47 := (- #35) -#49 := (div #47 #48) -#41 := (< 0::Int #24) -#43 := (< #35 0::Int) -#44 := (and #43 #41) -#40 := (< 0::Int #35) -#42 := (and #40 #41) -#45 := (or #42 #44) -#50 := (ite #45 #46 #49) -#51 := (ite #39 0::Int #50) -#52 := (= #36 #51) -#53 := (forall (vars (?v0 Int) (?v1 Int)) #52) -#266 := (iff #53 #263) -#199 := (and #41 #43) -#202 := (or #42 #199) -#215 := (ite #202 #46 #212) -#193 := (= 0::Int #24) -#190 := (= 0::Int #35) -#196 := (or #190 #193) -#218 := (ite #196 0::Int #215) -#221 := (= #36 #218) -#224 := (forall (vars (?v0 Int) (?v1 Int)) #221) -#264 := (iff #224 #263) -#261 := (iff #221 #260) -#258 := (= #218 #257) -#255 := (= #215 #254) -#252 := (iff #202 #251) -#249 := (iff #199 #248) -#246 := (iff #43 #245) -#247 := [rewrite]: #246 -#239 := (iff #41 #238) -#240 := [rewrite]: #239 -#250 := [monotonicity #240 #247]: #249 -#242 := (iff #42 #241) -#235 := (iff #40 #234) -#236 := [rewrite]: #235 -#243 := [monotonicity #236 #240]: #242 -#253 := [monotonicity #243 #250]: #252 -#256 := [monotonicity #253]: #255 -#231 := (iff #196 #39) -#229 := (iff #193 #38) -#230 := [rewrite]: #229 -#227 := (iff #190 #37) -#228 := [rewrite]: #227 -#232 := [monotonicity #228 #230]: #231 -#259 := [monotonicity #232 #256]: #258 -#262 := [monotonicity #259]: #261 -#265 := [quant-intro #262]: #264 -#225 := (iff #53 #224) -#222 := (iff #52 #221) -#219 := (= #51 #218) -#216 := (= #50 #215) -#213 := (= #49 #212) -#210 := (= #48 #209) -#211 := [rewrite]: #210 -#207 := (= #47 #206) -#208 := [rewrite]: #207 -#214 := [monotonicity #208 #211]: #213 -#203 := (iff #45 #202) -#200 := (iff #44 #199) -#201 := [rewrite]: #200 -#204 := [monotonicity #201]: #203 -#217 := [monotonicity #204 #214]: #216 -#197 := (iff #39 #196) -#194 := (iff #38 #193) -#195 := [rewrite]: #194 -#191 := (iff #37 #190) -#192 := [rewrite]: #191 -#198 := [monotonicity #192 #195]: #197 -#220 := [monotonicity #198 #217]: #219 -#223 := [monotonicity #220]: #222 -#226 := [quant-intro #223]: #225 -#267 := [trans #226 #265]: #266 -#189 := [asserted]: #53 -#268 := [mp #189 #267]: #263 -#338 := [mp~ #268 #324]: #263 -#363 := [mp #338 #362]: #360 -#394 := [mp #363 #393]: #391 -#909 := [mp #394 #908]: #904 -#774 := (not #904) -#775 := (or #774 #771) -#836 := (* -1::Int 3::Int) -#683 := (div #842 #836) -#684 := (* -1::Int #683) -#685 := (+ #11 #684) -#827 := (= #685 0::Int) -#831 := (<= 3::Int 0::Int) -#832 := (or #831 #825) -#826 := (not #832) -#662 := (or #833 #831) -#664 := (not #662) -#665 := (or #664 #826) -#818 := (ite #665 #824 #827) -#821 := (= 3::Int 0::Int) -#820 := (or #822 #821) -#823 := (ite #820 #819 #818) -#776 := (or #774 #823) -#778 := (iff #776 #775) -#779 := (iff #775 #775) -#757 := [rewrite]: #779 -#772 := (iff #823 #771) -#769 := (iff #818 #767) -#786 := (iff #827 #782) -#784 := (= #685 #783) -#780 := (= #684 #794) -#793 := (= #683 #792) -#790 := (= #836 -3::Int) -#791 := [rewrite]: #790 -#789 := [monotonicity #791]: #793 -#781 := [monotonicity #789]: #780 -#785 := [monotonicity #781]: #784 -#766 := [monotonicity #785]: #786 -#803 := (iff #665 #801) -#810 := (or #723 #808) -#802 := (iff #810 #801) -#796 := [rewrite]: #802 -#799 := (iff #665 #810) -#809 := (iff #826 #808) -#797 := (iff #832 #825) -#817 := (or false #825) -#798 := (iff #817 #825) -#795 := [rewrite]: #798 -#804 := (iff #832 #817) -#700 := (iff #831 false) -#715 := [rewrite]: #700 -#806 := [monotonicity #715]: #804 -#807 := [trans #806 #795]: #797 -#805 := [monotonicity #807]: #809 -#816 := (iff #664 #723) -#721 := (iff #662 #833) -#717 := (or #833 false) -#719 := (iff #717 #833) -#720 := [rewrite]: #719 -#718 := (iff #662 #717) -#711 := [monotonicity #715]: #718 -#722 := [trans #711 #720]: #721 -#813 := [monotonicity #722]: #816 -#800 := [monotonicity #813 #805]: #799 -#787 := [trans #800 #796]: #803 -#770 := [monotonicity #787 #766]: #769 -#812 := (iff #820 #822) -#707 := (or #822 false) -#716 := (iff #707 #822) -#811 := [rewrite]: #716 -#666 := (iff #820 #707) -#705 := (iff #821 false) -#706 := [rewrite]: #705 -#814 := [monotonicity #706]: #666 -#815 := [trans #814 #811]: #812 -#773 := [monotonicity #815 #770]: #772 -#768 := [monotonicity #773]: #778 -#758 := [trans #768 #757]: #778 -#777 := [quant-inst #9 #10]: #776 -#760 := [mp #777 #758]: #775 -#639 := [unit-resolution #760 #909]: #771 -#739 := (not #771) -#743 := (or #739 #740 #819) -#744 := [def-axiom]: #743 -#642 := [unit-resolution #744 #639]: #641 -#638 := [unit-resolution #642 #636]: #740 -#635 := [unit-resolution #638 #627]: false -#631 := [lemma #635]: #628 -#571 := [unit-resolution #631 #562]: #874 -#877 := (or #545 #876) -#875 := (or #880 #545 #876) -#881 := (or #880 #877) -#531 := (iff #881 #875) -#536 := [rewrite]: #531 -#871 := [quant-inst #11]: #881 -#872 := [mp #871 #536]: #875 -#572 := [unit-resolution #872 #896]: #877 -#563 := [unit-resolution #572 #571]: #545 -#480 := (= 0::Int #11) -#637 := (* -1::Int #11) -#640 := (+ #9 #637) -#646 := (>= #640 0::Int) -#658 := (= #9 #11) -#500 := (= #544 #11) -#496 := [symm #563]: #500 -#501 := [trans #498 #496]: #658 -#483 := (not #658) -#487 := (or #483 #646) -#488 := [th-lemma arith triangle-eq]: #487 -#491 := [unit-resolution #488 #501]: #646 -#492 := (not #646) -#493 := (or #825 #876 #492) -#485 := [th-lemma arith assign-bounds 1 1]: #493 -#494 := [unit-resolution #485 #571 #491]: #825 -#644 := (<= #640 0::Int) -#478 := (or #483 #644) -#475 := [th-lemma arith triangle-eq]: #478 -#476 := [unit-resolution #475 #501]: #644 -#512 := (not #644) -#489 := (or #819 #512 #808 #876) -#613 := (* -3::Int #828) -#748 := (mod #9 3::Int) -#612 := (* -1::Int #748) -#614 := (+ #612 #613) -#615 := (+ #9 #614) -#611 := (= #615 0::Int) -#80 := [true-axiom]: true -#573 := (or false #611) -#540 := [th-lemma arith]: #573 -#542 := [unit-resolution #540 #80]: #611 -#597 := (>= #615 0::Int) -#513 := (not #597) -#598 := (>= #748 0::Int) -#543 := (or false #598) -#534 := [th-lemma arith]: #543 -#547 := [unit-resolution #534 #80]: #598 -#761 := (<= #11 0::Int) -#550 := (not #761) -#548 := [hypothesis]: #874 -#549 := [hypothesis]: #746 -#551 := (or #819 #550 #876) -#541 := [th-lemma arith triangle-eq]: #551 -#552 := [unit-resolution #541 #549 #548]: #550 -#535 := [hypothesis]: #644 -#749 := (<= #830 0::Int) -#537 := [unit-resolution #642 #549]: #740 -#538 := (or #822 #767) -#745 := (or #739 #822 #767) -#741 := [def-axiom]: #745 -#517 := [unit-resolution #741 #639]: #538 -#519 := [unit-resolution #517 #537]: #767 -#524 := [hypothesis]: #825 -#525 := (or #822 #723 #808) -#526 := [th-lemma arith triangle-eq]: #525 -#527 := [unit-resolution #526 #537 #524]: #723 -#764 := (or #801 #833) -#759 := [def-axiom]: #764 -#528 := [unit-resolution #759 #527]: #801 -#765 := (not #801) -#750 := (not #767) -#756 := (or #750 #765 #824) -#729 := [def-axiom]: #756 -#529 := [unit-resolution #729 #528 #519]: #824 -#624 := (not #824) -#518 := (or #624 #749) -#530 := [th-lemma arith triangle-eq]: #518 -#511 := [unit-resolution #530 #529]: #749 -#515 := (not #749) -#514 := (not #598) -#503 := (or #513 #514 #761 #512 #515) -#505 := [th-lemma arith assign-bounds 1 2 1 3]: #503 -#506 := [unit-resolution #505 #511 #535 #552 #547]: #513 -#509 := (not #611) -#504 := (or #509 #597) -#510 := [th-lemma arith triangle-eq]: #504 -#484 := [unit-resolution #510 #506 #542]: false -#490 := [lemma #484]: #489 -#479 := [unit-resolution #490 #476 #494 #571]: #819 -#481 := [symm #479]: #480 -#469 := [trans #481 #563]: #482 -#472 := [trans #469 #477]: #471 -#917 := [monotonicity #472]: #473 -#919 := [symm #917]: #918 -#539 := (= f6 #560) -#19 := (:var 0 S2) -#20 := (f5 #19) -#882 := (pattern #20) -#21 := (f3 #20) -#104 := (= #19 #21) -#883 := (forall (vars (?v0 S2)) (:pat #882) #104) -#108 := (forall (vars (?v0 S2)) #104) -#884 := (iff #108 #883) -#886 := (iff #883 #883) -#887 := [rewrite]: #886 -#885 := [rewrite]: #884 -#888 := [trans #885 #887]: #884 -#331 := (~ #108 #108) -#329 := (~ #104 #104) -#330 := [refl]: #329 -#332 := [nnf-pos #330]: #331 -#22 := (= #21 #19) -#23 := (forall (vars (?v0 S2)) #22) -#109 := (iff #23 #108) -#106 := (iff #22 #104) -#107 := [rewrite]: #106 -#110 := [quant-intro #107]: #109 -#103 := [asserted]: #23 -#113 := [mp #103 #110]: #108 -#317 := [mp~ #113 #332]: #108 -#889 := [mp #317 #888]: #883 -#533 := (not #883) -#663 := (or #533 #539) -#870 := [quant-inst #8]: #663 -#470 := [unit-resolution #870 #889]: #539 -#920 := [trans #470 #919]: #16 -#921 := [unit-resolution #570 #920]: false -#922 := [lemma #921]: #16 -#927 := [monotonicity #922]: #926 -#928 := [trans #927 #923]: #822 -#929 := [unit-resolution #642 #928]: #819 -#931 := [monotonicity #929]: #930 -#933 := [symm #931]: #932 -#934 := [trans #922 #933]: #83 -#559 := (or #557 #97) -#558 := (or #557 #97 #468) -#486 := [def-axiom]: #558 -#556 := [unit-resolution #486 #105]: #559 -#495 := [unit-resolution #556 #922]: #557 -[unit-resolution #495 #934]: false -unsat -2e39fe3f9575e15a240203df63c5032154a66535 279 0 +#129 := [monotonicity #115 #126]: #128 +#133 := [trans #129 #131]: #132 +#121 := (iff #17 #111) +#116 := (and #111 true) +#119 := (iff #116 #111) +#120 := [rewrite]: #119 +#117 := (iff #17 #116) +#112 := (iff #15 #111) +#113 := [rewrite]: #112 +#118 := [monotonicity #113 #115]: #117 +#122 := [trans #118 #120]: #121 +#136 := [monotonicity #122 #133]: #135 +#139 := [monotonicity #136]: #138 +#142 := [monotonicity #139]: #141 +#145 := [monotonicity #142]: #144 +#148 := [monotonicity #145]: #147 +#151 := [monotonicity #148]: #150 +#108 := (iff #29 #107) +#105 := (iff #28 #102) +#99 := (= #96 f5) +#103 := (iff #99 #102) +#104 := [rewrite]: #103 +#100 := (iff #28 #99) +#97 := (= #27 #96) +#94 := (= #26 #93) +#91 := (= #25 #90) +#88 := (= #24 #87) +#85 := (= #23 -1::Int) +#86 := [rewrite]: #85 +#83 := (= #22 #82) +#84 := [rewrite]: #83 +#89 := [monotonicity #84 #86]: #88 +#79 := (iff #20 #78) +#76 := (iff #19 #75) +#77 := [rewrite]: #76 +#80 := [monotonicity #77]: #79 +#92 := [monotonicity #80 #89]: #91 +#73 := (iff #14 #11) +#68 := (or #11 false) +#71 := (iff #68 #11) +#72 := [rewrite]: #71 +#69 := (iff #14 #68) +#66 := (iff #13 false) +#67 := [rewrite]: #66 +#70 := [monotonicity #67]: #69 +#74 := [trans #70 #72]: #73 +#95 := [monotonicity #74 #92]: #94 +#98 := [monotonicity #95]: #97 +#101 := [monotonicity #98]: #100 +#106 := [trans #101 #104]: #105 +#109 := [monotonicity #106]: #108 +#153 := [trans #109 #151]: #152 +#65 := [asserted]: #29 +#154 := [mp #65 #153]: #149 +#693 := [unit-resolution #154 #689]: false +#682 := [lemma #693]: #389 +#723 := (or #11 #398) +#724 := [def-axiom]: #723 +#632 := [unit-resolution #724 #682]: #398 +#314 := (= #21 #137) +#708 := (f4 #725) +#703 := (= #708 0::Int) +#626 := (not #703) +#628 := (iff #389 #626) +#639 := (iff #11 #703) +#638 := (iff #703 #11) +#636 := (= #708 #9) +#633 := (= #725 f5) +#635 := [symm #690]: #633 +#637 := [monotonicity #635]: #636 +#634 := [monotonicity #637]: #638 +#625 := [symm #634]: #639 +#629 := [monotonicity #625]: #628 +#630 := [mp #682 #629]: #626 +#714 := (or #123 #703) +#35 := (:var 0 Int) +#37 := (f3 #35) +#735 := (pattern #37) +#180 := (>= #35 0::Int) +#38 := (f4 #37) +#43 := (= #38 0::Int) +#229 := (or #43 #180) +#742 := (forall (vars (?v0 Int)) (:pat #735) #229) +#234 := (forall (vars (?v0 Int)) #229) +#745 := (iff #234 #742) +#743 := (iff #229 #229) +#744 := [refl]: #743 +#746 := [quant-intro #744]: #745 +#247 := (~ #234 #234) +#255 := (~ #229 #229) +#256 := [refl]: #255 +#248 := [nnf-pos #256]: #247 +#42 := (< #35 0::Int) +#44 := (implies #42 #43) +#45 := (forall (vars (?v0 Int)) #44) +#237 := (iff #45 #234) +#200 := (= 0::Int #38) +#206 := (not #42) +#207 := (or #206 #200) +#212 := (forall (vars (?v0 Int)) #207) +#235 := (iff #212 #234) +#232 := (iff #207 #229) +#226 := (or #180 #43) +#230 := (iff #226 #229) +#231 := [rewrite]: #230 +#227 := (iff #207 #226) +#224 := (iff #200 #43) +#225 := [rewrite]: #224 +#222 := (iff #206 #180) +#182 := (not #180) +#217 := (not #182) +#220 := (iff #217 #180) +#221 := [rewrite]: #220 +#218 := (iff #206 #217) +#215 := (iff #42 #182) +#216 := [rewrite]: #215 +#219 := [monotonicity #216]: #218 +#223 := [trans #219 #221]: #222 +#228 := [monotonicity #223 #225]: #227 +#233 := [trans #228 #231]: #232 +#236 := [quant-intro #233]: #235 +#213 := (iff #45 #212) +#210 := (iff #44 #207) +#203 := (implies #42 #200) +#208 := (iff #203 #207) +#209 := [rewrite]: #208 +#204 := (iff #44 #203) +#201 := (iff #43 #200) +#202 := [rewrite]: #201 +#205 := [monotonicity #202]: #204 +#211 := [trans #205 #209]: #210 +#214 := [quant-intro #211]: #213 +#238 := [trans #214 #236]: #237 +#199 := [asserted]: #45 +#239 := [mp #199 #238]: #234 +#257 := [mp~ #239 #248]: #234 +#747 := [mp #257 #746]: #742 +#709 := (not #742) +#423 := (or #709 #123 #703) +#711 := (or #703 #123) +#424 := (or #709 #711) +#420 := (iff #424 #423) +#426 := (or #709 #714) +#697 := (iff #426 #423) +#419 := [rewrite]: #697 +#320 := (iff #424 #426) +#700 := (iff #711 #714) +#701 := [rewrite]: #700 +#696 := [monotonicity #701]: #320 +#694 := [trans #696 #419]: #420 +#425 := [quant-inst #9]: #424 +#698 := [mp #425 #694]: #423 +#627 := [unit-resolution #698 #747]: #714 +#631 := [unit-resolution #627 #630]: #123 +#611 := (or #11 #111 #124) +#612 := [th-lemma arith triangle-eq]: #611 +#614 := [unit-resolution #612 #682]: #134 +#615 := [unit-resolution #614 #631]: #111 +#400 := (or #134 #110) +#391 := [def-axiom]: #400 +#616 := [unit-resolution #391 #615]: #134 +#404 := (not #134) +#721 := (or #404 #314) +#378 := [def-axiom]: #721 +#617 := [unit-resolution #378 #616]: #314 +#618 := [trans #617 #632]: #651 +#619 := (not #651) +#620 := (or #619 #642) +#621 := [th-lemma arith triangle-eq]: #620 +#622 := [unit-resolution #621 #618]: #642 +#652 := (>= #640 0::Int) +#623 := (or #619 #652) +#613 := [th-lemma arith triangle-eq]: #623 +#624 := [unit-resolution #613 #618]: #652 +#603 := [th-lemma arith eq-propagate 1 1 1 1 #624 #622 #648 #646]: #602 +#605 := [symm #603]: #411 +#606 := [monotonicity #605]: #691 +#607 := [symm #606]: #688 +#608 := [trans #690 #607]: #146 +[unit-resolution #154 #608]: false +unsat +527e5e3123950986e94b94da9ebd83dc07302cc9 81 0 #2 := false decl f3 :: (-> Int S2) #8 := 0::Int -#11 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := (f4 0::Int 0::Int) -#10 := (f3 #9) -#12 := (= #10 #11) -#804 := (= #9 0::Int) -#19 := (:var 0 Int) -#30 := (:var 1 Int) -#49 := (f4 #30 #19) -#884 := (pattern #49) -#179 := -1::Int -#183 := (* -1::Int #19) -#180 := (* -1::Int #30) -#244 := (mod #180 #183) -#374 := (+ #49 #244) -#375 := (= #374 0::Int) -#50 := (mod #30 #19) -#371 := (* -1::Int #50) -#372 := (+ #49 #371) -#373 := (= #372 0::Int) -#218 := (>= #30 0::Int) -#211 := (<= #19 0::Int) -#318 := (or #211 #218) -#319 := (not #318) -#207 := (<= #30 0::Int) -#316 := (or #207 #211) -#317 := (not #316) -#322 := (or #317 #319) -#376 := (ite #322 #373 #375) -#370 := (= #49 0::Int) -#32 := (= #30 0::Int) -#377 := (ite #32 #370 #376) -#369 := (= #30 #49) -#33 := (= #19 0::Int) -#378 := (ite #33 #369 #377) -#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #378) -#381 := (forall (vars (?v0 Int) (?v1 Int)) #378) -#888 := (iff #381 #885) -#886 := (iff #378 #378) -#887 := [refl]: #886 -#889 := [quant-intro #887]: #888 -#250 := (* -1::Int #244) -#338 := (ite #322 #50 #250) -#341 := (ite #32 0::Int #338) -#344 := (ite #33 #30 #341) -#347 := (= #49 #344) -#350 := (forall (vars (?v0 Int) (?v1 Int)) #347) -#382 := (iff #350 #381) -#379 := (iff #347 #378) -#380 := [rewrite]: #379 -#383 := [quant-intro #380]: #382 -#219 := (not #218) -#212 := (not #211) -#222 := (and #212 #219) -#208 := (not #207) -#215 := (and #208 #212) -#225 := (or #215 #222) -#270 := (ite #225 #50 #250) -#273 := (ite #32 0::Int #270) -#276 := (ite #33 #30 #273) -#279 := (= #49 #276) -#282 := (forall (vars (?v0 Int) (?v1 Int)) #279) -#351 := (iff #282 #350) -#348 := (iff #279 #347) -#345 := (= #276 #344) -#342 := (= #273 #341) -#339 := (= #270 #338) -#323 := (iff #225 #322) -#320 := (iff #222 #319) -#321 := [rewrite]: #320 -#301 := (iff #215 #317) -#302 := [rewrite]: #301 -#324 := [monotonicity #302 #321]: #323 -#340 := [monotonicity #324]: #339 -#343 := [monotonicity #340]: #342 -#346 := [monotonicity #343]: #345 -#349 := [monotonicity #346]: #348 -#352 := [quant-intro #349]: #351 -#299 := (~ #282 #282) -#313 := (~ #279 #279) -#314 := [refl]: #313 -#300 := [nnf-pos #314]: #299 -#43 := (- #19) -#42 := (- #30) -#51 := (mod #42 #43) -#52 := (- #51) -#36 := (< 0::Int #19) -#38 := (< #30 0::Int) -#39 := (and #38 #36) -#35 := (< 0::Int #30) -#37 := (and #35 #36) -#40 := (or #37 #39) -#53 := (ite #40 #50 #52) -#54 := (ite #32 0::Int #53) -#55 := (ite #33 #30 #54) -#56 := (= #49 #55) -#57 := (forall (vars (?v0 Int) (?v1 Int)) #56) -#285 := (iff #57 #282) -#173 := (and #36 #38) -#176 := (or #37 #173) -#255 := (ite #176 #50 #250) -#164 := (= 0::Int #30) -#258 := (ite #164 0::Int #255) -#167 := (= 0::Int #19) -#261 := (ite #167 #30 #258) -#264 := (= #49 #261) -#267 := (forall (vars (?v0 Int) (?v1 Int)) #264) -#283 := (iff #267 #282) -#280 := (iff #264 #279) -#277 := (= #261 #276) -#274 := (= #258 #273) -#271 := (= #255 #270) -#226 := (iff #176 #225) -#223 := (iff #173 #222) -#220 := (iff #38 #219) -#221 := [rewrite]: #220 -#213 := (iff #36 #212) -#214 := [rewrite]: #213 -#224 := [monotonicity #214 #221]: #223 -#216 := (iff #37 #215) -#209 := (iff #35 #208) -#210 := [rewrite]: #209 -#217 := [monotonicity #210 #214]: #216 -#227 := [monotonicity #217 #224]: #226 -#272 := [monotonicity #227]: #271 -#201 := (iff #164 #32) -#202 := [rewrite]: #201 -#275 := [monotonicity #202 #272]: #274 -#203 := (iff #167 #33) -#204 := [rewrite]: #203 -#278 := [monotonicity #204 #275]: #277 -#281 := [monotonicity #278]: #280 -#284 := [quant-intro #281]: #283 -#268 := (iff #57 #267) -#265 := (iff #56 #264) -#262 := (= #55 #261) -#259 := (= #54 #258) -#256 := (= #53 #255) -#253 := (= #52 #250) -#247 := (- #244) -#251 := (= #247 #250) -#252 := [rewrite]: #251 -#248 := (= #52 #247) -#245 := (= #51 #244) -#184 := (= #43 #183) -#185 := [rewrite]: #184 -#181 := (= #42 #180) -#182 := [rewrite]: #181 -#246 := [monotonicity #182 #185]: #245 -#249 := [monotonicity #246]: #248 -#254 := [trans #249 #252]: #253 -#177 := (iff #40 #176) -#174 := (iff #39 #173) -#175 := [rewrite]: #174 -#178 := [monotonicity #175]: #177 -#257 := [monotonicity #178 #254]: #256 -#165 := (iff #32 #164) -#166 := [rewrite]: #165 -#260 := [monotonicity #166 #257]: #259 -#168 := (iff #33 #167) -#169 := [rewrite]: #168 -#263 := [monotonicity #169 #260]: #262 -#266 := [monotonicity #263]: #265 -#269 := [quant-intro #266]: #268 -#286 := [trans #269 #284]: #285 -#243 := [asserted]: #57 -#287 := [mp #243 #286]: #282 -#315 := [mp~ #287 #300]: #282 -#353 := [mp #315 #352]: #350 -#384 := [mp #353 #383]: #381 -#890 := [mp #384 #889]: #885 -#760 := (not #885) -#740 := (or #760 #804) -#811 := (* -1::Int 0::Int) -#812 := (mod #811 #811) -#813 := (+ #9 #812) -#808 := (= #813 0::Int) -#809 := (mod 0::Int 0::Int) -#814 := (* -1::Int #809) -#815 := (+ #9 #814) -#810 := (= #815 0::Int) -#833 := (>= 0::Int 0::Int) -#816 := (<= 0::Int 0::Int) -#657 := (or #816 #833) -#658 := (not #657) -#659 := (or #816 #816) -#801 := (not #659) -#802 := (or #801 #658) -#803 := (ite #802 #810 #808) -#798 := (= 0::Int 0::Int) -#799 := (ite #798 #804 #803) -#805 := (= 0::Int #9) -#806 := (ite #798 #805 #799) -#741 := (or #760 #806) -#744 := (iff #741 #740) -#746 := (iff #740 #740) -#747 := [rewrite]: #746 -#759 := (iff #806 #804) -#1 := true -#768 := (ite true #804 #804) -#757 := (iff #768 #804) -#758 := [rewrite]: #757 -#754 := (iff #806 #768) -#767 := (iff #799 #804) -#769 := (+ #9 #809) -#782 := (= #769 0::Int) -#761 := (ite true #804 #782) -#765 := (iff #761 #804) -#766 := [rewrite]: #765 -#762 := (iff #799 #761) -#770 := (iff #803 #782) -#784 := (ite false #810 #782) -#775 := (iff #784 #782) -#776 := [rewrite]: #775 -#773 := (iff #803 #784) -#783 := (iff #808 #782) -#771 := (= #813 #769) -#780 := (= #812 #809) -#791 := (= #811 0::Int) -#778 := [rewrite]: #791 -#772 := [monotonicity #778 #778]: #780 -#781 := [monotonicity #772]: #771 -#779 := [monotonicity #781]: #783 -#790 := (iff #802 false) -#693 := (or false false) -#696 := (iff #693 false) -#697 := [rewrite]: #696 -#694 := (iff #802 #693) -#692 := (iff #658 false) -#481 := (not true) -#840 := (iff #481 false) -#843 := [rewrite]: #840 -#689 := (iff #658 #481) -#789 := (iff #657 true) -#793 := (or true true) -#794 := (iff #793 true) -#797 := [rewrite]: #794 -#785 := (iff #657 #793) -#839 := (iff #833 true) -#841 := [rewrite]: #839 -#639 := (iff #816 true) -#792 := [rewrite]: #639 -#786 := [monotonicity #792 #841]: #785 -#674 := [trans #786 #797]: #789 -#691 := [monotonicity #674]: #689 -#685 := [trans #691 #843]: #692 -#788 := (iff #801 false) -#681 := (iff #801 #481) -#679 := (iff #659 true) -#795 := (iff #659 #793) -#796 := [monotonicity #792 #792]: #795 -#680 := [trans #796 #797]: #679 -#640 := [monotonicity #680]: #681 -#690 := [trans #640 #843]: #788 -#695 := [monotonicity #690 #685]: #694 -#787 := [trans #695 #697]: #790 -#774 := [monotonicity #787 #779]: #773 -#777 := [trans #774 #776]: #770 -#800 := (iff #798 true) -#807 := [rewrite]: #800 -#764 := [monotonicity #807 #777]: #762 -#763 := [trans #764 #766]: #767 -#636 := (iff #805 #804) -#638 := [rewrite]: #636 -#755 := [monotonicity #807 #638 #763]: #754 -#756 := [trans #755 #758]: #759 -#745 := [monotonicity #756]: #744 -#748 := [trans #745 #747]: #744 -#743 := [quant-inst #8 #8]: #741 -#749 := [mp #743 #748]: #740 -#751 := [unit-resolution #749 #890]: #804 -#752 := [monotonicity #751]: #12 -#13 := (not #12) -#77 := [asserted]: #13 -[unit-resolution #77 #752]: false -unsat -eaf623ea6157604982b5732ebda9f473145c7bd3 326 0 -#2 := false -decl f3 :: (-> Int S2) -decl f4 :: (-> Int Int Int) -#10 := 0::Int -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#11 := (f4 #9 0::Int) -#12 := (f3 #11) -#79 := (= f6 #12) -#450 := (f3 #9) -#785 := (= #450 #12) -#784 := (= #12 #450) -#781 := (= #11 #9) -#831 := (= #9 #11) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f4 #31 #20) -#892 := (pattern #50) -#187 := -1::Int -#191 := (* -1::Int #20) -#188 := (* -1::Int #31) -#252 := (mod #188 #191) -#382 := (+ #50 #252) -#383 := (= #382 0::Int) -#51 := (mod #31 #20) -#379 := (* -1::Int #51) -#380 := (+ #50 #379) -#381 := (= #380 0::Int) -#226 := (>= #31 0::Int) -#219 := (<= #20 0::Int) -#326 := (or #219 #226) -#327 := (not #326) -#215 := (<= #31 0::Int) -#324 := (or #215 #219) -#325 := (not #324) -#330 := (or #325 #327) -#384 := (ite #330 #381 #383) -#378 := (= #50 0::Int) -#33 := (= #31 0::Int) -#385 := (ite #33 #378 #384) -#377 := (= #31 #50) -#34 := (= #20 0::Int) -#386 := (ite #34 #377 #385) -#893 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #892) #386) -#389 := (forall (vars (?v0 Int) (?v1 Int)) #386) -#896 := (iff #389 #893) -#894 := (iff #386 #386) -#895 := [refl]: #894 -#897 := [quant-intro #895]: #896 -#258 := (* -1::Int #252) -#346 := (ite #330 #51 #258) -#349 := (ite #33 0::Int #346) -#352 := (ite #34 #31 #349) -#355 := (= #50 #352) -#358 := (forall (vars (?v0 Int) (?v1 Int)) #355) -#390 := (iff #358 #389) -#387 := (iff #355 #386) -#388 := [rewrite]: #387 -#391 := [quant-intro #388]: #390 -#227 := (not #226) -#220 := (not #219) -#230 := (and #220 #227) -#216 := (not #215) -#223 := (and #216 #220) -#233 := (or #223 #230) -#278 := (ite #233 #51 #258) -#281 := (ite #33 0::Int #278) -#284 := (ite #34 #31 #281) -#287 := (= #50 #284) -#290 := (forall (vars (?v0 Int) (?v1 Int)) #287) -#359 := (iff #290 #358) -#356 := (iff #287 #355) -#353 := (= #284 #352) -#350 := (= #281 #349) -#347 := (= #278 #346) -#331 := (iff #233 #330) -#328 := (iff #230 #327) -#329 := [rewrite]: #328 -#309 := (iff #223 #325) -#310 := [rewrite]: #309 -#332 := [monotonicity #310 #329]: #331 -#348 := [monotonicity #332]: #347 -#351 := [monotonicity #348]: #350 -#354 := [monotonicity #351]: #353 -#357 := [monotonicity #354]: #356 -#360 := [quant-intro #357]: #359 -#307 := (~ #290 #290) -#321 := (~ #287 #287) -#322 := [refl]: #321 -#308 := [nnf-pos #322]: #307 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#293 := (iff #58 #290) -#181 := (and #37 #39) -#184 := (or #38 #181) -#263 := (ite #184 #51 #258) -#172 := (= 0::Int #31) -#266 := (ite #172 0::Int #263) -#175 := (= 0::Int #20) -#269 := (ite #175 #31 #266) -#272 := (= #50 #269) -#275 := (forall (vars (?v0 Int) (?v1 Int)) #272) -#291 := (iff #275 #290) -#288 := (iff #272 #287) -#285 := (= #269 #284) -#282 := (= #266 #281) -#279 := (= #263 #278) -#234 := (iff #184 #233) -#231 := (iff #181 #230) -#228 := (iff #39 #227) -#229 := [rewrite]: #228 -#221 := (iff #37 #220) -#222 := [rewrite]: #221 -#232 := [monotonicity #222 #229]: #231 -#224 := (iff #38 #223) -#217 := (iff #36 #216) -#218 := [rewrite]: #217 -#225 := [monotonicity #218 #222]: #224 -#235 := [monotonicity #225 #232]: #234 -#280 := [monotonicity #235]: #279 -#209 := (iff #172 #33) -#210 := [rewrite]: #209 -#283 := [monotonicity #210 #280]: #282 -#211 := (iff #175 #34) -#212 := [rewrite]: #211 -#286 := [monotonicity #212 #283]: #285 -#289 := [monotonicity #286]: #288 -#292 := [quant-intro #289]: #291 -#276 := (iff #58 #275) -#273 := (iff #57 #272) -#270 := (= #56 #269) -#267 := (= #55 #266) -#264 := (= #54 #263) -#261 := (= #53 #258) -#255 := (- #252) -#259 := (= #255 #258) -#260 := [rewrite]: #259 -#256 := (= #53 #255) -#253 := (= #52 #252) -#192 := (= #44 #191) -#193 := [rewrite]: #192 -#189 := (= #43 #188) -#190 := [rewrite]: #189 -#254 := [monotonicity #190 #193]: #253 -#257 := [monotonicity #254]: #256 -#262 := [trans #257 #260]: #261 -#185 := (iff #41 #184) -#182 := (iff #40 #181) -#183 := [rewrite]: #182 -#186 := [monotonicity #183]: #185 -#265 := [monotonicity #186 #262]: #264 -#173 := (iff #33 #172) -#174 := [rewrite]: #173 -#268 := [monotonicity #174 #265]: #267 -#176 := (iff #34 #175) -#177 := [rewrite]: #176 -#271 := [monotonicity #177 #268]: #270 -#274 := [monotonicity #271]: #273 -#277 := [quant-intro #274]: #276 -#294 := [trans #277 #292]: #293 -#251 := [asserted]: #58 -#295 := [mp #251 #294]: #290 -#323 := [mp~ #295 #308]: #290 -#361 := [mp #323 #360]: #358 -#392 := [mp #361 #391]: #389 -#898 := [mp #392 #897]: #893 -#799 := (not #893) -#786 := (or #799 #831) -#840 := (* -1::Int 0::Int) -#846 := (* -1::Int #9) -#484 := (mod #846 #840) -#847 := (+ #11 #484) -#849 := (= #847 0::Int) -#489 := (mod #9 0::Int) -#490 := (* -1::Int #489) -#850 := (+ #11 #490) -#848 := (= #850 0::Int) -#851 := (>= #9 0::Int) -#837 := (<= 0::Int 0::Int) -#838 := (or #837 #851) -#560 := (not #838) -#561 := (<= #9 0::Int) -#562 := (or #561 #837) -#563 := (not #562) -#456 := (or #563 #560) -#833 := (ite #456 #848 #849) -#834 := (= #11 0::Int) -#556 := (= #9 0::Int) -#557 := (ite #556 #834 #833) -#835 := (= 0::Int 0::Int) -#832 := (ite #835 #831 #557) -#788 := (or #799 #832) -#777 := (iff #788 #786) -#789 := (iff #786 #786) -#790 := [rewrite]: #789 -#798 := (iff #832 #831) -#801 := (mod #846 0::Int) -#802 := (+ #11 #801) -#688 := (= #802 0::Int) -#699 := (ite #556 #834 #688) -#1 := true -#701 := (ite true #831 #699) -#704 := (iff #701 #831) -#705 := [rewrite]: #704 -#702 := (iff #832 #701) -#700 := (iff #557 #699) -#682 := (iff #833 #688) -#796 := (ite false #848 #688) -#794 := (iff #796 #688) -#797 := [rewrite]: #794 -#698 := (iff #833 #796) -#689 := (iff #849 #688) -#805 := (= #847 #802) -#803 := (= #484 #801) -#647 := (= #840 0::Int) -#800 := [rewrite]: #647 -#804 := [monotonicity #800]: #803 -#687 := [monotonicity #804]: #805 -#648 := [monotonicity #687]: #689 -#644 := (iff #456 false) -#807 := (or false false) -#808 := (iff #807 false) -#815 := [rewrite]: #808 -#813 := (iff #456 #807) -#812 := (iff #560 false) -#830 := (not true) -#821 := (iff #830 false) -#816 := [rewrite]: #821 -#810 := (iff #560 #830) -#667 := (iff #838 true) -#823 := (or true #851) -#665 := (iff #823 true) -#666 := [rewrite]: #665 -#818 := (iff #838 #823) -#547 := (iff #837 true) -#548 := [rewrite]: #547 -#824 := [monotonicity #548]: #818 -#809 := [trans #824 #666]: #667 -#811 := [monotonicity #809]: #810 -#806 := [trans #811 #816]: #812 -#817 := (iff #563 false) -#819 := (iff #563 #830) -#829 := (iff #562 true) -#549 := (or #561 true) -#543 := (iff #549 true) -#825 := [rewrite]: #543 -#827 := (iff #562 #549) -#828 := [monotonicity #548]: #827 -#826 := [trans #828 #825]: #829 -#820 := [monotonicity #826]: #819 -#822 := [trans #820 #816]: #817 -#814 := [monotonicity #822 #806]: #813 -#646 := [trans #814 #815]: #644 -#793 := [monotonicity #646 #648]: #698 -#697 := [trans #793 #797]: #682 -#693 := [monotonicity #697]: #700 -#836 := (iff #835 true) -#546 := [rewrite]: #836 -#703 := [monotonicity #546 #693]: #702 -#795 := [trans #703 #705]: #798 -#779 := [monotonicity #795]: #777 -#791 := [trans #779 #790]: #777 -#780 := [quant-inst #9 #10]: #788 -#787 := [mp #780 #791]: #786 -#792 := [unit-resolution #787 #898]: #831 -#782 := [symm #792]: #781 -#778 := [monotonicity #782]: #784 -#769 := [symm #778]: #785 -#535 := (= f6 #450) -#15 := (:var 0 S2) -#16 := (f5 #15) -#864 := (pattern #16) -#17 := (f3 #16) -#86 := (= #15 #17) -#865 := (forall (vars (?v0 S2)) (:pat #864) #86) -#90 := (forall (vars (?v0 S2)) #86) -#866 := (iff #90 #865) -#868 := (iff #865 #865) -#869 := [rewrite]: #868 -#867 := [rewrite]: #866 -#870 := [trans #867 #869]: #866 -#313 := (~ #90 #90) -#311 := (~ #86 #86) -#312 := [refl]: #311 -#314 := [nnf-pos #312]: #313 -#18 := (= #17 #15) -#19 := (forall (vars (?v0 S2)) #18) -#91 := (iff #19 #90) -#88 := (iff #18 #86) -#89 := [rewrite]: #88 -#92 := [quant-intro #89]: #91 -#85 := [asserted]: #19 -#95 := [mp #85 #92]: #90 -#299 := [mp~ #95 #314]: #90 -#871 := [mp #299 #870]: #865 -#528 := (not #865) -#539 := (or #528 #535) -#540 := [quant-inst #8]: #539 -#783 := [unit-resolution #540 #871]: #535 -#770 := [trans #783 #769]: #79 -#82 := (not #79) -#13 := (= #12 f6) -#14 := (not #13) -#83 := (iff #14 #82) -#80 := (iff #13 #79) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := [asserted]: #14 -#87 := [mp #78 #84]: #82 -[unit-resolution #87 #770]: false -unsat -acd2d715307b02a82f8d3d25d1935b122a84c3b3 309 0 -#2 := false -decl f3 :: (-> Int S2) -#8 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 1::Int -#10 := (f4 0::Int 1::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#805 := (= #10 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f4 #31 #20) -#884 := (pattern #50) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#245 := (mod #181 #184) -#375 := (+ #50 #245) -#376 := (= #375 0::Int) -#51 := (mod #31 #20) -#372 := (* -1::Int #51) -#373 := (+ #50 #372) -#374 := (= #373 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#377 := (ite #323 #374 #376) -#371 := (= #50 0::Int) -#33 := (= #31 0::Int) -#378 := (ite #33 #371 #377) -#370 := (= #31 #50) -#34 := (= #20 0::Int) -#379 := (ite #34 #370 #378) -#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379) -#382 := (forall (vars (?v0 Int) (?v1 Int)) #379) -#888 := (iff #382 #885) -#886 := (iff #379 #379) -#887 := [refl]: #886 -#889 := [quant-intro #887]: #888 -#251 := (* -1::Int #245) -#339 := (ite #323 #51 #251) -#342 := (ite #33 0::Int #339) -#345 := (ite #34 #31 #342) -#348 := (= #50 #345) -#351 := (forall (vars (?v0 Int) (?v1 Int)) #348) -#383 := (iff #351 #382) -#380 := (iff #348 #379) -#381 := [rewrite]: #380 -#384 := [quant-intro #381]: #383 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#271 := (ite #226 #51 #251) -#274 := (ite #33 0::Int #271) -#277 := (ite #34 #31 #274) -#280 := (= #50 #277) -#283 := (forall (vars (?v0 Int) (?v1 Int)) #280) -#352 := (iff #283 #351) -#349 := (iff #280 #348) -#346 := (= #277 #345) -#343 := (= #274 #342) -#340 := (= #271 #339) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#341 := [monotonicity #325]: #340 -#344 := [monotonicity #341]: #343 -#347 := [monotonicity #344]: #346 -#350 := [monotonicity #347]: #349 -#353 := [quant-intro #350]: #352 -#300 := (~ #283 #283) -#314 := (~ #280 #280) -#315 := [refl]: #314 -#301 := [nnf-pos #315]: #300 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#286 := (iff #58 #283) -#174 := (and #37 #39) -#177 := (or #38 #174) -#256 := (ite #177 #51 #251) -#165 := (= 0::Int #31) -#259 := (ite #165 0::Int #256) -#168 := (= 0::Int #20) -#262 := (ite #168 #31 #259) -#265 := (= #50 #262) -#268 := (forall (vars (?v0 Int) (?v1 Int)) #265) -#284 := (iff #268 #283) -#281 := (iff #265 #280) -#278 := (= #262 #277) -#275 := (= #259 #274) -#272 := (= #256 #271) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#273 := [monotonicity #228]: #272 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#276 := [monotonicity #203 #273]: #275 -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#279 := [monotonicity #205 #276]: #278 -#282 := [monotonicity #279]: #281 -#285 := [quant-intro #282]: #284 -#269 := (iff #58 #268) -#266 := (iff #57 #265) -#263 := (= #56 #262) -#260 := (= #55 #259) -#257 := (= #54 #256) -#254 := (= #53 #251) -#248 := (- #245) -#252 := (= #248 #251) -#253 := [rewrite]: #252 -#249 := (= #53 #248) -#246 := (= #52 #245) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#247 := [monotonicity #183 #186]: #246 -#250 := [monotonicity #247]: #249 -#255 := [trans #250 #253]: #254 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#258 := [monotonicity #179 #255]: #257 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#261 := [monotonicity #167 #258]: #260 -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#264 := [monotonicity #170 #261]: #263 -#267 := [monotonicity #264]: #266 -#270 := [quant-intro #267]: #269 -#287 := [trans #270 #285]: #286 -#244 := [asserted]: #58 -#288 := [mp #244 #287]: #283 -#316 := [mp~ #288 #301]: #283 -#354 := [mp #316 #353]: #351 -#385 := [mp #354 #384]: #382 -#890 := [mp #385 #889]: #885 -#728 := (not #885) -#729 := (or #728 #805) -#812 := (* -1::Int 1::Int) -#813 := (* -1::Int 0::Int) -#808 := (mod #813 #812) -#809 := (+ #10 #808) -#814 := (= #809 0::Int) -#815 := (mod 0::Int 1::Int) -#810 := (* -1::Int #815) -#816 := (+ #10 #810) -#657 := (= #816 0::Int) -#834 := (>= 0::Int 0::Int) -#658 := (<= 1::Int 0::Int) -#659 := (or #658 #834) -#801 := (not #659) -#802 := (<= 0::Int 0::Int) -#803 := (or #802 #658) -#804 := (not #803) -#798 := (or #804 #801) -#799 := (ite #798 #657 #814) -#806 := (= 0::Int 0::Int) -#800 := (ite #806 #805 #799) -#807 := (= 0::Int #10) -#636 := (= 1::Int 0::Int) -#638 := (ite #636 #807 #800) -#724 := (or #728 #638) -#703 := (iff #724 #729) -#705 := (iff #729 #729) -#598 := [rewrite]: #705 -#726 := (iff #638 #805) -#752 := (ite false #805 #805) -#731 := (iff #752 #805) -#732 := [rewrite]: #731 -#722 := (iff #638 #752) -#725 := (iff #800 #805) -#1 := true -#736 := (ite true #805 #805) -#733 := (iff #736 #805) -#739 := [rewrite]: #733 -#737 := (iff #800 #736) -#734 := (iff #799 #805) -#742 := (iff #799 #752) -#750 := (iff #814 #805) -#748 := (= #809 #10) -#764 := (+ #10 0::Int) -#767 := (= #764 #10) -#763 := [rewrite]: #767 -#746 := (= #809 #764) -#744 := (= #808 0::Int) -#756 := (mod 0::Int -1::Int) -#741 := (= #756 0::Int) -#743 := [rewrite]: #741 -#760 := (= #808 #756) -#758 := (= #812 -1::Int) -#759 := [rewrite]: #758 -#770 := (= #813 0::Int) -#777 := [rewrite]: #770 -#740 := [monotonicity #777 #759]: #760 -#745 := [trans #740 #743]: #744 -#747 := [monotonicity #745]: #746 -#749 := [trans #747 #763]: #748 -#751 := [monotonicity #749]: #750 -#755 := (iff #657 #805) -#768 := (= #816 #10) -#765 := (= #816 #764) -#761 := (= #810 0::Int) -#775 := (= #810 #813) -#773 := (= #815 0::Int) -#774 := [rewrite]: #773 -#776 := [monotonicity #774]: #775 -#762 := [trans #776 #777]: #761 -#766 := [monotonicity #762]: #765 -#754 := [trans #766 #763]: #768 -#757 := [monotonicity #754]: #755 -#779 := (iff #798 false) -#769 := (or false false) -#782 := (iff #769 false) -#783 := [rewrite]: #782 -#771 := (iff #798 #769) -#780 := (iff #801 false) -#482 := (not true) -#843 := (iff #482 false) -#829 := [rewrite]: #843 -#791 := (iff #801 #482) -#790 := (iff #659 true) -#693 := (or false true) -#696 := (iff #693 true) -#697 := [rewrite]: #696 -#694 := (iff #659 #693) -#841 := (iff #834 true) -#481 := [rewrite]: #841 -#680 := (iff #658 false) -#681 := [rewrite]: #680 -#695 := [monotonicity #681 #481]: #694 -#787 := [trans #695 #697]: #790 -#778 := [monotonicity #787]: #791 -#772 := [trans #778 #829]: #780 -#692 := (iff #804 false) -#689 := (iff #804 #482) -#789 := (iff #803 true) -#640 := (or true false) -#785 := (iff #640 true) -#786 := [rewrite]: #785 -#788 := (iff #803 #640) -#797 := (iff #802 true) -#679 := [rewrite]: #797 -#690 := [monotonicity #679 #681]: #788 -#674 := [trans #690 #786]: #789 -#691 := [monotonicity #674]: #689 -#685 := [trans #691 #829]: #692 -#781 := [monotonicity #685 #772]: #771 -#784 := [trans #781 #783]: #779 -#753 := [monotonicity #784 #757 #751]: #742 -#735 := [trans #753 #732]: #734 -#796 := (iff #806 true) -#794 := [rewrite]: #796 -#738 := [monotonicity #794 #735]: #737 -#721 := [trans #738 #739]: #725 -#793 := (iff #807 #805) -#795 := [rewrite]: #793 -#639 := (iff #636 false) -#792 := [rewrite]: #639 -#723 := [monotonicity #792 #795 #721]: #722 -#727 := [trans #723 #732]: #726 -#704 := [monotonicity #727]: #703 -#709 := [trans #704 #598]: #703 -#730 := [quant-inst #8 #9]: #724 -#710 := [mp #730 #709]: #729 -#716 := [unit-resolution #710 #890]: #805 -#712 := [monotonicity #716]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #712]: false -unsat -a77f50b29c69935853b053858b12886e75a3e1af 310 0 -#2 := false -decl f3 :: (-> Int S2) -#11 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) +#24 := (f3 0::Int) +#10 := 3::Int +#19 := (- 3::Int) +#18 := (- 0::Int) +#20 := (div #18 #19) +#17 := (div 0::Int 3::Int) +#14 := (< 0::Int 3::Int) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#21 := (ite #16 #17 #20) +#11 := (= 3::Int 0::Int) +#9 := (= 0::Int 0::Int) +#12 := (or #9 #11) +#22 := (ite #12 0::Int #21) +#23 := (f3 #22) +#25 := (= #23 #24) +#26 := (not #25) +#117 := (iff #26 false) +#1 := true +#112 := (not true) +#115 := (iff #112 false) +#116 := [rewrite]: #115 +#113 := (iff #26 #112) +#110 := (iff #25 true) +#105 := (= #24 #24) +#108 := (iff #105 true) +#109 := [rewrite]: #108 +#106 := (iff #25 #105) +#102 := (= #22 0::Int) +#97 := (ite true 0::Int 0::Int) +#100 := (= #97 0::Int) +#101 := [rewrite]: #100 +#98 := (= #22 #97) +#95 := (= #21 0::Int) +#90 := (ite #15 0::Int 0::Int) +#93 := (= #90 0::Int) +#94 := [rewrite]: #93 +#91 := (= #21 #90) +#88 := (= #20 0::Int) +#80 := -3::Int +#83 := (div 0::Int -3::Int) +#86 := (= #83 0::Int) +#87 := [rewrite]: #86 +#84 := (= #20 #83) +#81 := (= #19 -3::Int) +#82 := [rewrite]: #81 +#78 := (= #18 0::Int) +#79 := [rewrite]: #78 +#85 := [monotonicity #79 #82]: #84 +#89 := [trans #85 #87]: #88 +#76 := (= #17 0::Int) +#77 := [rewrite]: #76 +#74 := (iff #16 #15) +#75 := [rewrite]: #74 +#92 := [monotonicity #75 #77 #89]: #91 +#96 := [trans #92 #94]: #95 +#72 := (iff #12 true) +#67 := (or true false) +#70 := (iff #67 true) +#71 := [rewrite]: #70 +#68 := (iff #12 #67) +#65 := (iff #11 false) +#66 := [rewrite]: #65 +#63 := (iff #9 true) +#64 := [rewrite]: #63 +#69 := [monotonicity #64 #66]: #68 +#73 := [trans #69 #71]: #72 +#99 := [monotonicity #73 #96]: #98 +#103 := [trans #99 #101]: #102 +#104 := [monotonicity #103]: #25 +#107 := [monotonicity #104]: #106 +#111 := [trans #107 #109]: #110 +#114 := [monotonicity #111]: #113 +#118 := [trans #114 #116]: #117 +#62 := [asserted]: #26 +[mp #62 #118]: false +unsat +b6bcc3a997f628b30a8c56db4557945cb134a0bb 135 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#27 := (f3 0::Int) +#11 := 3::Int +#22 := (- 3::Int) #8 := 1::Int -#9 := (f4 1::Int 1::Int) -#10 := (f3 #9) -#13 := (= #10 #12) -#799 := (= #9 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f4 #31 #20) -#884 := (pattern #50) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#245 := (mod #181 #184) -#375 := (+ #50 #245) -#376 := (= #375 0::Int) -#51 := (mod #31 #20) -#372 := (* -1::Int #51) -#373 := (+ #50 #372) -#374 := (= #373 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#377 := (ite #323 #374 #376) -#371 := (= #50 0::Int) -#33 := (= #31 0::Int) -#378 := (ite #33 #371 #377) -#370 := (= #31 #50) -#34 := (= #20 0::Int) -#379 := (ite #34 #370 #378) -#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379) -#382 := (forall (vars (?v0 Int) (?v1 Int)) #379) -#888 := (iff #382 #885) -#886 := (iff #379 #379) -#887 := [refl]: #886 -#889 := [quant-intro #887]: #888 -#251 := (* -1::Int #245) -#339 := (ite #323 #51 #251) -#342 := (ite #33 0::Int #339) -#345 := (ite #34 #31 #342) -#348 := (= #50 #345) -#351 := (forall (vars (?v0 Int) (?v1 Int)) #348) -#383 := (iff #351 #382) -#380 := (iff #348 #379) -#381 := [rewrite]: #380 -#384 := [quant-intro #381]: #383 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#271 := (ite #226 #51 #251) -#274 := (ite #33 0::Int #271) -#277 := (ite #34 #31 #274) -#280 := (= #50 #277) -#283 := (forall (vars (?v0 Int) (?v1 Int)) #280) -#352 := (iff #283 #351) -#349 := (iff #280 #348) -#346 := (= #277 #345) -#343 := (= #274 #342) -#340 := (= #271 #339) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#341 := [monotonicity #325]: #340 -#344 := [monotonicity #341]: #343 -#347 := [monotonicity #344]: #346 -#350 := [monotonicity #347]: #349 -#353 := [quant-intro #350]: #352 -#300 := (~ #283 #283) -#314 := (~ #280 #280) -#315 := [refl]: #314 -#301 := [nnf-pos #315]: #300 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#286 := (iff #58 #283) -#174 := (and #37 #39) -#177 := (or #38 #174) -#256 := (ite #177 #51 #251) -#165 := (= 0::Int #31) -#259 := (ite #165 0::Int #256) -#168 := (= 0::Int #20) -#262 := (ite #168 #31 #259) -#265 := (= #50 #262) -#268 := (forall (vars (?v0 Int) (?v1 Int)) #265) -#284 := (iff #268 #283) -#281 := (iff #265 #280) -#278 := (= #262 #277) -#275 := (= #259 #274) -#272 := (= #256 #271) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#273 := [monotonicity #228]: #272 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#276 := [monotonicity #203 #273]: #275 -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#279 := [monotonicity #205 #276]: #278 -#282 := [monotonicity #279]: #281 -#285 := [quant-intro #282]: #284 -#269 := (iff #58 #268) -#266 := (iff #57 #265) -#263 := (= #56 #262) -#260 := (= #55 #259) -#257 := (= #54 #256) -#254 := (= #53 #251) -#248 := (- #245) -#252 := (= #248 #251) -#253 := [rewrite]: #252 -#249 := (= #53 #248) -#246 := (= #52 #245) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#247 := [monotonicity #183 #186]: #246 -#250 := [monotonicity #247]: #249 -#255 := [trans #250 #253]: #254 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#258 := [monotonicity #179 #255]: #257 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#261 := [monotonicity #167 #258]: #260 -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#264 := [monotonicity #170 #261]: #263 -#267 := [monotonicity #264]: #266 -#270 := [quant-intro #267]: #269 -#287 := [trans #270 #285]: #286 -#244 := [asserted]: #58 -#288 := [mp #244 #287]: #283 -#316 := [mp~ #288 #301]: #283 -#354 := [mp #316 #353]: #351 -#385 := [mp #354 #384]: #382 -#890 := [mp #385 #889]: #885 -#703 := (not #885) -#704 := (or #703 #799) -#812 := (* -1::Int 1::Int) -#813 := (mod #812 #812) -#808 := (+ #9 #813) -#809 := (= #808 0::Int) -#814 := (mod 1::Int 1::Int) -#815 := (* -1::Int #814) -#810 := (+ #9 #815) -#816 := (= #810 0::Int) -#657 := (>= 1::Int 0::Int) -#658 := (<= 1::Int 0::Int) -#659 := (or #658 #657) -#801 := (not #659) -#802 := (or #658 #658) -#803 := (not #802) -#804 := (or #803 #801) -#798 := (ite #804 #816 #809) -#805 := (= 1::Int 0::Int) -#806 := (ite #805 #799 #798) -#800 := (= 1::Int #9) -#807 := (ite #805 #800 #806) -#705 := (or #703 #807) -#709 := (iff #705 #704) -#711 := (iff #704 #704) -#716 := [rewrite]: #711 -#724 := (iff #807 #799) -#792 := (= #9 1::Int) -#723 := (ite false #792 #799) -#728 := (iff #723 #799) -#729 := [rewrite]: #728 -#726 := (iff #807 #723) -#721 := (iff #806 #799) -#737 := (ite false #799 #799) -#739 := (iff #737 #799) -#725 := [rewrite]: #739 -#738 := (iff #806 #737) -#735 := (iff #798 #799) -#1 := true -#742 := (ite true #799 #799) -#732 := (iff #742 #799) -#734 := [rewrite]: #732 -#753 := (iff #798 #742) -#751 := (iff #809 #799) -#749 := (= #808 #9) -#765 := (+ #9 0::Int) -#763 := (= #765 #9) -#768 := [rewrite]: #763 -#747 := (= #808 #765) -#745 := (= #813 0::Int) -#760 := (mod -1::Int -1::Int) -#743 := (= #760 0::Int) -#744 := [rewrite]: #743 -#740 := (= #813 #760) -#759 := (= #812 -1::Int) -#756 := [rewrite]: #759 -#741 := [monotonicity #756 #756]: #740 -#746 := [trans #741 #744]: #745 -#748 := [monotonicity #746]: #747 -#750 := [trans #748 #768]: #749 -#752 := [monotonicity #750]: #751 -#757 := (iff #816 #799) -#754 := (= #810 #9) -#766 := (= #810 #765) -#762 := (= #815 0::Int) -#775 := (* -1::Int 0::Int) -#777 := (= #775 0::Int) -#761 := [rewrite]: #777 -#776 := (= #815 #775) -#773 := (= #814 0::Int) -#774 := [rewrite]: #773 -#770 := [monotonicity #774]: #776 -#764 := [trans #770 #761]: #762 -#767 := [monotonicity #764]: #766 -#755 := [trans #767 #768]: #754 -#758 := [monotonicity #755]: #757 -#779 := (iff #804 true) -#769 := (or true false) -#782 := (iff #769 true) -#783 := [rewrite]: #782 -#771 := (iff #804 #769) -#780 := (iff #801 false) -#482 := (not true) -#843 := (iff #482 false) -#829 := [rewrite]: #843 -#791 := (iff #801 #482) -#790 := (iff #659 true) -#693 := (or false true) -#696 := (iff #693 true) -#697 := [rewrite]: #696 -#694 := (iff #659 #693) -#692 := (iff #657 true) -#685 := [rewrite]: #692 -#795 := (iff #658 false) -#796 := [rewrite]: #795 -#695 := [monotonicity #796 #685]: #694 -#787 := [trans #695 #697]: #790 -#778 := [monotonicity #787]: #791 -#772 := [trans #778 #829]: #780 -#689 := (iff #803 true) -#690 := (not false) -#789 := (iff #690 true) -#674 := [rewrite]: #789 -#785 := (iff #803 #690) -#640 := (iff #802 false) -#794 := (or false false) -#680 := (iff #794 false) -#681 := [rewrite]: #680 -#797 := (iff #802 #794) -#679 := [monotonicity #796 #796]: #797 -#788 := [trans #679 #681]: #640 -#786 := [monotonicity #788]: #785 -#691 := [trans #786 #674]: #689 -#781 := [monotonicity #691 #772]: #771 -#784 := [trans #781 #783]: #779 -#731 := [monotonicity #784 #758 #752]: #753 -#736 := [trans #731 #734]: #735 -#636 := (iff #805 false) -#638 := [rewrite]: #636 -#733 := [monotonicity #638 #736]: #738 -#722 := [trans #733 #725]: #721 -#639 := (iff #800 #792) -#793 := [rewrite]: #639 -#727 := [monotonicity #638 #793 #722]: #726 -#730 := [trans #727 #729]: #724 -#710 := [monotonicity #730]: #709 -#712 := [trans #710 #716]: #709 -#598 := [quant-inst #8 #8]: #705 -#713 := [mp #598 #712]: #704 -#717 := [unit-resolution #713 #890]: #799 -#718 := [monotonicity #717]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #718]: false -unsat -0b8020dc224bc16c2ca4d4c9672c839314b04736 321 0 -#2 := false -decl f3 :: (-> Int S2) -#12 := 0::Int -#13 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 1::Int -#8 := 3::Int -#10 := (f4 3::Int 1::Int) -#11 := (f3 #10) -#14 := (= #11 #13) -#807 := (= #10 0::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#51 := (f4 #32 #21) -#885 := (pattern #51) -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#246 := (mod #182 #185) -#376 := (+ #51 #246) -#377 := (= #376 0::Int) -#52 := (mod #32 #21) -#373 := (* -1::Int #52) -#374 := (+ #51 #373) -#375 := (= #374 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#378 := (ite #324 #375 #377) -#372 := (= #51 0::Int) -#34 := (= #32 0::Int) -#379 := (ite #34 #372 #378) -#371 := (= #32 #51) -#35 := (= #21 0::Int) -#380 := (ite #35 #371 #379) -#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380) -#383 := (forall (vars (?v0 Int) (?v1 Int)) #380) -#889 := (iff #383 #886) -#887 := (iff #380 #380) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#252 := (* -1::Int #246) -#340 := (ite #324 #52 #252) -#343 := (ite #34 0::Int #340) -#346 := (ite #35 #32 #343) -#349 := (= #51 #346) -#352 := (forall (vars (?v0 Int) (?v1 Int)) #349) -#384 := (iff #352 #383) -#381 := (iff #349 #380) -#382 := [rewrite]: #381 -#385 := [quant-intro #382]: #384 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#272 := (ite #227 #52 #252) -#275 := (ite #34 0::Int #272) -#278 := (ite #35 #32 #275) -#281 := (= #51 #278) -#284 := (forall (vars (?v0 Int) (?v1 Int)) #281) -#353 := (iff #284 #352) -#350 := (iff #281 #349) -#347 := (= #278 #346) -#344 := (= #275 #343) -#341 := (= #272 #340) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#342 := [monotonicity #326]: #341 -#345 := [monotonicity #342]: #344 -#348 := [monotonicity #345]: #347 -#351 := [monotonicity #348]: #350 -#354 := [quant-intro #351]: #353 -#301 := (~ #284 #284) -#315 := (~ #281 #281) -#316 := [refl]: #315 -#302 := [nnf-pos #316]: #301 -#45 := (- #21) -#44 := (- #32) -#53 := (mod #44 #45) -#54 := (- #53) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#55 := (ite #42 #52 #54) -#56 := (ite #34 0::Int #55) -#57 := (ite #35 #32 #56) -#58 := (= #51 #57) -#59 := (forall (vars (?v0 Int) (?v1 Int)) #58) -#287 := (iff #59 #284) -#175 := (and #38 #40) -#178 := (or #39 #175) -#257 := (ite #178 #52 #252) -#166 := (= 0::Int #32) -#260 := (ite #166 0::Int #257) -#169 := (= 0::Int #21) -#263 := (ite #169 #32 #260) -#266 := (= #51 #263) -#269 := (forall (vars (?v0 Int) (?v1 Int)) #266) -#285 := (iff #269 #284) -#282 := (iff #266 #281) -#279 := (= #263 #278) -#276 := (= #260 #275) -#273 := (= #257 #272) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#274 := [monotonicity #229]: #273 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#277 := [monotonicity #204 #274]: #276 -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#280 := [monotonicity #206 #277]: #279 -#283 := [monotonicity #280]: #282 -#286 := [quant-intro #283]: #285 -#270 := (iff #59 #269) -#267 := (iff #58 #266) -#264 := (= #57 #263) -#261 := (= #56 #260) -#258 := (= #55 #257) -#255 := (= #54 #252) -#249 := (- #246) -#253 := (= #249 #252) -#254 := [rewrite]: #253 -#250 := (= #54 #249) -#247 := (= #53 #246) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#248 := [monotonicity #184 #187]: #247 -#251 := [monotonicity #248]: #250 -#256 := [trans #251 #254]: #255 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#259 := [monotonicity #180 #256]: #258 -#167 := (iff #34 #166) +#21 := (- 1::Int) +#23 := (div #21 #22) +#20 := (div 1::Int 3::Int) +#15 := (< 0::Int 3::Int) +#17 := (< 1::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 1::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 3::Int 0::Int) +#10 := (= 1::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (f3 #25) +#28 := (= #26 #27) +#29 := (not #28) +#171 := (iff #29 false) +#77 := (and #15 #17) +#80 := (or #16 #77) +#98 := (ite #80 0::Int 1::Int) +#108 := (f3 #98) +#114 := (= #27 #108) +#119 := (not #114) +#169 := (iff #119 false) +#1 := true +#164 := (not true) +#167 := (iff #164 false) #168 := [rewrite]: #167 -#262 := [monotonicity #168 #259]: #261 -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#265 := [monotonicity #171 #262]: #264 -#268 := [monotonicity #265]: #267 -#271 := [quant-intro #268]: #270 -#288 := [trans #271 #286]: #287 -#245 := [asserted]: #59 -#289 := [mp #245 #288]: #284 -#317 := [mp~ #289 #302]: #284 -#355 := [mp #317 #354]: #352 -#386 := [mp #355 #385]: #383 -#891 := [mp #386 #890]: #886 -#715 := (not #886) -#718 := (or #715 #807) -#813 := (* -1::Int 1::Int) -#814 := (* -1::Int 3::Int) -#809 := (mod #814 #813) -#810 := (+ #10 #809) -#815 := (= #810 0::Int) -#816 := (mod 3::Int 1::Int) -#811 := (* -1::Int #816) -#817 := (+ #10 #811) -#658 := (= #817 0::Int) -#659 := (>= 3::Int 0::Int) -#660 := (<= 1::Int 0::Int) -#802 := (or #660 #659) -#803 := (not #802) -#804 := (<= 3::Int 0::Int) -#805 := (or #804 #660) -#799 := (not #805) -#800 := (or #799 #803) -#806 := (ite #800 #658 #815) -#801 := (= 3::Int 0::Int) -#808 := (ite #801 #807 #806) -#637 := (= 3::Int #10) -#639 := (= 1::Int 0::Int) -#640 := (ite #639 #637 #808) -#719 := (or #715 #640) -#716 := (iff #719 #718) -#701 := (iff #718 #718) -#647 := [rewrite]: #701 -#713 := (iff #640 #807) -#797 := (= #10 3::Int) -#599 := (ite false #797 #807) -#712 := (iff #599 #807) -#717 := [rewrite]: #712 -#710 := (iff #640 #599) -#705 := (iff #808 #807) -#729 := (ite false #807 #807) -#731 := (iff #729 #807) -#704 := [rewrite]: #731 -#730 := (iff #808 #729) -#727 := (iff #806 #807) -#1 := true -#740 := (ite true #807 #807) -#723 := (iff #740 #807) -#724 := [rewrite]: #723 -#726 := (iff #806 #740) -#739 := (iff #815 #807) -#737 := (= #810 #10) -#758 := (+ #10 0::Int) -#757 := (= #758 #10) -#761 := [rewrite]: #757 -#735 := (= #810 #758) -#732 := (= #809 0::Int) -#746 := -3::Int -#751 := (mod -3::Int -1::Int) -#743 := (= #751 0::Int) -#754 := [rewrite]: #743 -#752 := (= #809 #751) -#749 := (= #813 -1::Int) -#750 := [rewrite]: #749 -#747 := (= #814 -3::Int) -#748 := [rewrite]: #747 -#753 := [monotonicity #748 #750]: #752 -#733 := [trans #753 #754]: #732 -#736 := [monotonicity #733]: #735 -#738 := [trans #736 #761]: #737 -#734 := [monotonicity #738]: #739 -#744 := (iff #658 #807) -#741 := (= #817 #10) -#759 := (= #817 #758) -#755 := (= #811 0::Int) -#766 := (* -1::Int 0::Int) -#764 := (= #766 0::Int) -#769 := [rewrite]: #764 -#767 := (= #811 #766) -#763 := (= #816 0::Int) -#765 := [rewrite]: #763 -#768 := [monotonicity #765]: #767 -#756 := [trans #768 #769]: #755 -#760 := [monotonicity #756]: #759 -#742 := [trans #760 #761]: #741 -#745 := [monotonicity #742]: #744 -#778 := (iff #800 true) -#774 := (or true false) -#777 := (iff #774 true) -#771 := [rewrite]: #777 -#775 := (iff #800 #774) -#780 := (iff #803 false) -#483 := (not true) -#844 := (iff #483 false) -#830 := [rewrite]: #844 -#783 := (iff #803 #483) -#772 := (iff #802 true) -#792 := (or false true) -#773 := (iff #792 true) -#770 := [rewrite]: #773 -#779 := (iff #802 #792) -#791 := (iff #659 true) -#788 := [rewrite]: #791 -#641 := (iff #660 false) -#789 := [rewrite]: #641 -#781 := [monotonicity #789 #788]: #779 -#782 := [trans #781 #770]: #772 -#784 := [monotonicity #782]: #783 -#785 := [trans #784 #830]: #780 -#697 := (iff #799 true) -#693 := (not false) -#695 := (iff #693 true) -#696 := [rewrite]: #695 -#686 := (iff #799 #693) -#690 := (iff #805 false) -#691 := (or false false) -#790 := (iff #691 false) -#675 := [rewrite]: #790 -#786 := (iff #805 #691) -#681 := (iff #804 false) -#682 := [rewrite]: #681 -#787 := [monotonicity #682 #789]: #786 -#692 := [trans #787 #675]: #690 -#694 := [monotonicity #692]: #686 -#698 := [trans #694 #696]: #697 -#776 := [monotonicity #698 #785]: #775 -#762 := [trans #776 #771]: #778 -#722 := [monotonicity #762 #745 #734]: #726 -#728 := [trans #722 #724]: #727 -#798 := (iff #801 false) -#680 := [rewrite]: #798 -#725 := [monotonicity #680 #728]: #730 -#706 := [trans #725 #704]: #705 -#796 := (iff #637 #797) -#795 := [rewrite]: #796 -#793 := (iff #639 false) -#794 := [rewrite]: #793 -#711 := [monotonicity #794 #795 #706]: #710 -#714 := [trans #711 #717]: #713 -#721 := [monotonicity #714]: #716 -#702 := [trans #721 #647]: #716 -#720 := [quant-inst #8 #9]: #719 -#683 := [mp #720 #702]: #718 -#708 := [unit-resolution #683 #891]: #807 -#703 := [monotonicity #708]: #14 -#15 := (not #14) -#79 := [asserted]: #15 -[unit-resolution #79 #703]: false -unsat -beef9b82cbe8a31ac2e4568749757bdaef5ecf77 324 0 -#2 := false -#13 := 0::Int -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#812 := (>= #9 0::Int) -#694 := (not #812) -#801 := (= #9 0::Int) -#661 := (<= #9 0::Int) -#683 := (not #661) -#755 := (or #683 #801 #694) -#712 := (not #755) -decl f4 :: (-> Int Int Int) -#10 := 1::Int -#11 := (f4 #9 1::Int) -#800 := (= #11 0::Int) -#702 := (not #800) -decl f3 :: (-> Int S2) -#14 := (f3 0::Int) -#12 := (f3 #11) -#15 := (= #12 #14) -#685 := [hypothesis]: #800 -#644 := [monotonicity #685]: #15 -#16 := (not #15) -#80 := [asserted]: #16 -#690 := [unit-resolution #80 #644]: false -#700 := [lemma #690]: #702 -#701 := (or #712 #800) -#182 := -1::Int -#824 := (* -1::Int #9) -#763 := (mod #824 -1::Int) -#767 := (+ #11 #763) -#765 := (= #767 0::Int) -#736 := (ite #755 #800 #765) -#22 := (:var 0 Int) -#33 := (:var 1 Int) -#52 := (f4 #33 #22) -#886 := (pattern #52) -#186 := (* -1::Int #22) -#183 := (* -1::Int #33) -#247 := (mod #183 #186) -#377 := (+ #52 #247) -#378 := (= #377 0::Int) -#53 := (mod #33 #22) -#374 := (* -1::Int #53) -#375 := (+ #52 #374) -#376 := (= #375 0::Int) -#221 := (>= #33 0::Int) -#214 := (<= #22 0::Int) -#321 := (or #214 #221) -#322 := (not #321) -#210 := (<= #33 0::Int) -#319 := (or #210 #214) -#320 := (not #319) -#325 := (or #320 #322) -#379 := (ite #325 #376 #378) -#373 := (= #52 0::Int) -#35 := (= #33 0::Int) -#380 := (ite #35 #373 #379) -#372 := (= #33 #52) -#36 := (= #22 0::Int) -#381 := (ite #36 #372 #380) -#887 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #886) #381) -#384 := (forall (vars (?v0 Int) (?v1 Int)) #381) -#890 := (iff #384 #887) -#888 := (iff #381 #381) -#889 := [refl]: #888 -#891 := [quant-intro #889]: #890 -#253 := (* -1::Int #247) -#341 := (ite #325 #53 #253) -#344 := (ite #35 0::Int #341) -#347 := (ite #36 #33 #344) -#350 := (= #52 #347) -#353 := (forall (vars (?v0 Int) (?v1 Int)) #350) -#385 := (iff #353 #384) -#382 := (iff #350 #381) -#383 := [rewrite]: #382 -#386 := [quant-intro #383]: #385 -#222 := (not #221) -#215 := (not #214) -#225 := (and #215 #222) -#211 := (not #210) -#218 := (and #211 #215) -#228 := (or #218 #225) -#273 := (ite #228 #53 #253) -#276 := (ite #35 0::Int #273) -#279 := (ite #36 #33 #276) -#282 := (= #52 #279) -#285 := (forall (vars (?v0 Int) (?v1 Int)) #282) -#354 := (iff #285 #353) -#351 := (iff #282 #350) -#348 := (= #279 #347) -#345 := (= #276 #344) -#342 := (= #273 #341) -#326 := (iff #228 #325) -#323 := (iff #225 #322) -#324 := [rewrite]: #323 -#304 := (iff #218 #320) -#305 := [rewrite]: #304 -#327 := [monotonicity #305 #324]: #326 -#343 := [monotonicity #327]: #342 -#346 := [monotonicity #343]: #345 -#349 := [monotonicity #346]: #348 -#352 := [monotonicity #349]: #351 -#355 := [quant-intro #352]: #354 -#302 := (~ #285 #285) -#316 := (~ #282 #282) -#317 := [refl]: #316 -#303 := [nnf-pos #317]: #302 -#46 := (- #22) -#45 := (- #33) -#54 := (mod #45 #46) -#55 := (- #54) -#39 := (< 0::Int #22) -#41 := (< #33 0::Int) -#42 := (and #41 #39) -#38 := (< 0::Int #33) -#40 := (and #38 #39) -#43 := (or #40 #42) -#56 := (ite #43 #53 #55) -#57 := (ite #35 0::Int #56) -#58 := (ite #36 #33 #57) -#59 := (= #52 #58) -#60 := (forall (vars (?v0 Int) (?v1 Int)) #59) -#288 := (iff #60 #285) -#176 := (and #39 #41) -#179 := (or #40 #176) -#258 := (ite #179 #53 #253) -#167 := (= 0::Int #33) -#261 := (ite #167 0::Int #258) -#170 := (= 0::Int #22) -#264 := (ite #170 #33 #261) -#267 := (= #52 #264) -#270 := (forall (vars (?v0 Int) (?v1 Int)) #267) -#286 := (iff #270 #285) -#283 := (iff #267 #282) -#280 := (= #264 #279) -#277 := (= #261 #276) -#274 := (= #258 #273) -#229 := (iff #179 #228) -#226 := (iff #176 #225) -#223 := (iff #41 #222) -#224 := [rewrite]: #223 -#216 := (iff #39 #215) +#165 := (iff #119 #164) +#162 := (iff #114 true) +#157 := (= #27 #27) +#160 := (iff #157 true) +#161 := [rewrite]: #160 +#158 := (iff #114 #157) +#111 := (= #108 #27) +#154 := (= #98 0::Int) +#149 := (ite true 0::Int 1::Int) +#152 := (= #149 0::Int) +#153 := [rewrite]: #152 +#150 := (= #98 #149) +#147 := (iff #80 true) +#142 := (or true false) +#145 := (iff #142 true) +#146 := [rewrite]: #145 +#143 := (iff #80 #142) +#140 := (iff #77 false) +#135 := (and true false) +#138 := (iff #135 false) +#139 := [rewrite]: #138 +#136 := (iff #77 #135) +#133 := (iff #17 false) +#134 := [rewrite]: #133 +#124 := (iff #15 true) +#125 := [rewrite]: #124 +#137 := [monotonicity #125 #134]: #136 +#141 := [trans #137 #139]: #140 +#131 := (iff #16 true) +#126 := (and true true) +#129 := (iff #126 true) +#130 := [rewrite]: #129 +#127 := (iff #16 #126) +#122 := (iff #14 true) +#123 := [rewrite]: #122 +#128 := [monotonicity #123 #125]: #127 +#132 := [trans #128 #130]: #131 +#144 := [monotonicity #132 #141]: #143 +#148 := [trans #144 #146]: #147 +#151 := [monotonicity #148]: #150 +#155 := [trans #151 #153]: #154 +#156 := [monotonicity #155]: #111 +#159 := [monotonicity #156]: #158 +#163 := [trans #159 #161]: #162 +#166 := [monotonicity #163]: #165 +#170 := [trans #166 #168]: #169 +#120 := (iff #29 #119) +#117 := (iff #28 #114) +#115 := (iff #111 #114) +#116 := [rewrite]: #115 +#112 := (iff #28 #111) +#109 := (= #26 #108) +#106 := (= #25 #98) +#101 := (ite false 0::Int #98) +#104 := (= #101 #98) +#105 := [rewrite]: #104 +#102 := (= #25 #101) +#99 := (= #24 #98) +#96 := (= #23 1::Int) +#88 := -3::Int +#85 := -1::Int +#91 := (div -1::Int -3::Int) +#94 := (= #91 1::Int) +#95 := [rewrite]: #94 +#92 := (= #23 #91) +#89 := (= #22 -3::Int) +#90 := [rewrite]: #89 +#86 := (= #21 -1::Int) +#87 := [rewrite]: #86 +#93 := [monotonicity #87 #90]: #92 +#97 := [trans #93 #95]: #96 +#83 := (= #20 0::Int) +#84 := [rewrite]: #83 +#81 := (iff #19 #80) +#78 := (iff #18 #77) +#79 := [rewrite]: #78 +#82 := [monotonicity #79]: #81 +#100 := [monotonicity #82 #84 #97]: #99 +#75 := (iff #13 false) +#70 := (or false false) +#73 := (iff #70 false) +#74 := [rewrite]: #73 +#71 := (iff #13 #70) +#68 := (iff #12 false) +#69 := [rewrite]: #68 +#66 := (iff #10 false) +#67 := [rewrite]: #66 +#72 := [monotonicity #67 #69]: #71 +#76 := [trans #72 #74]: #75 +#103 := [monotonicity #76 #100]: #102 +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107]: #109 +#113 := [monotonicity #110]: #112 +#118 := [trans #113 #116]: #117 +#121 := [monotonicity #118]: #120 +#172 := [trans #121 #170]: #171 +#65 := [asserted]: #29 +[mp #65 #172]: false +unsat +ec979d4232e8803cddce0557ed6997ff67bffe05 83 0 +#2 := false +decl f3 :: (-> Int S2) +#23 := 1::Int +#24 := (f3 1::Int) +#8 := 3::Int +#18 := (- 3::Int) +#19 := (div #18 #18) +#17 := (div 3::Int 3::Int) +#9 := 0::Int +#12 := (< 0::Int 3::Int) +#14 := (< 3::Int 0::Int) +#15 := (and #14 #12) +#13 := (and #12 #12) +#16 := (or #13 #15) +#20 := (ite #16 #17 #19) +#10 := (= 3::Int 0::Int) +#11 := (or #10 #10) +#21 := (ite #11 0::Int #20) +#22 := (f3 #21) +#25 := (= #22 #24) +#26 := (not #25) +#119 := (iff #26 false) +#1 := true +#114 := (not true) +#117 := (iff #114 false) +#118 := [rewrite]: #117 +#115 := (iff #26 #114) +#112 := (iff #25 true) +#107 := (= #24 #24) +#110 := (iff #107 true) +#111 := [rewrite]: #110 +#108 := (iff #25 #107) +#104 := (= #21 1::Int) +#99 := (ite false 0::Int 1::Int) +#102 := (= #99 1::Int) +#103 := [rewrite]: #102 +#100 := (= #21 #99) +#97 := (= #20 1::Int) +#74 := (and #12 #14) +#77 := (or #12 #74) +#92 := (ite #77 1::Int 1::Int) +#95 := (= #92 1::Int) +#96 := [rewrite]: #95 +#93 := (= #20 #92) +#90 := (= #19 1::Int) +#82 := -3::Int +#85 := (div -3::Int -3::Int) +#88 := (= #85 1::Int) +#89 := [rewrite]: #88 +#86 := (= #19 #85) +#83 := (= #18 -3::Int) +#84 := [rewrite]: #83 +#87 := [monotonicity #84 #84]: #86 +#91 := [trans #87 #89]: #90 +#80 := (= #17 1::Int) +#81 := [rewrite]: #80 +#78 := (iff #16 #77) +#75 := (iff #15 #74) +#76 := [rewrite]: #75 +#72 := (iff #13 #12) +#73 := [rewrite]: #72 +#79 := [monotonicity #73 #76]: #78 +#94 := [monotonicity #79 #81 #91]: #93 +#98 := [trans #94 #96]: #97 +#70 := (iff #11 false) +#65 := (or false false) +#68 := (iff #65 false) +#69 := [rewrite]: #68 +#66 := (iff #11 #65) +#63 := (iff #10 false) +#64 := [rewrite]: #63 +#67 := [monotonicity #64 #64]: #66 +#71 := [trans #67 #69]: #70 +#101 := [monotonicity #71 #98]: #100 +#105 := [trans #101 #103]: #104 +#106 := [monotonicity #105]: #25 +#109 := [monotonicity #106]: #108 +#113 := [trans #109 #111]: #112 +#116 := [monotonicity #113]: #115 +#120 := [trans #116 #118]: #119 +#62 := [asserted]: #26 +[mp #62 #120]: false +unsat +7e6d147ebdbd2ef1c1366775850a7558514783c8 299 0 +#2 := false +#10 := 0::Int +#12 := 3::Int +decl f3 :: (-> S2 Int) +decl f4 :: S2 +#8 := f4 +#9 := (f3 f4) +#402 := (mod #9 3::Int) +#403 := (>= #402 0::Int) +#1 := true +#62 := [true-axiom]: true +#663 := (or false #403) +#664 := [th-lemma arith]: #663 +#662 := [unit-resolution #664 #62]: #403 +#84 := -3::Int +#80 := -1::Int +#81 := (* -1::Int #9) +#87 := (div #81 -3::Int) +#21 := (div #9 3::Int) +#115 := (>= #9 0::Int) +#116 := (not #115) +#102 := (<= #9 0::Int) +#103 := (not #102) +#126 := (or #103 #116) +#129 := (ite #126 #21 #87) +#11 := (= #9 0::Int) +#132 := (ite #11 0::Int #129) +#139 := (* -1::Int #132) +#140 := (+ #9 #139) +#138 := (>= #140 0::Int) +#145 := (not #138) +#23 := (- 3::Int) +#22 := (- #9) +#24 := (div #22 #23) +#16 := (< 0::Int 3::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= 3::Int 0::Int) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (<= #26 #9) +#28 := (not #27) +#148 := (iff #28 #145) +#74 := (and #16 #18) +#77 := (or #17 #74) +#90 := (ite #77 #21 #87) +#93 := (ite #11 0::Int #90) +#96 := (<= #93 #9) +#99 := (not #96) +#146 := (iff #99 #145) +#143 := (iff #96 #138) +#135 := (<= #132 #9) +#141 := (iff #135 #138) +#142 := [rewrite]: #141 +#136 := (iff #96 #135) +#133 := (= #93 #132) +#130 := (= #90 #129) +#127 := (iff #77 #126) +#124 := (iff #74 #116) +#119 := (and true #116) +#122 := (iff #119 #116) +#123 := [rewrite]: #122 +#120 := (iff #74 #119) +#117 := (iff #18 #116) +#118 := [rewrite]: #117 +#106 := (iff #16 true) +#107 := [rewrite]: #106 +#121 := [monotonicity #107 #118]: #120 +#125 := [trans #121 #123]: #124 +#113 := (iff #17 #103) +#108 := (and #103 true) +#111 := (iff #108 #103) +#112 := [rewrite]: #111 +#109 := (iff #17 #108) +#104 := (iff #15 #103) +#105 := [rewrite]: #104 +#110 := [monotonicity #105 #107]: #109 +#114 := [trans #110 #112]: #113 +#128 := [monotonicity #114 #125]: #127 +#131 := [monotonicity #128]: #130 +#134 := [monotonicity #131]: #133 +#137 := [monotonicity #134]: #136 +#144 := [trans #137 #142]: #143 +#147 := [monotonicity #144]: #146 +#100 := (iff #28 #99) +#97 := (iff #27 #96) +#94 := (= #26 #93) +#91 := (= #25 #90) +#88 := (= #24 #87) +#85 := (= #23 -3::Int) +#86 := [rewrite]: #85 +#82 := (= #22 #81) +#83 := [rewrite]: #82 +#89 := [monotonicity #83 #86]: #88 +#78 := (iff #20 #77) +#75 := (iff #19 #74) +#76 := [rewrite]: #75 +#79 := [monotonicity #76]: #78 +#92 := [monotonicity #79 #89]: #91 +#72 := (iff #14 #11) +#67 := (or #11 false) +#70 := (iff #67 #11) +#71 := [rewrite]: #70 +#68 := (iff #14 #67) +#65 := (iff #13 false) +#66 := [rewrite]: #65 +#69 := [monotonicity #66]: #68 +#73 := [trans #69 #71]: #72 +#95 := [monotonicity #73 #92]: #94 +#98 := [monotonicity #95]: #97 +#101 := [monotonicity #98]: #100 +#149 := [trans #101 #147]: #148 +#64 := [asserted]: #28 +#150 := [mp #64 #149]: #145 +#507 := (+ #21 #139) +#661 := (>= #507 0::Int) +#506 := (= #21 #132) +#395 := (= #129 #132) +#712 := (not #11) +#344 := (<= #132 0::Int) +#309 := (= #132 0::Int) +#709 := [hypothesis]: #11 +#386 := (or #712 #309) +#387 := [def-axiom]: #386 +#349 := [unit-resolution #387 #709]: #309 +#350 := (not #309) +#710 := (or #350 #344) +#708 := [th-lemma arith triangle-eq]: #710 +#711 := [unit-resolution #708 #349]: #344 +#697 := (or #712 #115) +#698 := [th-lemma arith triangle-eq]: #697 +#420 := [unit-resolution #698 #709]: #115 +#421 := [th-lemma arith farkas -1 1 1 #420 #150 #711]: false +#422 := [lemma #421]: #712 +#719 := (or #11 #395) +#720 := [def-axiom]: #719 +#665 := [unit-resolution #720 #422]: #395 +#310 := (= #21 #129) +decl f5 :: (-> Int S2) +#721 := (f5 #9) +#717 := (f3 #721) +#723 := (= #717 0::Int) +#542 := (not #723) +#557 := (iff #712 #542) +#654 := (iff #11 #723) +#558 := (iff #723 #11) +#508 := (= #717 #9) +#548 := (= #721 f4) +#722 := (= f4 #721) +#29 := (:var 0 S2) +#30 := (f3 #29) +#724 := (pattern #30) +#31 := (f5 #30) +#152 := (= #29 #31) +#725 := (forall (vars (?v0 S2)) (:pat #724) #152) +#155 := (forall (vars (?v0 S2)) #152) +#726 := (iff #155 #725) +#728 := (iff #725 #725) +#729 := [rewrite]: #728 +#727 := [rewrite]: #726 +#730 := [trans #727 #729]: #726 +#249 := (~ #155 #155) +#247 := (~ #152 #152) +#248 := [refl]: #247 +#250 := [nnf-pos #248]: #249 +#32 := (= #31 #29) +#33 := (forall (vars (?v0 S2)) #32) +#156 := (iff #33 #155) +#153 := (iff #32 #152) +#154 := [rewrite]: #153 +#157 := [quant-intro #154]: #156 +#151 := [asserted]: #33 +#160 := [mp #151 #157]: #155 +#239 := [mp~ #160 #250]: #155 +#731 := [mp #239 #730]: #725 +#713 := (not #725) +#373 := (or #713 #722) +#378 := [quant-inst #8]: #373 +#547 := [unit-resolution #378 #731]: #722 +#549 := [symm #547]: #548 +#656 := [monotonicity #549]: #508 +#653 := [monotonicity #656]: #558 +#657 := [symm #653]: #654 +#559 := [monotonicity #657]: #557 +#560 := [mp #422 #559]: #542 +#374 := (or #115 #723) +#34 := (:var 0 Int) +#36 := (f5 #34) +#732 := (pattern #36) +#176 := (>= #34 0::Int) +#37 := (f3 #36) +#42 := (= #37 0::Int) +#225 := (or #42 #176) +#739 := (forall (vars (?v0 Int)) (:pat #732) #225) +#230 := (forall (vars (?v0 Int)) #225) +#742 := (iff #230 #739) +#740 := (iff #225 #225) +#741 := [refl]: #740 +#743 := [quant-intro #741]: #742 +#243 := (~ #230 #230) +#251 := (~ #225 #225) +#252 := [refl]: #251 +#244 := [nnf-pos #252]: #243 +#41 := (< #34 0::Int) +#43 := (implies #41 #42) +#44 := (forall (vars (?v0 Int)) #43) +#233 := (iff #44 #230) +#196 := (= 0::Int #37) +#202 := (not #41) +#203 := (or #202 #196) +#208 := (forall (vars (?v0 Int)) #203) +#231 := (iff #208 #230) +#228 := (iff #203 #225) +#222 := (or #176 #42) +#226 := (iff #222 #225) +#227 := [rewrite]: #226 +#223 := (iff #203 #222) +#220 := (iff #196 #42) +#221 := [rewrite]: #220 +#218 := (iff #202 #176) +#178 := (not #176) +#213 := (not #178) +#216 := (iff #213 #176) #217 := [rewrite]: #216 -#227 := [monotonicity #217 #224]: #226 -#219 := (iff #40 #218) -#212 := (iff #38 #211) -#213 := [rewrite]: #212 -#220 := [monotonicity #213 #217]: #219 -#230 := [monotonicity #220 #227]: #229 -#275 := [monotonicity #230]: #274 -#204 := (iff #167 #35) +#214 := (iff #202 #213) +#211 := (iff #41 #178) +#212 := [rewrite]: #211 +#215 := [monotonicity #212]: #214 +#219 := [trans #215 #217]: #218 +#224 := [monotonicity #219 #221]: #223 +#229 := [trans #224 #227]: #228 +#232 := [quant-intro #229]: #231 +#209 := (iff #44 #208) +#206 := (iff #43 #203) +#199 := (implies #41 #196) +#204 := (iff #199 #203) #205 := [rewrite]: #204 -#278 := [monotonicity #205 #275]: #277 -#206 := (iff #170 #36) -#207 := [rewrite]: #206 -#281 := [monotonicity #207 #278]: #280 -#284 := [monotonicity #281]: #283 -#287 := [quant-intro #284]: #286 -#271 := (iff #60 #270) -#268 := (iff #59 #267) -#265 := (= #58 #264) -#262 := (= #57 #261) -#259 := (= #56 #258) -#256 := (= #55 #253) -#250 := (- #247) -#254 := (= #250 #253) -#255 := [rewrite]: #254 -#251 := (= #55 #250) -#248 := (= #54 #247) -#187 := (= #46 #186) -#188 := [rewrite]: #187 -#184 := (= #45 #183) -#185 := [rewrite]: #184 -#249 := [monotonicity #185 #188]: #248 -#252 := [monotonicity #249]: #251 -#257 := [trans #252 #255]: #256 -#180 := (iff #43 #179) -#177 := (iff #42 #176) -#178 := [rewrite]: #177 -#181 := [monotonicity #178]: #180 -#260 := [monotonicity #181 #257]: #259 -#168 := (iff #35 #167) -#169 := [rewrite]: #168 -#263 := [monotonicity #169 #260]: #262 -#171 := (iff #36 #170) +#200 := (iff #43 #199) +#197 := (iff #42 #196) +#198 := [rewrite]: #197 +#201 := [monotonicity #198]: #200 +#207 := [trans #201 #205]: #206 +#210 := [quant-intro #207]: #209 +#234 := [trans #210 #232]: #233 +#195 := [asserted]: #44 +#235 := [mp #195 #234]: #230 +#253 := [mp~ #235 #244]: #230 +#744 := [mp #253 #743]: #739 +#699 := (not #739) +#362 := (or #699 #115 #723) +#714 := (or #723 #115) +#363 := (or #699 #714) +#705 := (iff #363 #362) +#365 := (or #699 #374) +#703 := (iff #365 #362) +#704 := [rewrite]: #703 +#701 := (iff #363 #365) +#715 := (iff #714 #374) +#358 := [rewrite]: #715 +#702 := [monotonicity #358]: #701 +#700 := [trans #702 #704]: #705 +#364 := [quant-inst #9]: #363 +#706 := [mp #364 #700]: #362 +#553 := [unit-resolution #706 #744]: #374 +#561 := [unit-resolution #553 #560]: #115 +#562 := (or #11 #103 #116) +#563 := [th-lemma arith triangle-eq]: #562 +#564 := [unit-resolution #563 #561 #422]: #103 +#397 := (or #126 #102) +#388 := [def-axiom]: #397 +#565 := [unit-resolution #388 #564]: #126 +#328 := (not #126) +#716 := (or #328 #310) +#718 := [def-axiom]: #716 +#658 := [unit-resolution #718 #565]: #310 +#655 := [trans #658 #665]: #506 +#659 := (not #506) +#646 := (or #659 #661) +#648 := [th-lemma arith triangle-eq]: #646 +#640 := [unit-resolution #648 #655]: #661 +#696 := (* -1::Int #402) +#692 := (* -3::Int #21) +#406 := (+ #692 #696) +#407 := (+ #9 #406) +#688 := (>= #407 0::Int) +#695 := (= #407 0::Int) +#637 := (or false #695) +#639 := [th-lemma arith]: #637 +#649 := [unit-resolution #639 #62]: #695 +#650 := (not #695) +#651 := (or #650 #688) +#647 := [th-lemma arith triangle-eq]: #651 +#652 := [unit-resolution #647 #649]: #688 +[th-lemma arith farkas 2 1 3 3 1 #561 #652 #640 #150 #662]: false +unsat +73ec717ba0bbdd95adecb13ea22d00aede55f061 489 0 +#2 := false +decl f3 :: (-> Int S2) +#10 := 0::Int +#29 := (f3 0::Int) +decl f5 :: S2 +#8 := f5 +#30 := (= f5 #29) +decl f4 :: (-> S2 Int) +#9 := (f4 f5) +#385 := (f3 #9) +#662 := (= #385 #29) +#631 := (= #29 #385) +#629 := (= 0::Int #9) +#11 := (= #9 0::Int) +#12 := 3::Int +#429 := (mod #9 3::Int) +#663 := (>= #429 0::Int) +#1 := true +#66 := [true-axiom]: true +#624 := (or false #663) +#619 := [th-lemma arith]: #624 +#625 := [unit-resolution #619 #66]: #663 +#88 := -3::Int +#84 := -1::Int +#85 := (* -1::Int #9) +#91 := (div #85 -3::Int) +#21 := (div #9 3::Int) +#141 := (>= #9 0::Int) +#142 := (not #141) +#128 := (<= #9 0::Int) +#129 := (not #128) +#152 := (or #129 #142) +#155 := (ite #152 #21 #91) +#158 := (ite #11 0::Int #155) +#628 := (* -1::Int #158) +#634 := (+ #9 #628) +#620 := (<= #634 0::Int) +#633 := (= #9 #158) +#161 := (f3 #158) +#708 := (f4 #161) +#577 := (= #708 #158) +#703 := (= #158 #708) +#706 := (>= #158 0::Int) +#709 := (= #708 0::Int) +#608 := (not #709) +#739 := (not #11) +#609 := (iff #739 #608) +#611 := (iff #11 #709) +#605 := (iff #709 #11) +#493 := (= #708 #9) +#598 := (= #161 f5) +#164 := (= f5 #161) +#664 := (= #29 #161) +#675 := (= #161 #29) +#336 := (= #158 0::Int) +#729 := (f4 #29) +#727 := (= #729 0::Int) +#38 := (:var 0 Int) +#40 := (f3 #38) +#759 := (pattern #40) +#203 := (>= #38 0::Int) +#205 := (not #203) +#41 := (f4 #40) +#186 := (= #38 #41) +#211 := (or #186 #205) +#760 := (forall (vars (?v0 Int)) (:pat #759) #211) +#216 := (forall (vars (?v0 Int)) #211) +#763 := (iff #216 #760) +#761 := (iff #211 #211) +#762 := [refl]: #761 +#764 := [quant-intro #762]: #763 +#268 := (~ #216 #216) +#267 := (~ #211 #211) +#264 := [refl]: #267 +#269 := [nnf-pos #264]: #268 +#42 := (= #41 #38) +#39 := (<= 0::Int #38) +#43 := (implies #39 #42) +#44 := (forall (vars (?v0 Int)) #43) +#219 := (iff #44 #216) +#193 := (not #39) +#194 := (or #193 #186) +#199 := (forall (vars (?v0 Int)) #194) +#217 := (iff #199 #216) +#214 := (iff #194 #211) +#208 := (or #205 #186) +#212 := (iff #208 #211) +#213 := [rewrite]: #212 +#209 := (iff #194 #208) +#206 := (iff #193 #205) +#202 := (iff #39 #203) +#204 := [rewrite]: #202 +#207 := [monotonicity #204]: #206 +#210 := [monotonicity #207]: #209 +#215 := [trans #210 #213]: #214 +#218 := [quant-intro #215]: #217 +#200 := (iff #44 #199) +#197 := (iff #43 #194) +#190 := (implies #39 #186) +#195 := (iff #190 #194) +#196 := [rewrite]: #195 +#191 := (iff #43 #190) +#188 := (iff #42 #186) +#189 := [rewrite]: #188 +#192 := [monotonicity #189]: #191 +#198 := [trans #192 #196]: #197 +#201 := [quant-intro #198]: #200 +#220 := [trans #201 #218]: #219 +#185 := [asserted]: #44 +#221 := [mp #185 #220]: #216 +#265 := [mp~ #221 #269]: #216 +#765 := [mp #265 #764]: #760 +#721 := (not #760) +#443 := (or #721 #727) +#389 := (>= 0::Int 0::Int) +#390 := (not #389) +#730 := (= 0::Int #729) +#731 := (or #730 #390) +#444 := (or #721 #731) +#722 := (iff #444 #443) +#723 := (iff #443 #443) +#433 := [rewrite]: #723 +#343 := (iff #731 #727) +#725 := (or #727 false) +#449 := (iff #725 #727) +#450 := [rewrite]: #449 +#447 := (iff #731 #725) +#738 := (iff #390 false) +#736 := (not true) +#737 := (iff #736 false) +#735 := [rewrite]: #737 +#376 := (iff #390 #736) +#371 := (iff #389 true) +#734 := [rewrite]: #371 +#377 := [monotonicity #734]: #376 +#724 := [trans #377 #735]: #738 +#732 := (iff #730 #727) +#733 := [rewrite]: #732 +#448 := [monotonicity #733 #724]: #447 +#720 := [trans #448 #450]: #343 +#719 := [monotonicity #720]: #722 +#434 := [trans #719 #433]: #722 +#718 := [quant-inst #10]: #444 +#435 := [mp #718 #434]: #443 +#590 := [unit-resolution #435 #765]: #727 +#685 := (= #9 #729) +#748 := (not #164) +#588 := [hypothesis]: #748 +#401 := (or #30 #164) +#122 := (not #30) +#170 := (iff #122 #164) +#23 := (- 3::Int) +#22 := (- #9) +#24 := (div #22 #23) +#16 := (< 0::Int 3::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= 3::Int 0::Int) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (f3 #26) +#28 := (= #27 f5) +#31 := (iff #28 #30) +#32 := (not #31) +#175 := (iff #32 #170) +#78 := (and #16 #18) +#81 := (or #17 #78) +#94 := (ite #81 #21 #91) +#97 := (ite #11 0::Int #94) +#100 := (f3 #97) +#106 := (= f5 #100) +#123 := (iff #106 #122) +#173 := (iff #123 #170) +#167 := (iff #164 #122) +#171 := (iff #167 #170) #172 := [rewrite]: #171 -#266 := [monotonicity #172 #263]: #265 -#269 := [monotonicity #266]: #268 -#272 := [quant-intro #269]: #271 -#289 := [trans #272 #287]: #288 -#246 := [asserted]: #60 -#290 := [mp #246 #289]: #285 -#318 := [mp~ #290 #303]: #285 -#356 := [mp #318 #355]: #353 -#387 := [mp #356 #386]: #384 -#892 := [mp #387 #891]: #887 -#735 := (not #887) -#741 := (or #735 #736) -#820 := (* -1::Int 1::Int) -#813 := (mod #824 #820) -#814 := (+ #11 #813) -#815 := (= #814 0::Int) -#810 := (mod #9 1::Int) -#811 := (* -1::Int #810) -#816 := (+ #11 #811) -#817 := (= #816 0::Int) -#818 := (<= 1::Int 0::Int) -#659 := (or #818 #812) -#660 := (not #659) -#803 := (or #661 #818) -#804 := (not #803) -#805 := (or #804 #660) -#806 := (ite #805 #817 #815) -#807 := (ite #801 #800 #806) -#808 := (= #9 #11) -#802 := (= 1::Int 0::Int) -#809 := (ite #802 #808 #807) -#727 := (or #735 #809) -#724 := (iff #727 #741) -#728 := (iff #741 #741) -#729 := [rewrite]: #728 -#739 := (iff #809 #736) -#696 := (or #683 #694) -#742 := (or #696 #801) -#743 := (ite #742 #800 #765) -#737 := (iff #743 #736) -#733 := (iff #742 #755) -#734 := [rewrite]: #733 -#738 := [monotonicity #734]: #737 -#754 := (iff #809 #743) -#749 := (ite false #808 #743) -#752 := (iff #749 #743) -#753 := [rewrite]: #752 -#750 := (iff #809 #749) -#747 := (iff #807 #743) -#757 := (ite #696 #800 #765) -#761 := (ite #801 #800 #757) -#745 := (iff #761 #743) -#746 := [rewrite]: #745 -#758 := (iff #807 #761) -#759 := (iff #806 #757) -#770 := (iff #815 #765) -#768 := (= #814 #767) -#764 := (= #813 #763) -#772 := (= #820 -1::Int) -#779 := [rewrite]: #772 -#766 := [monotonicity #779]: #764 -#769 := [monotonicity #766]: #768 -#756 := [monotonicity #769]: #770 -#777 := (iff #817 #800) -#775 := (= #816 #11) -#783 := (+ #11 0::Int) -#781 := (= #783 #11) -#786 := [rewrite]: #781 -#784 := (= #816 #783) -#771 := (= #811 0::Int) -#789 := (* -1::Int 0::Int) -#782 := (= #789 0::Int) -#774 := [rewrite]: #782 -#793 := (= #811 #789) -#699 := (= #810 0::Int) -#792 := [rewrite]: #699 -#780 := [monotonicity #792]: #793 -#773 := [trans #780 #774]: #771 -#785 := [monotonicity #773]: #784 -#776 := [trans #785 #786]: #775 -#778 := [monotonicity #776]: #777 -#697 := (iff #805 #696) -#687 := (iff #660 #694) -#691 := (iff #659 #812) -#692 := (or false #812) -#791 := (iff #692 #812) -#676 := [rewrite]: #791 -#787 := (iff #659 #692) -#641 := (iff #818 false) -#794 := [rewrite]: #641 -#788 := [monotonicity #794]: #787 -#693 := [trans #788 #676]: #691 -#695 := [monotonicity #693]: #687 -#642 := (iff #804 #683) -#681 := (iff #803 #661) -#795 := (or #661 false) -#796 := (iff #795 #661) -#799 := [rewrite]: #796 -#797 := (iff #803 #795) -#798 := [monotonicity #794]: #797 -#682 := [trans #798 #799]: #681 -#790 := [monotonicity #682]: #642 -#698 := [monotonicity #790 #695]: #697 -#760 := [monotonicity #698 #778 #756]: #759 -#762 := [monotonicity #760]: #758 -#748 := [trans #762 #746]: #747 -#638 := (iff #802 false) -#640 := [rewrite]: #638 -#751 := [monotonicity #640 #748]: #750 -#744 := [trans #751 #753]: #754 -#740 := [trans #744 #738]: #739 -#725 := [monotonicity #740]: #724 -#730 := [trans #725 #729]: #724 -#723 := [quant-inst #9 #10]: #727 -#731 := [mp #723 #730]: #741 -#680 := [unit-resolution #731 #892]: #736 -#719 := (not #736) -#720 := (or #719 #712 #800) -#721 := [def-axiom]: #720 -#656 := [unit-resolution #721 #680]: #701 -#657 := [unit-resolution #656 #700]: #712 -#600 := (or #755 #812) -#711 := [def-axiom]: #600 -#662 := [unit-resolution #711 #657]: #812 -#726 := (or #755 #661) -#732 := [def-axiom]: #726 -#663 := [unit-resolution #732 #657]: #661 -#705 := (not #801) -#706 := (or #755 #705) -#707 := [def-axiom]: #706 -#664 := [unit-resolution #707 #657]: #705 -#665 := (or #801 #683 #694) -#666 := [th-lemma arith triangle-eq]: #665 -[unit-resolution #666 #664 #663 #662]: false -unsat -9fbefb874a9c8d1ffb3917c9db0286d637e8beaf 310 0 +#168 := (iff #123 #167) +#165 := (iff #106 #164) +#162 := (= #100 #161) +#159 := (= #97 #158) +#156 := (= #94 #155) +#153 := (iff #81 #152) +#150 := (iff #78 #142) +#145 := (and true #142) +#148 := (iff #145 #142) +#149 := [rewrite]: #148 +#146 := (iff #78 #145) +#143 := (iff #18 #142) +#144 := [rewrite]: #143 +#132 := (iff #16 true) +#133 := [rewrite]: #132 +#147 := [monotonicity #133 #144]: #146 +#151 := [trans #147 #149]: #150 +#139 := (iff #17 #129) +#134 := (and #129 true) +#137 := (iff #134 #129) +#138 := [rewrite]: #137 +#135 := (iff #17 #134) +#130 := (iff #15 #129) +#131 := [rewrite]: #130 +#136 := [monotonicity #131 #133]: #135 +#140 := [trans #136 #138]: #139 +#154 := [monotonicity #140 #151]: #153 +#157 := [monotonicity #154]: #156 +#160 := [monotonicity #157]: #159 +#163 := [monotonicity #160]: #162 +#166 := [monotonicity #163]: #165 +#169 := [monotonicity #166]: #168 +#174 := [trans #169 #172]: #173 +#126 := (iff #32 #123) +#114 := (iff #30 #106) +#119 := (not #114) +#124 := (iff #119 #123) +#125 := [rewrite]: #124 +#120 := (iff #32 #119) +#117 := (iff #31 #114) +#111 := (iff #106 #30) +#115 := (iff #111 #114) +#116 := [rewrite]: #115 +#112 := (iff #31 #111) +#109 := (iff #28 #106) +#103 := (= #100 f5) +#107 := (iff #103 #106) +#108 := [rewrite]: #107 +#104 := (iff #28 #103) +#101 := (= #27 #100) +#98 := (= #26 #97) +#95 := (= #25 #94) +#92 := (= #24 #91) +#89 := (= #23 -3::Int) +#90 := [rewrite]: #89 +#86 := (= #22 #85) +#87 := [rewrite]: #86 +#93 := [monotonicity #87 #90]: #92 +#82 := (iff #20 #81) +#79 := (iff #19 #78) +#80 := [rewrite]: #79 +#83 := [monotonicity #80]: #82 +#96 := [monotonicity #83 #93]: #95 +#76 := (iff #14 #11) +#71 := (or #11 false) +#74 := (iff #71 #11) +#75 := [rewrite]: #74 +#72 := (iff #14 #71) +#69 := (iff #13 false) +#70 := [rewrite]: #69 +#73 := [monotonicity #70]: #72 +#77 := [trans #73 #75]: #76 +#99 := [monotonicity #77 #96]: #98 +#102 := [monotonicity #99]: #101 +#105 := [monotonicity #102]: #104 +#110 := [trans #105 #108]: #109 +#113 := [monotonicity #110]: #112 +#118 := [trans #113 #116]: #117 +#121 := [monotonicity #118]: #120 +#127 := [trans #121 #125]: #126 +#176 := [trans #127 #174]: #175 +#68 := [asserted]: #32 +#177 := [mp #68 #176]: #170 +#749 := (not #170) +#405 := (or #30 #164 #749) +#741 := [def-axiom]: #405 +#742 := [unit-resolution #741 #177]: #401 +#589 := [unit-resolution #742 #588]: #30 +#682 := [monotonicity #589]: #685 +#686 := [trans #682 #590]: #11 +#413 := (or #739 #336) +#414 := [def-axiom]: #413 +#673 := [unit-resolution #414 #686]: #336 +#667 := [monotonicity #673]: #675 +#666 := [symm #667]: #664 +#676 := [trans #589 #666]: #164 +#677 := [unit-resolution #588 #676]: false +#678 := [lemma #677]: #164 +#599 := [symm #678]: #598 +#604 := [monotonicity #599]: #493 +#606 := [monotonicity #604]: #605 +#607 := [symm #606]: #611 +#612 := [monotonicity #607]: #609 +#600 := [hypothesis]: #739 +#613 := [mp #600 #612]: #608 +#697 := (or #706 #709) +#46 := (= #41 0::Int) +#252 := (or #46 #203) +#766 := (forall (vars (?v0 Int)) (:pat #759) #252) +#257 := (forall (vars (?v0 Int)) #252) +#769 := (iff #257 #766) +#767 := (iff #252 #252) +#768 := [refl]: #767 +#770 := [quant-intro #768]: #769 +#270 := (~ #257 #257) +#278 := (~ #252 #252) +#279 := [refl]: #278 +#271 := [nnf-pos #279]: #270 +#45 := (< #38 0::Int) +#47 := (implies #45 #46) +#48 := (forall (vars (?v0 Int)) #47) +#260 := (iff #48 #257) +#223 := (= 0::Int #41) +#229 := (not #45) +#230 := (or #229 #223) +#235 := (forall (vars (?v0 Int)) #230) +#258 := (iff #235 #257) +#255 := (iff #230 #252) +#249 := (or #203 #46) +#253 := (iff #249 #252) +#254 := [rewrite]: #253 +#250 := (iff #230 #249) +#247 := (iff #223 #46) +#248 := [rewrite]: #247 +#245 := (iff #229 #203) +#240 := (not #205) +#243 := (iff #240 #203) +#244 := [rewrite]: #243 +#241 := (iff #229 #240) +#238 := (iff #45 #205) +#239 := [rewrite]: #238 +#242 := [monotonicity #239]: #241 +#246 := [trans #242 #244]: #245 +#251 := [monotonicity #246 #248]: #250 +#256 := [trans #251 #254]: #255 +#259 := [quant-intro #256]: #258 +#236 := (iff #48 #235) +#233 := (iff #47 #230) +#226 := (implies #45 #223) +#231 := (iff #226 #230) +#232 := [rewrite]: #231 +#227 := (iff #47 #226) +#224 := (iff #46 #223) +#225 := [rewrite]: #224 +#228 := [monotonicity #225]: #227 +#234 := [trans #228 #232]: #233 +#237 := [quant-intro #234]: #236 +#261 := [trans #237 #259]: #260 +#222 := [asserted]: #48 +#262 := [mp #222 #261]: #257 +#280 := [mp~ #262 #271]: #257 +#771 := [mp #280 #770]: #766 +#693 := (not #766) +#694 := (or #693 #706 #709) +#710 := (or #709 #706) +#700 := (or #693 #710) +#687 := (iff #700 #694) +#695 := (or #693 #697) +#533 := (iff #695 #694) +#534 := [rewrite]: #533 +#702 := (iff #700 #695) +#698 := (iff #710 #697) +#699 := [rewrite]: #698 +#531 := [monotonicity #699]: #702 +#688 := [trans #531 #534]: #687 +#701 := [quant-inst #158]: #700 +#690 := [mp #701 #688]: #694 +#614 := [unit-resolution #690 #771]: #697 +#610 := [unit-resolution #614 #613]: #706 +#707 := (not #706) +#704 := (or #703 #707) +#705 := (or #721 #703 #707) +#711 := (or #721 #704) +#553 := (iff #711 #705) +#554 := [rewrite]: #553 +#552 := [quant-inst #158]: #711 +#696 := [mp #552 #554]: #705 +#615 := [unit-resolution #696 #765]: #704 +#595 := [unit-resolution #615 #610]: #703 +#601 := [symm #595]: #577 +#541 := (= #9 #708) +#596 := [symm #604]: #541 +#602 := [trans #596 #601]: #633 +#597 := (not #633) +#603 := (or #597 #620) +#571 := [th-lemma arith triangle-eq]: #603 +#578 := [unit-resolution #571 #602]: #620 +#618 := (+ #21 #628) +#622 := (>= #618 0::Int) +#617 := (= #21 #158) +#422 := (= #155 #158) +#746 := (or #11 #422) +#747 := [def-axiom]: #746 +#537 := [unit-resolution #747 #600]: #422 +#337 := (= #21 #155) +#691 := (f4 #385) +#689 := (= #691 0::Int) +#594 := (not #689) +#549 := (iff #739 #594) +#593 := (iff #11 #689) +#582 := (iff #689 #11) +#579 := (= #691 #9) +#570 := (= #385 f5) +#726 := (= f5 #385) +#33 := (:var 0 S2) +#34 := (f4 #33) +#751 := (pattern #34) +#35 := (f3 #34) +#179 := (= #33 #35) +#752 := (forall (vars (?v0 S2)) (:pat #751) #179) +#182 := (forall (vars (?v0 S2)) #179) +#753 := (iff #182 #752) +#755 := (iff #752 #752) +#756 := [rewrite]: #755 +#754 := [rewrite]: #753 +#757 := [trans #754 #756]: #753 +#276 := (~ #182 #182) +#274 := (~ #179 #179) +#275 := [refl]: #274 +#277 := [nnf-pos #275]: #276 +#36 := (= #35 #33) +#37 := (forall (vars (?v0 S2)) #36) +#183 := (iff #37 #182) +#180 := (iff #36 #179) +#181 := [rewrite]: #180 +#184 := [quant-intro #181]: #183 +#178 := [asserted]: #37 +#187 := [mp #178 #184]: #182 +#266 := [mp~ #187 #277]: #182 +#758 := [mp #266 #757]: #752 +#391 := (not #752) +#392 := (or #391 #726) +#728 := [quant-inst #8]: #392 +#568 := [unit-resolution #728 #758]: #726 +#572 := [symm #568]: #570 +#581 := [monotonicity #572]: #579 +#583 := [monotonicity #581]: #582 +#573 := [symm #583]: #593 +#550 := [monotonicity #573]: #549 +#555 := [mp #600 #550]: #594 +#574 := (or #141 #689) +#535 := (or #693 #141 #689) +#692 := (or #689 #141) +#683 := (or #693 #692) +#586 := (iff #683 #535) +#680 := (or #693 #574) +#569 := (iff #680 #535) +#584 := [rewrite]: #569 +#681 := (iff #683 #680) +#575 := (iff #692 #574) +#576 := [rewrite]: #575 +#684 := [monotonicity #576]: #681 +#587 := [trans #684 #584]: #586 +#585 := [quant-inst #9]: #683 +#580 := [mp #585 #587]: #535 +#556 := [unit-resolution #580 #771]: #574 +#557 := [unit-resolution #556 #555]: #141 +#558 := (or #11 #129 #142) +#559 := [th-lemma arith triangle-eq]: #558 +#560 := [unit-resolution #559 #600]: #152 +#561 := [unit-resolution #560 #557]: #129 +#424 := (or #152 #128) +#415 := [def-axiom]: #424 +#562 := [unit-resolution #415 #561]: #152 +#355 := (not #152) +#743 := (or #355 #337) +#745 := [def-axiom]: #743 +#563 := [unit-resolution #745 #562]: #337 +#564 := [trans #563 #537]: #617 +#565 := (not #617) +#566 := (or #565 #622) +#551 := [th-lemma arith triangle-eq]: #566 +#567 := [unit-resolution #551 #564]: #622 +#656 := (* -1::Int #429) +#672 := (* -3::Int #21) +#657 := (+ #672 #656) +#659 := (+ #9 #657) +#658 := (>= #659 0::Int) +#665 := (= #659 0::Int) +#528 := (or false #665) +#529 := [th-lemma arith]: #528 +#536 := [unit-resolution #529 #66]: #665 +#538 := (not #665) +#539 := (or #538 #658) +#540 := [th-lemma arith triangle-eq]: #539 +#542 := [unit-resolution #540 #536]: #658 +#543 := [th-lemma arith farkas 2 1 3 3 1 #561 #542 #567 #578 #625]: false +#544 := [lemma #543]: #11 +#630 := [symm #544]: #629 +#632 := [monotonicity #630]: #631 +#616 := [symm #632]: #662 +#621 := [trans #568 #616]: #30 +#740 := (or #122 #748) +#744 := (or #122 #748 #749) +#750 := [def-axiom]: #744 +#400 := [unit-resolution #750 #177]: #740 +#627 := [unit-resolution #400 #678]: #122 +[unit-resolution #627 #621]: false +unsat +1f21dc1a1f14ef0634d3f8992746cd150b8c3799 78 0 #2 := false decl f3 :: (-> Int S2) #8 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#9 := 3::Int -#10 := (f4 0::Int 3::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#800 := (= #10 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f4 #31 #20) -#885 := (pattern #50) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#245 := (mod #181 #184) -#375 := (+ #50 #245) -#376 := (= #375 0::Int) -#51 := (mod #31 #20) -#372 := (* -1::Int #51) -#373 := (+ #50 #372) -#374 := (= #373 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#377 := (ite #323 #374 #376) -#371 := (= #50 0::Int) -#33 := (= #31 0::Int) -#378 := (ite #33 #371 #377) -#370 := (= #31 #50) -#34 := (= #20 0::Int) -#379 := (ite #34 #370 #378) -#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379) -#382 := (forall (vars (?v0 Int) (?v1 Int)) #379) -#889 := (iff #382 #886) -#887 := (iff #379 #379) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#251 := (* -1::Int #245) -#339 := (ite #323 #51 #251) -#342 := (ite #33 0::Int #339) -#345 := (ite #34 #31 #342) -#348 := (= #50 #345) -#351 := (forall (vars (?v0 Int) (?v1 Int)) #348) -#383 := (iff #351 #382) -#380 := (iff #348 #379) -#381 := [rewrite]: #380 -#384 := [quant-intro #381]: #383 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#271 := (ite #226 #51 #251) -#274 := (ite #33 0::Int #271) -#277 := (ite #34 #31 #274) -#280 := (= #50 #277) -#283 := (forall (vars (?v0 Int) (?v1 Int)) #280) -#352 := (iff #283 #351) -#349 := (iff #280 #348) -#346 := (= #277 #345) -#343 := (= #274 #342) -#340 := (= #271 #339) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#341 := [monotonicity #325]: #340 -#344 := [monotonicity #341]: #343 -#347 := [monotonicity #344]: #346 -#350 := [monotonicity #347]: #349 -#353 := [quant-intro #350]: #352 -#300 := (~ #283 #283) -#314 := (~ #280 #280) -#315 := [refl]: #314 -#301 := [nnf-pos #315]: #300 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#286 := (iff #58 #283) -#174 := (and #37 #39) -#177 := (or #38 #174) -#256 := (ite #177 #51 #251) -#165 := (= 0::Int #31) -#259 := (ite #165 0::Int #256) -#168 := (= 0::Int #20) -#262 := (ite #168 #31 #259) -#265 := (= #50 #262) -#268 := (forall (vars (?v0 Int) (?v1 Int)) #265) -#284 := (iff #268 #283) -#281 := (iff #265 #280) -#278 := (= #262 #277) -#275 := (= #259 #274) -#272 := (= #256 #271) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#273 := [monotonicity #228]: #272 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#276 := [monotonicity #203 #273]: #275 -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#279 := [monotonicity #205 #276]: #278 -#282 := [monotonicity #279]: #281 -#285 := [quant-intro #282]: #284 -#269 := (iff #58 #268) -#266 := (iff #57 #265) -#263 := (= #56 #262) -#260 := (= #55 #259) -#257 := (= #54 #256) -#254 := (= #53 #251) -#248 := (- #245) -#252 := (= #248 #251) -#253 := [rewrite]: #252 -#249 := (= #53 #248) -#246 := (= #52 #245) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#247 := [monotonicity #183 #186]: #246 -#250 := [monotonicity #247]: #249 -#255 := [trans #250 #253]: #254 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#258 := [monotonicity #179 #255]: #257 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#261 := [monotonicity #167 #258]: #260 -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#264 := [monotonicity #170 #261]: #263 -#267 := [monotonicity #264]: #266 -#270 := [quant-intro #267]: #269 -#287 := [trans #270 #285]: #286 -#244 := [asserted]: #58 -#288 := [mp #244 #287]: #283 -#316 := [mp~ #288 #301]: #283 -#354 := [mp #316 #353]: #351 -#385 := [mp #354 #384]: #382 -#891 := [mp #385 #890]: #886 -#729 := (not #886) -#730 := (or #729 #800) -#812 := (* -1::Int 3::Int) -#813 := (* -1::Int 0::Int) -#814 := (mod #813 #812) -#809 := (+ #10 #814) -#810 := (= #809 0::Int) -#815 := (mod 0::Int 3::Int) -#816 := (* -1::Int #815) -#811 := (+ #10 #816) -#817 := (= #811 0::Int) -#834 := (>= 0::Int 0::Int) -#658 := (<= 3::Int 0::Int) -#659 := (or #658 #834) -#660 := (not #659) -#802 := (<= 0::Int 0::Int) -#803 := (or #802 #658) -#804 := (not #803) -#805 := (or #804 #660) -#799 := (ite #805 #817 #810) -#806 := (= 0::Int 0::Int) -#807 := (ite #806 #800 #799) -#801 := (= 0::Int #10) -#808 := (= 3::Int 0::Int) -#637 := (ite #808 #801 #807) -#725 := (or #729 #637) -#704 := (iff #725 #730) -#706 := (iff #730 #730) -#599 := [rewrite]: #706 -#727 := (iff #637 #800) -#753 := (ite false #800 #800) -#732 := (iff #753 #800) -#733 := [rewrite]: #732 -#723 := (iff #637 #753) -#726 := (iff #807 #800) -#1 := true -#737 := (ite true #800 #800) -#734 := (iff #737 #800) -#740 := [rewrite]: #734 -#738 := (iff #807 #737) -#735 := (iff #799 #800) -#743 := (iff #799 #753) -#751 := (iff #810 #800) -#749 := (= #809 #10) -#763 := (+ #10 0::Int) -#767 := (= #763 #10) -#768 := [rewrite]: #767 -#747 := (= #809 #763) -#745 := (= #814 0::Int) -#758 := -3::Int -#757 := (mod 0::Int -3::Int) -#742 := (= #757 0::Int) -#744 := [rewrite]: #742 -#761 := (= #814 #757) -#759 := (= #812 -3::Int) -#760 := [rewrite]: #759 -#777 := (= #813 0::Int) -#771 := [rewrite]: #777 -#741 := [monotonicity #771 #760]: #761 -#746 := [trans #741 #744]: #745 -#748 := [monotonicity #746]: #747 -#750 := [trans #748 #768]: #749 -#752 := [monotonicity #750]: #751 -#755 := (iff #817 #800) -#764 := (= #811 #10) -#765 := (= #811 #763) -#778 := (= #816 0::Int) -#775 := (= #816 #813) -#785 := (= #815 0::Int) -#774 := [rewrite]: #785 -#776 := [monotonicity #774]: #775 -#762 := [trans #776 #771]: #778 -#766 := [monotonicity #762]: #765 -#769 := [trans #766 #768]: #764 -#756 := [monotonicity #769]: #755 -#784 := (iff #805 false) -#773 := (or false false) -#782 := (iff #773 false) -#783 := [rewrite]: #782 -#770 := (iff #805 #773) -#779 := (iff #660 false) -#482 := (not true) -#841 := (iff #482 false) -#844 := [rewrite]: #841 -#788 := (iff #660 #482) -#698 := (iff #659 true) -#686 := (or false true) -#696 := (iff #686 true) -#697 := [rewrite]: #696 -#694 := (iff #659 #686) -#840 := (iff #834 true) -#842 := [rewrite]: #840 -#680 := (iff #658 false) -#681 := [rewrite]: #680 -#695 := [monotonicity #681 #842]: #694 -#791 := [trans #695 #697]: #698 -#792 := [monotonicity #791]: #788 -#781 := [trans #792 #844]: #779 -#692 := (iff #804 false) -#675 := (iff #804 #482) -#787 := (iff #803 true) -#682 := (or true false) -#691 := (iff #682 true) -#786 := [rewrite]: #691 -#641 := (iff #803 #682) -#795 := (iff #802 true) -#798 := [rewrite]: #795 -#789 := [monotonicity #798 #681]: #641 -#790 := [trans #789 #786]: #787 -#690 := [monotonicity #790]: #675 -#693 := [trans #690 #844]: #692 -#772 := [monotonicity #693 #781]: #770 -#780 := [trans #772 #783]: #784 -#754 := [monotonicity #780 #756 #752]: #743 -#736 := [trans #754 #733]: #735 -#796 := (iff #806 true) -#797 := [rewrite]: #796 -#739 := [monotonicity #797 #736]: #738 -#722 := [trans #739 #740]: #726 -#793 := (iff #801 #800) -#794 := [rewrite]: #793 -#639 := (iff #808 false) -#640 := [rewrite]: #639 -#724 := [monotonicity #640 #794 #722]: #723 -#728 := [trans #724 #733]: #727 -#705 := [monotonicity #728]: #704 -#710 := [trans #705 #599]: #704 -#731 := [quant-inst #8 #9]: #725 -#711 := [mp #731 #710]: #730 -#717 := [unit-resolution #711 #891]: #800 -#713 := [monotonicity #717]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #713]: false -unsat -e4bde0ae05cc3d53da641b07fe2928d0ca73206a 336 0 -#2 := false -decl f3 :: (-> Int S2) +#21 := (f3 0::Int) +#14 := (- 0::Int) +#15 := (mod #14 #14) +#16 := (- #15) +#13 := (mod 0::Int 0::Int) +#10 := (< 0::Int 0::Int) +#11 := (and #10 #10) +#12 := (or #11 #11) +#17 := (ite #12 #13 #16) +#9 := (= 0::Int 0::Int) +#18 := (ite #9 0::Int #17) +#19 := (ite #9 0::Int #18) +#20 := (f3 #19) +#22 := (= #20 #21) +#23 := (not #22) +#114 := (iff #23 false) +#1 := true +#109 := (not true) +#112 := (iff #109 false) +#113 := [rewrite]: #112 +#110 := (iff #23 #109) +#107 := (iff #22 true) +#102 := (= #21 #21) +#105 := (iff #102 true) +#106 := [rewrite]: #105 +#103 := (iff #22 #102) +#99 := (= #19 0::Int) +#94 := (ite true 0::Int 0::Int) +#97 := (= #94 0::Int) +#98 := [rewrite]: #97 +#95 := (= #19 #94) +#92 := (= #18 0::Int) +#78 := -1::Int +#79 := (* -1::Int #13) +#84 := (ite #10 #13 #79) +#87 := (ite true 0::Int #84) +#90 := (= #87 0::Int) +#91 := [rewrite]: #90 +#88 := (= #18 #87) +#85 := (= #17 #84) +#82 := (= #16 #79) +#75 := (- #13) +#80 := (= #75 #79) +#81 := [rewrite]: #80 +#76 := (= #16 #75) +#73 := (= #15 #13) +#71 := (= #14 0::Int) +#72 := [rewrite]: #71 +#74 := [monotonicity #72 #72]: #73 +#77 := [monotonicity #74]: #76 +#83 := [trans #77 #81]: #82 +#69 := (iff #12 #10) +#64 := (or #10 #10) +#67 := (iff #64 #10) +#68 := [rewrite]: #67 +#65 := (iff #12 #64) +#62 := (iff #11 #10) +#63 := [rewrite]: #62 +#66 := [monotonicity #63 #63]: #65 +#70 := [trans #66 #68]: #69 +#86 := [monotonicity #70 #83]: #85 +#60 := (iff #9 true) +#61 := [rewrite]: #60 +#89 := [monotonicity #61 #86]: #88 +#93 := [trans #89 #91]: #92 +#96 := [monotonicity #61 #93]: #95 +#100 := [trans #96 #98]: #99 +#101 := [monotonicity #100]: #22 +#104 := [monotonicity #101]: #103 +#108 := [trans #104 #106]: #107 +#111 := [monotonicity #108]: #110 +#115 := [trans #111 #113]: #114 +#59 := [asserted]: #23 +[mp #59 #115]: false +unsat +18c694d062a2e495b90f6c40f36cef6e909d6c58 115 0 +#2 := false +decl f4 :: (-> S2 Int) +#30 := (:var 0 S2) +#31 := (f4 #30) +#695 := (pattern #31) +decl f3 :: (-> Int S2) +#32 := (f3 #31) +#122 := (= #30 #32) +#696 := (forall (vars (?v0 S2)) (:pat #695) #122) +#126 := (forall (vars (?v0 S2)) #122) +#697 := (iff #126 #696) +#699 := (iff #696 #696) +#700 := [rewrite]: #699 +#698 := [rewrite]: #697 +#701 := [trans #698 #700]: #697 +#220 := (~ #126 #126) +#218 := (~ #122 #122) +#219 := [refl]: #218 +#221 := [nnf-pos #219]: #220 +#33 := (= #32 #30) +#34 := (forall (vars (?v0 S2)) #33) +#127 := (iff #34 #126) +#124 := (iff #33 #122) +#125 := [rewrite]: #124 +#128 := [quant-intro #125]: #127 +#121 := [asserted]: #34 +#131 := [mp #121 #128]: #126 +#210 := [mp~ #131 #221]: #126 +#702 := [mp #210 #701]: #696 +decl f5 :: S2 +#10 := f5 +#11 := (f4 f5) +#107 := (f3 #11) +#113 := (= f5 #107) +#118 := (not #113) +#8 := 0::Int +#21 := (- 0::Int) +#20 := (- #11) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod #11 0::Int) +#14 := (< 0::Int 0::Int) +#16 := (< #11 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int #11) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= #11 0::Int) +#25 := (ite #12 0::Int #24) +#9 := (= 0::Int 0::Int) +#26 := (ite #9 #11 #25) +#27 := (f3 #26) +#28 := (= #27 f5) +#29 := (not #28) +#119 := (iff #29 #118) +#116 := (iff #28 #113) +#110 := (= #107 f5) +#114 := (iff #110 #113) +#115 := [rewrite]: #114 +#111 := (iff #28 #110) +#108 := (= #27 #107) +#105 := (= #26 #11) +#77 := -1::Int +#78 := (* -1::Int #11) +#83 := (mod #78 0::Int) +#89 := (* -1::Int #83) +#71 := (and #14 #16) +#74 := (or #15 #71) +#94 := (ite #74 #19 #89) +#68 := (= 0::Int #11) +#97 := (ite #68 0::Int #94) +#1 := true +#100 := (ite true #11 #97) +#103 := (= #100 #11) +#104 := [rewrite]: #103 +#101 := (= #26 #100) +#98 := (= #25 #97) +#95 := (= #24 #94) +#92 := (= #23 #89) +#86 := (- #83) +#90 := (= #86 #89) +#91 := [rewrite]: #90 +#87 := (= #23 #86) +#84 := (= #22 #83) +#81 := (= #21 0::Int) +#82 := [rewrite]: #81 +#79 := (= #20 #78) +#80 := [rewrite]: #79 +#85 := [monotonicity #80 #82]: #84 +#88 := [monotonicity #85]: #87 +#93 := [trans #88 #91]: #92 +#75 := (iff #18 #74) +#72 := (iff #17 #71) +#73 := [rewrite]: #72 +#76 := [monotonicity #73]: #75 +#96 := [monotonicity #76 #93]: #95 +#69 := (iff #12 #68) +#70 := [rewrite]: #69 +#99 := [monotonicity #70 #96]: #98 +#66 := (iff #9 true) +#67 := [rewrite]: #66 +#102 := [monotonicity #67 #99]: #101 +#106 := [trans #102 #104]: #105 +#109 := [monotonicity #106]: #108 +#112 := [monotonicity #109]: #111 +#117 := [trans #112 #115]: #116 +#120 := [monotonicity #117]: #119 +#65 := [asserted]: #29 +#123 := [mp #65 #120]: #118 +#281 := (not #696) +#367 := (or #281 #113) +#368 := [quant-inst #10]: #367 +[unit-resolution #368 #123 #702]: false +unsat +2713378ea3e2d16536aee750f4c4dea73990d05c 86 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#25 := (f3 0::Int) #8 := 1::Int -#12 := (f3 1::Int) -decl f4 :: (-> Int Int Int) -#9 := 3::Int -#10 := (f4 1::Int 3::Int) -#11 := (f3 #10) -#13 := (= #11 #12) -#797 := (= #10 1::Int) -#21 := (:var 0 Int) -#32 := (:var 1 Int) -#51 := (f4 #32 #21) -#885 := (pattern #51) -#20 := 0::Int -#181 := -1::Int -#185 := (* -1::Int #21) -#182 := (* -1::Int #32) -#246 := (mod #182 #185) -#376 := (+ #51 #246) -#377 := (= #376 0::Int) -#52 := (mod #32 #21) -#373 := (* -1::Int #52) -#374 := (+ #51 #373) -#375 := (= #374 0::Int) -#220 := (>= #32 0::Int) -#213 := (<= #21 0::Int) -#320 := (or #213 #220) -#321 := (not #320) -#209 := (<= #32 0::Int) -#318 := (or #209 #213) -#319 := (not #318) -#324 := (or #319 #321) -#378 := (ite #324 #375 #377) -#372 := (= #51 0::Int) -#34 := (= #32 0::Int) -#379 := (ite #34 #372 #378) -#371 := (= #32 #51) -#35 := (= #21 0::Int) -#380 := (ite #35 #371 #379) -#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380) -#383 := (forall (vars (?v0 Int) (?v1 Int)) #380) -#889 := (iff #383 #886) -#887 := (iff #380 #380) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#252 := (* -1::Int #246) -#340 := (ite #324 #52 #252) -#343 := (ite #34 0::Int #340) -#346 := (ite #35 #32 #343) -#349 := (= #51 #346) -#352 := (forall (vars (?v0 Int) (?v1 Int)) #349) -#384 := (iff #352 #383) -#381 := (iff #349 #380) -#382 := [rewrite]: #381 -#385 := [quant-intro #382]: #384 -#221 := (not #220) -#214 := (not #213) -#224 := (and #214 #221) -#210 := (not #209) -#217 := (and #210 #214) -#227 := (or #217 #224) -#272 := (ite #227 #52 #252) -#275 := (ite #34 0::Int #272) -#278 := (ite #35 #32 #275) -#281 := (= #51 #278) -#284 := (forall (vars (?v0 Int) (?v1 Int)) #281) -#353 := (iff #284 #352) -#350 := (iff #281 #349) -#347 := (= #278 #346) -#344 := (= #275 #343) -#341 := (= #272 #340) -#325 := (iff #227 #324) -#322 := (iff #224 #321) -#323 := [rewrite]: #322 -#303 := (iff #217 #319) -#304 := [rewrite]: #303 -#326 := [monotonicity #304 #323]: #325 -#342 := [monotonicity #326]: #341 -#345 := [monotonicity #342]: #344 -#348 := [monotonicity #345]: #347 -#351 := [monotonicity #348]: #350 -#354 := [quant-intro #351]: #353 -#301 := (~ #284 #284) -#315 := (~ #281 #281) -#316 := [refl]: #315 -#302 := [nnf-pos #316]: #301 -#45 := (- #21) -#44 := (- #32) -#53 := (mod #44 #45) -#54 := (- #53) -#38 := (< 0::Int #21) -#40 := (< #32 0::Int) -#41 := (and #40 #38) -#37 := (< 0::Int #32) -#39 := (and #37 #38) -#42 := (or #39 #41) -#55 := (ite #42 #52 #54) -#56 := (ite #34 0::Int #55) -#57 := (ite #35 #32 #56) -#58 := (= #51 #57) -#59 := (forall (vars (?v0 Int) (?v1 Int)) #58) -#287 := (iff #59 #284) -#175 := (and #38 #40) -#178 := (or #39 #175) -#257 := (ite #178 #52 #252) -#166 := (= 0::Int #32) -#260 := (ite #166 0::Int #257) -#169 := (= 0::Int #21) -#263 := (ite #169 #32 #260) -#266 := (= #51 #263) -#269 := (forall (vars (?v0 Int) (?v1 Int)) #266) -#285 := (iff #269 #284) -#282 := (iff #266 #281) -#279 := (= #263 #278) -#276 := (= #260 #275) -#273 := (= #257 #272) -#228 := (iff #178 #227) -#225 := (iff #175 #224) -#222 := (iff #40 #221) -#223 := [rewrite]: #222 -#215 := (iff #38 #214) -#216 := [rewrite]: #215 -#226 := [monotonicity #216 #223]: #225 -#218 := (iff #39 #217) -#211 := (iff #37 #210) -#212 := [rewrite]: #211 -#219 := [monotonicity #212 #216]: #218 -#229 := [monotonicity #219 #226]: #228 -#274 := [monotonicity #229]: #273 -#203 := (iff #166 #34) -#204 := [rewrite]: #203 -#277 := [monotonicity #204 #274]: #276 -#205 := (iff #169 #35) -#206 := [rewrite]: #205 -#280 := [monotonicity #206 #277]: #279 -#283 := [monotonicity #280]: #282 -#286 := [quant-intro #283]: #285 -#270 := (iff #59 #269) -#267 := (iff #58 #266) -#264 := (= #57 #263) -#261 := (= #56 #260) -#258 := (= #55 #257) -#255 := (= #54 #252) -#249 := (- #246) -#253 := (= #249 #252) -#254 := [rewrite]: #253 -#250 := (= #54 #249) -#247 := (= #53 #246) -#186 := (= #45 #185) -#187 := [rewrite]: #186 -#183 := (= #44 #182) -#184 := [rewrite]: #183 -#248 := [monotonicity #184 #187]: #247 -#251 := [monotonicity #248]: #250 -#256 := [trans #251 #254]: #255 -#179 := (iff #42 #178) -#176 := (iff #41 #175) -#177 := [rewrite]: #176 -#180 := [monotonicity #177]: #179 -#259 := [monotonicity #180 #256]: #258 -#167 := (iff #34 #166) -#168 := [rewrite]: #167 -#262 := [monotonicity #168 #259]: #261 -#170 := (iff #35 #169) -#171 := [rewrite]: #170 -#265 := [monotonicity #171 #262]: #264 -#268 := [monotonicity #265]: #267 -#271 := [quant-intro #268]: #270 -#288 := [trans #271 #286]: #287 -#245 := [asserted]: #59 -#289 := [mp #245 #288]: #284 -#317 := [mp~ #289 #302]: #284 -#355 := [mp #317 #354]: #352 -#386 := [mp #355 #385]: #383 -#891 := [mp #386 #890]: #886 -#709 := (not #886) -#677 := (or #709 #797) -#814 := (* -1::Int 3::Int) -#809 := (* -1::Int 1::Int) -#810 := (mod #809 #814) -#815 := (+ #10 #810) -#816 := (= #815 0::Int) -#811 := (mod 1::Int 3::Int) -#817 := (* -1::Int #811) -#658 := (+ #10 #817) -#659 := (= #658 0::Int) -#835 := (>= 1::Int 0::Int) -#660 := (<= 3::Int 0::Int) -#802 := (or #660 #835) -#803 := (not #802) -#804 := (<= 1::Int 0::Int) -#805 := (or #804 #660) -#799 := (not #805) -#800 := (or #799 #803) -#806 := (ite #800 #659 #816) -#807 := (= #10 0::Int) -#801 := (= 1::Int 0::Int) -#808 := (ite #801 #807 #806) -#637 := (= 1::Int #10) -#639 := (= 3::Int 0::Int) -#640 := (ite #639 #637 #808) -#684 := (or #709 #640) -#674 := (iff #684 #677) -#678 := (iff #677 #677) -#685 := [rewrite]: #678 -#708 := (iff #640 #797) -#701 := (ite false #797 #797) -#683 := (iff #701 #797) -#707 := [rewrite]: #683 -#647 := (iff #640 #701) -#716 := (iff #808 #797) -#714 := (ite false #807 #797) -#719 := (iff #714 #797) -#720 := [rewrite]: #719 -#715 := (iff #808 #714) -#717 := (iff #806 #797) -#729 := -2::Int -#730 := (= #10 -2::Int) -#1 := true -#706 := (ite true #797 #730) -#711 := (iff #706 #797) -#712 := [rewrite]: #711 -#599 := (iff #806 #706) -#704 := (iff #816 #730) -#754 := 2::Int -#734 := (+ 2::Int #10) -#724 := (= #734 0::Int) -#725 := (iff #724 #730) -#731 := [rewrite]: #725 -#727 := (iff #816 #724) -#722 := (= #815 #734) -#737 := (+ #10 2::Int) -#740 := (= #737 #734) -#726 := [rewrite]: #740 -#738 := (= #815 #737) -#735 := (= #810 2::Int) -#749 := -3::Int -#752 := (mod -1::Int -3::Int) -#732 := (= #752 2::Int) -#733 := [rewrite]: #732 -#753 := (= #810 #752) -#750 := (= #814 -3::Int) -#751 := [rewrite]: #750 -#766 := (= #809 -1::Int) -#767 := [rewrite]: #766 -#743 := [monotonicity #767 #751]: #753 -#736 := [trans #743 #733]: #735 -#739 := [monotonicity #736]: #738 -#723 := [trans #739 #726]: #722 -#728 := [monotonicity #723]: #727 -#705 := [trans #728 #731]: #704 -#747 := (iff #659 #797) -#758 := (+ -1::Int #10) -#741 := (= #758 0::Int) -#745 := (iff #741 #797) -#746 := [rewrite]: #745 -#742 := (iff #659 #741) -#757 := (= #658 #758) -#769 := (+ #10 -1::Int) -#759 := (= #769 #758) -#760 := [rewrite]: #759 -#755 := (= #658 #769) -#768 := (= #817 -1::Int) -#763 := (= #817 #809) -#778 := (= #811 1::Int) -#762 := [rewrite]: #778 -#765 := [monotonicity #762]: #763 -#764 := [trans #765 #767]: #768 -#756 := [monotonicity #764]: #755 -#761 := [trans #756 #760]: #757 -#744 := [monotonicity #761]: #742 -#748 := [trans #744 #746]: #747 -#777 := (iff #800 true) -#780 := (or true false) -#775 := (iff #780 true) -#776 := [rewrite]: #775 -#785 := (iff #800 #780) -#783 := (iff #803 false) -#483 := (not true) -#844 := (iff #483 false) -#830 := [rewrite]: #844 -#772 := (iff #803 #483) -#773 := (iff #802 true) -#791 := (or false true) -#779 := (iff #791 true) -#781 := [rewrite]: #779 -#788 := (iff #802 #791) -#842 := (iff #835 true) -#482 := [rewrite]: #842 -#641 := (iff #660 false) -#789 := [rewrite]: #641 -#792 := [monotonicity #789 #482]: #788 -#770 := [trans #792 #781]: #773 -#782 := [monotonicity #770]: #772 -#784 := [trans #782 #830]: #783 -#697 := (iff #799 true) -#693 := (not false) -#695 := (iff #693 true) -#696 := [rewrite]: #695 -#686 := (iff #799 #693) -#690 := (iff #805 false) -#691 := (or false false) -#790 := (iff #691 false) -#675 := [rewrite]: #790 -#786 := (iff #805 #691) -#681 := (iff #804 false) -#682 := [rewrite]: #681 -#787 := [monotonicity #682 #789]: #786 -#692 := [trans #787 #675]: #690 -#694 := [monotonicity #692]: #686 -#698 := [trans #694 #696]: #697 -#774 := [monotonicity #698 #784]: #785 -#771 := [trans #774 #776]: #777 -#710 := [monotonicity #771 #748 #705]: #599 -#713 := [trans #710 #712]: #717 -#798 := (iff #801 false) -#680 := [rewrite]: #798 -#718 := [monotonicity #680 #713]: #715 -#721 := [trans #718 #720]: #716 -#796 := (iff #637 #797) -#795 := [rewrite]: #796 -#793 := (iff #639 false) -#794 := [rewrite]: #793 -#702 := [monotonicity #794 #795 #721]: #647 -#703 := [trans #702 #707]: #708 -#676 := [monotonicity #703]: #674 -#687 := [trans #676 #685]: #674 -#643 := [quant-inst #8 #9]: #684 -#688 := [mp #643 #687]: #677 -#679 := [unit-resolution #688 #891]: #797 -#700 := [monotonicity #679]: #13 -#14 := (not #13) -#79 := [asserted]: #14 -[unit-resolution #79 #700]: false -unsat -1120ebc08fbef118a46bc94c7a17d1ff3c4dbb08 311 0 -#2 := false -decl f3 :: (-> Int S2) -#11 := 0::Int -#12 := (f3 0::Int) -decl f4 :: (-> Int Int Int) -#8 := 3::Int -#9 := (f4 3::Int 3::Int) -#10 := (f3 #9) -#13 := (= #10 #12) -#799 := (= #9 0::Int) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f4 #31 #20) -#885 := (pattern #50) -#180 := -1::Int -#184 := (* -1::Int #20) -#181 := (* -1::Int #31) -#245 := (mod #181 #184) -#375 := (+ #50 #245) -#376 := (= #375 0::Int) -#51 := (mod #31 #20) -#372 := (* -1::Int #51) -#373 := (+ #50 #372) -#374 := (= #373 0::Int) -#219 := (>= #31 0::Int) -#212 := (<= #20 0::Int) -#319 := (or #212 #219) -#320 := (not #319) -#208 := (<= #31 0::Int) -#317 := (or #208 #212) -#318 := (not #317) -#323 := (or #318 #320) -#377 := (ite #323 #374 #376) -#371 := (= #50 0::Int) -#33 := (= #31 0::Int) -#378 := (ite #33 #371 #377) -#370 := (= #31 #50) -#34 := (= #20 0::Int) -#379 := (ite #34 #370 #378) -#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379) -#382 := (forall (vars (?v0 Int) (?v1 Int)) #379) -#889 := (iff #382 #886) -#887 := (iff #379 #379) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#251 := (* -1::Int #245) -#339 := (ite #323 #51 #251) -#342 := (ite #33 0::Int #339) -#345 := (ite #34 #31 #342) -#348 := (= #50 #345) -#351 := (forall (vars (?v0 Int) (?v1 Int)) #348) -#383 := (iff #351 #382) -#380 := (iff #348 #379) -#381 := [rewrite]: #380 -#384 := [quant-intro #381]: #383 -#220 := (not #219) -#213 := (not #212) -#223 := (and #213 #220) -#209 := (not #208) -#216 := (and #209 #213) -#226 := (or #216 #223) -#271 := (ite #226 #51 #251) -#274 := (ite #33 0::Int #271) -#277 := (ite #34 #31 #274) -#280 := (= #50 #277) -#283 := (forall (vars (?v0 Int) (?v1 Int)) #280) -#352 := (iff #283 #351) -#349 := (iff #280 #348) -#346 := (= #277 #345) -#343 := (= #274 #342) -#340 := (= #271 #339) -#324 := (iff #226 #323) -#321 := (iff #223 #320) -#322 := [rewrite]: #321 -#302 := (iff #216 #318) -#303 := [rewrite]: #302 -#325 := [monotonicity #303 #322]: #324 -#341 := [monotonicity #325]: #340 -#344 := [monotonicity #341]: #343 -#347 := [monotonicity #344]: #346 -#350 := [monotonicity #347]: #349 -#353 := [quant-intro #350]: #352 -#300 := (~ #283 #283) -#314 := (~ #280 #280) -#315 := [refl]: #314 -#301 := [nnf-pos #315]: #300 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#286 := (iff #58 #283) -#174 := (and #37 #39) -#177 := (or #38 #174) -#256 := (ite #177 #51 #251) -#165 := (= 0::Int #31) -#259 := (ite #165 0::Int #256) -#168 := (= 0::Int #20) -#262 := (ite #168 #31 #259) -#265 := (= #50 #262) -#268 := (forall (vars (?v0 Int) (?v1 Int)) #265) -#284 := (iff #268 #283) -#281 := (iff #265 #280) -#278 := (= #262 #277) -#275 := (= #259 #274) -#272 := (= #256 #271) -#227 := (iff #177 #226) -#224 := (iff #174 #223) -#221 := (iff #39 #220) -#222 := [rewrite]: #221 -#214 := (iff #37 #213) -#215 := [rewrite]: #214 -#225 := [monotonicity #215 #222]: #224 -#217 := (iff #38 #216) -#210 := (iff #36 #209) -#211 := [rewrite]: #210 -#218 := [monotonicity #211 #215]: #217 -#228 := [monotonicity #218 #225]: #227 -#273 := [monotonicity #228]: #272 -#202 := (iff #165 #33) -#203 := [rewrite]: #202 -#276 := [monotonicity #203 #273]: #275 -#204 := (iff #168 #34) -#205 := [rewrite]: #204 -#279 := [monotonicity #205 #276]: #278 -#282 := [monotonicity #279]: #281 -#285 := [quant-intro #282]: #284 -#269 := (iff #58 #268) -#266 := (iff #57 #265) -#263 := (= #56 #262) -#260 := (= #55 #259) -#257 := (= #54 #256) -#254 := (= #53 #251) -#248 := (- #245) -#252 := (= #248 #251) -#253 := [rewrite]: #252 -#249 := (= #53 #248) -#246 := (= #52 #245) -#185 := (= #44 #184) -#186 := [rewrite]: #185 -#182 := (= #43 #181) -#183 := [rewrite]: #182 -#247 := [monotonicity #183 #186]: #246 -#250 := [monotonicity #247]: #249 -#255 := [trans #250 #253]: #254 -#178 := (iff #41 #177) -#175 := (iff #40 #174) -#176 := [rewrite]: #175 -#179 := [monotonicity #176]: #178 -#258 := [monotonicity #179 #255]: #257 -#166 := (iff #33 #165) -#167 := [rewrite]: #166 -#261 := [monotonicity #167 #258]: #260 -#169 := (iff #34 #168) -#170 := [rewrite]: #169 -#264 := [monotonicity #170 #261]: #263 -#267 := [monotonicity #264]: #266 -#270 := [quant-intro #267]: #269 -#287 := [trans #270 #285]: #286 -#244 := [asserted]: #58 -#288 := [mp #244 #287]: #283 -#316 := [mp~ #288 #301]: #283 -#354 := [mp #316 #353]: #351 -#385 := [mp #354 #384]: #382 -#891 := [mp #385 #890]: #886 -#704 := (not #886) -#705 := (or #704 #799) -#812 := (* -1::Int 3::Int) -#813 := (mod #812 #812) -#814 := (+ #9 #813) -#809 := (= #814 0::Int) -#810 := (mod 3::Int 3::Int) -#815 := (* -1::Int #810) -#816 := (+ #9 #815) -#811 := (= #816 0::Int) -#817 := (>= 3::Int 0::Int) -#658 := (<= 3::Int 0::Int) -#659 := (or #658 #817) -#660 := (not #659) -#802 := (or #658 #658) -#803 := (not #802) -#804 := (or #803 #660) -#805 := (ite #804 #811 #809) -#800 := (= 3::Int 0::Int) -#806 := (ite #800 #799 #805) -#807 := (= 3::Int #9) -#801 := (ite #800 #807 #806) -#706 := (or #704 #801) -#710 := (iff #706 #705) -#712 := (iff #705 #705) -#717 := [rewrite]: #712 -#725 := (iff #801 #799) -#640 := (= #9 3::Int) -#724 := (ite false #640 #799) -#729 := (iff #724 #799) -#730 := [rewrite]: #729 -#727 := (iff #801 #724) -#722 := (iff #806 #799) -#738 := (ite false #799 #799) -#740 := (iff #738 #799) -#726 := [rewrite]: #740 -#739 := (iff #806 #738) -#736 := (iff #805 #799) -#1 := true -#743 := (ite true #799 #799) -#733 := (iff #743 #799) -#735 := [rewrite]: #733 -#754 := (iff #805 #743) -#752 := (iff #809 #799) -#750 := (= #814 #9) -#765 := (+ #9 0::Int) -#768 := (= #765 #9) -#764 := [rewrite]: #768 -#748 := (= #814 #765) -#746 := (= #813 0::Int) -#759 := -3::Int -#761 := (mod -3::Int -3::Int) -#744 := (= #761 0::Int) -#745 := [rewrite]: #744 -#741 := (= #813 #761) -#760 := (= #812 -3::Int) -#757 := [rewrite]: #760 -#742 := [monotonicity #757 #757]: #741 -#747 := [trans #742 #745]: #746 -#749 := [monotonicity #747]: #748 -#751 := [trans #749 #764]: #750 -#753 := [monotonicity #751]: #752 -#756 := (iff #811 #799) -#769 := (= #816 #9) -#766 := (= #816 #765) -#762 := (= #815 0::Int) -#775 := (* -1::Int 0::Int) -#771 := (= #775 0::Int) -#778 := [rewrite]: #771 -#776 := (= #815 #775) -#785 := (= #810 0::Int) -#774 := [rewrite]: #785 -#777 := [monotonicity #774]: #776 -#763 := [trans #777 #778]: #762 -#767 := [monotonicity #763]: #766 -#755 := [trans #767 #764]: #769 -#758 := [monotonicity #755]: #756 -#784 := (iff #804 true) -#773 := (or true false) -#782 := (iff #773 true) -#783 := [rewrite]: #782 -#770 := (iff #804 #773) -#779 := (iff #660 false) -#482 := (not true) -#841 := (iff #482 false) -#844 := [rewrite]: #841 -#788 := (iff #660 #482) -#698 := (iff #659 true) -#686 := (or false true) -#696 := (iff #686 true) -#697 := [rewrite]: #696 -#694 := (iff #659 #686) -#692 := (iff #817 true) -#693 := [rewrite]: #692 -#794 := (iff #658 false) -#796 := [rewrite]: #794 -#695 := [monotonicity #796 #693]: #694 -#791 := [trans #695 #697]: #698 -#792 := [monotonicity #791]: #788 -#781 := [trans #792 #844]: #779 -#675 := (iff #803 true) -#789 := (not false) -#787 := (iff #789 true) -#790 := [rewrite]: #787 -#691 := (iff #803 #789) -#682 := (iff #802 false) -#797 := (or false false) -#680 := (iff #797 false) -#681 := [rewrite]: #680 -#795 := (iff #802 #797) -#798 := [monotonicity #796 #796]: #795 -#641 := [trans #798 #681]: #682 -#786 := [monotonicity #641]: #691 -#690 := [trans #786 #790]: #675 -#772 := [monotonicity #690 #781]: #770 -#780 := [trans #772 #783]: #784 -#732 := [monotonicity #780 #758 #753]: #754 -#737 := [trans #732 #735]: #736 -#808 := (iff #800 false) -#637 := [rewrite]: #808 -#734 := [monotonicity #637 #737]: #739 -#723 := [trans #734 #726]: #722 -#639 := (iff #807 #640) -#793 := [rewrite]: #639 -#728 := [monotonicity #637 #793 #723]: #727 -#731 := [trans #728 #730]: #725 -#711 := [monotonicity #731]: #710 -#713 := [trans #711 #717]: #710 -#599 := [quant-inst #8 #8]: #706 -#714 := [mp #599 #713]: #705 -#718 := [unit-resolution #714 #891]: #799 -#719 := [monotonicity #718]: #13 -#14 := (not #13) -#78 := [asserted]: #14 -[unit-resolution #78 #719]: false -unsat -f05688f0b5f9f483f17f9e461ed5ff3d814bfbb3 452 0 -#2 := false -#10 := 3::Int -decl f4 :: (-> S2 Int) -decl f5 :: S2 -#8 := f5 -#9 := (f4 f5) -#547 := (mod #9 3::Int) -#741 := (>= #547 3::Int) -#742 := (not #741) -#1 := true -#76 := [true-axiom]: true -#729 := (or false #742) -#725 := [th-lemma arith]: #729 -#726 := [unit-resolution #725 #76]: #742 -#19 := 0::Int -#192 := -1::Int -#526 := (* -1::Int #547) -decl f3 :: (-> Int Int Int) -#11 := (f3 #9 3::Int) -#861 := (+ #11 #526) -#808 := (<= #861 0::Int) -#863 := (= #861 0::Int) -#561 := -3::Int -#542 := (* -1::Int #9) -#840 := (mod #542 -3::Int) -#551 := (+ #11 #840) -#554 := (= #551 0::Int) -#532 := (<= #9 0::Int) -#849 := (not #532) -#520 := (>= #9 0::Int) -#853 := (not #520) -#567 := (or #853 #849) -#548 := (ite #567 #863 #554) -#862 := (= #11 0::Int) -#868 := (= #9 0::Int) -#831 := (ite #868 #862 #548) -#20 := (:var 0 Int) -#31 := (:var 1 Int) -#50 := (f3 #31 #20) -#897 := (pattern #50) -#196 := (* -1::Int #20) -#193 := (* -1::Int #31) -#257 := (mod #193 #196) -#387 := (+ #50 #257) -#388 := (= #387 0::Int) -#51 := (mod #31 #20) -#384 := (* -1::Int #51) -#385 := (+ #50 #384) -#386 := (= #385 0::Int) -#231 := (>= #31 0::Int) -#224 := (<= #20 0::Int) -#331 := (or #224 #231) -#332 := (not #331) -#220 := (<= #31 0::Int) -#329 := (or #220 #224) -#330 := (not #329) -#335 := (or #330 #332) -#389 := (ite #335 #386 #388) -#383 := (= #50 0::Int) -#33 := (= #31 0::Int) -#390 := (ite #33 #383 #389) -#382 := (= #31 #50) -#34 := (= #20 0::Int) -#391 := (ite #34 #382 #390) -#898 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #897) #391) -#394 := (forall (vars (?v0 Int) (?v1 Int)) #391) -#901 := (iff #394 #898) -#899 := (iff #391 #391) -#900 := [refl]: #899 -#902 := [quant-intro #900]: #901 -#263 := (* -1::Int #257) -#351 := (ite #335 #51 #263) -#354 := (ite #33 0::Int #351) -#357 := (ite #34 #31 #354) -#360 := (= #50 #357) -#363 := (forall (vars (?v0 Int) (?v1 Int)) #360) -#395 := (iff #363 #394) -#392 := (iff #360 #391) -#393 := [rewrite]: #392 -#396 := [quant-intro #393]: #395 -#232 := (not #231) -#225 := (not #224) -#235 := (and #225 #232) -#221 := (not #220) -#228 := (and #221 #225) -#238 := (or #228 #235) -#283 := (ite #238 #51 #263) -#286 := (ite #33 0::Int #283) -#289 := (ite #34 #31 #286) -#292 := (= #50 #289) -#295 := (forall (vars (?v0 Int) (?v1 Int)) #292) -#364 := (iff #295 #363) -#361 := (iff #292 #360) -#358 := (= #289 #357) -#355 := (= #286 #354) -#352 := (= #283 #351) -#336 := (iff #238 #335) -#333 := (iff #235 #332) -#334 := [rewrite]: #333 -#314 := (iff #228 #330) -#315 := [rewrite]: #314 -#337 := [monotonicity #315 #334]: #336 -#353 := [monotonicity #337]: #352 -#356 := [monotonicity #353]: #355 -#359 := [monotonicity #356]: #358 -#362 := [monotonicity #359]: #361 -#365 := [quant-intro #362]: #364 -#312 := (~ #295 #295) -#326 := (~ #292 #292) -#327 := [refl]: #326 -#313 := [nnf-pos #327]: #312 -#44 := (- #20) -#43 := (- #31) -#52 := (mod #43 #44) -#53 := (- #52) -#37 := (< 0::Int #20) -#39 := (< #31 0::Int) -#40 := (and #39 #37) -#36 := (< 0::Int #31) -#38 := (and #36 #37) -#41 := (or #38 #40) -#54 := (ite #41 #51 #53) -#55 := (ite #33 0::Int #54) -#56 := (ite #34 #31 #55) -#57 := (= #50 #56) -#58 := (forall (vars (?v0 Int) (?v1 Int)) #57) -#298 := (iff #58 #295) -#186 := (and #37 #39) -#189 := (or #38 #186) -#268 := (ite #189 #51 #263) -#177 := (= 0::Int #31) -#271 := (ite #177 0::Int #268) -#180 := (= 0::Int #20) -#274 := (ite #180 #31 #271) -#277 := (= #50 #274) -#280 := (forall (vars (?v0 Int) (?v1 Int)) #277) -#296 := (iff #280 #295) -#293 := (iff #277 #292) -#290 := (= #274 #289) -#287 := (= #271 #286) -#284 := (= #268 #283) -#239 := (iff #189 #238) -#236 := (iff #186 #235) -#233 := (iff #39 #232) -#234 := [rewrite]: #233 -#226 := (iff #37 #225) -#227 := [rewrite]: #226 -#237 := [monotonicity #227 #234]: #236 -#229 := (iff #38 #228) -#222 := (iff #36 #221) -#223 := [rewrite]: #222 -#230 := [monotonicity #223 #227]: #229 -#240 := [monotonicity #230 #237]: #239 -#285 := [monotonicity #240]: #284 -#214 := (iff #177 #33) -#215 := [rewrite]: #214 -#288 := [monotonicity #215 #285]: #287 -#216 := (iff #180 #34) -#217 := [rewrite]: #216 -#291 := [monotonicity #217 #288]: #290 -#294 := [monotonicity #291]: #293 -#297 := [quant-intro #294]: #296 -#281 := (iff #58 #280) -#278 := (iff #57 #277) -#275 := (= #56 #274) -#272 := (= #55 #271) -#269 := (= #54 #268) -#266 := (= #53 #263) -#260 := (- #257) -#264 := (= #260 #263) -#265 := [rewrite]: #264 -#261 := (= #53 #260) -#258 := (= #52 #257) -#197 := (= #44 #196) -#198 := [rewrite]: #197 -#194 := (= #43 #193) -#195 := [rewrite]: #194 -#259 := [monotonicity #195 #198]: #258 -#262 := [monotonicity #259]: #261 -#267 := [trans #262 #265]: #266 -#190 := (iff #41 #189) -#187 := (iff #40 #186) -#188 := [rewrite]: #187 -#191 := [monotonicity #188]: #190 -#270 := [monotonicity #191 #267]: #269 -#178 := (iff #33 #177) -#179 := [rewrite]: #178 -#273 := [monotonicity #179 #270]: #272 -#181 := (iff #34 #180) -#182 := [rewrite]: #181 -#276 := [monotonicity #182 #273]: #275 -#279 := [monotonicity #276]: #278 -#282 := [quant-intro #279]: #281 -#299 := [trans #282 #297]: #298 -#256 := [asserted]: #58 -#300 := [mp #256 #299]: #295 -#328 := [mp~ #300 #313]: #295 -#366 := [mp #328 #365]: #363 -#397 := [mp #366 #396]: #394 -#903 := [mp #397 #902]: #898 -#829 := (not #898) -#670 := (or #829 #831) -#541 := (* -1::Int 3::Int) -#473 := (mod #542 #541) -#546 := (+ #11 #473) -#543 := (= #546 0::Int) -#650 := (<= 3::Int 0::Int) -#857 := (or #650 #520) -#531 := (not #857) -#864 := (or #532 #650) -#865 := (not #864) -#866 := (or #865 #531) -#867 := (ite #866 #863 #543) -#858 := (ite #868 #862 #867) -#518 := (= #9 #11) -#523 := (= 3::Int 0::Int) -#859 := (ite #523 #518 #858) -#671 := (or #829 #859) -#814 := (iff #671 #670) -#816 := (iff #670 #670) -#817 := [rewrite]: #816 -#828 := (iff #859 #831) -#825 := (ite false #518 #831) -#822 := (iff #825 #831) -#827 := [rewrite]: #822 -#826 := (iff #859 #825) -#835 := (iff #858 #831) -#830 := (iff #867 #548) -#832 := (iff #543 #554) -#552 := (= #546 #551) -#837 := (= #473 #840) -#562 := (= #541 -3::Int) -#836 := [rewrite]: #562 -#841 := [monotonicity #836]: #837 -#553 := [monotonicity #841]: #552 -#833 := [monotonicity #553]: #832 -#838 := (iff #866 #567) -#843 := (or #849 #853) -#568 := (iff #843 #567) -#461 := [rewrite]: #568 -#565 := (iff #866 #843) -#856 := (iff #531 #853) -#495 := (iff #857 #520) -#851 := (or false #520) -#854 := (iff #851 #520) -#494 := [rewrite]: #854 -#489 := (iff #857 #851) -#503 := (iff #650 false) -#844 := [rewrite]: #503 -#852 := [monotonicity #844]: #489 -#855 := [trans #852 #494]: #495 -#842 := [monotonicity #855]: #856 -#850 := (iff #865 #849) -#847 := (iff #864 #532) -#507 := (or #532 false) -#510 := (iff #507 #532) -#846 := [rewrite]: #510 -#508 := (iff #864 #507) -#509 := [monotonicity #844]: #508 -#848 := [trans #509 #846]: #847 -#845 := [monotonicity #848]: #850 -#566 := [monotonicity #845 #842]: #565 -#839 := [trans #566 #461]: #838 -#834 := [monotonicity #839 #833]: #830 -#824 := [monotonicity #834]: #835 -#519 := (iff #523 false) -#860 := [rewrite]: #519 -#821 := [monotonicity #860 #824]: #826 -#823 := [trans #821 #827]: #828 -#815 := [monotonicity #823]: #814 -#811 := [trans #815 #817]: #814 -#672 := [quant-inst #9 #10]: #671 -#812 := [mp #672 #811]: #670 -#727 := [unit-resolution #812 #903]: #831 -#705 := (not #868) -#704 := (not #831) -#714 := (or #704 #705) -#709 := (not #862) -#818 := (<= #11 0::Int) -#730 := (not #818) -#83 := (>= #11 3::Int) -#12 := (< #11 3::Int) -#13 := (not #12) -#90 := (iff #13 #83) -#81 := (not #83) -#85 := (not #81) -#88 := (iff #85 #83) +#18 := (- 1::Int) +#17 := (- 0::Int) +#19 := (mod #17 #18) +#20 := (- #19) +#16 := (mod 0::Int 1::Int) +#13 := (< 0::Int 1::Int) +#12 := (< 0::Int 0::Int) +#14 := (and #12 #13) +#15 := (or #14 #14) +#21 := (ite #15 #16 #20) +#11 := (= 0::Int 0::Int) +#22 := (ite #11 0::Int #21) +#10 := (= 1::Int 0::Int) +#23 := (ite #10 0::Int #22) +#24 := (f3 #23) +#26 := (= #24 #25) +#27 := (not #26) +#122 := (iff #27 false) +#1 := true +#117 := (not true) +#120 := (iff #117 false) +#121 := [rewrite]: #120 +#118 := (iff #27 #117) +#115 := (iff #26 true) +#110 := (= #25 #25) +#113 := (iff #110 true) +#114 := [rewrite]: #113 +#111 := (iff #26 #110) +#107 := (= #23 0::Int) +#102 := (ite false 0::Int 0::Int) +#105 := (= #102 0::Int) +#106 := [rewrite]: #105 +#103 := (= #23 #102) +#100 := (= #22 0::Int) +#95 := (ite true 0::Int 0::Int) +#98 := (= #95 0::Int) +#99 := [rewrite]: #98 +#96 := (= #22 #95) +#93 := (= #21 0::Int) +#88 := (ite #14 0::Int 0::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #21 #88) +#86 := (= #20 0::Int) +#72 := (= #17 0::Int) +#73 := [rewrite]: #72 +#84 := (= #20 #17) +#82 := (= #19 0::Int) +#74 := -1::Int +#77 := (mod 0::Int -1::Int) +#80 := (= #77 0::Int) +#81 := [rewrite]: #80 +#78 := (= #19 #77) +#75 := (= #18 -1::Int) +#76 := [rewrite]: #75 +#79 := [monotonicity #73 #76]: #78 +#83 := [trans #79 #81]: #82 +#85 := [monotonicity #83]: #84 +#87 := [trans #85 #73]: #86 +#70 := (= #16 0::Int) +#71 := [rewrite]: #70 +#68 := (iff #15 #14) +#69 := [rewrite]: #68 +#90 := [monotonicity #69 #71 #87]: #89 +#94 := [trans #90 #92]: #93 +#66 := (iff #11 true) +#67 := [rewrite]: #66 +#97 := [monotonicity #67 #94]: #96 +#101 := [trans #97 #99]: #100 +#64 := (iff #10 false) +#65 := [rewrite]: #64 +#104 := [monotonicity #65 #101]: #103 +#108 := [trans #104 #106]: #107 +#109 := [monotonicity #108]: #26 +#112 := [monotonicity #109]: #111 +#116 := [trans #112 #114]: #115 +#119 := [monotonicity #116]: #118 +#123 := [trans #119 #121]: #122 +#63 := [asserted]: #27 +[mp #63 #123]: false +unsat +a1075089dc52af4042f6a4669e72797d6209efe9 90 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#24 := (f3 0::Int) +#8 := 1::Int +#17 := (- 1::Int) +#18 := (mod #17 #17) +#19 := (- #18) +#16 := (mod 1::Int 1::Int) +#11 := (< 0::Int 1::Int) +#13 := (< 1::Int 0::Int) +#14 := (and #13 #11) +#12 := (and #11 #11) +#15 := (or #12 #14) +#20 := (ite #15 #16 #19) +#10 := (= 1::Int 0::Int) +#21 := (ite #10 0::Int #20) +#22 := (ite #10 1::Int #21) +#23 := (f3 #22) +#25 := (= #23 #24) +#26 := (not #25) +#126 := (iff #26 false) +#1 := true +#121 := (not true) +#124 := (iff #121 false) +#125 := [rewrite]: #124 +#122 := (iff #26 #121) +#119 := (iff #25 true) +#114 := (= #24 #24) +#117 := (iff #114 true) +#118 := [rewrite]: #117 +#115 := (iff #25 #114) +#111 := (= #22 0::Int) +#106 := (ite false 1::Int 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #22 #106) +#104 := (= #21 0::Int) +#99 := (ite false 0::Int 0::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #21 #99) +#97 := (= #20 0::Int) +#67 := (and #11 #13) +#70 := (or #11 #67) +#92 := (ite #70 0::Int 0::Int) +#95 := (= #92 0::Int) +#96 := [rewrite]: #95 +#93 := (= #20 #92) +#90 := (= #19 0::Int) +#85 := (- 0::Int) +#88 := (= #85 0::Int) #89 := [rewrite]: #88 -#86 := (iff #13 #85) -#82 := (iff #12 #81) -#84 := [rewrite]: #82 +#86 := (= #19 #85) +#83 := (= #18 0::Int) +#75 := -1::Int +#78 := (mod -1::Int -1::Int) +#81 := (= #78 0::Int) +#82 := [rewrite]: #81 +#79 := (= #18 #78) +#76 := (= #17 -1::Int) +#77 := [rewrite]: #76 +#80 := [monotonicity #77 #77]: #79 +#84 := [trans #80 #82]: #83 #87 := [monotonicity #84]: #86 #91 := [trans #87 #89]: #90 -#78 := [asserted]: #13 -#92 := [mp #78 #91]: #83 -#731 := (or #730 #81) -#732 := [th-lemma arith farkas 1 1]: #731 -#728 := [unit-resolution #732 #92]: #730 -#733 := (or #709 #818) -#713 := [th-lemma arith triangle-eq]: #733 -#659 := [unit-resolution #713 #728]: #709 -#698 := (or #704 #705 #862) -#706 := [def-axiom]: #698 -#695 := [unit-resolution #706 #659]: #714 -#719 := [unit-resolution #695 #727]: #705 -#707 := (or #704 #868 #548) -#708 := [def-axiom]: #707 -#720 := [unit-resolution #708 #719 #727]: #548 -decl f6 :: (-> Int S2) -#455 := (f6 #9) -#791 := (f4 #455) -#793 := (= #791 0::Int) -#699 := (not #793) -#700 := (iff #705 #699) -#690 := (iff #868 #793) -#686 := (iff #793 #868) -#696 := (= #791 #9) -#721 := (= #455 f5) -#540 := (= f5 #455) -#14 := (:var 0 S2) -#15 := (f4 #14) -#869 := (pattern #15) -#16 := (f6 #15) -#80 := (= #14 #16) -#870 := (forall (vars (?v0 S2)) (:pat #869) #80) -#95 := (forall (vars (?v0 S2)) #80) -#871 := (iff #95 #870) -#873 := (iff #870 #870) -#874 := [rewrite]: #873 -#872 := [rewrite]: #871 -#875 := [trans #872 #874]: #871 -#318 := (~ #95 #95) -#316 := (~ #80 #80) -#317 := [refl]: #316 -#319 := [nnf-pos #317]: #318 -#17 := (= #16 #14) -#18 := (forall (vars (?v0 S2)) #17) -#96 := (iff #18 #95) -#93 := (iff #17 #80) -#94 := [rewrite]: #93 -#97 := [quant-intro #94]: #96 -#79 := [asserted]: #18 -#100 := [mp #79 #97]: #95 -#304 := [mp~ #100 #319]: #95 -#876 := [mp #304 #875]: #870 -#533 := (not #870) -#544 := (or #533 #540) -#545 := [quant-inst #8]: #544 -#715 := [unit-resolution #545 #876]: #540 -#689 := [symm #715]: #721 -#655 := [monotonicity #689]: #696 -#688 := [monotonicity #655]: #686 -#697 := [symm #688]: #690 -#701 := [monotonicity #697]: #700 -#711 := [mp #719 #701]: #699 -#782 := (or #520 #793) -#22 := (f6 #20) -#877 := (pattern #22) -#117 := (>= #20 0::Int) -#23 := (f4 #22) -#28 := (= #23 0::Int) -#165 := (or #28 #117) -#884 := (forall (vars (?v0 Int)) (:pat #877) #165) -#170 := (forall (vars (?v0 Int)) #165) -#887 := (iff #170 #884) -#885 := (iff #165 #165) -#886 := [refl]: #885 -#888 := [quant-intro #886]: #887 -#308 := (~ #170 #170) -#320 := (~ #165 #165) -#321 := [refl]: #320 -#309 := [nnf-pos #321]: #308 -#27 := (< #20 0::Int) -#29 := (implies #27 #28) -#30 := (forall (vars (?v0 Int)) #29) -#173 := (iff #30 #170) -#136 := (= 0::Int #23) -#142 := (not #27) -#143 := (or #142 #136) -#148 := (forall (vars (?v0 Int)) #143) -#171 := (iff #148 #170) -#168 := (iff #143 #165) -#162 := (or #117 #28) -#166 := (iff #162 #165) -#167 := [rewrite]: #166 -#163 := (iff #143 #162) -#160 := (iff #136 #28) -#161 := [rewrite]: #160 -#158 := (iff #142 #117) -#118 := (not #117) -#153 := (not #118) -#156 := (iff #153 #117) -#157 := [rewrite]: #156 -#154 := (iff #142 #153) -#151 := (iff #27 #118) +#73 := (= #16 0::Int) +#74 := [rewrite]: #73 +#71 := (iff #15 #70) +#68 := (iff #14 #67) +#69 := [rewrite]: #68 +#65 := (iff #12 #11) +#66 := [rewrite]: #65 +#72 := [monotonicity #66 #69]: #71 +#94 := [monotonicity #72 #74 #91]: #93 +#98 := [trans #94 #96]: #97 +#63 := (iff #10 false) +#64 := [rewrite]: #63 +#101 := [monotonicity #64 #98]: #100 +#105 := [trans #101 #103]: #104 +#108 := [monotonicity #64 #105]: #107 +#112 := [trans #108 #110]: #111 +#113 := [monotonicity #112]: #25 +#116 := [monotonicity #113]: #115 +#120 := [trans #116 #118]: #119 +#123 := [monotonicity #120]: #122 +#127 := [trans #123 #125]: #126 +#62 := [asserted]: #26 +[mp #62 #127]: false +unsat +63c9d4e9b322eec0fd3bd7dd16ba42cd509506b7 97 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#28 := (f3 0::Int) +#8 := 1::Int +#21 := (- 1::Int) +#11 := 3::Int +#20 := (- 3::Int) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod 3::Int 1::Int) +#14 := (< 0::Int 1::Int) +#16 := (< 3::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 3::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= 3::Int 0::Int) +#25 := (ite #12 0::Int #24) +#10 := (= 1::Int 0::Int) +#26 := (ite #10 3::Int #25) +#27 := (f3 #26) +#29 := (= #27 #28) +#30 := (not #29) +#133 := (iff #30 false) +#1 := true +#128 := (not true) +#131 := (iff #128 false) +#132 := [rewrite]: #131 +#129 := (iff #30 #128) +#126 := (iff #29 true) +#121 := (= #28 #28) +#124 := (iff #121 true) +#125 := [rewrite]: #124 +#122 := (iff #29 #121) +#118 := (= #26 0::Int) +#113 := (ite false 3::Int 0::Int) +#116 := (= #113 0::Int) +#117 := [rewrite]: #116 +#114 := (= #26 #113) +#111 := (= #25 0::Int) +#106 := (ite false 0::Int 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #25 #106) +#104 := (= #24 0::Int) +#71 := (and #14 #16) +#74 := (or #15 #71) +#99 := (ite #74 0::Int 0::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #24 #99) +#97 := (= #23 0::Int) +#92 := (- 0::Int) +#95 := (= #92 0::Int) +#96 := [rewrite]: #95 +#93 := (= #23 #92) +#90 := (= #22 0::Int) +#82 := -1::Int +#79 := -3::Int +#85 := (mod -3::Int -1::Int) +#88 := (= #85 0::Int) +#89 := [rewrite]: #88 +#86 := (= #22 #85) +#83 := (= #21 -1::Int) +#84 := [rewrite]: #83 +#80 := (= #20 -3::Int) +#81 := [rewrite]: #80 +#87 := [monotonicity #81 #84]: #86 +#91 := [trans #87 #89]: #90 +#94 := [monotonicity #91]: #93 +#98 := [trans #94 #96]: #97 +#77 := (= #19 0::Int) +#78 := [rewrite]: #77 +#75 := (iff #18 #74) +#72 := (iff #17 #71) +#73 := [rewrite]: #72 +#76 := [monotonicity #73]: #75 +#101 := [monotonicity #76 #78 #98]: #100 +#105 := [trans #101 #103]: #104 +#69 := (iff #12 false) +#70 := [rewrite]: #69 +#108 := [monotonicity #70 #105]: #107 +#112 := [trans #108 #110]: #111 +#67 := (iff #10 false) +#68 := [rewrite]: #67 +#115 := [monotonicity #68 #112]: #114 +#119 := [trans #115 #117]: #118 +#120 := [monotonicity #119]: #29 +#123 := [monotonicity #120]: #122 +#127 := [trans #123 #125]: #126 +#130 := [monotonicity #127]: #129 +#134 := [trans #130 #132]: #133 +#66 := [asserted]: #30 +[mp #66 #134]: false +unsat +baacef3aba2d9193028d7d390c9e488f80e40513 170 0 +#2 := false +#9 := 0::Int +decl f4 :: (-> S2 Int) +decl f5 :: S2 +#11 := f5 +#12 := (f4 f5) +#144 := (>= #12 0::Int) +#145 := (not #144) +#131 := (<= #12 0::Int) +#132 := (not #131) +#13 := (= #12 0::Int) +#163 := (or #13 #132 #145) +#429 := (not #163) +#81 := -1::Int +#82 := (* -1::Int #12) +#87 := (mod #82 -1::Int) +#93 := (* -1::Int #87) +#168 := (ite #163 0::Int #93) +#341 := (= #168 0::Int) +#706 := (not #341) +decl f3 :: (-> Int S2) +#171 := (f3 #168) +#29 := (f3 0::Int) +#174 := (= #29 #171) +#698 := (= #171 #29) +#697 := [hypothesis]: #341 +#704 := [monotonicity #697]: #698 +#705 := [symm #704]: #174 +#177 := (not #174) +#8 := 1::Int +#22 := (- 1::Int) +#21 := (- #12) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod #12 1::Int) +#15 := (< 0::Int 1::Int) +#17 := (< #12 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #12) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#26 := (ite #13 0::Int #25) +#10 := (= 1::Int 0::Int) +#27 := (ite #10 #12 #26) +#28 := (f3 #27) +#30 := (= #28 #29) +#31 := (not #30) +#180 := (iff #31 #177) +#73 := (and #15 #17) +#76 := (or #16 #73) +#70 := (= 0::Int #12) +#104 := (or #70 #76) +#105 := (ite #104 0::Int #93) +#117 := (f3 #105) +#123 := (= #29 #117) +#128 := (not #123) +#178 := (iff #128 #177) +#175 := (iff #123 #174) +#172 := (= #117 #171) +#169 := (= #105 #168) +#166 := (iff #104 #163) +#157 := (or #132 #145) +#160 := (or #13 #157) +#164 := (iff #160 #163) +#165 := [rewrite]: #164 +#161 := (iff #104 #160) +#158 := (iff #76 #157) +#153 := (iff #73 #145) +#1 := true +#148 := (and true #145) +#151 := (iff #148 #145) #152 := [rewrite]: #151 -#155 := [monotonicity #152]: #154 -#159 := [trans #155 #157]: #158 -#164 := [monotonicity #159 #161]: #163 -#169 := [trans #164 #167]: #168 -#172 := [quant-intro #169]: #171 -#149 := (iff #30 #148) -#146 := (iff #29 #143) -#139 := (implies #27 #136) -#144 := (iff #139 #143) -#145 := [rewrite]: #144 -#140 := (iff #29 #139) -#137 := (iff #28 #136) -#138 := [rewrite]: #137 -#141 := [monotonicity #138]: #140 -#147 := [trans #141 #145]: #146 -#150 := [quant-intro #147]: #149 -#174 := [trans #150 #172]: #173 -#135 := [asserted]: #30 -#175 := [mp #135 #174]: #170 -#322 := [mp~ #175 #309]: #170 -#889 := [mp #322 #888]: #884 -#795 := (not #884) -#796 := (or #795 #520 #793) -#785 := (or #793 #520) -#792 := (or #795 #785) -#790 := (iff #792 #796) -#786 := (or #795 #782) -#789 := (iff #786 #796) -#783 := [rewrite]: #789 -#787 := (iff #792 #786) -#784 := (iff #785 #782) -#794 := [rewrite]: #784 -#788 := [monotonicity #794]: #787 -#774 := [trans #788 #783]: #790 -#797 := [quant-inst #9]: #792 -#775 := [mp #797 #774]: #796 -#691 := [unit-resolution #775 #889]: #782 -#712 := [unit-resolution #691 #711]: #520 -#667 := (or #868 #849 #853) -#668 := [th-lemma arith triangle-eq]: #667 -#673 := [unit-resolution #668 #719]: #843 -#674 := [unit-resolution #673 #712]: #849 -#649 := (or #567 #532) -#651 := [def-axiom]: #649 -#675 := [unit-resolution #651 #674]: #567 -#652 := (not #567) -#692 := (not #548) -#693 := (or #692 #652 #863) -#694 := [def-axiom]: #693 -#676 := [unit-resolution #694 #675 #720]: #863 -#703 := (not #863) -#677 := (or #703 #808) -#678 := [th-lemma arith triangle-eq]: #677 -#679 := [unit-resolution #678 #676]: #808 -[th-lemma arith farkas -1 1 1 #92 #679 #726]: false -unsat -318d5be50bbd50da7b7b7962a11c2c98ae8be85c 662 0 -#2 := false -#10 := 3::Int -decl f5 :: (-> S2 Int) -decl f6 :: S2 -#8 := f6 -#9 := (f5 f6) -#883 := (mod #9 3::Int) -#706 := (>= #883 3::Int) -#707 := (not #706) -#1 := true -#79 := [true-axiom]: true -#666 := (or false #707) -#667 := [th-lemma arith]: #666 -#669 := [unit-resolution #667 #79]: #707 -#104 := (>= #9 3::Int) -#102 := (not #104) -#619 := [hypothesis]: #102 -#22 := 0::Int -#220 := -1::Int -#881 := (* -1::Int #883) -decl f4 :: (-> Int Int Int) -#11 := (f4 #9 3::Int) -#884 := (+ #11 #881) -#824 := (<= #884 0::Int) -#870 := (= #884 0::Int) -#864 := (= #9 0::Int) -#809 := (not #864) -decl f3 :: (-> Int S2) -#12 := (f3 #11) -#82 := (= f6 #12) -#572 := (not #82) -#574 := (or #572 #104) -#113 := (iff #82 #104) -#14 := (< #9 3::Int) -#13 := (= #12 f6) -#15 := (iff #13 #14) -#16 := (not #15) -#116 := (iff #16 #113) -#96 := (not #14) -#97 := (iff #82 #96) -#114 := (iff #97 #113) -#111 := (iff #96 #104) -#106 := (not #102) -#109 := (iff #106 #104) -#110 := [rewrite]: #109 -#107 := (iff #96 #106) -#103 := (iff #14 #102) -#105 := [rewrite]: #103 -#108 := [monotonicity #105]: #107 -#112 := [trans #108 #110]: #111 -#115 := [monotonicity #112]: #114 -#100 := (iff #16 #97) -#88 := (iff #14 #82) -#93 := (not #88) -#98 := (iff #93 #97) +#149 := (iff #73 #148) +#146 := (iff #17 #145) +#147 := [rewrite]: #146 +#135 := (iff #15 true) +#136 := [rewrite]: #135 +#150 := [monotonicity #136 #147]: #149 +#154 := [trans #150 #152]: #153 +#142 := (iff #16 #132) +#137 := (and #132 true) +#140 := (iff #137 #132) +#141 := [rewrite]: #140 +#138 := (iff #16 #137) +#133 := (iff #14 #132) +#134 := [rewrite]: #133 +#139 := [monotonicity #134 #136]: #138 +#143 := [trans #139 #141]: #142 +#159 := [monotonicity #143 #154]: #158 +#155 := (iff #70 #13) +#156 := [rewrite]: #155 +#162 := [monotonicity #156 #159]: #161 +#167 := [trans #162 #165]: #166 +#170 := [monotonicity #167]: #169 +#173 := [monotonicity #170]: #172 +#176 := [monotonicity #173]: #175 +#179 := [monotonicity #176]: #178 +#129 := (iff #31 #128) +#126 := (iff #30 #123) +#120 := (= #117 #29) +#124 := (iff #120 #123) +#125 := [rewrite]: #124 +#121 := (iff #30 #120) +#118 := (= #28 #117) +#115 := (= #27 #105) +#110 := (ite false #12 #105) +#113 := (= #110 #105) +#114 := [rewrite]: #113 +#111 := (= #27 #110) +#108 := (= #26 #105) +#98 := (ite #76 0::Int #93) +#101 := (ite #70 0::Int #98) +#106 := (= #101 #105) +#107 := [rewrite]: #106 +#102 := (= #26 #101) +#99 := (= #25 #98) +#96 := (= #24 #93) +#90 := (- #87) +#94 := (= #90 #93) +#95 := [rewrite]: #94 +#91 := (= #24 #90) +#88 := (= #23 #87) +#85 := (= #22 -1::Int) +#86 := [rewrite]: #85 +#83 := (= #21 #82) +#84 := [rewrite]: #83 +#89 := [monotonicity #84 #86]: #88 +#92 := [monotonicity #89]: #91 +#97 := [trans #92 #95]: #96 +#79 := (= #20 0::Int) +#80 := [rewrite]: #79 +#77 := (iff #19 #76) +#74 := (iff #18 #73) +#75 := [rewrite]: #74 +#78 := [monotonicity #75]: #77 +#100 := [monotonicity #78 #80 #97]: #99 +#71 := (iff #13 #70) +#72 := [rewrite]: #71 +#103 := [monotonicity #72 #100]: #102 +#109 := [trans #103 #107]: #108 +#68 := (iff #10 false) +#69 := [rewrite]: #68 +#112 := [monotonicity #69 #109]: #111 +#116 := [trans #112 #114]: #115 +#119 := [monotonicity #116]: #118 +#122 := [monotonicity #119]: #121 +#127 := [trans #122 #125]: #126 +#130 := [monotonicity #127]: #129 +#181 := [trans #130 #179]: #180 +#67 := [asserted]: #31 +#182 := [mp #67 #181]: #177 +#699 := [unit-resolution #182 #705]: false +#535 := [lemma #699]: #706 +#747 := (or #429 #341) +#749 := [def-axiom]: #747 +#658 := [unit-resolution #749 #535]: #429 +#431 := (or #163 #144) +#432 := [def-axiom]: #431 +#655 := [unit-resolution #432 #658]: #144 +#419 := (or #163 #131) +#430 := [def-axiom]: #419 +#659 := [unit-resolution #430 #658]: #131 +#342 := (not #13) +#427 := (or #163 #342) +#428 := [def-axiom]: #427 +#639 := [unit-resolution #428 #658]: #342 +#640 := [th-lemma arith triangle-eq]: #163 +[unit-resolution #640 #639 #659 #655]: false +unsat +52940ae1c337d10436c752f28c341997638bfaa6 86 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#25 := (f3 0::Int) +#8 := 3::Int +#18 := (- 3::Int) +#17 := (- 0::Int) +#19 := (mod #17 #18) +#20 := (- #19) +#16 := (mod 0::Int 3::Int) +#13 := (< 0::Int 3::Int) +#12 := (< 0::Int 0::Int) +#14 := (and #12 #13) +#15 := (or #14 #14) +#21 := (ite #15 #16 #20) +#11 := (= 0::Int 0::Int) +#22 := (ite #11 0::Int #21) +#10 := (= 3::Int 0::Int) +#23 := (ite #10 0::Int #22) +#24 := (f3 #23) +#26 := (= #24 #25) +#27 := (not #26) +#122 := (iff #27 false) +#1 := true +#117 := (not true) +#120 := (iff #117 false) +#121 := [rewrite]: #120 +#118 := (iff #27 #117) +#115 := (iff #26 true) +#110 := (= #25 #25) +#113 := (iff #110 true) +#114 := [rewrite]: #113 +#111 := (iff #26 #110) +#107 := (= #23 0::Int) +#102 := (ite false 0::Int 0::Int) +#105 := (= #102 0::Int) +#106 := [rewrite]: #105 +#103 := (= #23 #102) +#100 := (= #22 0::Int) +#95 := (ite true 0::Int 0::Int) +#98 := (= #95 0::Int) #99 := [rewrite]: #98 -#94 := (iff #16 #93) -#91 := (iff #15 #88) -#85 := (iff #82 #14) -#89 := (iff #85 #88) +#96 := (= #22 #95) +#93 := (= #21 0::Int) +#88 := (ite #14 0::Int 0::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #21 #88) +#86 := (= #20 0::Int) +#72 := (= #17 0::Int) +#73 := [rewrite]: #72 +#84 := (= #20 #17) +#82 := (= #19 0::Int) +#74 := -3::Int +#77 := (mod 0::Int -3::Int) +#80 := (= #77 0::Int) +#81 := [rewrite]: #80 +#78 := (= #19 #77) +#75 := (= #18 -3::Int) +#76 := [rewrite]: #75 +#79 := [monotonicity #73 #76]: #78 +#83 := [trans #79 #81]: #82 +#85 := [monotonicity #83]: #84 +#87 := [trans #85 #73]: #86 +#70 := (= #16 0::Int) +#71 := [rewrite]: #70 +#68 := (iff #15 #14) +#69 := [rewrite]: #68 +#90 := [monotonicity #69 #71 #87]: #89 +#94 := [trans #90 #92]: #93 +#66 := (iff #11 true) +#67 := [rewrite]: #66 +#97 := [monotonicity #67 #94]: #96 +#101 := [trans #97 #99]: #100 +#64 := (iff #10 false) +#65 := [rewrite]: #64 +#104 := [monotonicity #65 #101]: #103 +#108 := [trans #104 #106]: #107 +#109 := [monotonicity #108]: #26 +#112 := [monotonicity #109]: #111 +#116 := [trans #112 #114]: #115 +#119 := [monotonicity #116]: #118 +#123 := [trans #119 #121]: #122 +#63 := [asserted]: #27 +[mp #63 #123]: false +unsat +eea72e0b08b81263eac13f5c3a2599d4713d6590 145 0 +#2 := false +decl f3 :: (-> Int S2) +#11 := 1::Int +#28 := (f3 1::Int) +#8 := 3::Int +#21 := (- 3::Int) +#20 := (- 1::Int) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod 1::Int 3::Int) +#9 := 0::Int +#14 := (< 0::Int 3::Int) +#16 := (< 1::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 1::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= 1::Int 0::Int) +#25 := (ite #12 0::Int #24) +#10 := (= 3::Int 0::Int) +#26 := (ite #10 1::Int #25) +#27 := (f3 #26) +#29 := (= #27 #28) +#30 := (not #29) +#181 := (iff #30 false) +#96 := -2::Int +#71 := (and #14 #16) +#74 := (or #15 #71) +#101 := (ite #74 1::Int -2::Int) +#118 := (f3 #101) +#124 := (= #28 #118) +#129 := (not #124) +#179 := (iff #129 false) +#1 := true +#174 := (not true) +#177 := (iff #174 false) +#178 := [rewrite]: #177 +#175 := (iff #129 #174) +#172 := (iff #124 true) +#167 := (= #28 #28) +#170 := (iff #167 true) +#171 := [rewrite]: #170 +#168 := (iff #124 #167) +#121 := (= #118 #28) +#164 := (= #101 1::Int) +#159 := (ite true 1::Int -2::Int) +#162 := (= #159 1::Int) +#163 := [rewrite]: #162 +#160 := (= #101 #159) +#157 := (iff #74 true) +#152 := (or true false) +#155 := (iff #152 true) +#156 := [rewrite]: #155 +#153 := (iff #74 #152) +#150 := (iff #71 false) +#145 := (and true false) +#148 := (iff #145 false) +#149 := [rewrite]: #148 +#146 := (iff #71 #145) +#143 := (iff #16 false) +#144 := [rewrite]: #143 +#134 := (iff #14 true) +#135 := [rewrite]: #134 +#147 := [monotonicity #135 #144]: #146 +#151 := [trans #147 #149]: #150 +#141 := (iff #15 true) +#136 := (and true true) +#139 := (iff #136 true) +#140 := [rewrite]: #139 +#137 := (iff #15 #136) +#132 := (iff #13 true) +#133 := [rewrite]: #132 +#138 := [monotonicity #133 #135]: #137 +#142 := [trans #138 #140]: #141 +#154 := [monotonicity #142 #151]: #153 +#158 := [trans #154 #156]: #157 +#161 := [monotonicity #158]: #160 +#165 := [trans #161 #163]: #164 +#166 := [monotonicity #165]: #121 +#169 := [monotonicity #166]: #168 +#173 := [trans #169 #171]: #172 +#176 := [monotonicity #173]: #175 +#180 := [trans #176 #178]: #179 +#130 := (iff #30 #129) +#127 := (iff #29 #124) +#125 := (iff #121 #124) +#126 := [rewrite]: #125 +#122 := (iff #29 #121) +#119 := (= #27 #118) +#116 := (= #26 #101) +#111 := (ite false 1::Int #101) +#114 := (= #111 #101) +#115 := [rewrite]: #114 +#112 := (= #26 #111) +#109 := (= #25 #101) +#104 := (ite false 0::Int #101) +#107 := (= #104 #101) +#108 := [rewrite]: #107 +#105 := (= #25 #104) +#102 := (= #24 #101) +#99 := (= #23 -2::Int) +#88 := 2::Int +#93 := (- 2::Int) +#97 := (= #93 -2::Int) +#98 := [rewrite]: #97 +#94 := (= #23 #93) +#91 := (= #22 2::Int) +#82 := -3::Int +#79 := -1::Int +#85 := (mod -1::Int -3::Int) +#89 := (= #85 2::Int) #90 := [rewrite]: #89 -#86 := (iff #15 #85) -#83 := (iff #13 #82) +#86 := (= #22 #85) +#83 := (= #21 -3::Int) #84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 +#80 := (= #20 -1::Int) +#81 := [rewrite]: #80 +#87 := [monotonicity #81 #84]: #86 #92 := [trans #87 #90]: #91 #95 := [monotonicity #92]: #94 -#101 := [trans #95 #99]: #100 -#117 := [trans #101 #115]: #116 -#81 := [asserted]: #16 -#118 := [mp #81 #117]: #113 -#483 := (not #113) -#573 := (or #572 #104 #483) -#501 := [def-axiom]: #573 -#571 := [unit-resolution #501 #118]: #574 -#636 := [unit-resolution #571 #619]: #572 -#753 := (or #809 #82) -#575 := (f3 #9) -#750 := (= #575 #12) -#746 := (= #12 #575) -#771 := (= #11 #9) -#770 := (= 0::Int #9) -#764 := [hypothesis]: #864 -#765 := [symm #764]: #770 -#590 := (= #11 0::Int) -#767 := (or #809 #590) -#840 := -3::Int -#880 := (* -1::Int #9) -#841 := (mod #880 -3::Int) -#679 := (+ #11 #841) -#834 := (= #679 0::Int) -#871 := (>= #9 0::Int) -#700 := (not #871) -#596 := (<= #9 0::Int) -#853 := (not #596) -#844 := (or #853 #700) -#835 := (ite #844 #870 #834) -#721 := (ite #864 #590 #835) -#23 := (:var 0 Int) -#34 := (:var 1 Int) -#53 := (f4 #34 #23) -#925 := (pattern #53) -#224 := (* -1::Int #23) -#221 := (* -1::Int #34) -#285 := (mod #221 #224) -#415 := (+ #53 #285) -#416 := (= #415 0::Int) -#54 := (mod #34 #23) -#412 := (* -1::Int #54) -#413 := (+ #53 #412) -#414 := (= #413 0::Int) -#259 := (>= #34 0::Int) -#252 := (<= #23 0::Int) -#359 := (or #252 #259) -#360 := (not #359) -#248 := (<= #34 0::Int) -#357 := (or #248 #252) -#358 := (not #357) -#363 := (or #358 #360) -#417 := (ite #363 #414 #416) -#411 := (= #53 0::Int) -#36 := (= #34 0::Int) -#418 := (ite #36 #411 #417) -#410 := (= #34 #53) -#37 := (= #23 0::Int) -#419 := (ite #37 #410 #418) -#926 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #925) #419) -#422 := (forall (vars (?v0 Int) (?v1 Int)) #419) -#929 := (iff #422 #926) -#927 := (iff #419 #419) -#928 := [refl]: #927 -#930 := [quant-intro #928]: #929 -#291 := (* -1::Int #285) -#379 := (ite #363 #54 #291) -#382 := (ite #36 0::Int #379) -#385 := (ite #37 #34 #382) -#388 := (= #53 #385) -#391 := (forall (vars (?v0 Int) (?v1 Int)) #388) -#423 := (iff #391 #422) -#420 := (iff #388 #419) -#421 := [rewrite]: #420 -#424 := [quant-intro #421]: #423 -#260 := (not #259) -#253 := (not #252) -#263 := (and #253 #260) -#249 := (not #248) -#256 := (and #249 #253) -#266 := (or #256 #263) -#311 := (ite #266 #54 #291) -#314 := (ite #36 0::Int #311) -#317 := (ite #37 #34 #314) -#320 := (= #53 #317) -#323 := (forall (vars (?v0 Int) (?v1 Int)) #320) -#392 := (iff #323 #391) -#389 := (iff #320 #388) -#386 := (= #317 #385) -#383 := (= #314 #382) -#380 := (= #311 #379) -#364 := (iff #266 #363) -#361 := (iff #263 #360) -#362 := [rewrite]: #361 -#342 := (iff #256 #358) -#343 := [rewrite]: #342 -#365 := [monotonicity #343 #362]: #364 -#381 := [monotonicity #365]: #380 -#384 := [monotonicity #381]: #383 -#387 := [monotonicity #384]: #386 -#390 := [monotonicity #387]: #389 -#393 := [quant-intro #390]: #392 -#340 := (~ #323 #323) -#354 := (~ #320 #320) -#355 := [refl]: #354 -#341 := [nnf-pos #355]: #340 -#47 := (- #23) -#46 := (- #34) -#55 := (mod #46 #47) -#56 := (- #55) -#40 := (< 0::Int #23) -#42 := (< #34 0::Int) -#43 := (and #42 #40) -#39 := (< 0::Int #34) -#41 := (and #39 #40) -#44 := (or #41 #43) -#57 := (ite #44 #54 #56) -#58 := (ite #36 0::Int #57) -#59 := (ite #37 #34 #58) -#60 := (= #53 #59) -#61 := (forall (vars (?v0 Int) (?v1 Int)) #60) -#326 := (iff #61 #323) -#214 := (and #40 #42) -#217 := (or #41 #214) -#296 := (ite #217 #54 #291) -#205 := (= 0::Int #34) -#299 := (ite #205 0::Int #296) -#208 := (= 0::Int #23) -#302 := (ite #208 #34 #299) -#305 := (= #53 #302) -#308 := (forall (vars (?v0 Int) (?v1 Int)) #305) -#324 := (iff #308 #323) -#321 := (iff #305 #320) -#318 := (= #302 #317) -#315 := (= #299 #314) -#312 := (= #296 #311) -#267 := (iff #217 #266) -#264 := (iff #214 #263) -#261 := (iff #42 #260) -#262 := [rewrite]: #261 -#254 := (iff #40 #253) -#255 := [rewrite]: #254 -#265 := [monotonicity #255 #262]: #264 -#257 := (iff #41 #256) -#250 := (iff #39 #249) +#100 := [trans #95 #98]: #99 +#77 := (= #19 1::Int) +#78 := [rewrite]: #77 +#75 := (iff #18 #74) +#72 := (iff #17 #71) +#73 := [rewrite]: #72 +#76 := [monotonicity #73]: #75 +#103 := [monotonicity #76 #78 #100]: #102 +#69 := (iff #12 false) +#70 := [rewrite]: #69 +#106 := [monotonicity #70 #103]: #105 +#110 := [trans #106 #108]: #109 +#67 := (iff #10 false) +#68 := [rewrite]: #67 +#113 := [monotonicity #68 #110]: #112 +#117 := [trans #113 #115]: #116 +#120 := [monotonicity #117]: #119 +#123 := [monotonicity #120]: #122 +#128 := [trans #123 #126]: #127 +#131 := [monotonicity #128]: #130 +#182 := [trans #131 #180]: #181 +#66 := [asserted]: #30 +[mp #66 #182]: false +unsat +3921706a8683868f2784292da2026eadf56bd286 90 0 +#2 := false +decl f3 :: (-> Int S2) +#9 := 0::Int +#24 := (f3 0::Int) +#8 := 3::Int +#17 := (- 3::Int) +#18 := (mod #17 #17) +#19 := (- #18) +#16 := (mod 3::Int 3::Int) +#11 := (< 0::Int 3::Int) +#13 := (< 3::Int 0::Int) +#14 := (and #13 #11) +#12 := (and #11 #11) +#15 := (or #12 #14) +#20 := (ite #15 #16 #19) +#10 := (= 3::Int 0::Int) +#21 := (ite #10 0::Int #20) +#22 := (ite #10 3::Int #21) +#23 := (f3 #22) +#25 := (= #23 #24) +#26 := (not #25) +#126 := (iff #26 false) +#1 := true +#121 := (not true) +#124 := (iff #121 false) +#125 := [rewrite]: #124 +#122 := (iff #26 #121) +#119 := (iff #25 true) +#114 := (= #24 #24) +#117 := (iff #114 true) +#118 := [rewrite]: #117 +#115 := (iff #25 #114) +#111 := (= #22 0::Int) +#106 := (ite false 3::Int 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #22 #106) +#104 := (= #21 0::Int) +#99 := (ite false 0::Int 0::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #21 #99) +#97 := (= #20 0::Int) +#67 := (and #11 #13) +#70 := (or #11 #67) +#92 := (ite #70 0::Int 0::Int) +#95 := (= #92 0::Int) +#96 := [rewrite]: #95 +#93 := (= #20 #92) +#90 := (= #19 0::Int) +#85 := (- 0::Int) +#88 := (= #85 0::Int) +#89 := [rewrite]: #88 +#86 := (= #19 #85) +#83 := (= #18 0::Int) +#75 := -3::Int +#78 := (mod -3::Int -3::Int) +#81 := (= #78 0::Int) +#82 := [rewrite]: #81 +#79 := (= #18 #78) +#76 := (= #17 -3::Int) +#77 := [rewrite]: #76 +#80 := [monotonicity #77 #77]: #79 +#84 := [trans #80 #82]: #83 +#87 := [monotonicity #84]: #86 +#91 := [trans #87 #89]: #90 +#73 := (= #16 0::Int) +#74 := [rewrite]: #73 +#71 := (iff #15 #70) +#68 := (iff #14 #67) +#69 := [rewrite]: #68 +#65 := (iff #12 #11) +#66 := [rewrite]: #65 +#72 := [monotonicity #66 #69]: #71 +#94 := [monotonicity #72 #74 #91]: #93 +#98 := [trans #94 #96]: #97 +#63 := (iff #10 false) +#64 := [rewrite]: #63 +#101 := [monotonicity #64 #98]: #100 +#105 := [trans #101 #103]: #104 +#108 := [monotonicity #64 #105]: #107 +#112 := [trans #108 #110]: #111 +#113 := [monotonicity #112]: #25 +#116 := [monotonicity #113]: #115 +#120 := [trans #116 #118]: #119 +#123 := [monotonicity #120]: #122 +#127 := [trans #123 #125]: #126 +#62 := [asserted]: #26 +[mp #62 #127]: false +unsat +514d90db39c84cc7bf19d9cbc0eb437cde0db30b 305 0 +#2 := false +#8 := 3::Int +decl f3 :: (-> S2 Int) +decl f4 :: S2 +#11 := f4 +#12 := (f3 f4) +#20 := (mod #12 3::Int) +#690 := (>= #20 3::Int) +#691 := (not #690) +#1 := true +#63 := [true-axiom]: true +#525 := (or false #691) +#673 := [th-lemma arith]: #525 +#575 := [unit-resolution #673 #63]: #691 +#9 := 0::Int +#81 := -3::Int +#77 := -1::Int +#78 := (* -1::Int #12) +#84 := (mod #78 -3::Int) +#90 := (* -1::Int #84) +#129 := (>= #12 0::Int) +#130 := (not #129) +#116 := (<= #12 0::Int) +#117 := (not #116) +#140 := (or #117 #130) +#143 := (ite #140 #20 #90) +#13 := (= #12 0::Int) +#146 := (ite #13 0::Int #143) +#682 := (* -1::Int #146) +#564 := (+ #20 #682) +#566 := (>= #564 0::Int) +#679 := (= #20 #146) +#412 := (= #143 #146) +#392 := (not #13) +#326 := (= #146 0::Int) +#727 := (not #326) +#717 := (<= #146 0::Int) +#361 := (not #717) +#153 := (>= #146 3::Int) +#22 := (- 3::Int) +#21 := (- #12) +#23 := (mod #21 #22) +#24 := (- #23) +#15 := (< 0::Int 3::Int) +#17 := (< #12 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #12) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#26 := (ite #13 0::Int #25) +#10 := (= 3::Int 0::Int) +#27 := (ite #10 #12 #26) +#28 := (< #27 3::Int) +#29 := (not #28) +#165 := (iff #29 #153) +#71 := (and #15 #17) +#74 := (or #16 #71) +#95 := (ite #74 #20 #90) +#68 := (= 0::Int #12) +#98 := (ite #68 0::Int #95) +#108 := (< #98 3::Int) +#111 := (not #108) +#163 := (iff #111 #153) +#152 := (not #153) +#158 := (not #152) +#161 := (iff #158 #153) +#162 := [rewrite]: #161 +#159 := (iff #111 #158) +#156 := (iff #108 #152) +#149 := (< #146 3::Int) +#154 := (iff #149 #152) +#155 := [rewrite]: #154 +#150 := (iff #108 #149) +#147 := (= #98 #146) +#144 := (= #95 #143) +#141 := (iff #74 #140) +#138 := (iff #71 #130) +#133 := (and true #130) +#136 := (iff #133 #130) +#137 := [rewrite]: #136 +#134 := (iff #71 #133) +#131 := (iff #17 #130) +#132 := [rewrite]: #131 +#120 := (iff #15 true) +#121 := [rewrite]: #120 +#135 := [monotonicity #121 #132]: #134 +#139 := [trans #135 #137]: #138 +#127 := (iff #16 #117) +#122 := (and #117 true) +#125 := (iff #122 #117) +#126 := [rewrite]: #125 +#123 := (iff #16 #122) +#118 := (iff #14 #117) +#119 := [rewrite]: #118 +#124 := [monotonicity #119 #121]: #123 +#128 := [trans #124 #126]: #127 +#142 := [monotonicity #128 #139]: #141 +#145 := [monotonicity #142]: #144 +#114 := (iff #68 #13) +#115 := [rewrite]: #114 +#148 := [monotonicity #115 #145]: #147 +#151 := [monotonicity #148]: #150 +#157 := [trans #151 #155]: #156 +#160 := [monotonicity #157]: #159 +#164 := [trans #160 #162]: #163 +#112 := (iff #29 #111) +#109 := (iff #28 #108) +#106 := (= #27 #98) +#101 := (ite false #12 #98) +#104 := (= #101 #98) +#105 := [rewrite]: #104 +#102 := (= #27 #101) +#99 := (= #26 #98) +#96 := (= #25 #95) +#93 := (= #24 #90) +#87 := (- #84) +#91 := (= #87 #90) +#92 := [rewrite]: #91 +#88 := (= #24 #87) +#85 := (= #23 #84) +#82 := (= #22 -3::Int) +#83 := [rewrite]: #82 +#79 := (= #21 #78) +#80 := [rewrite]: #79 +#86 := [monotonicity #80 #83]: #85 +#89 := [monotonicity #86]: #88 +#94 := [trans #89 #92]: #93 +#75 := (iff #19 #74) +#72 := (iff #18 #71) +#73 := [rewrite]: #72 +#76 := [monotonicity #73]: #75 +#97 := [monotonicity #76 #94]: #96 +#69 := (iff #13 #68) +#70 := [rewrite]: #69 +#100 := [monotonicity #70 #97]: #99 +#66 := (iff #10 false) +#67 := [rewrite]: #66 +#103 := [monotonicity #67 #100]: #102 +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107]: #109 +#113 := [monotonicity #110]: #112 +#166 := [trans #113 #164]: #165 +#65 := [asserted]: #29 +#167 := [mp #65 #166]: #153 +#724 := (or #361 #152) +#726 := [th-lemma arith farkas 1 1]: #724 +#366 := [unit-resolution #726 #167]: #361 +#367 := [hypothesis]: #326 +#725 := (or #727 #717) +#728 := [th-lemma arith triangle-eq]: #725 +#714 := [unit-resolution #728 #367 #366]: false +#715 := [lemma #714]: #727 +#522 := (or #392 #326) +#729 := [def-axiom]: #522 +#670 := [unit-resolution #729 #715]: #392 +#403 := (or #13 #412) +#404 := [def-axiom]: #403 +#671 := [unit-resolution #404 #670]: #412 +#327 := (= #20 #143) +decl f5 :: (-> Int S2) +#736 := (f5 #12) +#738 := (f3 #736) +#739 := (= #738 0::Int) +#581 := (not #739) +#582 := (iff #392 #581) +#579 := (iff #13 #739) +#570 := (iff #739 #13) +#576 := (= #738 #12) +#559 := (= #736 f4) +#737 := (= f4 #736) +#30 := (:var 0 S2) +#31 := (f3 #30) +#741 := (pattern #31) +#32 := (f5 #31) +#169 := (= #30 #32) +#742 := (forall (vars (?v0 S2)) (:pat #741) #169) +#172 := (forall (vars (?v0 S2)) #169) +#743 := (iff #172 #742) +#745 := (iff #742 #742) +#746 := [rewrite]: #745 +#744 := [rewrite]: #743 +#747 := [trans #744 #746]: #743 +#266 := (~ #172 #172) +#264 := (~ #169 #169) +#265 := [refl]: #264 +#267 := [nnf-pos #265]: #266 +#33 := (= #32 #30) +#34 := (forall (vars (?v0 S2)) #33) +#173 := (iff #34 #172) +#170 := (iff #33 #169) +#171 := [rewrite]: #170 +#174 := [quant-intro #171]: #173 +#168 := [asserted]: #34 +#177 := [mp #168 #174]: #172 +#256 := [mp~ #177 #267]: #172 +#748 := [mp #256 #747]: #742 +#734 := (not #742) +#740 := (or #734 #737) +#730 := [quant-inst #11]: #740 +#674 := [unit-resolution #730 #748]: #737 +#574 := [symm #674]: #559 +#577 := [monotonicity #574]: #576 +#578 := [monotonicity #577]: #570 +#580 := [symm #578]: #579 +#675 := [monotonicity #580]: #582 +#672 := [mp #670 #675]: #581 +#395 := (or #129 #739) +#35 := (:var 0 Int) +#37 := (f5 #35) +#749 := (pattern #37) +#193 := (>= #35 0::Int) +#38 := (f3 #37) +#43 := (= #38 0::Int) +#242 := (or #43 #193) +#756 := (forall (vars (?v0 Int)) (:pat #749) #242) +#247 := (forall (vars (?v0 Int)) #242) +#759 := (iff #247 #756) +#757 := (iff #242 #242) +#758 := [refl]: #757 +#760 := [quant-intro #758]: #759 +#260 := (~ #247 #247) +#268 := (~ #242 #242) +#269 := [refl]: #268 +#261 := [nnf-pos #269]: #260 +#42 := (< #35 0::Int) +#44 := (implies #42 #43) +#45 := (forall (vars (?v0 Int)) #44) +#250 := (iff #45 #247) +#213 := (= 0::Int #38) +#219 := (not #42) +#220 := (or #219 #213) +#225 := (forall (vars (?v0 Int)) #220) +#248 := (iff #225 #247) +#245 := (iff #220 #242) +#239 := (or #193 #43) +#243 := (iff #239 #242) +#244 := [rewrite]: #243 +#240 := (iff #220 #239) +#237 := (iff #213 #43) +#238 := [rewrite]: #237 +#235 := (iff #219 #193) +#195 := (not #193) +#230 := (not #195) +#233 := (iff #230 #193) +#234 := [rewrite]: #233 +#231 := (iff #219 #230) +#228 := (iff #42 #195) +#229 := [rewrite]: #228 +#232 := [monotonicity #229]: #231 +#236 := [trans #232 #234]: #235 +#241 := [monotonicity #236 #238]: #240 +#246 := [trans #241 #244]: #245 +#249 := [quant-intro #246]: #248 +#226 := (iff #45 #225) +#223 := (iff #44 #220) +#216 := (implies #42 #213) +#221 := (iff #216 #220) +#222 := [rewrite]: #221 +#217 := (iff #44 #216) +#214 := (iff #43 #213) +#215 := [rewrite]: #214 +#218 := [monotonicity #215]: #217 +#224 := [trans #218 #222]: #223 +#227 := [quant-intro #224]: #226 +#251 := [trans #227 #249]: #250 +#212 := [asserted]: #45 +#252 := [mp #212 #251]: #247 +#270 := [mp~ #252 #261]: #247 +#761 := [mp #270 #760]: #756 +#732 := (not #756) +#375 := (or #732 #129 #739) +#390 := (or #739 #129) +#716 := (or #732 #390) +#720 := (iff #716 #375) +#380 := (or #732 #395) +#718 := (iff #380 #375) +#719 := [rewrite]: #718 +#381 := (iff #716 #380) +#731 := (iff #390 #395) +#391 := [rewrite]: #731 +#382 := [monotonicity #391]: #381 +#721 := [trans #382 #719]: #720 +#379 := [quant-inst #12]: #716 +#722 := [mp #379 #721]: #375 +#676 := [unit-resolution #722 #761]: #395 +#663 := [unit-resolution #676 #672]: #129 +#665 := (or #13 #117 #130) +#657 := [th-lemma arith triangle-eq]: #665 +#654 := [unit-resolution #657 #670]: #140 +#656 := [unit-resolution #654 #663]: #117 +#414 := (or #140 #116) +#405 := [def-axiom]: #414 +#666 := [unit-resolution #405 #656]: #140 +#345 := (not #140) +#419 := (or #345 #327) +#398 := [def-axiom]: #419 +#667 := [unit-resolution #398 #666]: #327 +#668 := [trans #667 #671]: #679 +#664 := (not #679) +#669 := (or #664 #566) +#658 := [th-lemma arith triangle-eq]: #669 +#659 := [unit-resolution #658 #668]: #566 +[th-lemma arith farkas -1 -1 1 #167 #659 #575]: false +unsat +2855a1e15b1d7788a0afdba64d4d2bd112ea0f3b 560 0 +#2 := false +#9 := 0::Int +decl f4 :: (-> S2 Int) +decl f5 :: S2 +#11 := f5 +#12 := (f4 f5) +#141 := (<= #12 0::Int) +#142 := (not #141) +#8 := 3::Int +#180 := (>= #12 3::Int) +#654 := 1::Int +#706 := (div #12 3::Int) +#555 := -2::Int +#565 := (* -2::Int #706) +#20 := (mod #12 3::Int) +#80 := -1::Int +#603 := (* -1::Int #20) +#566 := (+ #603 #565) +#549 := (+ #12 #566) +#567 := (>= #549 1::Int) +#84 := -3::Int +#605 := (* -3::Int #706) +#606 := (+ #603 #605) +#599 := (+ #12 #606) +#704 := (>= #599 0::Int) +#588 := (= #599 0::Int) +#1 := true +#66 := [true-axiom]: true +#629 := (or false #588) +#634 := [th-lemma arith]: #629 +#614 := [unit-resolution #634 #66]: #588 +#560 := (not #588) +#582 := (or #560 #704) +#583 := [th-lemma arith triangle-eq]: #582 +#584 := [unit-resolution #583 #614]: #704 +#658 := (+ #12 #603) +#659 := (<= #658 0::Int) +#540 := (not #659) +#657 := (= #12 #20) +#627 := (not #657) +decl f3 :: (-> Int S2) +#81 := (* -1::Int #12) +#87 := (mod #81 -3::Int) +#93 := (* -1::Int #87) +#154 := (>= #12 0::Int) +#155 := (not #154) +#165 := (or #142 #155) +#168 := (ite #165 #20 #93) +#13 := (= #12 0::Int) +#171 := (ite #13 0::Int #168) +#174 := (f3 #171) +#177 := (= f5 #174) +#769 := (not #177) +#181 := (not #180) +#548 := [hypothesis]: #181 +#424 := (or #769 #180) +#191 := (iff #177 #180) +#30 := (< #12 3::Int) +#22 := (- 3::Int) +#21 := (- #12) +#23 := (mod #21 #22) +#24 := (- #23) +#15 := (< 0::Int 3::Int) +#17 := (< #12 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #12) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#26 := (ite #13 0::Int #25) +#10 := (= 3::Int 0::Int) +#27 := (ite #10 #12 #26) +#28 := (f3 #27) +#29 := (= #28 f5) +#31 := (iff #29 #30) +#32 := (not #31) +#194 := (iff #32 #191) +#133 := (not #30) +#74 := (and #15 #17) +#77 := (or #16 #74) +#98 := (ite #77 #20 #93) +#71 := (= 0::Int #12) +#101 := (ite #71 0::Int #98) +#111 := (f3 #101) +#117 := (= f5 #111) +#134 := (iff #117 #133) +#192 := (iff #134 #191) +#189 := (iff #133 #180) +#184 := (not #181) +#187 := (iff #184 #180) +#188 := [rewrite]: #187 +#185 := (iff #133 #184) +#182 := (iff #30 #181) +#183 := [rewrite]: #182 +#186 := [monotonicity #183]: #185 +#190 := [trans #186 #188]: #189 +#178 := (iff #117 #177) +#175 := (= #111 #174) +#172 := (= #101 #171) +#169 := (= #98 #168) +#166 := (iff #77 #165) +#163 := (iff #74 #155) +#158 := (and true #155) +#161 := (iff #158 #155) +#162 := [rewrite]: #161 +#159 := (iff #74 #158) +#156 := (iff #17 #155) +#157 := [rewrite]: #156 +#145 := (iff #15 true) +#146 := [rewrite]: #145 +#160 := [monotonicity #146 #157]: #159 +#164 := [trans #160 #162]: #163 +#152 := (iff #16 #142) +#147 := (and #142 true) +#150 := (iff #147 #142) +#151 := [rewrite]: #150 +#148 := (iff #16 #147) +#143 := (iff #14 #142) +#144 := [rewrite]: #143 +#149 := [monotonicity #144 #146]: #148 +#153 := [trans #149 #151]: #152 +#167 := [monotonicity #153 #164]: #166 +#170 := [monotonicity #167]: #169 +#139 := (iff #71 #13) +#140 := [rewrite]: #139 +#173 := [monotonicity #140 #170]: #172 +#176 := [monotonicity #173]: #175 +#179 := [monotonicity #176]: #178 +#193 := [monotonicity #179 #190]: #192 +#137 := (iff #32 #134) +#125 := (iff #30 #117) +#130 := (not #125) +#135 := (iff #130 #134) +#136 := [rewrite]: #135 +#131 := (iff #32 #130) +#128 := (iff #31 #125) +#122 := (iff #117 #30) +#126 := (iff #122 #125) +#127 := [rewrite]: #126 +#123 := (iff #31 #122) +#120 := (iff #29 #117) +#114 := (= #111 f5) +#118 := (iff #114 #117) +#119 := [rewrite]: #118 +#115 := (iff #29 #114) +#112 := (= #28 #111) +#109 := (= #27 #101) +#104 := (ite false #12 #101) +#107 := (= #104 #101) +#108 := [rewrite]: #107 +#105 := (= #27 #104) +#102 := (= #26 #101) +#99 := (= #25 #98) +#96 := (= #24 #93) +#90 := (- #87) +#94 := (= #90 #93) +#95 := [rewrite]: #94 +#91 := (= #24 #90) +#88 := (= #23 #87) +#85 := (= #22 -3::Int) +#86 := [rewrite]: #85 +#82 := (= #21 #81) +#83 := [rewrite]: #82 +#89 := [monotonicity #83 #86]: #88 +#92 := [monotonicity #89]: #91 +#97 := [trans #92 #95]: #96 +#78 := (iff #19 #77) +#75 := (iff #18 #74) +#76 := [rewrite]: #75 +#79 := [monotonicity #76]: #78 +#100 := [monotonicity #79 #97]: #99 +#72 := (iff #13 #71) +#73 := [rewrite]: #72 +#103 := [monotonicity #73 #100]: #102 +#69 := (iff #10 false) +#70 := [rewrite]: #69 +#106 := [monotonicity #70 #103]: #105 +#110 := [trans #106 #108]: #109 +#113 := [monotonicity #110]: #112 +#116 := [monotonicity #113]: #115 +#121 := [trans #116 #119]: #120 +#124 := [monotonicity #121]: #123 +#129 := [trans #124 #127]: #128 +#132 := [monotonicity #129]: #131 +#138 := [trans #132 #136]: #137 +#195 := [trans #138 #193]: #194 +#68 := [asserted]: #32 +#196 := [mp #68 #195]: #191 +#765 := (not #191) +#759 := (or #769 #180 #765) +#419 := [def-axiom]: #759 +#760 := [unit-resolution #419 #196]: #424 +#528 := [unit-resolution #760 #548]: #769 +#628 := (or #627 #177) +#420 := (f3 #12) +#720 := (= #420 #174) +#713 := (= #174 #420) +#717 := (= #171 #12) +#617 := (= #20 #12) +#641 := [hypothesis]: #657 +#618 := [symm #641]: #617 +#619 := (= #171 #20) +#638 := (= #168 #20) +#356 := (= #20 #168) +#733 := (f4 #420) +#734 := (= #733 0::Int) +#648 := (not #734) +#421 := (not #13) +#649 := (iff #421 #648) +#645 := (iff #13 #734) +#656 := (iff #734 #13) +#665 := (= #733 #12) +#663 := (= #420 f5) +#761 := (= f5 #420) +#33 := (:var 0 S2) +#34 := (f4 #33) +#770 := (pattern #34) +#35 := (f3 #34) +#198 := (= #33 #35) +#771 := (forall (vars (?v0 S2)) (:pat #770) #198) +#201 := (forall (vars (?v0 S2)) #198) +#772 := (iff #201 #771) +#774 := (iff #771 #771) +#775 := [rewrite]: #774 +#773 := [rewrite]: #772 +#776 := [trans #773 #775]: #772 +#295 := (~ #201 #201) +#293 := (~ #198 #198) +#294 := [refl]: #293 +#296 := [nnf-pos #294]: #295 +#36 := (= #35 #33) +#37 := (forall (vars (?v0 S2)) #36) +#202 := (iff #37 #201) +#199 := (iff #36 #198) +#200 := [rewrite]: #199 +#203 := [quant-intro #200]: #202 +#197 := [asserted]: #37 +#206 := [mp #197 #203]: #201 +#285 := [mp~ #206 #296]: #201 +#777 := [mp #285 #776]: #771 +#408 := (not #771) +#409 := (or #408 #761) +#410 := [quant-inst #11]: #409 +#712 := [unit-resolution #410 #777]: #761 +#664 := [symm #712]: #663 +#666 := [monotonicity #664]: #665 +#667 := [monotonicity #666]: #656 +#646 := [symm #667]: #645 +#650 := [monotonicity #646]: #649 +#572 := [hypothesis]: #769 +#552 := (or #421 #177) +#573 := [hypothesis]: #13 +#716 := [symm #573]: #71 +#355 := (= #171 0::Int) +#551 := (or #421 #355) +#758 := [def-axiom]: #551 +#715 := [unit-resolution #758 #573]: #355 +#718 := [trans #715 #716]: #717 +#719 := [monotonicity #718]: #713 +#714 := [symm #719]: #720 +#721 := [trans #712 #714]: #177 +#550 := [unit-resolution #572 #721]: false +#553 := [lemma #550]: #552 +#661 := [unit-resolution #553 #572]: #421 +#651 := [mp #661 #650]: #648 +#731 := (or #154 #734) +#38 := (:var 0 Int) +#40 := (f3 #38) +#778 := (pattern #40) +#222 := (>= #38 0::Int) +#41 := (f4 #40) +#46 := (= #41 0::Int) +#271 := (or #46 #222) +#785 := (forall (vars (?v0 Int)) (:pat #778) #271) +#276 := (forall (vars (?v0 Int)) #271) +#788 := (iff #276 #785) +#786 := (iff #271 #271) +#787 := [refl]: #786 +#789 := [quant-intro #787]: #788 +#289 := (~ #276 #276) +#297 := (~ #271 #271) +#298 := [refl]: #297 +#290 := [nnf-pos #298]: #289 +#45 := (< #38 0::Int) +#47 := (implies #45 #46) +#48 := (forall (vars (?v0 Int)) #47) +#279 := (iff #48 #276) +#242 := (= 0::Int #41) +#248 := (not #45) +#249 := (or #248 #242) +#254 := (forall (vars (?v0 Int)) #249) +#277 := (iff #254 #276) +#274 := (iff #249 #271) +#268 := (or #222 #46) +#272 := (iff #268 #271) +#273 := [rewrite]: #272 +#269 := (iff #249 #268) +#266 := (iff #242 #46) +#267 := [rewrite]: #266 +#264 := (iff #248 #222) +#224 := (not #222) +#259 := (not #224) +#262 := (iff #259 #222) +#263 := [rewrite]: #262 +#260 := (iff #248 #259) +#257 := (iff #45 #224) +#258 := [rewrite]: #257 +#261 := [monotonicity #258]: #260 +#265 := [trans #261 #263]: #264 +#270 := [monotonicity #265 #267]: #269 +#275 := [trans #270 #273]: #274 +#278 := [quant-intro #275]: #277 +#255 := (iff #48 #254) +#252 := (iff #47 #249) +#245 := (implies #45 #242) +#250 := (iff #245 #249) #251 := [rewrite]: #250 -#258 := [monotonicity #251 #255]: #257 -#268 := [monotonicity #258 #265]: #267 -#313 := [monotonicity #268]: #312 -#242 := (iff #205 #36) -#243 := [rewrite]: #242 -#316 := [monotonicity #243 #313]: #315 -#244 := (iff #208 #37) -#245 := [rewrite]: #244 -#319 := [monotonicity #245 #316]: #318 -#322 := [monotonicity #319]: #321 -#325 := [quant-intro #322]: #324 -#309 := (iff #61 #308) -#306 := (iff #60 #305) -#303 := (= #59 #302) -#300 := (= #58 #299) -#297 := (= #57 #296) -#294 := (= #56 #291) -#288 := (- #285) -#292 := (= #288 #291) -#293 := [rewrite]: #292 -#289 := (= #56 #288) -#286 := (= #55 #285) -#225 := (= #47 #224) -#226 := [rewrite]: #225 -#222 := (= #46 #221) -#223 := [rewrite]: #222 -#287 := [monotonicity #223 #226]: #286 -#290 := [monotonicity #287]: #289 -#295 := [trans #290 #293]: #294 -#218 := (iff #44 #217) -#215 := (iff #43 #214) -#216 := [rewrite]: #215 -#219 := [monotonicity #216]: #218 -#298 := [monotonicity #219 #295]: #297 -#206 := (iff #36 #205) -#207 := [rewrite]: #206 -#301 := [monotonicity #207 #298]: #300 -#209 := (iff #37 #208) -#210 := [rewrite]: #209 -#304 := [monotonicity #210 #301]: #303 -#307 := [monotonicity #304]: #306 -#310 := [quant-intro #307]: #309 -#327 := [trans #310 #325]: #326 -#284 := [asserted]: #61 -#328 := [mp #284 #327]: #323 -#356 := [mp~ #328 #341]: #323 -#394 := [mp #356 #393]: #391 -#425 := [mp #394 #424]: #422 -#931 := [mp #425 #930]: #926 -#732 := (not #926) -#733 := (or #732 #721) -#517 := (* -1::Int 3::Int) -#882 := (mod #880 #517) -#522 := (+ #11 #882) -#523 := (= #522 0::Int) -#593 := (<= 3::Int 0::Int) -#594 := (or #593 #871) -#595 := (not #594) -#489 := (or #596 #593) -#866 := (not #489) -#867 := (or #866 #595) -#589 := (ite #867 #870 #523) -#868 := (ite #864 #590 #589) -#865 := (= #9 #11) -#869 := (= 3::Int 0::Int) -#579 := (ite #869 #865 #868) -#726 := (or #732 #579) -#735 := (iff #726 #733) -#737 := (iff #733 #733) -#738 := [rewrite]: #737 -#715 := (iff #579 #721) -#829 := (ite false #865 #721) -#827 := (iff #829 #721) -#830 := [rewrite]: #827 -#731 := (iff #579 #829) -#722 := (iff #868 #721) -#838 := (iff #589 #835) -#836 := (iff #523 #834) -#680 := (= #522 #679) -#848 := (= #882 #841) -#846 := (= #517 -3::Int) -#847 := [rewrite]: #846 -#677 := [monotonicity #847]: #848 -#833 := [monotonicity #677]: #680 -#837 := [monotonicity #833]: #836 -#845 := (iff #867 #844) -#842 := (iff #595 #700) -#698 := (iff #594 #871) -#850 := (or false #871) -#851 := (iff #850 #871) -#857 := [rewrite]: #851 -#855 := (iff #594 #850) -#582 := (iff #593 false) -#860 := [rewrite]: #582 -#856 := [monotonicity #860]: #855 -#699 := [trans #856 #857]: #698 -#843 := [monotonicity #699]: #842 -#854 := (iff #866 #853) -#863 := (iff #489 #596) -#861 := (or #596 false) -#862 := (iff #861 #596) -#859 := [rewrite]: #862 -#576 := (iff #489 #861) -#858 := [monotonicity #860]: #576 -#852 := [trans #858 #859]: #863 -#849 := [monotonicity #852]: #854 -#839 := [monotonicity #849 #843]: #845 -#720 := [monotonicity #839 #837]: #838 -#681 := [monotonicity #720]: #722 -#580 := (iff #869 false) -#581 := [rewrite]: #580 -#826 := [monotonicity #581 #681]: #731 -#730 := [trans #826 #830]: #715 -#736 := [monotonicity #730]: #735 -#831 := [trans #736 #738]: #735 -#734 := [quant-inst #9 #10]: #726 -#828 := [mp #734 #831]: #733 -#794 := [unit-resolution #828 #931]: #721 -#804 := (not #721) -#795 := (or #804 #809 #590) -#796 := [def-axiom]: #795 -#768 := [unit-resolution #796 #794]: #767 -#769 := [unit-resolution #768 #764]: #590 -#744 := [trans #769 #765]: #771 -#639 := [monotonicity #744]: #746 -#751 := [symm #639]: #750 -#554 := (= f6 #575) -#17 := (:var 0 S2) -#18 := (f5 #17) -#897 := (pattern #18) -#19 := (f3 #18) -#120 := (= #17 #19) -#898 := (forall (vars (?v0 S2)) (:pat #897) #120) -#123 := (forall (vars (?v0 S2)) #120) -#899 := (iff #123 #898) -#901 := (iff #898 #898) -#902 := [rewrite]: #901 -#900 := [rewrite]: #899 -#903 := [trans #900 #902]: #899 -#346 := (~ #123 #123) -#344 := (~ #120 #120) -#345 := [refl]: #344 -#347 := [nnf-pos #345]: #346 -#20 := (= #19 #17) -#21 := (forall (vars (?v0 S2)) #20) -#124 := (iff #21 #123) -#121 := (iff #20 #120) -#122 := [rewrite]: #121 -#125 := [quant-intro #122]: #124 -#119 := [asserted]: #21 -#128 := [mp #119 #125]: #123 -#332 := [mp~ #128 #347]: #123 -#904 := [mp #332 #903]: #898 -#548 := (not #898) -#678 := (or #548 #554) -#885 := [quant-inst #8]: #678 -#745 := [unit-resolution #885 #904]: #554 -#752 := [trans #745 #751]: #82 -#763 := [hypothesis]: #572 -#757 := [unit-resolution #763 #752]: false -#754 := [lemma #757]: #753 -#634 := [unit-resolution #754 #636]: #809 -#766 := (or #864 #870) -#787 := [hypothesis]: #809 -#812 := (not #844) -#802 := (not #870) -#788 := [hypothesis]: #802 -#772 := (or #864 #835) -#798 := (or #804 #864 #835) -#799 := [def-axiom]: #798 -#773 := [unit-resolution #799 #794]: #772 -#775 := [unit-resolution #773 #787]: #835 -#815 := (not #835) -#816 := (or #815 #812 #870) -#817 := [def-axiom]: #816 -#776 := [unit-resolution #817 #775 #788]: #812 -#819 := (or #844 #596) -#821 := [def-axiom]: #819 -#777 := [unit-resolution #821 #776]: #596 -#813 := (or #844 #871) -#810 := [def-axiom]: #813 -#778 := [unit-resolution #810 #776]: #871 -#779 := (or #864 #853 #700) -#774 := [th-lemma arith triangle-eq]: #779 -#780 := [unit-resolution #774 #778 #777 #787]: false -#762 := [lemma #780]: #766 -#623 := [unit-resolution #762 #634]: #870 -#624 := (or #802 #824) -#625 := [th-lemma arith triangle-eq]: #624 -#626 := [unit-resolution #625 #623]: #824 -#755 := (div #9 3::Int) -#747 := (* -3::Int #755) -#748 := (+ #747 #881) -#743 := (+ #9 #748) -#724 := (<= #743 0::Int) -#723 := (= #743 0::Int) -#670 := (or false #723) -#671 := [th-lemma arith]: #670 -#514 := [unit-resolution #671 #79]: #723 -#672 := (not #723) -#668 := (or #672 #724) -#673 := [th-lemma arith triangle-eq]: #668 -#652 := [unit-resolution #673 #514]: #724 -#630 := 1::Int -#621 := -2::Int -#627 := (* -2::Int #755) -#628 := (+ #627 #881) -#629 := (+ #9 #628) -#631 := (>= #629 1::Int) -#682 := (* -1::Int #11) -#684 := (+ #9 #682) -#685 := (<= #684 0::Int) -#614 := (not #685) -#676 := (not #865) -#694 := (or #676 #82) -#688 := [hypothesis]: #865 -#689 := [symm #688]: #771 -#690 := [monotonicity #689]: #746 -#691 := [symm #690]: #750 -#692 := [trans #745 #691]: #82 -#693 := [unit-resolution #763 #692]: false -#664 := [lemma #693]: #694 -#608 := [unit-resolution #664 #636]: #676 -#686 := (>= #684 0::Int) -#665 := (>= #755 0::Int) -#784 := (f5 #575) -#785 := (= #784 0::Int) -#600 := (not #785) -#601 := (iff #809 #600) -#599 := (iff #864 #785) -#597 := (iff #785 #864) -#604 := (= #784 #9) -#607 := (= #575 f6) -#606 := [symm #745]: #607 -#605 := [monotonicity #606]: #604 -#598 := [monotonicity #605]: #597 -#591 := [symm #598]: #599 -#592 := [monotonicity #591]: #601 -#602 := [mp #634 #592]: #600 -#786 := (or #785 #871) -#25 := (f3 #23) -#905 := (pattern #25) -#145 := (>= #23 0::Int) -#26 := (f5 #25) -#31 := (= #26 0::Int) -#193 := (or #31 #145) -#912 := (forall (vars (?v0 Int)) (:pat #905) #193) -#198 := (forall (vars (?v0 Int)) #193) -#915 := (iff #198 #912) -#913 := (iff #193 #193) -#914 := [refl]: #913 -#916 := [quant-intro #914]: #915 -#336 := (~ #198 #198) -#348 := (~ #193 #193) -#349 := [refl]: #348 -#337 := [nnf-pos #349]: #336 -#30 := (< #23 0::Int) -#32 := (implies #30 #31) -#33 := (forall (vars (?v0 Int)) #32) -#201 := (iff #33 #198) -#164 := (= 0::Int #26) -#170 := (not #30) -#171 := (or #170 #164) -#176 := (forall (vars (?v0 Int)) #171) -#199 := (iff #176 #198) -#196 := (iff #171 #193) -#190 := (or #145 #31) -#194 := (iff #190 #193) -#195 := [rewrite]: #194 -#191 := (iff #171 #190) -#188 := (iff #164 #31) -#189 := [rewrite]: #188 -#186 := (iff #170 #145) -#146 := (not #145) -#181 := (not #146) -#184 := (iff #181 #145) -#185 := [rewrite]: #184 -#182 := (iff #170 #181) -#179 := (iff #30 #146) -#180 := [rewrite]: #179 -#183 := [monotonicity #180]: #182 -#187 := [trans #183 #185]: #186 -#192 := [monotonicity #187 #189]: #191 -#197 := [trans #192 #195]: #196 -#200 := [quant-intro #197]: #199 -#177 := (iff #33 #176) -#174 := (iff #32 #171) -#167 := (implies #30 #164) -#172 := (iff #167 #171) -#173 := [rewrite]: #172 -#168 := (iff #32 #167) -#165 := (iff #31 #164) -#166 := [rewrite]: #165 -#169 := [monotonicity #166]: #168 -#175 := [trans #169 #173]: #174 -#178 := [quant-intro #175]: #177 -#202 := [trans #178 #200]: #201 -#163 := [asserted]: #33 -#203 := [mp #163 #202]: #198 -#350 := [mp~ #203 #337]: #198 -#917 := [mp #350 #916]: #912 -#872 := (not #912) -#789 := (or #872 #785 #871) -#790 := (or #872 #786) -#792 := (iff #790 #789) -#793 := [rewrite]: #792 -#791 := [quant-inst #9]: #790 -#783 := [mp #791 #793]: #789 -#583 := [unit-resolution #783 #917]: #786 -#584 := [unit-resolution #583 #602]: #871 -#660 := (or #665 #700) -#655 := (not #665) -#659 := [hypothesis]: #655 -#661 := [hypothesis]: #871 -#662 := [th-lemma arith farkas 1 3 1 1 #661 #659 #652 #669]: false -#663 := [lemma #662]: #660 -#585 := [unit-resolution #663 #584]: #665 -#648 := (not #824) -#633 := (or #686 #648 #655) -#656 := (not #686) -#657 := [hypothesis]: #656 -#683 := (>= #743 0::Int) -#642 := (or #672 #683) -#650 := [th-lemma arith triangle-eq]: #642 -#643 := [unit-resolution #650 #514]: #683 -#646 := [hypothesis]: #665 -#654 := [hypothesis]: #824 -#647 := [th-lemma arith farkas 1 -3 -1 1 #654 #646 #643 #657]: false -#635 := [lemma #647]: #633 -#577 := [unit-resolution #635 #626 #585]: #686 -#586 := (or #865 #614 #656) -#587 := [th-lemma arith triangle-eq]: #586 -#578 := [unit-resolution #587 #577 #608]: #614 -#820 := (>= #884 0::Int) -#588 := (or #802 #820) -#555 := [th-lemma arith triangle-eq]: #588 -#557 := [unit-resolution #555 #623]: #820 -#610 := (not #820) -#618 := (or #631 #610 #685) -#609 := (not #631) -#613 := [hypothesis]: #609 -#615 := [hypothesis]: #614 -#616 := [hypothesis]: #820 -#617 := [th-lemma arith farkas -2/3 -1/3 -1/3 1 #643 #616 #615 #613]: false -#603 := [lemma #617]: #618 -#558 := [unit-resolution #603 #557 #578]: #631 -#889 := (>= #11 0::Int) -#714 := (>= #883 0::Int) -#549 := (or false #714) -#562 := [th-lemma arith]: #549 -#563 := [unit-resolution #562 #79]: #714 -#564 := (not #714) -#565 := (or #889 #564 #610) -#566 := [th-lemma arith assign-bounds 1 1]: #565 -#556 := [unit-resolution #566 #557 #563]: #889 -#567 := [th-lemma arith farkas -1 -3 2 1 1 #556 #558 #652 #626 #619]: false -#550 := [lemma #567]: #104 -#559 := (f5 #12) -#560 := (= #11 #559) -#521 := (iff #560 #865) -#518 := (iff #771 #865) -#520 := [commutativity]: #518 -#527 := (iff #560 #771) -#528 := (= #559 #9) -#570 := (or #82 #102) -#568 := (or #82 #102 #483) -#569 := [def-axiom]: #568 -#561 := [unit-resolution #569 #118]: #570 -#545 := [unit-resolution #561 #550]: #82 -#526 := [symm #545]: #13 -#529 := [monotonicity #526]: #528 -#530 := [monotonicity #529]: #527 -#524 := [trans #530 #520]: #521 -#552 := (or #853 #102) -#553 := [th-lemma arith farkas 1 1]: #552 -#532 := [unit-resolution #553 #550]: #853 -#534 := (or #809 #596) -#539 := [th-lemma arith triangle-eq]: #534 -#540 := [unit-resolution #539 #532]: #809 -#541 := [unit-resolution #762 #540]: #870 -#542 := [unit-resolution #555 #541]: #820 -#543 := [unit-resolution #566 #542 #563]: #889 -#891 := (not #889) -#892 := (or #560 #891) -#127 := (= #23 #26) -#152 := (or #127 #146) -#906 := (forall (vars (?v0 Int)) (:pat #905) #152) -#157 := (forall (vars (?v0 Int)) #152) -#909 := (iff #157 #906) -#907 := (iff #152 #152) -#908 := [refl]: #907 -#910 := [quant-intro #908]: #909 -#334 := (~ #157 #157) -#333 := (~ #152 #152) -#330 := [refl]: #333 -#335 := [nnf-pos #330]: #334 -#27 := (= #26 #23) -#24 := (<= 0::Int #23) -#28 := (implies #24 #27) -#29 := (forall (vars (?v0 Int)) #28) -#160 := (iff #29 #157) -#134 := (not #24) -#135 := (or #134 #127) -#140 := (forall (vars (?v0 Int)) #135) -#158 := (iff #140 #157) -#155 := (iff #135 #152) -#149 := (or #146 #127) -#153 := (iff #149 #152) -#154 := [rewrite]: #153 -#150 := (iff #135 #149) -#147 := (iff #134 #146) -#143 := (iff #24 #145) -#144 := [rewrite]: #143 -#148 := [monotonicity #144]: #147 +#246 := (iff #47 #245) +#243 := (iff #46 #242) +#244 := [rewrite]: #243 +#247 := [monotonicity #244]: #246 +#253 := [trans #247 #251]: #252 +#256 := [quant-intro #253]: #255 +#280 := [trans #256 #278]: #279 +#241 := [asserted]: #48 +#281 := [mp #241 #280]: #276 +#299 := [mp~ #281 #290]: #276 +#790 := [mp #299 #789]: #785 +#739 := (not #785) +#736 := (or #739 #154 #734) +#449 := (or #734 #154) +#725 := (or #739 #449) +#724 := (iff #725 #736) +#727 := (or #739 #731) +#728 := (iff #727 #736) +#729 := [rewrite]: #728 +#722 := (iff #725 #727) +#735 := (iff #449 #731) +#732 := [rewrite]: #735 +#723 := [monotonicity #732]: #722 +#730 := [trans #723 #729]: #724 +#726 := [quant-inst #12]: #725 +#571 := [mp #726 #730]: #736 +#652 := [unit-resolution #571 #790]: #731 +#647 := [unit-resolution #652 #651]: #154 +#653 := (or #13 #142 #155) +#639 := [th-lemma arith triangle-eq]: #653 +#635 := [unit-resolution #639 #661]: #165 +#636 := [unit-resolution #635 #647]: #142 +#443 := (or #165 #141) +#434 := [def-axiom]: #443 +#637 := [unit-resolution #434 #636]: #165 +#374 := (not #165) +#448 := (or #374 #356) +#427 := [def-axiom]: #448 +#640 := [unit-resolution #427 #637]: #356 +#644 := [symm #640]: #638 +#642 := (= #171 #168) +#441 := (= #168 #171) +#432 := (or #13 #441) +#433 := [def-axiom]: #432 +#662 := [unit-resolution #433 #661]: #441 +#643 := [symm #662]: #642 +#512 := [trans #643 #644]: #619 +#623 := [trans #512 #618]: #717 +#624 := [monotonicity #623]: #713 +#625 := [symm #624]: #720 +#630 := [trans #712 #625]: #177 +#626 := [unit-resolution #572 #630]: false +#631 := [lemma #626]: #628 +#546 := [unit-resolution #631 #528]: #627 +#660 := (>= #658 0::Int) +#578 := (* -1::Int #706) +#579 := (+ #603 #578) +#580 := (+ #12 #579) +#581 := (>= #580 0::Int) +#545 := [unit-resolution #553 #528]: #421 +#541 := [mp #545 #650]: #648 +#532 := [unit-resolution #652 #541]: #154 +#534 := [unit-resolution #639 #545]: #165 +#535 := [unit-resolution #534 #532]: #142 +#570 := (or #581 #141) +#574 := (not #581) +#577 := [hypothesis]: #574 +#691 := (>= #20 3::Int) +#675 := (not #691) +#616 := (or false #675) +#622 := [th-lemma arith]: #616 +#590 := [unit-resolution #622 #66]: #675 +#632 := [hypothesis]: #142 +#585 := [th-lemma arith farkas -2/3 2/3 -1/3 1 #632 #590 #584 #577]: false +#586 := [lemma #585]: #570 +#533 := [unit-resolution #586 #535]: #581 +#575 := (or #574 #660) +#568 := (not #660) +#569 := [hypothesis]: #568 +#611 := (<= #599 0::Int) +#615 := (or #560 #611) +#596 := [th-lemma arith triangle-eq]: #615 +#620 := [unit-resolution #596 #614]: #611 +#592 := [hypothesis]: #581 +#613 := [th-lemma arith farkas -3/2 1/2 1 #592 #620 #569]: false +#576 := [lemma #613]: #575 +#536 := [unit-resolution #576 #533]: #660 +#524 := (or #657 #540 #568) +#527 := [th-lemma arith triangle-eq]: #524 +#529 := [unit-resolution #527 #536 #546]: #540 +#530 := [th-lemma arith #529 #584]: #567 +#562 := (not #567) +#563 := (or #562 #180) +#701 := (>= #20 0::Int) +#558 := (or false #701) +#559 := [th-lemma arith]: #558 +#557 := [unit-resolution #559 #66]: #701 +#547 := [hypothesis]: #567 +#561 := [th-lemma arith farkas -1 3 -2 1 #548 #547 #620 #557]: false +#564 := [lemma #561]: #563 +#525 := [unit-resolution #564 #548]: #562 +#526 := [unit-resolution #525 #530]: false +#531 := [lemma #526]: #180 +#501 := (or #181 #142) +#502 := [th-lemma arith farkas 1 1]: #501 +#503 := [unit-resolution #502 #531]: #142 +#411 := (f4 #174) +#747 := (= #171 #411) +#491 := (not #747) +#476 := (iff #627 #491) +#490 := (iff #657 #747) +#485 := (= #411 #171) +#488 := (iff #485 #747) +#489 := [commutativity]: #488 +#486 := (iff #657 #485) +#671 := (= #20 #171) +#521 := [hypothesis]: #421 +#500 := [unit-resolution #433 #521]: #441 +#504 := [unit-resolution #434 #503]: #165 +#493 := [unit-resolution #427 #504]: #356 +#505 := [trans #493 #500]: #671 +#482 := (= #12 #411) +#517 := (= #411 #12) +#513 := (= #174 f5) +#768 := (or #177 #181) +#766 := (or #177 #181 #765) +#767 := [def-axiom]: #766 +#763 := [unit-resolution #767 #196]: #768 +#511 := [unit-resolution #763 #531]: #177 +#514 := [symm #511]: #513 +#518 := [monotonicity #514]: #517 +#484 := [symm #518]: #482 +#487 := [monotonicity #484 #505]: #486 +#483 := [trans #487 #489]: #490 +#477 := [monotonicity #483]: #476 +#494 := (or #540 #181 #691) +#495 := [th-lemma arith assign-bounds -1 1]: #494 +#496 := [unit-resolution #495 #590 #531]: #540 +#497 := (or #627 #659) +#498 := [th-lemma arith triangle-eq]: #497 +#499 := [unit-resolution #498 #496]: #627 +#478 := [mp #499 #477]: #491 +#404 := (>= #171 0::Int) +#466 := (= #411 0::Int) +#519 := (not #466) +#520 := (iff #421 #519) +#523 := (iff #13 #466) +#522 := (iff #466 #13) +#515 := [monotonicity #518]: #522 +#516 := [symm #515]: #523 +#506 := [monotonicity #516]: #520 +#508 := [mp #521 #506]: #519 +#468 := (or #404 #466) +#740 := (or #739 #404 #466) +#467 := (or #466 #404) +#462 := (or #739 #467) +#453 := (iff #462 #740) +#737 := (or #739 #468) +#742 := (iff #737 #740) +#452 := [rewrite]: #742 +#741 := (iff #462 #737) +#469 := (iff #467 #468) +#362 := [rewrite]: #469 +#738 := [monotonicity #362]: #741 +#454 := [trans #738 #452]: #453 +#463 := [quant-inst #171]: #462 +#455 := [mp #463 #454]: #740 +#509 := [unit-resolution #455 #790]: #468 +#507 := [unit-resolution #509 #508]: #404 +#745 := (not #404) +#749 := (or #745 #747) +#205 := (= #38 #41) +#230 := (or #205 #224) +#779 := (forall (vars (?v0 Int)) (:pat #778) #230) +#235 := (forall (vars (?v0 Int)) #230) +#782 := (iff #235 #779) +#780 := (iff #230 #230) +#781 := [refl]: #780 +#783 := [quant-intro #781]: #782 +#287 := (~ #235 #235) +#286 := (~ #230 #230) +#283 := [refl]: #286 +#288 := [nnf-pos #283]: #287 +#42 := (= #41 #38) +#39 := (<= 0::Int #38) +#43 := (implies #39 #42) +#44 := (forall (vars (?v0 Int)) #43) +#238 := (iff #44 #235) +#212 := (not #39) +#213 := (or #212 #205) +#218 := (forall (vars (?v0 Int)) #213) +#236 := (iff #218 #235) +#233 := (iff #213 #230) +#227 := (or #224 #205) +#231 := (iff #227 #230) +#232 := [rewrite]: #231 +#228 := (iff #213 #227) +#225 := (iff #212 #224) +#221 := (iff #39 #222) +#223 := [rewrite]: #221 +#226 := [monotonicity #223]: #225 +#229 := [monotonicity #226]: #228 +#234 := [trans #229 #232]: #233 +#237 := [quant-intro #234]: #236 +#219 := (iff #44 #218) +#216 := (iff #43 #213) +#209 := (implies #39 #205) +#214 := (iff #209 #213) +#215 := [rewrite]: #214 +#210 := (iff #43 #209) +#207 := (iff #42 #205) +#208 := [rewrite]: #207 +#211 := [monotonicity #208]: #210 +#217 := [trans #211 #215]: #216 +#220 := [quant-intro #217]: #219 +#239 := [trans #220 #237]: #238 +#204 := [asserted]: #44 +#240 := [mp #204 #239]: #235 +#284 := [mp~ #240 #288]: #235 +#784 := [mp #284 #783]: #779 +#746 := (not #779) +#752 := (or #746 #745 #747) +#748 := (or #747 #745) +#390 := (or #746 #748) +#757 := (iff #390 #752) +#755 := (or #746 #749) +#756 := (iff #755 #752) +#754 := [rewrite]: #756 +#395 := (iff #390 #755) +#750 := (iff #748 #749) +#751 := [rewrite]: #750 +#396 := [monotonicity #751]: #395 +#743 := [trans #396 #754]: #757 +#753 := [quant-inst #171]: #390 +#744 := [mp #753 #743]: #752 +#510 := [unit-resolution #744 #784]: #749 +#492 := [unit-resolution #510 #507]: #747 +#480 := [unit-resolution #492 #478]: false +#479 := [lemma #480]: #13 +#681 := (or #421 #141) +#677 := [th-lemma arith triangle-eq]: #681 +[unit-resolution #677 #479 #503]: false +unsat +a73683b8b391e3ad74189bec3a2bead06af3f8bd 414 0 +#2 := false +#10 := 0::Int +decl f5 :: (-> S2 Int) +decl f3 :: S2 +#8 := f3 +#9 := (f5 f3) +#168 := (>= #9 0::Int) +#169 := (not #168) +#155 := (<= #9 0::Int) +#156 := (not #155) +#11 := (= #9 0::Int) +#191 := (or #11 #156 #169) +#776 := (not #191) +decl f4 :: (-> Int S2) +#89 := -1::Int +#90 := (* -1::Int #9) +#113 := (mod #90 -1::Int) +#119 := (* -1::Int #113) +#196 := (ite #191 0::Int #119) +#95 := (div #90 -1::Int) +#12 := 1::Int +#21 := (div #9 1::Int) +#179 := (or #156 #169) +#182 := (ite #179 #21 #95) +#185 := (ite #11 0::Int #182) +#199 := (+ #185 #196) +#202 := (f4 #199) +#205 := (= f3 #202) +#426 := (f4 #9) +#715 := (= #426 #202) +#718 := (= #202 #426) +#610 := (= #199 #9) +#628 := (= #185 #9) +#614 := (= #9 #185) +#706 := (* -1::Int #21) +#700 := (+ #9 #706) +#695 := (<= #700 0::Int) +#705 := (= #700 0::Int) +#1 := true +#71 := [true-axiom]: true +#665 := (or false #705) +#666 := [th-lemma arith]: #665 +#667 := [unit-resolution #666 #71]: #705 +#668 := (not #705) +#663 := (or #668 #695) +#669 := [th-lemma arith triangle-eq]: #663 +#655 := [unit-resolution #669 #667]: #695 +#696 := (>= #700 0::Int) +#651 := (or #668 #696) +#652 := [th-lemma arith triangle-eq]: #651 +#653 := [unit-resolution #652 #667]: #696 +#683 := (* -1::Int #185) +#661 := (+ #21 #683) +#662 := (<= #661 0::Int) +#672 := (= #21 #185) +#457 := (= #182 #185) +#567 := (not #11) +#735 := (<= #196 0::Int) +#782 := (= #196 0::Int) +#656 := [hypothesis]: #191 +#420 := (or #776 #782) +#761 := [def-axiom]: #420 +#657 := [unit-resolution #761 #656]: #782 +#658 := (not #782) +#659 := (or #658 #735) +#654 := [th-lemma arith triangle-eq]: #659 +#660 := [unit-resolution #654 #657]: #735 +#736 := (>= #196 0::Int) +#633 := (or #658 #736) +#634 := [th-lemma arith triangle-eq]: #633 +#635 := [unit-resolution #634 #657]: #736 +#621 := (not #735) +#619 := (not #736) +#622 := (or #567 #619 #621) +#726 := (= 0::Int #9) +#730 := [hypothesis]: #11 +#724 := [symm #730]: #726 +#727 := (= #199 0::Int) +#372 := (= #185 0::Int) +#774 := (or #567 #372) +#448 := [def-axiom]: #774 +#737 := [unit-resolution #448 #730]: #372 +#723 := (= #199 #185) +#569 := (= #185 #199) +#566 := [hypothesis]: #735 +#568 := [hypothesis]: #736 +#722 := [th-lemma arith eq-propagate -1 -1 #568 #566]: #569 +#725 := [symm #722]: #723 +#609 := [trans #725 #737]: #727 +#611 := [trans #609 #724]: #610 +#620 := [monotonicity #611]: #718 +#716 := [symm #620]: #715 +#427 := (= f3 #426) +#38 := (:var 0 S2) +#39 := (f5 #38) +#786 := (pattern #39) +#40 := (f4 #39) +#215 := (= #38 #40) +#787 := (forall (vars (?v0 S2)) (:pat #786) #215) +#218 := (forall (vars (?v0 S2)) #215) +#788 := (iff #218 #787) +#790 := (iff #787 #787) +#791 := [rewrite]: #790 +#789 := [rewrite]: #788 +#792 := [trans #789 #791]: #788 +#312 := (~ #218 #218) +#310 := (~ #215 #215) +#311 := [refl]: #310 +#313 := [nnf-pos #311]: #312 +#41 := (= #40 #38) +#42 := (forall (vars (?v0 S2)) #41) +#219 := (iff #42 #218) +#216 := (iff #41 #215) +#217 := [rewrite]: #216 +#220 := [quant-intro #217]: #219 +#214 := [asserted]: #42 +#223 := [mp #214 #220]: #218 +#302 := [mp~ #223 #313]: #218 +#793 := [mp #302 #792]: #787 +#765 := (not #787) +#766 := (or #765 #427) +#767 := [quant-inst #8]: #766 +#570 := [unit-resolution #767 #793]: #427 +#719 := [trans #570 #716]: #205 +#208 := (not #205) +#23 := (- 1::Int) +#22 := (- #9) +#29 := (mod #22 #23) +#30 := (- #29) +#28 := (mod #9 1::Int) +#16 := (< 0::Int 1::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#31 := (ite #20 #28 #30) +#32 := (ite #11 0::Int #31) +#13 := (= 1::Int 0::Int) +#33 := (ite #13 #9 #32) +#24 := (div #22 #23) +#25 := (ite #20 #21 #24) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (* #26 1::Int) +#34 := (+ #27 #33) +#35 := (f4 #34) +#36 := (= f3 #35) +#37 := (not #36) +#211 := (iff #37 #208) +#83 := (and #16 #18) +#86 := (or #17 #83) +#130 := (or #11 #86) +#131 := (ite #130 0::Int #119) +#98 := (ite #86 #21 #95) +#101 := (ite #11 0::Int #98) +#143 := (+ #101 #131) +#146 := (f4 #143) +#149 := (= f3 #146) +#152 := (not #149) +#209 := (iff #152 #208) +#206 := (iff #149 #205) +#203 := (= #146 #202) +#200 := (= #143 #199) +#197 := (= #131 #196) +#194 := (iff #130 #191) +#188 := (or #11 #179) +#192 := (iff #188 #191) +#193 := [rewrite]: #192 +#189 := (iff #130 #188) +#180 := (iff #86 #179) +#177 := (iff #83 #169) +#172 := (and true #169) +#175 := (iff #172 #169) +#176 := [rewrite]: #175 +#173 := (iff #83 #172) +#170 := (iff #18 #169) +#171 := [rewrite]: #170 +#159 := (iff #16 true) +#160 := [rewrite]: #159 +#174 := [monotonicity #160 #171]: #173 +#178 := [trans #174 #176]: #177 +#166 := (iff #17 #156) +#161 := (and #156 true) +#164 := (iff #161 #156) +#165 := [rewrite]: #164 +#162 := (iff #17 #161) +#157 := (iff #15 #156) +#158 := [rewrite]: #157 +#163 := [monotonicity #158 #160]: #162 +#167 := [trans #163 #165]: #166 +#181 := [monotonicity #167 #178]: #180 +#190 := [monotonicity #181]: #189 +#195 := [trans #190 #193]: #194 +#198 := [monotonicity #195]: #197 +#186 := (= #101 #185) +#183 := (= #98 #182) +#184 := [monotonicity #181]: #183 +#187 := [monotonicity #184]: #186 +#201 := [monotonicity #187 #198]: #200 +#204 := [monotonicity #201]: #203 +#207 := [monotonicity #204]: #206 +#210 := [monotonicity #207]: #209 +#153 := (iff #37 #152) +#150 := (iff #36 #149) +#147 := (= #35 #146) +#144 := (= #34 #143) +#141 := (= #33 #131) +#136 := (ite false #9 #131) +#139 := (= #136 #131) +#140 := [rewrite]: #139 +#137 := (= #33 #136) +#134 := (= #32 #131) +#124 := (ite #86 0::Int #119) +#127 := (ite #11 0::Int #124) +#132 := (= #127 #131) +#133 := [rewrite]: #132 +#128 := (= #32 #127) +#125 := (= #31 #124) +#122 := (= #30 #119) +#116 := (- #113) +#120 := (= #116 #119) +#121 := [rewrite]: #120 +#117 := (= #30 #116) +#114 := (= #29 #113) +#93 := (= #23 -1::Int) +#94 := [rewrite]: #93 +#91 := (= #22 #90) +#92 := [rewrite]: #91 +#115 := [monotonicity #92 #94]: #114 +#118 := [monotonicity #115]: #117 +#123 := [trans #118 #121]: #122 +#111 := (= #28 0::Int) +#112 := [rewrite]: #111 +#87 := (iff #20 #86) +#84 := (iff #19 #83) +#85 := [rewrite]: #84 +#88 := [monotonicity #85]: #87 +#126 := [monotonicity #88 #112 #123]: #125 +#129 := [monotonicity #126]: #128 +#135 := [trans #129 #133]: #134 +#74 := (iff #13 false) +#75 := [rewrite]: #74 +#138 := [monotonicity #75 #135]: #137 +#142 := [trans #138 #140]: #141 +#109 := (= #27 #101) +#104 := (* #101 1::Int) +#107 := (= #104 #101) +#108 := [rewrite]: #107 +#105 := (= #27 #104) +#102 := (= #26 #101) +#99 := (= #25 #98) +#96 := (= #24 #95) +#97 := [monotonicity #92 #94]: #96 +#100 := [monotonicity #88 #97]: #99 +#81 := (iff #14 #11) +#76 := (or #11 false) +#79 := (iff #76 #11) +#80 := [rewrite]: #79 +#77 := (iff #14 #76) +#78 := [monotonicity #75]: #77 +#82 := [trans #78 #80]: #81 +#103 := [monotonicity #82 #100]: #102 +#106 := [monotonicity #103]: #105 +#110 := [trans #106 #108]: #109 +#145 := [monotonicity #110 #142]: #144 +#148 := [monotonicity #145]: #147 #151 := [monotonicity #148]: #150 -#156 := [trans #151 #154]: #155 -#159 := [quant-intro #156]: #158 -#141 := (iff #29 #140) -#138 := (iff #28 #135) -#131 := (implies #24 #127) -#136 := (iff #131 #135) -#137 := [rewrite]: #136 -#132 := (iff #28 #131) -#129 := (iff #27 #127) -#130 := [rewrite]: #129 -#133 := [monotonicity #130]: #132 -#139 := [trans #133 #137]: #138 -#142 := [quant-intro #139]: #141 -#161 := [trans #142 #159]: #160 -#126 := [asserted]: #29 -#162 := [mp #126 #161]: #157 -#331 := [mp~ #162 #335]: #157 -#911 := [mp #331 #910]: #906 -#895 := (not #906) -#890 := (or #895 #560 #891) -#896 := (or #895 #892) -#546 := (iff #896 #890) -#551 := [rewrite]: #546 -#886 := [quant-inst #11]: #896 -#887 := [mp #886 #551]: #890 -#544 := [unit-resolution #887 #911]: #892 -#533 := [unit-resolution #544 #543]: #560 -#519 := [mp #533 #524]: #865 -#525 := (or #676 #685) -#499 := [th-lemma arith triangle-eq]: #525 -#504 := [unit-resolution #499 #519]: #685 -#505 := [unit-resolution #625 #541]: #824 -[th-lemma arith farkas 1 1 -1 1 #505 #504 #550 #669]: false -unsat -bf4ed7a0c67dc55dd17034c099d4eaab353230e6 827 0 +#154 := [monotonicity #151]: #153 +#212 := [trans #154 #210]: #211 +#73 := [asserted]: #37 +#213 := [mp #73 #212]: #208 +#604 := [unit-resolution #213 #719]: false +#615 := [lemma #604]: #622 +#528 := [unit-resolution #615 #635 #660]: #567 +#449 := (or #11 #457) +#781 := [def-axiom]: #449 +#639 := [unit-resolution #781 #528]: #457 +#373 := (= #21 #182) +#471 := (f5 #426) +#749 := (= #471 0::Int) +#649 := (not #749) +#645 := (iff #567 #649) +#647 := (iff #11 #749) +#643 := (iff #749 #11) +#646 := (= #471 #9) +#640 := (= #426 f3) +#641 := [symm #570]: #640 +#642 := [monotonicity #641]: #646 +#644 := [monotonicity #642]: #643 +#648 := [symm #644]: #647 +#650 := [monotonicity #648]: #645 +#630 := [mp #528 #650]: #649 +#739 := (or #168 #749) +#43 := (:var 0 Int) +#45 := (f4 #43) +#794 := (pattern #45) +#239 := (>= #43 0::Int) +#46 := (f5 #45) +#51 := (= #46 0::Int) +#288 := (or #51 #239) +#801 := (forall (vars (?v0 Int)) (:pat #794) #288) +#293 := (forall (vars (?v0 Int)) #288) +#804 := (iff #293 #801) +#802 := (iff #288 #288) +#803 := [refl]: #802 +#805 := [quant-intro #803]: #804 +#306 := (~ #293 #293) +#314 := (~ #288 #288) +#315 := [refl]: #314 +#307 := [nnf-pos #315]: #306 +#50 := (< #43 0::Int) +#52 := (implies #50 #51) +#53 := (forall (vars (?v0 Int)) #52) +#296 := (iff #53 #293) +#259 := (= 0::Int #46) +#265 := (not #50) +#266 := (or #265 #259) +#271 := (forall (vars (?v0 Int)) #266) +#294 := (iff #271 #293) +#291 := (iff #266 #288) +#285 := (or #239 #51) +#289 := (iff #285 #288) +#290 := [rewrite]: #289 +#286 := (iff #266 #285) +#283 := (iff #259 #51) +#284 := [rewrite]: #283 +#281 := (iff #265 #239) +#241 := (not #239) +#276 := (not #241) +#279 := (iff #276 #239) +#280 := [rewrite]: #279 +#277 := (iff #265 #276) +#274 := (iff #50 #241) +#275 := [rewrite]: #274 +#278 := [monotonicity #275]: #277 +#282 := [trans #278 #280]: #281 +#287 := [monotonicity #282 #284]: #286 +#292 := [trans #287 #290]: #291 +#295 := [quant-intro #292]: #294 +#272 := (iff #53 #271) +#269 := (iff #52 #266) +#262 := (implies #50 #259) +#267 := (iff #262 #266) +#268 := [rewrite]: #267 +#263 := (iff #52 #262) +#260 := (iff #51 #259) +#261 := [rewrite]: #260 +#264 := [monotonicity #261]: #263 +#270 := [trans #264 #268]: #269 +#273 := [quant-intro #270]: #272 +#297 := [trans #273 #295]: #296 +#258 := [asserted]: #53 +#298 := [mp #258 #297]: #293 +#316 := [mp~ #298 #307]: #293 +#806 := [mp #316 #805]: #801 +#750 := (not #801) +#740 := (or #750 #168 #749) +#738 := (or #749 #168) +#746 := (or #750 #738) +#734 := (iff #746 #740) +#588 := (or #750 #739) +#732 := (iff #588 #740) +#733 := [rewrite]: #732 +#589 := (iff #746 #588) +#744 := (iff #738 #739) +#745 := [rewrite]: #744 +#731 := [monotonicity #745]: #589 +#728 := [trans #731 #733]: #734 +#587 := [quant-inst #9]: #746 +#729 := [mp #587 #728]: #740 +#576 := [unit-resolution #729 #806]: #739 +#631 := [unit-resolution #576 #630]: #168 +#436 := (or #776 #11 #156 #169) +#777 := [def-axiom]: #436 +#612 := [unit-resolution #777 #631 #528 #656]: #156 +#459 := (or #179 #155) +#450 := [def-axiom]: #459 +#636 := [unit-resolution #450 #612]: #179 +#463 := (not #179) +#443 := (or #463 #373) +#778 := [def-axiom]: #443 +#637 := [unit-resolution #778 #636]: #373 +#632 := [trans #637 #639]: #672 +#638 := (not #672) +#606 := (or #638 #662) +#613 := [th-lemma arith triangle-eq]: #606 +#572 := [unit-resolution #613 #632]: #662 +#664 := (>= #661 0::Int) +#603 := (or #638 #664) +#605 := [th-lemma arith triangle-eq]: #603 +#607 := [unit-resolution #605 #632]: #664 +#616 := [th-lemma arith eq-propagate 1 1 1 1 #607 #572 #653 #655]: #614 +#608 := [symm #616]: #628 +#617 := [th-lemma arith eq-propagate -1 -1 #635 #660]: #569 +#618 := [symm #617]: #723 +#629 := [trans #618 #608]: #610 +#584 := [monotonicity #629]: #718 +#585 := [symm #584]: #715 +#590 := [trans #570 #585]: #205 +#591 := [unit-resolution #213 #590]: false +#592 := [lemma #591]: #776 +#435 := (or #191 #168) +#440 := [def-axiom]: #435 +#533 := [unit-resolution #440 #592]: #168 +#785 := (or #191 #155) +#775 := [def-axiom]: #785 +#534 := [unit-resolution #775 #592]: #155 +#784 := (or #191 #567) +#779 := [def-axiom]: #784 +#538 := [unit-resolution #779 #592]: #567 +#531 := [th-lemma arith triangle-eq]: #191 +[unit-resolution #531 #538 #534 #533]: false +unsat +9915a65ab7888a474bcd2f001f0a80c1938cedba 411 0 #2 := false decl f4 :: (-> Int S2) -decl f7 :: (-> Int Int Int) -#10 := 1::Int -decl f6 :: (-> S2 Int) +#93 := -3::Int +decl f5 :: (-> S2 Int) decl f3 :: S2 #8 := f3 -#9 := (f6 f3) -#13 := (f7 #9 1::Int) -decl f5 :: (-> Int Int Int) -#11 := (f5 #9 1::Int) -#85 := (+ #11 #13) -#88 := (f4 #85) -#91 := (= f3 #88) -#552 := (f6 #88) -#470 := (f4 #552) -#983 := (= #470 #88) -#473 := (= #88 #470) -#18 := (:var 0 S2) -#19 := (f6 #18) -#875 := (pattern #19) -#20 := (f4 #19) -#98 := (= #18 #20) -#876 := (forall (vars (?v0 S2)) (:pat #875) #98) -#102 := (forall (vars (?v0 S2)) #98) -#877 := (iff #102 #876) -#879 := (iff #876 #876) -#880 := [rewrite]: #879 -#878 := [rewrite]: #877 -#881 := [trans #878 #880]: #877 -#325 := (~ #102 #102) -#323 := (~ #98 #98) -#324 := [refl]: #323 -#326 := [nnf-pos #324]: #325 -#21 := (= #20 #18) -#22 := (forall (vars (?v0 S2)) #21) -#103 := (iff #22 #102) -#100 := (iff #21 #98) -#101 := [rewrite]: #100 -#104 := [quant-intro #101]: #103 -#97 := [asserted]: #22 -#107 := [mp #97 #104]: #102 -#311 := [mp~ #107 #326]: #102 -#882 := [mp #311 #881]: #876 -#539 := (not #876) -#931 := (or #539 #473) -#932 := [quant-inst #88]: #931 -#978 := [unit-resolution #932 #882]: #473 -#984 := [symm #978]: #983 -#985 := (= f3 #470) -#462 := (f4 #9) -#981 := (= #462 #470) -#979 := (= #470 #462) -#976 := (= #552 #9) -#23 := 0::Int -#974 := (= 0::Int #9) -#847 := (= #9 0::Int) -#935 := (= #462 #88) -#933 := (= #9 #85) -#916 := (= #11 #85) -#670 := (<= #13 0::Int) -#757 := (= #13 0::Int) -#844 := (<= #9 0::Int) -#676 := (not #844) -#572 := (>= #9 0::Int) -#825 := (not #572) -#718 := (or #825 #676 #847) -#494 := [hypothesis]: #825 -#630 := (f6 #462) -#633 := (= #630 0::Int) -#510 := (iff #633 #847) -#530 := (= #630 #9) -#480 := (= #9 #630) -#546 := (= f3 #462) -#550 := (or #539 #546) -#551 := [quant-inst #8]: #550 -#534 := [unit-resolution #551 #882]: #546 -#481 := [monotonicity #534]: #480 -#484 := [symm #481]: #530 -#485 := [monotonicity #484]: #510 -#639 := (or #572 #633) -#24 := (:var 0 Int) -#26 := (f4 #24) -#883 := (pattern #26) -#124 := (>= #24 0::Int) -#27 := (f6 #26) -#32 := (= #27 0::Int) -#172 := (or #32 #124) -#890 := (forall (vars (?v0 Int)) (:pat #883) #172) -#177 := (forall (vars (?v0 Int)) #172) -#893 := (iff #177 #890) -#891 := (iff #172 #172) -#892 := [refl]: #891 -#894 := [quant-intro #892]: #893 -#315 := (~ #177 #177) -#327 := (~ #172 #172) -#328 := [refl]: #327 -#316 := [nnf-pos #328]: #315 -#31 := (< #24 0::Int) -#33 := (implies #31 #32) -#34 := (forall (vars (?v0 Int)) #33) -#180 := (iff #34 #177) -#143 := (= 0::Int #27) -#149 := (not #31) -#150 := (or #149 #143) -#155 := (forall (vars (?v0 Int)) #150) -#178 := (iff #155 #177) -#175 := (iff #150 #172) -#169 := (or #124 #32) -#173 := (iff #169 #172) -#174 := [rewrite]: #173 -#170 := (iff #150 #169) -#167 := (iff #143 #32) -#168 := [rewrite]: #167 -#165 := (iff #149 #124) -#125 := (not #124) -#160 := (not #125) -#163 := (iff #160 #124) -#164 := [rewrite]: #163 -#161 := (iff #149 #160) -#158 := (iff #31 #125) +#9 := (f5 f3) +#89 := -1::Int +#90 := (* -1::Int #9) +#113 := (mod #90 -3::Int) +#119 := (* -1::Int #113) +#12 := 3::Int +#28 := (mod #9 3::Int) +#10 := 0::Int +#162 := (>= #9 0::Int) +#163 := (not #162) +#149 := (<= #9 0::Int) +#150 := (not #149) +#173 := (or #150 #163) +#185 := (ite #173 #28 #119) +#11 := (= #9 0::Int) +#188 := (ite #11 0::Int #185) +#96 := (div #90 -3::Int) +#21 := (div #9 3::Int) +#176 := (ite #173 #21 #96) +#179 := (ite #11 0::Int #176) +#182 := (* 3::Int #179) +#191 := (+ #182 #188) +#194 := (f4 #191) +#197 := (= f3 #194) +#413 := (f4 #9) +#714 := (= #413 #194) +#713 := (= #194 #413) +#618 := (= #191 #9) +#579 := (= #9 #191) +#693 := (* -1::Int #28) +#699 := (* -3::Int #21) +#700 := (+ #699 #693) +#684 := (+ #9 #700) +#688 := (<= #684 0::Int) +#698 := (= #684 0::Int) +#1 := true +#71 := [true-axiom]: true +#630 := (or false #698) +#625 := [th-lemma arith]: #630 +#631 := [unit-resolution #625 #71]: #698 +#599 := (not #698) +#606 := (or #599 #688) +#565 := [th-lemma arith triangle-eq]: #606 +#596 := [unit-resolution #565 #631]: #688 +#689 := (>= #684 0::Int) +#584 := (or #599 #689) +#585 := [th-lemma arith triangle-eq]: #584 +#588 := [unit-resolution #585 #631]: #689 +#660 := (* -1::Int #179) +#661 := (+ #21 #660) +#656 := (<= #661 0::Int) +#659 := (= #21 #179) +#450 := (= #176 #179) +#430 := (not #11) +#616 := (= 0::Int #9) +#716 := [hypothesis]: #11 +#617 := [symm #716]: #616 +#615 := (= #191 0::Int) +#562 := (<= #188 0::Int) +#774 := (= #188 0::Int) +#433 := (or #430 #774) +#769 := [def-axiom]: #433 +#718 := [unit-resolution #769 #716]: #774 +#719 := (not #774) +#717 := (or #719 #562) +#720 := [th-lemma arith triangle-eq]: #717 +#602 := [unit-resolution #720 #718]: #562 +#715 := (>= #188 0::Int) +#603 := (or #719 #715) +#604 := [th-lemma arith triangle-eq]: #603 +#563 := [unit-resolution #604 #718]: #715 +#559 := (<= #179 0::Int) +#364 := (= #179 0::Int) +#560 := (or #430 #364) +#767 := [def-axiom]: #560 +#711 := [unit-resolution #767 #716]: #364 +#613 := (not #364) +#708 := (or #613 #559) +#709 := [th-lemma arith triangle-eq]: #708 +#712 := [unit-resolution #709 #711]: #559 +#561 := (>= #179 0::Int) +#597 := (or #613 #561) +#612 := [th-lemma arith triangle-eq]: #597 +#614 := [unit-resolution #612 #711]: #561 +#608 := [th-lemma arith eq-propagate -3 -3 -1 -1 #614 #712 #563 #602]: #615 +#619 := [trans #608 #617]: #618 +#710 := [monotonicity #619]: #713 +#701 := [symm #710]: #714 +#754 := (= f3 #413) +#38 := (:var 0 S2) +#39 := (f5 #38) +#779 := (pattern #39) +#40 := (f4 #39) +#207 := (= #38 #40) +#780 := (forall (vars (?v0 S2)) (:pat #779) #207) +#210 := (forall (vars (?v0 S2)) #207) +#781 := (iff #210 #780) +#783 := (iff #780 #780) +#784 := [rewrite]: #783 +#782 := [rewrite]: #781 +#785 := [trans #782 #784]: #781 +#304 := (~ #210 #210) +#302 := (~ #207 #207) +#303 := [refl]: #302 +#305 := [nnf-pos #303]: #304 +#41 := (= #40 #38) +#42 := (forall (vars (?v0 S2)) #41) +#211 := (iff #42 #210) +#208 := (iff #41 #207) +#209 := [rewrite]: #208 +#212 := [quant-intro #209]: #211 +#206 := [asserted]: #42 +#215 := [mp #206 #212]: #210 +#294 := [mp~ #215 #305]: #210 +#786 := [mp #294 #785]: #780 +#419 := (not #780) +#420 := (or #419 #754) +#756 := [quant-inst #8]: #420 +#620 := [unit-resolution #756 #786]: #754 +#703 := [trans #620 #701]: #197 +#200 := (not #197) +#23 := (- 3::Int) +#22 := (- #9) +#29 := (mod #22 #23) +#30 := (- #29) +#16 := (< 0::Int 3::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#31 := (ite #20 #28 #30) +#32 := (ite #11 0::Int #31) +#13 := (= 3::Int 0::Int) +#33 := (ite #13 #9 #32) +#24 := (div #22 #23) +#25 := (ite #20 #21 #24) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (* #26 3::Int) +#34 := (+ #27 #33) +#35 := (f4 #34) +#36 := (= f3 #35) +#37 := (not #36) +#203 := (iff #37 #200) +#83 := (and #16 #18) +#86 := (or #17 #83) +#124 := (ite #86 #28 #119) +#127 := (ite #11 0::Int #124) +#99 := (ite #86 #21 #96) +#102 := (ite #11 0::Int #99) +#108 := (* 3::Int #102) +#137 := (+ #108 #127) +#140 := (f4 #137) +#143 := (= f3 #140) +#146 := (not #143) +#201 := (iff #146 #200) +#198 := (iff #143 #197) +#195 := (= #140 #194) +#192 := (= #137 #191) +#189 := (= #127 #188) +#186 := (= #124 #185) +#174 := (iff #86 #173) +#171 := (iff #83 #163) +#166 := (and true #163) +#169 := (iff #166 #163) +#170 := [rewrite]: #169 +#167 := (iff #83 #166) +#164 := (iff #18 #163) +#165 := [rewrite]: #164 +#153 := (iff #16 true) +#154 := [rewrite]: #153 +#168 := [monotonicity #154 #165]: #167 +#172 := [trans #168 #170]: #171 +#160 := (iff #17 #150) +#155 := (and #150 true) +#158 := (iff #155 #150) #159 := [rewrite]: #158 -#162 := [monotonicity #159]: #161 -#166 := [trans #162 #164]: #165 -#171 := [monotonicity #166 #168]: #170 -#176 := [trans #171 #174]: #175 -#179 := [quant-intro #176]: #178 -#156 := (iff #34 #155) -#153 := (iff #33 #150) -#146 := (implies #31 #143) -#151 := (iff #146 #150) +#156 := (iff #17 #155) +#151 := (iff #15 #150) #152 := [rewrite]: #151 -#147 := (iff #33 #146) -#144 := (iff #32 #143) -#145 := [rewrite]: #144 -#148 := [monotonicity #145]: #147 -#154 := [trans #148 #152]: #153 -#157 := [quant-intro #154]: #156 -#181 := [trans #157 #179]: #180 -#142 := [asserted]: #34 -#182 := [mp #142 #181]: #177 -#329 := [mp~ #182 #316]: #177 -#895 := [mp #329 #894]: #890 -#853 := (not #890) -#641 := (or #853 #572 #633) -#637 := (or #633 #572) -#629 := (or #853 #637) -#616 := (iff #629 #641) -#634 := (or #853 #639) -#636 := (iff #634 #641) -#626 := [rewrite]: #636 -#635 := (iff #629 #634) -#640 := (iff #637 #639) -#638 := [rewrite]: #640 -#631 := [monotonicity #638]: #635 -#618 := [trans #631 #626]: #616 -#632 := [quant-inst #9]: #629 -#619 := [mp #632 #618]: #641 -#511 := [unit-resolution #619 #895]: #639 -#477 := [unit-resolution #511 #494]: #633 -#486 := [mp #477 #485]: #847 -#763 := (not #847) -#479 := (or #763 #572) -#487 := [th-lemma arith triangle-eq]: #479 -#472 := [unit-resolution #487 #486 #494]: false -#469 := [lemma #472]: #572 -#474 := [hypothesis]: #763 -#504 := (or #847 #676 #825) -#506 := [th-lemma arith triangle-eq]: #504 -#475 := [unit-resolution #506 #474 #469]: #676 -#662 := (or #718 #844) -#663 := [def-axiom]: #662 -#463 := [unit-resolution #663 #475]: #718 -#667 := (not #718) -#466 := (or #667 #757) -#199 := -1::Int -#852 := (* -1::Int #9) -#784 := (mod #852 -1::Int) -#736 := (+ #13 #784) -#734 := (= #736 0::Int) -#679 := (ite #718 #757 #734) -#35 := (:var 1 Int) -#54 := (f7 #35 #24) -#903 := (pattern #54) -#203 := (* -1::Int #24) -#200 := (* -1::Int #35) -#264 := (mod #200 #203) -#394 := (+ #54 #264) -#395 := (= #394 0::Int) -#55 := (mod #35 #24) -#391 := (* -1::Int #55) -#392 := (+ #54 #391) -#393 := (= #392 0::Int) -#238 := (>= #35 0::Int) -#231 := (<= #24 0::Int) -#338 := (or #231 #238) -#339 := (not #338) -#227 := (<= #35 0::Int) -#336 := (or #227 #231) -#337 := (not #336) -#342 := (or #337 #339) -#396 := (ite #342 #393 #395) -#390 := (= #54 0::Int) -#37 := (= #35 0::Int) -#397 := (ite #37 #390 #396) -#389 := (= #35 #54) -#38 := (= #24 0::Int) -#398 := (ite #38 #389 #397) -#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #398) -#401 := (forall (vars (?v0 Int) (?v1 Int)) #398) -#907 := (iff #401 #904) -#905 := (iff #398 #398) -#906 := [refl]: #905 -#908 := [quant-intro #906]: #907 -#270 := (* -1::Int #264) -#358 := (ite #342 #55 #270) -#361 := (ite #37 0::Int #358) -#364 := (ite #38 #35 #361) -#367 := (= #54 #364) -#370 := (forall (vars (?v0 Int) (?v1 Int)) #367) -#402 := (iff #370 #401) -#399 := (iff #367 #398) -#400 := [rewrite]: #399 -#403 := [quant-intro #400]: #402 -#239 := (not #238) -#232 := (not #231) -#242 := (and #232 #239) -#228 := (not #227) -#235 := (and #228 #232) -#245 := (or #235 #242) -#290 := (ite #245 #55 #270) -#293 := (ite #37 0::Int #290) -#296 := (ite #38 #35 #293) -#299 := (= #54 #296) -#302 := (forall (vars (?v0 Int) (?v1 Int)) #299) -#371 := (iff #302 #370) -#368 := (iff #299 #367) -#365 := (= #296 #364) -#362 := (= #293 #361) -#359 := (= #290 #358) -#343 := (iff #245 #342) -#340 := (iff #242 #339) -#341 := [rewrite]: #340 -#321 := (iff #235 #337) -#322 := [rewrite]: #321 -#344 := [monotonicity #322 #341]: #343 -#360 := [monotonicity #344]: #359 -#363 := [monotonicity #360]: #362 -#366 := [monotonicity #363]: #365 -#369 := [monotonicity #366]: #368 -#372 := [quant-intro #369]: #371 -#319 := (~ #302 #302) -#333 := (~ #299 #299) -#334 := [refl]: #333 -#320 := [nnf-pos #334]: #319 -#48 := (- #24) -#47 := (- #35) -#56 := (mod #47 #48) -#57 := (- #56) -#41 := (< 0::Int #24) -#43 := (< #35 0::Int) -#44 := (and #43 #41) -#40 := (< 0::Int #35) -#42 := (and #40 #41) -#45 := (or #42 #44) -#58 := (ite #45 #55 #57) -#59 := (ite #37 0::Int #58) -#60 := (ite #38 #35 #59) -#61 := (= #54 #60) -#62 := (forall (vars (?v0 Int) (?v1 Int)) #61) -#305 := (iff #62 #302) -#193 := (and #41 #43) -#196 := (or #42 #193) -#275 := (ite #196 #55 #270) -#184 := (= 0::Int #35) -#278 := (ite #184 0::Int #275) -#187 := (= 0::Int #24) -#281 := (ite #187 #35 #278) -#284 := (= #54 #281) -#287 := (forall (vars (?v0 Int) (?v1 Int)) #284) -#303 := (iff #287 #302) -#300 := (iff #284 #299) -#297 := (= #281 #296) -#294 := (= #278 #293) -#291 := (= #275 #290) -#246 := (iff #196 #245) -#243 := (iff #193 #242) -#240 := (iff #43 #239) -#241 := [rewrite]: #240 -#233 := (iff #41 #232) -#234 := [rewrite]: #233 -#244 := [monotonicity #234 #241]: #243 -#236 := (iff #42 #235) -#229 := (iff #40 #228) -#230 := [rewrite]: #229 -#237 := [monotonicity #230 #234]: #236 -#247 := [monotonicity #237 #244]: #246 -#292 := [monotonicity #247]: #291 -#221 := (iff #184 #37) -#222 := [rewrite]: #221 -#295 := [monotonicity #222 #292]: #294 -#223 := (iff #187 #38) -#224 := [rewrite]: #223 -#298 := [monotonicity #224 #295]: #297 -#301 := [monotonicity #298]: #300 -#304 := [quant-intro #301]: #303 -#288 := (iff #62 #287) -#285 := (iff #61 #284) -#282 := (= #60 #281) -#279 := (= #59 #278) -#276 := (= #58 #275) -#273 := (= #57 #270) -#267 := (- #264) -#271 := (= #267 #270) -#272 := [rewrite]: #271 -#268 := (= #57 #267) -#265 := (= #56 #264) -#204 := (= #48 #203) -#205 := [rewrite]: #204 -#201 := (= #47 #200) -#202 := [rewrite]: #201 -#266 := [monotonicity #202 #205]: #265 -#269 := [monotonicity #266]: #268 -#274 := [trans #269 #272]: #273 -#197 := (iff #45 #196) -#194 := (iff #44 #193) -#195 := [rewrite]: #194 -#198 := [monotonicity #195]: #197 -#277 := [monotonicity #198 #274]: #276 -#185 := (iff #37 #184) -#186 := [rewrite]: #185 -#280 := [monotonicity #186 #277]: #279 -#188 := (iff #38 #187) -#189 := [rewrite]: #188 -#283 := [monotonicity #189 #280]: #282 -#286 := [monotonicity #283]: #285 -#289 := [quant-intro #286]: #288 -#306 := [trans #289 #304]: #305 -#263 := [asserted]: #62 -#307 := [mp #263 #306]: #302 -#335 := [mp~ #307 #320]: #302 -#373 := [mp #335 #372]: #370 -#404 := [mp #373 #403]: #401 -#909 := [mp #404 #908]: #904 -#684 := (not #904) -#685 := (or #684 #679) -#516 := (* -1::Int 1::Int) -#772 := (mod #852 #516) -#750 := (+ #13 #772) -#751 := (= #750 0::Int) -#780 := (mod #9 1::Int) -#753 := (* -1::Int #780) -#754 := (+ #13 #753) -#755 := (= #754 0::Int) -#573 := (<= 1::Int 0::Int) -#574 := (or #573 #572) -#468 := (not #574) -#845 := (or #844 #573) -#567 := (not #845) -#568 := (or #567 #468) -#756 := (ite #568 #755 #751) -#752 := (ite #847 #757 #756) -#758 := (= #9 #13) -#843 := (= 1::Int 0::Int) -#744 := (ite #843 #758 #752) -#686 := (or #684 #744) -#688 := (iff #686 #685) -#690 := (iff #685 #685) -#675 := [rewrite]: #690 -#682 := (iff #744 #679) -#811 := (or #825 #676) -#727 := (or #811 #847) -#695 := (ite #727 #757 #734) -#680 := (iff #695 #679) -#673 := (iff #727 #718) -#674 := [rewrite]: #673 -#681 := [monotonicity #674]: #680 -#717 := (iff #744 #695) -#696 := (ite false #758 #695) -#706 := (iff #696 #695) -#707 := [rewrite]: #706 -#703 := (iff #744 #696) -#692 := (iff #752 #695) -#665 := (ite #811 #757 #734) -#725 := (ite #847 #757 #665) -#702 := (iff #725 #695) -#661 := [rewrite]: #702 -#726 := (iff #752 #725) -#720 := (iff #756 #665) -#739 := (iff #751 #734) -#737 := (= #750 #736) -#732 := (= #772 #784) -#816 := (= #516 -1::Int) -#698 := [rewrite]: #816 -#733 := [monotonicity #698]: #732 -#738 := [monotonicity #733]: #737 -#719 := [monotonicity #738]: #739 -#735 := (iff #755 #757) -#729 := (= #754 #13) -#722 := (+ #13 0::Int) -#617 := (= #722 #13) -#728 := [rewrite]: #617 -#723 := (= #754 #722) -#743 := (= #753 0::Int) -#742 := (* -1::Int 0::Int) -#747 := (= #742 0::Int) -#748 := [rewrite]: #747 -#745 := (= #753 #742) -#740 := (= #780 0::Int) -#741 := [rewrite]: #740 -#746 := [monotonicity #741]: #745 -#749 := [trans #746 #748]: #743 -#724 := [monotonicity #749]: #723 -#730 := [trans #724 #728]: #729 -#731 := [monotonicity #730]: #735 -#815 := (iff #568 #811) -#655 := (or #676 #825) -#812 := (iff #655 #811) -#814 := [rewrite]: #812 -#657 := (iff #568 #655) -#819 := (iff #468 #825) -#818 := (iff #574 #572) -#820 := (or false #572) -#823 := (iff #820 #572) -#817 := [rewrite]: #823 -#821 := (iff #574 #820) -#830 := (iff #573 false) -#831 := [rewrite]: #830 -#822 := [monotonicity #831]: #821 -#824 := [trans #822 #817]: #818 -#826 := [monotonicity #824]: #819 -#677 := (iff #567 #676) -#829 := (iff #845 #844) -#832 := (or #844 false) -#833 := (iff #832 #844) -#834 := [rewrite]: #833 -#827 := (iff #845 #832) -#828 := [monotonicity #831]: #827 -#835 := [trans #828 #834]: #829 -#678 := [monotonicity #835]: #677 -#658 := [monotonicity #678 #826]: #657 -#813 := [trans #658 #814]: #815 -#701 := [monotonicity #813 #731 #719]: #720 -#721 := [monotonicity #701]: #726 -#694 := [trans #721 #661]: #692 -#559 := (iff #843 false) -#560 := [rewrite]: #559 -#705 := [monotonicity #560 #694]: #703 -#697 := [trans #705 #707]: #717 -#683 := [trans #697 #681]: #682 -#689 := [monotonicity #683]: #688 -#691 := [trans #689 #675]: #688 -#687 := [quant-inst #9 #10]: #686 -#652 := [mp #687 #691]: #685 -#465 := [unit-resolution #652 #909]: #679 -#642 := (not #679) -#643 := (or #642 #667 #757) -#644 := [def-axiom]: #643 -#464 := [unit-resolution #644 #465]: #466 -#467 := [unit-resolution #464 #463]: #757 -#648 := (not #757) -#910 := (or #648 #670) -#911 := [th-lemma arith triangle-eq]: #910 -#912 := [unit-resolution #911 #467]: #670 -#671 := (>= #13 0::Int) -#913 := (or #648 #671) -#914 := [th-lemma arith triangle-eq]: #913 -#915 := [unit-resolution #914 #467]: #671 -#917 := [th-lemma arith eq-propagate -1 -1 #915 #912]: #916 -#929 := (= #9 #11) -#862 := (div #9 1::Int) -#848 := (* -1::Int #862) -#849 := (+ #11 #848) -#781 := (<= #849 0::Int) -#571 := (= #849 0::Int) -#793 := (or #811 #844) -#794 := [def-axiom]: #793 -#918 := [unit-resolution #794 #475]: #811 -#699 := (div #852 -1::Int) -#807 := (* -1::Int #699) -#805 := (+ #11 #807) -#708 := (= #805 0::Int) -#704 := (ite #811 #571 #708) -#542 := (or #847 #704) -#846 := (= #11 0::Int) -#714 := (ite #847 #846 #704) -#36 := (f5 #35 #24) -#896 := (pattern #36) -#206 := (div #200 #203) -#378 := (* -1::Int #206) -#379 := (+ #36 #378) -#380 := (= #379 0::Int) -#46 := (div #35 #24) -#375 := (* -1::Int #46) -#376 := (+ #36 #375) -#377 := (= #376 0::Int) -#381 := (ite #342 #377 #380) -#374 := (= #36 0::Int) -#39 := (or #37 #38) -#382 := (ite #39 #374 #381) -#897 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #896) #382) -#385 := (forall (vars (?v0 Int) (?v1 Int)) #382) -#900 := (iff #385 #897) -#898 := (iff #382 #382) -#899 := [refl]: #898 -#901 := [quant-intro #899]: #900 -#345 := (ite #342 #46 #206) -#348 := (ite #39 0::Int #345) -#351 := (= #36 #348) -#354 := (forall (vars (?v0 Int) (?v1 Int)) #351) -#386 := (iff #354 #385) -#383 := (iff #351 #382) -#384 := [rewrite]: #383 -#387 := [quant-intro #384]: #386 -#248 := (ite #245 #46 #206) -#251 := (ite #39 0::Int #248) -#254 := (= #36 #251) -#257 := (forall (vars (?v0 Int) (?v1 Int)) #254) -#355 := (iff #257 #354) -#352 := (iff #254 #351) -#349 := (= #251 #348) -#346 := (= #248 #345) -#347 := [monotonicity #344]: #346 -#350 := [monotonicity #347]: #349 -#353 := [monotonicity #350]: #352 -#356 := [quant-intro #353]: #355 -#317 := (~ #257 #257) -#330 := (~ #254 #254) -#331 := [refl]: #330 -#318 := [nnf-pos #331]: #317 -#49 := (div #47 #48) -#50 := (ite #45 #46 #49) -#51 := (ite #39 0::Int #50) -#52 := (= #36 #51) -#53 := (forall (vars (?v0 Int) (?v1 Int)) #52) -#260 := (iff #53 #257) -#209 := (ite #196 #46 #206) -#190 := (or #184 #187) -#212 := (ite #190 0::Int #209) -#215 := (= #36 #212) -#218 := (forall (vars (?v0 Int) (?v1 Int)) #215) -#258 := (iff #218 #257) -#255 := (iff #215 #254) -#252 := (= #212 #251) -#249 := (= #209 #248) -#250 := [monotonicity #247]: #249 -#225 := (iff #190 #39) -#226 := [monotonicity #222 #224]: #225 -#253 := [monotonicity #226 #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [quant-intro #256]: #258 -#219 := (iff #53 #218) -#216 := (iff #52 #215) -#213 := (= #51 #212) -#210 := (= #50 #209) -#207 := (= #49 #206) -#208 := [monotonicity #202 #205]: #207 -#211 := [monotonicity #198 #208]: #210 -#191 := (iff #39 #190) -#192 := [monotonicity #186 #189]: #191 -#214 := [monotonicity #192 #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [quant-intro #217]: #219 -#261 := [trans #220 #259]: #260 -#183 := [asserted]: #53 -#262 := [mp #183 #261]: #257 -#332 := [mp~ #262 #318]: #257 -#357 := [mp #332 #356]: #354 -#388 := [mp #357 #387]: #385 -#902 := [mp #388 #901]: #897 -#809 := (not #897) -#806 := (or #809 #714) -#500 := (div #852 #516) -#501 := (* -1::Int #500) -#861 := (+ #11 #501) -#859 := (= #861 0::Int) -#842 := (ite #568 #571 #859) -#557 := (or #847 #843) -#558 := (ite #557 #846 #842) -#810 := (or #809 #558) -#799 := (iff #810 #806) -#788 := (iff #806 #806) -#790 := [rewrite]: #788 -#715 := (iff #558 #714) -#712 := (iff #842 #704) -#710 := (iff #859 #708) -#808 := (= #861 #805) -#709 := (= #501 #807) -#700 := (= #500 #699) -#659 := [monotonicity #698]: #700 -#804 := [monotonicity #659]: #709 -#693 := [monotonicity #804]: #808 -#711 := [monotonicity #693]: #710 -#713 := [monotonicity #813 #711]: #712 -#837 := (iff #557 #847) -#838 := (or #847 false) -#836 := (iff #838 #847) -#840 := [rewrite]: #836 -#839 := (iff #557 #838) -#554 := [monotonicity #560]: #839 -#841 := [trans #554 #840]: #837 -#716 := [monotonicity #841 #713]: #715 -#791 := [monotonicity #716]: #799 -#800 := [trans #791 #790]: #799 -#797 := [quant-inst #9 #10]: #810 -#801 := [mp #797 #800]: #806 -#536 := [unit-resolution #801 #902]: #714 -#762 := (not #714) -#766 := (or #762 #847 #704) -#767 := [def-axiom]: #766 -#543 := [unit-resolution #767 #536]: #542 -#919 := [unit-resolution #543 #474]: #704 -#795 := (not #811) -#782 := (not #704) -#787 := (or #782 #795 #571) -#773 := [def-axiom]: #787 -#920 := [unit-resolution #773 #919 #918]: #571 -#777 := (not #571) -#921 := (or #777 #781) -#922 := [th-lemma arith triangle-eq]: #921 -#923 := [unit-resolution #922 #920]: #781 -#783 := (>= #849 0::Int) -#498 := (or #777 #783) -#499 := [th-lemma arith triangle-eq]: #498 -#924 := [unit-resolution #499 #920]: #783 -#606 := (+ #9 #848) -#610 := (<= #606 0::Int) -#605 := (= #606 0::Int) -#1 := true -#80 := [true-axiom]: true -#563 := (or false #605) -#555 := [th-lemma arith]: #563 -#564 := [unit-resolution #555 #80]: #605 -#488 := (not #605) -#490 := (or #488 #610) -#491 := [th-lemma arith triangle-eq]: #490 -#925 := [unit-resolution #491 #564]: #610 -#587 := (>= #606 0::Int) -#926 := (or #488 #587) -#927 := [th-lemma arith triangle-eq]: #926 -#928 := [unit-resolution #927 #564]: #587 -#930 := [th-lemma arith eq-propagate 1 1 -1 -1 #928 #925 #924 #923]: #929 -#934 := [trans #930 #917]: #933 -#936 := [monotonicity #934]: #935 -#937 := [trans #534 #936]: #91 -#94 := (not #91) -#12 := (* #11 1::Int) -#14 := (+ #12 #13) -#15 := (f4 #14) -#16 := (= f3 #15) -#17 := (not #16) -#95 := (iff #17 #94) -#92 := (iff #16 #91) -#89 := (= #15 #88) -#86 := (= #14 #85) -#83 := (= #12 #11) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#90 := [monotonicity #87]: #89 -#93 := [monotonicity #90]: #92 -#96 := [monotonicity #93]: #95 -#82 := [asserted]: #17 -#99 := [mp #82 #96]: #94 -#938 := [unit-resolution #99 #937]: false -#939 := [lemma #938]: #847 -#975 := [symm #939]: #974 -#514 := (= #552 0::Int) -#860 := (>= #552 0::Int) -#664 := (or #718 #763) -#666 := [def-axiom]: #664 -#471 := [unit-resolution #666 #939]: #718 -#476 := [unit-resolution #464 #471]: #757 -#940 := [unit-resolution #914 #476]: #671 -#798 := (>= #11 0::Int) -#497 := (not #610) -#565 := (not #798) -#556 := [hypothesis]: #565 -#768 := (not #846) -#566 := (or #768 #798) -#533 := [th-lemma arith triangle-eq]: #566 -#535 := [unit-resolution #533 #556]: #768 -#527 := (or #763 #846) -#764 := (or #762 #763 #846) -#765 := [def-axiom]: #764 -#540 := [unit-resolution #765 #536]: #527 -#541 := [unit-resolution #540 #535]: #763 -#544 := [unit-resolution #543 #541]: #704 -#519 := (not #633) -#520 := (iff #763 #519) -#517 := (iff #847 #633) -#545 := (= #462 f3) -#528 := [symm #534]: #545 -#531 := [monotonicity #528]: #530 -#512 := [monotonicity #531]: #510 -#518 := [symm #512]: #517 -#521 := [monotonicity #518]: #520 -#522 := [mp #541 #521]: #519 -#523 := [unit-resolution #511 #522]: #572 -#507 := [unit-resolution #506 #541]: #655 -#505 := [unit-resolution #507 #523]: #676 -#508 := [unit-resolution #794 #505]: #811 -#496 := [unit-resolution #773 #508 #544]: #571 -#502 := [unit-resolution #499 #496]: #783 -#503 := (not #783) -#478 := (or #497 #825 #798 #503) -#482 := [th-lemma arith assign-bounds 1 1 -1]: #478 -#483 := [unit-resolution #482 #523 #502 #556]: #497 -#493 := [unit-resolution #491 #483 #564]: false -#489 := [lemma #493]: #798 -#532 := (* -1::Int #552) -#867 := (+ #13 #532) -#869 := (+ #11 #867) -#850 := (<= #869 0::Int) -#526 := (= #869 0::Int) -#547 := (>= #85 0::Int) -#941 := (not #671) -#942 := (or #547 #565 #941) -#943 := [th-lemma arith assign-bounds -1 -1]: #942 -#944 := [unit-resolution #943 #940 #489]: #547 -#548 := (not #547) -#537 := (or #526 #548) -#106 := (= #24 #27) -#131 := (or #106 #125) -#884 := (forall (vars (?v0 Int)) (:pat #883) #131) -#136 := (forall (vars (?v0 Int)) #131) -#887 := (iff #136 #884) -#885 := (iff #131 #131) -#886 := [refl]: #885 -#888 := [quant-intro #886]: #887 -#313 := (~ #136 #136) -#312 := (~ #131 #131) -#309 := [refl]: #312 -#314 := [nnf-pos #309]: #313 -#28 := (= #27 #24) -#25 := (<= 0::Int #24) -#29 := (implies #25 #28) -#30 := (forall (vars (?v0 Int)) #29) -#139 := (iff #30 #136) -#113 := (not #25) -#114 := (or #113 #106) -#119 := (forall (vars (?v0 Int)) #114) -#137 := (iff #119 #136) -#134 := (iff #114 #131) -#128 := (or #125 #106) -#132 := (iff #128 #131) -#133 := [rewrite]: #132 -#129 := (iff #114 #128) -#126 := (iff #113 #125) -#122 := (iff #25 #124) -#123 := [rewrite]: #122 -#127 := [monotonicity #123]: #126 -#130 := [monotonicity #127]: #129 -#135 := [trans #130 #133]: #134 -#138 := [quant-intro #135]: #137 -#120 := (iff #30 #119) -#117 := (iff #29 #114) -#110 := (implies #25 #106) -#115 := (iff #110 #114) -#116 := [rewrite]: #115 -#111 := (iff #29 #110) -#108 := (iff #28 #106) -#109 := [rewrite]: #108 -#112 := [monotonicity #109]: #111 -#118 := [trans #112 #116]: #117 -#121 := [quant-intro #118]: #120 -#140 := [trans #121 #138]: #139 -#105 := [asserted]: #30 -#141 := [mp #105 #140]: #136 -#310 := [mp~ #141 #314]: #136 -#889 := [mp #310 #888]: #884 -#871 := (not #884) -#872 := (or #871 #526 #548) -#549 := (= #85 #552) -#553 := (or #549 #548) -#873 := (or #871 #553) -#525 := (iff #873 #872) -#874 := (or #871 #537) -#529 := (iff #874 #872) -#865 := [rewrite]: #529 -#864 := (iff #873 #874) -#538 := (iff #553 #537) -#656 := (iff #549 #526) -#863 := [rewrite]: #656 -#870 := [monotonicity #863]: #538 -#524 := [monotonicity #870]: #864 -#866 := [trans #524 #865]: #525 -#868 := [quant-inst #85]: #873 -#509 := [mp #868 #866]: #872 -#945 := [unit-resolution #509 #889]: #537 -#946 := [unit-resolution #945 #944]: #526 -#947 := (not #526) -#948 := (or #947 #850) -#949 := [th-lemma arith triangle-eq]: #948 -#950 := [unit-resolution #949 #946]: #850 -#951 := (not #850) -#952 := (or #860 #941 #951 #565) -#953 := [th-lemma arith assign-bounds -1 1 -1]: #952 -#954 := [unit-resolution #953 #950 #489 #940]: #860 -#858 := (<= #552 0::Int) -#955 := [unit-resolution #911 #476]: #670 -#802 := (<= #11 0::Int) -#956 := [unit-resolution #540 #939]: #846 -#957 := (or #768 #802) -#958 := [th-lemma arith triangle-eq]: #957 -#959 := [unit-resolution #958 #956]: #802 -#513 := (>= #869 0::Int) -#960 := (or #947 #513) -#961 := [th-lemma arith triangle-eq]: #960 -#962 := [unit-resolution #961 #946]: #513 -#965 := (not #802) -#964 := (not #513) -#963 := (not #670) -#966 := (or #858 #963 #964 #965) -#967 := [th-lemma arith assign-bounds -1 1 -1]: #966 -#968 := [unit-resolution #967 #962 #959 #955]: #858 -#970 := (not #860) -#969 := (not #858) -#971 := (or #514 #969 #970) -#972 := [th-lemma arith triangle-eq]: #971 -#973 := [unit-resolution #972 #968 #954]: #514 -#977 := [trans #973 #975]: #976 -#980 := [monotonicity #977]: #979 -#982 := [symm #980]: #981 -#986 := [trans #534 #982]: #985 -#987 := [trans #986 #984]: #91 -[unit-resolution #99 #987]: false -unsat -14ea837cc40eb6dd6a11b7a7e54b897ec75d15ed 873 0 -#2 := false -decl f4 :: (-> Int S2) -decl f7 :: (-> Int Int Int) -#10 := 3::Int -decl f6 :: (-> S2 Int) -decl f3 :: S2 -#8 := f3 -#9 := (f6 f3) -#13 := (f7 #9 3::Int) -decl f5 :: (-> Int Int Int) -#11 := (f5 #9 3::Int) -#83 := (* 3::Int #11) -#86 := (+ #83 #13) -#89 := (f4 #86) -#92 := (= f3 #89) -#463 := (f4 #9) -#1031 := (= #463 #89) -#1029 := (= #89 #463) -#1027 := (= #86 #9) -#23 := 0::Int -#1023 := (= 0::Int #9) -#832 := (= #9 0::Int) -#481 := (f6 #89) -#554 := (= #86 #481) -#943 := (not #554) -#844 := (div #9 3::Int) -#200 := -1::Int -#848 := (* -1::Int #844) -#845 := (+ #11 #848) -#781 := (<= #845 0::Int) -#849 := (= #845 0::Int) -#840 := (<= #9 0::Int) -#828 := (not #840) -#559 := (>= #9 0::Int) -#700 := (not #559) -#806 := (or #700 #828) -#594 := [hypothesis]: #700 -#671 := (f6 #463) -#672 := (= #671 0::Int) -#535 := (iff #672 #832) -#558 := (= #671 #9) -#596 := (= #9 #671) -#548 := (= f3 #463) -#18 := (:var 0 S2) -#19 := (f6 #18) -#877 := (pattern #19) -#20 := (f4 #19) -#99 := (= #18 #20) -#878 := (forall (vars (?v0 S2)) (:pat #877) #99) -#103 := (forall (vars (?v0 S2)) #99) -#879 := (iff #103 #878) -#881 := (iff #878 #878) -#882 := [rewrite]: #881 -#880 := [rewrite]: #879 -#883 := [trans #880 #882]: #879 -#326 := (~ #103 #103) -#324 := (~ #99 #99) -#325 := [refl]: #324 -#327 := [nnf-pos #325]: #326 -#21 := (= #20 #18) -#22 := (forall (vars (?v0 S2)) #21) -#104 := (iff #22 #103) -#101 := (iff #21 #99) -#102 := [rewrite]: #101 -#105 := [quant-intro #102]: #104 -#98 := [asserted]: #22 -#108 := [mp #98 #105]: #103 -#312 := [mp~ #108 #327]: #103 -#884 := [mp #312 #883]: #878 -#541 := (not #878) -#552 := (or #541 #548) -#553 := [quant-inst #8]: #552 -#557 := [unit-resolution #553 #884]: #548 -#597 := [monotonicity #557]: #596 -#590 := [symm #597]: #558 -#498 := [monotonicity #590]: #535 -#656 := (or #559 #672) -#24 := (:var 0 Int) -#26 := (f4 #24) -#885 := (pattern #26) -#125 := (>= #24 0::Int) -#27 := (f6 #26) -#32 := (= #27 0::Int) -#173 := (or #32 #125) -#892 := (forall (vars (?v0 Int)) (:pat #885) #173) -#178 := (forall (vars (?v0 Int)) #173) -#895 := (iff #178 #892) -#893 := (iff #173 #173) -#894 := [refl]: #893 -#896 := [quant-intro #894]: #895 -#316 := (~ #178 #178) -#328 := (~ #173 #173) -#329 := [refl]: #328 -#317 := [nnf-pos #329]: #316 -#31 := (< #24 0::Int) -#33 := (implies #31 #32) -#34 := (forall (vars (?v0 Int)) #33) -#181 := (iff #34 #178) -#144 := (= 0::Int #27) -#150 := (not #31) -#151 := (or #150 #144) -#156 := (forall (vars (?v0 Int)) #151) -#179 := (iff #156 #178) -#176 := (iff #151 #173) -#170 := (or #125 #32) -#174 := (iff #170 #173) -#175 := [rewrite]: #174 -#171 := (iff #151 #170) -#168 := (iff #144 #32) -#169 := [rewrite]: #168 -#166 := (iff #150 #125) -#126 := (not #125) -#161 := (not #126) -#164 := (iff #161 #125) -#165 := [rewrite]: #164 -#162 := (iff #150 #161) -#159 := (iff #31 #126) -#160 := [rewrite]: #159 -#163 := [monotonicity #160]: #162 -#167 := [trans #163 #165]: #166 -#172 := [monotonicity #167 #169]: #171 -#177 := [trans #172 #175]: #176 -#180 := [quant-intro #177]: #179 -#157 := (iff #34 #156) -#154 := (iff #33 #151) -#147 := (implies #31 #144) -#152 := (iff #147 #151) -#153 := [rewrite]: #152 -#148 := (iff #33 #147) -#145 := (iff #32 #144) -#146 := [rewrite]: #145 -#149 := [monotonicity #146]: #148 -#155 := [trans #149 #153]: #154 -#158 := [quant-intro #155]: #157 -#182 := [trans #158 #180]: #181 -#143 := [asserted]: #34 -#183 := [mp #143 #182]: #178 -#330 := [mp~ #183 #317]: #178 -#897 := [mp #330 #896]: #892 -#859 := (not #892) -#645 := (or #859 #559 #672) -#673 := (or #672 #559) -#646 := (or #859 #673) -#648 := (iff #646 #645) -#649 := (or #859 #656) -#494 := (iff #649 #645) -#652 := [rewrite]: #494 -#650 := (iff #646 #649) -#674 := (iff #673 #656) -#644 := [rewrite]: #674 -#651 := [monotonicity #644]: #650 -#653 := [trans #651 #652]: #648 -#647 := [quant-inst #9]: #646 -#632 := [mp #647 #653]: #645 -#546 := [unit-resolution #632 #897]: #656 -#595 := [unit-resolution #546 #594]: #672 -#500 := [mp #595 #498]: #832 -#755 := (not #832) -#501 := (or #755 #559) -#504 := [th-lemma arith triangle-eq]: #501 -#499 := [unit-resolution #504 #500 #594]: false -#505 := [lemma #499]: #559 -#480 := [hypothesis]: #755 -#547 := (or #832 #828 #700) -#530 := [th-lemma arith triangle-eq]: #547 -#489 := [unit-resolution #530 #480 #505]: #828 -#775 := (or #806 #840) -#776 := [def-axiom]: #775 -#488 := [unit-resolution #776 #489]: #806 -#712 := -3::Int -#469 := (* -1::Int #9) -#714 := (div #469 -3::Int) -#717 := (* -1::Int #714) -#808 := (+ #11 #717) -#801 := (= #808 0::Int) -#792 := (ite #806 #849 #801) -#563 := (or #832 #792) -#839 := (= #11 0::Int) -#804 := (ite #832 #839 #792) -#35 := (:var 1 Int) -#36 := (f5 #35 #24) -#898 := (pattern #36) -#204 := (* -1::Int #24) -#201 := (* -1::Int #35) -#207 := (div #201 #204) -#379 := (* -1::Int #207) -#380 := (+ #36 #379) -#381 := (= #380 0::Int) -#46 := (div #35 #24) -#376 := (* -1::Int #46) -#377 := (+ #36 #376) -#378 := (= #377 0::Int) -#239 := (>= #35 0::Int) -#232 := (<= #24 0::Int) -#339 := (or #232 #239) -#340 := (not #339) -#228 := (<= #35 0::Int) -#337 := (or #228 #232) -#338 := (not #337) -#343 := (or #338 #340) -#382 := (ite #343 #378 #381) -#375 := (= #36 0::Int) -#38 := (= #24 0::Int) -#37 := (= #35 0::Int) -#39 := (or #37 #38) -#383 := (ite #39 #375 #382) -#899 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #898) #383) -#386 := (forall (vars (?v0 Int) (?v1 Int)) #383) -#902 := (iff #386 #899) -#900 := (iff #383 #383) -#901 := [refl]: #900 -#903 := [quant-intro #901]: #902 -#346 := (ite #343 #46 #207) -#349 := (ite #39 0::Int #346) -#352 := (= #36 #349) -#355 := (forall (vars (?v0 Int) (?v1 Int)) #352) -#387 := (iff #355 #386) -#384 := (iff #352 #383) -#385 := [rewrite]: #384 -#388 := [quant-intro #385]: #387 -#240 := (not #239) -#233 := (not #232) -#243 := (and #233 #240) -#229 := (not #228) -#236 := (and #229 #233) -#246 := (or #236 #243) -#249 := (ite #246 #46 #207) -#252 := (ite #39 0::Int #249) -#255 := (= #36 #252) -#258 := (forall (vars (?v0 Int) (?v1 Int)) #255) -#356 := (iff #258 #355) -#353 := (iff #255 #352) -#350 := (= #252 #349) -#347 := (= #249 #346) -#344 := (iff #246 #343) -#341 := (iff #243 #340) -#342 := [rewrite]: #341 -#322 := (iff #236 #338) -#323 := [rewrite]: #322 -#345 := [monotonicity #323 #342]: #344 -#348 := [monotonicity #345]: #347 -#351 := [monotonicity #348]: #350 -#354 := [monotonicity #351]: #353 -#357 := [quant-intro #354]: #356 -#318 := (~ #258 #258) -#331 := (~ #255 #255) -#332 := [refl]: #331 -#319 := [nnf-pos #332]: #318 -#48 := (- #24) -#47 := (- #35) -#49 := (div #47 #48) -#41 := (< 0::Int #24) -#43 := (< #35 0::Int) -#44 := (and #43 #41) -#40 := (< 0::Int #35) -#42 := (and #40 #41) -#45 := (or #42 #44) -#50 := (ite #45 #46 #49) -#51 := (ite #39 0::Int #50) -#52 := (= #36 #51) -#53 := (forall (vars (?v0 Int) (?v1 Int)) #52) -#261 := (iff #53 #258) -#194 := (and #41 #43) -#197 := (or #42 #194) -#210 := (ite #197 #46 #207) -#188 := (= 0::Int #24) -#185 := (= 0::Int #35) -#191 := (or #185 #188) -#213 := (ite #191 0::Int #210) -#216 := (= #36 #213) -#219 := (forall (vars (?v0 Int) (?v1 Int)) #216) -#259 := (iff #219 #258) -#256 := (iff #216 #255) -#253 := (= #213 #252) -#250 := (= #210 #249) -#247 := (iff #197 #246) -#244 := (iff #194 #243) -#241 := (iff #43 #240) -#242 := [rewrite]: #241 -#234 := (iff #41 #233) -#235 := [rewrite]: #234 -#245 := [monotonicity #235 #242]: #244 -#237 := (iff #42 #236) -#230 := (iff #40 #229) -#231 := [rewrite]: #230 -#238 := [monotonicity #231 #235]: #237 -#248 := [monotonicity #238 #245]: #247 -#251 := [monotonicity #248]: #250 -#226 := (iff #191 #39) -#224 := (iff #188 #38) -#225 := [rewrite]: #224 -#222 := (iff #185 #37) -#223 := [rewrite]: #222 -#227 := [monotonicity #223 #225]: #226 -#254 := [monotonicity #227 #251]: #253 -#257 := [monotonicity #254]: #256 -#260 := [quant-intro #257]: #259 -#220 := (iff #53 #219) -#217 := (iff #52 #216) -#214 := (= #51 #213) -#211 := (= #50 #210) -#208 := (= #49 #207) -#205 := (= #48 #204) -#206 := [rewrite]: #205 -#202 := (= #47 #201) -#203 := [rewrite]: #202 -#209 := [monotonicity #203 #206]: #208 -#198 := (iff #45 #197) -#195 := (iff #44 #194) -#196 := [rewrite]: #195 +#157 := [monotonicity #152 #154]: #156 +#161 := [trans #157 #159]: #160 +#175 := [monotonicity #161 #172]: #174 +#187 := [monotonicity #175]: #186 +#190 := [monotonicity #187]: #189 +#183 := (= #108 #182) +#180 := (= #102 #179) +#177 := (= #99 #176) +#178 := [monotonicity #175]: #177 +#181 := [monotonicity #178]: #180 +#184 := [monotonicity #181]: #183 +#193 := [monotonicity #184 #190]: #192 +#196 := [monotonicity #193]: #195 #199 := [monotonicity #196]: #198 -#212 := [monotonicity #199 #209]: #211 -#192 := (iff #39 #191) -#189 := (iff #38 #188) -#190 := [rewrite]: #189 -#186 := (iff #37 #185) -#187 := [rewrite]: #186 -#193 := [monotonicity #187 #190]: #192 -#215 := [monotonicity #193 #212]: #214 -#218 := [monotonicity #215]: #217 -#221 := [quant-intro #218]: #220 -#262 := [trans #221 #260]: #261 -#184 := [asserted]: #53 -#263 := [mp #184 #262]: #258 -#333 := [mp~ #263 #319]: #258 -#358 := [mp #333 #357]: #355 -#389 := [mp #358 #388]: #386 -#904 := [mp #389 #903]: #899 -#794 := (not #899) -#795 := (or #794 #804) -#576 := (* -1::Int 3::Int) -#846 := (div #469 #576) -#847 := (* -1::Int #846) -#569 := (+ #11 #847) -#570 := (= #569 0::Int) -#560 := (<= 3::Int 0::Int) -#561 := (or #560 #559) -#562 := (not #561) -#841 := (or #840 #560) -#556 := (not #841) -#838 := (or #556 #562) -#842 := (ite #838 #849 #570) -#843 := (= 3::Int 0::Int) -#833 := (or #832 #843) -#834 := (ite #833 #839 #842) -#796 := (or #794 #834) -#791 := (iff #796 #795) -#782 := (iff #795 #795) -#783 := [rewrite]: #782 -#800 := (iff #834 #804) -#802 := (iff #842 #792) -#793 := (iff #570 #801) -#812 := (= #569 #808) -#718 := (= #847 #717) -#715 := (= #846 #714) -#713 := (= #576 -3::Int) -#706 := [rewrite]: #713 -#716 := [monotonicity #706]: #715 -#811 := [monotonicity #716]: #718 -#799 := [monotonicity #811]: #812 -#790 := [monotonicity #799]: #793 -#695 := (iff #838 #806) -#661 := (or #828 #700) -#807 := (iff #661 #806) -#810 := [rewrite]: #807 -#809 := (iff #838 #661) -#701 := (iff #562 #700) -#815 := (iff #561 #559) -#660 := (or false #559) -#816 := (iff #660 #559) -#817 := [rewrite]: #816 -#813 := (iff #561 #660) -#822 := (iff #560 false) -#823 := [rewrite]: #822 -#814 := [monotonicity #823]: #813 -#818 := [trans #814 #817]: #815 -#702 := [monotonicity #818]: #701 -#657 := (iff #556 #828) -#827 := (iff #841 #840) -#824 := (or #840 false) -#820 := (iff #824 #840) -#826 := [rewrite]: #820 -#825 := (iff #841 #824) -#819 := [monotonicity #823]: #825 -#821 := [trans #819 #826]: #827 -#659 := [monotonicity #821]: #657 -#711 := [monotonicity #659 #702]: #809 -#710 := [trans #711 #810]: #695 -#803 := [monotonicity #710 #790]: #802 -#679 := (iff #833 #832) -#835 := (or #832 false) -#837 := (iff #835 #832) -#678 := [rewrite]: #837 -#836 := (iff #833 #835) -#829 := (iff #843 false) -#830 := [rewrite]: #829 -#831 := [monotonicity #830]: #836 -#680 := [trans #831 #678]: #679 -#805 := [monotonicity #680 #803]: #800 -#798 := [monotonicity #805]: #791 -#785 := [trans #798 #783]: #791 -#797 := [quant-inst #9 #10]: #796 -#786 := [mp #797 #785]: #795 -#580 := [unit-resolution #786 #904]: #804 -#753 := (not #804) -#758 := (or #753 #832 #792) -#759 := [def-axiom]: #758 -#564 := [unit-resolution #759 #580]: #563 -#473 := [unit-resolution #564 #480]: #792 -#778 := (not #806) -#766 := (not #792) -#767 := (or #766 #778 #849) -#768 := [def-axiom]: #767 -#470 := [unit-resolution #768 #473 #488]: #849 -#771 := (not #849) -#471 := (or #771 #781) -#946 := [th-lemma arith triangle-eq]: #471 -#947 := [unit-resolution #946 #470]: #781 -#777 := (mod #9 3::Int) -#749 := (* -1::Int #777) -#750 := (+ #13 #749) -#675 := (<= #750 0::Int) -#745 := (= #750 0::Int) -#762 := (mod #469 -3::Int) -#732 := (+ #13 #762) -#734 := (= #732 0::Int) -#739 := (ite #806 #745 #734) -#949 := (or #832 #739) -#724 := (= #13 0::Int) -#741 := (ite #832 #724 #739) -#54 := (f7 #35 #24) -#905 := (pattern #54) -#265 := (mod #201 #204) -#395 := (+ #54 #265) -#396 := (= #395 0::Int) -#55 := (mod #35 #24) -#392 := (* -1::Int #55) -#393 := (+ #54 #392) -#394 := (= #393 0::Int) -#397 := (ite #343 #394 #396) -#391 := (= #54 0::Int) -#398 := (ite #37 #391 #397) -#390 := (= #35 #54) -#399 := (ite #38 #390 #398) -#906 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #905) #399) -#402 := (forall (vars (?v0 Int) (?v1 Int)) #399) -#909 := (iff #402 #906) -#907 := (iff #399 #399) -#908 := [refl]: #907 -#910 := [quant-intro #908]: #909 -#271 := (* -1::Int #265) -#359 := (ite #343 #55 #271) -#362 := (ite #37 0::Int #359) -#365 := (ite #38 #35 #362) -#368 := (= #54 #365) -#371 := (forall (vars (?v0 Int) (?v1 Int)) #368) -#403 := (iff #371 #402) -#400 := (iff #368 #399) -#401 := [rewrite]: #400 -#404 := [quant-intro #401]: #403 -#291 := (ite #246 #55 #271) -#294 := (ite #37 0::Int #291) -#297 := (ite #38 #35 #294) -#300 := (= #54 #297) -#303 := (forall (vars (?v0 Int) (?v1 Int)) #300) -#372 := (iff #303 #371) -#369 := (iff #300 #368) -#366 := (= #297 #365) -#363 := (= #294 #362) -#360 := (= #291 #359) -#361 := [monotonicity #345]: #360 -#364 := [monotonicity #361]: #363 -#367 := [monotonicity #364]: #366 -#370 := [monotonicity #367]: #369 -#373 := [quant-intro #370]: #372 -#320 := (~ #303 #303) -#334 := (~ #300 #300) -#335 := [refl]: #334 -#321 := [nnf-pos #335]: #320 -#56 := (mod #47 #48) -#57 := (- #56) -#58 := (ite #45 #55 #57) -#59 := (ite #37 0::Int #58) -#60 := (ite #38 #35 #59) -#61 := (= #54 #60) -#62 := (forall (vars (?v0 Int) (?v1 Int)) #61) -#306 := (iff #62 #303) -#276 := (ite #197 #55 #271) -#279 := (ite #185 0::Int #276) -#282 := (ite #188 #35 #279) -#285 := (= #54 #282) -#288 := (forall (vars (?v0 Int) (?v1 Int)) #285) -#304 := (iff #288 #303) -#301 := (iff #285 #300) -#298 := (= #282 #297) -#295 := (= #279 #294) -#292 := (= #276 #291) -#293 := [monotonicity #248]: #292 -#296 := [monotonicity #223 #293]: #295 -#299 := [monotonicity #225 #296]: #298 -#302 := [monotonicity #299]: #301 -#305 := [quant-intro #302]: #304 -#289 := (iff #62 #288) -#286 := (iff #61 #285) -#283 := (= #60 #282) -#280 := (= #59 #279) -#277 := (= #58 #276) -#274 := (= #57 #271) -#268 := (- #265) -#272 := (= #268 #271) -#273 := [rewrite]: #272 -#269 := (= #57 #268) -#266 := (= #56 #265) -#267 := [monotonicity #203 #206]: #266 -#270 := [monotonicity #267]: #269 -#275 := [trans #270 #273]: #274 -#278 := [monotonicity #199 #275]: #277 -#281 := [monotonicity #187 #278]: #280 -#284 := [monotonicity #190 #281]: #283 -#287 := [monotonicity #284]: #286 -#290 := [quant-intro #287]: #289 -#307 := [trans #290 #305]: #306 -#264 := [asserted]: #62 -#308 := [mp #264 #307]: #303 -#336 := [mp~ #308 #321]: #303 -#374 := [mp #336 #373]: #371 -#405 := [mp #374 #404]: #402 -#911 := [mp #405 #910]: #906 -#704 := (not #906) -#663 := (or #704 #741) -#744 := (mod #469 #576) -#747 := (+ #13 #744) -#748 := (= #747 0::Int) -#751 := (ite #838 #745 #748) -#725 := (ite #832 #724 #751) -#726 := (= #9 #13) -#619 := (ite #843 #726 #725) -#694 := (or #704 #619) -#698 := (iff #694 #663) -#707 := (iff #663 #663) -#708 := [rewrite]: #707 -#729 := (iff #619 #741) -#722 := (ite false #726 #741) -#728 := (iff #722 #741) -#723 := [rewrite]: #728 -#703 := (iff #619 #722) -#721 := (iff #725 #741) -#740 := (iff #751 #739) -#735 := (iff #748 #734) -#737 := (= #747 #732) -#730 := (= #744 #762) -#731 := [monotonicity #706]: #730 -#733 := [monotonicity #731]: #737 -#738 := [monotonicity #733]: #735 -#736 := [monotonicity #710 #738]: #740 -#667 := [monotonicity #736]: #721 -#727 := [monotonicity #830 #667]: #703 -#697 := [trans #727 #723]: #729 -#705 := [monotonicity #697]: #698 -#709 := [trans #705 #708]: #698 -#696 := [quant-inst #9 #10]: #694 -#719 := [mp #696 #709]: #663 -#948 := [unit-resolution #719 #911]: #741 -#693 := (not #741) -#662 := (or #693 #832 #739) -#664 := [def-axiom]: #662 -#950 := [unit-resolution #664 #948]: #949 -#951 := [unit-resolution #950 #480]: #739 -#683 := (not #739) -#684 := (or #683 #778 #745) -#685 := [def-axiom]: #684 -#952 := [unit-resolution #685 #951 #488]: #745 -#688 := (not #745) -#953 := (or #688 #675) -#954 := [th-lemma arith triangle-eq]: #953 -#955 := [unit-resolution #954 #952]: #675 -#761 := (>= #845 0::Int) -#519 := (or #771 #761) -#520 := [th-lemma arith triangle-eq]: #519 -#956 := [unit-resolution #520 #470]: #761 -#676 := (>= #750 0::Int) -#957 := (or #688 #676) -#958 := [th-lemma arith triangle-eq]: #957 -#959 := [unit-resolution #958 #952]: #676 -#916 := (not #781) -#917 := (not #675) -#523 := (not #761) -#924 := (not #676) -#944 := (or #943 #924 #523 #917 #916) -#493 := (f4 #481) -#937 := (= #493 #89) -#495 := (= #89 #493) -#478 := (or #541 #495) -#482 := [quant-inst #89]: #478 -#466 := [unit-resolution #482 #884]: #495 -#938 := [symm #466]: #937 -#939 := (= f3 #493) -#935 := (= #463 #493) -#933 := (= #9 #481) -#467 := [hypothesis]: #554 -#475 := (= #9 #86) -#476 := (* -1::Int #86) -#472 := (+ #9 #476) -#464 := (>= #472 0::Int) -#465 := [hypothesis]: #781 -#621 := (* -3::Int #844) -#624 := (+ #749 #621) -#625 := (+ #9 #624) -#627 := (>= #625 0::Int) -#620 := (= #625 0::Int) -#1 := true -#80 := [true-axiom]: true -#598 := (or false #620) -#583 := [th-lemma arith]: #598 -#584 := [unit-resolution #583 #80]: #620 -#506 := (not #620) -#468 := (or #506 #627) -#912 := [th-lemma arith triangle-eq]: #468 -#913 := [unit-resolution #912 #584]: #627 -#914 := [hypothesis]: #675 -#915 := (not #627) -#918 := (or #464 #915 #916 #917) -#919 := [th-lemma arith assign-bounds -1 3 1]: #918 -#920 := [unit-resolution #919 #914 #913 #465]: #464 -#477 := (<= #472 0::Int) -#921 := [hypothesis]: #761 -#626 := (<= #625 0::Int) -#508 := (or #506 #626) -#509 := [th-lemma arith triangle-eq]: #508 -#922 := [unit-resolution #509 #584]: #626 -#923 := [hypothesis]: #676 -#522 := (not #626) -#925 := (or #477 #522 #523 #924) -#926 := [th-lemma arith assign-bounds -1 3 1]: #925 -#927 := [unit-resolution #926 #923 #922 #921]: #477 -#929 := (not #464) -#928 := (not #477) -#930 := (or #475 #928 #929) -#931 := [th-lemma arith triangle-eq]: #930 -#932 := [unit-resolution #931 #927 #920]: #475 -#934 := [trans #932 #467]: #933 -#936 := [monotonicity #934]: #935 -#940 := [trans #557 #936]: #939 -#941 := [trans #940 #938]: #92 -#95 := (not #92) -#12 := (* #11 3::Int) -#14 := (+ #12 #13) -#15 := (f4 #14) -#16 := (= f3 #15) -#17 := (not #16) -#96 := (iff #17 #95) -#93 := (iff #16 #92) -#90 := (= #15 #89) -#87 := (= #14 #86) -#84 := (= #12 #83) +#202 := [monotonicity #199]: #201 +#147 := (iff #37 #146) +#144 := (iff #36 #143) +#141 := (= #35 #140) +#138 := (= #34 #137) +#135 := (= #33 #127) +#130 := (ite false #9 #127) +#133 := (= #130 #127) +#134 := [rewrite]: #133 +#131 := (= #33 #130) +#128 := (= #32 #127) +#125 := (= #31 #124) +#122 := (= #30 #119) +#116 := (- #113) +#120 := (= #116 #119) +#121 := [rewrite]: #120 +#117 := (= #30 #116) +#114 := (= #29 #113) +#94 := (= #23 -3::Int) +#95 := [rewrite]: #94 +#91 := (= #22 #90) +#92 := [rewrite]: #91 +#115 := [monotonicity #92 #95]: #114 +#118 := [monotonicity #115]: #117 +#123 := [trans #118 #121]: #122 +#87 := (iff #20 #86) +#84 := (iff #19 #83) #85 := [rewrite]: #84 #88 := [monotonicity #85]: #87 -#91 := [monotonicity #88]: #90 -#94 := [monotonicity #91]: #93 -#97 := [monotonicity #94]: #96 -#82 := [asserted]: #17 -#100 := [mp #82 #97]: #95 -#942 := [unit-resolution #100 #941]: false -#945 := [lemma #942]: #944 -#960 := [unit-resolution #945 #959 #956 #955 #947]: #943 -#555 := (* -1::Int #481) -#486 := (+ #86 #555) -#487 := (<= #486 0::Int) -#534 := (+ #13 #555) -#869 := (+ #83 #534) -#518 := (<= #869 0::Int) -#871 := (= #869 0::Int) -#549 := (>= #86 0::Int) -#788 := (>= #11 0::Int) -#600 := (>= #777 3::Int) -#612 := (not #600) -#585 := (or false #612) -#587 := [th-lemma arith]: #585 -#586 := [unit-resolution #587 #80]: #612 -#588 := (not #788) -#577 := [hypothesis]: #588 -#754 := (not #839) -#578 := (or #754 #788) -#579 := [th-lemma arith triangle-eq]: #578 -#571 := [unit-resolution #579 #577]: #754 -#581 := (or #755 #839) -#756 := (or #753 #755 #839) -#757 := [def-axiom]: #756 -#572 := [unit-resolution #757 #580]: #581 -#582 := [unit-resolution #572 #571]: #755 -#565 := [unit-resolution #564 #582]: #792 -#542 := (not #672) -#543 := (iff #755 #542) -#538 := (iff #832 #672) -#566 := (= #463 f3) -#567 := [symm #557]: #566 -#568 := [monotonicity #567]: #558 -#537 := [monotonicity #568]: #535 -#529 := [symm #537]: #538 -#544 := [monotonicity #529]: #543 -#545 := [mp #582 #544]: #542 -#536 := [unit-resolution #546 #545]: #559 -#532 := [unit-resolution #530 #582]: #661 -#533 := [unit-resolution #532 #536]: #828 -#512 := [unit-resolution #776 #533]: #806 -#514 := [unit-resolution #768 #512 #565]: #849 -#521 := [unit-resolution #520 #514]: #761 -#524 := (or #522 #700 #600 #788 #523) -#513 := [th-lemma arith assign-bounds 1 1 3 -3]: #524 -#525 := [unit-resolution #513 #536 #521 #577 #586]: #522 -#507 := [unit-resolution #509 #525 #584]: false -#510 := [lemma #507]: #788 -#720 := (>= #13 0::Int) -#613 := (>= #777 0::Int) -#961 := (or false #613) -#962 := [th-lemma arith]: #961 -#963 := [unit-resolution #962 #80]: #613 -#964 := (not #613) -#965 := (or #720 #964 #924) -#966 := [th-lemma arith assign-bounds 1 1]: #965 -#967 := [unit-resolution #966 #959 #963]: #720 -#968 := (not #720) -#969 := (or #549 #968 #588) -#970 := [th-lemma arith assign-bounds 1 3]: #969 -#971 := [unit-resolution #970 #967 #510]: #549 -#550 := (not #549) -#872 := (or #550 #871) -#107 := (= #24 #27) -#132 := (or #107 #126) -#886 := (forall (vars (?v0 Int)) (:pat #885) #132) -#137 := (forall (vars (?v0 Int)) #132) -#889 := (iff #137 #886) -#887 := (iff #132 #132) -#888 := [refl]: #887 -#890 := [quant-intro #888]: #889 -#314 := (~ #137 #137) -#313 := (~ #132 #132) -#310 := [refl]: #313 -#315 := [nnf-pos #310]: #314 -#28 := (= #27 #24) -#25 := (<= 0::Int #24) -#29 := (implies #25 #28) -#30 := (forall (vars (?v0 Int)) #29) -#140 := (iff #30 #137) -#114 := (not #25) -#115 := (or #114 #107) -#120 := (forall (vars (?v0 Int)) #115) -#138 := (iff #120 #137) -#135 := (iff #115 #132) -#129 := (or #126 #107) -#133 := (iff #129 #132) -#134 := [rewrite]: #133 -#130 := (iff #115 #129) -#127 := (iff #114 #126) -#123 := (iff #25 #125) -#124 := [rewrite]: #123 -#128 := [monotonicity #124]: #127 -#131 := [monotonicity #128]: #130 -#136 := [trans #131 #134]: #135 -#139 := [quant-intro #136]: #138 -#121 := (iff #30 #120) -#118 := (iff #29 #115) -#111 := (implies #25 #107) -#116 := (iff #111 #115) -#117 := [rewrite]: #116 -#112 := (iff #29 #111) -#109 := (iff #28 #107) +#126 := [monotonicity #88 #123]: #125 +#129 := [monotonicity #126]: #128 +#74 := (iff #13 false) +#75 := [rewrite]: #74 +#132 := [monotonicity #75 #129]: #131 +#136 := [trans #132 #134]: #135 +#111 := (= #27 #108) +#105 := (* #102 3::Int) +#109 := (= #105 #108) #110 := [rewrite]: #109 -#113 := [monotonicity #110]: #112 -#119 := [trans #113 #117]: #118 -#122 := [quant-intro #119]: #121 -#141 := [trans #122 #139]: #140 -#106 := [asserted]: #30 -#142 := [mp #106 #141]: #137 -#311 := [mp~ #142 #315]: #137 -#891 := [mp #311 #890]: #886 -#876 := (not #886) -#866 := (or #876 #550 #871) -#551 := (or #554 #550) -#526 := (or #876 #551) -#515 := (iff #526 #866) -#867 := (or #876 #872) -#511 := (iff #867 #866) -#852 := [rewrite]: #511 -#527 := (iff #526 #867) -#875 := (iff #551 #872) -#865 := (or #871 #550) -#873 := (iff #865 #872) -#874 := [rewrite]: #873 -#539 := (iff #551 #865) -#528 := (iff #554 #871) -#658 := [rewrite]: #528 -#540 := [monotonicity #658]: #539 -#870 := [trans #540 #874]: #875 -#868 := [monotonicity #870]: #527 -#516 := [trans #868 #852]: #515 -#531 := [quant-inst #86]: #526 -#517 := [mp #531 #516]: #866 -#972 := [unit-resolution #517 #891]: #872 -#973 := [unit-resolution #972 #971]: #871 -#974 := (not #871) -#975 := (or #974 #518) -#976 := [th-lemma arith triangle-eq]: #975 -#977 := [unit-resolution #976 #973]: #518 -#978 := (not #518) -#979 := (or #487 #978) -#980 := [th-lemma arith assign-bounds -1]: #979 -#981 := [unit-resolution #980 #977]: #487 -#474 := (>= #486 0::Int) -#854 := (>= #869 0::Int) -#982 := (or #974 #854) -#983 := [th-lemma arith triangle-eq]: #982 -#984 := [unit-resolution #983 #973]: #854 -#985 := (not #854) -#986 := (or #474 #985) -#987 := [th-lemma arith assign-bounds -1]: #986 -#988 := [unit-resolution #987 #984]: #474 -#990 := (not #474) -#989 := (not #487) -#991 := (or #554 #989 #990) -#992 := [th-lemma arith triangle-eq]: #991 -#993 := [unit-resolution #992 #988 #981 #960]: false -#994 := [lemma #993]: #832 -#1024 := [symm #994]: #1023 -#1025 := (= #86 0::Int) -#855 := (= #481 0::Int) -#575 := (>= #481 0::Int) -#479 := (or #755 #724) -#654 := (or #693 #755 #724) -#655 := [def-axiom]: #654 -#484 := [unit-resolution #655 #948]: #479 -#485 := [unit-resolution #484 #994]: #724 -#665 := (not #724) -#490 := (or #665 #720) -#492 := [th-lemma arith triangle-eq]: #490 -#995 := [unit-resolution #492 #485]: #720 -#996 := [unit-resolution #970 #995 #510]: #549 -#997 := [unit-resolution #972 #996]: #871 -#998 := [unit-resolution #976 #997]: #518 -#999 := (or #575 #968 #978 #588) -#1000 := [th-lemma arith assign-bounds 1 1 3]: #999 -#1001 := [unit-resolution #1000 #998 #510 #995]: #575 -#574 := (<= #481 0::Int) -#699 := (<= #13 0::Int) -#1002 := (or #665 #699) -#1003 := [th-lemma arith triangle-eq]: #1002 -#1004 := [unit-resolution #1003 #485]: #699 -#787 := (<= #11 0::Int) -#1005 := [unit-resolution #572 #994]: #839 -#1006 := (or #754 #787) -#1007 := [th-lemma arith triangle-eq]: #1006 -#1008 := [unit-resolution #1007 #1005]: #787 -#1009 := [unit-resolution #983 #997]: #854 -#1011 := (not #787) -#1010 := (not #699) -#1012 := (or #574 #1010 #985 #1011) -#1013 := [th-lemma arith assign-bounds -1 1 -3]: #1012 -#1014 := [unit-resolution #1013 #1009 #1008 #1004]: #574 -#1016 := (not #575) -#1015 := (not #574) -#1017 := (or #855 #1015 #1016) -#1018 := [th-lemma arith triangle-eq]: #1017 -#1019 := [unit-resolution #1018 #1014 #1001]: #855 -#1020 := [unit-resolution #980 #998]: #487 -#1021 := [unit-resolution #987 #1009]: #474 -#1022 := [unit-resolution #992 #1021 #1020]: #554 -#1026 := [trans #1022 #1019]: #1025 -#1028 := [trans #1026 #1024]: #1027 -#1030 := [monotonicity #1028]: #1029 -#1032 := [symm #1030]: #1031 -#1033 := [trans #557 #1032]: #92 -[unit-resolution #100 #1033]: false +#106 := (= #27 #105) +#103 := (= #26 #102) +#100 := (= #25 #99) +#97 := (= #24 #96) +#98 := [monotonicity #92 #95]: #97 +#101 := [monotonicity #88 #98]: #100 +#81 := (iff #14 #11) +#76 := (or #11 false) +#79 := (iff #76 #11) +#80 := [rewrite]: #79 +#77 := (iff #14 #76) +#78 := [monotonicity #75]: #77 +#82 := [trans #78 #80]: #81 +#104 := [monotonicity #82 #101]: #103 +#107 := [monotonicity #104]: #106 +#112 := [trans #107 #110]: #111 +#139 := [monotonicity #112 #136]: #138 +#142 := [monotonicity #139]: #141 +#145 := [monotonicity #142]: #144 +#148 := [monotonicity #145]: #147 +#204 := [trans #148 #202]: #203 +#73 := [asserted]: #37 +#205 := [mp #73 #204]: #200 +#695 := [unit-resolution #205 #703]: false +#692 := [lemma #695]: #430 +#441 := (or #11 #450) +#442 := [def-axiom]: #441 +#598 := [unit-resolution #442 #692]: #450 +#365 := (= #21 #176) +#737 := (f5 #413) +#738 := (= #737 0::Int) +#632 := (not #738) +#633 := (iff #430 #632) +#628 := (iff #11 #738) +#626 := (iff #738 #11) +#647 := (= #737 #9) +#651 := (= #413 f3) +#652 := [symm #620]: #651 +#653 := [monotonicity #652]: #647 +#627 := [monotonicity #653]: #626 +#521 := [symm #627]: #628 +#634 := [monotonicity #521]: #633 +#639 := [mp #692 #634]: #632 +#739 := (or #162 #738) +#43 := (:var 0 Int) +#45 := (f4 #43) +#787 := (pattern #45) +#231 := (>= #43 0::Int) +#46 := (f5 #45) +#51 := (= #46 0::Int) +#280 := (or #51 #231) +#794 := (forall (vars (?v0 Int)) (:pat #787) #280) +#285 := (forall (vars (?v0 Int)) #280) +#797 := (iff #285 #794) +#795 := (iff #280 #280) +#796 := [refl]: #795 +#798 := [quant-intro #796]: #797 +#298 := (~ #285 #285) +#306 := (~ #280 #280) +#307 := [refl]: #306 +#299 := [nnf-pos #307]: #298 +#50 := (< #43 0::Int) +#52 := (implies #50 #51) +#53 := (forall (vars (?v0 Int)) #52) +#288 := (iff #53 #285) +#251 := (= 0::Int #46) +#257 := (not #50) +#258 := (or #257 #251) +#263 := (forall (vars (?v0 Int)) #258) +#286 := (iff #263 #285) +#283 := (iff #258 #280) +#277 := (or #231 #51) +#281 := (iff #277 #280) +#282 := [rewrite]: #281 +#278 := (iff #258 #277) +#275 := (iff #251 #51) +#276 := [rewrite]: #275 +#273 := (iff #257 #231) +#233 := (not #231) +#268 := (not #233) +#271 := (iff #268 #231) +#272 := [rewrite]: #271 +#269 := (iff #257 #268) +#266 := (iff #50 #233) +#267 := [rewrite]: #266 +#270 := [monotonicity #267]: #269 +#274 := [trans #270 #272]: #273 +#279 := [monotonicity #274 #276]: #278 +#284 := [trans #279 #282]: #283 +#287 := [quant-intro #284]: #286 +#264 := (iff #53 #263) +#261 := (iff #52 #258) +#254 := (implies #50 #251) +#259 := (iff #254 #258) +#260 := [rewrite]: #259 +#255 := (iff #52 #254) +#252 := (iff #51 #251) +#253 := [rewrite]: #252 +#256 := [monotonicity #253]: #255 +#262 := [trans #256 #260]: #261 +#265 := [quant-intro #262]: #264 +#289 := [trans #265 #287]: #288 +#250 := [asserted]: #53 +#290 := [mp #250 #289]: #285 +#308 := [mp~ #290 #299]: #285 +#799 := [mp #308 #798]: #794 +#463 := (not #794) +#582 := (or #463 #162 #738) +#733 := (or #738 #162) +#724 := (or #463 #733) +#729 := (iff #724 #582) +#726 := (or #463 #739) +#722 := (iff #726 #582) +#728 := [rewrite]: #722 +#727 := (iff #724 #726) +#580 := (iff #733 #739) +#581 := [rewrite]: #580 +#721 := [monotonicity #581]: #727 +#723 := [trans #721 #728]: #729 +#725 := [quant-inst #9]: #724 +#730 := [mp #725 #723]: #582 +#635 := [unit-resolution #730 #799]: #739 +#636 := [unit-resolution #635 #639]: #162 +#637 := (or #11 #150 #163) +#640 := [th-lemma arith triangle-eq]: #637 +#641 := [unit-resolution #640 #692]: #173 +#642 := [unit-resolution #641 #636]: #150 +#452 := (or #173 #149) +#443 := [def-axiom]: #452 +#638 := [unit-resolution #443 #642]: #173 +#383 := (not #173) +#457 := (or #383 #365) +#436 := [def-axiom]: #457 +#600 := [unit-resolution #436 #638]: #365 +#607 := [trans #600 #598]: #659 +#609 := (not #659) +#610 := (or #609 #656) +#611 := [th-lemma arith triangle-eq]: #610 +#621 := [unit-resolution #611 #607]: #656 +#662 := (>= #661 0::Int) +#589 := (or #609 #662) +#590 := [th-lemma arith triangle-eq]: #589 +#591 := [unit-resolution #590 #607]: #662 +#644 := (* -1::Int #188) +#645 := (+ #28 #644) +#646 := (<= #645 0::Int) +#648 := (= #28 #188) +#775 := (= #185 #188) +#429 := (or #11 #775) +#770 := [def-axiom]: #429 +#650 := [unit-resolution #770 #692]: #775 +#776 := (= #28 #185) +#772 := (or #383 #776) +#778 := [def-axiom]: #772 +#643 := [unit-resolution #778 #638]: #776 +#623 := [trans #643 #650]: #648 +#569 := (not #648) +#624 := (or #569 #646) +#605 := [th-lemma arith triangle-eq]: #624 +#629 := [unit-resolution #605 #623]: #646 +#649 := (>= #645 0::Int) +#592 := (or #569 #649) +#593 := [th-lemma arith triangle-eq]: #592 +#594 := [unit-resolution #593 #623]: #649 +#595 := [th-lemma arith eq-propagate 1 1 3 3 1 1 #594 #629 #591 #621 #588 #596]: #579 +#556 := [symm #595]: #618 +#557 := [monotonicity #556]: #713 +#564 := [symm #557]: #714 +#566 := [trans #620 #564]: #197 +[unit-resolution #205 #566]: false unsat 34a7ceb02d535a80474ebf3499258caaaf0b3c6d 74 0 #2 := false @@ -26439,16909 +21415,6734 @@ #33 := [asserted]: #13 [mp #33 #49]: false unsat -9ce15ee2c485c15c28a4c003e8c335d04c1523a1 254 0 -#2 := false -decl f3 :: (-> Int Int Int) -#13 := (:var 0 Int) -#12 := (:var 1 Int) -#14 := (f3 #12 #13) -#749 := (pattern #14) +c3a19f1e9eadfa9e1e60ed3204d9afca1d3962d0 64 0 +#2 := false #8 := 0::Int -#87 := -1::Int -#91 := (* -1::Int #13) -#88 := (* -1::Int #12) -#94 := (div #88 #91) -#251 := (* -1::Int #94) -#252 := (+ #14 #251) -#253 := (= #252 0::Int) -#24 := (div #12 #13) -#248 := (* -1::Int #24) -#249 := (+ #14 #248) -#250 := (= #249 0::Int) -#126 := (>= #12 0::Int) -#119 := (<= #13 0::Int) -#211 := (or #119 #126) -#212 := (not #211) -#115 := (<= #12 0::Int) -#209 := (or #115 #119) -#210 := (not #209) -#215 := (or #210 #212) -#254 := (ite #215 #250 #253) -#247 := (= #14 0::Int) -#16 := (= #13 0::Int) -#15 := (= #12 0::Int) -#17 := (or #15 #16) -#255 := (ite #17 #247 #254) -#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #255) -#258 := (forall (vars (?v0 Int) (?v1 Int)) #255) -#753 := (iff #258 #750) -#751 := (iff #255 #255) -#752 := [refl]: #751 -#754 := [quant-intro #752]: #753 -#218 := (ite #215 #24 #94) -#221 := (ite #17 0::Int #218) -#224 := (= #14 #221) -#227 := (forall (vars (?v0 Int) (?v1 Int)) #224) -#259 := (iff #227 #258) -#256 := (iff #224 #255) -#257 := [rewrite]: #256 -#260 := [quant-intro #257]: #259 -#127 := (not #126) -#120 := (not #119) -#130 := (and #120 #127) -#116 := (not #115) -#123 := (and #116 #120) -#133 := (or #123 #130) -#136 := (ite #133 #24 #94) -#139 := (ite #17 0::Int #136) -#142 := (= #14 #139) -#145 := (forall (vars (?v0 Int) (?v1 Int)) #142) -#228 := (iff #145 #227) -#225 := (iff #142 #224) -#222 := (= #139 #221) -#219 := (= #136 #218) -#216 := (iff #133 #215) -#213 := (iff #130 #212) -#214 := [rewrite]: #213 -#203 := (iff #123 #210) -#204 := [rewrite]: #203 -#217 := [monotonicity #204 #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [monotonicity #220]: #222 -#226 := [monotonicity #223]: #225 -#229 := [quant-intro #226]: #228 -#207 := (~ #145 #145) -#205 := (~ #142 #142) -#206 := [refl]: #205 -#208 := [nnf-pos #206]: #207 -#26 := (- #13) -#25 := (- #12) -#27 := (div #25 #26) -#19 := (< 0::Int #13) -#21 := (< #12 0::Int) -#22 := (and #21 #19) -#18 := (< 0::Int #12) -#20 := (and #18 #19) -#23 := (or #20 #22) -#28 := (ite #23 #24 #27) -#29 := (ite #17 0::Int #28) -#30 := (= #14 #29) -#31 := (forall (vars (?v0 Int) (?v1 Int)) #30) -#148 := (iff #31 #145) -#81 := (and #19 #21) -#84 := (or #20 #81) -#97 := (ite #84 #24 #94) -#75 := (= 0::Int #13) -#72 := (= 0::Int #12) -#78 := (or #72 #75) -#100 := (ite #78 0::Int #97) -#103 := (= #14 #100) -#106 := (forall (vars (?v0 Int) (?v1 Int)) #103) -#146 := (iff #106 #145) -#143 := (iff #103 #142) -#140 := (= #100 #139) -#137 := (= #97 #136) -#134 := (iff #84 #133) -#131 := (iff #81 #130) -#128 := (iff #21 #127) -#129 := [rewrite]: #128 -#121 := (iff #19 #120) -#122 := [rewrite]: #121 -#132 := [monotonicity #122 #129]: #131 -#124 := (iff #20 #123) -#117 := (iff #18 #116) -#118 := [rewrite]: #117 -#125 := [monotonicity #118 #122]: #124 -#135 := [monotonicity #125 #132]: #134 -#138 := [monotonicity #135]: #137 -#113 := (iff #78 #17) -#111 := (iff #75 #16) -#112 := [rewrite]: #111 -#109 := (iff #72 #15) -#110 := [rewrite]: #109 -#114 := [monotonicity #110 #112]: #113 -#141 := [monotonicity #114 #138]: #140 -#144 := [monotonicity #141]: #143 -#147 := [quant-intro #144]: #146 -#107 := (iff #31 #106) -#104 := (iff #30 #103) -#101 := (= #29 #100) -#98 := (= #28 #97) -#95 := (= #27 #94) -#92 := (= #26 #91) -#93 := [rewrite]: #92 -#89 := (= #25 #88) -#90 := [rewrite]: #89 -#96 := [monotonicity #90 #93]: #95 -#85 := (iff #23 #84) -#82 := (iff #22 #81) -#83 := [rewrite]: #82 -#86 := [monotonicity #83]: #85 -#99 := [monotonicity #86 #96]: #98 -#79 := (iff #17 #78) -#76 := (iff #16 #75) -#77 := [rewrite]: #76 -#73 := (iff #15 #72) +#15 := (- 0::Int) +#16 := (div #15 #15) +#14 := (div 0::Int 0::Int) +#11 := (< 0::Int 0::Int) +#12 := (and #11 #11) +#13 := (or #12 #12) +#17 := (ite #13 #14 #16) +#9 := (= 0::Int 0::Int) +#10 := (or #9 #9) +#18 := (ite #10 0::Int #17) +#19 := (= #18 0::Int) +#20 := (not #19) +#85 := (iff #20 false) +#1 := true +#80 := (not true) +#83 := (iff #80 false) +#84 := [rewrite]: #83 +#81 := (iff #20 #80) +#78 := (iff #19 true) +#41 := (iff #9 true) +#42 := [rewrite]: #41 +#76 := (iff #19 #9) +#70 := (ite true 0::Int #14) +#73 := (= #70 0::Int) #74 := [rewrite]: #73 -#80 := [monotonicity #74 #77]: #79 -#102 := [monotonicity #80 #99]: #101 -#105 := [monotonicity #102]: #104 -#108 := [quant-intro #105]: #107 -#149 := [trans #108 #147]: #148 -#71 := [asserted]: #31 -#150 := [mp #71 #149]: #145 -#199 := [mp~ #150 #208]: #145 -#230 := [mp #199 #229]: #227 -#261 := [mp #230 #260]: #258 -#755 := [mp #261 #754]: #750 -#9 := (f3 0::Int 0::Int) -#10 := (= #9 0::Int) -#11 := (not #10) -#60 := [asserted]: #11 -#707 := (not #750) -#708 := (or #707 #10) -#335 := (* -1::Int 0::Int) -#420 := (div #335 #335) -#421 := (* -1::Int #420) -#422 := (+ #9 #421) -#413 := (= #422 0::Int) -#424 := (div 0::Int 0::Int) -#425 := (* -1::Int #424) -#353 := (+ #9 #425) -#426 := (= #353 0::Int) -#423 := (>= 0::Int 0::Int) -#427 := (<= 0::Int 0::Int) -#406 := (or #427 #423) -#741 := (not #406) -#743 := (or #427 #427) -#400 := (not #743) -#530 := (or #400 #741) -#737 := (ite #530 #426 #413) -#411 := (= 0::Int 0::Int) -#412 := (or #411 #411) -#744 := (ite #412 #10 #737) -#703 := (or #707 #744) -#550 := (iff #703 #708) -#552 := (iff #708 #708) -#694 := [rewrite]: #552 -#701 := (iff #744 #10) -#1 := true -#711 := (ite true #10 #426) -#705 := (iff #711 #10) -#706 := [rewrite]: #705 -#715 := (iff #744 #711) -#710 := (iff #737 #426) -#433 := (ite false #426 #426) -#713 := (iff #433 #426) -#428 := [rewrite]: #713 -#434 := (iff #737 #433) -#431 := (iff #413 #426) -#717 := (= #422 #353) -#716 := (= #421 #425) -#441 := (= #420 #424) -#718 := (= #335 0::Int) -#719 := [rewrite]: #718 -#442 := [monotonicity #719 #719]: #441 -#720 := [monotonicity #442]: #716 -#721 := [monotonicity #720]: #717 -#432 := [monotonicity #721]: #431 -#448 := (iff #530 false) -#722 := (or false false) -#446 := (iff #722 false) -#447 := [rewrite]: #446 -#723 := (iff #530 #722) -#733 := (iff #741 false) -#389 := (not true) -#727 := (iff #389 false) -#728 := [rewrite]: #727 -#375 := (iff #741 #389) -#734 := (iff #406 true) -#747 := (or true true) -#738 := (iff #747 true) -#398 := [rewrite]: #738 -#369 := (iff #406 #747) -#725 := (iff #423 true) -#731 := [rewrite]: #725 -#399 := (iff #427 true) -#740 := [rewrite]: #399 -#732 := [monotonicity #740 #731]: #369 -#374 := [trans #732 #398]: #734 -#735 := [monotonicity #374]: #375 -#736 := [trans #735 #728]: #733 -#729 := (iff #400 false) -#390 := (iff #400 #389) -#387 := (iff #743 true) -#383 := (iff #743 #747) -#724 := [monotonicity #740 #740]: #383 -#388 := [trans #724 #398]: #387 -#726 := [monotonicity #388]: #390 -#730 := [trans #726 #728]: #729 -#445 := [monotonicity #730 #736]: #723 -#341 := [trans #445 #447]: #448 -#712 := [monotonicity #341 #432]: #434 -#714 := [trans #712 #428]: #710 -#403 := (iff #412 true) -#742 := (iff #412 #747) -#745 := (iff #411 true) -#746 := [rewrite]: #745 -#748 := [monotonicity #746 #746]: #742 -#739 := [trans #748 #398]: #403 -#704 := [monotonicity #739 #714]: #715 -#702 := [trans #704 #706]: #701 -#551 := [monotonicity #702]: #550 -#695 := [trans #551 #694]: #550 -#709 := [quant-inst #8 #8]: #703 -#696 := [mp #709 #695]: #708 -[unit-resolution #696 #60 #755]: false -unsat -8c864635f2131bf56f7aae6736c04969e8015d95 267 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#750 := (pattern #15) -#9 := 0::Int -#88 := -1::Int -#92 := (* -1::Int #14) -#89 := (* -1::Int #13) -#95 := (div #89 #92) -#252 := (* -1::Int #95) -#253 := (+ #15 #252) -#254 := (= #253 0::Int) -#25 := (div #13 #14) -#249 := (* -1::Int #25) -#250 := (+ #15 #249) -#251 := (= #250 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#255 := (ite #216 #251 #254) -#248 := (= #15 0::Int) -#17 := (= #14 0::Int) -#16 := (= #13 0::Int) -#18 := (or #16 #17) -#256 := (ite #18 #248 #255) -#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#754 := (iff #259 #751) -#752 := (iff #256 #256) -#753 := [refl]: #752 -#755 := [quant-intro #753]: #754 -#219 := (ite #216 #25 #95) -#222 := (ite #18 0::Int #219) -#225 := (= #15 #222) -#228 := (forall (vars (?v0 Int) (?v1 Int)) #225) -#260 := (iff #228 #259) -#257 := (iff #225 #256) -#258 := [rewrite]: #257 -#261 := [quant-intro #258]: #260 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#137 := (ite #134 #25 #95) -#140 := (ite #18 0::Int #137) -#143 := (= #15 #140) -#146 := (forall (vars (?v0 Int) (?v1 Int)) #143) -#229 := (iff #146 #228) -#226 := (iff #143 #225) -#223 := (= #140 #222) -#220 := (= #137 #219) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#221 := [monotonicity #218]: #220 -#224 := [monotonicity #221]: #223 -#227 := [monotonicity #224]: #226 -#230 := [quant-intro #227]: #229 -#208 := (~ #146 #146) -#206 := (~ #143 #143) -#207 := [refl]: #206 -#209 := [nnf-pos #207]: #208 -#27 := (- #14) -#26 := (- #13) -#28 := (div #26 #27) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#29 := (ite #24 #25 #28) -#30 := (ite #18 0::Int #29) -#31 := (= #15 #30) -#32 := (forall (vars (?v0 Int) (?v1 Int)) #31) -#149 := (iff #32 #146) -#82 := (and #20 #22) -#85 := (or #21 #82) -#98 := (ite #85 #25 #95) -#76 := (= 0::Int #14) -#73 := (= 0::Int #13) -#79 := (or #73 #76) -#101 := (ite #79 0::Int #98) -#104 := (= #15 #101) -#107 := (forall (vars (?v0 Int) (?v1 Int)) #104) -#147 := (iff #107 #146) -#144 := (iff #104 #143) -#141 := (= #101 #140) -#138 := (= #98 #137) -#135 := (iff #85 #134) -#132 := (iff #82 #131) -#129 := (iff #22 #128) -#130 := [rewrite]: #129 -#122 := (iff #20 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #21 #124) -#118 := (iff #19 #117) -#119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#139 := [monotonicity #136]: #138 -#114 := (iff #79 #18) -#112 := (iff #76 #17) -#113 := [rewrite]: #112 -#110 := (iff #73 #16) -#111 := [rewrite]: #110 -#115 := [monotonicity #111 #113]: #114 -#142 := [monotonicity #115 #139]: #141 -#145 := [monotonicity #142]: #144 -#148 := [quant-intro #145]: #147 -#108 := (iff #32 #107) -#105 := (iff #31 #104) -#102 := (= #30 #101) -#99 := (= #29 #98) -#96 := (= #28 #95) -#93 := (= #27 #92) -#94 := [rewrite]: #93 -#90 := (= #26 #89) -#91 := [rewrite]: #90 -#97 := [monotonicity #91 #94]: #96 -#86 := (iff #24 #85) -#83 := (iff #23 #82) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#100 := [monotonicity #87 #97]: #99 -#80 := (iff #18 #79) -#77 := (iff #17 #76) +#71 := (= #18 #70) +#68 := (= #17 #14) +#63 := (ite #11 #14 #14) +#66 := (= #63 #14) +#67 := [rewrite]: #66 +#64 := (= #17 #63) +#61 := (= #16 #14) +#59 := (= #15 0::Int) +#60 := [rewrite]: #59 +#62 := [monotonicity #60 #60]: #61 +#57 := (iff #13 #11) +#52 := (or #11 #11) +#55 := (iff #52 #11) +#56 := [rewrite]: #55 +#53 := (iff #13 #52) +#50 := (iff #12 #11) +#51 := [rewrite]: #50 +#54 := [monotonicity #51 #51]: #53 +#58 := [trans #54 #56]: #57 +#65 := [monotonicity #58 #62]: #64 +#69 := [trans #65 #67]: #68 +#48 := (iff #10 true) +#43 := (or true true) +#46 := (iff #43 true) +#47 := [rewrite]: #46 +#44 := (iff #10 #43) +#45 := [monotonicity #42 #42]: #44 +#49 := [trans #45 #47]: #48 +#72 := [monotonicity #49 #69]: #71 +#75 := [trans #72 #74]: #19 +#77 := [monotonicity #75]: #76 +#79 := [trans #77 #42]: #78 +#82 := [monotonicity #79]: #81 +#86 := [trans #82 #84]: #85 +#40 := [asserted]: #20 +[mp #40 #86]: false +unsat +c39d13f4d2f865f3613c6b94cb5e51281b48ea9a 69 0 +#2 := false +#9 := 0::Int +#21 := (- 0::Int) +decl f3 :: Int +#8 := f3 +#20 := (- f3) +#22 := (div #20 #21) +#19 := (div f3 0::Int) +#14 := (< 0::Int 0::Int) +#16 := (< f3 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int f3) +#15 := (and #13 #14) +#18 := (or #15 #17) +#23 := (ite #18 #19 #22) +#11 := (= 0::Int 0::Int) +#10 := (= f3 0::Int) +#12 := (or #10 #11) +#24 := (ite #12 0::Int #23) +#25 := (= #24 0::Int) +#26 := (not #25) +#89 := (iff #26 false) +#1 := true +#84 := (not true) +#87 := (iff #84 false) +#88 := [rewrite]: #87 +#85 := (iff #26 #84) +#82 := (iff #25 true) +#47 := (iff #11 true) +#48 := [rewrite]: #47 +#80 := (iff #25 #11) +#62 := -1::Int +#63 := (* -1::Int f3) +#68 := (div #63 0::Int) +#56 := (and #14 #16) +#59 := (or #15 #56) +#71 := (ite #59 #19 #68) +#74 := (ite true 0::Int #71) +#77 := (= #74 0::Int) #78 := [rewrite]: #77 -#74 := (iff #16 #73) -#75 := [rewrite]: #74 -#81 := [monotonicity #75 #78]: #80 -#103 := [monotonicity #81 #100]: #102 -#106 := [monotonicity #103]: #105 -#109 := [quant-intro #106]: #108 -#150 := [trans #109 #148]: #149 -#72 := [asserted]: #32 -#151 := [mp #72 #150]: #146 -#200 := [mp~ #151 #209]: #146 -#231 := [mp #200 #230]: #228 -#262 := [mp #231 #261]: #259 -#756 := [mp #262 #755]: #751 -decl f4 :: Int -#8 := f4 -#10 := (f3 f4 0::Int) -#11 := (= #10 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#692 := (not #751) -#693 := (or #692 #11) -#336 := (* -1::Int 0::Int) -#421 := (* -1::Int f4) -#422 := (div #421 #336) -#423 := (* -1::Int #422) -#414 := (+ #10 #423) -#425 := (= #414 0::Int) -#426 := (div f4 0::Int) -#354 := (* -1::Int #426) -#427 := (+ #10 #354) -#424 := (= #427 0::Int) -#428 := (>= f4 0::Int) -#407 := (<= 0::Int 0::Int) -#742 := (or #407 #428) -#744 := (not #742) -#401 := (<= f4 0::Int) -#531 := (or #401 #407) -#738 := (not #531) -#412 := (or #738 #744) -#413 := (ite #412 #424 #425) -#745 := (= 0::Int 0::Int) -#746 := (= f4 0::Int) -#747 := (or #746 #745) -#748 := (ite #747 #11 #413) -#699 := (or #692 #748) -#694 := (iff #699 #693) -#530 := (iff #693 #693) -#532 := [rewrite]: #530 -#697 := (iff #748 #11) -#433 := (div #421 0::Int) -#713 := (* -1::Int #433) -#711 := (+ #10 #713) -#716 := (= #711 0::Int) -#1 := true -#551 := (ite true #11 #716) -#695 := (iff #551 #11) -#696 := [rewrite]: #695 -#552 := (iff #748 #551) -#704 := (iff #413 #716) -#707 := (ite false #424 #716) -#708 := (iff #707 #716) -#709 := [rewrite]: #708 -#702 := (iff #413 #707) -#705 := (iff #425 #716) -#715 := (= #414 #711) -#714 := (= #423 #713) -#434 := (= #422 #433) -#722 := (= #336 0::Int) -#432 := [rewrite]: #722 -#435 := [monotonicity #432]: #434 -#429 := [monotonicity #435]: #714 -#712 := [monotonicity #429]: #715 -#706 := [monotonicity #712]: #705 -#721 := (iff #412 false) -#719 := (or false false) -#443 := (iff #719 false) -#717 := [rewrite]: #443 -#720 := (iff #412 #719) -#449 := (iff #744 false) -#731 := (not true) -#370 := (iff #731 false) -#733 := [rewrite]: #370 -#447 := (iff #744 #731) -#724 := (iff #742 true) -#376 := (or true #428) -#737 := (iff #376 true) -#723 := [rewrite]: #737 -#736 := (iff #742 #376) -#725 := (iff #407 true) -#388 := [rewrite]: #725 -#734 := [monotonicity #388]: #736 -#446 := [trans #734 #723]: #724 -#448 := [monotonicity #446]: #447 -#342 := [trans #448 #733]: #449 -#735 := (iff #738 false) -#726 := (iff #738 #731) -#729 := (iff #531 true) -#389 := (or #401 true) -#727 := (iff #389 true) -#728 := [rewrite]: #727 -#390 := (iff #531 #389) -#391 := [monotonicity #388]: #390 -#730 := [trans #391 #728]: #729 -#732 := [monotonicity #730]: #726 -#375 := [trans #732 #733]: #735 -#442 := [monotonicity #375 #342]: #720 -#718 := [trans #442 #717]: #721 -#703 := [monotonicity #718 #706]: #702 -#710 := [trans #703 #709]: #704 -#741 := (iff #747 true) -#739 := (or #746 true) -#740 := (iff #739 true) -#400 := [rewrite]: #740 -#399 := (iff #747 #739) -#743 := (iff #745 true) -#749 := [rewrite]: #743 -#404 := [monotonicity #749]: #399 -#384 := [trans #404 #400]: #741 -#553 := [monotonicity #384 #710]: #552 -#698 := [trans #553 #696]: #697 -#701 := [monotonicity #698]: #694 -#533 := [trans #701 #532]: #694 -#700 := [quant-inst #8 #9]: #699 -#686 := [mp #700 #533]: #693 -[unit-resolution #686 #61 #756]: false -unsat -5b04feaa787b42fcdecf376c99ee15421d3ebc84 291 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#749 := (pattern #15) +#75 := (= #24 #74) +#72 := (= #23 #71) +#69 := (= #22 #68) +#66 := (= #21 0::Int) +#67 := [rewrite]: #66 +#64 := (= #20 #63) +#65 := [rewrite]: #64 +#70 := [monotonicity #65 #67]: #69 +#60 := (iff #18 #59) +#57 := (iff #17 #56) +#58 := [rewrite]: #57 +#61 := [monotonicity #58]: #60 +#73 := [monotonicity #61 #70]: #72 +#54 := (iff #12 true) +#49 := (or #10 true) +#52 := (iff #49 true) +#53 := [rewrite]: #52 +#50 := (iff #12 #49) +#51 := [monotonicity #48]: #50 +#55 := [trans #51 #53]: #54 +#76 := [monotonicity #55 #73]: #75 +#79 := [trans #76 #78]: #25 +#81 := [monotonicity #79]: #80 +#83 := [trans #81 #48]: #82 +#86 := [monotonicity #83]: #85 +#90 := [trans #86 #88]: #89 +#46 := [asserted]: #26 +[mp #46 #90]: false +unsat +bea53353954aa4070bfc4dfeef54e3441dcd8b82 73 0 +#2 := false #8 := 0::Int -#88 := -1::Int -#92 := (* -1::Int #14) -#89 := (* -1::Int #13) -#95 := (div #89 #92) -#252 := (* -1::Int #95) -#253 := (+ #15 #252) -#254 := (= #253 0::Int) -#25 := (div #13 #14) -#249 := (* -1::Int #25) -#250 := (+ #15 #249) -#251 := (= #250 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#255 := (ite #216 #251 #254) -#248 := (= #15 0::Int) -#17 := (= #14 0::Int) -#16 := (= #13 0::Int) -#18 := (or #16 #17) -#256 := (ite #18 #248 #255) -#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#753 := (iff #259 #750) -#751 := (iff #256 #256) -#752 := [refl]: #751 -#754 := [quant-intro #752]: #753 -#219 := (ite #216 #25 #95) -#222 := (ite #18 0::Int #219) -#225 := (= #15 #222) -#228 := (forall (vars (?v0 Int) (?v1 Int)) #225) -#260 := (iff #228 #259) -#257 := (iff #225 #256) -#258 := [rewrite]: #257 -#261 := [quant-intro #258]: #260 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#137 := (ite #134 #25 #95) -#140 := (ite #18 0::Int #137) -#143 := (= #15 #140) -#146 := (forall (vars (?v0 Int) (?v1 Int)) #143) -#229 := (iff #146 #228) -#226 := (iff #143 #225) -#223 := (= #140 #222) -#220 := (= #137 #219) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#221 := [monotonicity #218]: #220 -#224 := [monotonicity #221]: #223 -#227 := [monotonicity #224]: #226 -#230 := [quant-intro #227]: #229 -#208 := (~ #146 #146) -#206 := (~ #143 #143) -#207 := [refl]: #206 -#209 := [nnf-pos #207]: #208 -#27 := (- #14) -#26 := (- #13) -#28 := (div #26 #27) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#29 := (ite #24 #25 #28) -#30 := (ite #18 0::Int #29) -#31 := (= #15 #30) -#32 := (forall (vars (?v0 Int) (?v1 Int)) #31) -#149 := (iff #32 #146) -#82 := (and #20 #22) -#85 := (or #21 #82) -#98 := (ite #85 #25 #95) -#76 := (= 0::Int #14) -#73 := (= 0::Int #13) -#79 := (or #73 #76) -#101 := (ite #79 0::Int #98) -#104 := (= #15 #101) -#107 := (forall (vars (?v0 Int) (?v1 Int)) #104) -#147 := (iff #107 #146) -#144 := (iff #104 #143) -#141 := (= #101 #140) -#138 := (= #98 #137) -#135 := (iff #85 #134) -#132 := (iff #82 #131) -#129 := (iff #22 #128) -#130 := [rewrite]: #129 -#122 := (iff #20 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #21 #124) -#118 := (iff #19 #117) -#119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#139 := [monotonicity #136]: #138 -#114 := (iff #79 #18) -#112 := (iff #76 #17) -#113 := [rewrite]: #112 -#110 := (iff #73 #16) -#111 := [rewrite]: #110 -#115 := [monotonicity #111 #113]: #114 -#142 := [monotonicity #115 #139]: #141 -#145 := [monotonicity #142]: #144 -#148 := [quant-intro #145]: #147 -#108 := (iff #32 #107) -#105 := (iff #31 #104) -#102 := (= #30 #101) -#99 := (= #29 #98) -#96 := (= #28 #95) -#93 := (= #27 #92) -#94 := [rewrite]: #93 -#90 := (= #26 #89) -#91 := [rewrite]: #90 -#97 := [monotonicity #91 #94]: #96 -#86 := (iff #24 #85) -#83 := (iff #23 #82) +#10 := 1::Int +#19 := (- 1::Int) +#18 := (- 0::Int) +#20 := (div #18 #19) +#17 := (div 0::Int 1::Int) +#14 := (< 0::Int 1::Int) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#21 := (ite #16 #17 #20) +#11 := (= 1::Int 0::Int) +#9 := (= 0::Int 0::Int) +#12 := (or #9 #11) +#22 := (ite #12 0::Int #21) +#23 := (= #22 0::Int) +#24 := (not #23) +#94 := (iff #24 false) +#1 := true +#89 := (not true) +#92 := (iff #89 false) +#93 := [rewrite]: #92 +#90 := (iff #24 #89) +#87 := (iff #23 true) +#45 := (iff #9 true) +#46 := [rewrite]: #45 +#85 := (iff #23 #9) +#79 := (ite true 0::Int 0::Int) +#82 := (= #79 0::Int) +#83 := [rewrite]: #82 +#80 := (= #22 #79) +#77 := (= #21 0::Int) +#72 := (ite #15 0::Int 0::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #21 #72) +#70 := (= #20 0::Int) +#62 := -1::Int +#65 := (div 0::Int -1::Int) +#68 := (= #65 0::Int) +#69 := [rewrite]: #68 +#66 := (= #20 #65) +#63 := (= #19 -1::Int) +#64 := [rewrite]: #63 +#60 := (= #18 0::Int) +#61 := [rewrite]: #60 +#67 := [monotonicity #61 #64]: #66 +#71 := [trans #67 #69]: #70 +#58 := (= #17 0::Int) +#59 := [rewrite]: #58 +#56 := (iff #16 #15) +#57 := [rewrite]: #56 +#74 := [monotonicity #57 #59 #71]: #73 +#78 := [trans #74 #76]: #77 +#54 := (iff #12 true) +#49 := (or true false) +#52 := (iff #49 true) +#53 := [rewrite]: #52 +#50 := (iff #12 #49) +#47 := (iff #11 false) +#48 := [rewrite]: #47 +#51 := [monotonicity #46 #48]: #50 +#55 := [trans #51 #53]: #54 +#81 := [monotonicity #55 #78]: #80 +#84 := [trans #81 #83]: #23 +#86 := [monotonicity #84]: #85 +#88 := [trans #86 #46]: #87 +#91 := [monotonicity #88]: #90 +#95 := [trans #91 #93]: #94 +#44 := [asserted]: #24 +[mp #44 #95]: false +unsat +9f6a38ce629880be5bf8c7f73c6606884657520c 77 0 +#2 := false +#8 := 1::Int +#18 := (- 1::Int) +#19 := (div #18 #18) +#17 := (div 1::Int 1::Int) +#9 := 0::Int +#12 := (< 0::Int 1::Int) +#14 := (< 1::Int 0::Int) +#15 := (and #14 #12) +#13 := (and #12 #12) +#16 := (or #13 #15) +#20 := (ite #16 #17 #19) +#10 := (= 1::Int 0::Int) +#11 := (or #10 #10) +#21 := (ite #11 0::Int #20) +#22 := (= #21 1::Int) +#23 := (not #22) +#98 := (iff #23 false) +#1 := true +#93 := (not true) +#96 := (iff #93 false) +#97 := [rewrite]: #96 +#94 := (iff #23 #93) +#91 := (iff #22 true) +#86 := (= 1::Int 1::Int) +#89 := (iff #86 true) +#90 := [rewrite]: #89 +#87 := (iff #22 #86) +#80 := (ite false 0::Int 1::Int) +#83 := (= #80 1::Int) #84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#100 := [monotonicity #87 #97]: #99 -#80 := (iff #18 #79) -#77 := (iff #17 #76) -#78 := [rewrite]: #77 -#74 := (iff #16 #73) -#75 := [rewrite]: #74 -#81 := [monotonicity #75 #78]: #80 -#103 := [monotonicity #81 #100]: #102 -#106 := [monotonicity #103]: #105 -#109 := [quant-intro #106]: #108 -#150 := [trans #109 #148]: #149 -#72 := [asserted]: #32 -#151 := [mp #72 #150]: #146 -#200 := [mp~ #151 #209]: #146 -#231 := [mp #200 #230]: #228 -#262 := [mp #231 #261]: #259 -#755 := [mp #262 #754]: #750 -#9 := 1::Int -#10 := (f3 0::Int 1::Int) -#11 := (= #10 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#584 := (not #750) -#585 := (or #584 #11) -#336 := (* -1::Int 1::Int) -#420 := (* -1::Int 0::Int) -#421 := (div #420 #336) -#422 := (* -1::Int #421) -#413 := (+ #10 #422) -#424 := (= #413 0::Int) -#425 := (div 0::Int 1::Int) -#426 := (* -1::Int #425) -#423 := (+ #10 #426) -#427 := (= #423 0::Int) -#406 := (>= 0::Int 0::Int) -#741 := (<= 1::Int 0::Int) -#743 := (or #741 #406) -#400 := (not #743) -#530 := (<= 0::Int 0::Int) -#737 := (or #530 #741) -#411 := (not #737) -#412 := (or #411 #400) -#744 := (ite #412 #427 #424) -#745 := (= 1::Int 0::Int) -#746 := (= 0::Int 0::Int) -#747 := (or #746 #745) -#742 := (ite #747 #11 #744) -#578 := (or #584 #742) -#587 := (iff #578 #585) -#589 := (iff #585 #585) -#590 := [rewrite]: #589 -#567 := (iff #742 #11) -#1 := true -#681 := (ite true #11 #11) -#679 := (iff #681 #11) -#682 := [rewrite]: #679 -#583 := (iff #742 #681) -#574 := (iff #744 #11) -#689 := (ite false #11 #11) -#572 := (iff #689 #11) -#573 := [rewrite]: #572 -#687 := (iff #744 #689) -#686 := (iff #424 #11) -#532 := (= #413 #10) -#704 := (+ #10 0::Int) -#701 := (= #704 #10) -#702 := [rewrite]: #701 -#529 := (= #413 #704) -#693 := (= #422 0::Int) -#710 := (= #420 0::Int) -#714 := [rewrite]: #710 -#698 := (= #422 #420) -#691 := (= #421 0::Int) -#552 := (div 0::Int -1::Int) -#696 := (= #552 0::Int) -#697 := [rewrite]: #696 -#694 := (= #421 #552) -#550 := (= #336 -1::Int) -#551 := [rewrite]: #550 -#695 := [monotonicity #714 #551]: #694 -#692 := [trans #695 #697]: #691 -#699 := [monotonicity #692]: #698 -#700 := [trans #699 #714]: #693 -#531 := [monotonicity #700]: #529 -#685 := [trans #531 #702]: #532 -#688 := [monotonicity #685]: #686 -#703 := (iff #427 #11) -#707 := (= #423 #10) -#705 := (= #423 #704) -#711 := (= #426 0::Int) -#713 := (= #426 #420) -#434 := (= #425 0::Int) -#712 := [rewrite]: #434 -#428 := [monotonicity #712]: #713 -#715 := [trans #428 #714]: #711 -#706 := [monotonicity #715]: #705 -#708 := [trans #706 #702]: #707 -#709 := [monotonicity #708]: #703 -#432 := (iff #412 false) -#716 := (or false false) -#721 := (iff #716 false) -#431 := [rewrite]: #721 -#720 := (iff #412 #716) -#441 := (iff #400 false) -#731 := (not true) -#734 := (iff #731 false) -#374 := [rewrite]: #734 -#718 := (iff #400 #731) -#448 := (iff #743 true) -#722 := (or false true) -#446 := (iff #722 true) -#447 := [rewrite]: #446 -#723 := (iff #743 #722) -#733 := (iff #406 true) -#736 := [rewrite]: #733 -#726 := (iff #741 false) -#727 := [rewrite]: #726 -#445 := [monotonicity #727 #736]: #723 -#342 := [trans #445 #447]: #448 -#719 := [monotonicity #342]: #718 -#442 := [trans #719 #374]: #441 -#375 := (iff #411 false) -#369 := (iff #411 #731) -#730 := (iff #737 true) -#739 := (or true false) -#383 := (iff #739 true) -#724 := [rewrite]: #383 -#728 := (iff #737 #739) -#389 := (iff #530 true) -#390 := [rewrite]: #389 -#729 := [monotonicity #390 #727]: #728 -#725 := [trans #729 #724]: #730 -#732 := [monotonicity #725]: #369 -#735 := [trans #732 #374]: #375 -#717 := [monotonicity #735 #442]: #720 -#433 := [trans #717 #431]: #432 -#690 := [monotonicity #433 #709 #688]: #687 -#533 := [trans #690 #573]: #574 -#387 := (iff #747 true) -#399 := (iff #747 #739) -#398 := (iff #745 false) -#403 := [rewrite]: #398 -#748 := (iff #746 true) -#738 := [rewrite]: #748 -#740 := [monotonicity #738 #403]: #399 -#388 := [trans #740 #724]: #387 -#678 := [monotonicity #388 #533]: #583 -#582 := [trans #678 #682]: #567 -#588 := [monotonicity #582]: #587 -#683 := [trans #588 #590]: #587 -#586 := [quant-inst #8 #9]: #578 -#680 := [mp #586 #683]: #585 -[unit-resolution #680 #61 #755]: false -unsat -ca32959e06f9134641deb61724af7aaee2701280 279 0 -#2 := false -decl f3 :: (-> Int Int Int) -#13 := (:var 0 Int) -#12 := (:var 1 Int) -#14 := (f3 #12 #13) -#734 := (pattern #14) -#15 := 0::Int -#79 := -1::Int -#83 := (* -1::Int #13) -#80 := (* -1::Int #12) -#86 := (div #80 #83) -#237 := (* -1::Int #86) -#238 := (+ #14 #237) -#239 := (= #238 0::Int) -#25 := (div #12 #13) -#234 := (* -1::Int #25) -#235 := (+ #14 #234) -#236 := (= #235 0::Int) -#112 := (>= #12 0::Int) -#105 := (<= #13 0::Int) -#197 := (or #105 #112) -#198 := (not #197) -#101 := (<= #12 0::Int) -#195 := (or #101 #105) -#196 := (not #195) -#201 := (or #196 #198) -#240 := (ite #201 #236 #239) -#233 := (= #14 0::Int) -#17 := (= #13 0::Int) -#16 := (= #12 0::Int) -#18 := (or #16 #17) -#241 := (ite #18 #233 #240) -#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #241) -#244 := (forall (vars (?v0 Int) (?v1 Int)) #241) -#738 := (iff #244 #735) -#736 := (iff #241 #241) -#737 := [refl]: #736 -#739 := [quant-intro #737]: #738 -#204 := (ite #201 #25 #86) -#207 := (ite #18 0::Int #204) -#210 := (= #14 #207) -#213 := (forall (vars (?v0 Int) (?v1 Int)) #210) -#245 := (iff #213 #244) -#242 := (iff #210 #241) -#243 := [rewrite]: #242 -#246 := [quant-intro #243]: #245 -#113 := (not #112) -#106 := (not #105) -#116 := (and #106 #113) -#102 := (not #101) -#109 := (and #102 #106) -#119 := (or #109 #116) -#122 := (ite #119 #25 #86) -#125 := (ite #18 0::Int #122) -#128 := (= #14 #125) -#131 := (forall (vars (?v0 Int) (?v1 Int)) #128) -#214 := (iff #131 #213) -#211 := (iff #128 #210) -#208 := (= #125 #207) -#205 := (= #122 #204) -#202 := (iff #119 #201) -#199 := (iff #116 #198) -#200 := [rewrite]: #199 -#189 := (iff #109 #196) -#190 := [rewrite]: #189 -#203 := [monotonicity #190 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [monotonicity #206]: #208 -#212 := [monotonicity #209]: #211 -#215 := [quant-intro #212]: #214 -#193 := (~ #131 #131) -#191 := (~ #128 #128) -#192 := [refl]: #191 -#194 := [nnf-pos #192]: #193 -#27 := (- #13) -#26 := (- #12) -#28 := (div #26 #27) -#20 := (< 0::Int #13) -#22 := (< #12 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #12) -#21 := (and #19 #20) -#24 := (or #21 #23) -#29 := (ite #24 #25 #28) -#30 := (ite #18 0::Int #29) -#31 := (= #14 #30) -#32 := (forall (vars (?v0 Int) (?v1 Int)) #31) -#134 := (iff #32 #131) -#73 := (and #20 #22) -#76 := (or #21 #73) -#89 := (ite #76 #25 #86) -#92 := (ite #18 0::Int #89) -#95 := (= #14 #92) -#98 := (forall (vars (?v0 Int) (?v1 Int)) #95) -#132 := (iff #98 #131) -#129 := (iff #95 #128) -#126 := (= #92 #125) -#123 := (= #89 #122) -#120 := (iff #76 #119) -#117 := (iff #73 #116) -#114 := (iff #22 #113) -#115 := [rewrite]: #114 -#107 := (iff #20 #106) -#108 := [rewrite]: #107 -#118 := [monotonicity #108 #115]: #117 -#110 := (iff #21 #109) -#103 := (iff #19 #102) +#81 := (= #21 #80) +#78 := (= #20 1::Int) +#55 := (and #12 #14) +#58 := (or #12 #55) +#73 := (ite #58 1::Int 1::Int) +#76 := (= #73 1::Int) +#77 := [rewrite]: #76 +#74 := (= #20 #73) +#71 := (= #19 1::Int) +#63 := -1::Int +#66 := (div -1::Int -1::Int) +#69 := (= #66 1::Int) +#70 := [rewrite]: #69 +#67 := (= #19 #66) +#64 := (= #18 -1::Int) +#65 := [rewrite]: #64 +#68 := [monotonicity #65 #65]: #67 +#72 := [trans #68 #70]: #71 +#61 := (= #17 1::Int) +#62 := [rewrite]: #61 +#59 := (iff #16 #58) +#56 := (iff #15 #55) +#57 := [rewrite]: #56 +#53 := (iff #13 #12) +#54 := [rewrite]: #53 +#60 := [monotonicity #54 #57]: #59 +#75 := [monotonicity #60 #62 #72]: #74 +#79 := [trans #75 #77]: #78 +#51 := (iff #11 false) +#46 := (or false false) +#49 := (iff #46 false) +#50 := [rewrite]: #49 +#47 := (iff #11 #46) +#44 := (iff #10 false) +#45 := [rewrite]: #44 +#48 := [monotonicity #45 #45]: #47 +#52 := [trans #48 #50]: #51 +#82 := [monotonicity #52 #79]: #81 +#85 := [trans #82 #84]: #22 +#88 := [monotonicity #85]: #87 +#92 := [trans #88 #90]: #91 +#95 := [monotonicity #92]: #94 +#99 := [trans #95 #97]: #98 +#43 := [asserted]: #23 +[mp #43 #99]: false +unsat +519fa461c6409fb549ed180638c452bbb592389a 84 0 +#2 := false +#8 := 3::Int +#11 := 1::Int +#22 := (- 1::Int) +#21 := (- 3::Int) +#23 := (div #21 #22) +#20 := (div 3::Int 1::Int) +#9 := 0::Int +#15 := (< 0::Int 1::Int) +#17 := (< 3::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 3::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 1::Int 0::Int) +#10 := (= 3::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (= #25 3::Int) +#27 := (not #26) +#105 := (iff #27 false) +#1 := true +#100 := (not true) +#103 := (iff #100 false) #104 := [rewrite]: #103 -#111 := [monotonicity #104 #108]: #110 -#121 := [monotonicity #111 #118]: #120 +#101 := (iff #27 #100) +#98 := (iff #26 true) +#93 := (= 3::Int 3::Int) +#96 := (iff #93 true) +#97 := [rewrite]: #96 +#94 := (iff #26 #93) +#87 := (ite false 0::Int 3::Int) +#90 := (= #87 3::Int) +#91 := [rewrite]: #90 +#88 := (= #25 #87) +#85 := (= #24 3::Int) +#59 := (and #15 #17) +#62 := (or #16 #59) +#80 := (ite #62 3::Int 3::Int) +#83 := (= #80 3::Int) +#84 := [rewrite]: #83 +#81 := (= #24 #80) +#78 := (= #23 3::Int) +#70 := -1::Int +#67 := -3::Int +#73 := (div -3::Int -1::Int) +#76 := (= #73 3::Int) +#77 := [rewrite]: #76 +#74 := (= #23 #73) +#71 := (= #22 -1::Int) +#72 := [rewrite]: #71 +#68 := (= #21 -3::Int) +#69 := [rewrite]: #68 +#75 := [monotonicity #69 #72]: #74 +#79 := [trans #75 #77]: #78 +#65 := (= #20 3::Int) +#66 := [rewrite]: #65 +#63 := (iff #19 #62) +#60 := (iff #18 #59) +#61 := [rewrite]: #60 +#64 := [monotonicity #61]: #63 +#82 := [monotonicity #64 #66 #79]: #81 +#86 := [trans #82 #84]: #85 +#57 := (iff #13 false) +#52 := (or false false) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #13 #52) +#50 := (iff #12 false) +#51 := [rewrite]: #50 +#48 := (iff #10 false) +#49 := [rewrite]: #48 +#54 := [monotonicity #49 #51]: #53 +#58 := [trans #54 #56]: #57 +#89 := [monotonicity #58 #86]: #88 +#92 := [trans #89 #91]: #26 +#95 := [monotonicity #92]: #94 +#99 := [trans #95 #97]: #98 +#102 := [monotonicity #99]: #101 +#106 := [trans #102 #104]: #105 +#47 := [asserted]: #27 +[mp #47 #106]: false +unsat +8d9d1f916dc7c49723b00373e1ef641d98863a50 174 0 +#2 := false +#9 := 0::Int +decl f3 :: Int +#8 := f3 +#89 := (<= f3 0::Int) +#102 := (>= f3 0::Int) +#103 := (not #102) +#90 := (not #89) +#113 := (or #90 #103) +#140 := (not #113) +#63 := -1::Int +#64 := (* -1::Int f3) +#69 := (div #64 -1::Int) +#11 := 1::Int +#20 := (div f3 1::Int) +#116 := (ite #113 #20 #69) +#138 := (= #20 #116) +#246 := (not #138) +#10 := (= f3 0::Int) +#119 := (ite #10 0::Int #116) +#122 := (= f3 #119) +#137 := (= #116 #119) +#149 := (not #10) +#136 := (= #119 0::Int) +#163 := (iff #136 #122) +#161 := (iff #122 #136) +#156 := (= 0::Int #119) +#159 := (iff #156 #136) +#160 := [commutativity]: #159 +#157 := (iff #122 #156) +#154 := [hypothesis]: #10 +#158 := [monotonicity #154]: #157 +#162 := [trans #158 #160]: #161 +#164 := [symm #162]: #163 +#150 := (or #149 #136) +#151 := [def-axiom]: #150 +#155 := [unit-resolution #151 #154]: #136 +#165 := [mp #155 #164]: #122 +#125 := (not #122) +#22 := (- 1::Int) +#21 := (- f3) +#23 := (div #21 #22) +#15 := (< 0::Int 1::Int) +#17 := (< f3 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int f3) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 1::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (= #25 f3) +#27 := (not #26) +#128 := (iff #27 #125) +#57 := (and #15 #17) +#60 := (or #16 #57) +#72 := (ite #60 #20 #69) +#75 := (ite #10 0::Int #72) +#81 := (= f3 #75) +#86 := (not #81) +#126 := (iff #86 #125) +#123 := (iff #81 #122) +#120 := (= #75 #119) +#117 := (= #72 #116) +#114 := (iff #60 #113) +#111 := (iff #57 #103) +#1 := true +#106 := (and true #103) +#109 := (iff #106 #103) +#110 := [rewrite]: #109 +#107 := (iff #57 #106) +#104 := (iff #17 #103) +#105 := [rewrite]: #104 +#93 := (iff #15 true) +#94 := [rewrite]: #93 +#108 := [monotonicity #94 #105]: #107 +#112 := [trans #108 #110]: #111 +#100 := (iff #16 #90) +#95 := (and #90 true) +#98 := (iff #95 #90) +#99 := [rewrite]: #98 +#96 := (iff #16 #95) +#91 := (iff #14 #90) +#92 := [rewrite]: #91 +#97 := [monotonicity #92 #94]: #96 +#101 := [trans #97 #99]: #100 +#115 := [monotonicity #101 #112]: #114 +#118 := [monotonicity #115]: #117 +#121 := [monotonicity #118]: #120 #124 := [monotonicity #121]: #123 #127 := [monotonicity #124]: #126 -#130 := [monotonicity #127]: #129 -#133 := [quant-intro #130]: #132 -#99 := (iff #32 #98) -#96 := (iff #31 #95) -#93 := (= #30 #92) -#90 := (= #29 #89) -#87 := (= #28 #86) -#84 := (= #27 #83) -#85 := [rewrite]: #84 -#81 := (= #26 #80) -#82 := [rewrite]: #81 -#88 := [monotonicity #82 #85]: #87 -#77 := (iff #24 #76) -#74 := (iff #23 #73) -#75 := [rewrite]: #74 -#78 := [monotonicity #75]: #77 -#91 := [monotonicity #78 #88]: #90 -#94 := [monotonicity #91]: #93 -#97 := [monotonicity #94]: #96 -#100 := [quant-intro #97]: #99 -#135 := [trans #100 #133]: #134 -#72 := [asserted]: #32 -#136 := [mp #72 #135]: #131 -#185 := [mp~ #136 #194]: #131 -#216 := [mp #185 #215]: #213 -#247 := [mp #216 #246]: #244 -#740 := [mp #247 #739]: #735 -#8 := 1::Int -#9 := (f3 1::Int 1::Int) -#10 := (= #9 1::Int) -#11 := (not #10) -#61 := [asserted]: #11 -#571 := (not #735) -#572 := (or #571 #10) -#321 := (* -1::Int 1::Int) -#405 := (div #321 #321) -#406 := (* -1::Int #405) -#407 := (+ #9 #406) -#398 := (= #407 0::Int) -#409 := (div 1::Int 1::Int) -#410 := (* -1::Int #409) -#411 := (+ #9 #410) -#408 := (= #411 0::Int) -#412 := (>= 1::Int 0::Int) -#391 := (<= 1::Int 0::Int) -#726 := (or #391 #412) -#728 := (not #726) -#385 := (or #391 #391) -#515 := (not #385) -#722 := (or #515 #728) -#396 := (ite #722 #408 #398) -#397 := (= #9 0::Int) -#729 := (= 1::Int 0::Int) -#730 := (or #729 #729) -#731 := (ite #730 #397 #396) -#573 := (or #571 #731) -#575 := (iff #573 #572) -#665 := (iff #572 #572) -#669 := [rewrite]: #665 -#570 := (iff #731 #10) -#664 := (ite false #397 #10) -#567 := (iff #664 #10) -#569 := [rewrite]: #567 -#667 := (iff #731 #664) -#568 := (iff #396 #10) -#1 := true -#557 := (ite true #10 #10) -#518 := (iff #557 #10) -#666 := [rewrite]: #518 -#558 := (iff #396 #557) -#672 := (iff #398 #10) -#689 := (+ -1::Int #9) -#692 := (= #689 0::Int) -#694 := (iff #692 #10) -#535 := [rewrite]: #694 -#673 := (iff #398 #692) -#670 := (= #407 #689) -#699 := (+ #9 -1::Int) -#690 := (= #699 #689) -#691 := [rewrite]: #690 -#516 := (= #407 #699) -#685 := (= #406 -1::Int) -#697 := (= #321 -1::Int) -#698 := [rewrite]: #697 -#684 := (= #406 #321) -#677 := (= #405 1::Int) -#679 := (div -1::Int -1::Int) -#682 := (= #679 1::Int) -#676 := [rewrite]: #682 -#680 := (= #405 #679) -#681 := [monotonicity #698 #698]: #680 -#683 := [trans #681 #676]: #677 -#678 := [monotonicity #683]: #684 -#514 := [trans #678 #698]: #685 -#517 := [monotonicity #514]: #516 -#671 := [trans #517 #691]: #670 -#674 := [monotonicity #671]: #673 -#675 := [trans #674 #535]: #672 -#536 := (iff #408 #10) -#693 := (iff #408 #692) -#686 := (= #411 #689) -#696 := (= #411 #699) -#413 := (= #410 -1::Int) -#418 := (= #410 #321) -#416 := (= #409 1::Int) -#417 := [rewrite]: #416 -#419 := [monotonicity #417]: #418 -#695 := [trans #419 #698]: #413 -#700 := [monotonicity #695]: #696 -#687 := [trans #700 #691]: #686 -#688 := [monotonicity #687]: #693 -#537 := [trans #688 #535]: #536 -#702 := (iff #722 true) -#704 := (or true false) -#701 := (iff #704 true) -#705 := [rewrite]: #701 -#426 := (iff #722 #704) -#327 := (iff #728 false) -#708 := (not true) -#432 := (iff #708 false) -#433 := [rewrite]: #432 -#430 := (iff #728 #708) -#721 := (iff #726 true) -#719 := (or false true) -#720 := (iff #719 true) -#718 := [rewrite]: #720 -#359 := (iff #726 #719) -#354 := (iff #412 true) -#717 := [rewrite]: #354 -#368 := (iff #391 false) -#709 := [rewrite]: #368 -#360 := [monotonicity #709 #717]: #359 -#707 := [trans #360 #718]: #721 -#431 := [monotonicity #707]: #430 -#703 := [trans #431 #433]: #327 -#710 := (iff #515 true) -#711 := (not false) -#714 := (iff #711 true) -#715 := [rewrite]: #714 -#712 := (iff #515 #711) -#374 := (iff #385 false) -#733 := (or false false) -#388 := (iff #733 false) -#724 := [rewrite]: #388 -#372 := (iff #385 #733) -#373 := [monotonicity #709 #709]: #372 -#375 := [trans #373 #724]: #374 -#713 := [monotonicity #375]: #712 -#716 := [trans #713 #715]: #710 -#427 := [monotonicity #716 #703]: #426 -#706 := [trans #427 #705]: #702 -#559 := [monotonicity #706 #537 #675]: #558 -#663 := [trans #559 #666]: #568 -#384 := (iff #730 false) -#723 := (iff #730 #733) -#732 := (iff #729 false) -#727 := [rewrite]: #732 -#383 := [monotonicity #727 #727]: #723 -#725 := [trans #383 #724]: #384 -#552 := [monotonicity #725 #663]: #667 -#563 := [trans #552 #569]: #570 -#668 := [monotonicity #563]: #575 -#656 := [trans #668 #669]: #575 -#574 := [quant-inst #8 #8]: #573 -#658 := [mp #574 #656]: #572 -[unit-resolution #658 #61 #740]: false -unsat -4e490baf730f7c2e9689bb8a2892f4f8f052ba53 290 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#735 := (pattern #15) -#16 := 0::Int -#80 := -1::Int -#84 := (* -1::Int #14) -#81 := (* -1::Int #13) -#87 := (div #81 #84) -#238 := (* -1::Int #87) -#239 := (+ #15 #238) -#240 := (= #239 0::Int) -#26 := (div #13 #14) -#235 := (* -1::Int #26) -#236 := (+ #15 #235) -#237 := (= #236 0::Int) -#113 := (>= #13 0::Int) -#106 := (<= #14 0::Int) -#198 := (or #106 #113) -#199 := (not #198) -#102 := (<= #13 0::Int) -#196 := (or #102 #106) -#197 := (not #196) -#202 := (or #197 #199) -#241 := (ite #202 #237 #240) -#234 := (= #15 0::Int) -#18 := (= #14 0::Int) -#17 := (= #13 0::Int) -#19 := (or #17 #18) -#242 := (ite #19 #234 #241) -#736 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #735) #242) -#245 := (forall (vars (?v0 Int) (?v1 Int)) #242) -#739 := (iff #245 #736) -#737 := (iff #242 #242) -#738 := [refl]: #737 -#740 := [quant-intro #738]: #739 -#205 := (ite #202 #26 #87) -#208 := (ite #19 0::Int #205) -#211 := (= #15 #208) -#214 := (forall (vars (?v0 Int) (?v1 Int)) #211) -#246 := (iff #214 #245) -#243 := (iff #211 #242) -#244 := [rewrite]: #243 -#247 := [quant-intro #244]: #246 -#114 := (not #113) -#107 := (not #106) -#117 := (and #107 #114) -#103 := (not #102) -#110 := (and #103 #107) -#120 := (or #110 #117) -#123 := (ite #120 #26 #87) -#126 := (ite #19 0::Int #123) -#129 := (= #15 #126) -#132 := (forall (vars (?v0 Int) (?v1 Int)) #129) -#215 := (iff #132 #214) -#212 := (iff #129 #211) -#209 := (= #126 #208) -#206 := (= #123 #205) -#203 := (iff #120 #202) -#200 := (iff #117 #199) -#201 := [rewrite]: #200 -#190 := (iff #110 #197) -#191 := [rewrite]: #190 -#204 := [monotonicity #191 #201]: #203 -#207 := [monotonicity #204]: #206 -#210 := [monotonicity #207]: #209 -#213 := [monotonicity #210]: #212 -#216 := [quant-intro #213]: #215 -#194 := (~ #132 #132) -#192 := (~ #129 #129) -#193 := [refl]: #192 -#195 := [nnf-pos #193]: #194 -#28 := (- #14) -#27 := (- #13) -#29 := (div #27 #28) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #15 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#135 := (iff #33 #132) -#74 := (and #21 #23) -#77 := (or #22 #74) -#90 := (ite #77 #26 #87) -#93 := (ite #19 0::Int #90) -#96 := (= #15 #93) -#99 := (forall (vars (?v0 Int) (?v1 Int)) #96) -#133 := (iff #99 #132) -#130 := (iff #96 #129) -#127 := (= #93 #126) -#124 := (= #90 #123) -#121 := (iff #77 #120) -#118 := (iff #74 #117) -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#108 := (iff #21 #107) -#109 := [rewrite]: #108 -#119 := [monotonicity #109 #116]: #118 -#111 := (iff #22 #110) -#104 := (iff #20 #103) -#105 := [rewrite]: #104 -#112 := [monotonicity #105 #109]: #111 -#122 := [monotonicity #112 #119]: #121 -#125 := [monotonicity #122]: #124 -#128 := [monotonicity #125]: #127 -#131 := [monotonicity #128]: #130 -#134 := [quant-intro #131]: #133 -#100 := (iff #33 #99) -#97 := (iff #32 #96) -#94 := (= #31 #93) -#91 := (= #30 #90) -#88 := (= #29 #87) -#85 := (= #28 #84) -#86 := [rewrite]: #85 -#82 := (= #27 #81) -#83 := [rewrite]: #82 -#89 := [monotonicity #83 #86]: #88 -#78 := (iff #25 #77) -#75 := (iff #24 #74) -#76 := [rewrite]: #75 -#79 := [monotonicity #76]: #78 -#92 := [monotonicity #79 #89]: #91 -#95 := [monotonicity #92]: #94 -#98 := [monotonicity #95]: #97 -#101 := [quant-intro #98]: #100 -#136 := [trans #101 #134]: #135 -#73 := [asserted]: #33 -#137 := [mp #73 #136]: #132 -#186 := [mp~ #137 #195]: #132 -#217 := [mp #186 #216]: #214 -#248 := [mp #217 #247]: #245 -#741 := [mp #248 #740]: #736 -#8 := 3::Int -#9 := 1::Int -#10 := (f3 3::Int 1::Int) -#11 := (= #10 3::Int) -#12 := (not #11) -#62 := [asserted]: #12 -#651 := (not #736) -#648 := (or #651 #11) -#322 := (* -1::Int 1::Int) -#406 := (* -1::Int 3::Int) -#407 := (div #406 #322) -#408 := (* -1::Int #407) -#399 := (+ #10 #408) -#410 := (= #399 0::Int) -#411 := (div 3::Int 1::Int) -#412 := (* -1::Int #411) -#409 := (+ #10 #412) -#413 := (= #409 0::Int) -#392 := (>= 3::Int 0::Int) -#727 := (<= 1::Int 0::Int) -#729 := (or #727 #392) -#386 := (not #729) -#516 := (<= 3::Int 0::Int) -#723 := (or #516 #727) -#397 := (not #723) -#398 := (or #397 #386) -#730 := (ite #398 #413 #410) -#731 := (= #10 0::Int) -#732 := (= 1::Int 0::Int) -#733 := (= 3::Int 0::Int) -#728 := (or #733 #732) -#734 := (ite #728 #731 #730) -#650 := (or #651 #734) -#661 := (iff #650 #648) -#658 := (iff #648 #648) -#663 := [rewrite]: #658 -#657 := (iff #734 #11) -#575 := (ite false #731 #11) -#666 := (iff #575 #11) -#670 := [rewrite]: #666 -#576 := (iff #734 #575) -#573 := (iff #730 #11) -#1 := true -#568 := (ite true #11 #11) -#564 := (iff #568 #11) -#572 := [rewrite]: #564 -#570 := (iff #730 #568) -#668 := (iff #410 #11) -#690 := -3::Int -#695 := (+ -3::Int #10) -#681 := (= #695 0::Int) -#677 := (iff #681 #11) -#678 := [rewrite]: #677 -#664 := (iff #410 #681) -#667 := (= #399 #695) -#693 := (+ #10 -3::Int) -#536 := (= #693 #695) -#537 := [rewrite]: #536 -#560 := (= #399 #693) -#558 := (= #408 -3::Int) -#691 := (= #406 -3::Int) -#692 := [rewrite]: #691 -#673 := (= #408 #406) -#674 := (= #407 3::Int) -#515 := (div -3::Int -1::Int) -#671 := (= #515 3::Int) -#672 := [rewrite]: #671 -#517 := (= #407 #515) -#679 := (= #322 -1::Int) -#686 := [rewrite]: #679 -#518 := [monotonicity #692 #686]: #517 -#675 := [trans #518 #672]: #674 -#676 := [monotonicity #675]: #673 -#559 := [trans #676 #692]: #558 -#519 := [monotonicity #559]: #560 -#569 := [trans #519 #537]: #667 -#665 := [monotonicity #569]: #664 -#553 := [trans #665 #678]: #668 -#684 := (iff #413 #11) -#682 := (iff #413 #681) -#538 := (= #409 #695) -#694 := (= #409 #693) -#687 := (= #412 -3::Int) -#697 := (= #412 #406) -#696 := (= #411 3::Int) -#700 := [rewrite]: #696 -#701 := [monotonicity #700]: #697 -#688 := [trans #701 #692]: #687 -#689 := [monotonicity #688]: #694 -#680 := [trans #689 #537]: #538 -#683 := [monotonicity #680]: #682 -#685 := [trans #683 #678]: #684 -#699 := (iff #398 true) -#417 := (or true false) -#420 := (iff #417 true) -#698 := [rewrite]: #420 -#418 := (iff #398 #417) -#703 := (iff #386 false) -#705 := (not true) -#702 := (iff #705 false) -#706 := [rewrite]: #702 -#427 := (iff #386 #705) -#328 := (iff #729 true) -#709 := (or false true) -#433 := (iff #709 true) -#434 := [rewrite]: #433 -#431 := (iff #729 #709) -#722 := (iff #392 true) -#708 := [rewrite]: #722 -#713 := (iff #727 false) -#714 := [rewrite]: #713 -#432 := [monotonicity #714 #708]: #431 -#704 := [trans #432 #434]: #328 -#428 := [monotonicity #704]: #427 -#707 := [trans #428 #706]: #703 -#721 := (iff #397 true) -#355 := (not false) -#360 := (iff #355 true) -#361 := [rewrite]: #360 -#718 := (iff #397 #355) -#711 := (iff #723 false) -#385 := (or false false) -#710 := (iff #385 false) -#373 := [rewrite]: #710 -#715 := (iff #723 #385) -#376 := (iff #516 false) -#712 := [rewrite]: #376 -#716 := [monotonicity #712 #714]: #715 -#717 := [trans #716 #373]: #711 -#720 := [monotonicity #717]: #718 -#719 := [trans #720 #361]: #721 -#419 := [monotonicity #719 #707]: #418 -#414 := [trans #419 #698]: #699 -#571 := [monotonicity #414 #685 #553]: #570 -#574 := [trans #571 #572]: #573 -#374 := (iff #728 false) -#726 := (iff #728 #385) -#389 := (iff #732 false) -#725 := [rewrite]: #389 -#724 := (iff #733 false) -#384 := [rewrite]: #724 -#369 := [monotonicity #384 #725]: #726 -#375 := [trans #369 #373]: #374 -#669 := [monotonicity #375 #574]: #576 -#659 := [trans #669 #670]: #657 -#662 := [monotonicity #659]: #661 -#652 := [trans #662 #663]: #661 -#660 := [quant-inst #8 #9]: #650 -#653 := [mp #660 #652]: #648 -[unit-resolution #653 #62 #741]: false -unsat -3af8b375b2f7758b71c609be3059c3c3f068c4d0 327 0 -#2 := false -decl f3 :: (-> Int Int Int) -#9 := 1::Int -decl f4 :: Int -#8 := f4 -#10 := (f3 f4 1::Int) -#63 := (= f4 #10) -#16 := 0::Int -#728 := (= #10 0::Int) -#543 := (iff #728 #63) -#541 := (iff #63 #728) -#536 := (= 0::Int #10) -#539 := (iff #536 #728) -#540 := [commutativity]: #539 -#537 := (iff #63 #536) -#730 := (= f4 0::Int) -#408 := (div f4 1::Int) -#77 := -1::Int -#409 := (* -1::Int #408) -#406 := (+ #10 #409) -#410 := (= #406 0::Int) -#516 := (not #410) -#552 := (= #408 #10) -#590 := (= #10 #408) -#515 := (<= #406 0::Int) -#474 := [hypothesis]: #410 -#585 := (or #516 #515) -#586 := [th-lemma arith triangle-eq]: #585 -#587 := [unit-resolution #586 #474]: #515 -#668 := (>= #406 0::Int) -#592 := (or #516 #668) -#588 := [th-lemma arith triangle-eq]: #592 -#589 := [unit-resolution #588 #474]: #668 -#593 := [th-lemma arith eq-propagate 1 1 #589 #587]: #590 -#559 := [symm #593]: #552 -#578 := (= f4 #408) -#621 := (+ f4 #409) -#626 := (<= #621 0::Int) -#620 := (= #621 0::Int) -#1 := true -#60 := [true-axiom]: true -#594 := (or false #620) -#595 := [th-lemma arith]: #594 -#591 := [unit-resolution #595 #60]: #620 -#596 := (not #620) -#576 := (or #596 #626) -#522 := [th-lemma arith triangle-eq]: #576 -#577 := [unit-resolution #522 #591]: #626 -#627 := (>= #621 0::Int) -#558 := (or #596 #627) -#582 := [th-lemma arith triangle-eq]: #558 -#583 := [unit-resolution #582 #591]: #627 -#584 := [th-lemma arith eq-propagate 1 1 #583 #577]: #578 -#518 := [trans #584 #559]: #63 -#66 := (not #63) -#11 := (= #10 f4) -#12 := (not #11) -#67 := (iff #12 #66) -#64 := (iff #11 #63) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#62 := [asserted]: #12 -#71 := [mp #62 #68]: #66 -#549 := [unit-resolution #71 #518]: false -#551 := [lemma #549]: #516 -#403 := (* -1::Int f4) -#704 := (div #403 -1::Int) -#416 := (* -1::Int #704) -#696 := (+ #10 #416) -#697 := (= #696 0::Int) -#513 := (<= f4 0::Int) -#714 := (not #513) -#389 := (>= f4 0::Int) -#706 := (not #389) -#701 := (or #706 #714) -#687 := (ite #701 #410 #697) -#565 := (not #730) -#657 := [hypothesis]: #565 -#560 := (or #730 #687) -#684 := (ite #730 #728 #687) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#732 := (pattern #15) -#81 := (* -1::Int #14) -#78 := (* -1::Int #13) -#84 := (div #78 #81) -#235 := (* -1::Int #84) -#236 := (+ #15 #235) -#237 := (= #236 0::Int) -#26 := (div #13 #14) -#232 := (* -1::Int #26) -#233 := (+ #15 #232) -#234 := (= #233 0::Int) -#110 := (>= #13 0::Int) -#103 := (<= #14 0::Int) -#195 := (or #103 #110) -#196 := (not #195) -#99 := (<= #13 0::Int) -#193 := (or #99 #103) -#194 := (not #193) -#199 := (or #194 #196) -#238 := (ite #199 #234 #237) -#231 := (= #15 0::Int) -#18 := (= #14 0::Int) -#17 := (= #13 0::Int) -#19 := (or #17 #18) -#239 := (ite #19 #231 #238) -#733 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #732) #239) -#242 := (forall (vars (?v0 Int) (?v1 Int)) #239) -#736 := (iff #242 #733) -#734 := (iff #239 #239) -#735 := [refl]: #734 -#737 := [quant-intro #735]: #736 -#202 := (ite #199 #26 #84) -#205 := (ite #19 0::Int #202) -#208 := (= #15 #205) -#211 := (forall (vars (?v0 Int) (?v1 Int)) #208) -#243 := (iff #211 #242) -#240 := (iff #208 #239) -#241 := [rewrite]: #240 -#244 := [quant-intro #241]: #243 -#111 := (not #110) -#104 := (not #103) -#114 := (and #104 #111) -#100 := (not #99) -#107 := (and #100 #104) -#117 := (or #107 #114) -#120 := (ite #117 #26 #84) -#123 := (ite #19 0::Int #120) -#126 := (= #15 #123) -#129 := (forall (vars (?v0 Int) (?v1 Int)) #126) -#212 := (iff #129 #211) -#209 := (iff #126 #208) -#206 := (= #123 #205) -#203 := (= #120 #202) -#200 := (iff #117 #199) -#197 := (iff #114 #196) -#198 := [rewrite]: #197 -#187 := (iff #107 #194) -#188 := [rewrite]: #187 -#201 := [monotonicity #188 #198]: #200 -#204 := [monotonicity #201]: #203 -#207 := [monotonicity #204]: #206 -#210 := [monotonicity #207]: #209 -#213 := [quant-intro #210]: #212 -#191 := (~ #129 #129) -#189 := (~ #126 #126) -#190 := [refl]: #189 -#192 := [nnf-pos #190]: #191 -#28 := (- #14) -#27 := (- #13) -#29 := (div #27 #28) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #15 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#132 := (iff #33 #129) -#70 := (and #21 #23) -#74 := (or #22 #70) -#87 := (ite #74 #26 #84) -#90 := (ite #19 0::Int #87) -#93 := (= #15 #90) -#96 := (forall (vars (?v0 Int) (?v1 Int)) #93) -#130 := (iff #96 #129) -#127 := (iff #93 #126) -#124 := (= #90 #123) -#121 := (= #87 #120) -#118 := (iff #74 #117) -#115 := (iff #70 #114) -#112 := (iff #23 #111) -#113 := [rewrite]: #112 -#105 := (iff #21 #104) -#106 := [rewrite]: #105 -#116 := [monotonicity #106 #113]: #115 -#108 := (iff #22 #107) -#101 := (iff #20 #100) -#102 := [rewrite]: #101 -#109 := [monotonicity #102 #106]: #108 -#119 := [monotonicity #109 #116]: #118 -#122 := [monotonicity #119]: #121 -#125 := [monotonicity #122]: #124 -#128 := [monotonicity #125]: #127 -#131 := [quant-intro #128]: #130 -#97 := (iff #33 #96) -#94 := (iff #32 #93) -#91 := (= #31 #90) -#88 := (= #30 #87) -#85 := (= #29 #84) -#82 := (= #28 #81) +#87 := (iff #27 #86) +#84 := (iff #26 #81) +#78 := (= #75 f3) +#82 := (iff #78 #81) #83 := [rewrite]: #82 -#79 := (= #27 #78) -#80 := [rewrite]: #79 -#86 := [monotonicity #80 #83]: #85 -#75 := (iff #25 #74) -#72 := (iff #24 #70) -#73 := [rewrite]: #72 -#76 := [monotonicity #73]: #75 -#89 := [monotonicity #76 #86]: #88 -#92 := [monotonicity #89]: #91 -#95 := [monotonicity #92]: #94 -#98 := [quant-intro #95]: #97 -#133 := [trans #98 #131]: #132 -#69 := [asserted]: #33 -#134 := [mp #69 #133]: #129 -#183 := [mp~ #134 #192]: #129 -#214 := [mp #183 #213]: #211 -#245 := [mp #214 #244]: #242 -#738 := [mp #245 #737]: #733 -#691 := (not #733) -#686 := (or #691 #684) -#319 := (* -1::Int 1::Int) -#404 := (div #403 #319) -#405 := (* -1::Int #404) -#396 := (+ #10 #405) -#407 := (= #396 0::Int) -#724 := (<= 1::Int 0::Int) -#726 := (or #724 #389) -#383 := (not #726) -#720 := (or #513 #724) -#394 := (not #720) -#395 := (or #394 #383) -#727 := (ite #395 #410 #407) -#729 := (= 1::Int 0::Int) -#725 := (or #730 #729) -#731 := (ite #725 #728 #727) -#692 := (or #691 #731) -#534 := (iff #692 #686) -#677 := (iff #686 #686) -#678 := [rewrite]: #677 -#685 := (iff #731 #684) -#688 := (iff #727 #687) -#694 := (iff #407 #697) -#411 := (= #396 #696) -#417 := (= #405 #416) -#414 := (= #404 #704) -#703 := (= #319 -1::Int) -#700 := [rewrite]: #703 -#415 := [monotonicity #700]: #414 -#695 := [monotonicity #415]: #417 -#693 := [monotonicity #695]: #411 -#698 := [monotonicity #693]: #694 -#425 := (iff #395 #701) -#430 := (or #714 #706) -#702 := (iff #430 #701) -#424 := [rewrite]: #702 -#431 := (iff #395 #430) -#428 := (iff #383 #706) -#719 := (iff #726 #389) -#717 := (or false #389) -#718 := (iff #717 #389) -#716 := [rewrite]: #718 -#357 := (iff #726 #717) -#371 := (iff #724 false) -#372 := [rewrite]: #371 -#358 := [monotonicity #372]: #357 -#705 := [trans #358 #716]: #719 -#429 := [monotonicity #705]: #428 -#352 := (iff #394 #714) -#713 := (iff #720 #513) -#373 := (or #513 false) -#711 := (iff #373 #513) -#712 := [rewrite]: #711 -#709 := (iff #720 #373) -#710 := [monotonicity #372]: #709 -#708 := [trans #710 #712]: #713 -#715 := [monotonicity #708]: #352 -#325 := [monotonicity #715 #429]: #431 -#699 := [trans #325 #424]: #425 -#689 := [monotonicity #699 #698]: #688 -#707 := (iff #725 #730) -#386 := (or #730 false) -#723 := (iff #386 #730) -#366 := [rewrite]: #723 -#722 := (iff #725 #386) -#721 := (iff #729 false) -#381 := [rewrite]: #721 -#382 := [monotonicity #381]: #722 -#370 := [trans #382 #366]: #707 -#690 := [monotonicity #370 #689]: #685 -#535 := [monotonicity #690]: #534 -#679 := [trans #535 #678]: #534 -#533 := [quant-inst #8 #9]: #692 -#680 := [mp #533 #679]: #686 -#553 := [unit-resolution #680 #738]: #684 -#550 := (not #684) -#561 := (or #550 #730 #687) -#569 := [def-axiom]: #561 -#562 := [unit-resolution #569 #553]: #560 -#563 := [unit-resolution #562 #657]: #687 -#649 := (or #701 #730) -#676 := (not #701) -#648 := [hypothesis]: #676 -#674 := (or #701 #389) -#675 := [def-axiom]: #674 -#645 := [unit-resolution #675 #648]: #389 -#681 := (or #701 #513) -#682 := [def-axiom]: #681 -#647 := [unit-resolution #682 #648]: #513 -#658 := (or #730 #714 #706) -#659 := [th-lemma arith triangle-eq]: #658 -#655 := [unit-resolution #659 #657]: #430 -#660 := [unit-resolution #655 #647 #645]: false -#650 := [lemma #660]: #649 -#564 := [unit-resolution #650 #657]: #701 -#670 := (not #687) -#673 := (or #670 #676 #410) -#555 := [def-axiom]: #673 -#574 := [unit-resolution #555 #564 #563 #551]: false -#554 := [lemma #574]: #730 -#538 := [monotonicity #554]: #537 -#542 := [trans #538 #540]: #541 -#544 := [symm #542]: #543 -#575 := (or #565 #728) -#567 := (or #550 #565 #728) -#568 := [def-axiom]: #567 -#530 := [unit-resolution #568 #553]: #575 -#531 := [unit-resolution #530 #554]: #728 -#545 := [mp #531 #544]: #63 -[unit-resolution #71 #545]: false -unsat -6a8ee4256f7c15262363d462bd2dccb9364bb175 316 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#764 := (pattern #16) +#79 := (iff #26 #78) +#76 := (= #25 #75) +#73 := (= #24 #72) +#70 := (= #23 #69) +#67 := (= #22 -1::Int) +#68 := [rewrite]: #67 +#65 := (= #21 #64) +#66 := [rewrite]: #65 +#71 := [monotonicity #66 #68]: #70 +#61 := (iff #19 #60) +#58 := (iff #18 #57) +#59 := [rewrite]: #58 +#62 := [monotonicity #59]: #61 +#74 := [monotonicity #62 #71]: #73 +#55 := (iff #13 #10) +#50 := (or #10 false) +#53 := (iff #50 #10) +#54 := [rewrite]: #53 +#51 := (iff #13 #50) +#48 := (iff #12 false) +#49 := [rewrite]: #48 +#52 := [monotonicity #49]: #51 +#56 := [trans #52 #54]: #55 +#77 := [monotonicity #56 #74]: #76 +#80 := [monotonicity #77]: #79 +#85 := [trans #80 #83]: #84 +#88 := [monotonicity #85]: #87 +#129 := [trans #88 #127]: #128 +#47 := [asserted]: #27 +#130 := [mp #47 #129]: #125 +#166 := [unit-resolution #130 #165]: false +#167 := [lemma #166]: #149 +#152 := (or #10 #137) +#153 := [def-axiom]: #152 +#225 := [unit-resolution #153 #167]: #137 +#242 := (= f3 #116) +#226 := [hypothesis]: #138 +#224 := (= f3 #20) +#191 := (* -1::Int #20) +#192 := (+ f3 #191) +#197 := (<= #192 0::Int) +#190 := (= #192 0::Int) +#45 := [true-axiom]: true +#227 := (or false #190) +#228 := [th-lemma arith]: #227 +#229 := [unit-resolution #228 #45]: #190 +#230 := (not #190) +#231 := (or #230 #197) +#232 := [th-lemma arith triangle-eq]: #231 +#233 := [unit-resolution #232 #229]: #197 +#198 := (>= #192 0::Int) +#234 := (or #230 #198) +#235 := [th-lemma arith triangle-eq]: #234 +#236 := [unit-resolution #235 #229]: #198 +#238 := (not #198) +#237 := (not #197) +#239 := (or #224 #237 #238) +#240 := [th-lemma arith triangle-eq]: #239 +#241 := [unit-resolution #240 #236 #233]: #224 +#243 := [trans #241 #226]: #242 +#244 := [trans #243 #225]: #122 +#245 := [unit-resolution #130 #244]: false +#247 := [lemma #245]: #246 +#145 := (or #140 #138) +#146 := [def-axiom]: #145 +#221 := [unit-resolution #146 #247]: #140 +#134 := (or #113 #89) +#135 := [def-axiom]: #134 +#222 := [unit-resolution #135 #221]: #89 +#132 := (or #113 #102) +#133 := [def-axiom]: #132 +#223 := [unit-resolution #133 #221]: #102 +#248 := (or #10 #90 #103) +#249 := [th-lemma arith triangle-eq]: #248 +#250 := [unit-resolution #249 #167]: #113 +[unit-resolution #250 #223 #222]: false +unsat +7116e1ffcf5d8f75fc236e1967d4dc10ce43d95d 102 0 +#2 := false #8 := 0::Int -#63 := -1::Int -#107 := (* -1::Int #15) -#104 := (* -1::Int #14) -#110 := (div #104 #107) -#267 := (* -1::Int #110) -#268 := (+ #16 #267) -#269 := (= #268 0::Int) -#26 := (div #14 #15) -#264 := (* -1::Int #26) -#265 := (+ #16 #264) -#266 := (= #265 0::Int) -#142 := (>= #14 0::Int) -#135 := (<= #15 0::Int) -#227 := (or #135 #142) -#228 := (not #227) -#131 := (<= #14 0::Int) -#225 := (or #131 #135) -#226 := (not #225) -#231 := (or #226 #228) -#270 := (ite #231 #266 #269) -#263 := (= #16 0::Int) -#18 := (= #15 0::Int) -#17 := (= #14 0::Int) -#19 := (or #17 #18) -#271 := (ite #19 #263 #270) -#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #271) -#274 := (forall (vars (?v0 Int) (?v1 Int)) #271) -#768 := (iff #274 #765) -#766 := (iff #271 #271) -#767 := [refl]: #766 -#769 := [quant-intro #767]: #768 -#234 := (ite #231 #26 #110) -#237 := (ite #19 0::Int #234) -#240 := (= #16 #237) -#243 := (forall (vars (?v0 Int) (?v1 Int)) #240) -#275 := (iff #243 #274) -#272 := (iff #240 #271) -#273 := [rewrite]: #272 -#276 := [quant-intro #273]: #275 -#143 := (not #142) -#136 := (not #135) -#146 := (and #136 #143) -#132 := (not #131) -#139 := (and #132 #136) -#149 := (or #139 #146) -#152 := (ite #149 #26 #110) -#155 := (ite #19 0::Int #152) -#158 := (= #16 #155) -#161 := (forall (vars (?v0 Int) (?v1 Int)) #158) -#244 := (iff #161 #243) -#241 := (iff #158 #240) -#238 := (= #155 #237) -#235 := (= #152 #234) -#232 := (iff #149 #231) -#229 := (iff #146 #228) -#230 := [rewrite]: #229 -#219 := (iff #139 #226) -#220 := [rewrite]: #219 -#233 := [monotonicity #220 #230]: #232 -#236 := [monotonicity #233]: #235 -#239 := [monotonicity #236]: #238 -#242 := [monotonicity #239]: #241 -#245 := [quant-intro #242]: #244 -#223 := (~ #161 #161) -#221 := (~ #158 #158) -#222 := [refl]: #221 -#224 := [nnf-pos #222]: #223 -#28 := (- #15) -#27 := (- #14) -#29 := (div #27 #28) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #16 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#164 := (iff #33 #161) -#98 := (and #21 #23) -#101 := (or #22 #98) -#113 := (ite #101 #26 #110) -#92 := (= 0::Int #15) -#89 := (= 0::Int #14) -#95 := (or #89 #92) -#116 := (ite #95 0::Int #113) -#119 := (= #16 #116) -#122 := (forall (vars (?v0 Int) (?v1 Int)) #119) -#162 := (iff #122 #161) -#159 := (iff #119 #158) -#156 := (= #116 #155) -#153 := (= #113 #152) -#150 := (iff #101 #149) -#147 := (iff #98 #146) -#144 := (iff #23 #143) -#145 := [rewrite]: #144 -#137 := (iff #21 #136) -#138 := [rewrite]: #137 -#148 := [monotonicity #138 #145]: #147 -#140 := (iff #22 #139) -#133 := (iff #20 #132) -#134 := [rewrite]: #133 -#141 := [monotonicity #134 #138]: #140 -#151 := [monotonicity #141 #148]: #150 -#154 := [monotonicity #151]: #153 -#129 := (iff #95 #19) -#127 := (iff #92 #18) -#128 := [rewrite]: #127 -#125 := (iff #89 #17) -#126 := [rewrite]: #125 -#130 := [monotonicity #126 #128]: #129 -#157 := [monotonicity #130 #154]: #156 -#160 := [monotonicity #157]: #159 -#163 := [quant-intro #160]: #162 -#123 := (iff #33 #122) -#120 := (iff #32 #119) -#117 := (= #31 #116) -#114 := (= #30 #113) -#111 := (= #29 #110) -#108 := (= #28 #107) -#109 := [rewrite]: #108 -#105 := (= #27 #104) -#106 := [rewrite]: #105 -#112 := [monotonicity #106 #109]: #111 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#115 := [monotonicity #103 #112]: #114 -#96 := (iff #19 #95) -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#97 := [monotonicity #91 #94]: #96 -#118 := [monotonicity #97 #115]: #117 -#121 := [monotonicity #118]: #120 -#124 := [quant-intro #121]: #123 -#165 := [trans #124 #163]: #164 -#88 := [asserted]: #33 -#166 := [mp #88 #165]: #161 -#215 := [mp~ #166 #224]: #161 -#246 := [mp #215 #245]: #243 -#277 := [mp #246 #276]: #274 -#770 := [mp #277 #769]: #765 -#66 := (f3 0::Int -1::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := 1::Int -#10 := (- 1::Int) -#11 := (f3 0::Int #10) +#10 := 1::Int +#11 := (- 1::Int) +#20 := (- #11) +#19 := (- 0::Int) +#21 := (div #19 #20) +#18 := (div 0::Int #11) +#15 := (< 0::Int #11) +#14 := (< 0::Int 0::Int) +#16 := (and #14 #15) +#17 := (or #16 #16) +#22 := (ite #17 #18 #21) #12 := (= #11 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #11 #66) -#64 := (= #10 -1::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#599 := (not #765) -#600 := (or #599 #69) -#351 := (* -1::Int -1::Int) -#435 := (* -1::Int 0::Int) -#436 := (div #435 #351) -#437 := (* -1::Int #436) -#428 := (+ #66 #437) -#439 := (= #428 0::Int) -#440 := (div 0::Int -1::Int) -#441 := (* -1::Int #440) -#438 := (+ #66 #441) -#442 := (= #438 0::Int) -#421 := (>= 0::Int 0::Int) -#756 := (<= -1::Int 0::Int) -#758 := (or #756 #421) -#415 := (not #758) -#545 := (<= 0::Int 0::Int) -#752 := (or #545 #756) -#426 := (not #752) -#427 := (or #426 #415) -#759 := (ite #427 #442 #439) -#760 := (= -1::Int 0::Int) -#761 := (= 0::Int 0::Int) -#762 := (or #761 #760) -#757 := (ite #762 #69 #759) -#593 := (or #599 #757) -#602 := (iff #593 #600) -#604 := (iff #600 #600) -#605 := [rewrite]: #604 -#582 := (iff #757 #69) -#1 := true -#696 := (ite true #69 #69) -#694 := (iff #696 #69) -#697 := [rewrite]: #694 -#598 := (iff #757 #696) -#589 := (iff #759 #69) -#704 := (ite false #69 #69) -#587 := (iff #704 #69) -#588 := [rewrite]: #587 -#702 := (iff #759 #704) -#701 := (iff #439 #69) -#547 := (= #428 #66) -#719 := (+ #66 0::Int) -#716 := (= #719 #66) -#717 := [rewrite]: #716 -#544 := (= #428 #719) -#708 := (= #437 0::Int) -#725 := (= #435 0::Int) -#729 := [rewrite]: #725 -#713 := (= #437 #435) -#706 := (= #436 0::Int) -#567 := (div 0::Int 1::Int) -#711 := (= #567 0::Int) -#712 := [rewrite]: #711 -#709 := (= #436 #567) -#565 := (= #351 1::Int) -#566 := [rewrite]: #565 -#710 := [monotonicity #729 #566]: #709 -#707 := [trans #710 #712]: #706 -#714 := [monotonicity #707]: #713 -#715 := [trans #714 #729]: #708 -#546 := [monotonicity #715]: #544 -#700 := [trans #546 #717]: #547 -#703 := [monotonicity #700]: #701 -#718 := (iff #442 #69) -#722 := (= #438 #66) -#720 := (= #438 #719) -#726 := (= #441 0::Int) -#728 := (= #441 #435) -#449 := (= #440 0::Int) -#727 := [rewrite]: #449 -#443 := [monotonicity #727]: #728 -#730 := [trans #443 #729]: #726 -#721 := [monotonicity #730]: #720 -#723 := [trans #721 #717]: #722 -#724 := [monotonicity #723]: #718 -#447 := (iff #427 false) -#731 := (or false false) -#736 := (iff #731 false) -#446 := [rewrite]: #736 -#735 := (iff #427 #731) -#456 := (iff #415 false) -#749 := (not true) -#750 := (iff #749 false) -#748 := [rewrite]: #750 -#733 := (iff #415 #749) -#463 := (iff #758 true) -#743 := (or true true) -#740 := (iff #743 true) -#746 := [rewrite]: #740 -#461 := (iff #758 #743) -#738 := (iff #421 true) -#460 := [rewrite]: #738 -#741 := (iff #756 true) -#742 := [rewrite]: #741 -#462 := [monotonicity #742 #460]: #461 -#357 := [trans #462 #746]: #463 -#734 := [monotonicity #357]: #733 -#457 := [trans #734 #748]: #456 -#751 := (iff #426 false) -#389 := (iff #426 #749) -#384 := (iff #752 true) -#744 := (iff #752 #743) -#404 := (iff #545 true) -#405 := [rewrite]: #404 -#745 := [monotonicity #405 #742]: #744 -#747 := [trans #745 #746]: #384 -#390 := [monotonicity #747]: #389 -#737 := [trans #390 #748]: #751 -#732 := [monotonicity #737 #457]: #735 -#448 := [trans #732 #446]: #447 -#705 := [monotonicity #448 #724 #703]: #702 -#548 := [trans #705 #588]: #589 -#402 := (iff #762 true) -#754 := (or true false) -#398 := (iff #754 true) -#739 := [rewrite]: #398 -#414 := (iff #762 #754) -#413 := (iff #760 false) -#418 := [rewrite]: #413 -#763 := (iff #761 true) -#753 := [rewrite]: #763 -#755 := [monotonicity #753 #418]: #414 -#403 := [trans #755 #739]: #402 -#693 := [monotonicity #403 #548]: #598 -#597 := [trans #693 #697]: #582 -#603 := [monotonicity #597]: #602 -#698 := [trans #603 #605]: #602 -#601 := [quant-inst #8 #63]: #593 -#695 := [mp #601 #698]: #600 -[unit-resolution #695 #87 #770]: false -unsat -beaa0a62fe76b86ad510bf8c2d69fe2ce8dbdc5f 310 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#749 := (pattern #15) -#16 := 0::Int -#63 := -1::Int -#98 := (* -1::Int #14) -#95 := (* -1::Int #13) -#101 := (div #95 #98) -#252 := (* -1::Int #101) -#253 := (+ #15 #252) -#254 := (= #253 0::Int) -#26 := (div #13 #14) -#249 := (* -1::Int #26) -#250 := (+ #15 #249) -#251 := (= #250 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#255 := (ite #216 #251 #254) -#248 := (= #15 0::Int) -#18 := (= #14 0::Int) -#17 := (= #13 0::Int) -#19 := (or #17 #18) -#256 := (ite #19 #248 #255) -#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#753 := (iff #259 #750) -#751 := (iff #256 #256) -#752 := [refl]: #751 -#754 := [quant-intro #752]: #753 -#219 := (ite #216 #26 #101) -#222 := (ite #19 0::Int #219) -#225 := (= #15 #222) -#228 := (forall (vars (?v0 Int) (?v1 Int)) #225) -#260 := (iff #228 #259) -#257 := (iff #225 #256) -#258 := [rewrite]: #257 -#261 := [quant-intro #258]: #260 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#137 := (ite #134 #26 #101) -#140 := (ite #19 0::Int #137) -#143 := (= #15 #140) -#146 := (forall (vars (?v0 Int) (?v1 Int)) #143) -#229 := (iff #146 #228) -#226 := (iff #143 #225) -#223 := (= #140 #222) -#220 := (= #137 #219) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#221 := [monotonicity #218]: #220 -#224 := [monotonicity #221]: #223 -#227 := [monotonicity #224]: #226 -#230 := [quant-intro #227]: #229 -#208 := (~ #146 #146) -#206 := (~ #143 #143) -#207 := [refl]: #206 -#209 := [nnf-pos #207]: #208 -#28 := (- #14) -#27 := (- #13) -#29 := (div #27 #28) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #15 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#149 := (iff #33 #146) -#89 := (and #21 #23) -#92 := (or #22 #89) -#104 := (ite #92 #26 #101) -#107 := (ite #19 0::Int #104) -#110 := (= #15 #107) -#113 := (forall (vars (?v0 Int) (?v1 Int)) #110) -#147 := (iff #113 #146) -#144 := (iff #110 #143) -#141 := (= #107 #140) -#138 := (= #104 #137) -#135 := (iff #92 #134) -#132 := (iff #89 #131) -#129 := (iff #23 #128) -#130 := [rewrite]: #129 -#122 := (iff #21 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #22 #124) -#118 := (iff #20 #117) -#119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#139 := [monotonicity #136]: #138 -#142 := [monotonicity #139]: #141 -#145 := [monotonicity #142]: #144 -#148 := [quant-intro #145]: #147 -#114 := (iff #33 #113) -#111 := (iff #32 #110) -#108 := (= #31 #107) -#105 := (= #30 #104) -#102 := (= #29 #101) -#99 := (= #28 #98) -#100 := [rewrite]: #99 -#96 := (= #27 #95) -#97 := [rewrite]: #96 -#103 := [monotonicity #97 #100]: #102 -#93 := (iff #25 #92) -#90 := (iff #24 #89) +#9 := (= 0::Int 0::Int) +#13 := (or #9 #12) +#23 := (ite #13 0::Int #22) +#24 := (= #23 0::Int) +#25 := (not #24) +#123 := (iff #25 false) +#1 := true +#118 := (not true) +#121 := (iff #118 false) +#122 := [rewrite]: #121 +#119 := (iff #25 #118) +#116 := (iff #24 true) +#46 := (iff #9 true) +#47 := [rewrite]: #46 +#114 := (iff #24 #9) +#108 := (ite true 0::Int 0::Int) +#111 := (= #108 0::Int) +#112 := [rewrite]: #111 +#109 := (= #23 #108) +#106 := (= #22 0::Int) +#48 := -1::Int +#65 := (< 0::Int -1::Int) +#68 := (and #14 #65) +#101 := (ite #68 0::Int 0::Int) +#104 := (= #101 0::Int) +#105 := [rewrite]: #104 +#102 := (= #22 #101) +#99 := (= #21 0::Int) +#94 := (div 0::Int 1::Int) +#97 := (= #94 0::Int) +#98 := [rewrite]: #97 +#95 := (= #21 #94) +#92 := (= #20 1::Int) +#87 := (- -1::Int) +#90 := (= #87 1::Int) #91 := [rewrite]: #90 -#94 := [monotonicity #91]: #93 -#106 := [monotonicity #94 #103]: #105 -#109 := [monotonicity #106]: #108 -#112 := [monotonicity #109]: #111 -#115 := [quant-intro #112]: #114 -#150 := [trans #115 #148]: #149 -#88 := [asserted]: #33 -#151 := [mp #88 #150]: #146 -#200 := [mp~ #151 #209]: #146 -#231 := [mp #200 #230]: #228 -#262 := [mp #231 #261]: #259 -#755 := [mp #262 #754]: #750 -#8 := 1::Int -#66 := (f3 1::Int -1::Int) -#69 := (= #66 -1::Int) -#82 := (not #69) -#9 := (- 1::Int) -#10 := (f3 1::Int #9) -#11 := (= #10 #9) -#12 := (not #11) -#85 := (iff #12 #82) -#72 := (= -1::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #12 #77) -#75 := (iff #11 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #11 #69) -#64 := (= #9 -1::Int) -#65 := [rewrite]: #64 -#67 := (= #10 #66) -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68 #65]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #12 -#87 := [mp #62 #86]: #82 -#680 := (not #750) -#684 := (or #680 #69) -#336 := (* -1::Int -1::Int) -#420 := (* -1::Int 1::Int) -#421 := (div #420 #336) -#422 := (* -1::Int #421) -#413 := (+ #66 #422) -#424 := (= #413 0::Int) -#425 := (div 1::Int -1::Int) -#426 := (* -1::Int #425) -#423 := (+ #66 #426) -#427 := (= #423 0::Int) -#406 := (>= 1::Int 0::Int) -#741 := (<= -1::Int 0::Int) -#743 := (or #741 #406) -#400 := (not #743) -#530 := (<= 1::Int 0::Int) -#737 := (or #530 #741) -#411 := (not #737) -#412 := (or #411 #400) -#744 := (ite #412 #427 #424) -#745 := (= #66 0::Int) -#746 := (= -1::Int 0::Int) -#747 := (= 1::Int 0::Int) -#742 := (or #747 #746) -#748 := (ite #742 #745 #744) -#671 := (or #680 #748) -#665 := (iff #671 #684) -#664 := (iff #684 #684) -#674 := [rewrite]: #664 -#590 := (iff #748 #69) -#578 := (ite false #745 #69) -#588 := (iff #578 #69) -#589 := [rewrite]: #588 -#586 := (iff #748 #578) -#584 := (iff #744 #69) -#678 := (ite false #69 #69) -#567 := (iff #678 #69) -#582 := [rewrite]: #567 -#679 := (iff #744 #678) -#681 := (iff #424 #69) -#702 := (+ 1::Int #66) -#550 := (= #702 0::Int) -#694 := (iff #550 #69) -#695 := [rewrite]: #694 -#574 := (iff #424 #550) -#572 := (= #413 #702) -#705 := (+ #66 1::Int) -#707 := (= #705 #702) -#708 := [rewrite]: #707 -#687 := (= #413 #705) -#688 := (= #422 1::Int) -#714 := (= #336 1::Int) -#711 := [rewrite]: #714 -#685 := (= #422 #336) -#531 := (= #421 -1::Int) -#698 := (div -1::Int 1::Int) -#700 := (= #698 -1::Int) -#529 := [rewrite]: #700 -#699 := (= #421 #698) -#691 := (= #420 -1::Int) -#692 := [rewrite]: #691 -#693 := [monotonicity #692 #711]: #699 -#532 := [trans #693 #529]: #531 -#686 := [monotonicity #532]: #685 -#689 := [trans #686 #711]: #688 -#690 := [monotonicity #689]: #687 -#573 := [trans #690 #708]: #572 -#533 := [monotonicity #573]: #574 -#583 := [trans #533 #695]: #681 -#696 := (iff #427 #69) -#551 := (iff #427 #550) -#703 := (= #423 #702) -#706 := (= #423 #705) -#715 := (= #426 1::Int) -#428 := (= #426 #336) -#712 := (= #425 -1::Int) -#713 := [rewrite]: #712 -#710 := [monotonicity #713]: #428 -#704 := [trans #710 #711]: #715 -#701 := [monotonicity #704]: #706 -#709 := [trans #701 #708]: #703 -#552 := [monotonicity #709]: #551 -#697 := [trans #552 #695]: #696 -#433 := (iff #412 false) -#399 := (or false false) -#724 := (iff #399 false) -#387 := [rewrite]: #724 -#431 := (iff #412 #399) -#717 := (iff #400 false) -#1 := true -#374 := (not true) -#733 := (iff #374 false) -#736 := [rewrite]: #733 -#716 := (iff #400 #374) -#441 := (iff #743 true) -#447 := (or true true) -#718 := (iff #447 true) -#719 := [rewrite]: #718 -#448 := (iff #743 #447) -#445 := (iff #406 true) -#446 := [rewrite]: #445 -#727 := (iff #741 true) -#728 := [rewrite]: #727 -#342 := [monotonicity #728 #446]: #448 -#442 := [trans #342 #719]: #441 -#720 := [monotonicity #442]: #716 -#721 := [trans #720 #736]: #717 -#722 := (iff #411 false) -#375 := (iff #411 #374) -#732 := (iff #737 true) -#729 := (or false true) -#731 := (iff #729 true) -#369 := [rewrite]: #731 -#730 := (iff #737 #729) -#390 := (iff #530 false) -#726 := [rewrite]: #390 -#725 := [monotonicity #726 #728]: #730 -#734 := [trans #725 #369]: #732 -#735 := [monotonicity #734]: #375 -#723 := [trans #735 #736]: #722 -#432 := [monotonicity #723 #721]: #431 -#434 := [trans #432 #387]: #433 -#682 := [monotonicity #434 #697 #583]: #679 -#585 := [trans #682 #582]: #584 -#388 := (iff #742 false) -#740 := (iff #742 #399) -#403 := (iff #746 false) -#739 := [rewrite]: #403 -#738 := (iff #747 false) -#398 := [rewrite]: #738 -#383 := [monotonicity #398 #739]: #740 -#389 := [trans #383 #387]: #388 -#587 := [monotonicity #389 #585]: #586 -#683 := [trans #587 #589]: #590 -#662 := [monotonicity #683]: #665 -#675 := [trans #662 #674]: #665 -#673 := [quant-inst #8 #63]: #671 -#676 := [mp #673 #675]: #684 -[unit-resolution #676 #87 #755]: false -unsat -d7870bb48e209893f272c06c1d45c5a7c1765225 306 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#17 := (f3 #15 #16) -#742 := (pattern #17) -#18 := 0::Int -#65 := -1::Int -#91 := (* -1::Int #16) -#88 := (* -1::Int #15) -#94 := (div #88 #91) -#245 := (* -1::Int #94) -#246 := (+ #17 #245) -#247 := (= #246 0::Int) -#28 := (div #15 #16) -#242 := (* -1::Int #28) -#243 := (+ #17 #242) -#244 := (= #243 0::Int) -#120 := (>= #15 0::Int) -#113 := (<= #16 0::Int) -#205 := (or #113 #120) -#206 := (not #205) -#109 := (<= #15 0::Int) -#203 := (or #109 #113) -#204 := (not #203) -#209 := (or #204 #206) -#248 := (ite #209 #244 #247) -#241 := (= #17 0::Int) -#20 := (= #16 0::Int) -#19 := (= #15 0::Int) -#21 := (or #19 #20) -#249 := (ite #21 #241 #248) -#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249) -#252 := (forall (vars (?v0 Int) (?v1 Int)) #249) -#746 := (iff #252 #743) -#744 := (iff #249 #249) -#745 := [refl]: #744 -#747 := [quant-intro #745]: #746 -#212 := (ite #209 #28 #94) -#215 := (ite #21 0::Int #212) -#218 := (= #17 #215) -#221 := (forall (vars (?v0 Int) (?v1 Int)) #218) -#253 := (iff #221 #252) -#250 := (iff #218 #249) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#121 := (not #120) -#114 := (not #113) -#124 := (and #114 #121) -#110 := (not #109) -#117 := (and #110 #114) -#127 := (or #117 #124) -#130 := (ite #127 #28 #94) -#133 := (ite #21 0::Int #130) -#136 := (= #17 #133) -#139 := (forall (vars (?v0 Int) (?v1 Int)) #136) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#216 := (= #133 #215) -#213 := (= #130 #212) -#210 := (iff #127 #209) -#207 := (iff #124 #206) -#208 := [rewrite]: #207 -#197 := (iff #117 #204) -#198 := [rewrite]: #197 -#211 := [monotonicity #198 #208]: #210 -#214 := [monotonicity #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [quant-intro #220]: #222 -#201 := (~ #139 #139) -#199 := (~ #136 #136) -#200 := [refl]: #199 -#202 := [nnf-pos #200]: #201 -#30 := (- #16) -#29 := (- #15) -#31 := (div #29 #30) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #17 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#142 := (iff #35 #139) -#81 := (and #23 #25) -#85 := (or #24 #81) -#97 := (ite #85 #28 #94) -#100 := (ite #21 0::Int #97) -#103 := (= #17 #100) -#106 := (forall (vars (?v0 Int) (?v1 Int)) #103) -#140 := (iff #106 #139) -#137 := (iff #103 #136) -#134 := (= #100 #133) -#131 := (= #97 #130) -#128 := (iff #85 #127) -#125 := (iff #81 #124) -#122 := (iff #25 #121) -#123 := [rewrite]: #122 -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#126 := [monotonicity #116 #123]: #125 -#118 := (iff #24 #117) -#111 := (iff #22 #110) -#112 := [rewrite]: #111 -#119 := [monotonicity #112 #116]: #118 -#129 := [monotonicity #119 #126]: #128 -#132 := [monotonicity #129]: #131 -#135 := [monotonicity #132]: #134 -#138 := [monotonicity #135]: #137 -#141 := [quant-intro #138]: #140 -#107 := (iff #35 #106) -#104 := (iff #34 #103) -#101 := (= #33 #100) -#98 := (= #32 #97) -#95 := (= #31 #94) -#92 := (= #30 #91) -#93 := [rewrite]: #92 -#89 := (= #29 #88) -#90 := [rewrite]: #89 -#96 := [monotonicity #90 #93]: #95 -#86 := (iff #27 #85) -#83 := (iff #26 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#99 := [monotonicity #87 #96]: #98 -#102 := [monotonicity #99]: #101 -#105 := [monotonicity #102]: #104 -#108 := [quant-intro #105]: #107 -#143 := [trans #108 #141]: #142 -#80 := [asserted]: #35 -#144 := [mp #80 #143]: #139 -#193 := [mp~ #144 #202]: #139 -#224 := [mp #193 #223]: #221 -#255 := [mp #224 #254]: #252 -#748 := [mp #255 #747]: #743 -#71 := -3::Int -#8 := 3::Int -#68 := (f3 3::Int -1::Int) -#74 := (= #68 -3::Int) -#77 := (not #74) -#12 := (- 3::Int) -#9 := 1::Int -#10 := (- 1::Int) -#11 := (f3 3::Int #10) -#13 := (= #11 #12) -#14 := (not #13) -#78 := (iff #14 #77) -#75 := (iff #13 #74) -#72 := (= #12 -3::Int) -#73 := [rewrite]: #72 -#69 := (= #11 #68) -#66 := (= #10 -1::Int) -#67 := [rewrite]: #66 +#88 := (= #20 #87) +#49 := (= #11 -1::Int) +#50 := [rewrite]: #49 +#89 := [monotonicity #50]: #88 +#93 := [trans #89 #91]: #92 +#85 := (= #19 0::Int) +#86 := [rewrite]: #85 +#96 := [monotonicity #86 #93]: #95 +#100 := [trans #96 #98]: #99 +#83 := (= #18 0::Int) +#78 := (div 0::Int -1::Int) +#81 := (= #78 0::Int) +#82 := [rewrite]: #81 +#79 := (= #18 #78) +#80 := [monotonicity #50]: #79 +#84 := [trans #80 #82]: #83 +#76 := (iff #17 #68) +#71 := (or #68 #68) +#74 := (iff #71 #68) +#75 := [rewrite]: #74 +#72 := (iff #17 #71) +#69 := (iff #16 #68) +#66 := (iff #15 #65) +#67 := [monotonicity #50]: #66 #70 := [monotonicity #67]: #69 -#76 := [monotonicity #70 #73]: #75 -#79 := [monotonicity #76]: #78 -#64 := [asserted]: #14 -#82 := [mp #64 #79]: #77 -#666 := (not #743) -#658 := (or #666 #74) -#329 := (* -1::Int -1::Int) -#413 := (* -1::Int 3::Int) -#414 := (div #413 #329) -#415 := (* -1::Int #414) -#406 := (+ #68 #415) -#417 := (= #406 0::Int) -#418 := (div 3::Int -1::Int) -#419 := (* -1::Int #418) -#416 := (+ #68 #419) -#420 := (= #416 0::Int) -#399 := (>= 3::Int 0::Int) -#734 := (<= -1::Int 0::Int) -#736 := (or #734 #399) -#393 := (not #736) -#523 := (<= 3::Int 0::Int) -#730 := (or #523 #734) -#404 := (not #730) -#405 := (or #404 #393) -#737 := (ite #405 #420 #417) -#738 := (= #68 0::Int) -#739 := (= -1::Int 0::Int) -#740 := (= 3::Int 0::Int) -#735 := (or #740 #739) -#741 := (ite #735 #738 #737) -#655 := (or #666 #741) -#667 := (iff #655 #658) -#669 := (iff #658 #658) -#665 := [rewrite]: #669 -#677 := (iff #741 #74) -#581 := (ite false #738 #74) -#676 := (iff #581 #74) -#673 := [rewrite]: #676 -#582 := (iff #741 #581) -#579 := (iff #737 #74) -#560 := (ite false #74 #74) -#578 := (iff #560 #74) -#571 := [rewrite]: #578 -#575 := (iff #737 #560) -#672 := (iff #417 #74) -#700 := (+ 3::Int #68) -#544 := (= #700 0::Int) -#688 := (iff #544 #74) -#689 := [rewrite]: #688 -#576 := (iff #417 #544) -#526 := (= #406 #700) -#699 := (+ #68 3::Int) -#701 := (= #699 #700) -#696 := [rewrite]: #701 -#566 := (= #406 #699) -#683 := (= #415 3::Int) -#421 := (* -1::Int -3::Int) -#704 := (= #421 3::Int) -#708 := [rewrite]: #704 -#682 := (= #415 #421) -#679 := (= #414 -3::Int) -#693 := (div -3::Int 1::Int) -#525 := (= #693 -3::Int) -#678 := [rewrite]: #525 -#522 := (= #414 #693) -#692 := (= #329 1::Int) -#686 := [rewrite]: #692 -#685 := (= #413 -3::Int) -#691 := [rewrite]: #685 -#524 := [monotonicity #691 #686]: #522 -#681 := [trans #524 #678]: #679 -#680 := [monotonicity #681]: #682 -#565 := [trans #680 #708]: #683 -#567 := [monotonicity #565]: #566 -#674 := [trans #567 #696]: #526 -#671 := [monotonicity #674]: #576 -#675 := [trans #671 #689]: #672 -#690 := (iff #420 #74) -#545 := (iff #420 #544) -#702 := (= #416 #700) -#694 := (= #416 #699) -#697 := (= #419 3::Int) -#703 := (= #419 #421) -#705 := (= #418 -3::Int) -#706 := [rewrite]: #705 -#707 := [monotonicity #706]: #703 -#698 := [trans #707 #708]: #697 -#695 := [monotonicity #698]: #694 -#543 := [trans #695 #696]: #702 -#687 := [monotonicity #543]: #545 -#684 := [trans #687 #689]: #690 -#426 := (iff #405 false) -#392 := (or false false) -#717 := (iff #392 false) -#380 := [rewrite]: #717 -#424 := (iff #405 #392) -#710 := (iff #393 false) -#1 := true -#367 := (not true) -#726 := (iff #367 false) -#729 := [rewrite]: #726 -#709 := (iff #393 #367) -#434 := (iff #736 true) -#440 := (or true true) -#711 := (iff #440 true) -#712 := [rewrite]: #711 -#441 := (iff #736 #440) -#438 := (iff #399 true) -#439 := [rewrite]: #438 -#720 := (iff #734 true) -#721 := [rewrite]: #720 -#335 := [monotonicity #721 #439]: #441 -#435 := [trans #335 #712]: #434 -#713 := [monotonicity #435]: #709 -#714 := [trans #713 #729]: #710 -#715 := (iff #404 false) -#368 := (iff #404 #367) -#725 := (iff #730 true) -#722 := (or false true) -#724 := (iff #722 true) -#362 := [rewrite]: #724 -#723 := (iff #730 #722) -#383 := (iff #523 false) -#719 := [rewrite]: #383 -#718 := [monotonicity #719 #721]: #723 -#727 := [trans #718 #362]: #725 -#728 := [monotonicity #727]: #368 -#716 := [trans #728 #729]: #715 -#425 := [monotonicity #716 #714]: #424 -#427 := [trans #425 #380]: #426 -#577 := [monotonicity #427 #684 #675]: #575 -#580 := [trans #577 #571]: #579 -#381 := (iff #735 false) -#733 := (iff #735 #392) -#396 := (iff #739 false) -#732 := [rewrite]: #396 -#731 := (iff #740 false) -#391 := [rewrite]: #731 -#376 := [monotonicity #391 #732]: #733 -#382 := [trans #376 #380]: #381 -#583 := [monotonicity #382 #580]: #582 -#664 := [trans #583 #673]: #677 -#668 := [monotonicity #664]: #667 -#670 := [trans #668 #665]: #667 -#657 := [quant-inst #8 #65]: #655 -#659 := [mp #657 #670]: #658 -[unit-resolution #659 #82 #748]: false -unsat -5ee37b7887579207f198e2d96f811691f176d723 350 0 -#2 := false -#18 := 0::Int -#9 := 1::Int -decl f4 :: Int -#8 := f4 -#65 := -1::Int -#71 := (* -1::Int f4) -#714 := (div #71 1::Int) -#712 := (* -1::Int #714) -decl f3 :: (-> Int Int Int) -#68 := (f3 f4 -1::Int) -#717 := (+ #68 #712) -#691 := (<= #717 0::Int) -#708 := (= #717 0::Int) -#744 := (= f4 0::Int) -#574 := (not #744) -#739 := (<= f4 0::Int) -#615 := [hypothesis]: #744 -#595 := (or #574 #739) -#541 := [th-lemma arith triangle-eq]: #595 -#596 := [unit-resolution #541 #615]: #739 -#80 := (+ f4 #68) -#338 := (<= #80 0::Int) -#577 := (not #338) -#422 := (>= #80 0::Int) -#743 := (>= f4 0::Int) -#684 := (not #708) -#689 := (>= #717 0::Int) -#621 := (not #689) -#630 := (not #422) -#631 := [hypothesis]: #630 -#622 := (or #621 #422) -#629 := [hypothesis]: #689 -#665 := (+ f4 #714) -#662 := (>= #665 0::Int) -#672 := (= #665 0::Int) -#1 := true -#62 := [true-axiom]: true -#632 := (or false #672) -#633 := [th-lemma arith]: #632 -#628 := [unit-resolution #633 #62]: #672 -#634 := (not #672) -#620 := (or #634 #662) -#616 := [th-lemma arith triangle-eq]: #620 -#617 := [unit-resolution #616 #628]: #662 -#618 := [th-lemma arith farkas 1 -1 1 #617 #631 #629]: false -#623 := [lemma #618]: #622 -#661 := [unit-resolution #623 #631]: #621 -#624 := (or #684 #689) -#619 := [th-lemma arith triangle-eq]: #624 -#625 := [unit-resolution #619 #661]: #684 -#599 := (or #744 #708) -#748 := (= #68 0::Int) -#696 := (ite #744 #748 #708) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#17 := (f3 #15 #16) -#751 := (pattern #17) -#100 := (* -1::Int #16) -#97 := (* -1::Int #15) -#103 := (div #97 #100) -#254 := (* -1::Int #103) -#255 := (+ #17 #254) -#256 := (= #255 0::Int) -#28 := (div #15 #16) -#251 := (* -1::Int #28) -#252 := (+ #17 #251) -#253 := (= #252 0::Int) -#129 := (>= #15 0::Int) -#122 := (<= #16 0::Int) -#214 := (or #122 #129) -#215 := (not #214) -#118 := (<= #15 0::Int) -#212 := (or #118 #122) -#213 := (not #212) -#218 := (or #213 #215) -#257 := (ite #218 #253 #256) -#250 := (= #17 0::Int) -#20 := (= #16 0::Int) -#19 := (= #15 0::Int) -#21 := (or #19 #20) -#258 := (ite #21 #250 #257) -#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258) -#261 := (forall (vars (?v0 Int) (?v1 Int)) #258) -#755 := (iff #261 #752) -#753 := (iff #258 #258) -#754 := [refl]: #753 -#756 := [quant-intro #754]: #755 -#221 := (ite #218 #28 #103) -#224 := (ite #21 0::Int #221) -#227 := (= #17 #224) -#230 := (forall (vars (?v0 Int) (?v1 Int)) #227) -#262 := (iff #230 #261) -#259 := (iff #227 #258) -#260 := [rewrite]: #259 -#263 := [quant-intro #260]: #262 -#130 := (not #129) -#123 := (not #122) -#133 := (and #123 #130) -#119 := (not #118) -#126 := (and #119 #123) -#136 := (or #126 #133) -#139 := (ite #136 #28 #103) -#142 := (ite #21 0::Int #139) -#145 := (= #17 #142) -#148 := (forall (vars (?v0 Int) (?v1 Int)) #145) -#231 := (iff #148 #230) -#228 := (iff #145 #227) -#225 := (= #142 #224) -#222 := (= #139 #221) -#219 := (iff #136 #218) -#216 := (iff #133 #215) -#217 := [rewrite]: #216 -#206 := (iff #126 #213) -#207 := [rewrite]: #206 -#220 := [monotonicity #207 #217]: #219 -#223 := [monotonicity #220]: #222 -#226 := [monotonicity #223]: #225 -#229 := [monotonicity #226]: #228 -#232 := [quant-intro #229]: #231 -#210 := (~ #148 #148) -#208 := (~ #145 #145) -#209 := [refl]: #208 -#211 := [nnf-pos #209]: #210 -#30 := (- #16) -#29 := (- #15) -#31 := (div #29 #30) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #17 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#151 := (iff #35 #148) -#91 := (and #23 #25) -#94 := (or #24 #91) -#106 := (ite #94 #28 #103) -#109 := (ite #21 0::Int #106) -#112 := (= #17 #109) -#115 := (forall (vars (?v0 Int) (?v1 Int)) #112) -#149 := (iff #115 #148) -#146 := (iff #112 #145) -#143 := (= #109 #142) -#140 := (= #106 #139) -#137 := (iff #94 #136) -#134 := (iff #91 #133) -#131 := (iff #25 #130) -#132 := [rewrite]: #131 -#124 := (iff #23 #123) -#125 := [rewrite]: #124 -#135 := [monotonicity #125 #132]: #134 -#127 := (iff #24 #126) -#120 := (iff #22 #119) -#121 := [rewrite]: #120 -#128 := [monotonicity #121 #125]: #127 -#138 := [monotonicity #128 #135]: #137 -#141 := [monotonicity #138]: #140 -#144 := [monotonicity #141]: #143 -#147 := [monotonicity #144]: #146 -#150 := [quant-intro #147]: #149 -#116 := (iff #35 #115) -#113 := (iff #34 #112) -#110 := (= #33 #109) -#107 := (= #32 #106) -#104 := (= #31 #103) -#101 := (= #30 #100) -#102 := [rewrite]: #101 -#98 := (= #29 #97) -#99 := [rewrite]: #98 -#105 := [monotonicity #99 #102]: #104 -#95 := (iff #27 #94) -#92 := (iff #26 #91) -#93 := [rewrite]: #92 -#96 := [monotonicity #93]: #95 -#108 := [monotonicity #96 #105]: #107 -#111 := [monotonicity #108]: #110 -#114 := [monotonicity #111]: #113 -#117 := [quant-intro #114]: #116 -#152 := [trans #117 #150]: #151 -#90 := [asserted]: #35 -#153 := [mp #90 #152]: #148 -#202 := [mp~ #153 #211]: #148 -#233 := [mp #202 #232]: #230 -#264 := [mp #233 #263]: #261 -#757 := [mp #264 #756]: #752 -#699 := (not #752) -#693 := (or #699 #696) -#423 := (* -1::Int -1::Int) -#424 := (div #71 #423) -#415 := (* -1::Int #424) -#426 := (+ #68 #415) -#427 := (= #426 0::Int) -#428 := (div f4 -1::Int) -#425 := (* -1::Int #428) -#429 := (+ #68 #425) -#408 := (= #429 0::Int) -#745 := (<= -1::Int 0::Int) -#402 := (or #745 #743) -#532 := (not #402) -#413 := (or #739 #745) -#414 := (not #413) -#746 := (or #414 #532) -#747 := (ite #746 #408 #427) -#749 := (= -1::Int 0::Int) -#750 := (or #744 #749) -#740 := (ite #750 #748 #747) -#694 := (or #699 #740) -#701 := (iff #694 #693) -#702 := (iff #693 #693) -#531 := [rewrite]: #702 -#697 := (iff #740 #696) -#553 := (iff #747 #708) -#709 := (ite false #408 #708) -#711 := (iff #709 #708) -#552 := [rewrite]: #711 -#710 := (iff #747 #709) -#703 := (iff #427 #708) -#706 := (= #426 #717) -#716 := (= #415 #712) -#715 := (= #424 #714) -#435 := (= #423 1::Int) -#436 := [rewrite]: #435 -#430 := [monotonicity #436]: #715 -#713 := [monotonicity #430]: #716 -#707 := [monotonicity #713]: #706 -#704 := [monotonicity #707]: #703 -#433 := (iff #746 false) -#444 := (or false false) -#719 := (iff #444 false) -#723 := [rewrite]: #719 -#718 := (iff #746 #444) -#721 := (iff #532 false) -#371 := (not true) -#376 := (iff #371 false) -#377 := [rewrite]: #376 -#344 := (iff #532 #371) -#449 := (iff #402 true) -#738 := (or true #743) -#447 := (iff #738 true) -#448 := [rewrite]: #447 -#724 := (iff #402 #738) -#391 := (iff #745 true) -#392 := [rewrite]: #391 -#725 := [monotonicity #392]: #724 -#450 := [trans #725 #448]: #449 -#720 := [monotonicity #450]: #344 -#443 := [trans #720 #377]: #721 -#737 := (iff #414 false) -#734 := (iff #414 #371) -#727 := (iff #413 true) -#728 := (or #739 true) -#731 := (iff #728 true) -#732 := [rewrite]: #731 -#729 := (iff #413 #728) -#730 := [monotonicity #392]: #729 -#733 := [trans #730 #732]: #727 -#736 := [monotonicity #733]: #734 -#735 := [trans #736 #377]: #737 -#722 := [monotonicity #735 #443]: #718 -#434 := [trans #722 #723]: #433 -#705 := [monotonicity #434 #704]: #710 -#554 := [trans #705 #552]: #553 -#389 := (iff #750 #744) -#741 := (or #744 false) -#385 := (iff #741 #744) -#726 := [rewrite]: #385 -#401 := (iff #750 #741) -#400 := (iff #749 false) -#405 := [rewrite]: #400 -#742 := [monotonicity #405]: #401 -#390 := [trans #742 #726]: #389 -#698 := [monotonicity #390 #554]: #697 -#695 := [monotonicity #698]: #701 -#533 := [trans #695 #531]: #701 -#700 := [quant-inst #8 #65]: #694 -#534 := [mp #700 #533]: #693 -#598 := [unit-resolution #534 #757]: #696 -#692 := (not #696) -#535 := (or #692 #744 #708) -#683 := [def-axiom]: #535 -#600 := [unit-resolution #683 #598]: #599 -#493 := [unit-resolution #600 #625]: #744 -#604 := (or #574 #743) -#605 := [th-lemma arith triangle-eq]: #604 -#606 := [unit-resolution #605 #493]: #743 -#688 := (>= #68 0::Int) -#611 := (or #574 #748) -#575 := (or #692 #574 #748) -#576 := [def-axiom]: #575 -#607 := [unit-resolution #576 #598]: #611 -#608 := [unit-resolution #607 #493]: #748 -#585 := (not #748) -#609 := (or #585 #688) -#612 := [th-lemma arith triangle-eq]: #609 -#613 := [unit-resolution #612 #608]: #688 -#614 := [th-lemma arith farkas 1 -1 1 #613 #631 #606]: false -#610 := [lemma #614]: #422 -#597 := (or #577 #630) -#81 := (= #80 0::Int) -#84 := (not #81) -#12 := (- f4) -#10 := (- 1::Int) -#11 := (f3 f4 #10) -#13 := (= #11 #12) -#14 := (not #13) -#87 := (iff #14 #84) -#74 := (= #68 #71) -#77 := (not #74) -#85 := (iff #77 #84) -#82 := (iff #74 #81) -#83 := [rewrite]: #82 -#86 := [monotonicity #83]: #85 -#78 := (iff #14 #77) -#75 := (iff #13 #74) -#72 := (= #12 #71) -#73 := [rewrite]: #72 -#69 := (= #11 #68) -#66 := (= #10 -1::Int) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#76 := [monotonicity #70 #73]: #75 -#79 := [monotonicity #76]: #78 -#88 := [trans #79 #86]: #87 -#64 := [asserted]: #14 -#89 := [mp #64 #88]: #84 -#601 := (or #81 #577 #630) -#602 := [th-lemma arith triangle-eq]: #601 -#603 := [unit-resolution #602 #89]: #597 -#571 := [unit-resolution #603 #610]: #577 -#687 := (<= #68 0::Int) -#578 := [unit-resolution #607 #615]: #748 -#537 := (or #585 #687) -#568 := [th-lemma arith triangle-eq]: #537 -#570 := [unit-resolution #568 #578]: #687 -#572 := [th-lemma arith farkas 1 -1 1 #570 #571 #596]: false -#579 := [lemma #572]: #574 -#582 := [unit-resolution #600 #579]: #708 -#583 := (or #684 #691) -#593 := [th-lemma arith triangle-eq]: #583 -#573 := [unit-resolution #593 #582]: #691 -#581 := (<= #665 0::Int) -#594 := (or #634 #581) -#549 := [th-lemma arith triangle-eq]: #594 -#550 := [unit-resolution #549 #628]: #581 -[th-lemma arith farkas 1 -1 1 #550 #571 #573]: false -unsat -8db711c99a743e7c5b35063fc01bbf7e9119b29e 292 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#750 := (pattern #15) -#8 := 0::Int -#88 := -1::Int -#92 := (* -1::Int #14) -#89 := (* -1::Int #13) -#95 := (div #89 #92) -#252 := (* -1::Int #95) -#253 := (+ #15 #252) -#254 := (= #253 0::Int) -#25 := (div #13 #14) -#249 := (* -1::Int #25) -#250 := (+ #15 #249) -#251 := (= #250 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#255 := (ite #216 #251 #254) -#248 := (= #15 0::Int) -#17 := (= #14 0::Int) -#16 := (= #13 0::Int) -#18 := (or #16 #17) -#256 := (ite #18 #248 #255) -#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#754 := (iff #259 #751) -#752 := (iff #256 #256) -#753 := [refl]: #752 -#755 := [quant-intro #753]: #754 -#219 := (ite #216 #25 #95) -#222 := (ite #18 0::Int #219) -#225 := (= #15 #222) -#228 := (forall (vars (?v0 Int) (?v1 Int)) #225) -#260 := (iff #228 #259) -#257 := (iff #225 #256) -#258 := [rewrite]: #257 -#261 := [quant-intro #258]: #260 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#137 := (ite #134 #25 #95) -#140 := (ite #18 0::Int #137) -#143 := (= #15 #140) -#146 := (forall (vars (?v0 Int) (?v1 Int)) #143) -#229 := (iff #146 #228) -#226 := (iff #143 #225) -#223 := (= #140 #222) -#220 := (= #137 #219) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#221 := [monotonicity #218]: #220 -#224 := [monotonicity #221]: #223 -#227 := [monotonicity #224]: #226 -#230 := [quant-intro #227]: #229 -#208 := (~ #146 #146) -#206 := (~ #143 #143) -#207 := [refl]: #206 -#209 := [nnf-pos #207]: #208 -#27 := (- #14) -#26 := (- #13) -#28 := (div #26 #27) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#29 := (ite #24 #25 #28) -#30 := (ite #18 0::Int #29) -#31 := (= #15 #30) -#32 := (forall (vars (?v0 Int) (?v1 Int)) #31) -#149 := (iff #32 #146) -#82 := (and #20 #22) -#85 := (or #21 #82) -#98 := (ite #85 #25 #95) -#76 := (= 0::Int #14) -#73 := (= 0::Int #13) -#79 := (or #73 #76) -#101 := (ite #79 0::Int #98) -#104 := (= #15 #101) -#107 := (forall (vars (?v0 Int) (?v1 Int)) #104) -#147 := (iff #107 #146) -#144 := (iff #104 #143) -#141 := (= #101 #140) -#138 := (= #98 #137) -#135 := (iff #85 #134) -#132 := (iff #82 #131) -#129 := (iff #22 #128) -#130 := [rewrite]: #129 -#122 := (iff #20 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #21 #124) -#118 := (iff #19 #117) -#119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#139 := [monotonicity #136]: #138 -#114 := (iff #79 #18) -#112 := (iff #76 #17) -#113 := [rewrite]: #112 -#110 := (iff #73 #16) -#111 := [rewrite]: #110 -#115 := [monotonicity #111 #113]: #114 -#142 := [monotonicity #115 #139]: #141 -#145 := [monotonicity #142]: #144 -#148 := [quant-intro #145]: #147 -#108 := (iff #32 #107) -#105 := (iff #31 #104) -#102 := (= #30 #101) -#99 := (= #29 #98) -#96 := (= #28 #95) -#93 := (= #27 #92) -#94 := [rewrite]: #93 -#90 := (= #26 #89) -#91 := [rewrite]: #90 -#97 := [monotonicity #91 #94]: #96 -#86 := (iff #24 #85) -#83 := (iff #23 #82) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#100 := [monotonicity #87 #97]: #99 -#80 := (iff #18 #79) -#77 := (iff #17 #76) -#78 := [rewrite]: #77 -#74 := (iff #16 #73) -#75 := [rewrite]: #74 -#81 := [monotonicity #75 #78]: #80 -#103 := [monotonicity #81 #100]: #102 -#106 := [monotonicity #103]: #105 -#109 := [quant-intro #106]: #108 -#150 := [trans #109 #148]: #149 -#72 := [asserted]: #32 -#151 := [mp #72 #150]: #146 -#200 := [mp~ #151 #209]: #146 -#231 := [mp #200 #230]: #228 -#262 := [mp #231 #261]: #259 -#756 := [mp #262 #755]: #751 -#9 := 3::Int -#10 := (f3 0::Int 3::Int) -#11 := (= #10 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#585 := (not #751) -#586 := (or #585 #11) -#336 := (* -1::Int 3::Int) -#421 := (* -1::Int 0::Int) -#422 := (div #421 #336) -#423 := (* -1::Int #422) -#414 := (+ #10 #423) -#425 := (= #414 0::Int) -#426 := (div 0::Int 3::Int) -#354 := (* -1::Int #426) -#427 := (+ #10 #354) -#424 := (= #427 0::Int) -#428 := (>= 0::Int 0::Int) -#407 := (<= 3::Int 0::Int) -#742 := (or #407 #428) -#744 := (not #742) -#401 := (<= 0::Int 0::Int) -#531 := (or #401 #407) -#738 := (not #531) -#412 := (or #738 #744) -#413 := (ite #412 #424 #425) -#745 := (= 3::Int 0::Int) -#746 := (= 0::Int 0::Int) -#747 := (or #746 #745) -#748 := (ite #747 #11 #413) -#579 := (or #585 #748) -#588 := (iff #579 #586) -#590 := (iff #586 #586) -#591 := [rewrite]: #590 -#568 := (iff #748 #11) -#1 := true -#682 := (ite true #11 #11) -#680 := (iff #682 #11) -#683 := [rewrite]: #680 -#584 := (iff #748 #682) -#575 := (iff #413 #11) -#690 := (ite false #11 #11) -#573 := (iff #690 #11) -#574 := [rewrite]: #573 -#688 := (iff #413 #690) -#687 := (iff #425 #11) -#533 := (= #414 #10) -#716 := (+ #10 0::Int) -#707 := (= #716 #10) -#702 := [rewrite]: #707 -#530 := (= #414 #716) -#694 := (= #423 0::Int) -#429 := (= #421 0::Int) -#711 := [rewrite]: #429 -#699 := (= #423 #421) -#692 := (= #422 0::Int) -#710 := -3::Int -#553 := (div 0::Int -3::Int) -#697 := (= #553 0::Int) -#698 := [rewrite]: #697 -#695 := (= #422 #553) -#551 := (= #336 -3::Int) -#552 := [rewrite]: #551 -#696 := [monotonicity #711 #552]: #695 -#693 := [trans #696 #698]: #692 -#700 := [monotonicity #693]: #699 -#701 := [trans #700 #711]: #694 -#532 := [monotonicity #701]: #530 -#686 := [trans #532 #702]: #533 -#689 := [monotonicity #686]: #687 -#709 := (iff #424 #11) -#703 := (= #427 #10) -#705 := (= #427 #716) -#715 := (= #354 0::Int) -#713 := (= #354 #421) -#434 := (= #426 0::Int) -#435 := [rewrite]: #434 -#714 := [monotonicity #435]: #713 -#712 := [trans #714 #711]: #715 -#706 := [monotonicity #712]: #705 -#708 := [trans #706 #702]: #703 -#704 := [monotonicity #708]: #709 -#432 := (iff #412 false) -#443 := (or false false) -#718 := (iff #443 false) -#722 := [rewrite]: #718 -#717 := (iff #412 #443) -#720 := (iff #744 false) -#726 := (not true) -#733 := (iff #726 false) -#735 := [rewrite]: #733 -#342 := (iff #744 #726) -#448 := (iff #742 true) -#737 := (or false true) -#446 := (iff #737 true) -#447 := [rewrite]: #446 -#723 := (iff #742 #737) -#736 := (iff #428 true) -#734 := [rewrite]: #736 -#391 := (iff #407 false) -#727 := [rewrite]: #391 -#724 := [monotonicity #727 #734]: #723 -#449 := [trans #724 #447]: #448 -#719 := [monotonicity #449]: #342 -#442 := [trans #719 #735]: #720 -#375 := (iff #738 false) -#732 := (iff #738 #726) -#730 := (iff #531 true) -#404 := (or true false) -#741 := (iff #404 true) -#384 := [rewrite]: #741 -#728 := (iff #531 #404) -#389 := (iff #401 true) -#390 := [rewrite]: #389 -#729 := [monotonicity #390 #727]: #728 -#731 := [trans #729 #384]: #730 -#370 := [monotonicity #731]: #732 -#376 := [trans #370 #735]: #375 -#721 := [monotonicity #376 #442]: #717 -#433 := [trans #721 #722]: #432 -#691 := [monotonicity #433 #704 #689]: #688 -#534 := [trans #691 #574]: #575 -#725 := (iff #747 true) -#740 := (iff #747 #404) -#739 := (iff #745 false) -#399 := [rewrite]: #739 -#743 := (iff #746 true) -#749 := [rewrite]: #743 -#400 := [monotonicity #749 #399]: #740 -#388 := [trans #400 #384]: #725 -#679 := [monotonicity #388 #534]: #584 -#583 := [trans #679 #683]: #568 -#589 := [monotonicity #583]: #588 -#684 := [trans #589 #591]: #588 -#587 := [quant-inst #8 #9]: #579 -#681 := [mp #587 #684]: #586 -[unit-resolution #681 #61 #756]: false -unsat -6aeb136b7e9b0d9bd350f376d5db91cb7cdd5fa1 317 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#766 := (pattern #16) -#8 := 0::Int -#104 := -1::Int -#108 := (* -1::Int #15) -#105 := (* -1::Int #14) -#111 := (div #105 #108) -#268 := (* -1::Int #111) -#269 := (+ #16 #268) -#270 := (= #269 0::Int) -#26 := (div #14 #15) -#265 := (* -1::Int #26) -#266 := (+ #16 #265) -#267 := (= #266 0::Int) -#143 := (>= #14 0::Int) -#136 := (<= #15 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #14 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#271 := (ite #232 #267 #270) -#264 := (= #16 0::Int) -#18 := (= #15 0::Int) -#17 := (= #14 0::Int) -#19 := (or #17 #18) -#272 := (ite #19 #264 #271) -#767 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #766) #272) -#275 := (forall (vars (?v0 Int) (?v1 Int)) #272) -#770 := (iff #275 #767) -#768 := (iff #272 #272) -#769 := [refl]: #768 -#771 := [quant-intro #769]: #770 -#235 := (ite #232 #26 #111) -#238 := (ite #19 0::Int #235) -#241 := (= #16 #238) -#244 := (forall (vars (?v0 Int) (?v1 Int)) #241) -#276 := (iff #244 #275) -#273 := (iff #241 #272) -#274 := [rewrite]: #273 -#277 := [quant-intro #274]: #276 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#153 := (ite #150 #26 #111) -#156 := (ite #19 0::Int #153) -#159 := (= #16 #156) -#162 := (forall (vars (?v0 Int) (?v1 Int)) #159) -#245 := (iff #162 #244) -#242 := (iff #159 #241) -#239 := (= #156 #238) -#236 := (= #153 #235) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [monotonicity #237]: #239 -#243 := [monotonicity #240]: #242 -#246 := [quant-intro #243]: #245 -#224 := (~ #162 #162) -#222 := (~ #159 #159) -#223 := [refl]: #222 -#225 := [nnf-pos #223]: #224 -#28 := (- #15) -#27 := (- #14) -#29 := (div #27 #28) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #16 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#165 := (iff #33 #162) -#98 := (and #21 #23) -#101 := (or #22 #98) -#114 := (ite #101 #26 #111) -#92 := (= 0::Int #15) -#89 := (= 0::Int #14) -#95 := (or #89 #92) -#117 := (ite #95 0::Int #114) -#120 := (= #16 #117) -#123 := (forall (vars (?v0 Int) (?v1 Int)) #120) -#163 := (iff #123 #162) -#160 := (iff #120 #159) -#157 := (= #117 #156) -#154 := (= #114 #153) -#151 := (iff #101 #150) -#148 := (iff #98 #147) -#145 := (iff #23 #144) -#146 := [rewrite]: #145 -#138 := (iff #21 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #22 #140) -#134 := (iff #20 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#155 := [monotonicity #152]: #154 -#130 := (iff #95 #19) -#128 := (iff #92 #18) -#129 := [rewrite]: #128 -#126 := (iff #89 #17) -#127 := [rewrite]: #126 -#131 := [monotonicity #127 #129]: #130 -#158 := [monotonicity #131 #155]: #157 -#161 := [monotonicity #158]: #160 -#164 := [quant-intro #161]: #163 -#124 := (iff #33 #123) -#121 := (iff #32 #120) -#118 := (= #31 #117) -#115 := (= #30 #114) -#112 := (= #29 #111) -#109 := (= #28 #108) -#110 := [rewrite]: #109 -#106 := (= #27 #105) -#107 := [rewrite]: #106 -#113 := [monotonicity #107 #110]: #112 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#116 := [monotonicity #103 #113]: #115 -#96 := (iff #19 #95) -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#97 := [monotonicity #91 #94]: #96 -#119 := [monotonicity #97 #116]: #118 -#122 := [monotonicity #119]: #121 -#125 := [quant-intro #122]: #124 -#166 := [trans #125 #164]: #165 -#88 := [asserted]: #33 -#167 := [mp #88 #166]: #162 -#216 := [mp~ #167 #225]: #162 -#247 := [mp #216 #246]: #244 -#278 := [mp #247 #277]: #275 -#772 := [mp #278 #771]: #767 -#63 := -3::Int -#66 := (f3 0::Int -3::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 0::Int #10) +#73 := [monotonicity #70 #70]: #72 +#77 := [trans #73 #75]: #76 +#103 := [monotonicity #77 #84 #100]: #102 +#107 := [trans #103 #105]: #106 +#63 := (iff #13 true) +#58 := (or true false) +#61 := (iff #58 true) +#62 := [rewrite]: #61 +#59 := (iff #13 #58) +#56 := (iff #12 false) +#51 := (= -1::Int 0::Int) +#54 := (iff #51 false) +#55 := [rewrite]: #54 +#52 := (iff #12 #51) +#53 := [monotonicity #50]: #52 +#57 := [trans #53 #55]: #56 +#60 := [monotonicity #47 #57]: #59 +#64 := [trans #60 #62]: #63 +#110 := [monotonicity #64 #107]: #109 +#113 := [trans #110 #112]: #24 +#115 := [monotonicity #113]: #114 +#117 := [trans #115 #47]: #116 +#120 := [monotonicity #117]: #119 +#124 := [trans #120 #122]: #123 +#45 := [asserted]: #25 +[mp #45 #124]: false +unsat +5c9ec68cb5c6bc2336555bc99c13f0ecae2167b7 104 0 +#2 := false +#8 := 1::Int +#11 := (- 1::Int) +#21 := (- #11) +#22 := (div #11 #21) +#20 := (div 1::Int #11) +#9 := 0::Int +#15 := (< 0::Int #11) +#17 := (< 1::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 1::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#23 := (ite #19 #20 #22) #12 := (= #11 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #11 #66) -#64 := (= #10 -3::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#599 := (not #767) -#601 := (or #599 #69) -#352 := (* -1::Int -3::Int) -#437 := (* -1::Int 0::Int) -#438 := (div #437 #352) -#439 := (* -1::Int #438) -#430 := (+ #66 #439) -#441 := (= #430 0::Int) -#442 := (div 0::Int -3::Int) -#370 := (* -1::Int #442) -#443 := (+ #66 #370) -#440 := (= #443 0::Int) -#444 := (>= 0::Int 0::Int) -#423 := (<= -3::Int 0::Int) -#758 := (or #423 #444) -#760 := (not #758) -#417 := (<= 0::Int 0::Int) -#547 := (or #417 #423) -#754 := (not #547) -#428 := (or #754 #760) -#429 := (ite #428 #440 #441) -#761 := (= -3::Int 0::Int) -#762 := (= 0::Int 0::Int) -#763 := (or #762 #761) -#764 := (ite #763 #69 #429) -#602 := (or #599 #764) -#603 := (iff #602 #601) -#605 := (iff #601 #601) -#606 := [rewrite]: #605 -#699 := (iff #764 #69) -#1 := true -#550 := (ite true #69 #69) -#695 := (iff #550 #69) -#696 := [rewrite]: #695 -#698 := (iff #764 #550) -#590 := (iff #429 #69) -#705 := (ite false #69 #69) -#707 := (iff #705 #69) -#589 := [rewrite]: #707 -#706 := (iff #429 #705) -#702 := (iff #441 #69) -#548 := (= #430 #66) -#732 := (+ #66 0::Int) -#723 := (= #732 #66) -#718 := [rewrite]: #723 -#717 := (= #430 #732) -#716 := (= #439 0::Int) -#445 := (= #437 0::Int) -#727 := [rewrite]: #445 -#709 := (= #439 #437) -#714 := (= #438 0::Int) -#568 := (div 0::Int 3::Int) -#712 := (= #568 0::Int) -#713 := [rewrite]: #712 -#569 := (= #438 #568) -#726 := (= #352 3::Int) -#567 := [rewrite]: #726 -#711 := [monotonicity #727 #567]: #569 -#708 := [trans #711 #713]: #714 -#715 := [monotonicity #708]: #709 -#710 := [trans #715 #727]: #716 -#546 := [monotonicity #710]: #717 -#549 := [trans #546 #718]: #548 -#703 := [monotonicity #549]: #702 -#725 := (iff #440 #69) -#719 := (= #443 #66) -#721 := (= #443 #732) -#731 := (= #370 0::Int) -#729 := (= #370 #437) -#450 := (= #442 0::Int) -#451 := [rewrite]: #450 -#730 := [monotonicity #451]: #729 -#728 := [trans #730 #727]: #731 -#722 := [monotonicity #728]: #721 -#724 := [trans #722 #718]: #719 -#720 := [monotonicity #724]: #725 -#448 := (iff #428 false) -#459 := (or false false) -#734 := (iff #459 false) -#738 := [rewrite]: #734 -#733 := (iff #428 #459) -#736 := (iff #760 false) -#749 := (not true) -#392 := (iff #749 false) -#752 := [rewrite]: #392 -#358 := (iff #760 #749) -#464 := (iff #758 true) -#744 := (or true true) -#747 := (iff #744 true) -#742 := [rewrite]: #747 -#462 := (iff #758 #744) -#739 := (iff #444 true) -#740 := [rewrite]: #739 -#407 := (iff #423 true) -#743 := [rewrite]: #407 -#463 := [monotonicity #743 #740]: #462 -#465 := [trans #463 #742]: #464 -#735 := [monotonicity #465]: #358 -#458 := [trans #735 #752]: #736 -#750 := (iff #754 false) -#751 := (iff #754 #749) -#748 := (iff #547 true) -#745 := (iff #547 #744) -#405 := (iff #417 true) -#406 := [rewrite]: #405 -#746 := [monotonicity #406 #743]: #745 -#386 := [trans #746 #742]: #748 -#391 := [monotonicity #386]: #751 -#753 := [trans #391 #752]: #750 -#737 := [monotonicity #753 #458]: #733 -#449 := [trans #737 #738]: #448 -#704 := [monotonicity #449 #720 #703]: #706 -#591 := [trans #704 #589]: #590 -#741 := (iff #763 true) -#420 := (or true false) -#757 := (iff #420 true) -#400 := [rewrite]: #757 -#756 := (iff #763 #420) -#755 := (iff #761 false) -#415 := [rewrite]: #755 -#759 := (iff #762 true) -#765 := [rewrite]: #759 -#416 := [monotonicity #765 #415]: #756 -#404 := [trans #416 #400]: #741 -#600 := [monotonicity #404 #591]: #698 -#584 := [trans #600 #696]: #699 -#604 := [monotonicity #584]: #603 -#607 := [trans #604 #606]: #603 -#595 := [quant-inst #8 #63]: #602 -#700 := [mp #595 #607]: #601 -[unit-resolution #700 #87 #772]: false -unsat -a6a62a3b765435aa1a5f654ae0aa2e6502518a55 309 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#740 := (pattern #16) -#11 := 0::Int -#79 := -1::Int -#83 := (* -1::Int #15) -#80 := (* -1::Int #14) -#86 := (div #80 #83) -#243 := (* -1::Int #86) -#244 := (+ #16 #243) -#245 := (= #244 0::Int) -#26 := (div #14 #15) -#240 := (* -1::Int #26) -#241 := (+ #16 #240) -#242 := (= #241 0::Int) -#118 := (>= #14 0::Int) -#111 := (<= #15 0::Int) -#203 := (or #111 #118) -#204 := (not #203) -#107 := (<= #14 0::Int) -#201 := (or #107 #111) -#202 := (not #201) -#207 := (or #202 #204) -#246 := (ite #207 #242 #245) -#239 := (= #16 0::Int) -#18 := (= #15 0::Int) -#17 := (= #14 0::Int) -#19 := (or #17 #18) -#247 := (ite #19 #239 #246) -#741 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #740) #247) -#250 := (forall (vars (?v0 Int) (?v1 Int)) #247) -#744 := (iff #250 #741) -#742 := (iff #247 #247) -#743 := [refl]: #742 -#745 := [quant-intro #743]: #744 -#210 := (ite #207 #26 #86) -#213 := (ite #19 0::Int #210) -#216 := (= #16 #213) -#219 := (forall (vars (?v0 Int) (?v1 Int)) #216) -#251 := (iff #219 #250) -#248 := (iff #216 #247) -#249 := [rewrite]: #248 -#252 := [quant-intro #249]: #251 -#119 := (not #118) -#112 := (not #111) -#122 := (and #112 #119) -#108 := (not #107) -#115 := (and #108 #112) -#125 := (or #115 #122) -#128 := (ite #125 #26 #86) -#131 := (ite #19 0::Int #128) -#134 := (= #16 #131) -#137 := (forall (vars (?v0 Int) (?v1 Int)) #134) -#220 := (iff #137 #219) -#217 := (iff #134 #216) -#214 := (= #131 #213) -#211 := (= #128 #210) -#208 := (iff #125 #207) -#205 := (iff #122 #204) -#206 := [rewrite]: #205 -#195 := (iff #115 #202) -#196 := [rewrite]: #195 -#209 := [monotonicity #196 #206]: #208 -#212 := [monotonicity #209]: #211 -#215 := [monotonicity #212]: #214 -#218 := [monotonicity #215]: #217 -#221 := [quant-intro #218]: #220 -#199 := (~ #137 #137) -#197 := (~ #134 #134) -#198 := [refl]: #197 -#200 := [nnf-pos #198]: #199 -#28 := (- #15) -#27 := (- #14) -#29 := (div #27 #28) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #16 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#140 := (iff #33 #137) -#73 := (and #21 #23) -#76 := (or #22 #73) -#89 := (ite #76 #26 #86) -#67 := (= 0::Int #15) -#64 := (= 0::Int #14) -#70 := (or #64 #67) -#92 := (ite #70 0::Int #89) -#95 := (= #16 #92) -#98 := (forall (vars (?v0 Int) (?v1 Int)) #95) -#138 := (iff #98 #137) -#135 := (iff #95 #134) -#132 := (= #92 #131) -#129 := (= #89 #128) -#126 := (iff #76 #125) -#123 := (iff #73 #122) -#120 := (iff #23 #119) -#121 := [rewrite]: #120 -#113 := (iff #21 #112) -#114 := [rewrite]: #113 -#124 := [monotonicity #114 #121]: #123 -#116 := (iff #22 #115) -#109 := (iff #20 #108) +#10 := (= 1::Int 0::Int) +#13 := (or #10 #12) +#24 := (ite #13 0::Int #23) +#25 := (= #24 #11) +#26 := (not #25) +#125 := (iff #26 false) +#1 := true +#120 := (not true) +#123 := (iff #120 false) +#124 := [rewrite]: #123 +#121 := (iff #26 #120) +#118 := (iff #25 true) +#49 := -1::Int +#113 := (= -1::Int -1::Int) +#116 := (iff #113 true) +#117 := [rewrite]: #116 +#114 := (iff #25 #113) +#50 := (= #11 -1::Int) +#51 := [rewrite]: #50 +#111 := (= #24 -1::Int) +#106 := (ite false 0::Int -1::Int) +#109 := (= #106 -1::Int) #110 := [rewrite]: #109 -#117 := [monotonicity #110 #114]: #116 -#127 := [monotonicity #117 #124]: #126 -#130 := [monotonicity #127]: #129 -#105 := (iff #70 #19) -#103 := (iff #67 #18) -#104 := [rewrite]: #103 -#101 := (iff #64 #17) -#102 := [rewrite]: #101 -#106 := [monotonicity #102 #104]: #105 -#133 := [monotonicity #106 #130]: #132 -#136 := [monotonicity #133]: #135 -#139 := [quant-intro #136]: #138 -#99 := (iff #33 #98) -#96 := (iff #32 #95) -#93 := (= #31 #92) -#90 := (= #30 #89) -#87 := (= #29 #86) -#84 := (= #28 #83) -#85 := [rewrite]: #84 -#81 := (= #27 #80) +#107 := (= #24 #106) +#104 := (= #23 -1::Int) +#66 := (< 0::Int -1::Int) +#72 := (and #17 #66) +#69 := (and #14 #66) +#75 := (or #69 #72) +#99 := (ite #75 -1::Int -1::Int) +#102 := (= #99 -1::Int) +#103 := [rewrite]: #102 +#100 := (= #23 #99) +#97 := (= #22 -1::Int) +#92 := (div -1::Int 1::Int) +#95 := (= #92 -1::Int) +#96 := [rewrite]: #95 +#93 := (= #22 #92) +#90 := (= #21 1::Int) +#85 := (- -1::Int) +#88 := (= #85 1::Int) +#89 := [rewrite]: #88 +#86 := (= #21 #85) +#87 := [monotonicity #51]: #86 +#91 := [trans #87 #89]: #90 +#94 := [monotonicity #51 #91]: #93 +#98 := [trans #94 #96]: #97 +#83 := (= #20 -1::Int) +#78 := (div 1::Int -1::Int) +#81 := (= #78 -1::Int) #82 := [rewrite]: #81 -#88 := [monotonicity #82 #85]: #87 -#77 := (iff #25 #76) -#74 := (iff #24 #73) -#75 := [rewrite]: #74 -#78 := [monotonicity #75]: #77 -#91 := [monotonicity #78 #88]: #90 -#71 := (iff #19 #70) -#68 := (iff #18 #67) -#69 := [rewrite]: #68 -#65 := (iff #17 #64) -#66 := [rewrite]: #65 -#72 := [monotonicity #66 #69]: #71 -#94 := [monotonicity #72 #91]: #93 -#97 := [monotonicity #94]: #96 -#100 := [quant-intro #97]: #99 -#141 := [trans #100 #139]: #140 -#63 := [asserted]: #33 -#142 := [mp #63 #141]: #137 -#191 := [mp~ #142 #200]: #137 -#222 := [mp #191 #221]: #219 -#253 := [mp #222 #252]: #250 -#746 := [mp #253 #745]: #741 -#9 := 3::Int -#8 := 1::Int -#10 := (f3 1::Int 3::Int) -#12 := (= #10 0::Int) -#13 := (not #12) -#62 := [asserted]: #13 -#666 := (not #741) -#667 := (or #666 #12) -#327 := (* -1::Int 3::Int) -#411 := (* -1::Int 1::Int) -#412 := (div #411 #327) -#413 := (* -1::Int #412) -#404 := (+ #10 #413) -#415 := (= #404 0::Int) -#416 := (div 1::Int 3::Int) -#417 := (* -1::Int #416) -#414 := (+ #10 #417) -#418 := (= #414 0::Int) -#397 := (>= 1::Int 0::Int) -#732 := (<= 3::Int 0::Int) -#734 := (or #732 #397) -#391 := (not #734) -#521 := (<= 1::Int 0::Int) -#728 := (or #521 #732) -#402 := (not #728) -#403 := (or #402 #391) -#735 := (ite #403 #418 #415) -#736 := (= 3::Int 0::Int) -#737 := (= 1::Int 0::Int) -#738 := (or #737 #736) -#733 := (ite #738 #12 #735) -#663 := (or #666 #733) -#657 := (iff #663 #667) -#659 := (iff #667 #667) -#660 := [rewrite]: #659 -#655 := (iff #733 #12) -#675 := (ite false #12 #12) -#656 := (iff #675 #12) -#653 := [rewrite]: #656 -#662 := (iff #733 #675) -#674 := (iff #735 #12) -#558 := (= #10 1::Int) -#1 := true -#577 := (ite true #12 #558) -#580 := (iff #577 #12) -#581 := [rewrite]: #580 -#578 := (iff #735 #577) -#576 := (iff #415 #558) -#564 := (+ -1::Int #10) -#669 := (= #564 0::Int) -#573 := (iff #669 #558) -#575 := [rewrite]: #573 -#670 := (iff #415 #669) -#672 := (= #404 #564) -#678 := (+ #10 -1::Int) -#565 := (= #678 #564) -#524 := [rewrite]: #565 -#681 := (= #404 #678) -#679 := (= #413 -1::Int) -#686 := (= #411 -1::Int) -#687 := [rewrite]: #686 -#676 := (= #413 #411) -#522 := (= #412 1::Int) -#688 := -3::Int -#689 := (div -1::Int -3::Int) -#691 := (= #689 1::Int) -#520 := [rewrite]: #691 -#690 := (= #412 #689) -#682 := (= #327 -3::Int) -#683 := [rewrite]: #682 -#684 := [monotonicity #687 #683]: #690 -#523 := [trans #684 #520]: #522 -#677 := [monotonicity #523]: #676 -#680 := [trans #677 #687]: #679 -#563 := [monotonicity #680]: #681 -#574 := [trans #563 #524]: #672 -#673 := [monotonicity #574]: #670 -#569 := [trans #673 #575]: #576 -#543 := (iff #418 #12) -#541 := (= #414 #10) -#693 := (+ #10 0::Int) -#694 := (= #693 #10) -#700 := [rewrite]: #694 -#698 := (= #414 #693) -#697 := (= #417 0::Int) -#705 := (* -1::Int 0::Int) -#695 := (= #705 0::Int) -#696 := [rewrite]: #695 -#702 := (= #417 #705) -#419 := (= #416 0::Int) -#701 := [rewrite]: #419 -#706 := [monotonicity #701]: #702 -#692 := [trans #706 #696]: #697 -#699 := [monotonicity #692]: #698 -#542 := [trans #699 #700]: #541 -#685 := [monotonicity #542]: #543 -#703 := (iff #403 true) -#712 := (or true false) -#424 := (iff #712 true) -#425 := [rewrite]: #424 -#422 := (iff #403 #712) -#711 := (iff #391 false) -#709 := (not true) -#433 := (iff #709 false) -#707 := [rewrite]: #433 -#710 := (iff #391 #709) -#439 := (iff #734 true) -#713 := (or false true) -#437 := (iff #713 true) -#438 := [rewrite]: #437 -#714 := (iff #734 #713) -#724 := (iff #397 true) -#727 := [rewrite]: #724 -#717 := (iff #732 false) -#718 := [rewrite]: #717 -#436 := [monotonicity #718 #727]: #714 -#333 := [trans #436 #438]: #439 -#432 := [monotonicity #333]: #710 -#708 := [trans #432 #707]: #711 -#366 := (iff #402 true) -#722 := (not false) -#725 := (iff #722 true) -#365 := [rewrite]: #725 -#360 := (iff #402 #722) -#721 := (iff #728 false) -#730 := (or false false) -#374 := (iff #730 false) -#715 := [rewrite]: #374 -#719 := (iff #728 #730) -#380 := (iff #521 false) -#381 := [rewrite]: #380 -#720 := [monotonicity #381 #718]: #719 -#716 := [trans #720 #715]: #721 -#723 := [monotonicity #716]: #360 -#726 := [trans #723 #365]: #366 -#423 := [monotonicity #726 #708]: #422 -#704 := [trans #423 #425]: #703 -#579 := [monotonicity #704 #685 #569]: #578 -#671 := [trans #579 #581]: #674 -#378 := (iff #738 false) -#390 := (iff #738 #730) -#389 := (iff #736 false) -#394 := [rewrite]: #389 -#739 := (iff #737 false) -#729 := [rewrite]: #739 -#731 := [monotonicity #729 #394]: #390 -#379 := [trans #731 #715]: #378 -#664 := [monotonicity #379 #671]: #662 -#665 := [trans #664 #653]: #655 -#658 := [monotonicity #665]: #657 -#654 := [trans #658 #660]: #657 -#668 := [quant-inst #8 #9]: #663 -#661 := [mp #668 #654]: #667 -[unit-resolution #661 #62 #746]: false -unsat -e8bc05d54be641b4942beaff512e603a9cfaa4dd 284 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#15 := (f3 #13 #14) -#725 := (pattern #15) -#16 := 0::Int -#70 := -1::Int -#74 := (* -1::Int #14) -#71 := (* -1::Int #13) -#77 := (div #71 #74) -#228 := (* -1::Int #77) -#229 := (+ #15 #228) -#230 := (= #229 0::Int) -#26 := (div #13 #14) -#225 := (* -1::Int #26) -#226 := (+ #15 #225) -#227 := (= #226 0::Int) -#103 := (>= #13 0::Int) -#96 := (<= #14 0::Int) -#188 := (or #96 #103) -#189 := (not #188) -#92 := (<= #13 0::Int) -#186 := (or #92 #96) -#187 := (not #186) -#192 := (or #187 #189) -#231 := (ite #192 #227 #230) -#224 := (= #15 0::Int) -#18 := (= #14 0::Int) -#17 := (= #13 0::Int) -#19 := (or #17 #18) -#232 := (ite #19 #224 #231) -#726 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #725) #232) -#235 := (forall (vars (?v0 Int) (?v1 Int)) #232) -#729 := (iff #235 #726) -#727 := (iff #232 #232) -#728 := [refl]: #727 -#730 := [quant-intro #728]: #729 -#195 := (ite #192 #26 #77) -#198 := (ite #19 0::Int #195) -#201 := (= #15 #198) -#204 := (forall (vars (?v0 Int) (?v1 Int)) #201) -#236 := (iff #204 #235) -#233 := (iff #201 #232) -#234 := [rewrite]: #233 -#237 := [quant-intro #234]: #236 -#104 := (not #103) -#97 := (not #96) -#107 := (and #97 #104) -#93 := (not #92) -#100 := (and #93 #97) -#110 := (or #100 #107) -#113 := (ite #110 #26 #77) -#116 := (ite #19 0::Int #113) -#119 := (= #15 #116) -#122 := (forall (vars (?v0 Int) (?v1 Int)) #119) -#205 := (iff #122 #204) -#202 := (iff #119 #201) -#199 := (= #116 #198) -#196 := (= #113 #195) -#193 := (iff #110 #192) -#190 := (iff #107 #189) -#191 := [rewrite]: #190 -#180 := (iff #100 #187) -#181 := [rewrite]: #180 -#194 := [monotonicity #181 #191]: #193 -#197 := [monotonicity #194]: #196 -#200 := [monotonicity #197]: #199 -#203 := [monotonicity #200]: #202 -#206 := [quant-intro #203]: #205 -#184 := (~ #122 #122) -#182 := (~ #119 #119) -#183 := [refl]: #182 -#185 := [nnf-pos #183]: #184 -#28 := (- #14) -#27 := (- #13) -#29 := (div #27 #28) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#30 := (ite #25 #26 #29) -#31 := (ite #19 0::Int #30) -#32 := (= #15 #31) -#33 := (forall (vars (?v0 Int) (?v1 Int)) #32) -#125 := (iff #33 #122) -#64 := (and #21 #23) -#67 := (or #22 #64) -#80 := (ite #67 #26 #77) -#83 := (ite #19 0::Int #80) -#86 := (= #15 #83) -#89 := (forall (vars (?v0 Int) (?v1 Int)) #86) -#123 := (iff #89 #122) -#120 := (iff #86 #119) -#117 := (= #83 #116) -#114 := (= #80 #113) -#111 := (iff #67 #110) -#108 := (iff #64 #107) -#105 := (iff #23 #104) -#106 := [rewrite]: #105 -#98 := (iff #21 #97) -#99 := [rewrite]: #98 -#109 := [monotonicity #99 #106]: #108 -#101 := (iff #22 #100) -#94 := (iff #20 #93) -#95 := [rewrite]: #94 -#102 := [monotonicity #95 #99]: #101 -#112 := [monotonicity #102 #109]: #111 -#115 := [monotonicity #112]: #114 -#118 := [monotonicity #115]: #117 -#121 := [monotonicity #118]: #120 -#124 := [quant-intro #121]: #123 -#90 := (iff #33 #89) -#87 := (iff #32 #86) -#84 := (= #31 #83) -#81 := (= #30 #80) -#78 := (= #29 #77) -#75 := (= #28 #74) -#76 := [rewrite]: #75 -#72 := (= #27 #71) -#73 := [rewrite]: #72 -#79 := [monotonicity #73 #76]: #78 -#68 := (iff #25 #67) -#65 := (iff #24 #64) -#66 := [rewrite]: #65 -#69 := [monotonicity #66]: #68 -#82 := [monotonicity #69 #79]: #81 -#85 := [monotonicity #82]: #84 -#88 := [monotonicity #85]: #87 -#91 := [quant-intro #88]: #90 -#126 := [trans #91 #124]: #125 -#63 := [asserted]: #33 -#127 := [mp #63 #126]: #122 -#176 := [mp~ #127 #185]: #122 -#207 := [mp #176 #206]: #204 -#238 := [mp #207 #237]: #235 -#731 := [mp #238 #730]: #726 -#10 := 1::Int -#8 := 3::Int -#9 := (f3 3::Int 3::Int) -#11 := (= #9 1::Int) -#12 := (not #11) -#62 := [asserted]: #12 -#566 := (not #726) -#659 := (or #566 #11) -#312 := (* -1::Int 3::Int) -#396 := (div #312 #312) -#397 := (* -1::Int #396) -#398 := (+ #9 #397) -#389 := (= #398 0::Int) -#400 := (div 3::Int 3::Int) -#401 := (* -1::Int #400) -#402 := (+ #9 #401) -#399 := (= #402 0::Int) -#403 := (>= 3::Int 0::Int) -#382 := (<= 3::Int 0::Int) -#717 := (or #382 #403) -#719 := (not #717) -#376 := (or #382 #382) -#506 := (not #376) -#713 := (or #506 #719) -#387 := (ite #713 #399 #389) -#388 := (= #9 0::Int) -#720 := (= 3::Int 0::Int) -#721 := (or #720 #720) -#722 := (ite #721 #388 #387) -#656 := (or #566 #722) -#647 := (iff #656 #659) -#641 := (iff #659 #659) -#638 := [rewrite]: #641 -#564 := (iff #722 #11) -#560 := (ite false #388 #11) -#562 := (iff #560 #11) -#563 := [rewrite]: #562 -#561 := (iff #722 #560) -#543 := (iff #387 #11) -#1 := true -#657 := (ite true #11 #11) -#655 := (iff #657 #11) -#658 := [rewrite]: #655 -#559 := (iff #387 #657) -#550 := (iff #389 #11) -#681 := (+ -1::Int #9) -#684 := (= #681 0::Int) -#526 := (iff #684 #11) -#527 := [rewrite]: #526 -#548 := (iff #389 #684) -#663 := (= #398 #681) -#687 := (+ #9 -1::Int) -#682 := (= #687 #681) -#677 := [rewrite]: #682 -#664 := (= #398 #687) -#661 := (= #397 -1::Int) -#409 := (* -1::Int 1::Int) -#689 := (= #409 -1::Int) -#404 := [rewrite]: #689 -#507 := (= #397 #409) -#676 := (= #396 1::Int) -#671 := -3::Int -#667 := (div -3::Int -3::Int) -#675 := (= #667 1::Int) -#669 := [rewrite]: #675 -#668 := (= #396 #667) -#672 := (= #312 -3::Int) -#673 := [rewrite]: #672 -#674 := [monotonicity #673 #673]: #668 -#505 := [trans #674 #669]: #676 -#508 := [monotonicity #505]: #507 -#662 := [trans #508 #404]: #661 -#665 := [monotonicity #662]: #664 -#666 := [trans #665 #677]: #663 -#549 := [monotonicity #666]: #548 -#509 := [trans #549 #527]: #550 -#528 := (iff #399 #11) -#679 := (iff #399 #684) -#678 := (= #402 #681) -#691 := (= #402 #687) -#686 := (= #401 -1::Int) -#410 := (= #401 #409) -#407 := (= #400 1::Int) -#408 := [rewrite]: #407 -#688 := [monotonicity #408]: #410 -#690 := [trans #688 #404]: #686 -#680 := [monotonicity #690]: #691 -#683 := [trans #680 #677]: #678 -#685 := [monotonicity #683]: #679 -#670 := [trans #685 #527]: #528 -#693 := (iff #713 true) -#695 := (or true false) -#692 := (iff #695 true) -#696 := [rewrite]: #692 -#417 := (iff #713 #695) -#318 := (iff #719 false) -#699 := (not true) -#423 := (iff #699 false) -#424 := [rewrite]: #423 -#421 := (iff #719 #699) -#712 := (iff #717 true) -#710 := (or false true) -#711 := (iff #710 true) -#709 := [rewrite]: #711 -#350 := (iff #717 #710) -#345 := (iff #403 true) -#708 := [rewrite]: #345 -#359 := (iff #382 false) -#700 := [rewrite]: #359 -#351 := [monotonicity #700 #708]: #350 -#698 := [trans #351 #709]: #712 -#422 := [monotonicity #698]: #421 -#694 := [trans #422 #424]: #318 -#701 := (iff #506 true) -#702 := (not false) -#705 := (iff #702 true) -#706 := [rewrite]: #705 -#703 := (iff #506 #702) -#365 := (iff #376 false) -#724 := (or false false) -#379 := (iff #724 false) -#715 := [rewrite]: #379 -#363 := (iff #376 #724) -#364 := [monotonicity #700 #700]: #363 -#366 := [trans #364 #715]: #365 -#704 := [monotonicity #366]: #703 -#707 := [trans #704 #706]: #701 -#418 := [monotonicity #707 #694]: #417 -#697 := [trans #418 #696]: #693 -#654 := [monotonicity #697 #670 #509]: #559 -#558 := [trans #654 #658]: #543 -#375 := (iff #721 false) -#714 := (iff #721 #724) -#723 := (iff #720 false) -#718 := [rewrite]: #723 -#374 := [monotonicity #718 #718]: #714 -#716 := [trans #374 #715]: #375 -#554 := [monotonicity #716 #558]: #561 -#565 := [trans #554 #563]: #564 -#649 := [monotonicity #565]: #647 -#640 := [trans #649 #638]: #647 -#660 := [quant-inst #8 #8]: #656 -#650 := [mp #660 #640]: #659 -[unit-resolution #650 #62 #731]: false -unsat -e5eddbef23d1553e8639810f42b39c3055238ad5 308 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#726 := (pattern #16) -#17 := 0::Int -#71 := -1::Int -#75 := (* -1::Int #15) -#72 := (* -1::Int #14) -#78 := (div #72 #75) -#229 := (* -1::Int #78) -#230 := (+ #16 #229) -#231 := (= #230 0::Int) -#27 := (div #14 #15) -#226 := (* -1::Int #27) -#227 := (+ #16 #226) -#228 := (= #227 0::Int) -#104 := (>= #14 0::Int) -#97 := (<= #15 0::Int) -#189 := (or #97 #104) -#190 := (not #189) -#93 := (<= #14 0::Int) -#187 := (or #93 #97) -#188 := (not #187) -#193 := (or #188 #190) -#232 := (ite #193 #228 #231) -#225 := (= #16 0::Int) -#19 := (= #15 0::Int) -#18 := (= #14 0::Int) -#20 := (or #18 #19) -#233 := (ite #20 #225 #232) -#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #233) -#236 := (forall (vars (?v0 Int) (?v1 Int)) #233) -#730 := (iff #236 #727) -#728 := (iff #233 #233) -#729 := [refl]: #728 -#731 := [quant-intro #729]: #730 -#196 := (ite #193 #27 #78) -#199 := (ite #20 0::Int #196) -#202 := (= #16 #199) -#205 := (forall (vars (?v0 Int) (?v1 Int)) #202) -#237 := (iff #205 #236) -#234 := (iff #202 #233) -#235 := [rewrite]: #234 -#238 := [quant-intro #235]: #237 -#105 := (not #104) -#98 := (not #97) -#108 := (and #98 #105) -#94 := (not #93) -#101 := (and #94 #98) -#111 := (or #101 #108) -#114 := (ite #111 #27 #78) -#117 := (ite #20 0::Int #114) -#120 := (= #16 #117) -#123 := (forall (vars (?v0 Int) (?v1 Int)) #120) -#206 := (iff #123 #205) -#203 := (iff #120 #202) -#200 := (= #117 #199) -#197 := (= #114 #196) -#194 := (iff #111 #193) -#191 := (iff #108 #190) -#192 := [rewrite]: #191 -#181 := (iff #101 #188) -#182 := [rewrite]: #181 -#195 := [monotonicity #182 #192]: #194 -#198 := [monotonicity #195]: #197 -#201 := [monotonicity #198]: #200 -#204 := [monotonicity #201]: #203 -#207 := [quant-intro #204]: #206 -#185 := (~ #123 #123) -#183 := (~ #120 #120) -#184 := [refl]: #183 -#186 := [nnf-pos #184]: #185 -#29 := (- #15) -#28 := (- #14) -#30 := (div #28 #29) -#22 := (< 0::Int #15) -#24 := (< #14 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #14) -#23 := (and #21 #22) -#26 := (or #23 #25) -#31 := (ite #26 #27 #30) -#32 := (ite #20 0::Int #31) -#33 := (= #16 #32) -#34 := (forall (vars (?v0 Int) (?v1 Int)) #33) -#126 := (iff #34 #123) -#65 := (and #22 #24) -#68 := (or #23 #65) -#81 := (ite #68 #27 #78) -#84 := (ite #20 0::Int #81) -#87 := (= #16 #84) -#90 := (forall (vars (?v0 Int) (?v1 Int)) #87) -#124 := (iff #90 #123) -#121 := (iff #87 #120) -#118 := (= #84 #117) -#115 := (= #81 #114) -#112 := (iff #68 #111) -#109 := (iff #65 #108) -#106 := (iff #24 #105) -#107 := [rewrite]: #106 -#99 := (iff #22 #98) -#100 := [rewrite]: #99 -#110 := [monotonicity #100 #107]: #109 -#102 := (iff #23 #101) -#95 := (iff #21 #94) -#96 := [rewrite]: #95 -#103 := [monotonicity #96 #100]: #102 -#113 := [monotonicity #103 #110]: #112 -#116 := [monotonicity #113]: #115 -#119 := [monotonicity #116]: #118 +#79 := (= #20 #78) +#80 := [monotonicity #51]: #79 +#84 := [trans #80 #82]: #83 +#76 := (iff #19 #75) +#73 := (iff #18 #72) +#67 := (iff #15 #66) +#68 := [monotonicity #51]: #67 +#74 := [monotonicity #68]: #73 +#70 := (iff #16 #69) +#71 := [monotonicity #68]: #70 +#77 := [monotonicity #71 #74]: #76 +#101 := [monotonicity #77 #84 #98]: #100 +#105 := [trans #101 #103]: #104 +#64 := (iff #13 false) +#59 := (or false false) +#62 := (iff #59 false) +#63 := [rewrite]: #62 +#60 := (iff #13 #59) +#57 := (iff #12 false) +#52 := (= -1::Int 0::Int) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #12 #52) +#54 := [monotonicity #51]: #53 +#58 := [trans #54 #56]: #57 +#47 := (iff #10 false) +#48 := [rewrite]: #47 +#61 := [monotonicity #48 #58]: #60 +#65 := [trans #61 #63]: #64 +#108 := [monotonicity #65 #105]: #107 +#112 := [trans #108 #110]: #111 +#115 := [monotonicity #112 #51]: #114 +#119 := [trans #115 #117]: #118 #122 := [monotonicity #119]: #121 -#125 := [quant-intro #122]: #124 -#91 := (iff #34 #90) -#88 := (iff #33 #87) -#85 := (= #32 #84) -#82 := (= #31 #81) -#79 := (= #30 #78) -#76 := (= #29 #75) -#77 := [rewrite]: #76 -#73 := (= #28 #72) -#74 := [rewrite]: #73 -#80 := [monotonicity #74 #77]: #79 -#69 := (iff #26 #68) -#66 := (iff #25 #65) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#83 := [monotonicity #70 #80]: #82 -#86 := [monotonicity #83]: #85 -#89 := [monotonicity #86]: #88 -#92 := [quant-intro #89]: #91 -#127 := [trans #92 #125]: #126 -#64 := [asserted]: #34 -#128 := [mp #64 #127]: #123 -#177 := [mp~ #128 #186]: #123 -#208 := [mp #177 #207]: #205 -#239 := [mp #208 #238]: #236 -#732 := [mp #239 #731]: #727 -#11 := 1::Int -#9 := 3::Int -#8 := 5::Int -#10 := (f3 5::Int 3::Int) -#12 := (= #10 1::Int) -#13 := (not #12) -#63 := [asserted]: #13 -#635 := (not #727) -#636 := (or #635 #12) -#313 := (* -1::Int 3::Int) -#397 := (* -1::Int 5::Int) -#398 := (div #397 #313) -#399 := (* -1::Int #398) -#390 := (+ #10 #399) -#401 := (= #390 0::Int) -#402 := (div 5::Int 3::Int) -#403 := (* -1::Int #402) -#400 := (+ #10 #403) -#404 := (= #400 0::Int) -#383 := (>= 5::Int 0::Int) -#718 := (<= 3::Int 0::Int) -#720 := (or #718 #383) -#377 := (not #720) -#507 := (<= 5::Int 0::Int) -#714 := (or #507 #718) -#388 := (not #714) -#389 := (or #388 #377) -#721 := (ite #389 #404 #401) -#722 := (= #10 0::Int) -#723 := (= 3::Int 0::Int) -#724 := (= 5::Int 0::Int) -#719 := (or #724 #723) -#725 := (ite #719 #722 #721) -#637 := (or #635 #725) -#638 := (iff #637 #636) -#625 := (iff #636 #636) -#627 := [rewrite]: #625 -#632 := (iff #725 #12) -#645 := (ite false #722 #12) -#647 := (iff #645 #12) -#631 := [rewrite]: #647 -#646 := (iff #725 #645) -#643 := (iff #721 #12) -#664 := 2::Int -#648 := (= #10 2::Int) -#1 := true -#651 := (ite true #12 #648) -#649 := (iff #651 #12) -#654 := [rewrite]: #649 -#652 := (iff #721 #651) -#639 := (iff #401 #648) -#655 := -2::Int -#563 := (+ -2::Int #10) -#660 := (= #563 0::Int) -#650 := (iff #660 #648) -#642 := [rewrite]: #650 -#657 := (iff #401 #660) -#566 := (= #390 #563) -#561 := (+ #10 -2::Int) -#564 := (= #561 #563) -#565 := [rewrite]: #564 -#562 := (= #390 #561) -#544 := (= #399 -2::Int) -#510 := (* -1::Int 2::Int) -#656 := (= #510 -2::Int) -#659 := [rewrite]: #656 -#658 := (= #399 #510) -#550 := (= #398 2::Int) -#508 := -3::Int -#670 := -5::Int -#663 := (div -5::Int -3::Int) -#667 := (= #663 2::Int) -#549 := [rewrite]: #667 -#665 := (= #398 #663) -#509 := (= #313 -3::Int) -#662 := [rewrite]: #509 -#677 := (= #397 -5::Int) -#506 := [rewrite]: #677 -#666 := [monotonicity #506 #662]: #665 -#551 := [trans #666 #549]: #550 -#560 := [monotonicity #551]: #658 -#559 := [trans #560 #659]: #544 -#555 := [monotonicity #559]: #562 -#567 := [trans #555 #565]: #566 -#661 := [monotonicity #567]: #657 -#641 := [trans #661 #642]: #639 -#675 := (iff #404 #12) -#686 := (+ -1::Int #10) -#672 := (= #686 0::Int) -#668 := (iff #672 #12) -#669 := [rewrite]: #668 -#673 := (iff #404 #672) -#529 := (= #400 #686) -#684 := (+ #10 -1::Int) -#527 := (= #684 #686) -#528 := [rewrite]: #527 -#685 := (= #400 #684) -#678 := (= #403 -1::Int) -#688 := (* -1::Int 1::Int) -#682 := (= #688 -1::Int) -#683 := [rewrite]: #682 -#692 := (= #403 #688) -#687 := (= #402 1::Int) -#691 := [rewrite]: #687 -#681 := [monotonicity #691]: #692 -#679 := [trans #681 #683]: #678 -#680 := [monotonicity #679]: #685 -#671 := [trans #680 #528]: #529 -#674 := [monotonicity #671]: #673 -#676 := [trans #674 #669]: #675 -#690 := (iff #389 true) -#408 := (or true false) -#411 := (iff #408 true) -#689 := [rewrite]: #411 -#409 := (iff #389 #408) -#694 := (iff #377 false) -#696 := (not true) -#693 := (iff #696 false) -#697 := [rewrite]: #693 -#418 := (iff #377 #696) -#319 := (iff #720 true) -#700 := (or false true) -#424 := (iff #700 true) -#425 := [rewrite]: #424 -#422 := (iff #720 #700) -#713 := (iff #383 true) -#699 := [rewrite]: #713 -#704 := (iff #718 false) -#705 := [rewrite]: #704 -#423 := [monotonicity #705 #699]: #422 -#695 := [trans #423 #425]: #319 -#419 := [monotonicity #695]: #418 -#698 := [trans #419 #697]: #694 -#712 := (iff #388 true) -#346 := (not false) -#351 := (iff #346 true) -#352 := [rewrite]: #351 -#709 := (iff #388 #346) -#702 := (iff #714 false) -#376 := (or false false) -#701 := (iff #376 false) -#364 := [rewrite]: #701 -#706 := (iff #714 #376) -#367 := (iff #507 false) -#703 := [rewrite]: #367 -#707 := [monotonicity #703 #705]: #706 -#708 := [trans #707 #364]: #702 -#711 := [monotonicity #708]: #709 -#710 := [trans #711 #352]: #712 -#410 := [monotonicity #710 #698]: #409 -#405 := [trans #410 #689]: #690 -#653 := [monotonicity #405 #676 #641]: #652 -#644 := [trans #653 #654]: #643 -#365 := (iff #719 false) -#717 := (iff #719 #376) -#380 := (iff #723 false) -#716 := [rewrite]: #380 -#715 := (iff #724 false) -#375 := [rewrite]: #715 -#360 := [monotonicity #375 #716]: #717 -#366 := [trans #360 #364]: #365 -#640 := [monotonicity #366 #644]: #646 -#634 := [trans #640 #631]: #632 -#624 := [monotonicity #634]: #638 -#628 := [trans #624 #627]: #638 -#633 := [quant-inst #8 #9]: #637 -#629 := [mp #633 #628]: #636 -[unit-resolution #629 #63 #732]: false -unsat -191c033321d69fed907f76825c4e08dd5071fdbf 307 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#17 := (f3 #15 #16) -#742 := (pattern #17) -#18 := 0::Int -#71 := -1::Int -#91 := (* -1::Int #16) -#88 := (* -1::Int #15) -#94 := (div #88 #91) -#245 := (* -1::Int #94) -#246 := (+ #17 #245) -#247 := (= #246 0::Int) -#28 := (div #15 #16) -#242 := (* -1::Int #28) -#243 := (+ #17 #242) -#244 := (= #243 0::Int) -#120 := (>= #15 0::Int) -#113 := (<= #16 0::Int) -#205 := (or #113 #120) -#206 := (not #205) -#109 := (<= #15 0::Int) -#203 := (or #109 #113) -#204 := (not #203) -#209 := (or #204 #206) -#248 := (ite #209 #244 #247) -#241 := (= #17 0::Int) -#20 := (= #16 0::Int) -#19 := (= #15 0::Int) -#21 := (or #19 #20) -#249 := (ite #21 #241 #248) -#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249) -#252 := (forall (vars (?v0 Int) (?v1 Int)) #249) -#746 := (iff #252 #743) -#744 := (iff #249 #249) -#745 := [refl]: #744 -#747 := [quant-intro #745]: #746 -#212 := (ite #209 #28 #94) -#215 := (ite #21 0::Int #212) -#218 := (= #17 #215) -#221 := (forall (vars (?v0 Int) (?v1 Int)) #218) -#253 := (iff #221 #252) -#250 := (iff #218 #249) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#121 := (not #120) -#114 := (not #113) -#124 := (and #114 #121) -#110 := (not #109) -#117 := (and #110 #114) -#127 := (or #117 #124) -#130 := (ite #127 #28 #94) -#133 := (ite #21 0::Int #130) -#136 := (= #17 #133) -#139 := (forall (vars (?v0 Int) (?v1 Int)) #136) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#216 := (= #133 #215) -#213 := (= #130 #212) -#210 := (iff #127 #209) -#207 := (iff #124 #206) -#208 := [rewrite]: #207 -#197 := (iff #117 #204) -#198 := [rewrite]: #197 -#211 := [monotonicity #198 #208]: #210 -#214 := [monotonicity #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [quant-intro #220]: #222 -#201 := (~ #139 #139) -#199 := (~ #136 #136) -#200 := [refl]: #199 -#202 := [nnf-pos #200]: #201 -#30 := (- #16) -#29 := (- #15) -#31 := (div #29 #30) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #17 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#142 := (iff #35 #139) -#81 := (and #23 #25) -#85 := (or #24 #81) -#97 := (ite #85 #28 #94) -#100 := (ite #21 0::Int #97) -#103 := (= #17 #100) -#106 := (forall (vars (?v0 Int) (?v1 Int)) #103) -#140 := (iff #106 #139) -#137 := (iff #103 #136) -#134 := (= #100 #133) -#131 := (= #97 #130) -#128 := (iff #85 #127) -#125 := (iff #81 #124) -#122 := (iff #25 #121) -#123 := [rewrite]: #122 -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#126 := [monotonicity #116 #123]: #125 -#118 := (iff #24 #117) -#111 := (iff #22 #110) -#112 := [rewrite]: #111 -#119 := [monotonicity #112 #116]: #118 -#129 := [monotonicity #119 #126]: #128 -#132 := [monotonicity #129]: #131 -#135 := [monotonicity #132]: #134 -#138 := [monotonicity #135]: #137 -#141 := [quant-intro #138]: #140 -#107 := (iff #35 #106) -#104 := (iff #34 #103) -#101 := (= #33 #100) -#98 := (= #32 #97) -#95 := (= #31 #94) -#92 := (= #30 #91) -#93 := [rewrite]: #92 -#89 := (= #29 #88) -#90 := [rewrite]: #89 -#96 := [monotonicity #90 #93]: #95 -#86 := (iff #27 #85) -#83 := (iff #26 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#99 := [monotonicity #87 #96]: #98 -#102 := [monotonicity #99]: #101 -#105 := [monotonicity #102]: #104 -#108 := [quant-intro #105]: #107 -#143 := [trans #108 #141]: #142 -#80 := [asserted]: #35 -#144 := [mp #80 #143]: #139 -#193 := [mp~ #144 #202]: #139 -#224 := [mp #193 #223]: #221 -#255 := [mp #224 #254]: #252 -#748 := [mp #255 #747]: #743 -#65 := -3::Int -#8 := 1::Int -#68 := (f3 1::Int -3::Int) -#74 := (= #68 -1::Int) -#77 := (not #74) -#12 := (- 1::Int) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 1::Int #10) -#13 := (= #11 #12) -#14 := (not #13) -#78 := (iff #14 #77) -#75 := (iff #13 #74) -#72 := (= #12 -1::Int) -#73 := [rewrite]: #72 -#69 := (= #11 #68) -#66 := (= #10 -3::Int) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#76 := [monotonicity #70 #73]: #75 -#79 := [monotonicity #76]: #78 -#64 := [asserted]: #14 -#82 := [mp #64 #79]: #77 -#658 := (not #743) -#655 := (or #658 #74) -#329 := (* -1::Int -3::Int) -#413 := (* -1::Int 1::Int) -#414 := (div #413 #329) -#415 := (* -1::Int #414) -#406 := (+ #68 #415) -#417 := (= #406 0::Int) -#418 := (div 1::Int -3::Int) -#419 := (* -1::Int #418) -#416 := (+ #68 #419) -#420 := (= #416 0::Int) -#399 := (>= 1::Int 0::Int) -#734 := (<= -3::Int 0::Int) -#736 := (or #734 #399) -#393 := (not #736) -#523 := (<= 1::Int 0::Int) -#730 := (or #523 #734) -#404 := (not #730) -#405 := (or #404 #393) -#737 := (ite #405 #420 #417) -#738 := (= #68 0::Int) -#739 := (= -3::Int 0::Int) -#740 := (= 1::Int 0::Int) -#735 := (or #740 #739) -#741 := (ite #735 #738 #737) -#657 := (or #658 #741) -#668 := (iff #657 #655) -#665 := (iff #655 #655) -#670 := [rewrite]: #665 -#664 := (iff #741 #74) -#571 := (ite false #738 #74) -#581 := (iff #571 #74) -#582 := [rewrite]: #581 -#673 := (iff #741 #571) -#583 := (iff #737 #74) -#579 := (iff #737 #571) -#577 := (iff #417 #74) -#566 := (+ 1::Int #68) -#671 := (= #566 0::Int) -#560 := (iff #671 #74) -#575 := [rewrite]: #560 -#672 := (iff #417 #671) -#674 := (= #406 #566) -#680 := (+ #68 1::Int) -#567 := (= #680 #566) -#526 := [rewrite]: #567 -#683 := (= #406 #680) -#681 := (= #415 1::Int) -#522 := (* -1::Int -1::Int) -#678 := (= #522 1::Int) -#679 := [rewrite]: #678 -#524 := (= #415 #522) -#686 := (= #414 -1::Int) -#690 := (div -1::Int 3::Int) -#691 := (= #690 -1::Int) -#692 := [rewrite]: #691 -#684 := (= #414 #690) -#688 := (= #329 3::Int) -#689 := [rewrite]: #688 -#545 := (= #413 -1::Int) -#687 := [rewrite]: #545 -#685 := [monotonicity #687 #689]: #684 -#693 := [trans #685 #692]: #686 -#525 := [monotonicity #693]: #524 -#682 := [trans #525 #679]: #681 -#565 := [monotonicity #682]: #683 -#576 := [trans #565 #526]: #674 -#675 := [monotonicity #576]: #672 -#578 := [trans #675 #575]: #577 -#543 := (iff #420 #738) -#696 := (= #416 #68) -#699 := (+ #68 0::Int) -#700 := (= #699 #68) -#701 := [rewrite]: #700 -#694 := (= #416 #699) -#697 := (= #419 0::Int) -#421 := (* -1::Int 0::Int) -#704 := (= #421 0::Int) -#708 := [rewrite]: #704 -#703 := (= #419 #421) -#705 := (= #418 0::Int) -#706 := [rewrite]: #705 -#707 := [monotonicity #706]: #703 -#698 := [trans #707 #708]: #697 -#695 := [monotonicity #698]: #694 -#702 := [trans #695 #701]: #696 -#544 := [monotonicity #702]: #543 -#426 := (iff #405 false) -#392 := (or false false) -#717 := (iff #392 false) -#380 := [rewrite]: #717 -#424 := (iff #405 #392) -#710 := (iff #393 false) -#1 := true -#367 := (not true) -#726 := (iff #367 false) -#729 := [rewrite]: #726 -#709 := (iff #393 #367) -#434 := (iff #736 true) -#440 := (or true true) -#711 := (iff #440 true) -#712 := [rewrite]: #711 -#441 := (iff #736 #440) -#438 := (iff #399 true) -#439 := [rewrite]: #438 -#720 := (iff #734 true) -#721 := [rewrite]: #720 -#335 := [monotonicity #721 #439]: #441 -#435 := [trans #335 #712]: #434 -#713 := [monotonicity #435]: #709 -#714 := [trans #713 #729]: #710 -#715 := (iff #404 false) -#368 := (iff #404 #367) -#725 := (iff #730 true) -#722 := (or false true) -#724 := (iff #722 true) -#362 := [rewrite]: #724 -#723 := (iff #730 #722) -#383 := (iff #523 false) -#719 := [rewrite]: #383 -#718 := [monotonicity #719 #721]: #723 -#727 := [trans #718 #362]: #725 -#728 := [monotonicity #727]: #368 -#716 := [trans #728 #729]: #715 -#425 := [monotonicity #716 #714]: #424 -#427 := [trans #425 #380]: #426 -#580 := [monotonicity #427 #544 #578]: #579 -#676 := [trans #580 #582]: #583 -#381 := (iff #735 false) -#733 := (iff #735 #392) -#396 := (iff #739 false) -#732 := [rewrite]: #396 -#731 := (iff #740 false) -#391 := [rewrite]: #731 -#376 := [monotonicity #391 #732]: #733 -#382 := [trans #376 #380]: #381 -#677 := [monotonicity #382 #676]: #673 -#666 := [trans #677 #582]: #664 -#669 := [monotonicity #666]: #668 -#659 := [trans #669 #670]: #668 -#667 := [quant-inst #8 #65]: #657 -#660 := [mp #667 #659]: #655 -[unit-resolution #660 #82 #748]: false -unsat -5ac842dfccd0a130b836d32f5bc0e4f0b730d4cf 306 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#17 := (f3 #15 #16) -#742 := (pattern #17) -#18 := 0::Int -#71 := -1::Int -#91 := (* -1::Int #16) -#88 := (* -1::Int #15) -#94 := (div #88 #91) -#245 := (* -1::Int #94) -#246 := (+ #17 #245) -#247 := (= #246 0::Int) -#28 := (div #15 #16) -#242 := (* -1::Int #28) -#243 := (+ #17 #242) -#244 := (= #243 0::Int) -#120 := (>= #15 0::Int) -#113 := (<= #16 0::Int) -#205 := (or #113 #120) -#206 := (not #205) -#109 := (<= #15 0::Int) -#203 := (or #109 #113) -#204 := (not #203) -#209 := (or #204 #206) -#248 := (ite #209 #244 #247) -#241 := (= #17 0::Int) -#20 := (= #16 0::Int) -#19 := (= #15 0::Int) -#21 := (or #19 #20) -#249 := (ite #21 #241 #248) -#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249) -#252 := (forall (vars (?v0 Int) (?v1 Int)) #249) -#746 := (iff #252 #743) -#744 := (iff #249 #249) -#745 := [refl]: #744 -#747 := [quant-intro #745]: #746 -#212 := (ite #209 #28 #94) -#215 := (ite #21 0::Int #212) -#218 := (= #17 #215) -#221 := (forall (vars (?v0 Int) (?v1 Int)) #218) -#253 := (iff #221 #252) -#250 := (iff #218 #249) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#121 := (not #120) -#114 := (not #113) -#124 := (and #114 #121) -#110 := (not #109) -#117 := (and #110 #114) -#127 := (or #117 #124) -#130 := (ite #127 #28 #94) -#133 := (ite #21 0::Int #130) -#136 := (= #17 #133) -#139 := (forall (vars (?v0 Int) (?v1 Int)) #136) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#216 := (= #133 #215) -#213 := (= #130 #212) -#210 := (iff #127 #209) -#207 := (iff #124 #206) -#208 := [rewrite]: #207 -#197 := (iff #117 #204) -#198 := [rewrite]: #197 -#211 := [monotonicity #198 #208]: #210 -#214 := [monotonicity #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [quant-intro #220]: #222 -#201 := (~ #139 #139) -#199 := (~ #136 #136) -#200 := [refl]: #199 -#202 := [nnf-pos #200]: #201 -#30 := (- #16) -#29 := (- #15) -#31 := (div #29 #30) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #17 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#142 := (iff #35 #139) -#81 := (and #23 #25) -#85 := (or #24 #81) -#97 := (ite #85 #28 #94) -#100 := (ite #21 0::Int #97) -#103 := (= #17 #100) -#106 := (forall (vars (?v0 Int) (?v1 Int)) #103) -#140 := (iff #106 #139) -#137 := (iff #103 #136) -#134 := (= #100 #133) -#131 := (= #97 #130) -#128 := (iff #85 #127) -#125 := (iff #81 #124) -#122 := (iff #25 #121) -#123 := [rewrite]: #122 -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#126 := [monotonicity #116 #123]: #125 -#118 := (iff #24 #117) -#111 := (iff #22 #110) -#112 := [rewrite]: #111 -#119 := [monotonicity #112 #116]: #118 -#129 := [monotonicity #119 #126]: #128 -#132 := [monotonicity #129]: #131 -#135 := [monotonicity #132]: #134 -#138 := [monotonicity #135]: #137 -#141 := [quant-intro #138]: #140 -#107 := (iff #35 #106) -#104 := (iff #34 #103) -#101 := (= #33 #100) -#98 := (= #32 #97) -#95 := (= #31 #94) -#92 := (= #30 #91) -#93 := [rewrite]: #92 -#89 := (= #29 #88) -#90 := [rewrite]: #89 -#96 := [monotonicity #90 #93]: #95 -#86 := (iff #27 #85) -#83 := (iff #26 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#99 := [monotonicity #87 #96]: #98 -#102 := [monotonicity #99]: #101 -#105 := [monotonicity #102]: #104 -#108 := [quant-intro #105]: #107 -#143 := [trans #108 #141]: #142 -#80 := [asserted]: #35 -#144 := [mp #80 #143]: #139 -#193 := [mp~ #144 #202]: #139 -#224 := [mp #193 #223]: #221 -#255 := [mp #224 #254]: #252 -#748 := [mp #255 #747]: #743 -#65 := -3::Int +#126 := [trans #122 #124]: #125 +#46 := [asserted]: #26 +[mp #46 #126]: false +unsat +a8c1cb5f3abdb5b9970e52ea21ab71e754348560 109 0 +#2 := false #8 := 3::Int -#68 := (f3 3::Int -3::Int) -#74 := (= #68 -1::Int) -#77 := (not #74) +#22 := (- 3::Int) #11 := 1::Int #12 := (- 1::Int) -#9 := (- 3::Int) -#10 := (f3 3::Int #9) -#13 := (= #10 #12) -#14 := (not #13) -#78 := (iff #14 #77) -#75 := (iff #13 #74) -#72 := (= #12 -1::Int) -#73 := [rewrite]: #72 -#69 := (= #10 #68) -#66 := (= #9 -3::Int) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#76 := [monotonicity #70 #73]: #75 -#79 := [monotonicity #76]: #78 -#64 := [asserted]: #14 -#82 := [mp #64 #79]: #77 -#666 := (not #743) -#658 := (or #666 #74) -#329 := (* -1::Int -3::Int) -#413 := (* -1::Int 3::Int) -#414 := (div #413 #329) -#415 := (* -1::Int #414) -#406 := (+ #68 #415) -#417 := (= #406 0::Int) -#418 := (div 3::Int -3::Int) -#419 := (* -1::Int #418) -#416 := (+ #68 #419) -#420 := (= #416 0::Int) -#399 := (>= 3::Int 0::Int) -#734 := (<= -3::Int 0::Int) -#736 := (or #734 #399) -#393 := (not #736) -#523 := (<= 3::Int 0::Int) -#730 := (or #523 #734) -#404 := (not #730) -#405 := (or #404 #393) -#737 := (ite #405 #420 #417) -#738 := (= #68 0::Int) -#739 := (= -3::Int 0::Int) -#740 := (= 3::Int 0::Int) -#735 := (or #740 #739) -#741 := (ite #735 #738 #737) -#655 := (or #666 #741) -#667 := (iff #655 #658) -#669 := (iff #658 #658) -#665 := [rewrite]: #669 -#677 := (iff #741 #74) -#581 := (ite false #738 #74) -#676 := (iff #581 #74) -#673 := [rewrite]: #676 -#582 := (iff #741 #581) -#579 := (iff #737 #74) -#560 := (ite false #74 #74) -#578 := (iff #560 #74) -#571 := [rewrite]: #578 -#575 := (iff #737 #560) -#672 := (iff #417 #74) -#700 := (+ 1::Int #68) -#544 := (= #700 0::Int) -#688 := (iff #544 #74) -#689 := [rewrite]: #688 -#576 := (iff #417 #544) -#526 := (= #406 #700) -#699 := (+ #68 1::Int) -#701 := (= #699 #700) -#696 := [rewrite]: #701 -#566 := (= #406 #699) -#683 := (= #415 1::Int) -#421 := (* -1::Int -1::Int) -#704 := (= #421 1::Int) -#708 := [rewrite]: #704 -#682 := (= #415 #421) -#679 := (= #414 -1::Int) -#693 := (div -3::Int 3::Int) -#525 := (= #693 -1::Int) -#678 := [rewrite]: #525 -#522 := (= #414 #693) -#692 := (= #329 3::Int) -#686 := [rewrite]: #692 -#685 := (= #413 -3::Int) -#691 := [rewrite]: #685 -#524 := [monotonicity #691 #686]: #522 -#681 := [trans #524 #678]: #679 -#680 := [monotonicity #681]: #682 -#565 := [trans #680 #708]: #683 -#567 := [monotonicity #565]: #566 -#674 := [trans #567 #696]: #526 -#671 := [monotonicity #674]: #576 -#675 := [trans #671 #689]: #672 -#690 := (iff #420 #74) -#545 := (iff #420 #544) -#702 := (= #416 #700) -#694 := (= #416 #699) -#697 := (= #419 1::Int) -#703 := (= #419 #421) -#705 := (= #418 -1::Int) -#706 := [rewrite]: #705 -#707 := [monotonicity #706]: #703 -#698 := [trans #707 #708]: #697 -#695 := [monotonicity #698]: #694 -#543 := [trans #695 #696]: #702 -#687 := [monotonicity #543]: #545 -#684 := [trans #687 #689]: #690 -#426 := (iff #405 false) -#392 := (or false false) -#717 := (iff #392 false) -#380 := [rewrite]: #717 -#424 := (iff #405 #392) -#710 := (iff #393 false) -#1 := true -#367 := (not true) -#726 := (iff #367 false) -#729 := [rewrite]: #726 -#709 := (iff #393 #367) -#434 := (iff #736 true) -#440 := (or true true) -#711 := (iff #440 true) -#712 := [rewrite]: #711 -#441 := (iff #736 #440) -#438 := (iff #399 true) -#439 := [rewrite]: #438 -#720 := (iff #734 true) -#721 := [rewrite]: #720 -#335 := [monotonicity #721 #439]: #441 -#435 := [trans #335 #712]: #434 -#713 := [monotonicity #435]: #709 -#714 := [trans #713 #729]: #710 -#715 := (iff #404 false) -#368 := (iff #404 #367) -#725 := (iff #730 true) -#722 := (or false true) -#724 := (iff #722 true) -#362 := [rewrite]: #724 -#723 := (iff #730 #722) -#383 := (iff #523 false) -#719 := [rewrite]: #383 -#718 := [monotonicity #719 #721]: #723 -#727 := [trans #718 #362]: #725 -#728 := [monotonicity #727]: #368 -#716 := [trans #728 #729]: #715 -#425 := [monotonicity #716 #714]: #424 -#427 := [trans #425 #380]: #426 -#577 := [monotonicity #427 #684 #675]: #575 -#580 := [trans #577 #571]: #579 -#381 := (iff #735 false) -#733 := (iff #735 #392) -#396 := (iff #739 false) -#732 := [rewrite]: #396 -#731 := (iff #740 false) -#391 := [rewrite]: #731 -#376 := [monotonicity #391 #732]: #733 -#382 := [trans #376 #380]: #381 -#583 := [monotonicity #382 #580]: #582 -#664 := [trans #583 #673]: #677 -#668 := [monotonicity #664]: #667 -#670 := [trans #668 #665]: #667 -#657 := [quant-inst #8 #65]: #655 -#659 := [mp #657 #670]: #658 -[unit-resolution #659 #82 #748]: false -unsat -ff5c5d19f29597667640ddc4ac233d7f220d9f19 321 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#18 := (f3 #16 #17) -#745 := (pattern #18) -#19 := 0::Int -#89 := -1::Int -#93 := (* -1::Int #17) -#90 := (* -1::Int #16) -#96 := (div #90 #93) -#247 := (* -1::Int #96) -#248 := (+ #18 #247) -#249 := (= #248 0::Int) -#29 := (div #16 #17) -#244 := (* -1::Int #29) -#245 := (+ #18 #244) -#246 := (= #245 0::Int) -#122 := (>= #16 0::Int) -#115 := (<= #17 0::Int) -#207 := (or #115 #122) -#208 := (not #207) -#111 := (<= #16 0::Int) -#205 := (or #111 #115) -#206 := (not #205) -#211 := (or #206 #208) -#250 := (ite #211 #246 #249) -#243 := (= #18 0::Int) -#21 := (= #17 0::Int) -#20 := (= #16 0::Int) -#22 := (or #20 #21) -#251 := (ite #22 #243 #250) -#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251) -#254 := (forall (vars (?v0 Int) (?v1 Int)) #251) -#749 := (iff #254 #746) -#747 := (iff #251 #251) -#748 := [refl]: #747 -#750 := [quant-intro #748]: #749 -#214 := (ite #211 #29 #96) -#217 := (ite #22 0::Int #214) -#220 := (= #18 #217) -#223 := (forall (vars (?v0 Int) (?v1 Int)) #220) -#255 := (iff #223 #254) -#252 := (iff #220 #251) -#253 := [rewrite]: #252 -#256 := [quant-intro #253]: #255 -#123 := (not #122) -#116 := (not #115) -#126 := (and #116 #123) +#23 := (- #12) +#24 := (div #22 #23) +#21 := (div 3::Int #12) +#9 := 0::Int +#16 := (< 0::Int #12) +#18 := (< 3::Int 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int 3::Int) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= #12 0::Int) +#10 := (= 3::Int 0::Int) +#14 := (or #10 #13) +#26 := (ite #14 0::Int #25) +#27 := (= #26 #22) +#28 := (not #27) +#130 := (iff #28 false) +#1 := true +#125 := (not true) +#128 := (iff #125 false) +#129 := [rewrite]: #128 +#126 := (iff #28 #125) +#123 := (iff #27 true) +#83 := -3::Int +#118 := (= -3::Int -3::Int) +#121 := (iff #118 true) +#122 := [rewrite]: #121 +#119 := (iff #27 #118) +#88 := (= #22 -3::Int) +#89 := [rewrite]: #88 +#116 := (= #26 -3::Int) +#111 := (ite false 0::Int -3::Int) +#114 := (= #111 -3::Int) +#115 := [rewrite]: #114 +#112 := (= #26 #111) +#109 := (= #25 -3::Int) +#51 := -1::Int +#68 := (< 0::Int -1::Int) +#74 := (and #18 #68) +#71 := (and #15 #68) +#77 := (or #71 #74) +#104 := (ite #77 -3::Int -3::Int) +#107 := (= #104 -3::Int) +#108 := [rewrite]: #107 +#105 := (= #25 #104) +#102 := (= #24 -3::Int) +#97 := (div -3::Int 1::Int) +#100 := (= #97 -3::Int) +#101 := [rewrite]: #100 +#98 := (= #24 #97) +#95 := (= #23 1::Int) +#90 := (- -1::Int) +#93 := (= #90 1::Int) +#94 := [rewrite]: #93 +#91 := (= #23 #90) +#52 := (= #12 -1::Int) +#53 := [rewrite]: #52 +#92 := [monotonicity #53]: #91 +#96 := [trans #92 #94]: #95 +#99 := [monotonicity #89 #96]: #98 +#103 := [trans #99 #101]: #102 +#86 := (= #21 -3::Int) +#80 := (div 3::Int -1::Int) +#84 := (= #80 -3::Int) +#85 := [rewrite]: #84 +#81 := (= #21 #80) +#82 := [monotonicity #53]: #81 +#87 := [trans #82 #85]: #86 +#78 := (iff #20 #77) +#75 := (iff #19 #74) +#69 := (iff #16 #68) +#70 := [monotonicity #53]: #69 +#76 := [monotonicity #70]: #75 +#72 := (iff #17 #71) +#73 := [monotonicity #70]: #72 +#79 := [monotonicity #73 #76]: #78 +#106 := [monotonicity #79 #87 #103]: #105 +#110 := [trans #106 #108]: #109 +#66 := (iff #14 false) +#61 := (or false false) +#64 := (iff #61 false) +#65 := [rewrite]: #64 +#62 := (iff #14 #61) +#59 := (iff #13 false) +#54 := (= -1::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #13 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#63 := [monotonicity #50 #60]: #62 +#67 := [trans #63 #65]: #66 +#113 := [monotonicity #67 #110]: #112 +#117 := [trans #113 #115]: #116 +#120 := [monotonicity #117 #89]: #119 +#124 := [trans #120 #122]: #123 +#127 := [monotonicity #124]: #126 +#131 := [trans #127 #129]: #130 +#48 := [asserted]: #28 +[mp #48 #131]: false +unsat +99124c49e46379cd9d9cbc824f6c48eaad703212 215 0 +#2 := false +#9 := 0::Int +#11 := 1::Int +decl f3 :: Int +#8 := f3 +#49 := -1::Int +#81 := (* -1::Int f3) +#91 := (div #81 1::Int) +#10 := (= f3 0::Int) +#149 := (ite #10 0::Int #91) +#157 := (+ f3 #149) +#177 := (>= #157 0::Int) +#274 := (not #177) +#255 := [hypothesis]: #177 +#176 := (<= #157 0::Int) +#251 := (* -1::Int #149) +#252 := (+ #91 #251) +#254 := (>= #252 0::Int) +#173 := (= #91 #149) +#175 := (not #10) +#156 := (= #157 0::Int) +#172 := (= #149 0::Int) +#180 := [hypothesis]: #10 +#170 := (or #175 #172) +#171 := [def-axiom]: #170 +#181 := [unit-resolution #171 #180]: #172 +#190 := (= #157 #149) +#188 := (= #149 #157) +#111 := (<= f3 0::Int) +#182 := (or #175 #111) +#183 := [th-lemma arith triangle-eq]: #182 +#184 := [unit-resolution #183 #180]: #111 +#124 := (>= f3 0::Int) +#185 := (or #175 #124) +#186 := [th-lemma arith triangle-eq]: #185 +#187 := [unit-resolution #186 #180]: #124 +#189 := [th-lemma arith eq-propagate 1 1 #187 #184]: #188 +#191 := [symm #189]: #190 +#192 := [trans #191 #181]: #156 +#161 := (not #156) +#22 := (- f3) +#12 := (- 1::Int) +#23 := (- #12) +#24 := (div #22 #23) +#21 := (div f3 #12) +#16 := (< 0::Int #12) +#18 := (< f3 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int f3) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= #12 0::Int) +#14 := (or #10 #13) +#26 := (ite #14 0::Int #25) +#27 := (= #26 #22) +#28 := (not #27) +#164 := (iff #28 #161) +#78 := (div f3 -1::Int) +#66 := (< 0::Int -1::Int) +#72 := (and #18 #66) +#69 := (and #15 #66) +#75 := (or #69 #72) +#94 := (ite #75 #78 #91) +#97 := (ite #10 0::Int #94) +#103 := (= #81 #97) +#108 := (not #103) +#162 := (iff #108 #161) +#159 := (iff #103 #156) +#152 := (= #81 #149) +#155 := (iff #152 #156) +#158 := [rewrite]: #155 +#153 := (iff #103 #152) +#150 := (= #97 #149) +#147 := (= #94 #91) +#142 := (ite false #78 #91) +#145 := (= #142 #91) +#146 := [rewrite]: #145 +#143 := (= #94 #142) +#140 := (iff #75 false) +#135 := (or false false) +#138 := (iff #135 false) +#139 := [rewrite]: #138 +#136 := (iff #75 #135) +#133 := (iff #72 false) +#125 := (not #124) +#128 := (and #125 false) +#131 := (iff #128 false) +#132 := [rewrite]: #131 +#129 := (iff #72 #128) +#115 := (iff #66 false) +#116 := [rewrite]: #115 +#126 := (iff #18 #125) +#127 := [rewrite]: #126 +#130 := [monotonicity #127 #116]: #129 +#134 := [trans #130 #132]: #133 +#122 := (iff #69 false) #112 := (not #111) -#119 := (and #112 #116) -#129 := (or #119 #126) -#132 := (ite #129 #29 #96) -#135 := (ite #22 0::Int #132) -#138 := (= #18 #135) -#141 := (forall (vars (?v0 Int) (?v1 Int)) #138) -#224 := (iff #141 #223) -#221 := (iff #138 #220) -#218 := (= #135 #217) -#215 := (= #132 #214) -#212 := (iff #129 #211) -#209 := (iff #126 #208) -#210 := [rewrite]: #209 -#199 := (iff #119 #206) -#200 := [rewrite]: #199 -#213 := [monotonicity #200 #210]: #212 -#216 := [monotonicity #213]: #215 -#219 := [monotonicity #216]: #218 -#222 := [monotonicity #219]: #221 -#225 := [quant-intro #222]: #224 -#203 := (~ #141 #141) -#201 := (~ #138 #138) -#202 := [refl]: #201 -#204 := [nnf-pos #202]: #203 -#31 := (- #17) -#30 := (- #16) -#32 := (div #30 #31) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#33 := (ite #28 #29 #32) -#34 := (ite #22 0::Int #33) -#35 := (= #18 #34) -#36 := (forall (vars (?v0 Int) (?v1 Int)) #35) -#144 := (iff #36 #141) -#82 := (and #24 #26) -#86 := (or #25 #82) -#99 := (ite #86 #29 #96) -#102 := (ite #22 0::Int #99) -#105 := (= #18 #102) -#108 := (forall (vars (?v0 Int) (?v1 Int)) #105) -#142 := (iff #108 #141) -#139 := (iff #105 #138) -#136 := (= #102 #135) -#133 := (= #99 #132) -#130 := (iff #86 #129) -#127 := (iff #82 #126) -#124 := (iff #26 #123) -#125 := [rewrite]: #124 -#117 := (iff #24 #116) -#118 := [rewrite]: #117 -#128 := [monotonicity #118 #125]: #127 -#120 := (iff #25 #119) -#113 := (iff #23 #112) +#117 := (and #112 false) +#120 := (iff #117 false) +#121 := [rewrite]: #120 +#118 := (iff #69 #117) +#113 := (iff #15 #112) #114 := [rewrite]: #113 -#121 := [monotonicity #114 #118]: #120 -#131 := [monotonicity #121 #128]: #130 -#134 := [monotonicity #131]: #133 -#137 := [monotonicity #134]: #136 -#140 := [monotonicity #137]: #139 -#143 := [quant-intro #140]: #142 -#109 := (iff #36 #108) -#106 := (iff #35 #105) -#103 := (= #34 #102) -#100 := (= #33 #99) -#97 := (= #32 #96) -#94 := (= #31 #93) -#95 := [rewrite]: #94 -#91 := (= #30 #90) -#92 := [rewrite]: #91 -#98 := [monotonicity #92 #95]: #97 -#87 := (iff #28 #86) -#84 := (iff #27 #82) -#85 := [rewrite]: #84 -#88 := [monotonicity #85]: #87 -#101 := [monotonicity #88 #98]: #100 -#104 := [monotonicity #101]: #103 -#107 := [monotonicity #104]: #106 -#110 := [quant-intro #107]: #109 -#145 := [trans #110 #143]: #144 -#81 := [asserted]: #36 -#146 := [mp #81 #145]: #141 -#195 := [mp~ #146 #204]: #141 -#226 := [mp #195 #225]: #223 -#257 := [mp #226 #256]: #254 -#751 := [mp #257 #750]: #746 -#72 := -2::Int -#66 := -3::Int -#8 := 5::Int -#69 := (f3 5::Int -3::Int) -#75 := (= #69 -2::Int) -#78 := (not #75) -#12 := 2::Int -#13 := (- 2::Int) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 5::Int #10) -#14 := (= #11 #13) -#15 := (not #14) -#79 := (iff #15 #78) -#76 := (iff #14 #75) -#73 := (= #13 -2::Int) -#74 := [rewrite]: #73 -#70 := (= #11 #69) -#67 := (= #10 -3::Int) -#68 := [rewrite]: #67 +#119 := [monotonicity #114 #116]: #118 +#123 := [trans #119 #121]: #122 +#137 := [monotonicity #123 #134]: #136 +#141 := [trans #137 #139]: #140 +#144 := [monotonicity #141]: #143 +#148 := [trans #144 #146]: #147 +#151 := [monotonicity #148]: #150 +#154 := [monotonicity #151]: #153 +#160 := [trans #154 #158]: #159 +#163 := [monotonicity #160]: #162 +#109 := (iff #28 #108) +#106 := (iff #27 #103) +#100 := (= #97 #81) +#104 := (iff #100 #103) +#105 := [rewrite]: #104 +#101 := (iff #27 #100) +#82 := (= #22 #81) +#83 := [rewrite]: #82 +#98 := (= #26 #97) +#95 := (= #25 #94) +#92 := (= #24 #91) +#89 := (= #23 1::Int) +#84 := (- -1::Int) +#87 := (= #84 1::Int) +#88 := [rewrite]: #87 +#85 := (= #23 #84) +#50 := (= #12 -1::Int) +#51 := [rewrite]: #50 +#86 := [monotonicity #51]: #85 +#90 := [trans #86 #88]: #89 +#93 := [monotonicity #83 #90]: #92 +#79 := (= #21 #78) +#80 := [monotonicity #51]: #79 +#76 := (iff #20 #75) +#73 := (iff #19 #72) +#67 := (iff #16 #66) +#68 := [monotonicity #51]: #67 +#74 := [monotonicity #68]: #73 +#70 := (iff #17 #69) #71 := [monotonicity #68]: #70 #77 := [monotonicity #71 #74]: #76 -#80 := [monotonicity #77]: #79 -#65 := [asserted]: #15 -#83 := [mp #65 #80]: #78 -#665 := (not #746) -#659 := (or #665 #75) -#331 := (* -1::Int -3::Int) -#416 := (* -1::Int 5::Int) -#417 := (div #416 #331) -#418 := (* -1::Int #417) -#409 := (+ #69 #418) -#420 := (= #409 0::Int) -#421 := (div 5::Int -3::Int) -#349 := (* -1::Int #421) -#422 := (+ #69 #349) -#419 := (= #422 0::Int) -#423 := (>= 5::Int 0::Int) -#402 := (<= -3::Int 0::Int) -#737 := (or #402 #423) -#739 := (not #737) -#396 := (<= 5::Int 0::Int) -#526 := (or #396 #402) -#733 := (not #526) -#407 := (or #733 #739) -#408 := (ite #407 #419 #420) -#740 := (= #69 0::Int) -#741 := (= -3::Int 0::Int) -#742 := (= 5::Int 0::Int) -#743 := (or #742 #741) -#738 := (ite #743 #740 #408) -#666 := (or #665 #738) -#651 := (iff #666 #659) -#654 := (iff #659 #659) -#655 := [rewrite]: #654 -#663 := (iff #738 #75) -#671 := (ite false #740 #75) -#673 := (iff #671 #75) -#662 := [rewrite]: #673 -#672 := (iff #738 #671) -#660 := (iff #408 #75) -#691 := (= #69 -1::Int) -#680 := (ite false #691 #75) -#661 := (iff #680 #75) -#658 := [rewrite]: #661 -#667 := (iff #408 #680) -#679 := (iff #420 #75) -#563 := (+ 2::Int #69) -#582 := (= #563 0::Int) -#585 := (iff #582 #75) -#586 := [rewrite]: #585 -#583 := (iff #420 #582) -#581 := (= #409 #563) -#674 := (+ #69 2::Int) -#578 := (= #674 #563) -#580 := [rewrite]: #578 -#675 := (= #409 #674) -#677 := (= #418 2::Int) -#686 := (* -1::Int -2::Int) -#570 := (= #686 2::Int) -#529 := [rewrite]: #570 -#568 := (= #418 #686) -#685 := (= #417 -2::Int) -#694 := -5::Int -#527 := (div -5::Int 3::Int) -#682 := (= #527 -2::Int) -#684 := [rewrite]: #682 -#528 := (= #417 #527) -#696 := (= #331 3::Int) -#525 := [rewrite]: #696 -#695 := (= #416 -5::Int) -#689 := [rewrite]: #695 -#681 := [monotonicity #689 #525]: #528 -#683 := [trans #681 #684]: #685 -#569 := [monotonicity #683]: #568 -#579 := [trans #569 #529]: #677 -#678 := [monotonicity #579]: #675 -#574 := [trans #678 #580]: #581 -#584 := [monotonicity #574]: #583 -#676 := [trans #584 #586]: #679 -#687 := (iff #419 #691) -#710 := 1::Int -#703 := (+ 1::Int #69) -#547 := (= #703 0::Int) -#692 := (iff #547 #691) -#693 := [rewrite]: #692 -#548 := (iff #419 #547) -#705 := (= #422 #703) -#702 := (+ #69 1::Int) -#704 := (= #702 #703) -#699 := [rewrite]: #704 -#697 := (= #422 #702) -#700 := (= #349 1::Int) -#709 := (* -1::Int -1::Int) -#707 := (= #709 1::Int) -#711 := [rewrite]: #707 -#424 := (= #349 #709) -#430 := (= #421 -1::Int) -#708 := [rewrite]: #430 -#706 := [monotonicity #708]: #424 -#701 := [trans #706 #711]: #700 -#698 := [monotonicity #701]: #697 -#546 := [trans #698 #699]: #705 -#690 := [monotonicity #546]: #548 -#688 := [trans #690 #693]: #687 -#428 := (iff #407 false) -#735 := (or false false) -#379 := (iff #735 false) -#720 := [rewrite]: #379 -#717 := (iff #407 #735) -#716 := (iff #739 false) -#1 := true -#730 := (not true) -#731 := (iff #730 false) -#729 := [rewrite]: #731 -#438 := (iff #739 #730) -#715 := (iff #737 true) -#442 := (or true true) -#337 := (iff #442 true) -#714 := [rewrite]: #337 -#443 := (iff #737 #442) -#719 := (iff #423 true) -#441 := [rewrite]: #719 -#722 := (iff #402 true) -#723 := [rewrite]: #722 -#444 := [monotonicity #723 #441]: #443 -#437 := [trans #444 #714]: #715 -#712 := [monotonicity #437]: #438 -#713 := [trans #712 #729]: #716 -#732 := (iff #733 false) -#370 := (iff #733 #730) -#365 := (iff #526 true) -#724 := (or false true) -#721 := (iff #724 true) -#727 := [rewrite]: #721 -#725 := (iff #526 #724) -#385 := (iff #396 false) -#386 := [rewrite]: #385 -#726 := [monotonicity #386 #723]: #725 -#728 := [trans #726 #727]: #365 -#371 := [monotonicity #728]: #370 -#718 := [trans #371 #729]: #732 -#427 := [monotonicity #718 #713]: #717 -#429 := [trans #427 #720]: #428 -#669 := [monotonicity #429 #688 #676]: #667 -#670 := [trans #669 #658]: #660 -#383 := (iff #743 false) -#395 := (iff #743 #735) -#394 := (iff #741 false) -#399 := [rewrite]: #394 -#744 := (iff #742 false) -#734 := [rewrite]: #744 -#736 := [monotonicity #734 #399]: #395 -#384 := [trans #736 #720]: #383 -#668 := [monotonicity #384 #670]: #672 -#664 := [trans #668 #662]: #663 -#653 := [monotonicity #664]: #651 -#656 := [trans #653 #655]: #651 -#650 := [quant-inst #8 #66]: #666 -#652 := [mp #650 #656]: #659 -[unit-resolution #652 #83 #751]: false -unsat -3b09e93d3eb1701446a8a6f0f64071b3ee25d56a 319 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#750 := (pattern #16) -#17 := 0::Int -#64 := -1::Int -#99 := (* -1::Int #15) -#96 := (* -1::Int #14) -#102 := (div #96 #99) -#253 := (* -1::Int #102) -#254 := (+ #16 #253) -#255 := (= #254 0::Int) -#27 := (div #14 #15) -#250 := (* -1::Int #27) -#251 := (+ #16 #250) -#252 := (= #251 0::Int) -#128 := (>= #14 0::Int) -#121 := (<= #15 0::Int) -#213 := (or #121 #128) -#214 := (not #213) -#117 := (<= #14 0::Int) -#211 := (or #117 #121) -#212 := (not #211) -#217 := (or #212 #214) -#256 := (ite #217 #252 #255) -#249 := (= #16 0::Int) -#19 := (= #15 0::Int) -#18 := (= #14 0::Int) -#20 := (or #18 #19) -#257 := (ite #20 #249 #256) -#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #257) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#754 := (iff #260 #751) -#752 := (iff #257 #257) -#753 := [refl]: #752 -#755 := [quant-intro #753]: #754 -#220 := (ite #217 #27 #102) -#223 := (ite #20 0::Int #220) -#226 := (= #16 #223) -#229 := (forall (vars (?v0 Int) (?v1 Int)) #226) -#261 := (iff #229 #260) -#258 := (iff #226 #257) -#259 := [rewrite]: #258 -#262 := [quant-intro #259]: #261 -#129 := (not #128) -#122 := (not #121) -#132 := (and #122 #129) -#118 := (not #117) -#125 := (and #118 #122) -#135 := (or #125 #132) -#138 := (ite #135 #27 #102) -#141 := (ite #20 0::Int #138) -#144 := (= #16 #141) -#147 := (forall (vars (?v0 Int) (?v1 Int)) #144) -#230 := (iff #147 #229) -#227 := (iff #144 #226) -#224 := (= #141 #223) -#221 := (= #138 #220) -#218 := (iff #135 #217) -#215 := (iff #132 #214) -#216 := [rewrite]: #215 -#205 := (iff #125 #212) -#206 := [rewrite]: #205 -#219 := [monotonicity #206 #216]: #218 -#222 := [monotonicity #219]: #221 -#225 := [monotonicity #222]: #224 -#228 := [monotonicity #225]: #227 -#231 := [quant-intro #228]: #230 -#209 := (~ #147 #147) -#207 := (~ #144 #144) -#208 := [refl]: #207 -#210 := [nnf-pos #208]: #209 -#29 := (- #15) -#28 := (- #14) -#30 := (div #28 #29) -#22 := (< 0::Int #15) -#24 := (< #14 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #14) -#23 := (and #21 #22) -#26 := (or #23 #25) -#31 := (ite #26 #27 #30) -#32 := (ite #20 0::Int #31) -#33 := (= #16 #32) -#34 := (forall (vars (?v0 Int) (?v1 Int)) #33) -#150 := (iff #34 #147) -#90 := (and #22 #24) -#93 := (or #23 #90) -#105 := (ite #93 #27 #102) -#108 := (ite #20 0::Int #105) -#111 := (= #16 #108) -#114 := (forall (vars (?v0 Int) (?v1 Int)) #111) -#148 := (iff #114 #147) -#145 := (iff #111 #144) -#142 := (= #108 #141) -#139 := (= #105 #138) -#136 := (iff #93 #135) -#133 := (iff #90 #132) -#130 := (iff #24 #129) +#96 := [monotonicity #77 #80 #93]: #95 +#64 := (iff #14 #10) +#59 := (or #10 false) +#62 := (iff #59 #10) +#63 := [rewrite]: #62 +#60 := (iff #14 #59) +#57 := (iff #13 false) +#52 := (= -1::Int 0::Int) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #13 #52) +#54 := [monotonicity #51]: #53 +#58 := [trans #54 #56]: #57 +#61 := [monotonicity #58]: #60 +#65 := [trans #61 #63]: #64 +#99 := [monotonicity #65 #96]: #98 +#102 := [monotonicity #99 #83]: #101 +#107 := [trans #102 #105]: #106 +#110 := [monotonicity #107]: #109 +#165 := [trans #110 #163]: #164 +#48 := [asserted]: #28 +#166 := [mp #48 #165]: #161 +#193 := [unit-resolution #166 #192]: false +#194 := [lemma #193]: #175 +#168 := (or #10 #173) +#169 := [def-axiom]: #168 +#256 := [unit-resolution #169 #194]: #173 +#257 := (not #173) +#258 := (or #257 #254) +#259 := [th-lemma arith triangle-eq]: #258 +#260 := [unit-resolution #259 #256]: #254 +#218 := (+ f3 #91) +#224 := (<= #218 0::Int) +#219 := (= #218 0::Int) +#1 := true +#46 := [true-axiom]: true +#261 := (or false #219) +#262 := [th-lemma arith]: #261 +#263 := [unit-resolution #262 #46]: #219 +#264 := (not #219) +#265 := (or #264 #224) +#266 := [th-lemma arith triangle-eq]: #265 +#267 := [unit-resolution #266 #263]: #224 +#269 := (not #224) +#268 := (not #254) +#270 := (or #176 #268 #269) +#271 := [th-lemma arith assign-bounds 1 -1]: #270 +#272 := [unit-resolution #271 #267 #260]: #176 +#273 := (not #176) +#277 := (or #273 #274) +#275 := (or #156 #273 #274) +#276 := [th-lemma arith triangle-eq]: #275 +#278 := [unit-resolution #276 #166]: #277 +#279 := [unit-resolution #278 #272 #255]: false +#280 := [lemma #279]: #274 +#253 := (<= #252 0::Int) +#281 := (or #257 #253) +#282 := [th-lemma arith triangle-eq]: #281 +#283 := [unit-resolution #282 #256]: #253 +#225 := (>= #218 0::Int) +#284 := (or #264 #225) +#285 := [th-lemma arith triangle-eq]: #284 +#286 := [unit-resolution #285 #263]: #225 +#288 := (not #225) +#287 := (not #253) +#289 := (or #177 #287 #288) +#290 := [th-lemma arith assign-bounds 1 -1]: #289 +#291 := [unit-resolution #290 #286 #283]: #177 +[unit-resolution #291 #280]: false +unsat +530d84b9b60629031058dc22de3bbb66e9dd68b7 73 0 +#2 := false +#8 := 0::Int +#10 := 3::Int +#19 := (- 3::Int) +#18 := (- 0::Int) +#20 := (div #18 #19) +#17 := (div 0::Int 3::Int) +#14 := (< 0::Int 3::Int) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#21 := (ite #16 #17 #20) +#11 := (= 3::Int 0::Int) +#9 := (= 0::Int 0::Int) +#12 := (or #9 #11) +#22 := (ite #12 0::Int #21) +#23 := (= #22 0::Int) +#24 := (not #23) +#94 := (iff #24 false) +#1 := true +#89 := (not true) +#92 := (iff #89 false) +#93 := [rewrite]: #92 +#90 := (iff #24 #89) +#87 := (iff #23 true) +#45 := (iff #9 true) +#46 := [rewrite]: #45 +#85 := (iff #23 #9) +#79 := (ite true 0::Int 0::Int) +#82 := (= #79 0::Int) +#83 := [rewrite]: #82 +#80 := (= #22 #79) +#77 := (= #21 0::Int) +#72 := (ite #15 0::Int 0::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #21 #72) +#70 := (= #20 0::Int) +#62 := -3::Int +#65 := (div 0::Int -3::Int) +#68 := (= #65 0::Int) +#69 := [rewrite]: #68 +#66 := (= #20 #65) +#63 := (= #19 -3::Int) +#64 := [rewrite]: #63 +#60 := (= #18 0::Int) +#61 := [rewrite]: #60 +#67 := [monotonicity #61 #64]: #66 +#71 := [trans #67 #69]: #70 +#58 := (= #17 0::Int) +#59 := [rewrite]: #58 +#56 := (iff #16 #15) +#57 := [rewrite]: #56 +#74 := [monotonicity #57 #59 #71]: #73 +#78 := [trans #74 #76]: #77 +#54 := (iff #12 true) +#49 := (or true false) +#52 := (iff #49 true) +#53 := [rewrite]: #52 +#50 := (iff #12 #49) +#47 := (iff #11 false) +#48 := [rewrite]: #47 +#51 := [monotonicity #46 #48]: #50 +#55 := [trans #51 #53]: #54 +#81 := [monotonicity #55 #78]: #80 +#84 := [trans #81 #83]: #23 +#86 := [monotonicity #84]: #85 +#88 := [trans #86 #46]: #87 +#91 := [monotonicity #88]: #90 +#95 := [trans #91 #93]: #94 +#44 := [asserted]: #24 +[mp #44 #95]: false +unsat +99c1933dfc0f818aac1f7a0114d4293293e0a0a1 102 0 +#2 := false +#8 := 0::Int +#10 := 3::Int +#11 := (- 3::Int) +#20 := (- #11) +#19 := (- 0::Int) +#21 := (div #19 #20) +#18 := (div 0::Int #11) +#15 := (< 0::Int #11) +#14 := (< 0::Int 0::Int) +#16 := (and #14 #15) +#17 := (or #16 #16) +#22 := (ite #17 #18 #21) +#12 := (= #11 0::Int) +#9 := (= 0::Int 0::Int) +#13 := (or #9 #12) +#23 := (ite #13 0::Int #22) +#24 := (= #23 0::Int) +#25 := (not #24) +#123 := (iff #25 false) +#1 := true +#118 := (not true) +#121 := (iff #118 false) +#122 := [rewrite]: #121 +#119 := (iff #25 #118) +#116 := (iff #24 true) +#46 := (iff #9 true) +#47 := [rewrite]: #46 +#114 := (iff #24 #9) +#108 := (ite true 0::Int 0::Int) +#111 := (= #108 0::Int) +#112 := [rewrite]: #111 +#109 := (= #23 #108) +#106 := (= #22 0::Int) +#48 := -3::Int +#65 := (< 0::Int -3::Int) +#68 := (and #14 #65) +#101 := (ite #68 0::Int 0::Int) +#104 := (= #101 0::Int) +#105 := [rewrite]: #104 +#102 := (= #22 #101) +#99 := (= #21 0::Int) +#94 := (div 0::Int 3::Int) +#97 := (= #94 0::Int) +#98 := [rewrite]: #97 +#95 := (= #21 #94) +#92 := (= #20 3::Int) +#87 := (- -3::Int) +#90 := (= #87 3::Int) +#91 := [rewrite]: #90 +#88 := (= #20 #87) +#49 := (= #11 -3::Int) +#50 := [rewrite]: #49 +#89 := [monotonicity #50]: #88 +#93 := [trans #89 #91]: #92 +#85 := (= #19 0::Int) +#86 := [rewrite]: #85 +#96 := [monotonicity #86 #93]: #95 +#100 := [trans #96 #98]: #99 +#83 := (= #18 0::Int) +#78 := (div 0::Int -3::Int) +#81 := (= #78 0::Int) +#82 := [rewrite]: #81 +#79 := (= #18 #78) +#80 := [monotonicity #50]: #79 +#84 := [trans #80 #82]: #83 +#76 := (iff #17 #68) +#71 := (or #68 #68) +#74 := (iff #71 #68) +#75 := [rewrite]: #74 +#72 := (iff #17 #71) +#69 := (iff #16 #68) +#66 := (iff #15 #65) +#67 := [monotonicity #50]: #66 +#70 := [monotonicity #67]: #69 +#73 := [monotonicity #70 #70]: #72 +#77 := [trans #73 #75]: #76 +#103 := [monotonicity #77 #84 #100]: #102 +#107 := [trans #103 #105]: #106 +#63 := (iff #13 true) +#58 := (or true false) +#61 := (iff #58 true) +#62 := [rewrite]: #61 +#59 := (iff #13 #58) +#56 := (iff #12 false) +#51 := (= -3::Int 0::Int) +#54 := (iff #51 false) +#55 := [rewrite]: #54 +#52 := (iff #12 #51) +#53 := [monotonicity #50]: #52 +#57 := [trans #53 #55]: #56 +#60 := [monotonicity #47 #57]: #59 +#64 := [trans #60 #62]: #63 +#110 := [monotonicity #64 #107]: #109 +#113 := [trans #110 #112]: #24 +#115 := [monotonicity #113]: #114 +#117 := [trans #115 #47]: #116 +#120 := [monotonicity #117]: #119 +#124 := [trans #120 #122]: #123 +#45 := [asserted]: #25 +[mp #45 #124]: false +unsat +9d138480c7d61fdc258e935f0608d147c435d8d1 113 0 +#2 := false +#9 := 0::Int +#11 := 3::Int +#22 := (- 3::Int) +#8 := 1::Int +#21 := (- 1::Int) +#23 := (div #21 #22) +#20 := (div 1::Int 3::Int) +#15 := (< 0::Int 3::Int) +#17 := (< 1::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 1::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 3::Int 0::Int) +#10 := (= 1::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (= #25 0::Int) +#27 := (not #26) +#134 := (iff #27 false) +#59 := (and #15 #17) +#62 := (or #16 #59) +#97 := (not #62) +#132 := (iff #97 false) +#1 := true +#127 := (not true) +#130 := (iff #127 false) #131 := [rewrite]: #130 -#123 := (iff #22 #122) +#128 := (iff #97 #127) +#125 := (iff #62 true) +#120 := (or true false) +#123 := (iff #120 true) #124 := [rewrite]: #123 -#134 := [monotonicity #124 #131]: #133 -#126 := (iff #23 #125) -#119 := (iff #21 #118) -#120 := [rewrite]: #119 -#127 := [monotonicity #120 #124]: #126 -#137 := [monotonicity #127 #134]: #136 -#140 := [monotonicity #137]: #139 -#143 := [monotonicity #140]: #142 -#146 := [monotonicity #143]: #145 -#149 := [quant-intro #146]: #148 -#115 := (iff #34 #114) -#112 := (iff #33 #111) -#109 := (= #32 #108) -#106 := (= #31 #105) -#103 := (= #30 #102) -#100 := (= #29 #99) +#121 := (iff #62 #120) +#118 := (iff #59 false) +#113 := (and true false) +#116 := (iff #113 false) +#117 := [rewrite]: #116 +#114 := (iff #59 #113) +#111 := (iff #17 false) +#112 := [rewrite]: #111 +#102 := (iff #15 true) +#103 := [rewrite]: #102 +#115 := [monotonicity #103 #112]: #114 +#119 := [trans #115 #117]: #118 +#109 := (iff #16 true) +#104 := (and true true) +#107 := (iff #104 true) +#108 := [rewrite]: #107 +#105 := (iff #16 #104) +#100 := (iff #14 true) #101 := [rewrite]: #100 -#97 := (= #28 #96) +#106 := [monotonicity #101 #103]: #105 +#110 := [trans #106 #108]: #109 +#122 := [monotonicity #110 #119]: #121 +#126 := [trans #122 #124]: #125 +#129 := [monotonicity #126]: #128 +#133 := [trans #129 #131]: #132 +#98 := (iff #27 #97) +#95 := (iff #26 #62) +#80 := (ite #62 0::Int 1::Int) +#90 := (= #80 0::Int) +#93 := (iff #90 #62) +#94 := [rewrite]: #93 +#91 := (iff #26 #90) +#88 := (= #25 #80) +#83 := (ite false 0::Int #80) +#86 := (= #83 #80) +#87 := [rewrite]: #86 +#84 := (= #25 #83) +#81 := (= #24 #80) +#78 := (= #23 1::Int) +#70 := -3::Int +#67 := -1::Int +#73 := (div -1::Int -3::Int) +#76 := (= #73 1::Int) +#77 := [rewrite]: #76 +#74 := (= #23 #73) +#71 := (= #22 -3::Int) +#72 := [rewrite]: #71 +#68 := (= #21 -1::Int) +#69 := [rewrite]: #68 +#75 := [monotonicity #69 #72]: #74 +#79 := [trans #75 #77]: #78 +#65 := (= #20 0::Int) +#66 := [rewrite]: #65 +#63 := (iff #19 #62) +#60 := (iff #18 #59) +#61 := [rewrite]: #60 +#64 := [monotonicity #61]: #63 +#82 := [monotonicity #64 #66 #79]: #81 +#57 := (iff #13 false) +#52 := (or false false) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #13 #52) +#50 := (iff #12 false) +#51 := [rewrite]: #50 +#48 := (iff #10 false) +#49 := [rewrite]: #48 +#54 := [monotonicity #49 #51]: #53 +#58 := [trans #54 #56]: #57 +#85 := [monotonicity #58 #82]: #84 +#89 := [trans #85 #87]: #88 +#92 := [monotonicity #89]: #91 +#96 := [trans #92 #94]: #95 +#99 := [monotonicity #96]: #98 +#135 := [trans #99 #133]: #134 +#47 := [asserted]: #27 +[mp #47 #135]: false +unsat +59082baebee56f4a9740d0c291f81d87438f8452 78 0 +#2 := false +#22 := 1::Int +#8 := 3::Int +#18 := (- 3::Int) +#19 := (div #18 #18) +#17 := (div 3::Int 3::Int) +#9 := 0::Int +#12 := (< 0::Int 3::Int) +#14 := (< 3::Int 0::Int) +#15 := (and #14 #12) +#13 := (and #12 #12) +#16 := (or #13 #15) +#20 := (ite #16 #17 #19) +#10 := (= 3::Int 0::Int) +#11 := (or #10 #10) +#21 := (ite #11 0::Int #20) +#23 := (= #21 1::Int) +#24 := (not #23) +#99 := (iff #24 false) +#1 := true +#94 := (not true) +#97 := (iff #94 false) #98 := [rewrite]: #97 -#104 := [monotonicity #98 #101]: #103 -#94 := (iff #26 #93) -#91 := (iff #25 #90) +#95 := (iff #24 #94) +#92 := (iff #23 true) +#87 := (= 1::Int 1::Int) +#90 := (iff #87 true) +#91 := [rewrite]: #90 +#88 := (iff #23 #87) +#81 := (ite false 0::Int 1::Int) +#84 := (= #81 1::Int) +#85 := [rewrite]: #84 +#82 := (= #21 #81) +#79 := (= #20 1::Int) +#56 := (and #12 #14) +#59 := (or #12 #56) +#74 := (ite #59 1::Int 1::Int) +#77 := (= #74 1::Int) +#78 := [rewrite]: #77 +#75 := (= #20 #74) +#72 := (= #19 1::Int) +#64 := -3::Int +#67 := (div -3::Int -3::Int) +#70 := (= #67 1::Int) +#71 := [rewrite]: #70 +#68 := (= #19 #67) +#65 := (= #18 -3::Int) +#66 := [rewrite]: #65 +#69 := [monotonicity #66 #66]: #68 +#73 := [trans #69 #71]: #72 +#62 := (= #17 1::Int) +#63 := [rewrite]: #62 +#60 := (iff #16 #59) +#57 := (iff #15 #56) +#58 := [rewrite]: #57 +#54 := (iff #13 #12) +#55 := [rewrite]: #54 +#61 := [monotonicity #55 #58]: #60 +#76 := [monotonicity #61 #63 #73]: #75 +#80 := [trans #76 #78]: #79 +#52 := (iff #11 false) +#47 := (or false false) +#50 := (iff #47 false) +#51 := [rewrite]: #50 +#48 := (iff #11 #47) +#45 := (iff #10 false) +#46 := [rewrite]: #45 +#49 := [monotonicity #46 #46]: #48 +#53 := [trans #49 #51]: #52 +#83 := [monotonicity #53 #80]: #82 +#86 := [trans #83 #85]: #23 +#89 := [monotonicity #86]: #88 +#93 := [trans #89 #91]: #92 +#96 := [monotonicity #93]: #95 +#100 := [trans #96 #98]: #99 +#44 := [asserted]: #24 +[mp #44 #100]: false +unsat +b2dbf88881de745f35b3193199fcda41f7406d84 115 0 +#2 := false +#26 := 1::Int +#11 := 3::Int +#22 := (- 3::Int) +#8 := 5::Int +#21 := (- 5::Int) +#23 := (div #21 #22) +#20 := (div 5::Int 3::Int) +#9 := 0::Int +#15 := (< 0::Int 3::Int) +#17 := (< 5::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 5::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#24 := (ite #19 #20 #23) +#12 := (= 3::Int 0::Int) +#10 := (= 5::Int 0::Int) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#27 := (= #25 1::Int) +#28 := (not #27) +#136 := (iff #28 false) +#60 := (and #15 #17) +#63 := (or #16 #60) +#99 := (not #63) +#134 := (iff #99 false) +#1 := true +#129 := (not true) +#132 := (iff #129 false) +#133 := [rewrite]: #132 +#130 := (iff #99 #129) +#127 := (iff #63 true) +#122 := (or true false) +#125 := (iff #122 true) +#126 := [rewrite]: #125 +#123 := (iff #63 #122) +#120 := (iff #60 false) +#115 := (and true false) +#118 := (iff #115 false) +#119 := [rewrite]: #118 +#116 := (iff #60 #115) +#113 := (iff #17 false) +#114 := [rewrite]: #113 +#104 := (iff #15 true) +#105 := [rewrite]: #104 +#117 := [monotonicity #105 #114]: #116 +#121 := [trans #117 #119]: #120 +#111 := (iff #16 true) +#106 := (and true true) +#109 := (iff #106 true) +#110 := [rewrite]: #109 +#107 := (iff #16 #106) +#102 := (iff #14 true) +#103 := [rewrite]: #102 +#108 := [monotonicity #103 #105]: #107 +#112 := [trans #108 #110]: #111 +#124 := [monotonicity #112 #121]: #123 +#128 := [trans #124 #126]: #127 +#131 := [monotonicity #128]: #130 +#135 := [trans #131 #133]: #134 +#100 := (iff #28 #99) +#97 := (iff #27 #63) +#77 := 2::Int +#82 := (ite #63 1::Int 2::Int) +#92 := (= #82 1::Int) +#95 := (iff #92 #63) +#96 := [rewrite]: #95 +#93 := (iff #27 #92) +#90 := (= #25 #82) +#85 := (ite false 0::Int #82) +#88 := (= #85 #82) +#89 := [rewrite]: #88 +#86 := (= #25 #85) +#83 := (= #24 #82) +#80 := (= #23 2::Int) +#71 := -3::Int +#68 := -5::Int +#74 := (div -5::Int -3::Int) +#78 := (= #74 2::Int) +#79 := [rewrite]: #78 +#75 := (= #23 #74) +#72 := (= #22 -3::Int) +#73 := [rewrite]: #72 +#69 := (= #21 -5::Int) +#70 := [rewrite]: #69 +#76 := [monotonicity #70 #73]: #75 +#81 := [trans #76 #79]: #80 +#66 := (= #20 1::Int) +#67 := [rewrite]: #66 +#64 := (iff #19 #63) +#61 := (iff #18 #60) +#62 := [rewrite]: #61 +#65 := [monotonicity #62]: #64 +#84 := [monotonicity #65 #67 #81]: #83 +#58 := (iff #13 false) +#53 := (or false false) +#56 := (iff #53 false) +#57 := [rewrite]: #56 +#54 := (iff #13 #53) +#51 := (iff #12 false) +#52 := [rewrite]: #51 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#55 := [monotonicity #50 #52]: #54 +#59 := [trans #55 #57]: #58 +#87 := [monotonicity #59 #84]: #86 +#91 := [trans #87 #89]: #90 +#94 := [monotonicity #91]: #93 +#98 := [trans #94 #96]: #97 +#101 := [monotonicity #98]: #100 +#137 := [trans #101 #135]: #136 +#48 := [asserted]: #28 +[mp #48 #137]: false +unsat +e8c50ca8f2d03b633ebd301c60837eeba13d5124 132 0 +#2 := false +#8 := 1::Int +#22 := (- 1::Int) +#11 := 3::Int +#12 := (- 3::Int) +#23 := (- #12) +#24 := (div #22 #23) +#21 := (div 1::Int #12) +#9 := 0::Int +#16 := (< 0::Int #12) +#18 := (< 1::Int 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int 1::Int) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= #12 0::Int) +#10 := (= 1::Int 0::Int) +#14 := (or #10 #13) +#26 := (ite #14 0::Int #25) +#27 := (= #26 #22) +#28 := (not #27) +#153 := (iff #28 false) +#51 := -3::Int +#68 := (< 0::Int -3::Int) +#74 := (and #18 #68) +#71 := (and #15 #68) +#77 := (or #71 #74) +#151 := (iff #77 false) +#61 := (or false false) +#64 := (iff #61 false) +#65 := [rewrite]: #64 +#149 := (iff #77 #61) +#147 := (iff #74 false) +#142 := (and false false) +#145 := (iff #142 false) +#146 := [rewrite]: #145 +#143 := (iff #74 #142) +#131 := (iff #68 false) +#132 := [rewrite]: #131 +#140 := (iff #18 false) +#141 := [rewrite]: #140 +#144 := [monotonicity #141 #132]: #143 +#148 := [trans #144 #146]: #147 +#138 := (iff #71 false) +#1 := true +#133 := (and true false) +#136 := (iff #133 false) +#137 := [rewrite]: #136 +#134 := (iff #71 #133) +#129 := (iff #15 true) +#130 := [rewrite]: #129 +#135 := [monotonicity #130 #132]: #134 +#139 := [trans #135 #137]: #138 +#150 := [monotonicity #139 #148]: #149 +#152 := [trans #150 #65]: #151 +#127 := (iff #28 #77) +#117 := (not #77) +#122 := (not #117) +#125 := (iff #122 #77) +#126 := [rewrite]: #125 +#123 := (iff #28 #122) +#120 := (iff #27 #117) +#87 := -1::Int +#104 := (ite #77 0::Int -1::Int) +#114 := (= #104 -1::Int) +#118 := (iff #114 #117) +#119 := [rewrite]: #118 +#115 := (iff #27 #114) +#88 := (= #22 -1::Int) +#89 := [rewrite]: #88 +#112 := (= #26 #104) +#107 := (ite false 0::Int #104) +#110 := (= #107 #104) +#111 := [rewrite]: #110 +#108 := (= #26 #107) +#105 := (= #25 #104) +#102 := (= #24 -1::Int) +#97 := (div -1::Int 3::Int) +#100 := (= #97 -1::Int) +#101 := [rewrite]: #100 +#98 := (= #24 #97) +#95 := (= #23 3::Int) +#90 := (- -3::Int) +#93 := (= #90 3::Int) +#94 := [rewrite]: #93 +#91 := (= #23 #90) +#52 := (= #12 -3::Int) +#53 := [rewrite]: #52 +#92 := [monotonicity #53]: #91 +#96 := [trans #92 #94]: #95 +#99 := [monotonicity #89 #96]: #98 +#103 := [trans #99 #101]: #102 +#85 := (= #21 0::Int) +#80 := (div 1::Int -3::Int) +#83 := (= #80 0::Int) +#84 := [rewrite]: #83 +#81 := (= #21 #80) +#82 := [monotonicity #53]: #81 +#86 := [trans #82 #84]: #85 +#78 := (iff #20 #77) +#75 := (iff #19 #74) +#69 := (iff #16 #68) +#70 := [monotonicity #53]: #69 +#76 := [monotonicity #70]: #75 +#72 := (iff #17 #71) +#73 := [monotonicity #70]: #72 +#79 := [monotonicity #73 #76]: #78 +#106 := [monotonicity #79 #86 #103]: #105 +#66 := (iff #14 false) +#62 := (iff #14 #61) +#59 := (iff #13 false) +#54 := (= -3::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #13 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#63 := [monotonicity #50 #60]: #62 +#67 := [trans #63 #65]: #66 +#109 := [monotonicity #67 #106]: #108 +#113 := [trans #109 #111]: #112 +#116 := [monotonicity #113 #89]: #115 +#121 := [trans #116 #119]: #120 +#124 := [monotonicity #121]: #123 +#128 := [trans #124 #126]: #127 +#154 := [trans #128 #152]: #153 +#48 := [asserted]: #28 +[mp #48 #154]: false +unsat +e161cbc5766adb3a07b2f61822dd61195f3dd163 109 0 +#2 := false +#25 := 1::Int +#26 := (- 1::Int) +#8 := 3::Int +#11 := (- 3::Int) +#21 := (- #11) +#22 := (div #11 #21) +#20 := (div 3::Int #11) +#9 := 0::Int +#15 := (< 0::Int #11) +#17 := (< 3::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 3::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#23 := (ite #19 #20 #22) +#12 := (= #11 0::Int) +#10 := (= 3::Int 0::Int) +#13 := (or #10 #12) +#24 := (ite #13 0::Int #23) +#27 := (= #24 #26) +#28 := (not #27) +#130 := (iff #28 false) +#1 := true +#125 := (not true) +#128 := (iff #125 false) +#129 := [rewrite]: #128 +#126 := (iff #28 #125) +#123 := (iff #27 true) +#83 := -1::Int +#118 := (= -1::Int -1::Int) +#121 := (iff #118 true) +#122 := [rewrite]: #121 +#119 := (iff #27 #118) +#116 := (= #26 -1::Int) +#117 := [rewrite]: #116 +#114 := (= #24 -1::Int) +#109 := (ite false 0::Int -1::Int) +#112 := (= #109 -1::Int) +#113 := [rewrite]: #112 +#110 := (= #24 #109) +#107 := (= #23 -1::Int) +#51 := -3::Int +#68 := (< 0::Int -3::Int) +#74 := (and #17 #68) +#71 := (and #14 #68) +#77 := (or #71 #74) +#102 := (ite #77 -1::Int -1::Int) +#105 := (= #102 -1::Int) +#106 := [rewrite]: #105 +#103 := (= #23 #102) +#100 := (= #22 -1::Int) +#95 := (div -3::Int 3::Int) +#98 := (= #95 -1::Int) +#99 := [rewrite]: #98 +#96 := (= #22 #95) +#93 := (= #21 3::Int) +#88 := (- -3::Int) +#91 := (= #88 3::Int) #92 := [rewrite]: #91 -#95 := [monotonicity #92]: #94 -#107 := [monotonicity #95 #104]: #106 -#110 := [monotonicity #107]: #109 -#113 := [monotonicity #110]: #112 -#116 := [quant-intro #113]: #115 -#151 := [trans #116 #149]: #150 -#89 := [asserted]: #34 -#152 := [mp #89 #151]: #147 -#201 := [mp~ #152 #210]: #147 -#232 := [mp #201 #231]: #229 -#263 := [mp #232 #262]: #260 -#756 := [mp #263 #755]: #751 -#10 := 3::Int -#67 := (f3 -1::Int 3::Int) -#70 := (= #67 -1::Int) -#83 := (not #70) +#89 := (= #21 #88) +#52 := (= #11 -3::Int) +#53 := [rewrite]: #52 +#90 := [monotonicity #53]: #89 +#94 := [trans #90 #92]: #93 +#97 := [monotonicity #53 #94]: #96 +#101 := [trans #97 #99]: #100 +#86 := (= #20 -1::Int) +#80 := (div 3::Int -3::Int) +#84 := (= #80 -1::Int) +#85 := [rewrite]: #84 +#81 := (= #20 #80) +#82 := [monotonicity #53]: #81 +#87 := [trans #82 #85]: #86 +#78 := (iff #19 #77) +#75 := (iff #18 #74) +#69 := (iff #15 #68) +#70 := [monotonicity #53]: #69 +#76 := [monotonicity #70]: #75 +#72 := (iff #16 #71) +#73 := [monotonicity #70]: #72 +#79 := [monotonicity #73 #76]: #78 +#104 := [monotonicity #79 #87 #101]: #103 +#108 := [trans #104 #106]: #107 +#66 := (iff #13 false) +#61 := (or false false) +#64 := (iff #61 false) +#65 := [rewrite]: #64 +#62 := (iff #13 #61) +#59 := (iff #12 false) +#54 := (= -3::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #12 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#63 := [monotonicity #50 #60]: #62 +#67 := [trans #63 #65]: #66 +#111 := [monotonicity #67 #108]: #110 +#115 := [trans #111 #113]: #114 +#120 := [monotonicity #115 #117]: #119 +#124 := [trans #120 #122]: #123 +#127 := [monotonicity #124]: #126 +#131 := [trans #127 #129]: #130 +#48 := [asserted]: #28 +[mp #48 #131]: false +unsat +17920425f93d8549a15817d71271ba90ab0e16ae 138 0 +#2 := false +#27 := 2::Int +#28 := (- 2::Int) +#11 := 3::Int +#12 := (- 3::Int) +#23 := (- #12) +#8 := 5::Int +#22 := (- 5::Int) +#24 := (div #22 #23) +#21 := (div 5::Int #12) +#9 := 0::Int +#16 := (< 0::Int #12) +#18 := (< 5::Int 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int 5::Int) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= #12 0::Int) +#10 := (= 5::Int 0::Int) +#14 := (or #10 #13) +#26 := (ite #14 0::Int #25) +#29 := (= #26 #28) +#30 := (not #29) +#159 := (iff #30 false) +#53 := -3::Int +#70 := (< 0::Int -3::Int) +#76 := (and #18 #70) +#73 := (and #15 #70) +#79 := (or #73 #76) +#157 := (iff #79 false) +#63 := (or false false) +#66 := (iff #63 false) +#67 := [rewrite]: #66 +#155 := (iff #79 #63) +#153 := (iff #76 false) +#148 := (and false false) +#151 := (iff #148 false) +#152 := [rewrite]: #151 +#149 := (iff #76 #148) +#137 := (iff #70 false) +#138 := [rewrite]: #137 +#146 := (iff #18 false) +#147 := [rewrite]: #146 +#150 := [monotonicity #147 #138]: #149 +#154 := [trans #150 #152]: #153 +#144 := (iff #73 false) +#1 := true +#139 := (and true false) +#142 := (iff #139 false) +#143 := [rewrite]: #142 +#140 := (iff #73 #139) +#135 := (iff #15 true) +#136 := [rewrite]: #135 +#141 := [monotonicity #136 #138]: #140 +#145 := [trans #141 #143]: #144 +#156 := [monotonicity #145 #154]: #155 +#158 := [trans #156 #67]: #157 +#133 := (iff #30 #79) +#123 := (not #79) +#128 := (not #123) +#131 := (iff #128 #79) +#132 := [rewrite]: #131 +#129 := (iff #30 #128) +#126 := (iff #29 #123) +#103 := -2::Int +#85 := -1::Int +#108 := (ite #79 -1::Int -2::Int) +#120 := (= #108 -2::Int) +#124 := (iff #120 #123) +#125 := [rewrite]: #124 +#121 := (iff #29 #120) +#118 := (= #28 -2::Int) +#119 := [rewrite]: #118 +#116 := (= #26 #108) +#111 := (ite false 0::Int #108) +#114 := (= #111 #108) +#115 := [rewrite]: #114 +#112 := (= #26 #111) +#109 := (= #25 #108) +#106 := (= #24 -2::Int) +#90 := -5::Int +#100 := (div -5::Int 3::Int) +#104 := (= #100 -2::Int) +#105 := [rewrite]: #104 +#101 := (= #24 #100) +#98 := (= #23 3::Int) +#93 := (- -3::Int) +#96 := (= #93 3::Int) +#97 := [rewrite]: #96 +#94 := (= #23 #93) +#54 := (= #12 -3::Int) +#55 := [rewrite]: #54 +#95 := [monotonicity #55]: #94 +#99 := [trans #95 #97]: #98 +#91 := (= #22 -5::Int) +#92 := [rewrite]: #91 +#102 := [monotonicity #92 #99]: #101 +#107 := [trans #102 #105]: #106 +#88 := (= #21 -1::Int) +#82 := (div 5::Int -3::Int) +#86 := (= #82 -1::Int) +#87 := [rewrite]: #86 +#83 := (= #21 #82) +#84 := [monotonicity #55]: #83 +#89 := [trans #84 #87]: #88 +#80 := (iff #20 #79) +#77 := (iff #19 #76) +#71 := (iff #16 #70) +#72 := [monotonicity #55]: #71 +#78 := [monotonicity #72]: #77 +#74 := (iff #17 #73) +#75 := [monotonicity #72]: #74 +#81 := [monotonicity #75 #78]: #80 +#110 := [monotonicity #81 #89 #107]: #109 +#68 := (iff #14 false) +#64 := (iff #14 #63) +#61 := (iff #13 false) +#56 := (= -3::Int 0::Int) +#59 := (iff #56 false) +#60 := [rewrite]: #59 +#57 := (iff #13 #56) +#58 := [monotonicity #55]: #57 +#62 := [trans #58 #60]: #61 +#51 := (iff #10 false) +#52 := [rewrite]: #51 +#65 := [monotonicity #52 #62]: #64 +#69 := [trans #65 #67]: #68 +#113 := [monotonicity #69 #110]: #112 +#117 := [trans #113 #115]: #116 +#122 := [monotonicity #117 #119]: #121 +#127 := [trans #122 #125]: #126 +#130 := [monotonicity #127]: #129 +#134 := [trans #130 #132]: #133 +#160 := [trans #134 #158]: #159 +#50 := [asserted]: #30 +[mp #50 #160]: false +unsat +a358eed5b14d12c6db4e25a50a2df755d735c9b5 150 0 +#2 := false +#8 := 1::Int +#9 := (- 1::Int) +#12 := 3::Int +#23 := (- 3::Int) +#22 := (- #9) +#24 := (div #22 #23) +#21 := (div #9 3::Int) +#10 := 0::Int +#16 := (< 0::Int 3::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= 3::Int 0::Int) +#11 := (= #9 0::Int) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#27 := (= #26 #9) +#28 := (not #27) +#171 := (iff #28 false) +#49 := -1::Int +#79 := (< -1::Int 0::Int) +#85 := (and #16 #79) +#68 := (< 0::Int -1::Int) +#74 := (and #16 #68) +#90 := (or #74 #85) +#134 := (not #90) +#169 := (iff #134 false) +#1 := true +#164 := (not true) +#167 := (iff #164 false) +#168 := [rewrite]: #167 +#165 := (iff #134 #164) +#162 := (iff #90 true) +#157 := (or false true) +#160 := (iff #157 true) +#161 := [rewrite]: #160 +#158 := (iff #90 #157) +#155 := (iff #85 true) +#150 := (and true true) +#153 := (iff #150 true) +#154 := [rewrite]: #153 +#151 := (iff #85 #150) +#148 := (iff #79 true) +#149 := [rewrite]: #148 +#137 := (iff #16 true) +#138 := [rewrite]: #137 +#152 := [monotonicity #138 #149]: #151 +#156 := [trans #152 #154]: #155 +#146 := (iff #74 false) +#141 := (and true false) +#144 := (iff #141 false) +#145 := [rewrite]: #144 +#142 := (iff #74 #141) +#139 := (iff #68 false) +#140 := [rewrite]: #139 +#143 := [monotonicity #138 #140]: #142 +#147 := [trans #143 #145]: #146 +#159 := [monotonicity #147 #156]: #158 +#163 := [trans #159 #161]: #162 +#166 := [monotonicity #163]: #165 +#170 := [trans #166 #168]: #169 +#135 := (iff #28 #134) +#132 := (iff #27 #90) +#117 := (ite #90 -1::Int 0::Int) +#127 := (= #117 -1::Int) +#130 := (iff #127 #90) +#131 := [rewrite]: #130 +#128 := (iff #27 #127) +#50 := (= #9 -1::Int) +#51 := [rewrite]: #50 +#125 := (= #26 #117) +#120 := (ite false 0::Int #117) +#123 := (= #120 #117) +#124 := [rewrite]: #123 +#121 := (= #26 #120) +#118 := (= #25 #117) +#115 := (= #24 0::Int) +#107 := -3::Int +#110 := (div 1::Int -3::Int) +#113 := (= #110 0::Int) +#114 := [rewrite]: #113 +#111 := (= #24 #110) +#108 := (= #23 -3::Int) +#109 := [rewrite]: #108 +#105 := (= #22 1::Int) +#100 := (- -1::Int) +#103 := (= #100 1::Int) +#104 := [rewrite]: #103 +#101 := (= #22 #100) +#102 := [monotonicity #51]: #101 +#106 := [trans #102 #104]: #105 +#112 := [monotonicity #106 #109]: #111 +#116 := [trans #112 #114]: #115 +#98 := (= #21 -1::Int) +#93 := (div -1::Int 3::Int) +#96 := (= #93 -1::Int) +#97 := [rewrite]: #96 +#94 := (= #21 #93) +#95 := [monotonicity #51]: #94 +#99 := [trans #95 #97]: #98 +#91 := (iff #20 #90) +#88 := (iff #19 #85) +#82 := (and #79 #16) +#86 := (iff #82 #85) +#87 := [rewrite]: #86 +#83 := (iff #19 #82) +#80 := (iff #18 #79) +#81 := [monotonicity #51]: #80 +#84 := [monotonicity #81]: #83 +#89 := [trans #84 #87]: #88 +#77 := (iff #17 #74) +#71 := (and #68 #16) +#75 := (iff #71 #74) +#76 := [rewrite]: #75 +#72 := (iff #17 #71) +#69 := (iff #15 #68) +#70 := [monotonicity #51]: #69 +#73 := [monotonicity #70]: #72 +#78 := [trans #73 #76]: #77 +#92 := [monotonicity #78 #89]: #91 +#119 := [monotonicity #92 #99 #116]: #118 +#66 := (iff #14 false) +#61 := (or false false) +#64 := (iff #61 false) +#65 := [rewrite]: #64 +#62 := (iff #14 #61) +#59 := (iff #13 false) +#60 := [rewrite]: #59 +#57 := (iff #11 false) +#52 := (= -1::Int 0::Int) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #11 #52) +#54 := [monotonicity #51]: #53 +#58 := [trans #54 #56]: #57 +#63 := [monotonicity #58 #60]: #62 +#67 := [trans #63 #65]: #66 +#122 := [monotonicity #67 #119]: #121 +#126 := [trans #122 #124]: #125 +#129 := [monotonicity #126 #51]: #128 +#133 := [trans #129 #131]: #132 +#136 := [monotonicity #133]: #135 +#172 := [trans #136 #170]: #171 +#48 := [asserted]: #28 +[mp #48 #172]: false +unsat +282152f210622b67ee14b9ad0372daa57d1c2fe0 122 0 +#2 := false +#25 := 1::Int +#26 := (- 1::Int) +#8 := 3::Int +#9 := (- 3::Int) +#21 := (- #9) +#22 := (div #21 #9) +#20 := (div #9 3::Int) +#10 := 0::Int +#15 := (< 0::Int 3::Int) +#17 := (< #9 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #9) +#16 := (and #14 #15) +#19 := (or #16 #18) +#23 := (ite #19 #20 #22) +#12 := (= 3::Int 0::Int) +#11 := (= #9 0::Int) +#13 := (or #11 #12) +#24 := (ite #13 0::Int #23) +#27 := (= #24 #26) +#28 := (not #27) +#143 := (iff #28 false) +#1 := true +#138 := (not true) +#141 := (iff #138 false) +#142 := [rewrite]: #141 +#139 := (iff #28 #138) +#136 := (iff #27 true) +#96 := -1::Int +#131 := (= -1::Int -1::Int) +#134 := (iff #131 true) +#135 := [rewrite]: #134 +#132 := (iff #27 #131) +#129 := (= #26 -1::Int) +#130 := [rewrite]: #129 +#127 := (= #24 -1::Int) +#122 := (ite false 0::Int -1::Int) +#125 := (= #122 -1::Int) +#126 := [rewrite]: #125 +#123 := (= #24 #122) +#120 := (= #23 -1::Int) +#49 := -3::Int +#79 := (< -3::Int 0::Int) +#85 := (and #15 #79) +#68 := (< 0::Int -3::Int) +#74 := (and #15 #68) +#90 := (or #74 #85) +#115 := (ite #90 -1::Int -1::Int) +#118 := (= #115 -1::Int) +#119 := [rewrite]: #118 +#116 := (= #23 #115) +#113 := (= #22 -1::Int) +#108 := (div 3::Int -3::Int) +#111 := (= #108 -1::Int) +#112 := [rewrite]: #111 +#109 := (= #22 #108) +#50 := (= #9 -3::Int) +#51 := [rewrite]: #50 +#106 := (= #21 3::Int) +#101 := (- -3::Int) +#104 := (= #101 3::Int) +#105 := [rewrite]: #104 +#102 := (= #21 #101) +#103 := [monotonicity #51]: #102 +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107 #51]: #109 +#114 := [trans #110 #112]: #113 +#99 := (= #20 -1::Int) +#93 := (div -3::Int 3::Int) +#97 := (= #93 -1::Int) +#98 := [rewrite]: #97 +#94 := (= #20 #93) +#95 := [monotonicity #51]: #94 +#100 := [trans #95 #98]: #99 +#91 := (iff #19 #90) +#88 := (iff #18 #85) +#82 := (and #79 #15) +#86 := (iff #82 #85) +#87 := [rewrite]: #86 +#83 := (iff #18 #82) +#80 := (iff #17 #79) +#81 := [monotonicity #51]: #80 +#84 := [monotonicity #81]: #83 +#89 := [trans #84 #87]: #88 +#77 := (iff #16 #74) +#71 := (and #68 #15) +#75 := (iff #71 #74) +#76 := [rewrite]: #75 +#72 := (iff #16 #71) +#69 := (iff #14 #68) +#70 := [monotonicity #51]: #69 +#73 := [monotonicity #70]: #72 +#78 := [trans #73 #76]: #77 +#92 := [monotonicity #78 #89]: #91 +#117 := [monotonicity #92 #100 #114]: #116 +#121 := [trans #117 #119]: #120 +#66 := (iff #13 false) +#61 := (or false false) +#64 := (iff #61 false) +#65 := [rewrite]: #64 +#62 := (iff #13 #61) +#59 := (iff #12 false) +#60 := [rewrite]: #59 +#57 := (iff #11 false) +#52 := (= -3::Int 0::Int) +#55 := (iff #52 false) +#56 := [rewrite]: #55 +#53 := (iff #11 #52) +#54 := [monotonicity #51]: #53 +#58 := [trans #54 #56]: #57 +#63 := [monotonicity #58 #60]: #62 +#67 := [trans #63 #65]: #66 +#124 := [monotonicity #67 #121]: #123 +#128 := [trans #124 #126]: #127 +#133 := [monotonicity #128 #130]: #132 +#137 := [trans #133 #135]: #136 +#140 := [monotonicity #137]: #139 +#144 := [trans #140 #142]: #143 +#48 := [asserted]: #28 +[mp #48 #144]: false +unsat +09bd21e8184625daa5375adf22f60c439ab0cf17 156 0 +#2 := false +#27 := 2::Int +#28 := (- 2::Int) +#12 := 3::Int +#23 := (- 3::Int) +#8 := 5::Int +#9 := (- 5::Int) +#22 := (- #9) +#24 := (div #22 #23) +#21 := (div #9 3::Int) +#10 := 0::Int +#16 := (< 0::Int 3::Int) +#18 := (< #9 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #9) +#17 := (and #15 #16) +#20 := (or #17 #19) +#25 := (ite #20 #21 #24) +#13 := (= 3::Int 0::Int) +#11 := (= #9 0::Int) +#14 := (or #11 #13) +#26 := (ite #14 0::Int #25) +#29 := (= #26 #28) +#30 := (not #29) +#177 := (iff #30 false) +#51 := -5::Int +#81 := (< -5::Int 0::Int) +#87 := (and #16 #81) +#70 := (< 0::Int -5::Int) +#76 := (and #16 #70) +#92 := (or #76 #87) +#140 := (not #92) +#175 := (iff #140 false) +#1 := true +#170 := (not true) +#173 := (iff #170 false) +#174 := [rewrite]: #173 +#171 := (iff #140 #170) +#168 := (iff #92 true) +#163 := (or false true) +#166 := (iff #163 true) +#167 := [rewrite]: #166 +#164 := (iff #92 #163) +#161 := (iff #87 true) +#156 := (and true true) +#159 := (iff #156 true) +#160 := [rewrite]: #159 +#157 := (iff #87 #156) +#154 := (iff #81 true) +#155 := [rewrite]: #154 +#143 := (iff #16 true) +#144 := [rewrite]: #143 +#158 := [monotonicity #144 #155]: #157 +#162 := [trans #158 #160]: #161 +#152 := (iff #76 false) +#147 := (and true false) +#150 := (iff #147 false) +#151 := [rewrite]: #150 +#148 := (iff #76 #147) +#145 := (iff #70 false) +#146 := [rewrite]: #145 +#149 := [monotonicity #144 #146]: #148 +#153 := [trans #149 #151]: #152 +#165 := [monotonicity #153 #162]: #164 +#169 := [trans #165 #167]: #168 +#172 := [monotonicity #169]: #171 +#176 := [trans #172 #174]: #175 +#141 := (iff #30 #140) +#138 := (iff #29 #92) +#98 := -2::Int +#116 := -1::Int +#121 := (ite #92 -2::Int -1::Int) +#133 := (= #121 -2::Int) +#136 := (iff #133 #92) +#137 := [rewrite]: #136 +#134 := (iff #29 #133) +#131 := (= #28 -2::Int) +#132 := [rewrite]: #131 +#129 := (= #26 #121) +#124 := (ite false 0::Int #121) +#127 := (= #124 #121) +#128 := [rewrite]: #127 +#125 := (= #26 #124) +#122 := (= #25 #121) +#119 := (= #24 -1::Int) +#110 := -3::Int +#113 := (div 5::Int -3::Int) +#117 := (= #113 -1::Int) +#118 := [rewrite]: #117 +#114 := (= #24 #113) +#111 := (= #23 -3::Int) +#112 := [rewrite]: #111 +#108 := (= #22 5::Int) +#103 := (- -5::Int) +#106 := (= #103 5::Int) +#107 := [rewrite]: #106 +#104 := (= #22 #103) +#52 := (= #9 -5::Int) +#53 := [rewrite]: #52 +#105 := [monotonicity #53]: #104 +#109 := [trans #105 #107]: #108 +#115 := [monotonicity #109 #112]: #114 +#120 := [trans #115 #118]: #119 +#101 := (= #21 -2::Int) +#95 := (div -5::Int 3::Int) +#99 := (= #95 -2::Int) +#100 := [rewrite]: #99 +#96 := (= #21 #95) +#97 := [monotonicity #53]: #96 +#102 := [trans #97 #100]: #101 +#93 := (iff #20 #92) +#90 := (iff #19 #87) +#84 := (and #81 #16) +#88 := (iff #84 #87) +#89 := [rewrite]: #88 +#85 := (iff #19 #84) +#82 := (iff #18 #81) +#83 := [monotonicity #53]: #82 +#86 := [monotonicity #83]: #85 +#91 := [trans #86 #89]: #90 +#79 := (iff #17 #76) +#73 := (and #70 #16) +#77 := (iff #73 #76) +#78 := [rewrite]: #77 +#74 := (iff #17 #73) +#71 := (iff #15 #70) +#72 := [monotonicity #53]: #71 +#75 := [monotonicity #72]: #74 +#80 := [trans #75 #78]: #79 +#94 := [monotonicity #80 #91]: #93 +#123 := [monotonicity #94 #102 #120]: #122 +#68 := (iff #14 false) +#63 := (or false false) +#66 := (iff #63 false) +#67 := [rewrite]: #66 +#64 := (iff #14 #63) +#61 := (iff #13 false) +#62 := [rewrite]: #61 +#59 := (iff #11 false) +#54 := (= -5::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #11 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#65 := [monotonicity #60 #62]: #64 +#69 := [trans #65 #67]: #68 +#126 := [monotonicity #69 #123]: #125 +#130 := [trans #126 #128]: #129 +#135 := [monotonicity #130 #132]: #134 +#139 := [trans #135 #137]: #138 +#142 := [monotonicity #139]: #141 +#178 := [trans #142 #176]: #177 +#50 := [asserted]: #30 +[mp #50 #178]: false +unsat +75a498a3ae15008c6ba6962bb8ff41e876585e27 156 0 +#2 := false +#10 := 0::Int +#12 := 3::Int +#13 := (- 3::Int) +#24 := (- #13) #8 := 1::Int #9 := (- 1::Int) -#11 := (f3 #9 3::Int) -#12 := (= #11 #9) -#13 := (not #12) -#86 := (iff #13 #83) -#73 := (= -1::Int #67) -#78 := (not #73) -#84 := (iff #78 #83) -#81 := (iff #73 #70) -#82 := [rewrite]: #81 -#85 := [monotonicity #82]: #84 -#79 := (iff #13 #78) -#76 := (iff #12 #73) -#74 := (iff #70 #73) -#75 := [rewrite]: #74 -#71 := (iff #12 #70) -#65 := (= #9 -1::Int) -#66 := [rewrite]: #65 -#68 := (= #11 #67) -#69 := [monotonicity #66]: #68 -#72 := [monotonicity #69 #66]: #71 -#77 := [trans #72 #75]: #76 -#80 := [monotonicity #77]: #79 -#87 := [trans #80 #85]: #86 -#63 := [asserted]: #13 -#88 := [mp #63 #87]: #83 -#676 := (not #751) -#677 := (or #676 #70) -#337 := (* -1::Int 3::Int) -#421 := (* -1::Int -1::Int) -#422 := (div #421 #337) -#423 := (* -1::Int #422) -#414 := (+ #67 #423) -#425 := (= #414 0::Int) -#426 := (div -1::Int 3::Int) -#427 := (* -1::Int #426) -#424 := (+ #67 #427) -#428 := (= #424 0::Int) -#407 := (>= -1::Int 0::Int) -#742 := (<= 3::Int 0::Int) -#744 := (or #742 #407) -#401 := (not #744) -#531 := (<= -1::Int 0::Int) -#738 := (or #531 #742) -#412 := (not #738) -#413 := (or #412 #401) -#745 := (ite #413 #428 #425) -#746 := (= #67 0::Int) -#747 := (= 3::Int 0::Int) -#748 := (= -1::Int 0::Int) -#743 := (or #748 #747) -#749 := (ite #743 #746 #745) -#673 := (or #676 #749) -#667 := (iff #673 #677) -#669 := (iff #677 #677) -#670 := [rewrite]: #669 -#665 := (iff #749 #70) -#685 := (ite false #746 #70) -#666 := (iff #685 #70) -#663 := [rewrite]: #666 -#672 := (iff #749 #685) -#684 := (iff #745 #70) -#1 := true -#587 := (ite true #70 #746) -#590 := (iff #587 #70) -#591 := [rewrite]: #590 -#588 := (iff #745 #587) -#586 := (iff #425 #746) -#583 := (= #414 #67) -#584 := (+ #67 0::Int) -#683 := (= #584 #67) -#568 := [rewrite]: #683 -#679 := (= #414 #584) -#534 := (= #423 0::Int) -#688 := (* -1::Int 0::Int) -#574 := (= #688 0::Int) -#575 := [rewrite]: #574 -#691 := (= #423 #688) -#689 := (= #422 0::Int) -#700 := -3::Int -#530 := (div 1::Int -3::Int) -#686 := (= #530 0::Int) -#687 := [rewrite]: #686 -#532 := (= #422 #530) -#694 := (= #337 -3::Int) -#701 := [rewrite]: #694 -#705 := (= #421 1::Int) -#706 := [rewrite]: #705 -#533 := [monotonicity #706 #701]: #532 -#690 := [trans #533 #687]: #689 -#573 := [monotonicity #690]: #691 -#682 := [trans #573 #575]: #534 -#680 := [monotonicity #682]: #679 -#585 := [trans #680 #568]: #583 -#579 := [monotonicity #585]: #586 -#693 := (iff #428 #70) -#704 := (+ 1::Int #67) -#695 := (= #704 0::Int) -#698 := (iff #695 #70) -#692 := [rewrite]: #698 -#696 := (iff #428 #695) -#552 := (= #424 #704) -#703 := (+ #67 1::Int) -#710 := (= #703 #704) -#551 := [rewrite]: #710 -#708 := (= #424 #703) -#707 := (= #427 1::Int) -#712 := (= #427 #421) -#711 := (= #426 -1::Int) -#715 := [rewrite]: #711 -#716 := [monotonicity #715]: #712 -#702 := [trans #716 #706]: #707 -#709 := [monotonicity #702]: #708 -#553 := [trans #709 #551]: #552 -#697 := [monotonicity #553]: #696 -#699 := [trans #697 #692]: #693 -#714 := (iff #413 true) -#432 := (or false true) -#435 := (iff #432 true) -#713 := [rewrite]: #435 -#433 := (iff #413 #432) -#718 := (iff #401 true) -#720 := (not false) -#717 := (iff #720 true) -#721 := [rewrite]: #717 -#442 := (iff #401 #720) -#343 := (iff #744 false) -#400 := (or false false) -#725 := (iff #400 false) -#388 := [rewrite]: #725 -#448 := (iff #744 #400) -#446 := (iff #407 false) -#447 := [rewrite]: #446 -#728 := (iff #742 false) -#729 := [rewrite]: #728 -#449 := [monotonicity #729 #447]: #448 -#719 := [trans #449 #388]: #343 -#443 := [monotonicity #719]: #442 -#722 := [trans #443 #721]: #718 -#723 := (iff #412 false) -#375 := (not true) -#734 := (iff #375 false) -#737 := [rewrite]: #734 -#376 := (iff #412 #375) -#733 := (iff #738 true) -#730 := (or true false) -#732 := (iff #730 true) -#370 := [rewrite]: #732 -#731 := (iff #738 #730) -#391 := (iff #531 true) -#727 := [rewrite]: #391 -#726 := [monotonicity #727 #729]: #731 -#735 := [trans #726 #370]: #733 -#736 := [monotonicity #735]: #376 -#724 := [trans #736 #737]: #723 -#434 := [monotonicity #724 #722]: #433 -#429 := [trans #434 #713]: #714 -#589 := [monotonicity #429 #699 #579]: #588 -#681 := [trans #589 #591]: #684 -#389 := (iff #743 false) -#741 := (iff #743 #400) -#404 := (iff #747 false) -#740 := [rewrite]: #404 -#739 := (iff #748 false) -#399 := [rewrite]: #739 -#384 := [monotonicity #399 #740]: #741 -#390 := [trans #384 #388]: #389 -#674 := [monotonicity #390 #681]: #672 -#675 := [trans #674 #663]: #665 -#668 := [monotonicity #675]: #667 -#664 := [trans #668 #670]: #667 -#678 := [quant-inst #64 #10]: #673 -#671 := [mp #678 #664]: #677 -[unit-resolution #671 #88 #756]: false -unsat -896650ef8f75fd8ef47b1c1a736049dce2114a91 309 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#17 := (f3 #15 #16) -#742 := (pattern #17) -#18 := 0::Int -#71 := -1::Int -#91 := (* -1::Int #16) -#88 := (* -1::Int #15) -#94 := (div #88 #91) -#245 := (* -1::Int #94) -#246 := (+ #17 #245) -#247 := (= #246 0::Int) -#28 := (div #15 #16) -#242 := (* -1::Int #28) -#243 := (+ #17 #242) -#244 := (= #243 0::Int) -#120 := (>= #15 0::Int) -#113 := (<= #16 0::Int) -#205 := (or #113 #120) -#206 := (not #205) -#109 := (<= #15 0::Int) -#203 := (or #109 #113) -#204 := (not #203) -#209 := (or #204 #206) -#248 := (ite #209 #244 #247) -#241 := (= #17 0::Int) -#20 := (= #16 0::Int) -#19 := (= #15 0::Int) -#21 := (or #19 #20) -#249 := (ite #21 #241 #248) -#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249) -#252 := (forall (vars (?v0 Int) (?v1 Int)) #249) -#746 := (iff #252 #743) -#744 := (iff #249 #249) -#745 := [refl]: #744 -#747 := [quant-intro #745]: #746 -#212 := (ite #209 #28 #94) -#215 := (ite #21 0::Int #212) -#218 := (= #17 #215) -#221 := (forall (vars (?v0 Int) (?v1 Int)) #218) -#253 := (iff #221 #252) -#250 := (iff #218 #249) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#121 := (not #120) -#114 := (not #113) -#124 := (and #114 #121) -#110 := (not #109) -#117 := (and #110 #114) -#127 := (or #117 #124) -#130 := (ite #127 #28 #94) -#133 := (ite #21 0::Int #130) -#136 := (= #17 #133) -#139 := (forall (vars (?v0 Int) (?v1 Int)) #136) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#216 := (= #133 #215) -#213 := (= #130 #212) -#210 := (iff #127 #209) -#207 := (iff #124 #206) -#208 := [rewrite]: #207 -#197 := (iff #117 #204) -#198 := [rewrite]: #197 -#211 := [monotonicity #198 #208]: #210 -#214 := [monotonicity #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [quant-intro #220]: #222 -#201 := (~ #139 #139) -#199 := (~ #136 #136) -#200 := [refl]: #199 -#202 := [nnf-pos #200]: #201 -#30 := (- #16) -#29 := (- #15) -#31 := (div #29 #30) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #17 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#142 := (iff #35 #139) -#81 := (and #23 #25) -#85 := (or #24 #81) -#97 := (ite #85 #28 #94) -#100 := (ite #21 0::Int #97) -#103 := (= #17 #100) -#106 := (forall (vars (?v0 Int) (?v1 Int)) #103) -#140 := (iff #106 #139) -#137 := (iff #103 #136) -#134 := (= #100 #133) -#131 := (= #97 #130) -#128 := (iff #85 #127) -#125 := (iff #81 #124) -#122 := (iff #25 #121) -#123 := [rewrite]: #122 -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#126 := [monotonicity #116 #123]: #125 -#118 := (iff #24 #117) -#111 := (iff #22 #110) -#112 := [rewrite]: #111 -#119 := [monotonicity #112 #116]: #118 -#129 := [monotonicity #119 #126]: #128 -#132 := [monotonicity #129]: #131 -#135 := [monotonicity #132]: #134 -#138 := [monotonicity #135]: #137 -#141 := [quant-intro #138]: #140 -#107 := (iff #35 #106) -#104 := (iff #34 #103) -#101 := (= #33 #100) -#98 := (= #32 #97) -#95 := (= #31 #94) -#92 := (= #30 #91) -#93 := [rewrite]: #92 -#89 := (= #29 #88) -#90 := [rewrite]: #89 -#96 := [monotonicity #90 #93]: #95 -#86 := (iff #27 #85) -#83 := (iff #26 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#99 := [monotonicity #87 #96]: #98 -#102 := [monotonicity #99]: #101 -#105 := [monotonicity #102]: #104 -#108 := [quant-intro #105]: #107 -#143 := [trans #108 #141]: #142 -#80 := [asserted]: #35 -#144 := [mp #80 #143]: #139 -#193 := [mp~ #144 #202]: #139 -#224 := [mp #193 #223]: #221 -#255 := [mp #224 #254]: #252 -#748 := [mp #255 #747]: #743 +#23 := (- #9) +#25 := (div #23 #24) +#22 := (div #9 #13) +#17 := (< 0::Int #13) +#19 := (< #9 0::Int) +#20 := (and #19 #17) +#16 := (< 0::Int #9) +#18 := (and #16 #17) +#21 := (or #18 #20) +#26 := (ite #21 #22 #25) +#14 := (= #13 0::Int) +#11 := (= #9 0::Int) +#15 := (or #11 #14) +#27 := (ite #15 0::Int #26) +#28 := (= #27 0::Int) +#29 := (not #28) +#177 := (iff #29 false) +#50 := -1::Int +#86 := (< -1::Int 0::Int) +#60 := -3::Int +#80 := (< 0::Int -3::Int) +#92 := (and #80 #86) +#77 := (< 0::Int -1::Int) +#83 := (and #77 #80) +#97 := (or #83 #92) +#175 := (iff #97 false) +#70 := (or false false) +#73 := (iff #70 false) +#74 := [rewrite]: #73 +#173 := (iff #97 #70) +#171 := (iff #92 false) +#1 := true +#166 := (and false true) +#169 := (iff #166 false) +#170 := [rewrite]: #169 +#167 := (iff #92 #166) +#164 := (iff #86 true) +#165 := [rewrite]: #164 +#155 := (iff #80 false) +#156 := [rewrite]: #155 +#168 := [monotonicity #156 #165]: #167 +#172 := [trans #168 #170]: #171 +#162 := (iff #83 false) +#157 := (and false false) +#160 := (iff #157 false) +#161 := [rewrite]: #160 +#158 := (iff #83 #157) +#153 := (iff #77 false) +#154 := [rewrite]: #153 +#159 := [monotonicity #154 #156]: #158 +#163 := [trans #159 #161]: #162 +#174 := [monotonicity #163 #172]: #173 +#176 := [trans #174 #74]: #175 +#151 := (iff #29 #97) +#141 := (not #97) +#146 := (not #141) +#149 := (iff #146 #97) +#150 := [rewrite]: #149 +#147 := (iff #29 #146) +#144 := (iff #28 #141) +#128 := (ite #97 1::Int 0::Int) +#138 := (= #128 0::Int) +#142 := (iff #138 #141) +#143 := [rewrite]: #142 +#139 := (iff #28 #138) +#136 := (= #27 #128) +#131 := (ite false 0::Int #128) +#134 := (= #131 #128) +#135 := [rewrite]: #134 +#132 := (= #27 #131) +#129 := (= #26 #128) +#126 := (= #25 0::Int) +#121 := (div 1::Int 3::Int) +#124 := (= #121 0::Int) +#125 := [rewrite]: #124 +#122 := (= #25 #121) +#119 := (= #24 3::Int) +#114 := (- -3::Int) +#117 := (= #114 3::Int) +#118 := [rewrite]: #117 +#115 := (= #24 #114) +#61 := (= #13 -3::Int) +#62 := [rewrite]: #61 +#116 := [monotonicity #62]: #115 +#120 := [trans #116 #118]: #119 +#112 := (= #23 1::Int) +#107 := (- -1::Int) +#110 := (= #107 1::Int) +#111 := [rewrite]: #110 +#108 := (= #23 #107) +#51 := (= #9 -1::Int) +#52 := [rewrite]: #51 +#109 := [monotonicity #52]: #108 +#113 := [trans #109 #111]: #112 +#123 := [monotonicity #113 #120]: #122 +#127 := [trans #123 #125]: #126 +#105 := (= #22 1::Int) +#100 := (div -1::Int -3::Int) +#103 := (= #100 1::Int) +#104 := [rewrite]: #103 +#101 := (= #22 #100) +#102 := [monotonicity #52 #62]: #101 +#106 := [trans #102 #104]: #105 +#98 := (iff #21 #97) +#95 := (iff #20 #92) +#89 := (and #86 #80) +#93 := (iff #89 #92) +#94 := [rewrite]: #93 +#90 := (iff #20 #89) +#81 := (iff #17 #80) +#82 := [monotonicity #62]: #81 +#87 := (iff #19 #86) +#88 := [monotonicity #52]: #87 +#91 := [monotonicity #88 #82]: #90 +#96 := [trans #91 #94]: #95 +#84 := (iff #18 #83) +#78 := (iff #16 #77) +#79 := [monotonicity #52]: #78 +#85 := [monotonicity #79 #82]: #84 +#99 := [monotonicity #85 #96]: #98 +#130 := [monotonicity #99 #106 #127]: #129 +#75 := (iff #15 false) +#71 := (iff #15 #70) +#68 := (iff #14 false) +#63 := (= -3::Int 0::Int) +#66 := (iff #63 false) +#67 := [rewrite]: #66 +#64 := (iff #14 #63) +#65 := [monotonicity #62]: #64 +#69 := [trans #65 #67]: #68 +#58 := (iff #11 false) +#53 := (= -1::Int 0::Int) +#56 := (iff #53 false) +#57 := [rewrite]: #56 +#54 := (iff #11 #53) +#55 := [monotonicity #52]: #54 +#59 := [trans #55 #57]: #58 +#72 := [monotonicity #59 #69]: #71 +#76 := [trans #72 #74]: #75 +#133 := [monotonicity #76 #130]: #132 +#137 := [trans #133 #135]: #136 +#140 := [monotonicity #137]: #139 +#145 := [trans #140 #143]: #144 +#148 := [monotonicity #145]: #147 +#152 := [trans #148 #150]: #151 +#178 := [trans #152 #176]: #177 +#49 := [asserted]: #29 +[mp #49 #178]: false +unsat +b0f55b14153bd1415b180d8eb26a6650d8024f22 112 0 +#2 := false +#23 := 1::Int #8 := 3::Int -#65 := -3::Int -#68 := (f3 -3::Int 3::Int) -#74 := (= #68 -1::Int) -#77 := (not #74) -#11 := 1::Int -#12 := (- 1::Int) #9 := (- 3::Int) -#10 := (f3 #9 3::Int) -#13 := (= #10 #12) -#14 := (not #13) -#78 := (iff #14 #77) -#75 := (iff #13 #74) -#72 := (= #12 -1::Int) -#73 := [rewrite]: #72 -#69 := (= #10 #68) -#66 := (= #9 -3::Int) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#76 := [monotonicity #70 #73]: #75 -#79 := [monotonicity #76]: #78 -#64 := [asserted]: #14 -#82 := [mp #64 #79]: #77 -#657 := (not #743) -#667 := (or #657 #74) -#329 := (* -1::Int 3::Int) -#413 := (* -1::Int -3::Int) -#414 := (div #413 #329) -#415 := (* -1::Int #414) -#406 := (+ #68 #415) -#417 := (= #406 0::Int) -#418 := (div -3::Int 3::Int) -#419 := (* -1::Int #418) -#416 := (+ #68 #419) -#420 := (= #416 0::Int) -#399 := (>= -3::Int 0::Int) -#734 := (<= 3::Int 0::Int) -#736 := (or #734 #399) -#393 := (not #736) -#523 := (<= -3::Int 0::Int) -#730 := (or #523 #734) -#404 := (not #730) -#405 := (or #404 #393) -#737 := (ite #405 #420 #417) -#738 := (= #68 0::Int) -#739 := (= 3::Int 0::Int) -#740 := (= -3::Int 0::Int) -#735 := (or #740 #739) -#741 := (ite #735 #738 #737) -#668 := (or #657 #741) -#665 := (iff #668 #667) -#659 := (iff #667 #667) -#660 := [rewrite]: #659 -#658 := (iff #741 #74) -#676 := (ite false #738 #74) -#664 := (iff #676 #74) -#666 := [rewrite]: #664 -#673 := (iff #741 #676) -#582 := (iff #737 #74) -#1 := true -#578 := (ite true #74 #74) -#580 := (iff #578 #74) -#581 := [rewrite]: #580 -#571 := (iff #737 #578) -#575 := (iff #417 #74) -#702 := (+ 1::Int #68) -#688 := (= #702 0::Int) -#684 := (iff #688 #74) -#685 := [rewrite]: #684 -#675 := (iff #417 #688) -#671 := (= #406 #702) -#700 := (+ #68 1::Int) -#543 := (= #700 #702) -#544 := [rewrite]: #543 -#674 := (= #406 #700) -#567 := (= #415 1::Int) -#704 := (* -1::Int -1::Int) -#698 := (= #704 1::Int) -#699 := [rewrite]: #698 -#565 := (= #415 #704) -#680 := (= #414 -1::Int) -#525 := (div 3::Int -3::Int) -#681 := (= #525 -1::Int) -#682 := [rewrite]: #681 -#678 := (= #414 #525) -#522 := (= #329 -3::Int) -#524 := [rewrite]: #522 -#686 := (= #413 3::Int) -#693 := [rewrite]: #686 -#679 := [monotonicity #693 #524]: #678 -#683 := [trans #679 #682]: #680 -#566 := [monotonicity #683]: #565 -#526 := [trans #566 #699]: #567 -#576 := [monotonicity #526]: #674 -#672 := [trans #576 #544]: #671 -#560 := [monotonicity #672]: #675 -#577 := [trans #560 #685]: #575 -#691 := (iff #420 #74) -#689 := (iff #420 #688) -#545 := (= #416 #702) -#701 := (= #416 #700) -#694 := (= #419 1::Int) -#708 := (= #419 #704) -#703 := (= #418 -1::Int) -#707 := [rewrite]: #703 -#697 := [monotonicity #707]: #708 -#695 := [trans #697 #699]: #694 -#696 := [monotonicity #695]: #701 -#687 := [trans #696 #544]: #545 -#690 := [monotonicity #687]: #689 -#692 := [trans #690 #685]: #691 -#706 := (iff #405 true) -#424 := (or false true) -#427 := (iff #424 true) -#705 := [rewrite]: #427 -#425 := (iff #405 #424) -#710 := (iff #393 true) -#712 := (not false) -#709 := (iff #712 true) -#713 := [rewrite]: #709 -#434 := (iff #393 #712) -#335 := (iff #736 false) -#392 := (or false false) -#717 := (iff #392 false) -#380 := [rewrite]: #717 -#440 := (iff #736 #392) -#438 := (iff #399 false) -#439 := [rewrite]: #438 -#720 := (iff #734 false) -#721 := [rewrite]: #720 -#441 := [monotonicity #721 #439]: #440 -#711 := [trans #441 #380]: #335 -#435 := [monotonicity #711]: #434 -#714 := [trans #435 #713]: #710 -#715 := (iff #404 false) -#367 := (not true) -#726 := (iff #367 false) -#729 := [rewrite]: #726 -#368 := (iff #404 #367) -#725 := (iff #730 true) -#722 := (or true false) -#724 := (iff #722 true) -#362 := [rewrite]: #724 -#723 := (iff #730 #722) -#383 := (iff #523 true) -#719 := [rewrite]: #383 -#718 := [monotonicity #719 #721]: #723 -#727 := [trans #718 #362]: #725 -#728 := [monotonicity #727]: #368 -#716 := [trans #728 #729]: #715 -#426 := [monotonicity #716 #714]: #425 -#421 := [trans #426 #705]: #706 -#579 := [monotonicity #421 #692 #577]: #571 -#583 := [trans #579 #581]: #582 -#381 := (iff #735 false) -#733 := (iff #735 #392) -#396 := (iff #739 false) -#732 := [rewrite]: #396 -#731 := (iff #740 false) -#391 := [rewrite]: #731 -#376 := [monotonicity #391 #732]: #733 -#382 := [trans #376 #380]: #381 -#677 := [monotonicity #382 #583]: #673 -#655 := [trans #677 #666]: #658 -#670 := [monotonicity #655]: #665 -#661 := [trans #670 #660]: #665 -#669 := [quant-inst #65 #8]: #668 -#662 := [mp #669 #661]: #667 -[unit-resolution #662 #82 #748]: false -unsat -5e9e5ffc31aa8934508da0815460298eed868a8c 324 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#18 := (f3 #16 #17) -#745 := (pattern #18) -#19 := 0::Int -#89 := -1::Int -#93 := (* -1::Int #17) -#90 := (* -1::Int #16) -#96 := (div #90 #93) -#247 := (* -1::Int #96) -#248 := (+ #18 #247) -#249 := (= #248 0::Int) -#29 := (div #16 #17) -#244 := (* -1::Int #29) -#245 := (+ #18 #244) -#246 := (= #245 0::Int) -#122 := (>= #16 0::Int) -#115 := (<= #17 0::Int) -#207 := (or #115 #122) -#208 := (not #207) -#111 := (<= #16 0::Int) -#205 := (or #111 #115) -#206 := (not #205) -#211 := (or #206 #208) -#250 := (ite #211 #246 #249) -#243 := (= #18 0::Int) -#21 := (= #17 0::Int) -#20 := (= #16 0::Int) -#22 := (or #20 #21) -#251 := (ite #22 #243 #250) -#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251) -#254 := (forall (vars (?v0 Int) (?v1 Int)) #251) -#749 := (iff #254 #746) -#747 := (iff #251 #251) -#748 := [refl]: #747 -#750 := [quant-intro #748]: #749 -#214 := (ite #211 #29 #96) -#217 := (ite #22 0::Int #214) -#220 := (= #18 #217) -#223 := (forall (vars (?v0 Int) (?v1 Int)) #220) -#255 := (iff #223 #254) -#252 := (iff #220 #251) -#253 := [rewrite]: #252 -#256 := [quant-intro #253]: #255 -#123 := (not #122) -#116 := (not #115) -#126 := (and #116 #123) -#112 := (not #111) -#119 := (and #112 #116) -#129 := (or #119 #126) -#132 := (ite #129 #29 #96) -#135 := (ite #22 0::Int #132) -#138 := (= #18 #135) -#141 := (forall (vars (?v0 Int) (?v1 Int)) #138) -#224 := (iff #141 #223) -#221 := (iff #138 #220) -#218 := (= #135 #217) -#215 := (= #132 #214) -#212 := (iff #129 #211) -#209 := (iff #126 #208) -#210 := [rewrite]: #209 -#199 := (iff #119 #206) -#200 := [rewrite]: #199 -#213 := [monotonicity #200 #210]: #212 -#216 := [monotonicity #213]: #215 -#219 := [monotonicity #216]: #218 -#222 := [monotonicity #219]: #221 -#225 := [quant-intro #222]: #224 -#203 := (~ #141 #141) -#201 := (~ #138 #138) -#202 := [refl]: #201 -#204 := [nnf-pos #202]: #203 -#31 := (- #17) -#30 := (- #16) -#32 := (div #30 #31) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#33 := (ite #28 #29 #32) -#34 := (ite #22 0::Int #33) -#35 := (= #18 #34) -#36 := (forall (vars (?v0 Int) (?v1 Int)) #35) -#144 := (iff #36 #141) -#82 := (and #24 #26) -#86 := (or #25 #82) -#99 := (ite #86 #29 #96) -#102 := (ite #22 0::Int #99) -#105 := (= #18 #102) -#108 := (forall (vars (?v0 Int) (?v1 Int)) #105) -#142 := (iff #108 #141) -#139 := (iff #105 #138) -#136 := (= #102 #135) -#133 := (= #99 #132) -#130 := (iff #86 #129) -#127 := (iff #82 #126) -#124 := (iff #26 #123) +#19 := (- #9) +#20 := (div #19 #19) +#18 := (div #9 #9) +#10 := 0::Int +#13 := (< 0::Int #9) +#15 := (< #9 0::Int) +#16 := (and #15 #13) +#14 := (and #13 #13) +#17 := (or #14 #16) +#21 := (ite #17 #18 #20) +#11 := (= #9 0::Int) +#12 := (or #11 #11) +#22 := (ite #12 0::Int #21) +#24 := (= #22 1::Int) +#25 := (not #24) +#133 := (iff #25 false) +#1 := true +#128 := (not true) +#131 := (iff #128 false) +#132 := [rewrite]: #131 +#129 := (iff #25 #128) +#126 := (iff #24 true) +#121 := (= 1::Int 1::Int) +#124 := (iff #121 true) #125 := [rewrite]: #124 -#117 := (iff #24 #116) -#118 := [rewrite]: #117 -#128 := [monotonicity #118 #125]: #127 -#120 := (iff #25 #119) -#113 := (iff #23 #112) -#114 := [rewrite]: #113 -#121 := [monotonicity #114 #118]: #120 -#131 := [monotonicity #121 #128]: #130 -#134 := [monotonicity #131]: #133 -#137 := [monotonicity #134]: #136 -#140 := [monotonicity #137]: #139 -#143 := [quant-intro #140]: #142 -#109 := (iff #36 #108) -#106 := (iff #35 #105) -#103 := (= #34 #102) -#100 := (= #33 #99) -#97 := (= #32 #96) -#94 := (= #31 #93) -#95 := [rewrite]: #94 -#91 := (= #30 #90) -#92 := [rewrite]: #91 -#98 := [monotonicity #92 #95]: #97 -#87 := (iff #28 #86) -#84 := (iff #27 #82) -#85 := [rewrite]: #84 -#88 := [monotonicity #85]: #87 -#101 := [monotonicity #88 #98]: #100 -#104 := [monotonicity #101]: #103 -#107 := [monotonicity #104]: #106 -#110 := [quant-intro #107]: #109 -#145 := [trans #110 #143]: #144 -#81 := [asserted]: #36 -#146 := [mp #81 #145]: #141 -#195 := [mp~ #146 #204]: #141 -#226 := [mp #195 #225]: #223 -#257 := [mp #226 #256]: #254 -#751 := [mp #257 #750]: #746 -#72 := -2::Int -#10 := 3::Int -#66 := -5::Int -#69 := (f3 -5::Int 3::Int) -#75 := (= #69 -2::Int) -#78 := (not #75) -#12 := 2::Int -#13 := (- 2::Int) +#122 := (iff #24 #121) +#115 := (ite false 0::Int 1::Int) +#118 := (= #115 1::Int) +#119 := [rewrite]: #118 +#116 := (= #22 #115) +#113 := (= #21 1::Int) +#46 := -3::Int +#73 := (< -3::Int 0::Int) +#63 := (< 0::Int -3::Int) +#79 := (and #63 #73) +#84 := (or #63 #79) +#108 := (ite #84 1::Int 1::Int) +#111 := (= #108 1::Int) +#112 := [rewrite]: #111 +#109 := (= #21 #108) +#106 := (= #20 1::Int) +#101 := (div 3::Int 3::Int) +#104 := (= #101 1::Int) +#105 := [rewrite]: #104 +#102 := (= #20 #101) +#99 := (= #19 3::Int) +#94 := (- -3::Int) +#97 := (= #94 3::Int) +#98 := [rewrite]: #97 +#95 := (= #19 #94) +#47 := (= #9 -3::Int) +#48 := [rewrite]: #47 +#96 := [monotonicity #48]: #95 +#100 := [trans #96 #98]: #99 +#103 := [monotonicity #100 #100]: #102 +#107 := [trans #103 #105]: #106 +#92 := (= #18 1::Int) +#87 := (div -3::Int -3::Int) +#90 := (= #87 1::Int) +#91 := [rewrite]: #90 +#88 := (= #18 #87) +#89 := [monotonicity #48 #48]: #88 +#93 := [trans #89 #91]: #92 +#85 := (iff #17 #84) +#82 := (iff #16 #79) +#76 := (and #73 #63) +#80 := (iff #76 #79) +#81 := [rewrite]: #80 +#77 := (iff #16 #76) +#64 := (iff #13 #63) +#65 := [monotonicity #48]: #64 +#74 := (iff #15 #73) +#75 := [monotonicity #48]: #74 +#78 := [monotonicity #75 #65]: #77 +#83 := [trans #78 #81]: #82 +#71 := (iff #14 #63) +#66 := (and #63 #63) +#69 := (iff #66 #63) +#70 := [rewrite]: #69 +#67 := (iff #14 #66) +#68 := [monotonicity #65 #65]: #67 +#72 := [trans #68 #70]: #71 +#86 := [monotonicity #72 #83]: #85 +#110 := [monotonicity #86 #93 #107]: #109 +#114 := [trans #110 #112]: #113 +#61 := (iff #12 false) +#56 := (or false false) +#59 := (iff #56 false) +#60 := [rewrite]: #59 +#57 := (iff #12 #56) +#54 := (iff #11 false) +#49 := (= -3::Int 0::Int) +#52 := (iff #49 false) +#53 := [rewrite]: #52 +#50 := (iff #11 #49) +#51 := [monotonicity #48]: #50 +#55 := [trans #51 #53]: #54 +#58 := [monotonicity #55 #55]: #57 +#62 := [trans #58 #60]: #61 +#117 := [monotonicity #62 #114]: #116 +#120 := [trans #117 #119]: #24 +#123 := [monotonicity #120]: #122 +#127 := [trans #123 #125]: #126 +#130 := [monotonicity #127]: #129 +#134 := [trans #130 #132]: #133 +#45 := [asserted]: #25 +[mp #45 #134]: false +unsat +cebc167e67bf5c5c55d952431648797ef2d30dde 158 0 +#2 := false +#28 := 1::Int +#12 := 3::Int +#13 := (- 3::Int) +#24 := (- #13) #8 := 5::Int #9 := (- 5::Int) -#11 := (f3 #9 3::Int) -#14 := (= #11 #13) -#15 := (not #14) -#79 := (iff #15 #78) -#76 := (iff #14 #75) -#73 := (= #13 -2::Int) -#74 := [rewrite]: #73 -#70 := (= #11 #69) -#67 := (= #9 -5::Int) +#23 := (- #9) +#25 := (div #23 #24) +#22 := (div #9 #13) +#10 := 0::Int +#17 := (< 0::Int #13) +#19 := (< #9 0::Int) +#20 := (and #19 #17) +#16 := (< 0::Int #9) +#18 := (and #16 #17) +#21 := (or #18 #20) +#26 := (ite #21 #22 #25) +#14 := (= #13 0::Int) +#11 := (= #9 0::Int) +#15 := (or #11 #14) +#27 := (ite #15 0::Int #26) +#29 := (= #27 1::Int) +#30 := (not #29) +#179 := (iff #30 false) +#51 := -5::Int +#87 := (< -5::Int 0::Int) +#61 := -3::Int +#81 := (< 0::Int -3::Int) +#93 := (and #81 #87) +#78 := (< 0::Int -5::Int) +#84 := (and #78 #81) +#98 := (or #84 #93) +#177 := (iff #98 false) +#71 := (or false false) +#74 := (iff #71 false) +#75 := [rewrite]: #74 +#175 := (iff #98 #71) +#173 := (iff #93 false) +#1 := true +#168 := (and false true) +#171 := (iff #168 false) +#172 := [rewrite]: #171 +#169 := (iff #93 #168) +#166 := (iff #87 true) +#167 := [rewrite]: #166 +#157 := (iff #81 false) +#158 := [rewrite]: #157 +#170 := [monotonicity #158 #167]: #169 +#174 := [trans #170 #172]: #173 +#164 := (iff #84 false) +#159 := (and false false) +#162 := (iff #159 false) +#163 := [rewrite]: #162 +#160 := (iff #84 #159) +#155 := (iff #78 false) +#156 := [rewrite]: #155 +#161 := [monotonicity #156 #158]: #160 +#165 := [trans #161 #163]: #164 +#176 := [monotonicity #165 #174]: #175 +#178 := [trans #176 #75]: #177 +#153 := (iff #30 #98) +#143 := (not #98) +#148 := (not #143) +#151 := (iff #148 #98) +#152 := [rewrite]: #151 +#149 := (iff #30 #148) +#146 := (iff #29 #143) +#104 := 2::Int +#130 := (ite #98 2::Int 1::Int) +#140 := (= #130 1::Int) +#144 := (iff #140 #143) +#145 := [rewrite]: #144 +#141 := (iff #29 #140) +#138 := (= #27 #130) +#133 := (ite false 0::Int #130) +#136 := (= #133 #130) +#137 := [rewrite]: #136 +#134 := (= #27 #133) +#131 := (= #26 #130) +#128 := (= #25 1::Int) +#123 := (div 5::Int 3::Int) +#126 := (= #123 1::Int) +#127 := [rewrite]: #126 +#124 := (= #25 #123) +#121 := (= #24 3::Int) +#116 := (- -3::Int) +#119 := (= #116 3::Int) +#120 := [rewrite]: #119 +#117 := (= #24 #116) +#62 := (= #13 -3::Int) +#63 := [rewrite]: #62 +#118 := [monotonicity #63]: #117 +#122 := [trans #118 #120]: #121 +#114 := (= #23 5::Int) +#109 := (- -5::Int) +#112 := (= #109 5::Int) +#113 := [rewrite]: #112 +#110 := (= #23 #109) +#52 := (= #9 -5::Int) +#53 := [rewrite]: #52 +#111 := [monotonicity #53]: #110 +#115 := [trans #111 #113]: #114 +#125 := [monotonicity #115 #122]: #124 +#129 := [trans #125 #127]: #128 +#107 := (= #22 2::Int) +#101 := (div -5::Int -3::Int) +#105 := (= #101 2::Int) +#106 := [rewrite]: #105 +#102 := (= #22 #101) +#103 := [monotonicity #53 #63]: #102 +#108 := [trans #103 #106]: #107 +#99 := (iff #21 #98) +#96 := (iff #20 #93) +#90 := (and #87 #81) +#94 := (iff #90 #93) +#95 := [rewrite]: #94 +#91 := (iff #20 #90) +#82 := (iff #17 #81) +#83 := [monotonicity #63]: #82 +#88 := (iff #19 #87) +#89 := [monotonicity #53]: #88 +#92 := [monotonicity #89 #83]: #91 +#97 := [trans #92 #95]: #96 +#85 := (iff #18 #84) +#79 := (iff #16 #78) +#80 := [monotonicity #53]: #79 +#86 := [monotonicity #80 #83]: #85 +#100 := [monotonicity #86 #97]: #99 +#132 := [monotonicity #100 #108 #129]: #131 +#76 := (iff #15 false) +#72 := (iff #15 #71) +#69 := (iff #14 false) +#64 := (= -3::Int 0::Int) +#67 := (iff #64 false) #68 := [rewrite]: #67 -#71 := [monotonicity #68]: #70 -#77 := [monotonicity #71 #74]: #76 -#80 := [monotonicity #77]: #79 -#65 := [asserted]: #15 -#83 := [mp #65 #80]: #78 -#650 := (not #746) -#651 := (or #650 #75) -#331 := (* -1::Int 3::Int) -#416 := (* -1::Int -5::Int) -#417 := (div #416 #331) -#418 := (* -1::Int #417) -#409 := (+ #69 #418) -#420 := (= #409 0::Int) -#421 := (div -5::Int 3::Int) -#349 := (* -1::Int #421) -#422 := (+ #69 #349) -#419 := (= #422 0::Int) -#423 := (>= -5::Int 0::Int) -#402 := (<= 3::Int 0::Int) -#737 := (or #402 #423) -#739 := (not #737) -#396 := (<= -5::Int 0::Int) -#526 := (or #396 #402) -#733 := (not #526) -#407 := (or #733 #739) -#408 := (ite #407 #419 #420) -#740 := (= #69 0::Int) -#741 := (= 3::Int 0::Int) -#742 := (= -5::Int 0::Int) -#743 := (or #742 #741) -#738 := (ite #743 #740 #408) -#653 := (or #650 #738) -#655 := (iff #653 #651) -#652 := (iff #651 #651) -#657 := [rewrite]: #652 -#659 := (iff #738 #75) -#673 := (ite false #740 #75) -#664 := (iff #673 #75) -#665 := [rewrite]: #664 -#662 := (iff #738 #673) -#672 := (iff #408 #75) -#679 := (= #69 -1::Int) -#1 := true -#661 := (ite true #75 #679) -#670 := (iff #661 #75) -#671 := [rewrite]: #670 -#658 := (iff #408 #661) -#667 := (iff #420 #679) -#529 := 1::Int -#580 := (+ 1::Int #69) -#584 := (= #580 0::Int) -#676 := (iff #584 #679) -#680 := [rewrite]: #676 -#585 := (iff #420 #584) -#582 := (= #409 #580) -#678 := (+ #69 1::Int) -#581 := (= #678 #580) -#574 := [rewrite]: #581 -#563 := (= #409 #678) -#674 := (= #418 1::Int) -#568 := (* -1::Int -1::Int) -#677 := (= #568 1::Int) -#579 := [rewrite]: #677 -#569 := (= #418 #568) -#683 := (= #417 -1::Int) -#696 := -3::Int -#528 := (div 5::Int -3::Int) -#684 := (= #528 -1::Int) -#685 := [rewrite]: #684 -#681 := (= #417 #528) -#525 := (= #331 -3::Int) -#527 := [rewrite]: #525 -#695 := (= #416 5::Int) -#689 := [rewrite]: #695 -#682 := [monotonicity #689 #527]: #681 -#686 := [trans #682 #685]: #683 -#570 := [monotonicity #686]: #569 -#675 := [trans #570 #579]: #674 -#578 := [monotonicity #675]: #563 -#583 := [trans #578 #574]: #582 -#586 := [monotonicity #583]: #585 -#669 := [trans #586 #680]: #667 -#688 := (iff #419 #75) -#699 := (+ 2::Int #69) -#690 := (= #699 0::Int) -#693 := (iff #690 #75) -#687 := [rewrite]: #693 -#691 := (iff #419 #690) -#547 := (= #422 #699) -#698 := (+ #69 2::Int) -#705 := (= #698 #699) -#546 := [rewrite]: #705 -#703 := (= #422 #698) -#702 := (= #349 2::Int) -#710 := (* -1::Int -2::Int) -#700 := (= #710 2::Int) -#701 := [rewrite]: #700 -#707 := (= #349 #710) -#424 := (= #421 -2::Int) -#706 := [rewrite]: #424 -#711 := [monotonicity #706]: #707 -#697 := [trans #711 #701]: #702 -#704 := [monotonicity #697]: #703 -#548 := [trans #704 #546]: #547 -#692 := [monotonicity #548]: #691 -#694 := [trans #692 #687]: #688 -#708 := (iff #407 true) -#717 := (or false true) -#429 := (iff #717 true) -#430 := [rewrite]: #429 -#427 := (iff #407 #717) -#716 := (iff #739 true) -#714 := (not false) -#438 := (iff #714 true) -#712 := [rewrite]: #438 -#715 := (iff #739 #714) -#444 := (iff #737 false) -#735 := (or false false) -#379 := (iff #735 false) -#720 := [rewrite]: #379 -#442 := (iff #737 #735) -#719 := (iff #423 false) -#441 := [rewrite]: #719 -#722 := (iff #402 false) -#723 := [rewrite]: #722 -#443 := [monotonicity #723 #441]: #442 -#337 := [trans #443 #720]: #444 -#437 := [monotonicity #337]: #715 -#713 := [trans #437 #712]: #716 -#732 := (iff #733 false) -#730 := (not true) -#731 := (iff #730 false) -#729 := [rewrite]: #731 -#370 := (iff #733 #730) -#365 := (iff #526 true) -#724 := (or true false) -#721 := (iff #724 true) -#727 := [rewrite]: #721 -#725 := (iff #526 #724) -#385 := (iff #396 true) -#386 := [rewrite]: #385 -#726 := [monotonicity #386 #723]: #725 -#728 := [trans #726 #727]: #365 -#371 := [monotonicity #728]: #370 -#718 := [trans #371 #729]: #732 -#428 := [monotonicity #718 #713]: #427 -#709 := [trans #428 #430]: #708 -#660 := [monotonicity #709 #694 #669]: #658 -#668 := [trans #660 #671]: #672 -#383 := (iff #743 false) -#395 := (iff #743 #735) -#394 := (iff #741 false) -#399 := [rewrite]: #394 -#744 := (iff #742 false) -#734 := [rewrite]: #744 -#736 := [monotonicity #734 #399]: #395 -#384 := [trans #736 #720]: #383 -#663 := [monotonicity #384 #668]: #662 -#666 := [trans #663 #665]: #659 -#656 := [monotonicity #666]: #655 -#643 := [trans #656 #657]: #655 -#654 := [quant-inst #66 #10]: #653 -#644 := [mp #654 #643]: #651 -[unit-resolution #644 #83 #751]: false -unsat -7de568581f12c6417657495045816e0055a747d5 337 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#18 := (f3 #16 #17) -#769 := (pattern #18) -#13 := 0::Int -#65 := -1::Int -#112 := (* -1::Int #17) -#109 := (* -1::Int #16) -#115 := (div #109 #112) -#272 := (* -1::Int #115) -#273 := (+ #18 #272) -#274 := (= #273 0::Int) -#28 := (div #16 #17) -#269 := (* -1::Int #28) -#270 := (+ #18 #269) -#271 := (= #270 0::Int) -#147 := (>= #16 0::Int) -#140 := (<= #17 0::Int) -#232 := (or #140 #147) -#233 := (not #232) -#136 := (<= #16 0::Int) -#230 := (or #136 #140) -#231 := (not #230) -#236 := (or #231 #233) -#275 := (ite #236 #271 #274) -#268 := (= #18 0::Int) -#20 := (= #17 0::Int) -#19 := (= #16 0::Int) -#21 := (or #19 #20) -#276 := (ite #21 #268 #275) -#770 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #769) #276) -#279 := (forall (vars (?v0 Int) (?v1 Int)) #276) -#773 := (iff #279 #770) -#771 := (iff #276 #276) -#772 := [refl]: #771 -#774 := [quant-intro #772]: #773 -#239 := (ite #236 #28 #115) -#242 := (ite #21 0::Int #239) -#245 := (= #18 #242) -#248 := (forall (vars (?v0 Int) (?v1 Int)) #245) -#280 := (iff #248 #279) -#277 := (iff #245 #276) -#278 := [rewrite]: #277 -#281 := [quant-intro #278]: #280 -#148 := (not #147) -#141 := (not #140) -#151 := (and #141 #148) -#137 := (not #136) -#144 := (and #137 #141) -#154 := (or #144 #151) -#157 := (ite #154 #28 #115) -#160 := (ite #21 0::Int #157) -#163 := (= #18 #160) -#166 := (forall (vars (?v0 Int) (?v1 Int)) #163) -#249 := (iff #166 #248) -#246 := (iff #163 #245) -#243 := (= #160 #242) -#240 := (= #157 #239) -#237 := (iff #154 #236) -#234 := (iff #151 #233) -#235 := [rewrite]: #234 -#224 := (iff #144 #231) -#225 := [rewrite]: #224 -#238 := [monotonicity #225 #235]: #237 -#241 := [monotonicity #238]: #240 -#244 := [monotonicity #241]: #243 -#247 := [monotonicity #244]: #246 -#250 := [quant-intro #247]: #249 -#228 := (~ #166 #166) -#226 := (~ #163 #163) -#227 := [refl]: #226 -#229 := [nnf-pos #227]: #228 -#30 := (- #17) -#29 := (- #16) -#31 := (div #29 #30) -#23 := (< 0::Int #17) -#25 := (< #16 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #16) -#24 := (and #22 #23) -#27 := (or #24 #26) -#32 := (ite #27 #28 #31) -#33 := (ite #21 0::Int #32) -#34 := (= #18 #33) -#35 := (forall (vars (?v0 Int) (?v1 Int)) #34) -#169 := (iff #35 #166) -#103 := (and #23 #25) -#106 := (or #24 #103) -#118 := (ite #106 #28 #115) -#97 := (= 0::Int #17) -#94 := (= 0::Int #16) -#100 := (or #94 #97) -#121 := (ite #100 0::Int #118) -#124 := (= #18 #121) -#127 := (forall (vars (?v0 Int) (?v1 Int)) #124) -#167 := (iff #127 #166) -#164 := (iff #124 #163) -#161 := (= #121 #160) -#158 := (= #118 #157) -#155 := (iff #106 #154) -#152 := (iff #103 #151) -#149 := (iff #25 #148) -#150 := [rewrite]: #149 -#142 := (iff #23 #141) +#65 := (iff #14 #64) +#66 := [monotonicity #63]: #65 +#70 := [trans #66 #68]: #69 +#59 := (iff #11 false) +#54 := (= -5::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #11 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#73 := [monotonicity #60 #70]: #72 +#77 := [trans #73 #75]: #76 +#135 := [monotonicity #77 #132]: #134 +#139 := [trans #135 #137]: #138 +#142 := [monotonicity #139]: #141 +#147 := [trans #142 #145]: #146 +#150 := [monotonicity #147]: #149 +#154 := [trans #150 #152]: #153 +#180 := [trans #154 #178]: #179 +#50 := [asserted]: #30 +[mp #50 #180]: false +unsat +cb26d273f6e817a53bda9b00a467150cd5bc2594 70 0 +#2 := false +#8 := 0::Int +#14 := (- 0::Int) +#15 := (mod #14 #14) +#16 := (- #15) +#13 := (mod 0::Int 0::Int) +#10 := (< 0::Int 0::Int) +#11 := (and #10 #10) +#12 := (or #11 #11) +#17 := (ite #12 #13 #16) +#9 := (= 0::Int 0::Int) +#18 := (ite #9 0::Int #17) +#19 := (ite #9 0::Int #18) +#20 := (= #19 0::Int) +#21 := (not #20) +#91 := (iff #21 false) +#1 := true +#86 := (not true) +#89 := (iff #86 false) +#90 := [rewrite]: #89 +#87 := (iff #21 #86) +#84 := (iff #20 true) +#42 := (iff #9 true) +#43 := [rewrite]: #42 +#82 := (iff #20 #9) +#76 := (ite true 0::Int 0::Int) +#79 := (= #76 0::Int) +#80 := [rewrite]: #79 +#77 := (= #19 #76) +#74 := (= #18 0::Int) +#60 := -1::Int +#61 := (* -1::Int #13) +#66 := (ite #10 #13 #61) +#69 := (ite true 0::Int #66) +#72 := (= #69 0::Int) +#73 := [rewrite]: #72 +#70 := (= #18 #69) +#67 := (= #17 #66) +#64 := (= #16 #61) +#57 := (- #13) +#62 := (= #57 #61) +#63 := [rewrite]: #62 +#58 := (= #16 #57) +#55 := (= #15 #13) +#53 := (= #14 0::Int) +#54 := [rewrite]: #53 +#56 := [monotonicity #54 #54]: #55 +#59 := [monotonicity #56]: #58 +#65 := [trans #59 #63]: #64 +#51 := (iff #12 #10) +#46 := (or #10 #10) +#49 := (iff #46 #10) +#50 := [rewrite]: #49 +#47 := (iff #12 #46) +#44 := (iff #11 #10) +#45 := [rewrite]: #44 +#48 := [monotonicity #45 #45]: #47 +#52 := [trans #48 #50]: #51 +#68 := [monotonicity #52 #65]: #67 +#71 := [monotonicity #43 #68]: #70 +#75 := [trans #71 #73]: #74 +#78 := [monotonicity #43 #75]: #77 +#81 := [trans #78 #80]: #20 +#83 := [monotonicity #81]: #82 +#85 := [trans #83 #43]: #84 +#88 := [monotonicity #85]: #87 +#92 := [trans #88 #90]: #91 +#41 := [asserted]: #21 +[mp #41 #92]: false +unsat +1ec64b4c0435485d0864f4fb378fed079f553a7b 80 0 +#2 := false +decl f3 :: Int +#10 := f3 +#8 := 0::Int +#20 := (- 0::Int) +#19 := (- f3) +#21 := (mod #19 #20) +#22 := (- #21) +#18 := (mod f3 0::Int) +#13 := (< 0::Int 0::Int) +#15 := (< f3 0::Int) +#16 := (and #15 #13) +#12 := (< 0::Int f3) +#14 := (and #12 #13) +#17 := (or #14 #16) +#23 := (ite #17 #18 #22) +#11 := (= f3 0::Int) +#24 := (ite #11 0::Int #23) +#9 := (= 0::Int 0::Int) +#25 := (ite #9 f3 #24) +#26 := (= #25 f3) +#27 := (not #26) +#100 := (iff #27 false) +#1 := true +#95 := (not true) +#98 := (iff #95 false) +#99 := [rewrite]: #98 +#96 := (iff #27 #95) +#93 := (iff #26 true) +#88 := (= f3 f3) +#91 := (iff #88 true) +#92 := [rewrite]: #91 +#89 := (iff #26 #88) +#59 := -1::Int +#60 := (* -1::Int f3) +#65 := (mod #60 0::Int) +#71 := (* -1::Int #65) +#53 := (and #13 #15) +#56 := (or #14 #53) +#76 := (ite #56 #18 #71) +#50 := (= 0::Int f3) +#79 := (ite #50 0::Int #76) +#82 := (ite true f3 #79) +#85 := (= #82 f3) +#86 := [rewrite]: #85 +#83 := (= #25 #82) +#80 := (= #24 #79) +#77 := (= #23 #76) +#74 := (= #22 #71) +#68 := (- #65) +#72 := (= #68 #71) +#73 := [rewrite]: #72 +#69 := (= #22 #68) +#66 := (= #21 #65) +#63 := (= #20 0::Int) +#64 := [rewrite]: #63 +#61 := (= #19 #60) +#62 := [rewrite]: #61 +#67 := [monotonicity #62 #64]: #66 +#70 := [monotonicity #67]: #69 +#75 := [trans #70 #73]: #74 +#57 := (iff #17 #56) +#54 := (iff #16 #53) +#55 := [rewrite]: #54 +#58 := [monotonicity #55]: #57 +#78 := [monotonicity #58 #75]: #77 +#51 := (iff #11 #50) +#52 := [rewrite]: #51 +#81 := [monotonicity #52 #78]: #80 +#48 := (iff #9 true) +#49 := [rewrite]: #48 +#84 := [monotonicity #49 #81]: #83 +#87 := [trans #84 #86]: #26 +#90 := [monotonicity #87]: #89 +#94 := [trans #90 #92]: #93 +#97 := [monotonicity #94]: #96 +#101 := [trans #97 #99]: #100 +#47 := [asserted]: #27 +[mp #47 #101]: false +unsat +57af3178bd4bde4a26173de026e5de08dfc9faa6 78 0 +#2 := false +#9 := 0::Int +#8 := 1::Int +#18 := (- 1::Int) +#17 := (- 0::Int) +#19 := (mod #17 #18) +#20 := (- #19) +#16 := (mod 0::Int 1::Int) +#13 := (< 0::Int 1::Int) +#12 := (< 0::Int 0::Int) +#14 := (and #12 #13) +#15 := (or #14 #14) +#21 := (ite #15 #16 #20) +#11 := (= 0::Int 0::Int) +#22 := (ite #11 0::Int #21) +#10 := (= 1::Int 0::Int) +#23 := (ite #10 0::Int #22) +#24 := (= #23 0::Int) +#25 := (not #24) +#99 := (iff #25 false) +#1 := true +#94 := (not true) +#97 := (iff #94 false) +#98 := [rewrite]: #97 +#95 := (iff #25 #94) +#92 := (iff #24 true) +#48 := (iff #11 true) +#49 := [rewrite]: #48 +#90 := (iff #24 #11) +#84 := (ite false 0::Int 0::Int) +#87 := (= #84 0::Int) +#88 := [rewrite]: #87 +#85 := (= #23 #84) +#82 := (= #22 0::Int) +#77 := (ite true 0::Int 0::Int) +#80 := (= #77 0::Int) +#81 := [rewrite]: #80 +#78 := (= #22 #77) +#75 := (= #21 0::Int) +#70 := (ite #14 0::Int 0::Int) +#73 := (= #70 0::Int) +#74 := [rewrite]: #73 +#71 := (= #21 #70) +#68 := (= #20 0::Int) +#54 := (= #17 0::Int) +#55 := [rewrite]: #54 +#66 := (= #20 #17) +#64 := (= #19 0::Int) +#56 := -1::Int +#59 := (mod 0::Int -1::Int) +#62 := (= #59 0::Int) +#63 := [rewrite]: #62 +#60 := (= #19 #59) +#57 := (= #18 -1::Int) +#58 := [rewrite]: #57 +#61 := [monotonicity #55 #58]: #60 +#65 := [trans #61 #63]: #64 +#67 := [monotonicity #65]: #66 +#69 := [trans #67 #55]: #68 +#52 := (= #16 0::Int) +#53 := [rewrite]: #52 +#50 := (iff #15 #14) +#51 := [rewrite]: #50 +#72 := [monotonicity #51 #53 #69]: #71 +#76 := [trans #72 #74]: #75 +#79 := [monotonicity #49 #76]: #78 +#83 := [trans #79 #81]: #82 +#46 := (iff #10 false) +#47 := [rewrite]: #46 +#86 := [monotonicity #47 #83]: #85 +#89 := [trans #86 #88]: #24 +#91 := [monotonicity #89]: #90 +#93 := [trans #91 #49]: #92 +#96 := [monotonicity #93]: #95 +#100 := [trans #96 #98]: #99 +#45 := [asserted]: #25 +[mp #45 #100]: false +unsat +1f0751610d262907ec6f1f51ed51a6cd0992f6da 85 0 +#2 := false +#9 := 0::Int +#8 := 1::Int +#17 := (- 1::Int) +#18 := (mod #17 #17) +#19 := (- #18) +#16 := (mod 1::Int 1::Int) +#11 := (< 0::Int 1::Int) +#13 := (< 1::Int 0::Int) +#14 := (and #13 #11) +#12 := (and #11 #11) +#15 := (or #12 #14) +#20 := (ite #15 #16 #19) +#10 := (= 1::Int 0::Int) +#21 := (ite #10 0::Int #20) +#22 := (ite #10 1::Int #21) +#23 := (= #22 0::Int) +#24 := (not #23) +#106 := (iff #24 false) +#1 := true +#101 := (not true) +#104 := (iff #101 false) +#105 := [rewrite]: #104 +#102 := (iff #24 #101) +#99 := (iff #23 true) +#94 := (= 0::Int 0::Int) +#97 := (iff #94 true) +#98 := [rewrite]: #97 +#95 := (iff #23 #94) +#88 := (ite false 1::Int 0::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #22 #88) +#86 := (= #21 0::Int) +#81 := (ite false 0::Int 0::Int) +#84 := (= #81 0::Int) +#85 := [rewrite]: #84 +#82 := (= #21 #81) +#79 := (= #20 0::Int) +#49 := (and #11 #13) +#52 := (or #11 #49) +#74 := (ite #52 0::Int 0::Int) +#77 := (= #74 0::Int) +#78 := [rewrite]: #77 +#75 := (= #20 #74) +#72 := (= #19 0::Int) +#67 := (- 0::Int) +#70 := (= #67 0::Int) +#71 := [rewrite]: #70 +#68 := (= #19 #67) +#65 := (= #18 0::Int) +#57 := -1::Int +#60 := (mod -1::Int -1::Int) +#63 := (= #60 0::Int) +#64 := [rewrite]: #63 +#61 := (= #18 #60) +#58 := (= #17 -1::Int) +#59 := [rewrite]: #58 +#62 := [monotonicity #59 #59]: #61 +#66 := [trans #62 #64]: #65 +#69 := [monotonicity #66]: #68 +#73 := [trans #69 #71]: #72 +#55 := (= #16 0::Int) +#56 := [rewrite]: #55 +#53 := (iff #15 #52) +#50 := (iff #14 #49) +#51 := [rewrite]: #50 +#47 := (iff #12 #11) +#48 := [rewrite]: #47 +#54 := [monotonicity #48 #51]: #53 +#76 := [monotonicity #54 #56 #73]: #75 +#80 := [trans #76 #78]: #79 +#45 := (iff #10 false) +#46 := [rewrite]: #45 +#83 := [monotonicity #46 #80]: #82 +#87 := [trans #83 #85]: #86 +#90 := [monotonicity #46 #87]: #89 +#93 := [trans #90 #92]: #23 +#96 := [monotonicity #93]: #95 +#100 := [trans #96 #98]: #99 +#103 := [monotonicity #100]: #102 +#107 := [trans #103 #105]: #106 +#44 := [asserted]: #24 +[mp #44 #107]: false +unsat +da01481f3f884bcc8fb68943f21adbedb119b252 92 0 +#2 := false +#9 := 0::Int +#8 := 1::Int +#21 := (- 1::Int) +#11 := 3::Int +#20 := (- 3::Int) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod 3::Int 1::Int) +#14 := (< 0::Int 1::Int) +#16 := (< 3::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 3::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= 3::Int 0::Int) +#25 := (ite #12 0::Int #24) +#10 := (= 1::Int 0::Int) +#26 := (ite #10 3::Int #25) +#27 := (= #26 0::Int) +#28 := (not #27) +#113 := (iff #28 false) +#1 := true +#108 := (not true) +#111 := (iff #108 false) +#112 := [rewrite]: #111 +#109 := (iff #28 #108) +#106 := (iff #27 true) +#101 := (= 0::Int 0::Int) +#104 := (iff #101 true) +#105 := [rewrite]: #104 +#102 := (iff #27 #101) +#95 := (ite false 3::Int 0::Int) +#98 := (= #95 0::Int) +#99 := [rewrite]: #98 +#96 := (= #26 #95) +#93 := (= #25 0::Int) +#88 := (ite false 0::Int 0::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #25 #88) +#86 := (= #24 0::Int) +#53 := (and #14 #16) +#56 := (or #15 #53) +#81 := (ite #56 0::Int 0::Int) +#84 := (= #81 0::Int) +#85 := [rewrite]: #84 +#82 := (= #24 #81) +#79 := (= #23 0::Int) +#74 := (- 0::Int) +#77 := (= #74 0::Int) +#78 := [rewrite]: #77 +#75 := (= #23 #74) +#72 := (= #22 0::Int) +#64 := -1::Int +#61 := -3::Int +#67 := (mod -3::Int -1::Int) +#70 := (= #67 0::Int) +#71 := [rewrite]: #70 +#68 := (= #22 #67) +#65 := (= #21 -1::Int) +#66 := [rewrite]: #65 +#62 := (= #20 -3::Int) +#63 := [rewrite]: #62 +#69 := [monotonicity #63 #66]: #68 +#73 := [trans #69 #71]: #72 +#76 := [monotonicity #73]: #75 +#80 := [trans #76 #78]: #79 +#59 := (= #19 0::Int) +#60 := [rewrite]: #59 +#57 := (iff #18 #56) +#54 := (iff #17 #53) +#55 := [rewrite]: #54 +#58 := [monotonicity #55]: #57 +#83 := [monotonicity #58 #60 #80]: #82 +#87 := [trans #83 #85]: #86 +#51 := (iff #12 false) +#52 := [rewrite]: #51 +#90 := [monotonicity #52 #87]: #89 +#94 := [trans #90 #92]: #93 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#97 := [monotonicity #50 #94]: #96 +#100 := [trans #97 #99]: #27 +#103 := [monotonicity #100]: #102 +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107]: #109 +#114 := [trans #110 #112]: #113 +#48 := [asserted]: #28 +[mp #48 #114]: false +unsat +eb6e7e04e393e3fdf7579776e17a2526d7e7757f 156 0 +#2 := false +#9 := 0::Int +decl f3 :: Int +#11 := f3 +#122 := (>= f3 0::Int) +#123 := (not #122) +#109 := (<= f3 0::Int) +#110 := (not #109) +#12 := (= f3 0::Int) +#141 := (or #12 #110 #123) +#172 := (not #141) +#62 := -1::Int +#63 := (* -1::Int f3) +#68 := (mod #63 -1::Int) +#74 := (* -1::Int #68) +#146 := (ite #141 0::Int #74) +#153 := (= #146 0::Int) +#157 := (not #153) +#8 := 1::Int +#21 := (- 1::Int) +#20 := (- f3) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod f3 1::Int) +#14 := (< 0::Int 1::Int) +#16 := (< f3 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int f3) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#25 := (ite #12 0::Int #24) +#10 := (= 1::Int 0::Int) +#26 := (ite #10 f3 #25) +#27 := (= #26 0::Int) +#28 := (not #27) +#160 := (iff #28 #157) +#54 := (and #14 #16) +#57 := (or #15 #54) +#51 := (= 0::Int f3) +#85 := (or #51 #57) +#86 := (ite #85 0::Int #74) +#101 := (= 0::Int #86) +#106 := (not #101) +#158 := (iff #106 #157) +#155 := (iff #101 #153) +#149 := (= 0::Int #146) +#152 := (iff #149 #153) +#154 := [rewrite]: #152 +#150 := (iff #101 #149) +#147 := (= #86 #146) +#144 := (iff #85 #141) +#135 := (or #110 #123) +#138 := (or #12 #135) +#142 := (iff #138 #141) #143 := [rewrite]: #142 -#153 := [monotonicity #143 #150]: #152 -#145 := (iff #24 #144) -#138 := (iff #22 #137) -#139 := [rewrite]: #138 -#146 := [monotonicity #139 #143]: #145 -#156 := [monotonicity #146 #153]: #155 -#159 := [monotonicity #156]: #158 -#134 := (iff #100 #21) -#132 := (iff #97 #20) -#133 := [rewrite]: #132 -#130 := (iff #94 #19) -#131 := [rewrite]: #130 -#135 := [monotonicity #131 #133]: #134 -#162 := [monotonicity #135 #159]: #161 -#165 := [monotonicity #162]: #164 -#168 := [quant-intro #165]: #167 -#128 := (iff #35 #127) -#125 := (iff #34 #124) -#122 := (= #33 #121) -#119 := (= #32 #118) -#116 := (= #31 #115) -#113 := (= #30 #112) +#139 := (iff #85 #138) +#136 := (iff #57 #135) +#131 := (iff #54 #123) +#1 := true +#126 := (and true #123) +#129 := (iff #126 #123) +#130 := [rewrite]: #129 +#127 := (iff #54 #126) +#124 := (iff #16 #123) +#125 := [rewrite]: #124 +#113 := (iff #14 true) #114 := [rewrite]: #113 -#110 := (= #29 #109) -#111 := [rewrite]: #110 -#117 := [monotonicity #111 #114]: #116 -#107 := (iff #27 #106) -#104 := (iff #26 #103) -#105 := [rewrite]: #104 +#128 := [monotonicity #114 #125]: #127 +#132 := [trans #128 #130]: #131 +#120 := (iff #15 #110) +#115 := (and #110 true) +#118 := (iff #115 #110) +#119 := [rewrite]: #118 +#116 := (iff #15 #115) +#111 := (iff #13 #110) +#112 := [rewrite]: #111 +#117 := [monotonicity #112 #114]: #116 +#121 := [trans #117 #119]: #120 +#137 := [monotonicity #121 #132]: #136 +#133 := (iff #51 #12) +#134 := [rewrite]: #133 +#140 := [monotonicity #134 #137]: #139 +#145 := [trans #140 #143]: #144 +#148 := [monotonicity #145]: #147 +#151 := [monotonicity #148]: #150 +#156 := [trans #151 #154]: #155 +#159 := [monotonicity #156]: #158 +#107 := (iff #28 #106) +#104 := (iff #27 #101) +#98 := (= #86 0::Int) +#102 := (iff #98 #101) +#103 := [rewrite]: #102 +#99 := (iff #27 #98) +#96 := (= #26 #86) +#91 := (ite false f3 #86) +#94 := (= #91 #86) +#95 := [rewrite]: #94 +#92 := (= #26 #91) +#89 := (= #25 #86) +#79 := (ite #57 0::Int #74) +#82 := (ite #51 0::Int #79) +#87 := (= #82 #86) +#88 := [rewrite]: #87 +#83 := (= #25 #82) +#80 := (= #24 #79) +#77 := (= #23 #74) +#71 := (- #68) +#75 := (= #71 #74) +#76 := [rewrite]: #75 +#72 := (= #23 #71) +#69 := (= #22 #68) +#66 := (= #21 -1::Int) +#67 := [rewrite]: #66 +#64 := (= #20 #63) +#65 := [rewrite]: #64 +#70 := [monotonicity #65 #67]: #69 +#73 := [monotonicity #70]: #72 +#78 := [trans #73 #76]: #77 +#60 := (= #19 0::Int) +#61 := [rewrite]: #60 +#58 := (iff #18 #57) +#55 := (iff #17 #54) +#56 := [rewrite]: #55 +#59 := [monotonicity #56]: #58 +#81 := [monotonicity #59 #61 #78]: #80 +#52 := (iff #12 #51) +#53 := [rewrite]: #52 +#84 := [monotonicity #53 #81]: #83 +#90 := [trans #84 #88]: #89 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#93 := [monotonicity #50 #90]: #92 +#97 := [trans #93 #95]: #96 +#100 := [monotonicity #97]: #99 +#105 := [trans #100 #103]: #104 #108 := [monotonicity #105]: #107 -#120 := [monotonicity #108 #117]: #119 -#101 := (iff #21 #100) -#98 := (iff #20 #97) -#99 := [rewrite]: #98 -#95 := (iff #19 #94) -#96 := [rewrite]: #95 -#102 := [monotonicity #96 #99]: #101 -#123 := [monotonicity #102 #120]: #122 -#126 := [monotonicity #123]: #125 -#129 := [quant-intro #126]: #128 -#170 := [trans #129 #168]: #169 -#93 := [asserted]: #35 -#171 := [mp #93 #170]: #166 -#220 := [mp~ #171 #229]: #166 -#251 := [mp #220 #250]: #248 -#282 := [mp #251 #281]: #279 -#775 := [mp #282 #774]: #770 -#68 := -3::Int -#71 := (f3 -1::Int -3::Int) -#74 := (= #71 0::Int) -#87 := (not #74) -#10 := 3::Int -#11 := (- 3::Int) +#161 := [trans #108 #159]: #160 +#48 := [asserted]: #28 +#162 := [mp #48 #161]: #157 +#175 := (or #172 #153) +#176 := [def-axiom]: #175 +#233 := [unit-resolution #176 #162]: #172 +#164 := (or #141 #122) +#165 := [def-axiom]: #164 +#234 := [unit-resolution #165 #233]: #122 +#166 := (or #141 #109) +#167 := [def-axiom]: #166 +#235 := [unit-resolution #167 #233]: #109 +#169 := (not #12) +#170 := (or #141 #169) +#171 := [def-axiom]: #170 +#236 := [unit-resolution #171 #233]: #169 +#237 := [th-lemma arith triangle-eq]: #141 +[unit-resolution #237 #236 #235 #234]: false +unsat +106013bb1f998104836223245ab92e3b99397a07 107 0 +#2 := false +#10 := 0::Int #8 := 1::Int #9 := (- 1::Int) -#12 := (f3 #9 #11) -#14 := (= #12 0::Int) -#15 := (not #14) -#90 := (iff #15 #87) -#77 := (= 0::Int #71) -#82 := (not #77) -#88 := (iff #82 #87) -#85 := (iff #77 #74) -#86 := [rewrite]: #85 -#89 := [monotonicity #86]: #88 -#83 := (iff #15 #82) -#80 := (iff #14 #77) -#78 := (iff #74 #77) -#79 := [rewrite]: #78 -#75 := (iff #14 #74) -#72 := (= #12 #71) -#69 := (= #11 -3::Int) -#70 := [rewrite]: #69 -#66 := (= #9 -1::Int) -#67 := [rewrite]: #66 +#19 := (- #9) +#18 := (- 0::Int) +#20 := (mod #18 #19) +#21 := (- #20) +#17 := (mod 0::Int #9) +#14 := (< 0::Int #9) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#22 := (ite #16 #17 #21) +#12 := (= 0::Int 0::Int) +#23 := (ite #12 0::Int #22) +#11 := (= #9 0::Int) +#24 := (ite #11 0::Int #23) +#25 := (= #24 0::Int) +#26 := (not #25) +#128 := (iff #26 false) +#1 := true +#123 := (not true) +#126 := (iff #123 false) +#127 := [rewrite]: #126 +#124 := (iff #26 #123) +#121 := (iff #25 true) +#57 := (iff #12 true) +#58 := [rewrite]: #57 +#119 := (iff #25 #12) +#113 := (ite false 0::Int 0::Int) +#116 := (= #113 0::Int) +#117 := [rewrite]: #116 +#114 := (= #24 #113) +#111 := (= #23 0::Int) +#106 := (ite true 0::Int 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #23 #106) +#104 := (= #22 0::Int) +#47 := -1::Int +#59 := (< 0::Int -1::Int) +#62 := (and #13 #59) +#99 := (ite #62 0::Int 0::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #22 #99) +#97 := (= #21 0::Int) +#79 := (= #18 0::Int) +#80 := [rewrite]: #79 +#95 := (= #21 #18) +#93 := (= #20 0::Int) +#88 := (mod 0::Int 1::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #20 #88) +#86 := (= #19 1::Int) +#81 := (- -1::Int) +#84 := (= #81 1::Int) +#85 := [rewrite]: #84 +#82 := (= #19 #81) +#48 := (= #9 -1::Int) +#49 := [rewrite]: #48 +#83 := [monotonicity #49]: #82 +#87 := [trans #83 #85]: #86 +#90 := [monotonicity #80 #87]: #89 +#94 := [trans #90 #92]: #93 +#96 := [monotonicity #94]: #95 +#98 := [trans #96 #80]: #97 +#77 := (= #17 0::Int) +#72 := (mod 0::Int -1::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #17 #72) +#74 := [monotonicity #49]: #73 +#78 := [trans #74 #76]: #77 +#70 := (iff #16 #62) +#65 := (or #62 #62) +#68 := (iff #65 #62) +#69 := [rewrite]: #68 +#66 := (iff #16 #65) +#63 := (iff #15 #62) +#60 := (iff #14 #59) +#61 := [monotonicity #49]: #60 +#64 := [monotonicity #61]: #63 +#67 := [monotonicity #64 #64]: #66 +#71 := [trans #67 #69]: #70 +#101 := [monotonicity #71 #78 #98]: #100 +#105 := [trans #101 #103]: #104 +#108 := [monotonicity #58 #105]: #107 +#112 := [trans #108 #110]: #111 +#55 := (iff #11 false) +#50 := (= -1::Int 0::Int) +#53 := (iff #50 false) +#54 := [rewrite]: #53 +#51 := (iff #11 #50) +#52 := [monotonicity #49]: #51 +#56 := [trans #52 #54]: #55 +#115 := [monotonicity #56 #112]: #114 +#118 := [trans #115 #117]: #25 +#120 := [monotonicity #118]: #119 +#122 := [trans #120 #58]: #121 +#125 := [monotonicity #122]: #124 +#129 := [trans #125 #127]: #128 +#46 := [asserted]: #26 +[mp #46 #129]: false +unsat +8d5198a1caadbe07ee33787baa9fbc0f66546c9a 111 0 +#2 := false +#10 := 0::Int +#8 := 1::Int +#9 := (- 1::Int) +#20 := (- #9) +#21 := (mod #9 #20) +#22 := (- #21) +#19 := (mod 1::Int #9) +#14 := (< 0::Int #9) +#16 := (< 1::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 1::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#23 := (ite #18 #19 #22) +#12 := (= 1::Int 0::Int) +#24 := (ite #12 0::Int #23) +#11 := (= #9 0::Int) +#25 := (ite #11 1::Int #24) +#26 := (= #25 0::Int) +#27 := (not #26) +#132 := (iff #27 false) +#1 := true +#127 := (not true) +#130 := (iff #127 false) +#131 := [rewrite]: #130 +#128 := (iff #27 #127) +#125 := (iff #26 true) +#120 := (= 0::Int 0::Int) +#123 := (iff #120 true) +#124 := [rewrite]: #123 +#121 := (iff #26 #120) +#114 := (ite false 1::Int 0::Int) +#117 := (= #114 0::Int) +#118 := [rewrite]: #117 +#115 := (= #25 #114) +#112 := (= #24 0::Int) +#107 := (ite false 0::Int 0::Int) +#110 := (= #107 0::Int) +#111 := [rewrite]: #110 +#108 := (= #24 #107) +#105 := (= #23 0::Int) +#48 := -1::Int +#60 := (< 0::Int -1::Int) +#66 := (and #16 #60) +#63 := (and #13 #60) +#69 := (or #63 #66) +#100 := (ite #69 0::Int 0::Int) +#103 := (= #100 0::Int) +#104 := [rewrite]: #103 +#101 := (= #23 #100) +#98 := (= #22 0::Int) +#93 := (- 0::Int) +#96 := (= #93 0::Int) +#97 := [rewrite]: #96 +#94 := (= #22 #93) +#91 := (= #21 0::Int) +#86 := (mod -1::Int 1::Int) +#89 := (= #86 0::Int) +#90 := [rewrite]: #89 +#87 := (= #21 #86) +#84 := (= #20 1::Int) +#79 := (- -1::Int) +#82 := (= #79 1::Int) +#83 := [rewrite]: #82 +#80 := (= #20 #79) +#49 := (= #9 -1::Int) +#50 := [rewrite]: #49 +#81 := [monotonicity #50]: #80 +#85 := [trans #81 #83]: #84 +#88 := [monotonicity #50 #85]: #87 +#92 := [trans #88 #90]: #91 +#95 := [monotonicity #92]: #94 +#99 := [trans #95 #97]: #98 +#77 := (= #19 0::Int) +#72 := (mod 1::Int -1::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #19 #72) +#74 := [monotonicity #50]: #73 +#78 := [trans #74 #76]: #77 +#70 := (iff #18 #69) +#67 := (iff #17 #66) +#61 := (iff #14 #60) +#62 := [monotonicity #50]: #61 +#68 := [monotonicity #62]: #67 +#64 := (iff #15 #63) +#65 := [monotonicity #62]: #64 +#71 := [monotonicity #65 #68]: #70 +#102 := [monotonicity #71 #78 #99]: #101 +#106 := [trans #102 #104]: #105 +#58 := (iff #12 false) +#59 := [rewrite]: #58 +#109 := [monotonicity #59 #106]: #108 +#113 := [trans #109 #111]: #112 +#56 := (iff #11 false) +#51 := (= -1::Int 0::Int) +#54 := (iff #51 false) +#55 := [rewrite]: #54 +#52 := (iff #11 #51) +#53 := [monotonicity #50]: #52 +#57 := [trans #53 #55]: #56 +#116 := [monotonicity #57 #113]: #115 +#119 := [trans #116 #118]: #26 +#122 := [monotonicity #119]: #121 +#126 := [trans #122 #124]: #125 +#129 := [monotonicity #126]: #128 +#133 := [trans #129 #131]: #132 +#47 := [asserted]: #27 +[mp #47 #133]: false +unsat +3e5306453747f88fb9407b2be361e50903b04cbd 116 0 +#2 := false +#10 := 0::Int +#8 := 1::Int +#9 := (- 1::Int) +#22 := (- #9) +#12 := 3::Int +#21 := (- 3::Int) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod 3::Int #9) +#15 := (< 0::Int #9) +#17 := (< 3::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 3::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= 3::Int 0::Int) +#26 := (ite #13 0::Int #25) +#11 := (= #9 0::Int) +#27 := (ite #11 3::Int #26) +#28 := (= #27 0::Int) +#29 := (not #28) +#137 := (iff #29 false) +#1 := true +#132 := (not true) +#135 := (iff #132 false) +#136 := [rewrite]: #135 +#133 := (iff #29 #132) +#130 := (iff #28 true) +#125 := (= 0::Int 0::Int) +#128 := (iff #125 true) +#129 := [rewrite]: #128 +#126 := (iff #28 #125) +#119 := (ite false 3::Int 0::Int) +#122 := (= #119 0::Int) +#123 := [rewrite]: #122 +#120 := (= #27 #119) +#117 := (= #26 0::Int) +#112 := (ite false 0::Int 0::Int) +#115 := (= #112 0::Int) +#116 := [rewrite]: #115 +#113 := (= #26 #112) +#110 := (= #25 0::Int) +#50 := -1::Int +#62 := (< 0::Int -1::Int) +#68 := (and #17 #62) +#65 := (and #14 #62) +#71 := (or #65 #68) +#105 := (ite #71 0::Int 0::Int) +#108 := (= #105 0::Int) +#109 := [rewrite]: #108 +#106 := (= #25 #105) +#103 := (= #24 0::Int) +#98 := (- 0::Int) +#101 := (= #98 0::Int) +#102 := [rewrite]: #101 +#99 := (= #24 #98) +#96 := (= #23 0::Int) +#81 := -3::Int +#91 := (mod -3::Int 1::Int) +#94 := (= #91 0::Int) +#95 := [rewrite]: #94 +#92 := (= #23 #91) +#89 := (= #22 1::Int) +#84 := (- -1::Int) +#87 := (= #84 1::Int) +#88 := [rewrite]: #87 +#85 := (= #22 #84) +#51 := (= #9 -1::Int) +#52 := [rewrite]: #51 +#86 := [monotonicity #52]: #85 +#90 := [trans #86 #88]: #89 +#82 := (= #21 -3::Int) +#83 := [rewrite]: #82 +#93 := [monotonicity #83 #90]: #92 +#97 := [trans #93 #95]: #96 +#100 := [monotonicity #97]: #99 +#104 := [trans #100 #102]: #103 +#79 := (= #20 0::Int) +#74 := (mod 3::Int -1::Int) +#77 := (= #74 0::Int) +#78 := [rewrite]: #77 +#75 := (= #20 #74) +#76 := [monotonicity #52]: #75 +#80 := [trans #76 #78]: #79 +#72 := (iff #19 #71) +#69 := (iff #18 #68) +#63 := (iff #15 #62) +#64 := [monotonicity #52]: #63 +#70 := [monotonicity #64]: #69 +#66 := (iff #16 #65) +#67 := [monotonicity #64]: #66 #73 := [monotonicity #67 #70]: #72 -#76 := [monotonicity #73]: #75 -#81 := [trans #76 #79]: #80 -#84 := [monotonicity #81]: #83 -#91 := [trans #84 #89]: #90 -#64 := [asserted]: #15 -#92 := [mp #64 #91]: #87 -#694 := (not #770) -#695 := (or #694 #74) -#356 := (* -1::Int -3::Int) -#440 := (* -1::Int -1::Int) -#441 := (div #440 #356) -#442 := (* -1::Int #441) -#433 := (+ #71 #442) -#444 := (= #433 0::Int) -#445 := (div -1::Int -3::Int) -#446 := (* -1::Int #445) -#443 := (+ #71 #446) -#447 := (= #443 0::Int) -#426 := (>= -1::Int 0::Int) -#761 := (<= -3::Int 0::Int) -#763 := (or #761 #426) -#420 := (not #763) -#550 := (<= -1::Int 0::Int) -#757 := (or #550 #761) -#431 := (not #757) -#432 := (or #431 #420) -#764 := (ite #432 #447 #444) -#765 := (= -3::Int 0::Int) -#766 := (= -1::Int 0::Int) -#767 := (or #766 #765) -#762 := (ite #767 #74 #764) -#696 := (or #694 #762) -#697 := (iff #696 #695) -#687 := (iff #695 #695) -#688 := [rewrite]: #687 -#682 := (iff #762 #74) -#700 := (ite false #74 #74) -#693 := (iff #700 #74) -#685 := [rewrite]: #693 -#704 := (iff #762 #700) -#610 := (iff #764 #74) -#714 := (= #71 1::Int) -#598 := (ite false #714 #74) -#608 := (iff #598 #74) -#609 := [rewrite]: #608 -#606 := (iff #764 #598) -#604 := (iff #444 #74) -#587 := (= #433 #71) -#701 := (+ #71 0::Int) -#699 := (= #701 #71) -#702 := [rewrite]: #699 -#603 := (= #433 #701) -#594 := (= #442 0::Int) -#709 := (* -1::Int 0::Int) -#592 := (= #709 0::Int) -#593 := [rewrite]: #592 -#707 := (= #442 #709) -#706 := (= #441 0::Int) -#720 := (div 1::Int 3::Int) -#552 := (= #720 0::Int) -#705 := [rewrite]: #552 -#549 := (= #441 #720) -#719 := (= #356 3::Int) -#713 := [rewrite]: #719 -#712 := (= #440 1::Int) -#718 := [rewrite]: #712 -#551 := [monotonicity #718 #713]: #549 -#708 := [trans #551 #705]: #706 -#710 := [monotonicity #708]: #707 -#553 := [trans #710 #593]: #594 -#698 := [monotonicity #553]: #603 -#602 := [trans #698 #702]: #587 -#605 := [monotonicity #602]: #604 -#717 := (iff #447 #714) -#722 := (+ -1::Int #71) -#570 := (= #722 0::Int) -#715 := (iff #570 #714) -#716 := [rewrite]: #715 -#571 := (iff #447 #570) -#723 := (= #443 #722) -#725 := (+ #71 -1::Int) -#727 := (= #725 #722) -#728 := [rewrite]: #727 -#726 := (= #443 #725) -#735 := (= #446 -1::Int) -#733 := (* -1::Int 1::Int) -#734 := (= #733 -1::Int) -#731 := [rewrite]: #734 -#448 := (= #446 #733) -#454 := (= #445 1::Int) -#732 := [rewrite]: #454 -#730 := [monotonicity #732]: #448 -#724 := [trans #730 #731]: #735 -#721 := [monotonicity #724]: #726 -#729 := [trans #721 #728]: #723 -#572 := [monotonicity #729]: #571 -#711 := [trans #572 #716]: #717 -#452 := (iff #432 false) -#759 := (or false false) -#403 := (iff #759 false) -#744 := [rewrite]: #403 -#741 := (iff #432 #759) -#740 := (iff #420 false) -#1 := true -#754 := (not true) -#755 := (iff #754 false) -#753 := [rewrite]: #755 -#462 := (iff #420 #754) -#739 := (iff #763 true) -#466 := (or true false) -#362 := (iff #466 true) -#738 := [rewrite]: #362 -#467 := (iff #763 #466) -#743 := (iff #426 false) -#465 := [rewrite]: #743 -#746 := (iff #761 true) -#747 := [rewrite]: #746 -#468 := [monotonicity #747 #465]: #467 -#461 := [trans #468 #738]: #739 -#736 := [monotonicity #461]: #462 -#737 := [trans #736 #753]: #740 -#756 := (iff #431 false) -#394 := (iff #431 #754) -#389 := (iff #757 true) -#748 := (or true true) -#745 := (iff #748 true) -#751 := [rewrite]: #745 -#749 := (iff #757 #748) -#409 := (iff #550 true) -#410 := [rewrite]: #409 -#750 := [monotonicity #410 #747]: #749 -#752 := [trans #750 #751]: #389 -#395 := [monotonicity #752]: #394 -#742 := [trans #395 #753]: #756 -#451 := [monotonicity #742 #737]: #741 -#453 := [trans #451 #744]: #452 -#607 := [monotonicity #453 #711 #605]: #606 -#703 := [trans #607 #609]: #610 -#407 := (iff #767 false) -#419 := (iff #767 #759) -#418 := (iff #765 false) -#423 := [rewrite]: #418 -#768 := (iff #766 false) -#758 := [rewrite]: #768 -#760 := [monotonicity #758 #423]: #419 -#408 := [trans #760 #744]: #407 -#691 := [monotonicity #408 #703]: #704 -#684 := [trans #691 #685]: #682 -#686 := [monotonicity #684]: #697 -#689 := [trans #686 #688]: #697 -#692 := [quant-inst #65 #68]: #696 -#683 := [mp #692 #689]: #695 -[unit-resolution #683 #92 #775]: false -unsat -67c5769d49bd3d505a24355d203b30bb2a6d4f8d 306 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#16 := (f3 #14 #15) -#751 := (pattern #16) -#17 := 0::Int -#96 := -1::Int -#100 := (* -1::Int #15) -#97 := (* -1::Int #14) -#103 := (div #97 #100) -#254 := (* -1::Int #103) -#255 := (+ #16 #254) -#256 := (= #255 0::Int) -#27 := (div #14 #15) -#251 := (* -1::Int #27) -#252 := (+ #16 #251) -#253 := (= #252 0::Int) -#129 := (>= #14 0::Int) -#122 := (<= #15 0::Int) -#214 := (or #122 #129) -#215 := (not #214) -#118 := (<= #14 0::Int) -#212 := (or #118 #122) -#213 := (not #212) -#218 := (or #213 #215) -#257 := (ite #218 #253 #256) -#250 := (= #16 0::Int) -#19 := (= #15 0::Int) -#18 := (= #14 0::Int) -#20 := (or #18 #19) -#258 := (ite #20 #250 #257) -#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258) -#261 := (forall (vars (?v0 Int) (?v1 Int)) #258) -#755 := (iff #261 #752) -#753 := (iff #258 #258) -#754 := [refl]: #753 -#756 := [quant-intro #754]: #755 -#221 := (ite #218 #27 #103) -#224 := (ite #20 0::Int #221) -#227 := (= #16 #224) -#230 := (forall (vars (?v0 Int) (?v1 Int)) #227) -#262 := (iff #230 #261) -#259 := (iff #227 #258) -#260 := [rewrite]: #259 -#263 := [quant-intro #260]: #262 -#130 := (not #129) -#123 := (not #122) -#133 := (and #123 #130) -#119 := (not #118) -#126 := (and #119 #123) -#136 := (or #126 #133) -#139 := (ite #136 #27 #103) -#142 := (ite #20 0::Int #139) -#145 := (= #16 #142) -#148 := (forall (vars (?v0 Int) (?v1 Int)) #145) -#231 := (iff #148 #230) -#228 := (iff #145 #227) -#225 := (= #142 #224) -#222 := (= #139 #221) -#219 := (iff #136 #218) -#216 := (iff #133 #215) -#217 := [rewrite]: #216 -#206 := (iff #126 #213) -#207 := [rewrite]: #206 -#220 := [monotonicity #207 #217]: #219 -#223 := [monotonicity #220]: #222 -#226 := [monotonicity #223]: #225 -#229 := [monotonicity #226]: #228 -#232 := [quant-intro #229]: #231 -#210 := (~ #148 #148) -#208 := (~ #145 #145) -#209 := [refl]: #208 -#211 := [nnf-pos #209]: #210 -#29 := (- #15) -#28 := (- #14) -#30 := (div #28 #29) -#22 := (< 0::Int #15) -#24 := (< #14 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #14) -#23 := (and #21 #22) -#26 := (or #23 #25) -#31 := (ite #26 #27 #30) -#32 := (ite #20 0::Int #31) -#33 := (= #16 #32) -#34 := (forall (vars (?v0 Int) (?v1 Int)) #33) -#151 := (iff #34 #148) -#90 := (and #22 #24) -#93 := (or #23 #90) -#106 := (ite #93 #27 #103) -#109 := (ite #20 0::Int #106) -#112 := (= #16 #109) -#115 := (forall (vars (?v0 Int) (?v1 Int)) #112) -#149 := (iff #115 #148) -#146 := (iff #112 #145) -#143 := (= #109 #142) -#140 := (= #106 #139) -#137 := (iff #93 #136) -#134 := (iff #90 #133) -#131 := (iff #24 #130) -#132 := [rewrite]: #131 -#124 := (iff #22 #123) -#125 := [rewrite]: #124 -#135 := [monotonicity #125 #132]: #134 -#127 := (iff #23 #126) -#120 := (iff #21 #119) -#121 := [rewrite]: #120 -#128 := [monotonicity #121 #125]: #127 -#138 := [monotonicity #128 #135]: #137 -#141 := [monotonicity #138]: #140 -#144 := [monotonicity #141]: #143 -#147 := [monotonicity #144]: #146 -#150 := [quant-intro #147]: #149 -#116 := (iff #34 #115) -#113 := (iff #33 #112) -#110 := (= #32 #109) -#107 := (= #31 #106) -#104 := (= #30 #103) -#101 := (= #29 #100) -#102 := [rewrite]: #101 -#98 := (= #28 #97) +#107 := [monotonicity #73 #80 #104]: #106 +#111 := [trans #107 #109]: #110 +#60 := (iff #13 false) +#61 := [rewrite]: #60 +#114 := [monotonicity #61 #111]: #113 +#118 := [trans #114 #116]: #117 +#58 := (iff #11 false) +#53 := (= -1::Int 0::Int) +#56 := (iff #53 false) +#57 := [rewrite]: #56 +#54 := (iff #11 #53) +#55 := [monotonicity #52]: #54 +#59 := [trans #55 #57]: #58 +#121 := [monotonicity #59 #118]: #120 +#124 := [trans #121 #123]: #28 +#127 := [monotonicity #124]: #126 +#131 := [trans #127 #129]: #130 +#134 := [monotonicity #131]: #133 +#138 := [trans #134 #136]: #137 +#49 := [asserted]: #29 +[mp #49 #138]: false +unsat +56a38afd92c36cbda7ea0320ace529eafcdd0527 180 0 +#2 := false +#10 := 0::Int +#8 := 1::Int +#9 := (- 1::Int) +#22 := (- #9) +decl f3 :: Int +#12 := f3 +#21 := (- f3) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod f3 #9) +#15 := (< 0::Int #9) +#17 := (< f3 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int f3) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= f3 0::Int) +#26 := (ite #13 0::Int #25) +#11 := (= #9 0::Int) +#27 := (ite #11 f3 #26) +#28 := (= #27 0::Int) +#29 := (not #28) +#200 := (iff #29 false) +#50 := -1::Int +#75 := (mod f3 -1::Int) +#63 := (< 0::Int -1::Int) +#69 := (and #17 #63) +#66 := (and #14 #63) +#72 := (or #66 #69) +#108 := (not #72) +#60 := (= 0::Int f3) +#109 := (or #60 #108) +#110 := (ite #109 0::Int #75) +#125 := (= 0::Int #110) +#130 := (not #125) +#198 := (iff #130 false) +#1 := true +#193 := (not true) +#196 := (iff #193 false) +#197 := [rewrite]: #196 +#194 := (iff #130 #193) +#191 := (iff #125 true) +#186 := (= 0::Int 0::Int) +#189 := (iff #186 true) +#190 := [rewrite]: #189 +#187 := (iff #125 #186) +#122 := (= #110 0::Int) +#180 := (ite true 0::Int #75) +#183 := (= #180 0::Int) +#184 := [rewrite]: #183 +#181 := (= #110 #180) +#178 := (iff #109 true) +#173 := (or #13 true) +#176 := (iff #173 true) +#177 := [rewrite]: #176 +#174 := (iff #109 #173) +#171 := (iff #108 true) +#166 := (not false) +#169 := (iff #166 true) +#170 := [rewrite]: #169 +#167 := (iff #108 #166) +#164 := (iff #72 false) +#159 := (or false false) +#162 := (iff #159 false) +#163 := [rewrite]: #162 +#160 := (iff #72 #159) +#157 := (iff #69 false) +#148 := (>= f3 0::Int) +#149 := (not #148) +#152 := (and #149 false) +#155 := (iff #152 false) +#156 := [rewrite]: #155 +#153 := (iff #69 #152) +#139 := (iff #63 false) +#140 := [rewrite]: #139 +#150 := (iff #17 #149) +#151 := [rewrite]: #150 +#154 := [monotonicity #151 #140]: #153 +#158 := [trans #154 #156]: #157 +#146 := (iff #66 false) +#135 := (<= f3 0::Int) +#136 := (not #135) +#141 := (and #136 false) +#144 := (iff #141 false) +#145 := [rewrite]: #144 +#142 := (iff #66 #141) +#137 := (iff #14 #136) +#138 := [rewrite]: #137 +#143 := [monotonicity #138 #140]: #142 +#147 := [trans #143 #145]: #146 +#161 := [monotonicity #147 #158]: #160 +#165 := [trans #161 #163]: #164 +#168 := [monotonicity #165]: #167 +#172 := [trans #168 #170]: #171 +#133 := (iff #60 #13) +#134 := [rewrite]: #133 +#175 := [monotonicity #134 #172]: #174 +#179 := [trans #175 #177]: #178 +#182 := [monotonicity #179]: #181 +#185 := [trans #182 #184]: #122 +#188 := [monotonicity #185]: #187 +#192 := [trans #188 #190]: #191 +#195 := [monotonicity #192]: #194 +#199 := [trans #195 #197]: #198 +#131 := (iff #29 #130) +#128 := (iff #28 #125) +#126 := (iff #122 #125) +#127 := [rewrite]: #126 +#123 := (iff #28 #122) +#120 := (= #27 #110) +#115 := (ite false f3 #110) +#118 := (= #115 #110) +#119 := [rewrite]: #118 +#116 := (= #27 #115) +#113 := (= #26 #110) +#102 := (ite #72 #75 0::Int) +#105 := (ite #60 0::Int #102) +#111 := (= #105 #110) +#112 := [rewrite]: #111 +#106 := (= #26 #105) +#103 := (= #25 #102) +#100 := (= #24 0::Int) +#95 := (- 0::Int) +#98 := (= #95 0::Int) #99 := [rewrite]: #98 -#105 := [monotonicity #99 #102]: #104 -#94 := (iff #26 #93) -#91 := (iff #25 #90) +#96 := (= #24 #95) +#93 := (= #23 0::Int) +#78 := (* -1::Int f3) +#88 := (mod #78 1::Int) +#91 := (= #88 0::Int) #92 := [rewrite]: #91 -#95 := [monotonicity #92]: #94 -#108 := [monotonicity #95 #105]: #107 -#111 := [monotonicity #108]: #110 -#114 := [monotonicity #111]: #113 -#117 := [quant-intro #114]: #116 -#152 := [trans #117 #150]: #151 -#89 := [asserted]: #34 -#153 := [mp #89 #152]: #148 -#202 := [mp~ #153 #211]: #148 -#233 := [mp #202 #232]: #230 -#264 := [mp #233 #263]: #261 -#757 := [mp #264 #756]: #752 -#11 := 1::Int -#64 := -3::Int -#67 := (f3 -3::Int -3::Int) -#70 := (= #67 1::Int) -#83 := (not #70) +#89 := (= #23 #88) +#86 := (= #22 1::Int) +#81 := (- -1::Int) +#84 := (= #81 1::Int) +#85 := [rewrite]: #84 +#82 := (= #22 #81) +#51 := (= #9 -1::Int) +#52 := [rewrite]: #51 +#83 := [monotonicity #52]: #82 +#87 := [trans #83 #85]: #86 +#79 := (= #21 #78) +#80 := [rewrite]: #79 +#90 := [monotonicity #80 #87]: #89 +#94 := [trans #90 #92]: #93 +#97 := [monotonicity #94]: #96 +#101 := [trans #97 #99]: #100 +#76 := (= #20 #75) +#77 := [monotonicity #52]: #76 +#73 := (iff #19 #72) +#70 := (iff #18 #69) +#64 := (iff #15 #63) +#65 := [monotonicity #52]: #64 +#71 := [monotonicity #65]: #70 +#67 := (iff #16 #66) +#68 := [monotonicity #65]: #67 +#74 := [monotonicity #68 #71]: #73 +#104 := [monotonicity #74 #77 #101]: #103 +#61 := (iff #13 #60) +#62 := [rewrite]: #61 +#107 := [monotonicity #62 #104]: #106 +#114 := [trans #107 #112]: #113 +#58 := (iff #11 false) +#53 := (= -1::Int 0::Int) +#56 := (iff #53 false) +#57 := [rewrite]: #56 +#54 := (iff #11 #53) +#55 := [monotonicity #52]: #54 +#59 := [trans #55 #57]: #58 +#117 := [monotonicity #59 #114]: #116 +#121 := [trans #117 #119]: #120 +#124 := [monotonicity #121]: #123 +#129 := [trans #124 #127]: #128 +#132 := [monotonicity #129]: #131 +#201 := [trans #132 #199]: #200 +#49 := [asserted]: #29 +[mp #49 #201]: false +unsat +aaecefccca197f785d6ec165e82f88f0ae2f4e23 78 0 +#2 := false +#9 := 0::Int +#8 := 3::Int +#18 := (- 3::Int) +#17 := (- 0::Int) +#19 := (mod #17 #18) +#20 := (- #19) +#16 := (mod 0::Int 3::Int) +#13 := (< 0::Int 3::Int) +#12 := (< 0::Int 0::Int) +#14 := (and #12 #13) +#15 := (or #14 #14) +#21 := (ite #15 #16 #20) +#11 := (= 0::Int 0::Int) +#22 := (ite #11 0::Int #21) +#10 := (= 3::Int 0::Int) +#23 := (ite #10 0::Int #22) +#24 := (= #23 0::Int) +#25 := (not #24) +#99 := (iff #25 false) +#1 := true +#94 := (not true) +#97 := (iff #94 false) +#98 := [rewrite]: #97 +#95 := (iff #25 #94) +#92 := (iff #24 true) +#48 := (iff #11 true) +#49 := [rewrite]: #48 +#90 := (iff #24 #11) +#84 := (ite false 0::Int 0::Int) +#87 := (= #84 0::Int) +#88 := [rewrite]: #87 +#85 := (= #23 #84) +#82 := (= #22 0::Int) +#77 := (ite true 0::Int 0::Int) +#80 := (= #77 0::Int) +#81 := [rewrite]: #80 +#78 := (= #22 #77) +#75 := (= #21 0::Int) +#70 := (ite #14 0::Int 0::Int) +#73 := (= #70 0::Int) +#74 := [rewrite]: #73 +#71 := (= #21 #70) +#68 := (= #20 0::Int) +#54 := (= #17 0::Int) +#55 := [rewrite]: #54 +#66 := (= #20 #17) +#64 := (= #19 0::Int) +#56 := -3::Int +#59 := (mod 0::Int -3::Int) +#62 := (= #59 0::Int) +#63 := [rewrite]: #62 +#60 := (= #19 #59) +#57 := (= #18 -3::Int) +#58 := [rewrite]: #57 +#61 := [monotonicity #55 #58]: #60 +#65 := [trans #61 #63]: #64 +#67 := [monotonicity #65]: #66 +#69 := [trans #67 #55]: #68 +#52 := (= #16 0::Int) +#53 := [rewrite]: #52 +#50 := (iff #15 #14) +#51 := [rewrite]: #50 +#72 := [monotonicity #51 #53 #69]: #71 +#76 := [trans #72 #74]: #75 +#79 := [monotonicity #49 #76]: #78 +#83 := [trans #79 #81]: #82 +#46 := (iff #10 false) +#47 := [rewrite]: #46 +#86 := [monotonicity #47 #83]: #85 +#89 := [trans #86 #88]: #24 +#91 := [monotonicity #89]: #90 +#93 := [trans #91 #49]: #92 +#96 := [monotonicity #93]: #95 +#100 := [trans #96 #98]: #99 +#45 := [asserted]: #25 +[mp #45 #100]: false +unsat +000d5a08395f518246c54a195994fc62266f45ed 107 0 +#2 := false +#10 := 0::Int #8 := 3::Int #9 := (- 3::Int) -#10 := (f3 #9 #9) -#12 := (= #10 1::Int) -#13 := (not #12) -#86 := (iff #13 #83) -#73 := (= 1::Int #67) -#78 := (not #73) -#84 := (iff #78 #83) -#81 := (iff #73 #70) -#82 := [rewrite]: #81 -#85 := [monotonicity #82]: #84 -#79 := (iff #13 #78) -#76 := (iff #12 #73) -#74 := (iff #70 #73) -#75 := [rewrite]: #74 -#71 := (iff #12 #70) -#68 := (= #10 #67) -#65 := (= #9 -3::Int) +#19 := (- #9) +#18 := (- 0::Int) +#20 := (mod #18 #19) +#21 := (- #20) +#17 := (mod 0::Int #9) +#14 := (< 0::Int #9) +#13 := (< 0::Int 0::Int) +#15 := (and #13 #14) +#16 := (or #15 #15) +#22 := (ite #16 #17 #21) +#12 := (= 0::Int 0::Int) +#23 := (ite #12 0::Int #22) +#11 := (= #9 0::Int) +#24 := (ite #11 0::Int #23) +#25 := (= #24 0::Int) +#26 := (not #25) +#128 := (iff #26 false) +#1 := true +#123 := (not true) +#126 := (iff #123 false) +#127 := [rewrite]: #126 +#124 := (iff #26 #123) +#121 := (iff #25 true) +#57 := (iff #12 true) +#58 := [rewrite]: #57 +#119 := (iff #25 #12) +#113 := (ite false 0::Int 0::Int) +#116 := (= #113 0::Int) +#117 := [rewrite]: #116 +#114 := (= #24 #113) +#111 := (= #23 0::Int) +#106 := (ite true 0::Int 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #23 #106) +#104 := (= #22 0::Int) +#47 := -3::Int +#59 := (< 0::Int -3::Int) +#62 := (and #13 #59) +#99 := (ite #62 0::Int 0::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #22 #99) +#97 := (= #21 0::Int) +#79 := (= #18 0::Int) +#80 := [rewrite]: #79 +#95 := (= #21 #18) +#93 := (= #20 0::Int) +#88 := (mod 0::Int 3::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #20 #88) +#86 := (= #19 3::Int) +#81 := (- -3::Int) +#84 := (= #81 3::Int) +#85 := [rewrite]: #84 +#82 := (= #19 #81) +#48 := (= #9 -3::Int) +#49 := [rewrite]: #48 +#83 := [monotonicity #49]: #82 +#87 := [trans #83 #85]: #86 +#90 := [monotonicity #80 #87]: #89 +#94 := [trans #90 #92]: #93 +#96 := [monotonicity #94]: #95 +#98 := [trans #96 #80]: #97 +#77 := (= #17 0::Int) +#72 := (mod 0::Int -3::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #17 #72) +#74 := [monotonicity #49]: #73 +#78 := [trans #74 #76]: #77 +#70 := (iff #16 #62) +#65 := (or #62 #62) +#68 := (iff #65 #62) +#69 := [rewrite]: #68 +#66 := (iff #16 #65) +#63 := (iff #15 #62) +#60 := (iff #14 #59) +#61 := [monotonicity #49]: #60 +#64 := [monotonicity #61]: #63 +#67 := [monotonicity #64 #64]: #66 +#71 := [trans #67 #69]: #70 +#101 := [monotonicity #71 #78 #98]: #100 +#105 := [trans #101 #103]: #104 +#108 := [monotonicity #58 #105]: #107 +#112 := [trans #108 #110]: #111 +#55 := (iff #11 false) +#50 := (= -3::Int 0::Int) +#53 := (iff #50 false) +#54 := [rewrite]: #53 +#51 := (iff #11 #50) +#52 := [monotonicity #49]: #51 +#56 := [trans #52 #54]: #55 +#115 := [monotonicity #56 #112]: #114 +#118 := [trans #115 #117]: #25 +#120 := [monotonicity #118]: #119 +#122 := [trans #120 #58]: #121 +#125 := [monotonicity #122]: #124 +#129 := [trans #125 #127]: #128 +#46 := [asserted]: #26 +[mp #46 #129]: false +unsat +54496e8e1bdde41302d50e03b35540e70008eccf 123 0 +#2 := false +#11 := 1::Int +#8 := 3::Int +#21 := (- 3::Int) +#20 := (- 1::Int) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod 1::Int 3::Int) +#9 := 0::Int +#14 := (< 0::Int 3::Int) +#16 := (< 1::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 1::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= 1::Int 0::Int) +#25 := (ite #12 0::Int #24) +#10 := (= 3::Int 0::Int) +#26 := (ite #10 1::Int #25) +#27 := (= #26 1::Int) +#28 := (not #27) +#144 := (iff #28 false) +#53 := (and #14 #16) +#56 := (or #15 #53) +#107 := (not #56) +#142 := (iff #107 false) +#1 := true +#137 := (not true) +#140 := (iff #137 false) +#141 := [rewrite]: #140 +#138 := (iff #107 #137) +#135 := (iff #56 true) +#130 := (or true false) +#133 := (iff #130 true) +#134 := [rewrite]: #133 +#131 := (iff #56 #130) +#128 := (iff #53 false) +#123 := (and true false) +#126 := (iff #123 false) +#127 := [rewrite]: #126 +#124 := (iff #53 #123) +#121 := (iff #16 false) +#122 := [rewrite]: #121 +#112 := (iff #14 true) +#113 := [rewrite]: #112 +#125 := [monotonicity #113 #122]: #124 +#129 := [trans #125 #127]: #128 +#119 := (iff #15 true) +#114 := (and true true) +#117 := (iff #114 true) +#118 := [rewrite]: #117 +#115 := (iff #15 #114) +#110 := (iff #13 true) +#111 := [rewrite]: #110 +#116 := [monotonicity #111 #113]: #115 +#120 := [trans #116 #118]: #119 +#132 := [monotonicity #120 #129]: #131 +#136 := [trans #132 #134]: #135 +#139 := [monotonicity #136]: #138 +#143 := [trans #139 #141]: #142 +#108 := (iff #28 #107) +#105 := (iff #27 #56) +#78 := -2::Int +#83 := (ite #56 1::Int -2::Int) +#100 := (= #83 1::Int) +#103 := (iff #100 #56) +#104 := [rewrite]: #103 +#101 := (iff #27 #100) +#98 := (= #26 #83) +#93 := (ite false 1::Int #83) +#96 := (= #93 #83) +#97 := [rewrite]: #96 +#94 := (= #26 #93) +#91 := (= #25 #83) +#86 := (ite false 0::Int #83) +#89 := (= #86 #83) +#90 := [rewrite]: #89 +#87 := (= #25 #86) +#84 := (= #24 #83) +#81 := (= #23 -2::Int) +#70 := 2::Int +#75 := (- 2::Int) +#79 := (= #75 -2::Int) +#80 := [rewrite]: #79 +#76 := (= #23 #75) +#73 := (= #22 2::Int) +#64 := -3::Int +#61 := -1::Int +#67 := (mod -1::Int -3::Int) +#71 := (= #67 2::Int) +#72 := [rewrite]: #71 +#68 := (= #22 #67) +#65 := (= #21 -3::Int) #66 := [rewrite]: #65 -#69 := [monotonicity #66 #66]: #68 -#72 := [monotonicity #69]: #71 -#77 := [trans #72 #75]: #76 -#80 := [monotonicity #77]: #79 -#87 := [trans #80 #85]: #86 -#63 := [asserted]: #13 -#88 := [mp #63 #87]: #83 -#588 := (not #752) -#589 := (or #588 #70) -#338 := (* -1::Int -3::Int) -#422 := (div #338 #338) -#423 := (* -1::Int #422) -#424 := (+ #67 #423) -#415 := (= #424 0::Int) -#426 := (div -3::Int -3::Int) -#427 := (* -1::Int #426) -#428 := (+ #67 #427) -#425 := (= #428 0::Int) -#429 := (>= -3::Int 0::Int) -#408 := (<= -3::Int 0::Int) -#743 := (or #408 #429) -#745 := (not #743) -#402 := (or #408 #408) -#532 := (not #402) -#739 := (or #532 #745) -#413 := (ite #739 #425 #415) -#414 := (= #67 0::Int) -#746 := (= -3::Int 0::Int) -#747 := (or #746 #746) -#748 := (ite #747 #414 #413) -#590 := (or #588 #748) -#592 := (iff #590 #589) -#682 := (iff #589 #589) -#686 := [rewrite]: #682 -#587 := (iff #748 #70) -#681 := (ite false #414 #70) -#584 := (iff #681 #70) -#586 := [rewrite]: #584 -#684 := (iff #748 #681) -#585 := (iff #413 #70) -#574 := (ite false #70 #70) -#535 := (iff #574 #70) -#683 := [rewrite]: #535 -#575 := (iff #413 #574) -#689 := (iff #415 #70) -#713 := (+ -1::Int #67) -#703 := (= #713 0::Int) -#710 := (iff #703 #70) -#705 := [rewrite]: #710 -#690 := (iff #415 #703) -#687 := (= #424 #713) -#430 := (+ #67 -1::Int) -#717 := (= #430 #713) -#706 := [rewrite]: #717 -#533 := (= #424 #430) -#702 := (= #423 -1::Int) -#723 := (* -1::Int 1::Int) -#435 := (= #723 -1::Int) -#436 := [rewrite]: #435 -#701 := (= #423 #723) -#694 := (= #422 1::Int) -#696 := (div 3::Int 3::Int) -#699 := (= #696 1::Int) -#693 := [rewrite]: #699 -#697 := (= #422 #696) -#553 := (= #338 3::Int) -#554 := [rewrite]: #553 -#698 := [monotonicity #554 #554]: #697 -#700 := [trans #698 #693]: #694 -#695 := [monotonicity #700]: #701 -#531 := [trans #695 #436]: #702 -#534 := [monotonicity #531]: #533 -#688 := [trans #534 #706]: #687 -#691 := [monotonicity #688]: #690 -#692 := [trans #691 #705]: #689 -#711 := (iff #425 #70) -#704 := (iff #425 #703) -#707 := (= #428 #713) -#712 := (= #428 #430) -#714 := (= #427 -1::Int) -#433 := (= #427 #723) -#722 := (= #426 1::Int) -#719 := [rewrite]: #722 -#434 := [monotonicity #719]: #433 -#715 := [trans #434 #436]: #714 -#716 := [monotonicity #715]: #712 -#708 := [trans #716 #706]: #707 -#709 := [monotonicity #708]: #704 -#552 := [trans #709 #705]: #711 -#444 := (iff #739 false) -#750 := (or false false) -#405 := (iff #750 false) -#741 := [rewrite]: #405 -#721 := (iff #739 #750) -#344 := (iff #745 false) -#1 := true -#731 := (not true) -#733 := (iff #731 false) -#371 := [rewrite]: #733 -#449 := (iff #745 #731) -#447 := (iff #743 true) -#737 := (or true false) -#724 := (iff #737 true) -#725 := [rewrite]: #724 -#735 := (iff #743 #737) -#376 := (iff #429 false) -#377 := [rewrite]: #376 -#385 := (iff #408 true) -#726 := [rewrite]: #385 -#738 := [monotonicity #726 #377]: #735 -#448 := [trans #738 #725]: #447 -#450 := [monotonicity #448]: #449 -#720 := [trans #450 #371]: #344 -#734 := (iff #532 false) -#732 := (iff #532 #731) -#729 := (iff #402 true) -#389 := (or true true) -#392 := (iff #389 true) -#728 := [rewrite]: #392 -#390 := (iff #402 #389) -#391 := [monotonicity #726 #726]: #390 -#730 := [trans #391 #728]: #729 -#727 := [monotonicity #730]: #732 -#736 := [trans #727 #371]: #734 -#443 := [monotonicity #736 #720]: #721 -#718 := [trans #443 #741]: #444 -#576 := [monotonicity #718 #552 #692]: #575 -#680 := [trans #576 #683]: #585 -#401 := (iff #747 false) -#740 := (iff #747 #750) -#749 := (iff #746 false) -#744 := [rewrite]: #749 -#400 := [monotonicity #744 #744]: #740 -#742 := [trans #400 #741]: #401 -#569 := [monotonicity #742 #680]: #684 -#580 := [trans #569 #586]: #587 -#685 := [monotonicity #580]: #592 -#673 := [trans #685 #686]: #592 -#591 := [quant-inst #64 #64]: #590 -#675 := [mp #591 #673]: #589 -[unit-resolution #675 #88 #757]: false -unsat -602bd1c64454e63be2273eaf718ba5b3413f9555 333 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#18 := (f3 #16 #17) -#756 := (pattern #18) -#19 := 0::Int -#101 := -1::Int -#105 := (* -1::Int #17) -#102 := (* -1::Int #16) -#108 := (div #102 #105) -#259 := (* -1::Int #108) -#260 := (+ #18 #259) -#261 := (= #260 0::Int) -#29 := (div #16 #17) -#256 := (* -1::Int #29) -#257 := (+ #18 #256) -#258 := (= #257 0::Int) -#134 := (>= #16 0::Int) -#127 := (<= #17 0::Int) -#219 := (or #127 #134) -#220 := (not #219) -#123 := (<= #16 0::Int) -#217 := (or #123 #127) -#218 := (not #217) -#223 := (or #218 #220) -#262 := (ite #223 #258 #261) -#255 := (= #18 0::Int) -#21 := (= #17 0::Int) -#20 := (= #16 0::Int) -#22 := (or #20 #21) -#263 := (ite #22 #255 #262) -#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #263) -#266 := (forall (vars (?v0 Int) (?v1 Int)) #263) -#760 := (iff #266 #757) -#758 := (iff #263 #263) -#759 := [refl]: #758 -#761 := [quant-intro #759]: #760 -#226 := (ite #223 #29 #108) -#229 := (ite #22 0::Int #226) -#232 := (= #18 #229) -#235 := (forall (vars (?v0 Int) (?v1 Int)) #232) -#267 := (iff #235 #266) -#264 := (iff #232 #263) -#265 := [rewrite]: #264 -#268 := [quant-intro #265]: #267 -#135 := (not #134) -#128 := (not #127) -#138 := (and #128 #135) -#124 := (not #123) -#131 := (and #124 #128) -#141 := (or #131 #138) -#144 := (ite #141 #29 #108) -#147 := (ite #22 0::Int #144) -#150 := (= #18 #147) -#153 := (forall (vars (?v0 Int) (?v1 Int)) #150) -#236 := (iff #153 #235) -#233 := (iff #150 #232) -#230 := (= #147 #229) -#227 := (= #144 #226) -#224 := (iff #141 #223) -#221 := (iff #138 #220) -#222 := [rewrite]: #221 -#211 := (iff #131 #218) -#212 := [rewrite]: #211 -#225 := [monotonicity #212 #222]: #224 -#228 := [monotonicity #225]: #227 -#231 := [monotonicity #228]: #230 -#234 := [monotonicity #231]: #233 -#237 := [quant-intro #234]: #236 -#215 := (~ #153 #153) -#213 := (~ #150 #150) -#214 := [refl]: #213 -#216 := [nnf-pos #214]: #215 -#31 := (- #17) -#30 := (- #16) -#32 := (div #30 #31) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#33 := (ite #28 #29 #32) -#34 := (ite #22 0::Int #33) -#35 := (= #18 #34) -#36 := (forall (vars (?v0 Int) (?v1 Int)) #35) -#156 := (iff #36 #153) -#95 := (and #24 #26) -#98 := (or #25 #95) -#111 := (ite #98 #29 #108) -#114 := (ite #22 0::Int #111) -#117 := (= #18 #114) -#120 := (forall (vars (?v0 Int) (?v1 Int)) #117) -#154 := (iff #120 #153) -#151 := (iff #117 #150) -#148 := (= #114 #147) -#145 := (= #111 #144) -#142 := (iff #98 #141) -#139 := (iff #95 #138) -#136 := (iff #26 #135) -#137 := [rewrite]: #136 -#129 := (iff #24 #128) -#130 := [rewrite]: #129 -#140 := [monotonicity #130 #137]: #139 -#132 := (iff #25 #131) -#125 := (iff #23 #124) -#126 := [rewrite]: #125 -#133 := [monotonicity #126 #130]: #132 -#143 := [monotonicity #133 #140]: #142 -#146 := [monotonicity #143]: #145 -#149 := [monotonicity #146]: #148 -#152 := [monotonicity #149]: #151 -#155 := [quant-intro #152]: #154 -#121 := (iff #36 #120) -#118 := (iff #35 #117) -#115 := (= #34 #114) -#112 := (= #33 #111) -#109 := (= #32 #108) -#106 := (= #31 #105) -#107 := [rewrite]: #106 -#103 := (= #30 #102) -#104 := [rewrite]: #103 -#110 := [monotonicity #104 #107]: #109 -#99 := (iff #28 #98) -#96 := (iff #27 #95) -#97 := [rewrite]: #96 -#100 := [monotonicity #97]: #99 -#113 := [monotonicity #100 #110]: #112 -#116 := [monotonicity #113]: #115 -#119 := [monotonicity #116]: #118 -#122 := [quant-intro #119]: #121 -#157 := [trans #122 #155]: #156 -#94 := [asserted]: #36 -#158 := [mp #94 #157]: #153 -#207 := [mp~ #158 #216]: #153 -#238 := [mp #207 #237]: #235 -#269 := [mp #238 #268]: #266 -#762 := [mp #269 #761]: #757 -#13 := 1::Int -#69 := -3::Int -#66 := -5::Int -#72 := (f3 -5::Int -3::Int) -#75 := (= #72 1::Int) -#88 := (not #75) -#10 := 3::Int -#11 := (- 3::Int) -#8 := 5::Int -#9 := (- 5::Int) -#12 := (f3 #9 #11) -#14 := (= #12 1::Int) -#15 := (not #14) -#91 := (iff #15 #88) -#78 := (= 1::Int #72) -#83 := (not #78) -#89 := (iff #83 #88) -#86 := (iff #78 #75) -#87 := [rewrite]: #86 -#90 := [monotonicity #87]: #89 -#84 := (iff #15 #83) -#81 := (iff #14 #78) -#79 := (iff #75 #78) -#80 := [rewrite]: #79 -#76 := (iff #14 #75) -#73 := (= #12 #72) -#70 := (= #11 -3::Int) -#71 := [rewrite]: #70 -#67 := (= #9 -5::Int) -#68 := [rewrite]: #67 -#74 := [monotonicity #68 #71]: #73 +#62 := (= #20 -1::Int) +#63 := [rewrite]: #62 +#69 := [monotonicity #63 #66]: #68 +#74 := [trans #69 #72]: #73 #77 := [monotonicity #74]: #76 #82 := [trans #77 #80]: #81 -#85 := [monotonicity #82]: #84 -#92 := [trans #85 #90]: #91 -#65 := [asserted]: #15 -#93 := [mp #65 #92]: #88 -#670 := (not #757) -#677 := (or #670 #75) -#343 := (* -1::Int -3::Int) -#427 := (* -1::Int -5::Int) -#428 := (div #427 #343) -#429 := (* -1::Int #428) -#420 := (+ #72 #429) -#431 := (= #420 0::Int) -#432 := (div -5::Int -3::Int) -#433 := (* -1::Int #432) -#430 := (+ #72 #433) -#434 := (= #430 0::Int) -#413 := (>= -5::Int 0::Int) -#748 := (<= -3::Int 0::Int) -#750 := (or #748 #413) -#407 := (not #750) -#537 := (<= -5::Int 0::Int) -#744 := (or #537 #748) -#418 := (not #744) -#419 := (or #418 #407) -#751 := (ite #419 #434 #431) -#752 := (= #72 0::Int) -#753 := (= -3::Int 0::Int) -#754 := (= -5::Int 0::Int) -#749 := (or #754 #753) -#755 := (ite #749 #752 #751) -#661 := (or #670 #755) -#664 := (iff #661 #677) -#666 := (iff #677 #677) -#667 := [rewrite]: #666 -#675 := (iff #755 #75) -#683 := (ite false #752 #75) -#673 := (iff #683 #75) -#674 := [rewrite]: #673 -#679 := (iff #755 #683) -#681 := (iff #751 #75) -#719 := 2::Int -#704 := (= #72 2::Int) -#678 := (ite false #704 #75) -#669 := (iff #678 #75) -#671 := [rewrite]: #669 -#680 := (iff #751 #678) -#687 := (iff #431 #75) -#589 := (+ -1::Int #72) -#594 := (= #589 0::Int) -#597 := (iff #594 #75) -#690 := [rewrite]: #597 -#595 := (iff #431 #594) -#585 := (= #420 #589) -#686 := (+ #72 -1::Int) -#591 := (= #686 #589) -#592 := [rewrite]: #591 -#689 := (= #420 #686) -#590 := (= #429 -1::Int) -#579 := (* -1::Int 1::Int) -#540 := (= #579 -1::Int) -#688 := [rewrite]: #540 -#580 := (= #429 #579) -#694 := (= #428 1::Int) -#539 := (div 5::Int 3::Int) -#695 := (= #539 1::Int) -#696 := [rewrite]: #695 -#692 := (= #428 #539) -#536 := (= #343 3::Int) -#538 := [rewrite]: #536 -#700 := (= #427 5::Int) -#707 := [rewrite]: #700 -#693 := [monotonicity #707 #538]: #692 -#697 := [trans #693 #696]: #694 -#581 := [monotonicity #697]: #580 -#685 := [trans #581 #688]: #590 -#574 := [monotonicity #685]: #689 -#593 := [trans #574 #592]: #585 -#596 := [monotonicity #593]: #595 -#691 := [trans #596 #690]: #687 -#705 := (iff #434 #704) -#722 := -2::Int -#710 := (+ -2::Int #72) -#701 := (= #710 0::Int) -#698 := (iff #701 #704) -#699 := [rewrite]: #698 -#702 := (iff #434 #701) -#558 := (= #430 #710) -#709 := (+ #72 -2::Int) -#716 := (= #709 #710) -#557 := [rewrite]: #716 -#714 := (= #430 #709) -#713 := (= #433 -2::Int) -#717 := (* -1::Int 2::Int) -#711 := (= #717 -2::Int) -#712 := [rewrite]: #711 -#721 := (= #433 #717) -#720 := (= #432 2::Int) -#435 := [rewrite]: #720 -#718 := [monotonicity #435]: #721 -#708 := [trans #718 #712]: #713 -#715 := [monotonicity #708]: #714 -#559 := [trans #715 #557]: #558 -#703 := [monotonicity #559]: #702 -#706 := [trans #703 #699]: #705 -#440 := (iff #419 false) -#406 := (or false false) -#731 := (iff #406 false) -#394 := [rewrite]: #731 -#438 := (iff #419 #406) -#724 := (iff #407 false) -#1 := true -#381 := (not true) -#740 := (iff #381 false) -#743 := [rewrite]: #740 -#723 := (iff #407 #381) -#448 := (iff #750 true) -#454 := (or true false) -#725 := (iff #454 true) -#726 := [rewrite]: #725 -#455 := (iff #750 #454) -#452 := (iff #413 false) -#453 := [rewrite]: #452 -#734 := (iff #748 true) -#735 := [rewrite]: #734 -#349 := [monotonicity #735 #453]: #455 -#449 := [trans #349 #726]: #448 -#727 := [monotonicity #449]: #723 -#728 := [trans #727 #743]: #724 -#729 := (iff #418 false) -#382 := (iff #418 #381) -#739 := (iff #744 true) -#736 := (or true true) -#738 := (iff #736 true) -#376 := [rewrite]: #738 -#737 := (iff #744 #736) -#397 := (iff #537 true) -#733 := [rewrite]: #397 -#732 := [monotonicity #733 #735]: #737 -#741 := [trans #732 #376]: #739 -#742 := [monotonicity #741]: #382 -#730 := [trans #742 #743]: #729 -#439 := [monotonicity #730 #728]: #438 -#441 := [trans #439 #394]: #440 -#672 := [monotonicity #441 #706 #691]: #680 -#682 := [trans #672 #671]: #681 -#395 := (iff #749 false) -#747 := (iff #749 #406) -#410 := (iff #753 false) -#746 := [rewrite]: #410 -#745 := (iff #754 false) -#405 := [rewrite]: #745 -#390 := [monotonicity #405 #746]: #747 -#396 := [trans #390 #394]: #395 -#684 := [monotonicity #396 #682]: #679 -#676 := [trans #684 #674]: #675 -#665 := [monotonicity #676]: #664 -#663 := [trans #665 #667]: #664 -#662 := [quant-inst #66 #69]: #661 -#668 := [mp #662 #663]: #677 -[unit-resolution #668 #93 #762]: false -unsat -9d955d673529089780c55958aa0742a5b1471d68 273 0 -#2 := false -decl f3 :: (-> Int Int Int) -#13 := (:var 0 Int) -#12 := (:var 1 Int) -#32 := (f3 #12 #13) -#756 := (pattern #32) -#8 := 0::Int -#87 := -1::Int -#91 := (* -1::Int #13) -#88 := (* -1::Int #12) -#152 := (mod #88 #91) -#267 := (+ #32 #152) -#268 := (= #267 0::Int) -#33 := (mod #12 #13) -#264 := (* -1::Int #33) -#265 := (+ #32 #264) -#266 := (= #265 0::Int) -#126 := (>= #12 0::Int) -#119 := (<= #13 0::Int) -#211 := (or #119 #126) -#212 := (not #211) -#115 := (<= #12 0::Int) -#209 := (or #115 #119) -#210 := (not #209) -#215 := (or #210 #212) -#269 := (ite #215 #266 #268) -#263 := (= #32 0::Int) -#15 := (= #12 0::Int) -#270 := (ite #15 #263 #269) -#262 := (= #12 #32) -#16 := (= #13 0::Int) -#271 := (ite #16 #262 #270) -#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271) -#274 := (forall (vars (?v0 Int) (?v1 Int)) #271) -#760 := (iff #274 #757) -#758 := (iff #271 #271) -#759 := [refl]: #758 -#761 := [quant-intro #759]: #760 -#158 := (* -1::Int #152) -#231 := (ite #215 #33 #158) -#234 := (ite #15 0::Int #231) -#237 := (ite #16 #12 #234) -#240 := (= #32 #237) -#243 := (forall (vars (?v0 Int) (?v1 Int)) #240) -#275 := (iff #243 #274) -#272 := (iff #240 #271) -#273 := [rewrite]: #272 -#276 := [quant-intro #273]: #275 -#127 := (not #126) -#120 := (not #119) -#130 := (and #120 #127) -#116 := (not #115) -#123 := (and #116 #120) -#133 := (or #123 #130) -#178 := (ite #133 #33 #158) -#181 := (ite #15 0::Int #178) -#184 := (ite #16 #12 #181) -#187 := (= #32 #184) -#190 := (forall (vars (?v0 Int) (?v1 Int)) #187) -#244 := (iff #190 #243) -#241 := (iff #187 #240) -#238 := (= #184 #237) -#235 := (= #181 #234) -#232 := (= #178 #231) -#216 := (iff #133 #215) -#213 := (iff #130 #212) -#214 := [rewrite]: #213 -#203 := (iff #123 #210) -#204 := [rewrite]: #203 -#217 := [monotonicity #204 #214]: #216 -#233 := [monotonicity #217]: #232 -#236 := [monotonicity #233]: #235 -#239 := [monotonicity #236]: #238 -#242 := [monotonicity #239]: #241 -#245 := [quant-intro #242]: #244 -#201 := (~ #190 #190) -#200 := (~ #187 #187) -#197 := [refl]: #200 -#202 := [nnf-pos #197]: #201 -#26 := (- #13) -#25 := (- #12) -#34 := (mod #25 #26) -#35 := (- #34) -#19 := (< 0::Int #13) -#21 := (< #12 0::Int) -#22 := (and #21 #19) -#18 := (< 0::Int #12) -#20 := (and #18 #19) -#23 := (or #20 #22) -#36 := (ite #23 #33 #35) -#37 := (ite #15 0::Int #36) -#38 := (ite #16 #12 #37) -#39 := (= #32 #38) -#40 := (forall (vars (?v0 Int) (?v1 Int)) #39) -#193 := (iff #40 #190) -#81 := (and #19 #21) -#84 := (or #20 #81) -#163 := (ite #84 #33 #158) -#72 := (= 0::Int #12) -#166 := (ite #72 0::Int #163) -#75 := (= 0::Int #13) -#169 := (ite #75 #12 #166) -#172 := (= #32 #169) -#175 := (forall (vars (?v0 Int) (?v1 Int)) #172) -#191 := (iff #175 #190) -#188 := (iff #172 #187) -#185 := (= #169 #184) -#182 := (= #166 #181) -#179 := (= #163 #178) -#134 := (iff #84 #133) -#131 := (iff #81 #130) -#128 := (iff #21 #127) -#129 := [rewrite]: #128 -#121 := (iff #19 #120) -#122 := [rewrite]: #121 -#132 := [monotonicity #122 #129]: #131 -#124 := (iff #20 #123) -#117 := (iff #18 #116) -#118 := [rewrite]: #117 -#125 := [monotonicity #118 #122]: #124 -#135 := [monotonicity #125 #132]: #134 -#180 := [monotonicity #135]: #179 -#109 := (iff #72 #15) -#110 := [rewrite]: #109 -#183 := [monotonicity #110 #180]: #182 -#111 := (iff #75 #16) -#112 := [rewrite]: #111 -#186 := [monotonicity #112 #183]: #185 -#189 := [monotonicity #186]: #188 -#192 := [quant-intro #189]: #191 -#176 := (iff #40 #175) -#173 := (iff #39 #172) -#170 := (= #38 #169) -#167 := (= #37 #166) -#164 := (= #36 #163) -#161 := (= #35 #158) -#155 := (- #152) -#159 := (= #155 #158) -#160 := [rewrite]: #159 -#156 := (= #35 #155) -#153 := (= #34 #152) -#92 := (= #26 #91) -#93 := [rewrite]: #92 -#89 := (= #25 #88) -#90 := [rewrite]: #89 -#154 := [monotonicity #90 #93]: #153 -#157 := [monotonicity #154]: #156 -#162 := [trans #157 #160]: #161 -#85 := (iff #23 #84) -#82 := (iff #22 #81) -#83 := [rewrite]: #82 -#86 := [monotonicity #83]: #85 -#165 := [monotonicity #86 #162]: #164 -#73 := (iff #15 #72) -#74 := [rewrite]: #73 -#168 := [monotonicity #74 #165]: #167 -#76 := (iff #16 #75) -#77 := [rewrite]: #76 -#171 := [monotonicity #77 #168]: #170 -#174 := [monotonicity #171]: #173 -#177 := [quant-intro #174]: #176 -#194 := [trans #177 #192]: #193 -#151 := [asserted]: #40 -#195 := [mp #151 #194]: #190 -#198 := [mp~ #195 #202]: #190 -#246 := [mp #198 #245]: #243 -#277 := [mp #246 #276]: #274 -#762 := [mp #277 #761]: #757 -#9 := (f3 0::Int 0::Int) -#10 := (= #9 0::Int) -#11 := (not #10) -#60 := [asserted]: #11 -#703 := (not #757) -#709 := (or #703 #10) -#335 := (* -1::Int 0::Int) -#420 := (mod #335 #335) -#421 := (+ #9 #420) -#422 := (= #421 0::Int) -#413 := (mod 0::Int 0::Int) -#424 := (* -1::Int #413) -#425 := (+ #9 #424) -#353 := (= #425 0::Int) -#426 := (>= 0::Int 0::Int) -#423 := (<= 0::Int 0::Int) -#427 := (or #423 #426) -#406 := (not #427) -#741 := (or #423 #423) -#743 := (not #741) -#400 := (or #743 #406) -#530 := (ite #400 #353 #422) -#737 := (= 0::Int 0::Int) -#411 := (ite #737 #10 #530) -#61 := (= 0::Int #9) -#412 := (ite #737 #61 #411) -#550 := (or #703 #412) -#552 := (iff #550 #709) -#695 := (iff #709 #709) -#696 := [rewrite]: #695 -#707 := (iff #412 #10) -#1 := true -#704 := (ite true #10 #10) -#701 := (iff #704 #10) -#702 := [rewrite]: #701 -#705 := (iff #412 #704) -#711 := (iff #411 #10) -#341 := (+ #9 #413) -#441 := (= #341 0::Int) -#712 := (ite true #10 #441) -#710 := (iff #712 #10) -#714 := [rewrite]: #710 -#713 := (iff #411 #712) -#433 := (iff #530 #441) -#720 := (ite false #353 #441) -#431 := (iff #720 #441) -#432 := [rewrite]: #431 -#717 := (iff #530 #720) -#442 := (iff #422 #441) -#718 := (= #421 #341) -#447 := (= #420 #413) -#445 := (= #335 0::Int) -#446 := [rewrite]: #445 -#448 := [monotonicity #446 #446]: #447 -#719 := [monotonicity #448]: #718 -#716 := [monotonicity #719]: #442 -#722 := (iff #400 false) -#374 := (or false false) -#733 := (iff #374 false) -#736 := [rewrite]: #733 -#375 := (iff #400 #374) -#732 := (iff #406 false) -#740 := (not true) -#387 := (iff #740 false) -#388 := [rewrite]: #387 -#731 := (iff #406 #740) -#730 := (iff #427 true) -#742 := (or true true) -#398 := (iff #742 true) -#403 := [rewrite]: #398 -#728 := (iff #427 #742) -#726 := (iff #426 true) -#727 := [rewrite]: #726 -#746 := (iff #423 true) -#747 := [rewrite]: #746 -#729 := [monotonicity #747 #727]: #728 -#725 := [trans #729 #403]: #730 -#369 := [monotonicity #725]: #731 -#734 := [trans #369 #388]: #732 -#389 := (iff #743 false) -#383 := (iff #743 #740) -#739 := (iff #741 true) -#748 := (iff #741 #742) -#738 := [monotonicity #747 #747]: #748 -#399 := [trans #738 #403]: #739 -#724 := [monotonicity #399]: #383 -#390 := [trans #724 #388]: #389 -#735 := [monotonicity #390 #734]: #375 -#723 := [trans #735 #736]: #722 -#721 := [monotonicity #723 #716]: #717 -#434 := [trans #721 #432]: #433 -#744 := (iff #737 true) -#745 := [rewrite]: #744 -#428 := [monotonicity #745 #434]: #713 -#715 := [trans #428 #714]: #711 -#67 := (iff #61 #10) -#68 := [rewrite]: #67 -#706 := [monotonicity #745 #68 #715]: #705 -#708 := [trans #706 #702]: #707 -#694 := [monotonicity #708]: #552 -#697 := [trans #694 #696]: #552 -#551 := [quant-inst #8 #8]: #550 -#691 := [mp #551 #697]: #709 -[unit-resolution #691 #60 #762]: false -unsat -ea8997dddba0ea4cee2a7011c7fb001434f88f23 281 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#33 := (f3 #13 #14) -#754 := (pattern #33) -#9 := 0::Int -#85 := -1::Int -#89 := (* -1::Int #14) -#86 := (* -1::Int #13) -#150 := (mod #86 #89) -#265 := (+ #33 #150) -#266 := (= #265 0::Int) -#34 := (mod #13 #14) -#262 := (* -1::Int #34) -#263 := (+ #33 #262) -#264 := (= #263 0::Int) -#124 := (>= #13 0::Int) -#117 := (<= #14 0::Int) -#209 := (or #117 #124) -#210 := (not #209) -#113 := (<= #13 0::Int) -#207 := (or #113 #117) -#208 := (not #207) -#213 := (or #208 #210) -#267 := (ite #213 #264 #266) -#261 := (= #33 0::Int) -#16 := (= #13 0::Int) -#268 := (ite #16 #261 #267) -#260 := (= #13 #33) -#17 := (= #14 0::Int) -#269 := (ite #17 #260 #268) -#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #269) -#272 := (forall (vars (?v0 Int) (?v1 Int)) #269) -#758 := (iff #272 #755) -#756 := (iff #269 #269) -#757 := [refl]: #756 -#759 := [quant-intro #757]: #758 -#156 := (* -1::Int #150) -#229 := (ite #213 #34 #156) -#232 := (ite #16 0::Int #229) -#235 := (ite #17 #13 #232) -#238 := (= #33 #235) -#241 := (forall (vars (?v0 Int) (?v1 Int)) #238) -#273 := (iff #241 #272) -#270 := (iff #238 #269) -#271 := [rewrite]: #270 -#274 := [quant-intro #271]: #273 -#125 := (not #124) -#118 := (not #117) -#128 := (and #118 #125) -#114 := (not #113) -#121 := (and #114 #118) -#131 := (or #121 #128) -#176 := (ite #131 #34 #156) -#179 := (ite #16 0::Int #176) -#182 := (ite #17 #13 #179) -#185 := (= #33 #182) -#188 := (forall (vars (?v0 Int) (?v1 Int)) #185) -#242 := (iff #188 #241) -#239 := (iff #185 #238) -#236 := (= #182 #235) -#233 := (= #179 #232) -#230 := (= #176 #229) -#214 := (iff #131 #213) -#211 := (iff #128 #210) -#212 := [rewrite]: #211 -#201 := (iff #121 #208) -#202 := [rewrite]: #201 -#215 := [monotonicity #202 #212]: #214 -#231 := [monotonicity #215]: #230 -#234 := [monotonicity #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [monotonicity #237]: #239 -#243 := [quant-intro #240]: #242 -#199 := (~ #188 #188) -#198 := (~ #185 #185) -#195 := [refl]: #198 -#200 := [nnf-pos #195]: #199 -#27 := (- #14) -#26 := (- #13) -#35 := (mod #26 #27) -#36 := (- #35) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#37 := (ite #24 #34 #36) -#38 := (ite #16 0::Int #37) -#39 := (ite #17 #13 #38) -#40 := (= #33 #39) -#41 := (forall (vars (?v0 Int) (?v1 Int)) #40) -#191 := (iff #41 #188) -#79 := (and #20 #22) -#82 := (or #21 #79) -#161 := (ite #82 #34 #156) -#69 := (= 0::Int #13) -#164 := (ite #69 0::Int #161) -#73 := (= 0::Int #14) -#167 := (ite #73 #13 #164) -#170 := (= #33 #167) -#173 := (forall (vars (?v0 Int) (?v1 Int)) #170) -#189 := (iff #173 #188) -#186 := (iff #170 #185) -#183 := (= #167 #182) -#180 := (= #164 #179) -#177 := (= #161 #176) -#132 := (iff #82 #131) -#129 := (iff #79 #128) -#126 := (iff #22 #125) -#127 := [rewrite]: #126 -#119 := (iff #20 #118) -#120 := [rewrite]: #119 -#130 := [monotonicity #120 #127]: #129 -#122 := (iff #21 #121) -#115 := (iff #19 #114) -#116 := [rewrite]: #115 -#123 := [monotonicity #116 #120]: #122 -#133 := [monotonicity #123 #130]: #132 -#178 := [monotonicity #133]: #177 -#107 := (iff #69 #16) -#108 := [rewrite]: #107 -#181 := [monotonicity #108 #178]: #180 -#109 := (iff #73 #17) -#110 := [rewrite]: #109 -#184 := [monotonicity #110 #181]: #183 -#187 := [monotonicity #184]: #186 -#190 := [quant-intro #187]: #189 -#174 := (iff #41 #173) -#171 := (iff #40 #170) -#168 := (= #39 #167) -#165 := (= #38 #164) -#162 := (= #37 #161) -#159 := (= #36 #156) -#153 := (- #150) -#157 := (= #153 #156) -#158 := [rewrite]: #157 -#154 := (= #36 #153) -#151 := (= #35 #150) -#90 := (= #27 #89) -#91 := [rewrite]: #90 -#87 := (= #26 #86) -#88 := [rewrite]: #87 -#152 := [monotonicity #88 #91]: #151 -#155 := [monotonicity #152]: #154 -#160 := [trans #155 #158]: #159 -#83 := (iff #24 #82) -#80 := (iff #23 #79) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#163 := [monotonicity #84 #160]: #162 -#71 := (iff #16 #69) -#72 := [rewrite]: #71 -#166 := [monotonicity #72 #163]: #165 -#74 := (iff #17 #73) -#75 := [rewrite]: #74 -#169 := [monotonicity #75 #166]: #168 -#172 := [monotonicity #169]: #171 -#175 := [quant-intro #172]: #174 -#192 := [trans #175 #190]: #191 -#149 := [asserted]: #41 -#193 := [mp #149 #192]: #188 -#196 := [mp~ #193 #200]: #188 -#244 := [mp #196 #243]: #241 -#275 := [mp #244 #274]: #272 -#760 := [mp #275 #759]: #755 -decl f4 :: Int -#8 := f4 -#10 := (f3 f4 0::Int) -#62 := (= f4 #10) -#65 := (not #62) -#11 := (= #10 f4) -#12 := (not #11) -#66 := (iff #12 #65) -#63 := (iff #11 #62) -#64 := [rewrite]: #63 -#67 := [monotonicity #64]: #66 -#61 := [asserted]: #12 -#70 := [mp #61 #67]: #65 -#548 := (not #755) -#549 := (or #548 #62) -#333 := (* -1::Int 0::Int) -#418 := (* -1::Int f4) -#419 := (mod #418 #333) -#420 := (+ #10 #419) -#411 := (= #420 0::Int) -#422 := (mod f4 0::Int) -#423 := (* -1::Int #422) -#351 := (+ #10 #423) -#424 := (= #351 0::Int) -#421 := (>= f4 0::Int) -#425 := (<= 0::Int 0::Int) -#404 := (or #425 #421) -#739 := (not #404) -#741 := (<= f4 0::Int) -#398 := (or #741 #425) -#528 := (not #398) -#735 := (or #528 #739) -#409 := (ite #735 #424 #411) -#410 := (= #10 0::Int) -#742 := (= f4 0::Int) -#743 := (ite #742 #410 #409) -#744 := (= 0::Int 0::Int) -#745 := (ite #744 #62 #743) -#550 := (or #548 #745) -#693 := (iff #550 #549) -#695 := (iff #549 #549) -#689 := [rewrite]: #695 -#701 := (iff #745 #62) -#439 := (mod #418 0::Int) -#718 := (+ #10 #439) -#429 := (= #718 0::Int) -#713 := (ite #742 #410 #429) -#1 := true -#704 := (ite true #62 #713) -#705 := (iff #704 #62) -#706 := [rewrite]: #705 -#699 := (iff #745 #704) -#702 := (iff #743 #713) -#712 := (iff #409 #429) -#432 := (ite false #424 #429) -#426 := (iff #432 #429) -#708 := [rewrite]: #426 -#710 := (iff #409 #432) -#430 := (iff #411 #429) -#715 := (= #420 #718) -#440 := (= #419 #439) -#716 := (= #333 0::Int) -#717 := [rewrite]: #716 -#714 := [monotonicity #717]: #440 -#719 := [monotonicity #714]: #715 -#431 := [monotonicity #719]: #430 -#446 := (iff #735 false) -#720 := (or false false) -#444 := (iff #720 false) -#445 := [rewrite]: #444 -#721 := (iff #735 #720) -#731 := (iff #739 false) -#386 := (not true) -#724 := (iff #386 false) -#725 := [rewrite]: #724 -#373 := (iff #739 #386) -#732 := (iff #404 true) -#728 := (or true #421) -#367 := (iff #728 true) -#730 := [rewrite]: #367 -#723 := (iff #404 #728) -#736 := (iff #425 true) -#396 := [rewrite]: #736 -#729 := [monotonicity #396]: #723 -#372 := [trans #729 #730]: #732 -#733 := [monotonicity #372]: #373 -#734 := [trans #733 #725]: #731 -#726 := (iff #528 false) -#387 := (iff #528 #386) -#722 := (iff #398 true) -#401 := (or #741 true) -#738 := (iff #401 true) -#381 := [rewrite]: #738 -#737 := (iff #398 #401) -#397 := [monotonicity #396]: #737 -#385 := [trans #397 #381]: #722 -#388 := [monotonicity #385]: #387 -#727 := [trans #388 #725]: #726 -#443 := [monotonicity #727 #734]: #721 -#339 := [trans #443 #445]: #446 -#711 := [monotonicity #339 #431]: #710 -#709 := [trans #711 #708]: #712 -#703 := [monotonicity #709]: #702 -#740 := (iff #744 true) -#746 := [rewrite]: #740 -#700 := [monotonicity #746 #703]: #699 -#707 := [trans #700 #706]: #701 -#694 := [monotonicity #707]: #693 -#690 := [trans #694 #689]: #693 -#692 := [quant-inst #8 #9]: #550 -#696 := [mp #692 #690]: #549 -[unit-resolution #696 #70 #760]: false -unsat -b2456294470b5bb8cf71e8629c4adcc89dacf753 303 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#33 := (f3 #13 #14) -#756 := (pattern #33) -#8 := 0::Int -#88 := -1::Int -#92 := (* -1::Int #14) -#89 := (* -1::Int #13) -#153 := (mod #89 #92) -#268 := (+ #33 #153) -#269 := (= #268 0::Int) -#34 := (mod #13 #14) -#265 := (* -1::Int #34) -#266 := (+ #33 #265) -#267 := (= #266 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#270 := (ite #216 #267 #269) -#264 := (= #33 0::Int) -#16 := (= #13 0::Int) -#271 := (ite #16 #264 #270) -#263 := (= #13 #33) -#17 := (= #14 0::Int) -#272 := (ite #17 #263 #271) -#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #272) -#275 := (forall (vars (?v0 Int) (?v1 Int)) #272) -#760 := (iff #275 #757) -#758 := (iff #272 #272) -#759 := [refl]: #758 -#761 := [quant-intro #759]: #760 -#159 := (* -1::Int #153) -#232 := (ite #216 #34 #159) -#235 := (ite #16 0::Int #232) -#238 := (ite #17 #13 #235) -#241 := (= #33 #238) -#244 := (forall (vars (?v0 Int) (?v1 Int)) #241) -#276 := (iff #244 #275) -#273 := (iff #241 #272) -#274 := [rewrite]: #273 -#277 := [quant-intro #274]: #276 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#179 := (ite #134 #34 #159) -#182 := (ite #16 0::Int #179) -#185 := (ite #17 #13 #182) -#188 := (= #33 #185) -#191 := (forall (vars (?v0 Int) (?v1 Int)) #188) -#245 := (iff #191 #244) -#242 := (iff #188 #241) -#239 := (= #185 #238) -#236 := (= #182 #235) -#233 := (= #179 #232) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#234 := [monotonicity #218]: #233 -#237 := [monotonicity #234]: #236 -#240 := [monotonicity #237]: #239 -#243 := [monotonicity #240]: #242 -#246 := [quant-intro #243]: #245 -#202 := (~ #191 #191) -#201 := (~ #188 #188) -#198 := [refl]: #201 -#203 := [nnf-pos #198]: #202 -#27 := (- #14) -#26 := (- #13) -#35 := (mod #26 #27) -#36 := (- #35) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#37 := (ite #24 #34 #36) -#38 := (ite #16 0::Int #37) -#39 := (ite #17 #13 #38) -#40 := (= #33 #39) -#41 := (forall (vars (?v0 Int) (?v1 Int)) #40) -#194 := (iff #41 #191) -#82 := (and #20 #22) -#85 := (or #21 #82) -#164 := (ite #85 #34 #159) -#73 := (= 0::Int #13) -#167 := (ite #73 0::Int #164) -#76 := (= 0::Int #14) -#170 := (ite #76 #13 #167) -#173 := (= #33 #170) -#176 := (forall (vars (?v0 Int) (?v1 Int)) #173) -#192 := (iff #176 #191) -#189 := (iff #173 #188) -#186 := (= #170 #185) -#183 := (= #167 #182) -#180 := (= #164 #179) -#135 := (iff #85 #134) -#132 := (iff #82 #131) -#129 := (iff #22 #128) -#130 := [rewrite]: #129 -#122 := (iff #20 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #21 #124) -#118 := (iff #19 #117) -#119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#181 := [monotonicity #136]: #180 -#110 := (iff #73 #16) -#111 := [rewrite]: #110 -#184 := [monotonicity #111 #181]: #183 -#112 := (iff #76 #17) -#113 := [rewrite]: #112 -#187 := [monotonicity #113 #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [quant-intro #190]: #192 -#177 := (iff #41 #176) -#174 := (iff #40 #173) -#171 := (= #39 #170) -#168 := (= #38 #167) -#165 := (= #37 #164) -#162 := (= #36 #159) -#156 := (- #153) -#160 := (= #156 #159) -#161 := [rewrite]: #160 -#157 := (= #36 #156) -#154 := (= #35 #153) -#93 := (= #27 #92) -#94 := [rewrite]: #93 -#90 := (= #26 #89) -#91 := [rewrite]: #90 -#155 := [monotonicity #91 #94]: #154 -#158 := [monotonicity #155]: #157 -#163 := [trans #158 #161]: #162 -#86 := (iff #24 #85) -#83 := (iff #23 #82) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#166 := [monotonicity #87 #163]: #165 -#74 := (iff #16 #73) -#75 := [rewrite]: #74 -#169 := [monotonicity #75 #166]: #168 -#77 := (iff #17 #76) +#59 := (= #19 1::Int) +#60 := [rewrite]: #59 +#57 := (iff #18 #56) +#54 := (iff #17 #53) +#55 := [rewrite]: #54 +#58 := [monotonicity #55]: #57 +#85 := [monotonicity #58 #60 #82]: #84 +#51 := (iff #12 false) +#52 := [rewrite]: #51 +#88 := [monotonicity #52 #85]: #87 +#92 := [trans #88 #90]: #91 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#95 := [monotonicity #50 #92]: #94 +#99 := [trans #95 #97]: #98 +#102 := [monotonicity #99]: #101 +#106 := [trans #102 #104]: #105 +#109 := [monotonicity #106]: #108 +#145 := [trans #109 #143]: #144 +#48 := [asserted]: #28 +[mp #48 #145]: false +unsat +2e12b506bd838c7a91cf9b35f04a675da557e17b 85 0 +#2 := false +#9 := 0::Int +#8 := 3::Int +#17 := (- 3::Int) +#18 := (mod #17 #17) +#19 := (- #18) +#16 := (mod 3::Int 3::Int) +#11 := (< 0::Int 3::Int) +#13 := (< 3::Int 0::Int) +#14 := (and #13 #11) +#12 := (and #11 #11) +#15 := (or #12 #14) +#20 := (ite #15 #16 #19) +#10 := (= 3::Int 0::Int) +#21 := (ite #10 0::Int #20) +#22 := (ite #10 3::Int #21) +#23 := (= #22 0::Int) +#24 := (not #23) +#106 := (iff #24 false) +#1 := true +#101 := (not true) +#104 := (iff #101 false) +#105 := [rewrite]: #104 +#102 := (iff #24 #101) +#99 := (iff #23 true) +#94 := (= 0::Int 0::Int) +#97 := (iff #94 true) +#98 := [rewrite]: #97 +#95 := (iff #23 #94) +#88 := (ite false 3::Int 0::Int) +#91 := (= #88 0::Int) +#92 := [rewrite]: #91 +#89 := (= #22 #88) +#86 := (= #21 0::Int) +#81 := (ite false 0::Int 0::Int) +#84 := (= #81 0::Int) +#85 := [rewrite]: #84 +#82 := (= #21 #81) +#79 := (= #20 0::Int) +#49 := (and #11 #13) +#52 := (or #11 #49) +#74 := (ite #52 0::Int 0::Int) +#77 := (= #74 0::Int) #78 := [rewrite]: #77 -#172 := [monotonicity #78 #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [quant-intro #175]: #177 -#195 := [trans #178 #193]: #194 -#152 := [asserted]: #41 -#196 := [mp #152 #195]: #191 -#199 := [mp~ #196 #203]: #191 -#247 := [mp #199 #246]: #244 -#278 := [mp #247 #277]: #275 -#762 := [mp #278 #761]: #757 -#9 := 1::Int -#10 := (f3 0::Int 1::Int) -#11 := (= #10 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#678 := (not #757) -#679 := (or #678 #11) -#336 := (* -1::Int 1::Int) -#420 := (* -1::Int 0::Int) -#421 := (mod #420 #336) -#422 := (+ #10 #421) -#413 := (= #422 0::Int) -#424 := (mod 0::Int 1::Int) -#425 := (* -1::Int #424) -#426 := (+ #10 #425) -#423 := (= #426 0::Int) -#427 := (>= 0::Int 0::Int) -#406 := (<= 1::Int 0::Int) -#741 := (or #406 #427) -#743 := (not #741) -#400 := (<= 0::Int 0::Int) -#530 := (or #400 #406) -#737 := (not #530) -#411 := (or #737 #743) -#412 := (ite #411 #423 #413) -#744 := (= 0::Int 0::Int) -#745 := (ite #744 #11 #412) -#62 := (= 0::Int #10) -#746 := (= 1::Int 0::Int) -#747 := (ite #746 #62 #745) -#682 := (or #678 #747) -#582 := (iff #682 #679) -#585 := (iff #679 #679) -#578 := [rewrite]: #585 -#681 := (iff #747 #11) -#699 := (ite false #11 #11) -#529 := (iff #699 #11) -#531 := [rewrite]: #529 -#574 := (iff #747 #699) -#572 := (iff #745 #11) -#1 := true -#686 := (ite true #11 #11) -#687 := (iff #686 #11) -#690 := [rewrite]: #687 -#688 := (iff #745 #686) -#532 := (iff #412 #11) -#693 := (iff #412 #699) -#692 := (iff #413 #11) -#697 := (= #422 #10) -#428 := (+ #10 0::Int) -#711 := (= #428 #10) -#715 := [rewrite]: #711 -#695 := (= #422 #428) -#552 := (= #421 0::Int) -#708 := (mod 0::Int -1::Int) -#550 := (= #708 0::Int) -#551 := [rewrite]: #550 -#703 := (= #421 #708) -#702 := (= #336 -1::Int) -#707 := [rewrite]: #702 -#433 := (= #420 0::Int) -#434 := [rewrite]: #433 -#709 := [monotonicity #434 #707]: #703 -#694 := [trans #709 #551]: #552 -#696 := [monotonicity #694]: #695 -#691 := [trans #696 #715]: #697 -#698 := [monotonicity #691]: #692 -#706 := (iff #423 #11) -#704 := (= #426 #10) -#710 := (= #426 #428) -#712 := (= #425 0::Int) -#431 := (= #425 #420) -#717 := (= #424 0::Int) -#721 := [rewrite]: #717 -#432 := [monotonicity #721]: #431 -#713 := [trans #432 #434]: #712 -#714 := [monotonicity #713]: #710 -#705 := [trans #714 #715]: #704 -#701 := [monotonicity #705]: #706 -#716 := (iff #411 false) -#342 := (or false false) -#441 := (iff #342 false) -#442 := [rewrite]: #441 -#718 := (iff #411 #342) -#447 := (iff #743 false) -#727 := (not true) -#730 := (iff #727 false) -#725 := [rewrite]: #730 -#445 := (iff #743 #727) -#722 := (iff #741 true) -#374 := (or false true) -#733 := (iff #374 true) -#736 := [rewrite]: #733 -#375 := (iff #741 #374) -#732 := (iff #427 true) -#734 := [rewrite]: #732 -#399 := (iff #406 false) -#740 := [rewrite]: #399 -#735 := [monotonicity #740 #734]: #375 -#723 := [trans #735 #736]: #722 -#446 := [monotonicity #723]: #445 -#448 := [trans #446 #725]: #447 -#731 := (iff #737 false) -#728 := (iff #737 #727) -#390 := (iff #530 true) -#383 := (or true false) -#388 := (iff #383 true) -#389 := [rewrite]: #388 -#724 := (iff #530 #383) -#403 := (iff #400 true) -#739 := [rewrite]: #403 -#387 := [monotonicity #739 #740]: #724 -#726 := [trans #387 #389]: #390 -#729 := [monotonicity #726]: #728 -#369 := [trans #729 #725]: #731 -#719 := [monotonicity #369 #448]: #718 -#720 := [trans #719 #442]: #716 -#700 := [monotonicity #720 #701 #698]: #693 -#685 := [trans #700 #531]: #532 -#738 := (iff #744 true) -#398 := [rewrite]: #738 -#689 := [monotonicity #398 #685]: #688 -#573 := [trans #689 #690]: #572 -#68 := (iff #62 #11) -#69 := [rewrite]: #68 -#742 := (iff #746 false) -#748 := [rewrite]: #742 -#533 := [monotonicity #748 #69 #573]: #574 -#583 := [trans #533 #531]: #681 -#584 := [monotonicity #583]: #582 -#586 := [trans #584 #578]: #582 -#567 := [quant-inst #8 #9]: #682 -#587 := [mp #567 #586]: #679 -[unit-resolution #587 #61 #762]: false -unsat -e9db2756594c83e73847951deaad9e2f60acdae2 304 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#33 := (f3 #13 #14) -#746 := (pattern #33) -#10 := 0::Int -#78 := -1::Int -#82 := (* -1::Int #14) -#79 := (* -1::Int #13) -#143 := (mod #79 #82) -#258 := (+ #33 #143) -#259 := (= #258 0::Int) -#34 := (mod #13 #14) -#255 := (* -1::Int #34) -#256 := (+ #33 #255) -#257 := (= #256 0::Int) -#117 := (>= #13 0::Int) -#110 := (<= #14 0::Int) -#202 := (or #110 #117) -#203 := (not #202) -#106 := (<= #13 0::Int) -#200 := (or #106 #110) -#201 := (not #200) -#206 := (or #201 #203) -#260 := (ite #206 #257 #259) -#254 := (= #33 0::Int) -#16 := (= #13 0::Int) -#261 := (ite #16 #254 #260) -#253 := (= #13 #33) -#17 := (= #14 0::Int) -#262 := (ite #17 #253 #261) -#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #262) -#265 := (forall (vars (?v0 Int) (?v1 Int)) #262) -#750 := (iff #265 #747) -#748 := (iff #262 #262) -#749 := [refl]: #748 -#751 := [quant-intro #749]: #750 -#149 := (* -1::Int #143) -#222 := (ite #206 #34 #149) -#225 := (ite #16 0::Int #222) -#228 := (ite #17 #13 #225) -#231 := (= #33 #228) -#234 := (forall (vars (?v0 Int) (?v1 Int)) #231) -#266 := (iff #234 #265) -#263 := (iff #231 #262) -#264 := [rewrite]: #263 -#267 := [quant-intro #264]: #266 -#118 := (not #117) -#111 := (not #110) -#121 := (and #111 #118) -#107 := (not #106) -#114 := (and #107 #111) -#124 := (or #114 #121) -#169 := (ite #124 #34 #149) -#172 := (ite #16 0::Int #169) -#175 := (ite #17 #13 #172) -#178 := (= #33 #175) -#181 := (forall (vars (?v0 Int) (?v1 Int)) #178) -#235 := (iff #181 #234) -#232 := (iff #178 #231) -#229 := (= #175 #228) -#226 := (= #172 #225) -#223 := (= #169 #222) -#207 := (iff #124 #206) -#204 := (iff #121 #203) -#205 := [rewrite]: #204 -#194 := (iff #114 #201) -#195 := [rewrite]: #194 -#208 := [monotonicity #195 #205]: #207 -#224 := [monotonicity #208]: #223 -#227 := [monotonicity #224]: #226 -#230 := [monotonicity #227]: #229 -#233 := [monotonicity #230]: #232 -#236 := [quant-intro #233]: #235 -#192 := (~ #181 #181) -#191 := (~ #178 #178) -#188 := [refl]: #191 -#193 := [nnf-pos #188]: #192 -#27 := (- #14) -#26 := (- #13) -#35 := (mod #26 #27) -#36 := (- #35) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#37 := (ite #24 #34 #36) -#38 := (ite #16 0::Int #37) -#39 := (ite #17 #13 #38) -#40 := (= #33 #39) -#41 := (forall (vars (?v0 Int) (?v1 Int)) #40) -#184 := (iff #41 #181) -#72 := (and #20 #22) -#75 := (or #21 #72) -#154 := (ite #75 #34 #149) -#63 := (= 0::Int #13) -#157 := (ite #63 0::Int #154) -#66 := (= 0::Int #14) -#160 := (ite #66 #13 #157) -#163 := (= #33 #160) -#166 := (forall (vars (?v0 Int) (?v1 Int)) #163) -#182 := (iff #166 #181) -#179 := (iff #163 #178) -#176 := (= #160 #175) -#173 := (= #157 #172) -#170 := (= #154 #169) -#125 := (iff #75 #124) -#122 := (iff #72 #121) -#119 := (iff #22 #118) -#120 := [rewrite]: #119 -#112 := (iff #20 #111) -#113 := [rewrite]: #112 -#123 := [monotonicity #113 #120]: #122 -#115 := (iff #21 #114) -#108 := (iff #19 #107) -#109 := [rewrite]: #108 -#116 := [monotonicity #109 #113]: #115 -#126 := [monotonicity #116 #123]: #125 -#171 := [monotonicity #126]: #170 -#100 := (iff #63 #16) -#101 := [rewrite]: #100 -#174 := [monotonicity #101 #171]: #173 -#102 := (iff #66 #17) -#103 := [rewrite]: #102 -#177 := [monotonicity #103 #174]: #176 -#180 := [monotonicity #177]: #179 -#183 := [quant-intro #180]: #182 -#167 := (iff #41 #166) -#164 := (iff #40 #163) -#161 := (= #39 #160) -#158 := (= #38 #157) -#155 := (= #37 #154) -#152 := (= #36 #149) -#146 := (- #143) -#150 := (= #146 #149) -#151 := [rewrite]: #150 -#147 := (= #36 #146) -#144 := (= #35 #143) -#83 := (= #27 #82) -#84 := [rewrite]: #83 -#80 := (= #26 #79) -#81 := [rewrite]: #80 -#145 := [monotonicity #81 #84]: #144 -#148 := [monotonicity #145]: #147 -#153 := [trans #148 #151]: #152 -#76 := (iff #24 #75) -#73 := (iff #23 #72) -#74 := [rewrite]: #73 -#77 := [monotonicity #74]: #76 -#156 := [monotonicity #77 #153]: #155 -#64 := (iff #16 #63) -#65 := [rewrite]: #64 -#159 := [monotonicity #65 #156]: #158 -#67 := (iff #17 #66) -#68 := [rewrite]: #67 -#162 := [monotonicity #68 #159]: #161 -#165 := [monotonicity #162]: #164 -#168 := [quant-intro #165]: #167 -#185 := [trans #168 #183]: #184 -#142 := [asserted]: #41 -#186 := [mp #142 #185]: #181 -#189 := [mp~ #186 #193]: #181 -#237 := [mp #189 #236]: #234 -#268 := [mp #237 #267]: #265 -#752 := [mp #268 #751]: #747 -#8 := 1::Int -#9 := (f3 1::Int 1::Int) -#11 := (= #9 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#572 := (not #747) -#574 := (or #572 #11) -#326 := (* -1::Int 1::Int) -#410 := (mod #326 #326) -#411 := (+ #9 #410) -#412 := (= #411 0::Int) -#403 := (mod 1::Int 1::Int) -#414 := (* -1::Int #403) -#415 := (+ #9 #414) -#416 := (= #415 0::Int) -#413 := (>= 1::Int 0::Int) -#417 := (<= 1::Int 0::Int) -#396 := (or #417 #413) -#731 := (not #396) -#733 := (or #417 #417) -#390 := (not #733) -#520 := (or #390 #731) -#727 := (ite #520 #416 #412) -#401 := (= 1::Int 0::Int) -#402 := (ite #401 #11 #727) -#734 := (= 1::Int #9) -#735 := (ite #401 #734 #402) -#575 := (or #572 #735) -#576 := (iff #575 #574) -#578 := (iff #574 #574) -#579 := [rewrite]: #578 -#672 := (iff #735 #11) -#738 := (= #9 1::Int) -#523 := (ite false #738 #11) -#668 := (iff #523 #11) -#669 := [rewrite]: #668 -#671 := (iff #735 #523) -#563 := (iff #402 #11) -#678 := (ite false #11 #11) -#680 := (iff #678 #11) -#562 := [rewrite]: #680 -#679 := (iff #402 #678) -#675 := (iff #727 #11) -#1 := true -#683 := (ite true #11 #11) -#521 := (iff #683 #11) -#522 := [rewrite]: #521 -#690 := (iff #727 #683) -#688 := (iff #412 #11) -#681 := (= #411 #9) -#700 := (+ #9 0::Int) -#705 := (= #700 #9) -#694 := [rewrite]: #705 -#686 := (= #411 #700) -#684 := (= #410 0::Int) -#693 := (mod -1::Int -1::Int) -#541 := (= #693 0::Int) -#542 := [rewrite]: #541 -#699 := (= #410 #693) -#697 := (= #326 -1::Int) -#698 := [rewrite]: #697 -#540 := [monotonicity #698 #698]: #699 -#685 := [trans #540 #542]: #684 -#687 := [monotonicity #685]: #686 -#682 := [trans #687 #694]: #681 -#689 := [monotonicity #682]: #688 -#691 := (iff #416 #11) -#695 := (= #415 #9) -#704 := (= #415 #700) -#703 := (= #414 0::Int) -#421 := (* -1::Int 0::Int) -#424 := (= #421 0::Int) -#702 := [rewrite]: #424 -#422 := (= #414 #421) -#707 := (= #403 0::Int) -#711 := [rewrite]: #707 -#423 := [monotonicity #711]: #422 -#418 := [trans #423 #702]: #703 -#701 := [monotonicity #418]: #704 -#696 := [trans #701 #694]: #695 -#692 := [monotonicity #696]: #691 -#706 := (iff #520 true) -#332 := (or true false) -#431 := (iff #332 true) -#432 := [rewrite]: #431 -#708 := (iff #520 #332) -#437 := (iff #731 false) -#726 := (not true) -#435 := (iff #726 false) -#436 := [rewrite]: #435 -#712 := (iff #731 #726) -#725 := (iff #396 true) -#359 := (or false true) -#364 := (iff #359 true) -#365 := [rewrite]: #364 -#722 := (iff #396 #359) -#715 := (iff #413 true) -#721 := [rewrite]: #715 -#388 := (iff #417 false) -#393 := [rewrite]: #388 -#724 := [monotonicity #393 #721]: #722 -#723 := [trans #724 #365]: #725 -#713 := [monotonicity #723]: #712 -#438 := [trans #713 #436]: #437 -#719 := (iff #390 true) -#379 := (not false) -#717 := (iff #379 true) -#718 := [rewrite]: #717 -#380 := (iff #390 #379) -#377 := (iff #733 false) -#729 := (or false false) -#373 := (iff #729 false) -#714 := [rewrite]: #373 -#389 := (iff #733 #729) -#730 := [monotonicity #393 #393]: #389 -#378 := [trans #730 #714]: #377 -#716 := [monotonicity #378]: #380 -#720 := [trans #716 #718]: #719 -#709 := [monotonicity #720 #438]: #708 -#710 := [trans #709 #432]: #706 -#519 := [monotonicity #710 #692 #689]: #690 -#676 := [trans #519 #522]: #675 -#736 := (iff #401 false) -#737 := [rewrite]: #736 -#677 := [monotonicity #737 #676]: #679 -#564 := [trans #677 #562]: #563 -#732 := (iff #734 #738) -#728 := [rewrite]: #732 -#573 := [monotonicity #737 #728 #564]: #671 -#557 := [trans #573 #669]: #672 -#577 := [monotonicity #557]: #576 -#580 := [trans #577 #579]: #576 -#568 := [quant-inst #8 #8]: #575 -#673 := [mp #568 #580]: #574 -[unit-resolution #673 #61 #752]: false -unsat -5a27e28e4534905d80bae8170a2a6b87f8d4215e 315 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#747 := (pattern #34) -#11 := 0::Int +#75 := (= #20 #74) +#72 := (= #19 0::Int) +#67 := (- 0::Int) +#70 := (= #67 0::Int) +#71 := [rewrite]: #70 +#68 := (= #19 #67) +#65 := (= #18 0::Int) +#57 := -3::Int +#60 := (mod -3::Int -3::Int) +#63 := (= #60 0::Int) +#64 := [rewrite]: #63 +#61 := (= #18 #60) +#58 := (= #17 -3::Int) +#59 := [rewrite]: #58 +#62 := [monotonicity #59 #59]: #61 +#66 := [trans #62 #64]: #65 +#69 := [monotonicity #66]: #68 +#73 := [trans #69 #71]: #72 +#55 := (= #16 0::Int) +#56 := [rewrite]: #55 +#53 := (iff #15 #52) +#50 := (iff #14 #49) +#51 := [rewrite]: #50 +#47 := (iff #12 #11) +#48 := [rewrite]: #47 +#54 := [monotonicity #48 #51]: #53 +#76 := [monotonicity #54 #56 #73]: #75 +#80 := [trans #76 #78]: #79 +#45 := (iff #10 false) +#46 := [rewrite]: #45 +#83 := [monotonicity #46 #80]: #82 +#87 := [trans #83 #85]: #86 +#90 := [monotonicity #46 #87]: #89 +#93 := [trans #90 #92]: #23 +#96 := [monotonicity #93]: #95 +#100 := [trans #96 #98]: #99 +#103 := [monotonicity #100]: #102 +#107 := [trans #103 #105]: #106 +#44 := [asserted]: #24 +[mp #44 #107]: false +unsat +a185dd1db6f642a5e7d15c4c9072da159f55df2d 124 0 +#2 := false +#27 := 2::Int +#8 := 3::Int +#21 := (- 3::Int) +#11 := 5::Int +#20 := (- 5::Int) +#22 := (mod #20 #21) +#23 := (- #22) +#19 := (mod 5::Int 3::Int) +#9 := 0::Int +#14 := (< 0::Int 3::Int) +#16 := (< 5::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 5::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#12 := (= 5::Int 0::Int) +#25 := (ite #12 0::Int #24) +#10 := (= 3::Int 0::Int) +#26 := (ite #10 5::Int #25) +#28 := (= #26 2::Int) +#29 := (not #28) +#145 := (iff #29 false) +#54 := (and #14 #16) +#57 := (or #15 #54) +#108 := (not #57) +#143 := (iff #108 false) +#1 := true +#138 := (not true) +#141 := (iff #138 false) +#142 := [rewrite]: #141 +#139 := (iff #108 #138) +#136 := (iff #57 true) +#131 := (or true false) +#134 := (iff #131 true) +#135 := [rewrite]: #134 +#132 := (iff #57 #131) +#129 := (iff #54 false) +#124 := (and true false) +#127 := (iff #124 false) +#128 := [rewrite]: #127 +#125 := (iff #54 #124) +#122 := (iff #16 false) +#123 := [rewrite]: #122 +#113 := (iff #14 true) +#114 := [rewrite]: #113 +#126 := [monotonicity #114 #123]: #125 +#130 := [trans #126 #128]: #129 +#120 := (iff #15 true) +#115 := (and true true) +#118 := (iff #115 true) +#119 := [rewrite]: #118 +#116 := (iff #15 #115) +#111 := (iff #13 true) +#112 := [rewrite]: #111 +#117 := [monotonicity #112 #114]: #116 +#121 := [trans #117 #119]: #120 +#133 := [monotonicity #121 #130]: #132 +#137 := [trans #133 #135]: #136 +#140 := [monotonicity #137]: #139 +#144 := [trans #140 #142]: #143 +#109 := (iff #29 #108) +#106 := (iff #28 #57) #79 := -1::Int -#83 := (* -1::Int #15) -#80 := (* -1::Int #14) -#144 := (mod #80 #83) -#259 := (+ #34 #144) -#260 := (= #259 0::Int) -#35 := (mod #14 #15) -#256 := (* -1::Int #35) -#257 := (+ #34 #256) -#258 := (= #257 0::Int) -#118 := (>= #14 0::Int) -#111 := (<= #15 0::Int) -#203 := (or #111 #118) -#204 := (not #203) -#107 := (<= #14 0::Int) -#201 := (or #107 #111) -#202 := (not #201) -#207 := (or #202 #204) -#261 := (ite #207 #258 #260) -#255 := (= #34 0::Int) -#17 := (= #14 0::Int) -#262 := (ite #17 #255 #261) -#254 := (= #14 #34) -#18 := (= #15 0::Int) -#263 := (ite #18 #254 #262) -#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263) -#266 := (forall (vars (?v0 Int) (?v1 Int)) #263) -#751 := (iff #266 #748) -#749 := (iff #263 #263) -#750 := [refl]: #749 -#752 := [quant-intro #750]: #751 -#150 := (* -1::Int #144) -#223 := (ite #207 #35 #150) -#226 := (ite #17 0::Int #223) -#229 := (ite #18 #14 #226) -#232 := (= #34 #229) -#235 := (forall (vars (?v0 Int) (?v1 Int)) #232) -#267 := (iff #235 #266) -#264 := (iff #232 #263) -#265 := [rewrite]: #264 -#268 := [quant-intro #265]: #267 -#119 := (not #118) -#112 := (not #111) -#122 := (and #112 #119) -#108 := (not #107) -#115 := (and #108 #112) -#125 := (or #115 #122) -#170 := (ite #125 #35 #150) -#173 := (ite #17 0::Int #170) -#176 := (ite #18 #14 #173) -#179 := (= #34 #176) -#182 := (forall (vars (?v0 Int) (?v1 Int)) #179) -#236 := (iff #182 #235) -#233 := (iff #179 #232) -#230 := (= #176 #229) -#227 := (= #173 #226) -#224 := (= #170 #223) -#208 := (iff #125 #207) -#205 := (iff #122 #204) -#206 := [rewrite]: #205 -#195 := (iff #115 #202) -#196 := [rewrite]: #195 -#209 := [monotonicity #196 #206]: #208 -#225 := [monotonicity #209]: #224 -#228 := [monotonicity #225]: #227 -#231 := [monotonicity #228]: #230 -#234 := [monotonicity #231]: #233 -#237 := [quant-intro #234]: #236 -#193 := (~ #182 #182) -#192 := (~ #179 #179) -#189 := [refl]: #192 -#194 := [nnf-pos #189]: #193 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#185 := (iff #42 #182) -#73 := (and #21 #23) -#76 := (or #22 #73) -#155 := (ite #76 #35 #150) -#64 := (= 0::Int #14) -#158 := (ite #64 0::Int #155) -#67 := (= 0::Int #15) -#161 := (ite #67 #14 #158) -#164 := (= #34 #161) -#167 := (forall (vars (?v0 Int) (?v1 Int)) #164) -#183 := (iff #167 #182) -#180 := (iff #164 #179) -#177 := (= #161 #176) -#174 := (= #158 #173) -#171 := (= #155 #170) -#126 := (iff #76 #125) -#123 := (iff #73 #122) -#120 := (iff #23 #119) -#121 := [rewrite]: #120 -#113 := (iff #21 #112) -#114 := [rewrite]: #113 -#124 := [monotonicity #114 #121]: #123 -#116 := (iff #22 #115) -#109 := (iff #20 #108) -#110 := [rewrite]: #109 -#117 := [monotonicity #110 #114]: #116 -#127 := [monotonicity #117 #124]: #126 -#172 := [monotonicity #127]: #171 -#101 := (iff #64 #17) -#102 := [rewrite]: #101 -#175 := [monotonicity #102 #172]: #174 -#103 := (iff #67 #18) -#104 := [rewrite]: #103 -#178 := [monotonicity #104 #175]: #177 -#181 := [monotonicity #178]: #180 -#184 := [quant-intro #181]: #183 -#168 := (iff #42 #167) -#165 := (iff #41 #164) -#162 := (= #40 #161) -#159 := (= #39 #158) -#156 := (= #38 #155) -#153 := (= #37 #150) -#147 := (- #144) -#151 := (= #147 #150) -#152 := [rewrite]: #151 -#148 := (= #37 #147) -#145 := (= #36 #144) -#84 := (= #28 #83) -#85 := [rewrite]: #84 -#81 := (= #27 #80) -#82 := [rewrite]: #81 -#146 := [monotonicity #82 #85]: #145 -#149 := [monotonicity #146]: #148 -#154 := [trans #149 #152]: #153 -#77 := (iff #25 #76) -#74 := (iff #24 #73) -#75 := [rewrite]: #74 -#78 := [monotonicity #75]: #77 -#157 := [monotonicity #78 #154]: #156 -#65 := (iff #17 #64) -#66 := [rewrite]: #65 -#160 := [monotonicity #66 #157]: #159 -#68 := (iff #18 #67) -#69 := [rewrite]: #68 -#163 := [monotonicity #69 #160]: #162 -#166 := [monotonicity #163]: #165 -#169 := [quant-intro #166]: #168 -#186 := [trans #169 #184]: #185 -#143 := [asserted]: #42 -#187 := [mp #143 #186]: #182 -#190 := [mp~ #187 #194]: #182 -#238 := [mp #190 #237]: #235 -#269 := [mp #238 #268]: #266 -#753 := [mp #269 #752]: #748 -#9 := 1::Int -#8 := 3::Int -#10 := (f3 3::Int 1::Int) -#12 := (= #10 0::Int) -#13 := (not #12) -#62 := [asserted]: #13 -#671 := (not #748) -#675 := (or #671 #12) -#327 := (* -1::Int 1::Int) -#411 := (* -1::Int 3::Int) -#412 := (mod #411 #327) -#413 := (+ #10 #412) -#404 := (= #413 0::Int) -#415 := (mod 3::Int 1::Int) -#416 := (* -1::Int #415) -#417 := (+ #10 #416) -#414 := (= #417 0::Int) -#418 := (>= 3::Int 0::Int) -#397 := (<= 1::Int 0::Int) -#732 := (or #397 #418) -#734 := (not #732) -#391 := (<= 3::Int 0::Int) -#521 := (or #391 #397) -#728 := (not #521) -#402 := (or #728 #734) -#403 := (ite #402 #414 #404) -#735 := (= 3::Int 0::Int) -#736 := (ite #735 #12 #403) -#737 := (= 3::Int #10) -#738 := (= 1::Int 0::Int) -#733 := (ite #738 #737 #736) -#662 := (or #671 #733) -#656 := (iff #662 #675) -#655 := (iff #675 #675) -#665 := [rewrite]: #655 -#581 := (iff #733 #12) -#394 := (= #10 3::Int) -#569 := (ite false #394 #12) -#579 := (iff #569 #12) -#580 := [rewrite]: #579 -#577 := (iff #733 #569) -#575 := (iff #736 #12) -#669 := (ite false #12 #12) -#558 := (iff #669 #12) -#573 := [rewrite]: #558 -#670 := (iff #736 #669) -#672 := (iff #403 #12) -#1 := true -#681 := (ite true #12 #12) -#565 := (iff #681 #12) -#524 := [rewrite]: #565 -#563 := (iff #403 #681) -#680 := (iff #404 #12) -#677 := (= #413 #10) -#692 := (+ #10 0::Int) -#699 := (= #692 #10) -#694 := [rewrite]: #699 -#523 := (= #413 #692) -#520 := (= #412 0::Int) -#685 := -3::Int -#683 := (mod -3::Int -1::Int) -#684 := (= #683 0::Int) -#691 := [rewrite]: #684 -#689 := (= #412 #683) -#688 := (= #327 -1::Int) -#682 := [rewrite]: #688 -#686 := (= #411 -3::Int) -#687 := [rewrite]: #686 -#690 := [monotonicity #687 #682]: #689 -#522 := [trans #690 #691]: #520 -#676 := [monotonicity #522]: #523 -#679 := [trans #676 #694]: #677 -#678 := [monotonicity #679]: #680 -#542 := (iff #414 #12) -#700 := (= #417 #10) -#693 := (= #417 #692) -#696 := (= #416 0::Int) -#701 := (* -1::Int 0::Int) -#706 := (= #701 0::Int) -#695 := [rewrite]: #706 -#705 := (= #416 #701) -#704 := (= #415 0::Int) -#419 := [rewrite]: #704 -#702 := [monotonicity #419]: #705 -#697 := [trans #702 #695]: #696 -#698 := [monotonicity #697]: #693 -#541 := [trans #698 #694]: #700 -#543 := [monotonicity #541]: #542 -#425 := (iff #402 true) -#708 := (or true false) -#423 := (iff #708 true) -#424 := [rewrite]: #423 -#712 := (iff #402 #708) -#707 := (iff #734 false) -#333 := (not true) -#432 := (iff #333 false) -#433 := [rewrite]: #432 -#709 := (iff #734 #333) -#438 := (iff #732 true) -#727 := (or false true) -#436 := (iff #727 true) -#437 := [rewrite]: #436 -#713 := (iff #732 #727) -#726 := (iff #418 true) -#724 := [rewrite]: #726 -#378 := (iff #397 false) -#379 := [rewrite]: #378 -#714 := [monotonicity #379 #724]: #713 -#439 := [trans #714 #437]: #438 -#710 := [monotonicity #439]: #709 -#711 := [trans #710 #433]: #707 -#365 := (iff #728 true) -#716 := (not false) -#723 := (iff #716 true) -#725 := [rewrite]: #723 -#722 := (iff #728 #716) -#720 := (iff #521 false) -#380 := (or false false) -#718 := (iff #380 false) -#719 := [rewrite]: #718 -#381 := (iff #521 #380) -#374 := (iff #391 false) -#715 := [rewrite]: #374 -#717 := [monotonicity #715 #379]: #381 -#721 := [trans #717 #719]: #720 -#360 := [monotonicity #721]: #722 -#366 := [trans #360 #725]: #365 -#422 := [monotonicity #366 #711]: #712 -#703 := [trans #422 #424]: #425 -#564 := [monotonicity #703 #543 #678]: #563 -#574 := [trans #564 #524]: #672 -#390 := (iff #735 false) -#731 := [rewrite]: #390 -#673 := [monotonicity #731 #574]: #670 -#576 := [trans #673 #573]: #575 -#389 := (iff #737 #394) -#730 := [rewrite]: #389 -#739 := (iff #738 false) -#729 := [rewrite]: #739 -#578 := [monotonicity #729 #730 #576]: #577 -#674 := [trans #578 #580]: #581 -#653 := [monotonicity #674]: #656 -#666 := [trans #653 #665]: #656 -#664 := [quant-inst #8 #9]: #662 -#667 := [mp #664 #666]: #675 -[unit-resolution #667 #62 #753]: false -unsat -1b99f23affb0dadf3316102e865176c5efc38d4f 313 0 -#2 := false -#11 := 0::Int -decl f4 :: Int -#8 := f4 -#735 := (= f4 0::Int) -#576 := (not #735) -#418 := (>= f4 0::Int) -#723 := (not #418) -#391 := (<= f4 0::Int) -#380 := (not #391) -#691 := (or #380 #723 #735) -#578 := (not #691) -#79 := -1::Int -#411 := (* -1::Int f4) -#703 := (mod #411 -1::Int) -decl f3 :: (-> Int Int Int) -#9 := 1::Int -#10 := (f3 f4 1::Int) -#701 := (+ #10 #703) -#706 := (= #701 0::Int) -#12 := (= #10 0::Int) -#523 := (ite #691 #12 #706) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#747 := (pattern #34) -#83 := (* -1::Int #15) -#80 := (* -1::Int #14) -#144 := (mod #80 #83) -#259 := (+ #34 #144) -#260 := (= #259 0::Int) -#35 := (mod #14 #15) -#256 := (* -1::Int #35) -#257 := (+ #34 #256) -#258 := (= #257 0::Int) -#118 := (>= #14 0::Int) -#111 := (<= #15 0::Int) -#203 := (or #111 #118) -#204 := (not #203) -#107 := (<= #14 0::Int) -#201 := (or #107 #111) -#202 := (not #201) -#207 := (or #202 #204) -#261 := (ite #207 #258 #260) -#255 := (= #34 0::Int) -#17 := (= #14 0::Int) -#262 := (ite #17 #255 #261) -#254 := (= #14 #34) -#18 := (= #15 0::Int) -#263 := (ite #18 #254 #262) -#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263) -#266 := (forall (vars (?v0 Int) (?v1 Int)) #263) -#751 := (iff #266 #748) -#749 := (iff #263 #263) -#750 := [refl]: #749 -#752 := [quant-intro #750]: #751 -#150 := (* -1::Int #144) -#223 := (ite #207 #35 #150) -#226 := (ite #17 0::Int #223) -#229 := (ite #18 #14 #226) -#232 := (= #34 #229) -#235 := (forall (vars (?v0 Int) (?v1 Int)) #232) -#267 := (iff #235 #266) -#264 := (iff #232 #263) -#265 := [rewrite]: #264 -#268 := [quant-intro #265]: #267 -#119 := (not #118) -#112 := (not #111) -#122 := (and #112 #119) -#108 := (not #107) -#115 := (and #108 #112) -#125 := (or #115 #122) -#170 := (ite #125 #35 #150) -#173 := (ite #17 0::Int #170) -#176 := (ite #18 #14 #173) -#179 := (= #34 #176) -#182 := (forall (vars (?v0 Int) (?v1 Int)) #179) -#236 := (iff #182 #235) -#233 := (iff #179 #232) -#230 := (= #176 #229) -#227 := (= #173 #226) -#224 := (= #170 #223) -#208 := (iff #125 #207) -#205 := (iff #122 #204) -#206 := [rewrite]: #205 -#195 := (iff #115 #202) -#196 := [rewrite]: #195 -#209 := [monotonicity #196 #206]: #208 -#225 := [monotonicity #209]: #224 -#228 := [monotonicity #225]: #227 -#231 := [monotonicity #228]: #230 -#234 := [monotonicity #231]: #233 -#237 := [quant-intro #234]: #236 -#193 := (~ #182 #182) -#192 := (~ #179 #179) -#189 := [refl]: #192 -#194 := [nnf-pos #189]: #193 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#185 := (iff #42 #182) -#73 := (and #21 #23) -#76 := (or #22 #73) -#155 := (ite #76 #35 #150) -#64 := (= 0::Int #14) -#158 := (ite #64 0::Int #155) -#67 := (= 0::Int #15) -#161 := (ite #67 #14 #158) -#164 := (= #34 #161) -#167 := (forall (vars (?v0 Int) (?v1 Int)) #164) -#183 := (iff #167 #182) -#180 := (iff #164 #179) -#177 := (= #161 #176) -#174 := (= #158 #173) -#171 := (= #155 #170) -#126 := (iff #76 #125) -#123 := (iff #73 #122) -#120 := (iff #23 #119) -#121 := [rewrite]: #120 -#113 := (iff #21 #112) -#114 := [rewrite]: #113 -#124 := [monotonicity #114 #121]: #123 -#116 := (iff #22 #115) -#109 := (iff #20 #108) -#110 := [rewrite]: #109 -#117 := [monotonicity #110 #114]: #116 -#127 := [monotonicity #117 #124]: #126 -#172 := [monotonicity #127]: #171 -#101 := (iff #64 #17) -#102 := [rewrite]: #101 -#175 := [monotonicity #102 #172]: #174 -#103 := (iff #67 #18) -#104 := [rewrite]: #103 -#178 := [monotonicity #104 #175]: #177 -#181 := [monotonicity #178]: #180 -#184 := [quant-intro #181]: #183 -#168 := (iff #42 #167) -#165 := (iff #41 #164) -#162 := (= #40 #161) -#159 := (= #39 #158) -#156 := (= #38 #155) -#153 := (= #37 #150) -#147 := (- #144) -#151 := (= #147 #150) -#152 := [rewrite]: #151 -#148 := (= #37 #147) -#145 := (= #36 #144) -#84 := (= #28 #83) -#85 := [rewrite]: #84 -#81 := (= #27 #80) -#82 := [rewrite]: #81 -#146 := [monotonicity #82 #85]: #145 -#149 := [monotonicity #146]: #148 -#154 := [trans #149 #152]: #153 -#77 := (iff #25 #76) -#74 := (iff #24 #73) -#75 := [rewrite]: #74 +#84 := (ite #57 2::Int -1::Int) +#101 := (= #84 2::Int) +#104 := (iff #101 #57) +#105 := [rewrite]: #104 +#102 := (iff #28 #101) +#99 := (= #26 #84) +#94 := (ite false 5::Int #84) +#97 := (= #94 #84) +#98 := [rewrite]: #97 +#95 := (= #26 #94) +#92 := (= #25 #84) +#87 := (ite false 0::Int #84) +#90 := (= #87 #84) +#91 := [rewrite]: #90 +#88 := (= #25 #87) +#85 := (= #24 #84) +#82 := (= #23 -1::Int) +#71 := 1::Int +#76 := (- 1::Int) +#80 := (= #76 -1::Int) +#81 := [rewrite]: #80 +#77 := (= #23 #76) +#74 := (= #22 1::Int) +#65 := -3::Int +#62 := -5::Int +#68 := (mod -5::Int -3::Int) +#72 := (= #68 1::Int) +#73 := [rewrite]: #72 +#69 := (= #22 #68) +#66 := (= #21 -3::Int) +#67 := [rewrite]: #66 +#63 := (= #20 -5::Int) +#64 := [rewrite]: #63 +#70 := [monotonicity #64 #67]: #69 +#75 := [trans #70 #73]: #74 #78 := [monotonicity #75]: #77 -#157 := [monotonicity #78 #154]: #156 -#65 := (iff #17 #64) -#66 := [rewrite]: #65 -#160 := [monotonicity #66 #157]: #159 -#68 := (iff #18 #67) -#69 := [rewrite]: #68 -#163 := [monotonicity #69 #160]: #162 -#166 := [monotonicity #163]: #165 -#169 := [quant-intro #166]: #168 -#186 := [trans #169 #184]: #185 -#143 := [asserted]: #42 -#187 := [mp #143 #186]: #182 -#190 := [mp~ #187 #194]: #182 -#238 := [mp #190 #237]: #235 -#269 := [mp #238 #268]: #266 -#753 := [mp #269 #752]: #748 -#678 := (not #748) -#681 := (or #678 #523) -#327 := (* -1::Int 1::Int) -#412 := (mod #411 #327) -#413 := (+ #10 #412) -#404 := (= #413 0::Int) -#415 := (mod f4 1::Int) -#416 := (* -1::Int #415) -#417 := (+ #10 #416) -#414 := (= #417 0::Int) -#397 := (<= 1::Int 0::Int) -#732 := (or #397 #418) -#734 := (not #732) -#521 := (or #391 #397) -#728 := (not #521) -#402 := (or #728 #734) -#403 := (ite #402 #414 #404) -#736 := (ite #735 #12 #403) -#737 := (= f4 #10) -#738 := (= 1::Int 0::Int) -#733 := (ite #738 #737 #736) -#563 := (or #678 #733) -#565 := (iff #563 #681) -#672 := (iff #681 #681) -#574 := [rewrite]: #672 -#679 := (iff #733 #523) -#366 := (or #380 #723) -#700 := (or #366 #735) -#541 := (ite #700 #12 #706) -#676 := (iff #541 #523) -#520 := (iff #700 #691) -#522 := [rewrite]: #520 -#677 := [monotonicity #522]: #676 -#690 := (iff #733 #541) -#687 := (ite false #737 #541) -#683 := (iff #687 #541) -#689 := [rewrite]: #683 -#688 := (iff #733 #687) -#685 := (iff #736 #541) -#697 := (ite #366 #12 #706) -#698 := (ite #735 #12 #697) -#542 := (iff #698 #541) -#543 := [rewrite]: #542 -#699 := (iff #736 #698) -#692 := (iff #403 #697) -#695 := (iff #404 #706) -#705 := (= #413 #701) -#704 := (= #412 #703) -#424 := (= #327 -1::Int) -#425 := [rewrite]: #424 -#419 := [monotonicity #425]: #704 -#702 := [monotonicity #419]: #705 -#696 := [monotonicity #702]: #695 -#422 := (iff #414 #12) -#708 := (= #417 #10) -#710 := (+ #10 0::Int) -#707 := (= #710 #10) -#711 := [rewrite]: #707 -#432 := (= #417 #710) -#333 := (= #416 0::Int) -#714 := (* -1::Int 0::Int) -#438 := (= #714 0::Int) -#439 := [rewrite]: #438 -#436 := (= #416 #714) -#727 := (= #415 0::Int) -#713 := [rewrite]: #727 -#437 := [monotonicity #713]: #436 -#709 := [trans #437 #439]: #333 -#433 := [monotonicity #709]: #432 -#712 := [trans #433 #711]: #708 -#423 := [monotonicity #712]: #422 -#726 := (iff #402 #366) -#725 := (iff #734 #723) -#722 := (iff #732 #418) -#718 := (or false #418) -#721 := (iff #718 #418) -#716 := [rewrite]: #721 -#719 := (iff #732 #718) -#389 := (iff #397 false) -#394 := [rewrite]: #389 -#720 := [monotonicity #394]: #719 -#360 := [trans #720 #716]: #722 -#365 := [monotonicity #360]: #725 -#381 := (iff #728 #380) -#378 := (iff #521 #391) -#730 := (or #391 false) -#374 := (iff #730 #391) -#715 := [rewrite]: #374 -#390 := (iff #521 #730) -#731 := [monotonicity #394]: #390 -#379 := [trans #731 #715]: #378 -#717 := [monotonicity #379]: #381 -#724 := [monotonicity #717 #365]: #726 -#693 := [monotonicity #724 #423 #696]: #692 -#694 := [monotonicity #693]: #699 -#686 := [trans #694 #543]: #685 -#739 := (iff #738 false) -#729 := [rewrite]: #739 -#682 := [monotonicity #729 #686]: #688 -#684 := [trans #682 #689]: #690 -#680 := [trans #684 #677]: #679 -#524 := [monotonicity #680]: #565 -#669 := [trans #524 #574]: #565 -#564 := [quant-inst #8 #9]: #563 -#670 := [mp #564 #669]: #681 -#663 := [unit-resolution #670 #753]: #523 -#671 := (not #523) -#668 := (or #671 #578) -#13 := (not #12) -#62 := [asserted]: #13 -#675 := (or #671 #578 #12) -#662 := [def-axiom]: #675 -#657 := [unit-resolution #662 #62]: #668 -#658 := [unit-resolution #657 #663]: #578 -#569 := (or #691 #576) -#577 := [def-axiom]: #569 -#659 := [unit-resolution #577 #658]: #576 -#673 := (or #691 #391) -#558 := [def-axiom]: #673 -#660 := [unit-resolution #558 #658]: #391 -#573 := (or #691 #418) -#575 := [def-axiom]: #573 -#654 := [unit-resolution #575 #658]: #418 -#661 := (or #735 #380 #723) -#645 := [th-lemma arith triangle-eq]: #661 -[unit-resolution #645 #654 #660 #659]: false -unsat -b6f64755653a305b62fdd8df3fd24f1d40f3cc04 322 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#771 := (pattern #34) -#8 := 0::Int -#63 := -1::Int -#107 := (* -1::Int #15) -#104 := (* -1::Int #14) -#168 := (mod #104 #107) -#283 := (+ #34 #168) -#284 := (= #283 0::Int) -#35 := (mod #14 #15) -#280 := (* -1::Int #35) -#281 := (+ #34 #280) -#282 := (= #281 0::Int) -#142 := (>= #14 0::Int) -#135 := (<= #15 0::Int) -#227 := (or #135 #142) -#228 := (not #227) -#131 := (<= #14 0::Int) -#225 := (or #131 #135) -#226 := (not #225) -#231 := (or #226 #228) -#285 := (ite #231 #282 #284) -#279 := (= #34 0::Int) -#17 := (= #14 0::Int) -#286 := (ite #17 #279 #285) -#278 := (= #14 #34) -#18 := (= #15 0::Int) -#287 := (ite #18 #278 #286) -#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287) -#290 := (forall (vars (?v0 Int) (?v1 Int)) #287) -#775 := (iff #290 #772) -#773 := (iff #287 #287) -#774 := [refl]: #773 -#776 := [quant-intro #774]: #775 -#174 := (* -1::Int #168) -#247 := (ite #231 #35 #174) -#250 := (ite #17 0::Int #247) -#253 := (ite #18 #14 #250) -#256 := (= #34 #253) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#291 := (iff #259 #290) -#288 := (iff #256 #287) -#289 := [rewrite]: #288 -#292 := [quant-intro #289]: #291 -#143 := (not #142) -#136 := (not #135) -#146 := (and #136 #143) -#132 := (not #131) -#139 := (and #132 #136) -#149 := (or #139 #146) -#194 := (ite #149 #35 #174) -#197 := (ite #17 0::Int #194) -#200 := (ite #18 #14 #197) -#203 := (= #34 #200) -#206 := (forall (vars (?v0 Int) (?v1 Int)) #203) -#260 := (iff #206 #259) -#257 := (iff #203 #256) -#254 := (= #200 #253) -#251 := (= #197 #250) -#248 := (= #194 #247) -#232 := (iff #149 #231) -#229 := (iff #146 #228) -#230 := [rewrite]: #229 -#219 := (iff #139 #226) -#220 := [rewrite]: #219 -#233 := [monotonicity #220 #230]: #232 -#249 := [monotonicity #233]: #248 -#252 := [monotonicity #249]: #251 -#255 := [monotonicity #252]: #254 -#258 := [monotonicity #255]: #257 -#261 := [quant-intro #258]: #260 -#217 := (~ #206 #206) -#216 := (~ #203 #203) -#213 := [refl]: #216 -#218 := [nnf-pos #213]: #217 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#209 := (iff #42 #206) -#98 := (and #21 #23) -#101 := (or #22 #98) -#179 := (ite #101 #35 #174) -#89 := (= 0::Int #14) -#182 := (ite #89 0::Int #179) -#92 := (= 0::Int #15) -#185 := (ite #92 #14 #182) -#188 := (= #34 #185) -#191 := (forall (vars (?v0 Int) (?v1 Int)) #188) -#207 := (iff #191 #206) -#204 := (iff #188 #203) -#201 := (= #185 #200) -#198 := (= #182 #197) -#195 := (= #179 #194) -#150 := (iff #101 #149) -#147 := (iff #98 #146) -#144 := (iff #23 #143) -#145 := [rewrite]: #144 -#137 := (iff #21 #136) -#138 := [rewrite]: #137 -#148 := [monotonicity #138 #145]: #147 -#140 := (iff #22 #139) -#133 := (iff #20 #132) -#134 := [rewrite]: #133 -#141 := [monotonicity #134 #138]: #140 -#151 := [monotonicity #141 #148]: #150 -#196 := [monotonicity #151]: #195 -#125 := (iff #89 #17) -#126 := [rewrite]: #125 -#199 := [monotonicity #126 #196]: #198 -#127 := (iff #92 #18) -#128 := [rewrite]: #127 -#202 := [monotonicity #128 #199]: #201 -#205 := [monotonicity #202]: #204 -#208 := [quant-intro #205]: #207 -#192 := (iff #42 #191) -#189 := (iff #41 #188) -#186 := (= #40 #185) -#183 := (= #39 #182) -#180 := (= #38 #179) -#177 := (= #37 #174) -#171 := (- #168) -#175 := (= #171 #174) -#176 := [rewrite]: #175 -#172 := (= #37 #171) -#169 := (= #36 #168) -#108 := (= #28 #107) -#109 := [rewrite]: #108 -#105 := (= #27 #104) -#106 := [rewrite]: #105 -#170 := [monotonicity #106 #109]: #169 -#173 := [monotonicity #170]: #172 -#178 := [trans #173 #176]: #177 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 +#83 := [trans #78 #81]: #82 +#60 := (= #19 2::Int) +#61 := [rewrite]: #60 +#58 := (iff #18 #57) +#55 := (iff #17 #54) +#56 := [rewrite]: #55 +#59 := [monotonicity #56]: #58 +#86 := [monotonicity #59 #61 #83]: #85 +#52 := (iff #12 false) +#53 := [rewrite]: #52 +#89 := [monotonicity #53 #86]: #88 +#93 := [trans #89 #91]: #92 +#50 := (iff #10 false) +#51 := [rewrite]: #50 +#96 := [monotonicity #51 #93]: #95 +#100 := [trans #96 #98]: #99 #103 := [monotonicity #100]: #102 -#181 := [monotonicity #103 #178]: #180 -#90 := (iff #17 #89) +#107 := [trans #103 #105]: #106 +#110 := [monotonicity #107]: #109 +#146 := [trans #110 #144]: #145 +#49 := [asserted]: #29 +[mp #49 #146]: false +unsat +7d327b19e01666c9f9c62ef0af0f737663d19d70 145 0 +#2 := false +#28 := 2::Int +#29 := (- 2::Int) +#8 := 3::Int +#9 := (- 3::Int) +#22 := (- #9) +#12 := 1::Int +#21 := (- 1::Int) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod 1::Int #9) +#10 := 0::Int +#15 := (< 0::Int #9) +#17 := (< 1::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 1::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= 1::Int 0::Int) +#26 := (ite #13 0::Int #25) +#11 := (= #9 0::Int) +#27 := (ite #11 1::Int #26) +#30 := (= #27 #29) +#31 := (not #30) +#166 := (iff #31 false) +#52 := -3::Int +#64 := (< 0::Int -3::Int) +#70 := (and #17 #64) +#67 := (and #14 #64) +#73 := (or #67 #70) +#164 := (iff #73 false) +#159 := (or false false) +#162 := (iff #159 false) +#163 := [rewrite]: #162 +#160 := (iff #73 #159) +#157 := (iff #70 false) +#152 := (and false false) +#155 := (iff #152 false) +#156 := [rewrite]: #155 +#153 := (iff #70 #152) +#141 := (iff #64 false) +#142 := [rewrite]: #141 +#150 := (iff #17 false) +#151 := [rewrite]: #150 +#154 := [monotonicity #151 #142]: #153 +#158 := [trans #154 #156]: #157 +#148 := (iff #67 false) +#1 := true +#143 := (and true false) +#146 := (iff #143 false) +#147 := [rewrite]: #146 +#144 := (iff #67 #143) +#139 := (iff #14 true) +#140 := [rewrite]: #139 +#145 := [monotonicity #140 #142]: #144 +#149 := [trans #145 #147]: #148 +#161 := [monotonicity #149 #158]: #160 +#165 := [trans #161 #163]: #164 +#137 := (iff #31 #73) +#127 := (not #73) +#132 := (not #127) +#135 := (iff #132 #73) +#136 := [rewrite]: #135 +#133 := (iff #31 #132) +#130 := (iff #30 #127) +#102 := -2::Int +#107 := (ite #73 1::Int -2::Int) +#124 := (= #107 -2::Int) +#128 := (iff #124 #127) +#129 := [rewrite]: #128 +#125 := (iff #30 #124) +#103 := (= #29 -2::Int) +#104 := [rewrite]: #103 +#122 := (= #27 #107) +#117 := (ite false 1::Int #107) +#120 := (= #117 #107) +#121 := [rewrite]: #120 +#118 := (= #27 #117) +#115 := (= #26 #107) +#110 := (ite false 0::Int #107) +#113 := (= #110 #107) +#114 := [rewrite]: #113 +#111 := (= #26 #110) +#108 := (= #25 #107) +#105 := (= #24 -2::Int) +#100 := (= #24 #29) +#98 := (= #23 2::Int) +#83 := -1::Int +#93 := (mod -1::Int 3::Int) +#96 := (= #93 2::Int) +#97 := [rewrite]: #96 +#94 := (= #23 #93) +#91 := (= #22 3::Int) +#86 := (- -3::Int) +#89 := (= #86 3::Int) +#90 := [rewrite]: #89 +#87 := (= #22 #86) +#53 := (= #9 -3::Int) +#54 := [rewrite]: #53 +#88 := [monotonicity #54]: #87 +#92 := [trans #88 #90]: #91 +#84 := (= #21 -1::Int) +#85 := [rewrite]: #84 +#95 := [monotonicity #85 #92]: #94 +#99 := [trans #95 #97]: #98 +#101 := [monotonicity #99]: #100 +#106 := [trans #101 #104]: #105 +#81 := (= #20 1::Int) +#76 := (mod 1::Int -3::Int) +#79 := (= #76 1::Int) +#80 := [rewrite]: #79 +#77 := (= #20 #76) +#78 := [monotonicity #54]: #77 +#82 := [trans #78 #80]: #81 +#74 := (iff #19 #73) +#71 := (iff #18 #70) +#65 := (iff #15 #64) +#66 := [monotonicity #54]: #65 +#72 := [monotonicity #66]: #71 +#68 := (iff #16 #67) +#69 := [monotonicity #66]: #68 +#75 := [monotonicity #69 #72]: #74 +#109 := [monotonicity #75 #82 #106]: #108 +#62 := (iff #13 false) +#63 := [rewrite]: #62 +#112 := [monotonicity #63 #109]: #111 +#116 := [trans #112 #114]: #115 +#60 := (iff #11 false) +#55 := (= -3::Int 0::Int) +#58 := (iff #55 false) +#59 := [rewrite]: #58 +#56 := (iff #11 #55) +#57 := [monotonicity #54]: #56 +#61 := [trans #57 #59]: #60 +#119 := [monotonicity #61 #116]: #118 +#123 := [trans #119 #121]: #122 +#126 := [monotonicity #123 #104]: #125 +#131 := [trans #126 #129]: #130 +#134 := [monotonicity #131]: #133 +#138 := [trans #134 #136]: #137 +#167 := [trans #138 #165]: #166 +#51 := [asserted]: #31 +[mp #51 #167]: false +unsat +82d6113024911b407663ddeabeafc31ab21bb4b0 111 0 +#2 := false +#10 := 0::Int +#8 := 3::Int +#9 := (- 3::Int) +#20 := (- #9) +#21 := (mod #9 #20) +#22 := (- #21) +#19 := (mod 3::Int #9) +#14 := (< 0::Int #9) +#16 := (< 3::Int 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int 3::Int) +#15 := (and #13 #14) +#18 := (or #15 #17) +#23 := (ite #18 #19 #22) +#12 := (= 3::Int 0::Int) +#24 := (ite #12 0::Int #23) +#11 := (= #9 0::Int) +#25 := (ite #11 3::Int #24) +#26 := (= #25 0::Int) +#27 := (not #26) +#132 := (iff #27 false) +#1 := true +#127 := (not true) +#130 := (iff #127 false) +#131 := [rewrite]: #130 +#128 := (iff #27 #127) +#125 := (iff #26 true) +#120 := (= 0::Int 0::Int) +#123 := (iff #120 true) +#124 := [rewrite]: #123 +#121 := (iff #26 #120) +#114 := (ite false 3::Int 0::Int) +#117 := (= #114 0::Int) +#118 := [rewrite]: #117 +#115 := (= #25 #114) +#112 := (= #24 0::Int) +#107 := (ite false 0::Int 0::Int) +#110 := (= #107 0::Int) +#111 := [rewrite]: #110 +#108 := (= #24 #107) +#105 := (= #23 0::Int) +#48 := -3::Int +#60 := (< 0::Int -3::Int) +#66 := (and #16 #60) +#63 := (and #13 #60) +#69 := (or #63 #66) +#100 := (ite #69 0::Int 0::Int) +#103 := (= #100 0::Int) +#104 := [rewrite]: #103 +#101 := (= #23 #100) +#98 := (= #22 0::Int) +#93 := (- 0::Int) +#96 := (= #93 0::Int) +#97 := [rewrite]: #96 +#94 := (= #22 #93) +#91 := (= #21 0::Int) +#86 := (mod -3::Int 3::Int) +#89 := (= #86 0::Int) +#90 := [rewrite]: #89 +#87 := (= #21 #86) +#84 := (= #20 3::Int) +#79 := (- -3::Int) +#82 := (= #79 3::Int) +#83 := [rewrite]: #82 +#80 := (= #20 #79) +#49 := (= #9 -3::Int) +#50 := [rewrite]: #49 +#81 := [monotonicity #50]: #80 +#85 := [trans #81 #83]: #84 +#88 := [monotonicity #50 #85]: #87 +#92 := [trans #88 #90]: #91 +#95 := [monotonicity #92]: #94 +#99 := [trans #95 #97]: #98 +#77 := (= #19 0::Int) +#72 := (mod 3::Int -3::Int) +#75 := (= #72 0::Int) +#76 := [rewrite]: #75 +#73 := (= #19 #72) +#74 := [monotonicity #50]: #73 +#78 := [trans #74 #76]: #77 +#70 := (iff #18 #69) +#67 := (iff #17 #66) +#61 := (iff #14 #60) +#62 := [monotonicity #50]: #61 +#68 := [monotonicity #62]: #67 +#64 := (iff #15 #63) +#65 := [monotonicity #62]: #64 +#71 := [monotonicity #65 #68]: #70 +#102 := [monotonicity #71 #78 #99]: #101 +#106 := [trans #102 #104]: #105 +#58 := (iff #12 false) +#59 := [rewrite]: #58 +#109 := [monotonicity #59 #106]: #108 +#113 := [trans #109 #111]: #112 +#56 := (iff #11 false) +#51 := (= -3::Int 0::Int) +#54 := (iff #51 false) +#55 := [rewrite]: #54 +#52 := (iff #11 #51) +#53 := [monotonicity #50]: #52 +#57 := [trans #53 #55]: #56 +#116 := [monotonicity #57 #113]: #115 +#119 := [trans #116 #118]: #26 +#122 := [monotonicity #119]: #121 +#126 := [trans #122 #124]: #125 +#129 := [monotonicity #126]: #128 +#133 := [trans #129 #131]: #132 +#47 := [asserted]: #27 +[mp #47 #133]: false +unsat +c4214ad6df5eccc4b53bd004dab0150c7519b10c 146 0 +#2 := false +#28 := 1::Int +#29 := (- 1::Int) +#8 := 3::Int +#9 := (- 3::Int) +#22 := (- #9) +#12 := 5::Int +#21 := (- 5::Int) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod 5::Int #9) +#10 := 0::Int +#15 := (< 0::Int #9) +#17 := (< 5::Int 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int 5::Int) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= 5::Int 0::Int) +#26 := (ite #13 0::Int #25) +#11 := (= #9 0::Int) +#27 := (ite #11 5::Int #26) +#30 := (= #27 #29) +#31 := (not #30) +#167 := (iff #31 false) +#52 := -3::Int +#64 := (< 0::Int -3::Int) +#70 := (and #17 #64) +#67 := (and #14 #64) +#73 := (or #67 #70) +#165 := (iff #73 false) +#160 := (or false false) +#163 := (iff #160 false) +#164 := [rewrite]: #163 +#161 := (iff #73 #160) +#158 := (iff #70 false) +#153 := (and false false) +#156 := (iff #153 false) +#157 := [rewrite]: #156 +#154 := (iff #70 #153) +#142 := (iff #64 false) +#143 := [rewrite]: #142 +#151 := (iff #17 false) +#152 := [rewrite]: #151 +#155 := [monotonicity #152 #143]: #154 +#159 := [trans #155 #157]: #158 +#149 := (iff #67 false) +#1 := true +#144 := (and true false) +#147 := (iff #144 false) +#148 := [rewrite]: #147 +#145 := (iff #67 #144) +#140 := (iff #14 true) +#141 := [rewrite]: #140 +#146 := [monotonicity #141 #143]: #145 +#150 := [trans #146 #148]: #149 +#162 := [monotonicity #150 #159]: #161 +#166 := [trans #162 #164]: #165 +#138 := (iff #31 #73) +#128 := (not #73) +#133 := (not #128) +#136 := (iff #133 #73) +#137 := [rewrite]: #136 +#134 := (iff #31 #133) +#131 := (iff #30 #128) +#103 := -1::Int +#79 := 2::Int +#108 := (ite #73 2::Int -1::Int) +#125 := (= #108 -1::Int) +#129 := (iff #125 #128) +#130 := [rewrite]: #129 +#126 := (iff #30 #125) +#104 := (= #29 -1::Int) +#105 := [rewrite]: #104 +#123 := (= #27 #108) +#118 := (ite false 5::Int #108) +#121 := (= #118 #108) +#122 := [rewrite]: #121 +#119 := (= #27 #118) +#116 := (= #26 #108) +#111 := (ite false 0::Int #108) +#114 := (= #111 #108) +#115 := [rewrite]: #114 +#112 := (= #26 #111) +#109 := (= #25 #108) +#106 := (= #24 -1::Int) +#101 := (= #24 #29) +#99 := (= #23 1::Int) +#84 := -5::Int +#94 := (mod -5::Int 3::Int) +#97 := (= #94 1::Int) +#98 := [rewrite]: #97 +#95 := (= #23 #94) +#92 := (= #22 3::Int) +#87 := (- -3::Int) +#90 := (= #87 3::Int) #91 := [rewrite]: #90 -#184 := [monotonicity #91 #181]: #183 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#187 := [monotonicity #94 #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [quant-intro #190]: #192 -#210 := [trans #193 #208]: #209 -#167 := [asserted]: #42 -#211 := [mp #167 #210]: #206 -#214 := [mp~ #211 #218]: #206 -#262 := [mp #214 #261]: #259 -#293 := [mp #262 #292]: #290 -#777 := [mp #293 #776]: #772 -#66 := (f3 0::Int -1::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := 1::Int -#10 := (- 1::Int) -#11 := (f3 0::Int #10) -#12 := (= #11 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) +#88 := (= #22 #87) +#53 := (= #9 -3::Int) +#54 := [rewrite]: #53 +#89 := [monotonicity #54]: #88 +#93 := [trans #89 #91]: #92 +#85 := (= #21 -5::Int) +#86 := [rewrite]: #85 +#96 := [monotonicity #86 #93]: #95 +#100 := [trans #96 #98]: #99 +#102 := [monotonicity #100]: #101 +#107 := [trans #102 #105]: #106 +#82 := (= #20 2::Int) +#76 := (mod 5::Int -3::Int) +#80 := (= #76 2::Int) #81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #11 #66) -#64 := (= #10 -1::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#548 := (not #772) -#696 := (or #548 #69) -#351 := (* -1::Int -1::Int) -#435 := (* -1::Int 0::Int) -#436 := (mod #435 #351) -#437 := (+ #66 #436) -#428 := (= #437 0::Int) -#439 := (mod 0::Int -1::Int) -#440 := (* -1::Int #439) -#441 := (+ #66 #440) -#438 := (= #441 0::Int) -#442 := (>= 0::Int 0::Int) -#421 := (<= -1::Int 0::Int) -#756 := (or #421 #442) -#758 := (not #756) -#415 := (<= 0::Int 0::Int) -#545 := (or #415 #421) -#752 := (not #545) -#426 := (or #752 #758) -#427 := (ite #426 #438 #428) -#759 := (= 0::Int 0::Int) -#760 := (ite #759 #69 #427) -#761 := (= -1::Int 0::Int) -#762 := (ite #761 #72 #760) -#598 := (or #548 #762) -#694 := (iff #598 #696) -#582 := (iff #696 #696) -#597 := [rewrite]: #582 -#588 := (iff #762 #69) -#706 := (ite false #69 #69) -#714 := (iff #706 #69) -#708 := [rewrite]: #714 -#705 := (iff #762 #706) -#704 := (iff #760 #69) -#1 := true -#546 := (ite true #69 #69) -#701 := (iff #546 #69) -#703 := [rewrite]: #701 -#547 := (iff #760 #546) -#715 := (iff #427 #69) -#707 := (iff #427 #706) -#711 := (iff #428 #69) -#709 := (= #437 #66) -#449 := (+ #66 0::Int) -#443 := (= #449 #66) -#725 := [rewrite]: #443 -#566 := (= #437 #449) -#724 := (= #436 0::Int) -#716 := (mod 0::Int 1::Int) -#723 := (= #716 0::Int) -#718 := [rewrite]: #723 -#717 := (= #436 #716) -#720 := (= #351 1::Int) -#721 := [rewrite]: #720 -#736 := (= #435 0::Int) -#446 := [rewrite]: #736 -#722 := [monotonicity #446 #721]: #717 -#565 := [trans #722 #718]: #724 -#567 := [monotonicity #565]: #566 -#710 := [trans #567 #725]: #709 -#712 := [monotonicity #710]: #711 -#730 := (iff #438 #69) -#729 := (= #441 #66) -#727 := (= #441 #449) -#447 := (= #440 0::Int) -#735 := (= #440 #435) -#457 := (= #439 0::Int) -#731 := [rewrite]: #457 -#732 := [monotonicity #731]: #735 -#448 := [trans #732 #446]: #447 -#728 := [monotonicity #448]: #727 -#726 := [trans #728 #725]: #729 -#719 := [monotonicity #726]: #730 -#734 := (iff #426 false) -#461 := (or false false) -#357 := (iff #461 false) -#733 := [rewrite]: #357 -#462 := (iff #426 #461) -#738 := (iff #758 false) -#742 := (not true) -#745 := (iff #742 false) -#740 := [rewrite]: #745 -#751 := (iff #758 #742) -#750 := (iff #756 true) -#398 := (or true true) -#403 := (iff #398 true) -#404 := [rewrite]: #403 -#389 := (iff #756 #398) -#747 := (iff #442 true) -#749 := [rewrite]: #747 -#414 := (iff #421 true) -#755 := [rewrite]: #414 -#390 := [monotonicity #755 #749]: #389 -#748 := [trans #390 #404]: #750 -#737 := [monotonicity #748]: #751 -#460 := [trans #737 #740]: #738 -#746 := (iff #752 false) -#743 := (iff #752 #742) -#405 := (iff #545 true) -#739 := (iff #545 #398) -#418 := (iff #415 true) -#754 := [rewrite]: #418 -#402 := [monotonicity #754 #755]: #739 -#741 := [trans #402 #404]: #405 -#744 := [monotonicity #741]: #743 -#384 := [trans #744 #740]: #746 -#463 := [monotonicity #384 #460]: #462 -#456 := [trans #463 #733]: #734 -#713 := [monotonicity #456 #719 #712]: #707 -#544 := [trans #713 #708]: #715 -#753 := (iff #759 true) -#413 := [rewrite]: #753 -#700 := [monotonicity #413 #544]: #547 -#702 := [trans #700 #703]: #704 -#757 := (iff #761 false) -#763 := [rewrite]: #757 -#587 := [monotonicity #763 #81 #702]: #705 -#589 := [trans #587 #708]: #588 -#697 := [monotonicity #589]: #694 -#599 := [trans #697 #597]: #694 -#693 := [quant-inst #8 #63]: #598 -#600 := [mp #693 #599]: #696 -[unit-resolution #600 #87 #777]: false -unsat -7554e53ad4bbf50aa6cebedfca61c8a301b15856 332 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#771 := (pattern #34) -#11 := 0::Int -#63 := -1::Int -#107 := (* -1::Int #15) -#104 := (* -1::Int #14) -#168 := (mod #104 #107) -#283 := (+ #34 #168) -#284 := (= #283 0::Int) -#35 := (mod #14 #15) -#280 := (* -1::Int #35) -#281 := (+ #34 #280) -#282 := (= #281 0::Int) -#142 := (>= #14 0::Int) -#135 := (<= #15 0::Int) -#227 := (or #135 #142) -#228 := (not #227) -#131 := (<= #14 0::Int) -#225 := (or #131 #135) -#226 := (not #225) -#231 := (or #226 #228) -#285 := (ite #231 #282 #284) -#279 := (= #34 0::Int) -#17 := (= #14 0::Int) -#286 := (ite #17 #279 #285) -#278 := (= #14 #34) -#18 := (= #15 0::Int) -#287 := (ite #18 #278 #286) -#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287) -#290 := (forall (vars (?v0 Int) (?v1 Int)) #287) -#775 := (iff #290 #772) -#773 := (iff #287 #287) -#774 := [refl]: #773 -#776 := [quant-intro #774]: #775 -#174 := (* -1::Int #168) -#247 := (ite #231 #35 #174) -#250 := (ite #17 0::Int #247) -#253 := (ite #18 #14 #250) -#256 := (= #34 #253) -#259 := (forall (vars (?v0 Int) (?v1 Int)) #256) -#291 := (iff #259 #290) -#288 := (iff #256 #287) -#289 := [rewrite]: #288 -#292 := [quant-intro #289]: #291 -#143 := (not #142) -#136 := (not #135) -#146 := (and #136 #143) -#132 := (not #131) -#139 := (and #132 #136) -#149 := (or #139 #146) -#194 := (ite #149 #35 #174) -#197 := (ite #17 0::Int #194) -#200 := (ite #18 #14 #197) -#203 := (= #34 #200) -#206 := (forall (vars (?v0 Int) (?v1 Int)) #203) -#260 := (iff #206 #259) -#257 := (iff #203 #256) -#254 := (= #200 #253) -#251 := (= #197 #250) -#248 := (= #194 #247) -#232 := (iff #149 #231) -#229 := (iff #146 #228) -#230 := [rewrite]: #229 -#219 := (iff #139 #226) -#220 := [rewrite]: #219 -#233 := [monotonicity #220 #230]: #232 -#249 := [monotonicity #233]: #248 -#252 := [monotonicity #249]: #251 -#255 := [monotonicity #252]: #254 -#258 := [monotonicity #255]: #257 -#261 := [quant-intro #258]: #260 -#217 := (~ #206 #206) -#216 := (~ #203 #203) -#213 := [refl]: #216 -#218 := [nnf-pos #213]: #217 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#209 := (iff #42 #206) -#98 := (and #21 #23) -#101 := (or #22 #98) -#179 := (ite #101 #35 #174) -#89 := (= 0::Int #14) -#182 := (ite #89 0::Int #179) -#92 := (= 0::Int #15) -#185 := (ite #92 #14 #182) -#188 := (= #34 #185) -#191 := (forall (vars (?v0 Int) (?v1 Int)) #188) -#207 := (iff #191 #206) -#204 := (iff #188 #203) -#201 := (= #185 #200) -#198 := (= #182 #197) -#195 := (= #179 #194) -#150 := (iff #101 #149) -#147 := (iff #98 #146) -#144 := (iff #23 #143) -#145 := [rewrite]: #144 -#137 := (iff #21 #136) -#138 := [rewrite]: #137 -#148 := [monotonicity #138 #145]: #147 -#140 := (iff #22 #139) -#133 := (iff #20 #132) -#134 := [rewrite]: #133 -#141 := [monotonicity #134 #138]: #140 -#151 := [monotonicity #141 #148]: #150 -#196 := [monotonicity #151]: #195 -#125 := (iff #89 #17) -#126 := [rewrite]: #125 -#199 := [monotonicity #126 #196]: #198 -#127 := (iff #92 #18) -#128 := [rewrite]: #127 -#202 := [monotonicity #128 #199]: #201 -#205 := [monotonicity #202]: #204 -#208 := [quant-intro #205]: #207 -#192 := (iff #42 #191) -#189 := (iff #41 #188) -#186 := (= #40 #185) -#183 := (= #39 #182) -#180 := (= #38 #179) -#177 := (= #37 #174) -#171 := (- #168) -#175 := (= #171 #174) -#176 := [rewrite]: #175 -#172 := (= #37 #171) -#169 := (= #36 #168) -#108 := (= #28 #107) -#109 := [rewrite]: #108 -#105 := (= #27 #104) -#106 := [rewrite]: #105 -#170 := [monotonicity #106 #109]: #169 -#173 := [monotonicity #170]: #172 -#178 := [trans #173 #176]: #177 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#181 := [monotonicity #103 #178]: #180 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#184 := [monotonicity #91 #181]: #183 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#187 := [monotonicity #94 #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [quant-intro #190]: #192 -#210 := [trans #193 #208]: #209 -#167 := [asserted]: #42 -#211 := [mp #167 #210]: #206 -#214 := [mp~ #211 #218]: #206 -#262 := [mp #214 #261]: #259 -#293 := [mp #262 #292]: #290 -#777 := [mp #293 #776]: #772 -#8 := 1::Int -#66 := (f3 1::Int -1::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := (- 1::Int) -#10 := (f3 1::Int #9) -#12 := (= #10 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #10 #66) -#64 := (= #9 -1::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#593 := (not #772) -#601 := (or #593 #69) -#351 := (* -1::Int -1::Int) -#435 := (* -1::Int 1::Int) -#436 := (mod #435 #351) -#437 := (+ #66 #436) -#428 := (= #437 0::Int) -#439 := (mod 1::Int -1::Int) -#440 := (* -1::Int #439) -#441 := (+ #66 #440) -#438 := (= #441 0::Int) -#442 := (>= 1::Int 0::Int) -#421 := (<= -1::Int 0::Int) -#756 := (or #421 #442) -#758 := (not #756) -#415 := (<= 1::Int 0::Int) -#545 := (or #415 #421) -#752 := (not #545) -#426 := (or #752 #758) -#427 := (ite #426 #438 #428) -#759 := (= 1::Int 0::Int) -#760 := (ite #759 #69 #427) -#761 := (= 1::Int #66) -#762 := (= -1::Int 0::Int) -#757 := (ite #762 #761 #760) -#602 := (or #593 #757) -#604 := (iff #602 #601) -#698 := (iff #601 #601) -#695 := [rewrite]: #698 -#599 := (iff #757 #69) -#418 := (= #66 1::Int) -#693 := (ite false #418 #69) -#582 := (iff #693 #69) -#597 := [rewrite]: #582 -#694 := (iff #757 #693) -#696 := (iff #760 #69) -#701 := (ite false #69 #69) -#702 := (iff #701 #69) -#705 := [rewrite]: #702 -#589 := (iff #760 #701) -#587 := (iff #427 #69) -#703 := (iff #427 #701) -#547 := (iff #428 #69) -#544 := (= #437 #66) -#719 := (+ #66 0::Int) -#716 := (= #719 #66) -#717 := [rewrite]: #716 -#708 := (= #437 #719) -#713 := (= #436 0::Int) -#710 := (mod -1::Int 1::Int) -#706 := (= #710 0::Int) -#707 := [rewrite]: #706 -#711 := (= #436 #710) -#567 := (= #351 1::Int) -#709 := [rewrite]: #567 -#565 := (= #435 -1::Int) -#566 := [rewrite]: #565 -#712 := [monotonicity #566 #709]: #711 -#714 := [trans #712 #707]: #713 -#715 := [monotonicity #714]: #708 -#546 := [trans #715 #717]: #544 -#700 := [monotonicity #546]: #547 -#718 := (iff #438 #69) -#722 := (= #441 #66) -#720 := (= #441 #719) -#726 := (= #440 0::Int) -#727 := (* -1::Int 0::Int) -#725 := (= #727 0::Int) -#729 := [rewrite]: #725 -#728 := (= #440 #727) -#448 := (= #439 0::Int) -#449 := [rewrite]: #448 -#443 := [monotonicity #449]: #728 -#730 := [trans #443 #729]: #726 -#721 := [monotonicity #730]: #720 -#723 := [trans #721 #717]: #722 -#724 := [monotonicity #723]: #718 -#446 := (iff #426 false) -#457 := (or false false) -#732 := (iff #457 false) -#736 := [rewrite]: #732 -#731 := (iff #426 #457) -#734 := (iff #758 false) -#1 := true -#740 := (not true) -#747 := (iff #740 false) -#749 := [rewrite]: #747 -#357 := (iff #758 #740) -#462 := (iff #756 true) -#751 := (or true true) -#460 := (iff #751 true) -#461 := [rewrite]: #460 -#737 := (iff #756 #751) -#750 := (iff #442 true) -#748 := [rewrite]: #750 -#402 := (iff #421 true) -#403 := [rewrite]: #402 -#738 := [monotonicity #403 #748]: #737 -#463 := [trans #738 #461]: #462 -#733 := [monotonicity #463]: #357 -#456 := [trans #733 #749]: #734 -#389 := (iff #752 false) -#746 := (iff #752 #740) -#744 := (iff #545 true) -#404 := (or false true) -#742 := (iff #404 true) -#743 := [rewrite]: #742 -#405 := (iff #545 #404) -#398 := (iff #415 false) -#739 := [rewrite]: #398 -#741 := [monotonicity #739 #403]: #405 -#745 := [trans #741 #743]: #744 -#384 := [monotonicity #745]: #746 -#390 := [trans #384 #749]: #389 -#735 := [monotonicity #390 #456]: #731 -#447 := [trans #735 #736]: #446 -#704 := [monotonicity #447 #724 #700]: #703 -#588 := [trans #704 #705]: #587 -#414 := (iff #759 false) -#755 := [rewrite]: #414 -#548 := [monotonicity #755 #588]: #589 -#598 := [trans #548 #705]: #696 -#413 := (iff #761 #418) -#754 := [rewrite]: #413 -#763 := (iff #762 false) -#753 := [rewrite]: #763 -#697 := [monotonicity #753 #754 #598]: #694 -#600 := [trans #697 #597]: #599 -#605 := [monotonicity #600]: #604 -#699 := [trans #605 #695]: #604 -#603 := [quant-inst #8 #63]: #602 -#686 := [mp #603 #699]: #601 -[unit-resolution #686 #87 #777]: false -unsat -768cdc3a48375ab653481018d34501c9146cb16e 334 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#35 := (f3 #15 #16) -#772 := (pattern #35) -#12 := 0::Int -#64 := -1::Int -#108 := (* -1::Int #16) -#105 := (* -1::Int #15) -#169 := (mod #105 #108) -#284 := (+ #35 #169) -#285 := (= #284 0::Int) -#36 := (mod #15 #16) -#281 := (* -1::Int #36) -#282 := (+ #35 #281) -#283 := (= #282 0::Int) -#143 := (>= #15 0::Int) -#136 := (<= #16 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #15 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #35 0::Int) -#18 := (= #15 0::Int) -#287 := (ite #18 #280 #286) -#279 := (= #15 #35) -#19 := (= #16 0::Int) -#288 := (ite #19 #279 #287) -#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#776 := (iff #291 #773) -#774 := (iff #288 #288) -#775 := [refl]: #774 -#777 := [quant-intro #775]: #776 -#175 := (* -1::Int #169) -#248 := (ite #232 #36 #175) -#251 := (ite #18 0::Int #248) -#254 := (ite #19 #15 #251) -#257 := (= #35 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #36 #175) -#198 := (ite #18 0::Int #195) -#201 := (ite #19 #15 #198) -#204 := (= #35 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#29 := (- #16) -#28 := (- #15) -#37 := (mod #28 #29) -#38 := (- #37) -#22 := (< 0::Int #16) -#24 := (< #15 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #15) -#23 := (and #21 #22) -#26 := (or #23 #25) -#39 := (ite #26 #36 #38) -#40 := (ite #18 0::Int #39) -#41 := (ite #19 #15 #40) -#42 := (= #35 #41) -#43 := (forall (vars (?v0 Int) (?v1 Int)) #42) -#210 := (iff #43 #207) -#99 := (and #22 #24) -#102 := (or #23 #99) -#180 := (ite #102 #36 #175) -#90 := (= 0::Int #15) -#183 := (ite #90 0::Int #180) -#93 := (= 0::Int #16) -#186 := (ite #93 #15 #183) -#189 := (= #35 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #102 #150) -#148 := (iff #99 #147) -#145 := (iff #24 #144) -#146 := [rewrite]: #145 -#138 := (iff #22 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #23 #140) -#134 := (iff #21 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #90 #18) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #93 #19) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #43 #192) -#190 := (iff #42 #189) -#187 := (= #41 #186) -#184 := (= #40 #183) -#181 := (= #39 #180) -#178 := (= #38 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #38 #172) -#170 := (= #37 #169) -#109 := (= #29 #108) -#110 := [rewrite]: #109 -#106 := (= #28 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#103 := (iff #26 #102) -#100 := (iff #25 #99) -#101 := [rewrite]: #100 -#104 := [monotonicity #101]: #103 -#182 := [monotonicity #104 #179]: #181 -#91 := (iff #18 #90) -#92 := [rewrite]: #91 -#185 := [monotonicity #92 #182]: #184 -#94 := (iff #19 #93) -#95 := [rewrite]: #94 -#188 := [monotonicity #95 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #43 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#778 := [mp #294 #777]: #773 +#77 := (= #20 #76) +#78 := [monotonicity #54]: #77 +#83 := [trans #78 #81]: #82 +#74 := (iff #19 #73) +#71 := (iff #18 #70) +#65 := (iff #15 #64) +#66 := [monotonicity #54]: #65 +#72 := [monotonicity #66]: #71 +#68 := (iff #16 #67) +#69 := [monotonicity #66]: #68 +#75 := [monotonicity #69 #72]: #74 +#110 := [monotonicity #75 #83 #107]: #109 +#62 := (iff #13 false) +#63 := [rewrite]: #62 +#113 := [monotonicity #63 #110]: #112 +#117 := [trans #113 #115]: #116 +#60 := (iff #11 false) +#55 := (= -3::Int 0::Int) +#58 := (iff #55 false) +#59 := [rewrite]: #58 +#56 := (iff #11 #55) +#57 := [monotonicity #54]: #56 +#61 := [trans #57 #59]: #60 +#120 := [monotonicity #61 #117]: #119 +#124 := [trans #120 #122]: #123 +#127 := [monotonicity #124 #105]: #126 +#132 := [trans #127 #130]: #131 +#135 := [monotonicity #132]: #134 +#139 := [trans #135 #137]: #138 +#168 := [trans #139 #166]: #167 +#51 := [asserted]: #31 +[mp #51 #168]: false +unsat +fac742ba4b7a09666d1c5cd8a1a25074910c56cc 156 0 +#2 := false +#28 := 2::Int #8 := 3::Int -#67 := (f3 3::Int -1::Int) -#70 := (= #67 0::Int) -#83 := (not #70) -#9 := 1::Int -#10 := (- 1::Int) -#11 := (f3 3::Int #10) -#13 := (= #11 0::Int) -#14 := (not #13) -#86 := (iff #14 #83) -#73 := (= 0::Int #67) -#78 := (not #73) -#84 := (iff #78 #83) -#81 := (iff #73 #70) -#82 := [rewrite]: #81 -#85 := [monotonicity #82]: #84 -#79 := (iff #14 #78) -#76 := (iff #13 #73) -#74 := (iff #70 #73) -#75 := [rewrite]: #74 -#71 := (iff #13 #70) -#68 := (= #11 #67) -#65 := (= #10 -1::Int) -#66 := [rewrite]: #65 -#69 := [monotonicity #66]: #68 -#72 := [monotonicity #69]: #71 -#77 := [trans #72 #75]: #76 -#80 := [monotonicity #77]: #79 -#87 := [trans #80 #85]: #86 -#63 := [asserted]: #14 -#88 := [mp #63 #87]: #83 -#602 := (not #773) -#603 := (or #602 #70) -#352 := (* -1::Int -1::Int) -#436 := (* -1::Int 3::Int) -#437 := (mod #436 #352) -#438 := (+ #67 #437) -#429 := (= #438 0::Int) -#440 := (mod 3::Int -1::Int) -#441 := (* -1::Int #440) -#442 := (+ #67 #441) -#439 := (= #442 0::Int) -#443 := (>= 3::Int 0::Int) -#422 := (<= -1::Int 0::Int) -#757 := (or #422 #443) -#759 := (not #757) -#416 := (<= 3::Int 0::Int) -#546 := (or #416 #422) -#753 := (not #546) -#427 := (or #753 #759) -#428 := (ite #427 #439 #429) -#760 := (= 3::Int 0::Int) -#761 := (ite #760 #70 #428) -#762 := (= 3::Int #67) -#763 := (= -1::Int 0::Int) -#758 := (ite #763 #762 #761) -#604 := (or #602 #758) -#606 := (iff #604 #603) -#696 := (iff #603 #603) -#700 := [rewrite]: #696 -#601 := (iff #758 #70) -#419 := (= #67 3::Int) -#695 := (ite false #419 #70) -#598 := (iff #695 #70) -#600 := [rewrite]: #598 -#698 := (iff #758 #695) -#599 := (iff #761 #70) -#704 := (ite false #70 #70) -#706 := (iff #704 #70) -#588 := [rewrite]: #706 -#549 := (iff #761 #704) -#589 := (iff #428 #70) -#705 := (iff #428 #704) -#701 := (iff #429 #70) -#547 := (= #438 #67) -#720 := (+ #67 0::Int) -#717 := (= #720 #67) -#718 := [rewrite]: #717 -#716 := (= #438 #720) -#715 := (= #437 0::Int) -#566 := -3::Int -#712 := (mod -3::Int 1::Int) -#708 := (= #712 0::Int) -#714 := [rewrite]: #708 -#713 := (= #437 #712) -#710 := (= #352 1::Int) -#711 := [rewrite]: #710 -#567 := (= #436 -3::Int) -#568 := [rewrite]: #567 -#707 := [monotonicity #568 #711]: #713 -#709 := [trans #707 #714]: #715 -#545 := [monotonicity #709]: #716 -#548 := [trans #545 #718]: #547 -#702 := [monotonicity #548]: #701 -#719 := (iff #439 #70) -#723 := (= #442 #67) -#721 := (= #442 #720) -#727 := (= #441 0::Int) -#728 := (* -1::Int 0::Int) -#726 := (= #728 0::Int) -#730 := [rewrite]: #726 -#729 := (= #441 #728) -#449 := (= #440 0::Int) -#450 := [rewrite]: #449 -#444 := [monotonicity #450]: #729 -#731 := [trans #444 #730]: #727 -#722 := [monotonicity #731]: #721 -#724 := [trans #722 #718]: #723 -#725 := [monotonicity #724]: #719 -#447 := (iff #427 false) -#458 := (or false false) -#733 := (iff #458 false) -#737 := [rewrite]: #733 -#732 := (iff #427 #458) -#735 := (iff #759 false) -#1 := true -#741 := (not true) -#748 := (iff #741 false) -#750 := [rewrite]: #748 -#358 := (iff #759 #741) -#463 := (iff #757 true) -#752 := (or true true) -#461 := (iff #752 true) -#462 := [rewrite]: #461 -#738 := (iff #757 #752) -#751 := (iff #443 true) -#749 := [rewrite]: #751 -#403 := (iff #422 true) -#404 := [rewrite]: #403 -#739 := [monotonicity #404 #749]: #738 -#464 := [trans #739 #462]: #463 -#734 := [monotonicity #464]: #358 -#457 := [trans #734 #750]: #735 -#390 := (iff #753 false) -#747 := (iff #753 #741) -#745 := (iff #546 true) -#405 := (or false true) -#743 := (iff #405 true) -#744 := [rewrite]: #743 -#406 := (iff #546 #405) -#399 := (iff #416 false) -#740 := [rewrite]: #399 -#742 := [monotonicity #740 #404]: #406 -#746 := [trans #742 #744]: #745 -#385 := [monotonicity #746]: #747 -#391 := [trans #385 #750]: #390 -#736 := [monotonicity #391 #457]: #732 -#448 := [trans #736 #737]: #447 -#703 := [monotonicity #448 #725 #702]: #705 -#590 := [trans #703 #588]: #589 -#415 := (iff #760 false) -#756 := [rewrite]: #415 -#697 := [monotonicity #756 #590]: #549 -#694 := [trans #697 #588]: #599 -#414 := (iff #762 #419) -#755 := [rewrite]: #414 -#764 := (iff #763 false) -#754 := [rewrite]: #764 -#583 := [monotonicity #754 #755 #694]: #698 -#594 := [trans #583 #600]: #601 -#699 := [monotonicity #594]: #606 -#687 := [trans #699 #700]: #606 -#605 := [quant-inst #8 #64]: #604 -#689 := [mp #605 #687]: #603 -[unit-resolution #689 #88 #778]: false -unsat -d313c8803fd67ab7c81ae803664ddc96f0a1cd58 311 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#35 := (f3 #15 #16) -#772 := (pattern #35) -#12 := 0::Int -#64 := -1::Int -#108 := (* -1::Int #16) -#105 := (* -1::Int #15) -#169 := (mod #105 #108) -#284 := (+ #35 #169) -#285 := (= #284 0::Int) -#36 := (mod #15 #16) -#281 := (* -1::Int #36) -#282 := (+ #35 #281) -#283 := (= #282 0::Int) -#143 := (>= #15 0::Int) -#136 := (<= #16 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #15 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #35 0::Int) -#18 := (= #15 0::Int) -#287 := (ite #18 #280 #286) -#279 := (= #15 #35) -#19 := (= #16 0::Int) -#288 := (ite #19 #279 #287) -#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#776 := (iff #291 #773) -#774 := (iff #288 #288) -#775 := [refl]: #774 -#777 := [quant-intro #775]: #776 -#175 := (* -1::Int #169) -#248 := (ite #232 #36 #175) -#251 := (ite #18 0::Int #248) -#254 := (ite #19 #15 #251) -#257 := (= #35 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #36 #175) -#198 := (ite #18 0::Int #195) -#201 := (ite #19 #15 #198) -#204 := (= #35 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#29 := (- #16) -#28 := (- #15) -#37 := (mod #28 #29) -#38 := (- #37) -#22 := (< 0::Int #16) -#24 := (< #15 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #15) -#23 := (and #21 #22) -#26 := (or #23 #25) -#39 := (ite #26 #36 #38) -#40 := (ite #18 0::Int #39) -#41 := (ite #19 #15 #40) -#42 := (= #35 #41) -#43 := (forall (vars (?v0 Int) (?v1 Int)) #42) -#210 := (iff #43 #207) -#99 := (and #22 #24) -#102 := (or #23 #99) -#180 := (ite #102 #36 #175) -#90 := (= 0::Int #15) -#183 := (ite #90 0::Int #180) -#93 := (= 0::Int #16) -#186 := (ite #93 #15 #183) -#189 := (= #35 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #102 #150) -#148 := (iff #99 #147) -#145 := (iff #24 #144) +#22 := (- 3::Int) +#11 := 1::Int +#12 := (- 1::Int) +#21 := (- #12) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod #12 3::Int) +#9 := 0::Int +#15 := (< 0::Int 3::Int) +#17 := (< #12 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #12) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= #12 0::Int) +#26 := (ite #13 0::Int #25) +#10 := (= 3::Int 0::Int) +#27 := (ite #10 #12 #26) +#29 := (= #27 2::Int) +#30 := (not #29) +#177 := (iff #30 false) +#53 := -1::Int +#74 := (< -1::Int 0::Int) +#80 := (and #15 #74) +#63 := (< 0::Int -1::Int) +#69 := (and #15 #63) +#85 := (or #69 #80) +#140 := (not #85) +#175 := (iff #140 false) +#1 := true +#170 := (not true) +#173 := (iff #170 false) +#174 := [rewrite]: #173 +#171 := (iff #140 #170) +#168 := (iff #85 true) +#163 := (or false true) +#166 := (iff #163 true) +#167 := [rewrite]: #166 +#164 := (iff #85 #163) +#161 := (iff #80 true) +#156 := (and true true) +#159 := (iff #156 true) +#160 := [rewrite]: #159 +#157 := (iff #80 #156) +#154 := (iff #74 true) +#155 := [rewrite]: #154 +#143 := (iff #15 true) +#144 := [rewrite]: #143 +#158 := [monotonicity #144 #155]: #157 +#162 := [trans #158 #160]: #161 +#152 := (iff #69 false) +#147 := (and true false) +#150 := (iff #147 false) +#151 := [rewrite]: #150 +#148 := (iff #69 #147) +#145 := (iff #63 false) #146 := [rewrite]: #145 -#138 := (iff #22 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #23 #140) -#134 := (iff #21 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #90 #18) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #93 #19) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #43 #192) -#190 := (iff #42 #189) -#187 := (= #41 #186) -#184 := (= #40 #183) -#181 := (= #39 #180) -#178 := (= #38 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #38 #172) -#170 := (= #37 #169) -#109 := (= #29 #108) -#110 := [rewrite]: #109 -#106 := (= #28 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#103 := (iff #26 #102) -#100 := (iff #25 #99) -#101 := [rewrite]: #100 -#104 := [monotonicity #101]: #103 -#182 := [monotonicity #104 #179]: #181 -#91 := (iff #18 #90) +#149 := [monotonicity #144 #146]: #148 +#153 := [trans #149 #151]: #152 +#165 := [monotonicity #153 #162]: #164 +#169 := [trans #165 #167]: #168 +#172 := [monotonicity #169]: #171 +#176 := [trans #172 #174]: #175 +#141 := (iff #30 #140) +#138 := (iff #29 #85) +#116 := (ite #85 2::Int -1::Int) +#133 := (= #116 2::Int) +#136 := (iff #133 #85) +#137 := [rewrite]: #136 +#134 := (iff #29 #133) +#131 := (= #27 #116) +#126 := (ite false -1::Int #116) +#129 := (= #126 #116) +#130 := [rewrite]: #129 +#127 := (= #27 #126) +#124 := (= #26 #116) +#119 := (ite false 0::Int #116) +#122 := (= #119 #116) +#123 := [rewrite]: #122 +#120 := (= #26 #119) +#117 := (= #25 #116) +#114 := (= #24 -1::Int) +#54 := (= #12 -1::Int) +#55 := [rewrite]: #54 +#112 := (= #24 #12) +#110 := (= #23 1::Int) +#102 := -3::Int +#105 := (mod 1::Int -3::Int) +#108 := (= #105 1::Int) +#109 := [rewrite]: #108 +#106 := (= #23 #105) +#103 := (= #22 -3::Int) +#104 := [rewrite]: #103 +#100 := (= #21 1::Int) +#95 := (- -1::Int) +#98 := (= #95 1::Int) +#99 := [rewrite]: #98 +#96 := (= #21 #95) +#97 := [monotonicity #55]: #96 +#101 := [trans #97 #99]: #100 +#107 := [monotonicity #101 #104]: #106 +#111 := [trans #107 #109]: #110 +#113 := [monotonicity #111]: #112 +#115 := [trans #113 #55]: #114 +#93 := (= #20 2::Int) +#88 := (mod -1::Int 3::Int) +#91 := (= #88 2::Int) #92 := [rewrite]: #91 -#185 := [monotonicity #92 #182]: #184 -#94 := (iff #19 #93) -#95 := [rewrite]: #94 -#188 := [monotonicity #95 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #43 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#778 := [mp #294 #777]: #773 -decl f4 :: Int -#8 := f4 -#67 := (f3 f4 -1::Int) -#70 := (= #67 0::Int) -#83 := (not #70) -#9 := 1::Int -#10 := (- 1::Int) -#11 := (f3 f4 #10) -#13 := (= #11 0::Int) -#14 := (not #13) -#86 := (iff #14 #83) -#73 := (= 0::Int #67) -#78 := (not #73) -#84 := (iff #78 #83) -#81 := (iff #73 #70) +#89 := (= #20 #88) +#90 := [monotonicity #55]: #89 +#94 := [trans #90 #92]: #93 +#86 := (iff #19 #85) +#83 := (iff #18 #80) +#77 := (and #74 #15) +#81 := (iff #77 #80) #82 := [rewrite]: #81 -#85 := [monotonicity #82]: #84 -#79 := (iff #14 #78) -#76 := (iff #13 #73) -#74 := (iff #70 #73) -#75 := [rewrite]: #74 -#71 := (iff #13 #70) -#68 := (= #11 #67) -#65 := (= #10 -1::Int) -#66 := [rewrite]: #65 -#69 := [monotonicity #66]: #68 -#72 := [monotonicity #69]: #71 -#77 := [trans #72 #75]: #76 -#80 := [monotonicity #77]: #79 -#87 := [trans #80 #85]: #86 -#63 := [asserted]: #14 -#88 := [mp #63 #87]: #83 -#716 := (not #773) -#545 := (or #716 #70) -#352 := (* -1::Int -1::Int) -#436 := (* -1::Int f4) -#437 := (mod #436 #352) -#438 := (+ #67 #437) -#429 := (= #438 0::Int) -#440 := (mod f4 -1::Int) -#441 := (* -1::Int #440) -#442 := (+ #67 #441) -#439 := (= #442 0::Int) -#443 := (>= f4 0::Int) -#422 := (<= -1::Int 0::Int) -#757 := (or #422 #443) -#759 := (not #757) -#416 := (<= f4 0::Int) -#546 := (or #416 #422) -#753 := (not #546) -#427 := (or #753 #759) -#428 := (ite #427 #439 #429) -#760 := (= f4 0::Int) -#761 := (ite #760 #70 #428) -#762 := (= f4 #67) -#763 := (= -1::Int 0::Int) -#758 := (ite #763 #762 #761) -#547 := (or #716 #758) -#701 := (iff #547 #545) -#704 := (iff #545 #545) -#705 := [rewrite]: #704 -#715 := (iff #758 #70) -#712 := (ite false #762 #70) -#708 := (iff #712 #70) -#714 := [rewrite]: #708 -#713 := (iff #758 #712) -#710 := (iff #761 #70) -#719 := (ite #760 #70 #70) -#567 := (iff #719 #70) -#568 := [rewrite]: #567 -#725 := (iff #761 #719) -#723 := (iff #428 #70) -#720 := (ite false #439 #70) -#717 := (iff #720 #70) -#718 := [rewrite]: #717 -#721 := (iff #428 #720) -#727 := (iff #429 #70) -#726 := (= #438 #67) -#449 := (+ #67 0::Int) -#729 := (= #449 #67) -#444 := [rewrite]: #729 -#450 := (= #438 #449) -#447 := (= #437 0::Int) -#458 := (mod #436 1::Int) -#733 := (= #458 0::Int) -#737 := [rewrite]: #733 -#732 := (= #437 #458) -#735 := (= #352 1::Int) -#457 := [rewrite]: #735 -#736 := [monotonicity #457]: #732 -#448 := [trans #736 #737]: #447 -#728 := [monotonicity #448]: #450 -#730 := [trans #728 #444]: #726 -#731 := [monotonicity #730]: #727 -#358 := (iff #427 false) -#739 := (or false false) -#463 := (iff #739 false) -#464 := [rewrite]: #463 -#461 := (iff #427 #739) -#752 := (iff #759 false) -#1 := true -#405 := (not true) -#743 := (iff #405 false) -#744 := [rewrite]: #743 -#751 := (iff #759 #405) -#390 := (iff #757 true) -#741 := (or true #443) -#748 := (iff #741 true) -#750 := [rewrite]: #748 -#747 := (iff #757 #741) -#414 := (iff #422 true) -#419 := [rewrite]: #414 -#385 := [monotonicity #419]: #747 -#391 := [trans #385 #750]: #390 -#749 := [monotonicity #391]: #751 -#738 := [trans #749 #744]: #752 -#745 := (iff #753 false) -#406 := (iff #753 #405) -#403 := (iff #546 true) -#755 := (or #416 true) -#399 := (iff #755 true) -#740 := [rewrite]: #399 -#415 := (iff #546 #755) -#756 := [monotonicity #419]: #415 -#404 := [trans #756 #740]: #403 -#742 := [monotonicity #404]: #406 -#746 := [trans #742 #744]: #745 -#462 := [monotonicity #746 #738]: #461 -#734 := [trans #462 #464]: #358 -#722 := [monotonicity #734 #731]: #721 -#724 := [trans #722 #718]: #723 -#566 := [monotonicity #724]: #725 -#711 := [trans #566 #568]: #710 -#764 := (iff #763 false) -#754 := [rewrite]: #764 -#707 := [monotonicity #754 #711]: #713 -#709 := [trans #707 #714]: #715 -#702 := [monotonicity #709]: #701 -#703 := [trans #702 #705]: #701 -#548 := [quant-inst #8 #64]: #547 -#706 := [mp #548 #703]: #545 -[unit-resolution #706 #88 #778]: false -unsat -4e6d1a0d0e4d1e5ccd22f2801665c723ffc6cafc 304 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#33 := (f3 #13 #14) -#757 := (pattern #33) -#8 := 0::Int -#88 := -1::Int -#92 := (* -1::Int #14) -#89 := (* -1::Int #13) -#153 := (mod #89 #92) -#268 := (+ #33 #153) -#269 := (= #268 0::Int) -#34 := (mod #13 #14) -#265 := (* -1::Int #34) -#266 := (+ #33 #265) -#267 := (= #266 0::Int) -#127 := (>= #13 0::Int) -#120 := (<= #14 0::Int) -#212 := (or #120 #127) -#213 := (not #212) -#116 := (<= #13 0::Int) -#210 := (or #116 #120) -#211 := (not #210) -#216 := (or #211 #213) -#270 := (ite #216 #267 #269) -#264 := (= #33 0::Int) -#16 := (= #13 0::Int) -#271 := (ite #16 #264 #270) -#263 := (= #13 #33) -#17 := (= #14 0::Int) -#272 := (ite #17 #263 #271) -#758 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #757) #272) -#275 := (forall (vars (?v0 Int) (?v1 Int)) #272) -#761 := (iff #275 #758) -#759 := (iff #272 #272) -#760 := [refl]: #759 -#762 := [quant-intro #760]: #761 -#159 := (* -1::Int #153) -#232 := (ite #216 #34 #159) -#235 := (ite #16 0::Int #232) -#238 := (ite #17 #13 #235) -#241 := (= #33 #238) -#244 := (forall (vars (?v0 Int) (?v1 Int)) #241) -#276 := (iff #244 #275) -#273 := (iff #241 #272) -#274 := [rewrite]: #273 -#277 := [quant-intro #274]: #276 -#128 := (not #127) -#121 := (not #120) -#131 := (and #121 #128) -#117 := (not #116) -#124 := (and #117 #121) -#134 := (or #124 #131) -#179 := (ite #134 #34 #159) -#182 := (ite #16 0::Int #179) -#185 := (ite #17 #13 #182) -#188 := (= #33 #185) -#191 := (forall (vars (?v0 Int) (?v1 Int)) #188) -#245 := (iff #191 #244) -#242 := (iff #188 #241) -#239 := (= #185 #238) -#236 := (= #182 #235) -#233 := (= #179 #232) -#217 := (iff #134 #216) -#214 := (iff #131 #213) -#215 := [rewrite]: #214 -#204 := (iff #124 #211) -#205 := [rewrite]: #204 -#218 := [monotonicity #205 #215]: #217 -#234 := [monotonicity #218]: #233 -#237 := [monotonicity #234]: #236 -#240 := [monotonicity #237]: #239 -#243 := [monotonicity #240]: #242 -#246 := [quant-intro #243]: #245 -#202 := (~ #191 #191) -#201 := (~ #188 #188) -#198 := [refl]: #201 -#203 := [nnf-pos #198]: #202 -#27 := (- #14) -#26 := (- #13) -#35 := (mod #26 #27) -#36 := (- #35) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#37 := (ite #24 #34 #36) -#38 := (ite #16 0::Int #37) -#39 := (ite #17 #13 #38) -#40 := (= #33 #39) -#41 := (forall (vars (?v0 Int) (?v1 Int)) #40) -#194 := (iff #41 #191) -#82 := (and #20 #22) -#85 := (or #21 #82) -#164 := (ite #85 #34 #159) -#73 := (= 0::Int #13) -#167 := (ite #73 0::Int #164) -#76 := (= 0::Int #14) -#170 := (ite #76 #13 #167) -#173 := (= #33 #170) -#176 := (forall (vars (?v0 Int) (?v1 Int)) #173) -#192 := (iff #176 #191) -#189 := (iff #173 #188) -#186 := (= #170 #185) -#183 := (= #167 #182) -#180 := (= #164 #179) -#135 := (iff #85 #134) -#132 := (iff #82 #131) -#129 := (iff #22 #128) -#130 := [rewrite]: #129 -#122 := (iff #20 #121) -#123 := [rewrite]: #122 -#133 := [monotonicity #123 #130]: #132 -#125 := (iff #21 #124) -#118 := (iff #19 #117) +#78 := (iff #18 #77) +#75 := (iff #17 #74) +#76 := [monotonicity #55]: #75 +#79 := [monotonicity #76]: #78 +#84 := [trans #79 #82]: #83 +#72 := (iff #16 #69) +#66 := (and #63 #15) +#70 := (iff #66 #69) +#71 := [rewrite]: #70 +#67 := (iff #16 #66) +#64 := (iff #14 #63) +#65 := [monotonicity #55]: #64 +#68 := [monotonicity #65]: #67 +#73 := [trans #68 #71]: #72 +#87 := [monotonicity #73 #84]: #86 +#118 := [monotonicity #87 #94 #115]: #117 +#61 := (iff #13 false) +#56 := (= -1::Int 0::Int) +#59 := (iff #56 false) +#60 := [rewrite]: #59 +#57 := (iff #13 #56) +#58 := [monotonicity #55]: #57 +#62 := [trans #58 #60]: #61 +#121 := [monotonicity #62 #118]: #120 +#125 := [trans #121 #123]: #124 +#51 := (iff #10 false) +#52 := [rewrite]: #51 +#128 := [monotonicity #52 #55 #125]: #127 +#132 := [trans #128 #130]: #131 +#135 := [monotonicity #132]: #134 +#139 := [trans #135 #137]: #138 +#142 := [monotonicity #139]: #141 +#178 := [trans #142 #176]: #177 +#50 := [asserted]: #30 +[mp #50 #178]: false +unsat +c22b2f1ee044330de34ce6ed88bd5a128a3b12e5 124 0 +#2 := false +#9 := 0::Int +#8 := 3::Int +#11 := (- 3::Int) +#20 := (- #11) +#21 := (mod #20 #11) +#22 := (- #21) +#19 := (mod #11 3::Int) +#14 := (< 0::Int 3::Int) +#16 := (< #11 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int #11) +#15 := (and #13 #14) +#18 := (or #15 #17) +#23 := (ite #18 #19 #22) +#12 := (= #11 0::Int) +#24 := (ite #12 0::Int #23) +#10 := (= 3::Int 0::Int) +#25 := (ite #10 #11 #24) +#26 := (= #25 0::Int) +#27 := (not #26) +#145 := (iff #27 false) +#1 := true +#140 := (not true) +#143 := (iff #140 false) +#144 := [rewrite]: #143 +#141 := (iff #27 #140) +#138 := (iff #26 true) +#133 := (= 0::Int 0::Int) +#136 := (iff #133 true) +#137 := [rewrite]: #136 +#134 := (iff #26 #133) +#50 := -3::Int +#127 := (ite false -3::Int 0::Int) +#130 := (= #127 0::Int) +#131 := [rewrite]: #130 +#128 := (= #25 #127) +#125 := (= #24 0::Int) +#120 := (ite false 0::Int 0::Int) +#123 := (= #120 0::Int) +#124 := [rewrite]: #123 +#121 := (= #24 #120) +#118 := (= #23 0::Int) +#71 := (< -3::Int 0::Int) +#77 := (and #14 #71) +#60 := (< 0::Int -3::Int) +#66 := (and #14 #60) +#82 := (or #66 #77) +#113 := (ite #82 0::Int 0::Int) +#116 := (= #113 0::Int) +#117 := [rewrite]: #116 +#114 := (= #23 #113) +#111 := (= #22 0::Int) +#106 := (- 0::Int) +#109 := (= #106 0::Int) +#110 := [rewrite]: #109 +#107 := (= #22 #106) +#104 := (= #21 0::Int) +#99 := (mod 3::Int -3::Int) +#102 := (= #99 0::Int) +#103 := [rewrite]: #102 +#100 := (= #21 #99) +#51 := (= #11 -3::Int) +#52 := [rewrite]: #51 +#97 := (= #20 3::Int) +#92 := (- -3::Int) +#95 := (= #92 3::Int) +#96 := [rewrite]: #95 +#93 := (= #20 #92) +#94 := [monotonicity #52]: #93 +#98 := [trans #94 #96]: #97 +#101 := [monotonicity #98 #52]: #100 +#105 := [trans #101 #103]: #104 +#108 := [monotonicity #105]: #107 +#112 := [trans #108 #110]: #111 +#90 := (= #19 0::Int) +#85 := (mod -3::Int 3::Int) +#88 := (= #85 0::Int) +#89 := [rewrite]: #88 +#86 := (= #19 #85) +#87 := [monotonicity #52]: #86 +#91 := [trans #87 #89]: #90 +#83 := (iff #18 #82) +#80 := (iff #17 #77) +#74 := (and #71 #14) +#78 := (iff #74 #77) +#79 := [rewrite]: #78 +#75 := (iff #17 #74) +#72 := (iff #16 #71) +#73 := [monotonicity #52]: #72 +#76 := [monotonicity #73]: #75 +#81 := [trans #76 #79]: #80 +#69 := (iff #15 #66) +#63 := (and #60 #14) +#67 := (iff #63 #66) +#68 := [rewrite]: #67 +#64 := (iff #15 #63) +#61 := (iff #13 #60) +#62 := [monotonicity #52]: #61 +#65 := [monotonicity #62]: #64 +#70 := [trans #65 #68]: #69 +#84 := [monotonicity #70 #81]: #83 +#115 := [monotonicity #84 #91 #112]: #114 +#119 := [trans #115 #117]: #118 +#58 := (iff #12 false) +#53 := (= -3::Int 0::Int) +#56 := (iff #53 false) +#57 := [rewrite]: #56 +#54 := (iff #12 #53) +#55 := [monotonicity #52]: #54 +#59 := [trans #55 #57]: #58 +#122 := [monotonicity #59 #119]: #121 +#126 := [trans #122 #124]: #125 +#48 := (iff #10 false) +#49 := [rewrite]: #48 +#129 := [monotonicity #49 #52 #126]: #128 +#132 := [trans #129 #131]: #26 +#135 := [monotonicity #132]: #134 +#139 := [trans #135 #137]: #138 +#142 := [monotonicity #139]: #141 +#146 := [trans #142 #144]: #145 +#47 := [asserted]: #27 +[mp #47 #146]: false +unsat +1702a8956e7405182723d9b7e49a559e524180e5 161 0 +#2 := false +#28 := 1::Int +#8 := 3::Int +#22 := (- 3::Int) +#11 := 5::Int +#12 := (- 5::Int) +#21 := (- #12) +#23 := (mod #21 #22) +#24 := (- #23) +#20 := (mod #12 3::Int) +#9 := 0::Int +#15 := (< 0::Int 3::Int) +#17 := (< #12 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int #12) +#16 := (and #14 #15) +#19 := (or #16 #18) +#25 := (ite #19 #20 #24) +#13 := (= #12 0::Int) +#26 := (ite #13 0::Int #25) +#10 := (= 3::Int 0::Int) +#27 := (ite #10 #12 #26) +#29 := (= #27 1::Int) +#30 := (not #29) +#182 := (iff #30 false) +#53 := -5::Int +#74 := (< -5::Int 0::Int) +#80 := (and #15 #74) +#63 := (< 0::Int -5::Int) +#69 := (and #15 #63) +#85 := (or #69 #80) +#145 := (not #85) +#180 := (iff #145 false) +#1 := true +#175 := (not true) +#178 := (iff #175 false) +#179 := [rewrite]: #178 +#176 := (iff #145 #175) +#173 := (iff #85 true) +#168 := (or false true) +#171 := (iff #168 true) +#172 := [rewrite]: #171 +#169 := (iff #85 #168) +#166 := (iff #80 true) +#161 := (and true true) +#164 := (iff #161 true) +#165 := [rewrite]: #164 +#162 := (iff #80 #161) +#159 := (iff #74 true) +#160 := [rewrite]: #159 +#148 := (iff #15 true) +#149 := [rewrite]: #148 +#163 := [monotonicity #149 #160]: #162 +#167 := [trans #163 #165]: #166 +#157 := (iff #69 false) +#152 := (and true false) +#155 := (iff #152 false) +#156 := [rewrite]: #155 +#153 := (iff #69 #152) +#150 := (iff #63 false) +#151 := [rewrite]: #150 +#154 := [monotonicity #149 #151]: #153 +#158 := [trans #154 #156]: #157 +#170 := [monotonicity #158 #167]: #169 +#174 := [trans #170 #172]: #173 +#177 := [monotonicity #174]: #176 +#181 := [trans #177 #179]: #180 +#146 := (iff #30 #145) +#143 := (iff #29 #85) +#116 := -2::Int +#121 := (ite #85 1::Int -2::Int) +#138 := (= #121 1::Int) +#141 := (iff #138 #85) +#142 := [rewrite]: #141 +#139 := (iff #29 #138) +#136 := (= #27 #121) +#131 := (ite false -5::Int #121) +#134 := (= #131 #121) +#135 := [rewrite]: #134 +#132 := (= #27 #131) +#129 := (= #26 #121) +#124 := (ite false 0::Int #121) +#127 := (= #124 #121) +#128 := [rewrite]: #127 +#125 := (= #26 #124) +#122 := (= #25 #121) +#119 := (= #24 -2::Int) +#108 := 2::Int +#113 := (- 2::Int) +#117 := (= #113 -2::Int) +#118 := [rewrite]: #117 +#114 := (= #24 #113) +#111 := (= #23 2::Int) +#102 := -3::Int +#105 := (mod 5::Int -3::Int) +#109 := (= #105 2::Int) +#110 := [rewrite]: #109 +#106 := (= #23 #105) +#103 := (= #22 -3::Int) +#104 := [rewrite]: #103 +#100 := (= #21 5::Int) +#95 := (- -5::Int) +#98 := (= #95 5::Int) +#99 := [rewrite]: #98 +#96 := (= #21 #95) +#54 := (= #12 -5::Int) +#55 := [rewrite]: #54 +#97 := [monotonicity #55]: #96 +#101 := [trans #97 #99]: #100 +#107 := [monotonicity #101 #104]: #106 +#112 := [trans #107 #110]: #111 +#115 := [monotonicity #112]: #114 +#120 := [trans #115 #118]: #119 +#93 := (= #20 1::Int) +#88 := (mod -5::Int 3::Int) +#91 := (= #88 1::Int) +#92 := [rewrite]: #91 +#89 := (= #20 #88) +#90 := [monotonicity #55]: #89 +#94 := [trans #90 #92]: #93 +#86 := (iff #19 #85) +#83 := (iff #18 #80) +#77 := (and #74 #15) +#81 := (iff #77 #80) +#82 := [rewrite]: #81 +#78 := (iff #18 #77) +#75 := (iff #17 #74) +#76 := [monotonicity #55]: #75 +#79 := [monotonicity #76]: #78 +#84 := [trans #79 #82]: #83 +#72 := (iff #16 #69) +#66 := (and #63 #15) +#70 := (iff #66 #69) +#71 := [rewrite]: #70 +#67 := (iff #16 #66) +#64 := (iff #14 #63) +#65 := [monotonicity #55]: #64 +#68 := [monotonicity #65]: #67 +#73 := [trans #68 #71]: #72 +#87 := [monotonicity #73 #84]: #86 +#123 := [monotonicity #87 #94 #120]: #122 +#61 := (iff #13 false) +#56 := (= -5::Int 0::Int) +#59 := (iff #56 false) +#60 := [rewrite]: #59 +#57 := (iff #13 #56) +#58 := [monotonicity #55]: #57 +#62 := [trans #58 #60]: #61 +#126 := [monotonicity #62 #123]: #125 +#130 := [trans #126 #128]: #129 +#51 := (iff #10 false) +#52 := [rewrite]: #51 +#133 := [monotonicity #52 #55 #130]: #132 +#137 := [trans #133 #135]: #136 +#140 := [monotonicity #137]: #139 +#144 := [trans #140 #142]: #143 +#147 := [monotonicity #144]: #146 +#183 := [trans #147 #181]: #182 +#50 := [asserted]: #30 +[mp #50 #183]: false +unsat +1974063c697470ee08048aa93c91e77e8294ad37 165 0 +#2 := false +#12 := 1::Int +#13 := (- 1::Int) +#8 := 3::Int +#9 := (- 3::Int) +#23 := (- #9) +#22 := (- #13) +#24 := (mod #22 #23) +#25 := (- #24) +#21 := (mod #13 #9) +#10 := 0::Int +#16 := (< 0::Int #9) +#18 := (< #13 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #13) +#17 := (and #15 #16) +#20 := (or #17 #19) +#26 := (ite #20 #21 #25) +#14 := (= #13 0::Int) +#27 := (ite #14 0::Int #26) +#11 := (= #9 0::Int) +#28 := (ite #11 #13 #27) +#29 := (= #28 #13) +#30 := (not #29) +#186 := (iff #30 false) +#61 := -1::Int +#80 := (< -1::Int 0::Int) +#51 := -3::Int +#74 := (< 0::Int -3::Int) +#86 := (and #74 #80) +#71 := (< 0::Int -1::Int) +#77 := (and #71 #74) +#91 := (or #77 #86) +#184 := (iff #91 false) +#179 := (or false false) +#182 := (iff #179 false) +#183 := [rewrite]: #182 +#180 := (iff #91 #179) +#177 := (iff #86 false) +#1 := true +#172 := (and false true) +#175 := (iff #172 false) +#176 := [rewrite]: #175 +#173 := (iff #86 #172) +#170 := (iff #80 true) +#171 := [rewrite]: #170 +#161 := (iff #74 false) +#162 := [rewrite]: #161 +#174 := [monotonicity #162 #171]: #173 +#178 := [trans #174 #176]: #177 +#168 := (iff #77 false) +#163 := (and false false) +#166 := (iff #163 false) +#167 := [rewrite]: #166 +#164 := (iff #77 #163) +#159 := (iff #71 false) +#160 := [rewrite]: #159 +#165 := [monotonicity #160 #162]: #164 +#169 := [trans #165 #167]: #168 +#181 := [monotonicity #169 #178]: #180 +#185 := [trans #181 #183]: #184 +#157 := (iff #30 #91) +#147 := (not #91) +#152 := (not #147) +#155 := (iff #152 #91) +#156 := [rewrite]: #155 +#153 := (iff #30 #152) +#150 := (iff #29 #147) +#97 := 2::Int +#127 := (ite #91 2::Int -1::Int) +#144 := (= #127 -1::Int) +#148 := (iff #144 #147) +#149 := [rewrite]: #148 +#145 := (iff #29 #144) +#62 := (= #13 -1::Int) +#63 := [rewrite]: #62 +#142 := (= #28 #127) +#137 := (ite false -1::Int #127) +#140 := (= #137 #127) +#141 := [rewrite]: #140 +#138 := (= #28 #137) +#135 := (= #27 #127) +#130 := (ite false 0::Int #127) +#133 := (= #130 #127) +#134 := [rewrite]: #133 +#131 := (= #27 #130) +#128 := (= #26 #127) +#125 := (= #25 -1::Int) +#123 := (= #25 #13) +#121 := (= #24 1::Int) +#116 := (mod 1::Int 3::Int) +#119 := (= #116 1::Int) +#120 := [rewrite]: #119 +#117 := (= #24 #116) +#114 := (= #23 3::Int) +#109 := (- -3::Int) +#112 := (= #109 3::Int) +#113 := [rewrite]: #112 +#110 := (= #23 #109) +#52 := (= #9 -3::Int) +#53 := [rewrite]: #52 +#111 := [monotonicity #53]: #110 +#115 := [trans #111 #113]: #114 +#107 := (= #22 1::Int) +#102 := (- -1::Int) +#105 := (= #102 1::Int) +#106 := [rewrite]: #105 +#103 := (= #22 #102) +#104 := [monotonicity #63]: #103 +#108 := [trans #104 #106]: #107 +#118 := [monotonicity #108 #115]: #117 +#122 := [trans #118 #120]: #121 +#124 := [monotonicity #122]: #123 +#126 := [trans #124 #63]: #125 +#100 := (= #21 2::Int) +#94 := (mod -1::Int -3::Int) +#98 := (= #94 2::Int) +#99 := [rewrite]: #98 +#95 := (= #21 #94) +#96 := [monotonicity #63 #53]: #95 +#101 := [trans #96 #99]: #100 +#92 := (iff #20 #91) +#89 := (iff #19 #86) +#83 := (and #80 #74) +#87 := (iff #83 #86) +#88 := [rewrite]: #87 +#84 := (iff #19 #83) +#75 := (iff #16 #74) +#76 := [monotonicity #53]: #75 +#81 := (iff #18 #80) +#82 := [monotonicity #63]: #81 +#85 := [monotonicity #82 #76]: #84 +#90 := [trans #85 #88]: #89 +#78 := (iff #17 #77) +#72 := (iff #15 #71) +#73 := [monotonicity #63]: #72 +#79 := [monotonicity #73 #76]: #78 +#93 := [monotonicity #79 #90]: #92 +#129 := [monotonicity #93 #101 #126]: #128 +#69 := (iff #14 false) +#64 := (= -1::Int 0::Int) +#67 := (iff #64 false) +#68 := [rewrite]: #67 +#65 := (iff #14 #64) +#66 := [monotonicity #63]: #65 +#70 := [trans #66 #68]: #69 +#132 := [monotonicity #70 #129]: #131 +#136 := [trans #132 #134]: #135 +#59 := (iff #11 false) +#54 := (= -3::Int 0::Int) +#57 := (iff #54 false) +#58 := [rewrite]: #57 +#55 := (iff #11 #54) +#56 := [monotonicity #53]: #55 +#60 := [trans #56 #58]: #59 +#139 := [monotonicity #60 #63 #136]: #138 +#143 := [trans #139 #141]: #142 +#146 := [monotonicity #143 #63]: #145 +#151 := [trans #146 #149]: #150 +#154 := [monotonicity #151]: #153 +#158 := [trans #154 #156]: #157 +#187 := [trans #158 #185]: #186 +#50 := [asserted]: #30 +[mp #50 #187]: false +unsat +230992a84e85c41a4507e3a0c4b596203478f52c 119 0 +#2 := false +#10 := 0::Int +#8 := 3::Int +#9 := (- 3::Int) +#18 := (- #9) +#19 := (mod #18 #18) +#20 := (- #19) +#17 := (mod #9 #9) +#12 := (< 0::Int #9) +#14 := (< #9 0::Int) +#15 := (and #14 #12) +#13 := (and #12 #12) +#16 := (or #13 #15) +#21 := (ite #16 #17 #20) +#11 := (= #9 0::Int) +#22 := (ite #11 0::Int #21) +#23 := (ite #11 #9 #22) +#24 := (= #23 0::Int) +#25 := (not #24) +#140 := (iff #25 false) +#1 := true +#135 := (not true) +#138 := (iff #135 false) +#139 := [rewrite]: #138 +#136 := (iff #25 #135) +#133 := (iff #24 true) +#128 := (= 0::Int 0::Int) +#131 := (iff #128 true) +#132 := [rewrite]: #131 +#129 := (iff #24 #128) +#46 := -3::Int +#122 := (ite false -3::Int 0::Int) +#125 := (= #122 0::Int) +#126 := [rewrite]: #125 +#123 := (= #23 #122) +#120 := (= #22 0::Int) +#115 := (ite false 0::Int 0::Int) +#118 := (= #115 0::Int) #119 := [rewrite]: #118 -#126 := [monotonicity #119 #123]: #125 -#136 := [monotonicity #126 #133]: #135 -#181 := [monotonicity #136]: #180 -#110 := (iff #73 #16) -#111 := [rewrite]: #110 -#184 := [monotonicity #111 #181]: #183 -#112 := (iff #76 #17) -#113 := [rewrite]: #112 -#187 := [monotonicity #113 #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [quant-intro #190]: #192 -#177 := (iff #41 #176) -#174 := (iff #40 #173) -#171 := (= #39 #170) -#168 := (= #38 #167) -#165 := (= #37 #164) -#162 := (= #36 #159) -#156 := (- #153) -#160 := (= #156 #159) -#161 := [rewrite]: #160 -#157 := (= #36 #156) -#154 := (= #35 #153) -#93 := (= #27 #92) -#94 := [rewrite]: #93 -#90 := (= #26 #89) +#116 := (= #22 #115) +#113 := (= #21 0::Int) +#66 := (< -3::Int 0::Int) +#56 := (< 0::Int -3::Int) +#72 := (and #56 #66) +#77 := (or #56 #72) +#108 := (ite #77 0::Int 0::Int) +#111 := (= #108 0::Int) +#112 := [rewrite]: #111 +#109 := (= #21 #108) +#106 := (= #20 0::Int) +#101 := (- 0::Int) +#104 := (= #101 0::Int) +#105 := [rewrite]: #104 +#102 := (= #20 #101) +#99 := (= #19 0::Int) +#94 := (mod 3::Int 3::Int) +#97 := (= #94 0::Int) +#98 := [rewrite]: #97 +#95 := (= #19 #94) +#92 := (= #18 3::Int) +#87 := (- -3::Int) +#90 := (= #87 3::Int) #91 := [rewrite]: #90 -#155 := [monotonicity #91 #94]: #154 -#158 := [monotonicity #155]: #157 -#163 := [trans #158 #161]: #162 -#86 := (iff #24 #85) -#83 := (iff #23 #82) +#88 := (= #18 #87) +#47 := (= #9 -3::Int) +#48 := [rewrite]: #47 +#89 := [monotonicity #48]: #88 +#93 := [trans #89 #91]: #92 +#96 := [monotonicity #93 #93]: #95 +#100 := [trans #96 #98]: #99 +#103 := [monotonicity #100]: #102 +#107 := [trans #103 #105]: #106 +#85 := (= #17 0::Int) +#80 := (mod -3::Int -3::Int) +#83 := (= #80 0::Int) #84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#166 := [monotonicity #87 #163]: #165 -#74 := (iff #16 #73) -#75 := [rewrite]: #74 -#169 := [monotonicity #75 #166]: #168 -#77 := (iff #17 #76) -#78 := [rewrite]: #77 -#172 := [monotonicity #78 #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [quant-intro #175]: #177 -#195 := [trans #178 #193]: #194 -#152 := [asserted]: #41 -#196 := [mp #152 #195]: #191 -#199 := [mp~ #196 #203]: #191 -#247 := [mp #199 #246]: #244 -#278 := [mp #247 #277]: #275 -#763 := [mp #278 #762]: #758 -#9 := 3::Int -#10 := (f3 0::Int 3::Int) -#11 := (= #10 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#679 := (not #758) -#680 := (or #679 #11) -#336 := (* -1::Int 3::Int) -#421 := (* -1::Int 0::Int) -#422 := (mod #421 #336) -#423 := (+ #10 #422) -#414 := (= #423 0::Int) -#425 := (mod 0::Int 3::Int) -#426 := (* -1::Int #425) -#354 := (+ #10 #426) -#427 := (= #354 0::Int) -#424 := (>= 0::Int 0::Int) -#428 := (<= 3::Int 0::Int) -#407 := (or #428 #424) -#742 := (not #407) -#744 := (<= 0::Int 0::Int) -#401 := (or #744 #428) -#531 := (not #401) -#738 := (or #531 #742) -#412 := (ite #738 #427 #414) -#413 := (= 0::Int 0::Int) -#745 := (ite #413 #11 #412) -#62 := (= 0::Int #10) -#746 := (= 3::Int 0::Int) -#747 := (ite #746 #62 #745) -#683 := (or #679 #747) -#583 := (iff #683 #680) -#586 := (iff #680 #680) -#579 := [rewrite]: #586 -#682 := (iff #747 #11) -#700 := (ite false #11 #11) -#530 := (iff #700 #11) -#532 := [rewrite]: #530 -#575 := (iff #747 #700) -#573 := (iff #745 #11) -#1 := true -#687 := (ite true #11 #11) -#688 := (iff #687 #11) -#691 := [rewrite]: #688 -#689 := (iff #745 #687) -#533 := (iff #412 #11) -#694 := (iff #412 #700) -#693 := (iff #414 #11) -#698 := (= #423 #10) -#714 := (+ #10 0::Int) -#715 := (= #714 #10) -#712 := [rewrite]: #715 -#696 := (= #423 #714) -#553 := (= #422 0::Int) -#702 := -3::Int -#709 := (mod 0::Int -3::Int) -#551 := (= #709 0::Int) -#552 := [rewrite]: #551 -#704 := (= #422 #709) -#703 := (= #336 -3::Int) -#708 := [rewrite]: #703 -#433 := (= #421 0::Int) -#434 := [rewrite]: #433 -#710 := [monotonicity #434 #708]: #704 -#695 := [trans #710 #552]: #553 -#697 := [monotonicity #695]: #696 -#692 := [trans #697 #712]: #698 -#699 := [monotonicity #692]: #693 -#706 := (iff #427 #11) -#716 := (= #354 #10) -#429 := (= #354 #714) -#435 := (= #426 0::Int) -#722 := (= #426 #421) -#721 := (= #425 0::Int) -#718 := [rewrite]: #721 -#432 := [monotonicity #718]: #722 -#713 := [trans #432 #434]: #435 -#711 := [monotonicity #713]: #429 -#705 := [trans #711 #712]: #716 -#707 := [monotonicity #705]: #706 -#443 := (iff #738 false) -#449 := (or false false) -#720 := (iff #449 false) -#442 := [rewrite]: #720 -#342 := (iff #738 #449) -#447 := (iff #742 false) -#727 := (not true) -#730 := (iff #727 false) -#731 := [rewrite]: #730 -#724 := (iff #742 #727) -#737 := (iff #407 true) -#735 := (or false true) -#736 := (iff #735 true) -#734 := [rewrite]: #736 -#375 := (iff #407 #735) -#370 := (iff #424 true) -#733 := [rewrite]: #370 -#740 := (iff #428 false) -#400 := [rewrite]: #740 -#376 := [monotonicity #400 #733]: #375 -#723 := [trans #376 #734]: #737 -#446 := [monotonicity #723]: #724 -#448 := [trans #446 #731]: #447 -#726 := (iff #531 false) -#728 := (iff #531 #727) -#390 := (iff #401 true) -#741 := (or true false) -#388 := (iff #741 true) -#389 := [rewrite]: #388 -#384 := (iff #401 #741) -#399 := (iff #744 true) -#404 := [rewrite]: #399 -#725 := [monotonicity #404 #400]: #384 -#391 := [trans #725 #389]: #390 -#729 := [monotonicity #391]: #728 -#732 := [trans #729 #731]: #726 -#719 := [monotonicity #732 #448]: #342 -#717 := [trans #719 #442]: #443 -#701 := [monotonicity #717 #707 #699]: #694 -#686 := [trans #701 #532]: #533 -#749 := (iff #413 true) -#739 := [rewrite]: #749 -#690 := [monotonicity #739 #686]: #689 -#574 := [trans #690 #691]: #573 -#68 := (iff #62 #11) -#69 := [rewrite]: #68 -#748 := (iff #746 false) -#743 := [rewrite]: #748 -#534 := [monotonicity #743 #69 #574]: #575 -#584 := [trans #534 #532]: #682 -#585 := [monotonicity #584]: #583 -#587 := [trans #585 #579]: #583 -#568 := [quant-inst #8 #9]: #683 -#588 := [mp #568 #587]: #680 -[unit-resolution #588 #61 #763]: false -unsat -8c07fa0d73a756ba84d0fe9fed90f7b86f2beac8 323 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#773 := (pattern #34) -#8 := 0::Int -#104 := -1::Int -#108 := (* -1::Int #15) -#105 := (* -1::Int #14) -#169 := (mod #105 #108) -#284 := (+ #34 #169) -#285 := (= #284 0::Int) -#35 := (mod #14 #15) -#281 := (* -1::Int #35) -#282 := (+ #34 #281) -#283 := (= #282 0::Int) -#143 := (>= #14 0::Int) -#136 := (<= #15 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #14 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #34 0::Int) -#17 := (= #14 0::Int) -#287 := (ite #17 #280 #286) -#279 := (= #14 #34) -#18 := (= #15 0::Int) -#288 := (ite #18 #279 #287) -#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#777 := (iff #291 #774) -#775 := (iff #288 #288) -#776 := [refl]: #775 -#778 := [quant-intro #776]: #777 -#175 := (* -1::Int #169) -#248 := (ite #232 #35 #175) -#251 := (ite #17 0::Int #248) -#254 := (ite #18 #14 #251) -#257 := (= #34 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #35 #175) -#198 := (ite #17 0::Int #195) -#201 := (ite #18 #14 #198) -#204 := (= #34 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#210 := (iff #42 #207) -#98 := (and #21 #23) -#101 := (or #22 #98) -#180 := (ite #101 #35 #175) -#89 := (= 0::Int #14) -#183 := (ite #89 0::Int #180) -#92 := (= 0::Int #15) -#186 := (ite #92 #14 #183) -#189 := (= #34 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #101 #150) -#148 := (iff #98 #147) -#145 := (iff #23 #144) -#146 := [rewrite]: #145 -#138 := (iff #21 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #22 #140) -#134 := (iff #20 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #89 #17) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #92 #18) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #42 #192) -#190 := (iff #41 #189) -#187 := (= #40 #186) -#184 := (= #39 #183) -#181 := (= #38 #180) -#178 := (= #37 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #37 #172) -#170 := (= #36 #169) -#109 := (= #28 #108) -#110 := [rewrite]: #109 -#106 := (= #27 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#182 := [monotonicity #103 #179]: #181 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#185 := [monotonicity #91 #182]: #184 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#188 := [monotonicity #94 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #42 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#779 := [mp #294 #778]: #774 -#63 := -3::Int -#66 := (f3 0::Int -3::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 0::Int #10) -#12 := (= #11 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) +#81 := (= #17 #80) +#82 := [monotonicity #48 #48]: #81 +#86 := [trans #82 #84]: #85 +#78 := (iff #16 #77) +#75 := (iff #15 #72) +#69 := (and #66 #56) #73 := (iff #69 #72) #74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #11 #66) -#64 := (= #10 -3::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 +#70 := (iff #15 #69) +#57 := (iff #12 #56) +#58 := [monotonicity #48]: #57 +#67 := (iff #14 #66) +#68 := [monotonicity #48]: #67 +#71 := [monotonicity #68 #58]: #70 #76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#591 := (not #774) -#550 := (or #591 #69) -#352 := (* -1::Int -3::Int) -#437 := (* -1::Int 0::Int) -#438 := (mod #437 #352) -#439 := (+ #66 #438) -#430 := (= #439 0::Int) -#441 := (mod 0::Int -3::Int) -#442 := (* -1::Int #441) -#370 := (+ #66 #442) -#443 := (= #370 0::Int) -#440 := (>= 0::Int 0::Int) -#444 := (<= -3::Int 0::Int) -#423 := (or #444 #440) -#758 := (not #423) -#760 := (<= 0::Int 0::Int) -#417 := (or #760 #444) -#547 := (not #417) -#754 := (or #547 #758) -#428 := (ite #754 #443 #430) -#429 := (= 0::Int 0::Int) -#761 := (ite #429 #69 #428) -#762 := (= -3::Int 0::Int) -#763 := (ite #762 #72 #761) -#698 := (or #591 #763) -#695 := (iff #698 #550) -#699 := (iff #550 #550) -#584 := [rewrite]: #699 -#589 := (iff #763 #69) -#714 := (ite false #69 #69) -#715 := (iff #714 #69) -#716 := [rewrite]: #715 -#704 := (iff #763 #714) -#705 := (iff #761 #69) -#1 := true -#546 := (ite true #69 #69) -#702 := (iff #546 #69) -#703 := [rewrite]: #702 -#548 := (iff #761 #546) -#710 := (iff #428 #69) -#708 := (iff #428 #714) -#712 := (iff #430 #69) -#569 := (= #439 #66) -#450 := (+ #66 0::Int) -#730 := (= #450 #66) -#445 := [rewrite]: #730 -#567 := (= #439 #450) -#720 := (= #438 0::Int) -#723 := (mod 0::Int 3::Int) -#724 := (= #723 0::Int) -#725 := [rewrite]: #724 -#718 := (= #438 #723) -#721 := (= #352 3::Int) -#722 := [rewrite]: #721 -#734 := (= #437 0::Int) -#738 := [rewrite]: #734 -#719 := [monotonicity #738 #722]: #718 -#726 := [trans #719 #725]: #720 -#568 := [monotonicity #726]: #567 -#711 := [trans #568 #445]: #569 -#713 := [monotonicity #711]: #712 -#728 := (iff #443 #69) -#727 := (= #370 #66) -#451 := (= #370 #450) -#448 := (= #442 0::Int) -#733 := (= #442 #437) -#458 := (= #441 0::Int) -#459 := [rewrite]: #458 -#737 := [monotonicity #459]: #733 -#449 := [trans #737 #738]: #448 -#729 := [monotonicity #449]: #451 -#731 := [trans #729 #445]: #727 -#732 := [monotonicity #731]: #728 -#735 := (iff #754 false) -#462 := (or false false) -#465 := (iff #462 false) -#358 := [rewrite]: #465 -#463 := (iff #754 #462) -#739 := (iff #758 false) -#743 := (not true) -#746 := (iff #743 false) -#747 := [rewrite]: #746 -#750 := (iff #758 #743) -#392 := (iff #423 true) -#757 := (or true true) -#404 := (iff #757 true) -#405 := [rewrite]: #404 -#751 := (iff #423 #757) -#386 := (iff #440 true) -#749 := [rewrite]: #386 -#756 := (iff #444 true) -#416 := [rewrite]: #756 -#391 := [monotonicity #416 #749]: #751 -#752 := [trans #391 #405]: #392 -#753 := [monotonicity #752]: #750 -#740 := [trans #753 #747]: #739 -#742 := (iff #547 false) -#744 := (iff #547 #743) -#406 := (iff #417 true) -#400 := (iff #417 #757) -#415 := (iff #760 true) -#420 := [rewrite]: #415 -#741 := [monotonicity #420 #416]: #400 -#407 := [trans #741 #405]: #406 -#745 := [monotonicity #407]: #744 -#748 := [trans #745 #747]: #742 -#464 := [monotonicity #748 #740]: #463 -#736 := [trans #464 #358]: #735 -#709 := [monotonicity #736 #732 #713]: #708 -#717 := [trans #709 #716]: #710 -#765 := (iff #429 true) -#755 := [rewrite]: #765 -#549 := [monotonicity #755 #717]: #548 -#706 := [trans #549 #703]: #705 -#764 := (iff #762 false) -#759 := [rewrite]: #764 -#707 := [monotonicity #759 #81 #706]: #704 -#590 := [trans #707 #716]: #589 -#696 := [monotonicity #590]: #695 -#599 := [trans #696 #584]: #695 -#600 := [quant-inst #8 #63]: #698 -#601 := [mp #600 #599]: #550 -[unit-resolution #601 #87 #779]: false -unsat -4b125b55545fc1a8ed3851433e86bbecb0071f7b 320 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#34 := (f3 #13 #14) -#742 := (pattern #34) -#16 := 0::Int -#80 := -1::Int -#84 := (* -1::Int #14) -#81 := (* -1::Int #13) -#139 := (mod #81 #84) -#254 := (+ #34 #139) -#255 := (= #254 0::Int) -#35 := (mod #13 #14) -#251 := (* -1::Int #35) -#252 := (+ #34 #251) -#253 := (= #252 0::Int) -#113 := (>= #13 0::Int) -#106 := (<= #14 0::Int) -#198 := (or #106 #113) -#199 := (not #198) -#102 := (<= #13 0::Int) -#196 := (or #102 #106) -#197 := (not #196) -#202 := (or #197 #199) -#256 := (ite #202 #253 #255) -#250 := (= #34 0::Int) -#17 := (= #13 0::Int) -#257 := (ite #17 #250 #256) -#249 := (= #13 #34) -#18 := (= #14 0::Int) -#258 := (ite #18 #249 #257) -#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #258) -#261 := (forall (vars (?v0 Int) (?v1 Int)) #258) -#746 := (iff #261 #743) -#744 := (iff #258 #258) -#745 := [refl]: #744 -#747 := [quant-intro #745]: #746 -#145 := (* -1::Int #139) -#218 := (ite #202 #35 #145) -#221 := (ite #17 0::Int #218) -#224 := (ite #18 #13 #221) -#227 := (= #34 #224) -#230 := (forall (vars (?v0 Int) (?v1 Int)) #227) -#262 := (iff #230 #261) -#259 := (iff #227 #258) -#260 := [rewrite]: #259 -#263 := [quant-intro #260]: #262 -#114 := (not #113) -#107 := (not #106) -#117 := (and #107 #114) -#103 := (not #102) -#110 := (and #103 #107) -#120 := (or #110 #117) -#165 := (ite #120 #35 #145) -#168 := (ite #17 0::Int #165) -#171 := (ite #18 #13 #168) -#174 := (= #34 #171) -#177 := (forall (vars (?v0 Int) (?v1 Int)) #174) -#231 := (iff #177 #230) -#228 := (iff #174 #227) -#225 := (= #171 #224) -#222 := (= #168 #221) -#219 := (= #165 #218) -#203 := (iff #120 #202) -#200 := (iff #117 #199) -#201 := [rewrite]: #200 -#190 := (iff #110 #197) -#191 := [rewrite]: #190 -#204 := [monotonicity #191 #201]: #203 -#220 := [monotonicity #204]: #219 -#223 := [monotonicity #220]: #222 -#226 := [monotonicity #223]: #225 -#229 := [monotonicity #226]: #228 -#232 := [quant-intro #229]: #231 -#188 := (~ #177 #177) -#187 := (~ #174 #174) -#184 := [refl]: #187 -#189 := [nnf-pos #184]: #188 -#28 := (- #14) -#27 := (- #13) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #13 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#180 := (iff #42 #177) -#74 := (and #21 #23) -#77 := (or #22 #74) -#150 := (ite #77 #35 #145) -#153 := (ite #17 0::Int #150) -#156 := (ite #18 #13 #153) -#159 := (= #34 #156) -#162 := (forall (vars (?v0 Int) (?v1 Int)) #159) -#178 := (iff #162 #177) -#175 := (iff #159 #174) -#172 := (= #156 #171) -#169 := (= #153 #168) -#166 := (= #150 #165) -#121 := (iff #77 #120) -#118 := (iff #74 #117) -#115 := (iff #23 #114) -#116 := [rewrite]: #115 -#108 := (iff #21 #107) -#109 := [rewrite]: #108 -#119 := [monotonicity #109 #116]: #118 -#111 := (iff #22 #110) -#104 := (iff #20 #103) -#105 := [rewrite]: #104 -#112 := [monotonicity #105 #109]: #111 -#122 := [monotonicity #112 #119]: #121 -#167 := [monotonicity #122]: #166 -#170 := [monotonicity #167]: #169 -#173 := [monotonicity #170]: #172 -#176 := [monotonicity #173]: #175 -#179 := [quant-intro #176]: #178 -#163 := (iff #42 #162) -#160 := (iff #41 #159) -#157 := (= #40 #156) -#154 := (= #39 #153) -#151 := (= #38 #150) -#148 := (= #37 #145) -#142 := (- #139) -#146 := (= #142 #145) -#147 := [rewrite]: #146 -#143 := (= #37 #142) -#140 := (= #36 #139) -#85 := (= #28 #84) -#86 := [rewrite]: #85 -#82 := (= #27 #81) -#83 := [rewrite]: #82 -#141 := [monotonicity #83 #86]: #140 -#144 := [monotonicity #141]: #143 -#149 := [trans #144 #147]: #148 -#78 := (iff #25 #77) -#75 := (iff #24 #74) -#76 := [rewrite]: #75 -#79 := [monotonicity #76]: #78 -#152 := [monotonicity #79 #149]: #151 -#155 := [monotonicity #152]: #154 -#158 := [monotonicity #155]: #157 -#161 := [monotonicity #158]: #160 -#164 := [quant-intro #161]: #163 -#181 := [trans #164 #179]: #180 -#138 := [asserted]: #42 -#182 := [mp #138 #181]: #177 -#185 := [mp~ #182 #189]: #177 -#233 := [mp #185 #232]: #230 -#264 := [mp #233 #263]: #261 -#748 := [mp #264 #747]: #743 -#8 := 1::Int -#9 := 3::Int -#10 := (f3 1::Int 3::Int) -#11 := (= #10 1::Int) -#12 := (not #11) -#62 := [asserted]: #12 -#652 := (not #743) -#653 := (or #652 #11) -#322 := (* -1::Int 3::Int) -#406 := (* -1::Int 1::Int) -#407 := (mod #406 #322) -#408 := (+ #10 #407) -#399 := (= #408 0::Int) -#410 := (mod 1::Int 3::Int) -#411 := (* -1::Int #410) -#412 := (+ #10 #411) -#409 := (= #412 0::Int) -#413 := (>= 1::Int 0::Int) -#392 := (<= 3::Int 0::Int) -#727 := (or #392 #413) -#729 := (not #727) -#386 := (<= 1::Int 0::Int) -#516 := (or #386 #392) -#723 := (not #516) -#397 := (or #723 #729) -#398 := (ite #397 #409 #399) -#730 := (= #10 0::Int) -#731 := (= 1::Int 0::Int) -#732 := (ite #731 #730 #398) -#63 := (= 1::Int #10) -#733 := (= 3::Int 0::Int) -#728 := (ite #733 #63 #732) -#654 := (or #652 #728) -#649 := (iff #654 #653) -#640 := (iff #653 #653) -#641 := [rewrite]: #640 -#658 := (iff #728 #11) -#648 := (ite false #11 #11) -#661 := (iff #648 #11) -#662 := [rewrite]: #661 -#650 := (iff #728 #648) -#659 := (iff #732 #11) -#576 := (ite false #730 #11) -#670 := (iff #576 #11) -#657 := [rewrite]: #670 -#669 := (iff #732 #576) -#574 := (iff #398 #11) -#569 := -2::Int -#664 := (= #10 -2::Int) -#1 := true -#570 := (ite true #11 #664) -#572 := (iff #570 #11) -#573 := [rewrite]: #572 -#571 := (iff #398 #570) -#553 := (iff #399 #664) -#679 := 2::Int -#675 := (+ 2::Int #10) -#560 := (= #675 0::Int) -#665 := (iff #560 #664) -#668 := [rewrite]: #665 -#519 := (iff #399 #560) -#558 := (= #408 #675) -#671 := (+ #10 2::Int) -#673 := (= #671 #675) -#676 := [rewrite]: #673 -#672 := (= #408 #671) -#517 := (= #407 2::Int) -#682 := -3::Int -#678 := (mod -1::Int -3::Int) -#686 := (= #678 2::Int) -#515 := [rewrite]: #686 -#684 := (= #407 #678) -#683 := (= #322 -3::Int) -#677 := [rewrite]: #683 -#414 := (= #406 -1::Int) -#696 := [rewrite]: #414 -#685 := [monotonicity #696 #677]: #684 -#518 := [trans #685 #515]: #517 -#674 := [monotonicity #518]: #672 -#559 := [trans #674 #676]: #558 -#667 := [monotonicity #559]: #519 -#568 := [trans #667 #668]: #553 -#680 := (iff #409 #11) -#692 := (+ -1::Int #10) -#689 := (= #692 0::Int) -#537 := (iff #689 #11) -#538 := [rewrite]: #537 -#695 := (iff #409 #689) -#693 := (= #412 #692) -#701 := (+ #10 -1::Int) -#687 := (= #701 #692) -#688 := [rewrite]: #687 -#690 := (= #412 #701) -#700 := (= #411 -1::Int) -#698 := (= #411 #406) -#419 := (= #410 1::Int) -#420 := [rewrite]: #419 -#699 := [monotonicity #420]: #698 -#697 := [trans #699 #696]: #700 -#691 := [monotonicity #697]: #690 -#694 := [trans #691 #688]: #693 -#536 := [monotonicity #694]: #695 -#681 := [trans #536 #538]: #680 -#417 := (iff #397 true) -#428 := (or true false) -#703 := (iff #428 true) -#707 := [rewrite]: #703 -#702 := (iff #397 #428) -#705 := (iff #729 false) -#432 := (not true) -#328 := (iff #432 false) -#704 := [rewrite]: #328 -#433 := (iff #729 #432) -#709 := (iff #727 true) -#361 := (or false true) -#722 := (iff #361 true) -#708 := [rewrite]: #722 -#721 := (iff #727 #361) -#720 := (iff #413 true) -#360 := [rewrite]: #720 -#726 := (iff #392 false) -#369 := [rewrite]: #726 -#719 := [monotonicity #369 #360]: #721 -#431 := [trans #719 #708]: #709 -#434 := [monotonicity #431]: #433 -#427 := [trans #434 #704]: #705 -#355 := (iff #723 true) -#714 := (not false) -#711 := (iff #714 true) -#717 := [rewrite]: #711 -#715 := (iff #723 #714) -#712 := (iff #516 false) -#710 := (or false false) -#375 := (iff #710 false) -#376 := [rewrite]: #375 -#373 := (iff #516 #710) -#725 := (iff #386 false) -#385 := [rewrite]: #725 -#374 := [monotonicity #385 #369]: #373 -#713 := [trans #374 #376]: #712 -#716 := [monotonicity #713]: #715 -#718 := [trans #716 #717]: #355 -#706 := [monotonicity #718 #427]: #702 -#418 := [trans #706 #707]: #417 -#564 := [monotonicity #418 #681 #568]: #571 -#575 := [trans #564 #573]: #574 -#384 := (iff #731 false) -#389 := [rewrite]: #384 -#666 := [monotonicity #389 #575]: #669 -#651 := [trans #666 #657]: #659 -#69 := (iff #63 #11) +#64 := (iff #13 #56) +#59 := (and #56 #56) +#62 := (iff #59 #56) +#63 := [rewrite]: #62 +#60 := (iff #13 #59) +#61 := [monotonicity #58 #58]: #60 +#65 := [trans #61 #63]: #64 +#79 := [monotonicity #65 #76]: #78 +#110 := [monotonicity #79 #86 #107]: #109 +#114 := [trans #110 #112]: #113 +#54 := (iff #11 false) +#49 := (= -3::Int 0::Int) +#52 := (iff #49 false) +#53 := [rewrite]: #52 +#50 := (iff #11 #49) +#51 := [monotonicity #48]: #50 +#55 := [trans #51 #53]: #54 +#117 := [monotonicity #55 #114]: #116 +#121 := [trans #117 #119]: #120 +#124 := [monotonicity #55 #48 #121]: #123 +#127 := [trans #124 #126]: #24 +#130 := [monotonicity #127]: #129 +#134 := [trans #130 #132]: #133 +#137 := [monotonicity #134]: #136 +#141 := [trans #137 #139]: #140 +#45 := [asserted]: #25 +[mp #45 #141]: false +unsat +41d81c01f2d4595c3188777c9ff27286d543d121 170 0 +#2 := false +#29 := 2::Int +#30 := (- 2::Int) +#8 := 3::Int +#9 := (- 3::Int) +#23 := (- #9) +#12 := 5::Int +#13 := (- 5::Int) +#22 := (- #13) +#24 := (mod #22 #23) +#25 := (- #24) +#21 := (mod #13 #9) +#10 := 0::Int +#16 := (< 0::Int #9) +#18 := (< #13 0::Int) +#19 := (and #18 #16) +#15 := (< 0::Int #13) +#17 := (and #15 #16) +#20 := (or #17 #19) +#26 := (ite #20 #21 #25) +#14 := (= #13 0::Int) +#27 := (ite #14 0::Int #26) +#11 := (= #9 0::Int) +#28 := (ite #11 #13 #27) +#31 := (= #28 #30) +#32 := (not #31) +#191 := (iff #32 false) +#63 := -5::Int +#82 := (< -5::Int 0::Int) +#53 := -3::Int +#76 := (< 0::Int -3::Int) +#88 := (and #76 #82) +#73 := (< 0::Int -5::Int) +#79 := (and #73 #76) +#93 := (or #79 #88) +#189 := (iff #93 false) +#184 := (or false false) +#187 := (iff #184 false) +#188 := [rewrite]: #187 +#185 := (iff #93 #184) +#182 := (iff #88 false) +#1 := true +#177 := (and false true) +#180 := (iff #177 false) +#181 := [rewrite]: #180 +#178 := (iff #88 #177) +#175 := (iff #82 true) +#176 := [rewrite]: #175 +#166 := (iff #76 false) +#167 := [rewrite]: #166 +#179 := [monotonicity #167 #176]: #178 +#183 := [trans #179 #181]: #182 +#173 := (iff #79 false) +#168 := (and false false) +#171 := (iff #168 false) +#172 := [rewrite]: #171 +#169 := (iff #79 #168) +#164 := (iff #73 false) +#165 := [rewrite]: #164 +#170 := [monotonicity #165 #167]: #169 +#174 := [trans #170 #172]: #173 +#186 := [monotonicity #174 #183]: #185 +#190 := [trans #186 #188]: #189 +#162 := (iff #32 #93) +#152 := (not #93) +#157 := (not #152) +#160 := (iff #157 #93) +#161 := [rewrite]: #160 +#158 := (iff #32 #157) +#155 := (iff #31 #152) +#127 := -2::Int +#99 := 1::Int +#132 := (ite #93 1::Int -2::Int) +#149 := (= #132 -2::Int) +#153 := (iff #149 #152) +#154 := [rewrite]: #153 +#150 := (iff #31 #149) +#128 := (= #30 -2::Int) +#129 := [rewrite]: #128 +#147 := (= #28 #132) +#142 := (ite false -5::Int #132) +#145 := (= #142 #132) +#146 := [rewrite]: #145 +#143 := (= #28 #142) +#140 := (= #27 #132) +#135 := (ite false 0::Int #132) +#138 := (= #135 #132) +#139 := [rewrite]: #138 +#136 := (= #27 #135) +#133 := (= #26 #132) +#130 := (= #25 -2::Int) +#125 := (= #25 #30) +#123 := (= #24 2::Int) +#118 := (mod 5::Int 3::Int) +#121 := (= #118 2::Int) +#122 := [rewrite]: #121 +#119 := (= #24 #118) +#116 := (= #23 3::Int) +#111 := (- -3::Int) +#114 := (= #111 3::Int) +#115 := [rewrite]: #114 +#112 := (= #23 #111) +#54 := (= #9 -3::Int) +#55 := [rewrite]: #54 +#113 := [monotonicity #55]: #112 +#117 := [trans #113 #115]: #116 +#109 := (= #22 5::Int) +#104 := (- -5::Int) +#107 := (= #104 5::Int) +#108 := [rewrite]: #107 +#105 := (= #22 #104) +#64 := (= #13 -5::Int) +#65 := [rewrite]: #64 +#106 := [monotonicity #65]: #105 +#110 := [trans #106 #108]: #109 +#120 := [monotonicity #110 #117]: #119 +#124 := [trans #120 #122]: #123 +#126 := [monotonicity #124]: #125 +#131 := [trans #126 #129]: #130 +#102 := (= #21 1::Int) +#96 := (mod -5::Int -3::Int) +#100 := (= #96 1::Int) +#101 := [rewrite]: #100 +#97 := (= #21 #96) +#98 := [monotonicity #65 #55]: #97 +#103 := [trans #98 #101]: #102 +#94 := (iff #20 #93) +#91 := (iff #19 #88) +#85 := (and #82 #76) +#89 := (iff #85 #88) +#90 := [rewrite]: #89 +#86 := (iff #19 #85) +#77 := (iff #16 #76) +#78 := [monotonicity #55]: #77 +#83 := (iff #18 #82) +#84 := [monotonicity #65]: #83 +#87 := [monotonicity #84 #78]: #86 +#92 := [trans #87 #90]: #91 +#80 := (iff #17 #79) +#74 := (iff #15 #73) +#75 := [monotonicity #65]: #74 +#81 := [monotonicity #75 #78]: #80 +#95 := [monotonicity #81 #92]: #94 +#134 := [monotonicity #95 #103 #131]: #133 +#71 := (iff #14 false) +#66 := (= -5::Int 0::Int) +#69 := (iff #66 false) #70 := [rewrite]: #69 -#734 := (iff #733 false) -#724 := [rewrite]: #734 -#660 := [monotonicity #724 #70 #651]: #650 -#663 := [trans #660 #662]: #658 -#656 := [monotonicity #663]: #649 -#643 := [trans #656 #641]: #649 -#655 := [quant-inst #8 #9]: #654 -#644 := [mp #655 #643]: #653 -[unit-resolution #644 #62 #748]: false -unsat -8af900968418033d3c8752b20b45c64c00fb3744 305 0 -#2 := false -decl f3 :: (-> Int Int Int) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#33 := (f3 #13 #14) -#747 := (pattern #33) -#10 := 0::Int -#78 := -1::Int -#82 := (* -1::Int #14) -#79 := (* -1::Int #13) -#143 := (mod #79 #82) -#258 := (+ #33 #143) -#259 := (= #258 0::Int) -#34 := (mod #13 #14) -#255 := (* -1::Int #34) -#256 := (+ #33 #255) -#257 := (= #256 0::Int) -#117 := (>= #13 0::Int) -#110 := (<= #14 0::Int) -#202 := (or #110 #117) -#203 := (not #202) -#106 := (<= #13 0::Int) -#200 := (or #106 #110) -#201 := (not #200) -#206 := (or #201 #203) -#260 := (ite #206 #257 #259) -#254 := (= #33 0::Int) -#16 := (= #13 0::Int) -#261 := (ite #16 #254 #260) -#253 := (= #13 #33) -#17 := (= #14 0::Int) -#262 := (ite #17 #253 #261) -#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #262) -#265 := (forall (vars (?v0 Int) (?v1 Int)) #262) -#751 := (iff #265 #748) -#749 := (iff #262 #262) -#750 := [refl]: #749 -#752 := [quant-intro #750]: #751 -#149 := (* -1::Int #143) -#222 := (ite #206 #34 #149) -#225 := (ite #16 0::Int #222) -#228 := (ite #17 #13 #225) -#231 := (= #33 #228) -#234 := (forall (vars (?v0 Int) (?v1 Int)) #231) -#266 := (iff #234 #265) -#263 := (iff #231 #262) -#264 := [rewrite]: #263 -#267 := [quant-intro #264]: #266 -#118 := (not #117) -#111 := (not #110) -#121 := (and #111 #118) -#107 := (not #106) -#114 := (and #107 #111) -#124 := (or #114 #121) -#169 := (ite #124 #34 #149) -#172 := (ite #16 0::Int #169) -#175 := (ite #17 #13 #172) -#178 := (= #33 #175) -#181 := (forall (vars (?v0 Int) (?v1 Int)) #178) -#235 := (iff #181 #234) -#232 := (iff #178 #231) -#229 := (= #175 #228) -#226 := (= #172 #225) -#223 := (= #169 #222) -#207 := (iff #124 #206) -#204 := (iff #121 #203) -#205 := [rewrite]: #204 -#194 := (iff #114 #201) -#195 := [rewrite]: #194 -#208 := [monotonicity #195 #205]: #207 -#224 := [monotonicity #208]: #223 -#227 := [monotonicity #224]: #226 -#230 := [monotonicity #227]: #229 -#233 := [monotonicity #230]: #232 -#236 := [quant-intro #233]: #235 -#192 := (~ #181 #181) -#191 := (~ #178 #178) -#188 := [refl]: #191 -#193 := [nnf-pos #188]: #192 -#27 := (- #14) -#26 := (- #13) -#35 := (mod #26 #27) -#36 := (- #35) -#20 := (< 0::Int #14) -#22 := (< #13 0::Int) -#23 := (and #22 #20) -#19 := (< 0::Int #13) -#21 := (and #19 #20) -#24 := (or #21 #23) -#37 := (ite #24 #34 #36) -#38 := (ite #16 0::Int #37) -#39 := (ite #17 #13 #38) -#40 := (= #33 #39) -#41 := (forall (vars (?v0 Int) (?v1 Int)) #40) -#184 := (iff #41 #181) -#72 := (and #20 #22) -#75 := (or #21 #72) -#154 := (ite #75 #34 #149) -#63 := (= 0::Int #13) -#157 := (ite #63 0::Int #154) -#66 := (= 0::Int #14) -#160 := (ite #66 #13 #157) -#163 := (= #33 #160) -#166 := (forall (vars (?v0 Int) (?v1 Int)) #163) -#182 := (iff #166 #181) -#179 := (iff #163 #178) -#176 := (= #160 #175) -#173 := (= #157 #172) -#170 := (= #154 #169) -#125 := (iff #75 #124) -#122 := (iff #72 #121) -#119 := (iff #22 #118) -#120 := [rewrite]: #119 -#112 := (iff #20 #111) -#113 := [rewrite]: #112 -#123 := [monotonicity #113 #120]: #122 -#115 := (iff #21 #114) -#108 := (iff #19 #107) -#109 := [rewrite]: #108 -#116 := [monotonicity #109 #113]: #115 -#126 := [monotonicity #116 #123]: #125 -#171 := [monotonicity #126]: #170 -#100 := (iff #63 #16) -#101 := [rewrite]: #100 -#174 := [monotonicity #101 #171]: #173 -#102 := (iff #66 #17) -#103 := [rewrite]: #102 -#177 := [monotonicity #103 #174]: #176 -#180 := [monotonicity #177]: #179 -#183 := [quant-intro #180]: #182 -#167 := (iff #41 #166) -#164 := (iff #40 #163) -#161 := (= #39 #160) -#158 := (= #38 #157) -#155 := (= #37 #154) -#152 := (= #36 #149) -#146 := (- #143) -#150 := (= #146 #149) -#151 := [rewrite]: #150 -#147 := (= #36 #146) -#144 := (= #35 #143) -#83 := (= #27 #82) -#84 := [rewrite]: #83 -#80 := (= #26 #79) -#81 := [rewrite]: #80 -#145 := [monotonicity #81 #84]: #144 -#148 := [monotonicity #145]: #147 -#153 := [trans #148 #151]: #152 -#76 := (iff #24 #75) -#73 := (iff #23 #72) -#74 := [rewrite]: #73 -#77 := [monotonicity #74]: #76 -#156 := [monotonicity #77 #153]: #155 -#64 := (iff #16 #63) -#65 := [rewrite]: #64 -#159 := [monotonicity #65 #156]: #158 -#67 := (iff #17 #66) -#68 := [rewrite]: #67 -#162 := [monotonicity #68 #159]: #161 -#165 := [monotonicity #162]: #164 -#168 := [quant-intro #165]: #167 -#185 := [trans #168 #183]: #184 -#142 := [asserted]: #41 -#186 := [mp #142 #185]: #181 -#189 := [mp~ #186 #193]: #181 -#237 := [mp #189 #236]: #234 -#268 := [mp #237 #267]: #265 -#753 := [mp #268 #752]: #748 +#67 := (iff #14 #66) +#68 := [monotonicity #65]: #67 +#72 := [trans #68 #70]: #71 +#137 := [monotonicity #72 #134]: #136 +#141 := [trans #137 #139]: #140 +#61 := (iff #11 false) +#56 := (= -3::Int 0::Int) +#59 := (iff #56 false) +#60 := [rewrite]: #59 +#57 := (iff #11 #56) +#58 := [monotonicity #55]: #57 +#62 := [trans #58 #60]: #61 +#144 := [monotonicity #62 #65 #141]: #143 +#148 := [trans #144 #146]: #147 +#151 := [monotonicity #148 #129]: #150 +#156 := [trans #151 #154]: #155 +#159 := [monotonicity #156]: #158 +#163 := [trans #159 #161]: #162 +#192 := [trans #163 #190]: #191 +#52 := [asserted]: #32 +[mp #52 #192]: false +unsat +37d641fb0d3f5af8883d250eb08e7f4e580b8a49 182 0 +#2 := false +#9 := 0::Int +decl f3 :: Int +#11 := f3 +#99 := (<= f3 0::Int) +#112 := (>= f3 0::Int) +#113 := (not #112) +#100 := (not #99) +#123 := (or #100 #113) +#160 := (not #123) +#64 := -3::Int +#60 := -1::Int +#61 := (* -1::Int f3) +#67 := (mod #61 -3::Int) +#73 := (* -1::Int #67) #8 := 3::Int -#9 := (f3 3::Int 3::Int) -#11 := (= #9 0::Int) -#12 := (not #11) -#61 := [asserted]: #12 -#573 := (not #748) -#575 := (or #573 #11) -#326 := (* -1::Int 3::Int) -#411 := (mod #326 #326) -#412 := (+ #9 #411) -#413 := (= #412 0::Int) -#404 := (mod 3::Int 3::Int) -#415 := (* -1::Int #404) -#416 := (+ #9 #415) -#344 := (= #416 0::Int) -#417 := (>= 3::Int 0::Int) -#414 := (<= 3::Int 0::Int) -#418 := (or #414 #417) -#397 := (not #418) -#732 := (or #414 #414) -#734 := (not #732) -#391 := (or #734 #397) -#521 := (ite #391 #344 #413) -#728 := (= 3::Int 0::Int) -#402 := (ite #728 #11 #521) -#403 := (= 3::Int #9) -#735 := (ite #728 #403 #402) -#576 := (or #573 #735) -#577 := (iff #576 #575) -#579 := (iff #575 #575) -#580 := [rewrite]: #579 -#673 := (iff #735 #11) -#733 := (= #9 3::Int) -#524 := (ite false #733 #11) -#669 := (iff #524 #11) -#670 := [rewrite]: #669 -#672 := (iff #735 #524) -#564 := (iff #402 #11) -#679 := (ite false #11 #11) -#681 := (iff #679 #11) -#563 := [rewrite]: #681 -#680 := (iff #402 #679) -#676 := (iff #521 #11) -#1 := true -#684 := (ite true #11 #11) -#522 := (iff #684 #11) -#523 := [rewrite]: #522 -#691 := (iff #521 #684) -#689 := (iff #413 #11) -#682 := (= #412 #9) -#419 := (+ #9 0::Int) -#702 := (= #419 #9) -#706 := [rewrite]: #702 -#687 := (= #412 #419) -#685 := (= #411 0::Int) -#693 := -3::Int -#694 := (mod -3::Int -3::Int) -#542 := (= #694 0::Int) -#543 := [rewrite]: #542 -#700 := (= #411 #694) -#698 := (= #326 -3::Int) -#699 := [rewrite]: #698 -#541 := [monotonicity #699 #699]: #700 -#686 := [trans #541 #543]: #685 -#688 := [monotonicity #686]: #687 -#683 := [trans #688 #706]: #682 -#690 := [monotonicity #683]: #689 -#697 := (iff #344 #11) -#695 := (= #416 #9) -#701 := (= #416 #419) -#703 := (= #415 0::Int) -#712 := (* -1::Int 0::Int) -#424 := (= #712 0::Int) -#425 := [rewrite]: #424 -#422 := (= #415 #712) -#711 := (= #404 0::Int) -#708 := [rewrite]: #711 -#423 := [monotonicity #708]: #422 -#704 := [trans #423 #425]: #703 -#705 := [monotonicity #704]: #701 -#696 := [trans #705 #706]: #695 -#692 := [monotonicity #696]: #697 -#433 := (iff #391 true) -#439 := (or true false) -#710 := (iff #439 true) -#432 := [rewrite]: #710 -#332 := (iff #391 #439) -#437 := (iff #397 false) -#724 := (not true) -#714 := (iff #724 false) -#436 := [rewrite]: #714 -#727 := (iff #397 #724) -#366 := (iff #418 true) -#722 := (or false true) -#725 := (iff #722 true) -#365 := [rewrite]: #725 -#360 := (iff #418 #722) -#721 := (iff #417 true) -#716 := [rewrite]: #721 -#729 := (iff #414 false) -#389 := [rewrite]: #729 -#723 := [monotonicity #389 #716]: #360 -#726 := [trans #723 #365]: #366 -#713 := [monotonicity #726]: #727 -#438 := [trans #713 #436]: #437 -#719 := (iff #734 true) -#379 := (not false) -#717 := (iff #379 true) -#718 := [rewrite]: #717 -#380 := (iff #734 #379) -#715 := (iff #732 false) -#394 := (or false false) -#731 := (iff #394 false) -#374 := [rewrite]: #731 -#730 := (iff #732 #394) -#390 := [monotonicity #389 #389]: #730 -#378 := [trans #390 #374]: #715 -#381 := [monotonicity #378]: #380 -#720 := [trans #381 #718]: #719 -#709 := [monotonicity #720 #438]: #332 -#707 := [trans #709 #432]: #433 -#520 := [monotonicity #707 #692 #690]: #691 -#677 := [trans #520 #523]: #676 -#736 := (iff #728 false) -#737 := [rewrite]: #736 -#678 := [monotonicity #737 #677]: #680 -#565 := [trans #678 #563]: #564 -#738 := (iff #403 #733) -#739 := [rewrite]: #738 -#574 := [monotonicity #737 #739 #565]: #672 -#558 := [trans #574 #670]: #673 -#578 := [monotonicity #558]: #577 -#581 := [trans #578 #580]: #577 -#569 := [quant-inst #8 #8]: #576 -#674 := [mp #569 #581]: #575 -[unit-resolution #674 #61 #753]: false -unsat -e06ff93350d55c82e0187108fc1a1d48234a7767 326 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#35 := (f3 #14 #15) -#734 := (pattern #35) -#17 := 0::Int -#71 := -1::Int -#75 := (* -1::Int #15) -#72 := (* -1::Int #14) -#130 := (mod #72 #75) -#245 := (+ #35 #130) -#246 := (= #245 0::Int) -#36 := (mod #14 #15) -#242 := (* -1::Int #36) -#243 := (+ #35 #242) -#244 := (= #243 0::Int) -#104 := (>= #14 0::Int) -#97 := (<= #15 0::Int) -#189 := (or #97 #104) -#190 := (not #189) -#93 := (<= #14 0::Int) -#187 := (or #93 #97) -#188 := (not #187) -#193 := (or #188 #190) -#247 := (ite #193 #244 #246) -#241 := (= #35 0::Int) -#18 := (= #14 0::Int) -#248 := (ite #18 #241 #247) -#240 := (= #14 #35) -#19 := (= #15 0::Int) -#249 := (ite #19 #240 #248) -#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #249) -#252 := (forall (vars (?v0 Int) (?v1 Int)) #249) -#738 := (iff #252 #735) -#736 := (iff #249 #249) -#737 := [refl]: #736 -#739 := [quant-intro #737]: #738 -#136 := (* -1::Int #130) -#209 := (ite #193 #36 #136) -#212 := (ite #18 0::Int #209) -#215 := (ite #19 #14 #212) -#218 := (= #35 #215) -#221 := (forall (vars (?v0 Int) (?v1 Int)) #218) -#253 := (iff #221 #252) -#250 := (iff #218 #249) -#251 := [rewrite]: #250 -#254 := [quant-intro #251]: #253 -#105 := (not #104) -#98 := (not #97) -#108 := (and #98 #105) -#94 := (not #93) -#101 := (and #94 #98) -#111 := (or #101 #108) -#156 := (ite #111 #36 #136) -#159 := (ite #18 0::Int #156) -#162 := (ite #19 #14 #159) -#165 := (= #35 #162) -#168 := (forall (vars (?v0 Int) (?v1 Int)) #165) -#222 := (iff #168 #221) -#219 := (iff #165 #218) -#216 := (= #162 #215) -#213 := (= #159 #212) -#210 := (= #156 #209) -#194 := (iff #111 #193) -#191 := (iff #108 #190) -#192 := [rewrite]: #191 -#181 := (iff #101 #188) -#182 := [rewrite]: #181 -#195 := [monotonicity #182 #192]: #194 -#211 := [monotonicity #195]: #210 -#214 := [monotonicity #211]: #213 -#217 := [monotonicity #214]: #216 -#220 := [monotonicity #217]: #219 -#223 := [quant-intro #220]: #222 -#179 := (~ #168 #168) -#178 := (~ #165 #165) -#175 := [refl]: #178 -#180 := [nnf-pos #175]: #179 -#29 := (- #15) -#28 := (- #14) -#37 := (mod #28 #29) -#38 := (- #37) -#22 := (< 0::Int #15) -#24 := (< #14 0::Int) -#25 := (and #24 #22) -#21 := (< 0::Int #14) -#23 := (and #21 #22) -#26 := (or #23 #25) -#39 := (ite #26 #36 #38) -#40 := (ite #18 0::Int #39) -#41 := (ite #19 #14 #40) -#42 := (= #35 #41) -#43 := (forall (vars (?v0 Int) (?v1 Int)) #42) -#171 := (iff #43 #168) -#65 := (and #22 #24) -#68 := (or #23 #65) -#141 := (ite #68 #36 #136) -#144 := (ite #18 0::Int #141) -#147 := (ite #19 #14 #144) -#150 := (= #35 #147) -#153 := (forall (vars (?v0 Int) (?v1 Int)) #150) -#169 := (iff #153 #168) -#166 := (iff #150 #165) -#163 := (= #147 #162) -#160 := (= #144 #159) -#157 := (= #141 #156) -#112 := (iff #68 #111) -#109 := (iff #65 #108) -#106 := (iff #24 #105) +#19 := (mod f3 3::Int) +#126 := (ite #123 #19 #73) +#158 := (= #19 #126) +#254 := (not #158) +#226 := (>= #19 3::Int) +#227 := (not #226) +#1 := true +#46 := [true-axiom]: true +#242 := (or false #227) +#243 := [th-lemma arith]: #242 +#244 := [unit-resolution #243 #46]: #227 +#12 := (= f3 0::Int) +#129 := (ite #12 0::Int #126) +#238 := (* -1::Int #129) +#239 := (+ #19 #238) +#241 := (>= #239 0::Int) +#237 := (= #19 #129) +#157 := (= #126 #129) +#167 := (not #12) +#156 := (= #129 0::Int) +#179 := (not #156) +#172 := (<= #129 0::Int) +#174 := (not #172) +#136 := (>= #129 3::Int) +#21 := (- 3::Int) +#20 := (- f3) +#22 := (mod #20 #21) +#23 := (- #22) +#14 := (< 0::Int 3::Int) +#16 := (< f3 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int f3) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#25 := (ite #12 0::Int #24) +#10 := (= 3::Int 0::Int) +#26 := (ite #10 f3 #25) +#27 := (< #26 3::Int) +#28 := (not #27) +#148 := (iff #28 #136) +#54 := (and #14 #16) +#57 := (or #15 #54) +#78 := (ite #57 #19 #73) +#51 := (= 0::Int f3) +#81 := (ite #51 0::Int #78) +#91 := (< #81 3::Int) +#94 := (not #91) +#146 := (iff #94 #136) +#135 := (not #136) +#141 := (not #135) +#144 := (iff #141 #136) +#145 := [rewrite]: #144 +#142 := (iff #94 #141) +#139 := (iff #91 #135) +#132 := (< #129 3::Int) +#137 := (iff #132 #135) +#138 := [rewrite]: #137 +#133 := (iff #91 #132) +#130 := (= #81 #129) +#127 := (= #78 #126) +#124 := (iff #57 #123) +#121 := (iff #54 #113) +#116 := (and true #113) +#119 := (iff #116 #113) +#120 := [rewrite]: #119 +#117 := (iff #54 #116) +#114 := (iff #16 #113) +#115 := [rewrite]: #114 +#103 := (iff #14 true) +#104 := [rewrite]: #103 +#118 := [monotonicity #104 #115]: #117 +#122 := [trans #118 #120]: #121 +#110 := (iff #15 #100) +#105 := (and #100 true) +#108 := (iff #105 #100) +#109 := [rewrite]: #108 +#106 := (iff #15 #105) +#101 := (iff #13 #100) +#102 := [rewrite]: #101 +#107 := [monotonicity #102 #104]: #106 +#111 := [trans #107 #109]: #110 +#125 := [monotonicity #111 #122]: #124 +#128 := [monotonicity #125]: #127 +#97 := (iff #51 #12) +#98 := [rewrite]: #97 +#131 := [monotonicity #98 #128]: #130 +#134 := [monotonicity #131]: #133 +#140 := [trans #134 #138]: #139 +#143 := [monotonicity #140]: #142 +#147 := [trans #143 #145]: #146 +#95 := (iff #28 #94) +#92 := (iff #27 #91) +#89 := (= #26 #81) +#84 := (ite false f3 #81) +#87 := (= #84 #81) +#88 := [rewrite]: #87 +#85 := (= #26 #84) +#82 := (= #25 #81) +#79 := (= #24 #78) +#76 := (= #23 #73) +#70 := (- #67) +#74 := (= #70 #73) +#75 := [rewrite]: #74 +#71 := (= #23 #70) +#68 := (= #22 #67) +#65 := (= #21 -3::Int) +#66 := [rewrite]: #65 +#62 := (= #20 #61) +#63 := [rewrite]: #62 +#69 := [monotonicity #63 #66]: #68 +#72 := [monotonicity #69]: #71 +#77 := [trans #72 #75]: #76 +#58 := (iff #18 #57) +#55 := (iff #17 #54) +#56 := [rewrite]: #55 +#59 := [monotonicity #56]: #58 +#80 := [monotonicity #59 #77]: #79 +#52 := (iff #12 #51) +#53 := [rewrite]: #52 +#83 := [monotonicity #53 #80]: #82 +#49 := (iff #10 false) +#50 := [rewrite]: #49 +#86 := [monotonicity #50 #83]: #85 +#90 := [trans #86 #88]: #89 +#93 := [monotonicity #90]: #92 +#96 := [monotonicity #93]: #95 +#149 := [trans #96 #147]: #148 +#48 := [asserted]: #28 +#150 := [mp #48 #149]: #136 +#175 := (or #174 #135) +#176 := [th-lemma arith farkas 1 1]: #175 +#177 := [unit-resolution #176 #150]: #174 +#178 := [hypothesis]: #156 +#180 := (or #179 #172) +#181 := [th-lemma arith triangle-eq]: #180 +#182 := [unit-resolution #181 #178 #177]: false +#183 := [lemma #182]: #179 +#168 := (or #167 #156) +#169 := [def-axiom]: #168 +#245 := [unit-resolution #169 #183]: #167 +#170 := (or #12 #157) +#171 := [def-axiom]: #170 +#246 := [unit-resolution #171 #245]: #157 +#247 := [hypothesis]: #158 +#248 := [trans #247 #246]: #237 +#249 := (not #237) +#250 := (or #249 #241) +#251 := [th-lemma arith triangle-eq]: #250 +#252 := [unit-resolution #251 #248]: #241 +#253 := [th-lemma arith farkas -1 -1 1 #150 #252 #244]: false +#255 := [lemma #253]: #254 +#163 := (or #160 #158) +#164 := [def-axiom]: #163 +#232 := [unit-resolution #164 #255]: #160 +#154 := (or #123 #99) +#155 := [def-axiom]: #154 +#233 := [unit-resolution #155 #232]: #99 +#152 := (or #123 #112) +#153 := [def-axiom]: #152 +#234 := [unit-resolution #153 #232]: #112 +#235 := (or #12 #100 #113) +#236 := [th-lemma arith triangle-eq]: #235 +#207 := [unit-resolution #236 #245]: #123 +[unit-resolution #207 #234 #233]: false +unsat +fcd3f8cba75d0af01f63efd762505b1dda18b530 187 0 +#2 := false +#8 := 3::Int +decl f3 :: Int +#11 := f3 +#19 := (mod f3 3::Int) +#233 := (>= #19 3::Int) +#234 := (not #233) +#1 := true +#48 := [true-axiom]: true +#248 := (or false #234) +#249 := [th-lemma arith]: #248 +#250 := [unit-resolution #249 #48]: #234 +#9 := 0::Int +#62 := -1::Int +#206 := (* -1::Int #19) +#245 := (+ f3 #206) +#246 := (<= #245 0::Int) +#244 := (= f3 #19) +#66 := -3::Int +#63 := (* -1::Int f3) +#69 := (mod #63 -3::Int) +#75 := (* -1::Int #69) +#132 := (>= f3 0::Int) +#133 := (not #132) +#119 := (<= f3 0::Int) +#120 := (not #119) +#143 := (or #120 #133) +#146 := (ite #143 #19 #75) +#262 := (= #146 #19) +#178 := (= #19 #146) +#113 := (>= f3 3::Int) +#12 := (= f3 0::Int) +#149 := (ite #12 0::Int #146) +#152 := (= f3 #149) +#155 := (not #152) +#114 := (not #113) +#158 := (or #114 #155) +#161 := (not #158) +#28 := (< f3 3::Int) +#21 := (- 3::Int) +#20 := (- f3) +#22 := (mod #20 #21) +#23 := (- #22) +#14 := (< 0::Int 3::Int) +#16 := (< f3 0::Int) +#17 := (and #16 #14) +#13 := (< 0::Int f3) +#15 := (and #13 #14) +#18 := (or #15 #17) +#24 := (ite #18 #19 #23) +#25 := (ite #12 0::Int #24) +#10 := (= 3::Int 0::Int) +#26 := (ite #10 f3 #25) +#27 := (= #26 f3) +#29 := (implies #27 #28) +#30 := (not #29) +#164 := (iff #30 #161) +#56 := (and #14 #16) +#59 := (or #15 #56) +#80 := (ite #59 #19 #75) +#53 := (= 0::Int f3) +#83 := (ite #53 0::Int #80) +#96 := (= f3 #83) +#104 := (not #96) +#105 := (or #28 #104) +#110 := (not #105) +#162 := (iff #110 #161) +#159 := (iff #105 #158) +#156 := (iff #104 #155) +#153 := (iff #96 #152) +#150 := (= #83 #149) +#147 := (= #80 #146) +#144 := (iff #59 #143) +#141 := (iff #56 #133) +#136 := (and true #133) +#139 := (iff #136 #133) +#140 := [rewrite]: #139 +#137 := (iff #56 #136) +#134 := (iff #16 #133) +#135 := [rewrite]: #134 +#123 := (iff #14 true) +#124 := [rewrite]: #123 +#138 := [monotonicity #124 #135]: #137 +#142 := [trans #138 #140]: #141 +#130 := (iff #15 #120) +#125 := (and #120 true) +#128 := (iff #125 #120) +#129 := [rewrite]: #128 +#126 := (iff #15 #125) +#121 := (iff #13 #120) +#122 := [rewrite]: #121 +#127 := [monotonicity #122 #124]: #126 +#131 := [trans #127 #129]: #130 +#145 := [monotonicity #131 #142]: #144 +#148 := [monotonicity #145]: #147 +#117 := (iff #53 #12) +#118 := [rewrite]: #117 +#151 := [monotonicity #118 #148]: #150 +#154 := [monotonicity #151]: #153 +#157 := [monotonicity #154]: #156 +#115 := (iff #28 #114) +#116 := [rewrite]: #115 +#160 := [monotonicity #116 #157]: #159 +#163 := [monotonicity #160]: #162 +#111 := (iff #30 #110) +#108 := (iff #29 #105) +#101 := (implies #96 #28) +#106 := (iff #101 #105) #107 := [rewrite]: #106 -#99 := (iff #22 #98) -#100 := [rewrite]: #99 -#110 := [monotonicity #100 #107]: #109 -#102 := (iff #23 #101) -#95 := (iff #21 #94) -#96 := [rewrite]: #95 -#103 := [monotonicity #96 #100]: #102 -#113 := [monotonicity #103 #110]: #112 -#158 := [monotonicity #113]: #157 -#161 := [monotonicity #158]: #160 -#164 := [monotonicity #161]: #163 -#167 := [monotonicity #164]: #166 -#170 := [quant-intro #167]: #169 -#154 := (iff #43 #153) -#151 := (iff #42 #150) -#148 := (= #41 #147) -#145 := (= #40 #144) -#142 := (= #39 #141) -#139 := (= #38 #136) -#133 := (- #130) -#137 := (= #133 #136) -#138 := [rewrite]: #137 -#134 := (= #38 #133) -#131 := (= #37 #130) -#76 := (= #29 #75) +#102 := (iff #29 #101) +#99 := (iff #27 #96) +#93 := (= #83 f3) +#97 := (iff #93 #96) +#98 := [rewrite]: #97 +#94 := (iff #27 #93) +#91 := (= #26 #83) +#86 := (ite false f3 #83) +#89 := (= #86 #83) +#90 := [rewrite]: #89 +#87 := (= #26 #86) +#84 := (= #25 #83) +#81 := (= #24 #80) +#78 := (= #23 #75) +#72 := (- #69) +#76 := (= #72 #75) #77 := [rewrite]: #76 -#73 := (= #28 #72) -#74 := [rewrite]: #73 -#132 := [monotonicity #74 #77]: #131 -#135 := [monotonicity #132]: #134 -#140 := [trans #135 #138]: #139 -#69 := (iff #26 #68) -#66 := (iff #25 #65) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#143 := [monotonicity #70 #140]: #142 -#146 := [monotonicity #143]: #145 -#149 := [monotonicity #146]: #148 -#152 := [monotonicity #149]: #151 -#155 := [quant-intro #152]: #154 -#172 := [trans #155 #170]: #171 -#129 := [asserted]: #43 -#173 := [mp #129 #172]: #168 -#176 := [mp~ #173 #180]: #168 -#224 := [mp #176 #223]: #221 -#255 := [mp #224 #254]: #252 -#740 := [mp #255 #739]: #735 -#11 := 2::Int -#9 := 3::Int -#8 := 5::Int -#10 := (f3 5::Int 3::Int) -#12 := (= #10 2::Int) -#13 := (not #12) -#63 := [asserted]: #13 -#633 := (not #735) -#635 := (or #633 #12) -#313 := (* -1::Int 3::Int) -#398 := (* -1::Int 5::Int) -#399 := (mod #398 #313) -#400 := (+ #10 #399) -#391 := (= #400 0::Int) -#402 := (mod 5::Int 3::Int) -#403 := (* -1::Int #402) -#331 := (+ #10 #403) -#404 := (= #331 0::Int) -#401 := (>= 5::Int 0::Int) -#405 := (<= 3::Int 0::Int) -#384 := (or #405 #401) -#719 := (not #384) -#721 := (<= 5::Int 0::Int) -#378 := (or #721 #405) -#508 := (not #378) -#715 := (or #508 #719) -#389 := (ite #715 #404 #391) -#390 := (= #10 0::Int) -#722 := (= 5::Int 0::Int) -#723 := (ite #722 #390 #389) -#724 := (= 5::Int #10) -#725 := (= 3::Int 0::Int) -#720 := (ite #725 #724 #723) -#636 := (or #633 #720) -#638 := (iff #636 #635) -#639 := (iff #635 #635) -#625 := [rewrite]: #639 -#648 := (iff #720 #12) -#381 := (= #10 5::Int) -#644 := (ite false #381 #12) -#647 := (iff #644 #12) -#641 := [rewrite]: #647 -#645 := (iff #720 #644) -#650 := (iff #723 #12) -#640 := (ite false #390 #12) -#653 := (iff #640 #12) -#654 := [rewrite]: #653 -#642 := (iff #723 #640) -#651 := (iff #389 #12) -#556 := (= #10 -1::Int) -#1 := true -#568 := (ite true #12 #556) -#662 := (iff #568 #12) -#649 := [rewrite]: #662 -#661 := (iff #389 #568) -#566 := (iff #391 #556) -#667 := 1::Int -#561 := (+ 1::Int #10) -#560 := (= #561 0::Int) -#564 := (iff #560 #556) -#565 := [rewrite]: #564 -#562 := (iff #391 #560) -#660 := (= #400 #561) -#552 := (+ #10 1::Int) -#656 := (= #552 #561) -#657 := [rewrite]: #656 -#511 := (= #400 #552) -#550 := (= #399 1::Int) -#507 := -3::Int -#677 := -5::Int -#663 := (mod -5::Int -3::Int) -#665 := (= #663 1::Int) -#668 := [rewrite]: #665 -#664 := (= #399 #663) -#509 := (= #313 -3::Int) -#510 := [rewrite]: #509 -#671 := (= #398 -5::Int) -#678 := [rewrite]: #671 -#666 := [monotonicity #678 #510]: #664 -#551 := [trans #666 #668]: #550 -#659 := [monotonicity #551]: #511 -#545 := [trans #659 #657]: #660 -#563 := [monotonicity #545]: #562 -#567 := [trans #563 #565]: #566 -#670 := (iff #404 #12) -#693 := -2::Int -#681 := (+ -2::Int #10) -#672 := (= #681 0::Int) -#675 := (iff #672 #12) -#669 := [rewrite]: #675 -#673 := (iff #404 #672) -#529 := (= #331 #681) -#680 := (+ #10 -2::Int) -#687 := (= #680 #681) -#528 := [rewrite]: #687 -#685 := (= #331 #680) -#684 := (= #403 -2::Int) -#688 := (* -1::Int 2::Int) -#682 := (= #688 -2::Int) -#683 := [rewrite]: #682 -#692 := (= #403 #688) -#691 := (= #402 2::Int) -#406 := [rewrite]: #691 -#689 := [monotonicity #406]: #692 -#679 := [trans #689 #683]: #684 -#686 := [monotonicity #679]: #685 -#530 := [trans #686 #528]: #529 -#674 := [monotonicity #530]: #673 -#676 := [trans #674 #669]: #670 -#412 := (iff #715 true) -#695 := (or true false) -#410 := (iff #695 true) -#411 := [rewrite]: #410 -#699 := (iff #715 #695) -#694 := (iff #719 false) -#319 := (not true) -#419 := (iff #319 false) -#420 := [rewrite]: #419 -#696 := (iff #719 #319) -#425 := (iff #384 true) -#714 := (or false true) -#423 := (iff #714 true) -#424 := [rewrite]: #423 -#700 := (iff #384 #714) -#713 := (iff #401 true) -#711 := [rewrite]: #713 -#365 := (iff #405 false) -#366 := [rewrite]: #365 -#701 := [monotonicity #366 #711]: #700 -#426 := [trans #701 #424]: #425 -#697 := [monotonicity #426]: #696 -#698 := [trans #697 #420]: #694 -#352 := (iff #508 true) -#703 := (not false) -#710 := (iff #703 true) -#712 := [rewrite]: #710 -#709 := (iff #508 #703) -#707 := (iff #378 false) -#367 := (or false false) -#705 := (iff #367 false) -#706 := [rewrite]: #705 -#368 := (iff #378 #367) -#361 := (iff #721 false) -#702 := [rewrite]: #361 -#704 := [monotonicity #702 #366]: #368 -#708 := [trans #704 #706]: #707 -#347 := [monotonicity #708]: #709 -#353 := [trans #347 #712]: #352 -#409 := [monotonicity #353 #698]: #699 -#690 := [trans #409 #411]: #412 -#658 := [monotonicity #690 #676 #567]: #661 -#643 := [trans #658 #649]: #651 -#377 := (iff #722 false) -#718 := [rewrite]: #377 -#652 := [monotonicity #718 #643]: #642 -#655 := [trans #652 #654]: #650 -#376 := (iff #724 #381) -#717 := [rewrite]: #376 -#726 := (iff #725 false) -#716 := [rewrite]: #726 -#646 := [monotonicity #716 #717 #655]: #645 -#632 := [trans #646 #641]: #648 -#634 := [monotonicity #632]: #638 -#626 := [trans #634 #625]: #638 -#637 := [quant-inst #8 #9]: #636 -#628 := [mp #637 #626]: #635 -[unit-resolution #628 #63 #740]: false -unsat -216c9ba1da8ff35ffdfffd11994f68f93a59b859 330 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#37 := (f3 #16 #17) -#751 := (pattern #37) -#19 := 0::Int -#89 := -1::Int -#93 := (* -1::Int #17) -#90 := (* -1::Int #16) -#148 := (mod #90 #93) -#263 := (+ #37 #148) -#264 := (= #263 0::Int) -#38 := (mod #16 #17) -#260 := (* -1::Int #38) -#261 := (+ #37 #260) -#262 := (= #261 0::Int) -#122 := (>= #16 0::Int) -#115 := (<= #17 0::Int) -#207 := (or #115 #122) -#208 := (not #207) -#111 := (<= #16 0::Int) -#205 := (or #111 #115) -#206 := (not #205) -#211 := (or #206 #208) -#265 := (ite #211 #262 #264) -#259 := (= #37 0::Int) -#20 := (= #16 0::Int) -#266 := (ite #20 #259 #265) -#258 := (= #16 #37) -#21 := (= #17 0::Int) -#267 := (ite #21 #258 #266) -#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #267) -#270 := (forall (vars (?v0 Int) (?v1 Int)) #267) -#755 := (iff #270 #752) -#753 := (iff #267 #267) -#754 := [refl]: #753 -#756 := [quant-intro #754]: #755 -#154 := (* -1::Int #148) -#227 := (ite #211 #38 #154) -#230 := (ite #20 0::Int #227) -#233 := (ite #21 #16 #230) -#236 := (= #37 #233) -#239 := (forall (vars (?v0 Int) (?v1 Int)) #236) -#271 := (iff #239 #270) -#268 := (iff #236 #267) -#269 := [rewrite]: #268 -#272 := [quant-intro #269]: #271 -#123 := (not #122) -#116 := (not #115) -#126 := (and #116 #123) -#112 := (not #111) -#119 := (and #112 #116) -#129 := (or #119 #126) -#174 := (ite #129 #38 #154) -#177 := (ite #20 0::Int #174) -#180 := (ite #21 #16 #177) -#183 := (= #37 #180) -#186 := (forall (vars (?v0 Int) (?v1 Int)) #183) -#240 := (iff #186 #239) -#237 := (iff #183 #236) -#234 := (= #180 #233) -#231 := (= #177 #230) -#228 := (= #174 #227) -#212 := (iff #129 #211) -#209 := (iff #126 #208) -#210 := [rewrite]: #209 -#199 := (iff #119 #206) -#200 := [rewrite]: #199 -#213 := [monotonicity #200 #210]: #212 -#229 := [monotonicity #213]: #228 -#232 := [monotonicity #229]: #231 -#235 := [monotonicity #232]: #234 -#238 := [monotonicity #235]: #237 -#241 := [quant-intro #238]: #240 -#197 := (~ #186 #186) -#196 := (~ #183 #183) -#193 := [refl]: #196 -#198 := [nnf-pos #193]: #197 -#31 := (- #17) -#30 := (- #16) -#39 := (mod #30 #31) -#40 := (- #39) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#41 := (ite #28 #38 #40) -#42 := (ite #20 0::Int #41) -#43 := (ite #21 #16 #42) -#44 := (= #37 #43) -#45 := (forall (vars (?v0 Int) (?v1 Int)) #44) -#189 := (iff #45 #186) -#82 := (and #24 #26) -#86 := (or #25 #82) -#159 := (ite #86 #38 #154) -#162 := (ite #20 0::Int #159) -#165 := (ite #21 #16 #162) -#168 := (= #37 #165) -#171 := (forall (vars (?v0 Int) (?v1 Int)) #168) -#187 := (iff #171 #186) -#184 := (iff #168 #183) -#181 := (= #165 #180) -#178 := (= #162 #177) -#175 := (= #159 #174) -#130 := (iff #86 #129) -#127 := (iff #82 #126) -#124 := (iff #26 #123) -#125 := [rewrite]: #124 -#117 := (iff #24 #116) -#118 := [rewrite]: #117 -#128 := [monotonicity #118 #125]: #127 -#120 := (iff #25 #119) -#113 := (iff #23 #112) -#114 := [rewrite]: #113 -#121 := [monotonicity #114 #118]: #120 -#131 := [monotonicity #121 #128]: #130 -#176 := [monotonicity #131]: #175 -#179 := [monotonicity #176]: #178 -#182 := [monotonicity #179]: #181 -#185 := [monotonicity #182]: #184 -#188 := [quant-intro #185]: #187 -#172 := (iff #45 #171) -#169 := (iff #44 #168) -#166 := (= #43 #165) -#163 := (= #42 #162) -#160 := (= #41 #159) -#157 := (= #40 #154) -#151 := (- #148) -#155 := (= #151 #154) -#156 := [rewrite]: #155 -#152 := (= #40 #151) -#149 := (= #39 #148) -#94 := (= #31 #93) -#95 := [rewrite]: #94 -#91 := (= #30 #90) -#92 := [rewrite]: #91 -#150 := [monotonicity #92 #95]: #149 -#153 := [monotonicity #150]: #152 -#158 := [trans #153 #156]: #157 -#87 := (iff #28 #86) -#84 := (iff #27 #82) -#85 := [rewrite]: #84 -#88 := [monotonicity #85]: #87 -#161 := [monotonicity #88 #158]: #160 -#164 := [monotonicity #161]: #163 -#167 := [monotonicity #164]: #166 -#170 := [monotonicity #167]: #169 -#173 := [quant-intro #170]: #172 -#190 := [trans #173 #188]: #189 -#147 := [asserted]: #45 -#191 := [mp #147 #190]: #186 -#194 := [mp~ #191 #198]: #186 -#242 := [mp #194 #241]: #239 -#273 := [mp #242 #272]: #270 -#757 := [mp #273 #756]: #752 -#72 := -2::Int -#66 := -3::Int -#8 := 1::Int -#69 := (f3 1::Int -3::Int) -#75 := (= #69 -2::Int) -#78 := (not #75) -#12 := 2::Int -#13 := (- 2::Int) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 1::Int #10) -#14 := (= #11 #13) -#15 := (not #14) -#79 := (iff #15 #78) -#76 := (iff #14 #75) -#73 := (= #13 -2::Int) -#74 := [rewrite]: #73 -#70 := (= #11 #69) -#67 := (= #10 -3::Int) +#73 := (= #23 #72) +#70 := (= #22 #69) +#67 := (= #21 -3::Int) #68 := [rewrite]: #67 -#71 := [monotonicity #68]: #70 -#77 := [monotonicity #71 #74]: #76 -#80 := [monotonicity #77]: #79 -#65 := [asserted]: #15 -#83 := [mp #65 #80]: #78 -#659 := (not #752) -#669 := (or #659 #75) -#331 := (* -1::Int -3::Int) -#415 := (* -1::Int 1::Int) -#416 := (mod #415 #331) -#417 := (+ #69 #416) -#408 := (= #417 0::Int) -#419 := (mod 1::Int -3::Int) -#420 := (* -1::Int #419) -#421 := (+ #69 #420) -#418 := (= #421 0::Int) -#422 := (>= 1::Int 0::Int) -#401 := (<= -3::Int 0::Int) -#736 := (or #401 #422) -#738 := (not #736) -#395 := (<= 1::Int 0::Int) -#525 := (or #395 #401) -#732 := (not #525) -#406 := (or #732 #738) -#407 := (ite #406 #418 #408) -#739 := (= #69 0::Int) -#740 := (= 1::Int 0::Int) -#741 := (ite #740 #739 #407) -#742 := (= 1::Int #69) -#737 := (= -3::Int 0::Int) -#743 := (ite #737 #742 #741) -#670 := (or #659 #743) -#667 := (iff #670 #669) -#661 := (iff #669 #669) -#662 := [rewrite]: #661 -#660 := (iff #743 #75) -#734 := (= #69 1::Int) -#677 := (ite false #734 #75) -#579 := (iff #677 #75) -#580 := [rewrite]: #579 -#666 := (iff #743 #677) -#675 := (iff #741 #75) -#582 := (ite false #739 #75) -#585 := (iff #582 #75) -#678 := [rewrite]: #585 -#583 := (iff #741 #582) -#573 := (iff #407 #75) -#562 := (iff #407 #677) -#673 := (iff #408 #75) -#683 := (+ 2::Int #69) -#568 := (= #683 0::Int) -#676 := (iff #568 #75) -#578 := [rewrite]: #676 -#569 := (iff #408 #568) -#685 := (= #417 #683) -#527 := (+ #69 2::Int) -#684 := (= #527 #683) -#682 := [rewrite]: #684 -#680 := (= #417 #527) -#524 := (= #416 2::Int) -#687 := (mod -1::Int 3::Int) -#688 := (= #687 2::Int) -#695 := [rewrite]: #688 -#693 := (= #416 #687) -#692 := (= #331 3::Int) -#686 := [rewrite]: #692 -#705 := (= #415 -1::Int) -#709 := [rewrite]: #705 -#694 := [monotonicity #709 #686]: #693 -#526 := [trans #694 #695]: #524 -#681 := [monotonicity #526]: #680 -#567 := [trans #681 #682]: #685 -#528 := [monotonicity #567]: #569 -#674 := [trans #528 #578]: #673 -#690 := (iff #418 #734) -#696 := (+ -1::Int #69) -#704 := (= #696 0::Int) -#547 := (iff #704 #734) -#689 := [rewrite]: #547 -#545 := (iff #418 #704) -#703 := (= #421 #696) -#699 := (+ #69 -1::Int) -#697 := (= #699 #696) -#702 := [rewrite]: #697 -#700 := (= #421 #699) -#706 := (= #420 -1::Int) -#708 := (= #420 #415) -#429 := (= #419 1::Int) -#707 := [rewrite]: #429 -#423 := [monotonicity #707]: #708 -#710 := [trans #423 #709]: #706 -#701 := [monotonicity #710]: #700 -#698 := [trans #701 #702]: #703 -#546 := [monotonicity #698]: #545 -#691 := [trans #546 #689]: #690 -#427 := (iff #406 false) -#711 := (or false false) -#716 := (iff #711 false) -#426 := [rewrite]: #716 -#715 := (iff #406 #711) -#436 := (iff #738 false) -#1 := true -#726 := (not true) -#729 := (iff #726 false) -#369 := [rewrite]: #729 -#713 := (iff #738 #726) -#443 := (iff #736 true) -#717 := (or true true) -#441 := (iff #717 true) -#442 := [rewrite]: #441 -#718 := (iff #736 #717) -#728 := (iff #422 true) -#731 := [rewrite]: #728 -#383 := (iff #401 true) -#384 := [rewrite]: #383 -#440 := [monotonicity #384 #731]: #718 -#337 := [trans #440 #442]: #443 -#714 := [monotonicity #337]: #713 -#437 := [trans #714 #369]: #436 -#370 := (iff #732 false) -#364 := (iff #732 #726) -#725 := (iff #525 true) -#385 := (or false true) -#723 := (iff #385 true) -#724 := [rewrite]: #723 -#721 := (iff #525 #385) -#719 := (iff #395 false) -#382 := [rewrite]: #719 -#722 := [monotonicity #382 #384]: #721 -#720 := [trans #722 #724]: #725 -#727 := [monotonicity #720]: #364 -#730 := [trans #727 #369]: #370 -#712 := [monotonicity #730 #437]: #715 -#428 := [trans #712 #426]: #427 -#577 := [monotonicity #428 #691 #674]: #562 -#581 := [trans #577 #580]: #573 -#735 := (iff #740 false) -#378 := [rewrite]: #735 -#584 := [monotonicity #378 #581]: #583 -#679 := [trans #584 #678]: #675 -#398 := (iff #742 #734) -#394 := [rewrite]: #398 -#733 := (iff #737 false) -#393 := [rewrite]: #733 -#668 := [monotonicity #393 #394 #679]: #666 -#657 := [trans #668 #580]: #660 -#672 := [monotonicity #657]: #667 -#663 := [trans #672 #662]: #667 -#671 := [quant-inst #8 #66]: #670 -#664 := [mp #671 #663]: #669 -[unit-resolution #664 #83 #757]: false -unsat -e4d7746f48f3d604f4d6994a010e44b10b471dbd 333 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#773 := (pattern #34) -#11 := 0::Int -#104 := -1::Int -#108 := (* -1::Int #15) -#105 := (* -1::Int #14) -#169 := (mod #105 #108) -#284 := (+ #34 #169) -#285 := (= #284 0::Int) -#35 := (mod #14 #15) -#281 := (* -1::Int #35) -#282 := (+ #34 #281) -#283 := (= #282 0::Int) -#143 := (>= #14 0::Int) -#136 := (<= #15 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #14 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #34 0::Int) -#17 := (= #14 0::Int) -#287 := (ite #17 #280 #286) -#279 := (= #14 #34) -#18 := (= #15 0::Int) -#288 := (ite #18 #279 #287) -#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#777 := (iff #291 #774) -#775 := (iff #288 #288) -#776 := [refl]: #775 -#778 := [quant-intro #776]: #777 -#175 := (* -1::Int #169) -#248 := (ite #232 #35 #175) -#251 := (ite #17 0::Int #248) -#254 := (ite #18 #14 #251) -#257 := (= #34 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #35 #175) -#198 := (ite #17 0::Int #195) -#201 := (ite #18 #14 #198) -#204 := (= #34 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#210 := (iff #42 #207) -#98 := (and #21 #23) -#101 := (or #22 #98) -#180 := (ite #101 #35 #175) -#89 := (= 0::Int #14) -#183 := (ite #89 0::Int #180) -#92 := (= 0::Int #15) -#186 := (ite #92 #14 #183) -#189 := (= #34 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #101 #150) -#148 := (iff #98 #147) -#145 := (iff #23 #144) -#146 := [rewrite]: #145 -#138 := (iff #21 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #22 #140) -#134 := (iff #20 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #89 #17) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #92 #18) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #42 #192) -#190 := (iff #41 #189) -#187 := (= #40 #186) -#184 := (= #39 #183) -#181 := (= #38 #180) -#178 := (= #37 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #37 #172) -#170 := (= #36 #169) -#109 := (= #28 #108) -#110 := [rewrite]: #109 -#106 := (= #27 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 +#64 := (= #20 #63) +#65 := [rewrite]: #64 +#71 := [monotonicity #65 #68]: #70 +#74 := [monotonicity #71]: #73 +#79 := [trans #74 #77]: #78 +#60 := (iff #18 #59) +#57 := (iff #17 #56) +#58 := [rewrite]: #57 +#61 := [monotonicity #58]: #60 +#82 := [monotonicity #61 #79]: #81 +#54 := (iff #12 #53) +#55 := [rewrite]: #54 +#85 := [monotonicity #55 #82]: #84 +#51 := (iff #10 false) +#52 := [rewrite]: #51 +#88 := [monotonicity #52 #85]: #87 +#92 := [trans #88 #90]: #91 +#95 := [monotonicity #92]: #94 +#100 := [trans #95 #98]: #99 #103 := [monotonicity #100]: #102 -#182 := [monotonicity #103 #179]: #181 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#185 := [monotonicity #91 #182]: #184 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#188 := [monotonicity #94 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #42 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#779 := [mp #294 #778]: #774 -#63 := -3::Int -#8 := 3::Int -#66 := (f3 3::Int -3::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := (- 3::Int) -#10 := (f3 3::Int #9) -#12 := (= #10 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #10 #66) -#64 := (= #9 -3::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#602 := (not #774) -#595 := (or #602 #69) -#352 := (* -1::Int -3::Int) -#437 := (* -1::Int 3::Int) -#438 := (mod #437 #352) -#439 := (+ #66 #438) -#430 := (= #439 0::Int) -#441 := (mod 3::Int -3::Int) -#442 := (* -1::Int #441) -#370 := (+ #66 #442) -#443 := (= #370 0::Int) -#440 := (>= 3::Int 0::Int) -#444 := (<= -3::Int 0::Int) -#423 := (or #444 #440) -#758 := (not #423) -#760 := (<= 3::Int 0::Int) -#417 := (or #760 #444) -#547 := (not #417) -#754 := (or #547 #758) -#428 := (ite #754 #443 #430) -#429 := (= 3::Int 0::Int) -#761 := (ite #429 #69 #428) -#762 := (= 3::Int #66) -#763 := (= -3::Int 0::Int) -#764 := (ite #763 #762 #761) -#603 := (or #602 #764) -#605 := (iff #603 #595) -#607 := (iff #595 #595) -#700 := [rewrite]: #607 -#599 := (iff #764 #69) -#415 := (= #66 3::Int) -#600 := (ite false #415 #69) -#699 := (iff #600 #69) -#584 := [rewrite]: #699 -#695 := (iff #764 #600) -#550 := (iff #761 #69) -#702 := (ite false #69 #69) -#706 := (iff #702 #69) -#704 := [rewrite]: #706 -#590 := (iff #761 #702) -#707 := (iff #428 #69) -#703 := (iff #428 #702) -#548 := (iff #430 #69) -#717 := (= #439 #66) -#732 := (+ #66 0::Int) -#723 := (= #732 #66) -#718 := [rewrite]: #723 -#716 := (= #439 #732) -#709 := (= #438 0::Int) -#711 := (mod -3::Int 3::Int) -#714 := (= #711 0::Int) -#708 := [rewrite]: #714 -#712 := (= #438 #711) -#568 := (= #352 3::Int) -#569 := [rewrite]: #568 -#726 := (= #437 -3::Int) -#567 := [rewrite]: #726 -#713 := [monotonicity #567 #569]: #712 -#715 := [trans #713 #708]: #709 -#710 := [monotonicity #715]: #716 -#546 := [trans #710 #718]: #717 -#549 := [monotonicity #546]: #548 -#725 := (iff #443 #69) -#719 := (= #370 #66) -#721 := (= #370 #732) -#731 := (= #442 0::Int) -#451 := (* -1::Int 0::Int) -#445 := (= #451 0::Int) -#727 := [rewrite]: #445 -#729 := (= #442 #451) -#449 := (= #441 0::Int) -#450 := [rewrite]: #449 -#730 := [monotonicity #450]: #729 -#728 := [trans #730 #727]: #731 -#722 := [monotonicity #728]: #721 -#724 := [trans #722 #718]: #719 -#720 := [monotonicity #724]: #725 -#738 := (iff #754 false) -#458 := (or false false) -#737 := (iff #458 false) -#734 := [rewrite]: #737 -#459 := (iff #754 #458) -#735 := (iff #758 false) -#1 := true -#747 := (not true) -#386 := (iff #747 false) -#749 := [rewrite]: #386 -#465 := (iff #758 #747) -#463 := (iff #423 true) -#750 := (or true true) -#740 := (iff #750 true) -#462 := [rewrite]: #740 -#753 := (iff #423 #750) -#392 := (iff #440 true) -#752 := [rewrite]: #392 -#741 := (iff #444 true) -#404 := [rewrite]: #741 -#739 := [monotonicity #404 #752]: #753 -#464 := [trans #739 #462]: #463 -#358 := [monotonicity #464]: #465 -#736 := [trans #358 #749]: #735 -#751 := (iff #547 false) -#742 := (iff #547 #747) -#745 := (iff #417 true) -#405 := (or false true) -#743 := (iff #405 true) -#744 := [rewrite]: #743 -#406 := (iff #417 #405) -#757 := (iff #760 false) -#400 := [rewrite]: #757 -#407 := [monotonicity #400 #404]: #406 -#746 := [trans #407 #744]: #745 -#748 := [monotonicity #746]: #742 -#391 := [trans #748 #749]: #751 -#733 := [monotonicity #391 #736]: #459 -#448 := [trans #733 #734]: #738 -#705 := [monotonicity #448 #720 #549]: #703 -#589 := [trans #705 #704]: #707 -#756 := (iff #429 false) -#416 := [rewrite]: #756 -#591 := [monotonicity #416 #589]: #590 -#698 := [trans #591 #704]: #550 -#755 := (iff #762 #415) -#420 := [rewrite]: #755 -#759 := (iff #763 false) -#765 := [rewrite]: #759 -#696 := [monotonicity #765 #420 #698]: #695 -#601 := [trans #696 #584]: #599 -#606 := [monotonicity #601]: #605 -#697 := [trans #606 #700]: #605 -#604 := [quant-inst #8 #63]: #603 -#701 := [mp #604 #697]: #595 -[unit-resolution #701 #87 #779]: false -unsat -62dc22cc0a1f11a224be0520d214fcdfef9b8378 339 0 -#2 := false -decl f3 :: (-> Int Int Int) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#37 := (f3 #16 #17) -#750 := (pattern #37) -#19 := 0::Int -#72 := -1::Int -#92 := (* -1::Int #17) -#89 := (* -1::Int #16) -#147 := (mod #89 #92) -#262 := (+ #37 #147) -#263 := (= #262 0::Int) -#38 := (mod #16 #17) -#259 := (* -1::Int #38) -#260 := (+ #37 #259) -#261 := (= #260 0::Int) -#121 := (>= #16 0::Int) -#114 := (<= #17 0::Int) -#206 := (or #114 #121) -#207 := (not #206) -#110 := (<= #16 0::Int) -#204 := (or #110 #114) -#205 := (not #204) -#210 := (or #205 #207) -#264 := (ite #210 #261 #263) -#258 := (= #37 0::Int) -#20 := (= #16 0::Int) -#265 := (ite #20 #258 #264) -#257 := (= #16 #37) -#21 := (= #17 0::Int) -#266 := (ite #21 #257 #265) -#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #266) -#269 := (forall (vars (?v0 Int) (?v1 Int)) #266) -#754 := (iff #269 #751) -#752 := (iff #266 #266) -#753 := [refl]: #752 -#755 := [quant-intro #753]: #754 -#153 := (* -1::Int #147) -#226 := (ite #210 #38 #153) -#229 := (ite #20 0::Int #226) -#232 := (ite #21 #16 #229) -#235 := (= #37 #232) -#238 := (forall (vars (?v0 Int) (?v1 Int)) #235) -#270 := (iff #238 #269) -#267 := (iff #235 #266) -#268 := [rewrite]: #267 -#271 := [quant-intro #268]: #270 -#122 := (not #121) -#115 := (not #114) -#125 := (and #115 #122) -#111 := (not #110) -#118 := (and #111 #115) -#128 := (or #118 #125) -#173 := (ite #128 #38 #153) -#176 := (ite #20 0::Int #173) -#179 := (ite #21 #16 #176) -#182 := (= #37 #179) -#185 := (forall (vars (?v0 Int) (?v1 Int)) #182) -#239 := (iff #185 #238) -#236 := (iff #182 #235) -#233 := (= #179 #232) -#230 := (= #176 #229) -#227 := (= #173 #226) -#211 := (iff #128 #210) -#208 := (iff #125 #207) -#209 := [rewrite]: #208 -#198 := (iff #118 #205) -#199 := [rewrite]: #198 -#212 := [monotonicity #199 #209]: #211 -#228 := [monotonicity #212]: #227 -#231 := [monotonicity #228]: #230 -#234 := [monotonicity #231]: #233 -#237 := [monotonicity #234]: #236 -#240 := [quant-intro #237]: #239 -#196 := (~ #185 #185) -#195 := (~ #182 #182) -#192 := [refl]: #195 -#197 := [nnf-pos #192]: #196 -#31 := (- #17) -#30 := (- #16) -#39 := (mod #30 #31) -#40 := (- #39) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#41 := (ite #28 #38 #40) -#42 := (ite #20 0::Int #41) -#43 := (ite #21 #16 #42) -#44 := (= #37 #43) -#45 := (forall (vars (?v0 Int) (?v1 Int)) #44) -#188 := (iff #45 #185) -#82 := (and #24 #26) -#86 := (or #25 #82) -#158 := (ite #86 #38 #153) -#161 := (ite #20 0::Int #158) -#164 := (ite #21 #16 #161) -#167 := (= #37 #164) -#170 := (forall (vars (?v0 Int) (?v1 Int)) #167) -#186 := (iff #170 #185) -#183 := (iff #167 #182) -#180 := (= #164 #179) -#177 := (= #161 #176) -#174 := (= #158 #173) -#129 := (iff #86 #128) -#126 := (iff #82 #125) -#123 := (iff #26 #122) -#124 := [rewrite]: #123 -#116 := (iff #24 #115) -#117 := [rewrite]: #116 -#127 := [monotonicity #117 #124]: #126 -#119 := (iff #25 #118) -#112 := (iff #23 #111) -#113 := [rewrite]: #112 -#120 := [monotonicity #113 #117]: #119 -#130 := [monotonicity #120 #127]: #129 -#175 := [monotonicity #130]: #174 -#178 := [monotonicity #175]: #177 -#181 := [monotonicity #178]: #180 -#184 := [monotonicity #181]: #183 -#187 := [quant-intro #184]: #186 -#171 := (iff #45 #170) -#168 := (iff #44 #167) -#165 := (= #43 #164) -#162 := (= #42 #161) -#159 := (= #41 #158) -#156 := (= #40 #153) -#150 := (- #147) -#154 := (= #150 #153) +#109 := [trans #103 #107]: #108 +#112 := [monotonicity #109]: #111 +#165 := [trans #112 #163]: #164 +#50 := [asserted]: #30 +#166 := [mp #50 #165]: #161 +#167 := [not-or-elim #166]: #113 +#251 := (or #120 #114) +#252 := [th-lemma arith farkas 1 1]: #251 +#253 := [unit-resolution #252 #167]: #120 +#174 := (or #143 #119) +#175 := [def-axiom]: #174 +#258 := [unit-resolution #175 #253]: #143 +#170 := (not #143) +#181 := (or #170 #178) +#182 := [def-axiom]: #181 +#259 := [unit-resolution #182 #258]: #178 +#263 := [symm #259]: #262 +#264 := (= f3 #146) +#260 := (= #149 #146) +#177 := (= #146 #149) +#185 := (not #12) +#254 := (or #185 #119) +#255 := [th-lemma arith triangle-eq]: #254 +#256 := [unit-resolution #255 #253]: #185 +#188 := (or #12 #177) +#189 := [def-axiom]: #188 +#257 := [unit-resolution #189 #256]: #177 +#261 := [symm #257]: #260 +#168 := [not-or-elim #166]: #152 +#265 := [trans #168 #261]: #264 +#266 := [trans #265 #263]: #244 +#267 := (not #244) +#268 := (or #267 #246) +#269 := [th-lemma arith triangle-eq]: #268 +#270 := [unit-resolution #269 #266]: #246 +[th-lemma arith farkas -1 1 1 #167 #270 #250]: false +unsat +b0d0143b1d623c3b7e34600e7103453eafcbef9f 326 0 +#2 := false +#9 := 0::Int +#71 := -1::Int +decl f3 :: Int +#8 := f3 +#72 := (* -1::Int f3) +#95 := (mod #72 -1::Int) +#101 := (* -1::Int #95) +#147 := (>= f3 0::Int) +#148 := (not #147) +#134 := (<= f3 0::Int) +#135 := (not #134) +#10 := (= f3 0::Int) +#170 := (or #10 #135 #148) +#175 := (ite #170 0::Int #101) +#288 := (<= #175 0::Int) +#220 := (= #175 0::Int) +#215 := (not #10) +#228 := (not #170) +#375 := [hypothesis]: #228 +#222 := (or #170 #215) +#223 := [def-axiom]: #222 +#376 := [unit-resolution #223 #375]: #215 +#226 := (or #170 #147) +#227 := [def-axiom]: #226 +#377 := [unit-resolution #227 #375]: #147 +#378 := (or #10 #148) +#185 := (* -1::Int #175) +#77 := (div #72 -1::Int) +#11 := 1::Int +#20 := (div f3 1::Int) +#158 := (or #135 #148) +#161 := (ite #158 #20 #77) +#164 := (ite #10 0::Int #161) +#184 := (* -1::Int #164) +#186 := (+ #184 #185) +#187 := (+ f3 #186) +#236 := (>= #187 0::Int) +#291 := (+ #20 #184) +#293 := (>= #291 0::Int) +#290 := (= #20 #164) +#205 := (= #161 #164) +#294 := [hypothesis]: #135 +#295 := (or #215 #134) +#296 := [th-lemma arith triangle-eq]: #295 +#297 := [unit-resolution #296 #294]: #215 +#218 := (or #10 #205) +#219 := [def-axiom]: #218 +#298 := [unit-resolution #219 #297]: #205 +#206 := (= #20 #161) +#202 := (or #158 #134) +#203 := [def-axiom]: #202 +#299 := [unit-resolution #203 #294]: #158 +#208 := (not #158) +#211 := (or #208 #206) +#212 := [def-axiom]: #211 +#300 := [unit-resolution #212 #299]: #206 +#301 := [trans #300 #298]: #290 +#302 := (not #290) +#303 := (or #302 #293) +#304 := [th-lemma arith triangle-eq]: #303 +#305 := [unit-resolution #304 #301]: #293 +#224 := (or #170 #134) +#225 := [def-axiom]: #224 +#306 := [unit-resolution #225 #294]: #170 +#231 := (or #228 #220) +#232 := [def-axiom]: #231 +#307 := [unit-resolution #232 #306]: #220 +#308 := (not #220) +#309 := (or #308 #288) +#310 := [th-lemma arith triangle-eq]: #309 +#311 := [unit-resolution #310 #307]: #288 +#258 := (* -1::Int #20) +#259 := (+ f3 #258) +#265 := (>= #259 0::Int) +#257 := (= #259 0::Int) +#1 := true +#53 := [true-axiom]: true +#312 := (or false #257) +#313 := [th-lemma arith]: #312 +#314 := [unit-resolution #313 #53]: #257 +#315 := (not #257) +#316 := (or #315 #265) +#317 := [th-lemma arith triangle-eq]: #316 +#318 := [unit-resolution #317 #314]: #265 +#321 := (not #265) +#320 := (not #293) +#319 := (not #288) +#322 := (or #236 #319 #320 #321) +#323 := [th-lemma arith assign-bounds 1 -1 -1]: #322 +#324 := [unit-resolution #323 #318 #311 #305]: #236 +#235 := (<= #187 0::Int) +#292 := (<= #291 0::Int) +#325 := (or #302 #292) +#326 := [th-lemma arith triangle-eq]: #325 +#327 := [unit-resolution #326 #301]: #292 +#289 := (>= #175 0::Int) +#328 := (or #308 #289) +#329 := [th-lemma arith triangle-eq]: #328 +#330 := [unit-resolution #329 #307]: #289 +#264 := (<= #259 0::Int) +#331 := (or #315 #264) +#332 := [th-lemma arith triangle-eq]: #331 +#333 := [unit-resolution #332 #314]: #264 +#336 := (not #264) +#335 := (not #292) +#334 := (not #289) +#337 := (or #235 #334 #335 #336) +#338 := [th-lemma arith assign-bounds 1 -1 -1]: #337 +#339 := [unit-resolution #338 #333 #330 #327]: #235 +#341 := (not #236) +#340 := (not #235) +#344 := (or #340 #341) +#188 := (= #187 0::Int) +#193 := (not #188) +#22 := (- 1::Int) +#21 := (- f3) +#28 := (mod #21 #22) +#29 := (- #28) +#27 := (mod f3 1::Int) +#15 := (< 0::Int 1::Int) +#17 := (< f3 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int f3) +#16 := (and #14 #15) +#19 := (or #16 #18) +#30 := (ite #19 #27 #29) +#31 := (ite #10 0::Int #30) +#12 := (= 1::Int 0::Int) +#32 := (ite #12 f3 #31) +#23 := (div #21 #22) +#24 := (ite #19 #20 #23) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (* #25 1::Int) +#33 := (+ #26 #32) +#34 := (= f3 #33) +#35 := (not #34) +#196 := (iff #35 #193) +#65 := (and #15 #17) +#68 := (or #16 #65) +#112 := (or #10 #68) +#113 := (ite #112 0::Int #101) +#80 := (ite #68 #20 #77) +#83 := (ite #10 0::Int #80) +#125 := (+ #83 #113) +#128 := (= f3 #125) +#131 := (not #128) +#194 := (iff #131 #193) +#191 := (iff #128 #188) +#178 := (+ #164 #175) +#181 := (= f3 #178) +#189 := (iff #181 #188) +#190 := [rewrite]: #189 +#182 := (iff #128 #181) +#179 := (= #125 #178) +#176 := (= #113 #175) +#173 := (iff #112 #170) +#167 := (or #10 #158) +#171 := (iff #167 #170) +#172 := [rewrite]: #171 +#168 := (iff #112 #167) +#159 := (iff #68 #158) +#156 := (iff #65 #148) +#151 := (and true #148) +#154 := (iff #151 #148) #155 := [rewrite]: #154 -#151 := (= #40 #150) -#148 := (= #39 #147) -#93 := (= #31 #92) -#94 := [rewrite]: #93 -#90 := (= #30 #89) -#91 := [rewrite]: #90 -#149 := [monotonicity #91 #94]: #148 -#152 := [monotonicity #149]: #151 -#157 := [trans #152 #155]: #156 -#87 := (iff #28 #86) -#84 := (iff #27 #82) -#85 := [rewrite]: #84 -#88 := [monotonicity #85]: #87 -#160 := [monotonicity #88 #157]: #159 +#152 := (iff #65 #151) +#149 := (iff #17 #148) +#150 := [rewrite]: #149 +#138 := (iff #15 true) +#139 := [rewrite]: #138 +#153 := [monotonicity #139 #150]: #152 +#157 := [trans #153 #155]: #156 +#145 := (iff #16 #135) +#140 := (and #135 true) +#143 := (iff #140 #135) +#144 := [rewrite]: #143 +#141 := (iff #16 #140) +#136 := (iff #14 #135) +#137 := [rewrite]: #136 +#142 := [monotonicity #137 #139]: #141 +#146 := [trans #142 #144]: #145 +#160 := [monotonicity #146 #157]: #159 +#169 := [monotonicity #160]: #168 +#174 := [trans #169 #172]: #173 +#177 := [monotonicity #174]: #176 +#165 := (= #83 #164) +#162 := (= #80 #161) #163 := [monotonicity #160]: #162 #166 := [monotonicity #163]: #165 -#169 := [monotonicity #166]: #168 -#172 := [quant-intro #169]: #171 -#189 := [trans #172 #187]: #188 -#146 := [asserted]: #45 -#190 := [mp #146 #189]: #185 -#193 := [mp~ #190 #197]: #185 -#241 := [mp #193 #240]: #238 -#272 := [mp #241 #271]: #269 -#756 := [mp #272 #755]: #751 -#66 := -3::Int -#8 := 5::Int -#69 := (f3 5::Int -3::Int) -#75 := (= #69 -1::Int) -#78 := (not #75) -#12 := 1::Int -#13 := (- 1::Int) -#9 := 3::Int -#10 := (- 3::Int) -#11 := (f3 5::Int #10) -#14 := (= #11 #13) -#15 := (not #14) -#79 := (iff #15 #78) -#76 := (iff #14 #75) -#73 := (= #13 -1::Int) -#74 := [rewrite]: #73 -#70 := (= #11 #69) -#67 := (= #10 -3::Int) -#68 := [rewrite]: #67 -#71 := [monotonicity #68]: #70 -#77 := [monotonicity #71 #74]: #76 -#80 := [monotonicity #77]: #79 -#65 := [asserted]: #15 -#83 := [mp #65 #80]: #78 -#657 := (not #751) -#664 := (or #657 #75) -#330 := (* -1::Int -3::Int) -#414 := (* -1::Int 5::Int) -#415 := (mod #414 #330) -#416 := (+ #69 #415) -#407 := (= #416 0::Int) -#418 := (mod 5::Int -3::Int) -#419 := (* -1::Int #418) -#420 := (+ #69 #419) -#417 := (= #420 0::Int) -#421 := (>= 5::Int 0::Int) -#400 := (<= -3::Int 0::Int) -#735 := (or #400 #421) -#737 := (not #735) -#394 := (<= 5::Int 0::Int) -#524 := (or #394 #400) -#731 := (not #524) -#405 := (or #731 #737) -#406 := (ite #405 #417 #407) -#738 := (= #69 0::Int) -#739 := (= 5::Int 0::Int) -#740 := (ite #739 #738 #406) -#741 := (= 5::Int #69) -#736 := (= -3::Int 0::Int) -#742 := (ite #736 #741 #740) -#648 := (or #657 #742) -#651 := (iff #648 #664) -#653 := (iff #664 #664) -#654 := [rewrite]: #653 -#662 := (iff #742 #75) -#733 := (= #69 5::Int) -#670 := (ite false #733 #75) -#660 := (iff #670 #75) -#661 := [rewrite]: #660 -#666 := (iff #742 #670) -#668 := (iff #740 #75) -#665 := (ite false #738 #75) -#656 := (iff #665 #75) -#658 := [rewrite]: #656 -#667 := (iff #740 #665) -#674 := (iff #406 #75) -#428 := 2::Int -#690 := (= #69 2::Int) -#581 := (ite false #690 #75) -#584 := (iff #581 #75) -#677 := [rewrite]: #584 -#582 := (iff #406 #581) -#572 := (iff #407 #75) -#527 := (+ 1::Int #69) -#676 := (= #527 0::Int) -#578 := (iff #676 #75) -#579 := [rewrite]: #578 -#561 := (iff #407 #676) -#672 := (= #416 #527) -#566 := (+ #69 1::Int) -#675 := (= #566 #527) -#577 := [rewrite]: #675 -#567 := (= #416 #566) -#681 := (= #415 1::Int) -#693 := -5::Int -#526 := (mod -5::Int 3::Int) -#682 := (= #526 1::Int) -#683 := [rewrite]: #682 -#679 := (= #415 #526) -#523 := (= #330 3::Int) -#525 := [rewrite]: #523 -#687 := (= #414 -5::Int) -#694 := [rewrite]: #687 -#680 := [monotonicity #694 #525]: #679 -#684 := [trans #680 #683]: #681 -#568 := [monotonicity #684]: #567 -#673 := [trans #568 #577]: #672 -#576 := [monotonicity #673]: #561 -#580 := [trans #576 #579]: #572 -#686 := (iff #417 #690) -#705 := -2::Int -#702 := (+ -2::Int #69) -#546 := (= #702 0::Int) -#691 := (iff #546 #690) -#685 := [rewrite]: #691 -#688 := (iff #417 #546) -#544 := (= #420 #702) -#695 := (+ #69 -2::Int) -#697 := (= #695 #702) -#703 := [rewrite]: #697 -#696 := (= #420 #695) -#699 := (= #419 -2::Int) -#422 := (* -1::Int 2::Int) -#709 := (= #422 -2::Int) -#698 := [rewrite]: #709 -#704 := (= #419 #422) -#706 := (= #418 2::Int) -#707 := [rewrite]: #706 -#708 := [monotonicity #707]: #704 -#700 := [trans #708 #698]: #699 -#701 := [monotonicity #700]: #696 -#545 := [trans #701 #703]: #544 -#689 := [monotonicity #545]: #688 -#692 := [trans #689 #685]: #686 -#426 := (iff #405 false) -#710 := (or false false) -#715 := (iff #710 false) -#425 := [rewrite]: #715 -#714 := (iff #405 #710) -#435 := (iff #737 false) -#1 := true -#725 := (not true) -#728 := (iff #725 false) -#368 := [rewrite]: #728 -#712 := (iff #737 #725) -#442 := (iff #735 true) -#716 := (or true true) -#440 := (iff #716 true) -#441 := [rewrite]: #440 -#717 := (iff #735 #716) -#727 := (iff #421 true) -#730 := [rewrite]: #727 -#382 := (iff #400 true) -#383 := [rewrite]: #382 -#439 := [monotonicity #383 #730]: #717 -#336 := [trans #439 #441]: #442 -#713 := [monotonicity #336]: #712 -#436 := [trans #713 #368]: #435 -#369 := (iff #731 false) -#363 := (iff #731 #725) -#724 := (iff #524 true) -#384 := (or false true) -#722 := (iff #384 true) -#723 := [rewrite]: #722 -#720 := (iff #524 #384) -#718 := (iff #394 false) -#381 := [rewrite]: #718 -#721 := [monotonicity #381 #383]: #720 -#719 := [trans #721 #723]: #724 -#726 := [monotonicity #719]: #363 -#729 := [trans #726 #368]: #369 -#711 := [monotonicity #729 #436]: #714 -#427 := [trans #711 #425]: #426 -#583 := [monotonicity #427 #692 #580]: #582 -#678 := [trans #583 #677]: #674 -#734 := (iff #739 false) -#377 := [rewrite]: #734 -#659 := [monotonicity #377 #678]: #667 -#669 := [trans #659 #658]: #668 -#397 := (iff #741 #733) -#393 := [rewrite]: #397 -#732 := (iff #736 false) -#392 := [rewrite]: #732 -#671 := [monotonicity #392 #393 #669]: #666 -#663 := [trans #671 #661]: #662 -#652 := [monotonicity #663]: #651 -#650 := [trans #652 #654]: #651 -#649 := [quant-inst #8 #66]: #648 -#655 := [mp #649 #650]: #664 -[unit-resolution #655 #83 #756]: false -unsat -5d7ad299834cafeb0e7528443dd40353cb086137 348 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#36 := (f3 #15 #16) -#758 := (pattern #36) -#18 := 0::Int -#65 := -1::Int -#100 := (* -1::Int #16) -#97 := (* -1::Int #15) -#155 := (mod #97 #100) -#270 := (+ #36 #155) -#271 := (= #270 0::Int) -#37 := (mod #15 #16) -#267 := (* -1::Int #37) -#268 := (+ #36 #267) -#269 := (= #268 0::Int) -#129 := (>= #15 0::Int) -#122 := (<= #16 0::Int) -#214 := (or #122 #129) -#215 := (not #214) -#118 := (<= #15 0::Int) -#212 := (or #118 #122) -#213 := (not #212) -#218 := (or #213 #215) -#272 := (ite #218 #269 #271) -#266 := (= #36 0::Int) -#19 := (= #15 0::Int) -#273 := (ite #19 #266 #272) -#265 := (= #15 #36) -#20 := (= #16 0::Int) -#274 := (ite #20 #265 #273) -#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #274) -#277 := (forall (vars (?v0 Int) (?v1 Int)) #274) -#762 := (iff #277 #759) -#760 := (iff #274 #274) -#761 := [refl]: #760 -#763 := [quant-intro #761]: #762 -#161 := (* -1::Int #155) -#234 := (ite #218 #37 #161) -#237 := (ite #19 0::Int #234) -#240 := (ite #20 #15 #237) -#243 := (= #36 #240) -#246 := (forall (vars (?v0 Int) (?v1 Int)) #243) -#278 := (iff #246 #277) -#275 := (iff #243 #274) -#276 := [rewrite]: #275 -#279 := [quant-intro #276]: #278 -#130 := (not #129) -#123 := (not #122) -#133 := (and #123 #130) -#119 := (not #118) -#126 := (and #119 #123) -#136 := (or #126 #133) -#181 := (ite #136 #37 #161) -#184 := (ite #19 0::Int #181) -#187 := (ite #20 #15 #184) -#190 := (= #36 #187) -#193 := (forall (vars (?v0 Int) (?v1 Int)) #190) -#247 := (iff #193 #246) -#244 := (iff #190 #243) -#241 := (= #187 #240) -#238 := (= #184 #237) -#235 := (= #181 #234) -#219 := (iff #136 #218) -#216 := (iff #133 #215) -#217 := [rewrite]: #216 -#206 := (iff #126 #213) -#207 := [rewrite]: #206 -#220 := [monotonicity #207 #217]: #219 -#236 := [monotonicity #220]: #235 -#239 := [monotonicity #236]: #238 -#242 := [monotonicity #239]: #241 -#245 := [monotonicity #242]: #244 -#248 := [quant-intro #245]: #247 -#204 := (~ #193 #193) -#203 := (~ #190 #190) -#200 := [refl]: #203 -#205 := [nnf-pos #200]: #204 -#30 := (- #16) -#29 := (- #15) -#38 := (mod #29 #30) -#39 := (- #38) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#40 := (ite #27 #37 #39) -#41 := (ite #19 0::Int #40) -#42 := (ite #20 #15 #41) -#43 := (= #36 #42) -#44 := (forall (vars (?v0 Int) (?v1 Int)) #43) -#196 := (iff #44 #193) -#91 := (and #23 #25) -#94 := (or #24 #91) -#166 := (ite #94 #37 #161) -#169 := (ite #19 0::Int #166) -#172 := (ite #20 #15 #169) -#175 := (= #36 #172) -#178 := (forall (vars (?v0 Int) (?v1 Int)) #175) -#194 := (iff #178 #193) -#191 := (iff #175 #190) -#188 := (= #172 #187) -#185 := (= #169 #184) -#182 := (= #166 #181) -#137 := (iff #94 #136) -#134 := (iff #91 #133) -#131 := (iff #25 #130) -#132 := [rewrite]: #131 -#124 := (iff #23 #123) -#125 := [rewrite]: #124 -#135 := [monotonicity #125 #132]: #134 -#127 := (iff #24 #126) -#120 := (iff #22 #119) -#121 := [rewrite]: #120 -#128 := [monotonicity #121 #125]: #127 -#138 := [monotonicity #128 #135]: #137 -#183 := [monotonicity #138]: #182 -#186 := [monotonicity #183]: #185 -#189 := [monotonicity #186]: #188 -#192 := [monotonicity #189]: #191 -#195 := [quant-intro #192]: #194 -#179 := (iff #44 #178) -#176 := (iff #43 #175) -#173 := (= #42 #172) -#170 := (= #41 #169) -#167 := (= #40 #166) -#164 := (= #39 #161) -#158 := (- #155) -#162 := (= #158 #161) -#163 := [rewrite]: #162 -#159 := (= #39 #158) -#156 := (= #38 #155) -#101 := (= #30 #100) -#102 := [rewrite]: #101 -#98 := (= #29 #97) -#99 := [rewrite]: #98 -#157 := [monotonicity #99 #102]: #156 -#160 := [monotonicity #157]: #159 -#165 := [trans #160 #163]: #164 -#95 := (iff #27 #94) -#92 := (iff #26 #91) -#93 := [rewrite]: #92 -#96 := [monotonicity #93]: #95 -#168 := [monotonicity #96 #165]: #167 -#171 := [monotonicity #168]: #170 -#174 := [monotonicity #171]: #173 -#177 := [monotonicity #174]: #176 -#180 := [quant-intro #177]: #179 -#197 := [trans #180 #195]: #196 -#154 := [asserted]: #44 -#198 := [mp #154 #197]: #193 -#201 := [mp~ #198 #205]: #193 -#249 := [mp #201 #248]: #246 -#280 := [mp #249 #279]: #277 -#764 := [mp #280 #763]: #759 -#12 := 2::Int -#10 := 3::Int -#68 := (f3 -1::Int 3::Int) -#71 := (= #68 2::Int) -#84 := (not #71) -#8 := 1::Int -#9 := (- 1::Int) -#11 := (f3 #9 3::Int) -#13 := (= #11 2::Int) -#14 := (not #13) -#87 := (iff #14 #84) -#74 := (= 2::Int #68) -#79 := (not #74) -#85 := (iff #79 #84) -#82 := (iff #74 #71) -#83 := [rewrite]: #82 -#86 := [monotonicity #83]: #85 -#80 := (iff #14 #79) -#77 := (iff #13 #74) -#75 := (iff #71 #74) -#76 := [rewrite]: #75 -#72 := (iff #13 #71) -#69 := (= #11 #68) -#66 := (= #9 -1::Int) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#73 := [monotonicity #70]: #72 -#78 := [trans #73 #76]: #77 -#81 := [monotonicity #78]: #80 -#88 := [trans #81 #86]: #87 -#64 := [asserted]: #14 -#89 := [mp #64 #88]: #84 -#672 := (not #759) -#656 := (or #672 #71) -#338 := (* -1::Int 3::Int) -#422 := (* -1::Int -1::Int) -#423 := (mod #422 #338) -#424 := (+ #68 #423) -#415 := (= #424 0::Int) -#426 := (mod -1::Int 3::Int) -#427 := (* -1::Int #426) -#428 := (+ #68 #427) -#425 := (= #428 0::Int) -#429 := (>= -1::Int 0::Int) -#408 := (<= 3::Int 0::Int) -#743 := (or #408 #429) -#745 := (not #743) -#402 := (<= -1::Int 0::Int) -#532 := (or #402 #408) -#739 := (not #532) -#413 := (or #739 #745) -#414 := (ite #413 #425 #415) -#746 := (= #68 0::Int) -#747 := (= -1::Int 0::Int) -#748 := (ite #747 #746 #414) -#749 := (= -1::Int #68) -#744 := (= 3::Int 0::Int) -#750 := (ite #744 #749 #748) -#657 := (or #672 #750) -#660 := (iff #657 #656) -#662 := (iff #656 #656) -#658 := [rewrite]: #662 -#671 := (iff #750 #71) -#741 := (= #68 -1::Int) -#674 := (ite false #741 #71) -#669 := (iff #674 #71) -#670 := [rewrite]: #669 -#679 := (iff #750 #674) -#677 := (iff #748 #71) -#675 := (ite false #746 #71) -#666 := (iff #675 #71) -#676 := [rewrite]: #666 -#667 := (iff #748 #675) -#686 := (iff #414 #71) -#1 := true -#590 := (ite true #71 #741) -#685 := (iff #590 #71) -#682 := [rewrite]: #685 -#591 := (iff #414 #590) -#588 := (iff #415 #741) -#683 := (+ 1::Int #68) -#569 := (= #683 0::Int) -#587 := (iff #569 #741) -#580 := [rewrite]: #587 -#584 := (iff #415 #569) -#681 := (= #424 #683) -#575 := (+ #68 1::Int) -#585 := (= #575 #683) -#680 := [rewrite]: #585 -#576 := (= #424 #575) -#692 := (= #423 1::Int) -#531 := -3::Int -#687 := (mod 1::Int -3::Int) -#691 := (= #687 1::Int) -#689 := [rewrite]: #691 -#688 := (= #423 #687) -#533 := (= #338 -3::Int) -#534 := [rewrite]: #533 -#695 := (= #422 1::Int) -#702 := [rewrite]: #695 -#690 := [monotonicity #702 #534]: #688 -#574 := [trans #690 #689]: #692 -#535 := [monotonicity #574]: #576 -#684 := [trans #535 #680]: #681 -#586 := [monotonicity #684]: #584 -#589 := [trans #586 #580]: #588 -#700 := (iff #425 #71) -#706 := -2::Int -#711 := (+ -2::Int #68) -#697 := (= #711 0::Int) -#693 := (iff #697 #71) -#694 := [rewrite]: #693 -#698 := (iff #425 #697) -#554 := (= #428 #711) -#709 := (+ #68 -2::Int) -#552 := (= #709 #711) -#553 := [rewrite]: #552 -#710 := (= #428 #709) -#703 := (= #427 -2::Int) -#716 := (* -1::Int 2::Int) -#707 := (= #716 -2::Int) -#708 := [rewrite]: #707 -#713 := (= #427 #716) -#430 := (= #426 2::Int) -#712 := [rewrite]: #430 -#717 := [monotonicity #712]: #713 -#704 := [trans #717 #708]: #703 -#705 := [monotonicity #704]: #710 -#696 := [trans #705 #553]: #554 -#699 := [monotonicity #696]: #698 -#701 := [trans #699 #694]: #700 -#714 := (iff #413 true) -#723 := (or false true) -#435 := (iff #723 true) -#436 := [rewrite]: #435 -#433 := (iff #413 #723) -#722 := (iff #745 true) -#720 := (not false) -#444 := (iff #720 true) -#718 := [rewrite]: #444 -#721 := (iff #745 #720) -#450 := (iff #743 false) -#724 := (or false false) -#448 := (iff #724 false) -#449 := [rewrite]: #448 -#725 := (iff #743 #724) -#735 := (iff #429 false) -#738 := [rewrite]: #735 -#390 := (iff #408 false) -#391 := [rewrite]: #390 -#447 := [monotonicity #391 #738]: #725 -#344 := [trans #447 #449]: #450 -#443 := [monotonicity #344]: #721 -#719 := [trans #443 #718]: #722 -#377 := (iff #739 false) -#733 := (not true) -#736 := (iff #733 false) -#376 := [rewrite]: #736 -#371 := (iff #739 #733) -#732 := (iff #532 true) -#392 := (or true false) -#730 := (iff #392 true) -#731 := [rewrite]: #730 -#728 := (iff #532 #392) -#726 := (iff #402 true) -#389 := [rewrite]: #726 -#729 := [monotonicity #389 #391]: #728 -#727 := [trans #729 #731]: #732 -#734 := [monotonicity #727]: #371 -#737 := [trans #734 #376]: #377 -#434 := [monotonicity #737 #719]: #433 -#715 := [trans #434 #436]: #714 -#592 := [monotonicity #715 #701 #589]: #591 -#673 := [trans #592 #682]: #686 -#742 := (iff #747 false) -#385 := [rewrite]: #742 -#664 := [monotonicity #385 #673]: #667 -#678 := [trans #664 #676]: #677 -#405 := (iff #749 #741) -#401 := [rewrite]: #405 -#740 := (iff #744 false) -#400 := [rewrite]: #740 -#668 := [monotonicity #400 #401 #678]: #679 -#665 := [trans #668 #670]: #671 -#661 := [monotonicity #665]: #660 -#663 := [trans #661 #658]: #660 -#659 := [quant-inst #65 #10]: #657 -#649 := [mp #659 #663]: #656 -[unit-resolution #649 #89 #764]: false -unsat -513cb6376361794229c618f4dacebc2dcd3ef34a 339 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#773 := (pattern #34) -#11 := 0::Int -#104 := -1::Int -#108 := (* -1::Int #15) -#105 := (* -1::Int #14) -#169 := (mod #105 #108) -#284 := (+ #34 #169) -#285 := (= #284 0::Int) -#35 := (mod #14 #15) -#281 := (* -1::Int #35) -#282 := (+ #34 #281) -#283 := (= #282 0::Int) -#143 := (>= #14 0::Int) -#136 := (<= #15 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #14 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #34 0::Int) -#17 := (= #14 0::Int) -#287 := (ite #17 #280 #286) -#279 := (= #14 #34) -#18 := (= #15 0::Int) -#288 := (ite #18 #279 #287) -#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#777 := (iff #291 #774) -#775 := (iff #288 #288) -#776 := [refl]: #775 -#778 := [quant-intro #776]: #777 -#175 := (* -1::Int #169) -#248 := (ite #232 #35 #175) -#251 := (ite #17 0::Int #248) -#254 := (ite #18 #14 #251) -#257 := (= #34 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #35 #175) -#198 := (ite #17 0::Int #195) -#201 := (ite #18 #14 #198) -#204 := (= #34 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#210 := (iff #42 #207) -#98 := (and #21 #23) -#101 := (or #22 #98) -#180 := (ite #101 #35 #175) -#89 := (= 0::Int #14) -#183 := (ite #89 0::Int #180) -#92 := (= 0::Int #15) -#186 := (ite #92 #14 #183) -#189 := (= #34 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #101 #150) -#148 := (iff #98 #147) -#145 := (iff #23 #144) -#146 := [rewrite]: #145 -#138 := (iff #21 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #22 #140) -#134 := (iff #20 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #89 #17) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #92 #18) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #42 #192) -#190 := (iff #41 #189) -#187 := (= #40 #186) -#184 := (= #39 #183) -#181 := (= #38 #180) -#178 := (= #37 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #37 #172) -#170 := (= #36 #169) -#109 := (= #28 #108) -#110 := [rewrite]: #109 -#106 := (= #27 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#182 := [monotonicity #103 #179]: #181 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#185 := [monotonicity #91 #182]: #184 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#188 := [monotonicity #94 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #42 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#779 := [mp #294 #778]: #774 -#8 := 3::Int -#63 := -3::Int -#66 := (f3 -3::Int 3::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#9 := (- 3::Int) -#10 := (f3 #9 3::Int) -#12 := (= #10 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #10 #66) -#64 := (= #9 -3::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#607 := (not #774) -#700 := (or #607 #69) -#352 := (* -1::Int 3::Int) -#437 := (* -1::Int -3::Int) -#438 := (mod #437 #352) -#439 := (+ #66 #438) -#430 := (= #439 0::Int) -#441 := (mod -3::Int 3::Int) -#442 := (* -1::Int #441) -#370 := (+ #66 #442) -#443 := (= #370 0::Int) -#440 := (>= -3::Int 0::Int) -#444 := (<= 3::Int 0::Int) -#423 := (or #444 #440) -#758 := (not #423) -#760 := (<= -3::Int 0::Int) -#417 := (or #760 #444) -#547 := (not #417) -#754 := (or #547 #758) -#428 := (ite #754 #443 #430) -#429 := (= -3::Int 0::Int) -#761 := (ite #429 #69 #428) -#762 := (= -3::Int #66) -#763 := (= 3::Int 0::Int) -#764 := (ite #763 #762 #761) -#697 := (or #607 #764) -#688 := (iff #697 #700) -#682 := (iff #700 #700) -#679 := [rewrite]: #682 -#605 := (iff #764 #69) -#415 := (= #66 -3::Int) -#601 := (ite false #415 #69) -#603 := (iff #601 #69) -#604 := [rewrite]: #603 -#602 := (iff #764 #601) -#584 := (iff #761 #69) -#698 := (ite false #69 #69) -#696 := (iff #698 #69) -#699 := [rewrite]: #696 -#600 := (iff #761 #698) -#591 := (iff #428 #69) -#1 := true -#706 := (ite true #69 #69) -#589 := (iff #706 #69) -#590 := [rewrite]: #589 -#704 := (iff #428 #706) -#703 := (iff #430 #69) -#549 := (= #439 #66) -#723 := (+ #66 0::Int) -#724 := (= #723 #66) -#725 := [rewrite]: #724 -#546 := (= #439 #723) -#710 := (= #438 0::Int) -#714 := (mod 3::Int -3::Int) -#715 := (= #714 0::Int) -#716 := [rewrite]: #715 -#708 := (= #438 #714) -#712 := (= #352 -3::Int) -#713 := [rewrite]: #712 -#569 := (= #437 3::Int) -#711 := [rewrite]: #569 -#709 := [monotonicity #711 #713]: #708 -#717 := [trans #709 #716]: #710 -#548 := [monotonicity #717]: #546 -#702 := [trans #548 #725]: #549 -#705 := [monotonicity #702]: #703 -#567 := (iff #443 #69) -#720 := (= #370 #66) -#718 := (= #370 #723) -#721 := (= #442 0::Int) -#445 := (* -1::Int 0::Int) -#728 := (= #445 0::Int) -#732 := [rewrite]: #728 -#727 := (= #442 #445) -#729 := (= #441 0::Int) -#730 := [rewrite]: #729 -#731 := [monotonicity #730]: #727 -#722 := [trans #731 #732]: #721 -#719 := [monotonicity #722]: #718 -#726 := [trans #719 #725]: #720 -#568 := [monotonicity #726]: #567 -#450 := (iff #754 true) -#737 := (or false true) -#448 := (iff #737 true) -#449 := [rewrite]: #448 -#734 := (iff #754 #737) -#459 := (iff #758 true) -#465 := (not false) -#736 := (iff #465 true) -#458 := [rewrite]: #736 -#358 := (iff #758 #465) -#463 := (iff #423 false) -#750 := (or false false) -#740 := (iff #750 false) -#462 := [rewrite]: #740 -#753 := (iff #423 #750) -#392 := (iff #440 false) -#752 := [rewrite]: #392 -#741 := (iff #444 false) -#404 := [rewrite]: #741 -#739 := [monotonicity #404 #752]: #753 -#464 := [trans #739 #462]: #463 -#735 := [monotonicity #464]: #358 -#733 := [trans #735 #458]: #459 -#751 := (iff #547 false) -#747 := (not true) -#386 := (iff #747 false) -#749 := [rewrite]: #386 -#742 := (iff #547 #747) -#745 := (iff #417 true) -#405 := (or true false) -#743 := (iff #405 true) -#744 := [rewrite]: #743 -#406 := (iff #417 #405) -#757 := (iff #760 true) -#400 := [rewrite]: #757 -#407 := [monotonicity #400 #404]: #406 -#746 := [trans #407 #744]: #745 -#748 := [monotonicity #746]: #742 -#391 := [trans #748 #749]: #751 -#738 := [monotonicity #391 #733]: #734 -#451 := [trans #738 #449]: #450 -#707 := [monotonicity #451 #568 #705]: #704 -#550 := [trans #707 #590]: #591 -#756 := (iff #429 false) -#416 := [rewrite]: #756 -#695 := [monotonicity #416 #550]: #600 -#599 := [trans #695 #699]: #584 -#755 := (iff #762 #415) -#420 := [rewrite]: #755 -#759 := (iff #763 false) -#765 := [rewrite]: #759 -#595 := [monotonicity #765 #420 #599]: #602 -#606 := [trans #595 #604]: #605 -#690 := [monotonicity #606]: #688 -#681 := [trans #690 #679]: #688 -#701 := [quant-inst #63 #8]: #697 -#691 := [mp #701 #681]: #700 -[unit-resolution #691 #87 #779]: false -unsat -117ddb585bc1c6246f02758b44ec466b148da99c 351 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#36 := (f3 #15 #16) -#759 := (pattern #36) -#18 := 0::Int -#97 := -1::Int -#101 := (* -1::Int #16) -#98 := (* -1::Int #15) -#156 := (mod #98 #101) -#271 := (+ #36 #156) -#272 := (= #271 0::Int) -#37 := (mod #15 #16) -#268 := (* -1::Int #37) -#269 := (+ #36 #268) -#270 := (= #269 0::Int) -#130 := (>= #15 0::Int) -#123 := (<= #16 0::Int) -#215 := (or #123 #130) -#216 := (not #215) -#119 := (<= #15 0::Int) -#213 := (or #119 #123) -#214 := (not #213) -#219 := (or #214 #216) -#273 := (ite #219 #270 #272) -#267 := (= #36 0::Int) -#19 := (= #15 0::Int) -#274 := (ite #19 #267 #273) -#266 := (= #15 #36) -#20 := (= #16 0::Int) -#275 := (ite #20 #266 #274) -#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275) -#278 := (forall (vars (?v0 Int) (?v1 Int)) #275) -#763 := (iff #278 #760) -#761 := (iff #275 #275) -#762 := [refl]: #761 -#764 := [quant-intro #762]: #763 -#162 := (* -1::Int #156) -#235 := (ite #219 #37 #162) -#238 := (ite #19 0::Int #235) -#241 := (ite #20 #15 #238) -#244 := (= #36 #241) -#247 := (forall (vars (?v0 Int) (?v1 Int)) #244) -#279 := (iff #247 #278) -#276 := (iff #244 #275) -#277 := [rewrite]: #276 -#280 := [quant-intro #277]: #279 -#131 := (not #130) -#124 := (not #123) -#134 := (and #124 #131) -#120 := (not #119) -#127 := (and #120 #124) -#137 := (or #127 #134) -#182 := (ite #137 #37 #162) -#185 := (ite #19 0::Int #182) -#188 := (ite #20 #15 #185) -#191 := (= #36 #188) -#194 := (forall (vars (?v0 Int) (?v1 Int)) #191) -#248 := (iff #194 #247) -#245 := (iff #191 #244) -#242 := (= #188 #241) -#239 := (= #185 #238) -#236 := (= #182 #235) -#220 := (iff #137 #219) -#217 := (iff #134 #216) -#218 := [rewrite]: #217 -#207 := (iff #127 #214) -#208 := [rewrite]: #207 -#221 := [monotonicity #208 #218]: #220 -#237 := [monotonicity #221]: #236 -#240 := [monotonicity #237]: #239 -#243 := [monotonicity #240]: #242 -#246 := [monotonicity #243]: #245 -#249 := [quant-intro #246]: #248 -#205 := (~ #194 #194) -#204 := (~ #191 #191) -#201 := [refl]: #204 -#206 := [nnf-pos #201]: #205 -#30 := (- #16) -#29 := (- #15) -#38 := (mod #29 #30) -#39 := (- #38) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#40 := (ite #27 #37 #39) -#41 := (ite #19 0::Int #40) -#42 := (ite #20 #15 #41) -#43 := (= #36 #42) -#44 := (forall (vars (?v0 Int) (?v1 Int)) #43) -#197 := (iff #44 #194) -#91 := (and #23 #25) -#94 := (or #24 #91) -#167 := (ite #94 #37 #162) -#170 := (ite #19 0::Int #167) -#173 := (ite #20 #15 #170) -#176 := (= #36 #173) -#179 := (forall (vars (?v0 Int) (?v1 Int)) #176) -#195 := (iff #179 #194) -#192 := (iff #176 #191) -#189 := (= #173 #188) -#186 := (= #170 #185) -#183 := (= #167 #182) -#138 := (iff #94 #137) -#135 := (iff #91 #134) -#132 := (iff #25 #131) -#133 := [rewrite]: #132 -#125 := (iff #23 #124) -#126 := [rewrite]: #125 -#136 := [monotonicity #126 #133]: #135 -#128 := (iff #24 #127) -#121 := (iff #22 #120) +#180 := [monotonicity #166 #177]: #179 +#183 := [monotonicity #180]: #182 +#192 := [trans #183 #190]: #191 +#195 := [monotonicity #192]: #194 +#132 := (iff #35 #131) +#129 := (iff #34 #128) +#126 := (= #33 #125) +#123 := (= #32 #113) +#118 := (ite false f3 #113) +#121 := (= #118 #113) #122 := [rewrite]: #121 -#129 := [monotonicity #122 #126]: #128 -#139 := [monotonicity #129 #136]: #138 -#184 := [monotonicity #139]: #183 -#187 := [monotonicity #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [monotonicity #190]: #192 -#196 := [quant-intro #193]: #195 -#180 := (iff #44 #179) -#177 := (iff #43 #176) -#174 := (= #42 #173) -#171 := (= #41 #170) -#168 := (= #40 #167) -#165 := (= #39 #162) -#159 := (- #156) -#163 := (= #159 #162) -#164 := [rewrite]: #163 -#160 := (= #39 #159) -#157 := (= #38 #156) -#102 := (= #30 #101) +#119 := (= #32 #118) +#116 := (= #31 #113) +#106 := (ite #68 0::Int #101) +#109 := (ite #10 0::Int #106) +#114 := (= #109 #113) +#115 := [rewrite]: #114 +#110 := (= #31 #109) +#107 := (= #30 #106) +#104 := (= #29 #101) +#98 := (- #95) +#102 := (= #98 #101) #103 := [rewrite]: #102 #99 := (= #29 #98) -#100 := [rewrite]: #99 -#158 := [monotonicity #100 #103]: #157 -#161 := [monotonicity #158]: #160 -#166 := [trans #161 #164]: #165 -#95 := (iff #27 #94) -#92 := (iff #26 #91) -#93 := [rewrite]: #92 -#96 := [monotonicity #93]: #95 -#169 := [monotonicity #96 #166]: #168 -#172 := [monotonicity #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [monotonicity #175]: #177 -#181 := [quant-intro #178]: #180 -#198 := [trans #181 #196]: #197 -#155 := [asserted]: #44 -#199 := [mp #155 #198]: #194 -#202 := [mp~ #199 #206]: #194 -#250 := [mp #202 #249]: #247 -#281 := [mp #250 #280]: #278 -#765 := [mp #281 #764]: #760 -#12 := 1::Int -#10 := 3::Int -#65 := -5::Int -#68 := (f3 -5::Int 3::Int) -#71 := (= #68 1::Int) -#84 := (not #71) -#8 := 5::Int -#9 := (- 5::Int) -#11 := (f3 #9 3::Int) -#13 := (= #11 1::Int) -#14 := (not #13) -#87 := (iff #14 #84) -#74 := (= 1::Int #68) -#79 := (not #74) -#85 := (iff #79 #84) -#82 := (iff #74 #71) -#83 := [rewrite]: #82 -#86 := [monotonicity #83]: #85 -#80 := (iff #14 #79) -#77 := (iff #13 #74) -#75 := (iff #71 #74) +#96 := (= #28 #95) +#75 := (= #22 -1::Int) #76 := [rewrite]: #75 -#72 := (iff #13 #71) -#69 := (= #11 #68) -#66 := (= #9 -5::Int) +#73 := (= #21 #72) +#74 := [rewrite]: #73 +#97 := [monotonicity #74 #76]: #96 +#100 := [monotonicity #97]: #99 +#105 := [trans #100 #103]: #104 +#93 := (= #27 0::Int) +#94 := [rewrite]: #93 +#69 := (iff #19 #68) +#66 := (iff #18 #65) #67 := [rewrite]: #66 #70 := [monotonicity #67]: #69 -#73 := [monotonicity #70]: #72 -#78 := [trans #73 #76]: #77 -#81 := [monotonicity #78]: #80 -#88 := [trans #81 #86]: #87 -#64 := [asserted]: #14 -#89 := [mp #64 #88]: #84 -#658 := (not #760) -#660 := (or #658 #71) -#339 := (* -1::Int 3::Int) -#423 := (* -1::Int -5::Int) -#424 := (mod #423 #339) -#425 := (+ #68 #424) -#416 := (= #425 0::Int) -#427 := (mod -5::Int 3::Int) -#428 := (* -1::Int #427) -#429 := (+ #68 #428) -#426 := (= #429 0::Int) -#430 := (>= -5::Int 0::Int) -#409 := (<= 3::Int 0::Int) -#744 := (or #409 #430) -#746 := (not #744) -#403 := (<= -5::Int 0::Int) -#533 := (or #403 #409) -#740 := (not #533) -#414 := (or #740 #746) -#415 := (ite #414 #426 #416) -#747 := (= #68 0::Int) -#748 := (= -5::Int 0::Int) -#749 := (ite #748 #747 #415) -#750 := (= -5::Int #68) -#745 := (= 3::Int 0::Int) -#751 := (ite #745 #750 #749) -#661 := (or #658 #751) -#663 := (iff #661 #660) -#664 := (iff #660 #660) -#650 := [rewrite]: #664 -#673 := (iff #751 #71) -#742 := (= #68 -5::Int) -#669 := (ite false #742 #71) -#672 := (iff #669 #71) -#666 := [rewrite]: #672 -#670 := (iff #751 #669) -#675 := (iff #749 #71) -#665 := (ite false #747 #71) -#678 := (iff #665 #71) -#679 := [rewrite]: #678 -#667 := (iff #749 #665) -#676 := (iff #415 #71) -#588 := -2::Int -#581 := (= #68 -2::Int) -#1 := true -#593 := (ite true #71 #581) -#687 := (iff #593 #71) -#674 := [rewrite]: #687 -#686 := (iff #415 #593) -#591 := (iff #416 #581) -#691 := 2::Int -#684 := (+ 2::Int #68) -#570 := (= #684 0::Int) -#589 := (iff #570 #581) -#590 := [rewrite]: #589 -#585 := (iff #416 #570) -#682 := (= #425 #684) -#576 := (+ #68 2::Int) -#586 := (= #576 #684) -#681 := [rewrite]: #586 -#577 := (= #425 #576) -#693 := (= #424 2::Int) -#703 := -3::Int -#535 := (mod 5::Int -3::Int) -#692 := (= #535 2::Int) -#690 := [rewrite]: #692 -#688 := (= #424 #535) -#532 := (= #339 -3::Int) -#534 := [rewrite]: #532 -#702 := (= #423 5::Int) -#696 := [rewrite]: #702 -#689 := [monotonicity #696 #534]: #688 -#575 := [trans #689 #690]: #693 -#536 := [monotonicity #575]: #577 -#685 := [trans #536 #681]: #682 -#587 := [monotonicity #685]: #585 -#592 := [trans #587 #590]: #591 -#695 := (iff #426 #71) -#706 := (+ -1::Int #68) -#697 := (= #706 0::Int) -#700 := (iff #697 #71) -#694 := [rewrite]: #700 -#698 := (iff #426 #697) -#554 := (= #429 #706) -#705 := (+ #68 -1::Int) -#712 := (= #705 #706) -#553 := [rewrite]: #712 -#710 := (= #429 #705) -#709 := (= #428 -1::Int) -#717 := (* -1::Int 1::Int) -#707 := (= #717 -1::Int) -#708 := [rewrite]: #707 -#714 := (= #428 #717) -#431 := (= #427 1::Int) -#713 := [rewrite]: #431 -#718 := [monotonicity #713]: #714 -#704 := [trans #718 #708]: #709 -#711 := [monotonicity #704]: #710 -#555 := [trans #711 #553]: #554 -#699 := [monotonicity #555]: #698 -#701 := [trans #699 #694]: #695 -#715 := (iff #414 true) -#724 := (or false true) -#436 := (iff #724 true) -#437 := [rewrite]: #436 -#434 := (iff #414 #724) -#723 := (iff #746 true) -#721 := (not false) -#445 := (iff #721 true) -#719 := [rewrite]: #445 -#722 := (iff #746 #721) -#451 := (iff #744 false) -#725 := (or false false) -#449 := (iff #725 false) -#450 := [rewrite]: #449 -#726 := (iff #744 #725) -#736 := (iff #430 false) -#739 := [rewrite]: #736 -#391 := (iff #409 false) -#392 := [rewrite]: #391 -#448 := [monotonicity #392 #739]: #726 -#345 := [trans #448 #450]: #451 -#444 := [monotonicity #345]: #722 -#720 := [trans #444 #719]: #723 -#378 := (iff #740 false) -#734 := (not true) -#737 := (iff #734 false) -#377 := [rewrite]: #737 -#372 := (iff #740 #734) -#733 := (iff #533 true) -#393 := (or true false) -#731 := (iff #393 true) -#732 := [rewrite]: #731 -#729 := (iff #533 #393) -#727 := (iff #403 true) -#390 := [rewrite]: #727 -#730 := [monotonicity #390 #392]: #729 -#728 := [trans #730 #732]: #733 -#735 := [monotonicity #728]: #372 -#738 := [trans #735 #377]: #378 -#435 := [monotonicity #738 #720]: #434 -#716 := [trans #435 #437]: #715 -#683 := [monotonicity #716 #701 #592]: #686 -#668 := [trans #683 #674]: #676 -#743 := (iff #748 false) -#386 := [rewrite]: #743 -#677 := [monotonicity #386 #668]: #667 -#680 := [trans #677 #679]: #675 -#406 := (iff #750 #742) -#402 := [rewrite]: #406 -#741 := (iff #745 false) -#401 := [rewrite]: #741 -#671 := [monotonicity #401 #402 #680]: #670 -#657 := [trans #671 #666]: #673 -#659 := [monotonicity #657]: #663 -#651 := [trans #659 #650]: #663 -#662 := [quant-inst #65 #10]: #661 -#653 := [mp #662 #651]: #660 -[unit-resolution #653 #89 #765]: false -unsat -e49f7307606e8c00bbcb83b5fb72cc73d56a411b 345 0 -#2 := false -decl f3 :: (-> Int Int Int) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#36 := (f3 #15 #16) -#761 := (pattern #36) -#18 := 0::Int -#65 := -1::Int -#103 := (* -1::Int #16) -#100 := (* -1::Int #15) -#158 := (mod #100 #103) -#273 := (+ #36 #158) -#274 := (= #273 0::Int) -#37 := (mod #15 #16) -#270 := (* -1::Int #37) -#271 := (+ #36 #270) -#272 := (= #271 0::Int) -#132 := (>= #15 0::Int) -#125 := (<= #16 0::Int) -#217 := (or #125 #132) -#218 := (not #217) -#121 := (<= #15 0::Int) -#215 := (or #121 #125) -#216 := (not #215) -#221 := (or #216 #218) -#275 := (ite #221 #272 #274) -#269 := (= #36 0::Int) -#19 := (= #15 0::Int) -#276 := (ite #19 #269 #275) -#268 := (= #15 #36) -#20 := (= #16 0::Int) -#277 := (ite #20 #268 #276) -#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #277) -#280 := (forall (vars (?v0 Int) (?v1 Int)) #277) -#765 := (iff #280 #762) -#763 := (iff #277 #277) -#764 := [refl]: #763 -#766 := [quant-intro #764]: #765 -#164 := (* -1::Int #158) -#237 := (ite #221 #37 #164) -#240 := (ite #19 0::Int #237) -#243 := (ite #20 #15 #240) -#246 := (= #36 #243) -#249 := (forall (vars (?v0 Int) (?v1 Int)) #246) -#281 := (iff #249 #280) -#278 := (iff #246 #277) -#279 := [rewrite]: #278 -#282 := [quant-intro #279]: #281 -#133 := (not #132) -#126 := (not #125) -#136 := (and #126 #133) -#122 := (not #121) -#129 := (and #122 #126) -#139 := (or #129 #136) -#184 := (ite #139 #37 #164) -#187 := (ite #19 0::Int #184) -#190 := (ite #20 #15 #187) -#193 := (= #36 #190) -#196 := (forall (vars (?v0 Int) (?v1 Int)) #193) -#250 := (iff #196 #249) -#247 := (iff #193 #246) -#244 := (= #190 #243) -#241 := (= #187 #240) -#238 := (= #184 #237) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#220 := [rewrite]: #219 -#209 := (iff #129 #216) -#210 := [rewrite]: #209 -#223 := [monotonicity #210 #220]: #222 -#239 := [monotonicity #223]: #238 -#242 := [monotonicity #239]: #241 -#245 := [monotonicity #242]: #244 -#248 := [monotonicity #245]: #247 -#251 := [quant-intro #248]: #250 -#207 := (~ #196 #196) -#206 := (~ #193 #193) -#203 := [refl]: #206 -#208 := [nnf-pos #203]: #207 -#30 := (- #16) -#29 := (- #15) -#38 := (mod #29 #30) -#39 := (- #38) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#40 := (ite #27 #37 #39) -#41 := (ite #19 0::Int #40) -#42 := (ite #20 #15 #41) -#43 := (= #36 #42) -#44 := (forall (vars (?v0 Int) (?v1 Int)) #43) -#199 := (iff #44 #196) -#94 := (and #23 #25) -#97 := (or #24 #94) -#169 := (ite #97 #37 #164) -#172 := (ite #19 0::Int #169) -#175 := (ite #20 #15 #172) -#178 := (= #36 #175) -#181 := (forall (vars (?v0 Int) (?v1 Int)) #178) -#197 := (iff #181 #196) -#194 := (iff #178 #193) -#191 := (= #175 #190) -#188 := (= #172 #187) -#185 := (= #169 #184) -#140 := (iff #97 #139) -#137 := (iff #94 #136) -#134 := (iff #25 #133) -#135 := [rewrite]: #134 -#127 := (iff #23 #126) -#128 := [rewrite]: #127 -#138 := [monotonicity #128 #135]: #137 -#130 := (iff #24 #129) -#123 := (iff #22 #122) -#124 := [rewrite]: #123 -#131 := [monotonicity #124 #128]: #130 -#141 := [monotonicity #131 #138]: #140 -#186 := [monotonicity #141]: #185 -#189 := [monotonicity #186]: #188 -#192 := [monotonicity #189]: #191 -#195 := [monotonicity #192]: #194 -#198 := [quant-intro #195]: #197 -#182 := (iff #44 #181) -#179 := (iff #43 #178) -#176 := (= #42 #175) -#173 := (= #41 #172) -#170 := (= #40 #169) -#167 := (= #39 #164) -#161 := (- #158) -#165 := (= #161 #164) -#166 := [rewrite]: #165 -#162 := (= #39 #161) -#159 := (= #38 #158) -#104 := (= #30 #103) -#105 := [rewrite]: #104 -#101 := (= #29 #100) -#102 := [rewrite]: #101 -#160 := [monotonicity #102 #105]: #159 -#163 := [monotonicity #160]: #162 -#168 := [trans #163 #166]: #167 -#98 := (iff #27 #97) -#95 := (iff #26 #94) -#96 := [rewrite]: #95 -#99 := [monotonicity #96]: #98 -#171 := [monotonicity #99 #168]: #170 -#174 := [monotonicity #171]: #173 -#177 := [monotonicity #174]: #176 -#180 := [monotonicity #177]: #179 -#183 := [quant-intro #180]: #182 -#200 := [trans #183 #198]: #199 -#157 := [asserted]: #44 -#201 := [mp #157 #200]: #196 -#204 := [mp~ #201 #208]: #196 -#252 := [mp #204 #251]: #249 -#283 := [mp #252 #282]: #280 -#767 := [mp #283 #766]: #762 -#68 := -3::Int -#71 := (f3 -1::Int -3::Int) -#74 := (= #71 -1::Int) -#87 := (not #74) -#8 := 1::Int -#9 := (- 1::Int) -#10 := 3::Int -#11 := (- 3::Int) -#12 := (f3 #9 #11) -#13 := (= #12 #9) -#14 := (not #13) -#90 := (iff #14 #87) -#77 := (= -1::Int #71) -#82 := (not #77) -#88 := (iff #82 #87) -#85 := (iff #77 #74) -#86 := [rewrite]: #85 -#89 := [monotonicity #86]: #88 -#83 := (iff #14 #82) -#80 := (iff #13 #77) -#78 := (iff #74 #77) -#79 := [rewrite]: #78 -#75 := (iff #13 #74) -#66 := (= #9 -1::Int) -#67 := [rewrite]: #66 -#72 := (= #12 #71) -#69 := (= #11 -3::Int) -#70 := [rewrite]: #69 -#73 := [monotonicity #67 #70]: #72 -#76 := [monotonicity #73 #67]: #75 -#81 := [trans #76 #79]: #80 -#84 := [monotonicity #81]: #83 -#91 := [trans #84 #89]: #90 -#64 := [asserted]: #14 -#92 := [mp #64 #91]: #87 -#682 := (not #762) -#671 := (or #682 #74) -#341 := (* -1::Int -3::Int) -#425 := (* -1::Int -1::Int) -#426 := (mod #425 #341) -#427 := (+ #71 #426) -#418 := (= #427 0::Int) -#429 := (mod -1::Int -3::Int) -#430 := (* -1::Int #429) -#431 := (+ #71 #430) -#428 := (= #431 0::Int) -#432 := (>= -1::Int 0::Int) -#411 := (<= -3::Int 0::Int) -#746 := (or #411 #432) -#748 := (not #746) -#405 := (<= -1::Int 0::Int) -#535 := (or #405 #411) -#742 := (not #535) -#416 := (or #742 #748) -#417 := (ite #416 #428 #418) -#749 := (= #71 0::Int) -#750 := (= -1::Int 0::Int) -#751 := (ite #750 #749 #417) -#752 := (= -3::Int 0::Int) -#747 := (ite #752 #77 #751) -#672 := (or #682 #747) -#674 := (iff #672 #671) -#675 := (iff #671 #671) -#659 := [rewrite]: #675 -#681 := (iff #747 #74) -#670 := (ite false #74 #74) -#679 := (iff #670 #74) -#680 := [rewrite]: #679 -#667 := (iff #747 #670) -#676 := (iff #751 #74) -#594 := (ite false #749 #74) -#685 := (iff #594 #74) -#689 := [rewrite]: #685 -#595 := (iff #751 #594) -#592 := (iff #417 #74) -#726 := 2::Int -#556 := (= #71 2::Int) -#587 := (ite false #556 #74) -#583 := (iff #587 #74) -#591 := [rewrite]: #583 -#589 := (iff #417 #587) -#687 := (iff #418 #74) -#692 := (+ 1::Int #71) -#538 := (= #692 0::Int) -#683 := (iff #538 #74) -#684 := [rewrite]: #683 -#686 := (iff #418 #538) -#578 := (= #427 #692) -#691 := (+ #71 1::Int) -#695 := (= #691 #692) -#577 := [rewrite]: #695 -#693 := (= #427 #691) -#537 := (= #426 1::Int) -#704 := (mod 1::Int 3::Int) -#534 := (= #704 1::Int) -#536 := [rewrite]: #534 -#698 := (= #426 #704) -#697 := (= #341 3::Int) -#703 := [rewrite]: #697 -#702 := (= #425 1::Int) -#696 := [rewrite]: #702 -#705 := [monotonicity #696 #703]: #698 -#690 := [trans #705 #536]: #537 -#694 := [monotonicity #690]: #693 -#579 := [trans #694 #577]: #578 -#588 := [monotonicity #579]: #686 -#572 := [trans #588 #684]: #687 -#700 := (iff #428 #556) -#718 := -2::Int -#711 := (+ -2::Int #71) -#708 := (= #711 0::Int) -#557 := (iff #708 #556) -#699 := [rewrite]: #557 -#714 := (iff #428 #708) -#712 := (= #431 #711) -#720 := (+ #71 -2::Int) -#706 := (= #720 #711) -#707 := [rewrite]: #706 -#709 := (= #431 #720) -#719 := (= #430 -2::Int) -#438 := (* -1::Int 2::Int) -#433 := (= #438 -2::Int) -#715 := [rewrite]: #433 -#439 := (= #430 #438) -#436 := (= #429 2::Int) -#437 := [rewrite]: #436 -#717 := [monotonicity #437]: #439 -#716 := [trans #717 #715]: #719 -#710 := [monotonicity #716]: #709 -#713 := [trans #710 #707]: #712 -#555 := [monotonicity #713]: #714 -#701 := [trans #555 #699]: #700 -#725 := (iff #416 false) -#723 := (or false false) -#447 := (iff #723 false) -#721 := [rewrite]: #447 -#724 := (iff #416 #723) -#453 := (iff #748 false) -#1 := true -#733 := (not true) -#730 := (iff #733 false) -#736 := [rewrite]: #730 -#451 := (iff #748 #733) -#728 := (iff #746 true) -#380 := (or true false) -#741 := (iff #380 true) -#727 := [rewrite]: #741 -#740 := (iff #746 #380) -#739 := (iff #432 false) -#379 := [rewrite]: #739 -#745 := (iff #411 true) -#388 := [rewrite]: #745 -#738 := [monotonicity #388 #379]: #740 -#450 := [trans #738 #727]: #728 -#452 := [monotonicity #450]: #451 -#347 := [trans #452 #736]: #453 -#374 := (iff #742 false) -#734 := (iff #742 #733) -#731 := (iff #535 true) -#729 := (or true true) -#394 := (iff #729 true) -#395 := [rewrite]: #394 -#392 := (iff #535 #729) -#744 := (iff #405 true) -#404 := [rewrite]: #744 -#393 := [monotonicity #404 #388]: #392 -#732 := [trans #393 #395]: #731 -#735 := [monotonicity #732]: #734 -#737 := [trans #735 #736]: #374 -#446 := [monotonicity #737 #347]: #724 -#722 := [trans #446 #721]: #725 -#590 := [monotonicity #722 #701 #572]: #589 -#593 := [trans #590 #591]: #592 -#403 := (iff #750 false) -#408 := [rewrite]: #403 -#688 := [monotonicity #408 #593]: #595 -#678 := [trans #688 #689]: #676 -#753 := (iff #752 false) -#743 := [rewrite]: #753 -#669 := [monotonicity #743 #86 #678]: #667 -#677 := [trans #669 #680]: #681 -#668 := [monotonicity #677]: #674 -#660 := [trans #668 #659]: #674 -#673 := [quant-inst #65 #68]: #672 -#662 := [mp #673 #660]: #671 -[unit-resolution #662 #92 #767]: false -unsat -a8f315f795d8dc3da5b76a3fe9d6ebfef481af33 324 0 -#2 := false -decl f3 :: (-> Int Int Int) -#15 := (:var 0 Int) -#14 := (:var 1 Int) -#34 := (f3 #14 #15) -#773 := (pattern #34) -#11 := 0::Int -#104 := -1::Int -#108 := (* -1::Int #15) -#105 := (* -1::Int #14) -#169 := (mod #105 #108) -#284 := (+ #34 #169) -#285 := (= #284 0::Int) -#35 := (mod #14 #15) -#281 := (* -1::Int #35) -#282 := (+ #34 #281) -#283 := (= #282 0::Int) -#143 := (>= #14 0::Int) -#136 := (<= #15 0::Int) -#228 := (or #136 #143) -#229 := (not #228) -#132 := (<= #14 0::Int) -#226 := (or #132 #136) -#227 := (not #226) -#232 := (or #227 #229) -#286 := (ite #232 #283 #285) -#280 := (= #34 0::Int) -#17 := (= #14 0::Int) -#287 := (ite #17 #280 #286) -#279 := (= #14 #34) -#18 := (= #15 0::Int) -#288 := (ite #18 #279 #287) -#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288) -#291 := (forall (vars (?v0 Int) (?v1 Int)) #288) -#777 := (iff #291 #774) -#775 := (iff #288 #288) -#776 := [refl]: #775 -#778 := [quant-intro #776]: #777 -#175 := (* -1::Int #169) -#248 := (ite #232 #35 #175) -#251 := (ite #17 0::Int #248) -#254 := (ite #18 #14 #251) -#257 := (= #34 #254) -#260 := (forall (vars (?v0 Int) (?v1 Int)) #257) -#292 := (iff #260 #291) -#289 := (iff #257 #288) -#290 := [rewrite]: #289 -#293 := [quant-intro #290]: #292 -#144 := (not #143) -#137 := (not #136) -#147 := (and #137 #144) -#133 := (not #132) -#140 := (and #133 #137) -#150 := (or #140 #147) -#195 := (ite #150 #35 #175) -#198 := (ite #17 0::Int #195) -#201 := (ite #18 #14 #198) -#204 := (= #34 #201) -#207 := (forall (vars (?v0 Int) (?v1 Int)) #204) -#261 := (iff #207 #260) -#258 := (iff #204 #257) -#255 := (= #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#233 := (iff #150 #232) -#230 := (iff #147 #229) -#231 := [rewrite]: #230 -#220 := (iff #140 #227) -#221 := [rewrite]: #220 -#234 := [monotonicity #221 #231]: #233 -#250 := [monotonicity #234]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [monotonicity #256]: #258 -#262 := [quant-intro #259]: #261 -#218 := (~ #207 #207) -#217 := (~ #204 #204) -#214 := [refl]: #217 -#219 := [nnf-pos #214]: #218 -#28 := (- #15) -#27 := (- #14) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #15) -#23 := (< #14 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #14) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #14 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#210 := (iff #42 #207) -#98 := (and #21 #23) -#101 := (or #22 #98) -#180 := (ite #101 #35 #175) -#89 := (= 0::Int #14) -#183 := (ite #89 0::Int #180) -#92 := (= 0::Int #15) -#186 := (ite #92 #14 #183) -#189 := (= #34 #186) -#192 := (forall (vars (?v0 Int) (?v1 Int)) #189) -#208 := (iff #192 #207) -#205 := (iff #189 #204) -#202 := (= #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#151 := (iff #101 #150) -#148 := (iff #98 #147) -#145 := (iff #23 #144) -#146 := [rewrite]: #145 -#138 := (iff #21 #137) -#139 := [rewrite]: #138 -#149 := [monotonicity #139 #146]: #148 -#141 := (iff #22 #140) -#134 := (iff #20 #133) -#135 := [rewrite]: #134 -#142 := [monotonicity #135 #139]: #141 -#152 := [monotonicity #142 #149]: #151 -#197 := [monotonicity #152]: #196 -#126 := (iff #89 #17) -#127 := [rewrite]: #126 -#200 := [monotonicity #127 #197]: #199 -#128 := (iff #92 #18) -#129 := [rewrite]: #128 -#203 := [monotonicity #129 #200]: #202 -#206 := [monotonicity #203]: #205 -#209 := [quant-intro #206]: #208 -#193 := (iff #42 #192) -#190 := (iff #41 #189) -#187 := (= #40 #186) -#184 := (= #39 #183) -#181 := (= #38 #180) -#178 := (= #37 #175) -#172 := (- #169) -#176 := (= #172 #175) -#177 := [rewrite]: #176 -#173 := (= #37 #172) -#170 := (= #36 #169) -#109 := (= #28 #108) -#110 := [rewrite]: #109 -#106 := (= #27 #105) -#107 := [rewrite]: #106 -#171 := [monotonicity #107 #110]: #170 -#174 := [monotonicity #171]: #173 -#179 := [trans #174 #177]: #178 -#102 := (iff #25 #101) -#99 := (iff #24 #98) -#100 := [rewrite]: #99 -#103 := [monotonicity #100]: #102 -#182 := [monotonicity #103 #179]: #181 -#90 := (iff #17 #89) -#91 := [rewrite]: #90 -#185 := [monotonicity #91 #182]: #184 -#93 := (iff #18 #92) -#94 := [rewrite]: #93 -#188 := [monotonicity #94 #185]: #187 -#191 := [monotonicity #188]: #190 -#194 := [quant-intro #191]: #193 -#211 := [trans #194 #209]: #210 -#168 := [asserted]: #42 -#212 := [mp #168 #211]: #207 -#215 := [mp~ #212 #219]: #207 -#263 := [mp #215 #262]: #260 -#294 := [mp #263 #293]: #291 -#779 := [mp #294 #778]: #774 -#63 := -3::Int -#66 := (f3 -3::Int -3::Int) -#69 := (= #66 0::Int) -#82 := (not #69) -#8 := 3::Int -#9 := (- 3::Int) -#10 := (f3 #9 #9) -#12 := (= #10 0::Int) -#13 := (not #12) -#85 := (iff #13 #82) -#72 := (= 0::Int #66) -#77 := (not #72) -#83 := (iff #77 #82) -#80 := (iff #72 #69) -#81 := [rewrite]: #80 -#84 := [monotonicity #81]: #83 -#78 := (iff #13 #77) -#75 := (iff #12 #72) -#73 := (iff #69 #72) -#74 := [rewrite]: #73 -#70 := (iff #12 #69) -#67 := (= #10 #66) -#64 := (= #9 -3::Int) -#65 := [rewrite]: #64 -#68 := [monotonicity #65 #65]: #67 -#71 := [monotonicity #68]: #70 -#76 := [trans #71 #74]: #75 -#79 := [monotonicity #76]: #78 -#86 := [trans #79 #84]: #85 -#62 := [asserted]: #13 -#87 := [mp #62 #86]: #82 -#550 := (not #774) -#698 := (or #550 #69) -#352 := (* -1::Int -3::Int) -#437 := (mod #352 #352) -#438 := (+ #66 #437) -#439 := (= #438 0::Int) -#430 := (mod -3::Int -3::Int) -#441 := (* -1::Int #430) -#442 := (+ #66 #441) -#370 := (= #442 0::Int) -#443 := (>= -3::Int 0::Int) -#440 := (<= -3::Int 0::Int) -#444 := (or #440 #443) -#423 := (not #444) -#758 := (or #440 #440) -#760 := (not #758) -#417 := (or #760 #423) -#547 := (ite #417 #370 #439) -#754 := (= -3::Int 0::Int) -#428 := (ite #754 #69 #547) -#429 := (= -3::Int #66) -#761 := (ite #754 #429 #428) -#600 := (or #550 #761) -#696 := (iff #600 #698) -#584 := (iff #698 #698) -#599 := [rewrite]: #584 -#590 := (iff #761 #69) -#759 := (= #66 -3::Int) -#705 := (ite false #759 #69) -#707 := (iff #705 #69) -#589 := [rewrite]: #707 -#706 := (iff #761 #705) -#702 := (iff #428 #69) -#708 := (ite false #69 #69) -#716 := (iff #708 #69) -#710 := [rewrite]: #716 -#548 := (iff #428 #708) -#717 := (iff #547 #69) -#709 := (iff #547 #708) -#713 := (iff #439 #69) -#711 := (= #438 #66) -#451 := (+ #66 0::Int) -#445 := (= #451 #66) -#727 := [rewrite]: #445 -#568 := (= #438 #451) -#726 := (= #437 0::Int) -#718 := (mod 3::Int 3::Int) -#725 := (= #718 0::Int) -#720 := [rewrite]: #725 -#719 := (= #437 #718) -#722 := (= #352 3::Int) -#723 := [rewrite]: #722 -#724 := [monotonicity #723 #723]: #719 -#567 := [trans #724 #720]: #726 -#569 := [monotonicity #567]: #568 -#712 := [trans #569 #727]: #711 -#714 := [monotonicity #712]: #713 -#732 := (iff #370 #69) -#731 := (= #442 #66) -#729 := (= #442 #451) -#449 := (= #441 0::Int) -#733 := (* -1::Int 0::Int) -#738 := (= #733 0::Int) -#448 := [rewrite]: #738 -#737 := (= #441 #733) -#458 := (= #430 0::Int) -#459 := [rewrite]: #458 -#734 := [monotonicity #459]: #737 -#450 := [trans #734 #448]: #449 -#730 := [monotonicity #450]: #729 -#728 := [trans #730 #727]: #731 -#721 := [monotonicity #728]: #732 -#735 := (iff #417 false) -#462 := (or false false) -#465 := (iff #462 false) -#358 := [rewrite]: #465 -#463 := (iff #417 #462) -#739 := (iff #423 false) -#1 := true -#405 := (not true) -#743 := (iff #405 false) -#744 := [rewrite]: #743 -#750 := (iff #423 #405) -#392 := (iff #444 true) -#748 := (or true false) -#751 := (iff #748 true) -#391 := [rewrite]: #751 -#386 := (iff #444 #748) -#747 := (iff #443 false) -#742 := [rewrite]: #747 -#755 := (iff #440 true) -#415 := [rewrite]: #755 -#749 := [monotonicity #415 #742]: #386 -#752 := [trans #749 #391]: #392 -#753 := [monotonicity #752]: #750 -#740 := [trans #753 #744]: #739 -#745 := (iff #760 false) -#406 := (iff #760 #405) -#741 := (iff #758 true) -#420 := (or true true) -#757 := (iff #420 true) -#400 := [rewrite]: #757 -#756 := (iff #758 #420) -#416 := [monotonicity #415 #415]: #756 -#404 := [trans #416 #400]: #741 -#407 := [monotonicity #404]: #406 -#746 := [trans #407 #744]: #745 -#464 := [monotonicity #746 #740]: #463 -#736 := [trans #464 #358]: #735 -#715 := [monotonicity #736 #721 #714]: #709 -#546 := [trans #715 #710]: #717 -#762 := (iff #754 false) -#763 := [rewrite]: #762 -#549 := [monotonicity #763 #546]: #548 -#703 := [trans #549 #710]: #702 -#764 := (iff #429 #759) -#765 := [rewrite]: #764 -#704 := [monotonicity #763 #765 #703]: #706 -#591 := [trans #704 #589]: #590 -#699 := [monotonicity #591]: #696 -#601 := [trans #699 #599]: #696 -#695 := [quant-inst #63 #63]: #600 -#602 := [mp #695 #601]: #698 -[unit-resolution #602 #87 #779]: false -unsat -ab60a5d229f921e05cbaa6708d883c31816e3a4a 342 0 -#2 := false -decl f3 :: (-> Int Int Int) -#18 := (:var 0 Int) -#17 := (:var 1 Int) -#38 := (f3 #17 #18) -#756 := (pattern #38) -#20 := 0::Int -#93 := -1::Int -#97 := (* -1::Int #18) -#94 := (* -1::Int #17) -#152 := (mod #94 #97) -#267 := (+ #38 #152) -#268 := (= #267 0::Int) -#39 := (mod #17 #18) -#264 := (* -1::Int #39) -#265 := (+ #38 #264) -#266 := (= #265 0::Int) -#126 := (>= #17 0::Int) -#119 := (<= #18 0::Int) -#211 := (or #119 #126) -#212 := (not #211) -#115 := (<= #17 0::Int) -#209 := (or #115 #119) -#210 := (not #209) -#215 := (or #210 #212) -#269 := (ite #215 #266 #268) -#263 := (= #38 0::Int) -#21 := (= #17 0::Int) -#270 := (ite #21 #263 #269) -#262 := (= #17 #38) -#22 := (= #18 0::Int) -#271 := (ite #22 #262 #270) -#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271) -#274 := (forall (vars (?v0 Int) (?v1 Int)) #271) -#760 := (iff #274 #757) -#758 := (iff #271 #271) -#759 := [refl]: #758 -#761 := [quant-intro #759]: #760 -#158 := (* -1::Int #152) -#231 := (ite #215 #39 #158) -#234 := (ite #21 0::Int #231) -#237 := (ite #22 #17 #234) -#240 := (= #38 #237) -#243 := (forall (vars (?v0 Int) (?v1 Int)) #240) -#275 := (iff #243 #274) -#272 := (iff #240 #271) -#273 := [rewrite]: #272 -#276 := [quant-intro #273]: #275 -#127 := (not #126) -#120 := (not #119) -#130 := (and #120 #127) -#116 := (not #115) -#123 := (and #116 #120) -#133 := (or #123 #130) -#178 := (ite #133 #39 #158) -#181 := (ite #21 0::Int #178) -#184 := (ite #22 #17 #181) -#187 := (= #38 #184) -#190 := (forall (vars (?v0 Int) (?v1 Int)) #187) -#244 := (iff #190 #243) -#241 := (iff #187 #240) -#238 := (= #184 #237) -#235 := (= #181 #234) -#232 := (= #178 #231) -#216 := (iff #133 #215) -#213 := (iff #130 #212) -#214 := [rewrite]: #213 -#203 := (iff #123 #210) -#204 := [rewrite]: #203 -#217 := [monotonicity #204 #214]: #216 -#233 := [monotonicity #217]: #232 -#236 := [monotonicity #233]: #235 -#239 := [monotonicity #236]: #238 -#242 := [monotonicity #239]: #241 -#245 := [quant-intro #242]: #244 -#201 := (~ #190 #190) -#200 := (~ #187 #187) -#197 := [refl]: #200 -#202 := [nnf-pos #197]: #201 -#32 := (- #18) -#31 := (- #17) -#40 := (mod #31 #32) -#41 := (- #40) -#25 := (< 0::Int #18) -#27 := (< #17 0::Int) -#28 := (and #27 #25) -#24 := (< 0::Int #17) -#26 := (and #24 #25) -#29 := (or #26 #28) -#42 := (ite #29 #39 #41) -#43 := (ite #21 0::Int #42) -#44 := (ite #22 #17 #43) -#45 := (= #38 #44) -#46 := (forall (vars (?v0 Int) (?v1 Int)) #45) -#193 := (iff #46 #190) -#86 := (and #25 #27) -#90 := (or #26 #86) -#163 := (ite #90 #39 #158) -#166 := (ite #21 0::Int #163) -#169 := (ite #22 #17 #166) -#172 := (= #38 #169) -#175 := (forall (vars (?v0 Int) (?v1 Int)) #172) -#191 := (iff #175 #190) -#188 := (iff #172 #187) -#185 := (= #169 #184) -#182 := (= #166 #181) -#179 := (= #163 #178) -#134 := (iff #90 #133) -#131 := (iff #86 #130) -#128 := (iff #27 #127) -#129 := [rewrite]: #128 -#121 := (iff #25 #120) -#122 := [rewrite]: #121 -#132 := [monotonicity #122 #129]: #131 -#124 := (iff #26 #123) -#117 := (iff #24 #116) -#118 := [rewrite]: #117 -#125 := [monotonicity #118 #122]: #124 -#135 := [monotonicity #125 #132]: #134 -#180 := [monotonicity #135]: #179 -#183 := [monotonicity #180]: #182 -#186 := [monotonicity #183]: #185 -#189 := [monotonicity #186]: #188 -#192 := [quant-intro #189]: #191 -#176 := (iff #46 #175) -#173 := (iff #45 #172) -#170 := (= #44 #169) -#167 := (= #43 #166) -#164 := (= #42 #163) -#161 := (= #41 #158) -#155 := (- #152) -#159 := (= #155 #158) -#160 := [rewrite]: #159 -#156 := (= #41 #155) -#153 := (= #40 #152) -#98 := (= #32 #97) -#99 := [rewrite]: #98 -#95 := (= #31 #94) -#96 := [rewrite]: #95 -#154 := [monotonicity #96 #99]: #153 -#157 := [monotonicity #154]: #156 -#162 := [trans #157 #160]: #161 -#91 := (iff #29 #90) -#88 := (iff #28 #86) -#89 := [rewrite]: #88 -#92 := [monotonicity #89]: #91 -#165 := [monotonicity #92 #162]: #164 -#168 := [monotonicity #165]: #167 -#171 := [monotonicity #168]: #170 -#174 := [monotonicity #171]: #173 -#177 := [quant-intro #174]: #176 -#194 := [trans #177 #192]: #193 -#151 := [asserted]: #46 -#195 := [mp #151 #194]: #190 -#198 := [mp~ #195 #202]: #190 -#246 := [mp #198 #245]: #243 -#277 := [mp #246 #276]: #274 -#762 := [mp #277 #761]: #757 -#76 := -2::Int -#70 := -3::Int -#67 := -5::Int -#73 := (f3 -5::Int -3::Int) -#79 := (= #73 -2::Int) -#82 := (not #79) -#13 := 2::Int -#14 := (- 2::Int) -#10 := 3::Int -#11 := (- 3::Int) -#8 := 5::Int -#9 := (- 5::Int) -#12 := (f3 #9 #11) -#15 := (= #12 #14) -#16 := (not #15) -#83 := (iff #16 #82) -#80 := (iff #15 #79) -#77 := (= #14 -2::Int) -#78 := [rewrite]: #77 -#74 := (= #12 #73) -#71 := (= #11 -3::Int) -#72 := [rewrite]: #71 -#68 := (= #9 -5::Int) -#69 := [rewrite]: #68 -#75 := [monotonicity #69 #72]: #74 -#81 := [monotonicity #75 #78]: #80 -#84 := [monotonicity #81]: #83 -#66 := [asserted]: #16 -#87 := [mp #66 #84]: #82 -#667 := (not #757) -#668 := (or #667 #79) -#335 := (* -1::Int -3::Int) -#420 := (* -1::Int -5::Int) -#421 := (mod #420 #335) -#422 := (+ #73 #421) -#413 := (= #422 0::Int) -#424 := (mod -5::Int -3::Int) -#425 := (* -1::Int #424) -#353 := (+ #73 #425) -#426 := (= #353 0::Int) -#423 := (>= -5::Int 0::Int) -#427 := (<= -3::Int 0::Int) -#406 := (or #427 #423) -#741 := (not #406) -#743 := (<= -5::Int 0::Int) -#400 := (or #743 #427) -#530 := (not #400) -#737 := (or #530 #741) -#411 := (ite #737 #426 #413) -#412 := (= #73 0::Int) -#744 := (= -5::Int 0::Int) -#745 := (ite #744 #412 #411) -#746 := (= -5::Int #73) -#747 := (= -3::Int 0::Int) -#742 := (ite #747 #746 #745) -#669 := (or #667 #742) -#670 := (iff #669 #668) -#655 := (iff #668 #668) -#657 := [rewrite]: #655 -#677 := (iff #742 #79) -#403 := (= #73 -5::Int) -#664 := (ite false #403 #79) -#676 := (iff #664 #79) -#672 := [rewrite]: #676 -#674 := (iff #742 #664) -#665 := (iff #745 #79) -#683 := (ite false #412 #79) -#671 := (iff #683 #79) -#673 := [rewrite]: #671 -#680 := (iff #745 #683) -#589 := (iff #411 #79) -#433 := 1::Int -#694 := (= #73 1::Int) -#585 := (ite false #694 #79) -#587 := (iff #585 #79) -#588 := [rewrite]: #587 -#578 := (iff #411 #585) -#582 := (iff #413 #79) -#572 := (+ 2::Int #73) -#583 := (= #572 0::Int) -#682 := (iff #583 #79) -#567 := [rewrite]: #682 -#678 := (iff #413 #583) -#533 := (= #422 #572) -#689 := (+ #73 2::Int) -#573 := (= #689 #572) -#574 := [rewrite]: #573 -#687 := (= #422 #689) -#686 := (= #421 2::Int) -#700 := (mod 5::Int 3::Int) -#532 := (= #700 2::Int) -#685 := [rewrite]: #532 -#529 := (= #421 #700) -#699 := (= #335 3::Int) -#693 := [rewrite]: #699 -#692 := (= #420 5::Int) -#698 := [rewrite]: #692 -#531 := [monotonicity #698 #693]: #529 -#688 := [trans #531 #685]: #686 -#690 := [monotonicity #688]: #687 -#681 := [trans #690 #574]: #533 -#679 := [monotonicity #681]: #678 -#584 := [trans #679 #567]: #582 -#697 := (iff #426 #694) -#702 := (+ -1::Int #73) -#550 := (= #702 0::Int) -#695 := (iff #550 #694) -#696 := [rewrite]: #695 -#551 := (iff #426 #550) -#703 := (= #353 #702) -#705 := (+ #73 -1::Int) -#707 := (= #705 #702) -#708 := [rewrite]: #707 -#706 := (= #353 #705) -#715 := (= #425 -1::Int) -#713 := (* -1::Int 1::Int) -#714 := (= #713 -1::Int) -#711 := [rewrite]: #714 -#428 := (= #425 #713) -#434 := (= #424 1::Int) -#712 := [rewrite]: #434 -#710 := [monotonicity #712]: #428 -#704 := [trans #710 #711]: #715 -#701 := [monotonicity #704]: #706 -#709 := [trans #701 #708]: #703 -#552 := [monotonicity #709]: #551 -#691 := [trans #552 #696]: #697 -#431 := (iff #737 false) -#442 := (or false false) -#717 := (iff #442 false) -#721 := [rewrite]: #717 -#716 := (iff #737 #442) -#719 := (iff #741 false) -#1 := true -#725 := (not true) -#732 := (iff #725 false) -#734 := [rewrite]: #732 -#341 := (iff #741 #725) -#447 := (iff #406 true) -#736 := (or true false) -#445 := (iff #736 true) -#446 := [rewrite]: #445 -#722 := (iff #406 #736) -#735 := (iff #423 false) -#733 := [rewrite]: #735 -#387 := (iff #427 true) -#388 := [rewrite]: #387 -#723 := [monotonicity #388 #733]: #722 -#448 := [trans #723 #446]: #447 -#718 := [monotonicity #448]: #341 -#441 := [trans #718 #734]: #719 -#374 := (iff #530 false) -#731 := (iff #530 #725) -#729 := (iff #400 true) -#389 := (or true true) -#727 := (iff #389 true) -#728 := [rewrite]: #727 -#390 := (iff #400 #389) -#383 := (iff #743 true) -#724 := [rewrite]: #383 -#726 := [monotonicity #724 #388]: #390 -#730 := [trans #726 #728]: #729 -#369 := [monotonicity #730]: #731 -#375 := [trans #369 #734]: #374 -#720 := [monotonicity #375 #441]: #716 -#432 := [trans #720 #721]: #431 -#586 := [monotonicity #432 #691 #584]: #578 -#590 := [trans #586 #588]: #589 -#399 := (iff #744 false) -#740 := [rewrite]: #399 -#684 := [monotonicity #740 #590]: #680 -#662 := [trans #684 #673]: #665 -#398 := (iff #746 #403) -#739 := [rewrite]: #398 -#748 := (iff #747 false) -#738 := [rewrite]: #748 -#675 := [monotonicity #738 #739 #662]: #674 -#666 := [trans #675 #672]: #677 -#654 := [monotonicity #666]: #670 -#658 := [trans #654 #657]: #670 -#663 := [quant-inst #67 #70]: #669 -#659 := [mp #663 #658]: #668 -[unit-resolution #659 #87 #762]: false -unsat -0c710ae5525793136d2145b7da68378d3667fa91 322 0 -#2 := false -#16 := 0::Int -decl f4 :: Int -#8 := f4 -#412 := (>= f4 0::Int) -#732 := (<= f4 0::Int) -#378 := (not #732) -#721 := (not #412) -#725 := (or #721 #378) -#688 := (not #725) -#9 := 3::Int -#413 := (mod f4 3::Int) -#82 := -1::Int -#414 := (* -1::Int #413) -decl f3 :: (-> Int Int Int) -#10 := (f3 f4 3::Int) -#342 := (+ #10 #414) -#415 := (= #342 0::Int) -#561 := (not #415) -#518 := (<= #342 0::Int) -#621 := (not #518) -#629 := (>= #413 3::Int) -#630 := (not #629) -#1 := true -#60 := [true-axiom]: true -#617 := (or false #630) -#618 := [th-lemma arith]: #617 -#619 := [unit-resolution #618 #60]: #630 -#620 := [hypothesis]: #518 -#67 := (>= #10 3::Int) -#11 := (< #10 3::Int) -#12 := (not #11) -#74 := (iff #12 #67) -#65 := (not #67) -#69 := (not #65) -#72 := (iff #69 #67) -#73 := [rewrite]: #72 -#70 := (iff #12 #69) -#66 := (iff #11 #65) -#68 := [rewrite]: #66 -#71 := [monotonicity #68]: #70 -#75 := [trans #71 #73]: #74 -#62 := [asserted]: #12 -#76 := [mp #62 #75]: #67 -#615 := [th-lemma arith farkas -1 1 1 #76 #620 #619]: false -#607 := [lemma #615]: #621 -#624 := (or #561 #518) -#635 := [th-lemma arith triangle-eq]: #624 -#613 := [unit-resolution #635 #607]: #561 -#612 := (or #688 #415) -#436 := -3::Int -#409 := (* -1::Int f4) -#707 := (mod #409 -3::Int) -#431 := (+ #10 #707) -#706 := (= #431 0::Int) -#421 := (ite #725 #415 #706) -#401 := (= #10 0::Int) -#733 := (= f4 0::Int) -#701 := (ite #733 #401 #421) -#14 := (:var 0 Int) -#13 := (:var 1 Int) -#34 := (f3 #13 #14) -#745 := (pattern #34) -#86 := (* -1::Int #14) -#83 := (* -1::Int #13) -#141 := (mod #83 #86) -#256 := (+ #34 #141) -#257 := (= #256 0::Int) -#35 := (mod #13 #14) -#253 := (* -1::Int #35) -#254 := (+ #34 #253) -#255 := (= #254 0::Int) -#115 := (>= #13 0::Int) -#108 := (<= #14 0::Int) -#200 := (or #108 #115) -#201 := (not #200) -#104 := (<= #13 0::Int) -#198 := (or #104 #108) -#199 := (not #198) -#204 := (or #199 #201) -#258 := (ite #204 #255 #257) -#252 := (= #34 0::Int) -#17 := (= #13 0::Int) -#259 := (ite #17 #252 #258) -#251 := (= #13 #34) -#18 := (= #14 0::Int) -#260 := (ite #18 #251 #259) -#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #260) -#263 := (forall (vars (?v0 Int) (?v1 Int)) #260) -#749 := (iff #263 #746) -#747 := (iff #260 #260) -#748 := [refl]: #747 -#750 := [quant-intro #748]: #749 -#147 := (* -1::Int #141) -#220 := (ite #204 #35 #147) -#223 := (ite #17 0::Int #220) -#226 := (ite #18 #13 #223) -#229 := (= #34 #226) -#232 := (forall (vars (?v0 Int) (?v1 Int)) #229) -#264 := (iff #232 #263) -#261 := (iff #229 #260) -#262 := [rewrite]: #261 -#265 := [quant-intro #262]: #264 -#116 := (not #115) -#109 := (not #108) -#119 := (and #109 #116) -#105 := (not #104) -#112 := (and #105 #109) -#122 := (or #112 #119) -#167 := (ite #122 #35 #147) -#170 := (ite #17 0::Int #167) -#173 := (ite #18 #13 #170) -#176 := (= #34 #173) -#179 := (forall (vars (?v0 Int) (?v1 Int)) #176) -#233 := (iff #179 #232) -#230 := (iff #176 #229) -#227 := (= #173 #226) -#224 := (= #170 #223) -#221 := (= #167 #220) -#205 := (iff #122 #204) -#202 := (iff #119 #201) -#203 := [rewrite]: #202 -#192 := (iff #112 #199) -#193 := [rewrite]: #192 -#206 := [monotonicity #193 #203]: #205 -#222 := [monotonicity #206]: #221 -#225 := [monotonicity #222]: #224 -#228 := [monotonicity #225]: #227 -#231 := [monotonicity #228]: #230 -#234 := [quant-intro #231]: #233 -#190 := (~ #179 #179) -#189 := (~ #176 #176) -#186 := [refl]: #189 -#191 := [nnf-pos #186]: #190 -#28 := (- #14) -#27 := (- #13) -#36 := (mod #27 #28) -#37 := (- #36) -#21 := (< 0::Int #14) -#23 := (< #13 0::Int) -#24 := (and #23 #21) -#20 := (< 0::Int #13) -#22 := (and #20 #21) -#25 := (or #22 #24) -#38 := (ite #25 #35 #37) -#39 := (ite #17 0::Int #38) -#40 := (ite #18 #13 #39) -#41 := (= #34 #40) -#42 := (forall (vars (?v0 Int) (?v1 Int)) #41) -#182 := (iff #42 #179) -#64 := (and #21 #23) -#79 := (or #22 #64) -#152 := (ite #79 #35 #147) -#155 := (ite #17 0::Int #152) -#158 := (ite #18 #13 #155) -#161 := (= #34 #158) -#164 := (forall (vars (?v0 Int) (?v1 Int)) #161) -#180 := (iff #164 #179) -#177 := (iff #161 #176) -#174 := (= #158 #173) -#171 := (= #155 #170) -#168 := (= #152 #167) -#123 := (iff #79 #122) -#120 := (iff #64 #119) -#117 := (iff #23 #116) -#118 := [rewrite]: #117 -#110 := (iff #21 #109) -#111 := [rewrite]: #110 -#121 := [monotonicity #111 #118]: #120 -#113 := (iff #22 #112) -#106 := (iff #20 #105) -#107 := [rewrite]: #106 -#114 := [monotonicity #107 #111]: #113 -#124 := [monotonicity #114 #121]: #123 -#169 := [monotonicity #124]: #168 -#172 := [monotonicity #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [monotonicity #175]: #177 -#181 := [quant-intro #178]: #180 -#165 := (iff #42 #164) -#162 := (iff #41 #161) -#159 := (= #40 #158) -#156 := (= #39 #155) -#153 := (= #38 #152) -#150 := (= #37 #147) -#144 := (- #141) -#148 := (= #144 #147) +#108 := [monotonicity #70 #94 #105]: #107 +#111 := [monotonicity #108]: #110 +#117 := [trans #111 #115]: #116 +#56 := (iff #12 false) +#57 := [rewrite]: #56 +#120 := [monotonicity #57 #117]: #119 +#124 := [trans #120 #122]: #123 +#91 := (= #26 #83) +#86 := (* #83 1::Int) +#89 := (= #86 #83) +#90 := [rewrite]: #89 +#87 := (= #26 #86) +#84 := (= #25 #83) +#81 := (= #24 #80) +#78 := (= #23 #77) +#79 := [monotonicity #74 #76]: #78 +#82 := [monotonicity #70 #79]: #81 +#63 := (iff #13 #10) +#58 := (or #10 false) +#61 := (iff #58 #10) +#62 := [rewrite]: #61 +#59 := (iff #13 #58) +#60 := [monotonicity #57]: #59 +#64 := [trans #60 #62]: #63 +#85 := [monotonicity #64 #82]: #84 +#88 := [monotonicity #85]: #87 +#92 := [trans #88 #90]: #91 +#127 := [monotonicity #92 #124]: #126 +#130 := [monotonicity #127]: #129 +#133 := [monotonicity #130]: #132 +#197 := [trans #133 #195]: #196 +#55 := [asserted]: #35 +#198 := [mp #55 #197]: #193 +#342 := (or #188 #340 #341) +#343 := [th-lemma arith triangle-eq]: #342 +#345 := [unit-resolution #343 #198]: #344 +#346 := [unit-resolution #345 #339 #324]: false +#347 := [lemma #346]: #134 +#363 := [th-lemma arith triangle-eq]: #170 +#379 := [unit-resolution #363 #347]: #378 +#380 := [unit-resolution #379 #377 #376]: false +#381 := [lemma #380]: #170 +#390 := [unit-resolution #232 #381]: #220 +#391 := [unit-resolution #310 #390]: #288 +#382 := (<= #164 0::Int) +#204 := (= #164 0::Int) +#383 := [hypothesis]: #147 +#384 := [unit-resolution #379 #383]: #10 +#216 := (or #215 #204) +#217 := [def-axiom]: #216 +#385 := [unit-resolution #217 #384]: #204 +#355 := (not #204) +#386 := (or #355 #382) +#387 := [th-lemma arith triangle-eq]: #386 +#388 := [unit-resolution #387 #385]: #382 +#359 := [hypothesis]: #340 +#361 := (or #215 #235) +#350 := [hypothesis]: #10 +#351 := [unit-resolution #223 #350]: #170 +#352 := [unit-resolution #232 #351]: #220 +#353 := [unit-resolution #329 #352]: #289 +#349 := (>= #164 0::Int) +#354 := [unit-resolution #217 #350]: #204 +#356 := (or #355 #349) +#357 := [th-lemma arith triangle-eq]: #356 +#358 := [unit-resolution #357 #354]: #349 +#360 := [th-lemma arith farkas 1 1 -1 1 #359 #358 #347 #353]: false +#362 := [lemma #360]: #361 +#348 := [unit-resolution #362 #359]: #215 +#364 := [unit-resolution #363 #348 #347]: #148 +#365 := [unit-resolution #227 #364]: #170 +#366 := [unit-resolution #232 #365]: #220 +#367 := [unit-resolution #329 #366]: #289 +#368 := [unit-resolution #219 #348]: #205 +#200 := (or #158 #147) +#201 := [def-axiom]: #200 +#369 := [unit-resolution #201 #364]: #158 +#370 := [unit-resolution #212 #369]: #206 +#371 := [trans #370 #368]: #290 +#372 := [unit-resolution #326 #371]: #292 +#373 := [unit-resolution #338 #333 #372 #359 #367]: false +#374 := [lemma #373]: #235 +#389 := [unit-resolution #345 #374]: #341 +#392 := [th-lemma arith farkas 1 1 -1 1 #391 #389 #383 #388]: false +#393 := [lemma #392]: #148 +#394 := (or #215 #147) +#395 := [th-lemma arith triangle-eq]: #394 +#396 := [unit-resolution #395 #393]: #215 +#397 := [unit-resolution #219 #396]: #205 +#398 := [unit-resolution #201 #393]: #158 +#399 := [unit-resolution #212 #398]: #206 +#400 := [trans #399 #397]: #290 +#401 := [unit-resolution #304 #400]: #293 +#402 := (or #319 #320 #321) +#403 := [unit-resolution #323 #389]: #402 +[unit-resolution #403 #318 #401 #391]: false +unsat +31fe1e25557ea7df409ade184e44a23cd64eda4c 308 0 +#2 := false +#9 := 0::Int +#75 := -3::Int +decl f3 :: Int +#8 := f3 +#71 := -1::Int +#72 := (* -1::Int f3) +#95 := (mod #72 -3::Int) +#101 := (* -1::Int #95) +#11 := 3::Int +#27 := (mod f3 3::Int) +#141 := (>= f3 0::Int) +#142 := (not #141) +#128 := (<= f3 0::Int) +#129 := (not #128) +#152 := (or #129 #142) +#164 := (ite #152 #27 #101) +#10 := (= f3 0::Int) +#167 := (ite #10 0::Int #164) +#177 := (* -1::Int #167) +#321 := (+ #27 #177) +#358 := (>= #321 0::Int) +#320 := (= #27 #167) +#213 := (= #164 #167) +#207 := (not #10) +#78 := (div #72 -3::Int) +#20 := (div f3 3::Int) +#155 := (ite #152 #20 #78) +#158 := (ite #10 0::Int #155) +#176 := (* -3::Int #158) +#178 := (+ #176 #177) +#179 := (+ f3 #178) +#225 := (>= #179 0::Int) +#228 := (<= #167 0::Int) +#212 := (= #167 0::Int) +#200 := (not #152) +#230 := [hypothesis]: #200 +#192 := (or #152 #141) +#193 := [def-axiom]: #192 +#231 := [unit-resolution #193 #230]: #141 +#194 := (or #152 #128) +#195 := [def-axiom]: #194 +#232 := [unit-resolution #195 #230]: #128 +#233 := (or #10 #129 #142) +#234 := [th-lemma arith triangle-eq]: #233 +#235 := [unit-resolution #234 #232 #231]: #10 +#220 := (or #207 #212) +#221 := [def-axiom]: #220 +#236 := [unit-resolution #221 #235]: #212 +#237 := (not #212) +#238 := (or #237 #228) +#239 := [th-lemma arith triangle-eq]: #238 +#240 := [unit-resolution #239 #236]: #228 +#226 := (<= #158 0::Int) +#196 := (= #158 0::Int) +#208 := (or #207 #196) +#209 := [def-axiom]: #208 +#241 := [unit-resolution #209 #235]: #196 +#242 := (not #196) +#243 := (or #242 #226) +#244 := [th-lemma arith triangle-eq]: #243 +#245 := [unit-resolution #244 #241]: #226 +#247 := (not #228) +#246 := (not #226) +#248 := (or #225 #142 #246 #247) +#249 := [th-lemma arith assign-bounds -1 3 1]: #248 +#250 := [unit-resolution #249 #231 #245 #240]: #225 +#224 := (<= #179 0::Int) +#229 := (>= #167 0::Int) +#251 := (or #237 #229) +#252 := [th-lemma arith triangle-eq]: #251 +#253 := [unit-resolution #252 #236]: #229 +#227 := (>= #158 0::Int) +#254 := (or #242 #227) +#255 := [th-lemma arith triangle-eq]: #254 +#256 := [unit-resolution #255 #241]: #227 +#258 := (not #229) +#257 := (not #227) +#259 := (or #224 #129 #257 #258) +#260 := [th-lemma arith assign-bounds -1 3 1]: #259 +#261 := [unit-resolution #260 #232 #256 #253]: #224 +#263 := (not #225) +#262 := (not #224) +#266 := (or #262 #263) +#180 := (= #179 0::Int) +#185 := (not #180) +#22 := (- 3::Int) +#21 := (- f3) +#28 := (mod #21 #22) +#29 := (- #28) +#15 := (< 0::Int 3::Int) +#17 := (< f3 0::Int) +#18 := (and #17 #15) +#14 := (< 0::Int f3) +#16 := (and #14 #15) +#19 := (or #16 #18) +#30 := (ite #19 #27 #29) +#31 := (ite #10 0::Int #30) +#12 := (= 3::Int 0::Int) +#32 := (ite #12 f3 #31) +#23 := (div #21 #22) +#24 := (ite #19 #20 #23) +#13 := (or #10 #12) +#25 := (ite #13 0::Int #24) +#26 := (* #25 3::Int) +#33 := (+ #26 #32) +#34 := (= f3 #33) +#35 := (not #34) +#188 := (iff #35 #185) +#65 := (and #15 #17) +#68 := (or #16 #65) +#106 := (ite #68 #27 #101) +#109 := (ite #10 0::Int #106) +#81 := (ite #68 #20 #78) +#84 := (ite #10 0::Int #81) +#90 := (* 3::Int #84) +#119 := (+ #90 #109) +#122 := (= f3 #119) +#125 := (not #122) +#186 := (iff #125 #185) +#183 := (iff #122 #180) +#161 := (* 3::Int #158) +#170 := (+ #161 #167) +#173 := (= f3 #170) +#181 := (iff #173 #180) +#182 := [rewrite]: #181 +#174 := (iff #122 #173) +#171 := (= #119 #170) +#168 := (= #109 #167) +#165 := (= #106 #164) +#153 := (iff #68 #152) +#150 := (iff #65 #142) +#1 := true +#145 := (and true #142) +#148 := (iff #145 #142) #149 := [rewrite]: #148 -#145 := (= #37 #144) -#142 := (= #36 #141) -#87 := (= #28 #86) -#88 := [rewrite]: #87 -#84 := (= #27 #83) -#85 := [rewrite]: #84 -#143 := [monotonicity #85 #88]: #142 -#146 := [monotonicity #143]: #145 -#151 := [trans #146 #149]: #150 -#80 := (iff #25 #79) -#77 := (iff #24 #64) -#78 := [rewrite]: #77 -#81 := [monotonicity #78]: #80 -#154 := [monotonicity #81 #151]: #153 +#146 := (iff #65 #145) +#143 := (iff #17 #142) +#144 := [rewrite]: #143 +#132 := (iff #15 true) +#133 := [rewrite]: #132 +#147 := [monotonicity #133 #144]: #146 +#151 := [trans #147 #149]: #150 +#139 := (iff #16 #129) +#134 := (and #129 true) +#137 := (iff #134 #129) +#138 := [rewrite]: #137 +#135 := (iff #16 #134) +#130 := (iff #14 #129) +#131 := [rewrite]: #130 +#136 := [monotonicity #131 #133]: #135 +#140 := [trans #136 #138]: #139 +#154 := [monotonicity #140 #151]: #153 +#166 := [monotonicity #154]: #165 +#169 := [monotonicity #166]: #168 +#162 := (= #90 #161) +#159 := (= #84 #158) +#156 := (= #81 #155) #157 := [monotonicity #154]: #156 #160 := [monotonicity #157]: #159 #163 := [monotonicity #160]: #162 -#166 := [quant-intro #163]: #165 -#183 := [trans #166 #181]: #182 -#140 := [asserted]: #42 -#184 := [mp #140 #183]: #179 -#187 := [mp~ #184 #191]: #179 -#235 := [mp #187 #234]: #232 -#266 := [mp #235 #265]: #263 -#751 := [mp #266 #750]: #746 -#690 := (not #746) -#691 := (or #690 #701) -#324 := (* -1::Int 3::Int) -#410 := (mod #409 #324) -#411 := (+ #10 #410) -#402 := (= #411 0::Int) -#416 := (<= 3::Int 0::Int) -#395 := (or #416 #412) -#730 := (not #395) -#389 := (or #732 #416) -#519 := (not #389) -#726 := (or #519 #730) -#400 := (ite #726 #415 #402) -#734 := (ite #733 #401 #400) -#735 := (= f4 #10) -#736 := (= 3::Int 0::Int) -#731 := (ite #736 #735 #734) -#696 := (or #690 #731) -#692 := (iff #696 #691) -#539 := (iff #691 #691) -#540 := [rewrite]: #539 -#694 := (iff #731 #701) -#699 := (ite false #735 #701) -#704 := (iff #699 #701) -#693 := [rewrite]: #704 -#703 := (iff #731 #699) -#702 := (iff #734 #701) -#422 := (iff #400 #421) -#710 := (iff #402 #706) -#705 := (= #411 #431) -#708 := (= #410 #707) -#437 := (= #324 -3::Int) -#330 := [rewrite]: #437 -#430 := [monotonicity #330]: #708 -#709 := [monotonicity #430]: #705 -#420 := [monotonicity #709]: #710 -#434 := (iff #726 #725) -#364 := (or #378 #721) -#711 := (iff #364 #725) -#712 := [rewrite]: #711 -#724 := (iff #726 #364) -#723 := (iff #730 #721) -#720 := (iff #395 #412) -#716 := (or false #412) -#719 := (iff #716 #412) -#714 := [rewrite]: #719 -#717 := (iff #395 #716) -#387 := (iff #416 false) -#392 := [rewrite]: #387 -#718 := [monotonicity #392]: #717 -#358 := [trans #718 #714]: #720 -#363 := [monotonicity #358]: #723 -#379 := (iff #519 #378) -#376 := (iff #389 #732) -#728 := (or #732 false) -#372 := (iff #728 #732) -#713 := [rewrite]: #372 -#388 := (iff #389 #728) -#729 := [monotonicity #392]: #388 -#377 := [trans #729 #713]: #376 -#715 := [monotonicity #377]: #379 -#722 := [monotonicity #715 #363]: #724 -#435 := [trans #722 #712]: #434 -#423 := [monotonicity #435 #420]: #422 -#417 := [monotonicity #423]: #702 -#737 := (iff #736 false) -#727 := [rewrite]: #737 -#700 := [monotonicity #727 #417]: #703 -#695 := [trans #700 #693]: #694 -#698 := [monotonicity #695]: #692 -#541 := [trans #698 #540]: #692 -#697 := [quant-inst #8 #9]: #696 -#683 := [mp #697 #541]: #691 -#614 := [unit-resolution #683 #751]: #701 -#668 := (not #733) -#667 := (not #701) -#609 := (or #667 #668) -#574 := (not #401) -#684 := (<= #10 0::Int) -#616 := (not #684) -#646 := (or #616 #65) -#647 := [th-lemma arith farkas 1 1]: #646 -#603 := [unit-resolution #647 #76]: #616 -#604 := (or #574 #684) -#605 := [th-lemma arith triangle-eq]: #604 -#608 := [unit-resolution #605 #603]: #574 -#671 := (or #667 #668 #401) -#556 := [def-axiom]: #671 -#610 := [unit-resolution #556 #608]: #609 -#611 := [unit-resolution #610 #614]: #668 -#571 := (or #667 #733 #421) -#573 := [def-axiom]: #571 -#606 := [unit-resolution #573 #611 #614]: #421 -#675 := (not #421) -#677 := (or #675 #688 #415) -#678 := [def-axiom]: #677 -#585 := [unit-resolution #678 #606]: #612 -#586 := [unit-resolution #585 #613]: #688 -#686 := (or #725 #412) -#680 := [def-axiom]: #686 -#587 := [unit-resolution #680 #586]: #412 -#681 := (or #725 #732) -#687 := [def-axiom]: #681 -#480 := [unit-resolution #687 #586]: #732 -#591 := (or #733 #378 #721) -#592 := [th-lemma arith triangle-eq]: #591 -#593 := [unit-resolution #592 #611]: #364 -[unit-resolution #593 #480 #587]: false -unsat -8e1905429e143174e0fcdce59027187ea0e3224c 340 0 -#2 := false -#9 := 3::Int -decl f3 :: (-> Int Int Int) -decl f4 :: Int -#8 := f4 -#10 := (f3 f4 3::Int) -#439 := (mod #10 3::Int) -#655 := (>= #439 3::Int) -#656 := (not #655) -#1 := true -#62 := [true-axiom]: true -#645 := (or false #656) -#640 := [th-lemma arith]: #645 -#646 := [unit-resolution #640 #62]: #656 -#18 := 0::Int -#107 := -1::Int -#434 := (* -1::Int #10) -#598 := (+ f4 #434) -#599 := (<= #598 0::Int) -#65 := (= f4 #10) -#82 := (>= f4 3::Int) -#80 := (not #82) -#71 := (not #65) -#87 := (or #71 #80) -#92 := (not #87) -#12 := (< f4 3::Int) -#11 := (= #10 f4) -#13 := (implies #11 #12) -#14 := (not #13) -#95 := (iff #14 #92) -#72 := (or #12 #71) -#77 := (not #72) -#93 := (iff #77 #92) -#90 := (iff #72 #87) -#84 := (or #80 #71) -#88 := (iff #84 #87) -#89 := [rewrite]: #88 -#85 := (iff #72 #84) -#81 := (iff #12 #80) -#83 := [rewrite]: #81 -#86 := [monotonicity #83]: #85 -#91 := [trans #86 #89]: #90 -#94 := [monotonicity #91]: #93 -#78 := (iff #14 #77) -#75 := (iff #13 #72) -#68 := (implies #65 #12) -#73 := (iff #68 #72) +#172 := [monotonicity #163 #169]: #171 +#175 := [monotonicity #172]: #174 +#184 := [trans #175 #182]: #183 +#187 := [monotonicity #184]: #186 +#126 := (iff #35 #125) +#123 := (iff #34 #122) +#120 := (= #33 #119) +#117 := (= #32 #109) +#112 := (ite false f3 #109) +#115 := (= #112 #109) +#116 := [rewrite]: #115 +#113 := (= #32 #112) +#110 := (= #31 #109) +#107 := (= #30 #106) +#104 := (= #29 #101) +#98 := (- #95) +#102 := (= #98 #101) +#103 := [rewrite]: #102 +#99 := (= #29 #98) +#96 := (= #28 #95) +#76 := (= #22 -3::Int) +#77 := [rewrite]: #76 +#73 := (= #21 #72) #74 := [rewrite]: #73 -#69 := (iff #13 #68) -#66 := (iff #11 #65) +#97 := [monotonicity #74 #77]: #96 +#100 := [monotonicity #97]: #99 +#105 := [trans #100 #103]: #104 +#69 := (iff #19 #68) +#66 := (iff #18 #65) #67 := [rewrite]: #66 #70 := [monotonicity #67]: #69 -#76 := [trans #70 #74]: #75 -#79 := [monotonicity #76]: #78 -#96 := [trans #79 #94]: #95 -#64 := [asserted]: #14 -#97 := [mp #64 #96]: #92 -#98 := [not-or-elim #97]: #65 -#632 := (or #71 #599) -#628 := [th-lemma arith triangle-eq]: #632 -#629 := [unit-resolution #628 #98]: #599 -#99 := [not-or-elim #97]: #82 -#436 := (f3 #10 3::Int) -#600 := (* -1::Int #436) -#601 := (+ #10 #600) -#602 := (<= #601 0::Int) -#761 := (= #10 #436) -#633 := (= #436 #10) -#630 := [symm #98]: #11 -#634 := [monotonicity #630]: #633 -#635 := [symm #634]: #761 -#636 := (not #761) -#631 := (or #636 #602) -#637 := [th-lemma arith triangle-eq]: #631 -#610 := [unit-resolution #637 #635]: #602 -#367 := (* -1::Int #439) -#440 := (+ #436 #367) -#705 := (<= #440 0::Int) -#437 := (= #440 0::Int) -#736 := -3::Int -#460 := (mod #434 -3::Int) -#355 := (+ #436 #460) -#455 := (= #355 0::Int) -#441 := (>= #10 0::Int) -#748 := (not #441) -#414 := (<= #10 0::Int) -#404 := (not #414) -#749 := (or #404 #748) -#734 := (ite #749 #437 #455) -#758 := (= #436 0::Int) -#759 := (= #10 0::Int) -#445 := (ite #759 #758 #734) -#16 := (:var 0 Int) -#15 := (:var 1 Int) -#36 := (f3 #15 #16) -#770 := (pattern #36) -#111 := (* -1::Int #16) -#108 := (* -1::Int #15) -#166 := (mod #108 #111) -#281 := (+ #36 #166) -#282 := (= #281 0::Int) -#37 := (mod #15 #16) -#278 := (* -1::Int #37) -#279 := (+ #36 #278) -#280 := (= #279 0::Int) -#140 := (>= #15 0::Int) -#133 := (<= #16 0::Int) -#225 := (or #133 #140) -#226 := (not #225) -#129 := (<= #15 0::Int) -#211 := (or #129 #133) -#212 := (not #211) -#229 := (or #212 #226) -#283 := (ite #229 #280 #282) -#277 := (= #36 0::Int) -#19 := (= #15 0::Int) -#284 := (ite #19 #277 #283) -#276 := (= #15 #36) -#20 := (= #16 0::Int) -#285 := (ite #20 #276 #284) -#771 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #770) #285) -#288 := (forall (vars (?v0 Int) (?v1 Int)) #285) -#774 := (iff #288 #771) -#772 := (iff #285 #285) -#773 := [refl]: #772 -#775 := [quant-intro #773]: #774 -#172 := (* -1::Int #166) -#245 := (ite #229 #37 #172) -#248 := (ite #19 0::Int #245) -#251 := (ite #20 #15 #248) -#254 := (= #36 #251) -#257 := (forall (vars (?v0 Int) (?v1 Int)) #254) -#289 := (iff #257 #288) -#286 := (iff #254 #285) -#287 := [rewrite]: #286 -#290 := [quant-intro #287]: #289 -#141 := (not #140) -#134 := (not #133) -#144 := (and #134 #141) -#130 := (not #129) -#137 := (and #130 #134) -#147 := (or #137 #144) -#192 := (ite #147 #37 #172) -#195 := (ite #19 0::Int #192) -#198 := (ite #20 #15 #195) -#201 := (= #36 #198) -#204 := (forall (vars (?v0 Int) (?v1 Int)) #201) -#258 := (iff #204 #257) -#255 := (iff #201 #254) -#252 := (= #198 #251) -#249 := (= #195 #248) -#246 := (= #192 #245) -#230 := (iff #147 #229) -#227 := (iff #144 #226) -#228 := [rewrite]: #227 -#219 := (iff #137 #212) -#220 := [rewrite]: #219 -#231 := [monotonicity #220 #228]: #230 -#247 := [monotonicity #231]: #246 -#250 := [monotonicity #247]: #249 -#253 := [monotonicity #250]: #252 -#256 := [monotonicity #253]: #255 -#259 := [quant-intro #256]: #258 -#217 := (~ #204 #204) -#216 := (~ #201 #201) -#213 := [refl]: #216 -#218 := [nnf-pos #213]: #217 -#30 := (- #16) -#29 := (- #15) -#38 := (mod #29 #30) -#39 := (- #38) -#23 := (< 0::Int #16) -#25 := (< #15 0::Int) -#26 := (and #25 #23) -#22 := (< 0::Int #15) -#24 := (and #22 #23) -#27 := (or #24 #26) -#40 := (ite #27 #37 #39) -#41 := (ite #19 0::Int #40) -#42 := (ite #20 #15 #41) -#43 := (= #36 #42) -#44 := (forall (vars (?v0 Int) (?v1 Int)) #43) -#207 := (iff #44 #204) -#101 := (and #23 #25) -#104 := (or #24 #101) -#177 := (ite #104 #37 #172) -#180 := (ite #19 0::Int #177) -#183 := (ite #20 #15 #180) -#186 := (= #36 #183) -#189 := (forall (vars (?v0 Int) (?v1 Int)) #186) -#205 := (iff #189 #204) -#202 := (iff #186 #201) -#199 := (= #183 #198) -#196 := (= #180 #195) -#193 := (= #177 #192) -#148 := (iff #104 #147) -#145 := (iff #101 #144) -#142 := (iff #25 #141) -#143 := [rewrite]: #142 -#135 := (iff #23 #134) -#136 := [rewrite]: #135 -#146 := [monotonicity #136 #143]: #145 -#138 := (iff #24 #137) -#131 := (iff #22 #130) -#132 := [rewrite]: #131 -#139 := [monotonicity #132 #136]: #138 -#149 := [monotonicity #139 #146]: #148 -#194 := [monotonicity #149]: #193 -#197 := [monotonicity #194]: #196 -#200 := [monotonicity #197]: #199 -#203 := [monotonicity #200]: #202 -#206 := [quant-intro #203]: #205 -#190 := (iff #44 #189) -#187 := (iff #43 #186) -#184 := (= #42 #183) -#181 := (= #41 #180) -#178 := (= #40 #177) -#175 := (= #39 #172) -#169 := (- #166) -#173 := (= #169 #172) -#174 := [rewrite]: #173 -#170 := (= #39 #169) -#167 := (= #38 #166) -#112 := (= #30 #111) -#113 := [rewrite]: #112 -#109 := (= #29 #108) -#110 := [rewrite]: #109 -#168 := [monotonicity #110 #113]: #167 -#171 := [monotonicity #168]: #170 -#176 := [trans #171 #174]: #175 -#105 := (iff #27 #104) -#102 := (iff #26 #101) -#103 := [rewrite]: #102 -#106 := [monotonicity #103]: #105 -#179 := [monotonicity #106 #176]: #178 -#182 := [monotonicity #179]: #181 -#185 := [monotonicity #182]: #184 -#188 := [monotonicity #185]: #187 -#191 := [quant-intro #188]: #190 -#208 := [trans #191 #206]: #207 -#165 := [asserted]: #44 -#209 := [mp #165 #208]: #204 -#214 := [mp~ #209 #218]: #204 -#260 := [mp #214 #259]: #257 -#291 := [mp #260 #290]: #288 -#776 := [mp #291 #775]: #771 -#729 := (not #771) -#718 := (or #729 #445) -#349 := (* -1::Int 3::Int) -#435 := (mod #434 #349) -#427 := (+ #436 #435) -#438 := (= #427 0::Int) -#420 := (<= 3::Int 0::Int) -#755 := (or #420 #441) -#757 := (not #755) -#544 := (or #414 #420) -#751 := (not #544) -#425 := (or #751 #757) -#426 := (ite #425 #437 #438) -#760 := (ite #759 #758 #426) -#756 := (= 3::Int 0::Int) -#762 := (ite #756 #761 #760) -#719 := (or #729 #762) -#715 := (iff #719 #718) -#721 := (iff #718 #718) -#722 := [rewrite]: #721 -#728 := (iff #762 #445) -#448 := (ite false #761 #445) -#442 := (iff #448 #445) -#724 := [rewrite]: #442 -#726 := (iff #762 #448) -#446 := (iff #760 #445) -#731 := (iff #426 #734) -#456 := (iff #438 #455) -#732 := (= #427 #355) -#461 := (= #435 #460) -#737 := (= #349 -3::Int) -#459 := [rewrite]: #737 -#462 := [monotonicity #459]: #461 -#733 := [monotonicity #462]: #732 -#730 := [monotonicity #733]: #456 -#747 := (iff #425 #749) -#388 := (iff #757 #748) -#383 := (iff #755 #441) -#742 := (or false #441) -#739 := (iff #742 #441) -#745 := [rewrite]: #739 -#743 := (iff #755 #742) -#417 := (iff #420 false) -#753 := [rewrite]: #417 -#744 := [monotonicity #753]: #743 -#746 := [trans #744 #745]: #383 -#389 := [monotonicity #746]: #388 -#740 := (iff #751 #404) -#402 := (iff #544 #414) -#413 := (or #414 false) -#738 := (iff #413 #414) -#401 := [rewrite]: #738 -#754 := (iff #544 #413) -#397 := [monotonicity #753]: #754 -#403 := [trans #397 #401]: #402 -#741 := [monotonicity #403]: #740 -#750 := [monotonicity #741 #389]: #747 -#735 := [monotonicity #750 #730]: #731 -#447 := [monotonicity #735]: #446 -#752 := (iff #756 false) -#412 := [rewrite]: #752 -#727 := [monotonicity #412 #447]: #726 -#725 := [trans #727 #724]: #728 -#716 := [monotonicity #725]: #715 -#717 := [trans #716 #722]: #715 -#720 := [quant-inst #10 #9]: #719 -#723 := [mp #720 #717]: #718 -#611 := [unit-resolution #723 #776]: #445 -#587 := (not #759) -#612 := (not #599) -#505 := (or #404 #80 #612) -#616 := [th-lemma arith assign-bounds 1 1]: #505 -#617 := [unit-resolution #616 #99 #629]: #404 -#618 := (or #587 #414) -#623 := [th-lemma arith triangle-eq]: #618 -#619 := [unit-resolution #623 #617]: #587 -#586 := (not #445) -#695 := (or #586 #759 #734) -#597 := [def-axiom]: #695 -#620 := [unit-resolution #597 #619 #611]: #734 -#564 := (or #749 #414) -#565 := [def-axiom]: #564 -#621 := [unit-resolution #565 #617]: #749 -#709 := (not #749) -#707 := (not #734) -#714 := (or #707 #709 #437) -#543 := [def-axiom]: #714 -#624 := [unit-resolution #543 #621 #620]: #437 -#699 := (not #437) -#625 := (or #699 #705) -#626 := [th-lemma arith triangle-eq]: #625 -#622 := [unit-resolution #626 #624]: #705 -[th-lemma arith farkas 1 1 -1 1 1 #622 #610 #99 #629 #646]: false -unsat -554a2c1ef3c9bdd0bc388bdfa3186ab7a764500e 567 0 -#2 := false -#19 := 0::Int -decl f5 :: (-> Int Int Int) -#9 := 1::Int -decl f3 :: Int -#8 := f3 -#12 := (f5 f3 1::Int) -#77 := -1::Int -#79 := (* -1::Int #12) -decl f4 :: (-> Int Int Int) -#10 := (f4 f3 1::Int) -#78 := (* -1::Int #10) -#80 := (+ #78 #79) -#81 := (+ f3 #80) -#423 := (>= #81 0::Int) -#596 := (<= #12 0::Int) -#667 := (= #12 0::Int) -#751 := (= f3 0::Int) -#746 := (>= f3 0::Int) -#449 := (not #746) -#414 := (<= f3 0::Int) -#735 := (not #414) -#635 := (or #735 #449 #751) -#615 := (not #635) -#582 := [hypothesis]: #615 -#609 := (or #635 #746) -#610 := [def-axiom]: #609 -#583 := [unit-resolution #610 #582]: #746 -#612 := (or #635 #414) -#608 := [def-axiom]: #612 -#584 := [unit-resolution #608 #582]: #414 -#570 := (not #751) -#613 := (or #635 #570) -#614 := [def-axiom]: #613 -#594 := [unit-resolution #614 #582]: #570 -#574 := (or #751 #735 #449) -#595 := [th-lemma arith triangle-eq]: #574 -#550 := [unit-resolution #595 #594 #584 #583]: false -#551 := [lemma #550]: #635 -#498 := (or #615 #667) -#425 := (* -1::Int f3) -#688 := (mod #425 -1::Int) -#655 := (+ #12 #688) -#636 := (= #655 0::Int) -#618 := (ite #635 #667 #636) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#37 := (f5 #16 #17) -#759 := (pattern #37) -#101 := (* -1::Int #17) -#98 := (* -1::Int #16) -#156 := (mod #98 #101) -#271 := (+ #37 #156) -#272 := (= #271 0::Int) -#38 := (mod #16 #17) -#268 := (* -1::Int #38) -#269 := (+ #37 #268) -#270 := (= #269 0::Int) -#130 := (>= #16 0::Int) -#123 := (<= #17 0::Int) -#215 := (or #123 #130) -#216 := (not #215) -#119 := (<= #16 0::Int) -#213 := (or #119 #123) -#214 := (not #213) -#219 := (or #214 #216) -#273 := (ite #219 #270 #272) -#267 := (= #37 0::Int) -#20 := (= #16 0::Int) -#274 := (ite #20 #267 #273) -#266 := (= #16 #37) -#21 := (= #17 0::Int) -#275 := (ite #21 #266 #274) -#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275) -#278 := (forall (vars (?v0 Int) (?v1 Int)) #275) -#763 := (iff #278 #760) -#761 := (iff #275 #275) -#762 := [refl]: #761 -#764 := [quant-intro #762]: #763 -#162 := (* -1::Int #156) -#235 := (ite #219 #38 #162) -#238 := (ite #20 0::Int #235) -#241 := (ite #21 #16 #238) -#244 := (= #37 #241) -#247 := (forall (vars (?v0 Int) (?v1 Int)) #244) -#279 := (iff #247 #278) -#276 := (iff #244 #275) -#277 := [rewrite]: #276 -#280 := [quant-intro #277]: #279 -#131 := (not #130) -#124 := (not #123) -#134 := (and #124 #131) -#120 := (not #119) -#127 := (and #120 #124) -#137 := (or #127 #134) -#182 := (ite #137 #38 #162) -#185 := (ite #20 0::Int #182) -#188 := (ite #21 #16 #185) -#191 := (= #37 #188) -#194 := (forall (vars (?v0 Int) (?v1 Int)) #191) -#248 := (iff #194 #247) -#245 := (iff #191 #244) -#242 := (= #188 #241) -#239 := (= #185 #238) -#236 := (= #182 #235) -#220 := (iff #137 #219) -#217 := (iff #134 #216) -#218 := [rewrite]: #217 -#207 := (iff #127 #214) -#208 := [rewrite]: #207 -#221 := [monotonicity #208 #218]: #220 -#237 := [monotonicity #221]: #236 -#240 := [monotonicity #237]: #239 -#243 := [monotonicity #240]: #242 -#246 := [monotonicity #243]: #245 -#249 := [quant-intro #246]: #248 -#205 := (~ #194 #194) -#204 := (~ #191 #191) -#201 := [refl]: #204 -#206 := [nnf-pos #201]: #205 -#31 := (- #17) -#30 := (- #16) -#39 := (mod #30 #31) -#40 := (- #39) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#41 := (ite #28 #38 #40) -#42 := (ite #20 0::Int #41) -#43 := (ite #21 #16 #42) -#44 := (= #37 #43) -#45 := (forall (vars (?v0 Int) (?v1 Int)) #44) -#197 := (iff #45 #194) -#92 := (and #24 #26) -#95 := (or #25 #92) -#167 := (ite #95 #38 #162) -#170 := (ite #20 0::Int #167) -#173 := (ite #21 #16 #170) -#176 := (= #37 #173) -#179 := (forall (vars (?v0 Int) (?v1 Int)) #176) -#195 := (iff #179 #194) -#192 := (iff #176 #191) -#189 := (= #173 #188) -#186 := (= #170 #185) -#183 := (= #167 #182) -#138 := (iff #95 #137) -#135 := (iff #92 #134) -#132 := (iff #26 #131) -#133 := [rewrite]: #132 -#125 := (iff #24 #124) -#126 := [rewrite]: #125 -#136 := [monotonicity #126 #133]: #135 -#128 := (iff #25 #127) -#121 := (iff #23 #120) -#122 := [rewrite]: #121 -#129 := [monotonicity #122 #126]: #128 -#139 := [monotonicity #129 #136]: #138 -#184 := [monotonicity #139]: #183 -#187 := [monotonicity #184]: #186 -#190 := [monotonicity #187]: #189 -#193 := [monotonicity #190]: #192 -#196 := [quant-intro #193]: #195 -#180 := (iff #45 #179) -#177 := (iff #44 #176) -#174 := (= #43 #173) -#171 := (= #42 #170) -#168 := (= #41 #167) -#165 := (= #40 #162) -#159 := (- #156) -#163 := (= #159 #162) -#164 := [rewrite]: #163 -#160 := (= #40 #159) -#157 := (= #39 #156) -#102 := (= #31 #101) -#103 := [rewrite]: #102 -#99 := (= #30 #98) -#100 := [rewrite]: #99 -#158 := [monotonicity #100 #103]: #157 -#161 := [monotonicity #158]: #160 -#166 := [trans #161 #164]: #165 -#96 := (iff #28 #95) -#93 := (iff #27 #92) -#94 := [rewrite]: #93 -#97 := [monotonicity #94]: #96 -#169 := [monotonicity #97 #166]: #168 -#172 := [monotonicity #169]: #171 -#175 := [monotonicity #172]: #174 -#178 := [monotonicity #175]: #177 -#181 := [quant-intro #178]: #180 -#198 := [trans #181 #196]: #197 -#155 := [asserted]: #45 -#199 := [mp #155 #198]: #194 -#202 := [mp~ #199 #206]: #194 -#250 := [mp #202 #249]: #247 -#281 := [mp #250 #280]: #278 -#765 := [mp #281 #764]: #760 -#625 := (not #760) -#620 := (or #625 #618) -#424 := (* -1::Int 1::Int) -#686 := (mod #425 #424) -#683 := (+ #12 #686) -#687 := (= #683 0::Int) -#532 := (mod f3 1::Int) -#674 := (* -1::Int #532) -#676 := (+ #12 #674) -#668 := (= #676 0::Int) -#403 := (<= 1::Int 0::Int) -#533 := (or #403 #746) -#740 := (not #533) -#415 := (or #414 #403) -#747 := (not #415) -#748 := (or #747 #740) -#665 := (ite #748 #668 #687) -#677 := (ite #751 #667 #665) -#678 := (= f3 #12) -#745 := (= 1::Int 0::Int) -#679 := (ite #745 #678 #677) -#626 := (or #625 #679) -#600 := (iff #626 #620) -#494 := (iff #620 #620) -#605 := [rewrite]: #494 -#623 := (iff #679 #618) -#345 := (or #735 #449) -#646 := (or #345 #751) -#647 := (ite #646 #667 #636) -#619 := (iff #647 #618) -#621 := (iff #646 #635) -#617 := [rewrite]: #621 -#622 := [monotonicity #617]: #619 -#634 := (iff #679 #647) -#628 := (ite false #678 #647) -#632 := (iff #628 #647) -#633 := [rewrite]: #632 -#630 := (iff #679 #628) -#649 := (iff #677 #647) -#640 := (ite #345 #667 #636) -#643 := (ite #751 #667 #640) -#648 := (iff #643 #647) -#638 := [rewrite]: #648 -#644 := (iff #677 #643) -#641 := (iff #665 #640) -#637 := (iff #687 #636) -#652 := (= #683 #655) -#653 := (= #686 #688) -#444 := (= #424 -1::Int) -#445 := [rewrite]: #444 -#654 := [monotonicity #445]: #653 -#656 := [monotonicity #654]: #652 -#639 := [monotonicity #656]: #637 -#650 := (iff #668 #667) -#659 := (= #676 #12) -#658 := (+ #12 0::Int) -#662 := (= #658 #12) -#663 := [rewrite]: #662 -#660 := (= #676 #658) -#673 := (= #674 0::Int) -#669 := (* -1::Int 0::Int) -#672 := (= #669 0::Int) -#666 := [rewrite]: #672 -#670 := (= #674 #669) -#675 := (= #532 0::Int) -#680 := [rewrite]: #675 -#671 := [monotonicity #680]: #670 -#657 := [trans #671 #666]: #673 -#661 := [monotonicity #657]: #660 -#664 := [trans #661 #663]: #659 -#651 := [monotonicity #664]: #650 -#721 := (iff #748 #345) -#450 := (iff #740 #449) -#726 := (iff #533 #746) -#378 := (or false #746) -#739 := (iff #378 #746) -#725 := [rewrite]: #739 -#738 := (iff #533 #378) -#393 := (iff #403 false) -#729 := [rewrite]: #393 -#736 := [monotonicity #729]: #738 -#448 := [trans #736 #725]: #726 -#451 := [monotonicity #448]: #450 -#737 := (iff #747 #735) -#734 := (iff #415 #414) -#730 := (or #414 false) -#733 := (iff #730 #414) -#728 := [rewrite]: #733 -#731 := (iff #415 #730) -#732 := [monotonicity #729]: #731 -#372 := [trans #732 #728]: #734 -#377 := [monotonicity #372]: #737 -#722 := [monotonicity #377 #451]: #721 -#642 := [monotonicity #722 #651 #639]: #641 -#645 := [monotonicity #642]: #644 -#627 := [trans #645 #638]: #649 -#406 := (iff #745 false) -#742 := [rewrite]: #406 -#631 := [monotonicity #742 #627]: #630 -#629 := [trans #631 #633]: #634 -#624 := [trans #629 #622]: #623 -#601 := [monotonicity #624]: #600 -#606 := [trans #601 #605]: #600 -#599 := [quant-inst #8 #9]: #626 -#607 := [mp #599 #606]: #620 -#505 := [unit-resolution #607 #765]: #618 -#602 := (not #618) -#603 := (or #602 #615 #667) -#598 := [def-axiom]: #603 -#501 := [unit-resolution #598 #505]: #498 -#502 := [unit-resolution #501 #551]: #667 -#579 := (not #667) -#488 := (or #579 #596) -#490 := [th-lemma arith triangle-eq]: #488 -#491 := [unit-resolution #490 #502]: #596 -#698 := (<= #10 0::Int) -#750 := (= #10 0::Int) -#453 := [hypothesis]: #570 -#702 := (not #345) -#426 := (div f3 1::Int) -#430 := (* -1::Int #426) -#409 := (+ #10 #430) -#744 := (= #409 0::Int) -#577 := (not #744) -#544 := (+ f3 #430) -#549 := (>= #544 0::Int) -#543 := (= #544 0::Int) -#1 := true -#63 := [true-axiom]: true -#493 := (or false #543) -#495 := [th-lemma arith]: #493 -#496 := [unit-resolution #495 #63]: #543 -#499 := (not #543) -#500 := (or #499 #549) -#504 := [th-lemma arith triangle-eq]: #500 -#497 := [unit-resolution #504 #496]: #549 -#534 := (<= #409 0::Int) -#489 := [hypothesis]: #744 -#492 := (or #577 #534) -#474 := [th-lemma arith triangle-eq]: #492 -#476 := [unit-resolution #474 #489]: #534 -#479 := (not #549) -#478 := (not #534) -#477 := (not #596) -#480 := (or #423 #477 #478 #479) -#481 := [th-lemma arith assign-bounds 1 1 -1]: #480 -#482 := [unit-resolution #481 #476 #491 #497]: #423 -#339 := (<= #81 0::Int) -#531 := (<= #544 0::Int) -#483 := (or #499 #531) -#484 := [th-lemma arith triangle-eq]: #483 -#485 := [unit-resolution #484 #496]: #531 -#542 := (>= #12 0::Int) -#486 := (or #579 #542) -#475 := [th-lemma arith triangle-eq]: #486 -#487 := [unit-resolution #475 #502]: #542 -#535 := (>= #409 0::Int) -#464 := (or #577 #535) -#466 := [th-lemma arith triangle-eq]: #464 -#467 := [unit-resolution #466 #489]: #535 -#470 := (not #531) -#469 := (not #535) -#468 := (not #542) -#471 := (or #339 #468 #469 #470) -#472 := [th-lemma arith assign-bounds 1 1 -1]: #471 -#465 := [unit-resolution #472 #467 #487 #485]: #339 -#458 := (not #423) -#473 := (not #339) -#462 := (or #473 #458) -#82 := (= #81 0::Int) -#85 := (not #82) -#11 := (* #10 1::Int) -#13 := (+ #11 #12) -#14 := (= f3 #13) -#15 := (not #14) -#88 := (iff #15 #85) -#68 := (+ #10 #12) -#71 := (= f3 #68) -#74 := (not #71) -#86 := (iff #74 #85) -#83 := (iff #71 #82) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#75 := (iff #15 #74) -#72 := (iff #14 #71) -#69 := (= #13 #68) -#66 := (= #11 #10) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#73 := [monotonicity #70]: #72 -#76 := [monotonicity #73]: #75 -#89 := [trans #76 #87]: #88 -#65 := [asserted]: #15 -#90 := [mp #65 #89]: #85 -#459 := (or #82 #473 #458) -#460 := [th-lemma arith triangle-eq]: #459 -#461 := [unit-resolution #460 #90]: #462 -#463 := [unit-resolution #461 #465 #482]: false -#452 := [lemma #463]: #577 -#719 := (div #425 -1::Int) -#724 := (* -1::Int #719) -#436 := (+ #10 #724) -#716 := (= #436 0::Int) -#717 := (ite #345 #744 #716) -#446 := (or #751 #717) -#707 := (ite #751 #750 #717) -#18 := (f4 #16 #17) -#752 := (pattern #18) -#104 := (div #98 #101) -#255 := (* -1::Int #104) -#256 := (+ #18 #255) -#257 := (= #256 0::Int) -#29 := (div #16 #17) -#252 := (* -1::Int #29) -#253 := (+ #18 #252) -#254 := (= #253 0::Int) -#258 := (ite #219 #254 #257) -#251 := (= #18 0::Int) -#22 := (or #20 #21) -#259 := (ite #22 #251 #258) -#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #259) -#262 := (forall (vars (?v0 Int) (?v1 Int)) #259) -#756 := (iff #262 #753) -#754 := (iff #259 #259) -#755 := [refl]: #754 -#757 := [quant-intro #755]: #756 -#222 := (ite #219 #29 #104) -#225 := (ite #22 0::Int #222) -#228 := (= #18 #225) -#231 := (forall (vars (?v0 Int) (?v1 Int)) #228) -#263 := (iff #231 #262) -#260 := (iff #228 #259) -#261 := [rewrite]: #260 -#264 := [quant-intro #261]: #263 -#140 := (ite #137 #29 #104) -#143 := (ite #22 0::Int #140) -#146 := (= #18 #143) -#149 := (forall (vars (?v0 Int) (?v1 Int)) #146) -#232 := (iff #149 #231) -#229 := (iff #146 #228) -#226 := (= #143 #225) -#223 := (= #140 #222) -#224 := [monotonicity #221]: #223 -#227 := [monotonicity #224]: #226 -#230 := [monotonicity #227]: #229 -#233 := [quant-intro #230]: #232 -#211 := (~ #149 #149) -#209 := (~ #146 #146) -#210 := [refl]: #209 -#212 := [nnf-pos #210]: #211 -#32 := (div #30 #31) -#33 := (ite #28 #29 #32) -#34 := (ite #22 0::Int #33) -#35 := (= #18 #34) -#36 := (forall (vars (?v0 Int) (?v1 Int)) #35) -#152 := (iff #36 #149) -#107 := (ite #95 #29 #104) -#110 := (ite #22 0::Int #107) -#113 := (= #18 #110) -#116 := (forall (vars (?v0 Int) (?v1 Int)) #113) -#150 := (iff #116 #149) -#147 := (iff #113 #146) -#144 := (= #110 #143) -#141 := (= #107 #140) -#142 := [monotonicity #139]: #141 -#145 := [monotonicity #142]: #144 -#148 := [monotonicity #145]: #147 -#151 := [quant-intro #148]: #150 -#117 := (iff #36 #116) -#114 := (iff #35 #113) -#111 := (= #34 #110) -#108 := (= #33 #107) -#105 := (= #32 #104) -#106 := [monotonicity #100 #103]: #105 -#109 := [monotonicity #97 #106]: #108 -#112 := [monotonicity #109]: #111 -#115 := [monotonicity #112]: #114 -#118 := [quant-intro #115]: #117 -#153 := [trans #118 #151]: #152 -#91 := [asserted]: #36 -#154 := [mp #91 #153]: #149 -#203 := [mp~ #154 #212]: #149 -#234 := [mp #203 #233]: #231 -#265 := [mp #234 #264]: #262 -#758 := [mp #265 #757]: #753 -#704 := (not #753) -#705 := (or #704 #707) -#416 := (div #425 #424) -#427 := (* -1::Int #416) -#428 := (+ #10 #427) -#429 := (= #428 0::Int) -#749 := (ite #748 #744 #429) -#741 := (or #751 #745) -#401 := (ite #741 #750 #749) -#710 := (or #704 #401) -#706 := (iff #710 #705) -#553 := (iff #705 #705) -#554 := [rewrite]: #553 -#708 := (iff #401 #707) -#714 := (iff #749 #717) -#431 := (iff #429 #716) -#437 := (= #428 #436) -#434 := (= #427 #724) -#723 := (= #416 #719) -#720 := [monotonicity #445]: #723 -#435 := [monotonicity #720]: #434 -#715 := [monotonicity #435]: #437 -#713 := [monotonicity #715]: #431 -#718 := [monotonicity #722 #713]: #714 -#391 := (iff #741 #751) -#402 := (or #751 false) -#727 := (iff #402 #751) -#390 := [rewrite]: #727 -#743 := (iff #741 #402) -#386 := [monotonicity #742]: #743 -#392 := [trans #386 #390]: #391 -#709 := [monotonicity #392 #718]: #708 -#712 := [monotonicity #709]: #706 -#555 := [trans #712 #554]: #706 -#711 := [quant-inst #8 #9]: #710 -#697 := [mp #711 #555]: #705 -#454 := [unit-resolution #697 #758]: #707 -#685 := (not #707) -#588 := (or #685 #751 #717) -#581 := [def-axiom]: #588 -#455 := [unit-resolution #581 #454]: #446 -#456 := [unit-resolution #455 #453]: #717 -#692 := (not #717) -#690 := (or #692 #702 #744) -#693 := [def-axiom]: #690 -#447 := [unit-resolution #693 #456 #452]: #702 -#700 := (or #345 #414) -#694 := [def-axiom]: #700 -#457 := [unit-resolution #694 #447]: #414 -#695 := (or #345 #746) -#701 := [def-axiom]: #695 -#438 := [unit-resolution #701 #447]: #746 -#439 := [unit-resolution #595 #438 #457 #453]: false -#440 := [lemma #439]: #751 -#432 := (or #570 #750) -#585 := (or #685 #570 #750) -#587 := [def-axiom]: #585 -#441 := [unit-resolution #587 #454]: #432 -#442 := [unit-resolution #441 #440]: #750 -#589 := (not #750) -#433 := (or #589 #698) -#443 := [th-lemma arith triangle-eq]: #433 -#410 := [unit-resolution #443 #442]: #698 -#412 := (or #570 #746) -#413 := [th-lemma arith triangle-eq]: #412 -#404 := [unit-resolution #413 #440]: #746 -#417 := (not #698) -#418 := (or #423 #417 #477 #449) -#419 := [th-lemma arith assign-bounds 1 1 -1]: #418 -#420 := [unit-resolution #419 #404 #410 #491]: #423 -#699 := (>= #10 0::Int) -#421 := (or #589 #699) -#411 := [th-lemma arith triangle-eq]: #421 -#422 := [unit-resolution #411 #442]: #699 -#405 := (or #570 #414) -#407 := [th-lemma arith triangle-eq]: #405 -#408 := [unit-resolution #407 #440]: #414 -#387 := (not #699) -#389 := (or #339 #387 #468 #735) -#394 := [th-lemma arith assign-bounds 1 1 -1]: #389 -#395 := [unit-resolution #394 #408 #422 #487]: #339 -[unit-resolution #461 #395 #420]: false -unsat -b7566ab9692699d99b59e9354d5e78d5af5e3d40 544 0 -#2 := false -#19 := 0::Int -decl f4 :: (-> Int Int Int) -#9 := 3::Int -decl f3 :: Int -#8 := f3 -#10 := (f4 f3 3::Int) -#701 := (>= #10 0::Int) -#752 := (= #10 0::Int) -#748 := (= f3 0::Int) -#688 := (not #748) -#560 := [hypothesis]: #688 -#743 := (<= f3 0::Int) -#747 := (>= f3 0::Int) -#451 := (not #747) -#375 := (not #743) -#454 := (or #375 #451) -#704 := (not #454) -#78 := -3::Int -#80 := -1::Int -#428 := (* -1::Int f3) -#448 := (div #428 -3::Int) -#723 := (* -1::Int #448) -#438 := (+ #10 #723) -#718 := (= #438 0::Int) -#432 := (div f3 3::Int) -#429 := (* -1::Int #432) -#433 := (+ #10 #429) -#412 := (= #433 0::Int) -#716 := (ite #454 #412 #718) -#562 := (or #748 #716) -#721 := (ite #748 #752 #716) -#17 := (:var 0 Int) -#16 := (:var 1 Int) -#18 := (f4 #16 #17) -#755 := (pattern #18) -#103 := (* -1::Int #17) -#100 := (* -1::Int #16) -#106 := (div #100 #103) -#257 := (* -1::Int #106) -#258 := (+ #18 #257) -#259 := (= #258 0::Int) -#29 := (div #16 #17) -#254 := (* -1::Int #29) -#255 := (+ #18 #254) -#256 := (= #255 0::Int) -#132 := (>= #16 0::Int) -#125 := (<= #17 0::Int) -#217 := (or #125 #132) -#218 := (not #217) -#121 := (<= #16 0::Int) -#215 := (or #121 #125) -#216 := (not #215) -#221 := (or #216 #218) -#260 := (ite #221 #256 #259) -#253 := (= #18 0::Int) -#21 := (= #17 0::Int) -#20 := (= #16 0::Int) -#22 := (or #20 #21) -#261 := (ite #22 #253 #260) -#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #261) -#264 := (forall (vars (?v0 Int) (?v1 Int)) #261) -#759 := (iff #264 #756) -#757 := (iff #261 #261) -#758 := [refl]: #757 -#760 := [quant-intro #758]: #759 -#224 := (ite #221 #29 #106) -#227 := (ite #22 0::Int #224) -#230 := (= #18 #227) -#233 := (forall (vars (?v0 Int) (?v1 Int)) #230) -#265 := (iff #233 #264) -#262 := (iff #230 #261) -#263 := [rewrite]: #262 -#266 := [quant-intro #263]: #265 -#133 := (not #132) -#126 := (not #125) -#136 := (and #126 #133) -#122 := (not #121) -#129 := (and #122 #126) -#139 := (or #129 #136) -#142 := (ite #139 #29 #106) -#145 := (ite #22 0::Int #142) -#148 := (= #18 #145) -#151 := (forall (vars (?v0 Int) (?v1 Int)) #148) -#234 := (iff #151 #233) -#231 := (iff #148 #230) -#228 := (= #145 #227) -#225 := (= #142 #224) -#222 := (iff #139 #221) -#219 := (iff #136 #218) -#220 := [rewrite]: #219 -#209 := (iff #129 #216) -#210 := [rewrite]: #209 -#223 := [monotonicity #210 #220]: #222 -#226 := [monotonicity #223]: #225 -#229 := [monotonicity #226]: #228 -#232 := [monotonicity #229]: #231 -#235 := [quant-intro #232]: #234 -#213 := (~ #151 #151) -#211 := (~ #148 #148) -#212 := [refl]: #211 -#214 := [nnf-pos #212]: #213 -#31 := (- #17) -#30 := (- #16) -#32 := (div #30 #31) -#24 := (< 0::Int #17) -#26 := (< #16 0::Int) -#27 := (and #26 #24) -#23 := (< 0::Int #16) -#25 := (and #23 #24) -#28 := (or #25 #27) -#33 := (ite #28 #29 #32) -#34 := (ite #22 0::Int #33) -#35 := (= #18 #34) -#36 := (forall (vars (?v0 Int) (?v1 Int)) #35) -#154 := (iff #36 #151) -#94 := (and #24 #26) -#97 := (or #25 #94) -#109 := (ite #97 #29 #106) -#112 := (ite #22 0::Int #109) -#115 := (= #18 #112) -#118 := (forall (vars (?v0 Int) (?v1 Int)) #115) -#152 := (iff #118 #151) -#149 := (iff #115 #148) -#146 := (= #112 #145) -#143 := (= #109 #142) -#140 := (iff #97 #139) -#137 := (iff #94 #136) -#134 := (iff #26 #133) -#135 := [rewrite]: #134 -#127 := (iff #24 #126) -#128 := [rewrite]: #127 -#138 := [monotonicity #128 #135]: #137 -#130 := (iff #25 #129) -#123 := (iff #23 #122) -#124 := [rewrite]: #123 -#131 := [monotonicity #124 #128]: #130 -#141 := [monotonicity #131 #138]: #140 -#144 := [monotonicity #141]: #143 -#147 := [monotonicity #144]: #146 -#150 := [monotonicity #147]: #149 -#153 := [quant-intro #150]: #152 -#119 := (iff #36 #118) -#116 := (iff #35 #115) -#113 := (= #34 #112) -#110 := (= #33 #109) -#107 := (= #32 #106) -#104 := (= #31 #103) -#105 := [rewrite]: #104 -#101 := (= #30 #100) -#102 := [rewrite]: #101 -#108 := [monotonicity #102 #105]: #107 -#98 := (iff #28 #97) -#95 := (iff #27 #94) -#96 := [rewrite]: #95 -#99 := [monotonicity #96]: #98 -#111 := [monotonicity #99 #108]: #110 -#114 := [monotonicity #111]: #113 -#117 := [monotonicity #114]: #116 -#120 := [quant-intro #117]: #119 -#155 := [trans #120 #153]: #154 -#93 := [asserted]: #36 -#156 := [mp #93 #155]: #151 -#205 := [mp~ #156 #214]: #151 -#236 := [mp #205 #235]: #233 -#267 := [mp #236 #266]: #264 -#761 := [mp #267 #760]: #756 -#712 := (not #756) -#707 := (or #712 #721) -#427 := (* -1::Int 3::Int) -#419 := (div #428 #427) -#430 := (* -1::Int #419) -#431 := (+ #10 #430) -#359 := (= #431 0::Int) -#749 := (<= 3::Int 0::Int) -#406 := (or #749 #747) -#536 := (not #406) -#417 := (or #743 #749) -#418 := (not #417) -#750 := (or #418 #536) -#751 := (ite #750 #412 #359) -#753 := (= 3::Int 0::Int) -#754 := (or #748 #753) -#744 := (ite #754 #752 #751) -#708 := (or #712 #744) -#714 := (iff #708 #707) -#715 := (iff #707 #707) -#556 := [rewrite]: #715 -#710 := (iff #744 #721) -#720 := (iff #751 #716) -#719 := (iff #359 #718) -#439 := (= #431 #438) -#727 := (= #430 #723) -#722 := (= #419 #448) -#725 := (= #427 -3::Int) -#447 := [rewrite]: #725 -#726 := [monotonicity #447]: #722 -#437 := [monotonicity #726]: #727 -#440 := [monotonicity #437]: #439 -#434 := [monotonicity #440]: #719 -#347 := (iff #750 #454) -#452 := (iff #536 #451) -#728 := (iff #406 #747) -#380 := (or false #747) -#739 := (iff #380 #747) -#742 := [rewrite]: #739 -#381 := (iff #406 #380) -#395 := (iff #749 false) -#396 := [rewrite]: #395 -#741 := [monotonicity #396]: #381 -#729 := [trans #741 #742]: #728 -#453 := [monotonicity #729]: #452 -#738 := (iff #418 #375) -#731 := (iff #417 #743) -#732 := (or #743 false) -#735 := (iff #732 #743) -#736 := [rewrite]: #735 -#733 := (iff #417 #732) -#734 := [monotonicity #396]: #733 -#737 := [trans #734 #736]: #731 -#740 := [monotonicity #737]: #738 -#724 := [monotonicity #740 #453]: #347 -#717 := [monotonicity #724 #434]: #720 -#393 := (iff #754 #748) -#745 := (or #748 false) -#389 := (iff #745 #748) -#730 := [rewrite]: #389 -#405 := (iff #754 #745) -#404 := (iff #753 false) -#409 := [rewrite]: #404 -#746 := [monotonicity #409]: #405 -#394 := [trans #746 #730]: #393 -#711 := [monotonicity #394 #717]: #710 -#709 := [monotonicity #711]: #714 -#557 := [trans #709 #556]: #714 -#713 := [quant-inst #8 #9]: #708 -#558 := [mp #713 #557]: #707 -#561 := [unit-resolution #558 #761]: #721 -#685 := (not #721) -#590 := (or #685 #748 #716) -#591 := [def-axiom]: #590 -#563 := [unit-resolution #591 #561]: #562 -#564 := [unit-resolution #563 #560]: #716 -#538 := (mod #428 -3::Int) -decl f5 :: (-> Int Int Int) -#12 := (f5 f3 3::Int) -#683 := (+ #12 #538) -#674 := (= #683 0::Int) -#706 := (mod f3 3::Int) -#690 := (* -1::Int #706) -#677 := (+ #12 #690) -#679 := (= #677 0::Int) -#676 := (ite #454 #679 #674) -#523 := (or #748 #676) -#668 := (= #12 0::Int) -#663 := (ite #748 #668 #676) -#37 := (f5 #16 #17) -#762 := (pattern #37) -#158 := (mod #100 #103) -#273 := (+ #37 #158) -#274 := (= #273 0::Int) -#38 := (mod #16 #17) -#270 := (* -1::Int #38) -#271 := (+ #37 #270) -#272 := (= #271 0::Int) -#275 := (ite #221 #272 #274) -#269 := (= #37 0::Int) -#276 := (ite #20 #269 #275) -#268 := (= #16 #37) -#277 := (ite #21 #268 #276) -#763 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #762) #277) -#280 := (forall (vars (?v0 Int) (?v1 Int)) #277) -#766 := (iff #280 #763) -#764 := (iff #277 #277) -#765 := [refl]: #764 -#767 := [quant-intro #765]: #766 -#164 := (* -1::Int #158) -#237 := (ite #221 #38 #164) -#240 := (ite #20 0::Int #237) -#243 := (ite #21 #16 #240) -#246 := (= #37 #243) -#249 := (forall (vars (?v0 Int) (?v1 Int)) #246) -#281 := (iff #249 #280) -#278 := (iff #246 #277) -#279 := [rewrite]: #278 -#282 := [quant-intro #279]: #281 -#184 := (ite #139 #38 #164) -#187 := (ite #20 0::Int #184) -#190 := (ite #21 #16 #187) -#193 := (= #37 #190) -#196 := (forall (vars (?v0 Int) (?v1 Int)) #193) -#250 := (iff #196 #249) -#247 := (iff #193 #246) -#244 := (= #190 #243) -#241 := (= #187 #240) -#238 := (= #184 #237) -#239 := [monotonicity #223]: #238 -#242 := [monotonicity #239]: #241 -#245 := [monotonicity #242]: #244 -#248 := [monotonicity #245]: #247 -#251 := [quant-intro #248]: #250 -#207 := (~ #196 #196) -#206 := (~ #193 #193) -#203 := [refl]: #206 -#208 := [nnf-pos #203]: #207 -#39 := (mod #30 #31) -#40 := (- #39) -#41 := (ite #28 #38 #40) -#42 := (ite #20 0::Int #41) -#43 := (ite #21 #16 #42) -#44 := (= #37 #43) -#45 := (forall (vars (?v0 Int) (?v1 Int)) #44) -#199 := (iff #45 #196) -#169 := (ite #97 #38 #164) -#172 := (ite #20 0::Int #169) -#175 := (ite #21 #16 #172) -#178 := (= #37 #175) -#181 := (forall (vars (?v0 Int) (?v1 Int)) #178) -#197 := (iff #181 #196) -#194 := (iff #178 #193) -#191 := (= #175 #190) -#188 := (= #172 #187) -#185 := (= #169 #184) -#186 := [monotonicity #141]: #185 -#189 := [monotonicity #186]: #188 -#192 := [monotonicity #189]: #191 -#195 := [monotonicity #192]: #194 -#198 := [quant-intro #195]: #197 -#182 := (iff #45 #181) -#179 := (iff #44 #178) -#176 := (= #43 #175) -#173 := (= #42 #172) -#170 := (= #41 #169) -#167 := (= #40 #164) -#161 := (- #158) -#165 := (= #161 #164) -#166 := [rewrite]: #165 -#162 := (= #40 #161) -#159 := (= #39 #158) -#160 := [monotonicity #102 #105]: #159 -#163 := [monotonicity #160]: #162 -#168 := [trans #163 #166]: #167 -#171 := [monotonicity #99 #168]: #170 -#174 := [monotonicity #171]: #173 -#177 := [monotonicity #174]: #176 -#180 := [monotonicity #177]: #179 -#183 := [quant-intro #180]: #182 -#200 := [trans #183 #198]: #199 -#157 := [asserted]: #45 -#201 := [mp #157 #200]: #196 -#204 := [mp~ #201 #208]: #196 -#252 := [mp #204 #251]: #249 -#283 := [mp #252 #282]: #280 -#768 := [mp #283 #767]: #763 -#658 := (not #763) -#655 := (or #658 #663) -#596 := (mod #428 #427) -#689 := (+ #12 #596) -#686 := (= #689 0::Int) -#671 := (ite #750 #679 #686) -#670 := (ite #748 #668 #671) -#680 := (= f3 #12) -#681 := (ite #753 #680 #670) -#659 := (or #658 #681) -#640 := (iff #659 #655) -#643 := (iff #655 #655) -#644 := [rewrite]: #643 -#656 := (iff #681 #663) -#666 := (ite false #680 #663) -#653 := (iff #666 #663) -#654 := [rewrite]: #653 -#662 := (iff #681 #666) -#664 := (iff #670 #663) -#660 := (iff #671 #676) -#675 := (iff #686 #674) -#672 := (= #689 #683) -#682 := (= #596 #538) -#678 := [monotonicity #447]: #682 -#673 := [monotonicity #678]: #672 -#669 := [monotonicity #673]: #675 -#661 := [monotonicity #724 #669]: #660 -#665 := [monotonicity #661]: #664 -#667 := [monotonicity #409 #665]: #662 -#657 := [trans #667 #654]: #656 -#642 := [monotonicity #657]: #640 -#645 := [trans #642 #644]: #640 -#639 := [quant-inst #8 #9]: #659 -#646 := [mp #639 #645]: #655 -#619 := [unit-resolution #646 #768]: #663 -#620 := (not #663) -#625 := (or #620 #748 #676) -#626 := [def-axiom]: #625 -#524 := [unit-resolution #626 #619]: #523 -#525 := [unit-resolution #524 #560]: #676 -#694 := (not #716) -#652 := (not #676) -#489 := (or #704 #652 #694) -#650 := (>= #677 0::Int) -#565 := [hypothesis]: #676 -#566 := [hypothesis]: #454 -#630 := (or #652 #704 #679) -#631 := [def-axiom]: #630 -#567 := [unit-resolution #631 #566 #565]: #679 -#635 := (not #679) -#491 := (or #635 #650) -#493 := [th-lemma arith triangle-eq]: #491 -#494 := [unit-resolution #493 #567]: #650 -#537 := (>= #433 0::Int) -#547 := [hypothesis]: #716 -#695 := (or #694 #704 #412) -#693 := [def-axiom]: #695 -#548 := [unit-resolution #693 #566 #547]: #412 -#579 := (not #412) -#492 := (or #579 #537) -#495 := [th-lemma arith triangle-eq]: #492 -#477 := [unit-resolution #495 #548]: #537 -#81 := (* -1::Int #12) -#79 := (* -3::Int #10) -#82 := (+ #79 #81) -#83 := (+ f3 #82) -#341 := (<= #83 0::Int) -#479 := (not #341) -#426 := (>= #83 0::Int) -#555 := (not #426) -#571 := [hypothesis]: #555 -#531 := (or #748 #426) -#552 := (or #704 #426 #652 #694) -#649 := (<= #677 0::Int) -#568 := (or #635 #649) -#569 := [th-lemma arith triangle-eq]: #568 -#570 := [unit-resolution #569 #567]: #649 -#613 := (* -3::Int #432) -#616 := (+ #613 #690) -#617 := (+ f3 #616) -#599 := (>= #617 0::Int) -#612 := (= #617 0::Int) -#1 := true -#63 := [true-axiom]: true -#532 := (or false #612) -#533 := [th-lemma arith]: #532 -#540 := [unit-resolution #533 #63]: #612 -#542 := (not #612) -#543 := (or #542 #599) -#544 := [th-lemma arith triangle-eq]: #543 -#546 := [unit-resolution #544 #540]: #599 -#535 := (<= #433 0::Int) -#549 := (or #579 #535) -#550 := [th-lemma arith triangle-eq]: #549 -#551 := [unit-resolution #550 #548]: #535 -#534 := [th-lemma arith farkas 3 -1 1 1 #551 #546 #571 #570]: false -#522 := [lemma #534]: #552 -#527 := [unit-resolution #522 #525 #571 #564]: #704 -#702 := (or #454 #743) -#703 := [def-axiom]: #702 -#528 := [unit-resolution #703 #527]: #743 -#697 := (or #454 #747) -#698 := [def-axiom]: #697 -#529 := [unit-resolution #698 #527]: #747 -#372 := (or #748 #375 #451) -#530 := [th-lemma arith triangle-eq]: #372 -#526 := [unit-resolution #530 #529 #528 #560]: false -#510 := [lemma #526]: #531 -#513 := [unit-resolution #510 #571]: #748 -#517 := (or #688 #747) -#519 := [th-lemma arith triangle-eq]: #517 -#520 := [unit-resolution #519 #513]: #747 -#647 := (<= #12 0::Int) -#518 := (or #688 #668) -#621 := (or #620 #688 #668) -#622 := [def-axiom]: #621 -#521 := [unit-resolution #622 #619]: #518 -#509 := [unit-resolution #521 #513]: #668 -#627 := (not #668) -#512 := (or #627 #647) -#514 := [th-lemma arith triangle-eq]: #512 -#515 := [unit-resolution #514 #509]: #647 -#700 := (<= #10 0::Int) -#511 := (or #688 #752) -#573 := (or #685 #688 #752) -#588 := [def-axiom]: #573 -#516 := [unit-resolution #588 #561]: #511 -#506 := [unit-resolution #516 #513]: #752 -#584 := (not #752) -#496 := (or #584 #700) -#498 := [th-lemma arith triangle-eq]: #496 -#499 := [unit-resolution #498 #506]: #700 -#502 := [th-lemma arith farkas -3 -1 -1 1 #499 #515 #571 #520]: false -#503 := [lemma #502]: #426 -#482 := (or #479 #555) -#84 := (= #83 0::Int) -#87 := (not #84) -#11 := (* #10 3::Int) -#13 := (+ #11 #12) -#14 := (= f3 #13) -#15 := (not #14) -#90 := (iff #15 #87) -#66 := (* 3::Int #10) -#69 := (+ #66 #12) -#72 := (= f3 #69) -#75 := (not #72) -#88 := (iff #75 #87) -#85 := (iff #72 #84) -#86 := [rewrite]: #85 +#108 := [monotonicity #70 #105]: #107 +#111 := [monotonicity #108]: #110 +#56 := (iff #12 false) +#57 := [rewrite]: #56 +#114 := [monotonicity #57 #111]: #113 +#118 := [trans #114 #116]: #117 +#93 := (= #26 #90) +#87 := (* #84 3::Int) +#91 := (= #87 #90) +#92 := [rewrite]: #91 +#88 := (= #26 #87) +#85 := (= #25 #84) +#82 := (= #24 #81) +#79 := (= #23 #78) +#80 := [monotonicity #74 #77]: #79 +#83 := [monotonicity #70 #80]: #82 +#63 := (iff #13 #10) +#58 := (or #10 false) +#61 := (iff #58 #10) +#62 := [rewrite]: #61 +#59 := (iff #13 #58) +#60 := [monotonicity #57]: #59 +#64 := [trans #60 #62]: #63 +#86 := [monotonicity #64 #83]: #85 #89 := [monotonicity #86]: #88 -#76 := (iff #15 #75) -#73 := (iff #14 #72) -#70 := (= #13 #69) -#67 := (= #11 #66) -#68 := [rewrite]: #67 -#71 := [monotonicity #68]: #70 -#74 := [monotonicity #71]: #73 -#77 := [monotonicity #74]: #76 -#91 := [trans #77 #89]: #90 -#65 := [asserted]: #15 -#92 := [mp #65 #91]: #87 -#480 := (or #84 #479 #555) -#481 := [th-lemma arith triangle-eq]: #480 -#483 := [unit-resolution #481 #92]: #482 -#484 := [unit-resolution #483 #503]: #479 -#507 := (<= #617 0::Int) -#485 := (or #542 #507) -#486 := [th-lemma arith triangle-eq]: #485 -#487 := [unit-resolution #486 #540]: #507 -#488 := [th-lemma arith farkas -1 1 3 1 #487 #484 #477 #494]: false -#478 := [lemma #488]: #489 -#500 := [unit-resolution #478 #525 #564]: #704 -#508 := [unit-resolution #703 #500]: #743 -#501 := [unit-resolution #698 #500]: #747 -#504 := [unit-resolution #530 #501 #508 #560]: false -#505 := [lemma #504]: #748 -#490 := [unit-resolution #516 #505]: #752 -#467 := (or #584 #701) -#469 := [th-lemma arith triangle-eq]: #467 -#470 := [unit-resolution #469 #490]: #701 -#648 := (>= #12 0::Int) -#471 := [unit-resolution #521 #505]: #668 -#472 := (or #627 #648) -#473 := [th-lemma arith triangle-eq]: #472 -#474 := [unit-resolution #473 #471]: #648 -#475 := (or #688 #743) -#468 := [th-lemma arith triangle-eq]: #475 -#476 := [unit-resolution #468 #505]: #743 -[th-lemma arith farkas -1/3 1/3 1/3 1 #476 #474 #484 #470]: false +#94 := [trans #89 #92]: #93 +#121 := [monotonicity #94 #118]: #120 +#124 := [monotonicity #121]: #123 +#127 := [monotonicity #124]: #126 +#189 := [trans #127 #187]: #188 +#55 := [asserted]: #35 +#190 := [mp #55 #189]: #185 +#264 := (or #180 #262 #263) +#265 := [th-lemma arith triangle-eq]: #264 +#267 := [unit-resolution #265 #190]: #266 +#268 := [unit-resolution #267 #261 #250]: false +#269 := [lemma #268]: #152 +#310 := [hypothesis]: #10 +#311 := (or #207 #128) +#312 := [th-lemma arith triangle-eq]: #311 +#313 := [unit-resolution #312 #310]: #128 +#314 := (or #207 #141) +#286 := [th-lemma arith triangle-eq]: #314 +#319 := [unit-resolution #286 #310]: #141 +#201 := (or #200 #129 #142) +#202 := [def-axiom]: #201 +#323 := [unit-resolution #202 #319 #313 #269]: false +#350 := [lemma #323]: #207 +#222 := (or #10 #213) +#223 := [def-axiom]: #222 +#359 := [unit-resolution #223 #350]: #213 +#214 := (= #27 #164) +#216 := (or #200 #214) +#217 := [def-axiom]: #216 +#326 := [unit-resolution #217 #269]: #214 +#360 := [trans #326 #359]: #320 +#328 := (not #320) +#361 := (or #328 #358) +#362 := [th-lemma arith triangle-eq]: #361 +#363 := [unit-resolution #362 #360]: #358 +#280 := (* -1::Int #27) +#279 := (* -3::Int #20) +#281 := (+ #279 #280) +#282 := (+ f3 #281) +#351 := (>= #282 0::Int) +#278 := (= #282 0::Int) +#53 := [true-axiom]: true +#332 := (or false #278) +#333 := [th-lemma arith]: #332 +#334 := [unit-resolution #333 #53]: #278 +#335 := (not #278) +#364 := (or #335 #351) +#365 := [th-lemma arith triangle-eq]: #364 +#366 := [unit-resolution #365 #334]: #351 +#348 := (or #10 #224) +#322 := (<= #321 0::Int) +#324 := [hypothesis]: #207 +#325 := [unit-resolution #223 #324]: #213 +#327 := [trans #326 #325]: #320 +#329 := (or #328 #322) +#330 := [th-lemma arith triangle-eq]: #329 +#331 := [unit-resolution #330 #327]: #322 +#285 := (<= #282 0::Int) +#336 := (or #335 #285) +#337 := [th-lemma arith triangle-eq]: #336 +#338 := [unit-resolution #337 #334]: #285 +#339 := [hypothesis]: #262 +#316 := (* -1::Int #158) +#317 := (+ #20 #316) +#318 := (<= #317 0::Int) +#315 := (= #20 #158) +#197 := (= #155 #158) +#210 := (or #10 #197) +#211 := [def-axiom]: #210 +#340 := [unit-resolution #211 #324]: #197 +#198 := (= #20 #155) +#203 := (or #200 #198) +#204 := [def-axiom]: #203 +#341 := [unit-resolution #204 #269]: #198 +#342 := [trans #341 #340]: #315 +#343 := (not #315) +#344 := (or #343 #318) +#345 := [th-lemma arith triangle-eq]: #344 +#346 := [unit-resolution #345 #342]: #318 +#347 := [th-lemma arith farkas 3 -1 1 1 #346 #339 #338 #331]: false +#349 := [lemma #347]: #348 +#367 := [unit-resolution #349 #350]: #224 +#368 := [unit-resolution #267 #367]: #263 +#357 := (>= #317 0::Int) +#369 := [unit-resolution #211 #350]: #197 +#370 := [trans #341 #369]: #315 +#371 := (or #343 #357) +#372 := [th-lemma arith triangle-eq]: #371 +#373 := [unit-resolution #372 #370]: #357 +[th-lemma arith farkas 3 -1 1 1 #373 #368 #366 #363]: false unsat cacbb4776a876130daed2cf13657b41ab1c7df25 75 0 #2 := false diff -r 679118e35378 -r a4d1b5eef12e src/HOL/SMT_Examples/SMT_Word_Examples.certs --- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs Sun Dec 19 18:55:21 2010 +0100 @@ -36,6 +36,12 @@ unsat 64c9fe73f7ca3832f4daec3b66d94e4f6c730fa5 1 0 unsat +d8e56ac599bc3827a065804e88fc36c63a5afcfb 1 0 +unsat +a3340f8171cd0db9c0dd45f33a3cb1a42e793eee 1 0 +unsat +a8dd16a0d6a6514edcc3baafb20317536ccd338c 1 0 +unsat d5adb105f62510f5a3181800d02bb2208b8170d6 1 0 unsat f9ac14ab5e87743181fef8830f46edfda6007e6e 1 0 @@ -46,5 +52,5 @@ unsat 56db2066218af38e5a0015563c6a360d4cba04a7 1 0 unsat -e8d71df84f80ee07d30baf7a7df718db9a4df777 1 0 +3bf2dcb45282e43fa4ebfc5c17aaa663f9ce6a76 1 0 unsat diff -r 679118e35378 -r a4d1b5eef12e src/HOL/SMT_Examples/SMT_Word_Examples.thy --- a/src/HOL/SMT_Examples/SMT_Word_Examples.thy Sun Dec 19 18:54:29 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Word_Examples.thy Sun Dec 19 18:55:21 2010 +0100 @@ -66,11 +66,11 @@ lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt -lemma "0b10011 << 2 = (0b1001100::8 word)" sorry (* FIXME *) +lemma "0b10011 << 2 = (0b1001100::8 word)" by smt -lemma "0b11001 >> 2 = (0b110::8 word)" sorry (* FIXME *) +lemma "0b11001 >> 2 = (0b110::8 word)" by smt -lemma "0b10011 >>> 2 = (0b100::8 word)" sorry (* FIXME *) +lemma "0b10011 >>> 2 = (0b100::8 word)" by smt lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt