# HG changeset patch # User boehmes # Date 1292594346 -3600 # Node ID d4cb4d0c14a7cd3a90d5fc7e31456081b64d3c18 # Parent 4ea9f2a8c0939228a0f9e29405b699638a28da3e updated SMT certificates diff -r 4ea9f2a8c093 -r d4cb4d0c14a7 src/HOL/Boogie/Examples/Boogie_Dijkstra.certs --- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs Fri Dec 17 14:36:33 2010 +0100 +++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs Fri Dec 17 14:59:06 2010 +0100 @@ -1,7198 +1,7196 @@ -4a18f08eb054c06c0e0f108571305a91f86ae528 7197 0 +2bcca4894d12c21351a258c93ec6b00e790bb1de 7195 0 #2 := false -decl f14 :: (-> S6 S3 Int) -decl f23 :: S3 -#171 := f23 -decl f15 :: S6 -#99 := f15 -#175 := (f14 f15 f23) -decl f11 :: S3 -#57 := f11 -#100 := (f14 f15 f11) -#7798 := (= #100 #175) -#7826 := (= #175 #100) -#6087 := (= f23 f11) -#6089 := (= f11 f23) +decl f13 :: (-> S5 S3 Int) +decl f22 :: S3 +#170 := f22 +decl f14 :: S5 +#98 := f14 +#174 := (f13 f14 f22) +decl f10 :: S3 +#56 := f10 +#99 := (f13 f14 f10) +#7797 := (= #99 #174) +#7825 := (= #174 #99) +#6086 := (= f22 f10) +#6088 := (= f10 f22) decl f3 :: (-> S2 S3 S1) decl ?v1!7 :: (-> S3 S3) -#6070 := (?v1!7 f23) -decl f16 :: S2 -#105 := f16 -#6082 := (f3 f16 #6070) +#6069 := (?v1!7 f22) +decl f15 :: S2 +#104 := f15 +#6081 := (f3 f15 #6069) decl f1 :: S1 #4 := f1 -#6083 := (= f1 #6082) -#6084 := (not #6083) -#45 := 0::Int -decl f10 :: (-> S5 Int) -decl f6 :: (-> S3 S3 S5) -#6075 := (f6 #6070 f23) -#6076 := (f10 #6075) -#1209 := -1::Int -#6077 := (* -1::Int #6076) -#6071 := (f14 f15 #6070) -#6072 := (* -1::Int #6071) -#6078 := (+ #6072 #6077) -#6079 := (+ #175 #6078) -#6080 := (= #6079 0::Int) -#6081 := (not #6080) -#6073 := (+ #175 #6072) -#6074 := (<= #6073 0::Int) -#6092 := (or #6074 #6081 #6084) -decl f25 :: (-> S3 Int) +#6082 := (= f1 #6081) +#6083 := (not #6082) +#44 := 0::Int +decl f9 :: (-> S4 Int) +decl f5 :: (-> S3 S3 S4) +#6074 := (f5 #6069 f22) +#6075 := (f9 #6074) +#1208 := -1::Int +#6076 := (* -1::Int #6075) +#6070 := (f13 f14 #6069) +#6071 := (* -1::Int #6070) +#6077 := (+ #6071 #6076) +#6078 := (+ #174 #6077) +#6079 := (= #6078 0::Int) +#6080 := (not #6079) +#6072 := (+ #174 #6071) +#6073 := (<= #6072 0::Int) +#6091 := (or #6073 #6080 #6083) +decl f24 :: (-> S3 Int) decl ?v0!15 :: S3 -#2274 := ?v0!15 -#2275 := (f25 ?v0!15) -#2276 := (>= #2275 0::Int) -#2277 := (not #2276) +#2273 := ?v0!15 +#2274 := (f24 ?v0!15) +#2275 := (>= #2274 0::Int) +#2276 := (not #2275) decl ?v0!20 :: S3 -#2347 := ?v0!20 -#13 := (:var 0 S3) -#2351 := (f6 #13 ?v0!20) -#4455 := (pattern #2351) -#190 := (f25 #13) -#4395 := (pattern #190) -decl f24 :: S2 -#180 := f24 -#200 := (f3 f24 #13) -#4421 := (pattern #200) -#2352 := (f10 #2351) -#2348 := (f25 ?v0!20) -#2349 := (* -1::Int #2348) -#2951 := (+ #2349 #2352) -#2952 := (+ #190 #2951) -#2955 := (= #2952 0::Int) -#3517 := (not #2955) -#2350 := (+ #190 #2349) -#2355 := (>= #2350 0::Int) -#808 := (= f1 #200) -#814 := (not #808) -#3518 := (or #814 #2355 #3517) -#4456 := (forall (vars (?v1 S3)) (:pat #4421 #4395 #4455) #3518) -#4461 := (not #4456) -#24 := (:var 1 S3) -#82 := (f6 #13 #24) -#4250 := (pattern #82) -#212 := (f25 #24) -#1504 := (* -1::Int #212) -#1505 := (+ #190 #1504) -#83 := (f10 #82) -#1535 := (+ #83 #1505) -#1533 := (>= #1535 0::Int) -#1232 := (* -1::Int #83) -decl f9 :: Int -#46 := f9 -#1235 := (+ f9 #1232) -#1236 := (<= #1235 0::Int) -#3509 := (or #814 #1236 #1533) -#4447 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3509) -#4452 := (not #4447) -#2927 := (= f11 ?v0!20) -#2359 := (+ f9 #2349) -#2360 := (<= #2359 0::Int) -#4464 := (or #2360 #2927 #4452 #4461) -#4467 := (not #4464) +#2346 := ?v0!20 +#12 := (:var 0 S3) +#2350 := (f5 #12 ?v0!20) +#4454 := (pattern #2350) +#189 := (f24 #12) +#4394 := (pattern #189) +decl f23 :: S2 +#179 := f23 +#199 := (f3 f23 #12) +#4420 := (pattern #199) +#2351 := (f9 #2350) +#2347 := (f24 ?v0!20) +#2348 := (* -1::Int #2347) +#2950 := (+ #2348 #2351) +#2951 := (+ #189 #2950) +#2954 := (= #2951 0::Int) +#3516 := (not #2954) +#2349 := (+ #189 #2348) +#2354 := (>= #2349 0::Int) +#807 := (= f1 #199) +#813 := (not #807) +#3517 := (or #813 #2354 #3516) +#4455 := (forall (vars (?v1 S3)) (:pat #4420 #4394 #4454) #3517) +#4460 := (not #4455) +#23 := (:var 1 S3) +#81 := (f5 #12 #23) +#4249 := (pattern #81) +#211 := (f24 #23) +#1503 := (* -1::Int #211) +#1504 := (+ #189 #1503) +#82 := (f9 #81) +#1534 := (+ #82 #1504) +#1532 := (>= #1534 0::Int) +#1231 := (* -1::Int #82) +decl f8 :: Int +#45 := f8 +#1234 := (+ f8 #1231) +#1235 := (<= #1234 0::Int) +#3508 := (or #813 #1235 #1532) +#4446 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3508) +#4451 := (not #4446) +#2926 := (= f10 ?v0!20) +#2358 := (+ f8 #2348) +#2359 := (<= #2358 0::Int) +#4463 := (or #2359 #2926 #4451 #4460) +#4466 := (not #4463) decl ?v0!19 :: S3 -#2317 := ?v0!19 +#2316 := ?v0!19 decl ?v1!18 :: S3 -#2316 := ?v1!18 -#2322 := (f6 ?v1!18 ?v0!19) -#2323 := (f10 #2322) -#2326 := (* -1::Int #2323) -#2320 := (f25 ?v1!18) -#2913 := (* -1::Int #2320) -#2914 := (+ #2913 #2326) -#2318 := (f25 ?v0!19) -#2915 := (+ #2318 #2914) -#2916 := (<= #2915 0::Int) -#2330 := (f3 f24 ?v1!18) -#2331 := (= f1 #2330) -#3472 := (not #2331) -#2327 := (+ f9 #2326) -#2328 := (<= #2327 0::Int) -#3487 := (or #2328 #3472 #2916) -#3492 := (not #3487) -#4470 := (or #3492 #4467) -#4473 := (not #4470) -#4438 := (pattern #190 #212) -#1503 := (>= #1505 0::Int) -#209 := (f3 f24 #24) -#828 := (= f1 #209) -#3449 := (not #828) -#3464 := (or #808 #3449 #1503) -#4439 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4438) #3464) -#4444 := (not #4439) -#4476 := (or #4444 #4473) -#4479 := (not #4476) +#2315 := ?v1!18 +#2321 := (f5 ?v1!18 ?v0!19) +#2322 := (f9 #2321) +#2325 := (* -1::Int #2322) +#2319 := (f24 ?v1!18) +#2912 := (* -1::Int #2319) +#2913 := (+ #2912 #2325) +#2317 := (f24 ?v0!19) +#2914 := (+ #2317 #2913) +#2915 := (<= #2914 0::Int) +#2329 := (f3 f23 ?v1!18) +#2330 := (= f1 #2329) +#3471 := (not #2330) +#2326 := (+ f8 #2325) +#2327 := (<= #2326 0::Int) +#3486 := (or #2327 #3471 #2915) +#3491 := (not #3486) +#4469 := (or #3491 #4466) +#4472 := (not #4469) +#4437 := (pattern #189 #211) +#1502 := (>= #1504 0::Int) +#208 := (f3 f23 #23) +#827 := (= f1 #208) +#3448 := (not #827) +#3463 := (or #807 #3448 #1502) +#4438 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4437) #3463) +#4443 := (not #4438) +#4475 := (or #4443 #4472) +#4478 := (not #4475) decl ?v1!16 :: S3 -#2289 := ?v1!16 -#2293 := (f25 ?v1!16) -#2887 := (* -1::Int #2293) +#2288 := ?v1!16 +#2292 := (f24 ?v1!16) +#2886 := (* -1::Int #2292) decl ?v0!17 :: S3 -#2290 := ?v0!17 -#2291 := (f25 ?v0!17) -#2888 := (+ #2291 #2887) -#2889 := (<= #2888 0::Int) -#2298 := (f3 f24 ?v1!16) -#2299 := (= f1 #2298) -#2296 := (f3 f24 ?v0!17) -#2297 := (= f1 #2296) -#3426 := (not #2297) -#3441 := (or #3426 #2299 #2889) -#3446 := (not #3441) -#4482 := (or #3446 #4479) -#4485 := (not #4482) -#1494 := (>= #190 0::Int) -#4430 := (forall (vars (?v0 S3)) (:pat #4395) #1494) -#4435 := (not #4430) -#4488 := (or #4435 #4485) -decl f7 :: (-> S5 S3) -decl f8 :: (-> S5 S3) -#5996 := (f6 f23 f23) -#7212 := (f8 #5996) -#14212 := (f6 #7212 ?v0!20) -#24393 := (f8 #14212) -#14775 := (?v1!7 ?v0!20) -#24670 := (f6 #14775 #24393) -#25043 := (f7 #24670) -#26214 := (f3 f16 #25043) -#26215 := (= f1 #26214) -#14787 := (f3 f16 #14775) -#27707 := (= #14787 #26214) -#27704 := (= #26214 #14787) -#29052 := (= #25043 #14775) -#14780 := (f6 #14775 ?v0!20) -#19039 := (f7 #14780) -#26819 := (= #19039 #14775) -#19044 := (= #14775 #19039) -#38 := (f6 #24 #13) -#4194 := (pattern #38) -#42 := (f7 #38) -#345 := (= #24 #42) -#4201 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #345) -#349 := (forall (vars (?v0 S3) (?v1 S3)) #345) -#4204 := (iff #349 #4201) -#4202 := (iff #345 #345) -#4203 := [refl]: #4202 -#4205 := [quant-intro #4203]: #4204 -#1849 := (~ #349 #349) -#1879 := (~ #345 #345) -#1880 := [refl]: #1879 -#1850 := [nnf-pos #1880]: #1849 -#43 := (= #42 #24) -#44 := (forall (vars (?v0 S3) (?v1 S3)) #43) -#350 := (iff #44 #349) -#347 := (iff #43 #345) -#348 := [rewrite]: #347 -#351 := [quant-intro #348]: #350 -#344 := [asserted]: #44 -#354 := [mp #344 #351]: #349 -#1881 := [mp~ #354 #1850]: #349 -#4206 := [mp #1881 #4205]: #4201 -#6830 := (not #4201) -#8631 := (or #6830 #19044) -#13595 := [quant-inst #14775 #2347]: #8631 -#26775 := [unit-resolution #13595 #4206]: #19044 -#26817 := [symm #26775]: #26819 -#26827 := (= #25043 #19039) -#26824 := (= #24670 #14780) -#27256 := (= #24393 ?v0!20) -#19043 := (f8 #14780) -#25095 := (= #19043 ?v0!20) -#19038 := (= ?v0!20 #19043) -#39 := (f8 #38) -#337 := (= #13 #39) -#4195 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #337) -#341 := (forall (vars (?v0 S3) (?v1 S3)) #337) -#4198 := (iff #341 #4195) -#4196 := (iff #337 #337) -#4197 := [refl]: #4196 -#4199 := [quant-intro #4197]: #4198 -#1847 := (~ #341 #341) -#1876 := (~ #337 #337) -#1877 := [refl]: #1876 -#1848 := [nnf-pos #1877]: #1847 -#40 := (= #39 #13) -#41 := (forall (vars (?v0 S3) (?v1 S3)) #40) -#342 := (iff #41 #341) -#339 := (iff #40 #337) -#340 := [rewrite]: #339 -#343 := [quant-intro #340]: #342 -#336 := [asserted]: #41 -#346 := [mp #336 #343]: #341 -#1878 := [mp~ #346 #1848]: #341 -#4200 := [mp #1878 #4199]: #4195 -#6825 := (not #4195) -#19045 := (or #6825 #19038) -#19046 := [quant-inst #14775 #2347]: #19045 -#25094 := [unit-resolution #19046 #4200]: #19038 -#25096 := [symm #25094]: #25095 -#26796 := (= #24393 #19043) -#23181 := (f6 #7212 #19043) -#23300 := (f8 #23181) -#26808 := (= #23300 #19043) -#23306 := (= #19043 #23300) -#26718 := (or #6825 #23306) -#26721 := [quant-inst #7212 #19043]: #26718 -#26804 := [unit-resolution #26721 #4200]: #23306 -#26809 := [symm #26804]: #26808 -#26805 := (= #24393 #23300) -#26802 := (= #23300 #24393) -#26800 := (= #23181 #14212) -#14132 := (f6 f23 ?v0!20) -#26774 := (= #14132 #14212) -#24029 := (= #14212 #14132) -#7785 := (= #7212 f23) -#7213 := (= f23 #7212) -#7264 := (or #6825 #7213) -#7265 := [quant-inst #171 #171]: #7264 -#7790 := [unit-resolution #7265 #4200]: #7213 -#7791 := [symm #7790]: #7785 -#24030 := [monotonicity #7791]: #24029 -#26716 := [symm #24030]: #26774 -#26778 := (= #23181 #14132) -#26777 := (= #14132 #23181) -#26753 := [monotonicity #7790 #25094]: #26777 -#26779 := [symm #26753]: #26778 -#26803 := [trans #26779 #26716]: #26800 -#26806 := [monotonicity #26803]: #26802 -#26807 := [symm #26806]: #26805 -#26823 := [trans #26807 #26809]: #26796 -#26797 := [trans #26823 #25096]: #27256 -#26825 := [monotonicity #26797]: #26824 -#26818 := [monotonicity #26825]: #26827 -#26820 := [trans #26818 #26817]: #29052 -#26815 := [monotonicity #26820]: #27704 -#26829 := [symm #26815]: #27707 -#14788 := (= f1 #14787) -#14789 := (not #14788) -#14781 := (f10 #14780) -#14782 := (* -1::Int #14781) -#14776 := (f14 f15 #14775) -#14777 := (* -1::Int #14776) -#14783 := (+ #14777 #14782) -#14075 := (f14 f15 ?v0!20) -#14784 := (+ #14075 #14783) -#14785 := (= #14784 0::Int) -#14786 := (not #14785) -#14778 := (+ #14075 #14777) -#14779 := (<= #14778 0::Int) -#14795 := (or #14779 #14786 #14789) -#14798 := (not #14795) -#14116 := (* -1::Int #14075) -#14792 := (+ f9 #14116) -#14793 := (<= #14792 0::Int) -#21436 := (not #14793) -#2361 := (not #2360) -#19784 := [hypothesis]: #2361 -#14117 := (+ #2348 #14116) -#19568 := (>= #14117 0::Int) -#14086 := (= #2348 #14075) -#14133 := (f10 #14132) -#14151 := (+ #14116 #14133) -#14152 := (+ #175 #14151) -#14153 := (>= #14152 0::Int) -#14137 := (* -1::Int #14133) -#14141 := (+ f9 #14137) -#14142 := (<= #14141 0::Int) -#14184 := (or #14142 #14153) -#4491 := (not #4488) -#1454 := (* -1::Int #175) -#5914 := (+ #100 #1454) -#7799 := (<= #5914 0::Int) -#27735 := (or #6074 #2360) -#25048 := (= #14775 #25043) -#23338 := (or #6830 #25048) -#23339 := [quant-inst #14775 #24393]: #23338 -#28985 := [unit-resolution #23339 #4206]: #25048 -#29063 := [symm #28985]: #29052 -#27699 := [monotonicity #29063]: #27704 -#27719 := [symm #27699]: #27707 -#6119 := (not #6074) -#10075 := [hypothesis]: #6119 -#23175 := (or #14153 #6074) -#11115 := (or #2276 #6074) -#7537 := (f14 f15 ?v0!15) -#7758 := (>= #7537 0::Int) -#102 := (f14 f15 #13) -#4274 := (pattern #102) -#1737 := (>= #102 0::Int) -#4275 := (forall (vars (?v0 S3)) (:pat #4274) #1737) -#4494 := (or #2277 #4491) -#4497 := (not #4494) -#204 := (f25 f11) -#205 := (= #204 0::Int) -#1491 := (not #205) -#4500 := (or #1491 #4497) -#4503 := (not #4500) -#4506 := (or #1491 #4503) -#4509 := (not #4506) -#794 := (= #102 #190) -#815 := (or #794 #814) -#4422 := (forall (vars (?v0 S3)) (:pat #4274 #4395 #4421) #815) -#4427 := (not #4422) -#4512 := (or #4427 #4509) -#4515 := (not #4512) +#2289 := ?v0!17 +#2290 := (f24 ?v0!17) +#2887 := (+ #2290 #2886) +#2888 := (<= #2887 0::Int) +#2297 := (f3 f23 ?v1!16) +#2298 := (= f1 #2297) +#2295 := (f3 f23 ?v0!17) +#2296 := (= f1 #2295) +#3425 := (not #2296) +#3440 := (or #3425 #2298 #2888) +#3445 := (not #3440) +#4481 := (or #3445 #4478) +#4484 := (not #4481) +#1493 := (>= #189 0::Int) +#4429 := (forall (vars (?v0 S3)) (:pat #4394) #1493) +#4434 := (not #4429) +#4487 := (or #4434 #4484) +decl f6 :: (-> S4 S3) +decl f7 :: (-> S4 S3) +#5995 := (f5 f22 f22) +#7211 := (f7 #5995) +#14211 := (f5 #7211 ?v0!20) +#24392 := (f7 #14211) +#14774 := (?v1!7 ?v0!20) +#24669 := (f5 #14774 #24392) +#25042 := (f6 #24669) +#26213 := (f3 f15 #25042) +#26214 := (= f1 #26213) +#14786 := (f3 f15 #14774) +#27706 := (= #14786 #26213) +#27703 := (= #26213 #14786) +#29051 := (= #25042 #14774) +#14779 := (f5 #14774 ?v0!20) +#19038 := (f6 #14779) +#26818 := (= #19038 #14774) +#19043 := (= #14774 #19038) +#37 := (f5 #23 #12) +#4193 := (pattern #37) +#41 := (f6 #37) +#344 := (= #23 #41) +#4200 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #344) +#348 := (forall (vars (?v0 S3) (?v1 S3)) #344) +#4203 := (iff #348 #4200) +#4201 := (iff #344 #344) +#4202 := [refl]: #4201 +#4204 := [quant-intro #4202]: #4203 +#1848 := (~ #348 #348) +#1878 := (~ #344 #344) +#1879 := [refl]: #1878 +#1849 := [nnf-pos #1879]: #1848 +#42 := (= #41 #23) +#43 := (forall (vars (?v0 S3) (?v1 S3)) #42) +#349 := (iff #43 #348) +#346 := (iff #42 #344) +#347 := [rewrite]: #346 +#350 := [quant-intro #347]: #349 +#343 := [asserted]: #43 +#353 := [mp #343 #350]: #348 +#1880 := [mp~ #353 #1849]: #348 +#4205 := [mp #1880 #4204]: #4200 +#6829 := (not #4200) +#8630 := (or #6829 #19043) +#13594 := [quant-inst #14774 #2346]: #8630 +#26774 := [unit-resolution #13594 #4205]: #19043 +#26816 := [symm #26774]: #26818 +#26826 := (= #25042 #19038) +#26823 := (= #24669 #14779) +#27255 := (= #24392 ?v0!20) +#19042 := (f7 #14779) +#25094 := (= #19042 ?v0!20) +#19037 := (= ?v0!20 #19042) +#38 := (f7 #37) +#336 := (= #12 #38) +#4194 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #336) +#340 := (forall (vars (?v0 S3) (?v1 S3)) #336) +#4197 := (iff #340 #4194) +#4195 := (iff #336 #336) +#4196 := [refl]: #4195 +#4198 := [quant-intro #4196]: #4197 +#1846 := (~ #340 #340) +#1875 := (~ #336 #336) +#1876 := [refl]: #1875 +#1847 := [nnf-pos #1876]: #1846 +#39 := (= #38 #12) +#40 := (forall (vars (?v0 S3) (?v1 S3)) #39) +#341 := (iff #40 #340) +#338 := (iff #39 #336) +#339 := [rewrite]: #338 +#342 := [quant-intro #339]: #341 +#335 := [asserted]: #40 +#345 := [mp #335 #342]: #340 +#1877 := [mp~ #345 #1847]: #340 +#4199 := [mp #1877 #4198]: #4194 +#6824 := (not #4194) +#19044 := (or #6824 #19037) +#19045 := [quant-inst #14774 #2346]: #19044 +#25093 := [unit-resolution #19045 #4199]: #19037 +#25095 := [symm #25093]: #25094 +#26795 := (= #24392 #19042) +#23180 := (f5 #7211 #19042) +#23299 := (f7 #23180) +#26807 := (= #23299 #19042) +#23305 := (= #19042 #23299) +#26717 := (or #6824 #23305) +#26720 := [quant-inst #7211 #19042]: #26717 +#26803 := [unit-resolution #26720 #4199]: #23305 +#26808 := [symm #26803]: #26807 +#26804 := (= #24392 #23299) +#26801 := (= #23299 #24392) +#26799 := (= #23180 #14211) +#14131 := (f5 f22 ?v0!20) +#26773 := (= #14131 #14211) +#24028 := (= #14211 #14131) +#7784 := (= #7211 f22) +#7212 := (= f22 #7211) +#7263 := (or #6824 #7212) +#7264 := [quant-inst #170 #170]: #7263 +#7789 := [unit-resolution #7264 #4199]: #7212 +#7790 := [symm #7789]: #7784 +#24029 := [monotonicity #7790]: #24028 +#26715 := [symm #24029]: #26773 +#26777 := (= #23180 #14131) +#26776 := (= #14131 #23180) +#26752 := [monotonicity #7789 #25093]: #26776 +#26778 := [symm #26752]: #26777 +#26802 := [trans #26778 #26715]: #26799 +#26805 := [monotonicity #26802]: #26801 +#26806 := [symm #26805]: #26804 +#26822 := [trans #26806 #26808]: #26795 +#26796 := [trans #26822 #25095]: #27255 +#26824 := [monotonicity #26796]: #26823 +#26817 := [monotonicity #26824]: #26826 +#26819 := [trans #26817 #26816]: #29051 +#26814 := [monotonicity #26819]: #27703 +#26828 := [symm #26814]: #27706 +#14787 := (= f1 #14786) +#14788 := (not #14787) +#14780 := (f9 #14779) +#14781 := (* -1::Int #14780) +#14775 := (f13 f14 #14774) +#14776 := (* -1::Int #14775) +#14782 := (+ #14776 #14781) +#14074 := (f13 f14 ?v0!20) +#14783 := (+ #14074 #14782) +#14784 := (= #14783 0::Int) +#14785 := (not #14784) +#14777 := (+ #14074 #14776) +#14778 := (<= #14777 0::Int) +#14794 := (or #14778 #14785 #14788) +#14797 := (not #14794) +#14115 := (* -1::Int #14074) +#14791 := (+ f8 #14115) +#14792 := (<= #14791 0::Int) +#21435 := (not #14792) +#2360 := (not #2359) +#19783 := [hypothesis]: #2360 +#14116 := (+ #2347 #14115) +#19567 := (>= #14116 0::Int) +#14085 := (= #2347 #14074) +#14132 := (f9 #14131) +#14150 := (+ #14115 #14132) +#14151 := (+ #174 #14150) +#14152 := (>= #14151 0::Int) +#14136 := (* -1::Int #14132) +#14140 := (+ f8 #14136) +#14141 := (<= #14140 0::Int) +#14183 := (or #14141 #14152) +#4490 := (not #4487) +#1453 := (* -1::Int #174) +#5913 := (+ #99 #1453) +#7798 := (<= #5913 0::Int) +#27734 := (or #6073 #2359) +#25047 := (= #14774 #25042) +#23337 := (or #6829 #25047) +#23338 := [quant-inst #14774 #24392]: #23337 +#28984 := [unit-resolution #23338 #4205]: #25047 +#29062 := [symm #28984]: #29051 +#27698 := [monotonicity #29062]: #27703 +#27718 := [symm #27698]: #27706 +#6118 := (not #6073) +#10074 := [hypothesis]: #6118 +#23174 := (or #14152 #6073) +#11114 := (or #2275 #6073) +#7536 := (f13 f14 ?v0!15) +#7757 := (>= #7536 0::Int) +#101 := (f13 f14 #12) +#4273 := (pattern #101) +#1736 := (>= #101 0::Int) +#4274 := (forall (vars (?v0 S3)) (:pat #4273) #1736) +#4493 := (or #2276 #4490) +#4496 := (not #4493) +#203 := (f24 f10) +#204 := (= #203 0::Int) +#1490 := (not #204) +#4499 := (or #1490 #4496) +#4502 := (not #4499) +#4505 := (or #1490 #4502) +#4508 := (not #4505) +#793 := (= #101 #189) +#814 := (or #793 #813) +#4421 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4420) #814) +#4426 := (not #4421) +#4511 := (or #4426 #4508) +#4514 := (not #4511) decl ?v0!14 :: S3 -#2249 := ?v0!14 -#2254 := (f14 f15 ?v0!14) -#2253 := (f25 ?v0!14) -#2859 := (= #2253 #2254) -#2250 := (f3 f24 ?v0!14) -#2251 := (= f1 #2250) -#2252 := (not #2251) -#2865 := (or #2252 #2859) -#2870 := (not #2865) -#4518 := (or #2870 #4515) -#4521 := (not #4518) -#1479 := (* -1::Int #190) -#1480 := (+ #102 #1479) -#1478 := (>= #1480 0::Int) -#4413 := (forall (vars (?v0 S3)) (:pat #4274 #4395) #1478) -#4418 := (not #4413) -#4524 := (or #4418 #4521) -#4527 := (not #4524) +#2248 := ?v0!14 +#2253 := (f13 f14 ?v0!14) +#2252 := (f24 ?v0!14) +#2858 := (= #2252 #2253) +#2249 := (f3 f23 ?v0!14) +#2250 := (= f1 #2249) +#2251 := (not #2250) +#2864 := (or #2251 #2858) +#2869 := (not #2864) +#4517 := (or #2869 #4514) +#4520 := (not #4517) +#1478 := (* -1::Int #189) +#1479 := (+ #101 #1478) +#1477 := (>= #1479 0::Int) +#4412 := (forall (vars (?v0 S3)) (:pat #4273 #4394) #1477) +#4417 := (not #4412) +#4523 := (or #4417 #4520) +#4526 := (not #4523) decl ?v0!13 :: S3 -#2231 := ?v0!13 -#2234 := (f14 f15 ?v0!13) -#2849 := (* -1::Int #2234) -#2232 := (f25 ?v0!13) -#2850 := (+ #2232 #2849) -#2851 := (<= #2850 0::Int) -#2856 := (not #2851) -#4530 := (or #2856 #4527) -#4533 := (not #4530) -#184 := (f6 f23 #13) -#4396 := (pattern #184) -#185 := (f10 #184) -#1622 := (+ #185 #1479) -#1623 := (+ #175 #1622) -#1624 := (= #1623 0::Int) -#1448 := (* -1::Int #185) -#1455 := (+ #1454 #1448) -#1456 := (+ #102 #1455) -#1457 := (<= #1456 0::Int) -#1449 := (+ f9 #1448) -#1450 := (<= #1449 0::Int) -#3418 := (or #1450 #1457 #1624) -#4405 := (forall (vars (?v0 S3)) (:pat #4396 #4274 #4395) #3418) -#4410 := (not #4405) -#3398 := (or #1450 #1457) -#3399 := (not #3398) -#3402 := (or #794 #3399) -#4397 := (forall (vars (?v0 S3)) (:pat #4274 #4395 #4396) #3402) -#4402 := (not #4397) +#2230 := ?v0!13 +#2233 := (f13 f14 ?v0!13) +#2848 := (* -1::Int #2233) +#2231 := (f24 ?v0!13) +#2849 := (+ #2231 #2848) +#2850 := (<= #2849 0::Int) +#2855 := (not #2850) +#4529 := (or #2855 #4526) +#4532 := (not #4529) +#183 := (f5 f22 #12) +#4395 := (pattern #183) +#184 := (f9 #183) +#1621 := (+ #184 #1478) +#1622 := (+ #174 #1621) +#1623 := (= #1622 0::Int) +#1447 := (* -1::Int #184) +#1454 := (+ #1453 #1447) +#1455 := (+ #101 #1454) +#1456 := (<= #1455 0::Int) +#1448 := (+ f8 #1447) +#1449 := (<= #1448 0::Int) +#3417 := (or #1449 #1456 #1623) +#4404 := (forall (vars (?v0 S3)) (:pat #4395 #4273 #4394) #3417) +#4409 := (not #4404) +#3397 := (or #1449 #1456) +#3398 := (not #3397) +#3401 := (or #793 #3398) +#4396 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4395) #3401) +#4401 := (not #4396) decl ?v0!12 :: S3 -#2207 := ?v0!12 -#2213 := (f3 f16 ?v0!12) -#2214 := (= f1 #2213) -#2208 := (f14 f15 ?v0!12) -#2209 := (* -1::Int #2208) -#2210 := (+ f9 #2209) -#2211 := (<= #2210 0::Int) -#1654 := (+ f9 #1454) -#1655 := (<= #1654 0::Int) -#106 := (f3 f16 #13) -#4316 := (pattern #106) -#1637 := (+ #102 #1454) -#1636 := (>= #1637 0::Int) -#534 := (= f1 #106) -#1643 := (or #534 #1636) -#4387 := (forall (vars (?v0 S3)) (:pat #4316 #4274) #1643) -#4392 := (not #4387) -decl f4 :: (-> S4 S2 S3 S1 S2) -decl f5 :: S4 -#8 := f5 -#774 := (f4 f5 f16 f23 f1) -#777 := (= f24 #774) -#996 := (not #777) -#172 := (f3 f16 f23) -#755 := (= f1 #172) -#4536 := (or #755 #996 #4392 #1655 #2211 #2214 #4402 #4410 #4533) -#4539 := (not #4536) +#2206 := ?v0!12 +#2212 := (f3 f15 ?v0!12) +#2213 := (= f1 #2212) +#2207 := (f13 f14 ?v0!12) +#2208 := (* -1::Int #2207) +#2209 := (+ f8 #2208) +#2210 := (<= #2209 0::Int) +#1653 := (+ f8 #1453) +#1654 := (<= #1653 0::Int) +#105 := (f3 f15 #12) +#4315 := (pattern #105) +#1636 := (+ #101 #1453) +#1635 := (>= #1636 0::Int) +#533 := (= f1 #105) +#1642 := (or #533 #1635) +#4386 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #1642) +#4391 := (not #4386) +decl f4 :: (-> S2 S3 S1 S2) +#773 := (f4 f15 f22 f1) +#776 := (= f23 #773) +#995 := (not #776) +#171 := (f3 f15 f22) +#754 := (= f1 #171) +#4535 := (or #754 #995 #4391 #1654 #2210 #2213 #4401 #4409 #4532) +#4538 := (not #4535) decl ?v0!11 :: S3 -#2141 := ?v0!11 +#2140 := ?v0!11 decl ?v1!10 :: S3 -#2140 := ?v1!10 -#2146 := (f6 ?v1!10 ?v0!11) -#2147 := (f10 #2146) -#2154 := (* -1::Int #2147) -decl f20 :: S6 -#138 := f20 -#2144 := (f14 f20 ?v1!10) -#2150 := (* -1::Int #2144) -#2806 := (+ #2150 #2154) -#2142 := (f14 f20 ?v0!11) -#2807 := (+ #2142 #2806) -#2808 := (<= #2807 0::Int) -#2155 := (+ f9 #2154) -#2156 := (<= #2155 0::Int) -#2151 := (+ f9 #2150) -#2152 := (<= #2151 0::Int) -#3362 := (or #2152 #2156 #2808) -#3367 := (not #3362) -#146 := (f14 f20 #24) -#1356 := (* -1::Int #146) -#143 := (f14 f20 #13) -#1357 := (+ #143 #1356) -#1363 := (+ #83 #1357) -#1386 := (>= #1363 0::Int) -#1343 := (* -1::Int #143) -#1344 := (+ f9 #1343) -#1345 := (<= #1344 0::Int) -#3330 := (or #1236 #1345 #1386) -#4349 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3330) -#4354 := (not #4349) -#158 := (f14 f20 f11) -#159 := (= #158 0::Int) -#4357 := (or #159 #4354) -#4360 := (not #4357) -#4363 := (or #4360 #3367) -#4366 := (not #4363) -#4325 := (pattern #143) +#2139 := ?v1!10 +#2145 := (f5 ?v1!10 ?v0!11) +#2146 := (f9 #2145) +#2153 := (* -1::Int #2146) +decl f19 :: S5 +#137 := f19 +#2143 := (f13 f19 ?v1!10) +#2149 := (* -1::Int #2143) +#2805 := (+ #2149 #2153) +#2141 := (f13 f19 ?v0!11) +#2806 := (+ #2141 #2805) +#2807 := (<= #2806 0::Int) +#2154 := (+ f8 #2153) +#2155 := (<= #2154 0::Int) +#2150 := (+ f8 #2149) +#2151 := (<= #2150 0::Int) +#3361 := (or #2151 #2155 #2807) +#3366 := (not #3361) +#145 := (f13 f19 #23) +#1355 := (* -1::Int #145) +#142 := (f13 f19 #12) +#1356 := (+ #142 #1355) +#1362 := (+ #82 #1356) +#1385 := (>= #1362 0::Int) +#1342 := (* -1::Int #142) +#1343 := (+ f8 #1342) +#1344 := (<= #1343 0::Int) +#3329 := (or #1235 #1344 #1385) +#4348 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3329) +#4353 := (not #4348) +#157 := (f13 f19 f10) +#158 := (= #157 0::Int) +#4356 := (or #158 #4353) +#4359 := (not #4356) +#4362 := (or #4359 #3366) +#4365 := (not #4362) +#4324 := (pattern #142) decl ?v1!9 :: (-> S3 S3) -#2117 := (?v1!9 #13) -#2120 := (f6 #2117 #13) -#2121 := (f10 #2120) -#2776 := (* -1::Int #2121) -#2118 := (f14 f20 #2117) -#2759 := (* -1::Int #2118) -#2777 := (+ #2759 #2776) -#2778 := (+ #143 #2777) -#2779 := (= #2778 0::Int) -#3300 := (not #2779) -#2760 := (+ #143 #2759) -#2761 := (<= #2760 0::Int) -#3301 := (or #2761 #3300) -#3302 := (not #3301) -#58 := (= #13 f11) -#3308 := (or #58 #1345 #3302) -#4341 := (forall (vars (?v0 S3)) (:pat #4325) #3308) -#4346 := (not #4341) -#4369 := (or #4346 #4366) -#4372 := (not #4369) +#2116 := (?v1!9 #12) +#2119 := (f5 #2116 #12) +#2120 := (f9 #2119) +#2775 := (* -1::Int #2120) +#2117 := (f13 f19 #2116) +#2758 := (* -1::Int #2117) +#2776 := (+ #2758 #2775) +#2777 := (+ #142 #2776) +#2778 := (= #2777 0::Int) +#3299 := (not #2778) +#2759 := (+ #142 #2758) +#2760 := (<= #2759 0::Int) +#3300 := (or #2760 #3299) +#3301 := (not #3300) +#57 := (= #12 f10) +#3307 := (or #57 #1344 #3301) +#4340 := (forall (vars (?v0 S3)) (:pat #4324) #3307) +#4345 := (not #4340) +#4368 := (or #4345 #4365) +#4371 := (not #4368) decl ?v0!8 :: S3 -#2077 := ?v0!8 -#2081 := (f6 #13 ?v0!8) -#4326 := (pattern #2081) -#2082 := (f10 #2081) -#2078 := (f14 f20 ?v0!8) -#2079 := (* -1::Int #2078) -#2729 := (+ #2079 #2082) -#2730 := (+ #143 #2729) -#2733 := (= #2730 0::Int) -#3264 := (not #2733) -#2080 := (+ #143 #2079) -#2085 := (>= #2080 0::Int) -#3265 := (or #2085 #3264) -#4327 := (forall (vars (?v1 S3)) (:pat #4325 #4326) #3265) -#4332 := (not #4327) -#2705 := (= f11 ?v0!8) -#2089 := (+ f9 #2079) -#2090 := (<= #2089 0::Int) -#4335 := (or #2090 #2705 #4332) -#4338 := (not #4335) -#4375 := (or #4338 #4372) -#4378 := (not #4375) -#1298 := (* -1::Int #102) -#1299 := (+ f9 #1298) -#1300 := (<= #1299 0::Int) -#3250 := (or #534 #1300) -#4317 := (forall (vars (?v0 S3)) (:pat #4316 #4274) #3250) -#4322 := (not #4317) -#625 := (= f15 f20) -#716 := (not #625) -decl f17 :: S2 -#133 := f17 -#622 := (= f16 f17) -#734 := (not #622) -decl f22 :: S6 -#141 := f22 -decl f21 :: S6 +#2076 := ?v0!8 +#2080 := (f5 #12 ?v0!8) +#4325 := (pattern #2080) +#2081 := (f9 #2080) +#2077 := (f13 f19 ?v0!8) +#2078 := (* -1::Int #2077) +#2728 := (+ #2078 #2081) +#2729 := (+ #142 #2728) +#2732 := (= #2729 0::Int) +#3263 := (not #2732) +#2079 := (+ #142 #2078) +#2084 := (>= #2079 0::Int) +#3264 := (or #2084 #3263) +#4326 := (forall (vars (?v1 S3)) (:pat #4324 #4325) #3264) +#4331 := (not #4326) +#2704 := (= f10 ?v0!8) +#2088 := (+ f8 #2078) +#2089 := (<= #2088 0::Int) +#4334 := (or #2089 #2704 #4331) +#4337 := (not #4334) +#4374 := (or #4337 #4371) +#4377 := (not #4374) +#1297 := (* -1::Int #101) +#1298 := (+ f8 #1297) +#1299 := (<= #1298 0::Int) +#3249 := (or #533 #1299) +#4316 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #3249) +#4321 := (not #4316) +#624 := (= f14 f19) +#715 := (not #624) +decl f16 :: S2 +#132 := f16 +#621 := (= f15 f16) +#733 := (not #621) +decl f21 :: S5 #140 := f21 -#142 := (= f21 f22) -#707 := (not #142) -decl f19 :: S3 -#136 := f19 +decl f20 :: S5 +#139 := f20 +#141 := (= f20 f21) +#706 := (not #141) decl f18 :: S3 #135 := f18 -#137 := (= f18 f19) -#725 := (not #137) -#4381 := (or #725 #707 #734 #716 #4322 #4378) -#4384 := (not #4381) -#4542 := (or #4384 #4539) -#4545 := (not #4542) -#2040 := (?v1!7 #13) -#2041 := (f14 f15 #2040) -#2664 := (* -1::Int #2041) -#2679 := (+ #102 #2664) -#2680 := (<= #2679 0::Int) -#2045 := (f6 #2040 #13) -#2046 := (f10 #2045) -#2665 := (* -1::Int #2046) -#2666 := (+ #2664 #2665) -#2667 := (+ #102 #2666) -#2668 := (= #2667 0::Int) -#3234 := (not #2668) -#2049 := (f3 f16 #2040) -#2050 := (= f1 #2049) -#3233 := (not #2050) -#3235 := (or #3233 #3234 #2680) -#3236 := (not #3235) -#3242 := (or #58 #1300 #3236) -#4308 := (forall (vars (?v0 S3)) (:pat #4274) #3242) -#4313 := (not #4308) -decl f12 :: (-> S3 Int) -#59 := (f12 #13) -#4219 := (pattern #59) +decl f17 :: S3 +#134 := f17 +#136 := (= f17 f18) +#724 := (not #136) +#4380 := (or #724 #706 #733 #715 #4321 #4377) +#4383 := (not #4380) +#4541 := (or #4383 #4538) +#4544 := (not #4541) +#2039 := (?v1!7 #12) +#2040 := (f13 f14 #2039) +#2663 := (* -1::Int #2040) +#2678 := (+ #101 #2663) +#2679 := (<= #2678 0::Int) +#2044 := (f5 #2039 #12) +#2045 := (f9 #2044) +#2664 := (* -1::Int #2045) +#2665 := (+ #2663 #2664) +#2666 := (+ #101 #2665) +#2667 := (= #2666 0::Int) +#3233 := (not #2667) +#2048 := (f3 f15 #2039) +#2049 := (= f1 #2048) +#3232 := (not #2049) +#3234 := (or #3232 #3233 #2679) +#3235 := (not #3234) +#3241 := (or #57 #1299 #3235) +#4307 := (forall (vars (?v0 S3)) (:pat #4273) #3241) +#4312 := (not #4307) +decl f11 :: (-> S3 Int) +#58 := (f11 #12) +#4218 := (pattern #58) decl ?v1!6 :: (-> S3 S3) -#2012 := (?v1!6 #13) -#2016 := (f12 #2012) -#2623 := (* -1::Int #2016) -#2013 := (f6 #2012 #13) -#2014 := (f10 #2013) -#2640 := (* -1::Int #2014) -#2641 := (+ #2640 #2623) -#2642 := (+ #59 #2641) -#2643 := (= #2642 0::Int) -#3206 := (not #2643) -#2624 := (+ #59 #2623) -#2625 := (<= #2624 0::Int) -decl f13 :: (-> S3 S1) -#2022 := (f13 #2012) -#2023 := (= f1 #2022) -#3205 := (not #2023) -#3207 := (or #3205 #2625 #3206) -#3208 := (not #3207) -#1260 := (* -1::Int #59) -#1261 := (+ f9 #1260) -#1262 := (<= #1261 0::Int) -#3214 := (or #58 #1262 #3208) -#4300 := (forall (vars (?v0 S3)) (:pat #4219) #3214) -#4305 := (not #4300) -#109 := (f3 f16 #24) -#4291 := (pattern #106 #109) -#112 := (f14 f15 #24) -#1312 := (* -1::Int #112) -#1313 := (+ #102 #1312) -#1316 := (>= #1313 0::Int) -#540 := (= f1 #109) -#3171 := (not #540) -#3186 := (or #534 #3171 #1316) -#4292 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4291) #3186) -#4297 := (not #4292) -#1314 := (+ #83 #1313) -#1709 := (>= #1314 0::Int) -#537 := (not #534) -#3163 := (or #537 #1236 #1709) -#4283 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3163) -#4288 := (not #4283) -#4280 := (not #4275) -#101 := (= #100 0::Int) -#1748 := (not #101) -#4548 := (or #1748 #4280 #4288 #4297 #4305 #4313 #4545) -#4551 := (not #4548) +#2011 := (?v1!6 #12) +#2015 := (f11 #2011) +#2622 := (* -1::Int #2015) +#2012 := (f5 #2011 #12) +#2013 := (f9 #2012) +#2639 := (* -1::Int #2013) +#2640 := (+ #2639 #2622) +#2641 := (+ #58 #2640) +#2642 := (= #2641 0::Int) +#3205 := (not #2642) +#2623 := (+ #58 #2622) +#2624 := (<= #2623 0::Int) +decl f12 :: (-> S3 S1) +#2021 := (f12 #2011) +#2022 := (= f1 #2021) +#3204 := (not #2022) +#3206 := (or #3204 #2624 #3205) +#3207 := (not #3206) +#1259 := (* -1::Int #58) +#1260 := (+ f8 #1259) +#1261 := (<= #1260 0::Int) +#3213 := (or #57 #1261 #3207) +#4299 := (forall (vars (?v0 S3)) (:pat #4218) #3213) +#4304 := (not #4299) +#108 := (f3 f15 #23) +#4290 := (pattern #105 #108) +#111 := (f13 f14 #23) +#1311 := (* -1::Int #111) +#1312 := (+ #101 #1311) +#1315 := (>= #1312 0::Int) +#539 := (= f1 #108) +#3170 := (not #539) +#3185 := (or #533 #3170 #1315) +#4291 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4290) #3185) +#4296 := (not #4291) +#1313 := (+ #82 #1312) +#1708 := (>= #1313 0::Int) +#536 := (not #533) +#3162 := (or #536 #1235 #1708) +#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3162) +#4287 := (not #4282) +#4279 := (not #4274) +#100 := (= #99 0::Int) +#1747 := (not #100) +#4547 := (or #1747 #4279 #4287 #4296 #4304 #4312 #4544) +#4550 := (not #4547) decl ?v0!5 :: S3 -#1968 := ?v0!5 -#1969 := (f6 #13 ?v0!5) -#4259 := (pattern #1969) -#67 := (f13 #13) -#4226 := (pattern #67) -#1971 := (f12 ?v0!5) -#1972 := (* -1::Int #1971) -#1970 := (f10 #1969) -#2591 := (+ #1970 #1972) -#2592 := (+ #59 #2591) -#2595 := (= #2592 0::Int) -#3124 := (not #2595) -#1976 := (+ #59 #1972) -#1977 := (>= #1976 0::Int) -#455 := (= f1 #67) -#458 := (not #455) -#3125 := (or #458 #1977 #3124) -#4260 := (forall (vars (?v1 S3)) (:pat #4226 #4219 #4259) #3125) -#4265 := (not #4260) -#2567 := (= f11 ?v0!5) -#1981 := (+ f9 #1972) -#1982 := (<= #1981 0::Int) -#4268 := (or #1982 #2567 #4265) -#4271 := (not #4268) -#4554 := (or #4271 #4551) -#4557 := (not #4554) -#78 := (f12 #24) -#1212 := (* -1::Int #78) -#1233 := (+ #1212 #83) -#1234 := (+ #59 #1233) -#1231 := (>= #1234 0::Int) -#3116 := (or #458 #1231 #1236) -#4251 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4250) #3116) -#4256 := (not #4251) -#4560 := (or #4256 #4557) -#4563 := (not #4560) +#1967 := ?v0!5 +#1968 := (f5 #12 ?v0!5) +#4258 := (pattern #1968) +#66 := (f12 #12) +#4225 := (pattern #66) +#1970 := (f11 ?v0!5) +#1971 := (* -1::Int #1970) +#1969 := (f9 #1968) +#2590 := (+ #1969 #1971) +#2591 := (+ #58 #2590) +#2594 := (= #2591 0::Int) +#3123 := (not #2594) +#1975 := (+ #58 #1971) +#1976 := (>= #1975 0::Int) +#454 := (= f1 #66) +#457 := (not #454) +#3124 := (or #457 #1976 #3123) +#4259 := (forall (vars (?v1 S3)) (:pat #4225 #4218 #4258) #3124) +#4264 := (not #4259) +#2566 := (= f10 ?v0!5) +#1980 := (+ f8 #1971) +#1981 := (<= #1980 0::Int) +#4267 := (or #1981 #2566 #4264) +#4270 := (not #4267) +#4553 := (or #4270 #4550) +#4556 := (not #4553) +#77 := (f11 #23) +#1211 := (* -1::Int #77) +#1232 := (+ #1211 #82) +#1233 := (+ #58 #1232) +#1230 := (>= #1233 0::Int) +#3115 := (or #457 #1230 #1235) +#4250 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3115) +#4255 := (not #4250) +#4559 := (or #4255 #4556) +#4562 := (not #4559) decl ?v1!3 :: S3 -#1937 := ?v1!3 -#1952 := (f12 ?v1!3) +#1936 := ?v1!3 +#1951 := (f11 ?v1!3) decl ?v0!4 :: S3 -#1938 := ?v0!4 -#1949 := (f12 ?v0!4) -#1950 := (* -1::Int #1949) -#2548 := (+ #1950 #1952) -#1939 := (f6 ?v1!3 ?v0!4) -#1940 := (f10 #1939) -#2549 := (+ #1940 #2548) -#2552 := (>= #2549 0::Int) -#1945 := (f13 ?v1!3) -#1946 := (= f1 #1945) -#3079 := (not #1946) -#1941 := (* -1::Int #1940) -#1942 := (+ f9 #1941) -#1943 := (<= #1942 0::Int) -#3094 := (or #1943 #3079 #2552) -#5223 := [hypothesis]: #1946 -#4227 := (forall (vars (?v0 S3)) (:pat #4226) #458) -#461 := (forall (vars (?v0 S3)) #458) -#4230 := (iff #461 #4227) -#4228 := (iff #458 #458) -#4229 := [refl]: #4228 -#4231 := [quant-intro #4229]: #4230 -#1859 := (~ #461 #461) -#1889 := (~ #458 #458) -#1890 := [refl]: #1889 -#1860 := [nnf-pos #1890]: #1859 -#60 := (= #59 0::Int) -#63 := (not #58) -#1806 := (or #63 #60) -#1809 := (forall (vars (?v0 S3)) #1806) -#1812 := (not #1809) -#1740 := (forall (vars (?v0 S3)) #1737) -#1743 := (not #1740) -#543 := (and #537 #540) -#549 := (not #543) -#1726 := (or #549 #1316) -#1731 := (forall (vars (?v0 S3) (?v1 S3)) #1726) -#1734 := (not #1731) -#1237 := (not #1236) -#1701 := (and #534 #1237) -#1706 := (not #1701) -#1712 := (or #1706 #1709) -#1715 := (forall (vars (?v0 S3) (?v1 S3)) #1712) -#1718 := (not #1715) -#1648 := (forall (vars (?v0 S3)) #1643) -#1651 := (not #1648) -#1458 := (not #1457) -#1451 := (not #1450) -#1461 := (and #1451 #1458) -#1619 := (not #1461) -#1627 := (or #1619 #1624) -#1630 := (forall (vars (?v0 S3)) #1627) -#1633 := (not #1630) -#1557 := (= #1535 0::Int) -#1560 := (not #1503) -#1569 := (and #808 #1560 #1557) -#1574 := (exists (vars (?v1 S3)) #1569) -#1546 := (+ f9 #1479) -#1547 := (<= #1546 0::Int) -#1548 := (not #1547) -#1551 := (and #63 #1548) -#1554 := (not #1551) -#1577 := (or #1554 #1574) -#1580 := (forall (vars (?v0 S3)) #1577) -#1525 := (and #808 #1237) -#1530 := (not #1525) -#1537 := (or #1530 #1533) -#1540 := (forall (vars (?v0 S3) (?v1 S3)) #1537) -#1543 := (not #1540) -#1583 := (or #1543 #1580) -#1586 := (and #1540 #1583) -#831 := (and #814 #828) -#837 := (not #831) -#1511 := (or #837 #1503) -#1516 := (forall (vars (?v0 S3) (?v1 S3)) #1511) -#1519 := (not #1516) -#1589 := (or #1519 #1586) -#1592 := (and #1516 #1589) -#1497 := (forall (vars (?v0 S3)) #1494) -#1500 := (not #1497) -#1595 := (or #1500 #1592) -#1598 := (and #1497 #1595) -#1601 := (or #1491 #1598) -#1604 := (and #205 #1601) -#820 := (forall (vars (?v0 S3)) #815) -#954 := (not #820) -#1607 := (or #954 #1604) -#1610 := (and #820 #1607) -#1483 := (forall (vars (?v0 S3)) #1478) -#1486 := (not #1483) -#1613 := (or #1486 #1610) -#1616 := (and #1483 #1613) -#1467 := (or #794 #1461) -#1472 := (forall (vars (?v0 S3)) #1467) -#1475 := (not #1472) -#1301 := (not #1300) -#1420 := (and #537 #1301) -#1425 := (exists (vars (?v0 S3)) #1420) -#1666 := (not #1425) -#1690 := (or #755 #996 #1666 #1475 #1616 #1633 #1651 #1655) -#1346 := (not #1345) -#1380 := (and #1237 #1346) -#1383 := (not #1380) -#1389 := (or #1383 #1386) -#1392 := (forall (vars (?v0 S3) (?v1 S3)) #1389) -#1395 := (not #1392) -#1403 := (or #159 #1395) -#1408 := (and #1392 #1403) -#1361 := (= #1363 0::Int) -#1355 := (>= #1357 0::Int) -#1358 := (not #1355) -#1365 := (and #1358 #1361) -#1368 := (exists (vars (?v1 S3)) #1365) -#1349 := (and #63 #1346) -#1352 := (not #1349) -#1371 := (or #1352 #1368) -#1374 := (forall (vars (?v0 S3)) #1371) -#1377 := (not #1374) -#1411 := (or #1377 #1408) -#1414 := (and #1374 #1411) -#1443 := (or #725 #707 #734 #716 #1414 #1425) -#1695 := (and #1443 #1690) -#1317 := (not #1316) -#1310 := (= #1314 0::Int) -#1326 := (and #534 #1310 #1317) -#1331 := (exists (vars (?v1 S3)) #1326) -#1304 := (and #63 #1301) -#1307 := (not #1304) -#1334 := (or #1307 #1331) -#1337 := (forall (vars (?v0 S3)) #1334) -#1340 := (not #1337) -#1272 := (= #1234 0::Int) -#1213 := (+ #59 #1212) -#1211 := (>= #1213 0::Int) -#1275 := (not #1211) -#1284 := (and #455 #1275 #1272) -#1289 := (exists (vars (?v1 S3)) #1284) -#1263 := (not #1262) -#1266 := (and #63 #1263) -#1269 := (not #1266) -#1292 := (or #1269 #1289) -#1295 := (forall (vars (?v0 S3)) #1292) -#1751 := (not #1295) -#1772 := (or #1748 #1751 #1340 #1695 #1718 #1734 #1743) -#1777 := (and #1295 #1772) -#1243 := (and #455 #1237) -#1248 := (not #1243) -#1251 := (or #1231 #1248) -#1254 := (forall (vars (?v0 S3) (?v1 S3)) #1251) -#1257 := (not #1254) -#1780 := (or #1257 #1777) -#1783 := (and #1254 #1780) -#75 := (f13 #24) -#467 := (= f1 #75) -#470 := (and #458 #467) -#476 := (not #470) -#1218 := (or #476 #1211) -#1223 := (forall (vars (?v0 S3) (?v1 S3)) #1218) -#1226 := (not #1223) -#1786 := (or #1226 #1783) -#1789 := (and #1223 #1786) -#1202 := (>= #59 0::Int) -#1203 := (forall (vars (?v0 S3)) #1202) -#1206 := (not #1203) -#1792 := (or #1206 #1789) -#1795 := (and #1203 #1792) -#71 := (f12 f11) -#72 := (= #71 0::Int) -#1197 := (not #72) -#1798 := (or #1197 #1795) -#1801 := (and #72 #1798) -#1161 := (not #461) -#441 := (= f9 #59) -#447 := (or #58 #441) -#452 := (forall (vars (?v0 S3)) #447) -#1170 := (not #452) -#1824 := (or #1170 #1161 #1801 #1812) -#1829 := (not #1824) +#1937 := ?v0!4 +#1948 := (f11 ?v0!4) +#1949 := (* -1::Int #1948) +#2547 := (+ #1949 #1951) +#1938 := (f5 ?v1!3 ?v0!4) +#1939 := (f9 #1938) +#2548 := (+ #1939 #2547) +#2551 := (>= #2548 0::Int) +#1944 := (f12 ?v1!3) +#1945 := (= f1 #1944) +#3078 := (not #1945) +#1940 := (* -1::Int #1939) +#1941 := (+ f8 #1940) +#1942 := (<= #1941 0::Int) +#3093 := (or #1942 #3078 #2551) +#5222 := [hypothesis]: #1945 +#4226 := (forall (vars (?v0 S3)) (:pat #4225) #457) +#460 := (forall (vars (?v0 S3)) #457) +#4229 := (iff #460 #4226) +#4227 := (iff #457 #457) +#4228 := [refl]: #4227 +#4230 := [quant-intro #4228]: #4229 +#1858 := (~ #460 #460) +#1888 := (~ #457 #457) +#1889 := [refl]: #1888 +#1859 := [nnf-pos #1889]: #1858 +#59 := (= #58 0::Int) +#62 := (not #57) +#1805 := (or #62 #59) +#1808 := (forall (vars (?v0 S3)) #1805) +#1811 := (not #1808) +#1739 := (forall (vars (?v0 S3)) #1736) +#1742 := (not #1739) +#542 := (and #536 #539) +#548 := (not #542) +#1725 := (or #548 #1315) +#1730 := (forall (vars (?v0 S3) (?v1 S3)) #1725) +#1733 := (not #1730) +#1236 := (not #1235) +#1700 := (and #533 #1236) +#1705 := (not #1700) +#1711 := (or #1705 #1708) +#1714 := (forall (vars (?v0 S3) (?v1 S3)) #1711) +#1717 := (not #1714) +#1647 := (forall (vars (?v0 S3)) #1642) +#1650 := (not #1647) +#1457 := (not #1456) +#1450 := (not #1449) +#1460 := (and #1450 #1457) +#1618 := (not #1460) +#1626 := (or #1618 #1623) +#1629 := (forall (vars (?v0 S3)) #1626) +#1632 := (not #1629) +#1556 := (= #1534 0::Int) +#1559 := (not #1502) +#1568 := (and #807 #1559 #1556) +#1573 := (exists (vars (?v1 S3)) #1568) +#1545 := (+ f8 #1478) +#1546 := (<= #1545 0::Int) +#1547 := (not #1546) +#1550 := (and #62 #1547) +#1553 := (not #1550) +#1576 := (or #1553 #1573) +#1579 := (forall (vars (?v0 S3)) #1576) +#1524 := (and #807 #1236) +#1529 := (not #1524) +#1536 := (or #1529 #1532) +#1539 := (forall (vars (?v0 S3) (?v1 S3)) #1536) +#1542 := (not #1539) +#1582 := (or #1542 #1579) +#1585 := (and #1539 #1582) +#830 := (and #813 #827) +#836 := (not #830) +#1510 := (or #836 #1502) +#1515 := (forall (vars (?v0 S3) (?v1 S3)) #1510) +#1518 := (not #1515) +#1588 := (or #1518 #1585) +#1591 := (and #1515 #1588) +#1496 := (forall (vars (?v0 S3)) #1493) +#1499 := (not #1496) +#1594 := (or #1499 #1591) +#1597 := (and #1496 #1594) +#1600 := (or #1490 #1597) +#1603 := (and #204 #1600) +#819 := (forall (vars (?v0 S3)) #814) +#953 := (not #819) +#1606 := (or #953 #1603) +#1609 := (and #819 #1606) +#1482 := (forall (vars (?v0 S3)) #1477) +#1485 := (not #1482) +#1612 := (or #1485 #1609) +#1615 := (and #1482 #1612) +#1466 := (or #793 #1460) +#1471 := (forall (vars (?v0 S3)) #1466) +#1474 := (not #1471) +#1300 := (not #1299) +#1419 := (and #536 #1300) +#1424 := (exists (vars (?v0 S3)) #1419) +#1665 := (not #1424) +#1689 := (or #754 #995 #1665 #1474 #1615 #1632 #1650 #1654) +#1345 := (not #1344) +#1379 := (and #1236 #1345) +#1382 := (not #1379) +#1388 := (or #1382 #1385) +#1391 := (forall (vars (?v0 S3) (?v1 S3)) #1388) +#1394 := (not #1391) +#1402 := (or #158 #1394) +#1407 := (and #1391 #1402) +#1360 := (= #1362 0::Int) +#1354 := (>= #1356 0::Int) +#1357 := (not #1354) +#1364 := (and #1357 #1360) +#1367 := (exists (vars (?v1 S3)) #1364) +#1348 := (and #62 #1345) +#1351 := (not #1348) +#1370 := (or #1351 #1367) +#1373 := (forall (vars (?v0 S3)) #1370) +#1376 := (not #1373) +#1410 := (or #1376 #1407) +#1413 := (and #1373 #1410) +#1442 := (or #724 #706 #733 #715 #1413 #1424) +#1694 := (and #1442 #1689) +#1316 := (not #1315) +#1309 := (= #1313 0::Int) +#1325 := (and #533 #1309 #1316) +#1330 := (exists (vars (?v1 S3)) #1325) +#1303 := (and #62 #1300) +#1306 := (not #1303) +#1333 := (or #1306 #1330) +#1336 := (forall (vars (?v0 S3)) #1333) +#1339 := (not #1336) +#1271 := (= #1233 0::Int) +#1212 := (+ #58 #1211) +#1210 := (>= #1212 0::Int) +#1274 := (not #1210) +#1283 := (and #454 #1274 #1271) +#1288 := (exists (vars (?v1 S3)) #1283) +#1262 := (not #1261) +#1265 := (and #62 #1262) +#1268 := (not #1265) +#1291 := (or #1268 #1288) +#1294 := (forall (vars (?v0 S3)) #1291) +#1750 := (not #1294) +#1771 := (or #1747 #1750 #1339 #1694 #1717 #1733 #1742) +#1776 := (and #1294 #1771) +#1242 := (and #454 #1236) +#1247 := (not #1242) +#1250 := (or #1230 #1247) +#1253 := (forall (vars (?v0 S3) (?v1 S3)) #1250) +#1256 := (not #1253) +#1779 := (or #1256 #1776) +#1782 := (and #1253 #1779) +#74 := (f12 #23) +#466 := (= f1 #74) +#469 := (and #457 #466) +#475 := (not #469) +#1217 := (or #475 #1210) +#1222 := (forall (vars (?v0 S3) (?v1 S3)) #1217) +#1225 := (not #1222) +#1785 := (or #1225 #1782) +#1788 := (and #1222 #1785) +#1201 := (>= #58 0::Int) +#1202 := (forall (vars (?v0 S3)) #1201) +#1205 := (not #1202) +#1791 := (or #1205 #1788) +#1794 := (and #1202 #1791) +#70 := (f11 f10) +#71 := (= #70 0::Int) +#1196 := (not #71) +#1797 := (or #1196 #1794) +#1800 := (and #71 #1797) +#1160 := (not #460) +#440 := (= f8 #58) +#446 := (or #57 #440) +#451 := (forall (vars (?v0 S3)) #446) +#1169 := (not #451) +#1823 := (or #1169 #1160 #1800 #1811) +#1828 := (not #1823) #1 := true -#217 := (+ #190 #83) -#224 := (= #212 #217) -#201 := (= #200 f1) -#225 := (and #201 #224) -#223 := (< #190 #212) -#226 := (and #223 #225) -#227 := (exists (vars (?v1 S3)) #226) -#221 := (< #190 f9) -#222 := (and #63 #221) -#228 := (implies #222 #227) -#229 := (forall (vars (?v0 S3)) #228) -#230 := (and #229 true) -#218 := (<= #212 #217) -#84 := (< #83 f9) -#216 := (and #201 #84) -#219 := (implies #216 #218) -#220 := (forall (vars (?v0 S3) (?v1 S3)) #219) -#231 := (implies #220 #230) -#232 := (and #220 #231) -#213 := (<= #212 #190) -#210 := (= #209 f1) -#208 := (not #201) -#211 := (and #208 #210) -#214 := (implies #211 #213) -#215 := (forall (vars (?v0 S3) (?v1 S3)) #214) -#233 := (implies #215 #232) -#234 := (and #215 #233) -#206 := (<= 0::Int #190) -#207 := (forall (vars (?v0 S3)) #206) -#235 := (implies #207 #234) -#236 := (and #207 #235) -#237 := (implies #205 #236) -#238 := (and #205 #237) -#195 := (= #190 #102) -#202 := (implies #201 #195) -#203 := (forall (vars (?v0 S3)) #202) -#239 := (implies #203 #238) -#240 := (and #203 #239) -#198 := (<= #190 #102) -#199 := (forall (vars (?v0 S3)) #198) -#241 := (implies #199 #240) -#242 := (and #199 #241) -#187 := (+ #175 #185) -#188 := (< #187 #102) -#186 := (< #185 f9) -#189 := (and #186 #188) -#194 := (not #189) -#196 := (implies #194 #195) -#197 := (forall (vars (?v0 S3)) #196) -#243 := (implies #197 #242) -#191 := (= #190 #187) -#192 := (implies #189 #191) -#193 := (forall (vars (?v0 S3)) #192) -#244 := (implies #193 #243) +#216 := (+ #189 #82) +#223 := (= #211 #216) +#200 := (= #199 f1) +#224 := (and #200 #223) +#222 := (< #189 #211) +#225 := (and #222 #224) +#226 := (exists (vars (?v1 S3)) #225) +#220 := (< #189 f8) +#221 := (and #62 #220) +#227 := (implies #221 #226) +#228 := (forall (vars (?v0 S3)) #227) +#229 := (and #228 true) +#217 := (<= #211 #216) +#83 := (< #82 f8) +#215 := (and #200 #83) +#218 := (implies #215 #217) +#219 := (forall (vars (?v0 S3) (?v1 S3)) #218) +#230 := (implies #219 #229) +#231 := (and #219 #230) +#212 := (<= #211 #189) +#209 := (= #208 f1) +#207 := (not #200) +#210 := (and #207 #209) +#213 := (implies #210 #212) +#214 := (forall (vars (?v0 S3) (?v1 S3)) #213) +#232 := (implies #214 #231) +#233 := (and #214 #232) +#205 := (<= 0::Int #189) +#206 := (forall (vars (?v0 S3)) #205) +#234 := (implies #206 #233) +#235 := (and #206 #234) +#236 := (implies #204 #235) +#237 := (and #204 #236) +#194 := (= #189 #101) +#201 := (implies #200 #194) +#202 := (forall (vars (?v0 S3)) #201) +#238 := (implies #202 #237) +#239 := (and #202 #238) +#197 := (<= #189 #101) +#198 := (forall (vars (?v0 S3)) #197) +#240 := (implies #198 #239) +#241 := (and #198 #240) +#186 := (+ #174 #184) +#187 := (< #186 #101) +#185 := (< #184 f8) +#188 := (and #185 #187) +#193 := (not #188) +#195 := (implies #193 #194) +#196 := (forall (vars (?v0 S3)) #195) +#242 := (implies #196 #241) +#190 := (= #189 #186) +#191 := (implies #188 #190) +#192 := (forall (vars (?v0 S3)) #191) +#243 := (implies #192 #242) decl f2 :: S1 #5 := f2 -#181 := (ite true f1 f2) -#182 := (f4 f5 f16 f23 #181) -#183 := (= f24 #182) -#245 := (implies #183 #244) -#177 := (<= #175 #102) -#107 := (= #106 f1) -#108 := (not #107) -#178 := (implies #108 #177) -#179 := (forall (vars (?v0 S3)) #178) -#246 := (implies #179 #245) -#176 := (< #175 f9) -#247 := (implies #176 #246) -#173 := (= #172 f1) -#174 := (not #173) -#248 := (implies #174 #247) -#121 := (< #102 f9) -#130 := (and #108 #121) -#131 := (exists (vars (?v0 S3)) #130) -#249 := (implies #131 #248) -#250 := (implies true #249) -#160 := (and #159 true) -#148 := (+ #143 #83) -#155 := (<= #146 #148) -#144 := (< #143 f9) -#154 := (and #144 #84) -#156 := (implies #154 #155) -#157 := (forall (vars (?v0 S3) (?v1 S3)) #156) -#161 := (implies #157 #160) -#162 := (and #157 #161) -#149 := (= #146 #148) -#147 := (< #143 #146) -#150 := (and #147 #149) -#151 := (exists (vars (?v1 S3)) #150) -#145 := (and #63 #144) -#152 := (implies #145 #151) -#153 := (forall (vars (?v0 S3)) #152) -#163 := (implies #153 #162) -#164 := (and #153 #163) -#165 := (implies #142 #164) -#139 := (= f20 f15) -#166 := (implies #139 #165) -#167 := (implies #137 #166) -#134 := (= f17 f16) -#168 := (implies #134 #167) -#132 := (not #131) -#169 := (implies #132 #168) -#170 := (implies true #169) -#251 := (and #170 #250) -#117 := (+ #102 #83) -#124 := (= #112 #117) -#125 := (and #107 #124) -#123 := (< #102 #112) -#126 := (and #123 #125) -#127 := (exists (vars (?v1 S3)) #126) -#122 := (and #63 #121) -#128 := (implies #122 #127) -#129 := (forall (vars (?v0 S3)) #128) -#252 := (implies #129 #251) -#118 := (<= #112 #117) -#116 := (and #107 #84) -#119 := (implies #116 #118) -#120 := (forall (vars (?v0 S3) (?v1 S3)) #119) -#253 := (implies #120 #252) -#113 := (<= #112 #102) -#110 := (= #109 f1) -#111 := (and #108 #110) -#114 := (implies #111 #113) -#115 := (forall (vars (?v0 S3) (?v1 S3)) #114) -#254 := (implies #115 #253) -#103 := (<= 0::Int #102) -#104 := (forall (vars (?v0 S3)) #103) -#255 := (implies #104 #254) -#256 := (implies #101 #255) -#257 := (implies true #256) -#86 := (+ #59 #83) -#93 := (= #78 #86) -#68 := (= #67 f1) -#94 := (and #68 #93) -#92 := (< #59 #78) -#95 := (and #92 #94) -#96 := (exists (vars (?v1 S3)) #95) -#90 := (< #59 f9) -#91 := (and #63 #90) -#97 := (implies #91 #96) -#98 := (forall (vars (?v0 S3)) #97) -#258 := (implies #98 #257) -#259 := (and #98 #258) -#87 := (<= #78 #86) -#85 := (and #68 #84) -#88 := (implies #85 #87) -#89 := (forall (vars (?v0 S3) (?v1 S3)) #88) -#260 := (implies #89 #259) -#261 := (and #89 #260) -#79 := (<= #78 #59) -#76 := (= #75 f1) -#69 := (not #68) -#77 := (and #69 #76) -#80 := (implies #77 #79) -#81 := (forall (vars (?v0 S3) (?v1 S3)) #80) -#262 := (implies #81 #261) -#263 := (and #81 #262) -#73 := (<= 0::Int #59) -#74 := (forall (vars (?v0 S3)) #73) -#264 := (implies #74 #263) -#265 := (and #74 #264) -#266 := (implies #72 #265) -#267 := (and #72 #266) -#70 := (forall (vars (?v0 S3)) #69) -#268 := (implies #70 #267) -#64 := (= #59 f9) -#65 := (implies #63 #64) -#66 := (forall (vars (?v0 S3)) #65) -#269 := (implies #66 #268) -#61 := (implies #58 #60) -#62 := (forall (vars (?v0 S3)) #61) -#270 := (implies #62 #269) -#271 := (implies true #270) -#272 := (not #271) -#1832 := (iff #272 #1829) -#854 := (+ #83 #190) -#872 := (= #212 #854) -#875 := (and #808 #872) -#878 := (and #223 #875) -#881 := (exists (vars (?v1 S3)) #878) -#887 := (not #222) -#888 := (or #887 #881) -#893 := (forall (vars (?v0 S3)) #888) -#857 := (<= #212 #854) -#849 := (and #84 #808) -#863 := (not #849) -#864 := (or #863 #857) -#869 := (forall (vars (?v0 S3) (?v1 S3)) #864) -#906 := (not #869) -#907 := (or #906 #893) -#912 := (and #869 #907) -#838 := (or #213 #837) -#843 := (forall (vars (?v0 S3) (?v1 S3)) #838) -#918 := (not #843) -#919 := (or #918 #912) -#924 := (and #843 #919) -#930 := (not #207) -#931 := (or #930 #924) -#936 := (and #207 #931) -#823 := (= 0::Int #204) -#942 := (not #823) -#943 := (or #942 #936) -#948 := (and #823 #943) -#955 := (or #954 #948) -#960 := (and #820 #955) -#966 := (not #199) -#967 := (or #966 #960) -#972 := (and #199 #967) -#800 := (or #189 #794) -#805 := (forall (vars (?v0 S3)) #800) -#978 := (not #805) -#979 := (or #978 #972) -#780 := (= #187 #190) -#786 := (or #194 #780) -#791 := (forall (vars (?v0 S3)) #786) -#987 := (not #791) -#988 := (or #987 #979) -#997 := (or #996 #988) -#764 := (or #177 #534) -#769 := (forall (vars (?v0 S3)) #764) -#1005 := (not #769) -#1006 := (or #1005 #997) -#1014 := (not #176) -#1015 := (or #1014 #1006) -#1023 := (or #755 #1015) -#611 := (and #121 #537) -#616 := (exists (vars (?v0 S3)) #611) -#619 := (not #616) -#1031 := (or #619 #1023) -#670 := (= 0::Int #158) -#628 := (+ #83 #143) -#655 := (<= #146 #628) -#652 := (and #84 #144) -#661 := (not #652) -#662 := (or #661 #655) -#667 := (forall (vars (?v0 S3) (?v1 S3)) #662) -#683 := (not #667) -#684 := (or #683 #670) -#689 := (and #667 #684) -#631 := (= #146 #628) -#634 := (and #147 #631) -#637 := (exists (vars (?v1 S3)) #634) -#643 := (not #145) -#644 := (or #643 #637) -#649 := (forall (vars (?v0 S3)) #644) -#695 := (not #649) -#696 := (or #695 #689) -#701 := (and #649 #696) -#708 := (or #707 #701) -#717 := (or #716 #708) -#726 := (or #725 #717) -#735 := (or #734 #726) -#743 := (or #616 #735) -#1043 := (and #743 #1031) -#566 := (+ #83 #102) -#584 := (= #112 #566) -#587 := (and #534 #584) -#590 := (and #123 #587) -#593 := (exists (vars (?v1 S3)) #590) -#599 := (not #122) -#600 := (or #599 #593) -#605 := (forall (vars (?v0 S3)) #600) -#1049 := (not #605) -#1050 := (or #1049 #1043) -#569 := (<= #112 #566) -#561 := (and #84 #534) -#575 := (not #561) -#576 := (or #575 #569) -#581 := (forall (vars (?v0 S3) (?v1 S3)) #576) -#1058 := (not #581) -#1059 := (or #1058 #1050) -#550 := (or #113 #549) -#555 := (forall (vars (?v0 S3) (?v1 S3)) #550) -#1067 := (not #555) -#1068 := (or #1067 #1059) -#1076 := (not #104) -#1077 := (or #1076 #1068) -#531 := (= 0::Int #100) -#1085 := (not #531) -#1086 := (or #1085 #1077) -#508 := (and #93 #455) -#513 := (and #92 #508) -#516 := (exists (vars (?v1 S3)) #513) -#522 := (not #91) -#523 := (or #522 #516) -#528 := (forall (vars (?v0 S3)) #523) -#1101 := (not #528) -#1102 := (or #1101 #1086) -#1107 := (and #528 #1102) -#488 := (and #84 #455) -#496 := (not #488) -#497 := (or #87 #496) -#502 := (forall (vars (?v0 S3) (?v1 S3)) #497) -#1113 := (not #502) -#1114 := (or #1113 #1107) -#1119 := (and #502 #1114) -#477 := (or #79 #476) -#482 := (forall (vars (?v0 S3) (?v1 S3)) #477) -#1125 := (not #482) -#1126 := (or #1125 #1119) -#1131 := (and #482 #1126) -#1137 := (not #74) -#1138 := (or #1137 #1131) -#1143 := (and #74 #1138) -#464 := (= 0::Int #71) -#1149 := (not #464) -#1150 := (or #1149 #1143) -#1155 := (and #464 #1150) -#1162 := (or #1161 #1155) -#1171 := (or #1170 #1162) -#427 := (= 0::Int #59) -#433 := (or #63 #427) -#438 := (forall (vars (?v0 S3)) #433) -#1179 := (not #438) -#1180 := (or #1179 #1171) -#1192 := (not #1180) -#1830 := (iff #1192 #1829) -#1827 := (iff #1180 #1824) -#1815 := (or #1161 #1801) -#1818 := (or #1170 #1815) -#1821 := (or #1812 #1818) -#1825 := (iff #1821 #1824) -#1826 := [rewrite]: #1825 -#1822 := (iff #1180 #1821) -#1819 := (iff #1171 #1818) -#1816 := (iff #1162 #1815) -#1802 := (iff #1155 #1801) -#1799 := (iff #1150 #1798) -#1796 := (iff #1143 #1795) -#1793 := (iff #1138 #1792) -#1790 := (iff #1131 #1789) -#1787 := (iff #1126 #1786) -#1784 := (iff #1119 #1783) -#1781 := (iff #1114 #1780) -#1778 := (iff #1107 #1777) -#1775 := (iff #1102 #1772) -#1754 := (or #1340 #1695) -#1757 := (or #1718 #1754) -#1760 := (or #1734 #1757) -#1763 := (or #1743 #1760) -#1766 := (or #1748 #1763) -#1769 := (or #1751 #1766) -#1773 := (iff #1769 #1772) -#1774 := [rewrite]: #1773 -#1770 := (iff #1102 #1769) -#1767 := (iff #1086 #1766) -#1764 := (iff #1077 #1763) -#1761 := (iff #1068 #1760) -#1758 := (iff #1059 #1757) -#1755 := (iff #1050 #1754) -#1696 := (iff #1043 #1695) -#1693 := (iff #1031 #1690) -#1669 := (or #1475 #1616) -#1672 := (or #1633 #1669) -#1675 := (or #996 #1672) -#1678 := (or #1651 #1675) -#1681 := (or #1655 #1678) -#1684 := (or #755 #1681) -#1687 := (or #1666 #1684) -#1691 := (iff #1687 #1690) -#1692 := [rewrite]: #1691 -#1688 := (iff #1031 #1687) -#1685 := (iff #1023 #1684) -#1682 := (iff #1015 #1681) -#1679 := (iff #1006 #1678) -#1676 := (iff #997 #1675) -#1673 := (iff #988 #1672) -#1670 := (iff #979 #1669) -#1617 := (iff #972 #1616) -#1614 := (iff #967 #1613) -#1611 := (iff #960 #1610) -#1608 := (iff #955 #1607) -#1605 := (iff #948 #1604) -#1602 := (iff #943 #1601) -#1599 := (iff #936 #1598) -#1596 := (iff #931 #1595) -#1593 := (iff #924 #1592) -#1590 := (iff #919 #1589) -#1587 := (iff #912 #1586) -#1584 := (iff #907 #1583) -#1581 := (iff #893 #1580) -#1578 := (iff #888 #1577) -#1575 := (iff #881 #1574) -#1572 := (iff #878 #1569) -#1563 := (and #808 #1557) -#1566 := (and #1560 #1563) -#1570 := (iff #1566 #1569) -#1571 := [rewrite]: #1570 -#1567 := (iff #878 #1566) -#1564 := (iff #875 #1563) -#1558 := (iff #872 #1557) -#1559 := [rewrite]: #1558 -#1565 := [monotonicity #1559]: #1564 -#1561 := (iff #223 #1560) -#1562 := [rewrite]: #1561 -#1568 := [monotonicity #1562 #1565]: #1567 -#1573 := [trans #1568 #1571]: #1572 -#1576 := [quant-intro #1573]: #1575 -#1555 := (iff #887 #1554) -#1552 := (iff #222 #1551) -#1549 := (iff #221 #1548) -#1550 := [rewrite]: #1549 -#1553 := [monotonicity #1550]: #1552 -#1556 := [monotonicity #1553]: #1555 -#1579 := [monotonicity #1556 #1576]: #1578 -#1582 := [quant-intro #1579]: #1581 -#1544 := (iff #906 #1543) -#1541 := (iff #869 #1540) -#1538 := (iff #864 #1537) -#1534 := (iff #857 #1533) -#1536 := [rewrite]: #1534 -#1531 := (iff #863 #1530) -#1528 := (iff #849 #1525) -#1522 := (and #1237 #808) -#1526 := (iff #1522 #1525) -#1527 := [rewrite]: #1526 -#1523 := (iff #849 #1522) -#1238 := (iff #84 #1237) -#1239 := [rewrite]: #1238 -#1524 := [monotonicity #1239]: #1523 -#1529 := [trans #1524 #1527]: #1528 -#1532 := [monotonicity #1529]: #1531 -#1539 := [monotonicity #1532 #1536]: #1538 -#1542 := [quant-intro #1539]: #1541 -#1545 := [monotonicity #1542]: #1544 -#1585 := [monotonicity #1545 #1582]: #1584 -#1588 := [monotonicity #1542 #1585]: #1587 -#1520 := (iff #918 #1519) -#1517 := (iff #843 #1516) -#1514 := (iff #838 #1511) -#1508 := (or #1503 #837) -#1512 := (iff #1508 #1511) -#1513 := [rewrite]: #1512 -#1509 := (iff #838 #1508) -#1506 := (iff #213 #1503) -#1507 := [rewrite]: #1506 -#1510 := [monotonicity #1507]: #1509 -#1515 := [trans #1510 #1513]: #1514 -#1518 := [quant-intro #1515]: #1517 -#1521 := [monotonicity #1518]: #1520 -#1591 := [monotonicity #1521 #1588]: #1590 -#1594 := [monotonicity #1518 #1591]: #1593 -#1501 := (iff #930 #1500) -#1498 := (iff #207 #1497) -#1495 := (iff #206 #1494) -#1496 := [rewrite]: #1495 -#1499 := [quant-intro #1496]: #1498 -#1502 := [monotonicity #1499]: #1501 -#1597 := [monotonicity #1502 #1594]: #1596 -#1600 := [monotonicity #1499 #1597]: #1599 -#1492 := (iff #942 #1491) -#1489 := (iff #823 #205) -#1490 := [rewrite]: #1489 -#1493 := [monotonicity #1490]: #1492 -#1603 := [monotonicity #1493 #1600]: #1602 -#1606 := [monotonicity #1490 #1603]: #1605 -#1609 := [monotonicity #1606]: #1608 -#1612 := [monotonicity #1609]: #1611 -#1487 := (iff #966 #1486) -#1484 := (iff #199 #1483) -#1481 := (iff #198 #1478) -#1482 := [rewrite]: #1481 -#1485 := [quant-intro #1482]: #1484 -#1488 := [monotonicity #1485]: #1487 -#1615 := [monotonicity #1488 #1612]: #1614 -#1618 := [monotonicity #1485 #1615]: #1617 -#1476 := (iff #978 #1475) -#1473 := (iff #805 #1472) -#1470 := (iff #800 #1467) -#1464 := (or #1461 #794) -#1468 := (iff #1464 #1467) -#1469 := [rewrite]: #1468 -#1465 := (iff #800 #1464) -#1462 := (iff #189 #1461) -#1459 := (iff #188 #1458) -#1460 := [rewrite]: #1459 -#1452 := (iff #186 #1451) -#1453 := [rewrite]: #1452 -#1463 := [monotonicity #1453 #1460]: #1462 -#1466 := [monotonicity #1463]: #1465 -#1471 := [trans #1466 #1469]: #1470 -#1474 := [quant-intro #1471]: #1473 -#1477 := [monotonicity #1474]: #1476 -#1671 := [monotonicity #1477 #1618]: #1670 -#1634 := (iff #987 #1633) -#1631 := (iff #791 #1630) -#1628 := (iff #786 #1627) -#1625 := (iff #780 #1624) -#1626 := [rewrite]: #1625 -#1620 := (iff #194 #1619) -#1621 := [monotonicity #1463]: #1620 -#1629 := [monotonicity #1621 #1626]: #1628 -#1632 := [quant-intro #1629]: #1631 -#1635 := [monotonicity #1632]: #1634 -#1674 := [monotonicity #1635 #1671]: #1673 -#1677 := [monotonicity #1674]: #1676 -#1652 := (iff #1005 #1651) -#1649 := (iff #769 #1648) -#1646 := (iff #764 #1643) -#1640 := (or #1636 #534) -#1644 := (iff #1640 #1643) -#1645 := [rewrite]: #1644 -#1641 := (iff #764 #1640) -#1638 := (iff #177 #1636) -#1639 := [rewrite]: #1638 -#1642 := [monotonicity #1639]: #1641 -#1647 := [trans #1642 #1645]: #1646 -#1650 := [quant-intro #1647]: #1649 -#1653 := [monotonicity #1650]: #1652 -#1680 := [monotonicity #1653 #1677]: #1679 -#1664 := (iff #1014 #1655) -#1656 := (not #1655) -#1659 := (not #1656) -#1662 := (iff #1659 #1655) -#1663 := [rewrite]: #1662 -#1660 := (iff #1014 #1659) -#1657 := (iff #176 #1656) -#1658 := [rewrite]: #1657 -#1661 := [monotonicity #1658]: #1660 -#1665 := [trans #1661 #1663]: #1664 -#1683 := [monotonicity #1665 #1680]: #1682 -#1686 := [monotonicity #1683]: #1685 -#1667 := (iff #619 #1666) -#1426 := (iff #616 #1425) -#1423 := (iff #611 #1420) -#1417 := (and #1301 #537) -#1421 := (iff #1417 #1420) -#1422 := [rewrite]: #1421 -#1418 := (iff #611 #1417) -#1302 := (iff #121 #1301) -#1303 := [rewrite]: #1302 -#1419 := [monotonicity #1303]: #1418 -#1424 := [trans #1419 #1422]: #1423 -#1427 := [quant-intro #1424]: #1426 -#1668 := [monotonicity #1427]: #1667 -#1689 := [monotonicity #1668 #1686]: #1688 -#1694 := [trans #1689 #1692]: #1693 -#1446 := (iff #743 #1443) -#1428 := (or #707 #1414) -#1431 := (or #716 #1428) -#1434 := (or #725 #1431) -#1437 := (or #734 #1434) -#1440 := (or #1425 #1437) -#1444 := (iff #1440 #1443) -#1445 := [rewrite]: #1444 -#1441 := (iff #743 #1440) -#1438 := (iff #735 #1437) -#1435 := (iff #726 #1434) -#1432 := (iff #717 #1431) -#1429 := (iff #708 #1428) -#1415 := (iff #701 #1414) -#1412 := (iff #696 #1411) -#1409 := (iff #689 #1408) -#1406 := (iff #684 #1403) -#1400 := (or #1395 #159) -#1404 := (iff #1400 #1403) -#1405 := [rewrite]: #1404 -#1401 := (iff #684 #1400) -#1398 := (iff #670 #159) -#1399 := [rewrite]: #1398 -#1396 := (iff #683 #1395) -#1393 := (iff #667 #1392) -#1390 := (iff #662 #1389) -#1387 := (iff #655 #1386) -#1388 := [rewrite]: #1387 -#1384 := (iff #661 #1383) -#1381 := (iff #652 #1380) -#1347 := (iff #144 #1346) -#1348 := [rewrite]: #1347 -#1382 := [monotonicity #1239 #1348]: #1381 -#1385 := [monotonicity #1382]: #1384 -#1391 := [monotonicity #1385 #1388]: #1390 -#1394 := [quant-intro #1391]: #1393 -#1397 := [monotonicity #1394]: #1396 -#1402 := [monotonicity #1397 #1399]: #1401 -#1407 := [trans #1402 #1405]: #1406 -#1410 := [monotonicity #1394 #1407]: #1409 -#1378 := (iff #695 #1377) -#1375 := (iff #649 #1374) -#1372 := (iff #644 #1371) -#1369 := (iff #637 #1368) -#1366 := (iff #634 #1365) -#1362 := (iff #631 #1361) -#1364 := [rewrite]: #1362 -#1359 := (iff #147 #1358) -#1360 := [rewrite]: #1359 -#1367 := [monotonicity #1360 #1364]: #1366 -#1370 := [quant-intro #1367]: #1369 -#1353 := (iff #643 #1352) -#1350 := (iff #145 #1349) -#1351 := [monotonicity #1348]: #1350 -#1354 := [monotonicity #1351]: #1353 -#1373 := [monotonicity #1354 #1370]: #1372 -#1376 := [quant-intro #1373]: #1375 -#1379 := [monotonicity #1376]: #1378 -#1413 := [monotonicity #1379 #1410]: #1412 -#1416 := [monotonicity #1376 #1413]: #1415 -#1430 := [monotonicity #1416]: #1429 -#1433 := [monotonicity #1430]: #1432 -#1436 := [monotonicity #1433]: #1435 -#1439 := [monotonicity #1436]: #1438 -#1442 := [monotonicity #1427 #1439]: #1441 -#1447 := [trans #1442 #1445]: #1446 -#1697 := [monotonicity #1447 #1694]: #1696 -#1341 := (iff #1049 #1340) -#1338 := (iff #605 #1337) -#1335 := (iff #600 #1334) -#1332 := (iff #593 #1331) -#1329 := (iff #590 #1326) -#1320 := (and #534 #1310) -#1323 := (and #1317 #1320) -#1327 := (iff #1323 #1326) -#1328 := [rewrite]: #1327 -#1324 := (iff #590 #1323) -#1321 := (iff #587 #1320) -#1311 := (iff #584 #1310) -#1315 := [rewrite]: #1311 -#1322 := [monotonicity #1315]: #1321 -#1318 := (iff #123 #1317) -#1319 := [rewrite]: #1318 -#1325 := [monotonicity #1319 #1322]: #1324 -#1330 := [trans #1325 #1328]: #1329 -#1333 := [quant-intro #1330]: #1332 -#1308 := (iff #599 #1307) -#1305 := (iff #122 #1304) -#1306 := [monotonicity #1303]: #1305 -#1309 := [monotonicity #1306]: #1308 -#1336 := [monotonicity #1309 #1333]: #1335 -#1339 := [quant-intro #1336]: #1338 -#1342 := [monotonicity #1339]: #1341 -#1756 := [monotonicity #1342 #1697]: #1755 -#1719 := (iff #1058 #1718) -#1716 := (iff #581 #1715) -#1713 := (iff #576 #1712) -#1710 := (iff #569 #1709) -#1711 := [rewrite]: #1710 -#1707 := (iff #575 #1706) -#1704 := (iff #561 #1701) -#1698 := (and #1237 #534) -#1702 := (iff #1698 #1701) -#1703 := [rewrite]: #1702 -#1699 := (iff #561 #1698) -#1700 := [monotonicity #1239]: #1699 -#1705 := [trans #1700 #1703]: #1704 -#1708 := [monotonicity #1705]: #1707 -#1714 := [monotonicity #1708 #1711]: #1713 -#1717 := [quant-intro #1714]: #1716 -#1720 := [monotonicity #1717]: #1719 -#1759 := [monotonicity #1720 #1756]: #1758 -#1735 := (iff #1067 #1734) -#1732 := (iff #555 #1731) -#1729 := (iff #550 #1726) -#1723 := (or #1316 #549) -#1727 := (iff #1723 #1726) -#1728 := [rewrite]: #1727 -#1724 := (iff #550 #1723) -#1721 := (iff #113 #1316) -#1722 := [rewrite]: #1721 -#1725 := [monotonicity #1722]: #1724 -#1730 := [trans #1725 #1728]: #1729 -#1733 := [quant-intro #1730]: #1732 -#1736 := [monotonicity #1733]: #1735 -#1762 := [monotonicity #1736 #1759]: #1761 -#1744 := (iff #1076 #1743) -#1741 := (iff #104 #1740) -#1738 := (iff #103 #1737) -#1739 := [rewrite]: #1738 -#1742 := [quant-intro #1739]: #1741 -#1745 := [monotonicity #1742]: #1744 -#1765 := [monotonicity #1745 #1762]: #1764 -#1749 := (iff #1085 #1748) -#1746 := (iff #531 #101) -#1747 := [rewrite]: #1746 -#1750 := [monotonicity #1747]: #1749 -#1768 := [monotonicity #1750 #1765]: #1767 -#1752 := (iff #1101 #1751) -#1296 := (iff #528 #1295) -#1293 := (iff #523 #1292) -#1290 := (iff #516 #1289) -#1287 := (iff #513 #1284) -#1278 := (and #1272 #455) -#1281 := (and #1275 #1278) -#1285 := (iff #1281 #1284) -#1286 := [rewrite]: #1285 -#1282 := (iff #513 #1281) -#1279 := (iff #508 #1278) -#1273 := (iff #93 #1272) -#1274 := [rewrite]: #1273 -#1280 := [monotonicity #1274]: #1279 -#1276 := (iff #92 #1275) -#1277 := [rewrite]: #1276 -#1283 := [monotonicity #1277 #1280]: #1282 -#1288 := [trans #1283 #1286]: #1287 -#1291 := [quant-intro #1288]: #1290 -#1270 := (iff #522 #1269) -#1267 := (iff #91 #1266) -#1264 := (iff #90 #1263) -#1265 := [rewrite]: #1264 -#1268 := [monotonicity #1265]: #1267 -#1271 := [monotonicity #1268]: #1270 -#1294 := [monotonicity #1271 #1291]: #1293 -#1297 := [quant-intro #1294]: #1296 -#1753 := [monotonicity #1297]: #1752 -#1771 := [monotonicity #1753 #1768]: #1770 -#1776 := [trans #1771 #1774]: #1775 -#1779 := [monotonicity #1297 #1776]: #1778 -#1258 := (iff #1113 #1257) -#1255 := (iff #502 #1254) -#1252 := (iff #497 #1251) -#1249 := (iff #496 #1248) -#1246 := (iff #488 #1243) -#1240 := (and #1237 #455) -#1244 := (iff #1240 #1243) -#1245 := [rewrite]: #1244 -#1241 := (iff #488 #1240) -#1242 := [monotonicity #1239]: #1241 -#1247 := [trans #1242 #1245]: #1246 -#1250 := [monotonicity #1247]: #1249 -#1230 := (iff #87 #1231) -#1229 := [rewrite]: #1230 -#1253 := [monotonicity #1229 #1250]: #1252 -#1256 := [quant-intro #1253]: #1255 -#1259 := [monotonicity #1256]: #1258 -#1782 := [monotonicity #1259 #1779]: #1781 -#1785 := [monotonicity #1256 #1782]: #1784 -#1227 := (iff #1125 #1226) -#1224 := (iff #482 #1223) -#1221 := (iff #477 #1218) -#1215 := (or #1211 #476) -#1219 := (iff #1215 #1218) -#1220 := [rewrite]: #1219 -#1216 := (iff #477 #1215) -#1210 := (iff #79 #1211) -#1214 := [rewrite]: #1210 -#1217 := [monotonicity #1214]: #1216 -#1222 := [trans #1217 #1220]: #1221 -#1225 := [quant-intro #1222]: #1224 -#1228 := [monotonicity #1225]: #1227 -#1788 := [monotonicity #1228 #1785]: #1787 -#1791 := [monotonicity #1225 #1788]: #1790 -#1207 := (iff #1137 #1206) -#1204 := (iff #74 #1203) -#1200 := (iff #73 #1202) -#1201 := [rewrite]: #1200 -#1205 := [quant-intro #1201]: #1204 -#1208 := [monotonicity #1205]: #1207 -#1794 := [monotonicity #1208 #1791]: #1793 -#1797 := [monotonicity #1205 #1794]: #1796 -#1198 := (iff #1149 #1197) -#1195 := (iff #464 #72) -#1196 := [rewrite]: #1195 -#1199 := [monotonicity #1196]: #1198 -#1800 := [monotonicity #1199 #1797]: #1799 -#1803 := [monotonicity #1196 #1800]: #1802 -#1817 := [monotonicity #1803]: #1816 -#1820 := [monotonicity #1817]: #1819 -#1813 := (iff #1179 #1812) -#1810 := (iff #438 #1809) -#1807 := (iff #433 #1806) -#1804 := (iff #427 #60) -#1805 := [rewrite]: #1804 -#1808 := [monotonicity #1805]: #1807 -#1811 := [quant-intro #1808]: #1810 -#1814 := [monotonicity #1811]: #1813 -#1823 := [monotonicity #1814 #1820]: #1822 -#1828 := [trans #1823 #1826]: #1827 -#1831 := [monotonicity #1828]: #1830 -#1193 := (iff #272 #1192) -#1190 := (iff #271 #1180) -#1185 := (implies true #1180) -#1188 := (iff #1185 #1180) -#1189 := [rewrite]: #1188 -#1186 := (iff #271 #1185) -#1183 := (iff #270 #1180) -#1176 := (implies #438 #1171) -#1181 := (iff #1176 #1180) -#1182 := [rewrite]: #1181 -#1177 := (iff #270 #1176) -#1174 := (iff #269 #1171) -#1167 := (implies #452 #1162) -#1172 := (iff #1167 #1171) -#1173 := [rewrite]: #1172 -#1168 := (iff #269 #1167) -#1165 := (iff #268 #1162) -#1158 := (implies #461 #1155) -#1163 := (iff #1158 #1162) -#1164 := [rewrite]: #1163 -#1159 := (iff #268 #1158) -#1156 := (iff #267 #1155) -#1153 := (iff #266 #1150) -#1146 := (implies #464 #1143) -#1151 := (iff #1146 #1150) -#1152 := [rewrite]: #1151 -#1147 := (iff #266 #1146) -#1144 := (iff #265 #1143) -#1141 := (iff #264 #1138) -#1134 := (implies #74 #1131) -#1139 := (iff #1134 #1138) -#1140 := [rewrite]: #1139 -#1135 := (iff #264 #1134) -#1132 := (iff #263 #1131) -#1129 := (iff #262 #1126) -#1122 := (implies #482 #1119) -#1127 := (iff #1122 #1126) -#1128 := [rewrite]: #1127 -#1123 := (iff #262 #1122) -#1120 := (iff #261 #1119) -#1117 := (iff #260 #1114) -#1110 := (implies #502 #1107) -#1115 := (iff #1110 #1114) -#1116 := [rewrite]: #1115 -#1111 := (iff #260 #1110) -#1108 := (iff #259 #1107) -#1105 := (iff #258 #1102) -#1098 := (implies #528 #1086) -#1103 := (iff #1098 #1102) -#1104 := [rewrite]: #1103 -#1099 := (iff #258 #1098) -#1096 := (iff #257 #1086) -#1091 := (implies true #1086) -#1094 := (iff #1091 #1086) -#1095 := [rewrite]: #1094 -#1092 := (iff #257 #1091) -#1089 := (iff #256 #1086) -#1082 := (implies #531 #1077) -#1087 := (iff #1082 #1086) -#1088 := [rewrite]: #1087 -#1083 := (iff #256 #1082) -#1080 := (iff #255 #1077) -#1073 := (implies #104 #1068) -#1078 := (iff #1073 #1077) -#1079 := [rewrite]: #1078 -#1074 := (iff #255 #1073) -#1071 := (iff #254 #1068) -#1064 := (implies #555 #1059) -#1069 := (iff #1064 #1068) -#1070 := [rewrite]: #1069 -#1065 := (iff #254 #1064) -#1062 := (iff #253 #1059) -#1055 := (implies #581 #1050) -#1060 := (iff #1055 #1059) -#1061 := [rewrite]: #1060 -#1056 := (iff #253 #1055) -#1053 := (iff #252 #1050) -#1046 := (implies #605 #1043) -#1051 := (iff #1046 #1050) -#1052 := [rewrite]: #1051 -#1047 := (iff #252 #1046) -#1044 := (iff #251 #1043) -#1041 := (iff #250 #1031) -#1036 := (implies true #1031) -#1039 := (iff #1036 #1031) -#1040 := [rewrite]: #1039 -#1037 := (iff #250 #1036) -#1034 := (iff #249 #1031) -#1028 := (implies #616 #1023) -#1032 := (iff #1028 #1031) -#1033 := [rewrite]: #1032 -#1029 := (iff #249 #1028) -#1026 := (iff #248 #1023) -#758 := (not #755) -#1020 := (implies #758 #1015) -#1024 := (iff #1020 #1023) -#1025 := [rewrite]: #1024 -#1021 := (iff #248 #1020) -#1018 := (iff #247 #1015) -#1011 := (implies #176 #1006) -#1016 := (iff #1011 #1015) -#1017 := [rewrite]: #1016 -#1012 := (iff #247 #1011) -#1009 := (iff #246 #1006) -#1002 := (implies #769 #997) -#1007 := (iff #1002 #1006) -#1008 := [rewrite]: #1007 -#1003 := (iff #246 #1002) -#1000 := (iff #245 #997) -#993 := (implies #777 #988) -#998 := (iff #993 #997) -#999 := [rewrite]: #998 -#994 := (iff #245 #993) -#991 := (iff #244 #988) -#984 := (implies #791 #979) -#989 := (iff #984 #988) -#990 := [rewrite]: #989 -#985 := (iff #244 #984) -#982 := (iff #243 #979) -#975 := (implies #805 #972) -#980 := (iff #975 #979) -#981 := [rewrite]: #980 -#976 := (iff #243 #975) -#973 := (iff #242 #972) -#970 := (iff #241 #967) -#963 := (implies #199 #960) -#968 := (iff #963 #967) -#969 := [rewrite]: #968 -#964 := (iff #241 #963) -#961 := (iff #240 #960) -#958 := (iff #239 #955) -#951 := (implies #820 #948) -#956 := (iff #951 #955) -#957 := [rewrite]: #956 -#952 := (iff #239 #951) -#949 := (iff #238 #948) -#946 := (iff #237 #943) -#939 := (implies #823 #936) -#944 := (iff #939 #943) -#945 := [rewrite]: #944 -#940 := (iff #237 #939) -#937 := (iff #236 #936) -#934 := (iff #235 #931) -#927 := (implies #207 #924) -#932 := (iff #927 #931) -#933 := [rewrite]: #932 -#928 := (iff #235 #927) -#925 := (iff #234 #924) -#922 := (iff #233 #919) -#915 := (implies #843 #912) -#920 := (iff #915 #919) -#921 := [rewrite]: #920 -#916 := (iff #233 #915) -#913 := (iff #232 #912) -#910 := (iff #231 #907) -#903 := (implies #869 #893) -#908 := (iff #903 #907) -#909 := [rewrite]: #908 -#904 := (iff #231 #903) -#901 := (iff #230 #893) -#896 := (and #893 true) -#899 := (iff #896 #893) -#900 := [rewrite]: #899 -#897 := (iff #230 #896) -#894 := (iff #229 #893) -#891 := (iff #228 #888) -#884 := (implies #222 #881) -#889 := (iff #884 #888) -#890 := [rewrite]: #889 -#885 := (iff #228 #884) -#882 := (iff #227 #881) -#879 := (iff #226 #878) -#876 := (iff #225 #875) -#873 := (iff #224 #872) -#855 := (= #217 #854) -#856 := [rewrite]: #855 -#874 := [monotonicity #856]: #873 -#809 := (iff #201 #808) -#810 := [rewrite]: #809 -#877 := [monotonicity #810 #874]: #876 -#880 := [monotonicity #877]: #879 -#883 := [quant-intro #880]: #882 -#886 := [monotonicity #883]: #885 -#892 := [trans #886 #890]: #891 -#895 := [quant-intro #892]: #894 -#898 := [monotonicity #895]: #897 -#902 := [trans #898 #900]: #901 -#870 := (iff #220 #869) -#867 := (iff #219 #864) -#860 := (implies #849 #857) -#865 := (iff #860 #864) -#866 := [rewrite]: #865 -#861 := (iff #219 #860) -#858 := (iff #218 #857) -#859 := [monotonicity #856]: #858 -#852 := (iff #216 #849) -#846 := (and #808 #84) -#850 := (iff #846 #849) -#851 := [rewrite]: #850 -#847 := (iff #216 #846) -#848 := [monotonicity #810]: #847 -#853 := [trans #848 #851]: #852 -#862 := [monotonicity #853 #859]: #861 -#868 := [trans #862 #866]: #867 -#871 := [quant-intro #868]: #870 -#905 := [monotonicity #871 #902]: #904 -#911 := [trans #905 #909]: #910 -#914 := [monotonicity #871 #911]: #913 -#844 := (iff #215 #843) -#841 := (iff #214 #838) -#834 := (implies #831 #213) -#839 := (iff #834 #838) -#840 := [rewrite]: #839 -#835 := (iff #214 #834) -#832 := (iff #211 #831) -#829 := (iff #210 #828) -#830 := [rewrite]: #829 -#826 := (iff #208 #814) -#827 := [monotonicity #810]: #826 -#833 := [monotonicity #827 #830]: #832 -#836 := [monotonicity #833]: #835 -#842 := [trans #836 #840]: #841 -#845 := [quant-intro #842]: #844 -#917 := [monotonicity #845 #914]: #916 -#923 := [trans #917 #921]: #922 -#926 := [monotonicity #845 #923]: #925 -#929 := [monotonicity #926]: #928 -#935 := [trans #929 #933]: #934 -#938 := [monotonicity #935]: #937 -#824 := (iff #205 #823) -#825 := [rewrite]: #824 -#941 := [monotonicity #825 #938]: #940 -#947 := [trans #941 #945]: #946 -#950 := [monotonicity #825 #947]: #949 -#821 := (iff #203 #820) -#818 := (iff #202 #815) -#811 := (implies #808 #794) -#816 := (iff #811 #815) -#817 := [rewrite]: #816 -#812 := (iff #202 #811) -#795 := (iff #195 #794) -#796 := [rewrite]: #795 -#813 := [monotonicity #810 #796]: #812 -#819 := [trans #813 #817]: #818 -#822 := [quant-intro #819]: #821 -#953 := [monotonicity #822 #950]: #952 -#959 := [trans #953 #957]: #958 -#962 := [monotonicity #822 #959]: #961 -#965 := [monotonicity #962]: #964 -#971 := [trans #965 #969]: #970 -#974 := [monotonicity #971]: #973 -#806 := (iff #197 #805) -#803 := (iff #196 #800) -#797 := (implies #194 #794) -#801 := (iff #797 #800) -#802 := [rewrite]: #801 -#798 := (iff #196 #797) -#799 := [monotonicity #796]: #798 -#804 := [trans #799 #802]: #803 -#807 := [quant-intro #804]: #806 -#977 := [monotonicity #807 #974]: #976 -#983 := [trans #977 #981]: #982 -#792 := (iff #193 #791) -#789 := (iff #192 #786) -#783 := (implies #189 #780) -#787 := (iff #783 #786) -#788 := [rewrite]: #787 -#784 := (iff #192 #783) -#781 := (iff #191 #780) -#782 := [rewrite]: #781 -#785 := [monotonicity #782]: #784 -#790 := [trans #785 #788]: #789 -#793 := [quant-intro #790]: #792 -#986 := [monotonicity #793 #983]: #985 -#992 := [trans #986 #990]: #991 -#778 := (iff #183 #777) -#775 := (= #182 #774) -#772 := (= #181 f1) -#773 := [rewrite]: #772 -#776 := [monotonicity #773]: #775 -#779 := [monotonicity #776]: #778 -#995 := [monotonicity #779 #992]: #994 -#1001 := [trans #995 #999]: #1000 -#770 := (iff #179 #769) -#767 := (iff #178 #764) -#761 := (implies #537 #177) -#765 := (iff #761 #764) -#766 := [rewrite]: #765 -#762 := (iff #178 #761) -#538 := (iff #108 #537) -#535 := (iff #107 #534) -#536 := [rewrite]: #535 -#539 := [monotonicity #536]: #538 -#763 := [monotonicity #539]: #762 -#768 := [trans #763 #766]: #767 -#771 := [quant-intro #768]: #770 -#1004 := [monotonicity #771 #1001]: #1003 -#1010 := [trans #1004 #1008]: #1009 -#1013 := [monotonicity #1010]: #1012 -#1019 := [trans #1013 #1017]: #1018 -#759 := (iff #174 #758) -#756 := (iff #173 #755) -#757 := [rewrite]: #756 -#760 := [monotonicity #757]: #759 -#1022 := [monotonicity #760 #1019]: #1021 -#1027 := [trans #1022 #1025]: #1026 -#617 := (iff #131 #616) -#614 := (iff #130 #611) -#608 := (and #537 #121) -#612 := (iff #608 #611) -#613 := [rewrite]: #612 -#609 := (iff #130 #608) -#610 := [monotonicity #539]: #609 -#615 := [trans #610 #613]: #614 -#618 := [quant-intro #615]: #617 -#1030 := [monotonicity #618 #1027]: #1029 -#1035 := [trans #1030 #1033]: #1034 -#1038 := [monotonicity #1035]: #1037 -#1042 := [trans #1038 #1040]: #1041 -#753 := (iff #170 #743) -#748 := (implies true #743) -#751 := (iff #748 #743) -#752 := [rewrite]: #751 -#749 := (iff #170 #748) -#746 := (iff #169 #743) -#740 := (implies #619 #735) -#744 := (iff #740 #743) -#745 := [rewrite]: #744 -#741 := (iff #169 #740) -#738 := (iff #168 #735) -#731 := (implies #622 #726) -#736 := (iff #731 #735) -#737 := [rewrite]: #736 -#732 := (iff #168 #731) -#729 := (iff #167 #726) -#722 := (implies #137 #717) -#727 := (iff #722 #726) -#728 := [rewrite]: #727 -#723 := (iff #167 #722) -#720 := (iff #166 #717) -#713 := (implies #625 #708) -#718 := (iff #713 #717) -#719 := [rewrite]: #718 -#714 := (iff #166 #713) -#711 := (iff #165 #708) -#704 := (implies #142 #701) -#709 := (iff #704 #708) -#710 := [rewrite]: #709 -#705 := (iff #165 #704) -#702 := (iff #164 #701) -#699 := (iff #163 #696) -#692 := (implies #649 #689) -#697 := (iff #692 #696) -#698 := [rewrite]: #697 -#693 := (iff #163 #692) -#690 := (iff #162 #689) -#687 := (iff #161 #684) -#680 := (implies #667 #670) -#685 := (iff #680 #684) -#686 := [rewrite]: #685 -#681 := (iff #161 #680) -#678 := (iff #160 #670) -#673 := (and #670 true) -#676 := (iff #673 #670) -#677 := [rewrite]: #676 -#674 := (iff #160 #673) -#671 := (iff #159 #670) -#672 := [rewrite]: #671 -#675 := [monotonicity #672]: #674 -#679 := [trans #675 #677]: #678 -#668 := (iff #157 #667) -#665 := (iff #156 #662) -#658 := (implies #652 #655) -#663 := (iff #658 #662) -#664 := [rewrite]: #663 -#659 := (iff #156 #658) -#656 := (iff #155 #655) -#629 := (= #148 #628) -#630 := [rewrite]: #629 -#657 := [monotonicity #630]: #656 -#653 := (iff #154 #652) -#654 := [rewrite]: #653 -#660 := [monotonicity #654 #657]: #659 -#666 := [trans #660 #664]: #665 -#669 := [quant-intro #666]: #668 -#682 := [monotonicity #669 #679]: #681 -#688 := [trans #682 #686]: #687 -#691 := [monotonicity #669 #688]: #690 -#650 := (iff #153 #649) -#647 := (iff #152 #644) -#640 := (implies #145 #637) -#645 := (iff #640 #644) -#646 := [rewrite]: #645 -#641 := (iff #152 #640) -#638 := (iff #151 #637) -#635 := (iff #150 #634) -#632 := (iff #149 #631) -#633 := [monotonicity #630]: #632 -#636 := [monotonicity #633]: #635 -#639 := [quant-intro #636]: #638 -#642 := [monotonicity #639]: #641 -#648 := [trans #642 #646]: #647 -#651 := [quant-intro #648]: #650 -#694 := [monotonicity #651 #691]: #693 -#700 := [trans #694 #698]: #699 -#703 := [monotonicity #651 #700]: #702 -#706 := [monotonicity #703]: #705 -#712 := [trans #706 #710]: #711 -#626 := (iff #139 #625) -#627 := [rewrite]: #626 -#715 := [monotonicity #627 #712]: #714 -#721 := [trans #715 #719]: #720 -#724 := [monotonicity #721]: #723 -#730 := [trans #724 #728]: #729 -#623 := (iff #134 #622) -#624 := [rewrite]: #623 -#733 := [monotonicity #624 #730]: #732 -#739 := [trans #733 #737]: #738 -#620 := (iff #132 #619) -#621 := [monotonicity #618]: #620 -#742 := [monotonicity #621 #739]: #741 -#747 := [trans #742 #745]: #746 -#750 := [monotonicity #747]: #749 -#754 := [trans #750 #752]: #753 -#1045 := [monotonicity #754 #1042]: #1044 -#606 := (iff #129 #605) -#603 := (iff #128 #600) -#596 := (implies #122 #593) -#601 := (iff #596 #600) -#602 := [rewrite]: #601 -#597 := (iff #128 #596) -#594 := (iff #127 #593) -#591 := (iff #126 #590) -#588 := (iff #125 #587) -#585 := (iff #124 #584) -#567 := (= #117 #566) -#568 := [rewrite]: #567 -#586 := [monotonicity #568]: #585 -#589 := [monotonicity #536 #586]: #588 -#592 := [monotonicity #589]: #591 -#595 := [quant-intro #592]: #594 -#598 := [monotonicity #595]: #597 -#604 := [trans #598 #602]: #603 -#607 := [quant-intro #604]: #606 -#1048 := [monotonicity #607 #1045]: #1047 -#1054 := [trans #1048 #1052]: #1053 -#582 := (iff #120 #581) -#579 := (iff #119 #576) -#572 := (implies #561 #569) -#577 := (iff #572 #576) -#578 := [rewrite]: #577 -#573 := (iff #119 #572) -#570 := (iff #118 #569) -#571 := [monotonicity #568]: #570 -#564 := (iff #116 #561) -#558 := (and #534 #84) -#562 := (iff #558 #561) -#563 := [rewrite]: #562 -#559 := (iff #116 #558) -#560 := [monotonicity #536]: #559 -#565 := [trans #560 #563]: #564 -#574 := [monotonicity #565 #571]: #573 -#580 := [trans #574 #578]: #579 -#583 := [quant-intro #580]: #582 -#1057 := [monotonicity #583 #1054]: #1056 -#1063 := [trans #1057 #1061]: #1062 -#556 := (iff #115 #555) -#553 := (iff #114 #550) -#546 := (implies #543 #113) -#551 := (iff #546 #550) -#552 := [rewrite]: #551 -#547 := (iff #114 #546) -#544 := (iff #111 #543) -#541 := (iff #110 #540) -#542 := [rewrite]: #541 -#545 := [monotonicity #539 #542]: #544 -#548 := [monotonicity #545]: #547 -#554 := [trans #548 #552]: #553 -#557 := [quant-intro #554]: #556 -#1066 := [monotonicity #557 #1063]: #1065 -#1072 := [trans #1066 #1070]: #1071 -#1075 := [monotonicity #1072]: #1074 -#1081 := [trans #1075 #1079]: #1080 -#532 := (iff #101 #531) -#533 := [rewrite]: #532 -#1084 := [monotonicity #533 #1081]: #1083 -#1090 := [trans #1084 #1088]: #1089 -#1093 := [monotonicity #1090]: #1092 -#1097 := [trans #1093 #1095]: #1096 -#529 := (iff #98 #528) -#526 := (iff #97 #523) -#519 := (implies #91 #516) -#524 := (iff #519 #523) -#525 := [rewrite]: #524 -#520 := (iff #97 #519) -#517 := (iff #96 #516) -#514 := (iff #95 #513) -#511 := (iff #94 #508) -#505 := (and #455 #93) -#509 := (iff #505 #508) -#510 := [rewrite]: #509 -#506 := (iff #94 #505) -#456 := (iff #68 #455) -#457 := [rewrite]: #456 -#507 := [monotonicity #457]: #506 -#512 := [trans #507 #510]: #511 -#515 := [monotonicity #512]: #514 -#518 := [quant-intro #515]: #517 -#521 := [monotonicity #518]: #520 -#527 := [trans #521 #525]: #526 -#530 := [quant-intro #527]: #529 -#1100 := [monotonicity #530 #1097]: #1099 -#1106 := [trans #1100 #1104]: #1105 -#1109 := [monotonicity #530 #1106]: #1108 -#503 := (iff #89 #502) -#500 := (iff #88 #497) -#493 := (implies #488 #87) -#498 := (iff #493 #497) -#499 := [rewrite]: #498 -#494 := (iff #88 #493) -#491 := (iff #85 #488) -#485 := (and #455 #84) -#489 := (iff #485 #488) -#490 := [rewrite]: #489 -#486 := (iff #85 #485) -#487 := [monotonicity #457]: #486 -#492 := [trans #487 #490]: #491 -#495 := [monotonicity #492]: #494 -#501 := [trans #495 #499]: #500 -#504 := [quant-intro #501]: #503 -#1112 := [monotonicity #504 #1109]: #1111 -#1118 := [trans #1112 #1116]: #1117 -#1121 := [monotonicity #504 #1118]: #1120 -#483 := (iff #81 #482) -#480 := (iff #80 #477) -#473 := (implies #470 #79) -#478 := (iff #473 #477) -#479 := [rewrite]: #478 -#474 := (iff #80 #473) -#471 := (iff #77 #470) -#468 := (iff #76 #467) -#469 := [rewrite]: #468 -#459 := (iff #69 #458) -#460 := [monotonicity #457]: #459 -#472 := [monotonicity #460 #469]: #471 -#475 := [monotonicity #472]: #474 -#481 := [trans #475 #479]: #480 -#484 := [quant-intro #481]: #483 -#1124 := [monotonicity #484 #1121]: #1123 -#1130 := [trans #1124 #1128]: #1129 -#1133 := [monotonicity #484 #1130]: #1132 -#1136 := [monotonicity #1133]: #1135 -#1142 := [trans #1136 #1140]: #1141 -#1145 := [monotonicity #1142]: #1144 -#465 := (iff #72 #464) -#466 := [rewrite]: #465 -#1148 := [monotonicity #466 #1145]: #1147 -#1154 := [trans #1148 #1152]: #1153 -#1157 := [monotonicity #466 #1154]: #1156 -#462 := (iff #70 #461) -#463 := [quant-intro #460]: #462 -#1160 := [monotonicity #463 #1157]: #1159 -#1166 := [trans #1160 #1164]: #1165 -#453 := (iff #66 #452) -#450 := (iff #65 #447) -#444 := (implies #63 #441) -#448 := (iff #444 #447) -#449 := [rewrite]: #448 -#445 := (iff #65 #444) -#442 := (iff #64 #441) -#443 := [rewrite]: #442 -#446 := [monotonicity #443]: #445 -#451 := [trans #446 #449]: #450 -#454 := [quant-intro #451]: #453 -#1169 := [monotonicity #454 #1166]: #1168 -#1175 := [trans #1169 #1173]: #1174 -#439 := (iff #62 #438) -#436 := (iff #61 #433) -#430 := (implies #58 #427) -#434 := (iff #430 #433) -#435 := [rewrite]: #434 -#431 := (iff #61 #430) -#428 := (iff #60 #427) -#429 := [rewrite]: #428 -#432 := [monotonicity #429]: #431 -#437 := [trans #432 #435]: #436 -#440 := [quant-intro #437]: #439 -#1178 := [monotonicity #440 #1175]: #1177 -#1184 := [trans #1178 #1182]: #1183 -#1187 := [monotonicity #1184]: #1186 -#1191 := [trans #1187 #1189]: #1190 -#1194 := [monotonicity #1191]: #1193 -#1833 := [trans #1194 #1831]: #1832 -#426 := [asserted]: #272 -#1834 := [mp #426 #1833]: #1829 -#1836 := [not-or-elim #1834]: #461 -#1891 := [mp~ #1836 #1860]: #461 -#4232 := [mp #1891 #4231]: #4227 -#5530 := (not #4227) -#5531 := (or #5530 #3079) -#5526 := [quant-inst #1937]: #5531 -#5338 := [unit-resolution #5526 #4232 #5223]: false -#5346 := [lemma #5338]: #3079 -#3846 := (or #3094 #1946) -#3850 := [def-axiom]: #3846 -#6496 := [unit-resolution #3850 #5346]: #3094 -#3099 := (not #3094) -#4566 := (or #3099 #4563) -#4569 := (not #4566) -#4241 := (pattern #67 #75) -#2520 := (not #467) -#3071 := (or #455 #2520 #1211) -#4242 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4241) #3071) -#4247 := (not #4242) -#4572 := (or #4247 #4569) -#4575 := (not #4572) +#180 := (ite true f1 f2) +#181 := (f4 f15 f22 #180) +#182 := (= f23 #181) +#244 := (implies #182 #243) +#176 := (<= #174 #101) +#106 := (= #105 f1) +#107 := (not #106) +#177 := (implies #107 #176) +#178 := (forall (vars (?v0 S3)) #177) +#245 := (implies #178 #244) +#175 := (< #174 f8) +#246 := (implies #175 #245) +#172 := (= #171 f1) +#173 := (not #172) +#247 := (implies #173 #246) +#120 := (< #101 f8) +#129 := (and #107 #120) +#130 := (exists (vars (?v0 S3)) #129) +#248 := (implies #130 #247) +#249 := (implies true #248) +#159 := (and #158 true) +#147 := (+ #142 #82) +#154 := (<= #145 #147) +#143 := (< #142 f8) +#153 := (and #143 #83) +#155 := (implies #153 #154) +#156 := (forall (vars (?v0 S3) (?v1 S3)) #155) +#160 := (implies #156 #159) +#161 := (and #156 #160) +#148 := (= #145 #147) +#146 := (< #142 #145) +#149 := (and #146 #148) +#150 := (exists (vars (?v1 S3)) #149) +#144 := (and #62 #143) +#151 := (implies #144 #150) +#152 := (forall (vars (?v0 S3)) #151) +#162 := (implies #152 #161) +#163 := (and #152 #162) +#164 := (implies #141 #163) +#138 := (= f19 f14) +#165 := (implies #138 #164) +#166 := (implies #136 #165) +#133 := (= f16 f15) +#167 := (implies #133 #166) +#131 := (not #130) +#168 := (implies #131 #167) +#169 := (implies true #168) +#250 := (and #169 #249) +#116 := (+ #101 #82) +#123 := (= #111 #116) +#124 := (and #106 #123) +#122 := (< #101 #111) +#125 := (and #122 #124) +#126 := (exists (vars (?v1 S3)) #125) +#121 := (and #62 #120) +#127 := (implies #121 #126) +#128 := (forall (vars (?v0 S3)) #127) +#251 := (implies #128 #250) +#117 := (<= #111 #116) +#115 := (and #106 #83) +#118 := (implies #115 #117) +#119 := (forall (vars (?v0 S3) (?v1 S3)) #118) +#252 := (implies #119 #251) +#112 := (<= #111 #101) +#109 := (= #108 f1) +#110 := (and #107 #109) +#113 := (implies #110 #112) +#114 := (forall (vars (?v0 S3) (?v1 S3)) #113) +#253 := (implies #114 #252) +#102 := (<= 0::Int #101) +#103 := (forall (vars (?v0 S3)) #102) +#254 := (implies #103 #253) +#255 := (implies #100 #254) +#256 := (implies true #255) +#85 := (+ #58 #82) +#92 := (= #77 #85) +#67 := (= #66 f1) +#93 := (and #67 #92) +#91 := (< #58 #77) +#94 := (and #91 #93) +#95 := (exists (vars (?v1 S3)) #94) +#89 := (< #58 f8) +#90 := (and #62 #89) +#96 := (implies #90 #95) +#97 := (forall (vars (?v0 S3)) #96) +#257 := (implies #97 #256) +#258 := (and #97 #257) +#86 := (<= #77 #85) +#84 := (and #67 #83) +#87 := (implies #84 #86) +#88 := (forall (vars (?v0 S3) (?v1 S3)) #87) +#259 := (implies #88 #258) +#260 := (and #88 #259) +#78 := (<= #77 #58) +#75 := (= #74 f1) +#68 := (not #67) +#76 := (and #68 #75) +#79 := (implies #76 #78) +#80 := (forall (vars (?v0 S3) (?v1 S3)) #79) +#261 := (implies #80 #260) +#262 := (and #80 #261) +#72 := (<= 0::Int #58) +#73 := (forall (vars (?v0 S3)) #72) +#263 := (implies #73 #262) +#264 := (and #73 #263) +#265 := (implies #71 #264) +#266 := (and #71 #265) +#69 := (forall (vars (?v0 S3)) #68) +#267 := (implies #69 #266) +#63 := (= #58 f8) +#64 := (implies #62 #63) +#65 := (forall (vars (?v0 S3)) #64) +#268 := (implies #65 #267) +#60 := (implies #57 #59) +#61 := (forall (vars (?v0 S3)) #60) +#269 := (implies #61 #268) +#270 := (implies true #269) +#271 := (not #270) +#1831 := (iff #271 #1828) +#853 := (+ #82 #189) +#871 := (= #211 #853) +#874 := (and #807 #871) +#877 := (and #222 #874) +#880 := (exists (vars (?v1 S3)) #877) +#886 := (not #221) +#887 := (or #886 #880) +#892 := (forall (vars (?v0 S3)) #887) +#856 := (<= #211 #853) +#848 := (and #83 #807) +#862 := (not #848) +#863 := (or #862 #856) +#868 := (forall (vars (?v0 S3) (?v1 S3)) #863) +#905 := (not #868) +#906 := (or #905 #892) +#911 := (and #868 #906) +#837 := (or #212 #836) +#842 := (forall (vars (?v0 S3) (?v1 S3)) #837) +#917 := (not #842) +#918 := (or #917 #911) +#923 := (and #842 #918) +#929 := (not #206) +#930 := (or #929 #923) +#935 := (and #206 #930) +#822 := (= 0::Int #203) +#941 := (not #822) +#942 := (or #941 #935) +#947 := (and #822 #942) +#954 := (or #953 #947) +#959 := (and #819 #954) +#965 := (not #198) +#966 := (or #965 #959) +#971 := (and #198 #966) +#799 := (or #188 #793) +#804 := (forall (vars (?v0 S3)) #799) +#977 := (not #804) +#978 := (or #977 #971) +#779 := (= #186 #189) +#785 := (or #193 #779) +#790 := (forall (vars (?v0 S3)) #785) +#986 := (not #790) +#987 := (or #986 #978) +#996 := (or #995 #987) +#763 := (or #176 #533) +#768 := (forall (vars (?v0 S3)) #763) +#1004 := (not #768) +#1005 := (or #1004 #996) +#1013 := (not #175) +#1014 := (or #1013 #1005) +#1022 := (or #754 #1014) +#610 := (and #120 #536) +#615 := (exists (vars (?v0 S3)) #610) +#618 := (not #615) +#1030 := (or #618 #1022) +#669 := (= 0::Int #157) +#627 := (+ #82 #142) +#654 := (<= #145 #627) +#651 := (and #83 #143) +#660 := (not #651) +#661 := (or #660 #654) +#666 := (forall (vars (?v0 S3) (?v1 S3)) #661) +#682 := (not #666) +#683 := (or #682 #669) +#688 := (and #666 #683) +#630 := (= #145 #627) +#633 := (and #146 #630) +#636 := (exists (vars (?v1 S3)) #633) +#642 := (not #144) +#643 := (or #642 #636) +#648 := (forall (vars (?v0 S3)) #643) +#694 := (not #648) +#695 := (or #694 #688) +#700 := (and #648 #695) +#707 := (or #706 #700) +#716 := (or #715 #707) +#725 := (or #724 #716) +#734 := (or #733 #725) +#742 := (or #615 #734) +#1042 := (and #742 #1030) +#565 := (+ #82 #101) +#583 := (= #111 #565) +#586 := (and #533 #583) +#589 := (and #122 #586) +#592 := (exists (vars (?v1 S3)) #589) +#598 := (not #121) +#599 := (or #598 #592) +#604 := (forall (vars (?v0 S3)) #599) +#1048 := (not #604) +#1049 := (or #1048 #1042) +#568 := (<= #111 #565) +#560 := (and #83 #533) +#574 := (not #560) +#575 := (or #574 #568) +#580 := (forall (vars (?v0 S3) (?v1 S3)) #575) +#1057 := (not #580) +#1058 := (or #1057 #1049) +#549 := (or #112 #548) +#554 := (forall (vars (?v0 S3) (?v1 S3)) #549) +#1066 := (not #554) +#1067 := (or #1066 #1058) +#1075 := (not #103) +#1076 := (or #1075 #1067) +#530 := (= 0::Int #99) +#1084 := (not #530) +#1085 := (or #1084 #1076) +#507 := (and #92 #454) +#512 := (and #91 #507) +#515 := (exists (vars (?v1 S3)) #512) +#521 := (not #90) +#522 := (or #521 #515) +#527 := (forall (vars (?v0 S3)) #522) +#1100 := (not #527) +#1101 := (or #1100 #1085) +#1106 := (and #527 #1101) +#487 := (and #83 #454) +#495 := (not #487) +#496 := (or #86 #495) +#501 := (forall (vars (?v0 S3) (?v1 S3)) #496) +#1112 := (not #501) +#1113 := (or #1112 #1106) +#1118 := (and #501 #1113) +#476 := (or #78 #475) +#481 := (forall (vars (?v0 S3) (?v1 S3)) #476) +#1124 := (not #481) +#1125 := (or #1124 #1118) +#1130 := (and #481 #1125) +#1136 := (not #73) +#1137 := (or #1136 #1130) +#1142 := (and #73 #1137) +#463 := (= 0::Int #70) +#1148 := (not #463) +#1149 := (or #1148 #1142) +#1154 := (and #463 #1149) +#1161 := (or #1160 #1154) +#1170 := (or #1169 #1161) +#426 := (= 0::Int #58) +#432 := (or #62 #426) +#437 := (forall (vars (?v0 S3)) #432) +#1178 := (not #437) +#1179 := (or #1178 #1170) +#1191 := (not #1179) +#1829 := (iff #1191 #1828) +#1826 := (iff #1179 #1823) +#1814 := (or #1160 #1800) +#1817 := (or #1169 #1814) +#1820 := (or #1811 #1817) +#1824 := (iff #1820 #1823) +#1825 := [rewrite]: #1824 +#1821 := (iff #1179 #1820) +#1818 := (iff #1170 #1817) +#1815 := (iff #1161 #1814) +#1801 := (iff #1154 #1800) +#1798 := (iff #1149 #1797) +#1795 := (iff #1142 #1794) +#1792 := (iff #1137 #1791) +#1789 := (iff #1130 #1788) +#1786 := (iff #1125 #1785) +#1783 := (iff #1118 #1782) +#1780 := (iff #1113 #1779) +#1777 := (iff #1106 #1776) +#1774 := (iff #1101 #1771) +#1753 := (or #1339 #1694) +#1756 := (or #1717 #1753) +#1759 := (or #1733 #1756) +#1762 := (or #1742 #1759) +#1765 := (or #1747 #1762) +#1768 := (or #1750 #1765) +#1772 := (iff #1768 #1771) +#1773 := [rewrite]: #1772 +#1769 := (iff #1101 #1768) +#1766 := (iff #1085 #1765) +#1763 := (iff #1076 #1762) +#1760 := (iff #1067 #1759) +#1757 := (iff #1058 #1756) +#1754 := (iff #1049 #1753) +#1695 := (iff #1042 #1694) +#1692 := (iff #1030 #1689) +#1668 := (or #1474 #1615) +#1671 := (or #1632 #1668) +#1674 := (or #995 #1671) +#1677 := (or #1650 #1674) +#1680 := (or #1654 #1677) +#1683 := (or #754 #1680) +#1686 := (or #1665 #1683) +#1690 := (iff #1686 #1689) +#1691 := [rewrite]: #1690 +#1687 := (iff #1030 #1686) +#1684 := (iff #1022 #1683) +#1681 := (iff #1014 #1680) +#1678 := (iff #1005 #1677) +#1675 := (iff #996 #1674) +#1672 := (iff #987 #1671) +#1669 := (iff #978 #1668) +#1616 := (iff #971 #1615) +#1613 := (iff #966 #1612) +#1610 := (iff #959 #1609) +#1607 := (iff #954 #1606) +#1604 := (iff #947 #1603) +#1601 := (iff #942 #1600) +#1598 := (iff #935 #1597) +#1595 := (iff #930 #1594) +#1592 := (iff #923 #1591) +#1589 := (iff #918 #1588) +#1586 := (iff #911 #1585) +#1583 := (iff #906 #1582) +#1580 := (iff #892 #1579) +#1577 := (iff #887 #1576) +#1574 := (iff #880 #1573) +#1571 := (iff #877 #1568) +#1562 := (and #807 #1556) +#1565 := (and #1559 #1562) +#1569 := (iff #1565 #1568) +#1570 := [rewrite]: #1569 +#1566 := (iff #877 #1565) +#1563 := (iff #874 #1562) +#1557 := (iff #871 #1556) +#1558 := [rewrite]: #1557 +#1564 := [monotonicity #1558]: #1563 +#1560 := (iff #222 #1559) +#1561 := [rewrite]: #1560 +#1567 := [monotonicity #1561 #1564]: #1566 +#1572 := [trans #1567 #1570]: #1571 +#1575 := [quant-intro #1572]: #1574 +#1554 := (iff #886 #1553) +#1551 := (iff #221 #1550) +#1548 := (iff #220 #1547) +#1549 := [rewrite]: #1548 +#1552 := [monotonicity #1549]: #1551 +#1555 := [monotonicity #1552]: #1554 +#1578 := [monotonicity #1555 #1575]: #1577 +#1581 := [quant-intro #1578]: #1580 +#1543 := (iff #905 #1542) +#1540 := (iff #868 #1539) +#1537 := (iff #863 #1536) +#1533 := (iff #856 #1532) +#1535 := [rewrite]: #1533 +#1530 := (iff #862 #1529) +#1527 := (iff #848 #1524) +#1521 := (and #1236 #807) +#1525 := (iff #1521 #1524) +#1526 := [rewrite]: #1525 +#1522 := (iff #848 #1521) +#1237 := (iff #83 #1236) +#1238 := [rewrite]: #1237 +#1523 := [monotonicity #1238]: #1522 +#1528 := [trans #1523 #1526]: #1527 +#1531 := [monotonicity #1528]: #1530 +#1538 := [monotonicity #1531 #1535]: #1537 +#1541 := [quant-intro #1538]: #1540 +#1544 := [monotonicity #1541]: #1543 +#1584 := [monotonicity #1544 #1581]: #1583 +#1587 := [monotonicity #1541 #1584]: #1586 +#1519 := (iff #917 #1518) +#1516 := (iff #842 #1515) +#1513 := (iff #837 #1510) +#1507 := (or #1502 #836) +#1511 := (iff #1507 #1510) +#1512 := [rewrite]: #1511 +#1508 := (iff #837 #1507) +#1505 := (iff #212 #1502) +#1506 := [rewrite]: #1505 +#1509 := [monotonicity #1506]: #1508 +#1514 := [trans #1509 #1512]: #1513 +#1517 := [quant-intro #1514]: #1516 +#1520 := [monotonicity #1517]: #1519 +#1590 := [monotonicity #1520 #1587]: #1589 +#1593 := [monotonicity #1517 #1590]: #1592 +#1500 := (iff #929 #1499) +#1497 := (iff #206 #1496) +#1494 := (iff #205 #1493) +#1495 := [rewrite]: #1494 +#1498 := [quant-intro #1495]: #1497 +#1501 := [monotonicity #1498]: #1500 +#1596 := [monotonicity #1501 #1593]: #1595 +#1599 := [monotonicity #1498 #1596]: #1598 +#1491 := (iff #941 #1490) +#1488 := (iff #822 #204) +#1489 := [rewrite]: #1488 +#1492 := [monotonicity #1489]: #1491 +#1602 := [monotonicity #1492 #1599]: #1601 +#1605 := [monotonicity #1489 #1602]: #1604 +#1608 := [monotonicity #1605]: #1607 +#1611 := [monotonicity #1608]: #1610 +#1486 := (iff #965 #1485) +#1483 := (iff #198 #1482) +#1480 := (iff #197 #1477) +#1481 := [rewrite]: #1480 +#1484 := [quant-intro #1481]: #1483 +#1487 := [monotonicity #1484]: #1486 +#1614 := [monotonicity #1487 #1611]: #1613 +#1617 := [monotonicity #1484 #1614]: #1616 +#1475 := (iff #977 #1474) +#1472 := (iff #804 #1471) +#1469 := (iff #799 #1466) +#1463 := (or #1460 #793) +#1467 := (iff #1463 #1466) +#1468 := [rewrite]: #1467 +#1464 := (iff #799 #1463) +#1461 := (iff #188 #1460) +#1458 := (iff #187 #1457) +#1459 := [rewrite]: #1458 +#1451 := (iff #185 #1450) +#1452 := [rewrite]: #1451 +#1462 := [monotonicity #1452 #1459]: #1461 +#1465 := [monotonicity #1462]: #1464 +#1470 := [trans #1465 #1468]: #1469 +#1473 := [quant-intro #1470]: #1472 +#1476 := [monotonicity #1473]: #1475 +#1670 := [monotonicity #1476 #1617]: #1669 +#1633 := (iff #986 #1632) +#1630 := (iff #790 #1629) +#1627 := (iff #785 #1626) +#1624 := (iff #779 #1623) +#1625 := [rewrite]: #1624 +#1619 := (iff #193 #1618) +#1620 := [monotonicity #1462]: #1619 +#1628 := [monotonicity #1620 #1625]: #1627 +#1631 := [quant-intro #1628]: #1630 +#1634 := [monotonicity #1631]: #1633 +#1673 := [monotonicity #1634 #1670]: #1672 +#1676 := [monotonicity #1673]: #1675 +#1651 := (iff #1004 #1650) +#1648 := (iff #768 #1647) +#1645 := (iff #763 #1642) +#1639 := (or #1635 #533) +#1643 := (iff #1639 #1642) +#1644 := [rewrite]: #1643 +#1640 := (iff #763 #1639) +#1637 := (iff #176 #1635) +#1638 := [rewrite]: #1637 +#1641 := [monotonicity #1638]: #1640 +#1646 := [trans #1641 #1644]: #1645 +#1649 := [quant-intro #1646]: #1648 +#1652 := [monotonicity #1649]: #1651 +#1679 := [monotonicity #1652 #1676]: #1678 +#1663 := (iff #1013 #1654) +#1655 := (not #1654) +#1658 := (not #1655) +#1661 := (iff #1658 #1654) +#1662 := [rewrite]: #1661 +#1659 := (iff #1013 #1658) +#1656 := (iff #175 #1655) +#1657 := [rewrite]: #1656 +#1660 := [monotonicity #1657]: #1659 +#1664 := [trans #1660 #1662]: #1663 +#1682 := [monotonicity #1664 #1679]: #1681 +#1685 := [monotonicity #1682]: #1684 +#1666 := (iff #618 #1665) +#1425 := (iff #615 #1424) +#1422 := (iff #610 #1419) +#1416 := (and #1300 #536) +#1420 := (iff #1416 #1419) +#1421 := [rewrite]: #1420 +#1417 := (iff #610 #1416) +#1301 := (iff #120 #1300) +#1302 := [rewrite]: #1301 +#1418 := [monotonicity #1302]: #1417 +#1423 := [trans #1418 #1421]: #1422 +#1426 := [quant-intro #1423]: #1425 +#1667 := [monotonicity #1426]: #1666 +#1688 := [monotonicity #1667 #1685]: #1687 +#1693 := [trans #1688 #1691]: #1692 +#1445 := (iff #742 #1442) +#1427 := (or #706 #1413) +#1430 := (or #715 #1427) +#1433 := (or #724 #1430) +#1436 := (or #733 #1433) +#1439 := (or #1424 #1436) +#1443 := (iff #1439 #1442) +#1444 := [rewrite]: #1443 +#1440 := (iff #742 #1439) +#1437 := (iff #734 #1436) +#1434 := (iff #725 #1433) +#1431 := (iff #716 #1430) +#1428 := (iff #707 #1427) +#1414 := (iff #700 #1413) +#1411 := (iff #695 #1410) +#1408 := (iff #688 #1407) +#1405 := (iff #683 #1402) +#1399 := (or #1394 #158) +#1403 := (iff #1399 #1402) +#1404 := [rewrite]: #1403 +#1400 := (iff #683 #1399) +#1397 := (iff #669 #158) +#1398 := [rewrite]: #1397 +#1395 := (iff #682 #1394) +#1392 := (iff #666 #1391) +#1389 := (iff #661 #1388) +#1386 := (iff #654 #1385) +#1387 := [rewrite]: #1386 +#1383 := (iff #660 #1382) +#1380 := (iff #651 #1379) +#1346 := (iff #143 #1345) +#1347 := [rewrite]: #1346 +#1381 := [monotonicity #1238 #1347]: #1380 +#1384 := [monotonicity #1381]: #1383 +#1390 := [monotonicity #1384 #1387]: #1389 +#1393 := [quant-intro #1390]: #1392 +#1396 := [monotonicity #1393]: #1395 +#1401 := [monotonicity #1396 #1398]: #1400 +#1406 := [trans #1401 #1404]: #1405 +#1409 := [monotonicity #1393 #1406]: #1408 +#1377 := (iff #694 #1376) +#1374 := (iff #648 #1373) +#1371 := (iff #643 #1370) +#1368 := (iff #636 #1367) +#1365 := (iff #633 #1364) +#1361 := (iff #630 #1360) +#1363 := [rewrite]: #1361 +#1358 := (iff #146 #1357) +#1359 := [rewrite]: #1358 +#1366 := [monotonicity #1359 #1363]: #1365 +#1369 := [quant-intro #1366]: #1368 +#1352 := (iff #642 #1351) +#1349 := (iff #144 #1348) +#1350 := [monotonicity #1347]: #1349 +#1353 := [monotonicity #1350]: #1352 +#1372 := [monotonicity #1353 #1369]: #1371 +#1375 := [quant-intro #1372]: #1374 +#1378 := [monotonicity #1375]: #1377 +#1412 := [monotonicity #1378 #1409]: #1411 +#1415 := [monotonicity #1375 #1412]: #1414 +#1429 := [monotonicity #1415]: #1428 +#1432 := [monotonicity #1429]: #1431 +#1435 := [monotonicity #1432]: #1434 +#1438 := [monotonicity #1435]: #1437 +#1441 := [monotonicity #1426 #1438]: #1440 +#1446 := [trans #1441 #1444]: #1445 +#1696 := [monotonicity #1446 #1693]: #1695 +#1340 := (iff #1048 #1339) +#1337 := (iff #604 #1336) +#1334 := (iff #599 #1333) +#1331 := (iff #592 #1330) +#1328 := (iff #589 #1325) +#1319 := (and #533 #1309) +#1322 := (and #1316 #1319) +#1326 := (iff #1322 #1325) +#1327 := [rewrite]: #1326 +#1323 := (iff #589 #1322) +#1320 := (iff #586 #1319) +#1310 := (iff #583 #1309) +#1314 := [rewrite]: #1310 +#1321 := [monotonicity #1314]: #1320 +#1317 := (iff #122 #1316) +#1318 := [rewrite]: #1317 +#1324 := [monotonicity #1318 #1321]: #1323 +#1329 := [trans #1324 #1327]: #1328 +#1332 := [quant-intro #1329]: #1331 +#1307 := (iff #598 #1306) +#1304 := (iff #121 #1303) +#1305 := [monotonicity #1302]: #1304 +#1308 := [monotonicity #1305]: #1307 +#1335 := [monotonicity #1308 #1332]: #1334 +#1338 := [quant-intro #1335]: #1337 +#1341 := [monotonicity #1338]: #1340 +#1755 := [monotonicity #1341 #1696]: #1754 +#1718 := (iff #1057 #1717) +#1715 := (iff #580 #1714) +#1712 := (iff #575 #1711) +#1709 := (iff #568 #1708) +#1710 := [rewrite]: #1709 +#1706 := (iff #574 #1705) +#1703 := (iff #560 #1700) +#1697 := (and #1236 #533) +#1701 := (iff #1697 #1700) +#1702 := [rewrite]: #1701 +#1698 := (iff #560 #1697) +#1699 := [monotonicity #1238]: #1698 +#1704 := [trans #1699 #1702]: #1703 +#1707 := [monotonicity #1704]: #1706 +#1713 := [monotonicity #1707 #1710]: #1712 +#1716 := [quant-intro #1713]: #1715 +#1719 := [monotonicity #1716]: #1718 +#1758 := [monotonicity #1719 #1755]: #1757 +#1734 := (iff #1066 #1733) +#1731 := (iff #554 #1730) +#1728 := (iff #549 #1725) +#1722 := (or #1315 #548) +#1726 := (iff #1722 #1725) +#1727 := [rewrite]: #1726 +#1723 := (iff #549 #1722) +#1720 := (iff #112 #1315) +#1721 := [rewrite]: #1720 +#1724 := [monotonicity #1721]: #1723 +#1729 := [trans #1724 #1727]: #1728 +#1732 := [quant-intro #1729]: #1731 +#1735 := [monotonicity #1732]: #1734 +#1761 := [monotonicity #1735 #1758]: #1760 +#1743 := (iff #1075 #1742) +#1740 := (iff #103 #1739) +#1737 := (iff #102 #1736) +#1738 := [rewrite]: #1737 +#1741 := [quant-intro #1738]: #1740 +#1744 := [monotonicity #1741]: #1743 +#1764 := [monotonicity #1744 #1761]: #1763 +#1748 := (iff #1084 #1747) +#1745 := (iff #530 #100) +#1746 := [rewrite]: #1745 +#1749 := [monotonicity #1746]: #1748 +#1767 := [monotonicity #1749 #1764]: #1766 +#1751 := (iff #1100 #1750) +#1295 := (iff #527 #1294) +#1292 := (iff #522 #1291) +#1289 := (iff #515 #1288) +#1286 := (iff #512 #1283) +#1277 := (and #1271 #454) +#1280 := (and #1274 #1277) +#1284 := (iff #1280 #1283) +#1285 := [rewrite]: #1284 +#1281 := (iff #512 #1280) +#1278 := (iff #507 #1277) +#1272 := (iff #92 #1271) +#1273 := [rewrite]: #1272 +#1279 := [monotonicity #1273]: #1278 +#1275 := (iff #91 #1274) +#1276 := [rewrite]: #1275 +#1282 := [monotonicity #1276 #1279]: #1281 +#1287 := [trans #1282 #1285]: #1286 +#1290 := [quant-intro #1287]: #1289 +#1269 := (iff #521 #1268) +#1266 := (iff #90 #1265) +#1263 := (iff #89 #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 +#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 +#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 +#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 +#1176 := (iff #269 #1175) +#1173 := (iff #268 #1170) +#1166 := (implies #451 #1161) +#1171 := (iff #1166 #1170) +#1172 := [rewrite]: #1171 +#1167 := (iff #268 #1166) +#1164 := (iff #267 #1161) +#1157 := (implies #460 #1154) +#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 +#1146 := (iff #265 #1145) +#1143 := (iff #264 #1142) +#1140 := (iff #263 #1137) +#1133 := (implies #73 #1130) +#1138 := (iff #1133 #1137) +#1139 := [rewrite]: #1138 +#1134 := (iff #263 #1133) +#1131 := (iff #262 #1130) +#1128 := (iff #261 #1125) +#1121 := (implies #481 #1118) +#1126 := (iff #1121 #1125) +#1127 := [rewrite]: #1126 +#1122 := (iff #261 #1121) +#1119 := (iff #260 #1118) +#1116 := (iff #259 #1113) +#1109 := (implies #501 #1106) +#1114 := (iff #1109 #1113) +#1115 := [rewrite]: #1114 +#1110 := (iff #259 #1109) +#1107 := (iff #258 #1106) +#1104 := (iff #257 #1101) +#1097 := (implies #527 #1085) +#1102 := (iff #1097 #1101) +#1103 := [rewrite]: #1102 +#1098 := (iff #257 #1097) +#1095 := (iff #256 #1085) +#1090 := (implies true #1085) +#1093 := (iff #1090 #1085) +#1094 := [rewrite]: #1093 +#1091 := (iff #256 #1090) +#1088 := (iff #255 #1085) +#1081 := (implies #530 #1076) +#1086 := (iff #1081 #1085) +#1087 := [rewrite]: #1086 +#1082 := (iff #255 #1081) +#1079 := (iff #254 #1076) +#1072 := (implies #103 #1067) +#1077 := (iff #1072 #1076) +#1078 := [rewrite]: #1077 +#1073 := (iff #254 #1072) +#1070 := (iff #253 #1067) +#1063 := (implies #554 #1058) +#1068 := (iff #1063 #1067) +#1069 := [rewrite]: #1068 +#1064 := (iff #253 #1063) +#1061 := (iff #252 #1058) +#1054 := (implies #580 #1049) +#1059 := (iff #1054 #1058) +#1060 := [rewrite]: #1059 +#1055 := (iff #252 #1054) +#1052 := (iff #251 #1049) +#1045 := (implies #604 #1042) +#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 +#1011 := (iff #246 #1010) +#1008 := (iff #245 #1005) +#1001 := (implies #768 #996) +#1006 := (iff #1001 #1005) +#1007 := [rewrite]: #1006 +#1002 := (iff #245 #1001) +#999 := (iff #244 #996) +#992 := (implies #776 #987) +#997 := (iff #992 #996) +#998 := [rewrite]: #997 +#993 := (iff #244 #992) +#990 := (iff #243 #987) +#983 := (implies #790 #978) +#988 := (iff #983 #987) +#989 := [rewrite]: #988 +#984 := (iff #243 #983) +#981 := (iff #242 #978) +#974 := (implies #804 #971) +#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 +#963 := (iff #240 #962) +#960 := (iff #239 #959) +#957 := (iff #238 #954) +#950 := (implies #819 #947) +#955 := (iff #950 #954) +#956 := [rewrite]: #955 +#951 := (iff #238 #950) +#948 := (iff #237 #947) +#945 := (iff #236 #942) +#938 := (implies #822 #935) +#943 := (iff #938 #942) +#944 := [rewrite]: #943 +#939 := (iff #236 #938) +#936 := (iff #235 #935) +#933 := (iff #234 #930) +#926 := (implies #206 #923) +#931 := (iff #926 #930) +#932 := [rewrite]: #931 +#927 := (iff #234 #926) +#924 := (iff #233 #923) +#921 := (iff #232 #918) +#914 := (implies #842 #911) +#919 := (iff #914 #918) +#920 := [rewrite]: #919 +#915 := (iff #232 #914) +#912 := (iff #231 #911) +#909 := (iff #230 #906) +#902 := (implies #868 #892) +#907 := (iff #902 #906) +#908 := [rewrite]: #907 +#903 := (iff #230 #902) +#900 := (iff #229 #892) +#895 := (and #892 true) +#898 := (iff #895 #892) +#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 +#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 +#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 +#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 +#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 +#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 +#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) +#772 := [rewrite]: #771 +#775 := [monotonicity #772]: #774 +#778 := [monotonicity #775]: #777 +#994 := [monotonicity #778 #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 +#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 +#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 +#1062 := [trans #1056 #1060]: #1061 +#555 := (iff #114 #554) +#552 := (iff #113 #549) +#545 := (implies #542 #112) +#550 := (iff #545 #549) +#551 := [rewrite]: #550 +#546 := (iff #113 #545) +#543 := (iff #110 #542) +#540 := (iff #109 #539) +#541 := [rewrite]: #540 +#544 := [monotonicity #538 #541]: #543 +#547 := [monotonicity #544]: #546 +#553 := [trans #547 #551]: #552 +#556 := [quant-intro #553]: #555 +#1065 := [monotonicity #556 #1062]: #1064 +#1071 := [trans #1065 #1069]: #1070 +#1074 := [monotonicity #1071]: #1073 +#1080 := [trans #1074 #1078]: #1079 +#531 := (iff #100 #530) +#532 := [rewrite]: #531 +#1083 := [monotonicity #532 #1080]: #1082 +#1089 := [trans #1083 #1087]: #1088 +#1092 := [monotonicity #1089]: #1091 +#1096 := [trans #1092 #1094]: #1095 +#528 := (iff #97 #527) +#525 := (iff #96 #522) +#518 := (implies #90 #515) +#523 := (iff #518 #522) +#524 := [rewrite]: #523 +#519 := (iff #96 #518) +#516 := (iff #95 #515) +#513 := (iff #94 #512) +#510 := (iff #93 #507) +#504 := (and #454 #92) +#508 := (iff #504 #507) +#509 := [rewrite]: #508 +#505 := (iff #93 #504) +#455 := (iff #67 #454) +#456 := [rewrite]: #455 +#506 := [monotonicity #456]: #505 +#511 := [trans #506 #509]: #510 +#514 := [monotonicity #511]: #513 +#517 := [quant-intro #514]: #516 +#520 := [monotonicity #517]: #519 +#526 := [trans #520 #524]: #525 +#529 := [quant-intro #526]: #528 +#1099 := [monotonicity #529 #1096]: #1098 +#1105 := [trans #1099 #1103]: #1104 +#1108 := [monotonicity #529 #1105]: #1107 +#502 := (iff #88 #501) +#499 := (iff #87 #496) +#492 := (implies #487 #86) +#497 := (iff #492 #496) +#498 := [rewrite]: #497 +#493 := (iff #87 #492) +#490 := (iff #84 #487) +#484 := (and #454 #83) +#488 := (iff #484 #487) +#489 := [rewrite]: #488 +#485 := (iff #84 #484) +#486 := [monotonicity #456]: #485 +#491 := [trans #486 #489]: #490 +#494 := [monotonicity #491]: #493 +#500 := [trans #494 #498]: #499 +#503 := [quant-intro #500]: #502 +#1111 := [monotonicity #503 #1108]: #1110 +#1117 := [trans #1111 #1115]: #1116 +#1120 := [monotonicity #503 #1117]: #1119 +#482 := (iff #80 #481) +#479 := (iff #79 #476) +#472 := (implies #469 #78) +#477 := (iff #472 #476) +#478 := [rewrite]: #477 +#473 := (iff #79 #472) +#470 := (iff #76 #469) +#467 := (iff #75 #466) +#468 := [rewrite]: #467 +#458 := (iff #68 #457) +#459 := [monotonicity #456]: #458 +#471 := [monotonicity #459 #468]: #470 +#474 := [monotonicity #471]: #473 +#480 := [trans #474 #478]: #479 +#483 := [quant-intro #480]: #482 +#1123 := [monotonicity #483 #1120]: #1122 +#1129 := [trans #1123 #1127]: #1128 +#1132 := [monotonicity #483 #1129]: #1131 +#1135 := [monotonicity #1132]: #1134 +#1141 := [trans #1135 #1139]: #1140 +#1144 := [monotonicity #1141]: #1143 +#464 := (iff #71 #463) +#465 := [rewrite]: #464 +#1147 := [monotonicity #465 #1144]: #1146 +#1153 := [trans #1147 #1151]: #1152 +#1156 := [monotonicity #465 #1153]: #1155 +#461 := (iff #69 #460) +#462 := [quant-intro #459]: #461 +#1159 := [monotonicity #462 #1156]: #1158 +#1165 := [trans #1159 #1163]: #1164 +#452 := (iff #65 #451) +#449 := (iff #64 #446) +#443 := (implies #62 #440) +#447 := (iff #443 #446) +#448 := [rewrite]: #447 +#444 := (iff #64 #443) +#441 := (iff #63 #440) +#442 := [rewrite]: #441 +#445 := [monotonicity #442]: #444 +#450 := [trans #445 #448]: #449 +#453 := [quant-intro #450]: #452 +#1168 := [monotonicity #453 #1165]: #1167 +#1174 := [trans #1168 #1172]: #1173 +#438 := (iff #61 #437) +#435 := (iff #60 #432) +#429 := (implies #57 #426) +#433 := (iff #429 #432) +#434 := [rewrite]: #433 +#430 := (iff #60 #429) +#427 := (iff #59 #426) +#428 := [rewrite]: #427 +#431 := [monotonicity #428]: #430 +#436 := [trans #431 #434]: #435 +#439 := [quant-intro #436]: #438 +#1177 := [monotonicity #439 #1174]: #1176 +#1183 := [trans #1177 #1181]: #1182 +#1186 := [monotonicity #1183]: #1185 +#1190 := [trans #1186 #1188]: #1189 +#1193 := [monotonicity #1190]: #1192 +#1832 := [trans #1193 #1830]: #1831 +#425 := [asserted]: #271 +#1833 := [mp #425 #1832]: #1828 +#1835 := [not-or-elim #1833]: #460 +#1890 := [mp~ #1835 #1859]: #460 +#4231 := [mp #1890 #4230]: #4226 +#5529 := (not #4226) +#5530 := (or #5529 #3078) +#5525 := [quant-inst #1936]: #5530 +#5337 := [unit-resolution #5525 #4231 #5222]: false +#5345 := [lemma #5337]: #3078 +#3845 := (or #3093 #1945) +#3849 := [def-axiom]: #3845 +#6495 := [unit-resolution #3849 #5345]: #3093 +#3098 := (not #3093) +#4565 := (or #3098 #4562) +#4568 := (not #4565) +#4240 := (pattern #66 #74) +#2519 := (not #466) +#3070 := (or #454 #2519 #1210) +#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3070) +#4246 := (not #4241) +#4571 := (or #4246 #4568) +#4574 := (not #4571) decl ?v1!1 :: S3 -#1910 := ?v1!1 -#1914 := (f12 ?v1!1) -#2535 := (* -1::Int #1914) +#1909 := ?v1!1 +#1913 := (f11 ?v1!1) +#2534 := (* -1::Int #1913) decl ?v0!2 :: S3 -#1911 := ?v0!2 -#1912 := (f12 ?v0!2) -#2536 := (+ #1912 #2535) -#2537 := (<= #2536 0::Int) -#1919 := (f13 ?v1!1) -#1920 := (= f1 #1919) -#1917 := (f13 ?v0!2) -#1918 := (= f1 #1917) -#2308 := (not #1918) -#2338 := (or #2308 #1920 #2537) -#2130 := (not #2338) -#4578 := (or #2130 #4575) -#4581 := (not #4578) -#4233 := (forall (vars (?v0 S3)) (:pat #4219) #1202) -#4238 := (not #4233) -#4584 := (or #4238 #4581) -#4587 := (not #4584) +#1910 := ?v0!2 +#1911 := (f11 ?v0!2) +#2535 := (+ #1911 #2534) +#2536 := (<= #2535 0::Int) +#1918 := (f12 ?v1!1) +#1919 := (= f1 #1918) +#1916 := (f12 ?v0!2) +#1917 := (= f1 #1916) +#2054 := (not #1917) +#2026 := (or #2054 #1919 #2536) +#1928 := (not #2026) +#4577 := (or #1928 #4574) +#4580 := (not #4577) +#4232 := (forall (vars (?v0 S3)) (:pat #4218) #1201) +#4237 := (not #4232) +#4583 := (or #4237 #4580) +#4586 := (not #4583) decl ?v0!0 :: S3 -#1895 := ?v0!0 -#1896 := (f12 ?v0!0) -#1897 := (>= #1896 0::Int) -#1898 := (not #1897) -#4590 := (or #1898 #4587) -#4593 := (not #4590) -#4596 := (or #1197 #4593) -#4599 := (not #4596) -#4606 := (forall (vars (?v0 S3)) (:pat #4219) #1806) -#4609 := (iff #1809 #4606) -#4607 := (iff #1806 #1806) -#4608 := [refl]: #4607 -#4610 := [quant-intro #4608]: #4609 -#2219 := (~ #1809 #1809) -#1901 := (~ #1806 #1806) -#1902 := [refl]: #1901 -#2220 := [nnf-pos #1902]: #2219 -#1839 := [not-or-elim #1834]: #1809 -#2307 := [mp~ #1839 #2220]: #1809 -#4611 := [mp #2307 #4610]: #4606 -#5325 := [hypothesis]: #1197 -#4785 := (not #4606) -#5261 := (or #4785 #72) -#5145 := (= f11 f11) -#5146 := (not #5145) -#5148 := (or #5146 #72) -#5229 := (or #4785 #5148) -#5263 := (iff #5229 #5261) -#5265 := (iff #5261 #5261) -#5260 := [rewrite]: #5265 -#5234 := (iff #5148 #72) -#5202 := (or false #72) -#5230 := (iff #5202 #72) -#5233 := [rewrite]: #5230 -#5203 := (iff #5148 #5202) -#5200 := (iff #5146 false) -#5197 := (not true) -#5194 := (iff #5197 false) -#5195 := [rewrite]: #5194 -#5198 := (iff #5146 #5197) -#5149 := (iff #5145 true) -#5196 := [rewrite]: #5149 -#5199 := [monotonicity #5196]: #5198 -#5201 := [trans #5199 #5195]: #5200 -#5204 := [monotonicity #5201]: #5203 -#5235 := [trans #5204 #5233]: #5234 -#5264 := [monotonicity #5235]: #5263 -#5270 := [trans #5264 #5260]: #5263 -#5262 := [quant-inst #57]: #5229 -#5296 := [mp #5262 #5270]: #5261 -#5326 := [unit-resolution #5296 #5325 #4611]: false -#5321 := [lemma #5326]: #72 -#4602 := (or #1197 #4599) -#3529 := (forall (vars (?v1 S3)) #3518) -#3536 := (not #3529) -#3514 := (forall (vars (?v0 S3) (?v1 S3)) #3509) -#3535 := (not #3514) -#3537 := (or #2360 #2927 #3535 #3536) -#3538 := (not #3537) -#3543 := (or #3492 #3538) -#3550 := (not #3543) -#3469 := (forall (vars (?v0 S3) (?v1 S3)) #3464) -#3549 := (not #3469) -#3551 := (or #3549 #3550) -#3552 := (not #3551) -#3557 := (or #3446 #3552) -#3563 := (not #3557) -#3564 := (or #1500 #3563) -#3565 := (not #3564) -#3570 := (or #2277 #3565) -#3576 := (not #3570) -#3577 := (or #1491 #3576) -#3578 := (not #3577) -#3583 := (or #1491 #3578) -#3589 := (not #3583) -#3590 := (or #954 #3589) -#3591 := (not #3590) -#3596 := (or #2870 #3591) -#3602 := (not #3596) -#3603 := (or #1486 #3602) -#3604 := (not #3603) -#3609 := (or #2856 #3604) -#3617 := (not #3609) -#3423 := (forall (vars (?v0 S3)) #3418) -#3616 := (not #3423) -#3405 := (forall (vars (?v0 S3)) #3402) -#3615 := (not #3405) -#3618 := (or #755 #996 #1651 #1655 #2211 #2214 #3615 #3616 #3617) -#3619 := (not #3618) -#3335 := (forall (vars (?v0 S3) (?v1 S3)) #3330) -#3341 := (not #3335) -#3342 := (or #159 #3341) -#3343 := (not #3342) -#3370 := (or #3343 #3367) -#3377 := (not #3370) -#3313 := (forall (vars (?v0 S3)) #3308) -#3376 := (not #3313) -#3378 := (or #3376 #3377) -#3379 := (not #3378) -#3276 := (forall (vars (?v1 S3)) #3265) -#3282 := (not #3276) -#3283 := (or #2090 #2705 #3282) -#3284 := (not #3283) -#3384 := (or #3284 #3379) -#3391 := (not #3384) -#3261 := (forall (vars (?v0 S3)) #3250) -#3390 := (not #3261) -#3392 := (or #725 #707 #734 #716 #3390 #3391) -#3393 := (not #3392) -#3624 := (or #3393 #3619) -#3634 := (not #3624) -#3247 := (forall (vars (?v0 S3)) #3242) -#3633 := (not #3247) -#3219 := (forall (vars (?v0 S3)) #3214) -#3632 := (not #3219) -#3191 := (forall (vars (?v0 S3) (?v1 S3)) #3186) -#3631 := (not #3191) -#3168 := (forall (vars (?v0 S3) (?v1 S3)) #3163) -#3630 := (not #3168) -#3635 := (or #1748 #1743 #3630 #3631 #3632 #3633 #3634) -#3636 := (not #3635) -#3136 := (forall (vars (?v1 S3)) #3125) -#3142 := (not #3136) -#3143 := (or #1982 #2567 #3142) -#3144 := (not #3143) -#3641 := (or #3144 #3636) -#3648 := (not #3641) -#3121 := (forall (vars (?v0 S3) (?v1 S3)) #3116) -#3647 := (not #3121) -#3649 := (or #3647 #3648) -#3650 := (not #3649) -#3655 := (or #3099 #3650) -#3662 := (not #3655) -#3076 := (forall (vars (?v0 S3) (?v1 S3)) #3071) -#3661 := (not #3076) -#3663 := (or #3661 #3662) -#3664 := (not #3663) -#3669 := (or #2130 #3664) -#3675 := (not #3669) -#3676 := (or #1206 #3675) -#3677 := (not #3676) -#3682 := (or #1898 #3677) -#3688 := (not #3682) -#3689 := (or #1197 #3688) -#3690 := (not #3689) -#3695 := (or #1197 #3690) -#4603 := (iff #3695 #4602) -#4600 := (iff #3690 #4599) -#4597 := (iff #3689 #4596) -#4594 := (iff #3688 #4593) -#4591 := (iff #3682 #4590) -#4588 := (iff #3677 #4587) -#4585 := (iff #3676 #4584) -#4582 := (iff #3675 #4581) -#4579 := (iff #3669 #4578) -#4576 := (iff #3664 #4575) -#4573 := (iff #3663 #4572) -#4570 := (iff #3662 #4569) -#4567 := (iff #3655 #4566) -#4564 := (iff #3650 #4563) -#4561 := (iff #3649 #4560) -#4558 := (iff #3648 #4557) -#4555 := (iff #3641 #4554) -#4552 := (iff #3636 #4551) -#4549 := (iff #3635 #4548) -#4546 := (iff #3634 #4545) -#4543 := (iff #3624 #4542) -#4540 := (iff #3619 #4539) -#4537 := (iff #3618 #4536) -#4534 := (iff #3617 #4533) -#4531 := (iff #3609 #4530) -#4528 := (iff #3604 #4527) -#4525 := (iff #3603 #4524) -#4522 := (iff #3602 #4521) -#4519 := (iff #3596 #4518) -#4516 := (iff #3591 #4515) -#4513 := (iff #3590 #4512) -#4510 := (iff #3589 #4509) -#4507 := (iff #3583 #4506) -#4504 := (iff #3578 #4503) -#4501 := (iff #3577 #4500) -#4498 := (iff #3576 #4497) -#4495 := (iff #3570 #4494) -#4492 := (iff #3565 #4491) -#4489 := (iff #3564 #4488) -#4486 := (iff #3563 #4485) -#4483 := (iff #3557 #4482) -#4480 := (iff #3552 #4479) -#4477 := (iff #3551 #4476) -#4474 := (iff #3550 #4473) -#4471 := (iff #3543 #4470) -#4468 := (iff #3538 #4467) -#4465 := (iff #3537 #4464) -#4462 := (iff #3536 #4461) -#4459 := (iff #3529 #4456) -#4457 := (iff #3518 #3518) -#4458 := [refl]: #4457 -#4460 := [quant-intro #4458]: #4459 -#4463 := [monotonicity #4460]: #4462 -#4453 := (iff #3535 #4452) -#4450 := (iff #3514 #4447) -#4448 := (iff #3509 #3509) -#4449 := [refl]: #4448 -#4451 := [quant-intro #4449]: #4450 -#4454 := [monotonicity #4451]: #4453 -#4466 := [monotonicity #4454 #4463]: #4465 -#4469 := [monotonicity #4466]: #4468 -#4472 := [monotonicity #4469]: #4471 -#4475 := [monotonicity #4472]: #4474 -#4445 := (iff #3549 #4444) -#4442 := (iff #3469 #4439) -#4440 := (iff #3464 #3464) -#4441 := [refl]: #4440 -#4443 := [quant-intro #4441]: #4442 -#4446 := [monotonicity #4443]: #4445 -#4478 := [monotonicity #4446 #4475]: #4477 -#4481 := [monotonicity #4478]: #4480 -#4484 := [monotonicity #4481]: #4483 -#4487 := [monotonicity #4484]: #4486 -#4436 := (iff #1500 #4435) -#4433 := (iff #1497 #4430) -#4431 := (iff #1494 #1494) -#4432 := [refl]: #4431 -#4434 := [quant-intro #4432]: #4433 -#4437 := [monotonicity #4434]: #4436 -#4490 := [monotonicity #4437 #4487]: #4489 -#4493 := [monotonicity #4490]: #4492 -#4496 := [monotonicity #4493]: #4495 -#4499 := [monotonicity #4496]: #4498 -#4502 := [monotonicity #4499]: #4501 -#4505 := [monotonicity #4502]: #4504 -#4508 := [monotonicity #4505]: #4507 -#4511 := [monotonicity #4508]: #4510 -#4428 := (iff #954 #4427) -#4425 := (iff #820 #4422) -#4423 := (iff #815 #815) -#4424 := [refl]: #4423 -#4426 := [quant-intro #4424]: #4425 -#4429 := [monotonicity #4426]: #4428 -#4514 := [monotonicity #4429 #4511]: #4513 -#4517 := [monotonicity #4514]: #4516 -#4520 := [monotonicity #4517]: #4519 -#4523 := [monotonicity #4520]: #4522 -#4419 := (iff #1486 #4418) -#4416 := (iff #1483 #4413) -#4414 := (iff #1478 #1478) -#4415 := [refl]: #4414 -#4417 := [quant-intro #4415]: #4416 -#4420 := [monotonicity #4417]: #4419 -#4526 := [monotonicity #4420 #4523]: #4525 -#4529 := [monotonicity #4526]: #4528 -#4532 := [monotonicity #4529]: #4531 -#4535 := [monotonicity #4532]: #4534 -#4411 := (iff #3616 #4410) -#4408 := (iff #3423 #4405) -#4406 := (iff #3418 #3418) -#4407 := [refl]: #4406 -#4409 := [quant-intro #4407]: #4408 -#4412 := [monotonicity #4409]: #4411 -#4403 := (iff #3615 #4402) -#4400 := (iff #3405 #4397) -#4398 := (iff #3402 #3402) -#4399 := [refl]: #4398 -#4401 := [quant-intro #4399]: #4400 -#4404 := [monotonicity #4401]: #4403 -#4393 := (iff #1651 #4392) -#4390 := (iff #1648 #4387) -#4388 := (iff #1643 #1643) -#4389 := [refl]: #4388 -#4391 := [quant-intro #4389]: #4390 -#4394 := [monotonicity #4391]: #4393 -#4538 := [monotonicity #4394 #4404 #4412 #4535]: #4537 -#4541 := [monotonicity #4538]: #4540 -#4385 := (iff #3393 #4384) -#4382 := (iff #3392 #4381) -#4379 := (iff #3391 #4378) -#4376 := (iff #3384 #4375) -#4373 := (iff #3379 #4372) -#4370 := (iff #3378 #4369) -#4367 := (iff #3377 #4366) -#4364 := (iff #3370 #4363) -#4361 := (iff #3343 #4360) -#4358 := (iff #3342 #4357) -#4355 := (iff #3341 #4354) -#4352 := (iff #3335 #4349) -#4350 := (iff #3330 #3330) -#4351 := [refl]: #4350 -#4353 := [quant-intro #4351]: #4352 -#4356 := [monotonicity #4353]: #4355 -#4359 := [monotonicity #4356]: #4358 -#4362 := [monotonicity #4359]: #4361 -#4365 := [monotonicity #4362]: #4364 -#4368 := [monotonicity #4365]: #4367 -#4347 := (iff #3376 #4346) -#4344 := (iff #3313 #4341) -#4342 := (iff #3308 #3308) -#4343 := [refl]: #4342 -#4345 := [quant-intro #4343]: #4344 -#4348 := [monotonicity #4345]: #4347 -#4371 := [monotonicity #4348 #4368]: #4370 -#4374 := [monotonicity #4371]: #4373 -#4339 := (iff #3284 #4338) -#4336 := (iff #3283 #4335) -#4333 := (iff #3282 #4332) -#4330 := (iff #3276 #4327) -#4328 := (iff #3265 #3265) -#4329 := [refl]: #4328 -#4331 := [quant-intro #4329]: #4330 -#4334 := [monotonicity #4331]: #4333 -#4337 := [monotonicity #4334]: #4336 -#4340 := [monotonicity #4337]: #4339 -#4377 := [monotonicity #4340 #4374]: #4376 -#4380 := [monotonicity #4377]: #4379 -#4323 := (iff #3390 #4322) -#4320 := (iff #3261 #4317) -#4318 := (iff #3250 #3250) -#4319 := [refl]: #4318 -#4321 := [quant-intro #4319]: #4320 -#4324 := [monotonicity #4321]: #4323 -#4383 := [monotonicity #4324 #4380]: #4382 -#4386 := [monotonicity #4383]: #4385 -#4544 := [monotonicity #4386 #4541]: #4543 -#4547 := [monotonicity #4544]: #4546 -#4314 := (iff #3633 #4313) -#4311 := (iff #3247 #4308) -#4309 := (iff #3242 #3242) -#4310 := [refl]: #4309 -#4312 := [quant-intro #4310]: #4311 -#4315 := [monotonicity #4312]: #4314 -#4306 := (iff #3632 #4305) -#4303 := (iff #3219 #4300) -#4301 := (iff #3214 #3214) -#4302 := [refl]: #4301 -#4304 := [quant-intro #4302]: #4303 -#4307 := [monotonicity #4304]: #4306 -#4298 := (iff #3631 #4297) -#4295 := (iff #3191 #4292) -#4293 := (iff #3186 #3186) -#4294 := [refl]: #4293 -#4296 := [quant-intro #4294]: #4295 -#4299 := [monotonicity #4296]: #4298 -#4289 := (iff #3630 #4288) -#4286 := (iff #3168 #4283) -#4284 := (iff #3163 #3163) -#4285 := [refl]: #4284 -#4287 := [quant-intro #4285]: #4286 -#4290 := [monotonicity #4287]: #4289 -#4281 := (iff #1743 #4280) -#4278 := (iff #1740 #4275) -#4276 := (iff #1737 #1737) -#4277 := [refl]: #4276 -#4279 := [quant-intro #4277]: #4278 -#4282 := [monotonicity #4279]: #4281 -#4550 := [monotonicity #4282 #4290 #4299 #4307 #4315 #4547]: #4549 -#4553 := [monotonicity #4550]: #4552 -#4272 := (iff #3144 #4271) -#4269 := (iff #3143 #4268) -#4266 := (iff #3142 #4265) -#4263 := (iff #3136 #4260) -#4261 := (iff #3125 #3125) -#4262 := [refl]: #4261 -#4264 := [quant-intro #4262]: #4263 -#4267 := [monotonicity #4264]: #4266 -#4270 := [monotonicity #4267]: #4269 -#4273 := [monotonicity #4270]: #4272 -#4556 := [monotonicity #4273 #4553]: #4555 -#4559 := [monotonicity #4556]: #4558 -#4257 := (iff #3647 #4256) -#4254 := (iff #3121 #4251) -#4252 := (iff #3116 #3116) -#4253 := [refl]: #4252 -#4255 := [quant-intro #4253]: #4254 -#4258 := [monotonicity #4255]: #4257 -#4562 := [monotonicity #4258 #4559]: #4561 -#4565 := [monotonicity #4562]: #4564 -#4568 := [monotonicity #4565]: #4567 -#4571 := [monotonicity #4568]: #4570 -#4248 := (iff #3661 #4247) -#4245 := (iff #3076 #4242) -#4243 := (iff #3071 #3071) -#4244 := [refl]: #4243 -#4246 := [quant-intro #4244]: #4245 -#4249 := [monotonicity #4246]: #4248 -#4574 := [monotonicity #4249 #4571]: #4573 -#4577 := [monotonicity #4574]: #4576 -#4580 := [monotonicity #4577]: #4579 -#4583 := [monotonicity #4580]: #4582 -#4239 := (iff #1206 #4238) -#4236 := (iff #1203 #4233) -#4234 := (iff #1202 #1202) -#4235 := [refl]: #4234 -#4237 := [quant-intro #4235]: #4236 -#4240 := [monotonicity #4237]: #4239 -#4586 := [monotonicity #4240 #4583]: #4585 -#4589 := [monotonicity #4586]: #4588 -#4592 := [monotonicity #4589]: #4591 -#4595 := [monotonicity #4592]: #4594 -#4598 := [monotonicity #4595]: #4597 -#4601 := [monotonicity #4598]: #4600 -#4604 := [monotonicity #4601]: #4603 -#2356 := (not #2355) -#2958 := (and #808 #2356 #2955) -#2961 := (not #2958) -#2964 := (forall (vars (?v1 S3)) #2961) -#2930 := (not #2927) -#2973 := (and #1540 #2361 #2930 #2964) -#2329 := (not #2328) -#2900 := (and #2329 #2331) -#2903 := (not #2900) -#2921 := (or #2903 #2916) -#2924 := (not #2921) -#2978 := (or #2924 #2973) -#2981 := (and #1516 #2978) -#2300 := (not #2299) -#2875 := (and #2297 #2300) -#2878 := (not #2875) -#2894 := (or #2878 #2889) -#2897 := (not #2894) -#2984 := (or #2897 #2981) -#2987 := (and #1497 #2984) -#2990 := (or #2277 #2987) -#2993 := (and #205 #2990) -#2996 := (or #1491 #2993) -#2999 := (and #820 #2996) -#3002 := (or #2870 #2999) -#3005 := (and #1483 #3002) -#3008 := (or #2856 #3005) -#2215 := (not #2214) -#2212 := (not #2211) -#3014 := (and #758 #777 #1472 #1630 #1648 #1656 #2212 #2215 #3008) -#2157 := (not #2156) -#2153 := (not #2152) -#2793 := (and #2153 #2157) -#2796 := (not #2793) -#2813 := (or #2796 #2808) -#2816 := (not #2813) -#2166 := (not #159) -#2176 := (and #2166 #1392) -#2822 := (or #2176 #2816) -#2766 := (not #2761) -#2784 := (and #2766 #2779) -#2787 := (or #1352 #2784) -#2790 := (forall (vars (?v0 S3)) #2787) -#2827 := (and #2790 #2822) -#2086 := (not #2085) -#2736 := (and #2086 #2733) -#2739 := (not #2736) -#2742 := (forall (vars (?v1 S3)) #2739) -#2708 := (not #2705) -#2091 := (not #2090) -#2748 := (and #2091 #2708 #2742) -#2830 := (or #2748 #2827) -#2192 := (not #1420) -#2195 := (forall (vars (?v0 S3)) #2192) -#2836 := (and #137 #142 #622 #625 #2195 #2830) -#3019 := (or #2836 #3014) -#2685 := (not #2680) -#2688 := (and #2050 #2668 #2685) -#2691 := (or #1307 #2688) -#2694 := (forall (vars (?v0 S3)) #2691) -#2630 := (not #2625) -#2648 := (and #2023 #2630 #2643) -#2651 := (or #1269 #2648) -#2654 := (forall (vars (?v0 S3)) #2651) -#3025 := (and #101 #1715 #1731 #1740 #2654 #2694 #3019) -#1978 := (not #1977) -#2598 := (and #455 #1978 #2595) -#2601 := (not #2598) -#2604 := (forall (vars (?v1 S3)) #2601) -#2570 := (not #2567) -#1983 := (not #1982) -#2610 := (and #1983 #2570 #2604) -#3030 := (or #2610 #3025) -#3033 := (and #1254 #3030) -#1944 := (not #1943) -#2555 := (and #1944 #1946) -#2558 := (not #2555) -#2561 := (or #2552 #2558) -#2564 := (not #2561) -#3036 := (or #2564 #3033) -#3039 := (and #1223 #3036) -#1921 := (not #1920) -#2523 := (and #1918 #1921) -#2526 := (not #2523) -#2542 := (or #2526 #2537) -#2545 := (not #2542) -#3042 := (or #2545 #3039) -#3045 := (and #1203 #3042) -#3048 := (or #1898 #3045) -#3051 := (and #72 #3048) -#3054 := (or #1197 #3051) -#3696 := (iff #3054 #3695) -#3693 := (iff #3051 #3690) -#3685 := (and #72 #3682) -#3691 := (iff #3685 #3690) -#3692 := [rewrite]: #3691 -#3686 := (iff #3051 #3685) -#3683 := (iff #3048 #3682) -#3680 := (iff #3045 #3677) -#3672 := (and #1203 #3669) -#3678 := (iff #3672 #3677) -#3679 := [rewrite]: #3678 -#3673 := (iff #3045 #3672) -#3670 := (iff #3042 #3669) -#3667 := (iff #3039 #3664) -#3658 := (and #3076 #3655) -#3665 := (iff #3658 #3664) -#3666 := [rewrite]: #3665 -#3659 := (iff #3039 #3658) -#3656 := (iff #3036 #3655) -#3653 := (iff #3033 #3650) -#3644 := (and #3121 #3641) -#3651 := (iff #3644 #3650) -#3652 := [rewrite]: #3651 -#3645 := (iff #3033 #3644) -#3642 := (iff #3030 #3641) -#3639 := (iff #3025 #3636) -#3627 := (and #101 #3168 #3191 #1740 #3219 #3247 #3624) -#3637 := (iff #3627 #3636) -#3638 := [rewrite]: #3637 -#3628 := (iff #3025 #3627) -#3625 := (iff #3019 #3624) -#3622 := (iff #3014 #3619) -#3612 := (and #758 #777 #3405 #3423 #1648 #1656 #2212 #2215 #3609) -#3620 := (iff #3612 #3619) -#3621 := [rewrite]: #3620 -#3613 := (iff #3014 #3612) -#3610 := (iff #3008 #3609) -#3607 := (iff #3005 #3604) -#3599 := (and #1483 #3596) -#3605 := (iff #3599 #3604) -#3606 := [rewrite]: #3605 -#3600 := (iff #3005 #3599) -#3597 := (iff #3002 #3596) -#3594 := (iff #2999 #3591) -#3586 := (and #820 #3583) -#3592 := (iff #3586 #3591) -#3593 := [rewrite]: #3592 -#3587 := (iff #2999 #3586) -#3584 := (iff #2996 #3583) -#3581 := (iff #2993 #3578) -#3573 := (and #205 #3570) -#3579 := (iff #3573 #3578) -#3580 := [rewrite]: #3579 -#3574 := (iff #2993 #3573) -#3571 := (iff #2990 #3570) -#3568 := (iff #2987 #3565) -#3560 := (and #1497 #3557) -#3566 := (iff #3560 #3565) -#3567 := [rewrite]: #3566 -#3561 := (iff #2987 #3560) -#3558 := (iff #2984 #3557) -#3555 := (iff #2981 #3552) -#3546 := (and #3469 #3543) -#3553 := (iff #3546 #3552) -#3554 := [rewrite]: #3553 -#3547 := (iff #2981 #3546) -#3544 := (iff #2978 #3543) -#3541 := (iff #2973 #3538) -#3532 := (and #3514 #2361 #2930 #3529) -#3539 := (iff #3532 #3538) -#3540 := [rewrite]: #3539 -#3533 := (iff #2973 #3532) -#3530 := (iff #2964 #3529) -#3527 := (iff #2961 #3518) -#3519 := (not #3518) -#3522 := (not #3519) -#3525 := (iff #3522 #3518) -#3526 := [rewrite]: #3525 -#3523 := (iff #2961 #3522) -#3520 := (iff #2958 #3519) -#3521 := [rewrite]: #3520 -#3524 := [monotonicity #3521]: #3523 -#3528 := [trans #3524 #3526]: #3527 -#3531 := [quant-intro #3528]: #3530 -#3515 := (iff #1540 #3514) -#3512 := (iff #1537 #3509) -#3495 := (or #814 #1236) -#3506 := (or #3495 #1533) -#3510 := (iff #3506 #3509) -#3511 := [rewrite]: #3510 -#3507 := (iff #1537 #3506) -#3504 := (iff #1530 #3495) -#3496 := (not #3495) -#3499 := (not #3496) -#3502 := (iff #3499 #3495) -#3503 := [rewrite]: #3502 -#3500 := (iff #1530 #3499) -#3497 := (iff #1525 #3496) -#3498 := [rewrite]: #3497 -#3501 := [monotonicity #3498]: #3500 -#3505 := [trans #3501 #3503]: #3504 -#3508 := [monotonicity #3505]: #3507 -#3513 := [trans #3508 #3511]: #3512 -#3516 := [quant-intro #3513]: #3515 -#3534 := [monotonicity #3516 #3531]: #3533 -#3542 := [trans #3534 #3540]: #3541 -#3493 := (iff #2924 #3492) -#3490 := (iff #2921 #3487) -#3473 := (or #2328 #3472) -#3484 := (or #3473 #2916) -#3488 := (iff #3484 #3487) -#3489 := [rewrite]: #3488 -#3485 := (iff #2921 #3484) -#3482 := (iff #2903 #3473) -#3474 := (not #3473) -#3477 := (not #3474) -#3480 := (iff #3477 #3473) -#3481 := [rewrite]: #3480 -#3478 := (iff #2903 #3477) -#3475 := (iff #2900 #3474) -#3476 := [rewrite]: #3475 -#3479 := [monotonicity #3476]: #3478 -#3483 := [trans #3479 #3481]: #3482 -#3486 := [monotonicity #3483]: #3485 -#3491 := [trans #3486 #3489]: #3490 -#3494 := [monotonicity #3491]: #3493 -#3545 := [monotonicity #3494 #3542]: #3544 -#3470 := (iff #1516 #3469) -#3467 := (iff #1511 #3464) -#3450 := (or #808 #3449) -#3461 := (or #3450 #1503) -#3465 := (iff #3461 #3464) -#3466 := [rewrite]: #3465 -#3462 := (iff #1511 #3461) -#3459 := (iff #837 #3450) -#3451 := (not #3450) -#3454 := (not #3451) -#3457 := (iff #3454 #3450) -#3458 := [rewrite]: #3457 -#3455 := (iff #837 #3454) -#3452 := (iff #831 #3451) -#3453 := [rewrite]: #3452 -#3456 := [monotonicity #3453]: #3455 -#3460 := [trans #3456 #3458]: #3459 -#3463 := [monotonicity #3460]: #3462 -#3468 := [trans #3463 #3466]: #3467 -#3471 := [quant-intro #3468]: #3470 -#3548 := [monotonicity #3471 #3545]: #3547 -#3556 := [trans #3548 #3554]: #3555 -#3447 := (iff #2897 #3446) -#3444 := (iff #2894 #3441) -#3427 := (or #3426 #2299) -#3438 := (or #3427 #2889) -#3442 := (iff #3438 #3441) -#3443 := [rewrite]: #3442 -#3439 := (iff #2894 #3438) -#3436 := (iff #2878 #3427) -#3428 := (not #3427) -#3431 := (not #3428) -#3434 := (iff #3431 #3427) -#3435 := [rewrite]: #3434 -#3432 := (iff #2878 #3431) -#3429 := (iff #2875 #3428) -#3430 := [rewrite]: #3429 -#3433 := [monotonicity #3430]: #3432 -#3437 := [trans #3433 #3435]: #3436 -#3440 := [monotonicity #3437]: #3439 -#3445 := [trans #3440 #3443]: #3444 -#3448 := [monotonicity #3445]: #3447 -#3559 := [monotonicity #3448 #3556]: #3558 -#3562 := [monotonicity #3559]: #3561 -#3569 := [trans #3562 #3567]: #3568 -#3572 := [monotonicity #3569]: #3571 -#3575 := [monotonicity #3572]: #3574 -#3582 := [trans #3575 #3580]: #3581 -#3585 := [monotonicity #3582]: #3584 -#3588 := [monotonicity #3585]: #3587 -#3595 := [trans #3588 #3593]: #3594 -#3598 := [monotonicity #3595]: #3597 -#3601 := [monotonicity #3598]: #3600 -#3608 := [trans #3601 #3606]: #3607 -#3611 := [monotonicity #3608]: #3610 -#3424 := (iff #1630 #3423) -#3421 := (iff #1627 #3418) -#3415 := (or #3398 #1624) -#3419 := (iff #3415 #3418) -#3420 := [rewrite]: #3419 -#3416 := (iff #1627 #3415) -#3413 := (iff #1619 #3398) -#3408 := (not #3399) -#3411 := (iff #3408 #3398) -#3412 := [rewrite]: #3411 -#3409 := (iff #1619 #3408) -#3400 := (iff #1461 #3399) -#3401 := [rewrite]: #3400 -#3410 := [monotonicity #3401]: #3409 -#3414 := [trans #3410 #3412]: #3413 -#3417 := [monotonicity #3414]: #3416 -#3422 := [trans #3417 #3420]: #3421 -#3425 := [quant-intro #3422]: #3424 -#3406 := (iff #1472 #3405) -#3403 := (iff #1467 #3402) -#3404 := [monotonicity #3401]: #3403 -#3407 := [quant-intro #3404]: #3406 -#3614 := [monotonicity #3407 #3425 #3611]: #3613 -#3623 := [trans #3614 #3621]: #3622 -#3396 := (iff #2836 #3393) -#3387 := (and #137 #142 #622 #625 #3261 #3384) -#3394 := (iff #3387 #3393) -#3395 := [rewrite]: #3394 -#3388 := (iff #2836 #3387) -#3385 := (iff #2830 #3384) -#3382 := (iff #2827 #3379) -#3373 := (and #3313 #3370) -#3380 := (iff #3373 #3379) -#3381 := [rewrite]: #3380 -#3374 := (iff #2827 #3373) -#3371 := (iff #2822 #3370) -#3368 := (iff #2816 #3367) -#3365 := (iff #2813 #3362) -#3348 := (or #2152 #2156) -#3359 := (or #3348 #2808) -#3363 := (iff #3359 #3362) -#3364 := [rewrite]: #3363 -#3360 := (iff #2813 #3359) -#3357 := (iff #2796 #3348) -#3349 := (not #3348) -#3352 := (not #3349) -#3355 := (iff #3352 #3348) -#3356 := [rewrite]: #3355 -#3353 := (iff #2796 #3352) -#3350 := (iff #2793 #3349) -#3351 := [rewrite]: #3350 -#3354 := [monotonicity #3351]: #3353 -#3358 := [trans #3354 #3356]: #3357 -#3361 := [monotonicity #3358]: #3360 -#3366 := [trans #3361 #3364]: #3365 -#3369 := [monotonicity #3366]: #3368 -#3346 := (iff #2176 #3343) -#3338 := (and #2166 #3335) -#3344 := (iff #3338 #3343) -#3345 := [rewrite]: #3344 -#3339 := (iff #2176 #3338) -#3336 := (iff #1392 #3335) -#3333 := (iff #1389 #3330) -#3316 := (or #1236 #1345) -#3327 := (or #3316 #1386) -#3331 := (iff #3327 #3330) -#3332 := [rewrite]: #3331 -#3328 := (iff #1389 #3327) -#3325 := (iff #1383 #3316) -#3317 := (not #3316) -#3320 := (not #3317) -#3323 := (iff #3320 #3316) -#3324 := [rewrite]: #3323 -#3321 := (iff #1383 #3320) -#3318 := (iff #1380 #3317) -#3319 := [rewrite]: #3318 -#3322 := [monotonicity #3319]: #3321 -#3326 := [trans #3322 #3324]: #3325 -#3329 := [monotonicity #3326]: #3328 -#3334 := [trans #3329 #3332]: #3333 -#3337 := [quant-intro #3334]: #3336 -#3340 := [monotonicity #3337]: #3339 -#3347 := [trans #3340 #3345]: #3346 -#3372 := [monotonicity #3347 #3369]: #3371 -#3314 := (iff #2790 #3313) -#3311 := (iff #2787 #3308) -#3289 := (or #58 #1345) -#3305 := (or #3289 #3302) -#3309 := (iff #3305 #3308) -#3310 := [rewrite]: #3309 -#3306 := (iff #2787 #3305) -#3303 := (iff #2784 #3302) -#3304 := [rewrite]: #3303 -#3298 := (iff #1352 #3289) -#3290 := (not #3289) -#3293 := (not #3290) -#3296 := (iff #3293 #3289) -#3297 := [rewrite]: #3296 -#3294 := (iff #1352 #3293) -#3291 := (iff #1349 #3290) -#3292 := [rewrite]: #3291 -#3295 := [monotonicity #3292]: #3294 -#3299 := [trans #3295 #3297]: #3298 -#3307 := [monotonicity #3299 #3304]: #3306 -#3312 := [trans #3307 #3310]: #3311 -#3315 := [quant-intro #3312]: #3314 -#3375 := [monotonicity #3315 #3372]: #3374 -#3383 := [trans #3375 #3381]: #3382 -#3287 := (iff #2748 #3284) -#3279 := (and #2091 #2708 #3276) -#3285 := (iff #3279 #3284) -#3286 := [rewrite]: #3285 -#3280 := (iff #2748 #3279) -#3277 := (iff #2742 #3276) -#3274 := (iff #2739 #3265) -#3266 := (not #3265) -#3269 := (not #3266) -#3272 := (iff #3269 #3265) -#3273 := [rewrite]: #3272 -#3270 := (iff #2739 #3269) -#3267 := (iff #2736 #3266) -#3268 := [rewrite]: #3267 -#3271 := [monotonicity #3268]: #3270 -#3275 := [trans #3271 #3273]: #3274 -#3278 := [quant-intro #3275]: #3277 -#3281 := [monotonicity #3278]: #3280 -#3288 := [trans #3281 #3286]: #3287 -#3386 := [monotonicity #3288 #3383]: #3385 -#3262 := (iff #2195 #3261) -#3259 := (iff #2192 #3250) -#3251 := (not #3250) -#3254 := (not #3251) -#3257 := (iff #3254 #3250) -#3258 := [rewrite]: #3257 -#3255 := (iff #2192 #3254) -#3252 := (iff #1420 #3251) -#3253 := [rewrite]: #3252 -#3256 := [monotonicity #3253]: #3255 -#3260 := [trans #3256 #3258]: #3259 -#3263 := [quant-intro #3260]: #3262 -#3389 := [monotonicity #3263 #3386]: #3388 -#3397 := [trans #3389 #3395]: #3396 -#3626 := [monotonicity #3397 #3623]: #3625 -#3248 := (iff #2694 #3247) -#3245 := (iff #2691 #3242) -#3222 := (or #58 #1300) -#3239 := (or #3222 #3236) -#3243 := (iff #3239 #3242) -#3244 := [rewrite]: #3243 -#3240 := (iff #2691 #3239) -#3237 := (iff #2688 #3236) -#3238 := [rewrite]: #3237 -#3231 := (iff #1307 #3222) -#3223 := (not #3222) -#3226 := (not #3223) -#3229 := (iff #3226 #3222) -#3230 := [rewrite]: #3229 -#3227 := (iff #1307 #3226) -#3224 := (iff #1304 #3223) -#3225 := [rewrite]: #3224 -#3228 := [monotonicity #3225]: #3227 -#3232 := [trans #3228 #3230]: #3231 -#3241 := [monotonicity #3232 #3238]: #3240 -#3246 := [trans #3241 #3244]: #3245 -#3249 := [quant-intro #3246]: #3248 -#3220 := (iff #2654 #3219) -#3217 := (iff #2651 #3214) -#3194 := (or #58 #1262) -#3211 := (or #3194 #3208) -#3215 := (iff #3211 #3214) -#3216 := [rewrite]: #3215 -#3212 := (iff #2651 #3211) -#3209 := (iff #2648 #3208) -#3210 := [rewrite]: #3209 -#3203 := (iff #1269 #3194) -#3195 := (not #3194) -#3198 := (not #3195) -#3201 := (iff #3198 #3194) -#3202 := [rewrite]: #3201 -#3199 := (iff #1269 #3198) -#3196 := (iff #1266 #3195) -#3197 := [rewrite]: #3196 -#3200 := [monotonicity #3197]: #3199 -#3204 := [trans #3200 #3202]: #3203 -#3213 := [monotonicity #3204 #3210]: #3212 -#3218 := [trans #3213 #3216]: #3217 -#3221 := [quant-intro #3218]: #3220 -#3192 := (iff #1731 #3191) -#3189 := (iff #1726 #3186) -#3172 := (or #534 #3171) -#3183 := (or #3172 #1316) -#3187 := (iff #3183 #3186) -#3188 := [rewrite]: #3187 -#3184 := (iff #1726 #3183) -#3181 := (iff #549 #3172) -#3173 := (not #3172) -#3176 := (not #3173) -#3179 := (iff #3176 #3172) -#3180 := [rewrite]: #3179 -#3177 := (iff #549 #3176) -#3174 := (iff #543 #3173) -#3175 := [rewrite]: #3174 -#3178 := [monotonicity #3175]: #3177 -#3182 := [trans #3178 #3180]: #3181 -#3185 := [monotonicity #3182]: #3184 -#3190 := [trans #3185 #3188]: #3189 -#3193 := [quant-intro #3190]: #3192 -#3169 := (iff #1715 #3168) -#3166 := (iff #1712 #3163) -#3149 := (or #537 #1236) -#3160 := (or #3149 #1709) -#3164 := (iff #3160 #3163) -#3165 := [rewrite]: #3164 -#3161 := (iff #1712 #3160) -#3158 := (iff #1706 #3149) -#3150 := (not #3149) -#3153 := (not #3150) -#3156 := (iff #3153 #3149) -#3157 := [rewrite]: #3156 -#3154 := (iff #1706 #3153) -#3151 := (iff #1701 #3150) -#3152 := [rewrite]: #3151 -#3155 := [monotonicity #3152]: #3154 -#3159 := [trans #3155 #3157]: #3158 -#3162 := [monotonicity #3159]: #3161 -#3167 := [trans #3162 #3165]: #3166 -#3170 := [quant-intro #3167]: #3169 -#3629 := [monotonicity #3170 #3193 #3221 #3249 #3626]: #3628 -#3640 := [trans #3629 #3638]: #3639 -#3147 := (iff #2610 #3144) -#3139 := (and #1983 #2570 #3136) -#3145 := (iff #3139 #3144) -#3146 := [rewrite]: #3145 -#3140 := (iff #2610 #3139) -#3137 := (iff #2604 #3136) -#3134 := (iff #2601 #3125) -#3126 := (not #3125) -#3129 := (not #3126) -#3132 := (iff #3129 #3125) -#3133 := [rewrite]: #3132 -#3130 := (iff #2601 #3129) -#3127 := (iff #2598 #3126) -#3128 := [rewrite]: #3127 -#3131 := [monotonicity #3128]: #3130 -#3135 := [trans #3131 #3133]: #3134 -#3138 := [quant-intro #3135]: #3137 -#3141 := [monotonicity #3138]: #3140 -#3148 := [trans #3141 #3146]: #3147 -#3643 := [monotonicity #3148 #3640]: #3642 -#3122 := (iff #1254 #3121) -#3119 := (iff #1251 #3116) -#3102 := (or #458 #1236) -#3113 := (or #1231 #3102) -#3117 := (iff #3113 #3116) -#3118 := [rewrite]: #3117 -#3114 := (iff #1251 #3113) -#3111 := (iff #1248 #3102) -#3103 := (not #3102) -#3106 := (not #3103) -#3109 := (iff #3106 #3102) -#3110 := [rewrite]: #3109 -#3107 := (iff #1248 #3106) -#3104 := (iff #1243 #3103) -#3105 := [rewrite]: #3104 -#3108 := [monotonicity #3105]: #3107 -#3112 := [trans #3108 #3110]: #3111 -#3115 := [monotonicity #3112]: #3114 -#3120 := [trans #3115 #3118]: #3119 -#3123 := [quant-intro #3120]: #3122 -#3646 := [monotonicity #3123 #3643]: #3645 -#3654 := [trans #3646 #3652]: #3653 -#3100 := (iff #2564 #3099) -#3097 := (iff #2561 #3094) -#3080 := (or #1943 #3079) -#3091 := (or #2552 #3080) -#3095 := (iff #3091 #3094) -#3096 := [rewrite]: #3095 -#3092 := (iff #2561 #3091) -#3089 := (iff #2558 #3080) -#3081 := (not #3080) -#3084 := (not #3081) -#3087 := (iff #3084 #3080) -#3088 := [rewrite]: #3087 -#3085 := (iff #2558 #3084) -#3082 := (iff #2555 #3081) -#3083 := [rewrite]: #3082 -#3086 := [monotonicity #3083]: #3085 -#3090 := [trans #3086 #3088]: #3089 -#3093 := [monotonicity #3090]: #3092 -#3098 := [trans #3093 #3096]: #3097 -#3101 := [monotonicity #3098]: #3100 -#3657 := [monotonicity #3101 #3654]: #3656 -#3077 := (iff #1223 #3076) -#3074 := (iff #1218 #3071) -#3057 := (or #455 #2520) -#3068 := (or #3057 #1211) -#3072 := (iff #3068 #3071) -#3073 := [rewrite]: #3072 -#3069 := (iff #1218 #3068) -#3066 := (iff #476 #3057) -#3058 := (not #3057) -#3061 := (not #3058) -#3064 := (iff #3061 #3057) -#3065 := [rewrite]: #3064 -#3062 := (iff #476 #3061) -#3059 := (iff #470 #3058) -#3060 := [rewrite]: #3059 -#3063 := [monotonicity #3060]: #3062 -#3067 := [trans #3063 #3065]: #3066 -#3070 := [monotonicity #3067]: #3069 -#3075 := [trans #3070 #3073]: #3074 -#3078 := [quant-intro #3075]: #3077 -#3660 := [monotonicity #3078 #3657]: #3659 -#3668 := [trans #3660 #3666]: #3667 -#2260 := (iff #2545 #2130) -#2241 := (iff #2542 #2338) -#1928 := (or #2308 #1920) -#2165 := (or #1928 #2537) -#2339 := (iff #2165 #2338) -#2240 := [rewrite]: #2339 -#2280 := (iff #2542 #2165) -#1960 := (iff #2526 #1928) -#1865 := (not #1928) -#2027 := (not #1865) -#2055 := (iff #2027 #1928) -#1959 := [rewrite]: #2055 -#2028 := (iff #2526 #2027) -#1866 := (iff #2523 #1865) -#1929 := [rewrite]: #1866 -#2054 := [monotonicity #1929]: #2028 -#2164 := [trans #2054 #1959]: #1960 -#2281 := [monotonicity #2164]: #2280 -#2129 := [trans #2281 #2240]: #2241 -#2261 := [monotonicity #2129]: #2260 -#3671 := [monotonicity #2261 #3668]: #3670 -#3674 := [monotonicity #3671]: #3673 -#3681 := [trans #3674 #3679]: #3680 -#3684 := [monotonicity #3681]: #3683 -#3687 := [monotonicity #3684]: #3686 -#3694 := [trans #3687 #3692]: #3693 -#3697 := [monotonicity #3694]: #3696 -#2353 := (+ #2352 #2350) -#2354 := (= #2353 0::Int) -#2357 := (and #808 #2356 #2354) -#2374 := (not #2357) -#2377 := (forall (vars (?v1 S3)) #2374) -#2362 := (= ?v0!20 f11) -#2363 := (not #2362) -#2364 := (and #2363 #2361) -#2365 := (not #2364) -#2371 := (not #2365) -#2381 := (and #2371 #2377) -#2386 := (and #1540 #2381) -#2319 := (* -1::Int #2318) -#2321 := (+ #2320 #2319) -#2324 := (+ #2323 #2321) -#2325 := (>= #2324 0::Int) -#2332 := (and #2331 #2329) -#2333 := (not #2332) -#2334 := (or #2333 #2325) -#2335 := (not #2334) -#2390 := (or #2335 #2386) -#2394 := (and #1516 #2390) -#2292 := (* -1::Int #2291) -#2294 := (+ #2293 #2292) -#2295 := (>= #2294 0::Int) -#2301 := (and #2300 #2297) -#2302 := (not #2301) -#2303 := (or #2302 #2295) -#2304 := (not #2303) -#2398 := (or #2304 #2394) -#2402 := (and #1497 #2398) -#2406 := (or #2277 #2402) -#2271 := (not #1491) -#2410 := (and #2271 #2406) -#2414 := (or #1491 #2410) -#2418 := (and #820 #2414) -#2255 := (= #2254 #2253) -#2256 := (or #2255 #2252) -#2257 := (not #2256) -#2422 := (or #2257 #2418) -#2426 := (and #1483 #2422) -#2233 := (* -1::Int #2232) -#2235 := (+ #2234 #2233) -#2236 := (>= #2235 0::Int) -#2237 := (not #2236) -#2430 := (or #2237 #2426) -#2216 := (and #2215 #2212) -#2204 := (not #996) -#2450 := (and #758 #2204 #2216 #1472 #2430 #1630 #1648 #1656) -#2143 := (* -1::Int #2142) -#2145 := (+ #2144 #2143) -#2148 := (+ #2147 #2145) -#2149 := (>= #2148 0::Int) -#2158 := (and #2157 #2153) -#2159 := (not #2158) -#2160 := (or #2159 #2149) -#2161 := (not #2160) -#2180 := (or #2161 #2176) -#2119 := (+ #2118 #1343) -#2122 := (+ #2121 #2119) -#2123 := (= #2122 0::Int) -#2124 := (>= #2119 0::Int) -#2125 := (not #2124) -#2126 := (and #2125 #2123) -#2131 := (or #1352 #2126) -#2134 := (forall (vars (?v0 S3)) #2131) -#2184 := (and #2134 #2180) -#2083 := (+ #2082 #2080) -#2084 := (= #2083 0::Int) -#2087 := (and #2086 #2084) -#2103 := (not #2087) -#2106 := (forall (vars (?v1 S3)) #2103) -#2092 := (= ?v0!8 f11) -#2093 := (not #2092) -#2094 := (and #2093 #2091) -#2095 := (not #2094) -#2100 := (not #2095) -#2110 := (and #2100 #2106) -#2188 := (or #2110 #2184) -#2074 := (not #716) -#2071 := (not #734) -#2068 := (not #707) -#2065 := (not #725) -#2198 := (and #2065 #2068 #2071 #2074 #2188 #2195) -#2454 := (or #2198 #2450) -#2042 := (+ #2041 #1298) -#2043 := (>= #2042 0::Int) -#2044 := (not #2043) -#2047 := (+ #2046 #2042) -#2048 := (= #2047 0::Int) -#2051 := (and #2050 #2048 #2044) -#2056 := (or #1307 #2051) -#2059 := (forall (vars (?v0 S3)) #2056) -#2015 := (+ #1260 #2014) -#2017 := (+ #2016 #2015) -#2018 := (= #2017 0::Int) -#2019 := (+ #2016 #1260) -#2020 := (>= #2019 0::Int) -#2021 := (not #2020) -#2024 := (and #2023 #2021 #2018) -#2029 := (or #1269 #2024) -#2032 := (forall (vars (?v0 S3)) #2029) -#2007 := (not #1748) -#2479 := (and #2007 #2032 #2059 #2454 #1715 #1731 #1740) -#1973 := (+ #1972 #1970) -#1974 := (+ #59 #1973) -#1975 := (= #1974 0::Int) -#1979 := (and #455 #1978 #1975) -#1995 := (not #1979) -#1998 := (forall (vars (?v1 S3)) #1995) -#1984 := (= ?v0!5 f11) -#1985 := (not #1984) -#1986 := (and #1985 #1983) -#1987 := (not #1986) -#1992 := (not #1987) -#2002 := (and #1992 #1998) -#2483 := (or #2002 #2479) -#2487 := (and #1254 #2483) -#1947 := (and #1946 #1944) -#1948 := (not #1947) -#1951 := (+ #1950 #1940) -#1953 := (+ #1952 #1951) -#1954 := (>= #1953 0::Int) -#1955 := (or #1954 #1948) -#1956 := (not #1955) -#2491 := (or #1956 #2487) -#2495 := (and #1223 #2491) -#1913 := (* -1::Int #1912) -#1915 := (+ #1914 #1913) -#1916 := (>= #1915 0::Int) -#1922 := (and #1921 #1918) -#1923 := (not #1922) -#1924 := (or #1923 #1916) -#1925 := (not #1924) -#2499 := (or #1925 #2495) -#2503 := (and #1203 #2499) -#2507 := (or #1898 #2503) -#1861 := (not #1197) -#2511 := (and #1861 #2507) -#2515 := (or #1197 #2511) -#3055 := (iff #2515 #3054) -#3052 := (iff #2511 #3051) -#3049 := (iff #2507 #3048) -#3046 := (iff #2503 #3045) -#3043 := (iff #2499 #3042) -#3040 := (iff #2495 #3039) -#3037 := (iff #2491 #3036) -#3034 := (iff #2487 #3033) -#3031 := (iff #2483 #3030) -#3028 := (iff #2479 #3025) -#3022 := (and #101 #2654 #2694 #3019 #1715 #1731 #1740) -#3026 := (iff #3022 #3025) -#3027 := [rewrite]: #3026 -#3023 := (iff #2479 #3022) -#3020 := (iff #2454 #3019) -#3017 := (iff #2450 #3014) -#3011 := (and #758 #777 #2216 #1472 #3008 #1630 #1648 #1656) -#3015 := (iff #3011 #3014) -#3016 := [rewrite]: #3015 -#3012 := (iff #2450 #3011) -#3009 := (iff #2430 #3008) -#3006 := (iff #2426 #3005) -#3003 := (iff #2422 #3002) -#3000 := (iff #2418 #2999) -#2997 := (iff #2414 #2996) -#2994 := (iff #2410 #2993) -#2991 := (iff #2406 #2990) -#2988 := (iff #2402 #2987) -#2985 := (iff #2398 #2984) -#2982 := (iff #2394 #2981) -#2979 := (iff #2390 #2978) -#2976 := (iff #2386 #2973) -#2936 := (and #2361 #2930) -#2967 := (and #2936 #2964) -#2970 := (and #1540 #2967) -#2974 := (iff #2970 #2973) -#2975 := [rewrite]: #2974 -#2971 := (iff #2386 #2970) -#2968 := (iff #2381 #2967) -#2965 := (iff #2377 #2964) -#2962 := (iff #2374 #2961) -#2959 := (iff #2357 #2958) -#2956 := (iff #2354 #2955) -#2953 := (= #2353 #2952) -#2954 := [rewrite]: #2953 -#2957 := [monotonicity #2954]: #2956 -#2960 := [monotonicity #2957]: #2959 -#2963 := [monotonicity #2960]: #2962 -#2966 := [quant-intro #2963]: #2965 -#2949 := (iff #2371 #2936) -#2941 := (not #2936) -#2944 := (not #2941) -#2947 := (iff #2944 #2936) -#2948 := [rewrite]: #2947 -#2945 := (iff #2371 #2944) -#2942 := (iff #2365 #2941) -#2939 := (iff #2364 #2936) -#2933 := (and #2930 #2361) -#2937 := (iff #2933 #2936) -#2938 := [rewrite]: #2937 -#2934 := (iff #2364 #2933) -#2931 := (iff #2363 #2930) -#2928 := (iff #2362 #2927) -#2929 := [rewrite]: #2928 -#2932 := [monotonicity #2929]: #2931 -#2935 := [monotonicity #2932]: #2934 -#2940 := [trans #2935 #2938]: #2939 -#2943 := [monotonicity #2940]: #2942 -#2946 := [monotonicity #2943]: #2945 -#2950 := [trans #2946 #2948]: #2949 -#2969 := [monotonicity #2950 #2966]: #2968 -#2972 := [monotonicity #2969]: #2971 -#2977 := [trans #2972 #2975]: #2976 -#2925 := (iff #2335 #2924) -#2922 := (iff #2334 #2921) -#2919 := (iff #2325 #2916) -#2906 := (+ #2320 #2323) -#2907 := (+ #2319 #2906) -#2910 := (>= #2907 0::Int) -#2917 := (iff #2910 #2916) -#2918 := [rewrite]: #2917 -#2911 := (iff #2325 #2910) -#2908 := (= #2324 #2907) -#2909 := [rewrite]: #2908 -#2912 := [monotonicity #2909]: #2911 -#2920 := [trans #2912 #2918]: #2919 -#2904 := (iff #2333 #2903) -#2901 := (iff #2332 #2900) -#2902 := [rewrite]: #2901 -#2905 := [monotonicity #2902]: #2904 -#2923 := [monotonicity #2905 #2920]: #2922 -#2926 := [monotonicity #2923]: #2925 -#2980 := [monotonicity #2926 #2977]: #2979 -#2983 := [monotonicity #2980]: #2982 -#2898 := (iff #2304 #2897) -#2895 := (iff #2303 #2894) -#2892 := (iff #2295 #2889) -#2881 := (+ #2292 #2293) -#2884 := (>= #2881 0::Int) -#2890 := (iff #2884 #2889) -#2891 := [rewrite]: #2890 -#2885 := (iff #2295 #2884) -#2882 := (= #2294 #2881) -#2883 := [rewrite]: #2882 -#2886 := [monotonicity #2883]: #2885 -#2893 := [trans #2886 #2891]: #2892 -#2879 := (iff #2302 #2878) -#2876 := (iff #2301 #2875) -#2877 := [rewrite]: #2876 -#2880 := [monotonicity #2877]: #2879 -#2896 := [monotonicity #2880 #2893]: #2895 -#2899 := [monotonicity #2896]: #2898 -#2986 := [monotonicity #2899 #2983]: #2985 -#2989 := [monotonicity #2986]: #2988 -#2992 := [monotonicity #2989]: #2991 -#2873 := (iff #2271 #205) -#2874 := [rewrite]: #2873 -#2995 := [monotonicity #2874 #2992]: #2994 -#2998 := [monotonicity #2995]: #2997 -#3001 := [monotonicity #2998]: #3000 -#2871 := (iff #2257 #2870) -#2868 := (iff #2256 #2865) -#2862 := (or #2859 #2252) -#2866 := (iff #2862 #2865) -#2867 := [rewrite]: #2866 -#2863 := (iff #2256 #2862) -#2860 := (iff #2255 #2859) -#2861 := [rewrite]: #2860 -#2864 := [monotonicity #2861]: #2863 -#2869 := [trans #2864 #2867]: #2868 -#2872 := [monotonicity #2869]: #2871 -#3004 := [monotonicity #2872 #3001]: #3003 -#3007 := [monotonicity #3004]: #3006 -#2857 := (iff #2237 #2856) -#2854 := (iff #2236 #2851) -#2843 := (+ #2233 #2234) -#2846 := (>= #2843 0::Int) -#2852 := (iff #2846 #2851) -#2853 := [rewrite]: #2852 -#2847 := (iff #2236 #2846) -#2844 := (= #2235 #2843) -#2845 := [rewrite]: #2844 -#2848 := [monotonicity #2845]: #2847 -#2855 := [trans #2848 #2853]: #2854 -#2858 := [monotonicity #2855]: #2857 -#3010 := [monotonicity #2858 #3007]: #3009 -#2841 := (iff #2204 #777) -#2842 := [rewrite]: #2841 -#3013 := [monotonicity #2842 #3010]: #3012 -#3018 := [trans #3013 #3016]: #3017 -#2839 := (iff #2198 #2836) -#2833 := (and #137 #142 #622 #625 #2830 #2195) -#2837 := (iff #2833 #2836) -#2838 := [rewrite]: #2837 -#2834 := (iff #2198 #2833) -#2831 := (iff #2188 #2830) -#2828 := (iff #2184 #2827) -#2825 := (iff #2180 #2822) -#2819 := (or #2816 #2176) -#2823 := (iff #2819 #2822) -#2824 := [rewrite]: #2823 -#2820 := (iff #2180 #2819) -#2817 := (iff #2161 #2816) -#2814 := (iff #2160 #2813) -#2811 := (iff #2149 #2808) -#2799 := (+ #2144 #2147) -#2800 := (+ #2143 #2799) -#2803 := (>= #2800 0::Int) -#2809 := (iff #2803 #2808) -#2810 := [rewrite]: #2809 -#2804 := (iff #2149 #2803) -#2801 := (= #2148 #2800) -#2802 := [rewrite]: #2801 -#2805 := [monotonicity #2802]: #2804 -#2812 := [trans #2805 #2810]: #2811 -#2797 := (iff #2159 #2796) -#2794 := (iff #2158 #2793) -#2795 := [rewrite]: #2794 -#2798 := [monotonicity #2795]: #2797 -#2815 := [monotonicity #2798 #2812]: #2814 -#2818 := [monotonicity #2815]: #2817 -#2821 := [monotonicity #2818]: #2820 -#2826 := [trans #2821 #2824]: #2825 -#2791 := (iff #2134 #2790) -#2788 := (iff #2131 #2787) -#2785 := (iff #2126 #2784) -#2782 := (iff #2123 #2779) -#2769 := (+ #2118 #2121) -#2770 := (+ #1343 #2769) -#2773 := (= #2770 0::Int) -#2780 := (iff #2773 #2779) -#2781 := [rewrite]: #2780 -#2774 := (iff #2123 #2773) -#2771 := (= #2122 #2770) -#2772 := [rewrite]: #2771 -#2775 := [monotonicity #2772]: #2774 -#2783 := [trans #2775 #2781]: #2782 -#2767 := (iff #2125 #2766) -#2764 := (iff #2124 #2761) -#2753 := (+ #1343 #2118) -#2756 := (>= #2753 0::Int) -#2762 := (iff #2756 #2761) -#2763 := [rewrite]: #2762 -#2757 := (iff #2124 #2756) -#2754 := (= #2119 #2753) -#2755 := [rewrite]: #2754 -#2758 := [monotonicity #2755]: #2757 -#2765 := [trans #2758 #2763]: #2764 -#2768 := [monotonicity #2765]: #2767 -#2786 := [monotonicity #2768 #2783]: #2785 -#2789 := [monotonicity #2786]: #2788 -#2792 := [quant-intro #2789]: #2791 -#2829 := [monotonicity #2792 #2826]: #2828 -#2751 := (iff #2110 #2748) -#2714 := (and #2091 #2708) -#2745 := (and #2714 #2742) -#2749 := (iff #2745 #2748) -#2750 := [rewrite]: #2749 -#2746 := (iff #2110 #2745) -#2743 := (iff #2106 #2742) -#2740 := (iff #2103 #2739) -#2737 := (iff #2087 #2736) -#2734 := (iff #2084 #2733) -#2731 := (= #2083 #2730) -#2732 := [rewrite]: #2731 -#2735 := [monotonicity #2732]: #2734 -#2738 := [monotonicity #2735]: #2737 -#2741 := [monotonicity #2738]: #2740 -#2744 := [quant-intro #2741]: #2743 -#2727 := (iff #2100 #2714) -#2719 := (not #2714) -#2722 := (not #2719) -#2725 := (iff #2722 #2714) -#2726 := [rewrite]: #2725 -#2723 := (iff #2100 #2722) -#2720 := (iff #2095 #2719) -#2717 := (iff #2094 #2714) -#2711 := (and #2708 #2091) -#2715 := (iff #2711 #2714) -#2716 := [rewrite]: #2715 -#2712 := (iff #2094 #2711) -#2709 := (iff #2093 #2708) -#2706 := (iff #2092 #2705) -#2707 := [rewrite]: #2706 -#2710 := [monotonicity #2707]: #2709 -#2713 := [monotonicity #2710]: #2712 -#2718 := [trans #2713 #2716]: #2717 -#2721 := [monotonicity #2718]: #2720 -#2724 := [monotonicity #2721]: #2723 -#2728 := [trans #2724 #2726]: #2727 -#2747 := [monotonicity #2728 #2744]: #2746 -#2752 := [trans #2747 #2750]: #2751 -#2832 := [monotonicity #2752 #2829]: #2831 -#2703 := (iff #2074 #625) -#2704 := [rewrite]: #2703 -#2701 := (iff #2071 #622) -#2702 := [rewrite]: #2701 -#2699 := (iff #2068 #142) -#2700 := [rewrite]: #2699 -#2697 := (iff #2065 #137) -#2698 := [rewrite]: #2697 -#2835 := [monotonicity #2698 #2700 #2702 #2704 #2832]: #2834 -#2840 := [trans #2835 #2838]: #2839 -#3021 := [monotonicity #2840 #3018]: #3020 -#2695 := (iff #2059 #2694) -#2692 := (iff #2056 #2691) -#2689 := (iff #2051 #2688) -#2686 := (iff #2044 #2685) -#2683 := (iff #2043 #2680) -#2673 := (+ #1298 #2041) -#2676 := (>= #2673 0::Int) -#2681 := (iff #2676 #2680) -#2682 := [rewrite]: #2681 -#2677 := (iff #2043 #2676) -#2674 := (= #2042 #2673) -#2675 := [rewrite]: #2674 -#2678 := [monotonicity #2675]: #2677 -#2684 := [trans #2678 #2682]: #2683 -#2687 := [monotonicity #2684]: #2686 -#2671 := (iff #2048 #2668) -#2657 := (+ #2041 #2046) -#2658 := (+ #1298 #2657) -#2661 := (= #2658 0::Int) -#2669 := (iff #2661 #2668) -#2670 := [rewrite]: #2669 -#2662 := (iff #2048 #2661) -#2659 := (= #2047 #2658) -#2660 := [rewrite]: #2659 -#2663 := [monotonicity #2660]: #2662 -#2672 := [trans #2663 #2670]: #2671 -#2690 := [monotonicity #2672 #2687]: #2689 -#2693 := [monotonicity #2690]: #2692 -#2696 := [quant-intro #2693]: #2695 -#2655 := (iff #2032 #2654) -#2652 := (iff #2029 #2651) -#2649 := (iff #2024 #2648) -#2646 := (iff #2018 #2643) -#2633 := (+ #2014 #2016) -#2634 := (+ #1260 #2633) -#2637 := (= #2634 0::Int) -#2644 := (iff #2637 #2643) -#2645 := [rewrite]: #2644 -#2638 := (iff #2018 #2637) -#2635 := (= #2017 #2634) -#2636 := [rewrite]: #2635 -#2639 := [monotonicity #2636]: #2638 -#2647 := [trans #2639 #2645]: #2646 -#2631 := (iff #2021 #2630) -#2628 := (iff #2020 #2625) -#2617 := (+ #1260 #2016) -#2620 := (>= #2617 0::Int) -#2626 := (iff #2620 #2625) -#2627 := [rewrite]: #2626 -#2621 := (iff #2020 #2620) -#2618 := (= #2019 #2617) -#2619 := [rewrite]: #2618 -#2622 := [monotonicity #2619]: #2621 -#2629 := [trans #2622 #2627]: #2628 -#2632 := [monotonicity #2629]: #2631 -#2650 := [monotonicity #2632 #2647]: #2649 -#2653 := [monotonicity #2650]: #2652 -#2656 := [quant-intro #2653]: #2655 -#2615 := (iff #2007 #101) -#2616 := [rewrite]: #2615 -#3024 := [monotonicity #2616 #2656 #2696 #3021]: #3023 -#3029 := [trans #3024 #3027]: #3028 -#2613 := (iff #2002 #2610) -#2576 := (and #1983 #2570) -#2607 := (and #2576 #2604) -#2611 := (iff #2607 #2610) -#2612 := [rewrite]: #2611 -#2608 := (iff #2002 #2607) -#2605 := (iff #1998 #2604) -#2602 := (iff #1995 #2601) -#2599 := (iff #1979 #2598) -#2596 := (iff #1975 #2595) -#2593 := (= #1974 #2592) -#2594 := [rewrite]: #2593 -#2597 := [monotonicity #2594]: #2596 -#2600 := [monotonicity #2597]: #2599 -#2603 := [monotonicity #2600]: #2602 -#2606 := [quant-intro #2603]: #2605 -#2589 := (iff #1992 #2576) -#2581 := (not #2576) -#2584 := (not #2581) -#2587 := (iff #2584 #2576) -#2588 := [rewrite]: #2587 -#2585 := (iff #1992 #2584) -#2582 := (iff #1987 #2581) -#2579 := (iff #1986 #2576) -#2573 := (and #2570 #1983) -#2577 := (iff #2573 #2576) -#2578 := [rewrite]: #2577 -#2574 := (iff #1986 #2573) -#2571 := (iff #1985 #2570) -#2568 := (iff #1984 #2567) -#2569 := [rewrite]: #2568 -#2572 := [monotonicity #2569]: #2571 -#2575 := [monotonicity #2572]: #2574 -#2580 := [trans #2575 #2578]: #2579 -#2583 := [monotonicity #2580]: #2582 -#2586 := [monotonicity #2583]: #2585 -#2590 := [trans #2586 #2588]: #2589 -#2609 := [monotonicity #2590 #2606]: #2608 -#2614 := [trans #2609 #2612]: #2613 -#3032 := [monotonicity #2614 #3029]: #3031 -#3035 := [monotonicity #3032]: #3034 -#2565 := (iff #1956 #2564) -#2562 := (iff #1955 #2561) -#2559 := (iff #1948 #2558) -#2556 := (iff #1947 #2555) -#2557 := [rewrite]: #2556 -#2560 := [monotonicity #2557]: #2559 -#2553 := (iff #1954 #2552) -#2550 := (= #1953 #2549) -#2551 := [rewrite]: #2550 -#2554 := [monotonicity #2551]: #2553 -#2563 := [monotonicity #2554 #2560]: #2562 -#2566 := [monotonicity #2563]: #2565 -#3038 := [monotonicity #2566 #3035]: #3037 -#3041 := [monotonicity #3038]: #3040 -#2546 := (iff #1925 #2545) -#2543 := (iff #1924 #2542) -#2540 := (iff #1916 #2537) -#2529 := (+ #1913 #1914) -#2532 := (>= #2529 0::Int) -#2538 := (iff #2532 #2537) -#2539 := [rewrite]: #2538 -#2533 := (iff #1916 #2532) -#2530 := (= #1915 #2529) -#2531 := [rewrite]: #2530 -#2534 := [monotonicity #2531]: #2533 -#2541 := [trans #2534 #2539]: #2540 -#2527 := (iff #1923 #2526) -#2524 := (iff #1922 #2523) -#2525 := [rewrite]: #2524 -#2528 := [monotonicity #2525]: #2527 -#2544 := [monotonicity #2528 #2541]: #2543 -#2547 := [monotonicity #2544]: #2546 -#3044 := [monotonicity #2547 #3041]: #3043 -#3047 := [monotonicity #3044]: #3046 -#3050 := [monotonicity #3047]: #3049 -#2521 := (iff #1861 #72) -#2522 := [rewrite]: #2521 -#3053 := [monotonicity #2522 #3050]: #3052 -#3056 := [monotonicity #3053]: #3055 -#1837 := (not #1801) -#2516 := (~ #1837 #2515) -#2512 := (not #1798) -#2513 := (~ #2512 #2511) -#2508 := (not #1795) -#2509 := (~ #2508 #2507) -#2504 := (not #1792) -#2505 := (~ #2504 #2503) -#2500 := (not #1789) -#2501 := (~ #2500 #2499) -#2496 := (not #1786) -#2497 := (~ #2496 #2495) -#2492 := (not #1783) -#2493 := (~ #2492 #2491) -#2488 := (not #1780) -#2489 := (~ #2488 #2487) -#2484 := (not #1777) -#2485 := (~ #2484 #2483) -#2480 := (not #1772) -#2481 := (~ #2480 #2479) -#2476 := (not #1743) -#2477 := (~ #2476 #1740) -#2474 := (~ #1740 #1740) -#2472 := (~ #1737 #1737) -#2473 := [refl]: #2472 -#2475 := [nnf-pos #2473]: #2474 -#2478 := [nnf-neg #2475]: #2477 -#2469 := (not #1734) -#2470 := (~ #2469 #1731) -#2467 := (~ #1731 #1731) -#2465 := (~ #1726 #1726) -#2466 := [refl]: #2465 -#2468 := [nnf-pos #2466]: #2467 -#2471 := [nnf-neg #2468]: #2470 -#2462 := (not #1718) -#2463 := (~ #2462 #1715) -#2460 := (~ #1715 #1715) -#2458 := (~ #1712 #1712) -#2459 := [refl]: #2458 -#2461 := [nnf-pos #2459]: #2460 -#2464 := [nnf-neg #2461]: #2463 -#2455 := (not #1695) -#2456 := (~ #2455 #2454) -#2451 := (not #1690) -#2452 := (~ #2451 #2450) -#2448 := (~ #1656 #1656) -#2449 := [refl]: #2448 -#2445 := (not #1651) -#2446 := (~ #2445 #1648) -#2443 := (~ #1648 #1648) -#2441 := (~ #1643 #1643) -#2442 := [refl]: #2441 -#2444 := [nnf-pos #2442]: #2443 -#2447 := [nnf-neg #2444]: #2446 -#2438 := (not #1633) -#2439 := (~ #2438 #1630) -#2436 := (~ #1630 #1630) -#2434 := (~ #1627 #1627) -#2435 := [refl]: #2434 -#2437 := [nnf-pos #2435]: #2436 -#2440 := [nnf-neg #2437]: #2439 -#2431 := (not #1616) -#2432 := (~ #2431 #2430) -#2427 := (not #1613) -#2428 := (~ #2427 #2426) -#2423 := (not #1610) -#2424 := (~ #2423 #2422) -#2419 := (not #1607) -#2420 := (~ #2419 #2418) -#2415 := (not #1604) -#2416 := (~ #2415 #2414) -#2411 := (not #1601) -#2412 := (~ #2411 #2410) -#2407 := (not #1598) -#2408 := (~ #2407 #2406) -#2403 := (not #1595) -#2404 := (~ #2403 #2402) -#2399 := (not #1592) -#2400 := (~ #2399 #2398) -#2395 := (not #1589) -#2396 := (~ #2395 #2394) -#2391 := (not #1586) -#2392 := (~ #2391 #2390) -#2387 := (not #1583) -#2388 := (~ #2387 #2386) -#2368 := (not #1580) -#2384 := (~ #2368 #2381) -#2358 := (exists (vars (?v1 S3)) #2357) -#2366 := (or #2365 #2358) -#2367 := (not #2366) -#2382 := (~ #2367 #2381) -#2378 := (not #2358) -#2379 := (~ #2378 #2377) -#2375 := (~ #2374 #2374) -#2376 := [refl]: #2375 -#2380 := [nnf-neg #2376]: #2379 -#2372 := (~ #2371 #2371) -#2373 := [refl]: #2372 -#2383 := [nnf-neg #2373 #2380]: #2382 -#2369 := (~ #2368 #2367) -#2370 := [sk]: #2369 -#2385 := [trans #2370 #2383]: #2384 -#2344 := (not #1543) -#2345 := (~ #2344 #1540) -#2342 := (~ #1540 #1540) -#2340 := (~ #1537 #1537) -#2341 := [refl]: #2340 -#2343 := [nnf-pos #2341]: #2342 -#2346 := [nnf-neg #2343]: #2345 -#2389 := [nnf-neg #2346 #2385]: #2388 -#2336 := (~ #1543 #2335) -#2337 := [sk]: #2336 -#2393 := [nnf-neg #2337 #2389]: #2392 -#2313 := (not #1519) -#2314 := (~ #2313 #1516) -#2311 := (~ #1516 #1516) -#2309 := (~ #1511 #1511) -#2310 := [refl]: #2309 -#2312 := [nnf-pos #2310]: #2311 -#2315 := [nnf-neg #2312]: #2314 -#2397 := [nnf-neg #2315 #2393]: #2396 -#2305 := (~ #1519 #2304) -#2306 := [sk]: #2305 -#2401 := [nnf-neg #2306 #2397]: #2400 -#2286 := (not #1500) -#2287 := (~ #2286 #1497) -#2284 := (~ #1497 #1497) -#2282 := (~ #1494 #1494) -#2283 := [refl]: #2282 -#2285 := [nnf-pos #2283]: #2284 -#2288 := [nnf-neg #2285]: #2287 -#2405 := [nnf-neg #2288 #2401]: #2404 -#2278 := (~ #1500 #2277) -#2279 := [sk]: #2278 -#2409 := [nnf-neg #2279 #2405]: #2408 -#2272 := (~ #2271 #2271) -#2273 := [refl]: #2272 -#2413 := [nnf-neg #2273 #2409]: #2412 -#2269 := (~ #1491 #1491) -#2270 := [refl]: #2269 -#2417 := [nnf-neg #2270 #2413]: #2416 -#2266 := (not #954) -#2267 := (~ #2266 #820) -#2264 := (~ #820 #820) -#2262 := (~ #815 #815) -#2263 := [refl]: #2262 -#2265 := [nnf-pos #2263]: #2264 -#2268 := [nnf-neg #2265]: #2267 -#2421 := [nnf-neg #2268 #2417]: #2420 -#2258 := (~ #954 #2257) -#2259 := [sk]: #2258 -#2425 := [nnf-neg #2259 #2421]: #2424 -#2246 := (not #1486) -#2247 := (~ #2246 #1483) -#2244 := (~ #1483 #1483) -#2242 := (~ #1478 #1478) -#2243 := [refl]: #2242 -#2245 := [nnf-pos #2243]: #2244 -#2248 := [nnf-neg #2245]: #2247 -#2429 := [nnf-neg #2248 #2425]: #2428 -#2238 := (~ #1486 #2237) -#2239 := [sk]: #2238 -#2433 := [nnf-neg #2239 #2429]: #2432 -#2228 := (not #1475) -#2229 := (~ #2228 #1472) -#2226 := (~ #1472 #1472) -#2224 := (~ #1467 #1467) -#2225 := [refl]: #2224 -#2227 := [nnf-pos #2225]: #2226 -#2230 := [nnf-neg #2227]: #2229 -#2221 := (not #1666) -#2222 := (~ #2221 #2216) -#2217 := (~ #1425 #2216) -#2218 := [sk]: #2217 -#2223 := [nnf-neg #2218]: #2222 -#2205 := (~ #2204 #2204) -#2206 := [refl]: #2205 -#2202 := (~ #758 #758) -#2203 := [refl]: #2202 -#2453 := [nnf-neg #2203 #2206 #2223 #2230 #2433 #2440 #2447 #2449]: #2452 -#2199 := (not #1443) -#2200 := (~ #2199 #2198) -#2196 := (~ #1666 #2195) -#2193 := (~ #2192 #2192) -#2194 := [refl]: #2193 -#2197 := [nnf-neg #2194]: #2196 -#2189 := (not #1414) -#2190 := (~ #2189 #2188) -#2185 := (not #1411) -#2186 := (~ #2185 #2184) -#2181 := (not #1408) -#2182 := (~ #2181 #2180) -#2177 := (not #1403) -#2178 := (~ #2177 #2176) -#2173 := (not #1395) -#2174 := (~ #2173 #1392) -#2171 := (~ #1392 #1392) -#2169 := (~ #1389 #1389) -#2170 := [refl]: #2169 -#2172 := [nnf-pos #2170]: #2171 -#2175 := [nnf-neg #2172]: #2174 -#2167 := (~ #2166 #2166) -#2168 := [refl]: #2167 -#2179 := [nnf-neg #2168 #2175]: #2178 -#2162 := (~ #1395 #2161) -#2163 := [sk]: #2162 -#2183 := [nnf-neg #2163 #2179]: #2182 -#2137 := (not #1377) -#2138 := (~ #2137 #2134) -#2135 := (~ #1374 #2134) -#2132 := (~ #1371 #2131) -#2127 := (~ #1368 #2126) -#2128 := [sk]: #2127 -#2115 := (~ #1352 #1352) -#2116 := [refl]: #2115 -#2133 := [monotonicity #2116 #2128]: #2132 -#2136 := [nnf-pos #2133]: #2135 -#2139 := [nnf-neg #2136]: #2138 -#2187 := [nnf-neg #2139 #2183]: #2186 -#2113 := (~ #1377 #2110) -#2088 := (exists (vars (?v1 S3)) #2087) -#2096 := (or #2095 #2088) -#2097 := (not #2096) -#2111 := (~ #2097 #2110) -#2107 := (not #2088) -#2108 := (~ #2107 #2106) -#2104 := (~ #2103 #2103) -#2105 := [refl]: #2104 -#2109 := [nnf-neg #2105]: #2108 -#2101 := (~ #2100 #2100) -#2102 := [refl]: #2101 -#2112 := [nnf-neg #2102 #2109]: #2111 -#2098 := (~ #1377 #2097) -#2099 := [sk]: #2098 -#2114 := [trans #2099 #2112]: #2113 -#2191 := [nnf-neg #2114 #2187]: #2190 -#2075 := (~ #2074 #2074) -#2076 := [refl]: #2075 -#2072 := (~ #2071 #2071) -#2073 := [refl]: #2072 -#2069 := (~ #2068 #2068) -#2070 := [refl]: #2069 -#2066 := (~ #2065 #2065) -#2067 := [refl]: #2066 -#2201 := [nnf-neg #2067 #2070 #2073 #2076 #2191 #2197]: #2200 -#2457 := [nnf-neg #2201 #2453]: #2456 -#2062 := (not #1340) -#2063 := (~ #2062 #2059) -#2060 := (~ #1337 #2059) -#2057 := (~ #1334 #2056) -#2052 := (~ #1331 #2051) -#2053 := [sk]: #2052 -#2038 := (~ #1307 #1307) -#2039 := [refl]: #2038 -#2058 := [monotonicity #2039 #2053]: #2057 -#2061 := [nnf-pos #2058]: #2060 -#2064 := [nnf-neg #2061]: #2063 -#2035 := (not #1751) -#2036 := (~ #2035 #2032) -#2033 := (~ #1295 #2032) -#2030 := (~ #1292 #2029) -#2025 := (~ #1289 #2024) -#2026 := [sk]: #2025 -#2010 := (~ #1269 #1269) -#2011 := [refl]: #2010 -#2031 := [monotonicity #2011 #2026]: #2030 -#2034 := [nnf-pos #2031]: #2033 -#2037 := [nnf-neg #2034]: #2036 -#2008 := (~ #2007 #2007) -#2009 := [refl]: #2008 -#2482 := [nnf-neg #2009 #2037 #2064 #2457 #2464 #2471 #2478]: #2481 -#2005 := (~ #1751 #2002) -#1980 := (exists (vars (?v1 S3)) #1979) -#1988 := (or #1987 #1980) -#1989 := (not #1988) -#2003 := (~ #1989 #2002) -#1999 := (not #1980) -#2000 := (~ #1999 #1998) -#1996 := (~ #1995 #1995) -#1997 := [refl]: #1996 -#2001 := [nnf-neg #1997]: #2000 -#1993 := (~ #1992 #1992) -#1994 := [refl]: #1993 -#2004 := [nnf-neg #1994 #2001]: #2003 -#1990 := (~ #1751 #1989) -#1991 := [sk]: #1990 -#2006 := [trans #1991 #2004]: #2005 -#2486 := [nnf-neg #2006 #2482]: #2485 -#1965 := (not #1257) -#1966 := (~ #1965 #1254) -#1963 := (~ #1254 #1254) -#1961 := (~ #1251 #1251) -#1962 := [refl]: #1961 -#1964 := [nnf-pos #1962]: #1963 -#1967 := [nnf-neg #1964]: #1966 -#2490 := [nnf-neg #1967 #2486]: #2489 -#1957 := (~ #1257 #1956) -#1958 := [sk]: #1957 -#2494 := [nnf-neg #1958 #2490]: #2493 -#1934 := (not #1226) -#1935 := (~ #1934 #1223) -#1932 := (~ #1223 #1223) -#1930 := (~ #1218 #1218) -#1931 := [refl]: #1930 -#1933 := [nnf-pos #1931]: #1932 -#1936 := [nnf-neg #1933]: #1935 -#2498 := [nnf-neg #1936 #2494]: #2497 -#1926 := (~ #1226 #1925) -#1927 := [sk]: #1926 -#2502 := [nnf-neg #1927 #2498]: #2501 -#1907 := (not #1206) -#1908 := (~ #1907 #1203) -#1905 := (~ #1203 #1203) -#1903 := (~ #1202 #1202) -#1904 := [refl]: #1903 -#1906 := [nnf-pos #1904]: #1905 -#1909 := [nnf-neg #1906]: #1908 -#2506 := [nnf-neg #1909 #2502]: #2505 -#1899 := (~ #1206 #1898) -#1900 := [sk]: #1899 -#2510 := [nnf-neg #1900 #2506]: #2509 -#1862 := (~ #1861 #1861) -#1894 := [refl]: #1862 -#2514 := [nnf-neg #1894 #2510]: #2513 -#1892 := (~ #1197 #1197) -#1893 := [refl]: #1892 -#2517 := [nnf-neg #1893 #2514]: #2516 -#1838 := [not-or-elim #1834]: #1837 -#2518 := [mp~ #1838 #2517]: #2515 -#2519 := [mp #2518 #3056]: #3054 -#3698 := [mp #2519 #3697]: #3695 -#4605 := [mp #3698 #4604]: #4602 -#6497 := [unit-resolution #4605 #5321]: #4599 -#3944 := (or #4596 #4590) -#3945 := [def-axiom]: #3944 -#6498 := [unit-resolution #3945 #6497]: #4590 -#6499 := (or #4593 #4587) -#5108 := [hypothesis]: #1898 -#5107 := (<= #1896 0::Int) -#4722 := (or #5107 #1897) -#5140 := [th-lemma arith farkas 1 1]: #4722 -#5141 := [unit-resolution #5140 #5108]: #5107 -#5100 := (not #5107) -#5115 := (or #5100 #1897) -#356 := (<= f9 0::Int) -#357 := (not #356) -#47 := (< 0::Int f9) -#358 := (iff #47 #357) -#359 := [rewrite]: #358 -#352 := [asserted]: #47 -#360 := [mp #352 #359]: #357 -#4719 := (* -1::Int #1896) -#4720 := (+ f9 #4719) -#4721 := (<= #4720 0::Int) -#3934 := (= f9 #1896) -#3913 := (= f11 ?v0!0) -#4912 := (not #3913) -#4909 := (= #1896 0::Int) -#5109 := (not #4909) -#5110 := (or #5109 #1897) -#5111 := [th-lemma arith triangle-eq]: #5110 -#5091 := [unit-resolution #5111 #5108]: #5109 -#4918 := (or #4785 #4912 #4909) -#3933 := (= ?v0!0 f11) -#4910 := (not #3933) -#4911 := (or #4910 #4909) -#4649 := (or #4785 #4911) -#5104 := (iff #4649 #4918) -#4716 := (or #4912 #4909) -#4935 := (or #4785 #4716) -#4981 := (iff #4935 #4918) -#5103 := [rewrite]: #4981 -#4979 := (iff #4649 #4935) -#4717 := (iff #4911 #4716) -#4915 := (iff #4910 #4912) -#3915 := (iff #3933 #3913) -#3916 := [rewrite]: #3915 -#4916 := [monotonicity #3916]: #4915 -#4784 := [monotonicity #4916]: #4717 -#4980 := [monotonicity #4784]: #4979 -#5105 := [trans #4980 #5103]: #5104 -#4932 := [quant-inst #1895]: #4649 -#5106 := [mp #4932 #5105]: #4918 -#5092 := [unit-resolution #5106 #4611 #5091]: #4912 -#3928 := (or #3913 #3934) -#4220 := (forall (vars (?v0 S3)) (:pat #4219) #447) -#4223 := (iff #452 #4220) -#4221 := (iff #447 #447) -#4222 := [refl]: #4221 -#4224 := [quant-intro #4222]: #4223 -#1857 := (~ #452 #452) -#1886 := (~ #447 #447) -#1887 := [refl]: #1886 -#1858 := [nnf-pos #1887]: #1857 -#1835 := [not-or-elim #1834]: #452 -#1888 := [mp~ #1835 #1858]: #452 -#4225 := [mp #1888 #4224]: #4220 -#3924 := (not #4220) -#3917 := (or #3924 #3913 #3934) -#3923 := (or #3933 #3934) -#3925 := (or #3924 #3923) -#4663 := (iff #3925 #3917) -#3910 := (or #3924 #3928) -#4647 := (iff #3910 #3917) -#4662 := [rewrite]: #4647 -#4645 := (iff #3925 #3910) -#3919 := (iff #3923 #3928) -#3920 := [monotonicity #3916]: #3919 -#4646 := [monotonicity #3920]: #4645 -#4644 := [trans #4646 #4662]: #4663 -#3908 := [quant-inst #1895]: #3925 -#4718 := [mp #3908 #4644]: #3917 -#5093 := [unit-resolution #4718 #4225]: #3928 -#5094 := [unit-resolution #5093 #5092]: #3934 -#5095 := (not #3934) -#5090 := (or #5095 #4721) -#5096 := [th-lemma arith triangle-eq]: #5090 -#5097 := [unit-resolution #5096 #5094]: #4721 -#5098 := [hypothesis]: #5107 -#5099 := [th-lemma arith farkas 1 -1 1 #5098 #5097 #360]: false -#5116 := [lemma #5099]: #5115 -#5142 := [unit-resolution #5116 #5141 #5108]: false -#5143 := [lemma #5142]: #1897 -#3939 := (or #4593 #1898 #4587) -#3940 := [def-axiom]: #3939 -#6500 := [unit-resolution #3940 #5143]: #6499 -#6501 := [unit-resolution #6500 #6498]: #4587 -#3963 := (or #4584 #4578) -#3964 := [def-axiom]: #3963 -#6502 := [unit-resolution #3964 #6501]: #4578 -#5818 := [hypothesis]: #1918 -#5331 := (or #5530 #2308) -#5336 := [quant-inst #1911]: #5331 -#5819 := [unit-resolution #5336 #4232 #5818]: false -#5820 := [lemma #5819]: #2308 -#3756 := (or #2338 #1918) -#3843 := [def-axiom]: #3756 -#6503 := [unit-resolution #3843 #5820]: #2338 -#3957 := (or #4581 #2130 #4575) -#3959 := [def-axiom]: #3957 -#6504 := [unit-resolution #3959 #6503 #6502]: #4575 -#3984 := (or #4572 #4566) -#3985 := [def-axiom]: #3984 -#6505 := [unit-resolution #3985 #6504]: #4566 -#3980 := (or #4569 #3099 #4563) -#3981 := [def-axiom]: #3980 -#6506 := [unit-resolution #3981 #6505 #6496]: #4563 -#3994 := (or #4560 #4554) -#4015 := [def-axiom]: #3994 -#6507 := [unit-resolution #4015 #6506]: #4554 -#5791 := (= f9 #1971) -#5855 := (not #5791) -#5853 := [hypothesis]: #4271 -#4160 := (or #4268 #1983) -#3834 := [def-axiom]: #4160 -#5854 := [unit-resolution #3834 #5853]: #1983 -#5856 := (or #5855 #1982) -#5857 := [th-lemma arith triangle-eq]: #5856 -#5858 := [unit-resolution #5857 #5854]: #5855 -#3835 := (or #4268 #2570) -#4167 := [def-axiom]: #3835 -#5859 := [unit-resolution #4167 #5853]: #2570 -#5811 := (or #3924 #2567 #5791) -#5792 := (or #1984 #5791) -#5806 := (or #3924 #5792) -#5670 := (iff #5806 #5811) -#5808 := (or #2567 #5791) -#5813 := (or #3924 #5808) -#5816 := (iff #5813 #5811) -#5669 := [rewrite]: #5816 -#5814 := (iff #5806 #5813) -#5809 := (iff #5792 #5808) -#5810 := [monotonicity #2569]: #5809 -#5815 := [monotonicity #5810]: #5814 -#5671 := [trans #5815 #5669]: #5670 -#5812 := [quant-inst #1968]: #5806 -#5476 := [mp #5812 #5671]: #5811 -#5860 := [unit-resolution #5476 #4225 #5859 #5858]: false -#5861 := [lemma #5860]: #4268 -#4002 := (or #4557 #4271 #4551) -#4003 := [def-axiom]: #4002 -#6508 := [unit-resolution #4003 #5861 #6507]: #4551 -#4035 := (or #4548 #4275) -#4031 := [def-axiom]: #4035 -#7122 := [unit-resolution #4031 #6508]: #4275 -#9554 := (or #4280 #7758) -#9555 := [quant-inst #2274]: #9554 -#9581 := [unit-resolution #9555 #7122]: #7758 -#7571 := (* -1::Int #7537) -#7572 := (+ #2275 #7571) -#9582 := (>= #7572 0::Int) -#7540 := (= #2275 #7537) -#10088 := [hypothesis]: #2277 -#11986 := (or #7540 #2276 #6074) -#9989 := (f6 #7212 ?v0!15) -#9990 := (f10 #9989) -#9991 := (* -1::Int #9990) -#7587 := (f6 f23 ?v0!15) -#7588 := (f10 #7587) -#10059 := (+ #7588 #9991) -#10063 := (>= #10059 0::Int) -#10058 := (= #7588 #9990) -#10066 := (= #9990 #7588) -#10064 := (= #9989 #7587) -#10065 := [monotonicity #7791]: #10064 -#10067 := [monotonicity #10065]: #10066 -#10068 := [symm #10067]: #10058 -#10069 := (not #10058) -#10070 := (or #10069 #10063) -#10071 := [th-lemma arith triangle-eq]: #10070 -#10072 := [unit-resolution #10071 #10068]: #10063 -#7969 := (f6 #6070 #7212) -#8218 := (f7 #7969) -#9082 := (f14 f15 #8218) -#9083 := (* -1::Int #9082) -#9456 := (+ #6071 #9083) -#9458 := (>= #9456 0::Int) -#9862 := (= #6071 #9082) -#8219 := (= #6070 #8218) -#8390 := (or #6830 #8219) -#8391 := [quant-inst #6070 #7212]: #8390 -#9281 := [unit-resolution #8391 #4206]: #8219 -#11948 := [monotonicity #9281]: #9862 -#11946 := (not #9862) -#11949 := (or #11946 #9458) -#11950 := [th-lemma arith triangle-eq]: #11949 -#11951 := [unit-resolution #11950 #11948]: #9458 -#10867 := (+ #100 #9083) -#10879 := (<= #10867 0::Int) -#10876 := (= #100 #9082) -#11957 := (= #9082 #100) -#10698 := (= #8218 f11) -#7318 := (= #6070 f11) -#7320 := (= f11 #6070) -#7299 := (?v1!7 #6070) -#7311 := (f3 f16 #7299) -#7312 := (= f1 #7311) -#7313 := (not #7312) -#7304 := (f6 #7299 #6070) -#7305 := (f10 #7304) -#7306 := (* -1::Int #7305) -#7300 := (f14 f15 #7299) -#7301 := (* -1::Int #7300) -#7307 := (+ #7301 #7306) -#7308 := (+ #6071 #7307) -#7309 := (= #7308 0::Int) -#7310 := (not #7309) -#7302 := (+ #6071 #7301) -#7303 := (<= #7302 0::Int) -#7323 := (or #7303 #7310 #7313) -#9608 := (or #2276 #6074 #7303) -#8252 := (not #7303) -#10073 := [hypothesis]: #8252 -#10111 := (or #7540 #2276 #6074 #7303) -#9126 := (>= #7300 0::Int) -#9129 := (or #4280 #9126) -#9300 := [quant-inst #7299]: #9129 -#10074 := [unit-resolution #9300 #7122]: #9126 -#7562 := (* -1::Int #2275) -#7613 := (+ #7562 #7588) -#7614 := (+ #175 #7613) -#9498 := (<= #7614 0::Int) -#7617 := (= #7614 0::Int) -#7592 := (* -1::Int #7588) -#7596 := (+ f9 #7592) -#7597 := (<= #7596 0::Int) -#9511 := (not #7597) -#7606 := (+ #7571 #7588) -#7607 := (+ #175 #7606) -#7608 := (>= #7607 0::Int) -#7639 := (or #7597 #7608) -#7642 := (not #7639) -#10076 := (not #7540) -#10077 := [hypothesis]: #10076 -#7645 := (or #7540 #7642) -#5789 := (or #4548 #4539) -#4723 := (?v1!7 ?v0!8) -#4999 := (f14 f20 #4723) -#5012 := (* -1::Int #4999) -#4724 := (f14 f15 #4723) -#5232 := (+ #4724 #5012) -#5237 := (>= #5232 0::Int) -#5231 := (= #4724 #4999) -#5721 := (= #4999 #4724) -#5716 := [hypothesis]: #4536 -#5717 := [hypothesis]: #4551 -#4024 := (or #4548 #4542) -#3992 := [def-axiom]: #4024 -#5718 := [unit-resolution #3992 #5717]: #4542 -#4029 := (or #4545 #4384 #4539) -#4030 := [def-axiom]: #4029 -#5719 := [unit-resolution #4030 #5718 #5716]: #4384 -#4135 := (or #4381 #625) -#4136 := [def-axiom]: #4135 -#5720 := [unit-resolution #4136 #5719]: #625 -#5715 := [symm #5720]: #139 -#5722 := [monotonicity #5715]: #5721 -#5723 := [symm #5722]: #5231 -#5724 := (not #5231) -#5725 := (or #5724 #5237) -#5738 := [th-lemma arith triangle-eq]: #5725 -#5739 := [unit-resolution #5738 #5723]: #5237 -#4706 := (* -1::Int #4724) -#4656 := (f14 f15 ?v0!8) -#4707 := (+ #4656 #4706) -#4708 := (<= #4707 0::Int) -#4889 := (not #4708) -#4715 := (f3 f16 #4723) -#4786 := (= f1 #4715) -#4787 := (not #4786) -#4709 := (f6 #4723 ?v0!8) -#4710 := (f10 #4709) -#4705 := (* -1::Int #4710) -#4791 := (+ #4705 #4706) -#4792 := (+ #4656 #4791) -#4774 := (= #4792 0::Int) -#4777 := (not #4774) -#4782 := (or #4708 #4777 #4787) -#4856 := (not #4782) -#4657 := (* -1::Int #4656) -#4658 := (+ f9 #4657) -#4638 := (<= #4658 0::Int) -#4994 := (not #4638) -#4137 := (or #4381 #4375) -#4134 := [def-axiom]: #4137 -#5740 := [unit-resolution #4134 #5719]: #4375 -#4033 := (or #4548 #101) -#4034 := [def-axiom]: #4033 -#5741 := [unit-resolution #4034 #5717]: #101 -#5742 := (= #158 #100) -#5737 := [monotonicity #5715]: #5742 -#5743 := [trans #5737 #5741]: #159 -#4147 := (or #4357 #2166) -#3810 := [def-axiom]: #4147 -#5744 := [unit-resolution #3810 #5743]: #4357 -#4036 := (or #4548 #4283) -#4016 := [def-axiom]: #4036 -#5745 := [unit-resolution #4016 #5717]: #4283 -#3851 := (or #4381 #4317) -#4133 := [def-axiom]: #3851 -#5746 := [unit-resolution #4133 #5719]: #4317 -#4977 := (or #3362 #4322 #4288 #716) -#4950 := [hypothesis]: #3367 -#4150 := (or #3362 #2153) -#4151 := [def-axiom]: #4150 -#4951 := [unit-resolution #4151 #4950]: #2153 -#4725 := (f14 f15 ?v1!10) -#4726 := (* -1::Int #4725) -#4727 := (+ f9 #4726) -#4728 := (<= #4727 0::Int) -#4729 := (f3 f16 ?v1!10) -#4730 := (= f1 #4729) -#4801 := (not #4730) -#3838 := (f14 f15 ?v0!11) -#3839 := (* -1::Int #3838) -#4803 := (+ #3839 #4725) -#4804 := (+ #2147 #4803) -#4807 := (>= #4804 0::Int) -#4960 := (not #4807) -#4934 := (+ #2144 #4726) -#4936 := (>= #4934 0::Int) -#4933 := (= #2144 #4725) -#4938 := (= #4725 #2144) -#4937 := [hypothesis]: #625 -#4939 := [monotonicity #4937]: #4938 -#4940 := [symm #4939]: #4933 -#4941 := (not #4933) -#4942 := (or #4941 #4936) -#4943 := [th-lemma arith triangle-eq]: #4942 -#4944 := [unit-resolution #4943 #4940]: #4936 -#4148 := (not #2808) -#4154 := (or #3362 #4148) -#3792 := [def-axiom]: #4154 -#4945 := [unit-resolution #3792 #4950]: #4148 -#4927 := (+ #2142 #3839) -#4931 := (<= #4927 0::Int) -#4926 := (= #2142 #3838) -#4948 := (= #3838 #2142) -#4949 := [monotonicity #4937]: #4948 -#4952 := [symm #4949]: #4926 -#4953 := (not #4926) -#4954 := (or #4953 #4931) -#4965 := [th-lemma arith triangle-eq]: #4954 -#4966 := [unit-resolution #4965 #4952]: #4931 -#4962 := (not #4936) -#4961 := (not #4931) -#4963 := (or #4960 #4961 #2808 #4962) -#4955 := [hypothesis]: #4936 -#4956 := [hypothesis]: #4148 -#4957 := [hypothesis]: #4931 -#4958 := [hypothesis]: #4807 -#4959 := [th-lemma arith farkas 1 -1 1 1 #4958 #4957 #4956 #4955]: false -#4964 := [lemma #4959]: #4963 -#4967 := [unit-resolution #4964 #4966 #4945 #4944]: #4960 -#4970 := (or #4801 #4807) -#4152 := (or #3362 #2157) -#4153 := [def-axiom]: #4152 -#4968 := [unit-resolution #4153 #4950]: #2157 -#4969 := [hypothesis]: #4283 -#4818 := (or #4288 #2156 #4801 #4807) -#4796 := (+ #4725 #3839) -#4797 := (+ #2147 #4796) -#4800 := (>= #4797 0::Int) -#4802 := (or #4801 #2156 #4800) -#4819 := (or #4288 #4802) -#4826 := (iff #4819 #4818) -#4813 := (or #2156 #4801 #4807) -#4821 := (or #4288 #4813) -#4824 := (iff #4821 #4818) -#4825 := [rewrite]: #4824 -#4822 := (iff #4819 #4821) -#4816 := (iff #4802 #4813) -#4810 := (or #4801 #2156 #4807) -#4814 := (iff #4810 #4813) -#4815 := [rewrite]: #4814 -#4811 := (iff #4802 #4810) -#4808 := (iff #4800 #4807) -#4805 := (= #4797 #4804) -#4806 := [rewrite]: #4805 -#4809 := [monotonicity #4806]: #4808 -#4812 := [monotonicity #4809]: #4811 -#4817 := [trans #4812 #4815]: #4816 -#4823 := [monotonicity #4817]: #4822 -#4827 := [trans #4823 #4825]: #4826 -#4820 := [quant-inst #2141 #2140]: #4819 -#4828 := [mp #4820 #4827]: #4818 -#4971 := [unit-resolution #4828 #4969 #4968]: #4970 -#4972 := [unit-resolution #4971 #4967]: #4801 -#4732 := (or #4728 #4730) -#4973 := [hypothesis]: #4317 -#4735 := (or #4322 #4728 #4730) -#4731 := (or #4730 #4728) -#4736 := (or #4322 #4731) -#4743 := (iff #4736 #4735) -#4738 := (or #4322 #4732) -#4741 := (iff #4738 #4735) -#4742 := [rewrite]: #4741 -#4739 := (iff #4736 #4738) -#4733 := (iff #4731 #4732) -#4734 := [rewrite]: #4733 -#4740 := [monotonicity #4734]: #4739 -#4744 := [trans #4740 #4742]: #4743 -#4737 := [quant-inst #2140]: #4736 -#4745 := [mp #4737 #4744]: #4735 -#4974 := [unit-resolution #4745 #4973]: #4732 -#4975 := [unit-resolution #4974 #4972]: #4728 -#4976 := [th-lemma arith farkas 1 -1 1 #4944 #4975 #4951]: false -#4978 := [lemma #4976]: #4977 -#5747 := [unit-resolution #4978 #5746 #5745 #5720]: #3362 -#4159 := (or #4366 #4360 #3367) -#4145 := [def-axiom]: #4159 -#5748 := [unit-resolution #4145 #5747 #5744]: #4366 -#3869 := (or #4369 #4363) -#3870 := [def-axiom]: #3869 -#5749 := [unit-resolution #3870 #5748]: #4369 -#4139 := (or #4378 #4338 #4372) -#4143 := [def-axiom]: #4139 -#5750 := [unit-resolution #4143 #5749 #5740]: #4338 -#4171 := (or #4335 #2091) -#4161 := [def-axiom]: #4171 -#5751 := [unit-resolution #4161 #5750]: #2091 -#4987 := (+ #2078 #4657) -#4989 := (>= #4987 0::Int) -#4986 := (= #2078 #4656) -#5414 := (= #4656 #2078) -#5752 := [monotonicity #5720]: #5414 -#5753 := [symm #5752]: #4986 -#5417 := (not #4986) -#5422 := (or #5417 #4989) -#5423 := [th-lemma arith triangle-eq]: #5422 -#5754 := [unit-resolution #5423 #5753]: #4989 -#4995 := (not #4989) -#4996 := (or #4994 #4995 #2090) -#4990 := [hypothesis]: #2091 -#4991 := [hypothesis]: #4638 -#4992 := [hypothesis]: #4989 -#4993 := [th-lemma arith farkas 1 -1 1 #4992 #4991 #4990]: false -#4997 := [lemma #4993]: #4996 -#5755 := [unit-resolution #4997 #5754 #5751]: #4994 -#5765 := (or #4638 #4856) -#3821 := (or #4335 #2708) -#3826 := [def-axiom]: #3821 -#5763 := [unit-resolution #3826 #5750]: #2708 -#4023 := (or #4548 #4308) -#4018 := [def-axiom]: #4023 -#5764 := [unit-resolution #4018 #5717]: #4308 -#4861 := (or #4313 #2705 #4638 #4856) -#4711 := (+ #4706 #4705) -#4712 := (+ #4656 #4711) -#4713 := (= #4712 0::Int) -#4714 := (not #4713) -#4788 := (or #4787 #4714 #4708) -#4789 := (not #4788) -#4790 := (or #2092 #4638 #4789) -#4862 := (or #4313 #4790) -#4885 := (iff #4862 #4861) -#4859 := (or #2705 #4638 #4856) -#4864 := (or #4313 #4859) -#4883 := (iff #4864 #4861) -#4884 := [rewrite]: #4883 -#4880 := (iff #4862 #4864) -#4854 := (iff #4790 #4859) -#4857 := (iff #4789 #4856) -#4799 := (iff #4788 #4782) -#4779 := (or #4787 #4777 #4708) -#4783 := (iff #4779 #4782) -#4798 := [rewrite]: #4783 -#4780 := (iff #4788 #4779) -#4778 := (iff #4714 #4777) -#4775 := (iff #4713 #4774) -#4793 := (= #4712 #4792) -#4794 := [rewrite]: #4793 -#4776 := [monotonicity #4794]: #4775 -#4773 := [monotonicity #4776]: #4778 -#4781 := [monotonicity #4773]: #4780 -#4855 := [trans #4781 #4798]: #4799 -#4858 := [monotonicity #4855]: #4857 -#4860 := [monotonicity #2707 #4858]: #4854 -#4882 := [monotonicity #4860]: #4880 -#4886 := [trans #4882 #4884]: #4885 -#4863 := [quant-inst #2077]: #4862 -#4881 := [mp #4863 #4886]: #4861 -#5766 := [unit-resolution #4881 #5764 #5763]: #5765 -#5767 := [unit-resolution #5766 #5755]: #4856 -#4890 := (or #4782 #4889) -#4891 := [def-axiom]: #4890 -#5768 := [unit-resolution #4891 #5767]: #4889 -#5013 := (+ #2078 #5012) -#5014 := (<= #5013 0::Int) -#5026 := (+ #4705 #5012) -#5027 := (+ #2078 #5026) -#5028 := (= #5027 0::Int) -#5050 := (<= #5027 0::Int) -#5236 := (<= #5232 0::Int) -#5769 := (or #5724 #5236) -#5770 := [th-lemma arith triangle-eq]: #5769 -#5771 := [unit-resolution #5770 #5723]: #5236 -#4887 := (<= #4792 0::Int) -#4906 := (or #4782 #4774) -#4908 := [def-axiom]: #4906 -#5772 := [unit-resolution #4908 #5767]: #4774 -#5773 := (or #4777 #4887) -#5774 := [th-lemma arith triangle-eq]: #5773 -#5775 := [unit-resolution #5774 #5772]: #4887 -#4988 := (<= #4987 0::Int) -#5418 := (or #5417 #4988) -#5419 := [th-lemma arith triangle-eq]: #5418 -#5776 := [unit-resolution #5419 #5753]: #4988 -#5360 := (not #5236) -#5359 := (not #4887) -#5358 := (not #4988) -#5361 := (or #5050 #5358 #5359 #5360) -#5352 := [hypothesis]: #5236 -#5353 := [hypothesis]: #4887 -#5354 := [hypothesis]: #4988 -#5355 := (not #5050) -#5356 := [hypothesis]: #5355 -#5357 := [th-lemma arith farkas -1 1 1 1 #5356 #5354 #5353 #5352]: false -#5362 := [lemma #5357]: #5361 -#5777 := [unit-resolution #5362 #5776 #5775 #5771]: #5050 -#5051 := (>= #5027 0::Int) -#4888 := (>= #4792 0::Int) -#5778 := (or #4777 #4888) -#5779 := [th-lemma arith triangle-eq]: #5778 -#5780 := [unit-resolution #5779 #5772]: #4888 -#5760 := (not #5237) -#5400 := (not #4888) -#5761 := (or #5051 #4995 #5400 #5760) -#5756 := [hypothesis]: #5237 -#5396 := [hypothesis]: #4888 -#5757 := (not #5051) -#5758 := [hypothesis]: #5757 -#5759 := [th-lemma arith farkas -1 1 1 1 #5758 #4992 #5396 #5756]: false -#5762 := [lemma #5759]: #5761 -#5781 := [unit-resolution #5762 #5754 #5780 #5739]: #5051 -#5782 := (or #5028 #5355 #5757) -#5783 := [th-lemma arith triangle-eq]: #5782 -#5784 := [unit-resolution #5783 #5781 #5777]: #5028 -#5033 := (not #5028) -#5036 := (or #5014 #5033) -#4162 := (or #4335 #4327) -#3822 := [def-axiom]: #4162 -#5785 := [unit-resolution #3822 #5750]: #4327 -#5039 := (or #4332 #5014 #5033) -#4998 := (+ #2079 #4710) -#5000 := (+ #4999 #4998) -#5001 := (= #5000 0::Int) -#5002 := (not #5001) -#5003 := (+ #4999 #2079) -#5004 := (>= #5003 0::Int) -#5005 := (or #5004 #5002) -#5040 := (or #4332 #5005) -#5047 := (iff #5040 #5039) -#5042 := (or #4332 #5036) -#5045 := (iff #5042 #5039) -#5046 := [rewrite]: #5045 -#5043 := (iff #5040 #5042) -#5037 := (iff #5005 #5036) -#5034 := (iff #5002 #5033) -#5031 := (iff #5001 #5028) -#5019 := (+ #4710 #4999) -#5020 := (+ #2079 #5019) -#5023 := (= #5020 0::Int) -#5029 := (iff #5023 #5028) -#5030 := [rewrite]: #5029 -#5024 := (iff #5001 #5023) -#5021 := (= #5000 #5020) -#5022 := [rewrite]: #5021 -#5025 := [monotonicity #5022]: #5024 -#5032 := [trans #5025 #5030]: #5031 -#5035 := [monotonicity #5032]: #5034 -#5017 := (iff #5004 #5014) -#5006 := (+ #2079 #4999) -#5009 := (>= #5006 0::Int) -#5015 := (iff #5009 #5014) -#5016 := [rewrite]: #5015 -#5010 := (iff #5004 #5009) -#5007 := (= #5003 #5006) -#5008 := [rewrite]: #5007 -#5011 := [monotonicity #5008]: #5010 -#5018 := [trans #5011 #5016]: #5017 -#5038 := [monotonicity #5018 #5035]: #5037 -#5044 := [monotonicity #5038]: #5043 -#5048 := [trans #5044 #5046]: #5047 -#5041 := [quant-inst #4723]: #5040 -#5049 := [mp #5041 #5048]: #5039 -#5786 := [unit-resolution #5049 #5785]: #5036 -#5787 := [unit-resolution #5786 #5784]: #5014 -#5788 := [th-lemma arith farkas 1 -1 1 1 #5754 #5787 #5768 #5739]: false -#5790 := [lemma #5788]: #5789 -#6509 := [unit-resolution #5790 #6508]: #4539 -#4045 := (or #4536 #4397) -#4040 := [def-axiom]: #4045 -#6510 := [unit-resolution #4040 #6509]: #4397 -#9500 := (or #4402 #7540 #7642) -#7593 := (+ #1454 #7592) -#7594 := (+ #7537 #7593) -#7595 := (<= #7594 0::Int) -#7636 := (or #7597 #7595) -#7637 := (not #7636) -#7538 := (= #7537 #2275) -#7638 := (or #7538 #7637) -#9501 := (or #4402 #7638) -#9508 := (iff #9501 #9500) -#9503 := (or #4402 #7645) -#9506 := (iff #9503 #9500) -#9507 := [rewrite]: #9506 -#9504 := (iff #9501 #9503) -#7646 := (iff #7638 #7645) -#7643 := (iff #7637 #7642) -#7640 := (iff #7636 #7639) -#7611 := (iff #7595 #7608) -#7599 := (+ #7537 #7592) -#7600 := (+ #1454 #7599) -#7603 := (<= #7600 0::Int) -#7609 := (iff #7603 #7608) -#7610 := [rewrite]: #7609 -#7604 := (iff #7595 #7603) -#7601 := (= #7594 #7600) -#7602 := [rewrite]: #7601 -#7605 := [monotonicity #7602]: #7604 -#7612 := [trans #7605 #7610]: #7611 -#7641 := [monotonicity #7612]: #7640 -#7644 := [monotonicity #7641]: #7643 -#7541 := (iff #7538 #7540) -#7542 := [rewrite]: #7541 -#7647 := [monotonicity #7542 #7644]: #7646 -#9505 := [monotonicity #7647]: #9504 -#9509 := [trans #9505 #9507]: #9508 -#9502 := [quant-inst #2274]: #9501 -#9510 := [mp #9502 #9509]: #9500 -#10078 := [unit-resolution #9510 #6510]: #7645 -#10079 := [unit-resolution #10078 #10077]: #7642 -#9512 := (or #7639 #9511) -#9513 := [def-axiom]: #9512 -#10080 := [unit-resolution #9513 #10079]: #9511 -#9514 := (not #7608) -#9515 := (or #7639 #9514) -#9516 := [def-axiom]: #9515 -#10081 := [unit-resolution #9516 #10079]: #9514 -#7620 := (or #7597 #7608 #7617) -#4046 := (or #4536 #4405) -#4019 := [def-axiom]: #4046 -#6514 := [unit-resolution #4019 #6509]: #4405 -#9487 := (or #4410 #7597 #7608 #7617) -#7589 := (+ #7588 #7562) -#7590 := (+ #175 #7589) -#7591 := (= #7590 0::Int) -#7598 := (or #7597 #7595 #7591) -#9488 := (or #4410 #7598) -#9495 := (iff #9488 #9487) -#9490 := (or #4410 #7620) -#9493 := (iff #9490 #9487) -#9494 := [rewrite]: #9493 -#9491 := (iff #9488 #9490) -#7621 := (iff #7598 #7620) -#7618 := (iff #7591 #7617) -#7615 := (= #7590 #7614) -#7616 := [rewrite]: #7615 -#7619 := [monotonicity #7616]: #7618 -#7622 := [monotonicity #7612 #7619]: #7621 -#9492 := [monotonicity #7622]: #9491 -#9496 := [trans #9492 #9494]: #9495 -#9489 := [quant-inst #2274]: #9488 -#9497 := [mp #9489 #9496]: #9487 -#10082 := [unit-resolution #9497 #6514]: #7620 -#10083 := [unit-resolution #10082 #10081 #10080]: #7617 -#10084 := (not #7617) -#10085 := (or #10084 #9498) -#10086 := [th-lemma arith triangle-eq]: #10085 -#10087 := [unit-resolution #10086 #10083]: #9498 -#10051 := (>= #9990 0::Int) -#10026 := (<= #9990 0::Int) -#10027 := (not #10026) -#9950 := (= ?v0!15 #7212) -#9969 := (not #9950) -#7669 := (f3 f16 ?v0!15) -#7670 := (= f1 #7669) -#5892 := (f3 #774 f23) -#5893 := (= f1 #5892) -#9953 := (ite #9950 #5893 #7670) -#9968 := (not #9953) -#8443 := (f4 f5 f16 #7212 #5892) -#9947 := (f3 #8443 ?v0!15) -#9948 := (= f1 #9947) -#9956 := (iff #9948 #9953) -#11 := (:var 1 S1) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#4172 := (pattern #14) -#18 := (f3 #9 #13) -#302 := (= f1 #18) -#299 := (= f1 #11) -#296 := (= #10 #13) -#305 := (ite #296 #299 #302) -#293 := (= f1 #14) -#308 := (iff #293 #305) -#4173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4172) #308) -#311 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #308) -#4176 := (iff #311 #4173) -#4174 := (iff #308 #308) -#4175 := [refl]: #4174 -#4177 := [quant-intro #4175]: #4176 -#1869 := (~ #311 #311) -#1867 := (~ #308 #308) -#1868 := [refl]: #1867 -#1870 := [nnf-pos #1868]: #1869 -#19 := (= #18 f1) -#17 := (= #11 f1) -#16 := (= #13 #10) -#20 := (ite #16 #17 #19) -#15 := (= #14 f1) -#21 := (iff #15 #20) -#22 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #21) -#312 := (iff #22 #311) -#309 := (iff #21 #308) -#306 := (iff #20 #305) -#303 := (iff #19 #302) -#304 := [rewrite]: #303 -#300 := (iff #17 #299) -#301 := [rewrite]: #300 -#297 := (iff #16 #296) -#298 := [rewrite]: #297 -#307 := [monotonicity #298 #301 #304]: #306 -#294 := (iff #15 #293) -#295 := [rewrite]: #294 -#310 := [monotonicity #295 #307]: #309 -#313 := [quant-intro #310]: #312 -#292 := [asserted]: #22 -#316 := [mp #292 #313]: #311 -#1841 := [mp~ #316 #1870]: #311 -#4178 := [mp #1841 #4177]: #4173 -#6291 := (not #4173) -#9959 := (or #6291 #9956) -#9945 := (= #7212 ?v0!15) -#9946 := (ite #9945 #5893 #7670) -#9949 := (iff #9948 #9946) -#9960 := (or #6291 #9949) -#9962 := (iff #9960 #9959) -#9964 := (iff #9959 #9959) -#9965 := [rewrite]: #9964 -#9957 := (iff #9949 #9956) -#9954 := (iff #9946 #9953) -#9951 := (iff #9945 #9950) -#9952 := [rewrite]: #9951 -#9955 := [monotonicity #9952]: #9954 -#9958 := [monotonicity #9955]: #9957 -#9963 := [monotonicity #9958]: #9962 -#9966 := [trans #9963 #9965]: #9962 -#9961 := [quant-inst #105 #7212 #5892 #2274]: #9960 -#9967 := [mp #9961 #9966]: #9959 -#10089 := [unit-resolution #9967 #4178]: #9956 -#9982 := (not #9948) -#7534 := (f3 f24 ?v0!15) -#7535 := (= f1 #7534) -#7536 := (not #7535) -#10098 := (iff #7536 #9982) -#10096 := (iff #7535 #9948) -#10094 := (iff #9948 #7535) -#10092 := (= #9947 #7534) -#9286 := (= #8443 f24) -#7005 := (= #774 f24) -#4054 := (or #4536 #777) -#4049 := [def-axiom]: #4054 -#6999 := [unit-resolution #4049 #6509]: #777 -#7006 := [symm #6999]: #7005 -#9284 := (= #8443 #774) -#7001 := (= #5892 f1) -#25 := (:var 0 S1) -#23 := (:var 2 S2) -#26 := (f4 f5 #23 #24 #25) -#4179 := (pattern #26) -#319 := (= f1 #25) -#27 := (f3 #26 #24) -#315 := (= f1 #27) -#322 := (iff #315 #319) -#4180 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4179) #322) -#325 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #322) -#4183 := (iff #325 #4180) -#4181 := (iff #322 #322) -#4182 := [refl]: #4181 -#4184 := [quant-intro #4182]: #4183 -#1843 := (~ #325 #325) -#1842 := (~ #322 #322) -#1871 := [refl]: #1842 -#1844 := [nnf-pos #1871]: #1843 -#29 := (= #25 f1) -#28 := (= #27 f1) -#30 := (iff #28 #29) -#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #30) -#326 := (iff #31 #325) -#323 := (iff #30 #322) -#320 := (iff #29 #319) -#321 := [rewrite]: #320 -#317 := (iff #28 #315) -#318 := [rewrite]: #317 -#324 := [monotonicity #318 #321]: #323 -#327 := [quant-intro #324]: #326 -#314 := [asserted]: #31 -#330 := [mp #314 #327]: #325 -#1872 := [mp~ #330 #1844]: #325 -#4185 := [mp #1872 #4184]: #4180 -#5904 := (not #4180) -#5905 := (or #5904 #5893) -#5891 := (= f1 f1) -#5894 := (iff #5893 #5891) -#5906 := (or #5904 #5894) -#5908 := (iff #5906 #5905) -#5910 := (iff #5905 #5905) -#5911 := [rewrite]: #5910 -#5902 := (iff #5894 #5893) -#5897 := (iff #5893 true) -#5900 := (iff #5897 #5893) -#5901 := [rewrite]: #5900 -#5898 := (iff #5894 #5897) -#5895 := (iff #5891 true) -#5896 := [rewrite]: #5895 -#5899 := [monotonicity #5896]: #5898 -#5903 := [trans #5899 #5901]: #5902 -#5909 := [monotonicity #5903]: #5908 -#5912 := [trans #5909 #5911]: #5908 -#5907 := [quant-inst #105 #171 #4]: #5906 -#5913 := [mp #5907 #5912]: #5905 -#7000 := [unit-resolution #5913 #4185]: #5893 -#7002 := [symm #7000]: #7001 -#9285 := [monotonicity #7791 #7002]: #9284 -#9287 := [trans #9285 #7006]: #9286 -#10093 := [monotonicity #9287]: #10092 -#10095 := [monotonicity #10093]: #10094 -#10097 := [symm #10095]: #10096 -#10099 := [monotonicity #10097]: #10098 -#7546 := (or #7536 #7540) -#4020 := (or #4536 #4530) -#4021 := [def-axiom]: #4020 -#7097 := [unit-resolution #4021 #6509]: #4530 -#6312 := (f6 f23 ?v0!13) -#6313 := (f10 #6312) -#6338 := (+ #2233 #6313) -#6339 := (+ #175 #6338) -#6360 := (>= #6339 0::Int) -#6342 := (= #6339 0::Int) -#6317 := (* -1::Int #6313) -#6321 := (+ f9 #6317) -#6322 := (<= #6321 0::Int) -#6389 := (not #6322) -#6331 := (+ #2849 #6313) -#6332 := (+ #175 #6331) -#6333 := (>= #6332 0::Int) -#6368 := (or #6322 #6333) -#6371 := (not #6368) -#6365 := (= #2232 #2234) -#6490 := (not #6365) -#6489 := [hypothesis]: #2856 -#6493 := (or #6490 #2851) -#6494 := [th-lemma arith triangle-eq]: #6493 -#6495 := [unit-resolution #6494 #6489]: #6490 -#6377 := (or #4402 #6365 #6371) -#6318 := (+ #1454 #6317) -#6319 := (+ #2234 #6318) -#6320 := (<= #6319 0::Int) -#6361 := (or #6322 #6320) -#6362 := (not #6361) -#6363 := (= #2234 #2232) -#6364 := (or #6363 #6362) -#6378 := (or #4402 #6364) -#6385 := (iff #6378 #6377) -#6374 := (or #6365 #6371) -#6380 := (or #4402 #6374) -#6383 := (iff #6380 #6377) -#6384 := [rewrite]: #6383 -#6381 := (iff #6378 #6380) -#6375 := (iff #6364 #6374) -#6372 := (iff #6362 #6371) -#6369 := (iff #6361 #6368) -#6336 := (iff #6320 #6333) -#6324 := (+ #2234 #6317) -#6325 := (+ #1454 #6324) -#6328 := (<= #6325 0::Int) -#6334 := (iff #6328 #6333) -#6335 := [rewrite]: #6334 -#6329 := (iff #6320 #6328) -#6326 := (= #6319 #6325) -#6327 := [rewrite]: #6326 -#6330 := [monotonicity #6327]: #6329 -#6337 := [trans #6330 #6335]: #6336 -#6370 := [monotonicity #6337]: #6369 -#6373 := [monotonicity #6370]: #6372 -#6366 := (iff #6363 #6365) -#6367 := [rewrite]: #6366 -#6376 := [monotonicity #6367 #6373]: #6375 -#6382 := [monotonicity #6376]: #6381 -#6386 := [trans #6382 #6384]: #6385 -#6379 := [quant-inst #2231]: #6378 -#6387 := [mp #6379 #6386]: #6377 -#6511 := [unit-resolution #6387 #6510 #6495]: #6371 -#6390 := (or #6368 #6389) -#6391 := [def-axiom]: #6390 -#6512 := [unit-resolution #6391 #6511]: #6389 -#6392 := (not #6333) -#6393 := (or #6368 #6392) -#6394 := [def-axiom]: #6393 -#6513 := [unit-resolution #6394 #6511]: #6392 -#6345 := (or #6322 #6333 #6342) -#6348 := (or #4410 #6322 #6333 #6342) -#6314 := (+ #6313 #2233) -#6315 := (+ #175 #6314) -#6316 := (= #6315 0::Int) -#6323 := (or #6322 #6320 #6316) -#6349 := (or #4410 #6323) -#6356 := (iff #6349 #6348) -#6351 := (or #4410 #6345) -#6354 := (iff #6351 #6348) -#6355 := [rewrite]: #6354 -#6352 := (iff #6349 #6351) -#6346 := (iff #6323 #6345) -#6343 := (iff #6316 #6342) -#6340 := (= #6315 #6339) -#6341 := [rewrite]: #6340 -#6344 := [monotonicity #6341]: #6343 -#6347 := [monotonicity #6337 #6344]: #6346 -#6353 := [monotonicity #6347]: #6352 -#6357 := [trans #6353 #6355]: #6356 -#6350 := [quant-inst #2231]: #6349 -#6358 := [mp #6350 #6357]: #6348 -#6515 := [unit-resolution #6358 #6514]: #6345 -#6516 := [unit-resolution #6515 #6513 #6512]: #6342 -#6517 := (not #6342) -#6518 := (or #6517 #6360) -#6519 := [th-lemma arith triangle-eq]: #6518 -#6520 := [unit-resolution #6519 #6516]: #6360 -#6388 := (>= #2850 0::Int) -#6521 := (or #6388 #2851) -#6522 := [th-lemma arith farkas 1 1]: #6521 -#6523 := [unit-resolution #6522 #6489]: #6388 -#6524 := [th-lemma arith farkas 1 -1 1 #6523 #6513 #6520]: false -#6525 := [lemma #6524]: #2851 -#4050 := (or #4533 #2856 #4527) -#4051 := [def-axiom]: #4050 -#7098 := [unit-resolution #4051 #6525 #7097]: #4527 -#4065 := (or #4524 #4518) -#4066 := [def-axiom]: #4065 -#7099 := [unit-resolution #4066 #7098]: #4518 -#6880 := (= #175 #2254) -#6697 := (= f23 ?v0!14) -#6527 := (f3 f16 ?v0!14) -#6528 := (= f1 #6527) -#6698 := (ite #6697 #5893 #6528) -#6270 := (f4 f5 f16 f23 #5892) -#6701 := (f3 #6270 ?v0!14) -#6702 := (= f1 #6701) -#6704 := (iff #6698 #6702) -#6707 := (or #6291 #6704) -#6703 := (iff #6702 #6698) -#6708 := (or #6291 #6703) -#6710 := (iff #6708 #6707) -#6712 := (iff #6707 #6707) -#6713 := [rewrite]: #6712 -#6705 := (iff #6703 #6704) -#6706 := [rewrite]: #6705 -#6711 := [monotonicity #6706]: #6710 -#6714 := [trans #6711 #6713]: #6710 -#6709 := [quant-inst #105 #171 #5892 #2249]: #6708 -#6715 := [mp #6709 #6714]: #6707 -#6997 := [unit-resolution #6715 #4178]: #6704 -#7013 := (= #2250 #6701) -#7009 := (= #6701 #2250) -#7007 := (= #6270 f24) -#7003 := (= #6270 #774) -#7004 := [monotonicity #7002]: #7003 -#7008 := [trans #7004 #7006]: #7007 -#7010 := [monotonicity #7008]: #7009 -#7014 := [symm #7010]: #7013 -#6995 := [hypothesis]: #2870 -#4128 := (or #2865 #2251) -#4129 := [def-axiom]: #4128 -#6998 := [unit-resolution #4129 #6995]: #2251 -#7015 := [trans #6998 #7014]: #6702 -#6728 := (not #6702) -#6727 := (not #6704) -#6729 := (or #6727 #6698 #6728) -#6730 := [def-axiom]: #6729 -#7016 := [unit-resolution #6730 #7015 #6997]: #6698 -#6556 := (f6 f23 ?v0!14) -#6557 := (f10 #6556) -#6487 := (* -1::Int #2254) -#6574 := (+ #6487 #6557) -#6575 := (+ #175 #6574) -#6576 := (>= #6575 0::Int) -#6604 := (not #6576) -#6558 := (* -1::Int #6557) -#6562 := (+ f9 #6558) -#6563 := (<= #6562 0::Int) -#6581 := (or #6563 #6576) -#6584 := (not #6581) -#4124 := (not #2859) -#4125 := (or #2865 #4124) -#4130 := [def-axiom]: #4125 -#6996 := [unit-resolution #4130 #6995]: #4124 -#6590 := (or #4402 #2859 #6584) -#6559 := (+ #1454 #6558) -#6560 := (+ #2254 #6559) -#6561 := (<= #6560 0::Int) -#6564 := (or #6563 #6561) -#6565 := (not #6564) -#6566 := (or #2255 #6565) -#6591 := (or #4402 #6566) -#6598 := (iff #6591 #6590) -#6587 := (or #2859 #6584) -#6593 := (or #4402 #6587) -#6596 := (iff #6593 #6590) -#6597 := [rewrite]: #6596 -#6594 := (iff #6591 #6593) -#6588 := (iff #6566 #6587) -#6585 := (iff #6565 #6584) -#6582 := (iff #6564 #6581) -#6579 := (iff #6561 #6576) -#6567 := (+ #2254 #6558) -#6568 := (+ #1454 #6567) -#6571 := (<= #6568 0::Int) -#6577 := (iff #6571 #6576) -#6578 := [rewrite]: #6577 -#6572 := (iff #6561 #6571) -#6569 := (= #6560 #6568) -#6570 := [rewrite]: #6569 -#6573 := [monotonicity #6570]: #6572 -#6580 := [trans #6573 #6578]: #6579 -#6583 := [monotonicity #6580]: #6582 -#6586 := [monotonicity #6583]: #6585 -#6589 := [monotonicity #2861 #6586]: #6588 -#6595 := [monotonicity #6589]: #6594 -#6599 := [trans #6595 #6597]: #6598 -#6592 := [quant-inst #2249]: #6591 -#6600 := [mp #6592 #6599]: #6590 -#7017 := [unit-resolution #6600 #6510 #6996]: #6584 -#6605 := (or #6581 #6604) -#6606 := [def-axiom]: #6605 -#7018 := [unit-resolution #6606 #7017]: #6604 -#6716 := (not #6698) -#6942 := (or #6697 #6576 #6716) -#6823 := (f7 #6556) -#6833 := (f14 f15 #6823) -#6848 := (* -1::Int #6833) -#6888 := (+ #175 #6848) -#6890 := (>= #6888 0::Int) -#6887 := (= #175 #6833) -#6894 := (= #6833 #175) -#6892 := (= #6823 f23) -#6824 := (= f23 #6823) -#6831 := (or #6830 #6824) -#6832 := [quant-inst #171 #2249]: #6831 -#6891 := [unit-resolution #6832 #4206]: #6824 -#6893 := [symm #6891]: #6892 -#6895 := [monotonicity #6893]: #6894 -#6896 := [symm #6895]: #6887 -#6897 := (not #6887) -#6898 := (or #6897 #6890) -#6899 := [th-lemma arith triangle-eq]: #6898 -#6900 := [unit-resolution #6899 #6896]: #6890 -#6901 := [hypothesis]: #6604 -#6820 := (>= #6557 0::Int) -#6774 := (<= #6557 0::Int) -#6775 := (not #6774) -#6717 := (not #6697) -#6902 := [hypothesis]: #6717 -#6780 := (or #6697 #6775) -#49 := (f10 #38) -#408 := (<= #49 0::Int) -#409 := (not #408) -#355 := (= #13 #24) -#415 := (or #355 #409) -#4213 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #415) -#420 := (forall (vars (?v0 S3) (?v1 S3)) #415) -#4216 := (iff #420 #4213) -#4214 := (iff #415 #415) -#4215 := [refl]: #4214 -#4217 := [quant-intro #4215]: #4216 -#1855 := (~ #420 #420) -#1854 := (~ #415 #415) -#1884 := [refl]: #1854 -#1856 := [nnf-pos #1884]: #1855 -#54 := (< 0::Int #49) -#48 := (= #24 #13) -#53 := (not #48) -#55 := (implies #53 #54) -#56 := (forall (vars (?v0 S3) (?v1 S3)) #55) -#423 := (iff #56 #420) -#400 := (or #54 #355) -#405 := (forall (vars (?v0 S3) (?v1 S3)) #400) -#421 := (iff #405 #420) -#418 := (iff #400 #415) -#412 := (or #409 #355) -#416 := (iff #412 #415) -#417 := [rewrite]: #416 -#413 := (iff #400 #412) -#410 := (iff #54 #409) -#411 := [rewrite]: #410 -#414 := [monotonicity #411]: #413 -#419 := [trans #414 #417]: #418 -#422 := [quant-intro #419]: #421 -#406 := (iff #56 #405) -#403 := (iff #55 #400) -#369 := (not #355) -#397 := (implies #369 #54) -#401 := (iff #397 #400) -#402 := [rewrite]: #401 -#398 := (iff #55 #397) -#395 := (iff #53 #369) -#361 := (iff #48 #355) -#362 := [rewrite]: #361 -#396 := [monotonicity #362]: #395 -#399 := [monotonicity #396]: #398 -#404 := [trans #399 #402]: #403 -#407 := [quant-intro #404]: #406 -#424 := [trans #407 #422]: #423 -#394 := [asserted]: #56 -#425 := [mp #394 #424]: #420 -#1885 := [mp~ #425 #1856]: #420 -#4218 := [mp #1885 #4217]: #4213 -#6783 := (not #4213) -#6784 := (or #6783 #6697 #6775) -#6776 := (= ?v0!14 f23) -#6777 := (or #6776 #6775) -#6785 := (or #6783 #6777) -#6792 := (iff #6785 #6784) -#6787 := (or #6783 #6780) -#6790 := (iff #6787 #6784) -#6791 := [rewrite]: #6790 -#6788 := (iff #6785 #6787) -#6781 := (iff #6777 #6780) -#6778 := (iff #6776 #6697) -#6779 := [rewrite]: #6778 -#6782 := [monotonicity #6779]: #6781 -#6789 := [monotonicity #6782]: #6788 -#6793 := [trans #6789 #6791]: #6792 -#6786 := [quant-inst #171 #2249]: #6785 -#6794 := [mp #6786 #6793]: #6784 -#6903 := [unit-resolution #6794 #4218]: #6780 -#6904 := [unit-resolution #6903 #6902]: #6775 -#6905 := (or #6820 #6774) -#6906 := [th-lemma arith farkas 1 1]: #6905 -#6907 := [unit-resolution #6906 #6904]: #6820 -#6821 := (f8 #6556) -#6828 := (f14 f15 #6821) -#6829 := (* -1::Int #6828) -#6878 := (+ #2254 #6829) -#6885 := (<= #6878 0::Int) -#6877 := (= #2254 #6828) -#6911 := (= #6828 #2254) -#6909 := (= #6821 ?v0!14) -#6822 := (= ?v0!14 #6821) -#6826 := (or #6825 #6822) -#6827 := [quant-inst #171 #2249]: #6826 -#6908 := [unit-resolution #6827 #4200]: #6822 -#6910 := [symm #6908]: #6909 -#6912 := [monotonicity #6910]: #6911 -#6913 := [symm #6912]: #6877 -#6914 := (not #6877) -#6915 := (or #6914 #6885) -#6916 := [th-lemma arith triangle-eq]: #6915 -#6917 := [unit-resolution #6916 #6913]: #6885 -#6849 := (+ #6828 #6848) -#6850 := (<= #6849 0::Int) -#6836 := (f3 f16 #6821) -#6837 := (= f1 #6836) -#6924 := (= #6527 #6836) -#6920 := (= #6836 #6527) -#6921 := [monotonicity #6910]: #6920 -#6925 := [symm #6921]: #6924 -#6918 := [hypothesis]: #6698 -#6720 := (or #6716 #6697 #6528) -#6721 := [def-axiom]: #6720 -#6919 := [unit-resolution #6721 #6902 #6918]: #6528 -#6926 := [trans #6919 #6925]: #6837 -#6839 := (f3 f16 #6823) -#6840 := (= f1 #6839) -#6934 := (not #6840) -#6935 := (iff #758 #6934) -#6932 := (iff #755 #6840) -#6930 := (iff #6840 #755) -#6928 := (= #6839 #172) -#6929 := [monotonicity #6893]: #6928 -#6931 := [monotonicity #6929]: #6930 -#6933 := [symm #6931]: #6932 -#6936 := [monotonicity #6933]: #6935 -#4052 := (or #4536 #758) -#4053 := [def-axiom]: #4052 -#6927 := [unit-resolution #4053 #6509]: #758 -#6937 := [mp #6927 #6936]: #6934 -#6838 := (not #6837) -#6858 := (or #6838 #6840 #6850) -#3962 := (or #4548 #4292) -#4017 := [def-axiom]: #3962 -#6938 := [unit-resolution #4017 #6508]: #4292 -#6863 := (or #4297 #6838 #6840 #6850) -#6834 := (+ #6833 #6829) -#6835 := (>= #6834 0::Int) -#6841 := (or #6840 #6838 #6835) -#6864 := (or #4297 #6841) -#6871 := (iff #6864 #6863) -#6866 := (or #4297 #6858) -#6869 := (iff #6866 #6863) -#6870 := [rewrite]: #6869 -#6867 := (iff #6864 #6866) -#6861 := (iff #6841 #6858) -#6855 := (or #6840 #6838 #6850) -#6859 := (iff #6855 #6858) -#6860 := [rewrite]: #6859 -#6856 := (iff #6841 #6855) -#6853 := (iff #6835 #6850) -#6842 := (+ #6829 #6833) -#6845 := (>= #6842 0::Int) -#6851 := (iff #6845 #6850) -#6852 := [rewrite]: #6851 -#6846 := (iff #6835 #6845) -#6843 := (= #6834 #6842) -#6844 := [rewrite]: #6843 -#6847 := [monotonicity #6844]: #6846 -#6854 := [trans #6847 #6852]: #6853 -#6857 := [monotonicity #6854]: #6856 -#6862 := [trans #6857 #6860]: #6861 -#6868 := [monotonicity #6862]: #6867 -#6872 := [trans #6868 #6870]: #6871 -#6865 := [quant-inst #6821 #6823]: #6864 -#6873 := [mp #6865 #6872]: #6863 -#6939 := [unit-resolution #6873 #6938]: #6858 -#6940 := [unit-resolution #6939 #6937 #6926]: #6850 -#6941 := [th-lemma arith farkas 1 1 1 -1 1 #6940 #6917 #6907 #6901 #6900]: false -#6943 := [lemma #6941]: #6942 -#7019 := [unit-resolution #6943 #7018 #7016]: #6697 -#7043 := [monotonicity #7019]: #6880 -#7041 := (= #2253 #175) -#7039 := (= #175 #2253) -#6796 := (= #6557 0::Int) -#6803 := (or #6717 #6796) -#50 := (= #49 0::Int) -#383 := (or #50 #369) -#4207 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4194) #383) -#388 := (forall (vars (?v0 S3) (?v1 S3)) #383) -#4210 := (iff #388 #4207) -#4208 := (iff #383 #383) -#4209 := [refl]: #4208 -#4211 := [quant-intro #4209]: #4210 -#1851 := (~ #388 #388) -#1882 := (~ #383 #383) -#1883 := [refl]: #1882 -#1852 := [nnf-pos #1883]: #1851 -#51 := (implies #48 #50) -#52 := (forall (vars (?v0 S3) (?v1 S3)) #51) -#391 := (iff #52 #388) -#363 := (= 0::Int #49) -#370 := (or #369 #363) -#375 := (forall (vars (?v0 S3) (?v1 S3)) #370) -#389 := (iff #375 #388) -#386 := (iff #370 #383) -#380 := (or #369 #50) -#384 := (iff #380 #383) -#385 := [rewrite]: #384 -#381 := (iff #370 #380) -#378 := (iff #363 #50) -#379 := [rewrite]: #378 -#382 := [monotonicity #379]: #381 -#387 := [trans #382 #385]: #386 -#390 := [quant-intro #387]: #389 -#376 := (iff #52 #375) -#373 := (iff #51 #370) -#366 := (implies #355 #363) -#371 := (iff #366 #370) -#372 := [rewrite]: #371 -#367 := (iff #51 #366) -#364 := (iff #50 #363) -#365 := [rewrite]: #364 -#368 := [monotonicity #362 #365]: #367 -#374 := [trans #368 #372]: #373 -#377 := [quant-intro #374]: #376 -#392 := [trans #377 #390]: #391 -#353 := [asserted]: #52 -#393 := [mp #353 #392]: #388 -#1853 := [mp~ #393 #1852]: #388 -#4212 := [mp #1853 #4211]: #4207 -#6808 := (not #4207) -#6809 := (or #6808 #6717 #6796) -#6795 := (not #6776) -#6797 := (or #6796 #6795) -#6810 := (or #6808 #6797) -#6817 := (iff #6810 #6809) -#6812 := (or #6808 #6803) -#6815 := (iff #6812 #6809) -#6816 := [rewrite]: #6815 -#6813 := (iff #6810 #6812) -#6806 := (iff #6797 #6803) -#6800 := (or #6796 #6717) -#6804 := (iff #6800 #6803) -#6805 := [rewrite]: #6804 -#6801 := (iff #6797 #6800) -#6798 := (iff #6795 #6717) -#6799 := [monotonicity #6779]: #6798 -#6802 := [monotonicity #6799]: #6801 -#6807 := [trans #6802 #6805]: #6806 -#6814 := [monotonicity #6807]: #6813 -#6818 := [trans #6814 #6816]: #6817 -#6811 := [quant-inst #171 #2249]: #6810 -#6819 := [mp #6811 #6818]: #6809 -#7020 := [unit-resolution #6819 #4212]: #6803 -#7021 := [unit-resolution #7020 #7019]: #6796 -#7022 := (not #6796) -#7023 := (or #7022 #6774) -#7024 := [th-lemma arith triangle-eq]: #7023 -#7025 := [unit-resolution #7024 #7021]: #6774 -#7026 := (or #7022 #6820) -#7027 := [th-lemma arith triangle-eq]: #7026 -#7028 := [unit-resolution #7027 #7021]: #6820 -#6425 := (* -1::Int #2253) -#6613 := (+ #6425 #6557) -#6614 := (+ #175 #6613) -#6634 := (<= #6614 0::Int) -#6617 := (= #6614 0::Int) -#6601 := (not #6563) -#6602 := (or #6581 #6601) -#6603 := [def-axiom]: #6602 -#7029 := [unit-resolution #6603 #7017]: #6601 -#6620 := (or #6563 #6576 #6617) -#6623 := (or #4410 #6563 #6576 #6617) -#6609 := (+ #6557 #6425) -#6610 := (+ #175 #6609) -#6611 := (= #6610 0::Int) -#6612 := (or #6563 #6561 #6611) -#6624 := (or #4410 #6612) -#6631 := (iff #6624 #6623) -#6626 := (or #4410 #6620) -#6629 := (iff #6626 #6623) -#6630 := [rewrite]: #6629 -#6627 := (iff #6624 #6626) -#6621 := (iff #6612 #6620) -#6618 := (iff #6611 #6617) -#6615 := (= #6610 #6614) -#6616 := [rewrite]: #6615 -#6619 := [monotonicity #6616]: #6618 -#6622 := [monotonicity #6580 #6619]: #6621 -#6628 := [monotonicity #6622]: #6627 -#6632 := [trans #6628 #6630]: #6631 -#6625 := [quant-inst #2249]: #6624 -#6633 := [mp #6625 #6632]: #6623 -#7030 := [unit-resolution #6633 #6514]: #6620 -#7031 := [unit-resolution #7030 #7018 #7029]: #6617 -#7032 := (not #6617) -#7033 := (or #7032 #6634) -#7034 := [th-lemma arith triangle-eq]: #7033 -#7035 := [unit-resolution #7034 #7031]: #6634 -#6635 := (>= #6614 0::Int) -#7036 := (or #7032 #6635) -#7037 := [th-lemma arith triangle-eq]: #7036 -#7038 := [unit-resolution #7037 #7031]: #6635 -#7040 := [th-lemma arith eq-propagate 1 1 -1 -1 #7038 #7035 #7028 #7025]: #7039 -#7042 := [symm #7040]: #7041 -#7044 := [trans #7042 #7043]: #2859 -#7045 := [unit-resolution #6996 #7044]: false -#7046 := [lemma #7045]: #2865 -#4061 := (or #4521 #2870 #4515) -#4062 := [def-axiom]: #4061 -#7100 := [unit-resolution #4062 #7046 #7099]: #4515 -#4071 := (or #4512 #4422) -#4073 := [def-axiom]: #4071 -#7101 := [unit-resolution #4073 #7100]: #4422 -#9467 := (or #4427 #7536 #7540) -#7539 := (or #7538 #7536) -#9468 := (or #4427 #7539) -#9475 := (iff #9468 #9467) -#9470 := (or #4427 #7546) -#9473 := (iff #9470 #9467) -#9474 := [rewrite]: #9473 -#9471 := (iff #9468 #9470) -#7549 := (iff #7539 #7546) -#7543 := (or #7540 #7536) -#7547 := (iff #7543 #7546) -#7548 := [rewrite]: #7547 -#7544 := (iff #7539 #7543) -#7545 := [monotonicity #7542]: #7544 -#7550 := [trans #7545 #7548]: #7549 -#9472 := [monotonicity #7550]: #9471 -#9476 := [trans #9472 #9474]: #9475 -#9469 := [quant-inst #2274]: #9468 -#9477 := [mp #9469 #9476]: #9467 -#10090 := [unit-resolution #9477 #7101]: #7546 -#10091 := [unit-resolution #10090 #10077]: #7536 -#10100 := [mp #10091 #10099]: #9982 -#9979 := (not #9956) -#9980 := (or #9979 #9948 #9968) -#9981 := [def-axiom]: #9980 -#10101 := [unit-resolution #9981 #10100 #10089]: #9968 -#10102 := (or #9953 #9969) -#6305 := (not #5893) -#9974 := (or #9953 #9969 #6305) -#9975 := [def-axiom]: #9974 -#10103 := [unit-resolution #9975 #7000]: #10102 -#10104 := [unit-resolution #10103 #10101]: #9969 -#10028 := (or #9950 #10027) -#10031 := (or #6783 #9950 #10027) -#10032 := (or #6783 #10028) -#10034 := (iff #10032 #10031) -#10035 := [rewrite]: #10034 -#10033 := [quant-inst #7212 #2274]: #10032 -#10036 := [mp #10033 #10035]: #10031 -#10105 := [unit-resolution #10036 #4218]: #10028 -#10106 := [unit-resolution #10105 #10104]: #10027 -#10107 := (or #10051 #10026) -#10108 := [th-lemma arith farkas 1 1]: #10107 -#10109 := [unit-resolution #10108 #10106]: #10051 -#10110 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10109 #10088 #10087 #10075 #10074 #10073 #10072]: false -#10112 := [lemma #10110]: #10111 -#9587 := [unit-resolution #10112 #10088 #10075 #10073]: #7540 -#9588 := (or #10076 #9582) -#9589 := [th-lemma arith triangle-eq]: #9588 -#9590 := [unit-resolution #9589 #9587]: #9582 -#9591 := [th-lemma arith farkas -1 1 1 #10088 #9590 #9581]: false -#9609 := [lemma #9591]: #9608 -#11953 := [unit-resolution #9609 #10088 #10075]: #7303 -#9480 := (or #7323 #8252) -#9478 := [def-axiom]: #9480 -#11954 := [unit-resolution #9478 #11953]: #7323 -#7326 := (not #7323) -#12704 := (or #7320 #7326) -#7316 := (+ f9 #6072) -#7317 := (<= #7316 0::Int) -#12698 := (not #7317) -#12701 := (or #12698 #6074) -#4037 := (or #4536 #1656) -#4038 := [def-axiom]: #4037 -#7831 := [unit-resolution #4038 #6509]: #1656 -#12699 := (or #12698 #1655 #6074) -#12700 := [th-lemma arith assign-bounds 1 1]: #12699 -#12702 := [unit-resolution #12700 #7831]: #12701 -#12703 := [unit-resolution #12702 #10075]: #12698 -#12666 := [unit-resolution #4018 #6508]: #4308 -#9212 := (or #4313 #7317 #7320 #7326) -#7314 := (or #7313 #7310 #7303) -#7315 := (not #7314) -#7319 := (or #7318 #7317 #7315) -#9449 := (or #4313 #7319) -#9462 := (iff #9449 #9212) -#7332 := (or #7317 #7320 #7326) -#9455 := (or #4313 #7332) -#9460 := (iff #9455 #9212) -#9461 := [rewrite]: #9460 -#9457 := (iff #9449 #9455) -#7335 := (iff #7319 #7332) -#7329 := (or #7320 #7317 #7326) -#7333 := (iff #7329 #7332) -#7334 := [rewrite]: #7333 -#7330 := (iff #7319 #7329) -#7327 := (iff #7315 #7326) -#7324 := (iff #7314 #7323) -#7325 := [rewrite]: #7324 -#7328 := [monotonicity #7325]: #7327 -#7321 := (iff #7318 #7320) -#7322 := [rewrite]: #7321 -#7331 := [monotonicity #7322 #7328]: #7330 -#7336 := [trans #7331 #7334]: #7335 -#9459 := [monotonicity #7336]: #9457 -#9463 := [trans #9459 #9461]: #9462 -#9454 := [quant-inst #6070]: #9449 -#9479 := [mp #9454 #9463]: #9212 -#12705 := [unit-resolution #9479 #12666 #12703]: #12704 -#11952 := [unit-resolution #12705 #11954]: #7320 -#11955 := [symm #11952]: #7318 -#9282 := (= #8218 #6070) -#9283 := [symm #9281]: #9282 -#11956 := [trans #9283 #11955]: #10698 -#11958 := [monotonicity #11956]: #11957 -#11959 := [symm #11958]: #10876 -#11945 := (not #10876) -#11960 := (or #11945 #10879) -#11961 := [th-lemma arith triangle-eq]: #11960 -#11962 := [unit-resolution #11961 #11959]: #10879 -#3918 := (>= #100 0::Int) -#7124 := [unit-resolution #4034 #6508]: #101 -#6990 := (or #1748 #3918) -#6991 := [th-lemma arith triangle-eq]: #6990 -#6992 := [unit-resolution #6991 #7124]: #3918 -#11982 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10109 #10088 #10087 #10075 #6992 #11962 #11951 #10072]: false -#11987 := [lemma #11982]: #11986 -#11110 := [unit-resolution #11987 #10088 #10075]: #7540 -#11964 := (not #9582) -#11918 := [hypothesis]: #11964 -#11919 := [hypothesis]: #7540 -#11920 := [unit-resolution #9589 #11919 #11918]: false -#11921 := [lemma #11920]: #9588 -#11111 := [unit-resolution #11921 #11110]: #9582 -#11114 := [th-lemma arith farkas -1 1 1 #10088 #11111 #9581]: false -#11113 := [lemma #11114]: #11115 -#23131 := [unit-resolution #11113 #10075]: #2276 -#4074 := (or #4512 #4506) -#4075 := [def-axiom]: #4074 -#12709 := [unit-resolution #4075 #7100]: #4506 -#5933 := (= #100 #204) -#12713 := (iff #5933 #205) -#12712 := [commutativity]: #1489 -#12710 := (iff #5933 #823) -#12711 := [monotonicity #7124]: #12710 -#12714 := [trans #12711 #12712]: #12713 -#5917 := (f6 f23 f11) -#5918 := (f10 #5917) -#7060 := (<= #5918 0::Int) -#7061 := (not #7060) -#6768 := (not #6089) -#3935 := (f3 f16 f11) -#3938 := (= f1 #3935) -#6719 := (ite #6089 #5893 #3938) -#6767 := (not #6719) -#6699 := (f3 #6270 f11) -#6700 := (= f1 #6699) -#6724 := (iff #6700 #6719) -#6731 := (or #6291 #6724) -#6684 := (ite #6087 #5893 #3938) -#6718 := (iff #6700 #6684) -#6732 := (or #6291 #6718) -#6734 := (iff #6732 #6731) -#6736 := (iff #6731 #6731) -#6764 := [rewrite]: #6736 -#6725 := (iff #6718 #6724) -#6722 := (iff #6684 #6719) -#6090 := (iff #6087 #6089) -#6091 := [rewrite]: #6090 -#6723 := [monotonicity #6091]: #6722 -#6726 := [monotonicity #6723]: #6725 -#6735 := [monotonicity #6726]: #6734 -#6765 := [trans #6735 #6764]: #6734 -#6733 := [quant-inst #105 #171 #5892 #57]: #6732 -#6766 := [mp #6733 #6765]: #6731 -#7092 := [unit-resolution #6766 #4178]: #6724 -#6984 := (not #6700) -#6359 := (f3 f24 f11) -#6477 := (= f1 #6359) -#6546 := (not #6477) -#7110 := (iff #6546 #6984) -#7108 := (iff #6477 #6700) -#7106 := (iff #6700 #6477) -#7104 := (= #6699 #6359) -#7105 := [monotonicity #7008]: #7104 -#7107 := [monotonicity #7105]: #7106 -#7109 := [symm #7107]: #7108 -#7111 := [monotonicity #7109]: #7110 -#7093 := (not #5933) -#7096 := [hypothesis]: #7093 -#6547 := (or #5933 #6546) -#6550 := (or #4427 #5933 #6546) -#6545 := (or #4427 #6547) -#6552 := (iff #6545 #6550) -#6553 := [rewrite]: #6552 -#6551 := [quant-inst #57]: #6545 -#6554 := [mp #6551 #6553]: #6550 -#7102 := [unit-resolution #6554 #7101]: #6547 -#7103 := [unit-resolution #7102 #7096]: #6546 -#7112 := [mp #7103 #7111]: #6984 -#6987 := (not #6724) -#6988 := (or #6987 #6700 #6767) -#6989 := [def-axiom]: #6988 -#7113 := [unit-resolution #6989 #7112 #7092]: #6767 -#7114 := (or #6719 #6768) -#6772 := (or #6719 #6768 #6305) -#6773 := [def-axiom]: #6772 -#7115 := [unit-resolution #6773 #7000]: #7114 -#7116 := [unit-resolution #7115 #7113]: #6768 -#7062 := (or #6089 #7061) -#7065 := (or #6783 #6089 #7061) -#7066 := (or #6783 #7062) -#7068 := (iff #7066 #7065) -#7069 := [rewrite]: #7068 -#7067 := [quant-inst #171 #57]: #7066 -#7070 := [mp #7067 #7069]: #7065 -#7117 := [unit-resolution #7070 #4218]: #7062 -#7118 := [unit-resolution #7117 #7116]: #7061 -#5925 := (* -1::Int #5918) -#5926 := (+ #1454 #5925) -#5927 := (+ #100 #5926) -#5928 := (<= #5927 0::Int) -#5955 := (not #5928) -#5929 := (+ f9 #5925) -#5930 := (<= #5929 0::Int) -#5935 := (or #5928 #5930) -#5938 := (not #5935) -#5941 := (or #5933 #5938) -#5944 := (or #4402 #5933 #5938) -#5931 := (or #5930 #5928) -#5932 := (not #5931) -#5934 := (or #5933 #5932) -#5945 := (or #4402 #5934) -#5952 := (iff #5945 #5944) -#5947 := (or #4402 #5941) -#5950 := (iff #5947 #5944) -#5951 := [rewrite]: #5950 -#5948 := (iff #5945 #5947) -#5942 := (iff #5934 #5941) -#5939 := (iff #5932 #5938) -#5936 := (iff #5931 #5935) -#5937 := [rewrite]: #5936 -#5940 := [monotonicity #5937]: #5939 -#5943 := [monotonicity #5940]: #5942 -#5949 := [monotonicity #5943]: #5948 -#5953 := [trans #5949 #5951]: #5952 -#5946 := [quant-inst #57]: #5945 -#5954 := [mp #5946 #5953]: #5944 -#7119 := [unit-resolution #5954 #6510]: #5941 -#7120 := [unit-resolution #7119 #7096]: #5938 -#5956 := (or #5935 #5955) -#5957 := [def-axiom]: #5956 -#7121 := [unit-resolution #5957 #7120]: #5955 -#6128 := (>= #175 0::Int) -#6131 := (or #4280 #6128) -#6132 := [quant-inst #171]: #6131 -#7123 := [unit-resolution #6132 #7122]: #6128 -#3921 := (<= #100 0::Int) -#7125 := (or #1748 #3921) -#7126 := [th-lemma arith triangle-eq]: #7125 -#7127 := [unit-resolution #7126 #7124]: #3921 -#7128 := [th-lemma arith farkas 1 1 1 1 #7127 #7123 #7121 #7118]: false -#7129 := [lemma #7128]: #5933 -#12715 := [mp #7129 #12714]: #205 -#4084 := (or #4509 #1491 #4503) -#4070 := [def-axiom]: #4084 -#12716 := [unit-resolution #4070 #12715 #12709]: #4503 -#4093 := (or #4500 #4494) -#4077 := [def-axiom]: #4093 -#12717 := [unit-resolution #4077 #12716]: #4494 -#4090 := (or #4497 #2277 #4491) -#4091 := [def-axiom]: #4090 -#12718 := [unit-resolution #4091 #12717]: #4494 -#23132 := [unit-resolution #12718 #23131]: #4491 -#4085 := (or #4488 #4482) -#4087 := [def-axiom]: #4085 -#23140 := [unit-resolution #4087 #23132]: #4482 -#12721 := (or #4485 #4479) -#10289 := [hypothesis]: #3446 -#3974 := (or #3441 #2300) -#3975 := [def-axiom]: #3974 -#9759 := [unit-resolution #3975 #10289]: #2300 -#10380 := (or #3441 #2299) -#10565 := (f6 #7212 ?v1!16) -#10566 := (f10 #10565) -#10583 := (* -1::Int #10566) -#8692 := (f6 f23 ?v1!16) -#8693 := (f10 #8692) -#10586 := (+ #8693 #10583) -#10588 := (>= #10586 0::Int) -#10582 := (= #8693 #10566) -#10593 := (= #10566 #8693) -#10591 := (= #10565 #8692) -#10592 := [monotonicity #7791]: #10591 -#10594 := [monotonicity #10592]: #10593 -#10595 := [symm #10594]: #10582 -#10596 := (not #10582) -#10597 := (or #10596 #10588) -#10598 := [th-lemma arith triangle-eq]: #10597 -#10599 := [unit-resolution #10598 #10595]: #10588 -#6008 := (f25 f23) -#6049 := (* -1::Int #6008) -#6418 := (+ #175 #6049) -#6419 := (>= #6418 0::Int) -#4063 := (or #4524 #4413) -#4064 := [def-axiom]: #4063 -#8194 := [unit-resolution #4064 #7098]: #4413 -#6423 := (or #4418 #6419) -#6424 := [quant-inst #171]: #6423 -#8195 := [unit-resolution #6424 #8194]: #6419 -#4117 := (not #2889) -#4118 := (or #3441 #4117) -#4119 := [def-axiom]: #4118 -#10292 := [unit-resolution #4119 #10289]: #4117 -#10224 := (+ #2291 #6049) -#10225 := (<= #10224 0::Int) -#10213 := (= #2291 #6008) -#10481 := (= ?v0!17 f23) -#8518 := (= ?v0!17 #7212) -#8511 := (f3 f16 ?v0!17) -#8512 := (= f1 #8511) -#8521 := (ite #8518 #5893 #8512) -#8515 := (f3 #8443 ?v0!17) -#8516 := (= f1 #8515) -#8524 := (iff #8516 #8521) -#9712 := (or #6291 #8524) -#8513 := (= #7212 ?v0!17) -#8514 := (ite #8513 #5893 #8512) -#8517 := (iff #8516 #8514) -#9707 := (or #6291 #8517) -#9714 := (iff #9707 #9712) -#9716 := (iff #9712 #9712) -#9717 := [rewrite]: #9716 -#8525 := (iff #8517 #8524) -#8522 := (iff #8514 #8521) -#8519 := (iff #8513 #8518) -#8520 := [rewrite]: #8519 -#8523 := [monotonicity #8520]: #8522 -#8526 := [monotonicity #8523]: #8525 -#9715 := [monotonicity #8526]: #9714 -#9723 := [trans #9715 #9717]: #9714 -#9713 := [quant-inst #105 #7212 #5892 #2290]: #9707 -#9724 := [mp #9713 #9723]: #9712 -#10293 := [unit-resolution #9724 #4178]: #8524 -#10322 := (= #2296 #8515) -#10295 := (= #8515 #2296) -#10232 := [monotonicity #9287]: #10295 -#10323 := [symm #10232]: #10322 -#4132 := (or #3441 #2297) -#3973 := [def-axiom]: #4132 -#10294 := [unit-resolution #3973 #10289]: #2297 -#10324 := [trans #10294 #10323]: #8516 -#9733 := (not #8516) -#9736 := (not #8524) -#9739 := (or #9736 #9733 #8521) -#9740 := [def-axiom]: #9739 -#10325 := [unit-resolution #9740 #10324 #10293]: #8521 -#9732 := (not #8512) -#8486 := (f14 f15 ?v0!17) -#8568 := (* -1::Int #8486) -#7514 := (f14 f15 #7212) -#10487 := (+ #7514 #8568) -#10488 := (>= #10487 0::Int) -#10613 := (not #10488) -#8447 := (= ?v1!16 #7212) -#9617 := (not #8447) -#8439 := (f3 f16 ?v1!16) -#8440 := (= f1 #8439) -#8450 := (ite #8447 #5893 #8440) -#9616 := (not #8450) -#8444 := (f3 #8443 ?v1!16) -#8445 := (= f1 #8444) -#8453 := (iff #8445 #8450) -#9585 := (or #6291 #8453) -#8441 := (= #7212 ?v1!16) -#8442 := (ite #8441 #5893 #8440) -#8446 := (iff #8445 #8442) -#9586 := (or #6291 #8446) -#9611 := (iff #9586 #9585) -#9607 := (iff #9585 #9585) -#9613 := [rewrite]: #9607 -#8454 := (iff #8446 #8453) -#8451 := (iff #8442 #8450) -#8448 := (iff #8441 #8447) -#8449 := [rewrite]: #8448 -#8452 := [monotonicity #8449]: #8451 -#8455 := [monotonicity #8452]: #8454 -#9612 := [monotonicity #8455]: #9611 -#9614 := [trans #9612 #9613]: #9611 -#9610 := [quant-inst #105 #7212 #5892 #2289]: #9586 -#9615 := [mp #9610 #9614]: #9585 -#10326 := [unit-resolution #9615 #4178]: #8453 -#9649 := (not #8445) -#10334 := (iff #2300 #9649) -#10332 := (iff #2299 #8445) -#10330 := (iff #8445 #2299) -#10328 := (= #8444 #2298) -#10329 := [monotonicity #9287]: #10328 -#10331 := [monotonicity #10329]: #10330 -#10333 := [symm #10331]: #10332 -#10335 := [monotonicity #10333]: #10334 -#10327 := [hypothesis]: #2300 -#10336 := [mp #10327 #10335]: #9649 -#9641 := (not #8453) -#9642 := (or #9641 #8445 #9616) -#9648 := [def-axiom]: #9642 -#10337 := [unit-resolution #9648 #10336 #10326]: #9616 -#10338 := (or #8450 #9617) -#9637 := (or #8450 #9617 #6305) -#9632 := [def-axiom]: #9637 -#10339 := [unit-resolution #9632 #7000]: #10338 -#10340 := [unit-resolution #10339 #10337]: #9617 -#8665 := (f14 f15 ?v1!16) -#8676 := (* -1::Int #8665) -#8924 := (+ #175 #8676) -#8925 := (<= #8924 0::Int) -#9638 := (not #8440) -#9639 := (or #8450 #8447 #9638) -#9640 := [def-axiom]: #9639 -#10309 := [unit-resolution #9640 #10340 #10337]: #9638 -#8930 := (or #8440 #8925) -#4055 := (or #4536 #4387) -#4041 := [def-axiom]: #4055 -#10314 := [unit-resolution #4041 #6509]: #4387 -#9985 := (or #4392 #8440 #8925) -#8913 := (+ #8665 #1454) -#8914 := (>= #8913 0::Int) -#8917 := (or #8440 #8914) -#9986 := (or #4392 #8917) -#10021 := (iff #9986 #9985) -#10017 := (or #4392 #8930) -#10020 := (iff #10017 #9985) -#10015 := [rewrite]: #10020 -#10018 := (iff #9986 #10017) -#8931 := (iff #8917 #8930) -#8928 := (iff #8914 #8925) -#8918 := (+ #1454 #8665) -#8921 := (>= #8918 0::Int) -#8926 := (iff #8921 #8925) -#8927 := [rewrite]: #8926 -#8922 := (iff #8914 #8921) -#8919 := (= #8913 #8918) -#8920 := [rewrite]: #8919 -#8923 := [monotonicity #8920]: #8922 -#8929 := [trans #8923 #8927]: #8928 -#8932 := [monotonicity #8929]: #8931 -#10019 := [monotonicity #8932]: #10018 -#10022 := [trans #10019 #10015]: #10021 -#10016 := [quant-inst #2289]: #9986 -#10023 := [mp #10016 #10022]: #9985 -#10308 := [unit-resolution #10023 #10314]: #8930 -#10315 := [unit-resolution #10308 #10309]: #8925 -#10587 := (not #8925) -#10634 := (or #10613 #10587 #2889 #8447) -#8718 := (+ #2887 #8693) -#8719 := (+ #175 #8718) -#8722 := (= #8719 0::Int) -#10619 := (not #8722) -#9836 := (<= #8719 0::Int) -#10612 := (not #9836) -#10600 := [hypothesis]: #9617 -#10602 := [hypothesis]: #4117 -#10589 := [hypothesis]: #10488 -#10614 := (or #10612 #2889 #10613 #8447) -#10590 := [hypothesis]: #9836 -#10567 := (<= #10566 0::Int) -#10568 := (not #10567) -#10572 := (or #6783 #8447 #10568) -#10569 := (or #8447 #10568) -#10573 := (or #6783 #10569) -#10575 := (iff #10573 #10572) -#10576 := [rewrite]: #10575 -#10574 := [quant-inst #7212 #2289]: #10573 -#10577 := [mp #10574 #10576]: #10572 -#10601 := [unit-resolution #10577 #4218 #10600]: #10568 -#8569 := (+ #2291 #8568) -#8570 := (<= #8569 0::Int) -#9749 := (or #4418 #8570) -#8558 := (+ #8486 #2292) -#8559 := (>= #8558 0::Int) -#9752 := (or #4418 #8559) -#9767 := (iff #9752 #9749) -#9769 := (iff #9749 #9749) -#9770 := [rewrite]: #9769 -#8573 := (iff #8559 #8570) -#8562 := (+ #2292 #8486) -#8565 := (>= #8562 0::Int) -#8571 := (iff #8565 #8570) -#8572 := [rewrite]: #8571 -#8566 := (iff #8559 #8565) -#8563 := (= #8558 #8562) -#8564 := [rewrite]: #8563 -#8567 := [monotonicity #8564]: #8566 -#8574 := [trans #8567 #8572]: #8573 -#9768 := [monotonicity #8574]: #9767 -#9771 := [trans #9768 #9770]: #9767 -#9766 := [quant-inst #2290]: #9752 -#9772 := [mp #9766 #9771]: #9749 -#10603 := [unit-resolution #9772 #8194]: #8570 -#7530 := (* -1::Int #7514) -#8424 := (+ #175 #7530) -#8430 := (>= #8424 0::Int) -#7337 := (= #175 #7514) -#10604 := (= #7514 #175) -#10605 := [monotonicity #7791]: #10604 -#10606 := [symm #10605]: #7337 -#10607 := (not #7337) -#10608 := (or #10607 #8430) -#10609 := [th-lemma arith triangle-eq]: #10608 -#10610 := [unit-resolution #10609 #10606]: #8430 -#10611 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10610 #10603 #10602 #10601 #10599 #10590 #10589]: false -#10615 := [lemma #10611]: #10614 -#10618 := [unit-resolution #10615 #10589 #10602 #10600]: #10612 -#10620 := (or #10619 #9836) -#10621 := [th-lemma arith triangle-eq]: #10620 -#10622 := [unit-resolution #10621 #10618]: #10619 -#8697 := (* -1::Int #8693) -#8701 := (+ f9 #8697) -#8702 := (<= #8701 0::Int) -#9850 := (not #8702) -#8711 := (+ #8676 #8693) -#8712 := (+ #175 #8711) -#8713 := (>= #8712 0::Int) -#8748 := (or #8702 #8713) -#8751 := (not #8748) -#8745 := (= #2293 #8665) -#10624 := (not #8745) -#8677 := (+ #2293 #8676) -#9849 := (>= #8677 0::Int) -#10585 := (not #9849) -#10580 := [hypothesis]: #8925 -#10616 := (or #10585 #2889 #10587 #10613) -#10581 := [hypothesis]: #9849 -#10584 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10610 #10603 #10602 #10581 #10580 #10589]: false -#10617 := [lemma #10584]: #10616 -#10623 := [unit-resolution #10617 #10589 #10580 #10602]: #10585 -#10625 := (or #10624 #9849) -#10626 := [th-lemma arith triangle-eq]: #10625 -#10627 := [unit-resolution #10626 #10623]: #10624 -#8754 := (or #8745 #8751) -#9838 := (or #4402 #8745 #8751) -#8698 := (+ #1454 #8697) -#8699 := (+ #8665 #8698) -#8700 := (<= #8699 0::Int) -#8741 := (or #8702 #8700) -#8742 := (not #8741) -#8743 := (= #8665 #2293) -#8744 := (or #8743 #8742) -#9839 := (or #4402 #8744) -#9846 := (iff #9839 #9838) -#9840 := (or #4402 #8754) -#9843 := (iff #9840 #9838) -#9844 := [rewrite]: #9843 -#9841 := (iff #9839 #9840) -#8755 := (iff #8744 #8754) -#8752 := (iff #8742 #8751) -#8749 := (iff #8741 #8748) -#8716 := (iff #8700 #8713) -#8704 := (+ #8665 #8697) -#8705 := (+ #1454 #8704) -#8708 := (<= #8705 0::Int) -#8714 := (iff #8708 #8713) -#8715 := [rewrite]: #8714 -#8709 := (iff #8700 #8708) -#8706 := (= #8699 #8705) -#8707 := [rewrite]: #8706 -#8710 := [monotonicity #8707]: #8709 -#8717 := [trans #8710 #8715]: #8716 -#8750 := [monotonicity #8717]: #8749 -#8753 := [monotonicity #8750]: #8752 -#8746 := (iff #8743 #8745) -#8747 := [rewrite]: #8746 -#8756 := [monotonicity #8747 #8753]: #8755 -#9842 := [monotonicity #8756]: #9841 -#9847 := [trans #9842 #9844]: #9846 -#9818 := [quant-inst #2289]: #9839 -#9848 := [mp #9818 #9847]: #9838 -#10628 := [unit-resolution #9848 #6510]: #8754 -#10629 := [unit-resolution #10628 #10627]: #8751 -#9845 := (or #8748 #9850) -#9851 := [def-axiom]: #9845 -#10630 := [unit-resolution #9851 #10629]: #9850 -#9852 := (not #8713) -#9853 := (or #8748 #9852) -#9854 := [def-axiom]: #9853 -#10631 := [unit-resolution #9854 #10629]: #9852 -#8725 := (or #8702 #8713 #8722) -#9824 := (or #4410 #8702 #8713 #8722) -#8694 := (+ #8693 #2887) -#8695 := (+ #175 #8694) -#8696 := (= #8695 0::Int) -#8703 := (or #8702 #8700 #8696) -#9825 := (or #4410 #8703) -#9831 := (iff #9825 #9824) -#9827 := (or #4410 #8725) -#9829 := (iff #9827 #9824) -#9830 := [rewrite]: #9829 -#9822 := (iff #9825 #9827) -#8726 := (iff #8703 #8725) -#8723 := (iff #8696 #8722) -#8720 := (= #8695 #8719) -#8721 := [rewrite]: #8720 -#8724 := [monotonicity #8721]: #8723 -#8727 := [monotonicity #8717 #8724]: #8726 -#9828 := [monotonicity #8727]: #9822 -#9832 := [trans #9828 #9830]: #9831 -#9826 := [quant-inst #2289]: #9825 -#9835 := [mp #9826 #9832]: #9824 -#10632 := [unit-resolution #9835 #6514]: #8725 -#10633 := [unit-resolution #10632 #10631 #10630 #10622]: false -#10635 := [lemma #10633]: #10634 -#10316 := [unit-resolution #10635 #10315 #10292 #10340]: #10613 -#10311 := (or #9732 #10488) -#10296 := [hypothesis]: #10613 -#10298 := [hypothesis]: #8512 -#7516 := (f3 f16 #7212) -#7517 := (= f1 #7516) -#10304 := (not #7517) -#10305 := (iff #758 #10304) -#10297 := (iff #755 #7517) -#10301 := (iff #7517 #755) -#10299 := (= #7516 #172) -#10300 := [monotonicity #7791]: #10299 -#10302 := [monotonicity #10300]: #10301 -#10303 := [symm #10302]: #10297 -#10306 := [monotonicity #10303]: #10305 -#10307 := [mp #6927 #10306]: #10304 -#10234 := (or #4297 #7517 #9732 #10488) -#10495 := (or #7517 #9732 #10488) -#10240 := (or #4297 #10495) -#10242 := (iff #10240 #10234) -#10243 := [rewrite]: #10242 -#10241 := [quant-inst #2290 #7212]: #10240 -#10244 := [mp #10241 #10243]: #10234 -#10310 := [unit-resolution #10244 #6938 #10307 #10298 #10296]: false -#10312 := [lemma #10310]: #10311 -#10317 := [unit-resolution #10312 #10316]: #9732 -#9725 := (not #8521) -#9728 := (or #9725 #8518 #8512) -#9729 := [def-axiom]: #9728 -#10318 := [unit-resolution #9729 #10317 #10325]: #8518 -#10319 := [trans #10318 #7791]: #10481 -#10320 := [monotonicity #10319]: #10213 -#10347 := (not #10213) -#10348 := (or #10347 #10225) -#10346 := [th-lemma arith triangle-eq]: #10348 -#10349 := [unit-resolution #10346 #10320]: #10225 -#10351 := (not #6419) -#10350 := (not #10225) -#10356 := (or #10585 #10350 #2889 #10587 #10351) -#10357 := [th-lemma arith assign-bounds -1 1 -1 1]: #10356 -#10355 := [unit-resolution #10357 #10292 #8195 #10315 #10349]: #10585 -#10358 := [unit-resolution #10626 #10355]: #10624 -#10359 := [unit-resolution #10628 #10358]: #8751 -#10184 := (or #8748 #8722) -#10180 := [hypothesis]: #10619 -#10181 := [hypothesis]: #8751 -#10182 := [unit-resolution #9851 #10181]: #9850 -#10177 := [unit-resolution #9854 #10181]: #9852 -#10183 := [unit-resolution #10632 #10177 #10182 #10180]: false -#10185 := [lemma #10183]: #10184 -#10360 := [unit-resolution #10185 #10359]: #8722 -#10377 := [unit-resolution #10621 #10360]: #9836 -#10378 := [unit-resolution #10577 #4218 #10340]: #10568 -#10379 := [th-lemma arith farkas 1 1 1 1 1 1 #10378 #10377 #10349 #10292 #8195 #10599]: false -#10381 := [lemma #10379]: #10380 -#9760 := [unit-resolution #10381 #9759 #10289]: false -#9761 := [lemma #9760]: #3441 -#4107 := (or #4485 #3446 #4479) -#4094 := [def-axiom]: #4107 -#12722 := [unit-resolution #4094 #9761]: #12721 -#23133 := [unit-resolution #12722 #23140]: #4479 -#4001 := (or #4476 #4470) -#4009 := [def-axiom]: #4001 -#23134 := [unit-resolution #4009 #23133]: #4470 -#23135 := (or #4473 #4467) -#14672 := (f6 f23 ?v0!19) -#14673 := (f10 #14672) -#14468 := (f14 f15 ?v0!19) -#14604 := (* -1::Int #14468) -#14720 := (+ #14604 #14673) -#14721 := (+ #175 #14720) -#14722 := (>= #14721 0::Int) -#14961 := (not #14722) -#14676 := (* -1::Int #14673) -#15460 := (+ #2323 #14676) -#15461 := (>= #15460 0::Int) -#15459 := (= #2323 #14673) -#15669 := (= #2322 #14672) -#15696 := (= ?v1!18 f23) -#13666 := (= ?v1!18 #7212) -#13659 := (f3 f16 ?v1!18) -#13660 := (= f1 #13659) -#13803 := (not #13660) -#13799 := (f14 f15 ?v1!18) -#14924 := (+ #13799 #14604) -#14925 := (+ #2323 #14924) -#14920 := (>= #14925 0::Int) -#15620 := (not #14920) -#14605 := (+ #2318 #14604) -#14606 := (<= #14605 0::Int) -#14819 := (or #4418 #14606) -#14571 := (+ #14468 #2319) -#14598 := (>= #14571 0::Int) -#14820 := (or #4418 #14598) -#14822 := (iff #14820 #14819) -#14824 := (iff #14819 #14819) -#14825 := [rewrite]: #14824 -#14623 := (iff #14598 #14606) -#14599 := (+ #2319 #14468) -#14602 := (>= #14599 0::Int) -#14607 := (iff #14602 #14606) -#14622 := [rewrite]: #14607 -#14597 := (iff #14598 #14602) -#14600 := (= #14571 #14599) -#14601 := [rewrite]: #14600 -#14603 := [monotonicity #14601]: #14597 -#14624 := [trans #14603 #14622]: #14623 -#14823 := [monotonicity #14624]: #14822 -#14773 := [trans #14823 #14825]: #14822 -#14821 := [quant-inst #2317]: #14820 -#14892 := [mp #14821 #14773]: #14819 -#15609 := [unit-resolution #14892 #8194]: #14606 -#4123 := (not #2916) -#15610 := [hypothesis]: #3492 -#3952 := (or #3487 #4123) -#3954 := [def-axiom]: #3952 -#15608 := [unit-resolution #3954 #15610]: #4123 -#13816 := (* -1::Int #13799) -#13817 := (+ #2320 #13816) -#13545 := (>= #13817 0::Int) -#13885 := (= #2320 #13799) -#4122 := (or #3487 #2331) -#4116 := [def-axiom]: #4122 -#15611 := [unit-resolution #4116 #15610]: #2331 -#13777 := (or #4427 #3472 #13885) -#13883 := (= #13799 #2320) -#13753 := (or #13883 #3472) -#13778 := (or #4427 #13753) -#13800 := (iff #13778 #13777) -#13751 := (or #3472 #13885) -#13792 := (or #4427 #13751) -#13802 := (iff #13792 #13777) -#13794 := [rewrite]: #13802 -#13797 := (iff #13778 #13792) -#13759 := (iff #13753 #13751) -#13754 := (or #13885 #3472) -#13757 := (iff #13754 #13751) -#13758 := [rewrite]: #13757 -#13755 := (iff #13753 #13754) -#13886 := (iff #13883 #13885) -#13887 := [rewrite]: #13886 -#13756 := [monotonicity #13887]: #13755 -#13760 := [trans #13756 #13758]: #13759 -#13801 := [monotonicity #13760]: #13797 -#13804 := [trans #13801 #13794]: #13800 -#13796 := [quant-inst #2316]: #13778 -#13805 := [mp #13796 #13804]: #13777 -#15616 := [unit-resolution #13805 #7101 #15611]: #13885 -#15617 := (not #13885) -#15618 := (or #15617 #13545) -#15602 := [th-lemma arith triangle-eq]: #15618 -#15619 := [unit-resolution #15602 #15616]: #13545 -#15615 := (not #14606) -#15612 := (not #13545) -#15621 := (or #15620 #15612 #15615 #2916) -#15623 := [th-lemma arith assign-bounds 1 -1 1]: #15621 -#15624 := [unit-resolution #15623 #15619 #15608 #15609]: #15620 -#15629 := (or #13803 #14920) -#4115 := (or #3487 #2329) -#4121 := [def-axiom]: #4115 -#15627 := [unit-resolution #4121 #15610]: #2329 -#15628 := [unit-resolution #4016 #6508]: #4283 -#13312 := (or #4288 #2328 #13803 #14920) -#14926 := (or #13803 #2328 #14920) -#13541 := (or #4288 #14926) -#15127 := (iff #13541 #13312) -#14927 := (or #2328 #13803 #14920) -#13547 := (or #4288 #14927) -#15125 := (iff #13547 #13312) -#15126 := [rewrite]: #15125 -#13649 := (iff #13541 #13547) -#14928 := (iff #14926 #14927) -#14929 := [rewrite]: #14928 -#15124 := [monotonicity #14929]: #13649 -#15128 := [trans #15124 #15126]: #15127 -#13544 := [quant-inst #2317 #2316]: #13541 -#15129 := [mp #13544 #15128]: #13312 -#15622 := [unit-resolution #15129 #15628 #15627]: #15629 -#15630 := [unit-resolution #15622 #15624]: #13803 -#13669 := (ite #13666 #5893 #13660) -#13663 := (f3 #8443 ?v1!18) -#13664 := (= f1 #13663) -#13672 := (iff #13664 #13669) -#15013 := (or #6291 #13672) -#13661 := (= #7212 ?v1!18) -#13662 := (ite #13661 #5893 #13660) -#13665 := (iff #13664 #13662) -#15018 := (or #6291 #13665) -#14891 := (iff #15018 #15013) -#15044 := (iff #15013 #15013) -#15045 := [rewrite]: #15044 -#13673 := (iff #13665 #13672) -#13670 := (iff #13662 #13669) -#13667 := (iff #13661 #13666) -#13668 := [rewrite]: #13667 -#13671 := [monotonicity #13668]: #13670 -#13674 := [monotonicity #13671]: #13673 -#15020 := [monotonicity #13674]: #14891 -#15061 := [trans #15020 #15045]: #14891 -#15019 := [quant-inst #105 #7212 #5892 #2316]: #15018 -#14890 := [mp #15019 #15061]: #15013 -#15631 := [unit-resolution #14890 #4178]: #13672 -#15691 := (= #2330 #13663) -#15625 := (= #13663 #2330) -#15626 := [monotonicity #9287]: #15625 -#15693 := [symm #15626]: #15691 -#15694 := [trans #15611 #15693]: #13664 -#13238 := (not #13664) -#12831 := (not #13672) -#12789 := (or #12831 #13238 #13669) -#13251 := [def-axiom]: #12789 -#15695 := [unit-resolution #13251 #15694 #15631]: #13669 -#15062 := (not #13669) -#15060 := (or #15062 #13666 #13660) -#15068 := [def-axiom]: #15060 -#15689 := [unit-resolution #15068 #15695 #15630]: #13666 -#15668 := [trans #15689 #7791]: #15696 -#15667 := [monotonicity #15668]: #15669 -#15671 := [monotonicity #15667]: #15459 -#15673 := (not #15459) -#15674 := (or #15673 #15461) -#15675 := [th-lemma arith triangle-eq]: #15674 -#15670 := [unit-resolution #15675 #15671]: #15461 -#15239 := (+ #2320 #6049) -#15241 := (>= #15239 0::Int) -#15451 := (= #2320 #6008) -#15762 := [monotonicity #15668]: #15451 -#15672 := (not #15451) -#15768 := (or #15672 #15241) -#15769 := [th-lemma arith triangle-eq]: #15768 -#15770 := [unit-resolution #15769 #15762]: #15241 -#6675 := (<= #6418 0::Int) -#6009 := (= #175 #6008) -#6548 := (f3 f24 f23) -#6549 := (= f1 #6548) -#8185 := (= #5892 #6548) -#8183 := (= #6548 #5892) -#8184 := [monotonicity #6999]: #8183 -#8186 := [symm #8184]: #8185 -#8187 := [trans #7000 #8186]: #6549 -#6555 := (not #6549) -#6607 := (or #6009 #6555) -#6688 := (or #4427 #6009 #6555) -#6689 := (or #4427 #6607) -#6691 := (iff #6689 #6688) -#6692 := [rewrite]: #6691 -#6690 := [quant-inst #171]: #6689 -#6693 := [mp #6690 #6692]: #6688 -#8188 := [unit-resolution #6693 #7101]: #6607 -#8189 := [unit-resolution #8188 #8187]: #6009 -#8190 := (not #6009) -#8191 := (or #8190 #6675) -#8192 := [th-lemma arith triangle-eq]: #8191 -#8193 := [unit-resolution #8192 #8189]: #6675 -#16340 := (not #15461) -#12653 := (not #6675) -#15771 := (not #15241) -#15767 := (or #14961 #15615 #2916 #15771 #12653 #16340) -#15775 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15767 -#15776 := [unit-resolution #15775 #15609 #8193 #15770 #15608 #15670]: #14961 -#14680 := (+ f9 #14676) -#14732 := (<= #14680 0::Int) -#15015 := (not #14732) -#16341 := (or #15015 #16340 #2328) -#16337 := [hypothesis]: #2329 -#16332 := [hypothesis]: #14732 -#16338 := [hypothesis]: #15461 -#16339 := [th-lemma arith farkas 1 -1 1 #16338 #16332 #16337]: false -#16342 := [lemma #16339]: #16341 -#15777 := [unit-resolution #16342 #15670 #15627]: #15015 -#14726 := (+ #2319 #14673) -#14727 := (+ #175 #14726) -#14744 := (= #14727 0::Int) -#15812 := (not #14744) -#14858 := (>= #14727 0::Int) -#15773 := (not #14858) -#15794 := (or #15773 #2916 #15771 #12653 #16340) -#15806 := [th-lemma arith assign-bounds 1 1 -1 1]: #15794 -#15807 := [unit-resolution #15806 #15770 #8193 #15608 #15670]: #15773 -#15813 := (or #15812 #14858) -#15814 := [th-lemma arith triangle-eq]: #15813 -#15848 := [unit-resolution #15814 #15807]: #15812 -#14769 := (or #14722 #14732 #14744) -#14893 := (or #4410 #14722 #14732 #14744) -#14674 := (+ #14673 #2319) -#14675 := (+ #175 #14674) -#14670 := (= #14675 0::Int) -#14677 := (+ #1454 #14676) -#14678 := (+ #14468 #14677) -#14679 := (<= #14678 0::Int) -#14733 := (or #14732 #14679 #14670) -#14894 := (or #4410 #14733) -#14861 := (iff #14894 #14893) -#14896 := (or #4410 #14769) -#14859 := (iff #14896 #14893) -#14860 := [rewrite]: #14859 -#14922 := (iff #14894 #14896) -#14771 := (iff #14733 #14769) -#14766 := (or #14732 #14722 #14744) -#14764 := (iff #14766 #14769) -#14770 := [rewrite]: #14764 -#14767 := (iff #14733 #14766) -#14745 := (iff #14670 #14744) -#14728 := (= #14675 #14727) -#14729 := [rewrite]: #14728 -#14765 := [monotonicity #14729]: #14745 -#14719 := (iff #14679 #14722) -#14734 := (+ #14468 #14676) -#14735 := (+ #1454 #14734) -#14738 := (<= #14735 0::Int) -#14723 := (iff #14738 #14722) -#14724 := [rewrite]: #14723 -#14739 := (iff #14679 #14738) -#14736 := (= #14678 #14735) -#14737 := [rewrite]: #14736 -#14740 := [monotonicity #14737]: #14739 -#14725 := [trans #14740 #14724]: #14719 -#14768 := [monotonicity #14725 #14765]: #14767 -#14772 := [trans #14768 #14770]: #14771 -#14923 := [monotonicity #14772]: #14922 -#14921 := [trans #14923 #14860]: #14861 -#14895 := [quant-inst #2317]: #14894 -#14862 := [mp #14895 #14921]: #14893 -#15846 := [unit-resolution #14862 #6514]: #14769 -#15847 := [unit-resolution #15846 #15848 #15777 #15776]: false -#15843 := [lemma #15847]: #3487 -#3990 := (or #4473 #3492 #4467) -#4005 := [def-axiom]: #3990 -#23150 := [unit-resolution #4005 #15843]: #23135 -#23151 := [unit-resolution #23150 #23134]: #4467 -#4109 := (or #4464 #2361) -#4111 := [def-axiom]: #4109 -#23152 := [unit-resolution #4111 #23151]: #2361 -#23153 := (= #9082 #6071) -#23154 := [monotonicity #9283]: #23153 -#23156 := [symm #23154]: #9862 -#23157 := [unit-resolution #11950 #23156]: #9458 -#9819 := (<= #9456 0::Int) -#23149 := (or #11946 #9819) -#23155 := [th-lemma arith triangle-eq]: #23149 -#23158 := [unit-resolution #23155 #23156]: #9819 -#23159 := (not #9819) -#23165 := (or #10879 #23159) -#7359 := (>= #6071 0::Int) -#7297 := (not #7359) -#7298 := [hypothesis]: #7297 -#7979 := (or #4280 #7359) -#7980 := [quant-inst #6070]: #7979 -#7485 := [unit-resolution #7980 #7122 #7298]: false -#7489 := [lemma #7485]: #7359 -#7054 := (not #3921) -#23160 := (or #10879 #7054 #7297 #23159) -#23162 := [th-lemma arith assign-bounds -1 1 -1]: #23160 -#23166 := [unit-resolution #23162 #7489 #7127]: #23165 -#23164 := [unit-resolution #23166 #23158]: #10879 -#3996 := (or #4464 #4456) -#3997 := [def-axiom]: #3996 -#23167 := [unit-resolution #3997 #23151]: #4456 -#24106 := (or #14184 #4461) -#8779 := (f25 #7212) -#9545 := (* -1::Int #8779) -#14039 := (+ #2348 #9545) -#14227 := (<= #14039 0::Int) -#10165 := (f3 f24 #7212) -#10166 := (= f1 #10165) -#11811 := (= #5892 #10165) -#11804 := (= #10165 #5892) -#11810 := [monotonicity #6999 #7791]: #11804 -#11812 := [symm #11810]: #11811 -#11813 := [trans #7000 #11812]: #10166 -#14213 := (f10 #14212) -#14239 := (* -1::Int #14213) -#14240 := (+ #9545 #14239) -#14241 := (+ #2348 #14240) -#14242 := (= #14241 0::Int) -#15157 := (>= #14241 0::Int) -#14158 := (+ #2349 #14133) -#14159 := (+ #175 #14158) -#14428 := (<= #14159 0::Int) -#14162 := (= #14159 0::Int) -#14187 := (not #14184) -#21312 := [hypothesis]: #14187 -#21317 := (or #14184 #14162) -#21306 := (not #14162) -#21307 := [hypothesis]: #21306 -#12473 := (not #14142) -#12480 := (or #14184 #12473) -#12481 := [def-axiom]: #12480 -#21313 := [unit-resolution #12481 #21312]: #12473 -#12470 := (not #14153) -#12479 := (or #14184 #12470) -#12482 := [def-axiom]: #12479 -#21314 := [unit-resolution #12482 #21312]: #12470 -#14165 := (or #14142 #14153 #14162) -#12412 := (or #4410 #14142 #14153 #14162) -#14134 := (+ #14133 #2349) -#14135 := (+ #175 #14134) -#14136 := (= #14135 0::Int) -#14138 := (+ #1454 #14137) -#14139 := (+ #14075 #14138) -#14140 := (<= #14139 0::Int) -#14143 := (or #14142 #14140 #14136) -#12436 := (or #4410 #14143) -#12441 := (iff #12436 #12412) -#12409 := (or #4410 #14165) -#12440 := (iff #12409 #12412) -#12435 := [rewrite]: #12440 -#12438 := (iff #12436 #12409) -#14166 := (iff #14143 #14165) -#14163 := (iff #14136 #14162) -#14160 := (= #14135 #14159) -#14161 := [rewrite]: #14160 -#14164 := [monotonicity #14161]: #14163 -#14156 := (iff #14140 #14153) -#14144 := (+ #14075 #14137) -#14145 := (+ #1454 #14144) -#14148 := (<= #14145 0::Int) -#14154 := (iff #14148 #14153) -#14155 := [rewrite]: #14154 -#14149 := (iff #14140 #14148) -#14146 := (= #14139 #14145) -#14147 := [rewrite]: #14146 -#14150 := [monotonicity #14147]: #14149 -#14157 := [trans #14150 #14155]: #14156 -#14167 := [monotonicity #14157 #14164]: #14166 -#12439 := [monotonicity #14167]: #12438 -#12443 := [trans #12439 #12435]: #12441 -#12437 := [quant-inst #2347]: #12436 -#12444 := [mp #12437 #12443]: #12412 -#21315 := [unit-resolution #12444 #6514]: #14165 -#21316 := [unit-resolution #21315 #21314 #21313 #21307]: false -#21318 := [lemma #21316]: #21317 -#24023 := [unit-resolution #21318 #21312]: #14162 -#24024 := (or #21306 #14428) -#24025 := [th-lemma arith triangle-eq]: #24024 -#24026 := [unit-resolution #24025 #24023]: #14428 -#17685 := (not #14428) -#24047 := (or #15157 #17685) -#9546 := (+ #6008 #9545) -#7446 := (>= #9546 0::Int) -#9544 := (= #6008 #8779) -#11875 := (= #8779 #6008) -#11876 := [monotonicity #7791]: #11875 -#11877 := [symm #11876]: #9544 -#11878 := (not #9544) -#24021 := (or #11878 #7446) -#24027 := [th-lemma arith triangle-eq]: #24021 -#24028 := [unit-resolution #24027 #11877]: #7446 -#13354 := (+ #14133 #14239) -#13587 := (>= #13354 0::Int) -#7924 := (= #14133 #14213) -#24031 := (= #14213 #14133) -#24038 := [monotonicity #24030]: #24031 -#24039 := [symm #24038]: #7924 -#24037 := (not #7924) -#24040 := (or #24037 #13587) -#24041 := [th-lemma arith triangle-eq]: #24040 -#24042 := [unit-resolution #24041 #24039]: #13587 -#24045 := (not #13587) -#24044 := (not #7446) -#24043 := (or #15157 #24044 #10351 #24045 #17685) -#24046 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24043 -#24048 := [unit-resolution #24046 #24042 #24028 #8195]: #24047 -#24036 := [unit-resolution #24048 #24026]: #15157 -#15135 := (<= #14241 0::Int) -#14429 := (>= #14159 0::Int) -#24049 := (or #21306 #14429) -#24050 := [th-lemma arith triangle-eq]: #24049 -#24051 := [unit-resolution #24050 #24023]: #14429 -#24055 := (not #14429) -#24059 := (or #15135 #24055) -#9547 := (<= #9546 0::Int) -#11879 := (or #11878 #9547) -#11880 := [th-lemma arith triangle-eq]: #11879 -#11881 := [unit-resolution #11880 #11877]: #9547 -#13355 := (<= #13354 0::Int) -#24052 := (or #24037 #13355) -#24035 := [th-lemma arith triangle-eq]: #24052 -#24053 := [unit-resolution #24035 #24039]: #13355 -#24054 := (not #13355) -#12652 := (not #9547) -#24056 := (or #15135 #12652 #12653 #24054 #24055) -#24057 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24056 -#24060 := [unit-resolution #24057 #24053 #11881 #8193]: #24059 -#24061 := [unit-resolution #24060 #24051]: #15135 -#24063 := (not #15157) -#24062 := (not #15135) -#24058 := (or #14242 #24062 #24063) -#24064 := [th-lemma arith triangle-eq]: #24058 -#24065 := [unit-resolution #24064 #24061 #24036]: #14242 -#14247 := (not #14242) -#10178 := (not #10166) -#14250 := (or #10178 #14227 #14247) -#24066 := [hypothesis]: #4456 -#12778 := (or #4461 #10178 #14227 #14247) -#14214 := (+ #2349 #14213) -#14215 := (+ #8779 #14214) -#14216 := (= #14215 0::Int) -#14217 := (not #14216) -#14218 := (+ #8779 #2349) -#14219 := (>= #14218 0::Int) -#14220 := (or #10178 #14219 #14217) -#12785 := (or #4461 #14220) -#12838 := (iff #12785 #12778) -#12849 := (or #4461 #14250) -#12872 := (iff #12849 #12778) -#12878 := [rewrite]: #12872 -#12876 := (iff #12785 #12849) -#14251 := (iff #14220 #14250) -#14248 := (iff #14217 #14247) -#14245 := (iff #14216 #14242) -#14232 := (+ #8779 #14213) -#14233 := (+ #2349 #14232) -#14236 := (= #14233 0::Int) -#14243 := (iff #14236 #14242) -#14244 := [rewrite]: #14243 -#14237 := (iff #14216 #14236) -#14234 := (= #14215 #14233) -#14235 := [rewrite]: #14234 -#14238 := [monotonicity #14235]: #14237 -#14246 := [trans #14238 #14244]: #14245 -#14249 := [monotonicity #14246]: #14248 -#14230 := (iff #14219 #14227) -#14221 := (+ #2349 #8779) -#14224 := (>= #14221 0::Int) -#14228 := (iff #14224 #14227) -#14229 := [rewrite]: #14228 -#14225 := (iff #14219 #14224) -#14222 := (= #14218 #14221) -#14223 := [rewrite]: #14222 -#14226 := [monotonicity #14223]: #14225 -#14231 := [trans #14226 #14229]: #14230 -#14252 := [monotonicity #14231 #14249]: #14251 -#12877 := [monotonicity #14252]: #12876 -#12904 := [trans #12877 #12878]: #12838 -#12842 := [quant-inst #7212]: #12785 -#12905 := [mp #12842 #12904]: #12778 -#24067 := [unit-resolution #12905 #24066]: #14250 -#24068 := [unit-resolution #24067 #24065 #11813]: #14227 -#12488 := (f6 f11 ?v0!20) -#17156 := (f8 #12488) -#22317 := (f6 #7212 #17156) -#22326 := (f10 #22317) -#22329 := (* -1::Int #22326) -#22458 := (+ #14133 #22329) -#17192 := (>= #22458 0::Int) -#17178 := (= #14133 #22326) -#24069 := (= #22326 #14133) -#24073 := (= #22317 #14132) -#24071 := (= #17156 ?v0!20) -#17157 := (= ?v0!20 #17156) -#17180 := (or #6825 #17157) -#17181 := [quant-inst #57 #2347]: #17180 -#24070 := [unit-resolution #17181 #4200]: #17157 -#24072 := [symm #24070]: #24071 -#24074 := [monotonicity #7791 #24072]: #24073 -#24075 := [monotonicity #24074]: #24069 -#24076 := [symm #24075]: #17178 -#24077 := (not #17178) -#24078 := (or #24077 #17192) -#24079 := [th-lemma arith triangle-eq]: #24078 -#24081 := [unit-resolution #24079 #24076]: #17192 -#22385 := (<= #22326 0::Int) -#22365 := (not #22385) -#22368 := (= #7212 #17156) -#22398 := (not #22368) -#20555 := (f3 f16 #17156) -#20572 := (= f1 #20555) -#23982 := (ite #22368 #5893 #20572) -#24002 := (not #23982) -#23983 := (f3 #8443 #17156) -#23988 := (= f1 #23983) -#23990 := (iff #23982 #23988) -#23994 := (or #6291 #23990) -#23989 := (iff #23988 #23982) -#23995 := (or #6291 #23989) -#23997 := (iff #23995 #23994) -#23993 := (iff #23994 #23994) -#23999 := [rewrite]: #23993 -#23991 := (iff #23989 #23990) -#23992 := [rewrite]: #23991 -#23998 := [monotonicity #23992]: #23997 -#24000 := [trans #23998 #23999]: #23997 -#23996 := [quant-inst #105 #7212 #5892 #17156]: #23995 -#24001 := [mp #23996 #24000]: #23994 -#24082 := [unit-resolution #24001 #4178]: #23990 -#24014 := (not #23988) -#10247 := (f3 f24 ?v0!20) -#10248 := (= f1 #10247) -#10249 := (not #10248) -#24095 := (iff #10249 #24014) -#24093 := (iff #10248 #23988) -#24090 := (iff #23988 #10248) -#24088 := (= #23983 #10247) -#24089 := [monotonicity #9287 #24072]: #24088 -#24092 := [monotonicity #24089]: #24090 -#24094 := [symm #24092]: #24093 -#24096 := [monotonicity #24094]: #24095 -#24709 := (not #14086) -#21437 := (not #19568) -#24083 := (or #14153 #21437 #24045 #24062 #24044 #10351) -#24084 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24083 -#24085 := [unit-resolution #24084 #24061 #24042 #21314 #24028 #8195]: #21437 -#24710 := (or #24709 #19568) -#24697 := [hypothesis]: #21437 -#24698 := [hypothesis]: #14086 -#24711 := [th-lemma arith triangle-eq]: #24710 -#24712 := [unit-resolution #24711 #24698 #24697]: false -#24713 := [lemma #24712]: #24710 -#24080 := [unit-resolution #24713 #24085]: #24709 -#14092 := (or #10249 #14086) -#12335 := (or #4427 #10249 #14086) -#14082 := (= #14075 #2348) -#14085 := (or #14082 #10249) -#12375 := (or #4427 #14085) -#12383 := (iff #12375 #12335) -#12378 := (or #4427 #14092) -#12380 := (iff #12378 #12335) -#12382 := [rewrite]: #12380 -#12379 := (iff #12375 #12378) -#14095 := (iff #14085 #14092) -#14089 := (or #14086 #10249) -#14093 := (iff #14089 #14092) -#14094 := [rewrite]: #14093 -#14090 := (iff #14085 #14089) -#14087 := (iff #14082 #14086) -#14088 := [rewrite]: #14087 -#14091 := [monotonicity #14088]: #14090 -#14096 := [trans #14091 #14094]: #14095 -#12374 := [monotonicity #14096]: #12379 -#12384 := [trans #12374 #12382]: #12383 -#12377 := [quant-inst #2347]: #12375 -#12403 := [mp #12377 #12384]: #12335 -#24086 := [unit-resolution #12403 #7101]: #14092 -#24087 := [unit-resolution #24086 #24080]: #10249 -#24091 := [mp #24087 #24096]: #24014 -#24013 := (not #23990) -#24016 := (or #24013 #24002 #23988) -#24017 := [def-axiom]: #24016 -#24097 := [unit-resolution #24017 #24091 #24082]: #24002 -#24098 := (or #23982 #22398) -#24009 := (or #23982 #22398 #6305) -#24010 := [def-axiom]: #24009 -#24099 := [unit-resolution #24010 #7000]: #24098 -#24100 := [unit-resolution #24099 #24097]: #22398 -#22370 := (or #22368 #22365) -#23959 := (or #6783 #22368 #22365) -#22366 := (= #17156 #7212) -#22367 := (or #22366 #22365) -#23960 := (or #6783 #22367) -#23967 := (iff #23960 #23959) -#23962 := (or #6783 #22370) -#23965 := (iff #23962 #23959) -#23966 := [rewrite]: #23965 -#23963 := (iff #23960 #23962) -#22371 := (iff #22367 #22370) -#22369 := (iff #22366 #22368) -#22364 := [rewrite]: #22369 -#22372 := [monotonicity #22364]: #22371 -#23964 := [monotonicity #22372]: #23963 -#23968 := [trans #23964 #23966]: #23967 -#23961 := [quant-inst #7212 #17156]: #23960 -#23969 := [mp #23961 #23968]: #23959 -#24101 := [unit-resolution #23969 #4218]: #22370 -#24104 := [unit-resolution #24101 #24100]: #22365 -#24105 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24028 #8195 #24104 #24081 #24026 #24068]: false -#24107 := [lemma #24105]: #24106 -#23168 := [unit-resolution #24107 #23167]: #14184 -#23148 := [hypothesis]: #12470 -#12483 := (or #14187 #14142 #14153) -#12484 := [def-axiom]: #12483 -#23161 := [unit-resolution #12484 #23148 #23168]: #14142 -#14190 := (or #14086 #14187) -#12445 := (or #4402 #14086 #14187) -#14181 := (or #14142 #14140) -#14182 := (not #14181) -#14183 := (or #14082 #14182) -#12464 := (or #4402 #14183) -#12469 := (iff #12464 #12445) -#12442 := (or #4402 #14190) -#12468 := (iff #12442 #12445) -#12463 := [rewrite]: #12468 -#12466 := (iff #12464 #12442) -#14191 := (iff #14183 #14190) -#14188 := (iff #14182 #14187) -#14185 := (iff #14181 #14184) -#14186 := [monotonicity #14157]: #14185 -#14189 := [monotonicity #14186]: #14188 -#14192 := [monotonicity #14088 #14189]: #14191 -#12467 := [monotonicity #14192]: #12466 -#12471 := [trans #12467 #12463]: #12469 -#12465 := [quant-inst #2347]: #12464 -#12472 := [mp #12465 #12471]: #12445 -#23169 := [unit-resolution #12472 #6510]: #14190 -#23147 := [unit-resolution #23169 #23168]: #14086 -#23170 := [unit-resolution #24713 #23147]: #19568 -#23171 := [unit-resolution #24084 #23148 #24042 #23170 #24028 #8195]: #24062 -#23163 := (or #15135 #15157) -#23172 := [th-lemma arith farkas 1 1]: #23163 -#23173 := [unit-resolution #23172 #23171]: #15157 -#23174 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24053 #23173 #11881 #8193 #23161 #10075 #23164 #23157 #6992 #23152]: false -#23176 := [lemma #23174]: #23175 -#27692 := [unit-resolution #23176 #10075]: #14153 -#27697 := [unit-resolution #12482 #27692]: #14184 -#27709 := [unit-resolution #12472 #6510 #27697]: #14086 -#27710 := [unit-resolution #24711 #27709]: #19568 -#21438 := (or #21436 #21437 #2360) -#21431 := [hypothesis]: #19568 -#21432 := [hypothesis]: #14793 -#21435 := [th-lemma arith farkas -1 1 1 #21432 #21431 #19784]: false -#21439 := [lemma #21435]: #21438 -#27711 := [unit-resolution #21439 #27710 #19784]: #21436 -#4112 := (or #4464 #2930) -#4110 := [def-axiom]: #4112 -#27712 := [unit-resolution #4110 #23151]: #2930 -#24436 := (or #4313 #2927 #14793 #14798) -#14790 := (or #14789 #14786 #14779) -#14791 := (not #14790) -#14794 := (or #2362 #14793 #14791) -#24445 := (or #4313 #14794) -#24451 := (iff #24445 #24436) -#14801 := (or #2927 #14793 #14798) -#24442 := (or #4313 #14801) -#24450 := (iff #24442 #24436) -#24446 := [rewrite]: #24450 -#24441 := (iff #24445 #24442) -#14802 := (iff #14794 #14801) -#14799 := (iff #14791 #14798) -#14796 := (iff #14790 #14795) -#14797 := [rewrite]: #14796 -#14800 := [monotonicity #14797]: #14799 -#14803 := [monotonicity #2929 #14800]: #14802 -#24448 := [monotonicity #14803]: #24441 -#24440 := [trans #24448 #24446]: #24451 -#24447 := [quant-inst #2347]: #24445 -#24463 := [mp #24447 #24440]: #24436 -#27714 := [unit-resolution #24463 #12666 #27712 #27711]: #14798 -#24467 := (or #14795 #14788) -#24453 := [def-axiom]: #24467 -#27679 := [unit-resolution #24453 #27714]: #14788 -#27720 := [trans #27679 #27719]: #26215 -#26243 := (not #26215) -#15537 := (>= #14784 0::Int) -#24465 := (or #14795 #14785) -#24466 := [def-axiom]: #24465 -#27716 := [unit-resolution #24466 #27714]: #14785 -#27717 := (or #14786 #15537) -#27715 := [th-lemma arith triangle-eq]: #27717 -#27718 := [unit-resolution #27715 #27716]: #15537 -#24449 := (not #14779) -#24464 := (or #14795 #24449) -#24443 := [def-axiom]: #24464 -#27700 := [unit-resolution #24443 #27714]: #24449 -#15513 := (<= #14784 0::Int) -#27698 := (or #14786 #15513) -#27701 := [th-lemma arith triangle-eq]: #27698 -#27702 := [unit-resolution #27701 #27716]: #15513 -#28965 := (not #15537) -#29082 := (not #15513) -#29113 := (or #26243 #29082 #4461 #14779 #21437 #28965) -#21417 := (f25 #14775) -#21447 := (* -1::Int #21417) -#21658 := (+ #14782 #21447) -#21659 := (+ #2348 #21658) -#17956 := (<= #21659 0::Int) -#29065 := (not #17956) -#18267 := (>= #21659 0::Int) -#21448 := (+ #14776 #21447) -#21449 := (>= #21448 0::Int) -#25333 := (or #4418 #21449) -#25340 := [quant-inst #14775]: #25333 -#28970 := [unit-resolution #25340 #8194]: #21449 -#28962 := [hypothesis]: #15537 -#28967 := (not #21449) -#28968 := (or #18267 #28965 #21437 #28967) -#28964 := [th-lemma arith assign-bounds -1 -1 -1]: #28968 -#28963 := [unit-resolution #28964 #28962 #21431 #28970]: #18267 -#21660 := (= #21659 0::Int) -#21665 := (not #21660) -#21645 := (+ #2348 #21447) -#21646 := (<= #21645 0::Int) -#28966 := (not #21646) -#28969 := [hypothesis]: #24449 -#28986 := (or #28966 #14779 #21437 #28967) -#29000 := [th-lemma arith assign-bounds -1 -1 -1]: #28986 -#29043 := [unit-resolution #29000 #28969 #21431 #28970]: #28966 -#21430 := (f3 f24 #14775) -#21410 := (= f1 #21430) -#25159 := (f3 f24 #25043) -#25148 := (= f1 #25159) -#29044 := (iff #25148 #21410) -#29047 := (iff #21410 #25148) -#29046 := (= #21430 #25159) -#29001 := [monotonicity #28985]: #29046 -#29042 := [monotonicity #29001]: #29047 -#29050 := [symm #29042]: #29044 -#30427 := (= #7212 #25043) -#30421 := (ite #30427 #5893 #26215) -#30489 := [hypothesis]: #26215 -#30493 := (or #30421 #26243) -#30465 := (not #30421) -#30485 := [hypothesis]: #30465 -#30466 := (not #30427) -#30486 := (or #30421 #30466) -#30471 := (or #30421 #30466 #6305) -#30472 := [def-axiom]: #30471 -#30487 := [unit-resolution #30472 #7000]: #30486 -#30488 := [unit-resolution #30487 #30485]: #30466 -#30490 := (or #30421 #30427) -#30473 := (or #30421 #30427 #26243) -#30474 := [def-axiom]: #30473 -#30491 := [unit-resolution #30474 #30489]: #30490 -#30492 := [unit-resolution #30491 #30488 #30485]: false -#30494 := [lemma #30492]: #30493 -#28984 := [unit-resolution #30494 #30489]: #30421 -#30260 := (or #25148 #30465) -#30450 := (f3 #8443 #25043) -#30255 := (= #30450 #25159) -#30251 := (= #25159 #30450) -#18325 := (= f24 #8443) -#18226 := (= #774 #8443) -#18327 := [symm #9285]: #18226 -#18324 := [trans #6999 #18327]: #18325 -#30252 := [monotonicity #18324]: #30251 -#30257 := [symm #30252]: #30255 -#30451 := (= f1 #30450) -#30453 := (iff #30421 #30451) -#30195 := (or #6291 #30453) -#30452 := (iff #30451 #30421) -#30193 := (or #6291 #30452) -#30200 := (iff #30193 #30195) -#30202 := (iff #30195 #30195) -#30191 := [rewrite]: #30202 -#30454 := (iff #30452 #30453) -#30455 := [rewrite]: #30454 -#30201 := [monotonicity #30455]: #30200 -#30203 := [trans #30201 #30191]: #30200 -#30199 := [quant-inst #105 #7212 #5892 #25043]: #30193 -#30204 := [mp #30199 #30203]: #30195 -#30247 := [unit-resolution #30204 #4178]: #30453 -#30205 := (not #30453) -#30249 := (or #30205 #30451) -#30248 := [hypothesis]: #30421 -#30210 := (or #30205 #30465 #30451) -#30211 := [def-axiom]: #30210 -#30250 := [unit-resolution #30211 #30248]: #30249 -#30241 := [unit-resolution #30250 #30247]: #30451 -#30258 := [trans #30241 #30257]: #25148 -#25160 := (not #25148) -#30242 := [hypothesis]: #25160 -#30259 := [unit-resolution #30242 #30258]: false -#30261 := [lemma #30259]: #30260 -#29045 := [unit-resolution #30261 #28984]: #25148 -#29051 := [mp #29045 #29050]: #21410 -#21416 := (not #21410) -#21668 := (or #21416 #21646 #21665) -#16841 := (or #4461 #21416 #21646 #21665) -#21632 := (+ #2349 #14781) -#21633 := (+ #21417 #21632) -#21634 := (= #21633 0::Int) -#21635 := (not #21634) -#21636 := (+ #21417 #2349) -#21637 := (>= #21636 0::Int) -#21638 := (or #21416 #21637 #21635) -#16842 := (or #4461 #21638) -#16875 := (iff #16842 #16841) -#16855 := (or #4461 #21668) -#16858 := (iff #16855 #16841) -#16853 := [rewrite]: #16858 -#16856 := (iff #16842 #16855) -#21669 := (iff #21638 #21668) -#21666 := (iff #21635 #21665) -#21663 := (iff #21634 #21660) -#21651 := (+ #14781 #21417) -#21652 := (+ #2349 #21651) -#21655 := (= #21652 0::Int) -#21661 := (iff #21655 #21660) -#21662 := [rewrite]: #21661 -#21656 := (iff #21634 #21655) -#21653 := (= #21633 #21652) -#21654 := [rewrite]: #21653 -#21657 := [monotonicity #21654]: #21656 -#21664 := [trans #21657 #21662]: #21663 -#21667 := [monotonicity #21664]: #21666 -#21649 := (iff #21637 #21646) -#21639 := (+ #2349 #21417) -#21642 := (>= #21639 0::Int) -#21647 := (iff #21642 #21646) -#21648 := [rewrite]: #21647 -#21643 := (iff #21637 #21642) -#21640 := (= #21636 #21639) -#21641 := [rewrite]: #21640 -#21644 := [monotonicity #21641]: #21643 -#21650 := [trans #21644 #21648]: #21649 -#21670 := [monotonicity #21650 #21667]: #21669 -#16863 := [monotonicity #21670]: #16856 -#16860 := [trans #16863 #16853]: #16875 -#16854 := [quant-inst #14775]: #16842 -#16904 := [mp #16854 #16860]: #16841 -#29062 := [unit-resolution #16904 #24066]: #21668 -#29060 := [unit-resolution #29062 #29051 #29043]: #21665 -#29049 := (not #18267) -#29061 := (or #21660 #29065 #29049) -#29064 := [th-lemma arith triangle-eq]: #29061 -#29072 := [unit-resolution #29064 #29060 #28963]: #29065 -#25330 := (<= #21448 0::Int) -#21418 := (= #14776 #21417) -#26210 := (f14 f15 #25043) -#25149 := (f25 #25043) -#26949 := (= #25149 #26210) -#29156 := (iff #26949 #21418) -#29078 := (= #21417 #14776) -#29070 := (iff #29078 #21418) -#29155 := [commutativity]: #29070 -#29081 := (iff #26949 #29078) -#29079 := (= #26210 #14776) -#29048 := [monotonicity #29063]: #29079 -#29074 := (= #25149 #21417) -#24501 := (= #21417 #25149) -#29080 := [monotonicity #28985]: #24501 -#29071 := [symm #29080]: #29074 -#29083 := [monotonicity #29071 #29048]: #29081 -#29154 := [trans #29083 #29155]: #29156 -#26989 := (or #25160 #26949) -#26992 := (or #4427 #25160 #26949) -#26983 := (= #26210 #25149) -#27002 := (or #26983 #25160) -#27009 := (or #4427 #27002) -#27014 := (iff #27009 #26992) -#27011 := (or #4427 #26989) -#26967 := (iff #27011 #26992) -#27013 := [rewrite]: #26967 -#27004 := (iff #27009 #27011) -#27005 := (iff #27002 #26989) -#26982 := (or #26949 #25160) -#26990 := (iff #26982 #26989) -#26991 := [rewrite]: #26990 -#26988 := (iff #27002 #26982) -#26986 := (iff #26983 #26949) -#26948 := [rewrite]: #26986 -#26987 := [monotonicity #26948]: #26988 -#27008 := [trans #26987 #26991]: #27005 -#27012 := [monotonicity #27008]: #27004 -#26966 := [trans #27012 #27013]: #27014 -#27010 := [quant-inst #25043]: #27009 -#27016 := [mp #27010 #26966]: #26992 -#29073 := [unit-resolution #27016 #7101]: #26989 -#29069 := [unit-resolution #29073 #29045]: #26949 -#29157 := [mp #29069 #29154]: #21418 -#29158 := (not #21418) -#29159 := (or #29158 #25330) -#29119 := [th-lemma arith triangle-eq]: #29159 -#29152 := [unit-resolution #29119 #29157]: #25330 -#14118 := (<= #14117 0::Int) -#13522 := (or #4418 #14118) -#14108 := (+ #14075 #2349) -#14109 := (>= #14108 0::Int) -#13552 := (or #4418 #14109) -#13519 := (iff #13552 #13522) -#13568 := (iff #13522 #13522) -#13576 := [rewrite]: #13568 -#14121 := (iff #14109 #14118) -#14110 := (+ #2349 #14075) -#14113 := (>= #14110 0::Int) -#14119 := (iff #14113 #14118) -#14120 := [rewrite]: #14119 -#14114 := (iff #14109 #14113) -#14111 := (= #14108 #14110) -#14112 := [rewrite]: #14111 -#14115 := [monotonicity #14112]: #14114 -#14122 := [trans #14115 #14120]: #14121 -#13571 := [monotonicity #14122]: #13519 -#13579 := [trans #13571 #13576]: #13519 -#13562 := [quant-inst #2347]: #13552 -#13577 := [mp #13562 #13579]: #13522 -#29111 := [unit-resolution #13577 #8194]: #14118 -#29160 := [hypothesis]: #15513 -#29110 := [th-lemma arith farkas -1 -1 -1 1 #29160 #29111 #29152 #29072]: false -#29114 := [lemma #29110]: #29113 -#27703 := [unit-resolution #29114 #27702 #23167 #27700 #27710 #27718]: #26243 -#27721 := [unit-resolution #27703 #27720]: false -#27736 := [lemma #27721]: #27735 -#26719 := [unit-resolution #27736 #19784]: #6074 -#6120 := (or #6092 #6119) -#6121 := [def-axiom]: #6120 -#26720 := [unit-resolution #6121 #26719]: #6092 -#6095 := (not #6092) -#12667 := (or #6089 #6095) -#6106 := (or #4313 #1655 #6089 #6095) -#6085 := (or #6084 #6081 #6074) -#6086 := (not #6085) -#6088 := (or #6087 #1655 #6086) -#6107 := (or #4313 #6088) -#6114 := (iff #6107 #6106) -#6101 := (or #1655 #6089 #6095) -#6109 := (or #4313 #6101) -#6112 := (iff #6109 #6106) -#6113 := [rewrite]: #6112 -#6110 := (iff #6107 #6109) -#6104 := (iff #6088 #6101) -#6098 := (or #6089 #1655 #6095) -#6102 := (iff #6098 #6101) -#6103 := [rewrite]: #6102 -#6099 := (iff #6088 #6098) -#6096 := (iff #6086 #6095) -#6093 := (iff #6085 #6092) -#6094 := [rewrite]: #6093 -#6097 := [monotonicity #6094]: #6096 -#6100 := [monotonicity #6091 #6097]: #6099 -#6105 := [trans #6100 #6103]: #6104 -#6111 := [monotonicity #6105]: #6110 -#6115 := [trans #6111 #6113]: #6114 -#6108 := [quant-inst #171]: #6107 -#6116 := [mp #6108 #6115]: #6106 -#12668 := [unit-resolution #6116 #12666 #7831]: #12667 -#26766 := [unit-resolution #12668 #26720]: #6089 -#26767 := [symm #26766]: #6087 -#26763 := [monotonicity #26767]: #7826 -#26770 := [symm #26763]: #7798 -#7793 := (not #7798) -#7823 := (or #7793 #7799) -#7829 := [th-lemma arith triangle-eq]: #7823 -#26765 := [unit-resolution #7829 #26770]: #7799 -#9970 := (not #7799) -#8365 := (or #2276 #9970) -#9901 := (not #9498) -#9583 := [hypothesis]: #7799 -#9655 := (or #9901 #2276 #9970) -#10029 := (= #9990 0::Int) -#9976 := (not #10029) -#9786 := (not #10051) -#9584 := [hypothesis]: #9498 -#6993 := (not #3918) -#9900 := (not #10063) -#9973 := (or #9786 #9900 #2276 #9901 #6993 #9970) -#9893 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9973 -#9899 := [unit-resolution #9893 #9584 #6992 #10072 #10088 #9583]: #9786 -#9860 := (or #9976 #10051) -#9972 := [th-lemma arith triangle-eq]: #9860 -#9654 := [unit-resolution #9972 #9899]: #9976 -#9971 := (or #10026 #9900 #2276 #9901 #6993 #9970) -#10042 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9971 -#10043 := [unit-resolution #10042 #9584 #6992 #10088 #10072 #9583]: #10026 -#9864 := [unit-resolution #10036 #4218 #10043]: #9950 -#9529 := (or #6808 #9969 #10029) -#10030 := (or #10029 #9969) -#9548 := (or #6808 #10030) -#9802 := (iff #9548 #9529) -#10037 := (or #9969 #10029) -#9499 := (or #6808 #10037) -#9536 := (iff #9499 #9529) -#9801 := [rewrite]: #9536 -#9538 := (iff #9548 #9499) -#10038 := (iff #10030 #10037) -#10039 := [rewrite]: #10038 -#9542 := [monotonicity #10039]: #9538 -#9803 := [trans #9542 #9801]: #9802 -#9540 := [quant-inst #7212 #2274]: #9548 -#9762 := [mp #9540 #9803]: #9529 -#9863 := [unit-resolution #9762 #4212 #9864 #9654]: false -#10143 := [lemma #9863]: #9655 -#9535 := [unit-resolution #10143 #10088 #9583]: #9901 -#9539 := [unit-resolution #10086 #9535]: #10084 -#8428 := (or #7639 #7617) -#9099 := [hypothesis]: #10084 -#8425 := [hypothesis]: #7642 -#8427 := [unit-resolution #9513 #8425]: #9511 -#8467 := [unit-resolution #9516 #8425]: #9514 -#8468 := [unit-resolution #10082 #8467 #8427 #9099]: false -#9344 := [lemma #8468]: #8428 -#9758 := [unit-resolution #9344 #9539]: #7639 -#9800 := [unit-resolution #10078 #9758]: #7540 -#9756 := [unit-resolution #11921 #9800]: #9582 -#9898 := [th-lemma arith farkas 1 -1 1 #9581 #10088 #9756]: false -#8323 := [lemma #9898]: #8365 -#26771 := [unit-resolution #8323 #26765]: #2276 -#26769 := [unit-resolution #12718 #26771]: #4491 -#26772 := [unit-resolution #4087 #26769]: #4482 -#26768 := [unit-resolution #12722 #26772]: #4479 -#26773 := [unit-resolution #4009 #26768]: #4470 -#26781 := [unit-resolution #23150 #26773]: #4467 -#26783 := [unit-resolution #3997 #26781]: #4456 -#26780 := [unit-resolution #24107 #26783]: #14184 -#26784 := [unit-resolution #12472 #6510 #26780]: #14086 -#26782 := [unit-resolution #24711 #26784]: #19568 -#26798 := [unit-resolution #21439 #26782 #19784]: #21436 -#26801 := [unit-resolution #4110 #26781]: #2930 -#26793 := [unit-resolution #24463 #12666 #26801 #26798]: #14798 -#26776 := [unit-resolution #24453 #26793]: #14788 -#26835 := [trans #26776 #26829]: #26215 -#26799 := [unit-resolution #24466 #26793]: #14785 -#26794 := [unit-resolution #27701 #26799]: #15513 -#26792 := [unit-resolution #24443 #26793]: #24449 -#26795 := [unit-resolution #27715 #26799]: #15537 -#26791 := [unit-resolution #29114 #26795 #26783 #26792 #26782 #26794]: #26243 -#26830 := [unit-resolution #26791 #26835]: false -#26831 := [lemma #26830]: #2360 -#8230 := [unit-resolution #4111 #26831]: #4464 -#8234 := [unit-resolution #23150 #8230]: #4473 -#8320 := [unit-resolution #4009 #8234]: #4476 -#8239 := [unit-resolution #12722 #8320]: #4485 -#8243 := [unit-resolution #4087 #8239]: #4488 -#8249 := [unit-resolution #12718 #8243]: #2277 -#8343 := [unit-resolution #11113 #8249]: #6074 -#8368 := [unit-resolution #6121 #8343]: #6092 -#8286 := [unit-resolution #12668 #8368]: #6089 -#8426 := [symm #8286]: #6087 -#8355 := [monotonicity #8426]: #7826 -#8359 := [symm #8355]: #7798 -#8361 := [unit-resolution #8323 #8249]: #9970 -[unit-resolution #7829 #8361 #8359]: false +#1894 := ?v0!0 +#1895 := (f11 ?v0!0) +#1896 := (>= #1895 0::Int) +#1897 := (not #1896) +#4589 := (or #1897 #4586) +#4592 := (not #4589) +#4595 := (or #1196 #4592) +#4598 := (not #4595) +#4605 := (forall (vars (?v0 S3)) (:pat #4218) #1805) +#4608 := (iff #1808 #4605) +#4606 := (iff #1805 #1805) +#4607 := [refl]: #4606 +#4609 := [quant-intro #4607]: #4608 +#1958 := (~ #1808 #1808) +#1900 := (~ #1805 #1805) +#1901 := [refl]: #1900 +#1959 := [nnf-pos #1901]: #1958 +#1838 := [not-or-elim #1833]: #1808 +#2053 := [mp~ #1838 #1959]: #1808 +#4610 := [mp #2053 #4609]: #4605 +#5324 := [hypothesis]: #1196 +#4784 := (not #4605) +#5260 := (or #4784 #71) +#5144 := (= f10 f10) +#5145 := (not #5144) +#5147 := (or #5145 #71) +#5228 := (or #4784 #5147) +#5262 := (iff #5228 #5260) +#5264 := (iff #5260 #5260) +#5259 := [rewrite]: #5264 +#5233 := (iff #5147 #71) +#5201 := (or false #71) +#5229 := (iff #5201 #71) +#5232 := [rewrite]: #5229 +#5202 := (iff #5147 #5201) +#5199 := (iff #5145 false) +#5196 := (not true) +#5193 := (iff #5196 false) +#5194 := [rewrite]: #5193 +#5197 := (iff #5145 #5196) +#5148 := (iff #5144 true) +#5195 := [rewrite]: #5148 +#5198 := [monotonicity #5195]: #5197 +#5200 := [trans #5198 #5194]: #5199 +#5203 := [monotonicity #5200]: #5202 +#5234 := [trans #5203 #5232]: #5233 +#5263 := [monotonicity #5234]: #5262 +#5269 := [trans #5263 #5259]: #5262 +#5261 := [quant-inst #56]: #5228 +#5295 := [mp #5261 #5269]: #5260 +#5325 := [unit-resolution #5295 #5324 #4610]: false +#5320 := [lemma #5325]: #71 +#4601 := (or #1196 #4598) +#3528 := (forall (vars (?v1 S3)) #3517) +#3535 := (not #3528) +#3513 := (forall (vars (?v0 S3) (?v1 S3)) #3508) +#3534 := (not #3513) +#3536 := (or #2359 #2926 #3534 #3535) +#3537 := (not #3536) +#3542 := (or #3491 #3537) +#3549 := (not #3542) +#3468 := (forall (vars (?v0 S3) (?v1 S3)) #3463) +#3548 := (not #3468) +#3550 := (or #3548 #3549) +#3551 := (not #3550) +#3556 := (or #3445 #3551) +#3562 := (not #3556) +#3563 := (or #1499 #3562) +#3564 := (not #3563) +#3569 := (or #2276 #3564) +#3575 := (not #3569) +#3576 := (or #1490 #3575) +#3577 := (not #3576) +#3582 := (or #1490 #3577) +#3588 := (not #3582) +#3589 := (or #953 #3588) +#3590 := (not #3589) +#3595 := (or #2869 #3590) +#3601 := (not #3595) +#3602 := (or #1485 #3601) +#3603 := (not #3602) +#3608 := (or #2855 #3603) +#3616 := (not #3608) +#3422 := (forall (vars (?v0 S3)) #3417) +#3615 := (not #3422) +#3404 := (forall (vars (?v0 S3)) #3401) +#3614 := (not #3404) +#3617 := (or #754 #995 #1650 #1654 #2210 #2213 #3614 #3615 #3616) +#3618 := (not #3617) +#3334 := (forall (vars (?v0 S3) (?v1 S3)) #3329) +#3340 := (not #3334) +#3341 := (or #158 #3340) +#3342 := (not #3341) +#3369 := (or #3342 #3366) +#3376 := (not #3369) +#3312 := (forall (vars (?v0 S3)) #3307) +#3375 := (not #3312) +#3377 := (or #3375 #3376) +#3378 := (not #3377) +#3275 := (forall (vars (?v1 S3)) #3264) +#3281 := (not #3275) +#3282 := (or #2089 #2704 #3281) +#3283 := (not #3282) +#3383 := (or #3283 #3378) +#3390 := (not #3383) +#3260 := (forall (vars (?v0 S3)) #3249) +#3389 := (not #3260) +#3391 := (or #724 #706 #733 #715 #3389 #3390) +#3392 := (not #3391) +#3623 := (or #3392 #3618) +#3633 := (not #3623) +#3246 := (forall (vars (?v0 S3)) #3241) +#3632 := (not #3246) +#3218 := (forall (vars (?v0 S3)) #3213) +#3631 := (not #3218) +#3190 := (forall (vars (?v0 S3) (?v1 S3)) #3185) +#3630 := (not #3190) +#3167 := (forall (vars (?v0 S3) (?v1 S3)) #3162) +#3629 := (not #3167) +#3634 := (or #1747 #1742 #3629 #3630 #3631 #3632 #3633) +#3635 := (not #3634) +#3135 := (forall (vars (?v1 S3)) #3124) +#3141 := (not #3135) +#3142 := (or #1981 #2566 #3141) +#3143 := (not #3142) +#3640 := (or #3143 #3635) +#3647 := (not #3640) +#3120 := (forall (vars (?v0 S3) (?v1 S3)) #3115) +#3646 := (not #3120) +#3648 := (or #3646 #3647) +#3649 := (not #3648) +#3654 := (or #3098 #3649) +#3661 := (not #3654) +#3075 := (forall (vars (?v0 S3) (?v1 S3)) #3070) +#3660 := (not #3075) +#3662 := (or #3660 #3661) +#3663 := (not #3662) +#3668 := (or #1928 #3663) +#3674 := (not #3668) +#3675 := (or #1205 #3674) +#3676 := (not #3675) +#3681 := (or #1897 #3676) +#3687 := (not #3681) +#3688 := (or #1196 #3687) +#3689 := (not #3688) +#3694 := (or #1196 #3689) +#4602 := (iff #3694 #4601) +#4599 := (iff #3689 #4598) +#4596 := (iff #3688 #4595) +#4593 := (iff #3687 #4592) +#4590 := (iff #3681 #4589) +#4587 := (iff #3676 #4586) +#4584 := (iff #3675 #4583) +#4581 := (iff #3674 #4580) +#4578 := (iff #3668 #4577) +#4575 := (iff #3663 #4574) +#4572 := (iff #3662 #4571) +#4569 := (iff #3661 #4568) +#4566 := (iff #3654 #4565) +#4563 := (iff #3649 #4562) +#4560 := (iff #3648 #4559) +#4557 := (iff #3647 #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) +#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) +#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) +#4431 := [refl]: #4430 +#4433 := [quant-intro #4431]: #4432 +#4436 := [monotonicity #4433]: #4435 +#4489 := [monotonicity #4436 #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) +#4414 := [refl]: #4413 +#4416 := [quant-intro #4414]: #4415 +#4419 := [monotonicity #4416]: #4418 +#4525 := [monotonicity #4419 #4522]: #4524 +#4528 := [monotonicity #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) +#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 +#4355 := [monotonicity #4352]: #4354 +#4358 := [monotonicity #4355]: #4357 +#4361 := [monotonicity #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) +#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) +#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 +#4272 := [monotonicity #4269]: #4271 +#4555 := [monotonicity #4272 #4552]: #4554 +#4558 := [monotonicity #4555]: #4557 +#4256 := (iff #3646 #4255) +#4253 := (iff #3120 #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) +#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) +#4234 := [refl]: #4233 +#4236 := [quant-intro #4234]: #4235 +#4239 := [monotonicity #4236]: #4238 +#4585 := [monotonicity #4239 #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) +#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) +#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) +#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) +#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) +#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) +#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 +#2962 := [monotonicity #2959]: #2961 +#2965 := [quant-intro #2962]: #2964 +#2948 := (iff #2370 #2935) +#2940 := (not #2935) +#2943 := (not #2940) +#2946 := (iff #2943 #2935) +#2947 := [rewrite]: #2946 +#2944 := (iff #2370 #2943) +#2941 := (iff #2364 #2940) +#2938 := (iff #2363 #2935) +#2932 := (and #2929 #2360) +#2936 := (iff #2932 #2935) +#2937 := [rewrite]: #2936 +#2933 := (iff #2363 #2932) +#2930 := (iff #2362 #2929) +#2927 := (iff #2361 #2926) +#2928 := [rewrite]: #2927 +#2931 := [monotonicity #2928]: #2930 +#2934 := [monotonicity #2931]: #2933 +#2939 := [trans #2934 #2937]: #2938 +#2942 := [monotonicity #2939]: #2941 +#2945 := [monotonicity #2942]: #2944 +#2949 := [trans #2945 #2947]: #2948 +#2968 := [monotonicity #2949 #2965]: #2967 +#2971 := [monotonicity #2968]: #2970 +#2976 := [trans #2971 #2974]: #2975 +#2924 := (iff #2334 #2923) +#2921 := (iff #2333 #2920) +#2918 := (iff #2324 #2915) +#2905 := (+ #2319 #2322) +#2906 := (+ #2318 #2905) +#2909 := (>= #2906 0::Int) +#2916 := (iff #2909 #2915) +#2917 := [rewrite]: #2916 +#2910 := (iff #2324 #2909) +#2907 := (= #2323 #2906) +#2908 := [rewrite]: #2907 +#2911 := [monotonicity #2908]: #2910 +#2919 := [trans #2911 #2917]: #2918 +#2903 := (iff #2332 #2902) +#2900 := (iff #2331 #2899) +#2901 := [rewrite]: #2900 +#2904 := [monotonicity #2901]: #2903 +#2922 := [monotonicity #2904 #2919]: #2921 +#2925 := [monotonicity #2922]: #2924 +#2979 := [monotonicity #2925 #2976]: #2978 +#2982 := [monotonicity #2979]: #2981 +#2897 := (iff #2303 #2896) +#2894 := (iff #2302 #2893) +#2891 := (iff #2294 #2888) +#2880 := (+ #2291 #2292) +#2883 := (>= #2880 0::Int) +#2889 := (iff #2883 #2888) +#2890 := [rewrite]: #2889 +#2884 := (iff #2294 #2883) +#2881 := (= #2293 #2880) +#2882 := [rewrite]: #2881 +#2885 := [monotonicity #2882]: #2884 +#2892 := [trans #2885 #2890]: #2891 +#2878 := (iff #2301 #2877) +#2875 := (iff #2300 #2874) +#2876 := [rewrite]: #2875 +#2879 := [monotonicity #2876]: #2878 +#2895 := [monotonicity #2879 #2892]: #2894 +#2898 := [monotonicity #2895]: #2897 +#2985 := [monotonicity #2898 #2982]: #2984 +#2988 := [monotonicity #2985]: #2987 +#2991 := [monotonicity #2988]: #2990 +#2872 := (iff #2270 #204) +#2873 := [rewrite]: #2872 +#2994 := [monotonicity #2873 #2991]: #2993 +#2997 := [monotonicity #2994]: #2996 +#3000 := [monotonicity #2997]: #2999 +#2870 := (iff #2256 #2869) +#2867 := (iff #2255 #2864) +#2861 := (or #2858 #2251) +#2865 := (iff #2861 #2864) +#2866 := [rewrite]: #2865 +#2862 := (iff #2255 #2861) +#2859 := (iff #2254 #2858) +#2860 := [rewrite]: #2859 +#2863 := [monotonicity #2860]: #2862 +#2868 := [trans #2863 #2866]: #2867 +#2871 := [monotonicity #2868]: #2870 +#3003 := [monotonicity #2871 #3000]: #3002 +#3006 := [monotonicity #3003]: #3005 +#2856 := (iff #2236 #2855) +#2853 := (iff #2235 #2850) +#2842 := (+ #2232 #2233) +#2845 := (>= #2842 0::Int) +#2851 := (iff #2845 #2850) +#2852 := [rewrite]: #2851 +#2846 := (iff #2235 #2845) +#2843 := (= #2234 #2842) +#2844 := [rewrite]: #2843 +#2847 := [monotonicity #2844]: #2846 +#2854 := [trans #2847 #2852]: #2853 +#2857 := [monotonicity #2854]: #2856 +#3009 := [monotonicity #2857 #3006]: #3008 +#2840 := (iff #2203 #776) +#2841 := [rewrite]: #2840 +#3012 := [monotonicity #2841 #3009]: #3011 +#3017 := [trans #3012 #3015]: #3016 +#2838 := (iff #2197 #2835) +#2832 := (and #136 #141 #621 #624 #2829 #2194) +#2836 := (iff #2832 #2835) +#2837 := [rewrite]: #2836 +#2833 := (iff #2197 #2832) +#2830 := (iff #2187 #2829) +#2827 := (iff #2183 #2826) +#2824 := (iff #2179 #2821) +#2818 := (or #2815 #2175) +#2822 := (iff #2818 #2821) +#2823 := [rewrite]: #2822 +#2819 := (iff #2179 #2818) +#2816 := (iff #2160 #2815) +#2813 := (iff #2159 #2812) +#2810 := (iff #2148 #2807) +#2798 := (+ #2143 #2146) +#2799 := (+ #2142 #2798) +#2802 := (>= #2799 0::Int) +#2808 := (iff #2802 #2807) +#2809 := [rewrite]: #2808 +#2803 := (iff #2148 #2802) +#2800 := (= #2147 #2799) +#2801 := [rewrite]: #2800 +#2804 := [monotonicity #2801]: #2803 +#2811 := [trans #2804 #2809]: #2810 +#2796 := (iff #2158 #2795) +#2793 := (iff #2157 #2792) +#2794 := [rewrite]: #2793 +#2797 := [monotonicity #2794]: #2796 +#2814 := [monotonicity #2797 #2811]: #2813 +#2817 := [monotonicity #2814]: #2816 +#2820 := [monotonicity #2817]: #2819 +#2825 := [trans #2820 #2823]: #2824 +#2790 := (iff #2133 #2789) +#2787 := (iff #2130 #2786) +#2784 := (iff #2125 #2783) +#2781 := (iff #2122 #2778) +#2768 := (+ #2117 #2120) +#2769 := (+ #1342 #2768) +#2772 := (= #2769 0::Int) +#2779 := (iff #2772 #2778) +#2780 := [rewrite]: #2779 +#2773 := (iff #2122 #2772) +#2770 := (= #2121 #2769) +#2771 := [rewrite]: #2770 +#2774 := [monotonicity #2771]: #2773 +#2782 := [trans #2774 #2780]: #2781 +#2766 := (iff #2124 #2765) +#2763 := (iff #2123 #2760) +#2752 := (+ #1342 #2117) +#2755 := (>= #2752 0::Int) +#2761 := (iff #2755 #2760) +#2762 := [rewrite]: #2761 +#2756 := (iff #2123 #2755) +#2753 := (= #2118 #2752) +#2754 := [rewrite]: #2753 +#2757 := [monotonicity #2754]: #2756 +#2764 := [trans #2757 #2762]: #2763 +#2767 := [monotonicity #2764]: #2766 +#2785 := [monotonicity #2767 #2782]: #2784 +#2788 := [monotonicity #2785]: #2787 +#2791 := [quant-intro #2788]: #2790 +#2828 := [monotonicity #2791 #2825]: #2827 +#2750 := (iff #2109 #2747) +#2713 := (and #2090 #2707) +#2744 := (and #2713 #2741) +#2748 := (iff #2744 #2747) +#2749 := [rewrite]: #2748 +#2745 := (iff #2109 #2744) +#2742 := (iff #2105 #2741) +#2739 := (iff #2102 #2738) +#2736 := (iff #2086 #2735) +#2733 := (iff #2083 #2732) +#2730 := (= #2082 #2729) +#2731 := [rewrite]: #2730 +#2734 := [monotonicity #2731]: #2733 +#2737 := [monotonicity #2734]: #2736 +#2740 := [monotonicity #2737]: #2739 +#2743 := [quant-intro #2740]: #2742 +#2726 := (iff #2099 #2713) +#2718 := (not #2713) +#2721 := (not #2718) +#2724 := (iff #2721 #2713) +#2725 := [rewrite]: #2724 +#2722 := (iff #2099 #2721) +#2719 := (iff #2094 #2718) +#2716 := (iff #2093 #2713) +#2710 := (and #2707 #2090) +#2714 := (iff #2710 #2713) +#2715 := [rewrite]: #2714 +#2711 := (iff #2093 #2710) +#2708 := (iff #2092 #2707) +#2705 := (iff #2091 #2704) +#2706 := [rewrite]: #2705 +#2709 := [monotonicity #2706]: #2708 +#2712 := [monotonicity #2709]: #2711 +#2717 := [trans #2712 #2715]: #2716 +#2720 := [monotonicity #2717]: #2719 +#2723 := [monotonicity #2720]: #2722 +#2727 := [trans #2723 #2725]: #2726 +#2746 := [monotonicity #2727 #2743]: #2745 +#2751 := [trans #2746 #2749]: #2750 +#2831 := [monotonicity #2751 #2828]: #2830 +#2702 := (iff #2073 #624) +#2703 := [rewrite]: #2702 +#2700 := (iff #2070 #621) +#2701 := [rewrite]: #2700 +#2698 := (iff #2067 #141) +#2699 := [rewrite]: #2698 +#2696 := (iff #2064 #136) +#2697 := [rewrite]: #2696 +#2834 := [monotonicity #2697 #2699 #2701 #2703 #2831]: #2833 +#2839 := [trans #2834 #2837]: #2838 +#3020 := [monotonicity #2839 #3017]: #3019 +#2694 := (iff #2058 #2693) +#2691 := (iff #2055 #2690) +#2688 := (iff #2050 #2687) +#2685 := (iff #2043 #2684) +#2682 := (iff #2042 #2679) +#2672 := (+ #1297 #2040) +#2675 := (>= #2672 0::Int) +#2680 := (iff #2675 #2679) +#2681 := [rewrite]: #2680 +#2676 := (iff #2042 #2675) +#2673 := (= #2041 #2672) +#2674 := [rewrite]: #2673 +#2677 := [monotonicity #2674]: #2676 +#2683 := [trans #2677 #2681]: #2682 +#2686 := [monotonicity #2683]: #2685 +#2670 := (iff #2047 #2667) +#2656 := (+ #2040 #2045) +#2657 := (+ #1297 #2656) +#2660 := (= #2657 0::Int) +#2668 := (iff #2660 #2667) +#2669 := [rewrite]: #2668 +#2661 := (iff #2047 #2660) +#2658 := (= #2046 #2657) +#2659 := [rewrite]: #2658 +#2662 := [monotonicity #2659]: #2661 +#2671 := [trans #2662 #2669]: #2670 +#2689 := [monotonicity #2671 #2686]: #2688 +#2692 := [monotonicity #2689]: #2691 +#2695 := [quant-intro #2692]: #2694 +#2654 := (iff #2031 #2653) +#2651 := (iff #2028 #2650) +#2648 := (iff #2023 #2647) +#2645 := (iff #2017 #2642) +#2632 := (+ #2013 #2015) +#2633 := (+ #1259 #2632) +#2636 := (= #2633 0::Int) +#2643 := (iff #2636 #2642) +#2644 := [rewrite]: #2643 +#2637 := (iff #2017 #2636) +#2634 := (= #2016 #2633) +#2635 := [rewrite]: #2634 +#2638 := [monotonicity #2635]: #2637 +#2646 := [trans #2638 #2644]: #2645 +#2630 := (iff #2020 #2629) +#2627 := (iff #2019 #2624) +#2616 := (+ #1259 #2015) +#2619 := (>= #2616 0::Int) +#2625 := (iff #2619 #2624) +#2626 := [rewrite]: #2625 +#2620 := (iff #2019 #2619) +#2617 := (= #2018 #2616) +#2618 := [rewrite]: #2617 +#2621 := [monotonicity #2618]: #2620 +#2628 := [trans #2621 #2626]: #2627 +#2631 := [monotonicity #2628]: #2630 +#2649 := [monotonicity #2631 #2646]: #2648 +#2652 := [monotonicity #2649]: #2651 +#2655 := [quant-intro #2652]: #2654 +#2614 := (iff #2006 #100) +#2615 := [rewrite]: #2614 +#3023 := [monotonicity #2615 #2655 #2695 #3020]: #3022 +#3028 := [trans #3023 #3026]: #3027 +#2612 := (iff #2001 #2609) +#2575 := (and #1982 #2569) +#2606 := (and #2575 #2603) +#2610 := (iff #2606 #2609) +#2611 := [rewrite]: #2610 +#2607 := (iff #2001 #2606) +#2604 := (iff #1997 #2603) +#2601 := (iff #1994 #2600) +#2598 := (iff #1978 #2597) +#2595 := (iff #1974 #2594) +#2592 := (= #1973 #2591) +#2593 := [rewrite]: #2592 +#2596 := [monotonicity #2593]: #2595 +#2599 := [monotonicity #2596]: #2598 +#2602 := [monotonicity #2599]: #2601 +#2605 := [quant-intro #2602]: #2604 +#2588 := (iff #1991 #2575) +#2580 := (not #2575) +#2583 := (not #2580) +#2586 := (iff #2583 #2575) +#2587 := [rewrite]: #2586 +#2584 := (iff #1991 #2583) +#2581 := (iff #1986 #2580) +#2578 := (iff #1985 #2575) +#2572 := (and #2569 #1982) +#2576 := (iff #2572 #2575) +#2577 := [rewrite]: #2576 +#2573 := (iff #1985 #2572) +#2570 := (iff #1984 #2569) +#2567 := (iff #1983 #2566) +#2568 := [rewrite]: #2567 +#2571 := [monotonicity #2568]: #2570 +#2574 := [monotonicity #2571]: #2573 +#2579 := [trans #2574 #2577]: #2578 +#2582 := [monotonicity #2579]: #2581 +#2585 := [monotonicity #2582]: #2584 +#2589 := [trans #2585 #2587]: #2588 +#2608 := [monotonicity #2589 #2605]: #2607 +#2613 := [trans #2608 #2611]: #2612 +#3031 := [monotonicity #2613 #3028]: #3030 +#3034 := [monotonicity #3031]: #3033 +#2564 := (iff #1955 #2563) +#2561 := (iff #1954 #2560) +#2558 := (iff #1947 #2557) +#2555 := (iff #1946 #2554) +#2556 := [rewrite]: #2555 +#2559 := [monotonicity #2556]: #2558 +#2552 := (iff #1953 #2551) +#2549 := (= #1952 #2548) +#2550 := [rewrite]: #2549 +#2553 := [monotonicity #2550]: #2552 +#2562 := [monotonicity #2553 #2559]: #2561 +#2565 := [monotonicity #2562]: #2564 +#3037 := [monotonicity #2565 #3034]: #3036 +#3040 := [monotonicity #3037]: #3039 +#2545 := (iff #1924 #2544) +#2542 := (iff #1923 #2541) +#2539 := (iff #1915 #2536) +#2528 := (+ #1912 #1913) +#2531 := (>= #2528 0::Int) +#2537 := (iff #2531 #2536) +#2538 := [rewrite]: #2537 +#2532 := (iff #1915 #2531) +#2529 := (= #1914 #2528) +#2530 := [rewrite]: #2529 +#2533 := [monotonicity #2530]: #2532 +#2540 := [trans #2533 #2538]: #2539 +#2526 := (iff #1922 #2525) +#2523 := (iff #1921 #2522) +#2524 := [rewrite]: #2523 +#2527 := [monotonicity #2524]: #2526 +#2543 := [monotonicity #2527 #2540]: #2542 +#2546 := [monotonicity #2543]: #2545 +#3043 := [monotonicity #2546 #3040]: #3042 +#3046 := [monotonicity #3043]: #3045 +#3049 := [monotonicity #3046]: #3048 +#2520 := (iff #1860 #71) +#2521 := [rewrite]: #2520 +#3052 := [monotonicity #2521 #3049]: #3051 +#3055 := [monotonicity #3052]: #3054 +#1836 := (not #1800) +#2515 := (~ #1836 #2514) +#2511 := (not #1797) +#2512 := (~ #2511 #2510) +#2507 := (not #1794) +#2508 := (~ #2507 #2506) +#2503 := (not #1791) +#2504 := (~ #2503 #2502) +#2499 := (not #1788) +#2500 := (~ #2499 #2498) +#2495 := (not #1785) +#2496 := (~ #2495 #2494) +#2491 := (not #1782) +#2492 := (~ #2491 #2490) +#2487 := (not #1779) +#2488 := (~ #2487 #2486) +#2483 := (not #1776) +#2484 := (~ #2483 #2482) +#2479 := (not #1771) +#2480 := (~ #2479 #2478) +#2475 := (not #1742) +#2476 := (~ #2475 #1739) +#2473 := (~ #1739 #1739) +#2471 := (~ #1736 #1736) +#2472 := [refl]: #2471 +#2474 := [nnf-pos #2472]: #2473 +#2477 := [nnf-neg #2474]: #2476 +#2468 := (not #1733) +#2469 := (~ #2468 #1730) +#2466 := (~ #1730 #1730) +#2464 := (~ #1725 #1725) +#2465 := [refl]: #2464 +#2467 := [nnf-pos #2465]: #2466 +#2470 := [nnf-neg #2467]: #2469 +#2461 := (not #1717) +#2462 := (~ #2461 #1714) +#2459 := (~ #1714 #1714) +#2457 := (~ #1711 #1711) +#2458 := [refl]: #2457 +#2460 := [nnf-pos #2458]: #2459 +#2463 := [nnf-neg #2460]: #2462 +#2454 := (not #1694) +#2455 := (~ #2454 #2453) +#2450 := (not #1689) +#2451 := (~ #2450 #2449) +#2447 := (~ #1655 #1655) +#2448 := [refl]: #2447 +#2444 := (not #1650) +#2445 := (~ #2444 #1647) +#2442 := (~ #1647 #1647) +#2440 := (~ #1642 #1642) +#2441 := [refl]: #2440 +#2443 := [nnf-pos #2441]: #2442 +#2446 := [nnf-neg #2443]: #2445 +#2437 := (not #1632) +#2438 := (~ #2437 #1629) +#2435 := (~ #1629 #1629) +#2433 := (~ #1626 #1626) +#2434 := [refl]: #2433 +#2436 := [nnf-pos #2434]: #2435 +#2439 := [nnf-neg #2436]: #2438 +#2430 := (not #1615) +#2431 := (~ #2430 #2429) +#2426 := (not #1612) +#2427 := (~ #2426 #2425) +#2422 := (not #1609) +#2423 := (~ #2422 #2421) +#2418 := (not #1606) +#2419 := (~ #2418 #2417) +#2414 := (not #1603) +#2415 := (~ #2414 #2413) +#2410 := (not #1600) +#2411 := (~ #2410 #2409) +#2406 := (not #1597) +#2407 := (~ #2406 #2405) +#2402 := (not #1594) +#2403 := (~ #2402 #2401) +#2398 := (not #1591) +#2399 := (~ #2398 #2397) +#2394 := (not #1588) +#2395 := (~ #2394 #2393) +#2390 := (not #1585) +#2391 := (~ #2390 #2389) +#2386 := (not #1582) +#2387 := (~ #2386 #2385) +#2367 := (not #1579) +#2383 := (~ #2367 #2380) +#2357 := (exists (vars (?v1 S3)) #2356) +#2365 := (or #2364 #2357) +#2366 := (not #2365) +#2381 := (~ #2366 #2380) +#2377 := (not #2357) +#2378 := (~ #2377 #2376) +#2374 := (~ #2373 #2373) +#2375 := [refl]: #2374 +#2379 := [nnf-neg #2375]: #2378 +#2371 := (~ #2370 #2370) +#2372 := [refl]: #2371 +#2382 := [nnf-neg #2372 #2379]: #2381 +#2368 := (~ #2367 #2366) +#2369 := [sk]: #2368 +#2384 := [trans #2369 #2382]: #2383 +#2343 := (not #1542) +#2344 := (~ #2343 #1539) +#2341 := (~ #1539 #1539) +#2339 := (~ #1536 #1536) +#2340 := [refl]: #2339 +#2342 := [nnf-pos #2340]: #2341 +#2345 := [nnf-neg #2342]: #2344 +#2388 := [nnf-neg #2345 #2384]: #2387 +#2335 := (~ #1542 #2334) +#2336 := [sk]: #2335 +#2392 := [nnf-neg #2336 #2388]: #2391 +#2312 := (not #1518) +#2313 := (~ #2312 #1515) +#2310 := (~ #1515 #1515) +#2308 := (~ #1510 #1510) +#2309 := [refl]: #2308 +#2311 := [nnf-pos #2309]: #2310 +#2314 := [nnf-neg #2311]: #2313 +#2396 := [nnf-neg #2314 #2392]: #2395 +#2304 := (~ #1518 #2303) +#2305 := [sk]: #2304 +#2400 := [nnf-neg #2305 #2396]: #2399 +#2285 := (not #1499) +#2286 := (~ #2285 #1496) +#2283 := (~ #1496 #1496) +#2281 := (~ #1493 #1493) +#2282 := [refl]: #2281 +#2284 := [nnf-pos #2282]: #2283 +#2287 := [nnf-neg #2284]: #2286 +#2404 := [nnf-neg #2287 #2400]: #2403 +#2277 := (~ #1499 #2276) +#2278 := [sk]: #2277 +#2408 := [nnf-neg #2278 #2404]: #2407 +#2271 := (~ #2270 #2270) +#2272 := [refl]: #2271 +#2412 := [nnf-neg #2272 #2408]: #2411 +#2268 := (~ #1490 #1490) +#2269 := [refl]: #2268 +#2416 := [nnf-neg #2269 #2412]: #2415 +#2265 := (not #953) +#2266 := (~ #2265 #819) +#2263 := (~ #819 #819) +#2261 := (~ #814 #814) +#2262 := [refl]: #2261 +#2264 := [nnf-pos #2262]: #2263 +#2267 := [nnf-neg #2264]: #2266 +#2420 := [nnf-neg #2267 #2416]: #2419 +#2257 := (~ #953 #2256) +#2258 := [sk]: #2257 +#2424 := [nnf-neg #2258 #2420]: #2423 +#2245 := (not #1485) +#2246 := (~ #2245 #1482) +#2243 := (~ #1482 #1482) +#2241 := (~ #1477 #1477) +#2242 := [refl]: #2241 +#2244 := [nnf-pos #2242]: #2243 +#2247 := [nnf-neg #2244]: #2246 +#2428 := [nnf-neg #2247 #2424]: #2427 +#2237 := (~ #1485 #2236) +#2238 := [sk]: #2237 +#2432 := [nnf-neg #2238 #2428]: #2431 +#2227 := (not #1474) +#2228 := (~ #2227 #1471) +#2225 := (~ #1471 #1471) +#2223 := (~ #1466 #1466) +#2224 := [refl]: #2223 +#2226 := [nnf-pos #2224]: #2225 +#2229 := [nnf-neg #2226]: #2228 +#2220 := (not #1665) +#2221 := (~ #2220 #2215) +#2216 := (~ #1424 #2215) +#2217 := [sk]: #2216 +#2222 := [nnf-neg #2217]: #2221 +#2204 := (~ #2203 #2203) +#2205 := [refl]: #2204 +#2201 := (~ #757 #757) +#2202 := [refl]: #2201 +#2452 := [nnf-neg #2202 #2205 #2222 #2229 #2432 #2439 #2446 #2448]: #2451 +#2198 := (not #1442) +#2199 := (~ #2198 #2197) +#2195 := (~ #1665 #2194) +#2192 := (~ #2191 #2191) +#2193 := [refl]: #2192 +#2196 := [nnf-neg #2193]: #2195 +#2188 := (not #1413) +#2189 := (~ #2188 #2187) +#2184 := (not #1410) +#2185 := (~ #2184 #2183) +#2180 := (not #1407) +#2181 := (~ #2180 #2179) +#2176 := (not #1402) +#2177 := (~ #2176 #2175) +#2172 := (not #1394) +#2173 := (~ #2172 #1391) +#2170 := (~ #1391 #1391) +#2168 := (~ #1388 #1388) +#2169 := [refl]: #2168 +#2171 := [nnf-pos #2169]: #2170 +#2174 := [nnf-neg #2171]: #2173 +#2166 := (~ #2165 #2165) +#2167 := [refl]: #2166 +#2178 := [nnf-neg #2167 #2174]: #2177 +#2161 := (~ #1394 #2160) +#2162 := [sk]: #2161 +#2182 := [nnf-neg #2162 #2178]: #2181 +#2136 := (not #1376) +#2137 := (~ #2136 #2133) +#2134 := (~ #1373 #2133) +#2131 := (~ #1370 #2130) +#2126 := (~ #1367 #2125) +#2127 := [sk]: #2126 +#2114 := (~ #1351 #1351) +#2115 := [refl]: #2114 +#2132 := [monotonicity #2115 #2127]: #2131 +#2135 := [nnf-pos #2132]: #2134 +#2138 := [nnf-neg #2135]: #2137 +#2186 := [nnf-neg #2138 #2182]: #2185 +#2112 := (~ #1376 #2109) +#2087 := (exists (vars (?v1 S3)) #2086) +#2095 := (or #2094 #2087) +#2096 := (not #2095) +#2110 := (~ #2096 #2109) +#2106 := (not #2087) +#2107 := (~ #2106 #2105) +#2103 := (~ #2102 #2102) +#2104 := [refl]: #2103 +#2108 := [nnf-neg #2104]: #2107 +#2100 := (~ #2099 #2099) +#2101 := [refl]: #2100 +#2111 := [nnf-neg #2101 #2108]: #2110 +#2097 := (~ #1376 #2096) +#2098 := [sk]: #2097 +#2113 := [trans #2098 #2111]: #2112 +#2190 := [nnf-neg #2113 #2186]: #2189 +#2074 := (~ #2073 #2073) +#2075 := [refl]: #2074 +#2071 := (~ #2070 #2070) +#2072 := [refl]: #2071 +#2068 := (~ #2067 #2067) +#2069 := [refl]: #2068 +#2065 := (~ #2064 #2064) +#2066 := [refl]: #2065 +#2200 := [nnf-neg #2066 #2069 #2072 #2075 #2190 #2196]: #2199 +#2456 := [nnf-neg #2200 #2452]: #2455 +#2061 := (not #1339) +#2062 := (~ #2061 #2058) +#2059 := (~ #1336 #2058) +#2056 := (~ #1333 #2055) +#2051 := (~ #1330 #2050) +#2052 := [sk]: #2051 +#2037 := (~ #1306 #1306) +#2038 := [refl]: #2037 +#2057 := [monotonicity #2038 #2052]: #2056 +#2060 := [nnf-pos #2057]: #2059 +#2063 := [nnf-neg #2060]: #2062 +#2034 := (not #1750) +#2035 := (~ #2034 #2031) +#2032 := (~ #1294 #2031) +#2029 := (~ #1291 #2028) +#2024 := (~ #1288 #2023) +#2025 := [sk]: #2024 +#2009 := (~ #1268 #1268) +#2010 := [refl]: #2009 +#2030 := [monotonicity #2010 #2025]: #2029 +#2033 := [nnf-pos #2030]: #2032 +#2036 := [nnf-neg #2033]: #2035 +#2007 := (~ #2006 #2006) +#2008 := [refl]: #2007 +#2481 := [nnf-neg #2008 #2036 #2063 #2456 #2463 #2470 #2477]: #2480 +#2004 := (~ #1750 #2001) +#1979 := (exists (vars (?v1 S3)) #1978) +#1987 := (or #1986 #1979) +#1988 := (not #1987) +#2002 := (~ #1988 #2001) +#1998 := (not #1979) +#1999 := (~ #1998 #1997) +#1995 := (~ #1994 #1994) +#1996 := [refl]: #1995 +#2000 := [nnf-neg #1996]: #1999 +#1992 := (~ #1991 #1991) +#1993 := [refl]: #1992 +#2003 := [nnf-neg #1993 #2000]: #2002 +#1989 := (~ #1750 #1988) +#1990 := [sk]: #1989 +#2005 := [trans #1990 #2003]: #2004 +#2485 := [nnf-neg #2005 #2481]: #2484 +#1964 := (not #1256) +#1965 := (~ #1964 #1253) +#1962 := (~ #1253 #1253) +#1960 := (~ #1250 #1250) +#1961 := [refl]: #1960 +#1963 := [nnf-pos #1961]: #1962 +#1966 := [nnf-neg #1963]: #1965 +#2489 := [nnf-neg #1966 #2485]: #2488 +#1956 := (~ #1256 #1955) +#1957 := [sk]: #1956 +#2493 := [nnf-neg #1957 #2489]: #2492 +#1933 := (not #1225) +#1934 := (~ #1933 #1222) +#1931 := (~ #1222 #1222) +#1929 := (~ #1217 #1217) +#1930 := [refl]: #1929 +#1932 := [nnf-pos #1930]: #1931 +#1935 := [nnf-neg #1932]: #1934 +#2497 := [nnf-neg #1935 #2493]: #2496 +#1925 := (~ #1225 #1924) +#1926 := [sk]: #1925 +#2501 := [nnf-neg #1926 #2497]: #2500 +#1906 := (not #1205) +#1907 := (~ #1906 #1202) +#1904 := (~ #1202 #1202) +#1902 := (~ #1201 #1201) +#1903 := [refl]: #1902 +#1905 := [nnf-pos #1903]: #1904 +#1908 := [nnf-neg #1905]: #1907 +#2505 := [nnf-neg #1908 #2501]: #2504 +#1898 := (~ #1205 #1897) +#1899 := [sk]: #1898 +#2509 := [nnf-neg #1899 #2505]: #2508 +#1861 := (~ #1860 #1860) +#1893 := [refl]: #1861 +#2513 := [nnf-neg #1893 #2509]: #2512 +#1891 := (~ #1196 #1196) +#1892 := [refl]: #1891 +#2516 := [nnf-neg #1892 #2513]: #2515 +#1837 := [not-or-elim #1833]: #1836 +#2517 := [mp~ #1837 #2516]: #2514 +#2518 := [mp #2517 #3055]: #3053 +#3697 := [mp #2518 #3696]: #3694 +#4604 := [mp #3697 #4603]: #4601 +#6496 := [unit-resolution #4604 #5320]: #4598 +#3943 := (or #4595 #4589) +#3944 := [def-axiom]: #3943 +#6497 := [unit-resolution #3944 #6496]: #4589 +#6498 := (or #4592 #4586) +#5107 := [hypothesis]: #1897 +#5106 := (<= #1895 0::Int) +#4721 := (or #5106 #1896) +#5139 := [th-lemma arith farkas 1 1]: #4721 +#5140 := [unit-resolution #5139 #5107]: #5106 +#5099 := (not #5106) +#5114 := (or #5099 #1896) +#355 := (<= f8 0::Int) +#356 := (not #355) +#46 := (< 0::Int f8) +#357 := (iff #46 #356) +#358 := [rewrite]: #357 +#351 := [asserted]: #46 +#359 := [mp #351 #358]: #356 +#4718 := (* -1::Int #1895) +#4719 := (+ f8 #4718) +#4720 := (<= #4719 0::Int) +#3933 := (= f8 #1895) +#3912 := (= f10 ?v0!0) +#4911 := (not #3912) +#4908 := (= #1895 0::Int) +#5108 := (not #4908) +#5109 := (or #5108 #1896) +#5110 := [th-lemma arith triangle-eq]: #5109 +#5090 := [unit-resolution #5110 #5107]: #5108 +#4917 := (or #4784 #4911 #4908) +#3932 := (= ?v0!0 f10) +#4909 := (not #3932) +#4910 := (or #4909 #4908) +#4648 := (or #4784 #4910) +#5103 := (iff #4648 #4917) +#4715 := (or #4911 #4908) +#4934 := (or #4784 #4715) +#4980 := (iff #4934 #4917) +#5102 := [rewrite]: #4980 +#4978 := (iff #4648 #4934) +#4716 := (iff #4910 #4715) +#4914 := (iff #4909 #4911) +#3914 := (iff #3932 #3912) +#3915 := [rewrite]: #3914 +#4915 := [monotonicity #3915]: #4914 +#4783 := [monotonicity #4915]: #4716 +#4979 := [monotonicity #4783]: #4978 +#5104 := [trans #4979 #5102]: #5103 +#4931 := [quant-inst #1894]: #4648 +#5105 := [mp #4931 #5104]: #4917 +#5091 := [unit-resolution #5105 #4610 #5090]: #4911 +#3927 := (or #3912 #3933) +#4219 := (forall (vars (?v0 S3)) (:pat #4218) #446) +#4222 := (iff #451 #4219) +#4220 := (iff #446 #446) +#4221 := [refl]: #4220 +#4223 := [quant-intro #4221]: #4222 +#1856 := (~ #451 #451) +#1885 := (~ #446 #446) +#1886 := [refl]: #1885 +#1857 := [nnf-pos #1886]: #1856 +#1834 := [not-or-elim #1833]: #451 +#1887 := [mp~ #1834 #1857]: #451 +#4224 := [mp #1887 #4223]: #4219 +#3923 := (not #4219) +#3916 := (or #3923 #3912 #3933) +#3922 := (or #3932 #3933) +#3924 := (or #3923 #3922) +#4662 := (iff #3924 #3916) +#3909 := (or #3923 #3927) +#4646 := (iff #3909 #3916) +#4661 := [rewrite]: #4646 +#4644 := (iff #3924 #3909) +#3918 := (iff #3922 #3927) +#3919 := [monotonicity #3915]: #3918 +#4645 := [monotonicity #3919]: #4644 +#4643 := [trans #4645 #4661]: #4662 +#3907 := [quant-inst #1894]: #3924 +#4717 := [mp #3907 #4643]: #3916 +#5092 := [unit-resolution #4717 #4224]: #3927 +#5093 := [unit-resolution #5092 #5091]: #3933 +#5094 := (not #3933) +#5089 := (or #5094 #4720) +#5095 := [th-lemma arith triangle-eq]: #5089 +#5096 := [unit-resolution #5095 #5093]: #4720 +#5097 := [hypothesis]: #5106 +#5098 := [th-lemma arith farkas 1 -1 1 #5097 #5096 #359]: false +#5115 := [lemma #5098]: #5114 +#5141 := [unit-resolution #5115 #5140 #5107]: false +#5142 := [lemma #5141]: #1896 +#3938 := (or #4592 #1897 #4586) +#3939 := [def-axiom]: #3938 +#6499 := [unit-resolution #3939 #5142]: #6498 +#6500 := [unit-resolution #6499 #6497]: #4586 +#3962 := (or #4583 #4577) +#3963 := [def-axiom]: #3962 +#6501 := [unit-resolution #3963 #6500]: #4577 +#5817 := [hypothesis]: #1917 +#5330 := (or #5529 #2054) +#5335 := [quant-inst #1910]: #5330 +#5818 := [unit-resolution #5335 #4231 #5817]: false +#5819 := [lemma #5818]: #2054 +#3755 := (or #2026 #1917) +#3842 := [def-axiom]: #3755 +#6502 := [unit-resolution #3842 #5819]: #2026 +#3956 := (or #4580 #1928 #4574) +#3958 := [def-axiom]: #3956 +#6503 := [unit-resolution #3958 #6502 #6501]: #4574 +#3983 := (or #4571 #4565) +#3984 := [def-axiom]: #3983 +#6504 := [unit-resolution #3984 #6503]: #4565 +#3979 := (or #4568 #3098 #4562) +#3980 := [def-axiom]: #3979 +#6505 := [unit-resolution #3980 #6504 #6495]: #4562 +#3993 := (or #4559 #4553) +#4014 := [def-axiom]: #3993 +#6506 := [unit-resolution #4014 #6505]: #4553 +#5790 := (= f8 #1970) +#5854 := (not #5790) +#5852 := [hypothesis]: #4270 +#4159 := (or #4267 #1982) +#3833 := [def-axiom]: #4159 +#5853 := [unit-resolution #3833 #5852]: #1982 +#5855 := (or #5854 #1981) +#5856 := [th-lemma arith triangle-eq]: #5855 +#5857 := [unit-resolution #5856 #5853]: #5854 +#3834 := (or #4267 #2569) +#4166 := [def-axiom]: #3834 +#5858 := [unit-resolution #4166 #5852]: #2569 +#5810 := (or #3923 #2566 #5790) +#5791 := (or #1983 #5790) +#5805 := (or #3923 #5791) +#5669 := (iff #5805 #5810) +#5807 := (or #2566 #5790) +#5812 := (or #3923 #5807) +#5815 := (iff #5812 #5810) +#5668 := [rewrite]: #5815 +#5813 := (iff #5805 #5812) +#5808 := (iff #5791 #5807) +#5809 := [monotonicity #2568]: #5808 +#5814 := [monotonicity #5809]: #5813 +#5670 := [trans #5814 #5668]: #5669 +#5811 := [quant-inst #1967]: #5805 +#5475 := [mp #5811 #5670]: #5810 +#5859 := [unit-resolution #5475 #4224 #5858 #5857]: false +#5860 := [lemma #5859]: #4267 +#4001 := (or #4556 #4270 #4550) +#4002 := [def-axiom]: #4001 +#6507 := [unit-resolution #4002 #5860 #6506]: #4550 +#4034 := (or #4547 #4274) +#4030 := [def-axiom]: #4034 +#7121 := [unit-resolution #4030 #6507]: #4274 +#9553 := (or #4279 #7757) +#9554 := [quant-inst #2273]: #9553 +#9580 := [unit-resolution #9554 #7121]: #7757 +#7570 := (* -1::Int #7536) +#7571 := (+ #2274 #7570) +#9581 := (>= #7571 0::Int) +#7539 := (= #2274 #7536) +#10087 := [hypothesis]: #2276 +#11985 := (or #7539 #2275 #6073) +#9988 := (f5 #7211 ?v0!15) +#9989 := (f9 #9988) +#9990 := (* -1::Int #9989) +#7586 := (f5 f22 ?v0!15) +#7587 := (f9 #7586) +#10058 := (+ #7587 #9990) +#10062 := (>= #10058 0::Int) +#10057 := (= #7587 #9989) +#10065 := (= #9989 #7587) +#10063 := (= #9988 #7586) +#10064 := [monotonicity #7790]: #10063 +#10066 := [monotonicity #10064]: #10065 +#10067 := [symm #10066]: #10057 +#10068 := (not #10057) +#10069 := (or #10068 #10062) +#10070 := [th-lemma arith triangle-eq]: #10069 +#10071 := [unit-resolution #10070 #10067]: #10062 +#7968 := (f5 #6069 #7211) +#8217 := (f6 #7968) +#9081 := (f13 f14 #8217) +#9082 := (* -1::Int #9081) +#9455 := (+ #6070 #9082) +#9457 := (>= #9455 0::Int) +#9861 := (= #6070 #9081) +#8218 := (= #6069 #8217) +#8389 := (or #6829 #8218) +#8390 := [quant-inst #6069 #7211]: #8389 +#9280 := [unit-resolution #8390 #4205]: #8218 +#11947 := [monotonicity #9280]: #9861 +#11945 := (not #9861) +#11948 := (or #11945 #9457) +#11949 := [th-lemma arith triangle-eq]: #11948 +#11950 := [unit-resolution #11949 #11947]: #9457 +#10866 := (+ #99 #9082) +#10878 := (<= #10866 0::Int) +#10875 := (= #99 #9081) +#11956 := (= #9081 #99) +#10697 := (= #8217 f10) +#7317 := (= #6069 f10) +#7319 := (= f10 #6069) +#7298 := (?v1!7 #6069) +#7310 := (f3 f15 #7298) +#7311 := (= f1 #7310) +#7312 := (not #7311) +#7303 := (f5 #7298 #6069) +#7304 := (f9 #7303) +#7305 := (* -1::Int #7304) +#7299 := (f13 f14 #7298) +#7300 := (* -1::Int #7299) +#7306 := (+ #7300 #7305) +#7307 := (+ #6070 #7306) +#7308 := (= #7307 0::Int) +#7309 := (not #7308) +#7301 := (+ #6070 #7300) +#7302 := (<= #7301 0::Int) +#7322 := (or #7302 #7309 #7312) +#9607 := (or #2275 #6073 #7302) +#8251 := (not #7302) +#10072 := [hypothesis]: #8251 +#10110 := (or #7539 #2275 #6073 #7302) +#9125 := (>= #7299 0::Int) +#9128 := (or #4279 #9125) +#9299 := [quant-inst #7298]: #9128 +#10073 := [unit-resolution #9299 #7121]: #9125 +#7561 := (* -1::Int #2274) +#7612 := (+ #7561 #7587) +#7613 := (+ #174 #7612) +#9497 := (<= #7613 0::Int) +#7616 := (= #7613 0::Int) +#7591 := (* -1::Int #7587) +#7595 := (+ f8 #7591) +#7596 := (<= #7595 0::Int) +#9510 := (not #7596) +#7605 := (+ #7570 #7587) +#7606 := (+ #174 #7605) +#7607 := (>= #7606 0::Int) +#7638 := (or #7596 #7607) +#7641 := (not #7638) +#10075 := (not #7539) +#10076 := [hypothesis]: #10075 +#7644 := (or #7539 #7641) +#5788 := (or #4547 #4538) +#4722 := (?v1!7 ?v0!8) +#4998 := (f13 f19 #4722) +#5011 := (* -1::Int #4998) +#4723 := (f13 f14 #4722) +#5231 := (+ #4723 #5011) +#5236 := (>= #5231 0::Int) +#5230 := (= #4723 #4998) +#5720 := (= #4998 #4723) +#5715 := [hypothesis]: #4535 +#5716 := [hypothesis]: #4550 +#4023 := (or #4547 #4541) +#3991 := [def-axiom]: #4023 +#5717 := [unit-resolution #3991 #5716]: #4541 +#4028 := (or #4544 #4383 #4538) +#4029 := [def-axiom]: #4028 +#5718 := [unit-resolution #4029 #5717 #5715]: #4383 +#4134 := (or #4380 #624) +#4135 := [def-axiom]: #4134 +#5719 := [unit-resolution #4135 #5718]: #624 +#5714 := [symm #5719]: #138 +#5721 := [monotonicity #5714]: #5720 +#5722 := [symm #5721]: #5230 +#5723 := (not #5230) +#5724 := (or #5723 #5236) +#5737 := [th-lemma arith triangle-eq]: #5724 +#5738 := [unit-resolution #5737 #5722]: #5236 +#4705 := (* -1::Int #4723) +#4655 := (f13 f14 ?v0!8) +#4706 := (+ #4655 #4705) +#4707 := (<= #4706 0::Int) +#4888 := (not #4707) +#4714 := (f3 f15 #4722) +#4785 := (= f1 #4714) +#4786 := (not #4785) +#4708 := (f5 #4722 ?v0!8) +#4709 := (f9 #4708) +#4704 := (* -1::Int #4709) +#4790 := (+ #4704 #4705) +#4791 := (+ #4655 #4790) +#4773 := (= #4791 0::Int) +#4776 := (not #4773) +#4781 := (or #4707 #4776 #4786) +#4855 := (not #4781) +#4656 := (* -1::Int #4655) +#4657 := (+ f8 #4656) +#4637 := (<= #4657 0::Int) +#4993 := (not #4637) +#4136 := (or #4380 #4374) +#4133 := [def-axiom]: #4136 +#5739 := [unit-resolution #4133 #5718]: #4374 +#4032 := (or #4547 #100) +#4033 := [def-axiom]: #4032 +#5740 := [unit-resolution #4033 #5716]: #100 +#5741 := (= #157 #99) +#5736 := [monotonicity #5714]: #5741 +#5742 := [trans #5736 #5740]: #158 +#4146 := (or #4356 #2165) +#3809 := [def-axiom]: #4146 +#5743 := [unit-resolution #3809 #5742]: #4356 +#4035 := (or #4547 #4282) +#4015 := [def-axiom]: #4035 +#5744 := [unit-resolution #4015 #5716]: #4282 +#3850 := (or #4380 #4316) +#4132 := [def-axiom]: #3850 +#5745 := [unit-resolution #4132 #5718]: #4316 +#4976 := (or #3361 #4321 #4287 #715) +#4949 := [hypothesis]: #3366 +#4149 := (or #3361 #2152) +#4150 := [def-axiom]: #4149 +#4950 := [unit-resolution #4150 #4949]: #2152 +#4724 := (f13 f14 ?v1!10) +#4725 := (* -1::Int #4724) +#4726 := (+ f8 #4725) +#4727 := (<= #4726 0::Int) +#4728 := (f3 f15 ?v1!10) +#4729 := (= f1 #4728) +#4800 := (not #4729) +#3837 := (f13 f14 ?v0!11) +#3838 := (* -1::Int #3837) +#4802 := (+ #3838 #4724) +#4803 := (+ #2146 #4802) +#4806 := (>= #4803 0::Int) +#4959 := (not #4806) +#4933 := (+ #2143 #4725) +#4935 := (>= #4933 0::Int) +#4932 := (= #2143 #4724) +#4937 := (= #4724 #2143) +#4936 := [hypothesis]: #624 +#4938 := [monotonicity #4936]: #4937 +#4939 := [symm #4938]: #4932 +#4940 := (not #4932) +#4941 := (or #4940 #4935) +#4942 := [th-lemma arith triangle-eq]: #4941 +#4943 := [unit-resolution #4942 #4939]: #4935 +#4147 := (not #2807) +#4153 := (or #3361 #4147) +#3791 := [def-axiom]: #4153 +#4944 := [unit-resolution #3791 #4949]: #4147 +#4926 := (+ #2141 #3838) +#4930 := (<= #4926 0::Int) +#4925 := (= #2141 #3837) +#4947 := (= #3837 #2141) +#4948 := [monotonicity #4936]: #4947 +#4951 := [symm #4948]: #4925 +#4952 := (not #4925) +#4953 := (or #4952 #4930) +#4964 := [th-lemma arith triangle-eq]: #4953 +#4965 := [unit-resolution #4964 #4951]: #4930 +#4961 := (not #4935) +#4960 := (not #4930) +#4962 := (or #4959 #4960 #2807 #4961) +#4954 := [hypothesis]: #4935 +#4955 := [hypothesis]: #4147 +#4956 := [hypothesis]: #4930 +#4957 := [hypothesis]: #4806 +#4958 := [th-lemma arith farkas 1 -1 1 1 #4957 #4956 #4955 #4954]: false +#4963 := [lemma #4958]: #4962 +#4966 := [unit-resolution #4963 #4965 #4944 #4943]: #4959 +#4969 := (or #4800 #4806) +#4151 := (or #3361 #2156) +#4152 := [def-axiom]: #4151 +#4967 := [unit-resolution #4152 #4949]: #2156 +#4968 := [hypothesis]: #4282 +#4817 := (or #4287 #2155 #4800 #4806) +#4795 := (+ #4724 #3838) +#4796 := (+ #2146 #4795) +#4799 := (>= #4796 0::Int) +#4801 := (or #4800 #2155 #4799) +#4818 := (or #4287 #4801) +#4825 := (iff #4818 #4817) +#4812 := (or #2155 #4800 #4806) +#4820 := (or #4287 #4812) +#4823 := (iff #4820 #4817) +#4824 := [rewrite]: #4823 +#4821 := (iff #4818 #4820) +#4815 := (iff #4801 #4812) +#4809 := (or #4800 #2155 #4806) +#4813 := (iff #4809 #4812) +#4814 := [rewrite]: #4813 +#4810 := (iff #4801 #4809) +#4807 := (iff #4799 #4806) +#4804 := (= #4796 #4803) +#4805 := [rewrite]: #4804 +#4808 := [monotonicity #4805]: #4807 +#4811 := [monotonicity #4808]: #4810 +#4816 := [trans #4811 #4814]: #4815 +#4822 := [monotonicity #4816]: #4821 +#4826 := [trans #4822 #4824]: #4825 +#4819 := [quant-inst #2140 #2139]: #4818 +#4827 := [mp #4819 #4826]: #4817 +#4970 := [unit-resolution #4827 #4968 #4967]: #4969 +#4971 := [unit-resolution #4970 #4966]: #4800 +#4731 := (or #4727 #4729) +#4972 := [hypothesis]: #4316 +#4734 := (or #4321 #4727 #4729) +#4730 := (or #4729 #4727) +#4735 := (or #4321 #4730) +#4742 := (iff #4735 #4734) +#4737 := (or #4321 #4731) +#4740 := (iff #4737 #4734) +#4741 := [rewrite]: #4740 +#4738 := (iff #4735 #4737) +#4732 := (iff #4730 #4731) +#4733 := [rewrite]: #4732 +#4739 := [monotonicity #4733]: #4738 +#4743 := [trans #4739 #4741]: #4742 +#4736 := [quant-inst #2139]: #4735 +#4744 := [mp #4736 #4743]: #4734 +#4973 := [unit-resolution #4744 #4972]: #4731 +#4974 := [unit-resolution #4973 #4971]: #4727 +#4975 := [th-lemma arith farkas 1 -1 1 #4943 #4974 #4950]: false +#4977 := [lemma #4975]: #4976 +#5746 := [unit-resolution #4977 #5745 #5744 #5719]: #3361 +#4158 := (or #4365 #4359 #3366) +#4144 := [def-axiom]: #4158 +#5747 := [unit-resolution #4144 #5746 #5743]: #4365 +#3868 := (or #4368 #4362) +#3869 := [def-axiom]: #3868 +#5748 := [unit-resolution #3869 #5747]: #4368 +#4138 := (or #4377 #4337 #4371) +#4142 := [def-axiom]: #4138 +#5749 := [unit-resolution #4142 #5748 #5739]: #4337 +#4170 := (or #4334 #2090) +#4160 := [def-axiom]: #4170 +#5750 := [unit-resolution #4160 #5749]: #2090 +#4986 := (+ #2077 #4656) +#4988 := (>= #4986 0::Int) +#4985 := (= #2077 #4655) +#5413 := (= #4655 #2077) +#5751 := [monotonicity #5719]: #5413 +#5752 := [symm #5751]: #4985 +#5416 := (not #4985) +#5421 := (or #5416 #4988) +#5422 := [th-lemma arith triangle-eq]: #5421 +#5753 := [unit-resolution #5422 #5752]: #4988 +#4994 := (not #4988) +#4995 := (or #4993 #4994 #2089) +#4989 := [hypothesis]: #2090 +#4990 := [hypothesis]: #4637 +#4991 := [hypothesis]: #4988 +#4992 := [th-lemma arith farkas 1 -1 1 #4991 #4990 #4989]: false +#4996 := [lemma #4992]: #4995 +#5754 := [unit-resolution #4996 #5753 #5750]: #4993 +#5764 := (or #4637 #4855) +#3820 := (or #4334 #2707) +#3825 := [def-axiom]: #3820 +#5762 := [unit-resolution #3825 #5749]: #2707 +#4022 := (or #4547 #4307) +#4017 := [def-axiom]: #4022 +#5763 := [unit-resolution #4017 #5716]: #4307 +#4860 := (or #4312 #2704 #4637 #4855) +#4710 := (+ #4705 #4704) +#4711 := (+ #4655 #4710) +#4712 := (= #4711 0::Int) +#4713 := (not #4712) +#4787 := (or #4786 #4713 #4707) +#4788 := (not #4787) +#4789 := (or #2091 #4637 #4788) +#4861 := (or #4312 #4789) +#4884 := (iff #4861 #4860) +#4858 := (or #2704 #4637 #4855) +#4863 := (or #4312 #4858) +#4882 := (iff #4863 #4860) +#4883 := [rewrite]: #4882 +#4879 := (iff #4861 #4863) +#4853 := (iff #4789 #4858) +#4856 := (iff #4788 #4855) +#4798 := (iff #4787 #4781) +#4778 := (or #4786 #4776 #4707) +#4782 := (iff #4778 #4781) +#4797 := [rewrite]: #4782 +#4779 := (iff #4787 #4778) +#4777 := (iff #4713 #4776) +#4774 := (iff #4712 #4773) +#4792 := (= #4711 #4791) +#4793 := [rewrite]: #4792 +#4775 := [monotonicity #4793]: #4774 +#4772 := [monotonicity #4775]: #4777 +#4780 := [monotonicity #4772]: #4779 +#4854 := [trans #4780 #4797]: #4798 +#4857 := [monotonicity #4854]: #4856 +#4859 := [monotonicity #2706 #4857]: #4853 +#4881 := [monotonicity #4859]: #4879 +#4885 := [trans #4881 #4883]: #4884 +#4862 := [quant-inst #2076]: #4861 +#4880 := [mp #4862 #4885]: #4860 +#5765 := [unit-resolution #4880 #5763 #5762]: #5764 +#5766 := [unit-resolution #5765 #5754]: #4855 +#4889 := (or #4781 #4888) +#4890 := [def-axiom]: #4889 +#5767 := [unit-resolution #4890 #5766]: #4888 +#5012 := (+ #2077 #5011) +#5013 := (<= #5012 0::Int) +#5025 := (+ #4704 #5011) +#5026 := (+ #2077 #5025) +#5027 := (= #5026 0::Int) +#5049 := (<= #5026 0::Int) +#5235 := (<= #5231 0::Int) +#5768 := (or #5723 #5235) +#5769 := [th-lemma arith triangle-eq]: #5768 +#5770 := [unit-resolution #5769 #5722]: #5235 +#4886 := (<= #4791 0::Int) +#4905 := (or #4781 #4773) +#4907 := [def-axiom]: #4905 +#5771 := [unit-resolution #4907 #5766]: #4773 +#5772 := (or #4776 #4886) +#5773 := [th-lemma arith triangle-eq]: #5772 +#5774 := [unit-resolution #5773 #5771]: #4886 +#4987 := (<= #4986 0::Int) +#5417 := (or #5416 #4987) +#5418 := [th-lemma arith triangle-eq]: #5417 +#5775 := [unit-resolution #5418 #5752]: #4987 +#5359 := (not #5235) +#5358 := (not #4886) +#5357 := (not #4987) +#5360 := (or #5049 #5357 #5358 #5359) +#5351 := [hypothesis]: #5235 +#5352 := [hypothesis]: #4886 +#5353 := [hypothesis]: #4987 +#5354 := (not #5049) +#5355 := [hypothesis]: #5354 +#5356 := [th-lemma arith farkas -1 1 1 1 #5355 #5353 #5352 #5351]: false +#5361 := [lemma #5356]: #5360 +#5776 := [unit-resolution #5361 #5775 #5774 #5770]: #5049 +#5050 := (>= #5026 0::Int) +#4887 := (>= #4791 0::Int) +#5777 := (or #4776 #4887) +#5778 := [th-lemma arith triangle-eq]: #5777 +#5779 := [unit-resolution #5778 #5771]: #4887 +#5759 := (not #5236) +#5399 := (not #4887) +#5760 := (or #5050 #4994 #5399 #5759) +#5755 := [hypothesis]: #5236 +#5395 := [hypothesis]: #4887 +#5756 := (not #5050) +#5757 := [hypothesis]: #5756 +#5758 := [th-lemma arith farkas -1 1 1 1 #5757 #4991 #5395 #5755]: false +#5761 := [lemma #5758]: #5760 +#5780 := [unit-resolution #5761 #5753 #5779 #5738]: #5050 +#5781 := (or #5027 #5354 #5756) +#5782 := [th-lemma arith triangle-eq]: #5781 +#5783 := [unit-resolution #5782 #5780 #5776]: #5027 +#5032 := (not #5027) +#5035 := (or #5013 #5032) +#4161 := (or #4334 #4326) +#3821 := [def-axiom]: #4161 +#5784 := [unit-resolution #3821 #5749]: #4326 +#5038 := (or #4331 #5013 #5032) +#4997 := (+ #2078 #4709) +#4999 := (+ #4998 #4997) +#5000 := (= #4999 0::Int) +#5001 := (not #5000) +#5002 := (+ #4998 #2078) +#5003 := (>= #5002 0::Int) +#5004 := (or #5003 #5001) +#5039 := (or #4331 #5004) +#5046 := (iff #5039 #5038) +#5041 := (or #4331 #5035) +#5044 := (iff #5041 #5038) +#5045 := [rewrite]: #5044 +#5042 := (iff #5039 #5041) +#5036 := (iff #5004 #5035) +#5033 := (iff #5001 #5032) +#5030 := (iff #5000 #5027) +#5018 := (+ #4709 #4998) +#5019 := (+ #2078 #5018) +#5022 := (= #5019 0::Int) +#5028 := (iff #5022 #5027) +#5029 := [rewrite]: #5028 +#5023 := (iff #5000 #5022) +#5020 := (= #4999 #5019) +#5021 := [rewrite]: #5020 +#5024 := [monotonicity #5021]: #5023 +#5031 := [trans #5024 #5029]: #5030 +#5034 := [monotonicity #5031]: #5033 +#5016 := (iff #5003 #5013) +#5005 := (+ #2078 #4998) +#5008 := (>= #5005 0::Int) +#5014 := (iff #5008 #5013) +#5015 := [rewrite]: #5014 +#5009 := (iff #5003 #5008) +#5006 := (= #5002 #5005) +#5007 := [rewrite]: #5006 +#5010 := [monotonicity #5007]: #5009 +#5017 := [trans #5010 #5015]: #5016 +#5037 := [monotonicity #5017 #5034]: #5036 +#5043 := [monotonicity #5037]: #5042 +#5047 := [trans #5043 #5045]: #5046 +#5040 := [quant-inst #4722]: #5039 +#5048 := [mp #5040 #5047]: #5038 +#5785 := [unit-resolution #5048 #5784]: #5035 +#5786 := [unit-resolution #5785 #5783]: #5013 +#5787 := [th-lemma arith farkas 1 -1 1 1 #5753 #5786 #5767 #5738]: false +#5789 := [lemma #5787]: #5788 +#6508 := [unit-resolution #5789 #6507]: #4538 +#4044 := (or #4535 #4396) +#4039 := [def-axiom]: #4044 +#6509 := [unit-resolution #4039 #6508]: #4396 +#9499 := (or #4401 #7539 #7641) +#7592 := (+ #1453 #7591) +#7593 := (+ #7536 #7592) +#7594 := (<= #7593 0::Int) +#7635 := (or #7596 #7594) +#7636 := (not #7635) +#7537 := (= #7536 #2274) +#7637 := (or #7537 #7636) +#9500 := (or #4401 #7637) +#9507 := (iff #9500 #9499) +#9502 := (or #4401 #7644) +#9505 := (iff #9502 #9499) +#9506 := [rewrite]: #9505 +#9503 := (iff #9500 #9502) +#7645 := (iff #7637 #7644) +#7642 := (iff #7636 #7641) +#7639 := (iff #7635 #7638) +#7610 := (iff #7594 #7607) +#7598 := (+ #7536 #7591) +#7599 := (+ #1453 #7598) +#7602 := (<= #7599 0::Int) +#7608 := (iff #7602 #7607) +#7609 := [rewrite]: #7608 +#7603 := (iff #7594 #7602) +#7600 := (= #7593 #7599) +#7601 := [rewrite]: #7600 +#7604 := [monotonicity #7601]: #7603 +#7611 := [trans #7604 #7609]: #7610 +#7640 := [monotonicity #7611]: #7639 +#7643 := [monotonicity #7640]: #7642 +#7540 := (iff #7537 #7539) +#7541 := [rewrite]: #7540 +#7646 := [monotonicity #7541 #7643]: #7645 +#9504 := [monotonicity #7646]: #9503 +#9508 := [trans #9504 #9506]: #9507 +#9501 := [quant-inst #2273]: #9500 +#9509 := [mp #9501 #9508]: #9499 +#10077 := [unit-resolution #9509 #6509]: #7644 +#10078 := [unit-resolution #10077 #10076]: #7641 +#9511 := (or #7638 #9510) +#9512 := [def-axiom]: #9511 +#10079 := [unit-resolution #9512 #10078]: #9510 +#9513 := (not #7607) +#9514 := (or #7638 #9513) +#9515 := [def-axiom]: #9514 +#10080 := [unit-resolution #9515 #10078]: #9513 +#7619 := (or #7596 #7607 #7616) +#4045 := (or #4535 #4404) +#4018 := [def-axiom]: #4045 +#6513 := [unit-resolution #4018 #6508]: #4404 +#9486 := (or #4409 #7596 #7607 #7616) +#7588 := (+ #7587 #7561) +#7589 := (+ #174 #7588) +#7590 := (= #7589 0::Int) +#7597 := (or #7596 #7594 #7590) +#9487 := (or #4409 #7597) +#9494 := (iff #9487 #9486) +#9489 := (or #4409 #7619) +#9492 := (iff #9489 #9486) +#9493 := [rewrite]: #9492 +#9490 := (iff #9487 #9489) +#7620 := (iff #7597 #7619) +#7617 := (iff #7590 #7616) +#7614 := (= #7589 #7613) +#7615 := [rewrite]: #7614 +#7618 := [monotonicity #7615]: #7617 +#7621 := [monotonicity #7611 #7618]: #7620 +#9491 := [monotonicity #7621]: #9490 +#9495 := [trans #9491 #9493]: #9494 +#9488 := [quant-inst #2273]: #9487 +#9496 := [mp #9488 #9495]: #9486 +#10081 := [unit-resolution #9496 #6513]: #7619 +#10082 := [unit-resolution #10081 #10080 #10079]: #7616 +#10083 := (not #7616) +#10084 := (or #10083 #9497) +#10085 := [th-lemma arith triangle-eq]: #10084 +#10086 := [unit-resolution #10085 #10082]: #9497 +#10050 := (>= #9989 0::Int) +#10025 := (<= #9989 0::Int) +#10026 := (not #10025) +#9949 := (= ?v0!15 #7211) +#9968 := (not #9949) +#7668 := (f3 f15 ?v0!15) +#7669 := (= f1 #7668) +#5891 := (f3 #773 f22) +#5892 := (= f1 #5891) +#9952 := (ite #9949 #5892 #7669) +#9967 := (not #9952) +#8442 := (f4 f15 #7211 #5891) +#9946 := (f3 #8442 ?v0!15) +#9947 := (= f1 #9946) +#9955 := (iff #9947 #9952) +#10 := (:var 1 S1) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#4171 := (pattern #13) +#17 := (f3 #8 #12) +#301 := (= f1 #17) +#298 := (= f1 #10) +#295 := (= #9 #12) +#304 := (ite #295 #298 #301) +#292 := (= f1 #13) +#307 := (iff #292 #304) +#4172 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4171) #307) +#310 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #307) +#4175 := (iff #310 #4172) +#4173 := (iff #307 #307) +#4174 := [refl]: #4173 +#4176 := [quant-intro #4174]: #4175 +#1868 := (~ #310 #310) +#1866 := (~ #307 #307) +#1867 := [refl]: #1866 +#1869 := [nnf-pos #1867]: #1868 +#18 := (= #17 f1) +#16 := (= #10 f1) +#15 := (= #12 #9) +#19 := (ite #15 #16 #18) +#14 := (= #13 f1) +#20 := (iff #14 #19) +#21 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #20) +#311 := (iff #21 #310) +#308 := (iff #20 #307) +#305 := (iff #19 #304) +#302 := (iff #18 #301) +#303 := [rewrite]: #302 +#299 := (iff #16 #298) +#300 := [rewrite]: #299 +#296 := (iff #15 #295) +#297 := [rewrite]: #296 +#306 := [monotonicity #297 #300 #303]: #305 +#293 := (iff #14 #292) +#294 := [rewrite]: #293 +#309 := [monotonicity #294 #306]: #308 +#312 := [quant-intro #309]: #311 +#291 := [asserted]: #21 +#315 := [mp #291 #312]: #310 +#1840 := [mp~ #315 #1869]: #310 +#4177 := [mp #1840 #4176]: #4172 +#6290 := (not #4172) +#9958 := (or #6290 #9955) +#9944 := (= #7211 ?v0!15) +#9945 := (ite #9944 #5892 #7669) +#9948 := (iff #9947 #9945) +#9959 := (or #6290 #9948) +#9961 := (iff #9959 #9958) +#9963 := (iff #9958 #9958) +#9964 := [rewrite]: #9963 +#9956 := (iff #9948 #9955) +#9953 := (iff #9945 #9952) +#9950 := (iff #9944 #9949) +#9951 := [rewrite]: #9950 +#9954 := [monotonicity #9951]: #9953 +#9957 := [monotonicity #9954]: #9956 +#9962 := [monotonicity #9957]: #9961 +#9965 := [trans #9962 #9964]: #9961 +#9960 := [quant-inst #104 #7211 #5891 #2273]: #9959 +#9966 := [mp #9960 #9965]: #9958 +#10088 := [unit-resolution #9966 #4177]: #9955 +#9981 := (not #9947) +#7533 := (f3 f23 ?v0!15) +#7534 := (= f1 #7533) +#7535 := (not #7534) +#10097 := (iff #7535 #9981) +#10095 := (iff #7534 #9947) +#10093 := (iff #9947 #7534) +#10091 := (= #9946 #7533) +#9285 := (= #8442 f23) +#7004 := (= #773 f23) +#4053 := (or #4535 #776) +#4048 := [def-axiom]: #4053 +#6998 := [unit-resolution #4048 #6508]: #776 +#7005 := [symm #6998]: #7004 +#9283 := (= #8442 #773) +#7000 := (= #5891 f1) +#24 := (:var 0 S1) +#22 := (:var 2 S2) +#25 := (f4 #22 #23 #24) +#4178 := (pattern #25) +#318 := (= f1 #24) +#26 := (f3 #25 #23) +#314 := (= f1 #26) +#321 := (iff #314 #318) +#4179 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4178) #321) +#324 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #321) +#4182 := (iff #324 #4179) +#4180 := (iff #321 #321) +#4181 := [refl]: #4180 +#4183 := [quant-intro #4181]: #4182 +#1842 := (~ #324 #324) +#1841 := (~ #321 #321) +#1870 := [refl]: #1841 +#1843 := [nnf-pos #1870]: #1842 +#28 := (= #24 f1) +#27 := (= #26 f1) +#29 := (iff #27 #28) +#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #29) +#325 := (iff #30 #324) +#322 := (iff #29 #321) +#319 := (iff #28 #318) +#320 := [rewrite]: #319 +#316 := (iff #27 #314) +#317 := [rewrite]: #316 +#323 := [monotonicity #317 #320]: #322 +#326 := [quant-intro #323]: #325 +#313 := [asserted]: #30 +#329 := [mp #313 #326]: #324 +#1871 := [mp~ #329 #1843]: #324 +#4184 := [mp #1871 #4183]: #4179 +#5903 := (not #4179) +#5904 := (or #5903 #5892) +#5890 := (= f1 f1) +#5893 := (iff #5892 #5890) +#5905 := (or #5903 #5893) +#5907 := (iff #5905 #5904) +#5909 := (iff #5904 #5904) +#5910 := [rewrite]: #5909 +#5901 := (iff #5893 #5892) +#5896 := (iff #5892 true) +#5899 := (iff #5896 #5892) +#5900 := [rewrite]: #5899 +#5897 := (iff #5893 #5896) +#5894 := (iff #5890 true) +#5895 := [rewrite]: #5894 +#5898 := [monotonicity #5895]: #5897 +#5902 := [trans #5898 #5900]: #5901 +#5908 := [monotonicity #5902]: #5907 +#5911 := [trans #5908 #5910]: #5907 +#5906 := [quant-inst #104 #170 #4]: #5905 +#5912 := [mp #5906 #5911]: #5904 +#6999 := [unit-resolution #5912 #4184]: #5892 +#7001 := [symm #6999]: #7000 +#9284 := [monotonicity #7790 #7001]: #9283 +#9286 := [trans #9284 #7005]: #9285 +#10092 := [monotonicity #9286]: #10091 +#10094 := [monotonicity #10092]: #10093 +#10096 := [symm #10094]: #10095 +#10098 := [monotonicity #10096]: #10097 +#7545 := (or #7535 #7539) +#4019 := (or #4535 #4529) +#4020 := [def-axiom]: #4019 +#7096 := [unit-resolution #4020 #6508]: #4529 +#6311 := (f5 f22 ?v0!13) +#6312 := (f9 #6311) +#6337 := (+ #2232 #6312) +#6338 := (+ #174 #6337) +#6359 := (>= #6338 0::Int) +#6341 := (= #6338 0::Int) +#6316 := (* -1::Int #6312) +#6320 := (+ f8 #6316) +#6321 := (<= #6320 0::Int) +#6388 := (not #6321) +#6330 := (+ #2848 #6312) +#6331 := (+ #174 #6330) +#6332 := (>= #6331 0::Int) +#6367 := (or #6321 #6332) +#6370 := (not #6367) +#6364 := (= #2231 #2233) +#6489 := (not #6364) +#6488 := [hypothesis]: #2855 +#6492 := (or #6489 #2850) +#6493 := [th-lemma arith triangle-eq]: #6492 +#6494 := [unit-resolution #6493 #6488]: #6489 +#6376 := (or #4401 #6364 #6370) +#6317 := (+ #1453 #6316) +#6318 := (+ #2233 #6317) +#6319 := (<= #6318 0::Int) +#6360 := (or #6321 #6319) +#6361 := (not #6360) +#6362 := (= #2233 #2231) +#6363 := (or #6362 #6361) +#6377 := (or #4401 #6363) +#6384 := (iff #6377 #6376) +#6373 := (or #6364 #6370) +#6379 := (or #4401 #6373) +#6382 := (iff #6379 #6376) +#6383 := [rewrite]: #6382 +#6380 := (iff #6377 #6379) +#6374 := (iff #6363 #6373) +#6371 := (iff #6361 #6370) +#6368 := (iff #6360 #6367) +#6335 := (iff #6319 #6332) +#6323 := (+ #2233 #6316) +#6324 := (+ #1453 #6323) +#6327 := (<= #6324 0::Int) +#6333 := (iff #6327 #6332) +#6334 := [rewrite]: #6333 +#6328 := (iff #6319 #6327) +#6325 := (= #6318 #6324) +#6326 := [rewrite]: #6325 +#6329 := [monotonicity #6326]: #6328 +#6336 := [trans #6329 #6334]: #6335 +#6369 := [monotonicity #6336]: #6368 +#6372 := [monotonicity #6369]: #6371 +#6365 := (iff #6362 #6364) +#6366 := [rewrite]: #6365 +#6375 := [monotonicity #6366 #6372]: #6374 +#6381 := [monotonicity #6375]: #6380 +#6385 := [trans #6381 #6383]: #6384 +#6378 := [quant-inst #2230]: #6377 +#6386 := [mp #6378 #6385]: #6376 +#6510 := [unit-resolution #6386 #6509 #6494]: #6370 +#6389 := (or #6367 #6388) +#6390 := [def-axiom]: #6389 +#6511 := [unit-resolution #6390 #6510]: #6388 +#6391 := (not #6332) +#6392 := (or #6367 #6391) +#6393 := [def-axiom]: #6392 +#6512 := [unit-resolution #6393 #6510]: #6391 +#6344 := (or #6321 #6332 #6341) +#6347 := (or #4409 #6321 #6332 #6341) +#6313 := (+ #6312 #2232) +#6314 := (+ #174 #6313) +#6315 := (= #6314 0::Int) +#6322 := (or #6321 #6319 #6315) +#6348 := (or #4409 #6322) +#6355 := (iff #6348 #6347) +#6350 := (or #4409 #6344) +#6353 := (iff #6350 #6347) +#6354 := [rewrite]: #6353 +#6351 := (iff #6348 #6350) +#6345 := (iff #6322 #6344) +#6342 := (iff #6315 #6341) +#6339 := (= #6314 #6338) +#6340 := [rewrite]: #6339 +#6343 := [monotonicity #6340]: #6342 +#6346 := [monotonicity #6336 #6343]: #6345 +#6352 := [monotonicity #6346]: #6351 +#6356 := [trans #6352 #6354]: #6355 +#6349 := [quant-inst #2230]: #6348 +#6357 := [mp #6349 #6356]: #6347 +#6514 := [unit-resolution #6357 #6513]: #6344 +#6515 := [unit-resolution #6514 #6512 #6511]: #6341 +#6516 := (not #6341) +#6517 := (or #6516 #6359) +#6518 := [th-lemma arith triangle-eq]: #6517 +#6519 := [unit-resolution #6518 #6515]: #6359 +#6387 := (>= #2849 0::Int) +#6520 := (or #6387 #2850) +#6521 := [th-lemma arith farkas 1 1]: #6520 +#6522 := [unit-resolution #6521 #6488]: #6387 +#6523 := [th-lemma arith farkas 1 -1 1 #6522 #6512 #6519]: false +#6524 := [lemma #6523]: #2850 +#4049 := (or #4532 #2855 #4526) +#4050 := [def-axiom]: #4049 +#7097 := [unit-resolution #4050 #6524 #7096]: #4526 +#4064 := (or #4523 #4517) +#4065 := [def-axiom]: #4064 +#7098 := [unit-resolution #4065 #7097]: #4517 +#6879 := (= #174 #2253) +#6696 := (= f22 ?v0!14) +#6526 := (f3 f15 ?v0!14) +#6527 := (= f1 #6526) +#6697 := (ite #6696 #5892 #6527) +#6269 := (f4 f15 f22 #5891) +#6700 := (f3 #6269 ?v0!14) +#6701 := (= f1 #6700) +#6703 := (iff #6697 #6701) +#6706 := (or #6290 #6703) +#6702 := (iff #6701 #6697) +#6707 := (or #6290 #6702) +#6709 := (iff #6707 #6706) +#6711 := (iff #6706 #6706) +#6712 := [rewrite]: #6711 +#6704 := (iff #6702 #6703) +#6705 := [rewrite]: #6704 +#6710 := [monotonicity #6705]: #6709 +#6713 := [trans #6710 #6712]: #6709 +#6708 := [quant-inst #104 #170 #5891 #2248]: #6707 +#6714 := [mp #6708 #6713]: #6706 +#6996 := [unit-resolution #6714 #4177]: #6703 +#7012 := (= #2249 #6700) +#7008 := (= #6700 #2249) +#7006 := (= #6269 f23) +#7002 := (= #6269 #773) +#7003 := [monotonicity #7001]: #7002 +#7007 := [trans #7003 #7005]: #7006 +#7009 := [monotonicity #7007]: #7008 +#7013 := [symm #7009]: #7012 +#6994 := [hypothesis]: #2869 +#4127 := (or #2864 #2250) +#4128 := [def-axiom]: #4127 +#6997 := [unit-resolution #4128 #6994]: #2250 +#7014 := [trans #6997 #7013]: #6701 +#6727 := (not #6701) +#6726 := (not #6703) +#6728 := (or #6726 #6697 #6727) +#6729 := [def-axiom]: #6728 +#7015 := [unit-resolution #6729 #7014 #6996]: #6697 +#6555 := (f5 f22 ?v0!14) +#6556 := (f9 #6555) +#6486 := (* -1::Int #2253) +#6573 := (+ #6486 #6556) +#6574 := (+ #174 #6573) +#6575 := (>= #6574 0::Int) +#6603 := (not #6575) +#6557 := (* -1::Int #6556) +#6561 := (+ f8 #6557) +#6562 := (<= #6561 0::Int) +#6580 := (or #6562 #6575) +#6583 := (not #6580) +#4123 := (not #2858) +#4124 := (or #2864 #4123) +#4129 := [def-axiom]: #4124 +#6995 := [unit-resolution #4129 #6994]: #4123 +#6589 := (or #4401 #2858 #6583) +#6558 := (+ #1453 #6557) +#6559 := (+ #2253 #6558) +#6560 := (<= #6559 0::Int) +#6563 := (or #6562 #6560) +#6564 := (not #6563) +#6565 := (or #2254 #6564) +#6590 := (or #4401 #6565) +#6597 := (iff #6590 #6589) +#6586 := (or #2858 #6583) +#6592 := (or #4401 #6586) +#6595 := (iff #6592 #6589) +#6596 := [rewrite]: #6595 +#6593 := (iff #6590 #6592) +#6587 := (iff #6565 #6586) +#6584 := (iff #6564 #6583) +#6581 := (iff #6563 #6580) +#6578 := (iff #6560 #6575) +#6566 := (+ #2253 #6557) +#6567 := (+ #1453 #6566) +#6570 := (<= #6567 0::Int) +#6576 := (iff #6570 #6575) +#6577 := [rewrite]: #6576 +#6571 := (iff #6560 #6570) +#6568 := (= #6559 #6567) +#6569 := [rewrite]: #6568 +#6572 := [monotonicity #6569]: #6571 +#6579 := [trans #6572 #6577]: #6578 +#6582 := [monotonicity #6579]: #6581 +#6585 := [monotonicity #6582]: #6584 +#6588 := [monotonicity #2860 #6585]: #6587 +#6594 := [monotonicity #6588]: #6593 +#6598 := [trans #6594 #6596]: #6597 +#6591 := [quant-inst #2248]: #6590 +#6599 := [mp #6591 #6598]: #6589 +#7016 := [unit-resolution #6599 #6509 #6995]: #6583 +#6604 := (or #6580 #6603) +#6605 := [def-axiom]: #6604 +#7017 := [unit-resolution #6605 #7016]: #6603 +#6715 := (not #6697) +#6941 := (or #6696 #6575 #6715) +#6822 := (f6 #6555) +#6832 := (f13 f14 #6822) +#6847 := (* -1::Int #6832) +#6887 := (+ #174 #6847) +#6889 := (>= #6887 0::Int) +#6886 := (= #174 #6832) +#6893 := (= #6832 #174) +#6891 := (= #6822 f22) +#6823 := (= f22 #6822) +#6830 := (or #6829 #6823) +#6831 := [quant-inst #170 #2248]: #6830 +#6890 := [unit-resolution #6831 #4205]: #6823 +#6892 := [symm #6890]: #6891 +#6894 := [monotonicity #6892]: #6893 +#6895 := [symm #6894]: #6886 +#6896 := (not #6886) +#6897 := (or #6896 #6889) +#6898 := [th-lemma arith triangle-eq]: #6897 +#6899 := [unit-resolution #6898 #6895]: #6889 +#6900 := [hypothesis]: #6603 +#6819 := (>= #6556 0::Int) +#6773 := (<= #6556 0::Int) +#6774 := (not #6773) +#6716 := (not #6696) +#6901 := [hypothesis]: #6716 +#6779 := (or #6696 #6774) +#48 := (f9 #37) +#407 := (<= #48 0::Int) +#408 := (not #407) +#354 := (= #12 #23) +#414 := (or #354 #408) +#4212 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #414) +#419 := (forall (vars (?v0 S3) (?v1 S3)) #414) +#4215 := (iff #419 #4212) +#4213 := (iff #414 #414) +#4214 := [refl]: #4213 +#4216 := [quant-intro #4214]: #4215 +#1854 := (~ #419 #419) +#1853 := (~ #414 #414) +#1883 := [refl]: #1853 +#1855 := [nnf-pos #1883]: #1854 +#53 := (< 0::Int #48) +#47 := (= #23 #12) +#52 := (not #47) +#54 := (implies #52 #53) +#55 := (forall (vars (?v0 S3) (?v1 S3)) #54) +#422 := (iff #55 #419) +#399 := (or #53 #354) +#404 := (forall (vars (?v0 S3) (?v1 S3)) #399) +#420 := (iff #404 #419) +#417 := (iff #399 #414) +#411 := (or #408 #354) +#415 := (iff #411 #414) +#416 := [rewrite]: #415 +#412 := (iff #399 #411) +#409 := (iff #53 #408) +#410 := [rewrite]: #409 +#413 := [monotonicity #410]: #412 +#418 := [trans #413 #416]: #417 +#421 := [quant-intro #418]: #420 +#405 := (iff #55 #404) +#402 := (iff #54 #399) +#368 := (not #354) +#396 := (implies #368 #53) +#400 := (iff #396 #399) +#401 := [rewrite]: #400 +#397 := (iff #54 #396) +#394 := (iff #52 #368) +#360 := (iff #47 #354) +#361 := [rewrite]: #360 +#395 := [monotonicity #361]: #394 +#398 := [monotonicity #395]: #397 +#403 := [trans #398 #401]: #402 +#406 := [quant-intro #403]: #405 +#423 := [trans #406 #421]: #422 +#393 := [asserted]: #55 +#424 := [mp #393 #423]: #419 +#1884 := [mp~ #424 #1855]: #419 +#4217 := [mp #1884 #4216]: #4212 +#6782 := (not #4212) +#6783 := (or #6782 #6696 #6774) +#6775 := (= ?v0!14 f22) +#6776 := (or #6775 #6774) +#6784 := (or #6782 #6776) +#6791 := (iff #6784 #6783) +#6786 := (or #6782 #6779) +#6789 := (iff #6786 #6783) +#6790 := [rewrite]: #6789 +#6787 := (iff #6784 #6786) +#6780 := (iff #6776 #6779) +#6777 := (iff #6775 #6696) +#6778 := [rewrite]: #6777 +#6781 := [monotonicity #6778]: #6780 +#6788 := [monotonicity #6781]: #6787 +#6792 := [trans #6788 #6790]: #6791 +#6785 := [quant-inst #170 #2248]: #6784 +#6793 := [mp #6785 #6792]: #6783 +#6902 := [unit-resolution #6793 #4217]: #6779 +#6903 := [unit-resolution #6902 #6901]: #6774 +#6904 := (or #6819 #6773) +#6905 := [th-lemma arith farkas 1 1]: #6904 +#6906 := [unit-resolution #6905 #6903]: #6819 +#6820 := (f7 #6555) +#6827 := (f13 f14 #6820) +#6828 := (* -1::Int #6827) +#6877 := (+ #2253 #6828) +#6884 := (<= #6877 0::Int) +#6876 := (= #2253 #6827) +#6910 := (= #6827 #2253) +#6908 := (= #6820 ?v0!14) +#6821 := (= ?v0!14 #6820) +#6825 := (or #6824 #6821) +#6826 := [quant-inst #170 #2248]: #6825 +#6907 := [unit-resolution #6826 #4199]: #6821 +#6909 := [symm #6907]: #6908 +#6911 := [monotonicity #6909]: #6910 +#6912 := [symm #6911]: #6876 +#6913 := (not #6876) +#6914 := (or #6913 #6884) +#6915 := [th-lemma arith triangle-eq]: #6914 +#6916 := [unit-resolution #6915 #6912]: #6884 +#6848 := (+ #6827 #6847) +#6849 := (<= #6848 0::Int) +#6835 := (f3 f15 #6820) +#6836 := (= f1 #6835) +#6923 := (= #6526 #6835) +#6919 := (= #6835 #6526) +#6920 := [monotonicity #6909]: #6919 +#6924 := [symm #6920]: #6923 +#6917 := [hypothesis]: #6697 +#6719 := (or #6715 #6696 #6527) +#6720 := [def-axiom]: #6719 +#6918 := [unit-resolution #6720 #6901 #6917]: #6527 +#6925 := [trans #6918 #6924]: #6836 +#6838 := (f3 f15 #6822) +#6839 := (= f1 #6838) +#6933 := (not #6839) +#6934 := (iff #757 #6933) +#6931 := (iff #754 #6839) +#6929 := (iff #6839 #754) +#6927 := (= #6838 #171) +#6928 := [monotonicity #6892]: #6927 +#6930 := [monotonicity #6928]: #6929 +#6932 := [symm #6930]: #6931 +#6935 := [monotonicity #6932]: #6934 +#4051 := (or #4535 #757) +#4052 := [def-axiom]: #4051 +#6926 := [unit-resolution #4052 #6508]: #757 +#6936 := [mp #6926 #6935]: #6933 +#6837 := (not #6836) +#6857 := (or #6837 #6839 #6849) +#3961 := (or #4547 #4291) +#4016 := [def-axiom]: #3961 +#6937 := [unit-resolution #4016 #6507]: #4291 +#6862 := (or #4296 #6837 #6839 #6849) +#6833 := (+ #6832 #6828) +#6834 := (>= #6833 0::Int) +#6840 := (or #6839 #6837 #6834) +#6863 := (or #4296 #6840) +#6870 := (iff #6863 #6862) +#6865 := (or #4296 #6857) +#6868 := (iff #6865 #6862) +#6869 := [rewrite]: #6868 +#6866 := (iff #6863 #6865) +#6860 := (iff #6840 #6857) +#6854 := (or #6839 #6837 #6849) +#6858 := (iff #6854 #6857) +#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) +#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 +#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) +#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 +#8922 := [monotonicity #8919]: #8921 +#8928 := [trans #8922 #8926]: #8927 +#8931 := [monotonicity #8928]: #8930 +#10018 := [monotonicity #8931]: #10017 +#10021 := [trans #10018 #10014]: #10020 +#10015 := [quant-inst #2288]: #9985 +#10022 := [mp #10015 #10021]: #9984 +#10307 := [unit-resolution #10022 #10313]: #8929 +#10314 := [unit-resolution #10307 #10308]: #8924 +#10586 := (not #8924) +#10633 := (or #10612 #10586 #2888 #8446) +#8717 := (+ #2886 #8692) +#8718 := (+ #174 #8717) +#8721 := (= #8718 0::Int) +#10618 := (not #8721) +#9835 := (<= #8718 0::Int) +#10611 := (not #9835) +#10599 := [hypothesis]: #9616 +#10601 := [hypothesis]: #4116 +#10588 := [hypothesis]: #10487 +#10613 := (or #10611 #2888 #10612 #8446) +#10589 := [hypothesis]: #9835 +#10566 := (<= #10565 0::Int) +#10567 := (not #10566) +#10571 := (or #6782 #8446 #10567) +#10568 := (or #8446 #10567) +#10572 := (or #6782 #10568) +#10574 := (iff #10572 #10571) +#10575 := [rewrite]: #10574 +#10573 := [quant-inst #7211 #2288]: #10572 +#10576 := [mp #10573 #10575]: #10571 +#10600 := [unit-resolution #10576 #4217 #10599]: #10567 +#8568 := (+ #2290 #8567) +#8569 := (<= #8568 0::Int) +#9748 := (or #4417 #8569) +#8557 := (+ #8485 #2291) +#8558 := (>= #8557 0::Int) +#9751 := (or #4417 #8558) +#9766 := (iff #9751 #9748) +#9768 := (iff #9748 #9748) +#9769 := [rewrite]: #9768 +#8572 := (iff #8558 #8569) +#8561 := (+ #2291 #8485) +#8564 := (>= #8561 0::Int) +#8570 := (iff #8564 #8569) +#8571 := [rewrite]: #8570 +#8565 := (iff #8558 #8564) +#8562 := (= #8557 #8561) +#8563 := [rewrite]: #8562 +#8566 := [monotonicity #8563]: #8565 +#8573 := [trans #8566 #8571]: #8572 +#9767 := [monotonicity #8573]: #9766 +#9770 := [trans #9767 #9769]: #9766 +#9765 := [quant-inst #2289]: #9751 +#9771 := [mp #9765 #9770]: #9748 +#10602 := [unit-resolution #9771 #8193]: #8569 +#7529 := (* -1::Int #7513) +#8423 := (+ #174 #7529) +#8429 := (>= #8423 0::Int) +#7336 := (= #174 #7513) +#10603 := (= #7513 #174) +#10604 := [monotonicity #7790]: #10603 +#10605 := [symm #10604]: #7336 +#10606 := (not #7336) +#10607 := (or #10606 #8429) +#10608 := [th-lemma arith triangle-eq]: #10607 +#10609 := [unit-resolution #10608 #10605]: #8429 +#10610 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10609 #10602 #10601 #10600 #10598 #10589 #10588]: false +#10614 := [lemma #10610]: #10613 +#10617 := [unit-resolution #10614 #10588 #10601 #10599]: #10611 +#10619 := (or #10618 #9835) +#10620 := [th-lemma arith triangle-eq]: #10619 +#10621 := [unit-resolution #10620 #10617]: #10618 +#8696 := (* -1::Int #8692) +#8700 := (+ f8 #8696) +#8701 := (<= #8700 0::Int) +#9849 := (not #8701) +#8710 := (+ #8675 #8692) +#8711 := (+ #174 #8710) +#8712 := (>= #8711 0::Int) +#8747 := (or #8701 #8712) +#8750 := (not #8747) +#8744 := (= #2292 #8664) +#10623 := (not #8744) +#8676 := (+ #2292 #8675) +#9848 := (>= #8676 0::Int) +#10584 := (not #9848) +#10579 := [hypothesis]: #8924 +#10615 := (or #10584 #2888 #10586 #10612) +#10580 := [hypothesis]: #9848 +#10583 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10609 #10602 #10601 #10580 #10579 #10588]: false +#10616 := [lemma #10583]: #10615 +#10622 := [unit-resolution #10616 #10588 #10579 #10601]: #10584 +#10624 := (or #10623 #9848) +#10625 := [th-lemma arith triangle-eq]: #10624 +#10626 := [unit-resolution #10625 #10622]: #10623 +#8753 := (or #8744 #8750) +#9837 := (or #4401 #8744 #8750) +#8697 := (+ #1453 #8696) +#8698 := (+ #8664 #8697) +#8699 := (<= #8698 0::Int) +#8740 := (or #8701 #8699) +#8741 := (not #8740) +#8742 := (= #8664 #2292) +#8743 := (or #8742 #8741) +#9838 := (or #4401 #8743) +#9845 := (iff #9838 #9837) +#9839 := (or #4401 #8753) +#9842 := (iff #9839 #9837) +#9843 := [rewrite]: #9842 +#9840 := (iff #9838 #9839) +#8754 := (iff #8743 #8753) +#8751 := (iff #8741 #8750) +#8748 := (iff #8740 #8747) +#8715 := (iff #8699 #8712) +#8703 := (+ #8664 #8696) +#8704 := (+ #1453 #8703) +#8707 := (<= #8704 0::Int) +#8713 := (iff #8707 #8712) +#8714 := [rewrite]: #8713 +#8708 := (iff #8699 #8707) +#8705 := (= #8698 #8704) +#8706 := [rewrite]: #8705 +#8709 := [monotonicity #8706]: #8708 +#8716 := [trans #8709 #8714]: #8715 +#8749 := [monotonicity #8716]: #8748 +#8752 := [monotonicity #8749]: #8751 +#8745 := (iff #8742 #8744) +#8746 := [rewrite]: #8745 +#8755 := [monotonicity #8746 #8752]: #8754 +#9841 := [monotonicity #8755]: #9840 +#9846 := [trans #9841 #9843]: #9845 +#9817 := [quant-inst #2288]: #9838 +#9847 := [mp #9817 #9846]: #9837 +#10627 := [unit-resolution #9847 #6509]: #8753 +#10628 := [unit-resolution #10627 #10626]: #8750 +#9844 := (or #8747 #9849) +#9850 := [def-axiom]: #9844 +#10629 := [unit-resolution #9850 #10628]: #9849 +#9851 := (not #8712) +#9852 := (or #8747 #9851) +#9853 := [def-axiom]: #9852 +#10630 := [unit-resolution #9853 #10628]: #9851 +#8724 := (or #8701 #8712 #8721) +#9823 := (or #4409 #8701 #8712 #8721) +#8693 := (+ #8692 #2886) +#8694 := (+ #174 #8693) +#8695 := (= #8694 0::Int) +#8702 := (or #8701 #8699 #8695) +#9824 := (or #4409 #8702) +#9830 := (iff #9824 #9823) +#9826 := (or #4409 #8724) +#9828 := (iff #9826 #9823) +#9829 := [rewrite]: #9828 +#9821 := (iff #9824 #9826) +#8725 := (iff #8702 #8724) +#8722 := (iff #8695 #8721) +#8719 := (= #8694 #8718) +#8720 := [rewrite]: #8719 +#8723 := [monotonicity #8720]: #8722 +#8726 := [monotonicity #8716 #8723]: #8725 +#9827 := [monotonicity #8726]: #9821 +#9831 := [trans #9827 #9829]: #9830 +#9825 := [quant-inst #2288]: #9824 +#9834 := [mp #9825 #9831]: #9823 +#10631 := [unit-resolution #9834 #6513]: #8724 +#10632 := [unit-resolution #10631 #10630 #10629 #10621]: false +#10634 := [lemma #10632]: #10633 +#10315 := [unit-resolution #10634 #10314 #10291 #10339]: #10612 +#10310 := (or #9731 #10487) +#10295 := [hypothesis]: #10612 +#10297 := [hypothesis]: #8511 +#7515 := (f3 f15 #7211) +#7516 := (= f1 #7515) +#10303 := (not #7516) +#10304 := (iff #757 #10303) +#10296 := (iff #754 #7516) +#10300 := (iff #7516 #754) +#10298 := (= #7515 #171) +#10299 := [monotonicity #7790]: #10298 +#10301 := [monotonicity #10299]: #10300 +#10302 := [symm #10301]: #10296 +#10305 := [monotonicity #10302]: #10304 +#10306 := [mp #6926 #10305]: #10303 +#10233 := (or #4296 #7516 #9731 #10487) +#10494 := (or #7516 #9731 #10487) +#10239 := (or #4296 #10494) +#10241 := (iff #10239 #10233) +#10242 := [rewrite]: #10241 +#10240 := [quant-inst #2289 #7211]: #10239 +#10243 := [mp #10240 #10242]: #10233 +#10309 := [unit-resolution #10243 #6937 #10306 #10297 #10295]: false +#10311 := [lemma #10309]: #10310 +#10316 := [unit-resolution #10311 #10315]: #9731 +#9724 := (not #8520) +#9727 := (or #9724 #8517 #8511) +#9728 := [def-axiom]: #9727 +#10317 := [unit-resolution #9728 #10316 #10324]: #8517 +#10318 := [trans #10317 #7790]: #10480 +#10319 := [monotonicity #10318]: #10212 +#10346 := (not #10212) +#10347 := (or #10346 #10224) +#10345 := [th-lemma arith triangle-eq]: #10347 +#10348 := [unit-resolution #10345 #10319]: #10224 +#10350 := (not #6418) +#10349 := (not #10224) +#10355 := (or #10584 #10349 #2888 #10586 #10350) +#10356 := [th-lemma arith assign-bounds -1 1 -1 1]: #10355 +#10354 := [unit-resolution #10356 #10291 #8194 #10314 #10348]: #10584 +#10357 := [unit-resolution #10625 #10354]: #10623 +#10358 := [unit-resolution #10627 #10357]: #8750 +#10183 := (or #8747 #8721) +#10179 := [hypothesis]: #10618 +#10180 := [hypothesis]: #8750 +#10181 := [unit-resolution #9850 #10180]: #9849 +#10176 := [unit-resolution #9853 #10180]: #9851 +#10182 := [unit-resolution #10631 #10176 #10181 #10179]: false +#10184 := [lemma #10182]: #10183 +#10359 := [unit-resolution #10184 #10358]: #8721 +#10376 := [unit-resolution #10620 #10359]: #9835 +#10377 := [unit-resolution #10576 #4217 #10339]: #10567 +#10378 := [th-lemma arith farkas 1 1 1 1 1 1 #10377 #10376 #10348 #10291 #8194 #10598]: false +#10380 := [lemma #10378]: #10379 +#9759 := [unit-resolution #10380 #9758 #10288]: false +#9760 := [lemma #9759]: #3440 +#4106 := (or #4484 #3445 #4478) +#4093 := [def-axiom]: #4106 +#12721 := [unit-resolution #4093 #9760]: #12720 +#23132 := [unit-resolution #12721 #23139]: #4478 +#4000 := (or #4475 #4469) +#4008 := [def-axiom]: #4000 +#23133 := [unit-resolution #4008 #23132]: #4469 +#23134 := (or #4472 #4466) +#14671 := (f5 f22 ?v0!19) +#14672 := (f9 #14671) +#14467 := (f13 f14 ?v0!19) +#14603 := (* -1::Int #14467) +#14719 := (+ #14603 #14672) +#14720 := (+ #174 #14719) +#14721 := (>= #14720 0::Int) +#14960 := (not #14721) +#14675 := (* -1::Int #14672) +#15459 := (+ #2322 #14675) +#15460 := (>= #15459 0::Int) +#15458 := (= #2322 #14672) +#15668 := (= #2321 #14671) +#15695 := (= ?v1!18 f22) +#13665 := (= ?v1!18 #7211) +#13658 := (f3 f15 ?v1!18) +#13659 := (= f1 #13658) +#13802 := (not #13659) +#13798 := (f13 f14 ?v1!18) +#14923 := (+ #13798 #14603) +#14924 := (+ #2322 #14923) +#14919 := (>= #14924 0::Int) +#15619 := (not #14919) +#14604 := (+ #2317 #14603) +#14605 := (<= #14604 0::Int) +#14818 := (or #4417 #14605) +#14570 := (+ #14467 #2318) +#14597 := (>= #14570 0::Int) +#14819 := (or #4417 #14597) +#14821 := (iff #14819 #14818) +#14823 := (iff #14818 #14818) +#14824 := [rewrite]: #14823 +#14622 := (iff #14597 #14605) +#14598 := (+ #2318 #14467) +#14601 := (>= #14598 0::Int) +#14606 := (iff #14601 #14605) +#14621 := [rewrite]: #14606 +#14596 := (iff #14597 #14601) +#14599 := (= #14570 #14598) +#14600 := [rewrite]: #14599 +#14602 := [monotonicity #14600]: #14596 +#14623 := [trans #14602 #14621]: #14622 +#14822 := [monotonicity #14623]: #14821 +#14772 := [trans #14822 #14824]: #14821 +#14820 := [quant-inst #2316]: #14819 +#14891 := [mp #14820 #14772]: #14818 +#15608 := [unit-resolution #14891 #8193]: #14605 +#4122 := (not #2915) +#15609 := [hypothesis]: #3491 +#3951 := (or #3486 #4122) +#3953 := [def-axiom]: #3951 +#15607 := [unit-resolution #3953 #15609]: #4122 +#13815 := (* -1::Int #13798) +#13816 := (+ #2319 #13815) +#13544 := (>= #13816 0::Int) +#13884 := (= #2319 #13798) +#4121 := (or #3486 #2330) +#4115 := [def-axiom]: #4121 +#15610 := [unit-resolution #4115 #15609]: #2330 +#13776 := (or #4426 #3471 #13884) +#13882 := (= #13798 #2319) +#13752 := (or #13882 #3471) +#13777 := (or #4426 #13752) +#13799 := (iff #13777 #13776) +#13750 := (or #3471 #13884) +#13791 := (or #4426 #13750) +#13801 := (iff #13791 #13776) +#13793 := [rewrite]: #13801 +#13796 := (iff #13777 #13791) +#13758 := (iff #13752 #13750) +#13753 := (or #13884 #3471) +#13756 := (iff #13753 #13750) +#13757 := [rewrite]: #13756 +#13754 := (iff #13752 #13753) +#13885 := (iff #13882 #13884) +#13886 := [rewrite]: #13885 +#13755 := [monotonicity #13886]: #13754 +#13759 := [trans #13755 #13757]: #13758 +#13800 := [monotonicity #13759]: #13796 +#13803 := [trans #13800 #13793]: #13799 +#13795 := [quant-inst #2315]: #13777 +#13804 := [mp #13795 #13803]: #13776 +#15615 := [unit-resolution #13804 #7100 #15610]: #13884 +#15616 := (not #13884) +#15617 := (or #15616 #13544) +#15601 := [th-lemma arith triangle-eq]: #15617 +#15618 := [unit-resolution #15601 #15615]: #13544 +#15614 := (not #14605) +#15611 := (not #13544) +#15620 := (or #15619 #15611 #15614 #2915) +#15622 := [th-lemma arith assign-bounds 1 -1 1]: #15620 +#15623 := [unit-resolution #15622 #15618 #15607 #15608]: #15619 +#15628 := (or #13802 #14919) +#4114 := (or #3486 #2328) +#4120 := [def-axiom]: #4114 +#15626 := [unit-resolution #4120 #15609]: #2328 +#15627 := [unit-resolution #4015 #6507]: #4282 +#13311 := (or #4287 #2327 #13802 #14919) +#14925 := (or #13802 #2327 #14919) +#13540 := (or #4287 #14925) +#15126 := (iff #13540 #13311) +#14926 := (or #2327 #13802 #14919) +#13546 := (or #4287 #14926) +#15124 := (iff #13546 #13311) +#15125 := [rewrite]: #15124 +#13648 := (iff #13540 #13546) +#14927 := (iff #14925 #14926) +#14928 := [rewrite]: #14927 +#15123 := [monotonicity #14928]: #13648 +#15127 := [trans #15123 #15125]: #15126 +#13543 := [quant-inst #2316 #2315]: #13540 +#15128 := [mp #13543 #15127]: #13311 +#15621 := [unit-resolution #15128 #15627 #15626]: #15628 +#15629 := [unit-resolution #15621 #15623]: #13802 +#13668 := (ite #13665 #5892 #13659) +#13662 := (f3 #8442 ?v1!18) +#13663 := (= f1 #13662) +#13671 := (iff #13663 #13668) +#15012 := (or #6290 #13671) +#13660 := (= #7211 ?v1!18) +#13661 := (ite #13660 #5892 #13659) +#13664 := (iff #13663 #13661) +#15017 := (or #6290 #13664) +#14890 := (iff #15017 #15012) +#15043 := (iff #15012 #15012) +#15044 := [rewrite]: #15043 +#13672 := (iff #13664 #13671) +#13669 := (iff #13661 #13668) +#13666 := (iff #13660 #13665) +#13667 := [rewrite]: #13666 +#13670 := [monotonicity #13667]: #13669 +#13673 := [monotonicity #13670]: #13672 +#15019 := [monotonicity #13673]: #14890 +#15060 := [trans #15019 #15044]: #14890 +#15018 := [quant-inst #104 #7211 #5891 #2315]: #15017 +#14889 := [mp #15018 #15060]: #15012 +#15630 := [unit-resolution #14889 #4177]: #13671 +#15690 := (= #2329 #13662) +#15624 := (= #13662 #2329) +#15625 := [monotonicity #9286]: #15624 +#15692 := [symm #15625]: #15690 +#15693 := [trans #15610 #15692]: #13663 +#13237 := (not #13663) +#12830 := (not #13671) +#12788 := (or #12830 #13237 #13668) +#13250 := [def-axiom]: #12788 +#15694 := [unit-resolution #13250 #15693 #15630]: #13668 +#15061 := (not #13668) +#15059 := (or #15061 #13665 #13659) +#15067 := [def-axiom]: #15059 +#15688 := [unit-resolution #15067 #15694 #15629]: #13665 +#15667 := [trans #15688 #7790]: #15695 +#15666 := [monotonicity #15667]: #15668 +#15670 := [monotonicity #15666]: #15458 +#15672 := (not #15458) +#15673 := (or #15672 #15460) +#15674 := [th-lemma arith triangle-eq]: #15673 +#15669 := [unit-resolution #15674 #15670]: #15460 +#15238 := (+ #2319 #6048) +#15240 := (>= #15238 0::Int) +#15450 := (= #2319 #6007) +#15761 := [monotonicity #15667]: #15450 +#15671 := (not #15450) +#15767 := (or #15671 #15240) +#15768 := [th-lemma arith triangle-eq]: #15767 +#15769 := [unit-resolution #15768 #15761]: #15240 +#6674 := (<= #6417 0::Int) +#6008 := (= #174 #6007) +#6547 := (f3 f23 f22) +#6548 := (= f1 #6547) +#8184 := (= #5891 #6547) +#8182 := (= #6547 #5891) +#8183 := [monotonicity #6998]: #8182 +#8185 := [symm #8183]: #8184 +#8186 := [trans #6999 #8185]: #6548 +#6554 := (not #6548) +#6606 := (or #6008 #6554) +#6687 := (or #4426 #6008 #6554) +#6688 := (or #4426 #6606) +#6690 := (iff #6688 #6687) +#6691 := [rewrite]: #6690 +#6689 := [quant-inst #170]: #6688 +#6692 := [mp #6689 #6691]: #6687 +#8187 := [unit-resolution #6692 #7100]: #6606 +#8188 := [unit-resolution #8187 #8186]: #6008 +#8189 := (not #6008) +#8190 := (or #8189 #6674) +#8191 := [th-lemma arith triangle-eq]: #8190 +#8192 := [unit-resolution #8191 #8188]: #6674 +#16339 := (not #15460) +#12652 := (not #6674) +#15770 := (not #15240) +#15766 := (or #14960 #15614 #2915 #15770 #12652 #16339) +#15774 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15766 +#15775 := [unit-resolution #15774 #15608 #8192 #15769 #15607 #15669]: #14960 +#14679 := (+ f8 #14675) +#14731 := (<= #14679 0::Int) +#15014 := (not #14731) +#16340 := (or #15014 #16339 #2327) +#16336 := [hypothesis]: #2328 +#16331 := [hypothesis]: #14731 +#16337 := [hypothesis]: #15460 +#16338 := [th-lemma arith farkas 1 -1 1 #16337 #16331 #16336]: false +#16341 := [lemma #16338]: #16340 +#15776 := [unit-resolution #16341 #15669 #15626]: #15014 +#14725 := (+ #2318 #14672) +#14726 := (+ #174 #14725) +#14743 := (= #14726 0::Int) +#15811 := (not #14743) +#14857 := (>= #14726 0::Int) +#15772 := (not #14857) +#15793 := (or #15772 #2915 #15770 #12652 #16339) +#15805 := [th-lemma arith assign-bounds 1 1 -1 1]: #15793 +#15806 := [unit-resolution #15805 #15769 #8192 #15607 #15669]: #15772 +#15812 := (or #15811 #14857) +#15813 := [th-lemma arith triangle-eq]: #15812 +#15847 := [unit-resolution #15813 #15806]: #15811 +#14768 := (or #14721 #14731 #14743) +#14892 := (or #4409 #14721 #14731 #14743) +#14673 := (+ #14672 #2318) +#14674 := (+ #174 #14673) +#14669 := (= #14674 0::Int) +#14676 := (+ #1453 #14675) +#14677 := (+ #14467 #14676) +#14678 := (<= #14677 0::Int) +#14732 := (or #14731 #14678 #14669) +#14893 := (or #4409 #14732) +#14860 := (iff #14893 #14892) +#14895 := (or #4409 #14768) +#14858 := (iff #14895 #14892) +#14859 := [rewrite]: #14858 +#14921 := (iff #14893 #14895) +#14770 := (iff #14732 #14768) +#14765 := (or #14731 #14721 #14743) +#14763 := (iff #14765 #14768) +#14769 := [rewrite]: #14763 +#14766 := (iff #14732 #14765) +#14744 := (iff #14669 #14743) +#14727 := (= #14674 #14726) +#14728 := [rewrite]: #14727 +#14764 := [monotonicity #14728]: #14744 +#14718 := (iff #14678 #14721) +#14733 := (+ #14467 #14675) +#14734 := (+ #1453 #14733) +#14737 := (<= #14734 0::Int) +#14722 := (iff #14737 #14721) +#14723 := [rewrite]: #14722 +#14738 := (iff #14678 #14737) +#14735 := (= #14677 #14734) +#14736 := [rewrite]: #14735 +#14739 := [monotonicity #14736]: #14738 +#14724 := [trans #14739 #14723]: #14718 +#14767 := [monotonicity #14724 #14764]: #14766 +#14771 := [trans #14767 #14769]: #14770 +#14922 := [monotonicity #14771]: #14921 +#14920 := [trans #14922 #14859]: #14860 +#14894 := [quant-inst #2316]: #14893 +#14861 := [mp #14894 #14920]: #14892 +#15845 := [unit-resolution #14861 #6513]: #14768 +#15846 := [unit-resolution #15845 #15847 #15776 #15775]: false +#15842 := [lemma #15846]: #3486 +#3989 := (or #4472 #3491 #4466) +#4004 := [def-axiom]: #3989 +#23149 := [unit-resolution #4004 #15842]: #23134 +#23150 := [unit-resolution #23149 #23133]: #4466 +#4108 := (or #4463 #2360) +#4110 := [def-axiom]: #4108 +#23151 := [unit-resolution #4110 #23150]: #2360 +#23152 := (= #9081 #6070) +#23153 := [monotonicity #9282]: #23152 +#23155 := [symm #23153]: #9861 +#23156 := [unit-resolution #11949 #23155]: #9457 +#9818 := (<= #9455 0::Int) +#23148 := (or #11945 #9818) +#23154 := [th-lemma arith triangle-eq]: #23148 +#23157 := [unit-resolution #23154 #23155]: #9818 +#23158 := (not #9818) +#23164 := (or #10878 #23158) +#7358 := (>= #6070 0::Int) +#7296 := (not #7358) +#7297 := [hypothesis]: #7296 +#7978 := (or #4279 #7358) +#7979 := [quant-inst #6069]: #7978 +#7484 := [unit-resolution #7979 #7121 #7297]: false +#7488 := [lemma #7484]: #7358 +#7053 := (not #3920) +#23159 := (or #10878 #7053 #7296 #23158) +#23161 := [th-lemma arith assign-bounds -1 1 -1]: #23159 +#23165 := [unit-resolution #23161 #7488 #7126]: #23164 +#23163 := [unit-resolution #23165 #23157]: #10878 +#3995 := (or #4463 #4455) +#3996 := [def-axiom]: #3995 +#23166 := [unit-resolution #3996 #23150]: #4455 +#24105 := (or #14183 #4460) +#8778 := (f24 #7211) +#9544 := (* -1::Int #8778) +#14038 := (+ #2347 #9544) +#14226 := (<= #14038 0::Int) +#10164 := (f3 f23 #7211) +#10165 := (= f1 #10164) +#11810 := (= #5891 #10164) +#11803 := (= #10164 #5891) +#11809 := [monotonicity #6998 #7790]: #11803 +#11811 := [symm #11809]: #11810 +#11812 := [trans #6999 #11811]: #10165 +#14212 := (f9 #14211) +#14238 := (* -1::Int #14212) +#14239 := (+ #9544 #14238) +#14240 := (+ #2347 #14239) +#14241 := (= #14240 0::Int) +#15156 := (>= #14240 0::Int) +#14157 := (+ #2348 #14132) +#14158 := (+ #174 #14157) +#14427 := (<= #14158 0::Int) +#14161 := (= #14158 0::Int) +#14186 := (not #14183) +#21311 := [hypothesis]: #14186 +#21316 := (or #14183 #14161) +#21305 := (not #14161) +#21306 := [hypothesis]: #21305 +#12472 := (not #14141) +#12479 := (or #14183 #12472) +#12480 := [def-axiom]: #12479 +#21312 := [unit-resolution #12480 #21311]: #12472 +#12469 := (not #14152) +#12478 := (or #14183 #12469) +#12481 := [def-axiom]: #12478 +#21313 := [unit-resolution #12481 #21311]: #12469 +#14164 := (or #14141 #14152 #14161) +#12411 := (or #4409 #14141 #14152 #14161) +#14133 := (+ #14132 #2348) +#14134 := (+ #174 #14133) +#14135 := (= #14134 0::Int) +#14137 := (+ #1453 #14136) +#14138 := (+ #14074 #14137) +#14139 := (<= #14138 0::Int) +#14142 := (or #14141 #14139 #14135) +#12435 := (or #4409 #14142) +#12440 := (iff #12435 #12411) +#12408 := (or #4409 #14164) +#12439 := (iff #12408 #12411) +#12434 := [rewrite]: #12439 +#12437 := (iff #12435 #12408) +#14165 := (iff #14142 #14164) +#14162 := (iff #14135 #14161) +#14159 := (= #14134 #14158) +#14160 := [rewrite]: #14159 +#14163 := [monotonicity #14160]: #14162 +#14155 := (iff #14139 #14152) +#14143 := (+ #14074 #14136) +#14144 := (+ #1453 #14143) +#14147 := (<= #14144 0::Int) +#14153 := (iff #14147 #14152) +#14154 := [rewrite]: #14153 +#14148 := (iff #14139 #14147) +#14145 := (= #14138 #14144) +#14146 := [rewrite]: #14145 +#14149 := [monotonicity #14146]: #14148 +#14156 := [trans #14149 #14154]: #14155 +#14166 := [monotonicity #14156 #14163]: #14165 +#12438 := [monotonicity #14166]: #12437 +#12442 := [trans #12438 #12434]: #12440 +#12436 := [quant-inst #2346]: #12435 +#12443 := [mp #12436 #12442]: #12411 +#21314 := [unit-resolution #12443 #6513]: #14164 +#21315 := [unit-resolution #21314 #21313 #21312 #21306]: false +#21317 := [lemma #21315]: #21316 +#24022 := [unit-resolution #21317 #21311]: #14161 +#24023 := (or #21305 #14427) +#24024 := [th-lemma arith triangle-eq]: #24023 +#24025 := [unit-resolution #24024 #24022]: #14427 +#17684 := (not #14427) +#24046 := (or #15156 #17684) +#9545 := (+ #6007 #9544) +#7445 := (>= #9545 0::Int) +#9543 := (= #6007 #8778) +#11874 := (= #8778 #6007) +#11875 := [monotonicity #7790]: #11874 +#11876 := [symm #11875]: #9543 +#11877 := (not #9543) +#24020 := (or #11877 #7445) +#24026 := [th-lemma arith triangle-eq]: #24020 +#24027 := [unit-resolution #24026 #11876]: #7445 +#13353 := (+ #14132 #14238) +#13586 := (>= #13353 0::Int) +#7923 := (= #14132 #14212) +#24030 := (= #14212 #14132) +#24037 := [monotonicity #24029]: #24030 +#24038 := [symm #24037]: #7923 +#24036 := (not #7923) +#24039 := (or #24036 #13586) +#24040 := [th-lemma arith triangle-eq]: #24039 +#24041 := [unit-resolution #24040 #24038]: #13586 +#24044 := (not #13586) +#24043 := (not #7445) +#24042 := (or #15156 #24043 #10350 #24044 #17684) +#24045 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24042 +#24047 := [unit-resolution #24045 #24041 #24027 #8194]: #24046 +#24035 := [unit-resolution #24047 #24025]: #15156 +#15134 := (<= #14240 0::Int) +#14428 := (>= #14158 0::Int) +#24048 := (or #21305 #14428) +#24049 := [th-lemma arith triangle-eq]: #24048 +#24050 := [unit-resolution #24049 #24022]: #14428 +#24054 := (not #14428) +#24058 := (or #15134 #24054) +#9546 := (<= #9545 0::Int) +#11878 := (or #11877 #9546) +#11879 := [th-lemma arith triangle-eq]: #11878 +#11880 := [unit-resolution #11879 #11876]: #9546 +#13354 := (<= #13353 0::Int) +#24051 := (or #24036 #13354) +#24034 := [th-lemma arith triangle-eq]: #24051 +#24052 := [unit-resolution #24034 #24038]: #13354 +#24053 := (not #13354) +#12651 := (not #9546) +#24055 := (or #15134 #12651 #12652 #24053 #24054) +#24056 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24055 +#24059 := [unit-resolution #24056 #24052 #11880 #8192]: #24058 +#24060 := [unit-resolution #24059 #24050]: #15134 +#24062 := (not #15156) +#24061 := (not #15134) +#24057 := (or #14241 #24061 #24062) +#24063 := [th-lemma arith triangle-eq]: #24057 +#24064 := [unit-resolution #24063 #24060 #24035]: #14241 +#14246 := (not #14241) +#10177 := (not #10165) +#14249 := (or #10177 #14226 #14246) +#24065 := [hypothesis]: #4455 +#12777 := (or #4460 #10177 #14226 #14246) +#14213 := (+ #2348 #14212) +#14214 := (+ #8778 #14213) +#14215 := (= #14214 0::Int) +#14216 := (not #14215) +#14217 := (+ #8778 #2348) +#14218 := (>= #14217 0::Int) +#14219 := (or #10177 #14218 #14216) +#12784 := (or #4460 #14219) +#12837 := (iff #12784 #12777) +#12848 := (or #4460 #14249) +#12871 := (iff #12848 #12777) +#12877 := [rewrite]: #12871 +#12875 := (iff #12784 #12848) +#14250 := (iff #14219 #14249) +#14247 := (iff #14216 #14246) +#14244 := (iff #14215 #14241) +#14231 := (+ #8778 #14212) +#14232 := (+ #2348 #14231) +#14235 := (= #14232 0::Int) +#14242 := (iff #14235 #14241) +#14243 := [rewrite]: #14242 +#14236 := (iff #14215 #14235) +#14233 := (= #14214 #14232) +#14234 := [rewrite]: #14233 +#14237 := [monotonicity #14234]: #14236 +#14245 := [trans #14237 #14243]: #14244 +#14248 := [monotonicity #14245]: #14247 +#14229 := (iff #14218 #14226) +#14220 := (+ #2348 #8778) +#14223 := (>= #14220 0::Int) +#14227 := (iff #14223 #14226) +#14228 := [rewrite]: #14227 +#14224 := (iff #14218 #14223) +#14221 := (= #14217 #14220) +#14222 := [rewrite]: #14221 +#14225 := [monotonicity #14222]: #14224 +#14230 := [trans #14225 #14228]: #14229 +#14251 := [monotonicity #14230 #14248]: #14250 +#12876 := [monotonicity #14251]: #12875 +#12903 := [trans #12876 #12877]: #12837 +#12841 := [quant-inst #7211]: #12784 +#12904 := [mp #12841 #12903]: #12777 +#24066 := [unit-resolution #12904 #24065]: #14249 +#24067 := [unit-resolution #24066 #24064 #11812]: #14226 +#12487 := (f5 f10 ?v0!20) +#17155 := (f7 #12487) +#22316 := (f5 #7211 #17155) +#22325 := (f9 #22316) +#22328 := (* -1::Int #22325) +#22457 := (+ #14132 #22328) +#17191 := (>= #22457 0::Int) +#17177 := (= #14132 #22325) +#24068 := (= #22325 #14132) +#24072 := (= #22316 #14131) +#24070 := (= #17155 ?v0!20) +#17156 := (= ?v0!20 #17155) +#17179 := (or #6824 #17156) +#17180 := [quant-inst #56 #2346]: #17179 +#24069 := [unit-resolution #17180 #4199]: #17156 +#24071 := [symm #24069]: #24070 +#24073 := [monotonicity #7790 #24071]: #24072 +#24074 := [monotonicity #24073]: #24068 +#24075 := [symm #24074]: #17177 +#24076 := (not #17177) +#24077 := (or #24076 #17191) +#24078 := [th-lemma arith triangle-eq]: #24077 +#24080 := [unit-resolution #24078 #24075]: #17191 +#22384 := (<= #22325 0::Int) +#22364 := (not #22384) +#22367 := (= #7211 #17155) +#22397 := (not #22367) +#20554 := (f3 f15 #17155) +#20571 := (= f1 #20554) +#23981 := (ite #22367 #5892 #20571) +#24001 := (not #23981) +#23982 := (f3 #8442 #17155) +#23987 := (= f1 #23982) +#23989 := (iff #23981 #23987) +#23993 := (or #6290 #23989) +#23988 := (iff #23987 #23981) +#23994 := (or #6290 #23988) +#23996 := (iff #23994 #23993) +#23992 := (iff #23993 #23993) +#23998 := [rewrite]: #23992 +#23990 := (iff #23988 #23989) +#23991 := [rewrite]: #23990 +#23997 := [monotonicity #23991]: #23996 +#23999 := [trans #23997 #23998]: #23996 +#23995 := [quant-inst #104 #7211 #5891 #17155]: #23994 +#24000 := [mp #23995 #23999]: #23993 +#24081 := [unit-resolution #24000 #4177]: #23989 +#24013 := (not #23987) +#10246 := (f3 f23 ?v0!20) +#10247 := (= f1 #10246) +#10248 := (not #10247) +#24094 := (iff #10248 #24013) +#24092 := (iff #10247 #23987) +#24089 := (iff #23987 #10247) +#24087 := (= #23982 #10246) +#24088 := [monotonicity #9286 #24071]: #24087 +#24091 := [monotonicity #24088]: #24089 +#24093 := [symm #24091]: #24092 +#24095 := [monotonicity #24093]: #24094 +#24708 := (not #14085) +#21436 := (not #19567) +#24082 := (or #14152 #21436 #24044 #24061 #24043 #10350) +#24083 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24082 +#24084 := [unit-resolution #24083 #24060 #24041 #21313 #24027 #8194]: #21436 +#24709 := (or #24708 #19567) +#24696 := [hypothesis]: #21436 +#24697 := [hypothesis]: #14085 +#24710 := [th-lemma arith triangle-eq]: #24709 +#24711 := [unit-resolution #24710 #24697 #24696]: false +#24712 := [lemma #24711]: #24709 +#24079 := [unit-resolution #24712 #24084]: #24708 +#14091 := (or #10248 #14085) +#12334 := (or #4426 #10248 #14085) +#14081 := (= #14074 #2347) +#14084 := (or #14081 #10248) +#12374 := (or #4426 #14084) +#12382 := (iff #12374 #12334) +#12377 := (or #4426 #14091) +#12379 := (iff #12377 #12334) +#12381 := [rewrite]: #12379 +#12378 := (iff #12374 #12377) +#14094 := (iff #14084 #14091) +#14088 := (or #14085 #10248) +#14092 := (iff #14088 #14091) +#14093 := [rewrite]: #14092 +#14089 := (iff #14084 #14088) +#14086 := (iff #14081 #14085) +#14087 := [rewrite]: #14086 +#14090 := [monotonicity #14087]: #14089 +#14095 := [trans #14090 #14093]: #14094 +#12373 := [monotonicity #14095]: #12378 +#12383 := [trans #12373 #12381]: #12382 +#12376 := [quant-inst #2346]: #12374 +#12402 := [mp #12376 #12383]: #12334 +#24085 := [unit-resolution #12402 #7100]: #14091 +#24086 := [unit-resolution #24085 #24079]: #10248 +#24090 := [mp #24086 #24095]: #24013 +#24012 := (not #23989) +#24015 := (or #24012 #24001 #23987) +#24016 := [def-axiom]: #24015 +#24096 := [unit-resolution #24016 #24090 #24081]: #24001 +#24097 := (or #23981 #22397) +#24008 := (or #23981 #22397 #6304) +#24009 := [def-axiom]: #24008 +#24098 := [unit-resolution #24009 #6999]: #24097 +#24099 := [unit-resolution #24098 #24096]: #22397 +#22369 := (or #22367 #22364) +#23958 := (or #6782 #22367 #22364) +#22365 := (= #17155 #7211) +#22366 := (or #22365 #22364) +#23959 := (or #6782 #22366) +#23966 := (iff #23959 #23958) +#23961 := (or #6782 #22369) +#23964 := (iff #23961 #23958) +#23965 := [rewrite]: #23964 +#23962 := (iff #23959 #23961) +#22370 := (iff #22366 #22369) +#22368 := (iff #22365 #22367) +#22363 := [rewrite]: #22368 +#22371 := [monotonicity #22363]: #22370 +#23963 := [monotonicity #22371]: #23962 +#23967 := [trans #23963 #23965]: #23966 +#23960 := [quant-inst #7211 #17155]: #23959 +#23968 := [mp #23960 #23967]: #23958 +#24100 := [unit-resolution #23968 #4217]: #22369 +#24103 := [unit-resolution #24100 #24099]: #22364 +#24104 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24027 #8194 #24103 #24080 #24025 #24067]: false +#24106 := [lemma #24104]: #24105 +#23167 := [unit-resolution #24106 #23166]: #14183 +#23147 := [hypothesis]: #12469 +#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) +#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 unsat diff -r 4ea9f2a8c093 -r d4cb4d0c14a7 src/HOL/Multivariate_Analysis/Integration.certs --- a/src/HOL/Multivariate_Analysis/Integration.certs Fri Dec 17 14:36:33 2010 +0100 +++ b/src/HOL/Multivariate_Analysis/Integration.certs Fri Dec 17 14:59:06 2010 +0100 @@ -1,275 +1,275 @@ -57b03a56df49326094be4946646336bc93948572 272 0 +8d81ff6f41bc1cff9f5c6454ee204d147f8e27b7 272 0 #2 := false -#46 := 0::Real -decl f16 :: (-> S3 S9 Real) -decl f17 :: S9 -#41 := f17 +#48 := 0::Real +decl f17 :: (-> S3 S10 Real) +decl f18 :: S10 +#43 := f18 decl f4 :: S3 #8 := f4 -#56 := (f16 f4 f17) -#92 := -1::Real -#136 := (* -1::Real #56) +#58 := (f17 f4 f18) +#94 := -1::Real +#138 := (* -1::Real #58) decl f5 :: (-> S4 S5 Real) decl f8 :: S5 #14 := f8 +decl f20 :: S4 +#54 := f20 +#55 := (f5 f20 f8) +#139 := (+ #55 #138) +#122 := (* -1::Real #55) +#129 := (+ #122 #58) +#189 := (<= #139 0::Real) +#196 := (ite #189 #129 #139) +#372 := (* -1::Real #196) +#373 := (+ #129 #372) +#374 := (<= #373 0::Real) +#356 := (= #129 #196) decl f19 :: S4 -#52 := f19 -#53 := (f5 f19 f8) -#137 := (+ #53 #136) -#120 := (* -1::Real #53) -#127 := (+ #120 #56) -#187 := (<= #137 0::Real) -#194 := (ite #187 #127 #137) -#370 := (* -1::Real #194) -#371 := (+ #127 #370) -#372 := (<= #371 0::Real) -#354 := (= #127 #194) -decl f18 :: S4 -#43 := f18 -#44 := (f5 f18 f8) +#45 := f19 +#46 := (f5 f19 f8) decl f9 :: S3 #18 := f9 -#42 := (f16 f9 f17) -#103 := (* -1::Real #42) -#104 := (+ #103 #44) -#93 := (* -1::Real #44) -#94 := (+ #42 #93) -#222 := (>= #94 0::Real) -#229 := (ite #222 #94 #104) -#366 := (* -1::Real #229) -#369 := (+ #104 #366) -#373 := (<= #369 0::Real) -#361 := (= #104 #229) -#223 := (not #222) -#374 := [hypothesis]: #222 -#180 := (+ #42 #136) -#181 := (<= #180 0::Real) -#205 := -3::Real -#240 := (* -3::Real #229) -#241 := (+ #120 #240) -#242 := (+ #44 #241) -#243 := (<= #242 0::Real) -#206 := (* -3::Real #194) -#207 := (+ #120 #206) -#208 := (+ #44 #207) -#209 := (<= #208 0::Real) -#184 := (not #181) -#262 := (or #184 #209 #243) -#267 := (not #262) -#63 := (<= #42 #56) -#64 := (implies #63 false) -#54 := (- #44 #53) -#50 := 3::Real -#57 := (- #56 #53) -#59 := (- #57) -#58 := (< #57 0::Real) -#60 := (ite #58 #59 #57) -#61 := (* #60 3::Real) -#62 := (< #61 #54) -#65 := (implies #62 #64) -#45 := (- #42 #44) -#48 := (- #45) -#47 := (< #45 0::Real) -#49 := (ite #47 #48 #45) -#51 := (* #49 3::Real) -#55 := (< #51 #54) -#66 := (implies #55 #65) -#67 := (not #66) -#270 := (iff #67 #267) -#121 := (+ #44 #120) -#130 := (< #127 0::Real) -#142 := (ite #130 #137 #127) -#148 := (* 3::Real #142) -#153 := (< #148 #121) -#162 := (not #153) -#156 := (not #63) -#163 := (or #156 #162) -#97 := (< #94 0::Real) -#109 := (ite #97 #104 #94) -#115 := (* 3::Real #109) -#124 := (< #115 #121) -#171 := (not #124) -#172 := (or #171 #163) -#177 := (not #172) -#268 := (iff #177 #267) -#265 := (iff #172 #262) -#256 := (or #184 #209) -#259 := (or #243 #256) -#263 := (iff #259 #262) -#264 := [rewrite]: #263 -#260 := (iff #172 #259) -#257 := (iff #163 #256) -#220 := (iff #162 #209) -#210 := (not #209) -#215 := (not #210) -#218 := (iff #215 #209) -#219 := [rewrite]: #218 -#216 := (iff #162 #215) -#213 := (iff #153 #210) -#199 := (* 3::Real #194) -#202 := (< #199 #121) -#211 := (iff #202 #210) -#212 := [rewrite]: #211 -#203 := (iff #153 #202) -#200 := (= #148 #199) -#197 := (= #142 #194) -#188 := (not #187) -#191 := (ite #188 #137 #127) -#195 := (= #191 #194) -#196 := [rewrite]: #195 -#192 := (= #142 #191) -#189 := (iff #130 #188) -#190 := [rewrite]: #189 -#193 := [monotonicity #190]: #192 -#198 := [trans #193 #196]: #197 -#201 := [monotonicity #198]: #200 -#204 := [monotonicity #201]: #203 -#214 := [trans #204 #212]: #213 -#217 := [monotonicity #214]: #216 -#221 := [trans #217 #219]: #220 -#185 := (iff #156 #184) -#182 := (iff #63 #181) -#183 := [rewrite]: #182 -#186 := [monotonicity #183]: #185 -#258 := [monotonicity #186 #221]: #257 -#254 := (iff #171 #243) -#244 := (not #243) -#249 := (not #244) -#252 := (iff #249 #243) -#253 := [rewrite]: #252 -#250 := (iff #171 #249) -#247 := (iff #124 #244) -#234 := (* 3::Real #229) -#237 := (< #234 #121) -#245 := (iff #237 #244) -#246 := [rewrite]: #245 -#238 := (iff #124 #237) -#235 := (= #115 #234) -#232 := (= #109 #229) -#226 := (ite #223 #104 #94) -#230 := (= #226 #229) -#231 := [rewrite]: #230 -#227 := (= #109 #226) -#224 := (iff #97 #223) -#225 := [rewrite]: #224 -#228 := [monotonicity #225]: #227 -#233 := [trans #228 #231]: #232 -#236 := [monotonicity #233]: #235 -#239 := [monotonicity #236]: #238 -#248 := [trans #239 #246]: #247 -#251 := [monotonicity #248]: #250 -#255 := [trans #251 #253]: #254 -#261 := [monotonicity #255 #258]: #260 -#266 := [trans #261 #264]: #265 -#269 := [monotonicity #266]: #268 -#178 := (iff #67 #177) -#175 := (iff #66 #172) -#168 := (implies #124 #163) -#173 := (iff #168 #172) -#174 := [rewrite]: #173 -#169 := (iff #66 #168) -#166 := (iff #65 #163) -#159 := (implies #153 #156) -#164 := (iff #159 #163) -#165 := [rewrite]: #164 -#160 := (iff #65 #159) -#157 := (iff #64 #156) -#158 := [rewrite]: #157 -#154 := (iff #62 #153) -#122 := (= #54 #121) -#123 := [rewrite]: #122 -#151 := (= #61 #148) -#145 := (* #142 3::Real) -#149 := (= #145 #148) -#150 := [rewrite]: #149 -#146 := (= #61 #145) -#143 := (= #60 #142) -#128 := (= #57 #127) -#129 := [rewrite]: #128 -#140 := (= #59 #137) -#133 := (- #127) -#138 := (= #133 #137) -#139 := [rewrite]: #138 -#134 := (= #59 #133) -#135 := [monotonicity #129]: #134 -#141 := [trans #135 #139]: #140 -#131 := (iff #58 #130) -#132 := [monotonicity #129]: #131 -#144 := [monotonicity #132 #141 #129]: #143 -#147 := [monotonicity #144]: #146 -#152 := [trans #147 #150]: #151 -#155 := [monotonicity #152 #123]: #154 -#161 := [monotonicity #155 #158]: #160 -#167 := [trans #161 #165]: #166 -#125 := (iff #55 #124) -#118 := (= #51 #115) -#112 := (* #109 3::Real) -#116 := (= #112 #115) -#117 := [rewrite]: #116 -#113 := (= #51 #112) -#110 := (= #49 #109) -#95 := (= #45 #94) -#96 := [rewrite]: #95 -#107 := (= #48 #104) -#100 := (- #94) -#105 := (= #100 #104) -#106 := [rewrite]: #105 -#101 := (= #48 #100) -#102 := [monotonicity #96]: #101 -#108 := [trans #102 #106]: #107 -#98 := (iff #47 #97) -#99 := [monotonicity #96]: #98 -#111 := [monotonicity #99 #108 #96]: #110 -#114 := [monotonicity #111]: #113 -#119 := [trans #114 #117]: #118 -#126 := [monotonicity #119 #123]: #125 -#170 := [monotonicity #126 #167]: #169 -#176 := [trans #170 #174]: #175 -#179 := [monotonicity #176]: #178 -#271 := [trans #179 #269]: #270 -#91 := [asserted]: #67 -#272 := [mp #91 #271]: #267 -#273 := [not-or-elim #272]: #181 -#275 := [not-or-elim #272]: #244 -#367 := (+ #94 #366) -#368 := (<= #367 0::Real) -#360 := (= #94 #229) -#362 := (or #223 #360) -#363 := [def-axiom]: #362 -#386 := [unit-resolution #363 #374]: #360 -#387 := (not #360) -#388 := (or #387 #368) -#389 := [th-lemma arith triangle-eq]: #388 -#390 := [unit-resolution #389 #386]: #368 -#382 := (or #188 #223) -#375 := [hypothesis]: #187 -#274 := [not-or-elim #272]: #210 -#356 := (or #188 #354) -#357 := [def-axiom]: #356 -#376 := [unit-resolution #357 #375]: #354 -#377 := (not #354) -#378 := (or #377 #372) -#379 := [th-lemma arith triangle-eq]: #378 -#380 := [unit-resolution #379 #376]: #372 -#381 := [th-lemma arith farkas -1 -3 1 -2 1 #273 #380 #274 #375 #374]: false -#383 := [lemma #381]: #382 -#391 := [unit-resolution #383 #374]: #188 -#392 := [th-lemma arith farkas 1/4 -3/4 1/4 -1/4 1 #391 #390 #275 #273 #374]: false -#393 := [lemma #392]: #223 -#364 := (or #222 #361) +#44 := (f17 f9 f18) +#105 := (* -1::Real #44) +#106 := (+ #105 #46) +#95 := (* -1::Real #46) +#96 := (+ #44 #95) +#224 := (>= #96 0::Real) +#231 := (ite #224 #96 #106) +#368 := (* -1::Real #231) +#371 := (+ #106 #368) +#375 := (<= #371 0::Real) +#363 := (= #106 #231) +#225 := (not #224) +#376 := [hypothesis]: #224 +#182 := (+ #44 #138) +#183 := (<= #182 0::Real) +#207 := -3::Real +#242 := (* -3::Real #231) +#243 := (+ #122 #242) +#244 := (+ #46 #243) +#245 := (<= #244 0::Real) +#208 := (* -3::Real #196) +#209 := (+ #122 #208) +#210 := (+ #46 #209) +#211 := (<= #210 0::Real) +#186 := (not #183) +#264 := (or #186 #211 #245) +#269 := (not #264) +#65 := (<= #44 #58) +#66 := (implies #65 false) +#56 := (- #46 #55) +#52 := 3::Real +#59 := (- #58 #55) +#61 := (- #59) +#60 := (< #59 0::Real) +#62 := (ite #60 #61 #59) +#63 := (* #62 3::Real) +#64 := (< #63 #56) +#67 := (implies #64 #66) +#47 := (- #44 #46) +#50 := (- #47) +#49 := (< #47 0::Real) +#51 := (ite #49 #50 #47) +#53 := (* #51 3::Real) +#57 := (< #53 #56) +#68 := (implies #57 #67) +#69 := (not #68) +#272 := (iff #69 #269) +#123 := (+ #46 #122) +#132 := (< #129 0::Real) +#144 := (ite #132 #139 #129) +#150 := (* 3::Real #144) +#155 := (< #150 #123) +#164 := (not #155) +#158 := (not #65) +#165 := (or #158 #164) +#99 := (< #96 0::Real) +#111 := (ite #99 #106 #96) +#117 := (* 3::Real #111) +#126 := (< #117 #123) +#173 := (not #126) +#174 := (or #173 #165) +#179 := (not #174) +#270 := (iff #179 #269) +#267 := (iff #174 #264) +#258 := (or #186 #211) +#261 := (or #245 #258) +#265 := (iff #261 #264) +#266 := [rewrite]: #265 +#262 := (iff #174 #261) +#259 := (iff #165 #258) +#222 := (iff #164 #211) +#212 := (not #211) +#217 := (not #212) +#220 := (iff #217 #211) +#221 := [rewrite]: #220 +#218 := (iff #164 #217) +#215 := (iff #155 #212) +#201 := (* 3::Real #196) +#204 := (< #201 #123) +#213 := (iff #204 #212) +#214 := [rewrite]: #213 +#205 := (iff #155 #204) +#202 := (= #150 #201) +#199 := (= #144 #196) +#190 := (not #189) +#193 := (ite #190 #139 #129) +#197 := (= #193 #196) +#198 := [rewrite]: #197 +#194 := (= #144 #193) +#191 := (iff #132 #190) +#192 := [rewrite]: #191 +#195 := [monotonicity #192]: #194 +#200 := [trans #195 #198]: #199 +#203 := [monotonicity #200]: #202 +#206 := [monotonicity #203]: #205 +#216 := [trans #206 #214]: #215 +#219 := [monotonicity #216]: #218 +#223 := [trans #219 #221]: #222 +#187 := (iff #158 #186) +#184 := (iff #65 #183) +#185 := [rewrite]: #184 +#188 := [monotonicity #185]: #187 +#260 := [monotonicity #188 #223]: #259 +#256 := (iff #173 #245) +#246 := (not #245) +#251 := (not #246) +#254 := (iff #251 #245) +#255 := [rewrite]: #254 +#252 := (iff #173 #251) +#249 := (iff #126 #246) +#236 := (* 3::Real #231) +#239 := (< #236 #123) +#247 := (iff #239 #246) +#248 := [rewrite]: #247 +#240 := (iff #126 #239) +#237 := (= #117 #236) +#234 := (= #111 #231) +#228 := (ite #225 #106 #96) +#232 := (= #228 #231) +#233 := [rewrite]: #232 +#229 := (= #111 #228) +#226 := (iff #99 #225) +#227 := [rewrite]: #226 +#230 := [monotonicity #227]: #229 +#235 := [trans #230 #233]: #234 +#238 := [monotonicity #235]: #237 +#241 := [monotonicity #238]: #240 +#250 := [trans #241 #248]: #249 +#253 := [monotonicity #250]: #252 +#257 := [trans #253 #255]: #256 +#263 := [monotonicity #257 #260]: #262 +#268 := [trans #263 #266]: #267 +#271 := [monotonicity #268]: #270 +#180 := (iff #69 #179) +#177 := (iff #68 #174) +#170 := (implies #126 #165) +#175 := (iff #170 #174) +#176 := [rewrite]: #175 +#171 := (iff #68 #170) +#168 := (iff #67 #165) +#161 := (implies #155 #158) +#166 := (iff #161 #165) +#167 := [rewrite]: #166 +#162 := (iff #67 #161) +#159 := (iff #66 #158) +#160 := [rewrite]: #159 +#156 := (iff #64 #155) +#124 := (= #56 #123) +#125 := [rewrite]: #124 +#153 := (= #63 #150) +#147 := (* #144 3::Real) +#151 := (= #147 #150) +#152 := [rewrite]: #151 +#148 := (= #63 #147) +#145 := (= #62 #144) +#130 := (= #59 #129) +#131 := [rewrite]: #130 +#142 := (= #61 #139) +#135 := (- #129) +#140 := (= #135 #139) +#141 := [rewrite]: #140 +#136 := (= #61 #135) +#137 := [monotonicity #131]: #136 +#143 := [trans #137 #141]: #142 +#133 := (iff #60 #132) +#134 := [monotonicity #131]: #133 +#146 := [monotonicity #134 #143 #131]: #145 +#149 := [monotonicity #146]: #148 +#154 := [trans #149 #152]: #153 +#157 := [monotonicity #154 #125]: #156 +#163 := [monotonicity #157 #160]: #162 +#169 := [trans #163 #167]: #168 +#127 := (iff #57 #126) +#120 := (= #53 #117) +#114 := (* #111 3::Real) +#118 := (= #114 #117) +#119 := [rewrite]: #118 +#115 := (= #53 #114) +#112 := (= #51 #111) +#97 := (= #47 #96) +#98 := [rewrite]: #97 +#109 := (= #50 #106) +#102 := (- #96) +#107 := (= #102 #106) +#108 := [rewrite]: #107 +#103 := (= #50 #102) +#104 := [monotonicity #98]: #103 +#110 := [trans #104 #108]: #109 +#100 := (iff #49 #99) +#101 := [monotonicity #98]: #100 +#113 := [monotonicity #101 #110 #98]: #112 +#116 := [monotonicity #113]: #115 +#121 := [trans #116 #119]: #120 +#128 := [monotonicity #121 #125]: #127 +#172 := [monotonicity #128 #169]: #171 +#178 := [trans #172 #176]: #177 +#181 := [monotonicity #178]: #180 +#273 := [trans #181 #271]: #272 +#93 := [asserted]: #69 +#274 := [mp #93 #273]: #269 +#275 := [not-or-elim #274]: #183 +#277 := [not-or-elim #274]: #246 +#369 := (+ #96 #368) +#370 := (<= #369 0::Real) +#362 := (= #96 #231) +#364 := (or #225 #362) #365 := [def-axiom]: #364 -#394 := [unit-resolution #365 #393]: #361 -#395 := (not #361) -#396 := (or #395 #373) -#397 := [th-lemma arith triangle-eq]: #396 -#398 := [unit-resolution #397 #394]: #373 -#399 := (not #373) -#400 := (or #187 #399 #243 #184 #222) -#401 := [th-lemma arith assign-bounds 3 1 1 2]: #400 -#402 := [unit-resolution #401 #273 #393 #275 #398]: #187 -#403 := [unit-resolution #357 #402]: #354 -#404 := [unit-resolution #379 #403]: #372 -[th-lemma arith farkas 2 2/3 1 1 1/3 1 #398 #275 #273 #393 #274 #404]: false +#388 := [unit-resolution #365 #376]: #362 +#389 := (not #362) +#390 := (or #389 #370) +#391 := [th-lemma arith triangle-eq]: #390 +#392 := [unit-resolution #391 #388]: #370 +#384 := (or #190 #225) +#377 := [hypothesis]: #189 +#276 := [not-or-elim #274]: #212 +#358 := (or #190 #356) +#359 := [def-axiom]: #358 +#378 := [unit-resolution #359 #377]: #356 +#379 := (not #356) +#380 := (or #379 #374) +#381 := [th-lemma arith triangle-eq]: #380 +#382 := [unit-resolution #381 #378]: #374 +#383 := [th-lemma arith farkas -1 -3 1 -2 1 #275 #382 #276 #377 #376]: false +#385 := [lemma #383]: #384 +#393 := [unit-resolution #385 #376]: #190 +#394 := [th-lemma arith farkas 1/4 -3/4 1/4 -1/4 1 #393 #392 #277 #275 #376]: false +#395 := [lemma #394]: #225 +#366 := (or #224 #363) +#367 := [def-axiom]: #366 +#396 := [unit-resolution #367 #395]: #363 +#397 := (not #363) +#398 := (or #397 #375) +#399 := [th-lemma arith triangle-eq]: #398 +#400 := [unit-resolution #399 #396]: #375 +#401 := (not #375) +#402 := (or #189 #401 #245 #186 #224) +#403 := [th-lemma arith assign-bounds 3 1 1 2]: #402 +#404 := [unit-resolution #403 #275 #395 #277 #400]: #189 +#405 := [unit-resolution #359 #404]: #356 +#406 := [unit-resolution #381 #405]: #374 +[th-lemma arith farkas 2 2/3 1 1 1/3 1 #400 #277 #275 #395 #276 #406]: false unsat a66e77fbacece8ec9b71617769b478381e4da6e9 349 0 #2 := false diff -r 4ea9f2a8c093 -r d4cb4d0c14a7 src/HOL/SMT_Examples/SMT_Examples.certs --- a/src/HOL/SMT_Examples/SMT_Examples.certs Fri Dec 17 14:36:33 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples.certs Fri Dec 17 14:59:06 2010 +0100 @@ -12981,199 +12981,198 @@ #104 := [not-or-elim #101]: #103 [unit-resolution #104 #576]: false unsat -60ddd77de436db09ff8cc70aa2e0eff7e14b8798 193 0 +21925946f04e63dea2f01d8f4ea201edb55fb97e 192 0 #2 := false decl f3 :: (-> S2 S3 S4) +decl f5 :: S3 +#26 := f5 +decl f8 :: S2 +#34 := f8 +#40 := (f3 f8 f5) +decl f4 :: (-> S2 S3 S4 S2) +decl f10 :: S4 +#37 := f10 +decl f7 :: S3 +#30 := f7 +decl f9 :: S4 +#35 := f9 decl f6 :: S3 #27 := f6 -decl f9 :: S2 -#35 := f9 -#41 := (f3 f9 f6) -decl f4 :: (-> S5 S2 S3 S4 S2) -decl f11 :: S4 -#38 := f11 -decl f8 :: S3 -#31 := f8 -decl f10 :: S4 -#36 := f10 -decl f7 :: S3 -#28 := f7 -decl f5 :: S5 -#8 := f5 -#37 := (f4 f5 f9 f7 f10) -#39 := (f4 f5 #37 f8 f11) -#40 := (f3 #39 f6) -#42 := (= #40 #41) -#243 := (f3 #37 f7) -#234 := (f4 f5 f9 f7 #243) -#572 := (f3 #234 f6) -#575 := (= #572 #41) -#580 := (= #41 #572) -#576 := (= #243 #572) -#29 := (= f6 f7) -#581 := (ite #29 #576 #580) -#13 := (:var 0 S3) -#11 := (:var 1 S4) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#595 := (pattern #14) -#16 := (f3 #9 #13) -#120 := (= #14 #16) -#119 := (= #11 #14) -#65 := (= #10 #13) -#105 := (ite #65 #119 #120) -#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105) -#112 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105) -#599 := (iff #112 #596) -#597 := (iff #105 #105) -#598 := [refl]: #597 -#600 := [quant-intro #598]: #599 -#68 := (ite #65 #11 #16) -#71 := (= #14 #68) -#74 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #71) -#109 := (iff #74 #112) -#106 := (iff #71 #105) -#111 := [rewrite]: #106 -#110 := [quant-intro #111]: #109 -#115 := (~ #74 #74) -#113 := (~ #71 #71) -#114 := [refl]: #113 -#116 := [nnf-pos #114]: #115 -#15 := (= #13 #10) -#17 := (ite #15 #11 #16) -#18 := (= #14 #17) -#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18) -#75 := (iff #19 #74) -#72 := (iff #18 #71) -#69 := (= #17 #68) -#66 := (iff #15 #65) -#67 := [rewrite]: #66 -#70 := [monotonicity #67]: #69 -#73 := [monotonicity #70]: #72 -#76 := [quant-intro #73]: #75 -#64 := [asserted]: #19 -#79 := [mp #64 #76]: #74 -#101 := [mp~ #79 #116]: #74 -#107 := [mp #101 #110]: #112 -#601 := [mp #107 #600]: #596 -#270 := (not #596) -#568 := (or #270 #581) -#571 := (= f7 f6) -#577 := (ite #571 #576 #575) -#569 := (or #270 #577) -#291 := (iff #569 #568) -#293 := (iff #568 #568) -#279 := [rewrite]: #293 -#579 := (iff #577 #581) -#218 := (iff #575 #580) -#219 := [rewrite]: #218 -#213 := (iff #571 #29) -#578 := [rewrite]: #213 -#582 := [monotonicity #578 #219]: #579 -#292 := [monotonicity #582]: #291 -#294 := [trans #292 #279]: #291 -#275 := [quant-inst #35 #28 #243 #27]: #569 -#185 := [mp #275 #294]: #568 -#530 := [unit-resolution #185 #601]: #581 -#564 := (not #581) -#517 := (or #564 #580) -#30 := (not #29) -#32 := (= f6 f8) -#33 := (not #32) -#34 := (and #30 #33) -#86 := (not #34) -#88 := (or #86 #42) -#91 := (not #88) -#43 := (implies #34 #42) -#44 := (not #43) -#92 := (iff #44 #91) -#89 := (iff #43 #88) -#90 := [rewrite]: #89 -#93 := [monotonicity #90]: #92 -#85 := [asserted]: #44 -#96 := [mp #85 #93]: #91 -#94 := [not-or-elim #96]: #34 -#95 := [and-elim #94]: #30 -#288 := (or #564 #29 #580) -#562 := [def-axiom]: #288 -#519 := [unit-resolution #562 #95]: #517 -#511 := [unit-resolution #519 #530]: #580 -#513 := [symm #511]: #575 -#514 := (= #40 #572) -#177 := (f3 #37 f6) -#523 := (= #177 #572) -#522 := (= #572 #177) -#529 := (= #234 #37) -#435 := (= #243 f10) -#586 := (= f10 #243) -#22 := (:var 0 S4) -#21 := (:var 1 S3) -#20 := (:var 2 S2) -#23 := (f4 f5 #20 #21 #22) -#602 := (pattern #23) -#24 := (f3 #23 #21) -#78 := (= #22 #24) -#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #602) #78) -#82 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #78) -#606 := (iff #82 #603) -#604 := (iff #78 #78) -#605 := [refl]: #604 -#607 := [quant-intro #605]: #606 -#103 := (~ #82 #82) -#102 := (~ #78 #78) -#117 := [refl]: #102 -#104 := [nnf-pos #117]: #103 -#25 := (= #24 #22) -#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25) -#83 := (iff #26 #82) -#80 := (iff #25 #78) -#81 := [rewrite]: #80 -#84 := [quant-intro #81]: #83 -#77 := [asserted]: #26 -#87 := [mp #77 #84]: #82 -#118 := [mp~ #87 #104]: #82 -#608 := [mp #118 #607]: #603 -#231 := (not #603) -#232 := (or #231 #586) -#233 := [quant-inst #35 #28 #36]: #232 -#434 := [unit-resolution #233 #608]: #586 -#436 := [symm #434]: #435 -#526 := [monotonicity #436]: #529 -#518 := [monotonicity #526]: #522 -#512 := [symm #518]: #523 -#264 := (= #40 #177) -#178 := (= f11 #40) -#268 := (ite #32 #178 #264) -#267 := (or #270 #268) -#265 := (= f8 f6) -#179 := (ite #265 #178 #264) -#271 := (or #270 #179) -#587 := (iff #271 #267) -#244 := (iff #267 #267) -#376 := [rewrite]: #244 -#269 := (iff #179 #268) -#266 := (iff #265 #32) -#257 := [rewrite]: #266 -#197 := [monotonicity #257]: #269 -#589 := [monotonicity #197]: #587 -#583 := [trans #589 #376]: #587 -#250 := [quant-inst #37 #31 #38 #27]: #271 -#255 := [mp #250 #583]: #267 -#508 := [unit-resolution #255 #601]: #268 -#256 := (not #268) -#510 := (or #256 #264) -#97 := [and-elim #94]: #33 -#592 := (or #256 #32 #264) -#593 := [def-axiom]: #592 -#520 := [unit-resolution #593 #97]: #510 -#521 := [unit-resolution #520 #508]: #264 -#515 := [trans #521 #512]: #514 -#509 := [trans #515 #513]: #42 -#98 := (not #42) -#99 := [not-or-elim #96]: #98 -[unit-resolution #99 #509]: false +#36 := (f4 f8 f6 f9) +#38 := (f4 #36 f7 f10) +#39 := (f3 #38 f5) +#41 := (= #39 #40) +#242 := (f3 #36 f6) +#233 := (f4 f8 f6 #242) +#571 := (f3 #233 f5) +#574 := (= #571 #40) +#579 := (= #40 #571) +#575 := (= #242 #571) +#28 := (= f5 f6) +#580 := (ite #28 #575 #579) +#12 := (:var 0 S3) +#10 := (:var 1 S4) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#594 := (pattern #13) +#15 := (f3 #8 #12) +#119 := (= #13 #15) +#118 := (= #10 #13) +#64 := (= #9 #12) +#104 := (ite #64 #118 #119) +#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104) +#111 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104) +#598 := (iff #111 #595) +#596 := (iff #104 #104) +#597 := [refl]: #596 +#599 := [quant-intro #597]: #598 +#67 := (ite #64 #10 #15) +#70 := (= #13 #67) +#73 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #70) +#108 := (iff #73 #111) +#105 := (iff #70 #104) +#110 := [rewrite]: #105 +#109 := [quant-intro #110]: #108 +#114 := (~ #73 #73) +#112 := (~ #70 #70) +#113 := [refl]: #112 +#115 := [nnf-pos #113]: #114 +#14 := (= #12 #9) +#16 := (ite #14 #10 #15) +#17 := (= #13 #16) +#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17) +#74 := (iff #18 #73) +#71 := (iff #17 #70) +#68 := (= #16 #67) +#65 := (iff #14 #64) +#66 := [rewrite]: #65 +#69 := [monotonicity #66]: #68 +#72 := [monotonicity #69]: #71 +#75 := [quant-intro #72]: #74 +#63 := [asserted]: #18 +#78 := [mp #63 #75]: #73 +#100 := [mp~ #78 #115]: #73 +#106 := [mp #100 #109]: #111 +#600 := [mp #106 #599]: #595 +#269 := (not #595) +#567 := (or #269 #580) +#570 := (= f6 f5) +#576 := (ite #570 #575 #574) +#568 := (or #269 #576) +#290 := (iff #568 #567) +#292 := (iff #567 #567) +#278 := [rewrite]: #292 +#578 := (iff #576 #580) +#217 := (iff #574 #579) +#218 := [rewrite]: #217 +#212 := (iff #570 #28) +#577 := [rewrite]: #212 +#581 := [monotonicity #577 #218]: #578 +#291 := [monotonicity #581]: #290 +#293 := [trans #291 #278]: #290 +#274 := [quant-inst #34 #27 #242 #26]: #568 +#184 := [mp #274 #293]: #567 +#529 := [unit-resolution #184 #600]: #580 +#563 := (not #580) +#516 := (or #563 #579) +#29 := (not #28) +#31 := (= f5 f7) +#32 := (not #31) +#33 := (and #29 #32) +#85 := (not #33) +#87 := (or #85 #41) +#90 := (not #87) +#42 := (implies #33 #41) +#43 := (not #42) +#91 := (iff #43 #90) +#88 := (iff #42 #87) +#89 := [rewrite]: #88 +#92 := [monotonicity #89]: #91 +#84 := [asserted]: #43 +#95 := [mp #84 #92]: #90 +#93 := [not-or-elim #95]: #33 +#94 := [and-elim #93]: #29 +#287 := (or #563 #28 #579) +#561 := [def-axiom]: #287 +#518 := [unit-resolution #561 #94]: #516 +#510 := [unit-resolution #518 #529]: #579 +#512 := [symm #510]: #574 +#513 := (= #39 #571) +#176 := (f3 #36 f5) +#522 := (= #176 #571) +#521 := (= #571 #176) +#528 := (= #233 #36) +#434 := (= #242 f9) +#585 := (= f9 #242) +#21 := (:var 0 S4) +#20 := (:var 1 S3) +#19 := (:var 2 S2) +#22 := (f4 #19 #20 #21) +#601 := (pattern #22) +#23 := (f3 #22 #20) +#77 := (= #21 #23) +#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #77) +#81 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #77) +#602 := (iff #81 #603) +#605 := (iff #603 #603) +#606 := [rewrite]: #605 +#604 := [rewrite]: #602 +#607 := [trans #604 #606]: #602 +#102 := (~ #81 #81) +#101 := (~ #77 #77) +#116 := [refl]: #101 +#103 := [nnf-pos #116]: #102 +#24 := (= #23 #21) +#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24) +#82 := (iff #25 #81) +#79 := (iff #24 #77) +#80 := [rewrite]: #79 +#83 := [quant-intro #80]: #82 +#76 := [asserted]: #25 +#86 := [mp #76 #83]: #81 +#117 := [mp~ #86 #103]: #81 +#608 := [mp #117 #607]: #603 +#230 := (not #603) +#231 := (or #230 #585) +#232 := [quant-inst #34 #27 #35]: #231 +#433 := [unit-resolution #232 #608]: #585 +#435 := [symm #433]: #434 +#525 := [monotonicity #435]: #528 +#517 := [monotonicity #525]: #521 +#511 := [symm #517]: #522 +#263 := (= #39 #176) +#177 := (= f10 #39) +#267 := (ite #31 #177 #263) +#266 := (or #269 #267) +#264 := (= f7 f5) +#178 := (ite #264 #177 #263) +#270 := (or #269 #178) +#586 := (iff #270 #266) +#243 := (iff #266 #266) +#375 := [rewrite]: #243 +#268 := (iff #178 #267) +#265 := (iff #264 #31) +#256 := [rewrite]: #265 +#196 := [monotonicity #256]: #268 +#588 := [monotonicity #196]: #586 +#582 := [trans #588 #375]: #586 +#249 := [quant-inst #36 #30 #37 #26]: #270 +#254 := [mp #249 #582]: #266 +#507 := [unit-resolution #254 #600]: #267 +#255 := (not #267) +#509 := (or #255 #263) +#96 := [and-elim #93]: #32 +#591 := (or #255 #31 #263) +#592 := [def-axiom]: #591 +#519 := [unit-resolution #592 #96]: #509 +#520 := [unit-resolution #519 #507]: #263 +#514 := [trans #520 #511]: #513 +#508 := [trans #514 #512]: #41 +#97 := (not #41) +#98 := [not-or-elim #95]: #97 +[unit-resolution #98 #508]: false unsat 10c4eb4ff6b9f0c880cfc3af0cd433a1ff110114 96 0 #2 := false @@ -14299,82 +14298,82 @@ unsat 8f8fbc61d0925864fffd8945e68a0401b7416686 1 0 unsat -4bafa9f250d1b4853cae936d5a014474439d5625 76 0 -#2 := false -decl f3 :: (-> Int S1) -#129 := 1::Int -#130 := (f3 1::Int) +a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0 +#2 := false +decl f28 :: (-> Int S1) +#107 := 1::Int +#108 := (f28 1::Int) decl f1 :: S1 #4 := f1 -#460 := (= f1 #130) -#464 := (not #460) -#131 := (= #130 f1) -#132 := (not #131) -#465 := (iff #132 #464) -#462 := (iff #131 #460) -#463 := [rewrite]: #462 -#466 := [monotonicity #463]: #465 -#459 := [asserted]: #132 -#469 := [mp #459 #466]: #464 -#8 := (:var 0 Int) -#9 := (f3 #8) -#997 := (pattern #9) -#153 := (= f1 #9) -#998 := (forall (vars (?v0 Int)) (:pat #997) #153) -#176 := (forall (vars (?v0 Int)) #153) -#1001 := (iff #176 #998) -#999 := (iff #153 #153) -#1000 := [refl]: #999 -#1002 := [quant-intro #1000]: #1001 -#497 := (~ #176 #176) -#495 := (~ #153 #153) -#496 := [refl]: #495 -#498 := [nnf-pos #496]: #497 -decl f4 :: (-> S2 S1) -decl f5 :: (-> Int S2 S2) -decl f6 :: S2 -#11 := f6 -#12 := (f5 #8 f6) -#13 := (f4 #12) -#14 := (= #13 f1) -#15 := (not #14) -#16 := (or #14 #15) -#10 := (= #9 f1) -#17 := (and #10 #16) -#18 := (forall (vars (?v0 Int)) #17) -#177 := (iff #18 #176) -#174 := (iff #17 #153) +#382 := (= f1 #108) +#386 := (not #382) +#109 := (= #108 f1) +#110 := (not #109) +#387 := (iff #110 #386) +#384 := (iff #109 #382) +#385 := [rewrite]: #384 +#388 := [monotonicity #385]: #387 +#381 := [asserted]: #110 +#391 := [mp #381 #388]: #386 +#96 := (:var 0 Int) +#97 := (f28 #96) +#965 := (pattern #97) +#354 := (= f1 #97) +#966 := (forall (vars (?v0 Int)) (:pat #965) #354) +#378 := (forall (vars (?v0 Int)) #354) +#969 := (iff #378 #966) +#967 := (iff #354 #354) +#968 := [refl]: #967 +#970 := [quant-intro #968]: #969 +#407 := (~ #378 #378) +#437 := (~ #354 #354) +#438 := [refl]: #437 +#408 := [nnf-pos #438]: #407 +decl f3 :: (-> S2 S1) +decl f29 :: (-> Int S2 S2) +decl f30 :: S2 +#99 := f30 +#100 := (f29 #96 f30) +#101 := (f3 #100) +#102 := (= #101 f1) +#103 := (not #102) +#104 := (or #102 #103) +#98 := (= #97 f1) +#105 := (and #98 #104) +#106 := (forall (vars (?v0 Int)) #105) +#379 := (iff #106 #378) +#376 := (iff #105 #354) #1 := true -#169 := (and #153 true) -#172 := (iff #169 #153) -#173 := [rewrite]: #172 -#170 := (iff #17 #169) -#167 := (iff #16 true) -#156 := (= f1 #13) -#159 := (not #156) -#162 := (or #156 #159) -#165 := (iff #162 true) -#166 := [rewrite]: #165 -#163 := (iff #16 #162) -#160 := (iff #15 #159) -#157 := (iff #14 #156) -#158 := [rewrite]: #157 -#161 := [monotonicity #158]: #160 -#164 := [monotonicity #158 #161]: #163 -#168 := [trans #164 #166]: #167 -#154 := (iff #10 #153) -#155 := [rewrite]: #154 -#171 := [monotonicity #155 #168]: #170 -#175 := [trans #171 #173]: #174 -#178 := [quant-intro #175]: #177 -#152 := [asserted]: #18 -#181 := [mp #152 #178]: #176 -#468 := [mp~ #181 #498]: #176 -#1003 := [mp #468 #1002]: #998 -#582 := (not #998) -#667 := (or #582 #460) -#668 := [quant-inst #129]: #667 -[unit-resolution #668 #1003 #469]: false +#371 := (and #354 true) +#374 := (iff #371 #354) +#375 := [rewrite]: #374 +#372 := (iff #105 #371) +#369 := (iff #104 true) +#358 := (= f1 #101) +#361 := (not #358) +#364 := (or #358 #361) +#367 := (iff #364 true) +#368 := [rewrite]: #367 +#365 := (iff #104 #364) +#362 := (iff #103 #361) +#359 := (iff #102 #358) +#360 := [rewrite]: #359 +#363 := [monotonicity #360]: #362 +#366 := [monotonicity #360 #363]: #365 +#370 := [trans #366 #368]: #369 +#356 := (iff #98 #354) +#357 := [rewrite]: #356 +#373 := [monotonicity #357 #370]: #372 +#377 := [trans #373 #375]: #376 +#380 := [quant-intro #377]: #379 +#353 := [asserted]: #106 +#383 := [mp #353 #380]: #378 +#439 := [mp~ #383 #408]: #378 +#971 := [mp #439 #970]: #966 +#494 := (not #966) +#579 := (or #494 #382) +#580 := [quant-inst #107]: #579 +[unit-resolution #580 #971 #391]: false unsat e4dd068db00f152c179631d20d9af452dbe0f45d 439 0 #2 := false @@ -14816,80 +14815,3 @@ #287 := [mp #270 #284]: #282 [unit-resolution #287 #630]: false unsat -a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0 -#2 := false -decl f28 :: (-> Int S1) -#107 := 1::Int -#108 := (f28 1::Int) -decl f1 :: S1 -#4 := f1 -#382 := (= f1 #108) -#386 := (not #382) -#109 := (= #108 f1) -#110 := (not #109) -#387 := (iff #110 #386) -#384 := (iff #109 #382) -#385 := [rewrite]: #384 -#388 := [monotonicity #385]: #387 -#381 := [asserted]: #110 -#391 := [mp #381 #388]: #386 -#96 := (:var 0 Int) -#97 := (f28 #96) -#965 := (pattern #97) -#354 := (= f1 #97) -#966 := (forall (vars (?v0 Int)) (:pat #965) #354) -#378 := (forall (vars (?v0 Int)) #354) -#969 := (iff #378 #966) -#967 := (iff #354 #354) -#968 := [refl]: #967 -#970 := [quant-intro #968]: #969 -#407 := (~ #378 #378) -#437 := (~ #354 #354) -#438 := [refl]: #437 -#408 := [nnf-pos #438]: #407 -decl f3 :: (-> S2 S1) -decl f29 :: (-> Int S2 S2) -decl f30 :: S2 -#99 := f30 -#100 := (f29 #96 f30) -#101 := (f3 #100) -#102 := (= #101 f1) -#103 := (not #102) -#104 := (or #102 #103) -#98 := (= #97 f1) -#105 := (and #98 #104) -#106 := (forall (vars (?v0 Int)) #105) -#379 := (iff #106 #378) -#376 := (iff #105 #354) -#1 := true -#371 := (and #354 true) -#374 := (iff #371 #354) -#375 := [rewrite]: #374 -#372 := (iff #105 #371) -#369 := (iff #104 true) -#358 := (= f1 #101) -#361 := (not #358) -#364 := (or #358 #361) -#367 := (iff #364 true) -#368 := [rewrite]: #367 -#365 := (iff #104 #364) -#362 := (iff #103 #361) -#359 := (iff #102 #358) -#360 := [rewrite]: #359 -#363 := [monotonicity #360]: #362 -#366 := [monotonicity #360 #363]: #365 -#370 := [trans #366 #368]: #369 -#356 := (iff #98 #354) -#357 := [rewrite]: #356 -#373 := [monotonicity #357 #370]: #372 -#377 := [trans #373 #375]: #376 -#380 := [quant-intro #377]: #379 -#353 := [asserted]: #106 -#383 := [mp #353 #380]: #378 -#439 := [mp~ #383 #408]: #378 -#971 := [mp #439 #970]: #966 -#494 := (not #966) -#579 := (or #494 #382) -#580 := [quant-inst #107]: #579 -[unit-resolution #580 #971 #391]: false -unsat diff -r 4ea9f2a8c093 -r d4cb4d0c14a7 src/HOL/SMT_Examples/SMT_Tests.certs --- a/src/HOL/SMT_Examples/SMT_Tests.certs Fri Dec 17 14:36:33 2010 +0100 +++ b/src/HOL/SMT_Examples/SMT_Tests.certs Fri Dec 17 14:59:06 2010 +0100 @@ -51097,597 +51097,591 @@ #244 := [quant-inst #28 #24 #29 #25]: #253 [unit-resolution #244 #588 #165]: false unsat -3a3e28b9a1ce272e3a845bbcea7eeac5abc8f586 159 0 +57b1778e367cf6f6921505d440f3fc4fb8332587 158 0 #2 := false decl f3 :: (-> S2 S3 S4) +decl f5 :: S3 +#26 := f5 +decl f4 :: (-> S2 S3 S4 S2) +decl f9 :: S4 +#33 := f9 decl f6 :: S3 #27 := f6 -decl f4 :: (-> S5 S2 S3 S4 S2) -decl f10 :: S4 -#34 := f10 -decl f7 :: S3 -#28 := f7 -decl f9 :: S4 -#32 := f9 -decl f8 :: S2 +decl f8 :: S4 #31 := f8 -decl f5 :: S5 -#8 := f5 -#33 := (f4 f5 f8 f6 f9) -#35 := (f4 f5 #33 f7 f10) -#36 := (f3 #35 f6) -#81 := (= f9 #36) -#177 := (f3 #33 f6) -#264 := (= #36 #177) -#581 := (iff #264 #81) -#218 := (iff #81 #264) -#571 := (= #177 #36) -#578 := (iff #571 #264) -#580 := [commutativity]: #578 -#577 := (iff #81 #571) -#243 := (= f9 #177) -#22 := (:var 0 S4) -#21 := (:var 1 S3) -#20 := (:var 2 S2) -#23 := (f4 f5 #20 #21 #22) -#602 := (pattern #23) -#24 := (f3 #23 #21) -#73 := (= #22 #24) -#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #602) #73) -#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #73) -#606 := (iff #77 #603) -#604 := (iff #73 #73) -#605 := [refl]: #604 -#607 := [quant-intro #605]: #606 -#103 := (~ #77 #77) -#102 := (~ #73 #73) -#115 := [refl]: #102 -#104 := [nnf-pos #115]: #103 -#25 := (= #24 #22) -#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25) -#78 := (iff #26 #77) -#75 := (iff #25 #73) -#76 := [rewrite]: #75 -#79 := [quant-intro #76]: #78 -#72 := [asserted]: #26 -#82 := [mp #72 #79]: #77 -#116 := [mp~ #82 #104]: #77 -#608 := [mp #116 #607]: #603 -#570 := (not #603) -#231 := (or #570 #243) -#232 := [quant-inst #31 #27 #32]: #231 -#576 := [unit-resolution #232 #608]: #243 -#213 := [monotonicity #576]: #577 -#219 := [trans #213 #580]: #218 -#579 := [symm #219]: #581 -#178 := (= f10 #36) -#29 := (= f6 f7) -#268 := (ite #29 #178 #264) -#13 := (:var 0 S3) -#11 := (:var 1 S4) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#595 := (pattern #14) -#16 := (f3 #9 #13) -#118 := (= #14 #16) -#117 := (= #11 #14) -#60 := (= #10 #13) -#105 := (ite #60 #117 #118) -#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105) -#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105) -#599 := (iff #110 #596) -#597 := (iff #105 #105) -#598 := [refl]: #597 -#600 := [quant-intro #598]: #599 -#63 := (ite #60 #11 #16) -#66 := (= #14 #63) -#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66) -#107 := (iff #69 #110) -#106 := (iff #66 #105) -#109 := [rewrite]: #106 -#108 := [quant-intro #109]: #107 -#113 := (~ #69 #69) -#111 := (~ #66 #66) -#112 := [refl]: #111 -#114 := [nnf-pos #112]: #113 -#15 := (= #13 #10) -#17 := (ite #15 #11 #16) -#18 := (= #14 #17) -#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18) -#70 := (iff #19 #69) -#67 := (iff #18 #66) -#64 := (= #17 #63) -#61 := (iff #15 #60) -#62 := [rewrite]: #61 -#65 := [monotonicity #62]: #64 -#68 := [monotonicity #65]: #67 -#71 := [quant-intro #68]: #70 -#59 := [asserted]: #19 -#74 := [mp #59 #71]: #69 -#101 := [mp~ #74 #114]: #69 -#119 := [mp #101 #108]: #110 -#601 := [mp #119 #600]: #596 -#270 := (not #596) -#267 := (or #270 #268) -#265 := (= f7 f6) -#179 := (ite #265 #178 #264) -#271 := (or #270 #179) -#587 := (iff #271 #267) -#244 := (iff #267 #267) -#376 := [rewrite]: #244 -#269 := (iff #179 #268) -#266 := (iff #265 #29) -#257 := [rewrite]: #266 -#197 := [monotonicity #257]: #269 -#589 := [monotonicity #197]: #587 -#583 := [trans #589 #376]: #587 -#250 := [quant-inst #33 #28 #34 #27]: #271 -#255 := [mp #250 #583]: #267 -#233 := [unit-resolution #255 #601]: #268 -#256 := (not #268) -#234 := (or #256 #264) -#30 := (not #29) -#88 := (or #29 #81) -#93 := (not #88) -#37 := (= #36 f9) -#38 := (implies #30 #37) -#39 := (not #38) -#94 := (iff #39 #93) -#91 := (iff #38 #88) -#85 := (implies #30 #81) -#89 := (iff #85 #88) -#90 := [rewrite]: #89 -#86 := (iff #38 #85) -#83 := (iff #37 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#92 := [trans #87 #90]: #91 -#95 := [monotonicity #92]: #94 -#80 := [asserted]: #39 -#98 := [mp #80 #95]: #93 -#96 := [not-or-elim #98]: #30 -#592 := (or #256 #29 #264) -#593 := [def-axiom]: #592 -#574 := [unit-resolution #593 #96]: #234 -#575 := [unit-resolution #574 #233]: #264 -#582 := [mp #575 #579]: #81 -#97 := (not #81) -#99 := [not-or-elim #98]: #97 -[unit-resolution #99 #582]: false -unsat -9624532c2fce6f30c8a21e62aa8e557532aee6d5 113 0 -#2 := false -decl f3 :: (-> S2 S3 S4) -decl f7 :: S3 -#28 := f7 -decl f4 :: (-> S5 S2 S3 S4 S2) -decl f10 :: S4 -#34 := f10 -decl f9 :: S4 -#32 := f9 -decl f6 :: S3 -#27 := f6 -decl f8 :: S2 -#31 := f8 -decl f5 :: S5 -#8 := f5 -#33 := (f4 f5 f8 f6 f9) -#35 := (f4 f5 #33 f7 f10) -#36 := (f3 #35 f7) -#81 := (= f10 #36) -#97 := (not #81) -#29 := (= f6 f7) -#88 := (or #29 #81) -#93 := (not #88) -#37 := (= #36 f10) -#30 := (not #29) -#38 := (implies #30 #37) -#39 := (not #38) -#94 := (iff #39 #93) -#91 := (iff #38 #88) -#85 := (implies #30 #81) -#89 := (iff #85 #88) -#90 := [rewrite]: #89 -#86 := (iff #38 #85) -#83 := (iff #37 #81) -#84 := [rewrite]: #83 -#87 := [monotonicity #84]: #86 -#92 := [trans #87 #90]: #91 -#95 := [monotonicity #92]: #94 -#80 := [asserted]: #39 -#98 := [mp #80 #95]: #93 -#99 := [not-or-elim #98]: #97 -#13 := (:var 0 S3) -#11 := (:var 1 S4) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#595 := (pattern #14) -#16 := (f3 #9 #13) -#118 := (= #14 #16) -#117 := (= #11 #14) -#60 := (= #10 #13) -#105 := (ite #60 #117 #118) -#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105) -#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105) -#599 := (iff #110 #596) -#597 := (iff #105 #105) -#598 := [refl]: #597 -#600 := [quant-intro #598]: #599 -#63 := (ite #60 #11 #16) -#66 := (= #14 #63) -#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66) -#107 := (iff #69 #110) -#106 := (iff #66 #105) -#109 := [rewrite]: #106 -#108 := [quant-intro #109]: #107 -#113 := (~ #69 #69) -#111 := (~ #66 #66) -#112 := [refl]: #111 -#114 := [nnf-pos #112]: #113 -#15 := (= #13 #10) -#17 := (ite #15 #11 #16) -#18 := (= #14 #17) -#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18) -#70 := (iff #19 #69) -#67 := (iff #18 #66) -#64 := (= #17 #63) -#61 := (iff #15 #60) -#62 := [rewrite]: #61 -#65 := [monotonicity #62]: #64 -#68 := [monotonicity #65]: #67 -#71 := [quant-intro #68]: #70 -#59 := [asserted]: #19 -#74 := [mp #59 #71]: #69 -#101 := [mp~ #74 #114]: #69 -#119 := [mp #101 #108]: #110 -#601 := [mp #119 #600]: #596 -#250 := (not #596) -#587 := (or #250 #81) -#177 := (f3 #33 f7) -#264 := (= #36 #177) -#178 := (= f7 f7) -#265 := (ite #178 #81 #264) -#589 := (or #250 #265) -#376 := (iff #589 #587) -#255 := (iff #587 #587) -#256 := [rewrite]: #255 -#267 := (iff #265 #81) -#1 := true -#257 := (ite true #81 #264) -#197 := (iff #257 #81) -#270 := [rewrite]: #197 -#268 := (iff #265 #257) -#179 := (iff #178 true) -#266 := [rewrite]: #179 -#269 := [monotonicity #266]: #268 -#271 := [trans #269 #270]: #267 -#583 := [monotonicity #271]: #376 -#590 := [trans #583 #256]: #376 -#244 := [quant-inst #33 #28 #34 #28]: #589 -#591 := [mp #244 #590]: #587 -[unit-resolution #591 #601 #99]: false -unsat -c87329d6ba7c190d060550d5a4c2a90769f50212 125 0 +decl f7 :: S2 +#30 := f7 +#32 := (f4 f7 f5 f8) +#34 := (f4 #32 f6 f9) +#35 := (f3 #34 f5) +#80 := (= f8 #35) +#176 := (f3 #32 f5) +#263 := (= #35 #176) +#580 := (iff #263 #80) +#217 := (iff #80 #263) +#570 := (= #176 #35) +#577 := (iff #570 #263) +#579 := [commutativity]: #577 +#576 := (iff #80 #570) +#242 := (= f8 #176) +#21 := (:var 0 S4) +#20 := (:var 1 S3) +#19 := (:var 2 S2) +#22 := (f4 #19 #20 #21) +#601 := (pattern #22) +#23 := (f3 #22 #20) +#72 := (= #21 #23) +#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #72) +#76 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #72) +#602 := (iff #76 #603) +#605 := (iff #603 #603) +#606 := [rewrite]: #605 +#604 := [rewrite]: #602 +#607 := [trans #604 #606]: #602 +#102 := (~ #76 #76) +#101 := (~ #72 #72) +#114 := [refl]: #101 +#103 := [nnf-pos #114]: #102 +#24 := (= #23 #21) +#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24) +#77 := (iff #25 #76) +#74 := (iff #24 #72) +#75 := [rewrite]: #74 +#78 := [quant-intro #75]: #77 +#71 := [asserted]: #25 +#81 := [mp #71 #78]: #76 +#115 := [mp~ #81 #103]: #76 +#608 := [mp #115 #607]: #603 +#569 := (not #603) +#230 := (or #569 #242) +#231 := [quant-inst #30 #26 #31]: #230 +#575 := [unit-resolution #231 #608]: #242 +#212 := [monotonicity #575]: #576 +#218 := [trans #212 #579]: #217 +#578 := [symm #218]: #580 +#177 := (= f9 #35) +#28 := (= f5 f6) +#267 := (ite #28 #177 #263) +#12 := (:var 0 S3) +#10 := (:var 1 S4) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#594 := (pattern #13) +#15 := (f3 #8 #12) +#117 := (= #13 #15) +#116 := (= #10 #13) +#59 := (= #9 #12) +#104 := (ite #59 #116 #117) +#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104) +#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104) +#598 := (iff #109 #595) +#596 := (iff #104 #104) +#597 := [refl]: #596 +#599 := [quant-intro #597]: #598 +#62 := (ite #59 #10 #15) +#65 := (= #13 #62) +#68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65) +#106 := (iff #68 #109) +#105 := (iff #65 #104) +#108 := [rewrite]: #105 +#107 := [quant-intro #108]: #106 +#112 := (~ #68 #68) +#110 := (~ #65 #65) +#111 := [refl]: #110 +#113 := [nnf-pos #111]: #112 +#14 := (= #12 #9) +#16 := (ite #14 #10 #15) +#17 := (= #13 #16) +#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17) +#69 := (iff #18 #68) +#66 := (iff #17 #65) +#63 := (= #16 #62) +#60 := (iff #14 #59) +#61 := [rewrite]: #60 +#64 := [monotonicity #61]: #63 +#67 := [monotonicity #64]: #66 +#70 := [quant-intro #67]: #69 +#58 := [asserted]: #18 +#73 := [mp #58 #70]: #68 +#100 := [mp~ #73 #113]: #68 +#118 := [mp #100 #107]: #109 +#600 := [mp #118 #599]: #595 +#269 := (not #595) +#266 := (or #269 #267) +#264 := (= f6 f5) +#178 := (ite #264 #177 #263) +#270 := (or #269 #178) +#586 := (iff #270 #266) +#243 := (iff #266 #266) +#375 := [rewrite]: #243 +#268 := (iff #178 #267) +#265 := (iff #264 #28) +#256 := [rewrite]: #265 +#196 := [monotonicity #256]: #268 +#588 := [monotonicity #196]: #586 +#582 := [trans #588 #375]: #586 +#249 := [quant-inst #32 #27 #33 #26]: #270 +#254 := [mp #249 #582]: #266 +#232 := [unit-resolution #254 #600]: #267 +#255 := (not #267) +#233 := (or #255 #263) +#29 := (not #28) +#87 := (or #28 #80) +#92 := (not #87) +#36 := (= #35 f8) +#37 := (implies #29 #36) +#38 := (not #37) +#93 := (iff #38 #92) +#90 := (iff #37 #87) +#84 := (implies #29 #80) +#88 := (iff #84 #87) +#89 := [rewrite]: #88 +#85 := (iff #37 #84) +#82 := (iff #36 #80) +#83 := [rewrite]: #82 +#86 := [monotonicity #83]: #85 +#91 := [trans #86 #89]: #90 +#94 := [monotonicity #91]: #93 +#79 := [asserted]: #38 +#97 := [mp #79 #94]: #92 +#95 := [not-or-elim #97]: #29 +#591 := (or #255 #28 #263) +#592 := [def-axiom]: #591 +#573 := [unit-resolution #592 #95]: #233 +#574 := [unit-resolution #573 #232]: #263 +#581 := [mp #574 #578]: #80 +#96 := (not #80) +#98 := [not-or-elim #97]: #96 +[unit-resolution #98 #581]: false +unsat +c5924477e9186eb5df53c29cfb676c83a60e811c 111 0 #2 := false decl f3 :: (-> S2 S3 S4) decl f6 :: S3 #27 := f6 -decl f4 :: (-> S5 S2 S3 S4 S2) -decl f10 :: S4 -#33 := f10 -decl f7 :: S3 -#28 := f7 +decl f4 :: (-> S2 S3 S4 S2) decl f9 :: S4 -#31 := f9 -decl f8 :: S2 -#30 := f8 -decl f5 :: S5 -#8 := f5 -#32 := (f4 f5 f8 f6 f9) -#34 := (f4 f5 #32 f7 f10) +#33 := f9 +decl f8 :: S4 +#31 := f8 +decl f5 :: S3 +#26 := f5 +decl f7 :: S2 +#30 := f7 +#32 := (f4 f7 f5 f8) +#34 := (f4 #32 f6 f9) #35 := (f3 #34 f6) -#80 := (= f10 #35) -#264 := (f3 #34 f7) -#572 := (= #264 #35) -#586 := (= #35 #264) -#29 := (= f6 f7) -#87 := (not #29) -#88 := (or #87 #80) -#93 := (not #88) -#36 := (= #35 f10) +#80 := (= f9 #35) +#96 := (not #80) +#28 := (= f5 f6) +#87 := (or #28 #80) +#92 := (not #87) +#36 := (= #35 f9) +#29 := (not #28) #37 := (implies #29 #36) #38 := (not #37) -#94 := (iff #38 #93) -#91 := (iff #37 #88) +#93 := (iff #38 #92) +#90 := (iff #37 #87) #84 := (implies #29 #80) -#89 := (iff #84 #88) -#90 := [rewrite]: #89 +#88 := (iff #84 #87) +#89 := [rewrite]: #88 #85 := (iff #37 #84) #82 := (iff #36 #80) #83 := [rewrite]: #82 #86 := [monotonicity #83]: #85 -#92 := [trans #86 #90]: #91 -#95 := [monotonicity #92]: #94 +#91 := [trans #86 #89]: #90 +#94 := [monotonicity #91]: #93 #79 := [asserted]: #38 -#98 := [mp #79 #95]: #93 -#96 := [not-or-elim #98]: #29 -#234 := [monotonicity #96]: #586 -#573 := [symm #234]: #572 -#265 := (= f10 #264) -#13 := (:var 0 S3) -#11 := (:var 1 S4) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#595 := (pattern #14) -#16 := (f3 #9 #13) -#118 := (= #14 #16) -#117 := (= #11 #14) -#59 := (= #10 #13) -#105 := (ite #59 #117 #118) -#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #595) #105) -#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #105) -#599 := (iff #110 #596) -#597 := (iff #105 #105) -#598 := [refl]: #597 -#600 := [quant-intro #598]: #599 -#62 := (ite #59 #11 #16) -#65 := (= #14 #62) +#97 := [mp #79 #94]: #92 +#98 := [not-or-elim #97]: #96 +#12 := (:var 0 S3) +#10 := (:var 1 S4) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#594 := (pattern #13) +#15 := (f3 #8 #12) +#117 := (= #13 #15) +#116 := (= #10 #13) +#59 := (= #9 #12) +#104 := (ite #59 #116 #117) +#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104) +#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104) +#598 := (iff #109 #595) +#596 := (iff #104 #104) +#597 := [refl]: #596 +#599 := [quant-intro #597]: #598 +#62 := (ite #59 #10 #15) +#65 := (= #13 #62) #68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65) -#107 := (iff #68 #110) -#106 := (iff #65 #105) -#109 := [rewrite]: #106 -#108 := [quant-intro #109]: #107 -#113 := (~ #68 #68) -#111 := (~ #65 #65) -#112 := [refl]: #111 -#114 := [nnf-pos #112]: #113 -#15 := (= #13 #10) -#17 := (ite #15 #11 #16) -#18 := (= #14 #17) -#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18) -#69 := (iff #19 #68) -#66 := (iff #18 #65) -#63 := (= #17 #62) -#60 := (iff #15 #59) +#106 := (iff #68 #109) +#105 := (iff #65 #104) +#108 := [rewrite]: #105 +#107 := [quant-intro #108]: #106 +#112 := (~ #68 #68) +#110 := (~ #65 #65) +#111 := [refl]: #110 +#113 := [nnf-pos #111]: #112 +#14 := (= #12 #9) +#16 := (ite #14 #10 #15) +#17 := (= #13 #16) +#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17) +#69 := (iff #18 #68) +#66 := (iff #17 #65) +#63 := (= #16 #62) +#60 := (iff #14 #59) #61 := [rewrite]: #60 #64 := [monotonicity #61]: #63 #67 := [monotonicity #64]: #66 #70 := [quant-intro #67]: #69 -#58 := [asserted]: #19 +#58 := [asserted]: #18 #73 := [mp #58 #70]: #68 -#101 := [mp~ #73 #114]: #68 -#119 := [mp #101 #108]: #110 -#601 := [mp #119 #600]: #596 -#583 := (not #596) -#255 := (or #583 #265) -#177 := (f3 #32 f7) -#178 := (= #264 #177) -#179 := (= f7 f7) -#266 := (ite #179 #265 #178) -#256 := (or #583 #266) -#591 := (iff #256 #255) -#593 := (iff #255 #255) -#588 := [rewrite]: #593 -#244 := (iff #266 #265) -#269 := (= #177 #264) -#1 := true -#267 := (ite true #265 #269) -#587 := (iff #267 #265) -#589 := [rewrite]: #587 -#271 := (iff #266 #267) -#197 := (iff #178 #269) -#270 := [rewrite]: #197 -#257 := (iff #179 true) -#268 := [rewrite]: #257 -#250 := [monotonicity #268 #270]: #271 -#376 := [trans #250 #589]: #244 -#592 := [monotonicity #376]: #591 -#594 := [trans #592 #588]: #591 -#590 := [quant-inst #32 #28 #33 #28]: #256 -#584 := [mp #590 #594]: #255 -#243 := [unit-resolution #584 #601]: #265 -#574 := [trans #243 #573]: #80 -#97 := (not #80) -#99 := [not-or-elim #98]: #97 -[unit-resolution #99 #574]: false -unsat -1d21028f73bdc0aae30ff8eb56a63829018f8e82 191 0 +#100 := [mp~ #73 #113]: #68 +#118 := [mp #100 #107]: #109 +#600 := [mp #118 #599]: #595 +#249 := (not #595) +#586 := (or #249 #80) +#176 := (f3 #32 f6) +#263 := (= #35 #176) +#177 := (= f6 f6) +#264 := (ite #177 #80 #263) +#588 := (or #249 #264) +#375 := (iff #588 #586) +#254 := (iff #586 #586) +#255 := [rewrite]: #254 +#266 := (iff #264 #80) +#1 := true +#256 := (ite true #80 #263) +#196 := (iff #256 #80) +#269 := [rewrite]: #196 +#267 := (iff #264 #256) +#178 := (iff #177 true) +#265 := [rewrite]: #178 +#268 := [monotonicity #265]: #267 +#270 := [trans #268 #269]: #266 +#582 := [monotonicity #270]: #375 +#589 := [trans #582 #255]: #375 +#243 := [quant-inst #32 #27 #33 #27]: #588 +#590 := [mp #243 #589]: #586 +[unit-resolution #590 #600 #98]: false +unsat +7e28540fd0d4f5814439be9d6e362d0c1457f76e 123 0 #2 := false decl f3 :: (-> S2 S3 S4) -decl f8 :: S3 -#29 := f8 -decl f9 :: S2 -#31 := f9 -#37 := (f3 f9 f8) -decl f4 :: (-> S5 S2 S3 S4 S2) -decl f11 :: S4 -#34 := f11 +decl f5 :: S3 +#26 := f5 +decl f4 :: (-> S2 S3 S4 S2) +decl f9 :: S4 +#32 := f9 +decl f6 :: S3 +#27 := f6 +decl f8 :: S4 +#30 := f8 +decl f7 :: S2 +#29 := f7 +#31 := (f4 f7 f5 f8) +#33 := (f4 #31 f6 f9) +#34 := (f3 #33 f5) +#79 := (= f9 #34) +#263 := (f3 #33 f6) +#571 := (= #263 #34) +#585 := (= #34 #263) +#28 := (= f5 f6) +#86 := (not #28) +#87 := (or #86 #79) +#92 := (not #87) +#35 := (= #34 f9) +#36 := (implies #28 #35) +#37 := (not #36) +#93 := (iff #37 #92) +#90 := (iff #36 #87) +#83 := (implies #28 #79) +#88 := (iff #83 #87) +#89 := [rewrite]: #88 +#84 := (iff #36 #83) +#81 := (iff #35 #79) +#82 := [rewrite]: #81 +#85 := [monotonicity #82]: #84 +#91 := [trans #85 #89]: #90 +#94 := [monotonicity #91]: #93 +#78 := [asserted]: #37 +#97 := [mp #78 #94]: #92 +#95 := [not-or-elim #97]: #28 +#233 := [monotonicity #95]: #585 +#572 := [symm #233]: #571 +#264 := (= f9 #263) +#12 := (:var 0 S3) +#10 := (:var 1 S4) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#594 := (pattern #13) +#15 := (f3 #8 #12) +#117 := (= #13 #15) +#116 := (= #10 #13) +#58 := (= #9 #12) +#104 := (ite #58 #116 #117) +#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104) +#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104) +#598 := (iff #109 #595) +#596 := (iff #104 #104) +#597 := [refl]: #596 +#599 := [quant-intro #597]: #598 +#61 := (ite #58 #10 #15) +#64 := (= #13 #61) +#67 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #64) +#106 := (iff #67 #109) +#105 := (iff #64 #104) +#108 := [rewrite]: #105 +#107 := [quant-intro #108]: #106 +#112 := (~ #67 #67) +#110 := (~ #64 #64) +#111 := [refl]: #110 +#113 := [nnf-pos #111]: #112 +#14 := (= #12 #9) +#16 := (ite #14 #10 #15) +#17 := (= #13 #16) +#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17) +#68 := (iff #18 #67) +#65 := (iff #17 #64) +#62 := (= #16 #61) +#59 := (iff #14 #58) +#60 := [rewrite]: #59 +#63 := [monotonicity #60]: #62 +#66 := [monotonicity #63]: #65 +#69 := [quant-intro #66]: #68 +#57 := [asserted]: #18 +#72 := [mp #57 #69]: #67 +#100 := [mp~ #72 #113]: #67 +#118 := [mp #100 #107]: #109 +#600 := [mp #118 #599]: #595 +#582 := (not #595) +#254 := (or #582 #264) +#176 := (f3 #31 f6) +#177 := (= #263 #176) +#178 := (= f6 f6) +#265 := (ite #178 #264 #177) +#255 := (or #582 #265) +#590 := (iff #255 #254) +#592 := (iff #254 #254) +#587 := [rewrite]: #592 +#243 := (iff #265 #264) +#268 := (= #176 #263) +#1 := true +#266 := (ite true #264 #268) +#586 := (iff #266 #264) +#588 := [rewrite]: #586 +#270 := (iff #265 #266) +#196 := (iff #177 #268) +#269 := [rewrite]: #196 +#256 := (iff #178 true) +#267 := [rewrite]: #256 +#249 := [monotonicity #267 #269]: #270 +#375 := [trans #249 #588]: #243 +#591 := [monotonicity #375]: #590 +#593 := [trans #591 #587]: #590 +#589 := [quant-inst #31 #27 #32 #27]: #255 +#583 := [mp #589 #593]: #254 +#242 := [unit-resolution #583 #600]: #264 +#573 := [trans #242 #572]: #79 +#96 := (not #79) +#98 := [not-or-elim #97]: #96 +[unit-resolution #98 #573]: false +unsat +6e80c9c78d8fedc6d33345078567183b7c70457d 190 0 +#2 := false +decl f3 :: (-> S2 S3 S4) decl f7 :: S3 #28 := f7 +decl f8 :: S2 +#30 := f8 +#36 := (f3 f8 f7) +decl f4 :: (-> S2 S3 S4 S2) decl f10 :: S4 -#32 := f10 +#33 := f10 decl f6 :: S3 #27 := f6 -decl f5 :: S5 -#8 := f5 -#33 := (f4 f5 f9 f6 f10) -#35 := (f4 f5 #33 f7 f11) -#36 := (f3 #35 f8) -#38 := (= #36 #37) -#587 := (f3 #33 f6) -#571 := (f4 f5 f9 f6 #587) -#207 := (f3 #571 f8) -#212 := (= #207 #37) -#563 := (= #37 #207) -#573 := (= #207 #587) -#172 := (= f6 f8) -#286 := (ite #172 #573 #563) -#13 := (:var 0 S3) -#11 := (:var 1 S4) -#10 := (:var 2 S3) -#9 := (:var 3 S2) -#12 := (f4 f5 #9 #10 #11) -#14 := (f3 #12 #13) -#589 := (pattern #14) -#16 := (f3 #9 #13) -#112 := (= #14 #16) -#111 := (= #11 #14) -#61 := (= #10 #13) -#99 := (ite #61 #111 #112) -#590 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #589) #99) -#104 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #99) -#593 := (iff #104 #590) -#591 := (iff #99 #99) -#592 := [refl]: #591 -#594 := [quant-intro #592]: #593 -#64 := (ite #61 #11 #16) -#67 := (= #14 #64) -#70 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #67) -#101 := (iff #70 #104) -#100 := (iff #67 #99) -#103 := [rewrite]: #100 -#102 := [quant-intro #103]: #101 -#107 := (~ #70 #70) -#105 := (~ #67 #67) -#106 := [refl]: #105 -#108 := [nnf-pos #106]: #107 -#15 := (= #13 #10) -#17 := (ite #15 #11 #16) -#18 := (= #14 #17) -#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #18) -#71 := (iff #19 #70) -#68 := (iff #18 #67) -#65 := (= #17 #64) -#62 := (iff #15 #61) -#63 := [rewrite]: #62 -#66 := [monotonicity #63]: #65 -#69 := [monotonicity #66]: #68 -#72 := [quant-intro #69]: #71 -#60 := [asserted]: #19 -#75 := [mp #60 #72]: #70 -#95 := [mp~ #75 #108]: #70 -#113 := [mp #95 #102]: #104 -#595 := [mp #113 #594]: #590 -#588 := (not #590) -#288 := (or #588 #286) -#213 := (= #587 #207) -#575 := (ite #172 #213 #212) -#179 := (or #588 #575) -#559 := (iff #179 #288) -#282 := (iff #288 #288) -#556 := [rewrite]: #282 -#287 := (iff #575 #286) -#269 := (iff #212 #563) -#285 := [rewrite]: #269 -#576 := (iff #213 #573) -#562 := [rewrite]: #576 -#273 := [monotonicity #562 #285]: #287 -#281 := [monotonicity #273]: #559 -#560 := [trans #281 #556]: #559 -#558 := [quant-inst #31 #27 #587 #29]: #179 -#557 := [mp #558 #560]: #288 -#517 := [unit-resolution #557 #595]: #286 -#561 := (not #286) -#508 := (or #561 #563) -#259 := (not #172) -#173 := (= f7 f8) -#260 := (not #173) -#171 := (= f6 f7) +decl f9 :: S4 +#31 := f9 +decl f5 :: S3 +#26 := f5 +#32 := (f4 f8 f5 f9) +#34 := (f4 #32 f6 f10) +#35 := (f3 #34 f7) +#37 := (= #35 #36) +#586 := (f3 #32 f5) +#570 := (f4 f8 f5 #586) +#206 := (f3 #570 f7) +#211 := (= #206 #36) +#562 := (= #36 #206) +#572 := (= #206 #586) +#171 := (= f5 f7) +#285 := (ite #171 #572 #562) +#12 := (:var 0 S3) +#10 := (:var 1 S4) +#9 := (:var 2 S3) +#8 := (:var 3 S2) +#11 := (f4 #8 #9 #10) +#13 := (f3 #11 #12) +#588 := (pattern #13) +#15 := (f3 #8 #12) +#111 := (= #13 #15) +#110 := (= #10 #13) +#60 := (= #9 #12) +#98 := (ite #60 #110 #111) +#589 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #588) #98) +#103 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #98) +#592 := (iff #103 #589) +#590 := (iff #98 #98) +#591 := [refl]: #590 +#593 := [quant-intro #591]: #592 +#63 := (ite #60 #10 #15) +#66 := (= #13 #63) +#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66) +#100 := (iff #69 #103) +#99 := (iff #66 #98) +#102 := [rewrite]: #99 +#101 := [quant-intro #102]: #100 +#106 := (~ #69 #69) +#104 := (~ #66 #66) +#105 := [refl]: #104 +#107 := [nnf-pos #105]: #106 +#14 := (= #12 #9) +#16 := (ite #14 #10 #15) +#17 := (= #13 #16) +#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17) +#70 := (iff #18 #69) +#67 := (iff #17 #66) +#64 := (= #16 #63) +#61 := (iff #14 #60) +#62 := [rewrite]: #61 +#65 := [monotonicity #62]: #64 +#68 := [monotonicity #65]: #67 +#71 := [quant-intro #68]: #70 +#59 := [asserted]: #18 +#74 := [mp #59 #71]: #69 +#94 := [mp~ #74 #107]: #69 +#112 := [mp #94 #101]: #103 +#594 := [mp #112 #593]: #589 +#587 := (not #589) +#287 := (or #587 #285) +#212 := (= #586 #206) +#574 := (ite #171 #212 #211) +#178 := (or #587 #574) +#558 := (iff #178 #287) +#281 := (iff #287 #287) +#555 := [rewrite]: #281 +#286 := (iff #574 #285) +#268 := (iff #211 #562) +#284 := [rewrite]: #268 +#575 := (iff #212 #572) +#561 := [rewrite]: #575 +#272 := [monotonicity #561 #284]: #286 +#280 := [monotonicity #272]: #558 +#559 := [trans #280 #555]: #558 +#557 := [quant-inst #30 #26 #586 #28]: #178 +#556 := [mp #557 #559]: #287 +#516 := [unit-resolution #556 #594]: #285 +#560 := (not #285) +#507 := (or #560 #562) #258 := (not #171) -#251 := (and #258 #259 #260) -#30 := (distinct f6 f7 f8) -#82 := (not #30) -#84 := (or #82 #38) -#87 := (not #84) -#39 := (implies #30 #38) -#40 := (not #39) -#88 := (iff #40 #87) -#85 := (iff #39 #84) -#86 := [rewrite]: #85 -#89 := [monotonicity #86]: #88 -#81 := [asserted]: #40 -#92 := [mp #81 #89]: #87 -#90 := [not-or-elim #92]: #30 -#238 := (or #82 #251) -#370 := [def-axiom]: #238 -#506 := [unit-resolution #370 #90]: #251 -#262 := (not #251) -#264 := (or #262 #259) -#261 := [def-axiom]: #264 -#507 := [unit-resolution #261 #506]: #259 -#272 := (or #561 #172 #563) -#274 := [def-axiom]: #272 -#509 := [unit-resolution #274 #507]: #508 -#503 := [unit-resolution #509 #517]: #563 -#487 := [symm #503]: #212 -#488 := (= #36 #207) -#250 := (f3 #33 f8) -#496 := (= #250 #207) -#499 := (= #207 #250) -#516 := (= #571 #33) -#514 := (= #587 f10) -#582 := (= f10 #587) -#22 := (:var 0 S4) -#21 := (:var 1 S3) -#20 := (:var 2 S2) -#23 := (f4 f5 #20 #21 #22) -#596 := (pattern #23) -#24 := (f3 #23 #21) -#74 := (= #22 #24) -#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #596) #74) -#78 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #74) -#600 := (iff #78 #597) -#598 := (iff #74 #74) -#599 := [refl]: #598 -#601 := [quant-intro #599]: #600 -#97 := (~ #78 #78) -#96 := (~ #74 #74) -#109 := [refl]: #96 -#98 := [nnf-pos #109]: #97 -#25 := (= #24 #22) -#26 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #25) -#79 := (iff #26 #78) -#76 := (iff #25 #74) -#77 := [rewrite]: #76 -#80 := [quant-intro #77]: #79 -#73 := [asserted]: #26 -#83 := [mp #73 #80]: #78 -#110 := [mp~ #83 #98]: #78 -#602 := [mp #110 #601]: #597 -#569 := (not #597) -#570 := (or #569 #582) -#565 := [quant-inst #31 #27 #32]: #570 -#504 := [unit-resolution #565 #602]: #582 -#515 := [symm #504]: #514 -#512 := [monotonicity #515]: #516 -#500 := [monotonicity #512]: #499 -#501 := [symm #500]: #496 -#584 := (= #36 #250) -#585 := (= f11 #36) -#586 := (ite #173 #585 #584) -#578 := (or #588 #586) -#236 := [quant-inst #33 #28 #34 #29]: #578 -#510 := [unit-resolution #236 #595]: #586 -#241 := (not #586) -#495 := (or #241 #584) -#265 := (or #262 #260) -#244 := [def-axiom]: #265 -#494 := [unit-resolution #244 #506]: #260 -#580 := (or #241 #173 #584) -#221 := [def-axiom]: #580 -#497 := [unit-resolution #221 #494]: #495 -#498 := [unit-resolution #497 #510]: #584 -#490 := [trans #498 #501]: #488 -#491 := [trans #490 #487]: #38 -#91 := (not #38) -#93 := [not-or-elim #92]: #91 -[unit-resolution #93 #491]: false +#172 := (= f6 f7) +#259 := (not #172) +#170 := (= f5 f6) +#257 := (not #170) +#250 := (and #257 #258 #259) +#29 := (distinct f5 f6 f7) +#81 := (not #29) +#83 := (or #81 #37) +#86 := (not #83) +#38 := (implies #29 #37) +#39 := (not #38) +#87 := (iff #39 #86) +#84 := (iff #38 #83) +#85 := [rewrite]: #84 +#88 := [monotonicity #85]: #87 +#80 := [asserted]: #39 +#91 := [mp #80 #88]: #86 +#89 := [not-or-elim #91]: #29 +#237 := (or #81 #250) +#369 := [def-axiom]: #237 +#505 := [unit-resolution #369 #89]: #250 +#261 := (not #250) +#263 := (or #261 #258) +#260 := [def-axiom]: #263 +#506 := [unit-resolution #260 #505]: #258 +#271 := (or #560 #171 #562) +#273 := [def-axiom]: #271 +#508 := [unit-resolution #273 #506]: #507 +#502 := [unit-resolution #508 #516]: #562 +#486 := [symm #502]: #211 +#487 := (= #35 #206) +#249 := (f3 #32 f7) +#495 := (= #249 #206) +#498 := (= #206 #249) +#515 := (= #570 #32) +#513 := (= #586 f9) +#581 := (= f9 #586) +#21 := (:var 0 S4) +#20 := (:var 1 S3) +#19 := (:var 2 S2) +#22 := (f4 #19 #20 #21) +#595 := (pattern #22) +#23 := (f3 #22 #20) +#73 := (= #21 #23) +#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #595) #73) +#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #73) +#596 := (iff #77 #597) +#599 := (iff #597 #597) +#600 := [rewrite]: #599 +#598 := [rewrite]: #596 +#601 := [trans #598 #600]: #596 +#96 := (~ #77 #77) +#95 := (~ #73 #73) +#108 := [refl]: #95 +#97 := [nnf-pos #108]: #96 +#24 := (= #23 #21) +#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24) +#78 := (iff #25 #77) +#75 := (iff #24 #73) +#76 := [rewrite]: #75 +#79 := [quant-intro #76]: #78 +#72 := [asserted]: #25 +#82 := [mp #72 #79]: #77 +#109 := [mp~ #82 #97]: #77 +#602 := [mp #109 #601]: #597 +#568 := (not #597) +#569 := (or #568 #581) +#564 := [quant-inst #30 #26 #31]: #569 +#503 := [unit-resolution #564 #602]: #581 +#514 := [symm #503]: #513 +#511 := [monotonicity #514]: #515 +#499 := [monotonicity #511]: #498 +#500 := [symm #499]: #495 +#583 := (= #35 #249) +#584 := (= f10 #35) +#585 := (ite #172 #584 #583) +#577 := (or #587 #585) +#235 := [quant-inst #32 #27 #33 #28]: #577 +#509 := [unit-resolution #235 #594]: #585 +#240 := (not #585) +#494 := (or #240 #583) +#264 := (or #261 #259) +#243 := [def-axiom]: #264 +#493 := [unit-resolution #243 #505]: #259 +#579 := (or #240 #172 #583) +#220 := [def-axiom]: #579 +#496 := [unit-resolution #220 #493]: #494 +#497 := [unit-resolution #496 #509]: #583 +#489 := [trans #497 #500]: #487 +#490 := [trans #489 #486]: #37 +#90 := (not #37) +#92 := [not-or-elim #91]: #90 +[unit-resolution #92 #490]: false unsat a8479ddc219a8a1f70834d2e3bfa9595c2e54d48 31 0 #2 := false @@ -52500,267 +52494,265 @@ #637 := [unit-resolution #308 #293]: #636 [unit-resolution #637 #635 #634]: false unsat -5515b772fc370cead501436e9e655f396708da26 261 0 +8df9cadd28b79979ba76c3dfed467a1319648283 259 0 #2 := false decl f5 :: (-> S4 S5 S1) -decl f13 :: S5 -#48 := f13 -decl f11 :: S4 -#44 := f11 -#628 := (f5 f11 f13) -decl f1 :: S1 -#4 := f1 -#341 := (= f1 #628) -decl f12 :: S4 -#45 := f12 -#339 := (f5 f12 f13) -#336 := (= f1 #339) -#626 := (or #336 #341) -decl f6 :: (-> S6 S4 S4 S4) -decl f7 :: S6 -#20 := f7 -#46 := (f6 f7 f11 f12) -#313 := (f5 #46 f13) -#445 := (= f1 #313) -#620 := (iff #445 #626) -#586 := (not #620) -#598 := (not #626) -#610 := (not #341) +decl f12 :: S5 +#47 := f12 decl f10 :: S4 #43 := f10 -#641 := (f5 f10 f13) -#642 := (= f1 #641) -#488 := (or #341 #642) -#613 := (not #488) -#51 := (f6 f7 f10 f11) -#340 := (f5 #51 f13) -#319 := (= f1 #340) -#596 := (iff #319 #488) -#588 := (not #596) -#581 := [hypothesis]: #588 -#24 := (:var 0 S5) -#22 := (:var 1 S4) -#21 := (:var 2 S4) -#23 := (f6 f7 #21 #22) -#25 := (f5 #23 #24) -#671 := (pattern #25) -#29 := (f5 #22 #24) -#103 := (= f1 #29) -#27 := (f5 #21 #24) -#100 := (= f1 #27) -#106 := (or #100 #103) -#96 := (= f1 #25) -#109 := (iff #96 #106) -#672 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #671) #109) -#112 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #109) -#675 := (iff #112 #672) -#673 := (iff #109 #109) -#674 := [refl]: #673 -#676 := [quant-intro #674]: #675 -#158 := (~ #112 #112) -#157 := (~ #109 #109) -#172 := [refl]: #157 -#159 := [nnf-pos #172]: #158 -#30 := (= #29 f1) -#28 := (= #27 f1) -#31 := (or #28 #30) -#26 := (= #25 f1) -#32 := (iff #26 #31) -#33 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #32) -#113 := (iff #33 #112) -#110 := (iff #32 #109) -#107 := (iff #31 #106) -#104 := (iff #30 #103) -#105 := [rewrite]: #104 -#101 := (iff #28 #100) -#102 := [rewrite]: #101 -#108 := [monotonicity #102 #105]: #107 -#98 := (iff #26 #96) -#99 := [rewrite]: #98 -#111 := [monotonicity #99 #108]: #110 -#114 := [quant-intro #111]: #113 -#95 := [asserted]: #33 -#117 := [mp #95 #114]: #112 -#173 := [mp~ #117 #159]: #112 -#677 := [mp #173 #676]: #672 -#652 := (not #672) -#594 := (or #652 #596) -#605 := (or #642 #341) -#487 := (iff #319 #605) -#597 := (or #652 #487) -#497 := (iff #597 #594) -#500 := (iff #594 #594) -#493 := [rewrite]: #500 -#498 := (iff #487 #596) -#489 := (iff #605 #488) -#448 := [rewrite]: #489 -#593 := [monotonicity #448]: #498 -#499 := [monotonicity #593]: #497 -#501 := [trans #499 #493]: #497 -#482 := [quant-inst #43 #44 #48]: #597 -#502 := [mp #482 #501]: #594 -#582 := [unit-resolution #502 #677 #581]: false -#583 := [lemma #582]: #596 -#659 := (not #319) -#656 := (or #319 #336) -#653 := (not #656) -#52 := (f6 f7 #51 f12) -#53 := (f5 #52 f13) -#139 := (= f1 #53) -#335 := (not #139) -#47 := (f6 f7 f10 #46) -#49 := (f5 #47 f13) -#135 := (= f1 #49) -#148 := (not #135) -#584 := [hypothesis]: #148 -#334 := (or #139 #135) -#149 := (iff #139 #148) -#54 := (= #53 f1) -#50 := (= #49 f1) -#55 := (iff #50 #54) -#56 := (not #55) -#152 := (iff #56 #149) -#142 := (iff #135 #139) -#145 := (not #142) -#150 := (iff #145 #149) -#151 := [rewrite]: #150 -#146 := (iff #56 #145) -#143 := (iff #55 #142) -#140 := (iff #54 #139) -#141 := [rewrite]: #140 -#137 := (iff #50 #135) -#138 := [rewrite]: #137 -#144 := [monotonicity #138 #141]: #143 -#147 := [monotonicity #144]: #146 -#153 := [trans #147 #151]: #152 -#134 := [asserted]: #56 -#156 := [mp #134 #153]: #149 -#246 := (not #149) -#333 := (or #139 #135 #246) -#247 := [def-axiom]: #333 -#248 := [unit-resolution #247 #156]: #334 -#578 := [unit-resolution #248 #584]: #139 -#569 := (or #335 #656) -#658 := (iff #139 #656) -#324 := (or #652 #658) -#325 := [quant-inst #51 #45 #48]: #324 -#585 := [unit-resolution #325 #677]: #658 -#654 := (not #658) -#296 := (or #654 #335 #656) -#639 := [def-axiom]: #296 -#570 := [unit-resolution #639 #585]: #569 -#572 := [unit-resolution #570 #578]: #656 -#662 := (not #336) -#602 := (or #652 #620) -#625 := (or #341 #336) -#629 := (iff #445 #625) -#622 := (or #652 #629) -#617 := (iff #622 #602) -#624 := (iff #602 #602) -#465 := [rewrite]: #624 -#621 := (iff #629 #620) -#630 := (iff #625 #626) -#619 := [rewrite]: #630 -#616 := [monotonicity #619]: #621 -#618 := [monotonicity #616]: #617 -#466 := [trans #618 #465]: #617 -#623 := [quant-inst #44 #45 #48]: #622 -#467 := [mp #623 #466]: #602 -#573 := [unit-resolution #467 #677]: #620 -#563 := (or #586 #598) -#361 := (not #445) -#645 := (or #445 #642) -#634 := (not #645) -#575 := (or #135 #634) -#282 := (iff #135 #645) -#287 := (or #652 #282) -#643 := (or #642 #445) -#644 := (iff #135 #643) -#288 := (or #652 #644) -#648 := (iff #288 #287) -#637 := (iff #287 #287) -#638 := [rewrite]: #637 -#647 := (iff #644 #282) -#640 := (iff #643 #645) -#646 := [rewrite]: #640 -#649 := [monotonicity #646]: #647 -#651 := [monotonicity #649]: #648 -#344 := [trans #651 #638]: #648 -#650 := [quant-inst #43 #46 #48]: #288 -#360 := [mp #650 #344]: #287 -#574 := [unit-resolution #360 #677]: #282 -#631 := (not #282) -#635 := (or #631 #135 #634) -#632 := [def-axiom]: #635 -#571 := [unit-resolution #632 #574]: #575 -#576 := [unit-resolution #571 #584]: #634 -#362 := (or #645 #361) -#348 := [def-axiom]: #362 -#562 := [unit-resolution #348 #576]: #361 -#580 := (or #586 #445 #598) -#577 := [def-axiom]: #580 -#565 := [unit-resolution #577 #562]: #563 -#566 := [unit-resolution #565 #573]: #598 -#609 := (or #626 #662) -#503 := [def-axiom]: #609 -#567 := [unit-resolution #503 #566]: #662 -#311 := (or #653 #319 #336) -#316 := [def-axiom]: #311 -#564 := [unit-resolution #316 #567 #572]: #319 -#363 := (not #642) -#254 := (or #645 #363) -#633 := [def-axiom]: #254 -#568 := [unit-resolution #633 #576]: #363 -#504 := (or #626 #610) -#505 := [def-axiom]: #504 -#548 := [unit-resolution #505 #566]: #610 -#614 := (or #613 #341 #642) -#608 := [def-axiom]: #614 -#549 := [unit-resolution #608 #548 #568]: #613 -#446 := (or #588 #659 #488) -#447 := [def-axiom]: #446 -#551 := [unit-resolution #447 #549 #564 #583]: false -#552 := [lemma #551]: #135 -#338 := (or #335 #148) -#326 := (or #335 #148 #246) -#337 := [def-axiom]: #326 -#266 := [unit-resolution #337 #156]: #338 -#553 := [unit-resolution #266 #552]: #335 -#554 := (or #139 #653) -#312 := (or #654 #139 #653) -#655 := [def-axiom]: #312 -#555 := [unit-resolution #655 #585]: #554 -#556 := [unit-resolution #555 #553]: #653 -#660 := (or #656 #659) -#661 := [def-axiom]: #660 -#557 := [unit-resolution #661 #556]: #659 -#615 := (or #588 #319 #613) -#444 := [def-axiom]: #615 -#558 := [unit-resolution #444 #557 #583]: #613 -#611 := (or #488 #610) -#612 := [def-axiom]: #611 -#559 := [unit-resolution #612 #558]: #610 -#657 := (or #656 #662) -#663 := [def-axiom]: #657 -#560 := [unit-resolution #663 #556]: #662 -#595 := (or #598 #336 #341) -#599 := [def-axiom]: #595 -#550 := [unit-resolution #599 #560 #559]: #598 -#561 := (or #148 #645) -#636 := (or #631 #148 #645) -#345 := [def-axiom]: #636 -#539 := [unit-resolution #345 #574]: #561 -#540 := [unit-resolution #539 #552]: #645 -#606 := (or #488 #363) -#607 := [def-axiom]: #606 -#542 := [unit-resolution #607 #558]: #363 -#356 := (or #634 #445 #642) -#357 := [def-axiom]: #356 -#543 := [unit-resolution #357 #542 #540]: #445 -#579 := (or #586 #361 #626) -#589 := [def-axiom]: #579 -#544 := [unit-resolution #589 #543 #550]: #586 -[unit-resolution #467 #677 #544]: false +#627 := (f5 f10 f12) +decl f1 :: S1 +#4 := f1 +#340 := (= f1 #627) +decl f11 :: S4 +#44 := f11 +#338 := (f5 f11 f12) +#335 := (= f1 #338) +#625 := (or #335 #340) +decl f6 :: (-> S4 S4 S4) +#45 := (f6 f10 f11) +#312 := (f5 #45 f12) +#444 := (= f1 #312) +#619 := (iff #444 #625) +#585 := (not #619) +#597 := (not #625) +#609 := (not #340) +decl f9 :: S4 +#42 := f9 +#640 := (f5 f9 f12) +#641 := (= f1 #640) +#487 := (or #340 #641) +#612 := (not #487) +#50 := (f6 f9 f10) +#339 := (f5 #50 f12) +#318 := (= f1 #339) +#595 := (iff #318 #487) +#587 := (not #595) +#580 := [hypothesis]: #587 +#23 := (:var 0 S5) +#21 := (:var 1 S4) +#20 := (:var 2 S4) +#22 := (f6 #20 #21) +#24 := (f5 #22 #23) +#670 := (pattern #24) +#28 := (f5 #21 #23) +#102 := (= f1 #28) +#26 := (f5 #20 #23) +#99 := (= f1 #26) +#105 := (or #99 #102) +#95 := (= f1 #24) +#108 := (iff #95 #105) +#671 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #670) #108) +#111 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #108) +#674 := (iff #111 #671) +#672 := (iff #108 #108) +#673 := [refl]: #672 +#675 := [quant-intro #673]: #674 +#157 := (~ #111 #111) +#156 := (~ #108 #108) +#171 := [refl]: #156 +#158 := [nnf-pos #171]: #157 +#29 := (= #28 f1) +#27 := (= #26 f1) +#30 := (or #27 #29) +#25 := (= #24 f1) +#31 := (iff #25 #30) +#32 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #31) +#112 := (iff #32 #111) +#109 := (iff #31 #108) +#106 := (iff #30 #105) +#103 := (iff #29 #102) +#104 := [rewrite]: #103 +#100 := (iff #27 #99) +#101 := [rewrite]: #100 +#107 := [monotonicity #101 #104]: #106 +#97 := (iff #25 #95) +#98 := [rewrite]: #97 +#110 := [monotonicity #98 #107]: #109 +#113 := [quant-intro #110]: #112 +#94 := [asserted]: #32 +#116 := [mp #94 #113]: #111 +#172 := [mp~ #116 #158]: #111 +#676 := [mp #172 #675]: #671 +#651 := (not #671) +#593 := (or #651 #595) +#604 := (or #641 #340) +#486 := (iff #318 #604) +#596 := (or #651 #486) +#496 := (iff #596 #593) +#499 := (iff #593 #593) +#492 := [rewrite]: #499 +#497 := (iff #486 #595) +#488 := (iff #604 #487) +#447 := [rewrite]: #488 +#592 := [monotonicity #447]: #497 +#498 := [monotonicity #592]: #496 +#500 := [trans #498 #492]: #496 +#481 := [quant-inst #42 #43 #47]: #596 +#501 := [mp #481 #500]: #593 +#581 := [unit-resolution #501 #676 #580]: false +#582 := [lemma #581]: #595 +#658 := (not #318) +#655 := (or #318 #335) +#652 := (not #655) +#51 := (f6 #50 f11) +#52 := (f5 #51 f12) +#138 := (= f1 #52) +#334 := (not #138) +#46 := (f6 f9 #45) +#48 := (f5 #46 f12) +#134 := (= f1 #48) +#147 := (not #134) +#583 := [hypothesis]: #147 +#333 := (or #138 #134) +#148 := (iff #138 #147) +#53 := (= #52 f1) +#49 := (= #48 f1) +#54 := (iff #49 #53) +#55 := (not #54) +#151 := (iff #55 #148) +#141 := (iff #134 #138) +#144 := (not #141) +#149 := (iff #144 #148) +#150 := [rewrite]: #149 +#145 := (iff #55 #144) +#142 := (iff #54 #141) +#139 := (iff #53 #138) +#140 := [rewrite]: #139 +#136 := (iff #49 #134) +#137 := [rewrite]: #136 +#143 := [monotonicity #137 #140]: #142 +#146 := [monotonicity #143]: #145 +#152 := [trans #146 #150]: #151 +#133 := [asserted]: #55 +#155 := [mp #133 #152]: #148 +#245 := (not #148) +#332 := (or #138 #134 #245) +#246 := [def-axiom]: #332 +#247 := [unit-resolution #246 #155]: #333 +#577 := [unit-resolution #247 #583]: #138 +#568 := (or #334 #655) +#657 := (iff #138 #655) +#323 := (or #651 #657) +#324 := [quant-inst #50 #44 #47]: #323 +#584 := [unit-resolution #324 #676]: #657 +#653 := (not #657) +#295 := (or #653 #334 #655) +#638 := [def-axiom]: #295 +#569 := [unit-resolution #638 #584]: #568 +#571 := [unit-resolution #569 #577]: #655 +#661 := (not #335) +#601 := (or #651 #619) +#624 := (or #340 #335) +#628 := (iff #444 #624) +#621 := (or #651 #628) +#616 := (iff #621 #601) +#623 := (iff #601 #601) +#464 := [rewrite]: #623 +#620 := (iff #628 #619) +#629 := (iff #624 #625) +#618 := [rewrite]: #629 +#615 := [monotonicity #618]: #620 +#617 := [monotonicity #615]: #616 +#465 := [trans #617 #464]: #616 +#622 := [quant-inst #43 #44 #47]: #621 +#466 := [mp #622 #465]: #601 +#572 := [unit-resolution #466 #676]: #619 +#562 := (or #585 #597) +#360 := (not #444) +#644 := (or #444 #641) +#633 := (not #644) +#574 := (or #134 #633) +#281 := (iff #134 #644) +#286 := (or #651 #281) +#642 := (or #641 #444) +#643 := (iff #134 #642) +#287 := (or #651 #643) +#647 := (iff #287 #286) +#636 := (iff #286 #286) +#637 := [rewrite]: #636 +#646 := (iff #643 #281) +#639 := (iff #642 #644) +#645 := [rewrite]: #639 +#648 := [monotonicity #645]: #646 +#650 := [monotonicity #648]: #647 +#343 := [trans #650 #637]: #647 +#649 := [quant-inst #42 #45 #47]: #287 +#359 := [mp #649 #343]: #286 +#573 := [unit-resolution #359 #676]: #281 +#630 := (not #281) +#634 := (or #630 #134 #633) +#631 := [def-axiom]: #634 +#570 := [unit-resolution #631 #573]: #574 +#575 := [unit-resolution #570 #583]: #633 +#361 := (or #644 #360) +#347 := [def-axiom]: #361 +#561 := [unit-resolution #347 #575]: #360 +#579 := (or #585 #444 #597) +#576 := [def-axiom]: #579 +#564 := [unit-resolution #576 #561]: #562 +#565 := [unit-resolution #564 #572]: #597 +#608 := (or #625 #661) +#502 := [def-axiom]: #608 +#566 := [unit-resolution #502 #565]: #661 +#310 := (or #652 #318 #335) +#315 := [def-axiom]: #310 +#563 := [unit-resolution #315 #566 #571]: #318 +#362 := (not #641) +#253 := (or #644 #362) +#632 := [def-axiom]: #253 +#567 := [unit-resolution #632 #575]: #362 +#503 := (or #625 #609) +#504 := [def-axiom]: #503 +#547 := [unit-resolution #504 #565]: #609 +#613 := (or #612 #340 #641) +#607 := [def-axiom]: #613 +#548 := [unit-resolution #607 #547 #567]: #612 +#445 := (or #587 #658 #487) +#446 := [def-axiom]: #445 +#550 := [unit-resolution #446 #548 #563 #582]: false +#551 := [lemma #550]: #134 +#337 := (or #334 #147) +#325 := (or #334 #147 #245) +#336 := [def-axiom]: #325 +#265 := [unit-resolution #336 #155]: #337 +#552 := [unit-resolution #265 #551]: #334 +#553 := (or #138 #652) +#311 := (or #653 #138 #652) +#654 := [def-axiom]: #311 +#554 := [unit-resolution #654 #584]: #553 +#555 := [unit-resolution #554 #552]: #652 +#659 := (or #655 #658) +#660 := [def-axiom]: #659 +#556 := [unit-resolution #660 #555]: #658 +#614 := (or #587 #318 #612) +#443 := [def-axiom]: #614 +#557 := [unit-resolution #443 #556 #582]: #612 +#610 := (or #487 #609) +#611 := [def-axiom]: #610 +#558 := [unit-resolution #611 #557]: #609 +#656 := (or #655 #661) +#662 := [def-axiom]: #656 +#559 := [unit-resolution #662 #555]: #661 +#594 := (or #597 #335 #340) +#598 := [def-axiom]: #594 +#549 := [unit-resolution #598 #559 #558]: #597 +#560 := (or #147 #644) +#635 := (or #630 #147 #644) +#344 := [def-axiom]: #635 +#538 := [unit-resolution #344 #573]: #560 +#539 := [unit-resolution #538 #551]: #644 +#605 := (or #487 #362) +#606 := [def-axiom]: #605 +#541 := [unit-resolution #606 #557]: #362 +#355 := (or #633 #444 #641) +#356 := [def-axiom]: #355 +#542 := [unit-resolution #356 #541 #539]: #444 +#578 := (or #585 #360 #625) +#588 := [def-axiom]: #578 +#543 := [unit-resolution #588 #542 #549]: #585 +[unit-resolution #466 #676 #543]: false unsat e18331b7b676705a2856a4af405fce965b0fd82f 153 0 #2 := false @@ -53532,288 +53524,286 @@ #642 := [unit-resolution #294 #632]: #280 [unit-resolution #642 #279 #641]: false unsat -875452e11949675636517f32afdb052ad9456477 282 0 +2197c1dae16f488eb4bfcbae6c35e5ab268a4235 280 0 #2 := false decl f3 :: (-> S2 S3 S1) -decl f13 :: S3 -#48 := f13 -decl f4 :: (-> S4 S2 S2 S2) -decl f11 :: S2 -#44 := f11 +decl f12 :: S3 +#47 := f12 +decl f4 :: (-> S2 S2 S2) decl f10 :: S2 #43 := f10 -decl f5 :: S4 -#8 := f5 -#51 := (f4 f5 f10 f11) -#319 := (f3 #51 f13) -decl f1 :: S1 -#4 := f1 -#656 := (= f1 #319) -#254 := (f3 f11 f13) -#633 := (= f1 #254) -#630 := (not #633) -#344 := (f3 f10 f13) -#360 := (= f1 #344) -#361 := (not #360) -#619 := (or #361 #630) -#620 := (not #619) -#616 := (iff #620 #656) -#587 := (not #616) -decl f12 :: S2 -#45 := f12 -#339 := (f3 f12 f13) -#336 := (= f1 #339) -#340 := (not #336) -#489 := (or #340 #630) -#498 := (not #489) -#46 := (f4 f5 f11 f12) -#651 := (f3 #46 f13) -#637 := (= f1 #651) -#499 := (iff #498 #637) -#592 := (not #499) -#572 := [hypothesis]: #592 -#12 := (:var 0 S3) -#10 := (:var 1 S2) -#9 := (:var 2 S2) -#11 := (f4 f5 #9 #10) -#13 := (f3 #11 #12) -#664 := (pattern #13) -#17 := (f3 #10 #12) -#83 := (= f1 #17) -#181 := (not #83) -#15 := (f3 #9 #12) -#80 := (= f1 #15) -#180 := (not #80) -#164 := (or #180 #181) -#165 := (not #164) -#77 := (= f1 #13) -#182 := (iff #77 #165) -#665 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #664) #182) -#185 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #182) -#668 := (iff #185 #665) -#666 := (iff #182 #182) -#667 := [refl]: #666 -#669 := [quant-intro #667]: #668 -#86 := (and #80 #83) -#89 := (iff #77 #86) -#92 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #89) -#186 := (iff #92 #185) -#183 := (iff #89 #182) -#166 := (iff #86 #165) -#167 := [rewrite]: #166 -#184 := [monotonicity #167]: #183 -#187 := [quant-intro #184]: #186 -#170 := (~ #92 #92) -#168 := (~ #89 #89) -#169 := [refl]: #168 -#171 := [nnf-pos #169]: #170 -#18 := (= #17 f1) -#16 := (= #15 f1) -#19 := (and #16 #18) -#14 := (= #13 f1) -#20 := (iff #14 #19) -#21 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #20) -#93 := (iff #21 #92) -#90 := (iff #20 #89) -#87 := (iff #19 #86) -#84 := (iff #18 #83) -#85 := [rewrite]: #84 -#81 := (iff #16 #80) -#82 := [rewrite]: #81 -#88 := [monotonicity #82 #85]: #87 -#78 := (iff #14 #77) -#79 := [rewrite]: #78 -#91 := [monotonicity #79 #88]: #90 -#94 := [quant-intro #91]: #93 -#76 := [asserted]: #21 -#97 := [mp #76 #94]: #92 -#155 := [mp~ #97 #171]: #92 -#188 := [mp #155 #187]: #185 -#670 := [mp #188 #669]: #665 -#311 := (not #665) -#503 := (or #311 #499) -#605 := (or #630 #340) -#487 := (not #605) -#488 := (iff #637 #487) -#504 := (or #311 #488) -#598 := (iff #504 #503) -#599 := (iff #503 #503) -#586 := [rewrite]: #599 -#501 := (iff #488 #499) -#597 := (iff #637 #498) -#500 := (iff #597 #499) -#493 := [rewrite]: #500 -#482 := (iff #488 #597) -#593 := (iff #487 #498) -#448 := (iff #605 #489) -#596 := [rewrite]: #448 -#594 := [monotonicity #596]: #593 -#497 := [monotonicity #594]: #482 -#502 := [trans #497 #493]: #501 -#595 := [monotonicity #502]: #598 -#588 := [trans #595 #586]: #598 -#505 := [quant-inst #44 #45 #48]: #504 -#580 := [mp #505 #588]: #503 -#573 := [unit-resolution #580 #670 #572]: false -#574 := [lemma #573]: #499 -#638 := (not #637) -#362 := (or #361 #638) -#348 := (not #362) -#47 := (f4 f5 f10 #46) -#49 := (f3 #47 f13) -#135 := (= f1 #49) -#148 := (not #135) -#575 := [hypothesis]: #148 -#576 := (or #135 #362) -#363 := (iff #135 #348) -#634 := (or #311 #363) -#356 := [quant-inst #43 #46 #48]: #634 -#571 := [unit-resolution #356 #670]: #363 -#346 := (not #363) -#347 := (or #346 #135 #362) -#349 := [def-axiom]: #347 -#562 := [unit-resolution #349 #571]: #576 -#563 := [unit-resolution #562 #575]: #362 -#602 := (or #311 #616) -#621 := (iff #656 #620) -#618 := (or #311 #621) -#623 := (iff #618 #602) -#466 := (iff #602 #602) -#467 := [rewrite]: #466 -#617 := (iff #621 #616) -#622 := [rewrite]: #617 -#465 := [monotonicity #622]: #623 -#609 := [trans #465 #467]: #623 -#624 := [quant-inst #43 #44 #48]: #618 -#610 := [mp #624 #609]: #602 -#565 := [unit-resolution #610 #670]: #616 -#551 := (or #587 #620) -#658 := (not #656) -#324 := (or #340 #658) -#660 := (not #324) -#52 := (f4 f5 #51 f12) -#53 := (f3 #52 f13) -#139 := (= f1 #53) -#334 := (or #139 #135) -#149 := (iff #139 #148) -#54 := (= #53 f1) -#50 := (= #49 f1) -#55 := (iff #50 #54) -#56 := (not #55) -#152 := (iff #56 #149) -#142 := (iff #135 #139) -#145 := (not #142) -#150 := (iff #145 #149) -#151 := [rewrite]: #150 -#146 := (iff #56 #145) -#143 := (iff #55 #142) -#140 := (iff #54 #139) -#141 := [rewrite]: #140 -#137 := (iff #50 #135) -#138 := [rewrite]: #137 -#144 := [monotonicity #138 #141]: #143 -#147 := [monotonicity #144]: #146 -#153 := [trans #147 #151]: #152 -#134 := [asserted]: #56 -#156 := [mp #134 #153]: #149 -#246 := (not #149) -#333 := (or #139 #135 #246) -#247 := [def-axiom]: #333 -#248 := [unit-resolution #247 #156]: #334 -#566 := [unit-resolution #248 #575]: #139 -#335 := (not #139) -#564 := (or #335 #660) -#657 := (iff #139 #660) -#316 := (or #311 #657) -#313 := (or #658 #340) -#445 := (not #313) -#652 := (iff #139 #445) -#654 := (or #311 #652) -#655 := (iff #654 #316) -#639 := (iff #316 #316) -#300 := [rewrite]: #639 -#663 := (iff #652 #657) -#661 := (iff #445 #660) -#325 := (iff #313 #324) -#659 := [rewrite]: #325 -#662 := [monotonicity #659]: #661 -#653 := [monotonicity #662]: #663 -#296 := [monotonicity #653]: #655 -#301 := [trans #296 #300]: #655 -#312 := [quant-inst #51 #45 #48]: #654 -#302 := [mp #312 #301]: #316 -#567 := [unit-resolution #302 #670]: #657 -#640 := (not #657) -#647 := (or #640 #335 #660) -#649 := [def-axiom]: #647 -#568 := [unit-resolution #649 #567]: #564 -#548 := [unit-resolution #568 #566]: #660 -#642 := (or #324 #656) -#643 := [def-axiom]: #642 -#549 := [unit-resolution #643 #548]: #656 -#581 := (or #587 #620 #658) -#582 := [def-axiom]: #581 -#552 := [unit-resolution #582 #549]: #551 -#553 := [unit-resolution #552 #565]: #620 -#611 := (or #619 #360) -#577 := [def-axiom]: #611 -#554 := [unit-resolution #577 #553]: #360 -#636 := (or #348 #361 #638) -#345 := [def-axiom]: #636 -#555 := [unit-resolution #345 #554 #563]: #638 -#303 := (or #324 #336) -#641 := [def-axiom]: #303 -#556 := [unit-resolution #641 #548]: #336 -#579 := (or #619 #633) -#589 := [def-axiom]: #579 -#557 := [unit-resolution #589 #553]: #633 -#614 := (or #498 #340 #630) -#608 := [def-axiom]: #614 -#558 := [unit-resolution #608 #557 #556]: #498 -#446 := (or #592 #489 #637) -#447 := [def-axiom]: #446 -#559 := [unit-resolution #447 #558 #555 #574]: false -#560 := [lemma #559]: #135 -#550 := (or #148 #348) -#627 := (or #346 #148 #348) -#628 := [def-axiom]: #627 -#561 := [unit-resolution #628 #571]: #550 -#539 := [unit-resolution #561 #560]: #348 -#635 := (or #362 #637) -#632 := [def-axiom]: #635 -#540 := [unit-resolution #632 #539]: #637 -#615 := (or #592 #498 #638) -#444 := [def-axiom]: #615 -#542 := [unit-resolution #444 #540 #574]: #498 -#607 := (or #489 #633) -#613 := [def-axiom]: #607 -#543 := [unit-resolution #613 #542]: #633 -#357 := (or #362 #360) -#631 := [def-axiom]: #357 -#544 := [unit-resolution #631 #539]: #360 -#590 := (or #620 #361 #630) -#591 := [def-axiom]: #590 -#545 := [unit-resolution #591 #544 #543]: #620 -#338 := (or #335 #148) -#326 := (or #335 #148 #246) -#337 := [def-axiom]: #326 -#266 := [unit-resolution #337 #156]: #338 -#546 := [unit-resolution #266 #560]: #335 -#541 := (or #139 #324) -#646 := (or #640 #139 #324) -#282 := [def-axiom]: #646 -#547 := [unit-resolution #282 #567]: #541 -#533 := [unit-resolution #547 #546]: #324 -#612 := (or #489 #336) -#606 := [def-axiom]: #612 -#529 := [unit-resolution #606 #542]: #336 -#644 := (or #660 #340 #658) -#645 := [def-axiom]: #644 -#530 := [unit-resolution #645 #529 #533]: #658 -#583 := (or #587 #619 #656) -#584 := [def-axiom]: #583 -#531 := [unit-resolution #584 #530 #545]: #587 -[unit-resolution #610 #670 #531]: false +decl f9 :: S2 +#42 := f9 +#50 := (f4 f9 f10) +#318 := (f3 #50 f12) +decl f1 :: S1 +#4 := f1 +#655 := (= f1 #318) +#253 := (f3 f10 f12) +#632 := (= f1 #253) +#629 := (not #632) +#343 := (f3 f9 f12) +#359 := (= f1 #343) +#360 := (not #359) +#618 := (or #360 #629) +#619 := (not #618) +#615 := (iff #619 #655) +#586 := (not #615) +decl f11 :: S2 +#44 := f11 +#338 := (f3 f11 f12) +#335 := (= f1 #338) +#339 := (not #335) +#488 := (or #339 #629) +#497 := (not #488) +#45 := (f4 f10 f11) +#650 := (f3 #45 f12) +#636 := (= f1 #650) +#498 := (iff #497 #636) +#591 := (not #498) +#571 := [hypothesis]: #591 +#11 := (:var 0 S3) +#9 := (:var 1 S2) +#8 := (:var 2 S2) +#10 := (f4 #8 #9) +#12 := (f3 #10 #11) +#663 := (pattern #12) +#16 := (f3 #9 #11) +#82 := (= f1 #16) +#180 := (not #82) +#14 := (f3 #8 #11) +#79 := (= f1 #14) +#179 := (not #79) +#163 := (or #179 #180) +#164 := (not #163) +#76 := (= f1 #12) +#181 := (iff #76 #164) +#664 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #663) #181) +#184 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #181) +#667 := (iff #184 #664) +#665 := (iff #181 #181) +#666 := [refl]: #665 +#668 := [quant-intro #666]: #667 +#85 := (and #79 #82) +#88 := (iff #76 #85) +#91 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #88) +#185 := (iff #91 #184) +#182 := (iff #88 #181) +#165 := (iff #85 #164) +#166 := [rewrite]: #165 +#183 := [monotonicity #166]: #182 +#186 := [quant-intro #183]: #185 +#169 := (~ #91 #91) +#167 := (~ #88 #88) +#168 := [refl]: #167 +#170 := [nnf-pos #168]: #169 +#17 := (= #16 f1) +#15 := (= #14 f1) +#18 := (and #15 #17) +#13 := (= #12 f1) +#19 := (iff #13 #18) +#20 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #19) +#92 := (iff #20 #91) +#89 := (iff #19 #88) +#86 := (iff #18 #85) +#83 := (iff #17 #82) +#84 := [rewrite]: #83 +#80 := (iff #15 #79) +#81 := [rewrite]: #80 +#87 := [monotonicity #81 #84]: #86 +#77 := (iff #13 #76) +#78 := [rewrite]: #77 +#90 := [monotonicity #78 #87]: #89 +#93 := [quant-intro #90]: #92 +#75 := [asserted]: #20 +#96 := [mp #75 #93]: #91 +#154 := [mp~ #96 #170]: #91 +#187 := [mp #154 #186]: #184 +#669 := [mp #187 #668]: #664 +#310 := (not #664) +#502 := (or #310 #498) +#604 := (or #629 #339) +#486 := (not #604) +#487 := (iff #636 #486) +#503 := (or #310 #487) +#597 := (iff #503 #502) +#598 := (iff #502 #502) +#585 := [rewrite]: #598 +#500 := (iff #487 #498) +#596 := (iff #636 #497) +#499 := (iff #596 #498) +#492 := [rewrite]: #499 +#481 := (iff #487 #596) +#592 := (iff #486 #497) +#447 := (iff #604 #488) +#595 := [rewrite]: #447 +#593 := [monotonicity #595]: #592 +#496 := [monotonicity #593]: #481 +#501 := [trans #496 #492]: #500 +#594 := [monotonicity #501]: #597 +#587 := [trans #594 #585]: #597 +#504 := [quant-inst #43 #44 #47]: #503 +#579 := [mp #504 #587]: #502 +#572 := [unit-resolution #579 #669 #571]: false +#573 := [lemma #572]: #498 +#637 := (not #636) +#361 := (or #360 #637) +#347 := (not #361) +#46 := (f4 f9 #45) +#48 := (f3 #46 f12) +#134 := (= f1 #48) +#147 := (not #134) +#574 := [hypothesis]: #147 +#575 := (or #134 #361) +#362 := (iff #134 #347) +#633 := (or #310 #362) +#355 := [quant-inst #42 #45 #47]: #633 +#570 := [unit-resolution #355 #669]: #362 +#345 := (not #362) +#346 := (or #345 #134 #361) +#348 := [def-axiom]: #346 +#561 := [unit-resolution #348 #570]: #575 +#562 := [unit-resolution #561 #574]: #361 +#601 := (or #310 #615) +#620 := (iff #655 #619) +#617 := (or #310 #620) +#622 := (iff #617 #601) +#465 := (iff #601 #601) +#466 := [rewrite]: #465 +#616 := (iff #620 #615) +#621 := [rewrite]: #616 +#464 := [monotonicity #621]: #622 +#608 := [trans #464 #466]: #622 +#623 := [quant-inst #42 #43 #47]: #617 +#609 := [mp #623 #608]: #601 +#564 := [unit-resolution #609 #669]: #615 +#550 := (or #586 #619) +#657 := (not #655) +#323 := (or #339 #657) +#659 := (not #323) +#51 := (f4 #50 f11) +#52 := (f3 #51 f12) +#138 := (= f1 #52) +#333 := (or #138 #134) +#148 := (iff #138 #147) +#53 := (= #52 f1) +#49 := (= #48 f1) +#54 := (iff #49 #53) +#55 := (not #54) +#151 := (iff #55 #148) +#141 := (iff #134 #138) +#144 := (not #141) +#149 := (iff #144 #148) +#150 := [rewrite]: #149 +#145 := (iff #55 #144) +#142 := (iff #54 #141) +#139 := (iff #53 #138) +#140 := [rewrite]: #139 +#136 := (iff #49 #134) +#137 := [rewrite]: #136 +#143 := [monotonicity #137 #140]: #142 +#146 := [monotonicity #143]: #145 +#152 := [trans #146 #150]: #151 +#133 := [asserted]: #55 +#155 := [mp #133 #152]: #148 +#245 := (not #148) +#332 := (or #138 #134 #245) +#246 := [def-axiom]: #332 +#247 := [unit-resolution #246 #155]: #333 +#565 := [unit-resolution #247 #574]: #138 +#334 := (not #138) +#563 := (or #334 #659) +#656 := (iff #138 #659) +#315 := (or #310 #656) +#312 := (or #657 #339) +#444 := (not #312) +#651 := (iff #138 #444) +#653 := (or #310 #651) +#654 := (iff #653 #315) +#638 := (iff #315 #315) +#299 := [rewrite]: #638 +#662 := (iff #651 #656) +#660 := (iff #444 #659) +#324 := (iff #312 #323) +#658 := [rewrite]: #324 +#661 := [monotonicity #658]: #660 +#652 := [monotonicity #661]: #662 +#295 := [monotonicity #652]: #654 +#300 := [trans #295 #299]: #654 +#311 := [quant-inst #50 #44 #47]: #653 +#301 := [mp #311 #300]: #315 +#566 := [unit-resolution #301 #669]: #656 +#639 := (not #656) +#646 := (or #639 #334 #659) +#648 := [def-axiom]: #646 +#567 := [unit-resolution #648 #566]: #563 +#547 := [unit-resolution #567 #565]: #659 +#641 := (or #323 #655) +#642 := [def-axiom]: #641 +#548 := [unit-resolution #642 #547]: #655 +#580 := (or #586 #619 #657) +#581 := [def-axiom]: #580 +#551 := [unit-resolution #581 #548]: #550 +#552 := [unit-resolution #551 #564]: #619 +#610 := (or #618 #359) +#576 := [def-axiom]: #610 +#553 := [unit-resolution #576 #552]: #359 +#635 := (or #347 #360 #637) +#344 := [def-axiom]: #635 +#554 := [unit-resolution #344 #553 #562]: #637 +#302 := (or #323 #335) +#640 := [def-axiom]: #302 +#555 := [unit-resolution #640 #547]: #335 +#578 := (or #618 #632) +#588 := [def-axiom]: #578 +#556 := [unit-resolution #588 #552]: #632 +#613 := (or #497 #339 #629) +#607 := [def-axiom]: #613 +#557 := [unit-resolution #607 #556 #555]: #497 +#445 := (or #591 #488 #636) +#446 := [def-axiom]: #445 +#558 := [unit-resolution #446 #557 #554 #573]: false +#559 := [lemma #558]: #134 +#549 := (or #147 #347) +#626 := (or #345 #147 #347) +#627 := [def-axiom]: #626 +#560 := [unit-resolution #627 #570]: #549 +#538 := [unit-resolution #560 #559]: #347 +#634 := (or #361 #636) +#631 := [def-axiom]: #634 +#539 := [unit-resolution #631 #538]: #636 +#614 := (or #591 #497 #637) +#443 := [def-axiom]: #614 +#541 := [unit-resolution #443 #539 #573]: #497 +#606 := (or #488 #632) +#612 := [def-axiom]: #606 +#542 := [unit-resolution #612 #541]: #632 +#356 := (or #361 #359) +#630 := [def-axiom]: #356 +#543 := [unit-resolution #630 #538]: #359 +#589 := (or #619 #360 #629) +#590 := [def-axiom]: #589 +#544 := [unit-resolution #590 #543 #542]: #619 +#337 := (or #334 #147) +#325 := (or #334 #147 #245) +#336 := [def-axiom]: #325 +#265 := [unit-resolution #336 #155]: #337 +#545 := [unit-resolution #265 #559]: #334 +#540 := (or #138 #323) +#645 := (or #639 #138 #323) +#281 := [def-axiom]: #645 +#546 := [unit-resolution #281 #566]: #540 +#532 := [unit-resolution #546 #545]: #323 +#611 := (or #488 #335) +#605 := [def-axiom]: #611 +#528 := [unit-resolution #605 #541]: #335 +#643 := (or #659 #339 #657) +#644 := [def-axiom]: #643 +#529 := [unit-resolution #644 #528 #532]: #657 +#582 := (or #586 #618 #655) +#583 := [def-axiom]: #582 +#530 := [unit-resolution #583 #529 #544]: #586 +[unit-resolution #609 #669 #530]: false unsat 2b2ce778241d0cd9017eb9658fd16ee31fe3f28e 18 0 #2 := false