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

dropped some unused bindings

#2 := false
#55 := 0::int
decl uf_24 :: (-> T2 int)
decl ?x68!16 :: T2
#2296 := ?x68!16
#2300 := (uf_24 ?x68!16)
#1220 := -1::int
#2894 := (* -1::int #2300)
decl ?x67!17 :: T2
#2297 := ?x67!17
#2298 := (uf_24 ?x67!17)
#2895 := (+ #2298 #2894)
#2896 := (<= #2895 0::int)
#4133 := (not #2896)
decl uf_6 :: (-> T4 T2 T5)
decl uf_23 :: T4
#193 := uf_23
#2305 := (uf_6 uf_23 ?x68!16)
decl uf_8 :: T5
#33 := uf_8
#2306 := (= uf_8 #2305)
#2303 := (uf_6 uf_23 ?x67!17)
#2304 := (= uf_8 #2303)
#3433 := (not #2304)
#3448 := (or #3433 #2306 #2896)
#3453 := (not #3448)
decl uf_1 :: (-> T2 T2 T1)
decl ?x75!20 :: T2
#2354 := ?x75!20
#11 := (:var 0 T2)
#2358 := (uf_1 #11 ?x75!20)
#4486 := (pattern #2358)
#202 := (uf_24 #11)
#4426 := (pattern #202)
#212 := (uf_6 uf_23 #11)
#4452 := (pattern #212)
decl uf_10 :: (-> T1 int)
#2359 := (uf_10 #2358)
#2355 := (uf_24 ?x75!20)
#2356 := (* -1::int #2355)
#2958 := (+ #2356 #2359)
#2959 := (+ #202 #2958)
#2962 := (= #2959 0::int)
#3524 := (not #2962)
#2357 := (+ #202 #2356)
#2362 := (>= #2357 0::int)
#773 := (= uf_8 #212)
#779 := (not #773)
#3525 := (or #779 #2362 #3524)
#4487 := (forall (vars (?x76 T2)) (:pat #4452 #4426 #4486) #3525)
#4492 := (not #4487)
#10 := (:var 1 T2)
#90 := (uf_1 #11 #10)
#4281 := (pattern #90)
#224 := (uf_24 #10)
#1505 := (* -1::int #224)
#1506 := (+ #202 #1505)
#91 := (uf_10 #90)
#1536 := (+ #91 #1506)
#1534 := (>= #1536 0::int)
#1235 := (* -1::int #91)
decl uf_9 :: int
#56 := uf_9
#1236 := (+ uf_9 #1235)
#1237 := (<= #1236 0::int)
#3516 := (or #779 #1237 #1534)
#4478 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #4281) #3516)
#4483 := (not #4478)
decl uf_11 :: T2
#67 := uf_11
#2934 := (= uf_11 ?x75!20)
#2366 := (+ uf_9 #2356)
#2367 := (<= #2366 0::int)
#4495 := (or #2367 #2934 #4483 #4492)
#4498 := (not #4495)
decl ?x71!19 :: T2
#2324 := ?x71!19
decl ?x72!18 :: T2
#2323 := ?x72!18
#2329 := (uf_1 ?x72!18 ?x71!19)
#2330 := (uf_10 #2329)
#2333 := (* -1::int #2330)
#2327 := (uf_24 ?x72!18)
#2920 := (* -1::int #2327)
#2921 := (+ #2920 #2333)
#2325 := (uf_24 ?x71!19)
#2922 := (+ #2325 #2921)
#2923 := (<= #2922 0::int)
#2337 := (uf_6 uf_23 ?x72!18)
#2338 := (= uf_8 #2337)
#3479 := (not #2338)
#2334 := (+ uf_9 #2333)
#2335 := (<= #2334 0::int)
#3494 := (or #2335 #3479 #2923)
#3499 := (not #3494)
#4501 := (or #3499 #4498)
#4504 := (not #4501)
#4469 := (pattern #202 #224)
#1504 := (>= #1506 0::int)
#221 := (uf_6 uf_23 #10)
#793 := (= uf_8 #221)
#3456 := (not #793)
#3471 := (or #773 #3456 #1504)
#4470 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4469) #3471)
#4475 := (not #4470)
#4507 := (or #4475 #4504)
#7658 := [hypothesis]: #3499
#2336 := (not #2335)
#4131 := (or #3494 #2336)
#4137 := [def-axiom]: #4131
#17052 := [unit-resolution #4137 #7658]: #2336
#17077 := (or #3494 #2335)
decl uf_4 :: (-> T3 T2 int)
decl uf_14 :: T3
#107 := uf_14
#110 := (uf_4 uf_14 #11)
#4305 := (pattern #110)
#759 := (= #110 #202)
#780 := (or #759 #779)
#4453 := (forall (vars (?x63 T2)) (:pat #4305 #4426 #4452) #780)
#4510 := (not #4507)
#4513 := (or #3453 #4510)
#4516 := (not #4513)
#1495 := (>= #202 0::int)
#4461 := (forall (vars (?x65 T2)) (:pat #4426) #1495)
#4466 := (not #4461)
#4519 := (or #4466 #4516)
#4522 := (not #4519)
decl ?x65!15 :: T2
#2281 := ?x65!15
#2282 := (uf_24 ?x65!15)
#2283 := (>= #2282 0::int)
#2284 := (not #2283)
#4525 := (or #2284 #4522)
#4528 := (not #4525)
#216 := (uf_24 uf_11)
#217 := (= #216 0::int)
#1492 := (not #217)
#4531 := (or #1492 #4528)
#4534 := (not #4531)
#4537 := (or #1492 #4534)
#4540 := (not #4537)
#4458 := (not #4453)
#4543 := (or #4458 #4540)
#4546 := (not #4543)
decl ?x63!14 :: T2
#2256 := ?x63!14
#2261 := (uf_4 uf_14 ?x63!14)
#2260 := (uf_24 ?x63!14)
#2866 := (= #2260 #2261)
#2257 := (uf_6 uf_23 ?x63!14)
#2258 := (= uf_8 #2257)
#2259 := (not #2258)
#2872 := (or #2259 #2866)
#2877 := (not #2872)
#10222 := [hypothesis]: #2877
#4144 := (or #2872 #2258)
#4145 := [def-axiom]: #4144
#10559 := [unit-resolution #4145 #10222]: #2258
#4140 := (not #2866)
#4141 := (or #2872 #4140)
#4146 := [def-axiom]: #4141
#10294 := [unit-resolution #4146 #10222]: #4140
decl uf_3 :: (-> T1 T2)
decl uf_22 :: T2
#184 := uf_22
#4728 := (uf_1 uf_22 uf_22)
#9695 := (uf_3 #4728)
#10367 := (uf_1 #9695 ?x63!14)
#10448 := (uf_3 #10367)
#11132 := (uf_4 uf_14 #10448)
#13212 := (= #11132 #2261)
#12385 := (= #2261 #11132)
#10449 := (= ?x63!14 #10448)
#12 := (uf_1 #10 #11)
#4196 := (pattern #12)
#13 := (uf_3 #12)
#317 := (= #11 #13)
#4197 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #4196) #317)
#321 := (forall (vars (?x2 T2) (?x3 T2)) #317)
#4200 := (iff #321 #4197)
#4198 := (iff #317 #317)
#4199 := [refl]: #4198
#4201 := [quant-intro #4199]: #4200
#1843 := (~ #321 #321)
#1875 := (~ #317 #317)
#1876 := [refl]: #1875
#1841 := [nnf-pos #1876]: #1843
#14 := (= #13 #11)
#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
#322 := (iff #15 #321)
#319 := (iff #14 #317)
#320 := [rewrite]: #319
#323 := [quant-intro #320]: #322
#316 := [asserted]: #15
#326 := [mp #316 #323]: #321
#1877 := [mp~ #326 #1841]: #321
#4202 := [mp #1877 #4201]: #4197
#8139 := (not #4197)
#12947 := (or #8139 #10449)
#12948 := [quant-inst]: #12947
#13195 := [unit-resolution #12948 #4202]: #10449
#13203 := [monotonicity #13195]: #12385
#13213 := [symm #13203]: #13212
#13222 := (= #2260 #11132)
#188 := (uf_4 uf_14 uf_22)
#13623 := (= #188 #11132)
#13621 := (= #11132 #188)
#13610 := (= #10448 uf_22)
#10707 := (= #9695 uf_22)
#9696 := (= uf_22 #9695)
#9727 := (or #8139 #9696)
#9731 := [quant-inst]: #9727
#10706 := [unit-resolution #9731 #4202]: #9696
#10708 := [symm #10706]: #10707
#13609 := (= #10448 #9695)
#10319 := (= ?x63!14 #9695)
decl uf_15 :: T4
#113 := uf_15
#9518 := (uf_6 uf_15 ?x63!14)
#9519 := (= uf_8 #9518)
decl uf_7 :: (-> T4 T2 T5 T4)
#194 := (uf_7 uf_15 uf_22 uf_8)
#3894 := (uf_6 #194 uf_22)
#3895 := (= uf_8 #3894)
#10330 := (ite #10319 #3895 #9519)
#10323 := (uf_7 uf_15 #9695 #3894)
#10324 := (uf_6 #10323 ?x63!14)
#10327 := (= uf_8 #10324)
#10333 := (iff #10327 #10330)
#30 := (:var 1 T5)
#20 := (:var 2 T2)
#29 := (:var 3 T4)
#31 := (uf_7 #29 #20 #30)
#32 := (uf_6 #31 #11)
#4216 := (pattern #32)
#36 := (uf_6 #29 #11)
#335 := (= uf_8 #36)
#35 := (= #30 uf_8)
#24 := (= #11 #20)
#338 := (ite #24 #35 #335)
#34 := (= #32 uf_8)
#341 := (iff #34 #338)
#4217 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4216) #341)
#344 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #341)
#4220 := (iff #344 #4217)
#4218 := (iff #341 #341)
#4219 := [refl]: #4218
#4221 := [quant-intro #4219]: #4220
#1848 := (~ #344 #344)
#1884 := (~ #341 #341)
#1885 := [refl]: #1884
#1849 := [nnf-pos #1885]: #1848
#37 := (= #36 uf_8)
#38 := (ite #24 #35 #37)
#39 := (iff #34 #38)
#40 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #39)
#345 := (iff #40 #344)
#342 := (iff #39 #341)
#339 := (iff #38 #338)
#336 := (iff #37 #335)
#337 := [rewrite]: #336
#340 := [monotonicity #337]: #339
#343 := [monotonicity #340]: #342
#346 := [quant-intro #343]: #345
#333 := [asserted]: #40
#349 := [mp #333 #346]: #344
#1886 := [mp~ #349 #1849]: #344
#4222 := [mp #1886 #4221]: #4217
#4987 := (not #4217)
#13028 := (or #4987 #10333)
#4958 := (= #3894 uf_8)
#10322 := (ite #10319 #4958 #9519)
#10325 := (= #10324 uf_8)
#10326 := (iff #10325 #10322)
#13031 := (or #4987 #10326)
#13033 := (iff #13031 #13028)
#13035 := (iff #13028 #13028)
#13036 := [rewrite]: #13035
#10334 := (iff #10326 #10333)
#10331 := (iff #10322 #10330)
#4970 := (iff #4958 #3895)
#4971 := [rewrite]: #4970
#10332 := [monotonicity #4971]: #10331
#10328 := (iff #10325 #10327)
#10329 := [rewrite]: #10328
#10335 := [monotonicity #10329 #10332]: #10334
#13034 := [monotonicity #10335]: #13033
#13037 := [trans #13034 #13036]: #13033
#13032 := [quant-inst]: #13031
#13051 := [mp #13032 #13037]: #13028
#13579 := [unit-resolution #13051 #4222]: #10333
#13595 := (= #2257 #10324)
#13584 := (= #10324 #2257)
#13582 := (= #10323 uf_23)
#7680 := (= #194 uf_23)
#195 := (= uf_23 #194)
#4549 := (or #2877 #4546)
#4552 := (not #4549)
#1480 := (* -1::int #202)
#1481 := (+ #110 #1480)
#1479 := (>= #1481 0::int)
#4444 := (forall (vars (?x61 T2)) (:pat #4305 #4426) #1479)
#4449 := (not #4444)
#4555 := (or #4449 #4552)
#4558 := (not #4555)
decl ?x61!13 :: T2
#2238 := ?x61!13
#2241 := (uf_4 uf_14 ?x61!13)
#2856 := (* -1::int #2241)
#2239 := (uf_24 ?x61!13)
#2857 := (+ #2239 #2856)
#2858 := (<= #2857 0::int)
#2863 := (not #2858)
#4561 := (or #2863 #4558)
#4564 := (not #4561)
#196 := (uf_1 uf_22 #11)
#4427 := (pattern #196)
#197 := (uf_10 #196)
#1623 := (+ #197 #1480)
#1624 := (+ #188 #1623)
#1625 := (= #1624 0::int)
#1449 := (* -1::int #197)
#1455 := (* -1::int #188)
#1456 := (+ #1455 #1449)
#1457 := (+ #110 #1456)
#1458 := (<= #1457 0::int)
#1450 := (+ uf_9 #1449)
#1451 := (<= #1450 0::int)
#3425 := (or #1451 #1458 #1625)
#4436 := (forall (vars (?x59 T2)) (:pat #4427 #4305 #4426) #3425)
#4441 := (not #4436)
#3405 := (or #1451 #1458)
#3406 := (not #3405)
#3409 := (or #759 #3406)
#4428 := (forall (vars (?x60 T2)) (:pat #4305 #4426 #4427) #3409)
#4433 := (not #4428)
decl ?x48!12 :: T2
#2214 := ?x48!12
#2220 := (uf_6 uf_15 ?x48!12)
#2221 := (= uf_8 #2220)
#2215 := (uf_4 uf_14 ?x48!12)
#2216 := (* -1::int #2215)
#2217 := (+ uf_9 #2216)
#2218 := (<= #2217 0::int)
#1655 := (+ uf_9 #1455)
#1656 := (<= #1655 0::int)
#114 := (uf_6 uf_15 #11)
#4347 := (pattern #114)
#1638 := (+ #110 #1455)
#1637 := (>= #1638 0::int)
#478 := (= uf_8 #114)
#1644 := (or #478 #1637)
#4418 := (forall (vars (?x58 T2)) (:pat #4347 #4305) #1644)
#4423 := (not #4418)
#185 := (uf_6 uf_15 uf_22)
#728 := (= uf_8 #185)
#981 := (not #195)
#4567 := (or #981 #728 #4423 #1656 #2218 #2221 #4433 #4441 #4564)
#4570 := (not #4567)
decl ?x53!11 :: T2
#2148 := ?x53!11
decl ?x54!10 :: T2
#2147 := ?x54!10
#2153 := (uf_1 ?x54!10 ?x53!11)
#2154 := (uf_10 #2153)
#2161 := (* -1::int #2154)
decl uf_19 :: T3
#146 := uf_19
#2151 := (uf_4 uf_19 ?x54!10)
#2157 := (* -1::int #2151)
#2813 := (+ #2157 #2161)
#2149 := (uf_4 uf_19 ?x53!11)
#2814 := (+ #2149 #2813)
#2815 := (<= #2814 0::int)
#2162 := (+ uf_9 #2161)
#2163 := (<= #2162 0::int)
#2158 := (+ uf_9 #2157)
#2159 := (<= #2158 0::int)
#3369 := (or #2159 #2163 #2815)
#3374 := (not #3369)
#154 := (uf_4 uf_19 #10)
#1357 := (* -1::int #154)
#151 := (uf_4 uf_19 #11)
#1358 := (+ #151 #1357)
#1364 := (+ #91 #1358)
#1387 := (>= #1364 0::int)
#1344 := (* -1::int #151)
#1345 := (+ uf_9 #1344)
#1346 := (<= #1345 0::int)
#3337 := (or #1237 #1346 #1387)
#4380 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #4281) #3337)
#4385 := (not #4380)
#166 := (uf_4 uf_19 uf_11)
#167 := (= #166 0::int)
#4388 := (or #167 #4385)
#4391 := (not #4388)
#4394 := (or #4391 #3374)
#4397 := (not #4394)
#4356 := (pattern #151)
decl ?x50!9 :: (-> T2 T2)
#2124 := (?x50!9 #11)
#2127 := (uf_1 #2124 #11)
#2128 := (uf_10 #2127)
#2783 := (* -1::int #2128)
#2125 := (uf_4 uf_19 #2124)
#2766 := (* -1::int #2125)
#2784 := (+ #2766 #2783)
#2785 := (+ #151 #2784)
#2786 := (= #2785 0::int)
#3307 := (not #2786)
#2767 := (+ #151 #2766)
#2768 := (<= #2767 0::int)
#3308 := (or #2768 #3307)
#3309 := (not #3308)
#68 := (= #11 uf_11)
#3315 := (or #68 #1346 #3309)
#4372 := (forall (vars (?x49 T2)) (:pat #4356) #3315)
#4377 := (not #4372)
#4400 := (or #4377 #4397)
#4403 := (not #4400)
decl ?x49!8 :: T2
#2084 := ?x49!8
#2088 := (uf_1 #11 ?x49!8)
#4357 := (pattern #2088)
#2089 := (uf_10 #2088)
#2085 := (uf_4 uf_19 ?x49!8)
#2086 := (* -1::int #2085)
#2736 := (+ #2086 #2089)
#2737 := (+ #151 #2736)
#2740 := (= #2737 0::int)
#3271 := (not #2740)
#2087 := (+ #151 #2086)
#2092 := (>= #2087 0::int)
#3272 := (or #2092 #3271)
#4358 := (forall (vars (?x50 T2)) (:pat #4356 #4357) #3272)
#4363 := (not #4358)
#2712 := (= uf_11 ?x49!8)
#2096 := (+ uf_9 #2086)
#2097 := (<= #2096 0::int)
#4366 := (or #2097 #2712 #4363)
#4369 := (not #4366)
#4406 := (or #4369 #4403)
#4409 := (not #4406)
#1299 := (* -1::int #110)
#1300 := (+ uf_9 #1299)
#1301 := (<= #1300 0::int)
#3257 := (or #478 #1301)
#4348 := (forall (vars (?x48 T2)) (:pat #4347 #4305) #3257)
#4353 := (not #4348)
#569 := (= uf_14 uf_19)
#674 := (not #569)
decl uf_16 :: T4
#141 := uf_16
#566 := (= uf_15 uf_16)
#692 := (not #566)
decl uf_21 :: T3
#149 := uf_21
decl uf_20 :: T3
#148 := uf_20
#150 := (= uf_20 uf_21)
#665 := (not #150)
decl uf_18 :: T2
#144 := uf_18
decl uf_17 :: T2
#143 := uf_17
#145 := (= uf_17 uf_18)
#683 := (not #145)
#4412 := (or #683 #665 #692 #674 #4353 #4409)
#108 := (uf_4 uf_14 uf_11)
#109 := (= #108 0::int)
#4415 := (not #4412)
#4573 := (or #4415 #4570)
#4576 := (not #4573)
decl ?x47!7 :: (-> T2 T2)
#2047 := (?x47!7 #11)
#2048 := (uf_4 uf_14 #2047)
#2671 := (* -1::int #2048)
#2686 := (+ #110 #2671)
#2687 := (<= #2686 0::int)
#2052 := (uf_1 #2047 #11)
#2053 := (uf_10 #2052)
#2672 := (* -1::int #2053)
#2673 := (+ #2671 #2672)
#2674 := (+ #110 #2673)
#2675 := (= #2674 0::int)
#3241 := (not #2675)
#2056 := (uf_6 uf_15 #2047)
#2057 := (= uf_8 #2056)
#3240 := (not #2057)
#3242 := (or #3240 #3241 #2687)
#3243 := (not #3242)
#3249 := (or #68 #1301 #3243)
#4339 := (forall (vars (?x46 T2)) (:pat #4305) #3249)
#4344 := (not #4339)
decl uf_12 :: (-> T2 int)
#69 := (uf_12 #11)
#4257 := (pattern #69)
decl ?x38!6 :: (-> T2 T2)
#2020 := (?x38!6 #11)
#2024 := (uf_12 #2020)
#2630 := (* -1::int #2024)
#2021 := (uf_1 #2020 #11)
#2022 := (uf_10 #2021)
#2647 := (* -1::int #2022)
#2648 := (+ #2647 #2630)
#2649 := (+ #69 #2648)
#2650 := (= #2649 0::int)
#3213 := (not #2650)
#2631 := (+ #69 #2630)
#2632 := (<= #2631 0::int)
decl up_13 :: (-> T2 bool)
#2030 := (up_13 #2020)
#3212 := (not #2030)
#3214 := (or #3212 #2632 #3213)
#3215 := (not #3214)
#1261 := (* -1::int #69)
#1262 := (+ uf_9 #1261)
#1263 := (<= #1262 0::int)
#3221 := (or #68 #1263 #3215)
#4331 := (forall (vars (?x37 T2)) (:pat #4257) #3221)
#4336 := (not #4331)
#117 := (uf_6 uf_15 #10)
#4322 := (pattern #114 #117)
#120 := (uf_4 uf_14 #10)
#1313 := (* -1::int #120)
#1314 := (+ #110 #1313)
#1317 := (>= #1314 0::int)
#484 := (= uf_8 #117)
#3178 := (not #484)
#3193 := (or #478 #3178 #1317)
#4323 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #4322) #3193)
#4328 := (not #4323)
#1315 := (+ #91 #1314)
#1710 := (>= #1315 0::int)
#481 := (not #478)
#3170 := (or #481 #1237 #1710)
#4314 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #4281) #3170)
#4319 := (not #4314)
#1738 := (>= #110 0::int)
#4306 := (forall (vars (?x41 T2)) (:pat #4305) #1738)
#4311 := (not #4306)
#1749 := (not #109)
#4579 := (or #1749 #4311 #4319 #4328 #4336 #4344 #4576)
#4582 := (not #4579)
decl ?x37!5 :: T2
#1976 := ?x37!5
#1977 := (uf_1 #11 ?x37!5)
#4290 := (pattern #1977)
#77 := (up_13 #11)
#4250 := (pattern #77)
#1979 := (uf_12 ?x37!5)
#1980 := (* -1::int #1979)
#1978 := (uf_10 #1977)
#2598 := (+ #1978 #1980)
#2599 := (+ #69 #2598)
#2602 := (= #2599 0::int)
#3131 := (not #2602)
#1984 := (+ #69 #1980)
#1985 := (>= #1984 0::int)
#78 := (not #77)
#3132 := (or #78 #1985 #3131)
#4291 := (forall (vars (?x38 T2)) (:pat #4250 #4257 #4290) #3132)
#4296 := (not #4291)
#2574 := (= uf_11 ?x37!5)
#1989 := (+ uf_9 #1980)
#1990 := (<= #1989 0::int)
#4299 := (or #1990 #2574 #4296)
#5019 := (= uf_9 #1979)
#5185 := (not #5019)
#1991 := (not #1990)
#4302 := (not #4299)
#5183 := [hypothesis]: #4302
#4176 := (or #4299 #1991)
#3850 := [def-axiom]: #4176
#5184 := [unit-resolution #3850 #5183]: #1991
#5186 := (or #5185 #1990)
#5193 := [th-lemma]: #5186
#5194 := [unit-resolution #5193 #5184]: #5185
#2577 := (not #2574)
#3851 := (or #4299 #2577)
#4183 := [def-axiom]: #3851
#5192 := [unit-resolution #4183 #5183]: #2577
#437 := (= uf_9 #69)
#443 := (or #68 #437)
#4258 := (forall (vars (?x25 T2)) (:pat #4257) #443)
#448 := (forall (vars (?x25 T2)) #443)
#4261 := (iff #448 #4258)
#4259 := (iff #443 #443)
#4260 := [refl]: #4259
#4262 := [quant-intro #4260]: #4261
#1862 := (~ #448 #448)
#1900 := (~ #443 #443)
#1901 := [refl]: #1900
#1863 := [nnf-pos #1901]: #1862
#70 := (= #69 0::int)
#73 := (not #68)
#1807 := (or #73 #70)
#1810 := (forall (vars (?x24 T2)) #1807)
#1813 := (not #1810)
#1741 := (forall (vars (?x41 T2)) #1738)
#1744 := (not #1741)
#487 := (and #481 #484)
#493 := (not #487)
#1727 := (or #493 #1317)
#1732 := (forall (vars (?x42 T2) (?x43 T2)) #1727)
#1735 := (not #1732)
#1238 := (not #1237)
#1702 := (and #478 #1238)
#1707 := (not #1702)
#1713 := (or #1707 #1710)
#1716 := (forall (vars (?x44 T2) (?x45 T2)) #1713)
#1719 := (not #1716)
#1649 := (forall (vars (?x58 T2)) #1644)
#1652 := (not #1649)
#1459 := (not #1458)
#1452 := (not #1451)
#1462 := (and #1452 #1459)
#1620 := (not #1462)
#1628 := (or #1620 #1625)
#1631 := (forall (vars (?x59 T2)) #1628)
#1634 := (not #1631)
#1558 := (= #1536 0::int)
#1561 := (not #1504)
#1570 := (and #773 #1561 #1558)
#1575 := (exists (vars (?x76 T2)) #1570)
#1547 := (+ uf_9 #1480)
#1548 := (<= #1547 0::int)
#1549 := (not #1548)
#1552 := (and #73 #1549)
#1555 := (not #1552)
#1578 := (or #1555 #1575)
#1581 := (forall (vars (?x75 T2)) #1578)
#1526 := (and #773 #1238)
#1531 := (not #1526)
#1538 := (or #1531 #1534)
#1541 := (forall (vars (?x71 T2) (?x72 T2)) #1538)
#1544 := (not #1541)
#1584 := (or #1544 #1581)
#1587 := (and #1541 #1584)
#796 := (and #779 #793)
#802 := (not #796)
#1512 := (or #802 #1504)
#1517 := (forall (vars (?x67 T2) (?x68 T2)) #1512)
#1520 := (not #1517)
#1590 := (or #1520 #1587)
#1593 := (and #1517 #1590)
#1498 := (forall (vars (?x65 T2)) #1495)
#1501 := (not #1498)
#1596 := (or #1501 #1593)
#1599 := (and #1498 #1596)
#1602 := (or #1492 #1599)
#1605 := (and #217 #1602)
#785 := (forall (vars (?x63 T2)) #780)
#939 := (not #785)
#1608 := (or #939 #1605)
#1611 := (and #785 #1608)
#1484 := (forall (vars (?x61 T2)) #1479)
#1487 := (not #1484)
#1614 := (or #1487 #1611)
#1617 := (and #1484 #1614)
#1468 := (or #759 #1462)
#1473 := (forall (vars (?x60 T2)) #1468)
#1476 := (not #1473)
#1302 := (not #1301)
#1421 := (and #481 #1302)
#1426 := (exists (vars (?x48 T2)) #1421)
#1667 := (not #1426)
#1691 := (or #981 #728 #1667 #1476 #1617 #1634 #1652 #1656)
#1347 := (not #1346)
#1381 := (and #1238 #1347)
#1384 := (not #1381)
#1390 := (or #1384 #1387)
#1393 := (forall (vars (?x53 T2) (?x54 T2)) #1390)
#1396 := (not #1393)
#1404 := (or #167 #1396)
#1409 := (and #1393 #1404)
#1362 := (= #1364 0::int)
#1356 := (>= #1358 0::int)
#1359 := (not #1356)
#1366 := (and #1359 #1362)
#1369 := (exists (vars (?x50 T2)) #1366)
#1350 := (and #73 #1347)
#1353 := (not #1350)
#1372 := (or #1353 #1369)
#1375 := (forall (vars (?x49 T2)) #1372)
#1378 := (not #1375)
#1412 := (or #1378 #1409)
#1415 := (and #1375 #1412)
#1444 := (or #683 #665 #692 #674 #1415 #1426)
#1696 := (and #1444 #1691)
#1318 := (not #1317)
#1311 := (= #1315 0::int)
#1327 := (and #478 #1311 #1318)
#1332 := (exists (vars (?x47 T2)) #1327)
#1305 := (and #73 #1302)
#1308 := (not #1305)
#1335 := (or #1308 #1332)
#1338 := (forall (vars (?x46 T2)) #1335)
#1341 := (not #1338)
#86 := (uf_12 #10)
#1223 := (* -1::int #86)
#1250 := (+ #1223 #91)
#1251 := (+ #69 #1250)
#1273 := (= #1251 0::int)
#1224 := (+ #69 #1223)
#1222 := (>= #1224 0::int)
#1276 := (not #1222)
#1285 := (and #77 #1276 #1273)
#1290 := (exists (vars (?x38 T2)) #1285)
#1264 := (not #1263)
#1267 := (and #73 #1264)
#1270 := (not #1267)
#1293 := (or #1270 #1290)
#1296 := (forall (vars (?x37 T2)) #1293)
#1752 := (not #1296)
#1773 := (or #1749 #1752 #1341 #1696 #1719 #1735 #1744)
#1778 := (and #1296 #1773)
#1248 := (>= #1251 0::int)
#1241 := (and #77 #1238)
#1244 := (not #1241)
#1252 := (or #1244 #1248)
#1255 := (forall (vars (?x33 T2) (?x34 T2)) #1252)
#1258 := (not #1255)
#1781 := (or #1258 #1778)
#1784 := (and #1255 #1781)
#84 := (up_13 #10)
#85 := (and #78 #84)
#454 := (not #85)
#1226 := (or #454 #1222)
#1229 := (forall (vars (?x29 T2) (?x30 T2)) #1226)
#1232 := (not #1229)
#1787 := (or #1232 #1784)
#1790 := (and #1229 #1787)
#1213 := (>= #69 0::int)
#1214 := (forall (vars (?x27 T2)) #1213)
#1217 := (not #1214)
#1793 := (or #1217 #1790)
#1796 := (and #1214 #1793)
#80 := (uf_12 uf_11)
#81 := (= #80 0::int)
#1208 := (not #81)
#1799 := (or #1208 #1796)
#1802 := (and #81 #1799)
#1177 := (not #448)
#79 := (forall (vars (?x26 T2)) #78)
#1168 := (not #79)
#1825 := (or #1168 #1177 #1802 #1813)
#1830 := (not #1825)
#1 := true
#242 := (implies false true)
#229 := (+ #202 #91)
#236 := (= #224 #229)
#213 := (= #212 uf_8)
#237 := (and #213 #236)
#235 := (< #202 #224)
#238 := (and #235 #237)
#239 := (exists (vars (?x76 T2)) #238)
#233 := (< #202 uf_9)
#234 := (and #73 #233)
#240 := (implies #234 #239)
#241 := (forall (vars (?x75 T2)) #240)
#243 := (implies #241 #242)
#244 := (and #241 #243)
#230 := (<= #224 #229)
#92 := (< #91 uf_9)
#228 := (and #213 #92)
#231 := (implies #228 #230)
#232 := (forall (vars (?x71 T2) (?x72 T2)) #231)
#245 := (implies #232 #244)
#246 := (and #232 #245)
#225 := (<= #224 #202)
#222 := (= #221 uf_8)
#220 := (not #213)
#223 := (and #220 #222)
#226 := (implies #223 #225)
#227 := (forall (vars (?x67 T2) (?x68 T2)) #226)
#247 := (implies #227 #246)
#248 := (and #227 #247)
#218 := (<= 0::int #202)
#219 := (forall (vars (?x65 T2)) #218)
#249 := (implies #219 #248)
#250 := (and #219 #249)
#251 := (implies #217 #250)
#252 := (and #217 #251)
#253 := (implies true #252)
#254 := (implies true #253)
#207 := (= #202 #110)
#214 := (implies #213 #207)
#215 := (forall (vars (?x63 T2)) #214)
#255 := (implies #215 #254)
#256 := (and #215 #255)
#210 := (<= #202 #110)
#211 := (forall (vars (?x61 T2)) #210)
#257 := (implies #211 #256)
#258 := (and #211 #257)
#199 := (+ #188 #197)
#200 := (< #199 #110)
#198 := (< #197 uf_9)
#201 := (and #198 #200)
#206 := (not #201)
#208 := (implies #206 #207)
#209 := (forall (vars (?x60 T2)) #208)
#259 := (implies #209 #258)
#203 := (= #202 #199)
#204 := (implies #201 #203)
#205 := (forall (vars (?x59 T2)) #204)
#260 := (implies #205 #259)
#261 := (implies #195 #260)
#190 := (<= #188 #110)
#115 := (= #114 uf_8)
#116 := (not #115)
#191 := (implies #116 #190)
#192 := (forall (vars (?x58 T2)) #191)
#262 := (implies #192 #261)
#189 := (< #188 uf_9)
#263 := (implies #189 #262)
#186 := (= #185 uf_8)
#187 := (not #186)
#264 := (implies #187 #263)
#129 := (< #110 uf_9)
#138 := (and #116 #129)
#139 := (exists (vars (?x48 T2)) #138)
#265 := (implies #139 #264)
#266 := (implies true #265)
#267 := (implies true #266)
#168 := (implies #167 true)
#169 := (and #167 #168)
#156 := (+ #151 #91)
#163 := (<= #154 #156)
#152 := (< #151 uf_9)
#162 := (and #152 #92)
#164 := (implies #162 #163)
#165 := (forall (vars (?x53 T2) (?x54 T2)) #164)
#170 := (implies #165 #169)
#171 := (and #165 #170)
#157 := (= #154 #156)
#155 := (< #151 #154)
#158 := (and #155 #157)
#159 := (exists (vars (?x50 T2)) #158)
#153 := (and #73 #152)
#160 := (implies #153 #159)
#161 := (forall (vars (?x49 T2)) #160)
#172 := (implies #161 #171)
#173 := (and #161 #172)
#174 := (implies true #173)
#175 := (implies #150 #174)
#147 := (= uf_19 uf_14)
#176 := (implies #147 #175)
#177 := (implies #145 #176)
#142 := (= uf_16 uf_15)
#178 := (implies #142 #177)
#179 := (implies true #178)
#180 := (implies true #179)
#140 := (not #139)
#181 := (implies #140 #180)
#182 := (implies true #181)
#183 := (implies true #182)
#268 := (and #183 #267)
#269 := (implies true #268)
#125 := (+ #110 #91)
#132 := (= #120 #125)
#133 := (and #115 #132)
#131 := (< #110 #120)
#134 := (and #131 #133)
#135 := (exists (vars (?x47 T2)) #134)
#130 := (and #73 #129)
#136 := (implies #130 #135)
#137 := (forall (vars (?x46 T2)) #136)
#270 := (implies #137 #269)
#126 := (<= #120 #125)
#124 := (and #115 #92)
#127 := (implies #124 #126)
#128 := (forall (vars (?x44 T2) (?x45 T2)) #127)
#271 := (implies #128 #270)
#121 := (<= #120 #110)
#118 := (= #117 uf_8)
#119 := (and #116 #118)
#122 := (implies #119 #121)
#123 := (forall (vars (?x42 T2) (?x43 T2)) #122)
#272 := (implies #123 #271)
#111 := (<= 0::int #110)
#112 := (forall (vars (?x41 T2)) #111)
#273 := (implies #112 #272)
#274 := (implies #109 #273)
#275 := (implies true #274)
#276 := (implies true #275)
#94 := (+ #69 #91)
#101 := (= #86 #94)
#102 := (and #77 #101)
#100 := (< #69 #86)
#103 := (and #100 #102)
#104 := (exists (vars (?x38 T2)) #103)
#98 := (< #69 uf_9)
#99 := (and #73 #98)
#105 := (implies #99 #104)
#106 := (forall (vars (?x37 T2)) #105)
#277 := (implies #106 #276)
#278 := (and #106 #277)
#95 := (<= #86 #94)
#93 := (and #77 #92)
#96 := (implies #93 #95)
#97 := (forall (vars (?x33 T2) (?x34 T2)) #96)
#279 := (implies #97 #278)
#280 := (and #97 #279)
#87 := (<= #86 #69)
#88 := (implies #85 #87)
#89 := (forall (vars (?x29 T2) (?x30 T2)) #88)
#281 := (implies #89 #280)
#282 := (and #89 #281)
#82 := (<= 0::int #69)
#83 := (forall (vars (?x27 T2)) #82)
#283 := (implies #83 #282)
#284 := (and #83 #283)
#285 := (implies #81 #284)
#286 := (and #81 #285)
#287 := (implies true #286)
#288 := (implies #79 #287)
#74 := (= #69 uf_9)
#75 := (implies #73 #74)
#76 := (forall (vars (?x25 T2)) #75)
#289 := (implies #76 #288)
#71 := (implies #68 #70)
#72 := (forall (vars (?x24 T2)) #71)
#290 := (implies #72 #289)
#291 := (implies true #290)
#292 := (implies true #291)
#293 := (not #292)
#1833 := (iff #293 #1830)
#819 := (+ #91 #202)
#837 := (= #224 #819)
#840 := (and #773 #837)
#843 := (and #235 #840)
#846 := (exists (vars (?x76 T2)) #843)
#852 := (not #234)
#853 := (or #852 #846)
#858 := (forall (vars (?x75 T2)) #853)
#822 := (<= #224 #819)
#814 := (and #92 #773)
#828 := (not #814)
#829 := (or #828 #822)
#834 := (forall (vars (?x71 T2) (?x72 T2)) #829)
#880 := (not #834)
#881 := (or #880 #858)
#886 := (and #834 #881)
#803 := (or #225 #802)
#808 := (forall (vars (?x67 T2) (?x68 T2)) #803)
#892 := (not #808)
#893 := (or #892 #886)
#898 := (and #808 #893)
#904 := (not #219)
#905 := (or #904 #898)
#910 := (and #219 #905)
#788 := (= 0::int #216)
#916 := (not #788)
#917 := (or #916 #910)
#922 := (and #788 #917)
#940 := (or #939 #922)
#945 := (and #785 #940)
#951 := (not #211)
#952 := (or #951 #945)
#957 := (and #211 #952)
#765 := (or #201 #759)
#770 := (forall (vars (?x60 T2)) #765)
#963 := (not #770)
#964 := (or #963 #957)
#745 := (= #199 #202)
#751 := (or #206 #745)
#756 := (forall (vars (?x59 T2)) #751)
#972 := (not #756)
#973 := (or #972 #964)
#982 := (or #981 #973)
#737 := (or #190 #478)
#742 := (forall (vars (?x58 T2)) #737)
#990 := (not #742)
#991 := (or #990 #982)
#999 := (not #189)
#1000 := (or #999 #991)
#1008 := (or #728 #1000)
#555 := (and #129 #481)
#560 := (exists (vars (?x48 T2)) #555)
#563 := (not #560)
#1016 := (or #563 #1008)
#614 := (= 0::int #166)
#572 := (+ #91 #151)
#599 := (<= #154 #572)
#596 := (and #92 #152)
#605 := (not #596)
#606 := (or #605 #599)
#611 := (forall (vars (?x53 T2) (?x54 T2)) #606)
#634 := (not #611)
#635 := (or #634 #614)
#640 := (and #611 #635)
#575 := (= #154 #572)
#578 := (and #155 #575)
#581 := (exists (vars (?x50 T2)) #578)
#587 := (not #153)
#588 := (or #587 #581)
#593 := (forall (vars (?x49 T2)) #588)
#646 := (not #593)
#647 := (or #646 #640)
#652 := (and #593 #647)
#666 := (or #665 #652)
#675 := (or #674 #666)
#684 := (or #683 #675)
#693 := (or #692 #684)
#712 := (or #560 #693)
#1032 := (and #712 #1016)
#510 := (+ #91 #110)
#528 := (= #120 #510)
#531 := (and #478 #528)
#534 := (and #131 #531)
#537 := (exists (vars (?x47 T2)) #534)
#543 := (not #130)
#544 := (or #543 #537)
#549 := (forall (vars (?x46 T2)) #544)
#1045 := (not #549)
#1046 := (or #1045 #1032)
#513 := (<= #120 #510)
#505 := (and #92 #478)
#519 := (not #505)
#520 := (or #519 #513)
#525 := (forall (vars (?x44 T2) (?x45 T2)) #520)
#1054 := (not #525)
#1055 := (or #1054 #1046)
#494 := (or #121 #493)
#499 := (forall (vars (?x42 T2) (?x43 T2)) #494)
#1063 := (not #499)
#1064 := (or #1063 #1055)
#1072 := (not #112)
#1073 := (or #1072 #1064)
#475 := (= 0::int #108)
#1081 := (not #475)
#1082 := (or #1081 #1073)
#468 := (not #99)
#469 := (or #468 #104)
#472 := (forall (vars (?x37 T2)) #469)
#1101 := (not #472)
#1102 := (or #1101 #1082)
#1107 := (and #472 #1102)
#461 := (not #93)
#462 := (or #461 #95)
#465 := (forall (vars (?x33 T2) (?x34 T2)) #462)
#1113 := (not #465)
#1114 := (or #1113 #1107)
#1119 := (and #465 #1114)
#455 := (or #454 #87)
#458 := (forall (vars (?x29 T2) (?x30 T2)) #455)
#1125 := (not #458)
#1126 := (or #1125 #1119)
#1131 := (and #458 #1126)
#1137 := (not #83)
#1138 := (or #1137 #1131)
#1143 := (and #83 #1138)
#451 := (= 0::int #80)
#1149 := (not #451)
#1150 := (or #1149 #1143)
#1155 := (and #451 #1150)
#1169 := (or #1168 #1155)
#1178 := (or #1177 #1169)
#423 := (= 0::int #69)
#429 := (or #73 #423)
#434 := (forall (vars (?x24 T2)) #429)
#1186 := (not #434)
#1187 := (or #1186 #1178)
#1203 := (not #1187)
#1831 := (iff #1203 #1830)
#1828 := (iff #1187 #1825)
#1816 := (or #1168 #1802)
#1819 := (or #1177 #1816)
#1822 := (or #1813 #1819)
#1826 := (iff #1822 #1825)
#1827 := [rewrite]: #1826
#1823 := (iff #1187 #1822)
#1820 := (iff #1178 #1819)
#1817 := (iff #1169 #1816)
#1803 := (iff #1155 #1802)
#1800 := (iff #1150 #1799)
#1797 := (iff #1143 #1796)
#1794 := (iff #1138 #1793)
#1791 := (iff #1131 #1790)
#1788 := (iff #1126 #1787)
#1785 := (iff #1119 #1784)
#1782 := (iff #1114 #1781)
#1779 := (iff #1107 #1778)
#1776 := (iff #1102 #1773)
#1755 := (or #1341 #1696)
#1758 := (or #1719 #1755)
#1761 := (or #1735 #1758)
#1764 := (or #1744 #1761)
#1767 := (or #1749 #1764)
#1770 := (or #1752 #1767)
#1774 := (iff #1770 #1773)
#1775 := [rewrite]: #1774
#1771 := (iff #1102 #1770)
#1768 := (iff #1082 #1767)
#1765 := (iff #1073 #1764)
#1762 := (iff #1064 #1761)
#1759 := (iff #1055 #1758)
#1756 := (iff #1046 #1755)
#1697 := (iff #1032 #1696)
#1694 := (iff #1016 #1691)
#1670 := (or #1476 #1617)
#1673 := (or #1634 #1670)
#1676 := (or #981 #1673)
#1679 := (or #1652 #1676)
#1682 := (or #1656 #1679)
#1685 := (or #728 #1682)
#1688 := (or #1667 #1685)
#1692 := (iff #1688 #1691)
#1693 := [rewrite]: #1692
#1689 := (iff #1016 #1688)
#1686 := (iff #1008 #1685)
#1683 := (iff #1000 #1682)
#1680 := (iff #991 #1679)
#1677 := (iff #982 #1676)
#1674 := (iff #973 #1673)
#1671 := (iff #964 #1670)
#1618 := (iff #957 #1617)
#1615 := (iff #952 #1614)
#1612 := (iff #945 #1611)
#1609 := (iff #940 #1608)
#1606 := (iff #922 #1605)
#1603 := (iff #917 #1602)
#1600 := (iff #910 #1599)
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#1563 := [rewrite]: #1562
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#1551 := [rewrite]: #1550
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#1240 := [rewrite]: #1239
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#1508 := [rewrite]: #1507
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#1483 := [rewrite]: #1482
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#1454 := [rewrite]: #1453
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#1472 := [trans #1467 #1470]: #1471
#1475 := [quant-intro #1472]: #1474
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#1304 := [rewrite]: #1303
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#1361 := [rewrite]: #1360
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#1320 := [rewrite]: #1319
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#1278 := [rewrite]: #1277
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#1212 := [rewrite]: #1211
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#942 := [rewrite]: #941
#937 := (iff #255 #936)
#934 := (iff #254 #922)
#925 := (implies true #922)
#928 := (iff #925 #922)
#929 := [rewrite]: #928
#932 := (iff #254 #925)
#930 := (iff #253 #922)
#926 := (iff #253 #925)
#923 := (iff #252 #922)
#920 := (iff #251 #917)
#913 := (implies #788 #910)
#918 := (iff #913 #917)
#919 := [rewrite]: #918
#914 := (iff #251 #913)
#911 := (iff #250 #910)
#908 := (iff #249 #905)
#901 := (implies #219 #898)
#906 := (iff #901 #905)
#907 := [rewrite]: #906
#902 := (iff #249 #901)
#899 := (iff #248 #898)
#896 := (iff #247 #893)
#889 := (implies #808 #886)
#894 := (iff #889 #893)
#895 := [rewrite]: #894
#890 := (iff #247 #889)
#887 := (iff #246 #886)
#884 := (iff #245 #881)
#877 := (implies #834 #858)
#882 := (iff #877 #881)
#883 := [rewrite]: #882
#878 := (iff #245 #877)
#875 := (iff #244 #858)
#870 := (and #858 true)
#873 := (iff #870 #858)
#874 := [rewrite]: #873
#871 := (iff #244 #870)
#868 := (iff #243 true)
#863 := (implies #858 true)
#866 := (iff #863 true)
#867 := [rewrite]: #866
#864 := (iff #243 #863)
#861 := (iff #242 true)
#862 := [rewrite]: #861
#859 := (iff #241 #858)
#856 := (iff #240 #853)
#849 := (implies #234 #846)
#854 := (iff #849 #853)
#855 := [rewrite]: #854
#850 := (iff #240 #849)
#847 := (iff #239 #846)
#844 := (iff #238 #843)
#841 := (iff #237 #840)
#838 := (iff #236 #837)
#820 := (= #229 #819)
#821 := [rewrite]: #820
#839 := [monotonicity #821]: #838
#774 := (iff #213 #773)
#775 := [rewrite]: #774
#842 := [monotonicity #775 #839]: #841
#845 := [monotonicity #842]: #844
#848 := [quant-intro #845]: #847
#851 := [monotonicity #848]: #850
#857 := [trans #851 #855]: #856
#860 := [quant-intro #857]: #859
#865 := [monotonicity #860 #862]: #864
#869 := [trans #865 #867]: #868
#872 := [monotonicity #860 #869]: #871
#876 := [trans #872 #874]: #875
#835 := (iff #232 #834)
#832 := (iff #231 #829)
#825 := (implies #814 #822)
#830 := (iff #825 #829)
#831 := [rewrite]: #830
#826 := (iff #231 #825)
#823 := (iff #230 #822)
#824 := [monotonicity #821]: #823
#817 := (iff #228 #814)
#811 := (and #773 #92)
#815 := (iff #811 #814)
#816 := [rewrite]: #815
#812 := (iff #228 #811)
#813 := [monotonicity #775]: #812
#818 := [trans #813 #816]: #817
#827 := [monotonicity #818 #824]: #826
#833 := [trans #827 #831]: #832
#836 := [quant-intro #833]: #835
#879 := [monotonicity #836 #876]: #878
#885 := [trans #879 #883]: #884
#888 := [monotonicity #836 #885]: #887
#809 := (iff #227 #808)
#806 := (iff #226 #803)
#799 := (implies #796 #225)
#804 := (iff #799 #803)
#805 := [rewrite]: #804
#800 := (iff #226 #799)
#797 := (iff #223 #796)
#794 := (iff #222 #793)
#795 := [rewrite]: #794
#791 := (iff #220 #779)
#792 := [monotonicity #775]: #791
#798 := [monotonicity #792 #795]: #797
#801 := [monotonicity #798]: #800
#807 := [trans #801 #805]: #806
#810 := [quant-intro #807]: #809
#891 := [monotonicity #810 #888]: #890
#897 := [trans #891 #895]: #896
#900 := [monotonicity #810 #897]: #899
#903 := [monotonicity #900]: #902
#909 := [trans #903 #907]: #908
#912 := [monotonicity #909]: #911
#789 := (iff #217 #788)
#790 := [rewrite]: #789
#915 := [monotonicity #790 #912]: #914
#921 := [trans #915 #919]: #920
#924 := [monotonicity #790 #921]: #923
#927 := [monotonicity #924]: #926
#931 := [trans #927 #929]: #930
#933 := [monotonicity #931]: #932
#935 := [trans #933 #929]: #934
#786 := (iff #215 #785)
#783 := (iff #214 #780)
#776 := (implies #773 #759)
#781 := (iff #776 #780)
#782 := [rewrite]: #781
#777 := (iff #214 #776)
#760 := (iff #207 #759)
#761 := [rewrite]: #760
#778 := [monotonicity #775 #761]: #777
#784 := [trans #778 #782]: #783
#787 := [quant-intro #784]: #786
#938 := [monotonicity #787 #935]: #937
#944 := [trans #938 #942]: #943
#947 := [monotonicity #787 #944]: #946
#950 := [monotonicity #947]: #949
#956 := [trans #950 #954]: #955
#959 := [monotonicity #956]: #958
#771 := (iff #209 #770)
#768 := (iff #208 #765)
#762 := (implies #206 #759)
#766 := (iff #762 #765)
#767 := [rewrite]: #766
#763 := (iff #208 #762)
#764 := [monotonicity #761]: #763
#769 := [trans #764 #767]: #768
#772 := [quant-intro #769]: #771
#962 := [monotonicity #772 #959]: #961
#968 := [trans #962 #966]: #967
#757 := (iff #205 #756)
#754 := (iff #204 #751)
#748 := (implies #201 #745)
#752 := (iff #748 #751)
#753 := [rewrite]: #752
#749 := (iff #204 #748)
#746 := (iff #203 #745)
#747 := [rewrite]: #746
#750 := [monotonicity #747]: #749
#755 := [trans #750 #753]: #754
#758 := [quant-intro #755]: #757
#971 := [monotonicity #758 #968]: #970
#977 := [trans #971 #975]: #976
#980 := [monotonicity #977]: #979
#986 := [trans #980 #984]: #985
#743 := (iff #192 #742)
#740 := (iff #191 #737)
#734 := (implies #481 #190)
#738 := (iff #734 #737)
#739 := [rewrite]: #738
#735 := (iff #191 #734)
#482 := (iff #116 #481)
#479 := (iff #115 #478)
#480 := [rewrite]: #479
#483 := [monotonicity #480]: #482
#736 := [monotonicity #483]: #735
#741 := [trans #736 #739]: #740
#744 := [quant-intro #741]: #743
#989 := [monotonicity #744 #986]: #988
#995 := [trans #989 #993]: #994
#998 := [monotonicity #995]: #997
#1004 := [trans #998 #1002]: #1003
#732 := (iff #187 #731)
#729 := (iff #186 #728)
#730 := [rewrite]: #729
#733 := [monotonicity #730]: #732
#1007 := [monotonicity #733 #1004]: #1006
#1012 := [trans #1007 #1010]: #1011
#561 := (iff #139 #560)
#558 := (iff #138 #555)
#552 := (and #481 #129)
#556 := (iff #552 #555)
#557 := [rewrite]: #556
#553 := (iff #138 #552)
#554 := [monotonicity #483]: #553
#559 := [trans #554 #557]: #558
#562 := [quant-intro #559]: #561
#1015 := [monotonicity #562 #1012]: #1014
#1020 := [trans #1015 #1018]: #1019
#1023 := [monotonicity #1020]: #1022
#1027 := [trans #1023 #1025]: #1026
#1029 := [monotonicity #1027]: #1028
#1031 := [trans #1029 #1025]: #1030
#726 := (iff #183 #712)
#717 := (implies true #712)
#720 := (iff #717 #712)
#721 := [rewrite]: #720
#724 := (iff #183 #717)
#722 := (iff #182 #712)
#718 := (iff #182 #717)
#715 := (iff #181 #712)
#709 := (implies #563 #693)
#713 := (iff #709 #712)
#714 := [rewrite]: #713
#710 := (iff #181 #709)
#707 := (iff #180 #693)
#698 := (implies true #693)
#701 := (iff #698 #693)
#702 := [rewrite]: #701
#705 := (iff #180 #698)
#703 := (iff #179 #693)
#699 := (iff #179 #698)
#696 := (iff #178 #693)
#689 := (implies #566 #684)
#694 := (iff #689 #693)
#695 := [rewrite]: #694
#690 := (iff #178 #689)
#687 := (iff #177 #684)
#680 := (implies #145 #675)
#685 := (iff #680 #684)
#686 := [rewrite]: #685
#681 := (iff #177 #680)
#678 := (iff #176 #675)
#671 := (implies #569 #666)
#676 := (iff #671 #675)
#677 := [rewrite]: #676
#672 := (iff #176 #671)
#669 := (iff #175 #666)
#662 := (implies #150 #652)
#667 := (iff #662 #666)
#668 := [rewrite]: #667
#663 := (iff #175 #662)
#660 := (iff #174 #652)
#655 := (implies true #652)
#658 := (iff #655 #652)
#659 := [rewrite]: #658
#656 := (iff #174 #655)
#653 := (iff #173 #652)
#650 := (iff #172 #647)
#643 := (implies #593 #640)
#648 := (iff #643 #647)
#649 := [rewrite]: #648
#644 := (iff #172 #643)
#641 := (iff #171 #640)
#638 := (iff #170 #635)
#631 := (implies #611 #614)
#636 := (iff #631 #635)
#637 := [rewrite]: #636
#632 := (iff #170 #631)
#629 := (iff #169 #614)
#624 := (and #614 true)
#627 := (iff #624 #614)
#628 := [rewrite]: #627
#625 := (iff #169 #624)
#622 := (iff #168 true)
#617 := (implies #614 true)
#620 := (iff #617 true)
#621 := [rewrite]: #620
#618 := (iff #168 #617)
#615 := (iff #167 #614)
#616 := [rewrite]: #615
#619 := [monotonicity #616]: #618
#623 := [trans #619 #621]: #622
#626 := [monotonicity #616 #623]: #625
#630 := [trans #626 #628]: #629
#612 := (iff #165 #611)
#609 := (iff #164 #606)
#602 := (implies #596 #599)
#607 := (iff #602 #606)
#608 := [rewrite]: #607
#603 := (iff #164 #602)
#600 := (iff #163 #599)
#573 := (= #156 #572)
#574 := [rewrite]: #573
#601 := [monotonicity #574]: #600
#597 := (iff #162 #596)
#598 := [rewrite]: #597
#604 := [monotonicity #598 #601]: #603
#610 := [trans #604 #608]: #609
#613 := [quant-intro #610]: #612
#633 := [monotonicity #613 #630]: #632
#639 := [trans #633 #637]: #638
#642 := [monotonicity #613 #639]: #641
#594 := (iff #161 #593)
#591 := (iff #160 #588)
#584 := (implies #153 #581)
#589 := (iff #584 #588)
#590 := [rewrite]: #589
#585 := (iff #160 #584)
#582 := (iff #159 #581)
#579 := (iff #158 #578)
#576 := (iff #157 #575)
#577 := [monotonicity #574]: #576
#580 := [monotonicity #577]: #579
#583 := [quant-intro #580]: #582
#586 := [monotonicity #583]: #585
#592 := [trans #586 #590]: #591
#595 := [quant-intro #592]: #594
#645 := [monotonicity #595 #642]: #644
#651 := [trans #645 #649]: #650
#654 := [monotonicity #595 #651]: #653
#657 := [monotonicity #654]: #656
#661 := [trans #657 #659]: #660
#664 := [monotonicity #661]: #663
#670 := [trans #664 #668]: #669
#570 := (iff #147 #569)
#571 := [rewrite]: #570
#673 := [monotonicity #571 #670]: #672
#679 := [trans #673 #677]: #678
#682 := [monotonicity #679]: #681
#688 := [trans #682 #686]: #687
#567 := (iff #142 #566)
#568 := [rewrite]: #567
#691 := [monotonicity #568 #688]: #690
#697 := [trans #691 #695]: #696
#700 := [monotonicity #697]: #699
#704 := [trans #700 #702]: #703
#706 := [monotonicity #704]: #705
#708 := [trans #706 #702]: #707
#564 := (iff #140 #563)
#565 := [monotonicity #562]: #564
#711 := [monotonicity #565 #708]: #710
#716 := [trans #711 #714]: #715
#719 := [monotonicity #716]: #718
#723 := [trans #719 #721]: #722
#725 := [monotonicity #723]: #724
#727 := [trans #725 #721]: #726
#1034 := [monotonicity #727 #1031]: #1033
#1037 := [monotonicity #1034]: #1036
#1041 := [trans #1037 #1039]: #1040
#550 := (iff #137 #549)
#547 := (iff #136 #544)
#540 := (implies #130 #537)
#545 := (iff #540 #544)
#546 := [rewrite]: #545
#541 := (iff #136 #540)
#538 := (iff #135 #537)
#535 := (iff #134 #534)
#532 := (iff #133 #531)
#529 := (iff #132 #528)
#511 := (= #125 #510)
#512 := [rewrite]: #511
#530 := [monotonicity #512]: #529
#533 := [monotonicity #480 #530]: #532
#536 := [monotonicity #533]: #535
#539 := [quant-intro #536]: #538
#542 := [monotonicity #539]: #541
#548 := [trans #542 #546]: #547
#551 := [quant-intro #548]: #550
#1044 := [monotonicity #551 #1041]: #1043
#1050 := [trans #1044 #1048]: #1049
#526 := (iff #128 #525)
#523 := (iff #127 #520)
#516 := (implies #505 #513)
#521 := (iff #516 #520)
#522 := [rewrite]: #521
#517 := (iff #127 #516)
#514 := (iff #126 #513)
#515 := [monotonicity #512]: #514
#508 := (iff #124 #505)
#502 := (and #478 #92)
#506 := (iff #502 #505)
#507 := [rewrite]: #506
#503 := (iff #124 #502)
#504 := [monotonicity #480]: #503
#509 := [trans #504 #507]: #508
#518 := [monotonicity #509 #515]: #517
#524 := [trans #518 #522]: #523
#527 := [quant-intro #524]: #526
#1053 := [monotonicity #527 #1050]: #1052
#1059 := [trans #1053 #1057]: #1058
#500 := (iff #123 #499)
#497 := (iff #122 #494)
#490 := (implies #487 #121)
#495 := (iff #490 #494)
#496 := [rewrite]: #495
#491 := (iff #122 #490)
#488 := (iff #119 #487)
#485 := (iff #118 #484)
#486 := [rewrite]: #485
#489 := [monotonicity #483 #486]: #488
#492 := [monotonicity #489]: #491
#498 := [trans #492 #496]: #497
#501 := [quant-intro #498]: #500
#1062 := [monotonicity #501 #1059]: #1061
#1068 := [trans #1062 #1066]: #1067
#1071 := [monotonicity #1068]: #1070
#1077 := [trans #1071 #1075]: #1076
#476 := (iff #109 #475)
#477 := [rewrite]: #476
#1080 := [monotonicity #477 #1077]: #1079
#1086 := [trans #1080 #1084]: #1085
#1089 := [monotonicity #1086]: #1088
#1093 := [trans #1089 #1091]: #1092
#1095 := [monotonicity #1093]: #1094
#1097 := [trans #1095 #1091]: #1096
#473 := (iff #106 #472)
#470 := (iff #105 #469)
#471 := [rewrite]: #470
#474 := [quant-intro #471]: #473
#1100 := [monotonicity #474 #1097]: #1099
#1106 := [trans #1100 #1104]: #1105
#1109 := [monotonicity #474 #1106]: #1108
#466 := (iff #97 #465)
#463 := (iff #96 #462)
#464 := [rewrite]: #463
#467 := [quant-intro #464]: #466
#1112 := [monotonicity #467 #1109]: #1111
#1118 := [trans #1112 #1116]: #1117
#1121 := [monotonicity #467 #1118]: #1120
#459 := (iff #89 #458)
#456 := (iff #88 #455)
#457 := [rewrite]: #456
#460 := [quant-intro #457]: #459
#1124 := [monotonicity #460 #1121]: #1123
#1130 := [trans #1124 #1128]: #1129
#1133 := [monotonicity #460 #1130]: #1132
#1136 := [monotonicity #1133]: #1135
#1142 := [trans #1136 #1140]: #1141
#1145 := [monotonicity #1142]: #1144
#452 := (iff #81 #451)
#453 := [rewrite]: #452
#1148 := [monotonicity #453 #1145]: #1147
#1154 := [trans #1148 #1152]: #1153
#1157 := [monotonicity #453 #1154]: #1156
#1160 := [monotonicity #1157]: #1159
#1164 := [trans #1160 #1162]: #1163
#1167 := [monotonicity #1164]: #1166
#1173 := [trans #1167 #1171]: #1172
#449 := (iff #76 #448)
#446 := (iff #75 #443)
#440 := (implies #73 #437)
#444 := (iff #440 #443)
#445 := [rewrite]: #444
#441 := (iff #75 #440)
#438 := (iff #74 #437)
#439 := [rewrite]: #438
#442 := [monotonicity #439]: #441
#447 := [trans #442 #445]: #446
#450 := [quant-intro #447]: #449
#1176 := [monotonicity #450 #1173]: #1175
#1182 := [trans #1176 #1180]: #1181
#435 := (iff #72 #434)
#432 := (iff #71 #429)
#426 := (implies #68 #423)
#430 := (iff #426 #429)
#431 := [rewrite]: #430
#427 := (iff #71 #426)
#424 := (iff #70 #423)
#425 := [rewrite]: #424
#428 := [monotonicity #425]: #427
#433 := [trans #428 #431]: #432
#436 := [quant-intro #433]: #435
#1185 := [monotonicity #436 #1182]: #1184
#1191 := [trans #1185 #1189]: #1190
#1194 := [monotonicity #1191]: #1193
#1198 := [trans #1194 #1196]: #1197
#1200 := [monotonicity #1198]: #1199
#1202 := [trans #1200 #1196]: #1201
#1205 := [monotonicity #1202]: #1204
#1834 := [trans #1205 #1832]: #1833
#422 := [asserted]: #293
#1835 := [mp #422 #1834]: #1830
#1837 := [not-or-elim #1835]: #448
#1902 := [mp~ #1837 #1863]: #448
#4263 := [mp #1902 #4262]: #4258
#4706 := (not #4258)
#5054 := (or #4706 #2574 #5019)
#1992 := (= ?x37!5 uf_11)
#5025 := (or #1992 #5019)
#5056 := (or #4706 #5025)
#5111 := (iff #5056 #5054)
#5048 := (or #2574 #5019)
#5057 := (or #4706 #5048)
#5087 := (iff #5057 #5054)
#5088 := [rewrite]: #5087
#5059 := (iff #5056 #5057)
#5049 := (iff #5025 #5048)
#2575 := (iff #1992 #2574)
#2576 := [rewrite]: #2575
#5053 := [monotonicity #2576]: #5049
#5060 := [monotonicity #5053]: #5059
#5120 := [trans #5060 #5088]: #5111
#5047 := [quant-inst]: #5056
#5121 := [mp #5047 #5120]: #5054
#5195 := [unit-resolution #5121 #4263 #5192 #5194]: false
#5196 := [lemma #5195]: #4299
#4585 := (or #4302 #4582)
#4588 := (not #4585)
#3123 := (or #78 #1237 #1248)
#4282 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #4281) #3123)
#4287 := (not #4282)
#4591 := (or #4287 #4588)
#4594 := (not #4591)
decl ?x34!3 :: T2
#1946 := ?x34!3
#1953 := (uf_12 ?x34!3)
decl ?x33!4 :: T2
#1947 := ?x33!4
#1950 := (uf_12 ?x33!4)
#1951 := (* -1::int #1950)
#2561 := (+ #1951 #1953)
#1948 := (uf_1 ?x34!3 ?x33!4)
#1949 := (uf_10 #1948)
#2562 := (+ #1949 #2561)
#2565 := (>= #2562 0::int)
#1960 := (up_13 ?x34!3)
#3086 := (not #1960)
#1956 := (* -1::int #1949)
#1957 := (+ uf_9 #1956)
#1958 := (<= #1957 0::int)
#3101 := (or #1958 #3086 #2565)
#5147 := [hypothesis]: #1960
#4251 := (forall (vars (?x26 T2)) (:pat #4250) #78)
#4254 := (iff #79 #4251)
#4252 := (iff #78 #78)
#4253 := [refl]: #4252
#4255 := [quant-intro #4253]: #4254
#1860 := (~ #79 #79)
#1897 := (~ #78 #78)
#1898 := [refl]: #1897
#1861 := [nnf-pos #1898]: #1860
#1836 := [not-or-elim #1835]: #79
#1899 := [mp~ #1836 #1861]: #79
#4256 := [mp #1899 #4255]: #4251
#4844 := (not #4251)
#4845 := (or #4844 #3086)
#4846 := [quant-inst]: #4845
#5148 := [unit-resolution #4846 #4256 #5147]: false
#5157 := [lemma #5148]: #3086
#3862 := (or #3101 #1960)
#3866 := [def-axiom]: #3862
#4921 := [unit-resolution #3866 #5157]: #3101
#3106 := (not #3101)
#4597 := (or #3106 #4594)
#4600 := (not #4597)
#4272 := (pattern #77 #84)
#2527 := (not #84)
#3078 := (or #77 #2527 #1222)
#4273 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #4272) #3078)
#4278 := (not #4273)
#4603 := (or #4278 #4600)
#4606 := (not #4603)
decl ?x30!1 :: T2
#1921 := ?x30!1
#1925 := (uf_12 ?x30!1)
#2542 := (* -1::int #1925)
decl ?x29!2 :: T2
#1922 := ?x29!2
#1923 := (uf_12 ?x29!2)
#2543 := (+ #1923 #2542)
#2544 := (<= #2543 0::int)
#1929 := (up_13 ?x30!1)
#1928 := (up_13 ?x29!2)
#1968 := (not #1928)
#2171 := (or #1968 #1929 #2544)
#2248 := (not #2171)
#4609 := (or #2248 #4606)
#4612 := (not #4609)
#4264 := (forall (vars (?x27 T2)) (:pat #4257) #1213)
#4269 := (not #4264)
#4615 := (or #4269 #4612)
#4618 := (not #4615)
decl ?x27!0 :: T2
#1906 := ?x27!0
#1907 := (uf_12 ?x27!0)
#1908 := (>= #1907 0::int)
#1909 := (not #1908)
#4621 := (or #1909 #4618)
#4624 := (not #4621)
#4627 := (or #1208 #4624)
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#3627 := (iff #3619 #3626)
#3628 := [rewrite]: #3627
#3620 := (iff #3021 #3619)
#3617 := (iff #3015 #3616)
#3614 := (iff #3012 #3611)
#3606 := (and #1484 #3603)
#3612 := (iff #3606 #3611)
#3613 := [rewrite]: #3612
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#3604 := (iff #3009 #3603)
#3601 := (iff #3006 #3598)
#3593 := (and #785 #3590)
#3599 := (iff #3593 #3598)
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#3591 := (iff #3003 #3590)
#3588 := (iff #3000 #3585)
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#3586 := (iff #3580 #3585)
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#3578 := (iff #2997 #3577)
#3575 := (iff #2994 #3572)
#3567 := (and #1498 #3564)
#3573 := (iff #3567 #3572)
#3574 := [rewrite]: #3573
#3568 := (iff #2994 #3567)
#3565 := (iff #2991 #3564)
#3562 := (iff #2988 #3559)
#3553 := (and #3476 #3550)
#3560 := (iff #3553 #3559)
#3561 := [rewrite]: #3560
#3554 := (iff #2988 #3553)
#3551 := (iff #2985 #3550)
#3548 := (iff #2980 #3545)
#3539 := (and #3521 #2368 #2937 #3536)
#3546 := (iff #3539 #3545)
#3547 := [rewrite]: #3546
#3540 := (iff #2980 #3539)
#3537 := (iff #2971 #3536)
#3534 := (iff #2968 #3525)
#3526 := (not #3525)
#3529 := (not #3526)
#3532 := (iff #3529 #3525)
#3533 := [rewrite]: #3532
#3530 := (iff #2968 #3529)
#3527 := (iff #2965 #3526)
#3528 := [rewrite]: #3527
#3531 := [monotonicity #3528]: #3530
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#3538 := [quant-intro #3535]: #3537
#3522 := (iff #1541 #3521)
#3519 := (iff #1538 #3516)
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#3513 := (or #3502 #1534)
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#3518 := [rewrite]: #3517
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#3510 := [rewrite]: #3509
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#3512 := [trans #3508 #3510]: #3511
#3515 := [monotonicity #3512]: #3514
#3520 := [trans #3515 #3518]: #3519
#3523 := [quant-intro #3520]: #3522
#3541 := [monotonicity #3523 #3538]: #3540
#3549 := [trans #3541 #3547]: #3548
#3500 := (iff #2931 #3499)
#3497 := (iff #2928 #3494)
#3480 := (or #2335 #3479)
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#3496 := [rewrite]: #3495
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#3489 := (iff #2910 #3480)
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#3488 := [rewrite]: #3487
#3485 := (iff #2910 #3484)
#3482 := (iff #2907 #3481)
#3483 := [rewrite]: #3482
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#3490 := [trans #3486 #3488]: #3489
#3493 := [monotonicity #3490]: #3492
#3498 := [trans #3493 #3496]: #3497
#3501 := [monotonicity #3498]: #3500
#3552 := [monotonicity #3501 #3549]: #3551
#3477 := (iff #1517 #3476)
#3474 := (iff #1512 #3471)
#3457 := (or #773 #3456)
#3468 := (or #3457 #1504)
#3472 := (iff #3468 #3471)
#3473 := [rewrite]: #3472
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#3466 := (iff #802 #3457)
#3458 := (not #3457)
#3461 := (not #3458)
#3464 := (iff #3461 #3457)
#3465 := [rewrite]: #3464
#3462 := (iff #802 #3461)
#3459 := (iff #796 #3458)
#3460 := [rewrite]: #3459
#3463 := [monotonicity #3460]: #3462
#3467 := [trans #3463 #3465]: #3466
#3470 := [monotonicity #3467]: #3469
#3475 := [trans #3470 #3473]: #3474
#3478 := [quant-intro #3475]: #3477
#3555 := [monotonicity #3478 #3552]: #3554
#3563 := [trans #3555 #3561]: #3562
#3454 := (iff #2904 #3453)
#3451 := (iff #2901 #3448)
#3434 := (or #3433 #2306)
#3445 := (or #3434 #2896)
#3449 := (iff #3445 #3448)
#3450 := [rewrite]: #3449
#3446 := (iff #2901 #3445)
#3443 := (iff #2885 #3434)
#3435 := (not #3434)
#3438 := (not #3435)
#3441 := (iff #3438 #3434)
#3442 := [rewrite]: #3441
#3439 := (iff #2885 #3438)
#3436 := (iff #2882 #3435)
#3437 := [rewrite]: #3436
#3440 := [monotonicity #3437]: #3439
#3444 := [trans #3440 #3442]: #3443
#3447 := [monotonicity #3444]: #3446
#3452 := [trans #3447 #3450]: #3451
#3455 := [monotonicity #3452]: #3454
#3566 := [monotonicity #3455 #3563]: #3565
#3569 := [monotonicity #3566]: #3568
#3576 := [trans #3569 #3574]: #3575
#3579 := [monotonicity #3576]: #3578
#3582 := [monotonicity #3579]: #3581
#3589 := [trans #3582 #3587]: #3588
#3592 := [monotonicity #3589]: #3591
#3595 := [monotonicity #3592]: #3594
#3602 := [trans #3595 #3600]: #3601
#3605 := [monotonicity #3602]: #3604
#3608 := [monotonicity #3605]: #3607
#3615 := [trans #3608 #3613]: #3614
#3618 := [monotonicity #3615]: #3617
#3431 := (iff #1631 #3430)
#3428 := (iff #1628 #3425)
#3422 := (or #3405 #1625)
#3426 := (iff #3422 #3425)
#3427 := [rewrite]: #3426
#3423 := (iff #1628 #3422)
#3420 := (iff #1620 #3405)
#3415 := (not #3406)
#3418 := (iff #3415 #3405)
#3419 := [rewrite]: #3418
#3416 := (iff #1620 #3415)
#3407 := (iff #1462 #3406)
#3408 := [rewrite]: #3407
#3417 := [monotonicity #3408]: #3416
#3421 := [trans #3417 #3419]: #3420
#3424 := [monotonicity #3421]: #3423
#3429 := [trans #3424 #3427]: #3428
#3432 := [quant-intro #3429]: #3431
#3413 := (iff #1473 #3412)
#3410 := (iff #1468 #3409)
#3411 := [monotonicity #3408]: #3410
#3414 := [quant-intro #3411]: #3413
#3621 := [monotonicity #3414 #3432 #3618]: #3620
#3630 := [trans #3621 #3628]: #3629
#3403 := (iff #2843 #3400)
#3394 := (and #145 #150 #566 #569 #3268 #3391)
#3401 := (iff #3394 #3400)
#3402 := [rewrite]: #3401
#3395 := (iff #2843 #3394)
#3392 := (iff #2837 #3391)
#3389 := (iff #2834 #3386)
#3380 := (and #3320 #3377)
#3387 := (iff #3380 #3386)
#3388 := [rewrite]: #3387
#3381 := (iff #2834 #3380)
#3378 := (iff #2829 #3377)
#3375 := (iff #2823 #3374)
#3372 := (iff #2820 #3369)
#3355 := (or #2159 #2163)
#3366 := (or #3355 #2815)
#3370 := (iff #3366 #3369)
#3371 := [rewrite]: #3370
#3367 := (iff #2820 #3366)
#3364 := (iff #2803 #3355)
#3356 := (not #3355)
#3359 := (not #3356)
#3362 := (iff #3359 #3355)
#3363 := [rewrite]: #3362
#3360 := (iff #2803 #3359)
#3357 := (iff #2800 #3356)
#3358 := [rewrite]: #3357
#3361 := [monotonicity #3358]: #3360
#3365 := [trans #3361 #3363]: #3364
#3368 := [monotonicity #3365]: #3367
#3373 := [trans #3368 #3371]: #3372
#3376 := [monotonicity #3373]: #3375
#3353 := (iff #2183 #3350)
#3345 := (and #2173 #3342)
#3351 := (iff #3345 #3350)
#3352 := [rewrite]: #3351
#3346 := (iff #2183 #3345)
#3343 := (iff #1393 #3342)
#3340 := (iff #1390 #3337)
#3323 := (or #1237 #1346)
#3334 := (or #3323 #1387)
#3338 := (iff #3334 #3337)
#3339 := [rewrite]: #3338
#3335 := (iff #1390 #3334)
#3332 := (iff #1384 #3323)
#3324 := (not #3323)
#3327 := (not #3324)
#3330 := (iff #3327 #3323)
#3331 := [rewrite]: #3330
#3328 := (iff #1384 #3327)
#3325 := (iff #1381 #3324)
#3326 := [rewrite]: #3325
#3329 := [monotonicity #3326]: #3328
#3333 := [trans #3329 #3331]: #3332
#3336 := [monotonicity #3333]: #3335
#3341 := [trans #3336 #3339]: #3340
#3344 := [quant-intro #3341]: #3343
#3347 := [monotonicity #3344]: #3346
#3354 := [trans #3347 #3352]: #3353
#3379 := [monotonicity #3354 #3376]: #3378
#3321 := (iff #2797 #3320)
#3318 := (iff #2794 #3315)
#3296 := (or #68 #1346)
#3312 := (or #3296 #3309)
#3316 := (iff #3312 #3315)
#3317 := [rewrite]: #3316
#3313 := (iff #2794 #3312)
#3310 := (iff #2791 #3309)
#3311 := [rewrite]: #3310
#3305 := (iff #1353 #3296)
#3297 := (not #3296)
#3300 := (not #3297)
#3303 := (iff #3300 #3296)
#3304 := [rewrite]: #3303
#3301 := (iff #1353 #3300)
#3298 := (iff #1350 #3297)
#3299 := [rewrite]: #3298
#3302 := [monotonicity #3299]: #3301
#3306 := [trans #3302 #3304]: #3305
#3314 := [monotonicity #3306 #3311]: #3313
#3319 := [trans #3314 #3317]: #3318
#3322 := [quant-intro #3319]: #3321
#3382 := [monotonicity #3322 #3379]: #3381
#3390 := [trans #3382 #3388]: #3389
#3294 := (iff #2755 #3291)
#3286 := (and #2098 #2715 #3283)
#3292 := (iff #3286 #3291)
#3293 := [rewrite]: #3292
#3287 := (iff #2755 #3286)
#3284 := (iff #2749 #3283)
#3281 := (iff #2746 #3272)
#3273 := (not #3272)
#3276 := (not #3273)
#3279 := (iff #3276 #3272)
#3280 := [rewrite]: #3279
#3277 := (iff #2746 #3276)
#3274 := (iff #2743 #3273)
#3275 := [rewrite]: #3274
#3278 := [monotonicity #3275]: #3277
#3282 := [trans #3278 #3280]: #3281
#3285 := [quant-intro #3282]: #3284
#3288 := [monotonicity #3285]: #3287
#3295 := [trans #3288 #3293]: #3294
#3393 := [monotonicity #3295 #3390]: #3392
#3269 := (iff #2202 #3268)
#3266 := (iff #2199 #3257)
#3258 := (not #3257)
#3261 := (not #3258)
#3264 := (iff #3261 #3257)
#3265 := [rewrite]: #3264
#3262 := (iff #2199 #3261)
#3259 := (iff #1421 #3258)
#3260 := [rewrite]: #3259
#3263 := [monotonicity #3260]: #3262
#3267 := [trans #3263 #3265]: #3266
#3270 := [quant-intro #3267]: #3269
#3396 := [monotonicity #3270 #3393]: #3395
#3404 := [trans #3396 #3402]: #3403
#3633 := [monotonicity #3404 #3630]: #3632
#3255 := (iff #2701 #3254)
#3252 := (iff #2698 #3249)
#3229 := (or #68 #1301)
#3246 := (or #3229 #3243)
#3250 := (iff #3246 #3249)
#3251 := [rewrite]: #3250
#3247 := (iff #2698 #3246)
#3244 := (iff #2695 #3243)
#3245 := [rewrite]: #3244
#3238 := (iff #1308 #3229)
#3230 := (not #3229)
#3233 := (not #3230)
#3236 := (iff #3233 #3229)
#3237 := [rewrite]: #3236
#3234 := (iff #1308 #3233)
#3231 := (iff #1305 #3230)
#3232 := [rewrite]: #3231
#3235 := [monotonicity #3232]: #3234
#3239 := [trans #3235 #3237]: #3238
#3248 := [monotonicity #3239 #3245]: #3247
#3253 := [trans #3248 #3251]: #3252
#3256 := [quant-intro #3253]: #3255
#3227 := (iff #2661 #3226)
#3224 := (iff #2658 #3221)
#3201 := (or #68 #1263)
#3218 := (or #3201 #3215)
#3222 := (iff #3218 #3221)
#3223 := [rewrite]: #3222
#3219 := (iff #2658 #3218)
#3216 := (iff #2655 #3215)
#3217 := [rewrite]: #3216
#3210 := (iff #1270 #3201)
#3202 := (not #3201)
#3205 := (not #3202)
#3208 := (iff #3205 #3201)
#3209 := [rewrite]: #3208
#3206 := (iff #1270 #3205)
#3203 := (iff #1267 #3202)
#3204 := [rewrite]: #3203
#3207 := [monotonicity #3204]: #3206
#3211 := [trans #3207 #3209]: #3210
#3220 := [monotonicity #3211 #3217]: #3219
#3225 := [trans #3220 #3223]: #3224
#3228 := [quant-intro #3225]: #3227
#3199 := (iff #1732 #3198)
#3196 := (iff #1727 #3193)
#3179 := (or #478 #3178)
#3190 := (or #3179 #1317)
#3194 := (iff #3190 #3193)
#3195 := [rewrite]: #3194
#3191 := (iff #1727 #3190)
#3188 := (iff #493 #3179)
#3180 := (not #3179)
#3183 := (not #3180)
#3186 := (iff #3183 #3179)
#3187 := [rewrite]: #3186
#3184 := (iff #493 #3183)
#3181 := (iff #487 #3180)
#3182 := [rewrite]: #3181
#3185 := [monotonicity #3182]: #3184
#3189 := [trans #3185 #3187]: #3188
#3192 := [monotonicity #3189]: #3191
#3197 := [trans #3192 #3195]: #3196
#3200 := [quant-intro #3197]: #3199
#3176 := (iff #1716 #3175)
#3173 := (iff #1713 #3170)
#3156 := (or #481 #1237)
#3167 := (or #3156 #1710)
#3171 := (iff #3167 #3170)
#3172 := [rewrite]: #3171
#3168 := (iff #1713 #3167)
#3165 := (iff #1707 #3156)
#3157 := (not #3156)
#3160 := (not #3157)
#3163 := (iff #3160 #3156)
#3164 := [rewrite]: #3163
#3161 := (iff #1707 #3160)
#3158 := (iff #1702 #3157)
#3159 := [rewrite]: #3158
#3162 := [monotonicity #3159]: #3161
#3166 := [trans #3162 #3164]: #3165
#3169 := [monotonicity #3166]: #3168
#3174 := [trans #3169 #3172]: #3173
#3177 := [quant-intro #3174]: #3176
#3636 := [monotonicity #3177 #3200 #3228 #3256 #3633]: #3635
#3647 := [trans #3636 #3645]: #3646
#3154 := (iff #2617 #3151)
#3146 := (and #1991 #2577 #3143)
#3152 := (iff #3146 #3151)
#3153 := [rewrite]: #3152
#3147 := (iff #2617 #3146)
#3144 := (iff #2611 #3143)
#3141 := (iff #2608 #3132)
#3133 := (not #3132)
#3136 := (not #3133)
#3139 := (iff #3136 #3132)
#3140 := [rewrite]: #3139
#3137 := (iff #2608 #3136)
#3134 := (iff #2605 #3133)
#3135 := [rewrite]: #3134
#3138 := [monotonicity #3135]: #3137
#3142 := [trans #3138 #3140]: #3141
#3145 := [quant-intro #3142]: #3144
#3148 := [monotonicity #3145]: #3147
#3155 := [trans #3148 #3153]: #3154
#3650 := [monotonicity #3155 #3647]: #3649
#3129 := (iff #1255 #3128)
#3126 := (iff #1252 #3123)
#3109 := (or #78 #1237)
#3120 := (or #3109 #1248)
#3124 := (iff #3120 #3123)
#3125 := [rewrite]: #3124
#3121 := (iff #1252 #3120)
#3118 := (iff #1244 #3109)
#3110 := (not #3109)
#3113 := (not #3110)
#3116 := (iff #3113 #3109)
#3117 := [rewrite]: #3116
#3114 := (iff #1244 #3113)
#3111 := (iff #1241 #3110)
#3112 := [rewrite]: #3111
#3115 := [monotonicity #3112]: #3114
#3119 := [trans #3115 #3117]: #3118
#3122 := [monotonicity #3119]: #3121
#3127 := [trans #3122 #3125]: #3126
#3130 := [quant-intro #3127]: #3129
#3653 := [monotonicity #3130 #3650]: #3652
#3661 := [trans #3653 #3659]: #3660
#3107 := (iff #2571 #3106)
#3104 := (iff #2568 #3101)
#3087 := (or #1958 #3086)
#3098 := (or #3087 #2565)
#3102 := (iff #3098 #3101)
#3103 := [rewrite]: #3102
#3099 := (iff #2568 #3098)
#3096 := (iff #2558 #3087)
#3088 := (not #3087)
#3091 := (not #3088)
#3094 := (iff #3091 #3087)
#3095 := [rewrite]: #3094
#3092 := (iff #2558 #3091)
#3089 := (iff #2555 #3088)
#3090 := [rewrite]: #3089
#3093 := [monotonicity #3090]: #3092
#3097 := [trans #3093 #3095]: #3096
#3100 := [monotonicity #3097]: #3099
#3105 := [trans #3100 #3103]: #3104
#3108 := [monotonicity #3105]: #3107
#3664 := [monotonicity #3108 #3661]: #3663
#3084 := (iff #1229 #3083)
#3081 := (iff #1226 #3078)
#3064 := (or #77 #2527)
#3075 := (or #3064 #1222)
#3079 := (iff #3075 #3078)
#3080 := [rewrite]: #3079
#3076 := (iff #1226 #3075)
#3073 := (iff #454 #3064)
#3065 := (not #3064)
#3068 := (not #3065)
#3071 := (iff #3068 #3064)
#3072 := [rewrite]: #3071
#3069 := (iff #454 #3068)
#3066 := (iff #85 #3065)
#3067 := [rewrite]: #3066
#3070 := [monotonicity #3067]: #3069
#3074 := [trans #3070 #3072]: #3073
#3077 := [monotonicity #3074]: #3076
#3082 := [trans #3077 #3080]: #3081
#3085 := [quant-intro #3082]: #3084
#3667 := [monotonicity #3085 #3664]: #3666
#3675 := [trans #3667 #3673]: #3674
#2345 := (iff #2552 #2248)
#2137 := (iff #2549 #2171)
#1937 := (or #1968 #1929)
#2268 := (or #1937 #2544)
#2172 := (iff #2268 #2171)
#2136 := [rewrite]: #2172
#2226 := (iff #2549 #2268)
#2035 := (iff #2533 #1937)
#1868 := (not #1937)
#2314 := (not #1868)
#1913 := (iff #2314 #1937)
#2034 := [rewrite]: #1913
#2315 := (iff #2533 #2314)
#1869 := (iff #2530 #1868)
#1938 := [rewrite]: #1869
#1912 := [monotonicity #1938]: #2315
#2267 := [trans #1912 #2034]: #2035
#2227 := [monotonicity #2267]: #2226
#2247 := [trans #2227 #2136]: #2137
#2346 := [monotonicity #2247]: #2345
#3678 := [monotonicity #2346 #3675]: #3677
#3681 := [monotonicity #3678]: #3680
#3688 := [trans #3681 #3686]: #3687
#3691 := [monotonicity #3688]: #3690
#3694 := [monotonicity #3691]: #3693
#3701 := [trans #3694 #3699]: #3700
#3704 := [monotonicity #3701]: #3703
#2360 := (+ #2359 #2357)
#2361 := (= #2360 0::int)
#2364 := (and #773 #2363 #2361)
#2381 := (not #2364)
#2384 := (forall (vars (?x76 T2)) #2381)
#2369 := (= ?x75!20 uf_11)
#2370 := (not #2369)
#2371 := (and #2370 #2368)
#2372 := (not #2371)
#2378 := (not #2372)
#2388 := (and #2378 #2384)
#2393 := (and #1541 #2388)
#2326 := (* -1::int #2325)
#2328 := (+ #2327 #2326)
#2331 := (+ #2330 #2328)
#2332 := (>= #2331 0::int)
#2339 := (and #2338 #2336)
#2340 := (not #2339)
#2341 := (or #2340 #2332)
#2342 := (not #2341)
#2397 := (or #2342 #2393)
#2401 := (and #1517 #2397)
#2299 := (* -1::int #2298)
#2301 := (+ #2300 #2299)
#2302 := (>= #2301 0::int)
#2308 := (and #2307 #2304)
#2309 := (not #2308)
#2310 := (or #2309 #2302)
#2311 := (not #2310)
#2405 := (or #2311 #2401)
#2409 := (and #1498 #2405)
#2413 := (or #2284 #2409)
#2278 := (not #1492)
#2417 := (and #2278 #2413)
#2421 := (or #1492 #2417)
#2425 := (and #785 #2421)
#2262 := (= #2261 #2260)
#2263 := (or #2262 #2259)
#2264 := (not #2263)
#2429 := (or #2264 #2425)
#2433 := (and #1484 #2429)
#2240 := (* -1::int #2239)
#2242 := (+ #2241 #2240)
#2243 := (>= #2242 0::int)
#2244 := (not #2243)
#2437 := (or #2244 #2433)
#2223 := (and #2222 #2219)
#2209 := (not #981)
#2457 := (and #2209 #731 #2223 #1473 #2437 #1631 #1649 #1657)
#2150 := (* -1::int #2149)
#2152 := (+ #2151 #2150)
#2155 := (+ #2154 #2152)
#2156 := (>= #2155 0::int)
#2165 := (and #2164 #2160)
#2166 := (not #2165)
#2167 := (or #2166 #2156)
#2168 := (not #2167)
#2187 := (or #2168 #2183)
#2126 := (+ #2125 #1344)
#2129 := (+ #2128 #2126)
#2130 := (= #2129 0::int)
#2131 := (>= #2126 0::int)
#2132 := (not #2131)
#2133 := (and #2132 #2130)
#2138 := (or #1353 #2133)
#2141 := (forall (vars (?x49 T2)) #2138)
#2191 := (and #2141 #2187)
#2090 := (+ #2089 #2087)
#2091 := (= #2090 0::int)
#2094 := (and #2093 #2091)
#2110 := (not #2094)
#2113 := (forall (vars (?x50 T2)) #2110)
#2099 := (= ?x49!8 uf_11)
#2100 := (not #2099)
#2101 := (and #2100 #2098)
#2102 := (not #2101)
#2107 := (not #2102)
#2117 := (and #2107 #2113)
#2195 := (or #2117 #2191)
#2081 := (not #674)
#2078 := (not #692)
#2075 := (not #665)
#2072 := (not #683)
#2205 := (and #2072 #2075 #2078 #2081 #2195 #2202)
#2461 := (or #2205 #2457)
#2049 := (+ #2048 #1299)
#2050 := (>= #2049 0::int)
#2051 := (not #2050)
#2054 := (+ #2053 #2049)
#2055 := (= #2054 0::int)
#2058 := (and #2057 #2055 #2051)
#2063 := (or #1308 #2058)
#2066 := (forall (vars (?x46 T2)) #2063)
#2023 := (+ #1261 #2022)
#2025 := (+ #2024 #2023)
#2026 := (= #2025 0::int)
#2027 := (+ #2024 #1261)
#2028 := (>= #2027 0::int)
#2029 := (not #2028)
#2031 := (and #2030 #2029 #2026)
#2036 := (or #1270 #2031)
#2039 := (forall (vars (?x37 T2)) #2036)
#2015 := (not #1749)
#2486 := (and #2015 #2039 #2066 #2461 #1716 #1732 #1741)
#1981 := (+ #1980 #1978)
#1982 := (+ #69 #1981)
#1983 := (= #1982 0::int)
#1987 := (and #77 #1986 #1983)
#2003 := (not #1987)
#2006 := (forall (vars (?x38 T2)) #2003)
#1993 := (not #1992)
#1994 := (and #1993 #1991)
#1995 := (not #1994)
#2000 := (not #1995)
#2010 := (and #2000 #2006)
#2490 := (or #2010 #2486)
#2494 := (and #1255 #2490)
#1952 := (+ #1951 #1949)
#1954 := (+ #1953 #1952)
#1955 := (>= #1954 0::int)
#1961 := (and #1960 #1959)
#1962 := (not #1961)
#1963 := (or #1962 #1955)
#1964 := (not #1963)
#2498 := (or #1964 #2494)
#2502 := (and #1229 #2498)
#1924 := (* -1::int #1923)
#1926 := (+ #1925 #1924)
#1927 := (>= #1926 0::int)
#1931 := (and #1930 #1928)
#1932 := (not #1931)
#1933 := (or #1932 #1927)
#1934 := (not #1933)
#2506 := (or #1934 #2502)
#2510 := (and #1214 #2506)
#2514 := (or #1909 #2510)
#1864 := (not #1208)
#2518 := (and #1864 #2514)
#2522 := (or #1208 #2518)
#3062 := (iff #2522 #3061)
#3059 := (iff #2518 #3058)
#3056 := (iff #2514 #3055)
#3053 := (iff #2510 #3052)
#3050 := (iff #2506 #3049)
#3047 := (iff #2502 #3046)
#3044 := (iff #2498 #3043)
#3041 := (iff #2494 #3040)
#3038 := (iff #2490 #3037)
#3035 := (iff #2486 #3032)
#3029 := (and #109 #2661 #2701 #3026 #1716 #1732 #1741)
#3033 := (iff #3029 #3032)
#3034 := [rewrite]: #3033
#3030 := (iff #2486 #3029)
#3027 := (iff #2461 #3026)
#3024 := (iff #2457 #3021)
#3018 := (and #195 #731 #2223 #1473 #3015 #1631 #1649 #1657)
#3022 := (iff #3018 #3021)
#3023 := [rewrite]: #3022
#3019 := (iff #2457 #3018)
#3016 := (iff #2437 #3015)
#3013 := (iff #2433 #3012)
#3010 := (iff #2429 #3009)
#3007 := (iff #2425 #3006)
#3004 := (iff #2421 #3003)
#3001 := (iff #2417 #3000)
#2998 := (iff #2413 #2997)
#2995 := (iff #2409 #2994)
#2992 := (iff #2405 #2991)
#2989 := (iff #2401 #2988)
#2986 := (iff #2397 #2985)
#2983 := (iff #2393 #2980)
#2943 := (and #2368 #2937)
#2974 := (and #2943 #2971)
#2977 := (and #1541 #2974)
#2981 := (iff #2977 #2980)
#2982 := [rewrite]: #2981
#2978 := (iff #2393 #2977)
#2975 := (iff #2388 #2974)
#2972 := (iff #2384 #2971)
#2969 := (iff #2381 #2968)
#2966 := (iff #2364 #2965)
#2963 := (iff #2361 #2962)
#2960 := (= #2360 #2959)
#2961 := [rewrite]: #2960
#2964 := [monotonicity #2961]: #2963
#2967 := [monotonicity #2964]: #2966
#2970 := [monotonicity #2967]: #2969
#2973 := [quant-intro #2970]: #2972
#2956 := (iff #2378 #2943)
#2948 := (not #2943)
#2951 := (not #2948)
#2954 := (iff #2951 #2943)
#2955 := [rewrite]: #2954
#2952 := (iff #2378 #2951)
#2949 := (iff #2372 #2948)
#2946 := (iff #2371 #2943)
#2940 := (and #2937 #2368)
#2944 := (iff #2940 #2943)
#2945 := [rewrite]: #2944
#2941 := (iff #2371 #2940)
#2938 := (iff #2370 #2937)
#2935 := (iff #2369 #2934)
#2936 := [rewrite]: #2935
#2939 := [monotonicity #2936]: #2938
#2942 := [monotonicity #2939]: #2941
#2947 := [trans #2942 #2945]: #2946
#2950 := [monotonicity #2947]: #2949
#2953 := [monotonicity #2950]: #2952
#2957 := [trans #2953 #2955]: #2956
#2976 := [monotonicity #2957 #2973]: #2975
#2979 := [monotonicity #2976]: #2978
#2984 := [trans #2979 #2982]: #2983
#2932 := (iff #2342 #2931)
#2929 := (iff #2341 #2928)
#2926 := (iff #2332 #2923)
#2913 := (+ #2327 #2330)
#2914 := (+ #2326 #2913)
#2917 := (>= #2914 0::int)
#2924 := (iff #2917 #2923)
#2925 := [rewrite]: #2924
#2918 := (iff #2332 #2917)
#2915 := (= #2331 #2914)
#2916 := [rewrite]: #2915
#2919 := [monotonicity #2916]: #2918
#2927 := [trans #2919 #2925]: #2926
#2911 := (iff #2340 #2910)
#2908 := (iff #2339 #2907)
#2909 := [rewrite]: #2908
#2912 := [monotonicity #2909]: #2911
#2930 := [monotonicity #2912 #2927]: #2929
#2933 := [monotonicity #2930]: #2932
#2987 := [monotonicity #2933 #2984]: #2986
#2990 := [monotonicity #2987]: #2989
#2905 := (iff #2311 #2904)
#2902 := (iff #2310 #2901)
#2899 := (iff #2302 #2896)
#2888 := (+ #2299 #2300)
#2891 := (>= #2888 0::int)
#2897 := (iff #2891 #2896)
#2898 := [rewrite]: #2897
#2892 := (iff #2302 #2891)
#2889 := (= #2301 #2888)
#2890 := [rewrite]: #2889
#2893 := [monotonicity #2890]: #2892
#2900 := [trans #2893 #2898]: #2899
#2886 := (iff #2309 #2885)
#2883 := (iff #2308 #2882)
#2884 := [rewrite]: #2883
#2887 := [monotonicity #2884]: #2886
#2903 := [monotonicity #2887 #2900]: #2902
#2906 := [monotonicity #2903]: #2905
#2993 := [monotonicity #2906 #2990]: #2992
#2996 := [monotonicity #2993]: #2995
#2999 := [monotonicity #2996]: #2998
#2880 := (iff #2278 #217)
#2881 := [rewrite]: #2880
#3002 := [monotonicity #2881 #2999]: #3001
#3005 := [monotonicity #3002]: #3004
#3008 := [monotonicity #3005]: #3007
#2878 := (iff #2264 #2877)
#2875 := (iff #2263 #2872)
#2869 := (or #2866 #2259)
#2873 := (iff #2869 #2872)
#2874 := [rewrite]: #2873
#2870 := (iff #2263 #2869)
#2867 := (iff #2262 #2866)
#2868 := [rewrite]: #2867
#2871 := [monotonicity #2868]: #2870
#2876 := [trans #2871 #2874]: #2875
#2879 := [monotonicity #2876]: #2878
#3011 := [monotonicity #2879 #3008]: #3010
#3014 := [monotonicity #3011]: #3013
#2864 := (iff #2244 #2863)
#2861 := (iff #2243 #2858)
#2850 := (+ #2240 #2241)
#2853 := (>= #2850 0::int)
#2859 := (iff #2853 #2858)
#2860 := [rewrite]: #2859
#2854 := (iff #2243 #2853)
#2851 := (= #2242 #2850)
#2852 := [rewrite]: #2851
#2855 := [monotonicity #2852]: #2854
#2862 := [trans #2855 #2860]: #2861
#2865 := [monotonicity #2862]: #2864
#3017 := [monotonicity #2865 #3014]: #3016
#2848 := (iff #2209 #195)
#2849 := [rewrite]: #2848
#3020 := [monotonicity #2849 #3017]: #3019
#3025 := [trans #3020 #3023]: #3024
#2846 := (iff #2205 #2843)
#2840 := (and #145 #150 #566 #569 #2837 #2202)
#2844 := (iff #2840 #2843)
#2845 := [rewrite]: #2844
#2841 := (iff #2205 #2840)
#2838 := (iff #2195 #2837)
#2835 := (iff #2191 #2834)
#2832 := (iff #2187 #2829)
#2826 := (or #2823 #2183)
#2830 := (iff #2826 #2829)
#2831 := [rewrite]: #2830
#2827 := (iff #2187 #2826)
#2824 := (iff #2168 #2823)
#2821 := (iff #2167 #2820)
#2818 := (iff #2156 #2815)
#2806 := (+ #2151 #2154)
#2807 := (+ #2150 #2806)
#2810 := (>= #2807 0::int)
#2816 := (iff #2810 #2815)
#2817 := [rewrite]: #2816
#2811 := (iff #2156 #2810)
#2808 := (= #2155 #2807)
#2809 := [rewrite]: #2808
#2812 := [monotonicity #2809]: #2811
#2819 := [trans #2812 #2817]: #2818
#2804 := (iff #2166 #2803)
#2801 := (iff #2165 #2800)
#2802 := [rewrite]: #2801
#2805 := [monotonicity #2802]: #2804
#2822 := [monotonicity #2805 #2819]: #2821
#2825 := [monotonicity #2822]: #2824
#2828 := [monotonicity #2825]: #2827
#2833 := [trans #2828 #2831]: #2832
#2798 := (iff #2141 #2797)
#2795 := (iff #2138 #2794)
#2792 := (iff #2133 #2791)
#2789 := (iff #2130 #2786)
#2776 := (+ #2125 #2128)
#2777 := (+ #1344 #2776)
#2780 := (= #2777 0::int)
#2787 := (iff #2780 #2786)
#2788 := [rewrite]: #2787
#2781 := (iff #2130 #2780)
#2778 := (= #2129 #2777)
#2779 := [rewrite]: #2778
#2782 := [monotonicity #2779]: #2781
#2790 := [trans #2782 #2788]: #2789
#2774 := (iff #2132 #2773)
#2771 := (iff #2131 #2768)
#2760 := (+ #1344 #2125)
#2763 := (>= #2760 0::int)
#2769 := (iff #2763 #2768)
#2770 := [rewrite]: #2769
#2764 := (iff #2131 #2763)
#2761 := (= #2126 #2760)
#2762 := [rewrite]: #2761
#2765 := [monotonicity #2762]: #2764
#2772 := [trans #2765 #2770]: #2771
#2775 := [monotonicity #2772]: #2774
#2793 := [monotonicity #2775 #2790]: #2792
#2796 := [monotonicity #2793]: #2795
#2799 := [quant-intro #2796]: #2798
#2836 := [monotonicity #2799 #2833]: #2835
#2758 := (iff #2117 #2755)
#2721 := (and #2098 #2715)
#2752 := (and #2721 #2749)
#2756 := (iff #2752 #2755)
#2757 := [rewrite]: #2756
#2753 := (iff #2117 #2752)
#2750 := (iff #2113 #2749)
#2747 := (iff #2110 #2746)
#2744 := (iff #2094 #2743)
#2741 := (iff #2091 #2740)
#2738 := (= #2090 #2737)
#2739 := [rewrite]: #2738
#2742 := [monotonicity #2739]: #2741
#2745 := [monotonicity #2742]: #2744
#2748 := [monotonicity #2745]: #2747
#2751 := [quant-intro #2748]: #2750
#2734 := (iff #2107 #2721)
#2726 := (not #2721)
#2729 := (not #2726)
#2732 := (iff #2729 #2721)
#2733 := [rewrite]: #2732
#2730 := (iff #2107 #2729)
#2727 := (iff #2102 #2726)
#2724 := (iff #2101 #2721)
#2718 := (and #2715 #2098)
#2722 := (iff #2718 #2721)
#2723 := [rewrite]: #2722
#2719 := (iff #2101 #2718)
#2716 := (iff #2100 #2715)
#2713 := (iff #2099 #2712)
#2714 := [rewrite]: #2713
#2717 := [monotonicity #2714]: #2716
#2720 := [monotonicity #2717]: #2719
#2725 := [trans #2720 #2723]: #2724
#2728 := [monotonicity #2725]: #2727
#2731 := [monotonicity #2728]: #2730
#2735 := [trans #2731 #2733]: #2734
#2754 := [monotonicity #2735 #2751]: #2753
#2759 := [trans #2754 #2757]: #2758
#2839 := [monotonicity #2759 #2836]: #2838
#2710 := (iff #2081 #569)
#2711 := [rewrite]: #2710
#2708 := (iff #2078 #566)
#2709 := [rewrite]: #2708
#2706 := (iff #2075 #150)
#2707 := [rewrite]: #2706
#2704 := (iff #2072 #145)
#2705 := [rewrite]: #2704
#2842 := [monotonicity #2705 #2707 #2709 #2711 #2839]: #2841
#2847 := [trans #2842 #2845]: #2846
#3028 := [monotonicity #2847 #3025]: #3027
#2702 := (iff #2066 #2701)
#2699 := (iff #2063 #2698)
#2696 := (iff #2058 #2695)
#2693 := (iff #2051 #2692)
#2690 := (iff #2050 #2687)
#2680 := (+ #1299 #2048)
#2683 := (>= #2680 0::int)
#2688 := (iff #2683 #2687)
#2689 := [rewrite]: #2688
#2684 := (iff #2050 #2683)
#2681 := (= #2049 #2680)
#2682 := [rewrite]: #2681
#2685 := [monotonicity #2682]: #2684
#2691 := [trans #2685 #2689]: #2690
#2694 := [monotonicity #2691]: #2693
#2678 := (iff #2055 #2675)
#2664 := (+ #2048 #2053)
#2665 := (+ #1299 #2664)
#2668 := (= #2665 0::int)
#2676 := (iff #2668 #2675)
#2677 := [rewrite]: #2676
#2669 := (iff #2055 #2668)
#2666 := (= #2054 #2665)
#2667 := [rewrite]: #2666
#2670 := [monotonicity #2667]: #2669
#2679 := [trans #2670 #2677]: #2678
#2697 := [monotonicity #2679 #2694]: #2696
#2700 := [monotonicity #2697]: #2699
#2703 := [quant-intro #2700]: #2702
#2662 := (iff #2039 #2661)
#2659 := (iff #2036 #2658)
#2656 := (iff #2031 #2655)
#2653 := (iff #2026 #2650)
#2640 := (+ #2022 #2024)
#2641 := (+ #1261 #2640)
#2644 := (= #2641 0::int)
#2651 := (iff #2644 #2650)
#2652 := [rewrite]: #2651
#2645 := (iff #2026 #2644)
#2642 := (= #2025 #2641)
#2643 := [rewrite]: #2642
#2646 := [monotonicity #2643]: #2645
#2654 := [trans #2646 #2652]: #2653
#2638 := (iff #2029 #2637)
#2635 := (iff #2028 #2632)
#2624 := (+ #1261 #2024)
#2627 := (>= #2624 0::int)
#2633 := (iff #2627 #2632)
#2634 := [rewrite]: #2633
#2628 := (iff #2028 #2627)
#2625 := (= #2027 #2624)
#2626 := [rewrite]: #2625
#2629 := [monotonicity #2626]: #2628
#2636 := [trans #2629 #2634]: #2635
#2639 := [monotonicity #2636]: #2638
#2657 := [monotonicity #2639 #2654]: #2656
#2660 := [monotonicity #2657]: #2659
#2663 := [quant-intro #2660]: #2662
#2622 := (iff #2015 #109)
#2623 := [rewrite]: #2622
#3031 := [monotonicity #2623 #2663 #2703 #3028]: #3030
#3036 := [trans #3031 #3034]: #3035
#2620 := (iff #2010 #2617)
#2583 := (and #1991 #2577)
#2614 := (and #2583 #2611)
#2618 := (iff #2614 #2617)
#2619 := [rewrite]: #2618
#2615 := (iff #2010 #2614)
#2612 := (iff #2006 #2611)
#2609 := (iff #2003 #2608)
#2606 := (iff #1987 #2605)
#2603 := (iff #1983 #2602)
#2600 := (= #1982 #2599)
#2601 := [rewrite]: #2600
#2604 := [monotonicity #2601]: #2603
#2607 := [monotonicity #2604]: #2606
#2610 := [monotonicity #2607]: #2609
#2613 := [quant-intro #2610]: #2612
#2596 := (iff #2000 #2583)
#2588 := (not #2583)
#2591 := (not #2588)
#2594 := (iff #2591 #2583)
#2595 := [rewrite]: #2594
#2592 := (iff #2000 #2591)
#2589 := (iff #1995 #2588)
#2586 := (iff #1994 #2583)
#2580 := (and #2577 #1991)
#2584 := (iff #2580 #2583)
#2585 := [rewrite]: #2584
#2581 := (iff #1994 #2580)
#2578 := (iff #1993 #2577)
#2579 := [monotonicity #2576]: #2578
#2582 := [monotonicity #2579]: #2581
#2587 := [trans #2582 #2585]: #2586
#2590 := [monotonicity #2587]: #2589
#2593 := [monotonicity #2590]: #2592
#2597 := [trans #2593 #2595]: #2596
#2616 := [monotonicity #2597 #2613]: #2615
#2621 := [trans #2616 #2619]: #2620
#3039 := [monotonicity #2621 #3036]: #3038
#3042 := [monotonicity #3039]: #3041
#2572 := (iff #1964 #2571)
#2569 := (iff #1963 #2568)
#2566 := (iff #1955 #2565)
#2563 := (= #1954 #2562)
#2564 := [rewrite]: #2563
#2567 := [monotonicity #2564]: #2566
#2559 := (iff #1962 #2558)
#2556 := (iff #1961 #2555)
#2557 := [rewrite]: #2556
#2560 := [monotonicity #2557]: #2559
#2570 := [monotonicity #2560 #2567]: #2569
#2573 := [monotonicity #2570]: #2572
#3045 := [monotonicity #2573 #3042]: #3044
#3048 := [monotonicity #3045]: #3047
#2553 := (iff #1934 #2552)
#2550 := (iff #1933 #2549)
#2547 := (iff #1927 #2544)
#2536 := (+ #1924 #1925)
#2539 := (>= #2536 0::int)
#2545 := (iff #2539 #2544)
#2546 := [rewrite]: #2545
#2540 := (iff #1927 #2539)
#2537 := (= #1926 #2536)
#2538 := [rewrite]: #2537
#2541 := [monotonicity #2538]: #2540
#2548 := [trans #2541 #2546]: #2547
#2534 := (iff #1932 #2533)
#2531 := (iff #1931 #2530)
#2532 := [rewrite]: #2531
#2535 := [monotonicity #2532]: #2534
#2551 := [monotonicity #2535 #2548]: #2550
#2554 := [monotonicity #2551]: #2553
#3051 := [monotonicity #2554 #3048]: #3050
#3054 := [monotonicity #3051]: #3053
#3057 := [monotonicity #3054]: #3056
#2528 := (iff #1864 #81)
#2529 := [rewrite]: #2528
#3060 := [monotonicity #2529 #3057]: #3059
#3063 := [monotonicity #3060]: #3062
#1838 := (not #1802)
#2523 := (~ #1838 #2522)
#2519 := (not #1799)
#2520 := (~ #2519 #2518)
#2515 := (not #1796)
#2516 := (~ #2515 #2514)
#2511 := (not #1793)
#2512 := (~ #2511 #2510)
#2507 := (not #1790)
#2508 := (~ #2507 #2506)
#2503 := (not #1787)
#2504 := (~ #2503 #2502)
#2499 := (not #1784)
#2500 := (~ #2499 #2498)
#2495 := (not #1781)
#2496 := (~ #2495 #2494)
#2491 := (not #1778)
#2492 := (~ #2491 #2490)
#2487 := (not #1773)
#2488 := (~ #2487 #2486)
#2483 := (not #1744)
#2484 := (~ #2483 #1741)
#2481 := (~ #1741 #1741)
#2479 := (~ #1738 #1738)
#2480 := [refl]: #2479
#2482 := [nnf-pos #2480]: #2481
#2485 := [nnf-neg #2482]: #2484
#2476 := (not #1735)
#2477 := (~ #2476 #1732)
#2474 := (~ #1732 #1732)
#2472 := (~ #1727 #1727)
#2473 := [refl]: #2472
#2475 := [nnf-pos #2473]: #2474
#2478 := [nnf-neg #2475]: #2477
#2469 := (not #1719)
#2470 := (~ #2469 #1716)
#2467 := (~ #1716 #1716)
#2465 := (~ #1713 #1713)
#2466 := [refl]: #2465
#2468 := [nnf-pos #2466]: #2467
#2471 := [nnf-neg #2468]: #2470
#2462 := (not #1696)
#2463 := (~ #2462 #2461)
#2458 := (not #1691)
#2459 := (~ #2458 #2457)
#2455 := (~ #1657 #1657)
#2456 := [refl]: #2455
#2452 := (not #1652)
#2453 := (~ #2452 #1649)
#2450 := (~ #1649 #1649)
#2448 := (~ #1644 #1644)
#2449 := [refl]: #2448
#2451 := [nnf-pos #2449]: #2450
#2454 := [nnf-neg #2451]: #2453
#2445 := (not #1634)
#2446 := (~ #2445 #1631)
#2443 := (~ #1631 #1631)
#2441 := (~ #1628 #1628)
#2442 := [refl]: #2441
#2444 := [nnf-pos #2442]: #2443
#2447 := [nnf-neg #2444]: #2446
#2438 := (not #1617)
#2439 := (~ #2438 #2437)
#2434 := (not #1614)
#2435 := (~ #2434 #2433)
#2430 := (not #1611)
#2431 := (~ #2430 #2429)
#2426 := (not #1608)
#2427 := (~ #2426 #2425)
#2422 := (not #1605)
#2423 := (~ #2422 #2421)
#2418 := (not #1602)
#2419 := (~ #2418 #2417)
#2414 := (not #1599)
#2415 := (~ #2414 #2413)
#2410 := (not #1596)
#2411 := (~ #2410 #2409)
#2406 := (not #1593)
#2407 := (~ #2406 #2405)
#2402 := (not #1590)
#2403 := (~ #2402 #2401)
#2398 := (not #1587)
#2399 := (~ #2398 #2397)
#2394 := (not #1584)
#2395 := (~ #2394 #2393)
#2375 := (not #1581)
#2391 := (~ #2375 #2388)
#2365 := (exists (vars (?x76 T2)) #2364)
#2373 := (or #2372 #2365)
#2374 := (not #2373)
#2389 := (~ #2374 #2388)
#2385 := (not #2365)
#2386 := (~ #2385 #2384)
#2382 := (~ #2381 #2381)
#2383 := [refl]: #2382
#2387 := [nnf-neg #2383]: #2386
#2379 := (~ #2378 #2378)
#2380 := [refl]: #2379
#2390 := [nnf-neg #2380 #2387]: #2389
#2376 := (~ #2375 #2374)
#2377 := [sk]: #2376
#2392 := [trans #2377 #2390]: #2391
#2351 := (not #1544)
#2352 := (~ #2351 #1541)
#2349 := (~ #1541 #1541)
#2347 := (~ #1538 #1538)
#2348 := [refl]: #2347
#2350 := [nnf-pos #2348]: #2349
#2353 := [nnf-neg #2350]: #2352
#2396 := [nnf-neg #2353 #2392]: #2395
#2343 := (~ #1544 #2342)
#2344 := [sk]: #2343
#2400 := [nnf-neg #2344 #2396]: #2399
#2320 := (not #1520)
#2321 := (~ #2320 #1517)
#2318 := (~ #1517 #1517)
#2316 := (~ #1512 #1512)
#2317 := [refl]: #2316
#2319 := [nnf-pos #2317]: #2318
#2322 := [nnf-neg #2319]: #2321
#2404 := [nnf-neg #2322 #2400]: #2403
#2312 := (~ #1520 #2311)
#2313 := [sk]: #2312
#2408 := [nnf-neg #2313 #2404]: #2407
#2293 := (not #1501)
#2294 := (~ #2293 #1498)
#2291 := (~ #1498 #1498)
#2289 := (~ #1495 #1495)
#2290 := [refl]: #2289
#2292 := [nnf-pos #2290]: #2291
#2295 := [nnf-neg #2292]: #2294
#2412 := [nnf-neg #2295 #2408]: #2411
#2285 := (~ #1501 #2284)
#2286 := [sk]: #2285
#2416 := [nnf-neg #2286 #2412]: #2415
#2279 := (~ #2278 #2278)
#2280 := [refl]: #2279
#2420 := [nnf-neg #2280 #2416]: #2419
#2276 := (~ #1492 #1492)
#2277 := [refl]: #2276
#2424 := [nnf-neg #2277 #2420]: #2423
#2273 := (not #939)
#2274 := (~ #2273 #785)
#2271 := (~ #785 #785)
#2269 := (~ #780 #780)
#2270 := [refl]: #2269
#2272 := [nnf-pos #2270]: #2271
#2275 := [nnf-neg #2272]: #2274
#2428 := [nnf-neg #2275 #2424]: #2427
#2265 := (~ #939 #2264)
#2266 := [sk]: #2265
#2432 := [nnf-neg #2266 #2428]: #2431
#2253 := (not #1487)
#2254 := (~ #2253 #1484)
#2251 := (~ #1484 #1484)
#2249 := (~ #1479 #1479)
#2250 := [refl]: #2249
#2252 := [nnf-pos #2250]: #2251
#2255 := [nnf-neg #2252]: #2254
#2436 := [nnf-neg #2255 #2432]: #2435
#2245 := (~ #1487 #2244)
#2246 := [sk]: #2245
#2440 := [nnf-neg #2246 #2436]: #2439
#2235 := (not #1476)
#2236 := (~ #2235 #1473)
#2233 := (~ #1473 #1473)
#2231 := (~ #1468 #1468)
#2232 := [refl]: #2231
#2234 := [nnf-pos #2232]: #2233
#2237 := [nnf-neg #2234]: #2236
#2228 := (not #1667)
#2229 := (~ #2228 #2223)
#2224 := (~ #1426 #2223)
#2225 := [sk]: #2224
#2230 := [nnf-neg #2225]: #2229
#2212 := (~ #731 #731)
#2213 := [refl]: #2212
#2210 := (~ #2209 #2209)
#2211 := [refl]: #2210
#2460 := [nnf-neg #2211 #2213 #2230 #2237 #2440 #2447 #2454 #2456]: #2459
#2206 := (not #1444)
#2207 := (~ #2206 #2205)
#2203 := (~ #1667 #2202)
#2200 := (~ #2199 #2199)
#2201 := [refl]: #2200
#2204 := [nnf-neg #2201]: #2203
#2196 := (not #1415)
#2197 := (~ #2196 #2195)
#2192 := (not #1412)
#2193 := (~ #2192 #2191)
#2188 := (not #1409)
#2189 := (~ #2188 #2187)
#2184 := (not #1404)
#2185 := (~ #2184 #2183)
#2180 := (not #1396)
#2181 := (~ #2180 #1393)
#2178 := (~ #1393 #1393)
#2176 := (~ #1390 #1390)
#2177 := [refl]: #2176
#2179 := [nnf-pos #2177]: #2178
#2182 := [nnf-neg #2179]: #2181
#2174 := (~ #2173 #2173)
#2175 := [refl]: #2174
#2186 := [nnf-neg #2175 #2182]: #2185
#2169 := (~ #1396 #2168)
#2170 := [sk]: #2169
#2190 := [nnf-neg #2170 #2186]: #2189
#2144 := (not #1378)
#2145 := (~ #2144 #2141)
#2142 := (~ #1375 #2141)
#2139 := (~ #1372 #2138)
#2134 := (~ #1369 #2133)
#2135 := [sk]: #2134
#2122 := (~ #1353 #1353)
#2123 := [refl]: #2122
#2140 := [monotonicity #2123 #2135]: #2139
#2143 := [nnf-pos #2140]: #2142
#2146 := [nnf-neg #2143]: #2145
#2194 := [nnf-neg #2146 #2190]: #2193
#2120 := (~ #1378 #2117)
#2095 := (exists (vars (?x50 T2)) #2094)
#2103 := (or #2102 #2095)
#2104 := (not #2103)
#2118 := (~ #2104 #2117)
#2114 := (not #2095)
#2115 := (~ #2114 #2113)
#2111 := (~ #2110 #2110)
#2112 := [refl]: #2111
#2116 := [nnf-neg #2112]: #2115
#2108 := (~ #2107 #2107)
#2109 := [refl]: #2108
#2119 := [nnf-neg #2109 #2116]: #2118
#2105 := (~ #1378 #2104)
#2106 := [sk]: #2105
#2121 := [trans #2106 #2119]: #2120
#2198 := [nnf-neg #2121 #2194]: #2197
#2082 := (~ #2081 #2081)
#2083 := [refl]: #2082
#2079 := (~ #2078 #2078)
#2080 := [refl]: #2079
#2076 := (~ #2075 #2075)
#2077 := [refl]: #2076
#2073 := (~ #2072 #2072)
#2074 := [refl]: #2073
#2208 := [nnf-neg #2074 #2077 #2080 #2083 #2198 #2204]: #2207
#2464 := [nnf-neg #2208 #2460]: #2463
#2069 := (not #1341)
#2070 := (~ #2069 #2066)
#2067 := (~ #1338 #2066)
#2064 := (~ #1335 #2063)
#2059 := (~ #1332 #2058)
#2060 := [sk]: #2059
#2045 := (~ #1308 #1308)
#2046 := [refl]: #2045
#2065 := [monotonicity #2046 #2060]: #2064
#2068 := [nnf-pos #2065]: #2067
#2071 := [nnf-neg #2068]: #2070
#2042 := (not #1752)
#2043 := (~ #2042 #2039)
#2040 := (~ #1296 #2039)
#2037 := (~ #1293 #2036)
#2032 := (~ #1290 #2031)
#2033 := [sk]: #2032
#2018 := (~ #1270 #1270)
#2019 := [refl]: #2018
#2038 := [monotonicity #2019 #2033]: #2037
#2041 := [nnf-pos #2038]: #2040
#2044 := [nnf-neg #2041]: #2043
#2016 := (~ #2015 #2015)
#2017 := [refl]: #2016
#2489 := [nnf-neg #2017 #2044 #2071 #2464 #2471 #2478 #2485]: #2488
#2013 := (~ #1752 #2010)
#1988 := (exists (vars (?x38 T2)) #1987)
#1996 := (or #1995 #1988)
#1997 := (not #1996)
#2011 := (~ #1997 #2010)
#2007 := (not #1988)
#2008 := (~ #2007 #2006)
#2004 := (~ #2003 #2003)
#2005 := [refl]: #2004
#2009 := [nnf-neg #2005]: #2008
#2001 := (~ #2000 #2000)
#2002 := [refl]: #2001
#2012 := [nnf-neg #2002 #2009]: #2011
#1998 := (~ #1752 #1997)
#1999 := [sk]: #1998
#2014 := [trans #1999 #2012]: #2013
#2493 := [nnf-neg #2014 #2489]: #2492
#1973 := (not #1258)
#1974 := (~ #1973 #1255)
#1971 := (~ #1255 #1255)
#1969 := (~ #1252 #1252)
#1970 := [refl]: #1969
#1972 := [nnf-pos #1970]: #1971
#1975 := [nnf-neg #1972]: #1974
#2497 := [nnf-neg #1975 #2493]: #2496
#1965 := (~ #1258 #1964)
#1966 := [sk]: #1965
#2501 := [nnf-neg #1966 #2497]: #2500
#1943 := (not #1232)
#1944 := (~ #1943 #1229)
#1941 := (~ #1229 #1229)
#1939 := (~ #1226 #1226)
#1940 := [refl]: #1939
#1942 := [nnf-pos #1940]: #1941
#1945 := [nnf-neg #1942]: #1944
#2505 := [nnf-neg #1945 #2501]: #2504
#1935 := (~ #1232 #1934)
#1936 := [sk]: #1935
#2509 := [nnf-neg #1936 #2505]: #2508
#1918 := (not #1217)
#1919 := (~ #1918 #1214)
#1916 := (~ #1214 #1214)
#1914 := (~ #1213 #1213)
#1915 := [refl]: #1914
#1917 := [nnf-pos #1915]: #1916
#1920 := [nnf-neg #1917]: #1919
#2513 := [nnf-neg #1920 #2509]: #2512
#1910 := (~ #1217 #1909)
#1911 := [sk]: #1910
#2517 := [nnf-neg #1911 #2513]: #2516
#1865 := (~ #1864 #1864)
#1905 := [refl]: #1865
#2521 := [nnf-neg #1905 #2517]: #2520
#1903 := (~ #1208 #1208)
#1904 := [refl]: #1903
#2524 := [nnf-neg #1904 #2521]: #2523
#1839 := [not-or-elim #1835]: #1838
#2525 := [mp~ #1839 #2524]: #2522
#2526 := [mp #2525 #3063]: #3061
#3705 := [mp #2526 #3704]: #3702
#4636 := [mp #3705 #4635]: #4633
#4922 := [unit-resolution #4636 #4656]: #4630
#3960 := (or #4627 #4621)
#3961 := [def-axiom]: #3960
#4948 := [unit-resolution #3961 #4922]: #4621
#373 := (<= uf_9 0::int)
#374 := (not #373)
#57 := (< 0::int uf_9)
#375 := (iff #57 #374)
#376 := [rewrite]: #375
#369 := [asserted]: #57
#377 := [mp #369 #376]: #374
#4731 := (* -1::int #1907)
#4773 := (+ uf_9 #4731)
#4774 := (<= #4773 0::int)
#4662 := (= uf_9 #1907)
#4665 := (= uf_11 ?x27!0)
#4779 := (not #4665)
#4776 := (= #1907 0::int)
#4795 := (not #4776)
#4789 := [hypothesis]: #1909
#4796 := (or #4795 #1908)
#4797 := [th-lemma]: #4796
#4798 := [unit-resolution #4797 #4789]: #4795
#4767 := (or #3800 #4779 #4776)
#4663 := (= ?x27!0 uf_11)
#4777 := (not #4663)
#4778 := (or #4777 #4776)
#4762 := (or #3800 #4778)
#4791 := (iff #4762 #4767)
#4764 := (or #4779 #4776)
#4769 := (or #3800 #4764)
#4772 := (iff #4769 #4767)
#4790 := [rewrite]: #4772
#4770 := (iff #4762 #4769)
#4765 := (iff #4778 #4764)
#4780 := (iff #4777 #4779)
#4666 := (iff #4663 #4665)
#4718 := [rewrite]: #4666
#4763 := [monotonicity #4718]: #4780
#4766 := [monotonicity #4763]: #4765
#4771 := [monotonicity #4766]: #4770
#4792 := [trans #4771 #4790]: #4791
#4768 := [quant-inst]: #4762
#4793 := [mp #4768 #4792]: #4767
#4799 := [unit-resolution #4793 #4642 #4798]: #4779
#4722 := (or #4662 #4665)
#4707 := (or #4706 #4662 #4665)
#4664 := (or #4663 #4662)
#4708 := (or #4706 #4664)
#4714 := (iff #4708 #4707)
#4710 := (or #4706 #4722)
#4712 := (iff #4710 #4707)
#4713 := [rewrite]: #4712
#4705 := (iff #4708 #4710)
#4725 := (iff #4664 #4722)
#4719 := (or #4665 #4662)
#4723 := (iff #4719 #4722)
#4724 := [rewrite]: #4723
#4720 := (iff #4664 #4719)
#4721 := [monotonicity #4718]: #4720
#4726 := [trans #4721 #4724]: #4725
#4711 := [monotonicity #4726]: #4705
#4715 := [trans #4711 #4713]: #4714
#4709 := [quant-inst]: #4708
#4730 := [mp #4709 #4715]: #4707
#4851 := [unit-resolution #4730 #4263]: #4722
#4852 := [unit-resolution #4851 #4799]: #4662
#4853 := (not #4662)
#4854 := (or #4853 #4774)
#4855 := [th-lemma]: #4854
#4856 := [unit-resolution #4855 #4852]: #4774
#4794 := (<= #1907 0::int)
#4857 := (or #4794 #1908)
#4858 := [th-lemma]: #4857
#4859 := [unit-resolution #4858 #4789]: #4794
#4839 := [th-lemma #4859 #4856 #377]: false
#4840 := [lemma #4839]: #1908
#3955 := (or #4624 #1909 #4618)
#3956 := [def-axiom]: #3955
#5086 := [unit-resolution #3956 #4840 #4948]: #4618
#3979 := (or #4615 #4609)
#3980 := [def-axiom]: #3979
#5292 := [unit-resolution #3980 #5086]: #4609
#5416 := [hypothesis]: #1928
#5028 := (or #4844 #1968)
#5029 := [quant-inst]: #5028
#5422 := [unit-resolution #5029 #4256 #5416]: false
#5423 := [lemma #5422]: #1968
#3772 := (or #2171 #1928)
#3859 := [def-axiom]: #3772
#5293 := [unit-resolution #3859 #5423]: #2171
#3973 := (or #4612 #2248 #4606)
#3975 := [def-axiom]: #3973
#5417 := [unit-resolution #3975 #5293 #5292]: #4606
#4000 := (or #4603 #4597)
#4001 := [def-axiom]: #4000
#5418 := [unit-resolution #4001 #5417]: #4597
#3996 := (or #4600 #3106 #4594)
#3997 := [def-axiom]: #3996
#5452 := [unit-resolution #3997 #5418 #4921]: #4594
#4010 := (or #4591 #4585)
#4031 := [def-axiom]: #4010
#5507 := [unit-resolution #4031 #5452]: #4585
#4018 := (or #4588 #4302 #4582)
#4019 := [def-axiom]: #4018
#5496 := [unit-resolution #4019 #5507 #5196]: #4582
#4049 := (or #4579 #109)
#4050 := [def-axiom]: #4049
#5498 := [unit-resolution #4050 #5496]: #109
#9048 := (= #166 #108)
#9042 := [hypothesis]: #4415
#4151 := (or #4412 #569)
#4152 := [def-axiom]: #4151
#9043 := [unit-resolution #4152 #9042]: #569
#8965 := [symm #9043]: #147
#9049 := [monotonicity #8965]: #9048
#9047 := [trans #9049 #5498]: #167
#3867 := (or #4412 #4348)
#4149 := [def-axiom]: #3867
#9030 := [unit-resolution #4149 #9042]: #4348
#7181 := (or #3369 #4353 #674)
#9174 := [hypothesis]: #569
#9183 := [hypothesis]: #4348
#9172 := [hypothesis]: #3374
#4168 := (or #3369 #2164)
#4169 := [def-axiom]: #4168
#7182 := [unit-resolution #4169 #9172]: #2164
#9200 := (or #3369 #2163 #4353 #674)
#8980 := (uf_4 uf_14 ?x54!10)
#7073 := (uf_4 uf_14 ?x53!11)
#7171 := (* -1::int #7073)
#9058 := (+ #7171 #8980)
#9059 := (+ #2154 #9058)
#9062 := (>= #9059 0::int)
#8984 := (uf_6 uf_15 ?x54!10)
#8985 := (= uf_8 #8984)
#8981 := (* -1::int #8980)
#8982 := (+ uf_9 #8981)
#8983 := (<= #8982 0::int)
#9168 := (not #8983)
#4166 := (or #3369 #2160)
#4167 := [def-axiom]: #4166
#9173 := [unit-resolution #4167 #9172]: #2160
#9161 := (+ #2151 #8981)
#9163 := (>= #9161 0::int)
#9160 := (= #2151 #8980)
#9175 := (= #8980 #2151)
#9176 := [monotonicity #9174]: #9175
#9177 := [symm #9176]: #9160
#9178 := (not #9160)
#9179 := (or #9178 #9163)
#9180 := [th-lemma]: #9179
#9181 := [unit-resolution #9180 #9177]: #9163
#9169 := (not #9163)
#9170 := (or #9168 #9169 #2159)
#9164 := [hypothesis]: #2160
#9165 := [hypothesis]: #8983
#9166 := [hypothesis]: #9163
#9167 := [th-lemma #9166 #9165 #9164]: false
#9171 := [lemma #9167]: #9170
#9182 := [unit-resolution #9171 #9181 #9173]: #9168
#8987 := (or #8983 #8985)
#8990 := (or #4353 #8983 #8985)
#8986 := (or #8985 #8983)
#8991 := (or #4353 #8986)
#8998 := (iff #8991 #8990)
#8993 := (or #4353 #8987)
#8996 := (iff #8993 #8990)
#8997 := [rewrite]: #8996
#8994 := (iff #8991 #8993)
#8988 := (iff #8986 #8987)
#8989 := [rewrite]: #8988
#8995 := [monotonicity #8989]: #8994
#8999 := [trans #8995 #8997]: #8998
#8992 := [quant-inst]: #8991
#9000 := [mp #8992 #8999]: #8990
#9184 := [unit-resolution #9000 #9183]: #8987
#9185 := [unit-resolution #9184 #9182]: #8985
#9056 := (not #8985)
#9188 := (or #9056 #9062)
#9186 := [hypothesis]: #2164
#4052 := (or #4579 #4314)
#4032 := [def-axiom]: #4052
#9187 := [unit-resolution #4032 #5496]: #4314
#9073 := (or #4319 #2163 #9056 #9062)
#9051 := (+ #8980 #7171)
#9052 := (+ #2154 #9051)
#9055 := (>= #9052 0::int)
#9057 := (or #9056 #2163 #9055)
#9074 := (or #4319 #9057)
#9081 := (iff #9074 #9073)
#9068 := (or #2163 #9056 #9062)
#9076 := (or #4319 #9068)
#9079 := (iff #9076 #9073)
#9080 := [rewrite]: #9079
#9077 := (iff #9074 #9076)
#9071 := (iff #9057 #9068)
#9065 := (or #9056 #2163 #9062)
#9069 := (iff #9065 #9068)
#9070 := [rewrite]: #9069
#9066 := (iff #9057 #9065)
#9063 := (iff #9055 #9062)
#9060 := (= #9052 #9059)
#9061 := [rewrite]: #9060
#9064 := [monotonicity #9061]: #9063
#9067 := [monotonicity #9064]: #9066
#9072 := [trans #9067 #9070]: #9071
#9078 := [monotonicity #9072]: #9077
#9082 := [trans #9078 #9080]: #9081
#9075 := [quant-inst]: #9074
#9083 := [mp #9075 #9082]: #9073
#9189 := [unit-resolution #9083 #9187 #9186]: #9188
#9190 := [unit-resolution #9189 #9185]: #9062
#4164 := (not #2815)
#4170 := (or #3369 #4164)
#3808 := [def-axiom]: #4170
#9191 := [unit-resolution #3808 #9172]: #4164
#9155 := (+ #2149 #7171)
#9158 := (<= #9155 0::int)
#9154 := (= #2149 #7073)
#9192 := (= #7073 #2149)
#9193 := [monotonicity #9174]: #9192
#9194 := [symm #9193]: #9154
#9195 := (not #9154)
#9196 := (or #9195 #9158)
#9197 := [th-lemma]: #9196
#9198 := [unit-resolution #9197 #9194]: #9158
#9199 := [th-lemma #9198 #9191 #9181 #9190]: false
#9201 := [lemma #9199]: #9200
#7183 := [unit-resolution #9201 #7182 #9172 #9183 #9174]: false
#7082 := [lemma #7183]: #7181
#9031 := [unit-resolution #7082 #9030 #9043]: #3369
#4153 := (or #4412 #4406)
#4150 := [def-axiom]: #4153
#8964 := [unit-resolution #4150 #9042]: #4406
#9037 := (or #4412 #2097)
#5396 := (uf_4 uf_14 ?x49!8)
#5456 := (* -1::int #5396)
#5457 := (+ uf_9 #5456)
#5458 := (<= #5457 0::int)
#6793 := (not #5458)
#6788 := [hypothesis]: #2098
#6206 := (+ #2085 #5456)
#6232 := (>= #6206 0::int)
#5257 := (= #2085 #5396)
#9044 := (= #5396 #2085)
#9045 := [monotonicity #9043]: #9044
#8975 := [symm #9045]: #5257
#8976 := (not #5257)
#8977 := (or #8976 #6232)
#8978 := [th-lemma]: #8977
#8979 := [unit-resolution #8978 #8975]: #6232
#6794 := (not #6232)
#6792 := (or #6793 #6794 #2097)
#6786 := [hypothesis]: #6232
#6790 := [hypothesis]: #5458
#6791 := [th-lemma #6790 #6786 #6788]: false
#6816 := [lemma #6791]: #6792
#8974 := [unit-resolution #6816 #8979 #6788]: #6793
#6231 := (<= #6206 0::int)
#8961 := (or #8976 #6231)
#8962 := [th-lemma]: #8961
#8963 := [unit-resolution #8962 #8975]: #6231
#4163 := (or #4388 #2173)
#3826 := [def-axiom]: #4163
#9029 := [unit-resolution #3826 #9047]: #4388
#4175 := (or #4397 #4391 #3374)
#4161 := [def-axiom]: #4175
#9032 := [unit-resolution #4161 #9031 #9029]: #4397
#3885 := (or #4400 #4394)
#3886 := [def-axiom]: #3885
#9046 := [unit-resolution #3886 #9032]: #4400
#4155 := (or #4409 #4369 #4403)
#4159 := [def-axiom]: #4155
#9033 := [unit-resolution #4159 #9046 #8964]: #4369
#5178 := (?x47!7 ?x49!8)
#6376 := (uf_4 uf_19 #5178)
#6600 := (* -1::int #6376)
#5179 := (uf_4 uf_14 #5178)
#8481 := (+ #5179 #6600)
#6172 := (<= #8481 0::int)
#5887 := (= #5179 #6376)
#9028 := [monotonicity #9043]: #5887
#9034 := (not #5887)
#9035 := (or #9034 #6172)
#9036 := [th-lemma]: #9035
#9038 := [unit-resolution #9036 #9028]: #6172
#8515 := (>= #8481 0::int)
#9053 := (or #9034 #8515)
#9054 := [th-lemma]: #9053
#9109 := [unit-resolution #9054 #9028]: #8515
#9290 := (not #6172)
#9289 := (not #6231)
#8950 := (not #8515)
#9263 := (or #4366 #6794 #8950 #9289 #9290 #5458)
#5641 := (+ #5179 #5456)
#5665 := (>= #5641 0::int)
#7930 := (not #5665)
#5450 := (uf_1 #5178 ?x49!8)
#5451 := (uf_10 #5450)
#5631 := (+ #5456 #5451)
#5637 := (+ #5179 #5631)
#5526 := (= #5637 0::int)
#5525 := (not #5526)
#5508 := (uf_6 uf_15 #5178)
#5517 := (= uf_8 #5508)
#5518 := (not #5517)
#5697 := (or #5518 #5525 #5665)
#5707 := (not #5697)
#9240 := [hypothesis]: #6793
#9241 := [hypothesis]: #4369
#3837 := (or #4366 #2715)
#3842 := [def-axiom]: #3837
#9242 := [unit-resolution #3842 #9241]: #2715
#4039 := (or #4579 #4339)
#4034 := [def-axiom]: #4039
#9243 := [unit-resolution #4034 #5496]: #4339
#7629 := (or #4344 #2712 #5458 #5707)
#5424 := (* -1::int #5179)
#5425 := (+ #5396 #5424)
#5426 := (<= #5425 0::int)
#5509 := (* -1::int #5451)
#5514 := (+ #5424 #5509)
#5515 := (+ #5396 #5514)
#5513 := (= #5515 0::int)
#5516 := (not #5513)
#5523 := (or #5518 #5516 #5426)
#5524 := (not #5523)
#5522 := (or #2099 #5458 #5524)
#7083 := (or #4344 #5522)
#7435 := (iff #7083 #7629)
#5819 := (or #2712 #5458 #5707)
#7261 := (or #4344 #5819)
#7430 := (iff #7261 #7629)
#7436 := [rewrite]: #7430
#7210 := (iff #7083 #7261)
#5798 := (iff #5522 #5819)
#5801 := (iff #5524 #5707)
#5705 := (iff #5523 #5697)
#5638 := (iff #5426 #5665)
#5536 := (+ #5424 #5396)
#5639 := (<= #5536 0::int)
#5666 := (iff #5639 #5665)
#5703 := [rewrite]: #5666
#5640 := (iff #5426 #5639)
#5497 := (= #5425 #5536)
#5495 := [rewrite]: #5497
#5634 := [monotonicity #5495]: #5640
#5704 := [trans #5634 #5703]: #5638
#5534 := (iff #5516 #5525)
#5533 := (iff #5513 #5526)
#5499 := (+ #5396 #5509)
#5500 := (+ #5424 #5499)
#5504 := (= #5500 0::int)
#5527 := (iff #5504 #5526)
#5532 := [rewrite]: #5527
#5635 := (iff #5513 #5504)
#5505 := (= #5515 #5500)
#5506 := [rewrite]: #5505
#5636 := [monotonicity #5506]: #5635
#5531 := [trans #5636 #5532]: #5533
#5535 := [monotonicity #5531]: #5534
#5706 := [monotonicity #5535 #5704]: #5705
#5818 := [monotonicity #5706]: #5801
#5817 := [monotonicity #2714 #5818]: #5798
#6900 := [monotonicity #5817]: #7210
#7432 := [trans #6900 #7436]: #7435
#7217 := [quant-inst]: #7083
#7437 := [mp #7217 #7432]: #7629
#9244 := [unit-resolution #7437 #9243 #9242 #9240]: #5707
#7888 := (or #5697 #7930)
#7931 := [def-axiom]: #7888
#9239 := [unit-resolution #7931 #9244]: #7930
#6592 := (+ #2085 #6600)
#6591 := (<= #6592 0::int)
#6800 := (+ #5509 #6600)
#6802 := (+ #2085 #6800)
#6783 := (= #6802 0::int)
#8973 := (<= #6802 0::int)
#9282 := [hypothesis]: #6172
#9283 := [hypothesis]: #6231
#5866 := (>= #5637 0::int)
#7549 := (or #5697 #5526)
#7928 := [def-axiom]: #7549
#9245 := [unit-resolution #7928 #9244]: #5526
#9246 := (or #5525 #5866)
#9247 := [th-lemma]: #9246
#9248 := [unit-resolution #9247 #9245]: #5866
#9288 := (not #5866)
#9291 := (or #8973 #9288 #9289 #9290)
#9284 := [hypothesis]: #5866
#9285 := (not #8973)
#9286 := [hypothesis]: #9285
#9287 := [th-lemma #9286 #9284 #9283 #9282]: false
#9292 := [lemma #9287]: #9291
#9249 := [unit-resolution #9292 #9248 #9283 #9282]: #8973
#9256 := (or #6783 #9285)
#7263 := (>= #6802 0::int)
#8944 := [hypothesis]: #8515
#5863 := (<= #5637 0::int)
#9251 := (or #5525 #5863)
#9252 := [th-lemma]: #9251
#9253 := [unit-resolution #9252 #9245]: #5863
#8949 := (not #5863)
#8951 := (or #7263 #8949 #6794 #8950)
#8945 := [hypothesis]: #5863
#8946 := (not #7263)
#8947 := [hypothesis]: #8946
#8948 := [th-lemma #8947 #8945 #6786 #8944]: false
#8952 := [lemma #8948]: #8951
#9254 := [unit-resolution #8952 #9253 #6786 #8944]: #7263
#9255 := (or #6783 #9285 #8946)
#9250 := [th-lemma]: #9255
#9257 := [unit-resolution #9250 #9254]: #9256
#9258 := [unit-resolution #9257 #9249]: #6783
#6818 := (not #6783)
#6815 := (or #6591 #6818)
#4178 := (or #4366 #4358)
#3838 := [def-axiom]: #4178
#9259 := [unit-resolution #3838 #9241]: #4358
#8898 := (or #4363 #6591 #6818)
#6374 := (+ #2086 #5451)
#6377 := (+ #6376 #6374)
#6477 := (= #6377 0::int)
#6478 := (not #6477)
#6366 := (+ #6376 #2086)
#6479 := (>= #6366 0::int)
#6480 := (or #6479 #6478)
#8899 := (or #4363 #6480)
#8905 := (iff #8899 #8898)
#8124 := (or #4363 #6815)
#8903 := (iff #8124 #8898)
#8904 := [rewrite]: #8903
#8901 := (iff #8899 #8124)
#6821 := (iff #6480 #6815)
#6819 := (iff #6478 #6818)
#6782 := (iff #6477 #6783)
#6572 := (+ #5451 #6376)
#6011 := (+ #2086 #6572)
#6083 := (= #6011 0::int)
#6787 := (iff #6083 #6783)
#6789 := [rewrite]: #6787
#6797 := (iff #6477 #6083)
#6795 := (= #6377 #6011)
#6796 := [rewrite]: #6795
#6799 := [monotonicity #6796]: #6797
#6817 := [trans #6799 #6789]: #6782
#6820 := [monotonicity #6817]: #6819
#6626 := (iff #6479 #6591)
#6481 := (+ #2086 #6376)
#6597 := (>= #6481 0::int)
#6627 := (iff #6597 #6591)
#6628 := [rewrite]: #6627
#6598 := (iff #6479 #6597)
#6476 := (= #6366 #6481)
#6482 := [rewrite]: #6476
#6599 := [monotonicity #6482]: #6598
#6629 := [trans #6599 #6628]: #6626
#6784 := [monotonicity #6629 #6820]: #6821
#8902 := [monotonicity #6784]: #8901
#7262 := [trans #8902 #8904]: #8905
#8900 := [quant-inst]: #8899
#7283 := [mp #8900 #7262]: #8898
#9260 := [unit-resolution #7283 #9259]: #6815
#9264 := [unit-resolution #9260 #9258]: #6591
#9265 := [th-lemma #6786 #8944 #9264 #9239]: false
#9266 := [lemma #9265]: #9263
#9110 := [unit-resolution #9266 #9109 #9038 #9033 #8963 #8979 #8974]: false
#9111 := [lemma #9110]: #9037
#5419 := [unit-resolution #9111 #9042]: #2097
#4187 := (or #4366 #2098)
#4177 := [def-axiom]: #4187
#5867 := [unit-resolution #4177 #5419]: #4366
#5862 := [unit-resolution #4159 #5867 #8964]: #4403
#5363 := [unit-resolution #3886 #5862]: #4394
#7926 := [unit-resolution #4161 #5363 #9031]: #4391
#7932 := [unit-resolution #3826 #7926]: #2173
#7884 := [unit-resolution #7932 #9047]: false
#8887 := [lemma #7884]: #4412
#4040 := (or #4579 #4573)
#4008 := [def-axiom]: #4040
#10724 := [unit-resolution #4008 #5496]: #4573
#4045 := (or #4576 #4415 #4570)
#4046 := [def-axiom]: #4045
#10725 := [unit-resolution #4046 #10724]: #4573
#10726 := [unit-resolution #10725 #8887]: #4570
#4068 := (or #4567 #195)
#4069 := [def-axiom]: #4068
#13581 := [unit-resolution #4069 #10726]: #195
#13578 := [symm #13581]: #7680
#13576 := (= #10323 #194)
#48 := (:var 0 T5)
#47 := (:var 2 T4)
#49 := (uf_7 #47 #10 #48)
#4231 := (pattern #49)
#360 := (= uf_8 #48)
#50 := (uf_6 #49 #10)
#356 := (= uf_8 #50)
#363 := (iff #356 #360)
#4232 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4231) #363)
#366 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #363)
#4235 := (iff #366 #4232)
#4233 := (iff #363 #363)
#4234 := [refl]: #4233
#4236 := [quant-intro #4234]: #4235
#1852 := (~ #366 #366)
#1890 := (~ #363 #363)
#1891 := [refl]: #1890
#1853 := [nnf-pos #1891]: #1852
#52 := (= #48 uf_8)
#51 := (= #50 uf_8)
#53 := (iff #51 #52)
#54 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #53)
#367 := (iff #54 #366)
#364 := (iff #53 #363)
#361 := (iff #52 #360)
#362 := [rewrite]: #361
#358 := (iff #51 #356)
#359 := [rewrite]: #358
#365 := [monotonicity #359 #362]: #364
#368 := [quant-intro #365]: #367
#355 := [asserted]: #54
#371 := [mp #355 #368]: #366
#1892 := [mp~ #371 #1853]: #366
#4237 := [mp #1892 #4236]: #4232
#3883 := (not #4232)
#3893 := (or #3883 #3895)
#3909 := (= uf_8 uf_8)
#3896 := (iff #3895 #3909)
#3874 := (or #3883 #3896)
#3876 := (iff #3874 #3893)
#3877 := (iff #3893 #3893)
#3878 := [rewrite]: #3877
#3891 := (iff #3896 #3895)
#3899 := (iff #3895 true)
#3890 := (iff #3899 #3895)
#3882 := [rewrite]: #3890
#3888 := (iff #3896 #3899)
#3898 := (iff #3909 true)
#3897 := [rewrite]: #3898
#3889 := [monotonicity #3897]: #3888
#3892 := [trans #3889 #3882]: #3891
#3868 := [monotonicity #3892]: #3876
#3869 := [trans #3868 #3878]: #3876
#3875 := [quant-inst]: #3874
#3879 := [mp #3875 #3869]: #3893
#7677 := [unit-resolution #3879 #4237]: #3895
#7678 := [symm #7677]: #4958
#13577 := [monotonicity #10708 #7678]: #13576
#13583 := [trans #13577 #13578]: #13582
#13585 := [monotonicity #13583]: #13584
#13596 := [symm #13585]: #13595
#13580 := [hypothesis]: #2258
#13597 := [trans #13580 #13596]: #10327
#13450 := (not #10327)
#13447 := (not #10333)
#13451 := (or #13447 #13450 #10330)
#13454 := [def-axiom]: #13451
#13593 := [unit-resolution #13454 #13597 #13579]: #10330
#13335 := (not #9519)
#11136 := (uf_6 uf_15 #10448)
#11137 := (= uf_8 #11136)
#11138 := (not #11137)
#11133 := (* -1::int #11132)
#9701 := (uf_4 uf_14 #9695)
#11134 := (+ #9701 #11133)
#11135 := (>= #11134 0::int)
#13999 := (not #11135)
#9563 := (uf_1 uf_22 ?x63!14)
#9564 := (uf_10 #9563)
#9508 := (* -1::int #2261)
#9581 := (+ #9508 #9564)
#9582 := (+ #188 #9581)
#9583 := (>= #9582 0::int)
#12179 := (not #9583)
#9565 := (* -1::int #9564)
#9569 := (+ uf_9 #9565)
#9570 := (<= #9569 0::int)
#9588 := (or #9570 #9583)
#9591 := (not #9588)
#13188 := [hypothesis]: #4140
#4061 := (or #4567 #4428)
#4056 := [def-axiom]: #4061
#10727 := [unit-resolution #4056 #10726]: #4428
#13444 := (or #4433 #2866 #9591)
#9566 := (+ #1455 #9565)
#9567 := (+ #2261 #9566)
#9568 := (<= #9567 0::int)
#9571 := (or #9570 #9568)
#9572 := (not #9571)
#9573 := (or #2262 #9572)
#11618 := (or #4433 #9573)
#11883 := (iff #11618 #13444)
#9594 := (or #2866 #9591)
#11662 := (or #4433 #9594)
#11855 := (iff #11662 #13444)
#11841 := [rewrite]: #11855
#11663 := (iff #11618 #11662)
#9595 := (iff #9573 #9594)
#9592 := (iff #9572 #9591)
#9589 := (iff #9571 #9588)
#9586 := (iff #9568 #9583)
#9574 := (+ #2261 #9565)
#9575 := (+ #1455 #9574)
#9578 := (<= #9575 0::int)
#9584 := (iff #9578 #9583)
#9585 := [rewrite]: #9584
#9579 := (iff #9568 #9578)
#9576 := (= #9567 #9575)
#9577 := [rewrite]: #9576
#9580 := [monotonicity #9577]: #9579
#9587 := [trans #9580 #9585]: #9586
#9590 := [monotonicity #9587]: #9589
#9593 := [monotonicity #9590]: #9592
#9596 := [monotonicity #2868 #9593]: #9595
#11801 := [monotonicity #9596]: #11663
#11930 := [trans #11801 #11841]: #11883
#11417 := [quant-inst]: #11618
#12087 := [mp #11417 #11930]: #13444
#13594 := [unit-resolution #12087 #10727 #13188]: #9591
#12344 := (or #9588 #12179)
#11143 := [def-axiom]: #12344
#13599 := [unit-resolution #11143 #13594]: #12179
#14000 := (or #13999 #9583)
#13979 := [hypothesis]: #11135
#13980 := [hypothesis]: #12179
#10368 := (uf_10 #10367)
#10372 := (* -1::int #10368)
#11940 := (+ #9564 #10372)
#11942 := (>= #11940 0::int)
#9867 := (= #9564 #10368)
#13987 := (= #9563 #10367)
#13988 := [monotonicity #10706]: #13987
#13989 := [monotonicity #13988]: #9867
#13990 := (not #9867)
#13991 := (or #13990 #11942)
#13992 := [th-lemma]: #13991
#13993 := [unit-resolution #13992 #13989]: #11942
#11219 := (>= #10368 0::int)
#10318 := (= #10368 0::int)
#11983 := (not #10318)
#11981 := (not #11219)
#11982 := [hypothesis]: #11981
#11984 := (or #11983 #11219)
#11985 := [th-lemma]: #11984
#11986 := [unit-resolution #11985 #11982]: #11983
#10404 := (<= #10368 0::int)
#11987 := (or #11219 #10404)
#11988 := [th-lemma]: #11987
#11989 := [unit-resolution #11988 #11982]: #10404
#10405 := (not #10404)
#10410 := (or #10319 #10405)
#59 := (uf_10 #12)
#409 := (<= #59 0::int)
#410 := (not #409)
#58 := (= #10 #11)
#413 := (or #58 #410)
#4244 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #4196) #413)
#416 := (forall (vars (?x22 T2) (?x23 T2)) #413)
#4247 := (iff #416 #4244)
#4245 := (iff #413 #413)
#4246 := [refl]: #4245
#4248 := [quant-intro #4246]: #4247
#1858 := (~ #416 #416)
#1857 := (~ #413 #413)
#1895 := [refl]: #1857
#1859 := [nnf-pos #1895]: #1858
#64 := (< 0::int #59)
#63 := (not #58)
#65 := (implies #63 #64)
#66 := (forall (vars (?x22 T2) (?x23 T2)) #65)
#419 := (iff #66 #416)
#403 := (or #58 #64)
#406 := (forall (vars (?x22 T2) (?x23 T2)) #403)
#417 := (iff #406 #416)
#414 := (iff #403 #413)
#411 := (iff #64 #410)
#412 := [rewrite]: #411
#415 := [monotonicity #412]: #414
#418 := [quant-intro #415]: #417
#407 := (iff #66 #406)
#404 := (iff #65 #403)
#405 := [rewrite]: #404
#408 := [quant-intro #405]: #407
#420 := [trans #408 #418]: #419
#402 := [asserted]: #66
#421 := [mp #402 #420]: #416
#1896 := [mp~ #421 #1859]: #416
#4249 := [mp #1896 #4248]: #4244
#10302 := (not #4244)
#11162 := (or #10302 #10319 #10405)
#10406 := (= #9695 ?x63!14)
#10407 := (or #10406 #10405)
#11163 := (or #10302 #10407)
#11205 := (iff #11163 #11162)
#11188 := (or #10302 #10410)
#11203 := (iff #11188 #11162)
#11204 := [rewrite]: #11203
#11189 := (iff #11163 #11188)
#10411 := (iff #10407 #10410)
#10408 := (iff #10406 #10319)
#10409 := [rewrite]: #10408
#10412 := [monotonicity #10409]: #10411
#11202 := [monotonicity #10412]: #11189
#11206 := [trans #11202 #11204]: #11205
#11164 := [quant-inst]: #11163
#11201 := [mp #11164 #11206]: #11162
#11990 := [unit-resolution #11201 #4249]: #10410
#11991 := [unit-resolution #11990 #11989]: #10319
#10346 := (not #10319)
#10431 := (or #10318 #10346)
#60 := (= #59 0::int)
#393 := (or #63 #60)
#4238 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #4196) #393)
#396 := (forall (vars (?x20 T2) (?x21 T2)) #393)
#4241 := (iff #396 #4238)
#4239 := (iff #393 #393)
#4240 := [refl]: #4239
#4242 := [quant-intro #4240]: #4241
#1854 := (~ #396 #396)
#1893 := (~ #393 #393)
#1894 := [refl]: #1893
#1855 := [nnf-pos #1894]: #1854
#61 := (implies #58 #60)
#62 := (forall (vars (?x20 T2) (?x21 T2)) #61)
#399 := (iff #62 #396)
#372 := (= 0::int #59)
#383 := (or #63 #372)
#388 := (forall (vars (?x20 T2) (?x21 T2)) #383)
#397 := (iff #388 #396)
#394 := (iff #383 #393)
#391 := (iff #372 #60)
#392 := [rewrite]: #391
#395 := [monotonicity #392]: #394
#398 := [quant-intro #395]: #397
#389 := (iff #62 #388)
#386 := (iff #61 #383)
#380 := (implies #58 #372)
#384 := (iff #380 #383)
#385 := [rewrite]: #384
#381 := (iff #61 #380)
#378 := (iff #60 #372)
#379 := [rewrite]: #378
#382 := [monotonicity #379]: #381
#387 := [trans #382 #385]: #386
#390 := [quant-intro #387]: #389
#400 := [trans #390 #398]: #399
#370 := [asserted]: #62
#401 := [mp #370 #400]: #396
#1856 := [mp~ #401 #1855]: #396
#4243 := [mp #1856 #4242]: #4238
#6331 := (not #4238)
#11098 := (or #6331 #10318 #10346)
#10424 := (not #10406)
#10425 := (or #10424 #10318)
#11207 := (or #6331 #10425)
#11222 := (iff #11207 #11098)
#11209 := (or #6331 #10431)
#11220 := (iff #11209 #11098)
#11221 := [rewrite]: #11220
#11210 := (iff #11207 #11209)
#10434 := (iff #10425 #10431)
#10428 := (or #10346 #10318)
#10432 := (iff #10428 #10431)
#10433 := [rewrite]: #10432
#10429 := (iff #10425 #10428)
#10426 := (iff #10424 #10346)
#10427 := [monotonicity #10409]: #10426
#10430 := [monotonicity #10427]: #10429
#10435 := [trans #10430 #10433]: #10434
#11211 := [monotonicity #10435]: #11210
#11223 := [trans #11211 #11221]: #11222
#11208 := [quant-inst]: #11207
#11224 := [mp #11208 #11223]: #11098
#11992 := [unit-resolution #11224 #4243]: #10431
#11993 := [unit-resolution #11992 #11991 #11986]: false
#11994 := [lemma #11993]: #11219
#10057 := (+ #2261 #11133)
#11955 := (<= #10057 0::int)
#13994 := (not #12385)
#13995 := (or #13994 #11955)
#13996 := [th-lemma]: #13995
#13997 := [unit-resolution #13996 #13203]: #11955
#9707 := (* -1::int #9701)
#10565 := (+ #188 #9707)
#10581 := (>= #10565 0::int)
#9923 := (= #188 #9701)
#12919 := (= #9701 #188)
#12920 := [monotonicity #10708]: #12919
#12921 := [symm #12920]: #9923
#12922 := (not #9923)
#12923 := (or #12922 #10581)
#12924 := [th-lemma]: #12923
#12925 := [unit-resolution #12924 #12921]: #10581
#13998 := [th-lemma #12925 #13997 #11994 #13993 #13980 #13979]: false
#14001 := [lemma #13998]: #14000
#13600 := [unit-resolution #14001 #13599]: #13999
#13971 := (or #11138 #11135)
#13935 := [hypothesis]: #13999
#13936 := [hypothesis]: #11137
#9685 := (uf_6 uf_15 #9695)
#9686 := (= uf_8 #9685)
#13964 := (not #9686)
#13965 := (iff #731 #13964)
#13957 := (iff #728 #9686)
#13955 := (iff #9686 #728)
#13948 := (= #9685 #185)
#13954 := [monotonicity #10708]: #13948
#13956 := [monotonicity #13954]: #13955
#13958 := [symm #13956]: #13957
#13968 := [monotonicity #13958]: #13965
#4070 := (or #4567 #731)
#4065 := [def-axiom]: #4070
#13953 := [unit-resolution #4065 #10726]: #731
#13969 := [mp #13953 #13968]: #13964
#3978 := (or #4579 #4323)
#4033 := [def-axiom]: #3978
#13967 := [unit-resolution #4033 #5496]: #4323
#13906 := (or #4328 #9686 #11135 #11138)
#11139 := (or #9686 #11138 #11135)
#13907 := (or #4328 #11139)
#13933 := (iff #13907 #13906)
#11140 := (or #9686 #11135 #11138)
#13912 := (or #4328 #11140)
#13931 := (iff #13912 #13906)
#13932 := [rewrite]: #13931
#13929 := (iff #13907 #13912)
#11141 := (iff #11139 #11140)
#11142 := [rewrite]: #11141
#13930 := [monotonicity #11142]: #13929
#13928 := [trans #13930 #13932]: #13933
#13911 := [quant-inst]: #13907
#13934 := [mp #13911 #13928]: #13906
#13970 := [unit-resolution #13934 #13967 #13969 #13936 #13935]: false
#13972 := [lemma #13970]: #13971
#13598 := [unit-resolution #13972 #13600]: #11138
#13978 := (or #13335 #11137)
#13974 := (iff #9519 #11137)
#13973 := (iff #11137 #9519)
#13736 := (= #11136 #9518)
#13693 := (= #10448 ?x63!14)
#13735 := [symm #13195]: #13693
#13905 := [monotonicity #13735]: #13736
#13966 := [monotonicity #13905]: #13973
#13975 := [symm #13966]: #13974
#13619 := [hypothesis]: #9519
#13976 := [mp #13619 #13975]: #11137
#13625 := [hypothesis]: #11138
#13977 := [unit-resolution #13625 #13976]: false
#13982 := [lemma #13977]: #13978
#13601 := [unit-resolution #13982 #13598]: #13335
#13052 := (not #10330)
#13244 := (or #13052 #10319 #9519)
#13279 := [def-axiom]: #13244
#13602 := [unit-resolution #13279 #13601 #13593]: #10319
#13607 := [trans #13735 #13602]: #13609
#13611 := [trans #13607 #10708]: #13610
#13622 := [monotonicity #13611]: #13621
#13629 := [symm #13622]: #13623
#13634 := (= #2260 #188)
#4740 := (uf_24 uf_22)
#10619 := (= #4740 #188)
#4741 := (= #188 #4740)
#4729 := (uf_10 #4728)
#4748 := (>= #4729 0::int)
#4732 := (* -1::int #4729)
#4736 := (+ uf_9 #4732)
#4737 := (<= #4736 0::int)
#4753 := (or #4737 #4748)
#9615 := (= #4729 0::int)
#9682 := (or #6331 #9615)
#4959 := (= uf_22 uf_22)
#9598 := (not #4959)
#9599 := (or #9598 #9615)
#9683 := (or #6331 #9599)
#9749 := (iff #9683 #9682)
#9751 := (iff #9682 #9682)
#9752 := [rewrite]: #9751
#9631 := (iff #9599 #9615)
#9603 := (or false #9615)
#9606 := (iff #9603 #9615)
#9607 := [rewrite]: #9606
#9604 := (iff #9599 #9603)
#9602 := (iff #9598 false)
#9600 := (iff #9598 #8605)
#4968 := (iff #4959 true)
#4969 := [rewrite]: #4968
#9601 := [monotonicity #4969]: #9600
#9597 := [trans #9601 #8609]: #9602
#9605 := [monotonicity #9597]: #9604
#9632 := [trans #9605 #9607]: #9631
#9750 := [monotonicity #9632]: #9749
#9747 := [trans #9750 #9752]: #9749
#9748 := [quant-inst]: #9683
#9724 := [mp #9748 #9747]: #9682
#10718 := [unit-resolution #9724 #4243]: #9615
#10719 := (not #9615)
#10720 := (or #10719 #4748)
#10721 := [th-lemma]: #10720
#10722 := [unit-resolution #10721 #10718]: #4748
#9223 := (not #4748)
#9224 := (or #4753 #9223)
#9225 := [def-axiom]: #9224
#10723 := [unit-resolution #9225 #10722]: #4753
#4756 := (not #4753)
#4759 := (or #4741 #4756)
#7499 := (or #4433 #4741 #4756)
#4733 := (+ #1455 #4732)
#4734 := (+ #188 #4733)
#4735 := (<= #4734 0::int)
#4738 := (or #4737 #4735)
#4739 := (not #4738)
#4742 := (or #4741 #4739)
#7438 := (or #4433 #4742)
#9202 := (iff #7438 #7499)
#9040 := (or #4433 #4759)
#9159 := (iff #9040 #7499)
#9162 := [rewrite]: #9159
#9149 := (iff #7438 #9040)
#4760 := (iff #4742 #4759)
#4757 := (iff #4739 #4756)
#4754 := (iff #4738 #4753)
#4751 := (iff #4735 #4748)
#4745 := (<= #4732 0::int)
#4749 := (iff #4745 #4748)
#4750 := [rewrite]: #4749
#4746 := (iff #4735 #4745)
#4743 := (= #4734 #4732)
#4744 := [rewrite]: #4743
#4747 := [monotonicity #4744]: #4746
#4752 := [trans #4747 #4750]: #4751
#4755 := [monotonicity #4752]: #4754
#4758 := [monotonicity #4755]: #4757
#4761 := [monotonicity #4758]: #4760
#8886 := [monotonicity #4761]: #9149
#9203 := [trans #8886 #9162]: #9202
#9039 := [quant-inst]: #7438
#9204 := [mp #9039 #9203]: #7499
#10728 := [unit-resolution #9204 #10727]: #4759
#10729 := [unit-resolution #10728 #10723]: #4741
#13620 := [symm #10729]: #10619
#13608 := (= #2260 #4740)
#9704 := (= ?x63!14 uf_22)
#13603 := [trans #13602 #10708]: #9704
#13612 := [monotonicity #13603]: #13608
#13641 := [trans #13612 #13620]: #13634
#13633 := [trans #13641 #13629]: #13222
#13644 := [trans #13633 #13213]: #2866
#13646 := [unit-resolution #13188 #13644]: false
#13639 := [lemma #13646]: #2872
#10564 := [unit-resolution #13639 #10294 #10559]: false
#10587 := [lemma #10564]: #2872
#4036 := (or #4567 #4561)
#4037 := [def-axiom]: #4036
#10784 := [unit-resolution #4037 #10726]: #4561
#4062 := (or #4567 #4436)
#4035 := [def-axiom]: #4062
#10785 := [unit-resolution #4035 #10726]: #4436
#9537 := (or #2858 #4441 #4433)
#9339 := (uf_1 uf_22 ?x61!13)
#9340 := (uf_10 #9339)
#9365 := (+ #2240 #9340)
#9366 := (+ #188 #9365)
#9387 := (>= #9366 0::int)
#9369 := (= #9366 0::int)
#9344 := (* -1::int #9340)
#9348 := (+ uf_9 #9344)
#9349 := (<= #9348 0::int)
#9416 := (not #9349)
#9358 := (+ #2856 #9340)
#9359 := (+ #188 #9358)
#9360 := (>= #9359 0::int)
#9395 := (or #9349 #9360)
#9398 := (not #9395)
#9392 := (= #2239 #2241)
#9517 := (not #9392)
#9516 := [hypothesis]: #2863
#9520 := (or #9517 #2858)
#9521 := [th-lemma]: #9520
#9522 := [unit-resolution #9521 #9516]: #9517
#9523 := [hypothesis]: #4428
#9404 := (or #4433 #9392 #9398)
#9345 := (+ #1455 #9344)
#9346 := (+ #2241 #9345)
#9347 := (<= #9346 0::int)
#9388 := (or #9349 #9347)
#9389 := (not #9388)
#9390 := (= #2241 #2239)
#9391 := (or #9390 #9389)
#9405 := (or #4433 #9391)
#9412 := (iff #9405 #9404)
#9401 := (or #9392 #9398)
#9407 := (or #4433 #9401)
#9410 := (iff #9407 #9404)
#9411 := [rewrite]: #9410
#9408 := (iff #9405 #9407)
#9402 := (iff #9391 #9401)
#9399 := (iff #9389 #9398)
#9396 := (iff #9388 #9395)
#9363 := (iff #9347 #9360)
#9351 := (+ #2241 #9344)
#9352 := (+ #1455 #9351)
#9355 := (<= #9352 0::int)
#9361 := (iff #9355 #9360)
#9362 := [rewrite]: #9361
#9356 := (iff #9347 #9355)
#9353 := (= #9346 #9352)
#9354 := [rewrite]: #9353
#9357 := [monotonicity #9354]: #9356
#9364 := [trans #9357 #9362]: #9363
#9397 := [monotonicity #9364]: #9396
#9400 := [monotonicity #9397]: #9399
#9393 := (iff #9390 #9392)
#9394 := [rewrite]: #9393
#9403 := [monotonicity #9394 #9400]: #9402
#9409 := [monotonicity #9403]: #9408
#9413 := [trans #9409 #9411]: #9412
#9406 := [quant-inst]: #9405
#9414 := [mp #9406 #9413]: #9404
#9524 := [unit-resolution #9414 #9523 #9522]: #9398
#9417 := (or #9395 #9416)
#9418 := [def-axiom]: #9417
#9525 := [unit-resolution #9418 #9524]: #9416
#9419 := (not #9360)
#9420 := (or #9395 #9419)
#9421 := [def-axiom]: #9420
#9526 := [unit-resolution #9421 #9524]: #9419
#9372 := (or #9349 #9360 #9369)
#7593 := [hypothesis]: #4436
#9375 := (or #4441 #9349 #9360 #9369)
#9341 := (+ #9340 #2240)
#9342 := (+ #188 #9341)
#9343 := (= #9342 0::int)
#9350 := (or #9349 #9347 #9343)
#9376 := (or #4441 #9350)
#9383 := (iff #9376 #9375)
#9378 := (or #4441 #9372)
#9381 := (iff #9378 #9375)
#9382 := [rewrite]: #9381
#9379 := (iff #9376 #9378)
#9373 := (iff #9350 #9372)
#9370 := (iff #9343 #9369)
#9367 := (= #9342 #9366)
#9368 := [rewrite]: #9367
#9371 := [monotonicity #9368]: #9370
#9374 := [monotonicity #9364 #9371]: #9373
#9380 := [monotonicity #9374]: #9379
#9384 := [trans #9380 #9382]: #9383
#9377 := [quant-inst]: #9376
#9385 := [mp #9377 #9384]: #9375
#9527 := [unit-resolution #9385 #7593]: #9372
#9528 := [unit-resolution #9527 #9526 #9525]: #9369
#9529 := (not #9369)
#9530 := (or #9529 #9387)
#9531 := [th-lemma]: #9530
#9532 := [unit-resolution #9531 #9528]: #9387
#9415 := (>= #2857 0::int)
#9533 := (or #9415 #2858)
#9534 := [th-lemma]: #9533
#9535 := [unit-resolution #9534 #9516]: #9415
#9536 := [th-lemma #9535 #9526 #9532]: false
#9538 := [lemma #9536]: #9537
#10786 := [unit-resolution #9538 #10785 #10727]: #2858
#4066 := (or #4564 #2863 #4558)
#4067 := [def-axiom]: #4066
#10787 := [unit-resolution #4067 #10786 #10784]: #4558
#4081 := (or #4555 #4549)
#4082 := [def-axiom]: #4081
#25696 := [unit-resolution #4082 #10787]: #4549
#4077 := (or #4552 #2877 #4546)
#4078 := [def-axiom]: #4077
#25697 := [unit-resolution #4078 #25696]: #4549
#25698 := [unit-resolution #25697 #10587]: #4546
#4087 := (or #4543 #4453)
#4089 := [def-axiom]: #4087
#25699 := [unit-resolution #4089 #25698]: #4453
#17073 := (or #3494 #2335 #4458)
#4079 := (or #4555 #4444)
#4080 := [def-axiom]: #4079
#10788 := [unit-resolution #4080 #10787]: #4444
#4071 := (or #4567 #4418)
#4057 := [def-axiom]: #4071
#17666 := [unit-resolution #4057 #10726]: #4418
#17049 := (or #3494 #2335 #4441 #4423 #981 #4449 #4458)
#7717 := (or #3494 #4319 #2335 #4441 #4423 #981 #4449 #4458)
#6095 := (uf_4 uf_14 ?x72!18)
#6194 := (* -1::int #6095)
#6195 := (+ #2327 #6194)
#7308 := (>= #6195 0::int)
#6100 := (= #2327 #6095)
#4138 := (or #3494 #2338)
#4132 := [def-axiom]: #4138
#7656 := [unit-resolution #4132 #7658]: #2338
#7708 := [hypothesis]: #4453
#6849 := (or #4458 #3479 #6100)
#6096 := (= #6095 #2327)
#6099 := (or #6096 #3479)
#6850 := (or #4458 #6099)
#6859 := (iff #6850 #6849)
#6106 := (or #3479 #6100)
#6854 := (or #4458 #6106)
#6857 := (iff #6854 #6849)
#6858 := [rewrite]: #6857
#6855 := (iff #6850 #6854)
#6109 := (iff #6099 #6106)
#6103 := (or #6100 #3479)
#6107 := (iff #6103 #6106)
#6108 := [rewrite]: #6107
#6104 := (iff #6099 #6103)
#6101 := (iff #6096 #6100)
#6102 := [rewrite]: #6101
#6105 := [monotonicity #6102]: #6104
#6110 := [trans #6105 #6108]: #6109
#6856 := [monotonicity #6110]: #6855
#6860 := [trans #6856 #6858]: #6859
#6853 := [quant-inst]: #6850
#6861 := [mp #6853 #6860]: #6849
#7667 := [unit-resolution #6861 #7708 #7656]: #6100
#7668 := (not #6100)
#7666 := (or #7668 #7308)
#7669 := [th-lemma]: #7666
#7670 := [unit-resolution #7669 #7667]: #7308
#4139 := (not #2923)
#3968 := (or #3494 #4139)
#3970 := [def-axiom]: #3968
#7671 := [unit-resolution #3970 #7658]: #4139
#7057 := (uf_4 uf_14 ?x71!19)
#7092 := (* -1::int #7057)
#7093 := (+ #2325 #7092)
#7094 := (<= #7093 0::int)
#7672 := [hypothesis]: #4444
#7099 := (or #4449 #7094)
#7084 := (+ #7057 #2326)
#7085 := (>= #7084 0::int)
#7100 := (or #4449 #7085)
#7102 := (iff #7100 #7099)
#7104 := (iff #7099 #7099)
#7105 := [rewrite]: #7104
#7097 := (iff #7085 #7094)
#7086 := (+ #2326 #7057)
#7089 := (>= #7086 0::int)
#7095 := (iff #7089 #7094)
#7096 := [rewrite]: #7095
#7090 := (iff #7085 #7089)
#7087 := (= #7084 #7086)
#7088 := [rewrite]: #7087
#7091 := [monotonicity #7088]: #7090
#7098 := [trans #7091 #7096]: #7097
#7103 := [monotonicity #7098]: #7102
#7106 := [trans #7103 #7105]: #7102
#7101 := [quant-inst]: #7100
#7107 := [mp #7101 #7106]: #7099
#7673 := [unit-resolution #7107 #7672]: #7094
#7218 := (+ #6095 #7092)
#7219 := (+ #2330 #7218)
#7220 := (>= #7219 0::int)
#6129 := (uf_6 uf_15 ?x72!18)
#6130 := (= uf_8 #6129)
decl uf_2 :: (-> T1 T2)
#7303 := (uf_2 #2329)
#7315 := (uf_6 uf_15 #7303)
#7316 := (= uf_8 #7315)
#7618 := (iff #7316 #6130)
#7616 := (= #7315 #6129)
#7707 := (= #6129 #7315)
#7304 := (= ?x72!18 #7303)
#16 := (uf_2 #12)
#325 := (= #10 #16)
#4203 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #4196) #325)
#329 := (forall (vars (?x4 T2) (?x5 T2)) #325)
#4206 := (iff #329 #4203)
#4204 := (iff #325 #325)
#4205 := [refl]: #4204
#4207 := [quant-intro #4205]: #4206
#1844 := (~ #329 #329)
#1878 := (~ #325 #325)
#1879 := [refl]: #1878
#1845 := [nnf-pos #1879]: #1844
#17 := (= #16 #10)
#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
#330 := (iff #18 #329)
#327 := (iff #17 #325)
#328 := [rewrite]: #327
#331 := [quant-intro #328]: #330
#324 := [asserted]: #18
#334 := [mp #324 #331]: #329
#1880 := [mp~ #334 #1845]: #329
#4208 := [mp #1880 #4207]: #4203
#7310 := (not #4203)
#7311 := (or #7310 #7304)
#7312 := [quant-inst]: #7311
#7862 := [unit-resolution #7312 #4208]: #7304
#7751 := [monotonicity #7862]: #7707
#7710 := [symm #7751]: #7616
#7711 := [monotonicity #7710]: #7618
#7575 := [hypothesis]: #4418
#6147 := (= uf_22 ?x72!18)
#6150 := (ite #6147 #3895 #6130)
#4961 := (uf_7 uf_15 uf_22 #3894)
#6141 := (uf_6 #4961 ?x72!18)
#6144 := (= uf_8 #6141)
#6153 := (iff #6144 #6150)
#7188 := (or #4987 #6153)
#6139 := (= ?x72!18 uf_22)
#6140 := (ite #6139 #4958 #6130)
#6142 := (= #6141 uf_8)
#6143 := (iff #6142 #6140)
#7189 := (or #4987 #6143)
#7191 := (iff #7189 #7188)
#7193 := (iff #7188 #7188)
#7194 := [rewrite]: #7193
#6154 := (iff #6143 #6153)
#6151 := (iff #6140 #6150)
#6148 := (iff #6139 #6147)
#6149 := [rewrite]: #6148
#6152 := [monotonicity #6149 #4971]: #6151
#6145 := (iff #6142 #6144)
#6146 := [rewrite]: #6145
#6155 := [monotonicity #6146 #6152]: #6154
#7192 := [monotonicity #6155]: #7191
#7195 := [trans #7192 #7194]: #7191
#7190 := [quant-inst]: #7189
#7196 := [mp #7190 #7195]: #7188
#7674 := [unit-resolution #7196 #4222]: #6153
#7702 := (= #2337 #6141)
#7684 := (= #6141 #2337)
#7682 := (= #4961 uf_23)
#7718 := [hypothesis]: #195
#7681 := [symm #7718]: #7680
#7676 := (= #4961 #194)
#7679 := [monotonicity #7678]: #7676
#7683 := [trans #7679 #7681]: #7682
#7700 := [monotonicity #7683]: #7684
#7703 := [symm #7700]: #7702
#7704 := [trans #7656 #7703]: #6144
#7211 := (not #6144)
#7208 := (not #6153)
#7212 := (or #7208 #7211 #6150)
#7213 := [def-axiom]: #7212
#7705 := [unit-resolution #7213 #7704 #7674]: #6150
#7587 := [hypothesis]: #2336
#7197 := (not #6150)
#7876 := (not #7308)
#7626 := (not #7094)
#7627 := (or #7316 #7626 #2923 #7876 #4441 #2335 #7197 #4423)
#7857 := [hypothesis]: #7308
#7858 := [hypothesis]: #4139
#7108 := (uf_1 uf_22 ?x71!19)
#7109 := (uf_10 #7108)
#7113 := (* -1::int #7109)
#7842 := (+ #2330 #7113)
#7844 := (>= #7842 0::int)
#7841 := (= #2330 #7109)
#7843 := (= #2329 #7108)
#7559 := [hypothesis]: #6150
#7205 := (not #6130)
#7614 := (not #7316)
#7615 := [hypothesis]: #7614
#7625 := (or #7205 #7316)
#7620 := (iff #6130 #7316)
#7863 := (= #7303 ?x72!18)
#7864 := [symm #7862]: #7863
#7617 := [monotonicity #7864]: #7616
#7619 := [monotonicity #7617]: #7618
#7621 := [symm #7619]: #7620
#7613 := [hypothesis]: #6130
#7665 := [mp #7613 #7621]: #7316
#7624 := [unit-resolution #7615 #7665]: false
#7623 := [lemma #7624]: #7625
#7565 := [unit-resolution #7623 #7615]: #7205
#7201 := (or #7197 #6147 #6130)
#7202 := [def-axiom]: #7201
#7566 := [unit-resolution #7202 #7565 #7559]: #6147
#7567 := [symm #7566]: #6139
#7568 := [monotonicity #7567]: #7843
#7569 := [monotonicity #7568]: #7841
#7847 := (not #7841)
#7848 := (or #7847 #7844)
#7849 := [th-lemma]: #7848
#7576 := [unit-resolution #7849 #7569]: #7844
#7577 := [hypothesis]: #7094
#7127 := (+ #7092 #7109)
#7128 := (+ #188 #7127)
#7129 := (>= #7128 0::int)
#7134 := (+ #2326 #7109)
#7135 := (+ #188 #7134)
#7138 := (= #7135 0::int)
#7584 := (not #7138)
#7156 := (>= #7135 0::int)
#7875 := (not #7156)
#7309 := (uf_4 uf_14 #7303)
#7324 := (* -1::int #7309)
#7325 := (+ #188 #7324)
#7326 := (<= #7325 0::int)
#7331 := (or #7316 #7326)
#7334 := (or #4423 #7316 #7326)
#7313 := (+ #7309 #1455)
#7314 := (>= #7313 0::int)
#7317 := (or #7316 #7314)
#7335 := (or #4423 #7317)
#7342 := (iff #7335 #7334)
#7337 := (or #4423 #7331)
#7340 := (iff #7337 #7334)
#7341 := [rewrite]: #7340
#7338 := (iff #7335 #7337)
#7332 := (iff #7317 #7331)
#7329 := (iff #7314 #7326)
#7318 := (+ #1455 #7309)
#7321 := (>= #7318 0::int)
#7327 := (iff #7321 #7326)
#7328 := [rewrite]: #7327
#7322 := (iff #7314 #7321)
#7319 := (= #7313 #7318)
#7320 := [rewrite]: #7319
#7323 := [monotonicity #7320]: #7322
#7330 := [trans #7323 #7328]: #7329
#7333 := [monotonicity #7330]: #7332
#7339 := [monotonicity #7333]: #7338
#7343 := [trans #7339 #7341]: #7342
#7336 := [quant-inst]: #7335
#7344 := [mp #7336 #7343]: #7334
#7578 := [unit-resolution #7344 #7575]: #7331
#7579 := [unit-resolution #7578 #7615]: #7326
#7874 := (not #7326)
#7873 := (not #7844)
#7877 := (or #7873 #7874 #7875 #2923 #7876)
#7859 := [hypothesis]: #7156
#7860 := [hypothesis]: #7844
#7861 := [hypothesis]: #7326
#7503 := (+ #6095 #7324)
#7507 := (>= #7503 0::int)
#7502 := (= #6095 #7309)
#7865 := (= #7309 #6095)
#7866 := [monotonicity #7864]: #7865
#7867 := [symm #7866]: #7502
#7868 := (not #7502)
#7869 := (or #7868 #7507)
#7870 := [th-lemma]: #7869
#7871 := [unit-resolution #7870 #7867]: #7507
#7872 := [th-lemma #7871 #7861 #7860 #7859 #7858 #7857]: false
#7878 := [lemma #7872]: #7877
#7580 := [unit-resolution #7878 #7576 #7579 #7858 #7857]: #7875
#7585 := (or #7584 #7156)
#7581 := [th-lemma]: #7585
#7586 := [unit-resolution #7581 #7580]: #7584
#7117 := (+ uf_9 #7113)
#7118 := (<= #7117 0::int)
#7180 := (not #7118)
#7590 := (or #7180 #2335 #7873)
#7591 := [th-lemma]: #7590
#7592 := [unit-resolution #7591 #7576 #7587]: #7180
#7141 := (or #7118 #7129 #7138)
#7144 := (or #4441 #7118 #7129 #7138)
#7110 := (+ #7109 #2326)
#7111 := (+ #188 #7110)
#7112 := (= #7111 0::int)
#7114 := (+ #1455 #7113)
#7115 := (+ #7057 #7114)
#7116 := (<= #7115 0::int)
#7119 := (or #7118 #7116 #7112)
#7145 := (or #4441 #7119)
#7152 := (iff #7145 #7144)
#7147 := (or #4441 #7141)
#7150 := (iff #7147 #7144)
#7151 := [rewrite]: #7150
#7148 := (iff #7145 #7147)
#7142 := (iff #7119 #7141)
#7139 := (iff #7112 #7138)
#7136 := (= #7111 #7135)
#7137 := [rewrite]: #7136
#7140 := [monotonicity #7137]: #7139
#7132 := (iff #7116 #7129)
#7120 := (+ #7057 #7113)
#7121 := (+ #1455 #7120)
#7124 := (<= #7121 0::int)
#7130 := (iff #7124 #7129)
#7131 := [rewrite]: #7130
#7125 := (iff #7116 #7124)
#7122 := (= #7115 #7121)
#7123 := [rewrite]: #7122
#7126 := [monotonicity #7123]: #7125
#7133 := [trans #7126 #7131]: #7132
#7143 := [monotonicity #7133 #7140]: #7142
#7149 := [monotonicity #7143]: #7148
#7153 := [trans #7149 #7151]: #7152
#7146 := [quant-inst]: #7145
#7154 := [mp #7146 #7153]: #7144
#7594 := [unit-resolution #7154 #7593]: #7141
#7595 := [unit-resolution #7594 #7592 #7586]: #7129
#7632 := [th-lemma #7871 #7579 #7595 #7577 #7576 #7858 #7857]: false
#7628 := [lemma #7632]: #7627
#7706 := [unit-resolution #7628 #7673 #7671 #7670 #7593 #7587 #7705 #7575]: #7316
#7709 := [mp #7706 #7711]: #6130
#7713 := (or #7205 #7220)
#7712 := [hypothesis]: #4314
#7225 := (or #4319 #2335 #7205 #7220)
#7221 := (or #7205 #2335 #7220)
#7226 := (or #4319 #7221)
#7233 := (iff #7226 #7225)
#7222 := (or #2335 #7205 #7220)
#7228 := (or #4319 #7222)
#7231 := (iff #7228 #7225)
#7232 := [rewrite]: #7231
#7229 := (iff #7226 #7228)
#7223 := (iff #7221 #7222)
#7224 := [rewrite]: #7223
#7230 := [monotonicity #7224]: #7229
#7234 := [trans #7230 #7232]: #7233
#7227 := [quant-inst]: #7226
#7235 := [mp #7227 #7234]: #7225
#7714 := [unit-resolution #7235 #7712 #7587]: #7713
#7715 := [unit-resolution #7714 #7709]: #7220
#7716 := [th-lemma #7715 #7673 #7671 #7670]: false
#7761 := [lemma #7716]: #7717
#16979 := [unit-resolution #7761 #9187]: #17049
#17090 := [unit-resolution #16979 #10785 #17666 #13581 #10788]: #17073
#16348 := [unit-resolution #17090 #25699]: #17077
#17046 := [unit-resolution #16348 #17052 #7658]: false
#16349 := [lemma #17046]: #3494
#5169 := (uf_6 uf_23 ?x75!20)
#5170 := (= uf_8 #5169)
#21788 := (uf_6 #10323 ?x75!20)
#20832 := (= #21788 #5169)
#20857 := (= #5169 #21788)
#14425 := (= uf_23 #10323)
#14423 := (= #194 #10323)
#14424 := [symm #13577]: #14423
#14426 := [trans #13581 #14424]: #14425
#20702 := [monotonicity #14426]: #20857
#20877 := [symm #20702]: #20832
#21791 := (= uf_8 #21788)
#6014 := (uf_6 uf_15 ?x75!20)
#6015 := (= uf_8 #6014)
#21786 := (= ?x75!20 #9695)
#21794 := (ite #21786 #3895 #6015)
#21797 := (iff #21791 #21794)
#19678 := (or #4987 #21797)
#21787 := (ite #21786 #4958 #6015)
#21789 := (= #21788 uf_8)
#21790 := (iff #21789 #21787)
#19676 := (or #4987 #21790)
#19311 := (iff #19676 #19678)
#19682 := (iff #19678 #19678)
#19685 := [rewrite]: #19682
#21798 := (iff #21790 #21797)
#21795 := (iff #21787 #21794)
#21796 := [monotonicity #4971]: #21795
#21792 := (iff #21789 #21791)
#21793 := [rewrite]: #21792
#21799 := [monotonicity #21793 #21796]: #21798
#19681 := [monotonicity #21799]: #19311
#19733 := [trans #19681 #19685]: #19311
#19684 := [quant-inst]: #19676
#19731 := [mp #19684 #19733]: #19678
#20449 := [unit-resolution #19731 #4222]: #21797
#15125 := (uf_1 #9695 ?x75!20)
#15126 := (uf_10 #15125)
#19741 := (<= #15126 0::int)
#4781 := (* -1::int #4740)
#5008 := (+ #188 #4781)
#5009 := (>= #5008 0::int)
#9232 := (or #4449 #5009)
#7564 := [quant-inst]: #9232
#9311 := [unit-resolution #7564 #10788]: #5009
#11895 := (uf_24 #9695)
#10002 := (* -1::int #11895)
#14620 := (+ #2355 #10002)
#15146 := (<= #14620 0::int)
#14621 := (uf_6 uf_23 #9695)
#14622 := (= uf_8 #14621)
#21303 := (= #3894 #14621)
#21293 := (= #14621 #3894)
#21294 := [monotonicity #13581 #10708]: #21293
#21304 := [symm #21294]: #21303
#21305 := [trans #7677 #21304]: #14622
#15158 := (* -1::int #15126)
#15159 := (+ #10002 #15158)
#15160 := (+ #2355 #15159)
#15161 := (= #15160 0::int)
#23339 := (<= #15160 0::int)
#5042 := (<= #5008 0::int)
#10190 := (not #4741)
#10191 := (or #10190 #5042)
#10192 := [th-lemma]: #10191
#17097 := [unit-resolution #10192 #10729]: #5042
#10025 := (+ #4740 #10002)
#10040 := (<= #10025 0::int)
#9964 := (= #4740 #11895)
#17098 := (= #11895 #4740)
#17107 := [monotonicity #10708]: #17098
#17108 := [symm #17107]: #9964
#17109 := (not #9964)
#17110 := (or #17109 #10040)
#17111 := [th-lemma]: #17110
#17112 := [unit-resolution #17111 #17108]: #10040
#5826 := (uf_1 uf_22 ?x75!20)
#5827 := (uf_10 #5826)
#23569 := (+ #5827 #15158)
#23570 := (<= #23569 0::int)
#23568 := (= #5827 #15126)
#20561 := (= #5826 #15125)
#25948 := (= #15125 #5826)
#25949 := [monotonicity #10708]: #25948
#20537 := [symm #25949]: #20561
#20580 := [monotonicity #20537]: #23568
#25953 := (not #23568)
#25961 := (or #25953 #23570)
#25962 := [th-lemma]: #25961
#20545 := [unit-resolution #25962 #20580]: #23570
#5852 := (+ #2356 #5827)
#5853 := (+ #188 #5852)
#23301 := (>= #5853 0::int)
#20066 := [hypothesis]: #4498
#4125 := (or #4495 #2368)
#4127 := [def-axiom]: #4125
#20064 := [unit-resolution #4127 #20066]: #2368
#29068 := (or #23301 #2367)
#4860 := (>= #188 0::int)
#4051 := (or #4579 #4306)
#4047 := [def-axiom]: #4051
#10596 := [unit-resolution #4047 #5496]: #4306
#9276 := (or #4311 #4860)
#9277 := [quant-inst]: #9276
#12530 := [unit-resolution #9277 #10596]: #4860
#25950 := (= #15126 #5827)
#25951 := [monotonicity #25949]: #25950
#25952 := [symm #25951]: #23568
#25963 := [unit-resolution #25962 #25952]: #23570
#23340 := (>= #15160 0::int)
#10021 := (>= #10025 0::int)
#25933 := (or #17109 #10021)
#25934 := [th-lemma]: #25933
#25935 := [unit-resolution #25934 #17108]: #10021
#23571 := (>= #23569 0::int)
#25954 := (or #25953 #23571)
#25955 := [th-lemma]: #25954
#25956 := [unit-resolution #25955 #25952]: #23571
#23300 := (<= #5853 0::int)
#25968 := (not #23301)
#25609 := [hypothesis]: #25968
#29059 := (or #23300 #23301)
#29062 := [th-lemma]: #29059
#29061 := [unit-resolution #29062 #25609]: #23300
#25957 := (not #23571)
#25944 := (not #23300)
#8759 := (not #5009)
#25942 := (not #10021)
#25958 := (or #23340 #25942 #8759 #25944 #25957)
#25959 := [th-lemma]: #25958
#29063 := [unit-resolution #25959 #29061 #25956 #25935 #9311]: #23340
#24500 := [hypothesis]: #2368
#5831 := (* -1::int #5827)
#5835 := (+ uf_9 #5831)
#5836 := (<= #5835 0::int)
#25729 := (or #23301 #5836)
#23313 := (not #5836)
#25608 := [hypothesis]: #23313
#5856 := (= #5853 0::int)
#25937 := (not #5856)
#25964 := (or #25937 #23301)
#25965 := [th-lemma]: #25964
#25722 := [unit-resolution #25965 #25609]: #25937
#5775 := (uf_4 uf_14 ?x75!20)
#5810 := (* -1::int #5775)
#5845 := (+ #5810 #5827)
#5846 := (+ #188 #5845)
#5847 := (>= #5846 0::int)
#23316 := (not #5847)
#5811 := (+ #2355 #5810)
#5812 := (<= #5811 0::int)
#23280 := (or #4449 #5812)
#5802 := (+ #5775 #2356)
#5803 := (>= #5802 0::int)
#23281 := (or #4449 #5803)
#23283 := (iff #23281 #23280)
#23285 := (iff #23280 #23280)
#23286 := [rewrite]: #23285
#5815 := (iff #5803 #5812)
#5804 := (+ #2356 #5775)
#5807 := (>= #5804 0::int)
#5813 := (iff #5807 #5812)
#5814 := [rewrite]: #5813
#5808 := (iff #5803 #5807)
#5805 := (= #5802 #5804)
#5806 := [rewrite]: #5805
#5809 := [monotonicity #5806]: #5808
#5816 := [trans #5809 #5814]: #5815
#23284 := [monotonicity #5816]: #23283
#23287 := [trans #23284 #23286]: #23283
#23282 := [quant-inst]: #23281
#23288 := [mp #23282 #23287]: #23280
#25723 := [unit-resolution #23288 #10788]: #5812
#25724 := (not #5812)
#25725 := (or #23301 #23316 #25724)
#25726 := [th-lemma]: #25725
#25721 := [unit-resolution #25726 #25609 #25723]: #23316
#5859 := (or #5836 #5847 #5856)
#23289 := (or #4441 #5836 #5847 #5856)
#5828 := (+ #5827 #2356)
#5829 := (+ #188 #5828)
#5830 := (= #5829 0::int)
#5832 := (+ #1455 #5831)
#5833 := (+ #5775 #5832)
#5834 := (<= #5833 0::int)
#5837 := (or #5836 #5834 #5830)
#23290 := (or #4441 #5837)
#23297 := (iff #23290 #23289)
#23292 := (or #4441 #5859)
#23295 := (iff #23292 #23289)
#23296 := [rewrite]: #23295
#23293 := (iff #23290 #23292)
#5860 := (iff #5837 #5859)
#5857 := (iff #5830 #5856)
#5854 := (= #5829 #5853)
#5855 := [rewrite]: #5854
#5858 := [monotonicity #5855]: #5857
#5850 := (iff #5834 #5847)
#5838 := (+ #5775 #5831)
#5839 := (+ #1455 #5838)
#5842 := (<= #5839 0::int)
#5848 := (iff #5842 #5847)
#5849 := [rewrite]: #5848
#5843 := (iff #5834 #5842)
#5840 := (= #5833 #5839)
#5841 := [rewrite]: #5840
#5844 := [monotonicity #5841]: #5843
#5851 := [trans #5844 #5849]: #5850
#5861 := [monotonicity #5851 #5858]: #5860
#23294 := [monotonicity #5861]: #23293
#23298 := [trans #23294 #23296]: #23297
#23291 := [quant-inst]: #23290
#23299 := [mp #23291 #23298]: #23289
#25727 := [unit-resolution #23299 #10785]: #5859
#25728 := [unit-resolution #25727 #25721 #25722 #25608]: false
#25730 := [lemma #25728]: #25729
#29064 := [unit-resolution #25730 #25609]: #5836
#29069 := [th-lemma #29064 #24500 #29063 #17112 #17097 #25963 #12530]: false
#29071 := [lemma #29069]: #29068
#20448 := [unit-resolution #29071 #20064]: #23301
#25969 := (not #23570)
#8760 := (not #5042)
#25967 := (not #10040)
#25970 := (or #23339 #25967 #8760 #25968 #25969)
#25971 := [th-lemma]: #25970
#20530 := [unit-resolution #25971 #20448 #20545 #17112 #17097]: #23339
#20756 := [unit-resolution #25955 #20580]: #23571
#5878 := (or #5836 #5847)
#5881 := (not #5878)
#5780 := (= #2355 #5775)
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#24414 := (>= #5811 0::int)
#24509 := (not #24414)
#4128 := (or #4495 #2937)
#4126 := [def-axiom]: #4128
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#4012 := (or #4495 #4487)
#4013 := [def-axiom]: #4012
#20068 := [unit-resolution #4013 #20066]: #4487
#23167 := (or #24509 #4492 #2934 #2367)
#6043 := (?x47!7 ?x75!20)
#6048 := (uf_1 #6043 ?x75!20)
#24986 := (uf_2 #6048)
#25837 := (uf_6 uf_15 #24986)
#25838 := (= uf_8 #25837)
#21703 := (= #9695 #24986)
#22526 := (ite #21703 #3895 #25838)
#23044 := (not #22526)
#21277 := (uf_6 #10323 #24986)
#21622 := (= uf_8 #21277)
#22242 := (iff #21622 #22526)
#22524 := (or #4987 #22242)
#21246 := (= #24986 #9695)
#21220 := (ite #21246 #4958 #25838)
#21600 := (= #21277 uf_8)
#21601 := (iff #21600 #21220)
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#23042 := (iff #22524 #22524)
#23043 := [rewrite]: #23042
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#22529 := (iff #21220 #22526)
#22515 := (iff #21246 #21703)
#22520 := [rewrite]: #22515
#22530 := [monotonicity #22520 #4971]: #22529
#21227 := (iff #21600 #21622)
#21608 := [rewrite]: #21227
#22592 := [monotonicity #21608 #22530]: #22533
#23029 := [monotonicity #22592]: #23028
#23041 := [trans #23029 #23043]: #23028
#23025 := [quant-inst]: #23024
#22593 := [mp #23025 #23041]: #22524
#23122 := [unit-resolution #22593 #4222]: #22242
#23057 := (not #21622)
#24996 := (uf_6 uf_23 #24986)
#24997 := (= uf_8 #24996)
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#23151 := (= #21277 #24996)
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#23152 := [monotonicity #23149]: #23146
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#6050 := (* -1::int #6049)
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#6045 := (* -1::int #6044)
#6051 := (+ #6045 #6050)
#6052 := (+ #5775 #6051)
#18721 := (>= #6052 0::int)
#6053 := (= #6052 0::int)
#6055 := (uf_6 uf_15 #6043)
#6056 := (= uf_8 #6055)
#6057 := (not #6056)
#6054 := (not #6053)
#6046 := (+ #5775 #6045)
#6047 := (<= #6046 0::int)
#6063 := (or #6047 #6054 #6057)
#6066 := (not #6063)
#6060 := (+ uf_9 #5810)
#6061 := (<= #6060 0::int)
#24508 := (not #6061)
#24510 := (or #24508 #24509 #2367)
#24505 := [hypothesis]: #6061
#24507 := [th-lemma #24506 #24505 #24500]: false
#24511 := [lemma #24507]: #24510
#23125 := [unit-resolution #24511 #24506 #24500]: #24508
#23139 := (or #6061 #6066)
#23138 := [hypothesis]: #2937
#19063 := (or #4344 #2934 #6061 #6066)
#6058 := (or #6057 #6054 #6047)
#6059 := (not #6058)
#6062 := (or #2369 #6061 #6059)
#19066 := (or #4344 #6062)
#18390 := (iff #19066 #19063)
#6069 := (or #2934 #6061 #6066)
#19050 := (or #4344 #6069)
#19090 := (iff #19050 #19063)
#19045 := [rewrite]: #19090
#19051 := (iff #19066 #19050)
#6070 := (iff #6062 #6069)
#6067 := (iff #6059 #6066)
#6064 := (iff #6058 #6063)
#6065 := [rewrite]: #6064
#6068 := [monotonicity #6065]: #6067
#6071 := [monotonicity #2936 #6068]: #6070
#19061 := [monotonicity #6071]: #19051
#18720 := [trans #19061 #19045]: #18390
#18371 := [quant-inst]: #19066
#19065 := [mp #18371 #18720]: #19063
#23137 := [unit-resolution #19065 #9243 #23138]: #23139
#23140 := [unit-resolution #23137 #23125]: #6066
#19081 := (or #6063 #6053)
#12850 := [def-axiom]: #19081
#23135 := [unit-resolution #12850 #23140]: #6053
#23141 := (or #6054 #18721)
#23143 := [th-lemma]: #23141
#23144 := [unit-resolution #23143 #23135]: #18721
#25978 := [hypothesis]: #4487
#23633 := (<= #6052 0::int)
#23142 := (or #6054 #23633)
#23145 := [th-lemma]: #23142
#23147 := [unit-resolution #23145 #23135]: #23633
#19055 := (not #6047)
#18317 := (or #6063 #19055)
#19075 := [def-axiom]: #18317
#23148 := [unit-resolution #19075 #23140]: #19055
#30651 := (not #18721)
#30650 := (not #23633)
#30652 := (or #24998 #6047 #30650 #4492 #30651 #24509)
#28637 := (uf_1 #24986 ?x75!20)
#28638 := (uf_10 #28637)
#28651 := (* -1::int #28638)
#24990 := (uf_24 #24986)
#24991 := (* -1::int #24990)
#28652 := (+ #24991 #28651)
#28653 := (+ #2355 #28652)
#28682 := (>= #28653 0::int)
#28654 := (= #28653 0::int)
#19910 := (uf_3 #15125)
#22479 := (uf_1 #24986 #19910)
#22480 := (uf_10 #22479)
#22498 := (* -1::int #22480)
#22603 := (+ #22498 #24991)
#21494 := (uf_24 #19910)
#22604 := (+ #21494 #22603)
#30636 := (= #22604 0::int)
#30564 := [hypothesis]: #23633
#29534 := [hypothesis]: #18721
#29010 := (+ #6049 #28651)
#21152 := (<= #29010 0::int)
#21012 := (= #6049 #28638)
#30043 := (= #6048 #28637)
#24987 := (= #6043 #24986)
#20827 := (or #7310 #24987)
#20849 := [quant-inst]: #20827
#30089 := [unit-resolution #20849 #4208]: #24987
#30044 := [monotonicity #30089]: #30043
#30097 := [monotonicity #30044]: #21012
#30102 := (not #21012)
#30581 := (or #30102 #21152)
#30588 := [th-lemma]: #30581
#30589 := [unit-resolution #30588 #30097]: #21152
#29012 := (>= #29010 0::int)
#30590 := (or #30102 #29012)
#30591 := [th-lemma]: #30590
#30592 := [unit-resolution #30591 #30097]: #29012
#19879 := (+ #22480 #28651)
#21287 := (<= #19879 0::int)
#21209 := (= #22480 #28638)
#30596 := (= #22479 #28637)
#30594 := (= #19910 ?x75!20)
#19950 := (= ?x75!20 #19910)
#19896 := (or #8139 #19950)
#19953 := [quant-inst]: #19896
#30593 := [unit-resolution #19953 #4202]: #19950
#30595 := [symm #30593]: #30594
#30597 := [monotonicity #30595]: #30596
#30598 := [monotonicity #30597]: #21209
#30599 := (not #21209)
#30600 := (or #30599 #21287)
#30601 := [th-lemma]: #30600
#30602 := [unit-resolution #30601 #30598]: #21287
#20127 := (>= #19879 0::int)
#30603 := (or #30599 #20127)
#30604 := [th-lemma]: #30603
#30605 := [unit-resolution #30604 #30598]: #20127
#22047 := (* -1::int #21494)
#20392 := (+ #2355 #22047)
#20387 := (<= #20392 0::int)
#19773 := (= #2355 #21494)
#30606 := (= #21494 #2355)
#30607 := [monotonicity #30595]: #30606
#30608 := [symm #30607]: #19773
#30609 := (not #19773)
#30610 := (or #30609 #20387)
#30611 := [th-lemma]: #30610
#30612 := [unit-resolution #30611 #30608]: #20387
#20393 := (>= #20392 0::int)
#30613 := (or #30609 #20393)
#30614 := [th-lemma]: #30613
#30615 := [unit-resolution #30614 #30608]: #20393
#25833 := (uf_4 uf_14 #24986)
#25834 := (* -1::int #25833)
#21068 := (+ #6044 #25834)
#21067 := (<= #21068 0::int)
#21078 := (= #6044 #25833)
#30618 := (= #25833 #6044)
#30616 := (= #24986 #6043)
#30617 := [symm #30089]: #30616
#30619 := [monotonicity #30617]: #30618
#30620 := [symm #30619]: #21078
#30621 := (not #21078)
#30622 := (or #30621 #21067)
#30623 := [th-lemma]: #30622
#30624 := [unit-resolution #30623 #30620]: #21067
#21183 := (>= #21068 0::int)
#30625 := (or #30621 #21183)
#30626 := [th-lemma]: #30625
#30627 := [unit-resolution #30626 #30620]: #21183
#28762 := (+ #24990 #25834)
#28763 := (<= #28762 0::int)
#22244 := (or #4449 #28763)
#28754 := (+ #25833 #24991)
#28755 := (>= #28754 0::int)
#22245 := (or #4449 #28755)
#22246 := (iff #22245 #22244)
#22240 := (iff #22244 #22244)
#22286 := [rewrite]: #22240
#28766 := (iff #28755 #28763)
#28756 := (+ #24991 #25833)
#28759 := (>= #28756 0::int)
#28764 := (iff #28759 #28763)
#28765 := [rewrite]: #28764
#28760 := (iff #28755 #28759)
#28757 := (= #28754 #28756)
#28758 := [rewrite]: #28757
#28761 := [monotonicity #28758]: #28760
#28767 := [trans #28761 #28765]: #28766
#22285 := [monotonicity #28767]: #22246
#22287 := [trans #22285 #22286]: #22246
#22187 := [quant-inst]: #22245
#22288 := [mp #22187 #22287]: #22244
#30628 := [unit-resolution #22288 #10788]: #28763
#30563 := (>= #28762 0::int)
#28732 := (= #24990 #25833)
#30629 := [hypothesis]: #24997
#28738 := (or #24998 #28732)
#22151 := (or #4458 #24998 #28732)
#28728 := (= #25833 #24990)
#28729 := (or #28728 #24998)
#22180 := (or #4458 #28729)
#22189 := (iff #22180 #22151)
#22183 := (or #4458 #28738)
#22186 := (iff #22183 #22151)
#22188 := [rewrite]: #22186
#22179 := (iff #22180 #22183)
#28741 := (iff #28729 #28738)
#28735 := (or #28732 #24998)
#28739 := (iff #28735 #28738)
#28740 := [rewrite]: #28739
#28736 := (iff #28729 #28735)
#28733 := (iff #28728 #28732)
#28734 := [rewrite]: #28733
#28737 := [monotonicity #28734]: #28736
#28742 := [trans #28737 #28740]: #28741
#22185 := [monotonicity #28742]: #22179
#22184 := [trans #22185 #22188]: #22189
#22154 := [quant-inst]: #22180
#22243 := [mp #22154 #22184]: #22151
#30630 := [unit-resolution #22243 #25699]: #28738
#30631 := [unit-resolution #30630 #30629]: #28732
#30632 := (not #28732)
#30633 := (or #30632 #30563)
#30634 := [th-lemma]: #30633
#30635 := [unit-resolution #30634 #30631]: #30563
#30637 := [th-lemma #30635 #30628 #30627 #30624 #30615 #30612 #30605 #30602 #30592 #30589 #29534 #30564 #24506 #25723]: #30636
#30640 := (= #28653 #22604)
#30638 := (= #22604 #28653)
#30639 := [th-lemma #30615 #30612 #30605 #30602]: #30638
#30641 := [symm #30639]: #30640
#30642 := [trans #30641 #30637]: #28654
#28659 := (not #28654)
#30643 := (or #28659 #28682)
#30644 := [th-lemma]: #30643
#30645 := [unit-resolution #30644 #30642]: #28682
#16155 := (+ #2355 #24991)
#15436 := (<= #16155 0::int)
#28665 := (or #15436 #24998 #28659)
#21333 := (or #4492 #15436 #24998 #28659)
#28639 := (+ #2356 #28638)
#28640 := (+ #24990 #28639)
#28641 := (= #28640 0::int)
#28642 := (not #28641)
#15907 := (+ #24990 #2356)
#16051 := (>= #15907 0::int)
#28643 := (or #24998 #16051 #28642)
#21024 := (or #4492 #28643)
#20975 := (iff #21024 #21333)
#21318 := (or #4492 #28665)
#21314 := (iff #21318 #21333)
#21310 := [rewrite]: #21314
#21153 := (iff #21024 #21318)
#28668 := (iff #28643 #28665)
#28662 := (or #24998 #15436 #28659)
#28666 := (iff #28662 #28665)
#28667 := [rewrite]: #28666
#28663 := (iff #28643 #28662)
#28660 := (iff #28642 #28659)
#28657 := (iff #28641 #28654)
#28644 := (+ #24990 #28638)
#28645 := (+ #2356 #28644)
#28648 := (= #28645 0::int)
#28655 := (iff #28648 #28654)
#28656 := [rewrite]: #28655
#28649 := (iff #28641 #28648)
#28646 := (= #28640 #28645)
#28647 := [rewrite]: #28646
#28650 := [monotonicity #28647]: #28649
#28658 := [trans #28650 #28656]: #28657
#28661 := [monotonicity #28658]: #28660
#15965 := (iff #16051 #15436)
#13744 := (+ #2356 #24990)
#15070 := (>= #13744 0::int)
#14692 := (iff #15070 #15436)
#16264 := [rewrite]: #14692
#16123 := (iff #16051 #15070)
#16156 := (= #15907 #13744)
#15494 := [rewrite]: #16156
#15349 := [monotonicity #15494]: #16123
#16187 := [trans #15349 #16264]: #15965
#28664 := [monotonicity #16187 #28661]: #28663
#28669 := [trans #28664 #28667]: #28668
#21320 := [monotonicity #28669]: #21153
#21319 := [trans #21320 #21310]: #20975
#21323 := [quant-inst]: #21024
#20612 := [mp #21323 #21319]: #21333
#30646 := [unit-resolution #20612 #25978]: #28665
#30647 := [unit-resolution #30646 #30642 #30629]: #15436
#30648 := [hypothesis]: #19055
#30649 := [th-lemma #30648 #30589 #30564 #30647 #30645]: false
#30653 := [lemma #30649]: #30652
#23150 := [unit-resolution #30653 #23148 #23147 #25978 #23144 #24506]: #24998
#23131 := [mp #23150 #23124]: #23057
#23056 := (not #22242)
#23047 := (or #23056 #21622 #23044)
#23051 := [def-axiom]: #23047
#23132 := [unit-resolution #23051 #23131 #23122]: #23044
#23045 := (not #21703)
#23130 := (or #22526 #23045)
#3924 := (not #3895)
#23054 := (or #22526 #23045 #3924)
#23050 := [def-axiom]: #23054
#23157 := [unit-resolution #23050 #7677]: #23130
#23158 := [unit-resolution #23157 #23132]: #23045
#23164 := (or #22526 #21703)
#23162 := (= #6055 #25837)
#23129 := (= #25837 #6055)
#23156 := [monotonicity #30617]: #23129
#23128 := [symm #23156]: #23162
#19077 := (or #6063 #6056)
#19078 := [def-axiom]: #19077
#23133 := [unit-resolution #19078 #23140]: #6056
#23163 := [trans #23133 #23128]: #25838
#25839 := (not #25838)
#23055 := (or #22526 #21703 #25839)
#23053 := [def-axiom]: #23055
#23165 := [unit-resolution #23053 #23163]: #23164
#23169 := [unit-resolution #23165 #23158 #23132]: false
#23168 := [lemma #23169]: #23167
#19986 := [unit-resolution #23168 #20068 #20016 #20064]: #24509
#20023 := (or #20062 #24414)
#20453 := [th-lemma]: #20023
#20441 := [unit-resolution #20453 #19986]: #20062
#5884 := (or #5780 #5881)
#18349 := (or #4433 #5780 #5881)
#5875 := (or #5836 #5834)
#5876 := (not #5875)
#5776 := (= #5775 #2355)
#5877 := (or #5776 #5876)
#18388 := (or #4433 #5877)
#18375 := (iff #18388 #18349)
#18374 := (or #4433 #5884)
#18380 := (iff #18374 #18349)
#18414 := [rewrite]: #18380
#18370 := (iff #18388 #18374)
#5885 := (iff #5877 #5884)
#5882 := (iff #5876 #5881)
#5879 := (iff #5875 #5878)
#5880 := [monotonicity #5851]: #5879
#5883 := [monotonicity #5880]: #5882
#5781 := (iff #5776 #5780)
#5782 := [rewrite]: #5781
#5886 := [monotonicity #5782 #5883]: #5885
#18411 := [monotonicity #5886]: #18370
#18381 := [trans #18411 #18414]: #18375
#18415 := [quant-inst]: #18388
#18379 := [mp #18415 #18381]: #18349
#20748 := [unit-resolution #18379 #10727]: #5884
#20750 := [unit-resolution #20748 #20441]: #5881
#18373 := (or #5878 #23313)
#18372 := [def-axiom]: #18373
#20751 := [unit-resolution #18372 #20750]: #23313
#18384 := (or #5878 #23316)
#18417 := [def-axiom]: #18384
#20753 := [unit-resolution #18417 #20750]: #23316
#20775 := [unit-resolution #25727 #20753 #20751]: #5856
#25938 := (or #25937 #23300)
#25939 := [th-lemma]: #25938
#20664 := [unit-resolution #25939 #20775]: #23300
#20698 := [unit-resolution #25959 #20664 #20756 #25935 #9311]: #23340
#25974 := (not #23340)
#25973 := (not #23339)
#25975 := (or #15161 #25973 #25974)
#25976 := [th-lemma]: #25975
#20700 := [unit-resolution #25976 #20698 #20530]: #15161
#15166 := (not #15161)
#14623 := (not #14622)
#15169 := (or #14623 #15146 #15166)
#23321 := (or #4492 #14623 #15146 #15166)
#15133 := (+ #2356 #15126)
#15134 := (+ #11895 #15133)
#15135 := (= #15134 0::int)
#15136 := (not #15135)
#15137 := (+ #11895 #2356)
#15138 := (>= #15137 0::int)
#15139 := (or #14623 #15138 #15136)
#23322 := (or #4492 #15139)
#23336 := (iff #23322 #23321)
#23331 := (or #4492 #15169)
#23334 := (iff #23331 #23321)
#23335 := [rewrite]: #23334
#23332 := (iff #23322 #23331)
#15170 := (iff #15139 #15169)
#15167 := (iff #15136 #15166)
#15164 := (iff #15135 #15161)
#15151 := (+ #11895 #15126)
#15152 := (+ #2356 #15151)
#15155 := (= #15152 0::int)
#15162 := (iff #15155 #15161)
#15163 := [rewrite]: #15162
#15156 := (iff #15135 #15155)
#15153 := (= #15134 #15152)
#15154 := [rewrite]: #15153
#15157 := [monotonicity #15154]: #15156
#15165 := [trans #15157 #15163]: #15164
#15168 := [monotonicity #15165]: #15167
#15149 := (iff #15138 #15146)
#15140 := (+ #2356 #11895)
#15143 := (>= #15140 0::int)
#15147 := (iff #15143 #15146)
#15148 := [rewrite]: #15147
#15144 := (iff #15138 #15143)
#15141 := (= #15137 #15140)
#15142 := [rewrite]: #15141
#15145 := [monotonicity #15142]: #15144
#15150 := [trans #15145 #15148]: #15149
#15171 := [monotonicity #15150 #15168]: #15170
#23333 := [monotonicity #15171]: #23332
#23337 := [trans #23333 #23335]: #23336
#23330 := [quant-inst]: #23322
#23338 := [mp #23330 #23337]: #23321
#20754 := [unit-resolution #23338 #20068]: #15169
#20663 := [unit-resolution #20754 #20700 #21305]: #15146
#25941 := (not #15146)
#20620 := (or #19741 #25957 #25944 #25941 #25942 #8759)
#20724 := [th-lemma]: #20620
#20713 := [unit-resolution #20724 #20664 #25935 #20756 #20663 #9311]: #19741
#19738 := (not #19741)
#20001 := (or #10302 #19738 #21786)
#19729 := (= #9695 ?x75!20)
#19725 := (or #19729 #19738)
#19974 := (or #10302 #19725)
#19977 := (iff #19974 #20001)
#19723 := (or #19738 #21786)
#19976 := (or #10302 #19723)
#19980 := (iff #19976 #20001)
#19985 := [rewrite]: #19980
#19981 := (iff #19974 #19976)
#19759 := (iff #19725 #19723)
#19727 := (or #21786 #19738)
#19755 := (iff #19727 #19723)
#19757 := [rewrite]: #19755
#19728 := (iff #19725 #19727)
#19742 := (iff #19729 #21786)
#19724 := [rewrite]: #19742
#19726 := [monotonicity #19724]: #19728
#19753 := [trans #19726 #19757]: #19759
#19982 := [monotonicity #19753]: #19981
#19947 := [trans #19982 #19985]: #19977
#20005 := [quant-inst]: #19974
#19997 := [mp #20005 #19947]: #20001
#20716 := [unit-resolution #19997 #4249 #20713]: #21786
#19787 := (not #21786)
#20752 := (or #21794 #19787)
#19745 := (or #21794 #19787 #3924)
#19739 := [def-axiom]: #19745
#20774 := [unit-resolution #19739 #7677]: #20752
#20858 := [unit-resolution #20774 #20716]: #21794
#19746 := (not #21794)
#19695 := (not #21797)
#19694 := (or #19695 #21791 #19746)
#19761 := [def-axiom]: #19694
#20783 := [unit-resolution #19761 #20858 #20449]: #21791
#20859 := [trans #20783 #20877]: #5170
#5171 := (not #5170)
#5786 := (or #5171 #5780)
#18330 := (or #4458 #5171 #5780)
#5779 := (or #5776 #5171)
#18283 := (or #4458 #5779)
#18352 := (iff #18283 #18330)
#18337 := (or #4458 #5786)
#18335 := (iff #18337 #18330)
#18351 := [rewrite]: #18335
#18336 := (iff #18283 #18337)
#5789 := (iff #5779 #5786)
#5783 := (or #5780 #5171)
#5787 := (iff #5783 #5786)
#5788 := [rewrite]: #5787
#5784 := (iff #5779 #5783)
#5785 := [monotonicity #5782]: #5784
#5790 := [trans #5785 #5788]: #5789
#18331 := [monotonicity #5790]: #18336
#18358 := [trans #18331 #18351]: #18352
#18350 := [quant-inst]: #18283
#18412 := [mp #18350 #18358]: #18330
#20455 := [unit-resolution #18412 #25699]: #5786
#20452 := [unit-resolution #20455 #20441]: #5171
#20896 := [unit-resolution #20452 #20859]: false
#20973 := [lemma #20896]: #4495
#4006 := (or #4504 #3499 #4498)
#4021 := [def-axiom]: #4006
#19204 := [unit-resolution #4021 #20973 #16349]: #4504
#4017 := (or #4507 #4501)
#4025 := [def-axiom]: #4017
#19217 := [unit-resolution #4025 #19204]: #4507
#11869 := (or #2283 #4458)
#8633 := (uf_1 uf_22 ?x65!15)
#8634 := (uf_10 #8633)
#5075 := (* -1::int #2282)
#8695 := (+ #5075 #8634)
#8696 := (+ #188 #8695)
#13182 := (<= #8696 0::int)
#8699 := (= #8696 0::int)
#8635 := (* -1::int #8634)
#8639 := (+ uf_9 #8635)
#8640 := (<= #8639 0::int)
#13547 := (not #8640)
#8579 := (uf_4 uf_14 ?x65!15)
#8589 := (* -1::int #8579)
#8655 := (+ #8589 #8634)
#8656 := (+ #188 #8655)
#8657 := (>= #8656 0::int)
#8662 := (or #8640 #8657)
#8665 := (not #8662)
#8645 := (= #2282 #8579)
#13653 := (not #8645)
#8618 := (+ #2282 #8589)
#13938 := (>= #8618 0::int)
#14032 := (not #13938)
#8826 := [hypothesis]: #2284
#14033 := (or #14032 #2283)
#14029 := [hypothesis]: #13938
#8778 := (>= #8579 0::int)
#13651 := (or #4311 #8778)
#13643 := [quant-inst]: #13651
#14030 := [unit-resolution #13643 #10596]: #8778
#14031 := [th-lemma #8826 #14030 #14029]: false
#14034 := [lemma #14031]: #14033
#14041 := [unit-resolution #14034 #8826]: #14032
#13631 := (or #13653 #13938)
#13654 := [th-lemma]: #13631
#11935 := [unit-resolution #13654 #14041]: #13653
#13403 := (or #4433 #8645 #8665)
#8636 := (+ #1455 #8635)
#8637 := (+ #8579 #8636)
#8638 := (<= #8637 0::int)
#8641 := (or #8640 #8638)
#8642 := (not #8641)
#8643 := (= #8579 #2282)
#8644 := (or #8643 #8642)
#13406 := (or #4433 #8644)
#13514 := (iff #13406 #13403)
#8668 := (or #8645 #8665)
#12773 := (or #4433 #8668)
#13027 := (iff #12773 #13403)
#13487 := [rewrite]: #13027
#12976 := (iff #13406 #12773)
#8669 := (iff #8644 #8668)
#8666 := (iff #8642 #8665)
#8663 := (iff #8641 #8662)
#8660 := (iff #8638 #8657)
#8648 := (+ #8579 #8635)
#8649 := (+ #1455 #8648)
#8652 := (<= #8649 0::int)
#8658 := (iff #8652 #8657)
#8659 := [rewrite]: #8658
#8653 := (iff #8638 #8652)
#8650 := (= #8637 #8649)
#8651 := [rewrite]: #8650
#8654 := [monotonicity #8651]: #8653
#8661 := [trans #8654 #8659]: #8660
#8664 := [monotonicity #8661]: #8663
#8667 := [monotonicity #8664]: #8666
#8646 := (iff #8643 #8645)
#8647 := [rewrite]: #8646
#8670 := [monotonicity #8647 #8667]: #8669
#13475 := [monotonicity #8670]: #12976
#13534 := [trans #13475 #13487]: #13514
#12762 := [quant-inst]: #13406
#13535 := [mp #12762 #13534]: #13403
#11121 := [unit-resolution #13535 #10727 #11935]: #8665
#13548 := (or #8662 #13547)
#13558 := [def-axiom]: #13548
#11762 := [unit-resolution #13558 #11121]: #13547
#13559 := (not #8657)
#13562 := (or #8662 #13559)
#13563 := [def-axiom]: #13562
#11759 := [unit-resolution #13563 #11121]: #13559
#8702 := (or #8640 #8657 #8699)
#13329 := (or #4441 #8640 #8657 #8699)
#8691 := (+ #8634 #5075)
#8692 := (+ #188 #8691)
#8693 := (= #8692 0::int)
#8694 := (or #8640 #8638 #8693)
#13330 := (or #4441 #8694)
#13187 := (iff #13330 #13329)
#13332 := (or #4441 #8702)
#13183 := (iff #13332 #13329)
#13184 := [rewrite]: #13183
#13355 := (iff #13330 #13332)
#8703 := (iff #8694 #8702)
#8700 := (iff #8693 #8699)
#8697 := (= #8692 #8696)
#8698 := [rewrite]: #8697
#8701 := [monotonicity #8698]: #8700
#8704 := [monotonicity #8661 #8701]: #8703
#13107 := [monotonicity #8704]: #13355
#13265 := [trans #13107 #13184]: #13187
#13331 := [quant-inst]: #13330
#13285 := [mp #13331 #13265]: #13329
#14047 := [unit-resolution #13285 #10785]: #8702
#11757 := [unit-resolution #14047 #11759 #11762]: #8699
#14049 := (not #8699)
#14050 := (or #14049 #13182)
#14051 := [th-lemma]: #14050
#11817 := [unit-resolution #14051 #11757]: #13182
#13904 := (uf_1 #9695 ?x65!15)
#13630 := (uf_10 #13904)
#13902 := (* -1::int #13630)
#13836 := (+ #8634 #13902)
#14015 := (>= #13836 0::int)
#13832 := (= #8634 #13630)
#14026 := (= #13630 #8634)
#14022 := (= #13904 #8633)
#14023 := [monotonicity #10708]: #14022
#14027 := [monotonicity #14023]: #14026
#14028 := [symm #14027]: #13832
#14035 := (not #13832)
#14036 := (or #14035 #14015)
#14037 := [th-lemma]: #14036
#14038 := [unit-resolution #14037 #14028]: #14015
#13835 := (>= #13630 0::int)
#13660 := (<= #13630 0::int)
#13692 := (not #13660)
#13628 := (= ?x65!15 #9695)
#13668 := (not #13628)
#8269 := (uf_6 uf_15 ?x65!15)
#8270 := (= uf_8 #8269)
#13741 := (ite #13628 #3895 #8270)
#13822 := (not #13741)
#13691 := (uf_6 #10323 ?x65!15)
#13734 := (= uf_8 #13691)
#13768 := (iff #13734 #13741)
#13775 := (or #4987 #13768)
#13690 := (ite #13628 #4958 #8270)
#13689 := (= #13691 uf_8)
#13739 := (iff #13689 #13690)
#13769 := (or #4987 #13739)
#13699 := (iff #13769 #13775)
#13700 := (iff #13775 #13775)
#13746 := [rewrite]: #13700
#13770 := (iff #13739 #13768)
#13772 := (iff #13690 #13741)
#13773 := [monotonicity #4971]: #13772
#13738 := (iff #13689 #13734)
#13740 := [rewrite]: #13738
#13774 := [monotonicity #13740 #13773]: #13770
#13776 := [monotonicity #13774]: #13699
#13747 := [trans #13776 #13746]: #13699
#13777 := [quant-inst]: #13769
#13821 := [mp #13777 #13747]: #13775
#14053 := [unit-resolution #13821 #4222]: #13768
#13869 := (not #13734)
#5078 := (uf_6 uf_23 ?x65!15)
#5079 := (= uf_8 #5078)
#5080 := (not #5079)
#14062 := (iff #5080 #13869)
#14060 := (iff #5079 #13734)
#14058 := (iff #13734 #5079)
#14056 := (= #13691 #5078)
#14057 := [monotonicity #13583]: #14056
#14059 := [monotonicity #14057]: #14058
#14061 := [symm #14059]: #14060
#14063 := [monotonicity #14061]: #14062
#12807 := (or #4458 #5080 #8645)
#12793 := (or #8643 #5080)
#12815 := (or #4458 #12793)
#12826 := (iff #12815 #12807)
#12790 := (or #5080 #8645)
#12845 := (or #4458 #12790)
#12847 := (iff #12845 #12807)
#12848 := [rewrite]: #12847
#12846 := (iff #12815 #12845)
#12791 := (iff #12793 #12790)
#12794 := (or #8645 #5080)
#12785 := (iff #12794 #12790)
#12787 := [rewrite]: #12785
#12788 := (iff #12793 #12794)
#12789 := [monotonicity #8647]: #12788
#12814 := [trans #12789 #12787]: #12791
#12844 := [monotonicity #12814]: #12846
#12827 := [trans #12844 #12848]: #12826
#12816 := [quant-inst]: #12815
#12828 := [mp #12816 #12827]: #12807
#10280 := [unit-resolution #12828 #7708 #11935]: #5080
#10395 := [mp #10280 #14063]: #13869
#13829 := (not #13768)
#13844 := (or #13829 #13734 #13822)
#13874 := [def-axiom]: #13844
#11835 := [unit-resolution #13874 #10395 #14053]: #13822
#14066 := (or #13741 #13668)
#13827 := (or #13741 #13668 #3924)
#13840 := [def-axiom]: #13827
#14067 := [unit-resolution #13840 #7677]: #14066
#12190 := [unit-resolution #14067 #11835]: #13668
#13657 := (or #13628 #13692)
#14009 := (or #10302 #13628 #13692)
#13626 := (= #9695 ?x65!15)
#13627 := (or #13626 #13692)
#14004 := (or #10302 #13627)
#14021 := (iff #14004 #14009)
#14011 := (or #10302 #13657)
#14014 := (iff #14011 #14009)
#14020 := [rewrite]: #14014
#14012 := (iff #14004 #14011)
#13742 := (iff #13627 #13657)
#13642 := (iff #13626 #13628)
#13640 := [rewrite]: #13642
#13743 := [monotonicity #13640]: #13742
#14013 := [monotonicity #13743]: #14012
#14024 := [trans #14013 #14020]: #14021
#14010 := [quant-inst]: #14004
#14025 := [mp #14010 #14024]: #14009
#14069 := [unit-resolution #14025 #4249]: #13657
#12191 := [unit-resolution #14069 #12190]: #13692
#14071 := (or #13835 #13660)
#14072 := [th-lemma]: #14071
#12192 := [unit-resolution #14072 #12191]: #13835
#11148 := [th-lemma #12192 #14038 #8826 #11817 #12530]: false
#11885 := [lemma #11148]: #11869
#19815 := [unit-resolution #11885 #25699]: #2283
#4090 := (or #4543 #4537)
#4091 := [def-axiom]: #4090
#19829 := [unit-resolution #4091 #25698]: #4537
#19826 := (or #4540 #4534)
#10106 := (uf_1 #9695 uf_11)
#10107 := (uf_10 #10106)
#10111 := (* -1::int #10107)
#4883 := (uf_1 uf_22 uf_11)
#4884 := (uf_10 #4883)
#10686 := (+ #4884 #10111)
#10690 := (>= #10686 0::int)
#10685 := (= #4884 #10107)
#10711 := (= #10107 #4884)
#10709 := (= #10106 #4883)
#10710 := [monotonicity #10708]: #10709
#10712 := [monotonicity #10710]: #10711
#10713 := [symm #10712]: #10685
#10714 := (not #10685)
#10715 := (or #10714 #10690)
#10716 := [th-lemma]: #10715
#10717 := [unit-resolution #10716 #10713]: #10690
#3952 := (<= #108 0::int)
#5799 := (or #1749 #3952)
#5800 := [th-lemma]: #5799
#6367 := [unit-resolution #5800 #5498]: #3952
#4802 := (?x47!7 uf_22)
#4803 := (uf_4 uf_14 #4802)
#4804 := (* -1::int #4803)
#4805 := (+ #188 #4804)
#4806 := (<= #4805 0::int)
#9262 := (not #4806)
#4814 := (uf_6 uf_15 #4802)
#4815 := (= uf_8 #4814)
#4816 := (not #4815)
#4807 := (uf_1 #4802 uf_22)
#4808 := (uf_10 #4807)
#4809 := (* -1::int #4808)
#4810 := (+ #4804 #4809)
#4811 := (+ #188 #4810)
#4812 := (= #4811 0::int)
#4813 := (not #4812)
#4824 := (or #4806 #4813 #4816)
#4827 := (not #4824)
#4821 := (= uf_11 uf_22)
#8243 := (not #4821)
#10613 := [hypothesis]: #1492
#10629 := (or #8243 #217 #10190)
#10625 := (= #216 #108)
#10621 := (= #188 #108)
#4819 := (= uf_22 uf_11)
#10614 := [hypothesis]: #4821
#10615 := [symm #10614]: #4819
#10622 := [monotonicity #10615]: #10621
#10623 := (= #216 #188)
#10616 := [hypothesis]: #4741
#10620 := [symm #10616]: #10619
#10617 := (= #216 #4740)
#10618 := [monotonicity #10614]: #10617
#10624 := [trans #10618 #10620]: #10623
#10626 := [trans #10624 #10622]: #10625
#10627 := [trans #10626 #5498]: #217
#10628 := [unit-resolution #10613 #10627]: false
#10630 := [lemma #10628]: #10629
#10730 := [unit-resolution #10630 #10613 #10729]: #8243
#10732 := (or #4821 #4827)
#4053 := (or #4567 #1657)
#4054 := [def-axiom]: #4053
#10731 := [unit-resolution #4054 #10726]: #1657
#8960 := (or #4344 #1656 #4821 #4827)
#4817 := (or #4816 #4813 #4806)
#4818 := (not #4817)
#4820 := (or #4819 #1656 #4818)
#8966 := (or #4344 #4820)
#9267 := (iff #8966 #8960)
#4833 := (or #1656 #4821 #4827)
#9153 := (or #4344 #4833)
#8906 := (iff #9153 #8960)
#9205 := [rewrite]: #8906
#9156 := (iff #8966 #9153)
#4836 := (iff #4820 #4833)
#4830 := (or #4821 #1656 #4827)
#4834 := (iff #4830 #4833)
#4835 := [rewrite]: #4834
#4831 := (iff #4820 #4830)
#4828 := (iff #4818 #4827)
#4825 := (iff #4817 #4824)
#4826 := [rewrite]: #4825
#4829 := [monotonicity #4826]: #4828
#4822 := (iff #4819 #4821)
#4823 := [rewrite]: #4822
#4832 := [monotonicity #4823 #4829]: #4831
#4837 := [trans #4832 #4835]: #4836
#9157 := [monotonicity #4837]: #9156
#9268 := [trans #9157 #9205]: #9267
#9217 := [quant-inst]: #8966
#9238 := [mp #9217 #9268]: #8960
#10733 := [unit-resolution #9238 #9243 #10731]: #10732
#10734 := [unit-resolution #10733 #10730]: #4827
#9269 := (or #4824 #9262)
#9261 := [def-axiom]: #9269
#10735 := [unit-resolution #9261 #10734]: #9262
#6905 := (>= #4803 0::int)
#10502 := (not #6905)
#10503 := [hypothesis]: #10502
#10442 := (or #4311 #6905)
#10443 := [quant-inst]: #10442
#10607 := [unit-resolution #10443 #10596 #10503]: false
#10608 := [lemma #10607]: #6905
#4888 := (* -1::int #4884)
#4889 := (+ #1455 #4888)
#4890 := (+ #108 #4889)
#4891 := (<= #4890 0::int)
#9338 := (not #4891)
#4892 := (+ uf_9 #4888)
#4893 := (<= #4892 0::int)
#4927 := (or #4891 #4893)
#4930 := (not #4927)
#4925 := (= #108 #216)
#10743 := (not #4925)
#10744 := (iff #1492 #10743)
#10741 := (iff #217 #4925)
#10739 := (iff #4925 #217)
#10738 := [commutativity]: #1490
#10736 := (iff #4925 #788)
#10737 := [monotonicity #5498]: #10736
#10740 := [trans #10737 #10738]: #10739
#10742 := [symm #10740]: #10741
#10745 := [monotonicity #10742]: #10744
#10746 := [mp #10613 #10745]: #10743
#4933 := (or #4925 #4930)
#9308 := (or #4433 #4925 #4930)
#4923 := (or #4893 #4891)
#4924 := (not #4923)
#4926 := (or #4925 #4924)
#9309 := (or #4433 #4926)
#9334 := (iff #9309 #9308)
#9329 := (or #4433 #4933)
#9332 := (iff #9329 #9308)
#9333 := [rewrite]: #9332
#9330 := (iff #9309 #9329)
#4934 := (iff #4926 #4933)
#4931 := (iff #4924 #4930)
#4928 := (iff #4923 #4927)
#4929 := [rewrite]: #4928
#4932 := [monotonicity #4929]: #4931
#4935 := [monotonicity #4932]: #4934
#9331 := [monotonicity #4935]: #9330
#9335 := [trans #9331 #9333]: #9334
#9310 := [quant-inst]: #9309
#9336 := [mp #9310 #9335]: #9308
#10747 := [unit-resolution #9336 #10727]: #4933
#10748 := [unit-resolution #10747 #10746]: #4930
#9321 := (or #4927 #9338)
#9322 := [def-axiom]: #9321
#10749 := [unit-resolution #9322 #10748]: #9338
#10647 := (>= #10107 0::int)
#9978 := (<= #10107 0::int)
#9979 := (not #9978)
#10042 := (= uf_11 #9695)
#10207 := (not #10042)
#10754 := (iff #8243 #10207)
#10752 := (iff #4821 #10042)
#10750 := (iff #10042 #4821)
#10751 := [monotonicity #10708]: #10750
#10753 := [symm #10751]: #10752
#10755 := [monotonicity #10753]: #10754
#10756 := [mp #10730 #10755]: #10207
#10049 := (or #9979 #10042)
#10397 := (or #10302 #9979 #10042)
#10035 := (= #9695 uf_11)
#10036 := (or #10035 #9979)
#10418 := (or #10302 #10036)
#10633 := (iff #10418 #10397)
#10308 := (or #10302 #10049)
#10631 := (iff #10308 #10397)
#10632 := [rewrite]: #10631
#10609 := (iff #10418 #10308)
#10065 := (iff #10036 #10049)
#10046 := (or #10042 #9979)
#10050 := (iff #10046 #10049)
#10051 := [rewrite]: #10050
#10047 := (iff #10036 #10046)
#10044 := (iff #10035 #10042)
#10045 := [rewrite]: #10044
#10048 := [monotonicity #10045]: #10047
#10165 := [trans #10048 #10051]: #10065
#10612 := [monotonicity #10165]: #10609
#10634 := [trans #10612 #10632]: #10633
#10413 := [quant-inst]: #10418
#10635 := [mp #10413 #10634]: #10397
#10757 := [unit-resolution #10635 #4249]: #10049
#10758 := [unit-resolution #10757 #10756]: #9979
#10759 := (or #10647 #9978)
#10760 := [th-lemma]: #10759
#10761 := [unit-resolution #10760 #10758]: #10647
#10762 := [th-lemma #10761 #10749 #10608 #10735 #6367 #10717]: false
#10763 := [lemma #10762]: #217
#4100 := (or #4540 #1492 #4534)
#4086 := [def-axiom]: #4100
#19860 := [unit-resolution #4086 #10763]: #19826
#19861 := [unit-resolution #19860 #19829]: #4534
#4109 := (or #4531 #4525)
#4093 := [def-axiom]: #4109
#19854 := [unit-resolution #4093 #19861]: #4525
#4106 := (or #4528 #2284 #4522)
#4107 := [def-axiom]: #4106
#19851 := [unit-resolution #4107 #19854 #19815]: #4522
#4101 := (or #4519 #4513)
#4103 := [def-axiom]: #4101
#19863 := [unit-resolution #4103 #19851]: #4513
#4123 := (or #4516 #3453 #4510)
#4110 := [def-axiom]: #4123
#19864 := [unit-resolution #4110 #19863]: #4513
#19859 := [unit-resolution #19864 #19217]: #3453
#4134 := (or #3448 #4133)
#4135 := [def-axiom]: #4134
#19869 := [unit-resolution #4135 #19859]: #4133
#4148 := (or #3448 #2304)
#3989 := [def-axiom]: #4148
#19866 := [unit-resolution #3989 #19859]: #2304
#3990 := (or #3448 #2307)
#3991 := [def-axiom]: #3990
#19868 := [unit-resolution #3991 #19859]: #2307
#17736 := (or #3433 #2896 #2306)
#12004 := [hypothesis]: #4133
#6675 := (uf_1 uf_22 ?x68!16)
#6676 := (uf_10 #6675)
#6701 := (+ #2894 #6676)
#6702 := (+ #188 #6701)
#16997 := (<= #6702 0::int)
#6705 := (= #6702 0::int)
#6642 := (uf_4 uf_14 ?x68!16)
#6659 := (* -1::int #6642)
#6694 := (+ #6659 #6676)
#6695 := (+ #188 #6694)
#6696 := (>= #6695 0::int)
#6680 := (* -1::int #6676)
#6684 := (+ uf_9 #6680)
#6685 := (<= #6684 0::int)
#6731 := (or #6685 #6696)
#6734 := (not #6731)
#6728 := (= #2300 #6642)
#14098 := (not #6728)
#6660 := (+ #2300 #6659)
#17022 := (>= #6660 0::int)
#14117 := (not #17022)
#6472 := (+ #188 #6659)
#6473 := (<= #6472 0::int)
#6496 := (uf_6 uf_15 ?x68!16)
#6497 := (= uf_8 #6496)
#16679 := (not #6497)
#13671 := (= ?x68!16 #9695)
#13592 := (ite #13671 #3895 #6497)
#15564 := (not #13592)
#13670 := (uf_6 #10323 ?x68!16)
#13649 := (= uf_8 #13670)
#13820 := (iff #13592 #13649)
#14101 := (or #4987 #13820)
#13645 := (ite #13671 #4958 #6497)
#13647 := (= #13670 uf_8)
#13648 := (iff #13647 #13645)
#15296 := (or #4987 #13648)
#15178 := (iff #15296 #14101)
#15561 := (iff #14101 #14101)
#15556 := [rewrite]: #15561
#13826 := (iff #13648 #13820)
#13663 := (iff #13649 #13592)
#13819 := (iff #13663 #13820)
#13825 := [rewrite]: #13819
#13664 := (iff #13648 #13663)
#13638 := (iff #13645 #13592)
#13662 := [monotonicity #4971]: #13638
#13655 := (iff #13647 #13649)
#13661 := [rewrite]: #13655
#13665 := [monotonicity #13661 #13662]: #13664
#13828 := [trans #13665 #13825]: #13826
#15560 := [monotonicity #13828]: #15178
#15558 := [trans #15560 #15556]: #15178
#15177 := [quant-inst]: #15296
#15563 := [mp #15177 #15558]: #14101
#17427 := [unit-resolution #15563 #4222]: #13820
#16690 := (not #13649)
#17349 := (iff #2307 #16690)
#17657 := (iff #2306 #13649)
#17654 := (iff #13649 #2306)
#17353 := (= #13670 #2305)
#17653 := [monotonicity #13583]: #17353
#17655 := [monotonicity #17653]: #17654
#17300 := [symm #17655]: #17657
#17434 := [monotonicity #17300]: #17349
#17656 := [hypothesis]: #2307
#17463 := [mp #17656 #17434]: #16690
#16689 := (not #13820)
#16795 := (or #16689 #15564 #13649)
#16793 := [def-axiom]: #16795
#17402 := [unit-resolution #16793 #17463 #17427]: #15564
#15565 := (not #13671)
#17466 := (or #13592 #15565)
#15618 := (or #13592 #15565 #3924)
#15814 := [def-axiom]: #15618
#17660 := [unit-resolution #15814 #7677]: #17466
#17661 := [unit-resolution #17660 #17402]: #15565
#16681 := (or #13592 #13671 #16679)
#16685 := [def-axiom]: #16681
#17658 := [unit-resolution #16685 #17661 #17402]: #16679
#6530 := (or #6473 #6497)
#17091 := (or #4423 #6473 #6497)
#6493 := (+ #6642 #1455)
#6494 := (>= #6493 0::int)
#6495 := (or #6497 #6494)
#17092 := (or #4423 #6495)
#16354 := (iff #17092 #17091)
#17099 := (or #4423 #6530)
#16352 := (iff #17099 #17091)
#16353 := [rewrite]: #16352
#16351 := (iff #17092 #17099)
#6533 := (iff #6495 #6530)
#6527 := (or #6497 #6473)
#6531 := (iff #6527 #6530)
#6532 := [rewrite]: #6531
#6528 := (iff #6495 #6527)
#6525 := (iff #6494 #6473)
#6467 := (+ #1455 #6642)
#6469 := (>= #6467 0::int)
#6474 := (iff #6469 #6473)
#6524 := [rewrite]: #6474
#6470 := (iff #6494 #6469)
#6468 := (= #6493 #6467)
#6466 := [rewrite]: #6468
#6471 := [monotonicity #6466]: #6470
#6526 := [trans #6471 #6524]: #6525
#6529 := [monotonicity #6526]: #6528
#6534 := [trans #6529 #6532]: #6533
#17076 := [monotonicity #6534]: #16351
#16356 := [trans #17076 #16353]: #16354
#17101 := [quant-inst]: #17092
#16358 := [mp #17101 #16356]: #17091
#17669 := [unit-resolution #16358 #17666]: #6530
#17659 := [unit-resolution #17669 #17658]: #6473
#6393 := (+ #2298 #4781)
#18006 := (<= #6393 0::int)
#17296 := (= #2298 #4740)
#6449 := (= ?x67!17 uf_22)
#14077 := (= ?x67!17 #9695)
#6439 := (uf_6 uf_15 ?x67!17)
#6440 := (= uf_8 #6439)
#14085 := (ite #14077 #3895 #6440)
#14079 := (uf_6 #10323 ?x67!17)
#14082 := (= uf_8 #14079)
#14088 := (iff #14082 #14085)
#16842 := (or #4987 #14088)
#14078 := (ite #14077 #4958 #6440)
#14080 := (= #14079 uf_8)
#14081 := (iff #14080 #14078)
#16843 := (or #4987 #14081)
#16827 := (iff #16843 #16842)
#16829 := (iff #16842 #16842)
#16830 := [rewrite]: #16829
#14089 := (iff #14081 #14088)
#14086 := (iff #14078 #14085)
#14087 := [monotonicity #4971]: #14086
#14083 := (iff #14080 #14082)
#14084 := [rewrite]: #14083
#14090 := [monotonicity #14084 #14087]: #14089
#16828 := [monotonicity #14090]: #16827
#16825 := [trans #16828 #16830]: #16827
#16822 := [quant-inst]: #16843
#16780 := [mp #16822 #16825]: #16842
#17670 := [unit-resolution #16780 #4222]: #14088
#17684 := (= #2303 #14079)
#17672 := (= #14079 #2303)
#17688 := [monotonicity #13583]: #17672
#17680 := [symm #17688]: #17684
#17671 := [hypothesis]: #2304
#17705 := [trans #17671 #17680]: #14082
#16844 := (not #14082)
#16848 := (not #14088)
#16851 := (or #16848 #16844 #14085)
#16852 := [def-axiom]: #16851
#17703 := [unit-resolution #16852 #17705 #17670]: #14085
#16816 := (not #6440)
#6405 := (uf_4 uf_14 ?x67!17)
#17321 := (+ #6405 #9707)
#17316 := (<= #17321 0::int)
#14110 := (not #17316)
#14118 := (not #6473)
#17620 := (or #14110 #2896 #13671 #14118)
#17021 := (not #6685)
#5574 := (* -1::int #6405)
#5674 := (+ #2298 #5574)
#5698 := (<= #5674 0::int)
#16850 := (or #4449 #5698)
#5667 := (+ #6405 #2299)
#5668 := (>= #5667 0::int)
#16871 := (or #4449 #5668)
#16875 := (iff #16871 #16850)
#16878 := (iff #16850 #16850)
#16872 := [rewrite]: #16878
#5701 := (iff #5668 #5698)
#5669 := (+ #2299 #6405)
#5671 := (>= #5669 0::int)
#5699 := (iff #5671 #5698)
#5700 := [rewrite]: #5699
#5672 := (iff #5668 #5671)
#5664 := (= #5667 #5669)
#5670 := [rewrite]: #5664
#5673 := [monotonicity #5670]: #5672
#5702 := [trans #5673 #5700]: #5701
#16877 := [monotonicity #5702]: #16875
#16845 := [trans #16877 #16872]: #16875
#16831 := [quant-inst]: #16871
#16858 := [mp #16831 #16845]: #16850
#12150 := [unit-resolution #16858 #10788]: #5698
#14116 := [hypothesis]: #6473
#14115 := [hypothesis]: #17316
#14119 := (not #10581)
#14113 := (not #5698)
#14120 := (or #14117 #14118 #14113 #2896 #14110 #14119)
#14127 := [th-lemma]: #14120
#14128 := [unit-resolution #14127 #14115 #14116 #12150 #12004 #12925]: #14117
#14167 := (or #14098 #17022)
#14099 := [th-lemma]: #14167
#14170 := [unit-resolution #14099 #14128]: #14098
#6737 := (or #6728 #6734)
#17003 := (or #4433 #6728 #6734)
#6681 := (+ #1455 #6680)
#6682 := (+ #6642 #6681)
#6683 := (<= #6682 0::int)
#6724 := (or #6685 #6683)
#6725 := (not #6724)
#6726 := (= #6642 #2300)
#6727 := (or #6726 #6725)
#17006 := (or #4433 #6727)
#17015 := (iff #17006 #17003)
#16994 := (or #4433 #6737)
#17013 := (iff #16994 #17003)
#17012 := [rewrite]: #17013
#17007 := (iff #17006 #16994)
#6738 := (iff #6727 #6737)
#6735 := (iff #6725 #6734)
#6732 := (iff #6724 #6731)
#6699 := (iff #6683 #6696)
#6687 := (+ #6642 #6680)
#6688 := (+ #1455 #6687)
#6691 := (<= #6688 0::int)
#6697 := (iff #6691 #6696)
#6698 := [rewrite]: #6697
#6692 := (iff #6683 #6691)
#6689 := (= #6682 #6688)
#6690 := [rewrite]: #6689
#6693 := [monotonicity #6690]: #6692
#6700 := [trans #6693 #6698]: #6699
#6733 := [monotonicity #6700]: #6732
#6736 := [monotonicity #6733]: #6735
#6729 := (iff #6726 #6728)
#6730 := [rewrite]: #6729
#6739 := [monotonicity #6730 #6736]: #6738
#17008 := [monotonicity #6739]: #17007
#17016 := [trans #17008 #17012]: #17015
#17005 := [quant-inst]: #17006
#17017 := [mp #17005 #17016]: #17003
#14323 := [unit-resolution #17017 #10727]: #6737
#14462 := [unit-resolution #14323 #14170]: #6734
#17024 := (or #6731 #17021)
#17014 := [def-axiom]: #17024
#14131 := [unit-resolution #17014 #14462]: #17021
#17023 := (not #6696)
#17025 := (or #6731 #17023)
#17026 := [def-axiom]: #17025
#14463 := [unit-resolution #17026 #14462]: #17023
#6708 := (or #6685 #6696 #6705)
#16986 := (or #4441 #6685 #6696 #6705)
#6677 := (+ #6676 #2894)
#6678 := (+ #188 #6677)
#6679 := (= #6678 0::int)
#6686 := (or #6685 #6683 #6679)
#16942 := (or #4441 #6686)
#16967 := (iff #16942 #16986)
#16939 := (or #4441 #6708)
#16965 := (iff #16939 #16986)
#16966 := [rewrite]: #16965
#16958 := (iff #16942 #16939)
#6709 := (iff #6686 #6708)
#6706 := (iff #6679 #6705)
#6703 := (= #6678 #6702)
#6704 := [rewrite]: #6703
#6707 := [monotonicity #6704]: #6706
#6710 := [monotonicity #6700 #6707]: #6709
#16981 := [monotonicity #6710]: #16958
#16968 := [trans #16981 #16966]: #16967
#16943 := [quant-inst]: #16942
#16957 := [mp #16943 #16968]: #16986
#14091 := [unit-resolution #16957 #10785]: #6708
#15021 := [unit-resolution #14091 #14463 #14131]: #6705
#15016 := (not #6705)
#15301 := (or #15016 #16997)
#16191 := [th-lemma]: #15301
#16210 := [unit-resolution #16191 #15021]: #16997
#17555 := (uf_1 #9695 ?x68!16)
#17556 := (uf_10 #17555)
#11882 := (* -1::int #17556)
#11971 := (+ #6676 #11882)
#12082 := (>= #11971 0::int)
#12012 := (= #6676 #17556)
#16213 := (= #17556 #6676)
#15939 := (= #17555 #6675)
#16211 := [monotonicity #10708]: #15939
#16214 := [monotonicity #16211]: #16213
#16541 := [symm #16214]: #12012
#16559 := (not #12012)
#16520 := (or #16559 #12082)
#16540 := [th-lemma]: #16520
#16560 := [unit-resolution #16540 #16541]: #12082
#17561 := (<= #17556 0::int)
#17562 := (not #17561)
#16607 := [hypothesis]: #15565
#17589 := (or #10302 #13671 #17562)
#17574 := (= #9695 ?x68!16)
#17571 := (or #17574 #17562)
#17590 := (or #10302 #17571)
#11861 := (iff #17590 #17589)
#17587 := (or #13671 #17562)
#17606 := (or #10302 #17587)
#17600 := (iff #17606 #17589)
#17601 := [rewrite]: #17600
#17593 := (iff #17590 #17606)
#17569 := (iff #17571 #17587)
#17585 := (iff #17574 #13671)
#17586 := [rewrite]: #17585
#17588 := [monotonicity #17586]: #17569
#17599 := [monotonicity #17588]: #17593
#17598 := [trans #17599 #17601]: #11861
#17583 := [quant-inst]: #17590
#11866 := [mp #17583 #17598]: #17589
#17621 := [unit-resolution #11866 #4249 #16607]: #17562
#17166 := [th-lemma #12150 #12004 #14115 #12925 #17621 #16560 #16210]: false
#17622 := [lemma #17166]: #17620
#17722 := [unit-resolution #17622 #17661 #12004 #17659]: #14110
#18133 := (or #16816 #17316)
#18126 := [hypothesis]: #14110
#18130 := [hypothesis]: #6440
#18002 := (or #4328 #16816 #9686 #17316)
#17278 := (+ #9701 #5574)
#17277 := (>= #17278 0::int)
#17276 := (or #9686 #16816 #17277)
#18007 := (or #4328 #17276)
#17984 := (iff #18007 #18002)
#17337 := (or #16816 #9686 #17316)
#17982 := (or #4328 #17337)
#17989 := (iff #17982 #18002)
#17990 := [rewrite]: #17989
#17983 := (iff #18007 #17982)
#17345 := (iff #17276 #17337)
#17333 := (or #9686 #16816 #17316)
#17346 := (iff #17333 #17337)
#17341 := [rewrite]: #17346
#17336 := (iff #17276 #17333)
#17332 := (iff #17277 #17316)
#17303 := (+ #5574 #9701)
#17297 := (>= #17303 0::int)
#17320 := (iff #17297 #17316)
#17326 := [rewrite]: #17320
#17306 := (iff #17277 #17297)
#17304 := (= #17278 #17303)
#17305 := [rewrite]: #17304
#17317 := [monotonicity #17305]: #17306
#17325 := [trans #17317 #17326]: #17332
#17324 := [monotonicity #17325]: #17336
#17347 := [trans #17324 #17341]: #17345
#17971 := [monotonicity #17347]: #17983
#17988 := [trans #17971 #17990]: #17984
#17980 := [quant-inst]: #18007
#17991 := [mp #17980 #17988]: #18002
#18132 := [unit-resolution #17991 #13967 #13969 #18130 #18126]: false
#18134 := [lemma #18132]: #18133
#17723 := [unit-resolution #18134 #17722]: #16816
#16801 := (not #14085)
#16815 := (or #16801 #14077 #6440)
#16832 := [def-axiom]: #16815
#17724 := [unit-resolution #16832 #17723 #17703]: #14077
#17720 := [trans #17724 #10708]: #6449
#17697 := [monotonicity #17720]: #17296
#17700 := (not #17296)
#17701 := (or #17700 #18006)
#17693 := [th-lemma]: #17701
#17673 := [unit-resolution #17693 #17697]: #18006
#18044 := (not #18006)
#18045 := (or #18044 #14117 #2896 #14118)
#18043 := [hypothesis]: #18006
#18041 := [hypothesis]: #17022
#18042 := [th-lemma #18041 #12004 #14116 #9311 #18043]: false
#18046 := [lemma #18042]: #18045
#17699 := [unit-resolution #18046 #17673 #12004 #17659]: #14117
#17676 := [unit-resolution #14099 #17699]: #14098
#17677 := [unit-resolution #14323 #17676]: #6734
#17164 := (or #6731 #6705)
#17180 := [hypothesis]: #15016
#17209 := [hypothesis]: #6734
#17210 := [unit-resolution #17014 #17209]: #17021
#17207 := [unit-resolution #17026 #17209]: #17023
#17212 := [unit-resolution #14091 #17207 #17210 #17180]: false
#17211 := [lemma #17212]: #17164
#17678 := [unit-resolution #17211 #17677]: #6705
#17681 := [unit-resolution #16191 #17678]: #16997
#17675 := [unit-resolution #11866 #4249 #17661]: #17562
#17735 := [th-lemma #17673 #9311 #17675 #16560 #17681 #12004]: false
#17721 := [lemma #17735]: #17736
[unit-resolution #17721 #19868 #19866 #19869]: false
unsat