--- a/src/HOL/Boogie/Examples/VCC_Max.certs Mon Dec 20 09:06:37 2010 +0100
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs Mon Dec 20 09:31:47 2010 +0100
@@ -1,758 +1,1510 @@
-3b08169b1d21e7df09081614598ecffbfc739ade 7774 0
+d334e94512e2be06e90930c75ed763964895b7de 7803 0
#2 := false
-#161 := 0::Int
-decl f122 :: (-> S19 S20 Int)
+decl f121 :: (-> S19 S20 Int)
decl f77 :: (-> S20 Int S18 S20)
decl f19 :: S18
#50 := f19
decl ?v0!14 :: Int
-#18578 := ?v0!14
+#18614 := ?v0!14
decl f54 :: (-> S18 Int S20)
-decl f299 :: Int
-#3041 := f299
-#3042 := (f54 f19 f299)
-#18583 := (f77 #3042 ?v0!14 f19)
-decl f298 :: S19
-#3039 := f298
-#18584 := (f122 f298 #18583)
+decl f298 :: Int
+#3041 := f298
+#3042 := (f54 f19 f298)
+#18619 := (f77 #3042 ?v0!14 f19)
+decl f297 :: S19
+#3039 := f297
+#18620 := (f121 f297 #18619)
+decl f309 :: Int
+#3139 := f309
+#3257 := (f77 #3042 f309 f19)
+#3266 := (f121 f297 #3257)
+#30591 := (= #3266 #18620)
+#30624 := (not #30591)
+#161 := 0::Int
#4203 := -1::Int
-#18905 := (* -1::Int #18584)
-decl f310 :: Int
-#3139 := f310
-#3257 := (f77 #3042 f310 f19)
-#3266 := (f122 f298 #3257)
-#30336 := (+ #3266 #18905)
-#30338 := (>= #30336 0::Int)
-#30332 := (= #3266 #18584)
-#29868 := (= f310 ?v0!14)
-decl f308 :: Int
-#3131 := f308
-#29822 := (+ f308 #18905)
-#29823 := (>= #29822 0::Int)
-#30220 := (not #29823)
-decl f316 :: Int
-#3275 := f316
-#13534 := (* -1::Int f316)
-#24551 := (+ f308 #13534)
-#24552 := (<= #24551 0::Int)
-#30447 := (+ #3266 #13534)
-#30448 := (<= #30447 0::Int)
-#30446 := (= #3266 f316)
+#18941 := (* -1::Int #18620)
+#30619 := (+ #3266 #18941)
+#30621 := (>= #30619 0::Int)
+#30631 := (not #30621)
decl f315 :: Int
-#3268 := f315
-#12565 := (= f315 f316)
-#18906 := (+ f316 #18905)
-#18907 := (>= #18906 0::Int)
-#18892 := (* -1::Int ?v0!14)
-decl f318 :: Int
-#3285 := f318
-#18893 := (+ f318 #18892)
-#18894 := (<= #18893 0::Int)
-#18580 := (>= ?v0!14 0::Int)
-#22360 := (not #18580)
-#7596 := 4294967295::Int
-#18579 := (<= ?v0!14 4294967295::Int)
-#22359 := (not #18579)
-#22375 := (or #22359 #22360 #18894 #18907)
-#22380 := (not #22375)
+#3275 := f315
+#13570 := (* -1::Int f315)
+#30344 := (+ #3266 #13570)
+#30172 := (<= #30344 0::Int)
+#30343 := (= #3266 f315)
+decl f314 :: Int
+#3268 := f314
+#12601 := (= f314 f315)
+#18942 := (+ f315 #18941)
+#18943 := (>= #18942 0::Int)
+#18928 := (* -1::Int ?v0!14)
+decl f317 :: Int
+#3285 := f317
+#18929 := (+ f317 #18928)
+#18930 := (<= #18929 0::Int)
+#18616 := (>= ?v0!14 0::Int)
+#22396 := (not #18616)
+#7632 := 4294967295::Int
+#18615 := (<= ?v0!14 4294967295::Int)
+#22395 := (not #18615)
+#22411 := (or #22395 #22396 #18930 #18943)
+#22416 := (not #22411)
#202 := (:var 0 Int)
#3123 := (f77 #3042 #202 f19)
-#23327 := (pattern #3123)
-#15183 := (<= #202 4294967295::Int)
-#19577 := (not #15183)
-#3124 := (f122 f298 #3123)
-#13535 := (+ #3124 #13534)
-#13536 := (<= #13535 0::Int)
-#13515 := (* -1::Int f318)
-#13523 := (+ #202 #13515)
-#13522 := (>= #13523 0::Int)
+#23363 := (pattern #3123)
+#15219 := (<= #202 4294967295::Int)
+#19613 := (not #15219)
+#3124 := (f121 f297 #3123)
+#13571 := (+ #3124 #13570)
+#13572 := (<= #13571 0::Int)
+#13551 := (* -1::Int f317)
+#13559 := (+ #202 #13551)
+#13558 := (>= #13559 0::Int)
#4202 := (>= #202 0::Int)
-#5104 := (not #4202)
-#22341 := (or #5104 #13522 #13536 #19577)
-#23344 := (forall (vars (?v0 Int)) (:pat #23327) #22341)
-#23349 := (not #23344)
-decl f317 :: Int
-#3277 := f317
-#13556 := (* -1::Int f317)
-decl f297 :: Int
-#3036 := f297
-#13557 := (+ f297 #13556)
-#13558 := (<= #13557 0::Int)
-#3298 := (f77 #3042 f317 f19)
-#3299 := (f122 f298 #3298)
-#12607 := (= f316 #3299)
-#22326 := (not #12607)
-#22327 := (or #22326 #13558)
-#22328 := (not #22327)
-#23352 := (or #22328 #23349)
-#23355 := (not #23352)
-#23358 := (or #23355 #22380)
-#23361 := (not #23358)
-#13516 := (+ f297 #13515)
-#13514 := (>= #13516 0::Int)
-#13519 := (not #13514)
-#23364 := (or #13519 #23361)
-#23367 := (not #23364)
-#23370 := (or #13519 #23367)
-#23373 := (not #23370)
-#15863 := 4294967294::Int
-#15864 := (<= f310 4294967294::Int)
-#18561 := (not #15864)
-#13583 := (+ f310 #13515)
-#13582 := (= #13583 -1::Int)
-#13586 := (not #13582)
+#5124 := (not #4202)
+#22377 := (or #5124 #13558 #13572 #19613)
+#23380 := (forall (vars (?v0 Int)) (:pat #23363) #22377)
+#23385 := (not #23380)
+decl f316 :: Int
+#3277 := f316
+#13592 := (* -1::Int f316)
+decl f296 :: Int
+#3036 := f296
+#13593 := (+ f296 #13592)
+#13594 := (<= #13593 0::Int)
+#3298 := (f77 #3042 f316 f19)
+#3299 := (f121 f297 #3298)
+#12643 := (= f315 #3299)
+#22362 := (not #12643)
+#22363 := (or #22362 #13594)
+#22364 := (not #22363)
+#23388 := (or #22364 #23385)
+#23391 := (not #23388)
+#23394 := (or #23391 #22416)
+#23397 := (not #23394)
+#13552 := (+ f296 #13551)
+#13550 := (>= #13552 0::Int)
+#13555 := (not #13550)
+#23400 := (or #13555 #23397)
+#23403 := (not #23400)
+#23406 := (or #13555 #23403)
+#23409 := (not #23406)
+#15899 := 4294967294::Int
+#15900 := (<= f309 4294967294::Int)
+#18597 := (not #15900)
+#13619 := (+ f309 #13551)
+#13618 := (= #13619 -1::Int)
+#13622 := (not #13618)
#935 := 2::Int
-#13506 := (>= f318 2::Int)
-#22403 := (not #13506)
-#13498 := (>= f310 -1::Int)
-#18558 := (not #13498)
-#13489 := (>= f317 0::Int)
-#22402 := (not #13489)
-decl f302 :: (-> S19 S17 S17 Int S18 S1)
+#13542 := (>= f317 2::Int)
+#22439 := (not #13542)
+#13534 := (>= f309 -1::Int)
+#18594 := (not #13534)
+#13525 := (>= f316 0::Int)
+#22438 := (not #13525)
+decl f301 :: (-> S19 S17 S17 Int S18 S1)
decl f16 :: S18
#46 := f16
-decl f285 :: S17
-#3012 := f285
-decl f281 :: S17
-#3008 := f281
-#3287 := (f302 f298 f281 f285 f318 f16)
+decl f284 :: S17
+#3012 := f284
+decl f280 :: S17
+#3008 := f280
+#3287 := (f301 f297 f280 f284 f317 f16)
decl f1 :: S1
#4 := f1
-#12586 := (= f1 #3287)
-#12656 := (not #12586)
-#23376 := (or #12656 #22402 #18558 #22403 #13586 #18561 #23373)
-#23379 := (not #23376)
-#23382 := (or #18558 #18561 #23379)
-#23385 := (not #23382)
+#12622 := (= f1 #3287)
+#12692 := (not #12622)
+#23412 := (or #12692 #22438 #18594 #22439 #13622 #18597 #23409)
+#23415 := (not #23412)
+#23418 := (or #18594 #18597 #23415)
+#23421 := (not #23418)
#42 := 1::Int
-#13480 := (>= f310 1::Int)
-#13620 := (not #13480)
-#12568 := (= f310 f317)
-#12695 := (not #12568)
-#12704 := (not #12565)
-decl f287 :: S17
-#3014 := f287
+#13516 := (>= f309 1::Int)
+#13656 := (not #13516)
+#12604 := (= f309 f316)
+#12731 := (not #12604)
+#12740 := (not #12601)
+decl f286 :: S17
+#3014 := f286
+decl f281 :: S17
+#3009 := f281
+#3272 := (f301 f297 f281 f286 f309 f16)
+#12596 := (= f1 #3272)
+#12758 := (not #12596)
+decl f288 :: S17
+#3016 := f288
decl f282 :: S17
-#3009 := f282
-#3272 := (f302 f298 f282 f287 f310 f16)
-#12560 := (= f1 #3272)
-#12722 := (not #12560)
-decl f289 :: S17
-#3016 := f289
-decl f283 :: S17
-#3010 := f283
-#3270 := (f302 f298 f283 f289 f315 f19)
-#12557 := (= f1 #3270)
-#12731 := (not #12557)
-#12554 := (= #3266 f315)
-#12740 := (not #12554)
+#3010 := f282
+#3270 := (f301 f297 f282 f288 f314 f19)
+#12593 := (= f1 #3270)
+#12767 := (not #12593)
+#12590 := (= #3266 f314)
+#12776 := (not #12590)
decl f79 :: (-> S19 S20 S1)
-#3263 := (f79 f298 #3257)
-#12548 := (= f1 #3263)
-#18529 := (not #12548)
+#3263 := (f79 f297 #3257)
+#12584 := (= f1 #3263)
+#18565 := (not #12584)
decl f59 :: (-> S20 S18 S1)
#3258 := (f59 #3257 f19)
-#12539 := (= f1 #3258)
-#18520 := (not #12539)
-#23388 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #23385)
-#23391 := (not #23388)
-#13673 := (* -1::Int #3266)
-#13674 := (+ f308 #13673)
-#13672 := (>= #13674 0::Int)
-#13671 := (not #13672)
-decl f309 :: Int
-#3135 := f309
-#13477 := (>= f309 0::Int)
-#22443 := (not #13477)
-#12806 := (= f309 f317)
-#12812 := (not #12806)
-#12803 := (= f308 f316)
-#12821 := (not #12803)
-#23418 := (or #12821 #12812 #22443 #13620 #22402 #13671 #23385)
-#23421 := (not #23418)
-#28423 := [hypothesis]: #23421
-#24557 := (or #23418 #12803)
-#24558 := [def-axiom]: #24557
-#28430 := [unit-resolution #24558 #28423]: #12803
-#29525 := (or #12821 #24552)
-#29591 := [th-lemma arith triangle-eq]: #29525
-#29590 := [unit-resolution #29591 #28430]: #24552
-#24448 := (not #18907)
-#29594 := (or #23418 #22328)
-#13941 := (* -1::Int f309)
-#13942 := (+ f297 #13941)
-#13943 := (<= #13942 0::Int)
-#13944 := (not #13943)
-decl ?v0!15 :: Int
-#18702 := ?v0!15
-#18707 := (f77 #3042 ?v0!15 f19)
-#18708 := (f122 f298 #18707)
-#19053 := (* -1::Int #18708)
-decl f314 :: Int
-#3166 := f314
-#19054 := (+ f314 #19053)
-#19055 := (>= #19054 0::Int)
-#19040 := (* -1::Int ?v0!15)
-#19041 := (+ f297 #19040)
-#19042 := (<= #19041 0::Int)
-#18704 := (>= ?v0!15 0::Int)
-#22537 := (not #18704)
-#18703 := (<= ?v0!15 4294967295::Int)
-#22536 := (not #18703)
-#22552 := (or #22536 #22537 #19042 #19055)
-#22557 := (not #22552)
-#13406 := (* -1::Int f297)
-#13794 := (+ #202 #13406)
-#13793 := (>= #13794 0::Int)
-#3173 := (= #3124 f314)
-#22510 := (not #3173)
-#22511 := (or #22510 #5104 #13793 #19577)
-#23468 := (forall (vars (?v0 Int)) (:pat #23327) #22511)
-#23473 := (not #23468)
-#13805 := (* -1::Int f314)
-#13806 := (+ #3124 #13805)
-#13807 := (<= #13806 0::Int)
-#22502 := (or #5104 #13793 #13807 #19577)
-#23460 := (forall (vars (?v0 Int)) (:pat #23327) #22502)
-#23465 := (not #23460)
-#23476 := (or #23465 #23473)
-#23479 := (not #23476)
-#23482 := (or #23479 #22557)
-#23485 := (not #23482)
-#13501 := (* -1::Int f310)
-#13764 := (+ f297 #13501)
-#13765 := (<= #13764 0::Int)
-#13766 := (not #13765)
-#12242 := (= f308 f314)
-#12277 := (not #12242)
-decl f313 :: Int
-#3164 := f313
-#12239 := (= f309 f313)
-#12286 := (not #12239)
-decl f312 :: Int
-#3162 := f312
-#12236 := (= f310 f312)
-#12295 := (not #12236)
-decl f311 :: Int
-#3160 := f311
-#12233 := (= f308 f311)
-#12304 := (not #12233)
-#23488 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #23485)
-#23491 := (not #23488)
-#23394 := (or #18520 #18529 #23391)
-#23397 := (not #23394)
+#12575 := (= f1 #3258)
+#18556 := (not #12575)
+#23424 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #23421)
+#23427 := (not #23424)
+decl f36 :: (-> S19 S20 S20)
+decl f146 :: (-> S29 S20)
+decl f69 :: (-> S28 S20 S29)
+decl f70 :: (-> S19 S28)
+#3220 := (f70 f297)
+#27834 := (f69 #3220 #3257)
+#28494 := (f146 #27834)
+#28497 := (f36 f297 #28494)
+decl f37 :: S20
+#116 := f37
+#28498 := (= f37 #28497)
+decl f221 :: (-> S19 S20 S1)
+#28495 := (f221 f297 #28494)
+#28496 := (= f1 #28495)
+#28554 := (or #28496 #28498)
+#28557 := (not #28554)
+decl f147 :: (-> S29 S1)
+#28507 := (f147 #27834)
+#28508 := (= f1 #28507)
+#28509 := (not #28508)
+decl f38 :: (-> S19 S20 S1)
+#28504 := (f38 f297 #28494)
+#28505 := (= f1 #28504)
+#28506 := (not #28505)
+#28548 := (or #28506 #28509)
+#28551 := (not #28548)
+decl f23 :: (-> S18 S23)
+decl f24 :: (-> S20 S18)
+#28202 := (f24 #3257)
+#28512 := (f23 #28202)
+decl f25 :: S23
+#67 := f25
+#28530 := (= f25 #28512)
+#28545 := (not #28530)
+#28501 := (f24 #28494)
+#28502 := (f23 #28501)
+#28503 := (= f25 #28502)
+#28563 := (or #28503 #28545 #28551 #28557)
+#28568 := (not #28563)
+#28519 := (f36 f297 #3257)
+#28520 := (= f37 #28519)
+#28517 := (f221 f297 #3257)
+#28518 := (= f1 #28517)
+#28533 := (or #28518 #28520)
+#28536 := (not #28533)
+#28539 := (or #28530 #28536)
+#28542 := (not #28539)
+#28571 := (or #28542 #28568)
+#28574 := (not #28571)
decl f35 :: (-> S19 S20 S1)
-#3260 := (f35 f298 #3257)
-#12542 := (= f1 #3260)
-#18523 := (not #12542)
-#23400 := (or #18520 #18523 #23397)
-#23403 := (not #23400)
-#23406 := (or #18520 #18523 #23403)
-#23409 := (not #23406)
-#23412 := (or #22443 #13620 #13672 #23409)
-#23415 := (not #23412)
-#23424 := (or #23415 #23421)
-#23427 := (not #23424)
-#23430 := (or #18520 #18529 #22443 #13620 #23427)
-#23433 := (not #23430)
-#23436 := (or #18520 #18529 #23433)
-#23439 := (not #23436)
-#23442 := (or #18520 #18523 #23439)
-#23445 := (not #23442)
-#23448 := (or #18520 #18523 #23445)
-#23451 := (not #23448)
-#23454 := (or #22443 #13620 #13765 #23451)
-#23457 := (not #23454)
-#23494 := (or #23457 #23491)
-#23497 := (not #23494)
-#13970 := (* -1::Int f308)
-#13971 := (+ #3124 #13970)
-#13972 := (<= #13971 0::Int)
-#13959 := (+ #202 #13501)
-#13958 := (>= #13959 0::Int)
-#22318 := (or #5104 #13958 #13972 #19577)
-#23336 := (forall (vars (?v0 Int)) (:pat #23327) #22318)
-#23341 := (not #23336)
-#1374 := 255::Int
-#15849 := (<= f308 255::Int)
-#22587 := (not #15849)
-#15832 := (<= f309 4294967295::Int)
-#22586 := (not #15832)
-#15815 := (<= f310 4294967295::Int)
-#22585 := (not #15815)
-#14020 := (>= f308 0::Int)
-#22583 := (not #14020)
-#13998 := (>= f310 0::Int)
-#22582 := (not #13998)
-#13992 := (>= #13764 0::Int)
-#13995 := (not #13992)
-#13472 := (<= f297 0::Int)
-decl f303 :: (-> S19 S17 S17 S20 S18 S1)
-decl f18 :: (-> S18 S18)
-#51 := (f18 f19)
-decl f292 :: S17
-#3019 := f292
-decl f284 :: S17
-#3011 := f284
-#3250 := (f303 f298 f284 f292 #3042 #51)
-#12522 := (= f1 #3250)
-#22581 := (not #12522)
+#3260 := (f35 f297 #3257)
+#12578 := (= f1 #3260)
+#18559 := (not #12578)
+#28577 := (or #18559 #28574)
+#28580 := (not #28577)
+#28583 := (iff #12584 #28580)
+#29899 := (not #28583)
+#30296 := [hypothesis]: #29899
+#62 := (:var 0 S20)
+#86 := (:var 1 S19)
+#2438 := (f79 #86 #62)
+#2439 := (pattern #2438)
+#324 := (f70 #86)
+#2441 := (f69 #324 #62)
+#2445 := (f146 #2441)
+#2456 := (f221 #86 #2445)
+#10696 := (= f1 #2456)
+#2454 := (f36 #86 #2445)
+#10693 := (= f37 #2454)
+#10699 := (or #10693 #10696)
+#22070 := (not #10699)
+#2450 := (f24 #2445)
+#2451 := (f23 #2450)
+#10687 := (= f25 #2451)
+#2446 := (f38 #86 #2445)
+#10678 := (= f1 #2446)
+#10681 := (not #10678)
+#2442 := (f147 #2441)
+#10672 := (= f1 #2442)
+#10675 := (not #10672)
+#10684 := (or #10675 #10681)
+#22069 := (not #10684)
+#65 := (f24 #62)
+#66 := (f23 #65)
+#68 := (= #66 f25)
+#91 := (not #68)
+#22071 := (or #91 #22069 #10687 #22070)
+#22072 := (not #22071)
+#2462 := (f221 #86 #62)
+#10711 := (= f1 #2462)
+#182 := (f36 #86 #62)
+#3761 := (= f37 #182)
+#10714 := (or #3761 #10711)
+#22064 := (not #10714)
+#22065 := (or #68 #22064)
+#22066 := (not #22065)
+#22075 := (or #22066 #22072)
+#22081 := (not #22075)
+#186 := (f35 #86 #62)
+#3767 := (= f1 #186)
+#11297 := (not #3767)
+#22082 := (or #11297 #22081)
+#22083 := (not #22082)
+#10668 := (= f1 #2438)
+#22088 := (iff #10668 #22083)
+#22091 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22088)
+#10690 := (not #10687)
+#10732 := (and #68 #10684 #10690 #10699)
+#10717 := (and #91 #10714)
+#10738 := (or #10717 #10732)
+#10743 := (and #3767 #10738)
+#10746 := (iff #10668 #10743)
+#10749 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10746)
+#22092 := (iff #10749 #22091)
+#22089 := (iff #10746 #22088)
+#22086 := (iff #10743 #22083)
+#22078 := (and #3767 #22075)
+#22084 := (iff #22078 #22083)
+#22085 := [rewrite]: #22084
+#22079 := (iff #10743 #22078)
+#22076 := (iff #10738 #22075)
+#22073 := (iff #10732 #22072)
+#22074 := [rewrite]: #22073
+#22067 := (iff #10717 #22066)
+#22068 := [rewrite]: #22067
+#22077 := [monotonicity #22068 #22074]: #22076
+#22080 := [monotonicity #22077]: #22079
+#22087 := [trans #22080 #22085]: #22086
+#22090 := [monotonicity #22087]: #22089
+#22093 := [quant-intro #22090]: #22092
+#18014 := (~ #10749 #10749)
+#18012 := (~ #10746 #10746)
+#18013 := [refl]: #18012
+#18015 := [nnf-pos #18013]: #18014
+#2463 := (= #2462 f1)
+#183 := (= #182 f37)
+#2464 := (or #183 #2463)
+#2465 := (and #91 #2464)
+#2457 := (= #2456 f1)
+#2455 := (= #2454 f37)
+#2458 := (or #2455 #2457)
+#2452 := (= #2451 f25)
+#2453 := (not #2452)
+#2459 := (and #2453 #2458)
+#2447 := (= #2446 f1)
+#2448 := (not #2447)
+#2443 := (= #2442 f1)
+#2444 := (not #2443)
+#2449 := (or #2444 #2448)
+#2460 := (and #2449 #2459)
+#2461 := (and #68 #2460)
+#2466 := (or #2461 #2465)
+#187 := (= #186 f1)
+#2467 := (and #187 #2466)
+#2440 := (= #2438 f1)
+#2468 := (iff #2440 #2467)
+#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468)
+#10752 := (iff #2469 #10749)
+#10702 := (and #10690 #10699)
+#10705 := (and #10684 #10702)
+#10708 := (and #68 #10705)
+#10720 := (or #10708 #10717)
+#10723 := (and #3767 #10720)
+#10726 := (iff #10668 #10723)
+#10729 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10726)
+#10750 := (iff #10729 #10749)
+#10747 := (iff #10726 #10746)
+#10744 := (iff #10723 #10743)
+#10741 := (iff #10720 #10738)
+#10735 := (or #10732 #10717)
+#10739 := (iff #10735 #10738)
+#10740 := [rewrite]: #10739
+#10736 := (iff #10720 #10735)
+#10733 := (iff #10708 #10732)
+#10734 := [rewrite]: #10733
+#10737 := [monotonicity #10734]: #10736
+#10742 := [trans #10737 #10740]: #10741
+#10745 := [monotonicity #10742]: #10744
+#10748 := [monotonicity #10745]: #10747
+#10751 := [quant-intro #10748]: #10750
+#10730 := (iff #2469 #10729)
+#10727 := (iff #2468 #10726)
+#10724 := (iff #2467 #10723)
+#10721 := (iff #2466 #10720)
+#10718 := (iff #2465 #10717)
+#10715 := (iff #2464 #10714)
+#10712 := (iff #2463 #10711)
+#10713 := [rewrite]: #10712
+#3762 := (iff #183 #3761)
+#3763 := [rewrite]: #3762
+#10716 := [monotonicity #3763 #10713]: #10715
+#10719 := [monotonicity #10716]: #10718
+#10709 := (iff #2461 #10708)
+#10706 := (iff #2460 #10705)
+#10703 := (iff #2459 #10702)
+#10700 := (iff #2458 #10699)
+#10697 := (iff #2457 #10696)
+#10698 := [rewrite]: #10697
+#10694 := (iff #2455 #10693)
+#10695 := [rewrite]: #10694
+#10701 := [monotonicity #10695 #10698]: #10700
+#10691 := (iff #2453 #10690)
+#10688 := (iff #2452 #10687)
+#10689 := [rewrite]: #10688
+#10692 := [monotonicity #10689]: #10691
+#10704 := [monotonicity #10692 #10701]: #10703
+#10685 := (iff #2449 #10684)
+#10682 := (iff #2448 #10681)
+#10679 := (iff #2447 #10678)
+#10680 := [rewrite]: #10679
+#10683 := [monotonicity #10680]: #10682
+#10676 := (iff #2444 #10675)
+#10673 := (iff #2443 #10672)
+#10674 := [rewrite]: #10673
+#10677 := [monotonicity #10674]: #10676
+#10686 := [monotonicity #10677 #10683]: #10685
+#10707 := [monotonicity #10686 #10704]: #10706
+#10710 := [monotonicity #10707]: #10709
+#10722 := [monotonicity #10710 #10719]: #10721
+#3768 := (iff #187 #3767)
+#3769 := [rewrite]: #3768
+#10725 := [monotonicity #3769 #10722]: #10724
+#10670 := (iff #2440 #10668)
+#10671 := [rewrite]: #10670
+#10728 := [monotonicity #10671 #10725]: #10727
+#10731 := [quant-intro #10728]: #10730
+#10753 := [trans #10731 #10751]: #10752
+#10667 := [asserted]: #2469
+#10754 := [mp #10667 #10753]: #10749
+#18016 := [mp~ #10754 #18015]: #10749
+#22094 := [mp #18016 #22093]: #22091
+#28423 := (not #22091)
+#29896 := (or #28423 #28583)
+#28499 := (or #28498 #28496)
+#28500 := (not #28499)
+#28510 := (or #28509 #28506)
+#28511 := (not #28510)
+#28513 := (= #28512 f25)
+#28514 := (not #28513)
+#28515 := (or #28514 #28511 #28503 #28500)
+#28516 := (not #28515)
+#28521 := (or #28520 #28518)
+#28522 := (not #28521)
+#28523 := (or #28513 #28522)
+#28524 := (not #28523)
+#28525 := (or #28524 #28516)
+#28526 := (not #28525)
+#28527 := (or #18559 #28526)
+#28528 := (not #28527)
+#28529 := (iff #12584 #28528)
+#29897 := (or #28423 #28529)
+#29946 := (iff #29897 #29896)
+#29888 := (iff #29896 #29896)
+#29891 := [rewrite]: #29888
+#28584 := (iff #28529 #28583)
+#28581 := (iff #28528 #28580)
+#28578 := (iff #28527 #28577)
+#28575 := (iff #28526 #28574)
+#28572 := (iff #28525 #28571)
+#28569 := (iff #28516 #28568)
+#28566 := (iff #28515 #28563)
+#28560 := (or #28545 #28551 #28503 #28557)
+#28564 := (iff #28560 #28563)
+#28565 := [rewrite]: #28564
+#28561 := (iff #28515 #28560)
+#28558 := (iff #28500 #28557)
+#28555 := (iff #28499 #28554)
+#28556 := [rewrite]: #28555
+#28559 := [monotonicity #28556]: #28558
+#28552 := (iff #28511 #28551)
+#28549 := (iff #28510 #28548)
+#28550 := [rewrite]: #28549
+#28553 := [monotonicity #28550]: #28552
+#28546 := (iff #28514 #28545)
+#28531 := (iff #28513 #28530)
+#28532 := [rewrite]: #28531
+#28547 := [monotonicity #28532]: #28546
+#28562 := [monotonicity #28547 #28553 #28559]: #28561
+#28567 := [trans #28562 #28565]: #28566
+#28570 := [monotonicity #28567]: #28569
+#28543 := (iff #28524 #28542)
+#28540 := (iff #28523 #28539)
+#28537 := (iff #28522 #28536)
+#28534 := (iff #28521 #28533)
+#28535 := [rewrite]: #28534
+#28538 := [monotonicity #28535]: #28537
+#28541 := [monotonicity #28532 #28538]: #28540
+#28544 := [monotonicity #28541]: #28543
+#28573 := [monotonicity #28544 #28570]: #28572
+#28576 := [monotonicity #28573]: #28575
+#28579 := [monotonicity #28576]: #28578
+#28582 := [monotonicity #28579]: #28581
+#28585 := [monotonicity #28582]: #28584
+#29935 := [monotonicity #28585]: #29946
+#29933 := [trans #29935 #29891]: #29946
+#29945 := [quant-inst #3039 #3257]: #29897
+#29889 := [mp #29945 #29933]: #29896
+#30214 := [unit-resolution #29889 #22094 #30296]: false
+#30215 := [lemma #30214]: #28583
+#30322 := (or #29899 #12584)
+#30167 := [hypothesis]: #28563
+decl f127 :: (-> S20 Int)
+#3043 := (f127 #3042)
+decl f135 :: (-> S18 Int S18)
+#3040 := (f135 f19 f296)
+#3044 := (f54 #3040 #3043)
+#3047 := (f36 f297 #3044)
+#30199 := (= #3047 #28497)
+#30193 := (= #28497 #3047)
+#30284 := (= #28494 #3044)
+decl f154 :: (-> S18 Int)
+#24998 := (f154 #3040)
+decl f155 :: (-> S18 S18)
+#24996 := (f155 #3040)
+#27144 := (f135 #24996 #24998)
+#27145 := (f54 #27144 #3043)
+#28787 := (= #27145 #3044)
+#28807 := (= #27144 #3040)
+#28805 := (= #24998 f296)
+#24999 := (= f296 #24998)
+#369 := (:var 1 S18)
+#1401 := (f135 #369 #202)
+#1638 := (pattern #1401)
+#1649 := (f154 #1401)
+#8444 := (= #202 #1649)
+#8447 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8444)
+#17390 := (~ #8447 #8447)
+#17388 := (~ #8444 #8444)
+#17389 := [refl]: #17388
+#17391 := [nnf-pos #17389]: #17390
+#1650 := (= #1649 #202)
+#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650)
+#8448 := (iff #1651 #8447)
+#8445 := (iff #1650 #8444)
+#8446 := [rewrite]: #8445
+#8449 := [quant-intro #8446]: #8448
+#8443 := [asserted]: #1651
+#8452 := [mp #8443 #8449]: #8447
+#17392 := [mp~ #8452 #17391]: #8447
+#25005 := (not #8447)
+#25006 := (or #25005 #24999)
+#25007 := [quant-inst #50 #3036]: #25006
+#28406 := [unit-resolution #25007 #17392]: #24999
+#28806 := [symm #28406]: #28805
+#28385 := (= #24996 f19)
+#24997 := (= f19 #24996)
+#1652 := (f155 #1401)
+#8451 := (= #369 #1652)
+#8455 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8451)
+#17395 := (~ #8455 #8455)
+#17393 := (~ #8451 #8451)
+#17394 := [refl]: #17393
+#17396 := [nnf-pos #17394]: #17395
+#1653 := (= #1652 #369)
+#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653)
+#8456 := (iff #1654 #8455)
+#8453 := (iff #1653 #8451)
+#8454 := [rewrite]: #8453
+#8457 := [quant-intro #8454]: #8456
+#8450 := [asserted]: #1654
+#8460 := [mp #8450 #8457]: #8455
+#17397 := [mp~ #8460 #17396]: #8455
+#25000 := (not #8455)
+#25001 := (or #25000 #24997)
+#25002 := [quant-inst #50 #3036]: #25001
+#28384 := [unit-resolution #25002 #17397]: #24997
+#28386 := [symm #28384]: #28385
+#28808 := [monotonicity #28386 #28806]: #28807
+#28789 := [monotonicity #28808]: #28787
+#30282 := (= #28494 #27145)
+decl f136 :: (-> S20 S20 Int)
+decl f39 :: (-> Int S20)
decl f40 :: (-> S20 Int)
#3076 := (f40 #3042)
-#3248 := (f302 f298 f284 f292 #3076 #51)
-#12519 := (= f1 #3248)
-#22580 := (not #12519)
-decl f291 :: S17
-#3018 := f291
-#3246 := (f302 f298 f284 f291 f297 f16)
-#12516 := (= f1 #3246)
-#12997 := (not #12516)
-#3244 := (f302 f298 f284 f289 f308 f19)
-#12513 := (= f1 #3244)
-#13006 := (not #12513)
-#3242 := (f302 f298 f284 f287 f309 f16)
-#12510 := (= f1 #3242)
-#13015 := (not #12510)
-#3240 := (f302 f298 f284 f285 f310 f16)
-#12507 := (= f1 #3240)
-#13024 := (not #12507)
-decl f190 :: (-> S19 S19 S1)
-#3232 := (f190 f298 f298)
-#12479 := (= f1 #3232)
-#13938 := (not #12479)
-decl f214 :: (-> S17 S19 S1)
-#3157 := (f214 f284 f298)
-#12222 := (= f1 #3157)
-#15263 := (not #12222)
-#3152 := (f77 #3042 f309 f19)
-#3153 := (f122 f298 #3152)
-#12214 := (= f308 #3153)
-#22579 := (not #12214)
-#3098 := (f77 #3042 0::Int f19)
-#3108 := (f122 f298 #3098)
+#24833 := (f39 #3076)
+#27122 := (f24 #24833)
+#29367 := (f77 #24833 f309 #27122)
+#29368 := (f136 #29367 #24833)
+#29431 := (f77 #27145 #29368 #24996)
+#29452 := (f69 #3220 #29431)
+#29458 := (f146 #29452)
+#30280 := (= #29458 #27145)
+#29459 := (= #27145 #29458)
+#29460 := (not #29459)
+#29456 := (f147 #29452)
+#29457 := (= f1 #29456)
+decl f78 :: (-> S29 S1)
+#29453 := (f78 #29452)
+#29454 := (= f1 #29453)
+#29455 := (not #29454)
+#29449 := (f35 f297 #29431)
+#29450 := (= f1 #29449)
+#29451 := (not #29450)
+#29481 := (or #29451 #29455 #29457 #29460)
+#29484 := (not #29481)
+#29474 := (* -1::Int #29368)
+#29475 := (+ #24998 #29474)
+#29476 := (<= #29475 0::Int)
+#30241 := (not #29476)
+#29583 := (+ f309 #29474)
+#29585 := (>= #29583 0::Int)
+#29369 := (= f309 #29368)
+#55 := (:var 1 S20)
+#1433 := (f24 #55)
+#1434 := (f77 #55 #202 #1433)
+#1435 := (pattern #1434)
+#1436 := (f136 #1434 #55)
+#7824 := (= #202 #1436)
+#7828 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7824)
+#17105 := (~ #7828 #7828)
+#17103 := (~ #7824 #7824)
+#17104 := [refl]: #17103
+#17106 := [nnf-pos #17104]: #17105
+#1437 := (= #1436 #202)
+#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437)
+#7829 := (iff #1438 #7828)
+#7826 := (iff #1437 #7824)
+#7827 := [rewrite]: #7826
+#7830 := [quant-intro #7827]: #7829
+#7823 := [asserted]: #1438
+#7833 := [mp #7823 #7830]: #7828
+#17107 := [mp~ #7833 #17106]: #7828
+#27129 := (not #7828)
+#29432 := (or #27129 #29369)
+#29448 := [quant-inst #24833 #3139]: #29432
+#29674 := [unit-resolution #29448 #17107]: #29369
+#29675 := (not #29369)
+#30235 := (or #29675 #29585)
+#30236 := [th-lemma arith triangle-eq]: #30235
+#30237 := [unit-resolution #30236 #29674]: #29585
+#13537 := (* -1::Int f309)
+#13800 := (+ f296 #13537)
+#13801 := (<= #13800 0::Int)
+#13802 := (not #13801)
+#13709 := (* -1::Int #3266)
decl f307 :: Int
-#3107 := f307
-#3109 := (= f307 #3108)
-#13231 := (not #3109)
-#23500 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #23341 #23497)
-#23503 := (not #23500)
-#23506 := (or #13231 #13472 #23503)
-#23509 := (not #23506)
-#13452 := (* -1::Int #3124)
-#13453 := (+ f307 #13452)
-#13451 := (>= #13453 0::Int)
-#13439 := (>= #202 1::Int)
-#22307 := (or #5104 #13439 #13451 #19577)
-#23328 := (forall (vars (?v0 Int)) (:pat #23327) #22307)
-#23333 := (not #23328)
-#23512 := (or #23333 #23509)
+#3131 := f307
+#13710 := (+ f307 #13709)
+#13708 := (>= #13710 0::Int)
+#13707 := (not #13708)
+decl f308 :: Int
+#3135 := f308
+#13513 := (>= f308 0::Int)
+#22479 := (not #13513)
+#12842 := (= f308 f316)
+#12848 := (not #12842)
+#12839 := (= f307 f315)
+#12857 := (not #12839)
+#23454 := (or #12857 #12848 #22479 #13656 #22438 #13707 #23421)
+#23457 := (not #23454)
+#23430 := (or #18556 #18565 #23427)
+#23433 := (not #23430)
+#23436 := (or #18556 #18559 #23433)
+#23439 := (not #23436)
+#23442 := (or #18556 #18559 #23439)
+#23445 := (not #23442)
+#23448 := (or #22479 #13656 #13708 #23445)
+#23451 := (not #23448)
+#23460 := (or #23451 #23457)
+#23463 := (not #23460)
+#23466 := (or #18556 #18565 #22479 #13656 #23463)
+#23469 := (not #23466)
+#23472 := (or #18556 #18565 #23469)
+#23475 := (not #23472)
+#23478 := (or #18556 #18559 #23475)
+#23481 := (not #23478)
+#23484 := (or #18556 #18559 #23481)
+#23487 := (not #23484)
+#23490 := (or #22479 #13656 #13801 #23487)
+#23493 := (not #23490)
+decl ?v0!15 :: Int
+#18738 := ?v0!15
+#18743 := (f77 #3042 ?v0!15 f19)
+#18744 := (f121 f297 #18743)
+#19089 := (* -1::Int #18744)
+decl f313 :: Int
+#3166 := f313
+#19090 := (+ f313 #19089)
+#19091 := (>= #19090 0::Int)
+#19076 := (* -1::Int ?v0!15)
+#19077 := (+ f296 #19076)
+#19078 := (<= #19077 0::Int)
+#18740 := (>= ?v0!15 0::Int)
+#22573 := (not #18740)
+#18739 := (<= ?v0!15 4294967295::Int)
+#22572 := (not #18739)
+#22588 := (or #22572 #22573 #19078 #19091)
+#22593 := (not #22588)
+#13442 := (* -1::Int f296)
+#13830 := (+ #202 #13442)
+#13829 := (>= #13830 0::Int)
+#3173 := (= #3124 f313)
+#22546 := (not #3173)
+#22547 := (or #22546 #5124 #13829 #19613)
+#23504 := (forall (vars (?v0 Int)) (:pat #23363) #22547)
+#23509 := (not #23504)
+#13841 := (* -1::Int f313)
+#13842 := (+ #3124 #13841)
+#13843 := (<= #13842 0::Int)
+#22538 := (or #5124 #13829 #13843 #19613)
+#23496 := (forall (vars (?v0 Int)) (:pat #23363) #22538)
+#23501 := (not #23496)
+#23512 := (or #23501 #23509)
#23515 := (not #23512)
-decl ?v0!13 :: Int
-#18441 := ?v0!13
-#18451 := (>= ?v0!13 1::Int)
-#18446 := (f77 #3042 ?v0!13 f19)
-#18447 := (f122 f298 #18446)
-#18448 := (* -1::Int #18447)
-#18449 := (+ f307 #18448)
-#18450 := (>= #18449 0::Int)
-#18443 := (>= ?v0!13 0::Int)
-#22281 := (not #18443)
-#18442 := (<= ?v0!13 4294967295::Int)
-#22280 := (not #18442)
-#22296 := (or #22280 #22281 #18450 #18451)
-#22301 := (not #22296)
-#23518 := (or #22301 #23515)
+#23518 := (or #23515 #22593)
#23521 := (not #23518)
-#13433 := (>= f297 1::Int)
-#13436 := (not #13433)
-#23524 := (or #13436 #23521)
+#12278 := (= f307 f313)
+#12313 := (not #12278)
+decl f312 :: Int
+#3164 := f312
+#12275 := (= f308 f312)
+#12322 := (not #12275)
+decl f311 :: Int
+#3162 := f311
+#12272 := (= f309 f311)
+#12331 := (not #12272)
+decl f310 :: Int
+#3160 := f310
+#12269 := (= f307 f310)
+#12340 := (not #12269)
+#23524 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #23521)
#23527 := (not #23524)
-#23530 := (or #13436 #23527)
+#23530 := (or #23493 #23527)
#23533 := (not #23530)
-decl f286 :: S17
-#3013 := f286
-#3114 := (f302 f298 f286 f285 1::Int f16)
-#12165 := (= f1 #3114)
-#13204 := (not #12165)
-decl f288 :: S17
-#3015 := f288
-#3112 := (f302 f298 f288 f287 0::Int f16)
-#12162 := (= f1 #3112)
-#13213 := (not #12162)
+#14006 := (* -1::Int f307)
+#14007 := (+ #3124 #14006)
+#14008 := (<= #14007 0::Int)
+#13995 := (+ #202 #13537)
+#13994 := (>= #13995 0::Int)
+#22354 := (or #5124 #13994 #14008 #19613)
+#23372 := (forall (vars (?v0 Int)) (:pat #23363) #22354)
+#23377 := (not #23372)
+#1374 := 255::Int
+#15885 := (<= f307 255::Int)
+#22623 := (not #15885)
+#15868 := (<= f308 4294967295::Int)
+#22622 := (not #15868)
+#15851 := (<= f309 4294967295::Int)
+#22621 := (not #15851)
+#14056 := (>= f307 0::Int)
+#22619 := (not #14056)
+#14034 := (>= f309 0::Int)
+#22618 := (not #14034)
+#14028 := (>= #13800 0::Int)
+#14031 := (not #14028)
+#13977 := (* -1::Int f308)
+#13978 := (+ f296 #13977)
+#13979 := (<= #13978 0::Int)
+#13508 := (<= f296 0::Int)
+decl f302 :: (-> S19 S17 S17 S20 S18 S1)
+decl f18 :: (-> S18 S18)
+#51 := (f18 f19)
+decl f291 :: S17
+#3019 := f291
+decl f283 :: S17
+#3011 := f283
+#3250 := (f302 f297 f283 f291 #3042 #51)
+#12558 := (= f1 #3250)
+#22617 := (not #12558)
+#3248 := (f301 f297 f283 f291 #3076 #51)
+#12555 := (= f1 #3248)
+#22616 := (not #12555)
decl f290 :: S17
-#3017 := f290
-#3110 := (f302 f298 f290 f289 f307 f19)
-#12159 := (= f1 #3110)
-#13222 := (not #12159)
-#3104 := (f79 f298 #3098)
-#12153 := (= f1 #3104)
-#18418 := (not #12153)
-#3099 := (f59 #3098 f19)
-#12144 := (= f1 #3099)
-#18409 := (not #12144)
-#23536 := (or #13231 #18409 #18418 #13222 #13213 #13204 #23533)
+#3018 := f290
+#3246 := (f301 f297 f283 f290 f296 f16)
+#12552 := (= f1 #3246)
+#13033 := (not #12552)
+#3244 := (f301 f297 f283 f288 f307 f19)
+#12549 := (= f1 #3244)
+#13042 := (not #12549)
+#3242 := (f301 f297 f283 f286 f308 f16)
+#12546 := (= f1 #3242)
+#13051 := (not #12546)
+#3240 := (f301 f297 f283 f284 f309 f16)
+#12543 := (= f1 #3240)
+#13060 := (not #12543)
+decl f189 :: (-> S19 S19 S1)
+#3232 := (f189 f297 f297)
+#12515 := (= f1 #3232)
+#13974 := (not #12515)
+decl f213 :: (-> S17 S19 S1)
+#3157 := (f213 f283 f297)
+#12258 := (= f1 #3157)
+#15299 := (not #12258)
+#3152 := (f77 #3042 f308 f19)
+#3153 := (f121 f297 #3152)
+#12250 := (= f307 #3153)
+#22615 := (not #12250)
+#3098 := (f77 #3042 0::Int f19)
+#3108 := (f121 f297 #3098)
+decl f306 :: Int
+#3107 := f306
+#3109 := (= f306 #3108)
+#13267 := (not #3109)
+#23536 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #23377 #23533)
#23539 := (not #23536)
-#23542 := (or #18409 #18418 #23539)
+#23542 := (or #13267 #13508 #23539)
#23545 := (not #23542)
-#3101 := (f35 f298 #3098)
-#12147 := (= f1 #3101)
-#18412 := (not #12147)
-#23548 := (or #18409 #18412 #23545)
+#13488 := (* -1::Int #3124)
+#13489 := (+ f306 #13488)
+#13487 := (>= #13489 0::Int)
+#13475 := (>= #202 1::Int)
+#22343 := (or #5124 #13475 #13487 #19613)
+#23364 := (forall (vars (?v0 Int)) (:pat #23363) #22343)
+#23369 := (not #23364)
+#23548 := (or #23369 #23545)
#23551 := (not #23548)
-#23554 := (or #18409 #18412 #23551)
+decl ?v0!13 :: Int
+#18477 := ?v0!13
+#18487 := (>= ?v0!13 1::Int)
+#18482 := (f77 #3042 ?v0!13 f19)
+#18483 := (f121 f297 #18482)
+#18484 := (* -1::Int #18483)
+#18485 := (+ f306 #18484)
+#18486 := (>= #18485 0::Int)
+#18479 := (>= ?v0!13 0::Int)
+#22317 := (not #18479)
+#18478 := (<= ?v0!13 4294967295::Int)
+#22316 := (not #18478)
+#22332 := (or #22316 #22317 #18486 #18487)
+#22337 := (not #22332)
+#23554 := (or #22337 #23551)
#23557 := (not #23554)
-decl f212 :: (-> S19 S20 S20 S31 S1)
-decl f306 :: S31
-#3095 := f306
-decl f128 :: (-> S20 Int)
-#3043 := (f128 #3042)
-decl f136 :: (-> S18 Int S18)
-#3040 := (f136 f19 f297)
-#3044 := (f54 #3040 #3043)
-#3096 := (f212 f298 #3044 #3044 f306)
-#12141 := (= f1 #3096)
-#13264 := (not #12141)
-#23560 := (or #13264 #23557)
+#13469 := (>= f296 1::Int)
+#13472 := (not #13469)
+#23560 := (or #13472 #23557)
#23563 := (not #23560)
-decl f23 :: (-> S18 S23)
-decl f24 :: (-> S20 S18)
-#24844 := (f128 #3044)
-#26146 := (f54 #3040 #24844)
-#26550 := (f24 #26146)
-#26792 := (f23 #26550)
-decl f25 :: S23
-#67 := f25
-#26795 := (= f25 #26792)
-#26915 := (not #26795)
-#3053 := (f23 #3040)
-#12079 := (= f25 #3053)
-#12082 := (not #12079)
-#26897 := (iff #12082 #26915)
-#26913 := (iff #12079 #26795)
-#26911 := (iff #26795 #12079)
-#26909 := (= #26792 #3053)
-#26875 := (= #26550 #3040)
-#25081 := (f24 #3044)
-#28877 := (= #25081 #3040)
-#25084 := (= #3040 #25081)
-#369 := (:var 1 S18)
+#23566 := (or #13472 #23563)
+#23569 := (not #23566)
+decl f285 :: S17
+#3013 := f285
+#3114 := (f301 f297 f285 f284 1::Int f16)
+#12201 := (= f1 #3114)
+#13240 := (not #12201)
+decl f287 :: S17
+#3015 := f287
+#3112 := (f301 f297 f287 f286 0::Int f16)
+#12198 := (= f1 #3112)
+#13249 := (not #12198)
+decl f289 :: S17
+#3017 := f289
+#3110 := (f301 f297 f289 f288 f306 f19)
+#12195 := (= f1 #3110)
+#13258 := (not #12195)
+#3104 := (f79 f297 #3098)
+#12189 := (= f1 #3104)
+#18454 := (not #12189)
+#3099 := (f59 #3098 f19)
+#12180 := (= f1 #3099)
+#18445 := (not #12180)
+#23572 := (or #13267 #18445 #18454 #13258 #13249 #13240 #23569)
+#23575 := (not #23572)
+#27039 := (f24 #3098)
+#27040 := (= #24996 #27039)
+#27013 := (f59 #3098 #24996)
+#27014 := (= f1 #27013)
+#27042 := (iff #27014 #27040)
+#275 := (:var 0 S18)
+#2729 := (f59 #55 #275)
+#2730 := (pattern #2729)
+#11369 := (= f1 #2729)
+#9220 := (= #275 #1433)
+#11390 := (iff #9220 #11369)
+#23294 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11390)
+#11395 := (forall (vars (?v0 S20) (?v1 S18)) #11390)
+#23297 := (iff #11395 #23294)
+#23295 := (iff #11390 #11390)
+#23296 := [refl]: #23295
+#23298 := [quant-intro #23296]: #23297
+#18287 := (~ #11395 #11395)
+#18285 := (~ #11390 #11390)
+#18286 := [refl]: #18285
+#18288 := [nnf-pos #18286]: #18287
+#1939 := (= #1433 #275)
+#2731 := (= #2729 f1)
+#2736 := (iff #2731 #1939)
+#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736)
+#11396 := (iff #2737 #11395)
+#11393 := (iff #2736 #11390)
+#11386 := (iff #11369 #9220)
+#11391 := (iff #11386 #11390)
+#11392 := [rewrite]: #11391
+#11388 := (iff #2736 #11386)
+#9221 := (iff #1939 #9220)
+#9222 := [rewrite]: #9221
+#11371 := (iff #2731 #11369)
+#11372 := [rewrite]: #11371
+#11389 := [monotonicity #11372 #9222]: #11388
+#11394 := [trans #11389 #11392]: #11393
+#11397 := [quant-intro #11394]: #11396
+#11385 := [asserted]: #2737
+#11400 := [mp #11385 #11397]: #11395
+#18289 := [mp~ #11400 #18288]: #11395
+#23299 := [mp #18289 #23298]: #23294
+#26210 := (not #23294)
+#27513 := (or #26210 #27042)
+#27041 := (iff #27040 #27014)
+#27551 := (or #26210 #27041)
+#27552 := (iff #27551 #27513)
+#27592 := (iff #27513 #27513)
+#27593 := [rewrite]: #27592
+#27043 := (iff #27041 #27042)
+#27044 := [rewrite]: #27043
+#27594 := [monotonicity #27044]: #27552
+#27595 := [trans #27594 #27593]: #27552
+#27546 := [quant-inst #3098 #24996]: #27551
+#27596 := [mp #27546 #27595]: #27513
+#27640 := [unit-resolution #27596 #23299]: #27042
+#25112 := (f24 #3042)
+#27668 := (= #25112 #27039)
+#27682 := (= #27039 #25112)
+#27680 := (= #3098 #3042)
+#27070 := (f127 #24833)
+#27086 := (f54 #24996 #27070)
+#27410 := (= #27086 #3042)
+#27367 := (= #27070 f298)
+#28390 := (= #3043 f298)
+#25116 := (= f298 #3043)
#2761 := (f54 #369 #202)
-#23264 := (pattern #2761)
+#23300 := (pattern #2761)
+#2762 := (f127 #2761)
+#11445 := (= #202 #2762)
+#23301 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11445)
+#11449 := (forall (vars (?v0 S18) (?v1 Int)) #11445)
+#23304 := (iff #11449 #23301)
+#23302 := (iff #11445 #11445)
+#23303 := [refl]: #23302
+#23305 := [quant-intro #23303]: #23304
+#18302 := (~ #11449 #11449)
+#18300 := (~ #11445 #11445)
+#18301 := [refl]: #18300
+#18303 := [nnf-pos #18301]: #18302
+#2763 := (= #2762 #202)
+#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763)
+#11450 := (iff #2764 #11449)
+#11447 := (iff #2763 #11445)
+#11448 := [rewrite]: #11447
+#11451 := [quant-intro #11448]: #11450
+#11444 := [asserted]: #2764
+#11454 := [mp #11444 #11451]: #11449
+#18304 := [mp~ #11454 #18303]: #11449
+#23306 := [mp #18304 #23305]: #23301
+#25070 := (not #23301)
+#25121 := (or #25070 #25116)
+#25122 := [quant-inst #50 #3041]: #25121
+#28389 := [unit-resolution #25122 #23306]: #25116
+#28391 := [symm #28389]: #28390
+#27143 := (= #27070 #3043)
+#27141 := (= #24833 #3042)
+#24834 := (= #3042 #24833)
+#132 := (f40 #62)
+#23211 := (pattern #132)
+#133 := (f39 #132)
+#3682 := (= #62 #133)
+#23212 := (forall (vars (?v0 S20)) (:pat #23211) #3682)
+#3685 := (forall (vars (?v0 S20)) #3682)
+#23213 := (iff #3685 #23212)
+#23215 := (iff #23212 #23212)
+#23216 := [rewrite]: #23215
+#23214 := [rewrite]: #23213
+#23217 := [trans #23214 #23216]: #23213
+#16342 := (~ #3685 #3685)
+#16332 := (~ #3682 #3682)
+#16333 := [refl]: #16332
+#16398 := [nnf-pos #16333]: #16342
+#134 := (= #133 #62)
+#135 := (forall (vars (?v0 S20)) #134)
+#3686 := (iff #135 #3685)
+#3683 := (iff #134 #3682)
+#3684 := [rewrite]: #3683
+#3687 := [quant-intro #3684]: #3686
+#3681 := [asserted]: #135
+#3690 := [mp #3681 #3687]: #3685
+#16399 := [mp~ #3690 #16398]: #3685
+#23218 := [mp #16399 #23217]: #23212
+#24837 := (not #23212)
+#24838 := (or #24837 #24834)
+#24839 := [quant-inst #3042]: #24838
+#27140 := [unit-resolution #24839 #23218]: #24834
+#27142 := [symm #27140]: #27141
+#27275 := [monotonicity #27142]: #27143
+#27368 := [trans #27275 #28391]: #27367
+#27414 := [monotonicity #28386 #27368]: #27410
+#27415 := (= #3098 #27086)
+#27064 := (f77 #24833 0::Int #24996)
+#27089 := (= #27064 #27086)
+#27092 := (not #27089)
+decl f149 :: (-> S20 S20 S1)
+#27065 := (f149 #27064 #24833)
+#27066 := (= f1 #27065)
+#27067 := (not #27066)
+#27098 := (or #27067 #27092)
+#27103 := (not #27098)
+#28651 := [hypothesis]: #27098
+#289 := (:var 1 Int)
+#60 := (:var 2 S20)
+#1622 := (f77 #60 #289 #275)
+#1623 := (pattern #1622)
+#1624 := (f149 #1622 #60)
+#8390 := (= f1 #1624)
+#21232 := (not #8390)
+decl f150 :: (-> S18 Int)
+#1627 := (f150 #275)
+#1628 := (* #289 #1627)
+#1626 := (f127 #60)
+#1629 := (+ #1626 #1628)
+#1630 := (f54 #275 #1629)
+#1631 := (= #1622 #1630)
+#21231 := (not #1631)
+#21233 := (or #21231 #21232)
+#21234 := (not #21233)
+#21237 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21234)
+#8396 := (and #1631 #8390)
+#8401 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8396)
+#21238 := (iff #8401 #21237)
+#21235 := (iff #8396 #21234)
+#21236 := [rewrite]: #21235
+#21239 := [quant-intro #21236]: #21238
+#17365 := (~ #8401 #8401)
+#17363 := (~ #8396 #8396)
+#17364 := [refl]: #17363
+#17366 := [nnf-pos #17364]: #17365
+#1625 := (= #1624 f1)
+#1632 := (and #1625 #1631)
+#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632)
+#8402 := (iff #1633 #8401)
+#8399 := (iff #1632 #8396)
+#8393 := (and #8390 #1631)
+#8397 := (iff #8393 #8396)
+#8398 := [rewrite]: #8397
+#8394 := (iff #1632 #8393)
+#8391 := (iff #1625 #8390)
+#8392 := [rewrite]: #8391
+#8395 := [monotonicity #8392]: #8394
+#8400 := [trans #8395 #8398]: #8399
+#8403 := [quant-intro #8400]: #8402
+#8389 := [asserted]: #1633
+#8406 := [mp #8389 #8403]: #8401
+#17367 := [mp~ #8406 #17366]: #8401
+#21240 := [mp #17367 #21239]: #21237
+#27721 := (not #21237)
+#27728 := (or #27721 #27103)
+#27068 := (f150 #24996)
+#27069 := (* 0::Int #27068)
+#27071 := (+ #27070 #27069)
+#27072 := (f54 #24996 #27071)
+#27073 := (= #27064 #27072)
+#27074 := (not #27073)
+#27075 := (or #27074 #27067)
+#27076 := (not #27075)
+#27729 := (or #27721 #27076)
+#27730 := (iff #27729 #27728)
+#27736 := (iff #27728 #27728)
+#27737 := [rewrite]: #27736
+#27104 := (iff #27076 #27103)
+#27101 := (iff #27075 #27098)
+#27095 := (or #27092 #27067)
+#27099 := (iff #27095 #27098)
+#27100 := [rewrite]: #27099
+#27096 := (iff #27075 #27095)
+#27093 := (iff #27074 #27092)
+#27090 := (iff #27073 #27089)
+#27087 := (= #27072 #27086)
+#27084 := (= #27071 #27070)
+#27079 := (+ #27070 0::Int)
+#27082 := (= #27079 #27070)
+#27083 := [rewrite]: #27082
+#27080 := (= #27071 #27079)
+#27077 := (= #27069 0::Int)
+#27078 := [rewrite]: #27077
+#27081 := [monotonicity #27078]: #27080
+#27085 := [trans #27081 #27083]: #27084
+#27088 := [monotonicity #27085]: #27087
+#27091 := [monotonicity #27088]: #27090
+#27094 := [monotonicity #27091]: #27093
+#27097 := [monotonicity #27094]: #27096
+#27102 := [trans #27097 #27100]: #27101
+#27105 := [monotonicity #27102]: #27104
+#27731 := [monotonicity #27105]: #27730
+#27745 := [trans #27731 #27737]: #27730
+#27727 := [quant-inst #24833 #161 #24996]: #27729
+#27746 := [mp #27727 #27745]: #27728
+#28652 := [unit-resolution #27746 #21240 #28651]: false
+#28653 := [lemma #28652]: #27103
+#27748 := (or #27098 #27089)
+#27749 := [def-axiom]: #27748
+#27673 := [unit-resolution #27749 #28653]: #27089
+#27371 := (= #3098 #27064)
+#27409 := [monotonicity #27140 #28384]: #27371
+#27674 := [trans #27409 #27673]: #27415
+#27675 := [trans #27674 #27414]: #27680
+#27676 := [monotonicity #27675]: #27682
+#27669 := [symm #27676]: #27668
+#27670 := (= #24996 #25112)
+#25113 := (= f19 #25112)
#2765 := (f24 #2761)
-#11417 := (= #369 #2765)
-#23271 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11417)
-#11421 := (forall (vars (?v0 S18) (?v1 Int)) #11417)
-#23274 := (iff #11421 #23271)
-#23272 := (iff #11417 #11417)
-#23273 := [refl]: #23272
-#23275 := [quant-intro #23273]: #23274
-#18271 := (~ #11421 #11421)
-#18269 := (~ #11417 #11417)
-#18270 := [refl]: #18269
-#18272 := [nnf-pos #18270]: #18271
+#11453 := (= #369 #2765)
+#23307 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11453)
+#11457 := (forall (vars (?v0 S18) (?v1 Int)) #11453)
+#23310 := (iff #11457 #23307)
+#23308 := (iff #11453 #11453)
+#23309 := [refl]: #23308
+#23311 := [quant-intro #23309]: #23310
+#18307 := (~ #11457 #11457)
+#18305 := (~ #11453 #11453)
+#18306 := [refl]: #18305
+#18308 := [nnf-pos #18306]: #18307
#2766 := (= #2765 #369)
#2767 := (forall (vars (?v0 S18) (?v1 Int)) #2766)
-#11422 := (iff #2767 #11421)
-#11419 := (iff #2766 #11417)
-#11420 := [rewrite]: #11419
-#11423 := [quant-intro #11420]: #11422
-#11416 := [asserted]: #2767
-#11426 := [mp #11416 #11423]: #11421
-#18273 := [mp~ #11426 #18272]: #11421
-#23276 := [mp #18273 #23275]: #23271
-#25028 := (not #23271)
-#25089 := (or #25028 #25084)
-#25090 := [quant-inst #3040 #3043]: #25089
-#28876 := [unit-resolution #25090 #23276]: #25084
-#28878 := [symm #28876]: #28877
-#26873 := (= #26550 #25081)
-#26866 := (= #26146 #3044)
-#26153 := (= #3044 #26146)
+#11458 := (iff #2767 #11457)
+#11455 := (iff #2766 #11453)
+#11456 := [rewrite]: #11455
+#11459 := [quant-intro #11456]: #11458
+#11452 := [asserted]: #2767
+#11462 := [mp #11452 #11459]: #11457
+#18309 := [mp~ #11462 #18308]: #11457
+#23312 := [mp #18309 #23311]: #23307
+#25064 := (not #23307)
+#25118 := (or #25064 #25113)
+#25119 := [quant-inst #50 #3041]: #25118
+#27139 := [unit-resolution #25119 #23312]: #25113
+#27671 := [trans #28386 #27139]: #27670
+#27672 := [trans #27671 #27669]: #27040
+#27021 := (not #27014)
+#27677 := (iff #18445 #27021)
+#27722 := (iff #12180 #27014)
+#27750 := (iff #27014 #12180)
+#27744 := (= #27013 #3099)
+#27747 := [monotonicity #28386]: #27744
+#27751 := [monotonicity #27747]: #27750
+#27723 := [symm #27751]: #27722
+#27724 := [monotonicity #27723]: #27677
+#27667 := [hypothesis]: #18445
+#27725 := [mp #27667 #27724]: #27021
+#27604 := (not #27040)
+#27597 := (not #27042)
+#27605 := (or #27597 #27014 #27604)
+#27603 := [def-axiom]: #27605
+#27726 := [unit-resolution #27603 #27725 #27672 #27640]: false
+#27642 := [lemma #27726]: #12180
+#28945 := (or #27098 #12189)
+#26985 := (f69 #3220 #3098)
+#27775 := (f146 #26985)
+#27778 := (f36 f297 #27775)
+#27786 := (= f37 #27778)
+#27776 := (f221 f297 #27775)
+#27777 := (= f1 #27776)
+#28363 := (or #27777 #27786)
+#28365 := (not #28363)
+#28146 := (f147 #26985)
+#28147 := (= f1 #28146)
+#28148 := (not #28147)
+#28100 := (f38 f297 #27775)
+#28093 := (= f1 #28100)
+#28145 := (not #28093)
+#28326 := (or #28145 #28148)
+#28340 := (not #28326)
+#27920 := (f23 #27039)
+#28266 := (= f25 #27920)
+#28322 := (not #28266)
+#28095 := (f24 #27775)
+#28096 := (f23 #28095)
+#28097 := (= f25 #28096)
+#28345 := (or #28097 #28322 #28340 #28365)
+#28437 := (not #28345)
+#28209 := (f221 f297 #3098)
+#28207 := (= f1 #28209)
+#28196 := (f36 f297 #3098)
+#28197 := (= f37 #28196)
+#28195 := (or #28197 #28207)
+#28275 := (not #28195)
+#28271 := (or #28275 #28266)
+#28273 := (not #28271)
+#28440 := (or #28273 #28437)
+#28443 := (not #28440)
+#3101 := (f35 f297 #3098)
+#12183 := (= f1 #3101)
+#18448 := (not #12183)
+#28446 := (or #18448 #28443)
+#28377 := (not #28446)
+#28367 := (iff #12189 #28377)
+#28434 := (or #28423 #28367)
+#27787 := (or #27786 #27777)
+#28094 := (not #27787)
+#27921 := (or #28148 #28145)
+#27919 := (not #27921)
+#27931 := (= #27920 f25)
+#27965 := (not #27931)
+#27966 := (or #27965 #27919 #28097 #28094)
+#28208 := (not #27966)
+#28276 := (or #27931 #28275)
+#28274 := (not #28276)
+#28277 := (or #28274 #28208)
+#28278 := (not #28277)
+#28279 := (or #18448 #28278)
+#28264 := (not #28279)
+#28265 := (iff #12189 #28264)
+#28435 := (or #28423 #28265)
+#28448 := (iff #28435 #28434)
+#28450 := (iff #28434 #28434)
+#28451 := [rewrite]: #28450
+#28348 := (iff #28265 #28367)
+#28378 := (iff #28264 #28377)
+#28368 := (iff #28279 #28446)
+#28444 := (iff #28278 #28443)
+#28441 := (iff #28277 #28440)
+#28438 := (iff #28208 #28437)
+#28360 := (iff #27966 #28345)
+#28341 := (or #28322 #28340 #28097 #28365)
+#28346 := (iff #28341 #28345)
+#28347 := [rewrite]: #28346
+#28343 := (iff #27966 #28341)
+#28339 := (iff #28094 #28365)
+#28364 := (iff #27787 #28363)
+#28359 := [rewrite]: #28364
+#28342 := [monotonicity #28359]: #28339
+#28361 := (iff #27919 #28340)
+#28331 := (iff #27921 #28326)
+#28332 := [rewrite]: #28331
+#28362 := [monotonicity #28332]: #28361
+#28281 := (iff #27965 #28322)
+#28267 := (iff #27931 #28266)
+#28268 := [rewrite]: #28267
+#28325 := [monotonicity #28268]: #28281
+#28344 := [monotonicity #28325 #28362 #28342]: #28343
+#28436 := [trans #28344 #28347]: #28360
+#28439 := [monotonicity #28436]: #28438
+#28320 := (iff #28274 #28273)
+#28284 := (iff #28276 #28271)
+#28263 := (or #28266 #28275)
+#28272 := (iff #28263 #28271)
+#28283 := [rewrite]: #28272
+#28269 := (iff #28276 #28263)
+#28270 := [monotonicity #28268]: #28269
+#28282 := [trans #28270 #28283]: #28284
+#28321 := [monotonicity #28282]: #28320
+#28442 := [monotonicity #28321 #28439]: #28441
+#28445 := [monotonicity #28442]: #28444
+#28369 := [monotonicity #28445]: #28368
+#28213 := [monotonicity #28369]: #28378
+#28349 := [monotonicity #28213]: #28348
+#28449 := [monotonicity #28349]: #28448
+#28456 := [trans #28449 #28451]: #28448
+#28447 := [quant-inst #3039 #3098]: #28435
+#28457 := [mp #28447 #28456]: #28434
+#28776 := [unit-resolution #28457 #22094]: #28367
+#28625 := (not #28367)
+#28779 := (or #28625 #28446)
+#28778 := [hypothesis]: #18454
+#28626 := (or #28625 #12189 #28446)
+#28627 := [def-axiom]: #28626
+#28777 := [unit-resolution #28627 #28778]: #28779
+#28780 := [unit-resolution #28777 #28776]: #28446
+#28816 := (or #28377 #28443)
+decl f26 :: (-> S20 S21 S1)
+decl f27 :: (-> S19 S20 S21)
+#24880 := (f127 #3044)
+#26182 := (f54 #3040 #24880)
+#26775 := (f27 f297 #26182)
+#27233 := (f26 #27145 #26775)
+#27234 := (= f1 #27233)
+#26776 := (f26 #26182 #26775)
+#28795 := (= #26776 #27233)
+#28792 := (= #27233 #26776)
+#28790 := (= #27145 #26182)
+#26189 := (= #3044 #26182)
#3049 := (f59 #3044 #3040)
-#12073 := (= f1 #3049)
+#12109 := (= f1 #3049)
decl f34 :: (-> S18 S1)
#3056 := (f34 #3040)
-#12085 := (= f1 #3056)
-#3051 := (f35 f298 #3044)
-#12076 := (= f1 #3051)
-decl f36 :: (-> S19 S20 S20)
-#3047 := (f36 f298 #3044)
-decl f37 :: S20
-#116 := f37
-#12070 := (= f37 #3047)
-decl f38 :: (-> S19 S20 S1)
-#3045 := (f38 f298 #3044)
-#12066 := (= f1 #3045)
-#14192 := (and #12066 #12070 #12073 #12076 #12082 #12085)
+#12121 := (= f1 #3056)
+#3053 := (f23 #3040)
+#12115 := (= f25 #3053)
+#12118 := (not #12115)
+#3051 := (f35 f297 #3044)
+#12112 := (= f1 #3051)
+#12106 := (= f37 #3047)
+#3045 := (f38 f297 #3044)
+#12102 := (= f1 #3045)
+#14228 := (and #12102 #12106 #12109 #12112 #12118 #12121)
+decl f293 :: Int
+#3024 := f293
+#14284 := (* -1::Int f293)
+decl f89 :: Int
+#472 := f89
+#14285 := (+ f89 #14284)
+#14283 := (>= #14285 0::Int)
+#14281 := (>= f293 0::Int)
+#14288 := (and #14281 #14283)
+#14291 := (not #14288)
decl f294 :: Int
-#3024 := f294
-#14248 := (* -1::Int f294)
-decl f90 :: Int
-#472 := f90
-#14249 := (+ f90 #14248)
-#14247 := (>= #14249 0::Int)
-#14245 := (>= f294 0::Int)
-#14252 := (and #14245 #14247)
-#14255 := (not #14252)
+#3028 := f294
+#14270 := (* -1::Int f294)
+decl f87 :: Int
+#452 := f87
+#14271 := (+ f87 #14270)
+#14269 := (>= #14271 0::Int)
+#14267 := (>= f294 0::Int)
+#14274 := (and #14267 #14269)
+#14277 := (not #14274)
decl f295 :: Int
-#3028 := f295
-#14234 := (* -1::Int f295)
-decl f88 :: Int
-#452 := f88
-#14235 := (+ f88 #14234)
-#14233 := (>= #14235 0::Int)
-#14231 := (>= f295 0::Int)
-#14238 := (and #14231 #14233)
-#14241 := (not #14238)
-decl f296 :: Int
-#3032 := f296
-#14220 := (* -1::Int f296)
-#14221 := (+ f88 #14220)
-#14219 := (>= #14221 0::Int)
-#14217 := (>= f296 0::Int)
-#14224 := (and #14217 #14219)
-#14227 := (not #14224)
+#3032 := f295
+#14256 := (* -1::Int f295)
+#14257 := (+ f87 #14256)
+#14255 := (>= #14257 0::Int)
+#14253 := (>= f295 0::Int)
+#14260 := (and #14253 #14255)
+#14263 := (not #14260)
#1085 := 1099511627776::Int
-#14205 := (>= f297 1099511627776::Int)
-#14195 := (not #14192)
-decl f300 :: (-> S34 Int)
+#14241 := (>= f296 1099511627776::Int)
+#14231 := (not #14228)
+decl f299 :: (-> S34 Int)
#3070 := (:var 0 S34)
-#3071 := (f300 #3070)
+#3071 := (f299 #3070)
#3072 := (pattern #3071)
-decl f301 :: Int
-#3073 := f301
-#14182 := (* -1::Int f301)
-#14183 := (+ #3071 #14182)
-#14181 := (>= #14183 0::Int)
-#14180 := (not #14181)
-#14186 := (forall (vars (?v0 S34)) (:pat #3072) #14180)
-#14189 := (not #14186)
-#13473 := (not #13472)
-#14036 := (and #3109 #13473)
-#14041 := (not #14036)
-#14024 := (+ f90 #13970)
-#14023 := (>= #14024 0::Int)
-#14027 := (and #14020 #14023)
-#14030 := (not #14027)
-#14011 := (+ f88 #13941)
-#14010 := (>= #14011 0::Int)
-#14014 := (and #13477 #14010)
-#14017 := (not #14014)
-#13502 := (+ f88 #13501)
-#14001 := (>= #13502 0::Int)
-#14004 := (and #13998 #14001)
-#14007 := (not #14004)
-#4494 := (* -1::Int f88)
-#4495 := (+ #202 #4494)
-#4496 := (<= #4495 0::Int)
-#4503 := (and #4202 #4496)
-#5712 := (not #4503)
-#13981 := (or #5712 #13958 #13972)
-#13986 := (forall (vars (?v0 Int)) #13981)
-#13989 := (not #13986)
-#13950 := (and #12214 #13944)
-#13955 := (not #13950)
-#13795 := (not #13793)
-#13833 := (and #3173 #4202 #4496 #13795)
-#13838 := (exists (vars (?v0 Int)) #13833)
-#13816 := (or #5712 #13793 #13807)
-#13821 := (forall (vars (?v0 Int)) #13816)
-#13841 := (not #13821)
-#13847 := (or #13841 #13838)
-#13852 := (and #13821 #13847)
-#13482 := (and #13477 #13480)
-#13485 := (not #13482)
-decl f228 :: S1
-#2541 := f228
-#10924 := (= f1 f228)
-#12338 := (not #10924)
-#13879 := (or #12338 #12304 #12295 #12286 #12277 #13485 #13852)
-#13884 := (and #10924 #13879)
-#13909 := (or #13485 #13766 #13884)
-#13500 := (>= #13502 1::Int)
-#13589 := (and #13498 #13500)
-#13592 := (not #13589)
-#13559 := (not #13558)
-#13565 := (and #12607 #13559)
-#13545 := (or #5712 #13522 #13536)
-#13550 := (forall (vars (?v0 Int)) #13545)
-#13553 := (not #13550)
-#13570 := (or #13553 #13565)
-#13573 := (and #13550 #13570)
-#13576 := (or #13519 #13573)
-#13579 := (and #13514 #13576)
-#13508 := (and #13489 #13506)
-#13511 := (not #13508)
-#13607 := (or #12656 #13511 #13579 #13586 #13592)
-#13615 := (and #13498 #13500 #13607)
-#13491 := (and #13480 #13489)
-#13494 := (not #13491)
-#13726 := (or #12821 #12812 #13485 #13494 #13615 #13671)
-#12551 := (and #12539 #12548)
-#12749 := (not #12551)
-#13647 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #13615)
-#13655 := (and #12539 #12548 #13647)
-#12545 := (and #12539 #12542)
-#12761 := (not #12545)
-#13660 := (or #12761 #13655)
-#13666 := (and #12539 #12542 #13660)
-#13696 := (or #13485 #13666 #13672)
-#13731 := (and #13696 #13726)
-#13740 := (or #12749 #13485 #13731)
-#13748 := (and #12539 #12548 #13740)
-#13753 := (or #12761 #13748)
-#13759 := (and #12539 #12542 #13753)
-#13788 := (or #13485 #13759 #13765)
-#13914 := (and #13788 #13909)
-#12525 := (and #12519 #12522)
-#12988 := (not #12525)
+decl f300 :: Int
+#3073 := f300
+#14218 := (* -1::Int f300)
+#14219 := (+ #3071 #14218)
+#14217 := (>= #14219 0::Int)
+#14216 := (not #14217)
+#14222 := (forall (vars (?v0 S34)) (:pat #3072) #14216)
+#14225 := (not #14222)
+#13509 := (not #13508)
+#14072 := (and #3109 #13509)
+#14077 := (not #14072)
+#14060 := (+ f89 #14006)
+#14059 := (>= #14060 0::Int)
+#14063 := (and #14056 #14059)
+#14066 := (not #14063)
+#14047 := (+ f87 #13977)
+#14046 := (>= #14047 0::Int)
+#14050 := (and #13513 #14046)
+#14053 := (not #14050)
+#13538 := (+ f87 #13537)
+#14037 := (>= #13538 0::Int)
+#14040 := (and #14034 #14037)
+#14043 := (not #14040)
+#4514 := (* -1::Int f87)
+#4515 := (+ #202 #4514)
+#4516 := (<= #4515 0::Int)
+#4523 := (and #4202 #4516)
+#5738 := (not #4523)
+#14017 := (or #5738 #13994 #14008)
+#14022 := (forall (vars (?v0 Int)) #14017)
+#14025 := (not #14022)
+#13980 := (not #13979)
+#13986 := (and #12250 #13980)
+#13991 := (not #13986)
+#13831 := (not #13829)
+#13869 := (and #3173 #4202 #4516 #13831)
+#13874 := (exists (vars (?v0 Int)) #13869)
+#13852 := (or #5738 #13829 #13843)
+#13857 := (forall (vars (?v0 Int)) #13852)
+#13877 := (not #13857)
+#13883 := (or #13877 #13874)
+#13888 := (and #13857 #13883)
+#13518 := (and #13513 #13516)
+#13521 := (not #13518)
+decl f227 :: S1
+#2541 := f227
+#10960 := (= f1 f227)
+#12374 := (not #10960)
+#13915 := (or #12374 #12340 #12331 #12322 #12313 #13521 #13888)
+#13920 := (and #10960 #13915)
+#13945 := (or #13521 #13802 #13920)
+#13536 := (>= #13538 1::Int)
+#13625 := (and #13534 #13536)
+#13628 := (not #13625)
+#13595 := (not #13594)
+#13601 := (and #12643 #13595)
+#13581 := (or #5738 #13558 #13572)
+#13586 := (forall (vars (?v0 Int)) #13581)
+#13589 := (not #13586)
+#13606 := (or #13589 #13601)
+#13609 := (and #13586 #13606)
+#13612 := (or #13555 #13609)
+#13615 := (and #13550 #13612)
+#13544 := (and #13525 #13542)
+#13547 := (not #13544)
+#13643 := (or #12692 #13547 #13615 #13622 #13628)
+#13651 := (and #13534 #13536 #13643)
+#13527 := (and #13516 #13525)
+#13530 := (not #13527)
+#13762 := (or #12857 #12848 #13521 #13530 #13651 #13707)
+#12587 := (and #12575 #12584)
+#12785 := (not #12587)
+#13683 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #13651)
+#13691 := (and #12575 #12584 #13683)
+#12581 := (and #12575 #12578)
+#12797 := (not #12581)
+#13696 := (or #12797 #13691)
+#13702 := (and #12575 #12578 #13696)
+#13732 := (or #13521 #13702 #13708)
+#13767 := (and #13732 #13762)
+#13776 := (or #12785 #13521 #13767)
+#13784 := (and #12575 #12584 #13776)
+#13789 := (or #12797 #13784)
+#13795 := (and #12575 #12578 #13789)
+#13824 := (or #13521 #13795 #13801)
+#13950 := (and #13824 #13945)
+#12561 := (and #12555 #12558)
+#13024 := (not #12561)
decl f66 :: (-> S19 S1)
-#3067 := (f66 f298)
-#12109 := (= f1 #3067)
-#12228 := (and #12109 #12222)
-#12366 := (not #12228)
-#14107 := (or #12366 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13914 #13955 #13989 #13995 #14007 #14017 #14030 #14041)
-#14115 := (and #3109 #13473 #14107)
-#13461 := (or #5712 #13439 #13451)
-#13466 := (forall (vars (?v0 Int)) #13461)
-#13469 := (not #13466)
-#14120 := (or #13469 #14115)
-#14123 := (and #13466 #14120)
-#14126 := (or #13436 #14123)
-#14129 := (and #13433 #14126)
-#12156 := (and #12144 #12153)
-#13240 := (not #12156)
-#14150 := (or #13231 #13240 #13222 #13213 #13204 #14129)
-#14158 := (and #12144 #12153 #14150)
-#12150 := (and #12144 #12147)
-#13252 := (not #12150)
-#14163 := (or #13252 #14158)
-#14169 := (and #12144 #12147 #14163)
-#14174 := (or #13264 #14169)
-#14177 := (and #12141 #14174)
-#13407 := (+ f88 #13406)
-#13405 := (>= #13407 0::Int)
-#13403 := (>= f297 0::Int)
-#13410 := (and #13403 #13405)
-#13413 := (not #13410)
-decl f305 :: (-> Int S20 S1)
-#62 := (:var 0 S20)
-decl f304 :: Int
-#3084 := f304
-#3087 := (f305 f304 #62)
+#3067 := (f66 f297)
+#12145 := (= f1 #3067)
+#12264 := (and #12145 #12258)
+#12402 := (not #12264)
+#14143 := (or #12402 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13950 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
+#14151 := (and #3109 #13509 #14143)
+#13497 := (or #5738 #13475 #13487)
+#13502 := (forall (vars (?v0 Int)) #13497)
+#13505 := (not #13502)
+#14156 := (or #13505 #14151)
+#14159 := (and #13502 #14156)
+#14162 := (or #13472 #14159)
+#14165 := (and #13469 #14162)
+#12192 := (and #12180 #12189)
+#13276 := (not #12192)
+#14186 := (or #13267 #13276 #13258 #13249 #13240 #14165)
+#14194 := (and #12180 #12189 #14186)
+#12186 := (and #12180 #12183)
+#13288 := (not #12186)
+#14199 := (or #13288 #14194)
+#14205 := (and #12180 #12183 #14199)
+decl f211 :: (-> S19 S20 S20 S31 S1)
+decl f305 :: S31
+#3095 := f305
+#3096 := (f211 f297 #3044 #3044 f305)
+#12177 := (= f1 #3096)
+#13300 := (not #12177)
+#14210 := (or #13300 #14205)
+#14213 := (and #12177 #14210)
+#13443 := (+ f87 #13442)
+#13441 := (>= #13443 0::Int)
+#13439 := (>= f296 0::Int)
+#13446 := (and #13439 #13441)
+#13449 := (not #13446)
+decl f304 :: (-> Int S20 S1)
+decl f303 :: Int
+#3084 := f303
+#3087 := (f304 f303 #62)
#3088 := (pattern #3087)
-#12127 := (= f1 #3087)
-#12133 := (not #12127)
-#12138 := (forall (vars (?v0 S20)) (:pat #3088) #12133)
-#13285 := (not #12138)
-decl f293 :: S17
-#3020 := f293
-#3082 := (f302 f298 f293 f291 f297 f16)
-#12124 := (= f1 #3082)
-#13303 := (not #12124)
-#3079 := (f303 f298 f293 f292 #3042 #51)
-#12118 := (= f1 #3079)
-#3077 := (f302 f298 f293 f292 #3076 #51)
-#12115 := (= f1 #3077)
-#12121 := (and #12115 #12118)
-#13312 := (not #12121)
-#3065 := (f214 f293 f298)
-#12106 := (= f1 #3065)
-#12112 := (and #12106 #12109)
-#13330 := (not #12112)
-decl f215 :: (-> S19 S1)
-#3063 := (f215 f298)
-#12103 := (= f1 #3063)
-#13339 := (not #12103)
-decl f185 :: (-> S19 Int)
-#3085 := (f185 f298)
-#3086 := (= f304 #3085)
-#13294 := (not #3086)
-#14300 := (or #13294 #13339 #13330 #13312 #13303 #13285 #13413 #13472 #14177 #14189 #14195 #14205 #14227 #14241 #14255)
-#14305 := (not #14300)
+#12163 := (= f1 #3087)
+#12169 := (not #12163)
+#12174 := (forall (vars (?v0 S20)) (:pat #3088) #12169)
+#13321 := (not #12174)
+decl f292 :: S17
+#3020 := f292
+#3082 := (f301 f297 f292 f290 f296 f16)
+#12160 := (= f1 #3082)
+#13339 := (not #12160)
+#3079 := (f302 f297 f292 f291 #3042 #51)
+#12154 := (= f1 #3079)
+#3077 := (f301 f297 f292 f291 #3076 #51)
+#12151 := (= f1 #3077)
+#12157 := (and #12151 #12154)
+#13348 := (not #12157)
+#3065 := (f213 f292 f297)
+#12142 := (= f1 #3065)
+#12148 := (and #12142 #12145)
+#13366 := (not #12148)
+decl f214 :: (-> S19 S1)
+#3063 := (f214 f297)
+#12139 := (= f1 #3063)
+#13375 := (not #12139)
+decl f184 :: (-> S19 Int)
+#3085 := (f184 f297)
+#3086 := (= f303 #3085)
+#13330 := (not #3086)
+#14336 := (or #13330 #13375 #13366 #13348 #13339 #13321 #13449 #13508 #14213 #14225 #14231 #14241 #14263 #14277 #14291)
+#14341 := (not #14336)
#1 := true
-#3168 := (< #202 f297)
+#3168 := (< #202 f296)
#3174 := (and #3168 #3173)
-#454 := (<= #202 f88)
+#454 := (<= #202 f87)
#3175 := (and #454 #3174)
#327 := (<= 0::Int #202)
#3176 := (and #327 #3175)
#3177 := (exists (vars (?v0 Int)) #3176)
#3178 := (and #3177 true)
-#3169 := (<= #3124 f314)
+#3169 := (<= #3124 f313)
#3170 := (implies #3168 #3169)
#455 := (and #327 #454)
#3171 := (implies #455 #3170)
#3172 := (forall (vars (?v0 Int)) #3171)
#3179 := (implies #3172 #3178)
#3180 := (and #3172 #3179)
-#3167 := (= f314 f308)
+#3167 := (= f313 f307)
#3181 := (implies #3167 #3180)
-#3165 := (= f313 f309)
+#3165 := (= f312 f308)
#3182 := (implies #3165 #3181)
-#3163 := (= f312 f310)
+#3163 := (= f311 f309)
#3183 := (implies #3163 #3182)
-#3161 := (= f311 f308)
+#3161 := (= f310 f307)
#3184 := (implies #3161 #3183)
-#3136 := (<= 0::Int f309)
-#3143 := (<= 1::Int f310)
+#3136 := (<= 0::Int f308)
+#3143 := (<= 1::Int f309)
#3144 := (and #3143 #3136)
#3185 := (implies #3144 #3184)
#3186 := (implies #3144 #3185)
#3187 := (implies #3144 #3186)
-#2542 := (= f228 f1)
+#2542 := (= f227 f1)
#3188 := (implies #2542 #3187)
#3189 := (and #2542 #3188)
#3190 := (implies #3144 #3189)
#3191 := (implies #3144 #3190)
#3348 := (implies #3144 #3191)
#3349 := (implies #3144 #3348)
-#3347 := (<= f297 f310)
+#3347 := (<= f296 f309)
#3350 := (implies #3347 #3349)
#3351 := (implies #3144 #3350)
-#3300 := (= #3299 f316)
-#3297 := (< f317 f297)
+#3300 := (= #3299 f315)
+#3297 := (< f316 f296)
#3301 := (and #3297 #3300)
#3302 := (and #3301 true)
-#3293 := (<= #3124 f316)
-#3292 := (< #202 f318)
+#3293 := (<= #3124 f315)
+#3292 := (< #202 f317)
#3294 := (implies #3292 #3293)
#3295 := (implies #455 #3294)
#3296 := (forall (vars (?v0 Int)) #3295)
#3303 := (implies #3296 #3302)
#3304 := (and #3296 #3303)
-#3291 := (<= f318 f297)
+#3291 := (<= f317 f296)
#3305 := (implies #3291 #3304)
#3306 := (and #3291 #3305)
-#3279 := (<= 0::Int f317)
-#3289 := (<= 2::Int f318)
+#3279 := (<= 0::Int f316)
+#3289 := (<= 2::Int f317)
#3290 := (and #3289 #3279)
#3307 := (implies #3290 #3306)
#3288 := (= #3287 f1)
#3308 := (implies #3288 #3307)
-#3281 := (+ f310 1::Int)
-#3286 := (= f318 #3281)
+#3281 := (+ f309 1::Int)
+#3286 := (= f317 #3281)
#3309 := (implies #3286 #3308)
-#3283 := (<= #3281 f88)
+#3283 := (<= #3281 f87)
#3282 := (<= 0::Int #3281)
#3284 := (and #3282 #3283)
#3310 := (implies #3284 #3309)
#3311 := (and #3284 #3310)
#3280 := (and #3143 #3279)
#3312 := (implies #3280 #3311)
-#3329 := (= f317 f309)
+#3329 := (= f316 f308)
#3330 := (implies #3329 #3312)
-#3328 := (= f316 f308)
+#3328 := (= f315 f307)
#3331 := (implies #3328 #3330)
#3332 := (implies #3144 #3331)
#3333 := (implies #3144 #3332)
#3334 := (implies #3144 #3333)
-#3327 := (<= #3266 f308)
+#3327 := (<= #3266 f307)
#3335 := (implies #3327 #3334)
#3336 := (implies #3144 #3335)
-#3278 := (= f317 f310)
+#3278 := (= f316 f309)
#3313 := (implies #3278 #3312)
-#3276 := (= f316 f315)
+#3276 := (= f315 f314)
#3314 := (implies #3276 #3313)
#3274 := (and #3143 #3143)
#3315 := (implies #3274 #3314)
@@ -760,7 +1512,7 @@
#3316 := (implies #3273 #3315)
#3271 := (= #3270 f1)
#3317 := (implies #3271 #3316)
-#3269 := (= f315 #3266)
+#3269 := (= f314 #3266)
#3318 := (implies #3269 #3317)
#3264 := (= #3263 f1)
#3259 := (= #3258 f1)
@@ -773,7 +1525,7 @@
#3322 := (and #3262 #3321)
#3323 := (implies #3144 #3322)
#3324 := (implies #3144 #3323)
-#3267 := (< f308 #3266)
+#3267 := (< f307 #3266)
#3325 := (implies #3267 #3324)
#3326 := (implies #3144 #3325)
#3337 := (and #3326 #3336)
@@ -784,16 +1536,14 @@
#3342 := (and #3262 #3341)
#3343 := (implies #3144 #3342)
#3344 := (implies #3144 #3343)
-#3256 := (< f310 f297)
+#3256 := (< f309 f296)
#3345 := (implies #3256 #3344)
#3346 := (implies #3144 #3345)
#3352 := (and #3346 #3351)
#3353 := (implies #3144 #3352)
decl f52 :: (-> S19 S27)
-#3197 := (f52 f298)
+#3197 := (f52 f297)
#3254 := (= #3197 #3197)
-decl f70 :: (-> S19 S28)
-#3220 := (f70 f298)
#3253 := (= #3220 #3220)
#3255 := (and #3253 #3254)
#3354 := (implies #3255 #3353)
@@ -814,8 +1564,8 @@
#3159 := (and #3158 #3068)
#3360 := (implies #3159 #3359)
#3233 := (= #3232 f1)
-decl f184 :: (-> S19 S20 Int)
-#3228 := (f184 f298 #62)
+decl f183 :: (-> S19 S20 Int)
+#3228 := (f183 f297 #62)
#3229 := (pattern #3228)
#3230 := (<= #3228 #3228)
#3231 := (forall (vars (?v0 S20)) (:pat #3229) #3230)
@@ -823,10 +1573,9 @@
#3227 := (<= #3085 #3085)
#3235 := (and #3227 #3234)
#3361 := (implies #3235 #3360)
-decl f69 :: (-> S28 S20 S29)
#3221 := (f69 #3220 #62)
#3222 := (pattern #3221)
-#3210 := (f79 f298 #62)
+#3210 := (f79 f297 #62)
#3211 := (= #3210 f1)
#3223 := (= #3221 #3221)
#3224 := (and #3223 #3211)
@@ -843,7 +1592,7 @@
#3237 := (and #3219 #3236)
decl f30 :: (-> S24 S20 Int)
decl f31 :: (-> S19 S24)
-#3207 := (f31 f298)
+#3207 := (f31 f297)
#3208 := (f30 #3207 #62)
#3209 := (pattern #3208)
#3212 := (= #3208 #3208)
@@ -851,12 +1600,12 @@
#3214 := (implies #3211 #3213)
#3215 := (forall (vars (?v0 S20)) (:pat #3209) #3214)
#3238 := (and #3215 #3237)
-decl f273 :: S23
-#2903 := f273
-#3200 := (f36 f298 #62)
+decl f272 :: S23
+#2903 := f272
+#3200 := (f36 f297 #62)
#3201 := (f24 #3200)
#3202 := (f23 #3201)
-#3203 := (= #3202 f273)
+#3203 := (= #3202 f272)
#3204 := (not #3203)
#3205 := (implies #3204 #3204)
#3206 := (forall (vars (?v0 S20)) (:pat #3199) #3205)
@@ -873,43 +1622,43 @@
#3196 := (implies #3144 #3195)
#3366 := (and #3196 #3365)
#3367 := (implies #3144 #3366)
-#3154 := (= #3153 f308)
-#3151 := (< f309 f297)
+#3154 := (= #3153 f307)
+#3151 := (< f308 f296)
#3155 := (and #3151 #3154)
#3368 := (implies #3155 #3367)
-#3147 := (<= #3124 f308)
-#3146 := (< #202 f310)
+#3147 := (<= #3124 f307)
+#3146 := (< #202 f309)
#3148 := (implies #3146 #3147)
#3149 := (implies #455 #3148)
#3150 := (forall (vars (?v0 Int)) #3149)
#3369 := (implies #3150 #3368)
-#3145 := (<= f310 f297)
+#3145 := (<= f309 f296)
#3370 := (implies #3145 #3369)
#3371 := (implies #3144 #3370)
-#3141 := (<= f310 f88)
-#3140 := (<= 0::Int f310)
+#3141 := (<= f309 f87)
+#3140 := (<= 0::Int f309)
#3142 := (and #3140 #3141)
#3372 := (implies #3142 #3371)
-#3137 := (<= f309 f88)
+#3137 := (<= f308 f87)
#3138 := (and #3136 #3137)
#3373 := (implies #3138 #3372)
-#3133 := (<= f308 f90)
-#3132 := (<= 0::Int f308)
+#3133 := (<= f307 f89)
+#3132 := (<= 0::Int f307)
#3134 := (and #3132 #3133)
#3374 := (implies #3134 #3373)
-#3129 := (= #3108 f307)
-#3038 := (< 0::Int f297)
+#3129 := (= #3108 f306)
+#3038 := (< 0::Int f296)
#3130 := (and #3038 #3129)
#3375 := (implies #3130 #3374)
#3376 := (and #3130 #3375)
-#3125 := (<= #3124 f307)
+#3125 := (<= #3124 f306)
#3122 := (< #202 1::Int)
#3126 := (implies #3122 #3125)
#3127 := (implies #455 #3126)
#3128 := (forall (vars (?v0 Int)) #3127)
#3377 := (implies #3128 #3376)
#3378 := (and #3128 #3377)
-#3121 := (<= 1::Int f297)
+#3121 := (<= 1::Int f296)
#3379 := (implies #3121 #3378)
#3380 := (and #3121 #3379)
#3117 := (<= 0::Int 0::Int)
@@ -937,8 +1686,8 @@
#3097 := (= #3096 f1)
#3390 := (implies #3097 #3389)
#3391 := (and #3097 #3390)
-#3093 := (<= f297 f88)
-#3092 := (<= 0::Int f297)
+#3093 := (<= f296 f87)
+#3092 := (<= 0::Int f296)
#3094 := (and #3092 #3093)
#3392 := (implies #3094 #3391)
#3089 := (= #3087 f1)
@@ -952,7 +1701,7 @@
#3078 := (= #3077 f1)
#3081 := (and #3078 #3080)
#3396 := (implies #3081 #3395)
-#3074 := (< #3071 f301)
+#3074 := (< #3071 f300)
#3075 := (forall (vars (?v0 S34)) (:pat #3072) #3074)
#3397 := (implies #3075 #3396)
#3066 := (= #3065 f1)
@@ -974,2252 +1723,2278 @@
#3062 := (and #3046 #3061)
#3400 := (implies #3062 #3399)
#3401 := (implies #3038 #3400)
-#3037 := (< f297 1099511627776::Int)
+#3037 := (< f296 1099511627776::Int)
#3402 := (implies #3037 #3401)
-#3034 := (<= f296 f88)
-#3033 := (<= 0::Int f296)
+#3034 := (<= f295 f87)
+#3033 := (<= 0::Int f295)
#3035 := (and #3033 #3034)
#3403 := (implies #3035 #3402)
-#3030 := (<= f295 f88)
-#3029 := (<= 0::Int f295)
+#3030 := (<= f294 f87)
+#3029 := (<= 0::Int f294)
#3031 := (and #3029 #3030)
#3404 := (implies #3031 #3403)
-#3026 := (<= f294 f90)
-#3025 := (<= 0::Int f294)
+#3026 := (<= f293 f89)
+#3025 := (<= 0::Int f293)
#3027 := (and #3025 #3026)
#3405 := (implies #3027 #3404)
#3406 := (not #3405)
-#14308 := (iff #3406 #14305)
-#12245 := (not #3168)
-#12246 := (or #12245 #3169)
-#5703 := (not #455)
-#12252 := (or #5703 #12246)
-#12257 := (forall (vars (?v0 Int)) #12252)
-#12265 := (not #12257)
-#12266 := (or #3177 #12265)
-#12271 := (and #12257 #12266)
-#12278 := (or #12277 #12271)
-#12287 := (or #12286 #12278)
-#12296 := (or #12295 #12287)
-#12305 := (or #12304 #12296)
-#12196 := (and #3136 #3143)
-#12313 := (not #12196)
-#12314 := (or #12313 #12305)
-#12322 := (or #12313 #12314)
-#12330 := (or #12313 #12322)
-#12339 := (or #12338 #12330)
-#12344 := (and #10924 #12339)
-#12350 := (or #12313 #12344)
-#12358 := (or #12313 #12350)
-#12937 := (or #12313 #12358)
-#12945 := (or #12313 #12937)
-#12953 := (not #3347)
-#12954 := (or #12953 #12945)
-#12962 := (or #12313 #12954)
-#12610 := (and #3297 #12607)
-#12592 := (not #3292)
-#12593 := (or #12592 #3293)
-#12599 := (or #5703 #12593)
-#12604 := (forall (vars (?v0 Int)) #12599)
-#12623 := (not #12604)
-#12624 := (or #12623 #12610)
-#12629 := (and #12604 #12624)
-#12635 := (not #3291)
-#12636 := (or #12635 #12629)
-#12641 := (and #3291 #12636)
-#12589 := (and #3279 #3289)
-#12647 := (not #12589)
-#12648 := (or #12647 #12641)
-#12657 := (or #12656 #12648)
-#12571 := (+ 1::Int f310)
-#12583 := (= f318 #12571)
-#12665 := (not #12583)
-#12666 := (or #12665 #12657)
-#12577 := (<= #12571 f88)
-#12574 := (<= 0::Int #12571)
-#12580 := (and #12574 #12577)
-#12674 := (not #12580)
-#12675 := (or #12674 #12666)
-#12680 := (and #12580 #12675)
-#12686 := (not #3280)
-#12687 := (or #12686 #12680)
-#12813 := (or #12687 #12812)
-#12822 := (or #12821 #12813)
-#12830 := (or #12313 #12822)
-#12838 := (or #12313 #12830)
-#12846 := (or #12313 #12838)
-#12854 := (not #3327)
-#12855 := (or #12854 #12846)
-#12863 := (or #12313 #12855)
-#12696 := (or #12695 #12687)
-#12705 := (or #12704 #12696)
-#12713 := (not #3143)
-#12714 := (or #12713 #12705)
-#12723 := (or #12722 #12714)
+#14344 := (iff #3406 #14341)
+#12281 := (not #3168)
+#12282 := (or #12281 #3169)
+#5729 := (not #455)
+#12288 := (or #5729 #12282)
+#12293 := (forall (vars (?v0 Int)) #12288)
+#12301 := (not #12293)
+#12302 := (or #3177 #12301)
+#12307 := (and #12293 #12302)
+#12314 := (or #12313 #12307)
+#12323 := (or #12322 #12314)
+#12332 := (or #12331 #12323)
+#12341 := (or #12340 #12332)
+#12232 := (and #3136 #3143)
+#12349 := (not #12232)
+#12350 := (or #12349 #12341)
+#12358 := (or #12349 #12350)
+#12366 := (or #12349 #12358)
+#12375 := (or #12374 #12366)
+#12380 := (and #10960 #12375)
+#12386 := (or #12349 #12380)
+#12394 := (or #12349 #12386)
+#12973 := (or #12349 #12394)
+#12981 := (or #12349 #12973)
+#12989 := (not #3347)
+#12990 := (or #12989 #12981)
+#12998 := (or #12349 #12990)
+#12646 := (and #3297 #12643)
+#12628 := (not #3292)
+#12629 := (or #12628 #3293)
+#12635 := (or #5729 #12629)
+#12640 := (forall (vars (?v0 Int)) #12635)
+#12659 := (not #12640)
+#12660 := (or #12659 #12646)
+#12665 := (and #12640 #12660)
+#12671 := (not #3291)
+#12672 := (or #12671 #12665)
+#12677 := (and #3291 #12672)
+#12625 := (and #3279 #3289)
+#12683 := (not #12625)
+#12684 := (or #12683 #12677)
+#12693 := (or #12692 #12684)
+#12607 := (+ 1::Int f309)
+#12619 := (= f317 #12607)
+#12701 := (not #12619)
+#12702 := (or #12701 #12693)
+#12613 := (<= #12607 f87)
+#12610 := (<= 0::Int #12607)
+#12616 := (and #12610 #12613)
+#12710 := (not #12616)
+#12711 := (or #12710 #12702)
+#12716 := (and #12616 #12711)
+#12722 := (not #3280)
+#12723 := (or #12722 #12716)
+#12849 := (or #12723 #12848)
+#12858 := (or #12857 #12849)
+#12866 := (or #12349 #12858)
+#12874 := (or #12349 #12866)
+#12882 := (or #12349 #12874)
+#12890 := (not #3327)
+#12891 := (or #12890 #12882)
+#12899 := (or #12349 #12891)
#12732 := (or #12731 #12723)
#12741 := (or #12740 #12732)
+#12749 := (not #3143)
#12750 := (or #12749 #12741)
-#12755 := (and #12551 #12750)
-#12762 := (or #12761 #12755)
-#12767 := (and #12545 #12762)
-#12773 := (or #12313 #12767)
-#12781 := (or #12313 #12773)
-#12789 := (not #3267)
-#12790 := (or #12789 #12781)
-#12798 := (or #12313 #12790)
-#12868 := (and #12798 #12863)
-#12874 := (or #12313 #12868)
-#12882 := (or #12749 #12874)
-#12887 := (and #12551 #12882)
-#12893 := (or #12761 #12887)
-#12898 := (and #12545 #12893)
-#12904 := (or #12313 #12898)
-#12912 := (or #12313 #12904)
-#12920 := (not #3256)
-#12921 := (or #12920 #12912)
-#12929 := (or #12313 #12921)
-#12967 := (and #12929 #12962)
-#12973 := (or #12313 #12967)
-#12989 := (or #12988 #12973)
-#12998 := (or #12997 #12989)
-#13007 := (or #13006 #12998)
-#13016 := (or #13015 #13007)
-#13025 := (or #13024 #13016)
-#13033 := (or #12366 #13025)
-#12482 := (and #3231 #12479)
-#12485 := (and #3227 #12482)
-#13041 := (not #12485)
-#13042 := (or #13041 #13033)
-#13050 := (or #13041 #13042)
-#13058 := (or #12313 #13050)
-#13066 := (or #12313 #13058)
-#13074 := (or #12313 #13066)
-#13089 := (or #12313 #13074)
-#12217 := (and #3151 #12214)
-#13097 := (not #12217)
-#13098 := (or #13097 #13089)
-#12199 := (not #3146)
-#12200 := (or #12199 #3147)
-#12206 := (or #5703 #12200)
-#12211 := (forall (vars (?v0 Int)) #12206)
-#13106 := (not #12211)
-#13107 := (or #13106 #13098)
-#13115 := (not #3145)
-#13116 := (or #13115 #13107)
-#13124 := (or #12313 #13116)
-#13132 := (not #3142)
-#13133 := (or #13132 #13124)
-#13141 := (not #3138)
-#13142 := (or #13141 #13133)
-#13150 := (not #3134)
-#13151 := (or #13150 #13142)
-#12193 := (and #3038 #3109)
-#13159 := (not #12193)
-#13160 := (or #13159 #13151)
-#13165 := (and #12193 #13160)
-#12176 := (not #3122)
-#12177 := (or #12176 #3125)
-#12183 := (or #5703 #12177)
-#12188 := (forall (vars (?v0 Int)) #12183)
-#13171 := (not #12188)
-#13172 := (or #13171 #13165)
-#13177 := (and #12188 #13172)
-#13183 := (not #3121)
-#13184 := (or #13183 #13177)
-#13189 := (and #3121 #13184)
-#12170 := (and #3116 #3117)
-#12173 := (and #3116 #12170)
-#13195 := (not #12173)
-#13196 := (or #13195 #13189)
-#13205 := (or #13204 #13196)
-#13214 := (or #13213 #13205)
-#13223 := (or #13222 #13214)
-#13232 := (or #13231 #13223)
+#12759 := (or #12758 #12750)
+#12768 := (or #12767 #12759)
+#12777 := (or #12776 #12768)
+#12786 := (or #12785 #12777)
+#12791 := (and #12587 #12786)
+#12798 := (or #12797 #12791)
+#12803 := (and #12581 #12798)
+#12809 := (or #12349 #12803)
+#12817 := (or #12349 #12809)
+#12825 := (not #3267)
+#12826 := (or #12825 #12817)
+#12834 := (or #12349 #12826)
+#12904 := (and #12834 #12899)
+#12910 := (or #12349 #12904)
+#12918 := (or #12785 #12910)
+#12923 := (and #12587 #12918)
+#12929 := (or #12797 #12923)
+#12934 := (and #12581 #12929)
+#12940 := (or #12349 #12934)
+#12948 := (or #12349 #12940)
+#12956 := (not #3256)
+#12957 := (or #12956 #12948)
+#12965 := (or #12349 #12957)
+#13003 := (and #12965 #12998)
+#13009 := (or #12349 #13003)
+#13025 := (or #13024 #13009)
+#13034 := (or #13033 #13025)
+#13043 := (or #13042 #13034)
+#13052 := (or #13051 #13043)
+#13061 := (or #13060 #13052)
+#13069 := (or #12402 #13061)
+#12518 := (and #3231 #12515)
+#12521 := (and #3227 #12518)
+#13077 := (not #12521)
+#13078 := (or #13077 #13069)
+#13086 := (or #13077 #13078)
+#13094 := (or #12349 #13086)
+#13102 := (or #12349 #13094)
+#13110 := (or #12349 #13102)
+#13125 := (or #12349 #13110)
+#12253 := (and #3151 #12250)
+#13133 := (not #12253)
+#13134 := (or #13133 #13125)
+#12235 := (not #3146)
+#12236 := (or #12235 #3147)
+#12242 := (or #5729 #12236)
+#12247 := (forall (vars (?v0 Int)) #12242)
+#13142 := (not #12247)
+#13143 := (or #13142 #13134)
+#13151 := (not #3145)
+#13152 := (or #13151 #13143)
+#13160 := (or #12349 #13152)
+#13168 := (not #3142)
+#13169 := (or #13168 #13160)
+#13177 := (not #3138)
+#13178 := (or #13177 #13169)
+#13186 := (not #3134)
+#13187 := (or #13186 #13178)
+#12229 := (and #3038 #3109)
+#13195 := (not #12229)
+#13196 := (or #13195 #13187)
+#13201 := (and #12229 #13196)
+#12212 := (not #3122)
+#12213 := (or #12212 #3125)
+#12219 := (or #5729 #12213)
+#12224 := (forall (vars (?v0 Int)) #12219)
+#13207 := (not #12224)
+#13208 := (or #13207 #13201)
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-#13745 := (and #12551 #13740)
-#13749 := (iff #13745 #13748)
-#13750 := [rewrite]: #13749
-#13746 := (iff #12887 #13745)
-#13743 := (iff #12882 #13740)
-#13734 := (or #13485 #13731)
-#13737 := (or #12749 #13734)
-#13741 := (iff #13737 #13740)
-#13742 := [rewrite]: #13741
-#13738 := (iff #12882 #13737)
-#13735 := (iff #12874 #13734)
-#13732 := (iff #12868 #13731)
-#13729 := (iff #12863 #13726)
-#13623 := (or #13494 #13615)
-#13705 := (or #13623 #12812)
-#13708 := (or #12821 #13705)
-#13711 := (or #13485 #13708)
-#13714 := (or #13485 #13711)
-#13717 := (or #13485 #13714)
-#13720 := (or #13671 #13717)
-#13723 := (or #13485 #13720)
-#13727 := (iff #13723 #13726)
-#13728 := [rewrite]: #13727
-#13724 := (iff #12863 #13723)
-#13721 := (iff #12855 #13720)
-#13718 := (iff #12846 #13717)
-#13715 := (iff #12838 #13714)
-#13712 := (iff #12830 #13711)
-#13709 := (iff #12822 #13708)
-#13706 := (iff #12813 #13705)
-#13624 := (iff #12687 #13623)
-#13618 := (iff #12680 #13615)
-#13612 := (and #13589 #13607)
-#13616 := (iff #13612 #13615)
-#13617 := [rewrite]: #13616
-#13613 := (iff #12680 #13612)
-#13610 := (iff #12675 #13607)
-#13595 := (or #13511 #13579)
-#13598 := (or #12656 #13595)
-#13601 := (or #13586 #13598)
-#13604 := (or #13592 #13601)
-#13608 := (iff #13604 #13607)
-#13609 := [rewrite]: #13608
-#13605 := (iff #12675 #13604)
-#13602 := (iff #12666 #13601)
-#13599 := (iff #12657 #13598)
-#13596 := (iff #12648 #13595)
-#13580 := (iff #12641 #13579)
-#13577 := (iff #12636 #13576)
-#13574 := (iff #12629 #13573)
-#13571 := (iff #12624 #13570)
-#13568 := (iff #12610 #13565)
-#13562 := (and #13559 #12607)
-#13566 := (iff #13562 #13565)
-#13567 := [rewrite]: #13566
-#13563 := (iff #12610 #13562)
-#13560 := (iff #3297 #13559)
-#13561 := [rewrite]: #13560
-#13564 := [monotonicity #13561]: #13563
-#13569 := [trans #13564 #13567]: #13568
-#13554 := (iff #12623 #13553)
-#13551 := (iff #12604 #13550)
-#13548 := (iff #12599 #13545)
-#13539 := (or #13522 #13536)
-#13542 := (or #5712 #13539)
-#13546 := (iff #13542 #13545)
-#13547 := [rewrite]: #13546
-#13543 := (iff #12599 #13542)
-#13540 := (iff #12593 #13539)
-#13537 := (iff #3293 #13536)
-#13538 := [rewrite]: #13537
-#13532 := (iff #12592 #13522)
-#13524 := (not #13522)
-#13527 := (not #13524)
-#13530 := (iff #13527 #13522)
-#13531 := [rewrite]: #13530
-#13528 := (iff #12592 #13527)
-#13525 := (iff #3292 #13524)
-#13526 := [rewrite]: #13525
-#13529 := [monotonicity #13526]: #13528
-#13533 := [trans #13529 #13531]: #13532
-#13541 := [monotonicity #13533 #13538]: #13540
-#13544 := [monotonicity #5714 #13541]: #13543
-#13549 := [trans #13544 #13547]: #13548
-#13552 := [quant-intro #13549]: #13551
-#13555 := [monotonicity #13552]: #13554
-#13572 := [monotonicity #13555 #13569]: #13571
-#13575 := [monotonicity #13552 #13572]: #13574
-#13520 := (iff #12635 #13519)
-#13517 := (iff #3291 #13514)
-#13518 := [rewrite]: #13517
-#13521 := [monotonicity #13518]: #13520
-#13578 := [monotonicity #13521 #13575]: #13577
-#13581 := [monotonicity #13518 #13578]: #13580
-#13512 := (iff #12647 #13511)
-#13509 := (iff #12589 #13508)
-#13505 := (iff #3289 #13506)
-#13507 := [rewrite]: #13505
-#13488 := (iff #3279 #13489)
-#13490 := [rewrite]: #13488
-#13510 := [monotonicity #13490 #13507]: #13509
-#13513 := [monotonicity #13510]: #13512
-#13597 := [monotonicity #13513 #13581]: #13596
+#4525 := [monotonicity #4201 #4518]: #4524
+#5740 := [monotonicity #4525]: #5739
+#13851 := [monotonicity #5740 #13848]: #13850
+#13856 := [trans #13851 #13854]: #13855
+#13859 := [quant-intro #13856]: #13858
+#13879 := [monotonicity #13859]: #13878
+#13875 := (iff #3177 #13874)
+#13872 := (iff #3176 #13869)
+#13860 := (and #13831 #3173)
+#13863 := (and #4516 #13860)
+#13866 := (and #4202 #13863)
+#13870 := (iff #13866 #13869)
+#13871 := [rewrite]: #13870
+#13867 := (iff #3176 #13866)
+#13864 := (iff #3175 #13863)
+#13861 := (iff #3174 #13860)
+#13862 := [monotonicity #13833]: #13861
+#13865 := [monotonicity #4518 #13862]: #13864
+#13868 := [monotonicity #4201 #13865]: #13867
+#13873 := [trans #13868 #13871]: #13872
+#13876 := [quant-intro #13873]: #13875
+#13882 := [monotonicity #13876 #13879]: #13881
+#13887 := [trans #13882 #13885]: #13886
+#13890 := [monotonicity #13859 #13887]: #13889
+#13893 := [monotonicity #13890]: #13892
+#13896 := [monotonicity #13893]: #13895
+#13899 := [monotonicity #13896]: #13898
+#13902 := [monotonicity #13899]: #13901
+#13522 := (iff #12349 #13521)
+#13519 := (iff #12232 #13518)
+#13515 := (iff #3143 #13516)
+#13517 := [rewrite]: #13515
+#13512 := (iff #3136 #13513)
+#13514 := [rewrite]: #13512
+#13520 := [monotonicity #13514 #13517]: #13519
+#13523 := [monotonicity #13520]: #13522
+#13905 := [monotonicity #13523 #13902]: #13904
+#13908 := [monotonicity #13523 #13905]: #13907
+#13911 := [monotonicity #13523 #13908]: #13910
+#13914 := [monotonicity #13911]: #13913
+#13919 := [trans #13914 #13917]: #13918
+#13922 := [monotonicity #13919]: #13921
+#13929 := [monotonicity #13523 #13922]: #13928
+#13932 := [monotonicity #13523 #13929]: #13931
+#13935 := [monotonicity #13523 #13932]: #13934
+#13938 := [monotonicity #13523 #13935]: #13937
+#13925 := (iff #12989 #13802)
+#13923 := (iff #3347 #13801)
+#13924 := [rewrite]: #13923
+#13926 := [monotonicity #13924]: #13925
+#13941 := [monotonicity #13926 #13938]: #13940
+#13944 := [monotonicity #13523 #13941]: #13943
+#13949 := [trans #13944 #13947]: #13948
+#13827 := (iff #12965 #13824)
+#13812 := (or #13521 #13795)
+#13815 := (or #13521 #13812)
+#13818 := (or #13801 #13815)
+#13821 := (or #13521 #13818)
+#13825 := (iff #13821 #13824)
+#13826 := [rewrite]: #13825
+#13822 := (iff #12965 #13821)
+#13819 := (iff #12957 #13818)
+#13816 := (iff #12948 #13815)
+#13813 := (iff #12940 #13812)
+#13798 := (iff #12934 #13795)
+#13792 := (and #12581 #13789)
+#13796 := (iff #13792 #13795)
+#13797 := [rewrite]: #13796
+#13793 := (iff #12934 #13792)
+#13790 := (iff #12929 #13789)
+#13787 := (iff #12923 #13784)
+#13781 := (and #12587 #13776)
+#13785 := (iff #13781 #13784)
+#13786 := [rewrite]: #13785
+#13782 := (iff #12923 #13781)
+#13779 := (iff #12918 #13776)
+#13770 := (or #13521 #13767)
+#13773 := (or #12785 #13770)
+#13777 := (iff #13773 #13776)
+#13778 := [rewrite]: #13777
+#13774 := (iff #12918 #13773)
+#13771 := (iff #12910 #13770)
+#13768 := (iff #12904 #13767)
+#13765 := (iff #12899 #13762)
+#13659 := (or #13530 #13651)
+#13741 := (or #13659 #12848)
+#13744 := (or #12857 #13741)
+#13747 := (or #13521 #13744)
+#13750 := (or #13521 #13747)
+#13753 := (or #13521 #13750)
+#13756 := (or #13707 #13753)
+#13759 := (or #13521 #13756)
+#13763 := (iff #13759 #13762)
+#13764 := [rewrite]: #13763
+#13760 := (iff #12899 #13759)
+#13757 := (iff #12891 #13756)
+#13754 := (iff #12882 #13753)
+#13751 := (iff #12874 #13750)
+#13748 := (iff #12866 #13747)
+#13745 := (iff #12858 #13744)
+#13742 := (iff #12849 #13741)
+#13660 := (iff #12723 #13659)
+#13654 := (iff #12716 #13651)
+#13648 := (and #13625 #13643)
+#13652 := (iff #13648 #13651)
+#13653 := [rewrite]: #13652
+#13649 := (iff #12716 #13648)
+#13646 := (iff #12711 #13643)
+#13631 := (or #13547 #13615)
+#13634 := (or #12692 #13631)
+#13637 := (or #13622 #13634)
+#13640 := (or #13628 #13637)
+#13644 := (iff #13640 #13643)
+#13645 := [rewrite]: #13644
+#13641 := (iff #12711 #13640)
+#13638 := (iff #12702 #13637)
+#13635 := (iff #12693 #13634)
+#13632 := (iff #12684 #13631)
+#13616 := (iff #12677 #13615)
+#13613 := (iff #12672 #13612)
+#13610 := (iff #12665 #13609)
+#13607 := (iff #12660 #13606)
+#13604 := (iff #12646 #13601)
+#13598 := (and #13595 #12643)
+#13602 := (iff #13598 #13601)
+#13603 := [rewrite]: #13602
+#13599 := (iff #12646 #13598)
+#13596 := (iff #3297 #13595)
+#13597 := [rewrite]: #13596
#13600 := [monotonicity #13597]: #13599
-#13587 := (iff #12665 #13586)
-#13584 := (iff #12583 #13582)
-#13585 := [rewrite]: #13584
-#13588 := [monotonicity #13585]: #13587
-#13603 := [monotonicity #13588 #13600]: #13602
-#13593 := (iff #12674 #13592)
-#13590 := (iff #12580 #13589)
-#13503 := (iff #12577 #13500)
-#13504 := [rewrite]: #13503
-#13497 := (iff #12574 #13498)
-#13499 := [rewrite]: #13497
-#13591 := [monotonicity #13499 #13504]: #13590
-#13594 := [monotonicity #13591]: #13593
-#13606 := [monotonicity #13594 #13603]: #13605
-#13611 := [trans #13606 #13609]: #13610
-#13614 := [monotonicity #13591 #13611]: #13613
-#13619 := [trans #13614 #13617]: #13618
-#13495 := (iff #12686 #13494)
-#13492 := (iff #3280 #13491)
-#13493 := [monotonicity #13481 #13490]: #13492
-#13496 := [monotonicity #13493]: #13495
-#13625 := [monotonicity #13496 #13619]: #13624
-#13707 := [monotonicity #13625]: #13706
-#13710 := [monotonicity #13707]: #13709
-#13713 := [monotonicity #13487 #13710]: #13712
-#13716 := [monotonicity #13487 #13713]: #13715
-#13719 := [monotonicity #13487 #13716]: #13718
-#13703 := (iff #12854 #13671)
-#13701 := (iff #3327 #13672)
-#13702 := [rewrite]: #13701
-#13704 := [monotonicity #13702]: #13703
-#13722 := [monotonicity #13704 #13719]: #13721
-#13725 := [monotonicity #13487 #13722]: #13724
-#13730 := [trans #13725 #13728]: #13729
-#13699 := (iff #12798 #13696)
-#13684 := (or #13485 #13666)
-#13687 := (or #13485 #13684)
-#13690 := (or #13672 #13687)
-#13693 := (or #13485 #13690)
-#13697 := (iff #13693 #13696)
-#13698 := [rewrite]: #13697
-#13694 := (iff #12798 #13693)
-#13691 := (iff #12790 #13690)
-#13688 := (iff #12781 #13687)
-#13685 := (iff #12773 #13684)
-#13669 := (iff #12767 #13666)
-#13663 := (and #12545 #13660)
-#13667 := (iff #13663 #13666)
-#13668 := [rewrite]: #13667
-#13664 := (iff #12767 #13663)
-#13661 := (iff #12762 #13660)
-#13658 := (iff #12755 #13655)
-#13652 := (and #12551 #13647)
-#13656 := (iff #13652 #13655)
-#13657 := [rewrite]: #13656
-#13653 := (iff #12755 #13652)
-#13650 := (iff #12750 #13647)
-#13626 := (or #12695 #13623)
-#13629 := (or #12704 #13626)
-#13632 := (or #13620 #13629)
-#13635 := (or #12722 #13632)
-#13638 := (or #12731 #13635)
-#13641 := (or #12740 #13638)
-#13644 := (or #12749 #13641)
-#13648 := (iff #13644 #13647)
-#13649 := [rewrite]: #13648
-#13645 := (iff #12750 #13644)
-#13642 := (iff #12741 #13641)
-#13639 := (iff #12732 #13638)
-#13636 := (iff #12723 #13635)
-#13633 := (iff #12714 #13632)
-#13630 := (iff #12705 #13629)
-#13627 := (iff #12696 #13626)
-#13628 := [monotonicity #13625]: #13627
-#13631 := [monotonicity #13628]: #13630
-#13621 := (iff #12713 #13620)
-#13622 := [monotonicity #13481]: #13621
-#13634 := [monotonicity #13622 #13631]: #13633
-#13637 := [monotonicity #13634]: #13636
-#13640 := [monotonicity #13637]: #13639
-#13643 := [monotonicity #13640]: #13642
-#13646 := [monotonicity #13643]: #13645
-#13651 := [trans #13646 #13649]: #13650
-#13654 := [monotonicity #13651]: #13653
-#13659 := [trans #13654 #13657]: #13658
-#13662 := [monotonicity #13659]: #13661
-#13665 := [monotonicity #13662]: #13664
-#13670 := [trans #13665 #13668]: #13669
-#13686 := [monotonicity #13487 #13670]: #13685
-#13689 := [monotonicity #13487 #13686]: #13688
-#13682 := (iff #12789 #13672)
-#13677 := (not #13671)
-#13680 := (iff #13677 #13672)
-#13681 := [rewrite]: #13680
-#13678 := (iff #12789 #13677)
-#13675 := (iff #3267 #13671)
-#13676 := [rewrite]: #13675
+#13605 := [trans #13600 #13603]: #13604
+#13590 := (iff #12659 #13589)
+#13587 := (iff #12640 #13586)
+#13584 := (iff #12635 #13581)
+#13575 := (or #13558 #13572)
+#13578 := (or #5738 #13575)
+#13582 := (iff #13578 #13581)
+#13583 := [rewrite]: #13582
+#13579 := (iff #12635 #13578)
+#13576 := (iff #12629 #13575)
+#13573 := (iff #3293 #13572)
+#13574 := [rewrite]: #13573
+#13568 := (iff #12628 #13558)
+#13560 := (not #13558)
+#13563 := (not #13560)
+#13566 := (iff #13563 #13558)
+#13567 := [rewrite]: #13566
+#13564 := (iff #12628 #13563)
+#13561 := (iff #3292 #13560)
+#13562 := [rewrite]: #13561
+#13565 := [monotonicity #13562]: #13564
+#13569 := [trans #13565 #13567]: #13568
+#13577 := [monotonicity #13569 #13574]: #13576
+#13580 := [monotonicity #5740 #13577]: #13579
+#13585 := [trans #13580 #13583]: #13584
+#13588 := [quant-intro #13585]: #13587
+#13591 := [monotonicity #13588]: #13590
+#13608 := [monotonicity #13591 #13605]: #13607
+#13611 := [monotonicity #13588 #13608]: #13610
+#13556 := (iff #12671 #13555)
+#13553 := (iff #3291 #13550)
+#13554 := [rewrite]: #13553
+#13557 := [monotonicity #13554]: #13556
+#13614 := [monotonicity #13557 #13611]: #13613
+#13617 := [monotonicity #13554 #13614]: #13616
+#13548 := (iff #12683 #13547)
+#13545 := (iff #12625 #13544)
+#13541 := (iff #3289 #13542)
+#13543 := [rewrite]: #13541
+#13524 := (iff #3279 #13525)
+#13526 := [rewrite]: #13524
+#13546 := [monotonicity #13526 #13543]: #13545
+#13549 := [monotonicity #13546]: #13548
+#13633 := [monotonicity #13549 #13617]: #13632
+#13636 := [monotonicity #13633]: #13635
+#13623 := (iff #12701 #13622)
+#13620 := (iff #12619 #13618)
+#13621 := [rewrite]: #13620
+#13624 := [monotonicity #13621]: #13623
+#13639 := [monotonicity #13624 #13636]: #13638
+#13629 := (iff #12710 #13628)
+#13626 := (iff #12616 #13625)
+#13539 := (iff #12613 #13536)
+#13540 := [rewrite]: #13539
+#13533 := (iff #12610 #13534)
+#13535 := [rewrite]: #13533
+#13627 := [monotonicity #13535 #13540]: #13626
+#13630 := [monotonicity #13627]: #13629
+#13642 := [monotonicity #13630 #13639]: #13641
+#13647 := [trans #13642 #13645]: #13646
+#13650 := [monotonicity #13627 #13647]: #13649
+#13655 := [trans #13650 #13653]: #13654
+#13531 := (iff #12722 #13530)
+#13528 := (iff #3280 #13527)
+#13529 := [monotonicity #13517 #13526]: #13528
+#13532 := [monotonicity #13529]: #13531
+#13661 := [monotonicity #13532 #13655]: #13660
+#13743 := [monotonicity #13661]: #13742
+#13746 := [monotonicity #13743]: #13745
+#13749 := [monotonicity #13523 #13746]: #13748
+#13752 := [monotonicity #13523 #13749]: #13751
+#13755 := [monotonicity #13523 #13752]: #13754
+#13739 := (iff #12890 #13707)
+#13737 := (iff #3327 #13708)
+#13738 := [rewrite]: #13737
+#13740 := [monotonicity #13738]: #13739
+#13758 := [monotonicity #13740 #13755]: #13757
+#13761 := [monotonicity #13523 #13758]: #13760
+#13766 := [trans #13761 #13764]: #13765
+#13735 := (iff #12834 #13732)
+#13720 := (or #13521 #13702)
+#13723 := (or #13521 #13720)
+#13726 := (or #13708 #13723)
+#13729 := (or #13521 #13726)
+#13733 := (iff #13729 #13732)
+#13734 := [rewrite]: #13733
+#13730 := (iff #12834 #13729)
+#13727 := (iff #12826 #13726)
+#13724 := (iff #12817 #13723)
+#13721 := (iff #12809 #13720)
+#13705 := (iff #12803 #13702)
+#13699 := (and #12581 #13696)
+#13703 := (iff #13699 #13702)
+#13704 := [rewrite]: #13703
+#13700 := (iff #12803 #13699)
+#13697 := (iff #12798 #13696)
+#13694 := (iff #12791 #13691)
+#13688 := (and #12587 #13683)
+#13692 := (iff #13688 #13691)
+#13693 := [rewrite]: #13692
+#13689 := (iff #12791 #13688)
+#13686 := (iff #12786 #13683)
+#13662 := (or #12731 #13659)
+#13665 := (or #12740 #13662)
+#13668 := (or #13656 #13665)
+#13671 := (or #12758 #13668)
+#13674 := (or #12767 #13671)
+#13677 := (or #12776 #13674)
+#13680 := (or #12785 #13677)
+#13684 := (iff #13680 #13683)
+#13685 := [rewrite]: #13684
+#13681 := (iff #12786 #13680)
+#13678 := (iff #12777 #13677)
+#13675 := (iff #12768 #13674)
+#13672 := (iff #12759 #13671)
+#13669 := (iff #12750 #13668)
+#13666 := (iff #12741 #13665)
+#13663 := (iff #12732 #13662)
+#13664 := [monotonicity #13661]: #13663
+#13667 := [monotonicity #13664]: #13666
+#13657 := (iff #12749 #13656)
+#13658 := [monotonicity #13517]: #13657
+#13670 := [monotonicity #13658 #13667]: #13669
+#13673 := [monotonicity #13670]: #13672
+#13676 := [monotonicity #13673]: #13675
#13679 := [monotonicity #13676]: #13678
-#13683 := [trans #13679 #13681]: #13682
-#13692 := [monotonicity #13683 #13689]: #13691
-#13695 := [monotonicity #13487 #13692]: #13694
-#13700 := [trans #13695 #13698]: #13699
-#13733 := [monotonicity #13700 #13730]: #13732
-#13736 := [monotonicity #13487 #13733]: #13735
-#13739 := [monotonicity #13736]: #13738
-#13744 := [trans #13739 #13742]: #13743
-#13747 := [monotonicity #13744]: #13746
-#13752 := [trans #13747 #13750]: #13751
-#13755 := [monotonicity #13752]: #13754
-#13758 := [monotonicity #13755]: #13757
-#13763 := [trans #13758 #13761]: #13762
-#13778 := [monotonicity #13487 #13763]: #13777
-#13781 := [monotonicity #13487 #13778]: #13780
-#13774 := (iff #12920 #13765)
-#13769 := (not #13766)
-#13772 := (iff #13769 #13765)
-#13773 := [rewrite]: #13772
-#13770 := (iff #12920 #13769)
-#13767 := (iff #3256 #13766)
-#13768 := [rewrite]: #13767
-#13771 := [monotonicity #13768]: #13770
-#13775 := [trans #13771 #13773]: #13774
-#13784 := [monotonicity #13775 #13781]: #13783
-#13787 := [monotonicity #13487 #13784]: #13786
-#13792 := [trans #13787 #13790]: #13791
-#13916 := [monotonicity #13792 #13913]: #13915
-#14046 := [monotonicity #13487 #13916]: #14045
-#14049 := [monotonicity #14046]: #14048
-#14052 := [monotonicity #14049]: #14051
+#13682 := [monotonicity #13679]: #13681
+#13687 := [trans #13682 #13685]: #13686
+#13690 := [monotonicity #13687]: #13689
+#13695 := [trans #13690 #13693]: #13694
+#13698 := [monotonicity #13695]: #13697
+#13701 := [monotonicity #13698]: #13700
+#13706 := [trans #13701 #13704]: #13705
+#13722 := [monotonicity #13523 #13706]: #13721
+#13725 := [monotonicity #13523 #13722]: #13724
+#13718 := (iff #12825 #13708)
+#13713 := (not #13707)
+#13716 := (iff #13713 #13708)
+#13717 := [rewrite]: #13716
+#13714 := (iff #12825 #13713)
+#13711 := (iff #3267 #13707)
+#13712 := [rewrite]: #13711
+#13715 := [monotonicity #13712]: #13714
+#13719 := [trans #13715 #13717]: #13718
+#13728 := [monotonicity #13719 #13725]: #13727
+#13731 := [monotonicity #13523 #13728]: #13730
+#13736 := [trans #13731 #13734]: #13735
+#13769 := [monotonicity #13736 #13766]: #13768
+#13772 := [monotonicity #13523 #13769]: #13771
+#13775 := [monotonicity #13772]: #13774
+#13780 := [trans #13775 #13778]: #13779
+#13783 := [monotonicity #13780]: #13782
+#13788 := [trans #13783 #13786]: #13787
+#13791 := [monotonicity #13788]: #13790
+#13794 := [monotonicity #13791]: #13793
+#13799 := [trans #13794 #13797]: #13798
+#13814 := [monotonicity #13523 #13799]: #13813
+#13817 := [monotonicity #13523 #13814]: #13816
+#13810 := (iff #12956 #13801)
+#13805 := (not #13802)
+#13808 := (iff #13805 #13801)
+#13809 := [rewrite]: #13808
+#13806 := (iff #12956 #13805)
+#13803 := (iff #3256 #13802)
+#13804 := [rewrite]: #13803
+#13807 := [monotonicity #13804]: #13806
+#13811 := [trans #13807 #13809]: #13810
+#13820 := [monotonicity #13811 #13817]: #13819
+#13823 := [monotonicity #13523 #13820]: #13822
+#13828 := [trans #13823 #13826]: #13827
+#13952 := [monotonicity #13828 #13949]: #13951
+#14082 := [monotonicity #13523 #13952]: #14081
+#14085 := [monotonicity #14082]: #14084
+#14088 := [monotonicity #14085]: #14087
+#14091 := [monotonicity #14088]: #14090
+#14094 := [monotonicity #14091]: #14093
+#14097 := [monotonicity #14094]: #14096
+#14100 := [monotonicity #14097]: #14099
+#13975 := (iff #13077 #13974)
+#13972 := (iff #12521 #12515)
+#13964 := (and true #12515)
+#13967 := (and true #13964)
+#13970 := (iff #13967 #12515)
+#13971 := [rewrite]: #13970
+#13968 := (iff #12521 #13967)
+#13965 := (iff #12518 #13964)
+#13960 := (iff #3231 true)
+#13955 := (forall (vars (?v0 S20)) (:pat #3229) true)
+#13958 := (iff #13955 true)
+#13959 := [elim-unused]: #13958
+#13956 := (iff #3231 #13955)
+#13953 := (iff #3230 true)
+#13954 := [rewrite]: #13953
+#13957 := [quant-intro #13954]: #13956
+#13961 := [trans #13957 #13959]: #13960
+#13966 := [monotonicity #13961]: #13965
+#13962 := (iff #3227 true)
+#13963 := [rewrite]: #13962
+#13969 := [monotonicity #13963 #13966]: #13968
+#13973 := [trans #13969 #13971]: #13972
+#13976 := [monotonicity #13973]: #13975
+#14103 := [monotonicity #13976 #14100]: #14102
+#14106 := [monotonicity #13976 #14103]: #14105
+#14109 := [monotonicity #13523 #14106]: #14108
+#14112 := [monotonicity #13523 #14109]: #14111
+#14115 := [monotonicity #13523 #14112]: #14114
+#14118 := [monotonicity #13523 #14115]: #14117
+#13992 := (iff #13133 #13991)
+#13989 := (iff #12253 #13986)
+#13983 := (and #13980 #12250)
+#13987 := (iff #13983 #13986)
+#13988 := [rewrite]: #13987
+#13984 := (iff #12253 #13983)
+#13981 := (iff #3151 #13980)
+#13982 := [rewrite]: #13981
+#13985 := [monotonicity #13982]: #13984
+#13990 := [trans #13985 #13988]: #13989
+#13993 := [monotonicity #13990]: #13992
+#14121 := [monotonicity #13993 #14118]: #14120
+#14026 := (iff #13142 #14025)
+#14023 := (iff #12247 #14022)
+#14020 := (iff #12242 #14017)
+#14011 := (or #13994 #14008)
+#14014 := (or #5738 #14011)
+#14018 := (iff #14014 #14017)
+#14019 := [rewrite]: #14018
+#14015 := (iff #12242 #14014)
+#14012 := (iff #12236 #14011)
+#14009 := (iff #3147 #14008)
+#14010 := [rewrite]: #14009
+#14004 := (iff #12235 #13994)
+#13996 := (not #13994)
+#13999 := (not #13996)
+#14002 := (iff #13999 #13994)
+#14003 := [rewrite]: #14002
+#14000 := (iff #12235 #13999)
+#13997 := (iff #3146 #13996)
+#13998 := [rewrite]: #13997
+#14001 := [monotonicity #13998]: #14000
+#14005 := [trans #14001 #14003]: #14004
+#14013 := [monotonicity #14005 #14010]: #14012
+#14016 := [monotonicity #5740 #14013]: #14015
+#14021 := [trans #14016 #14019]: #14020
+#14024 := [quant-intro #14021]: #14023
+#14027 := [monotonicity #14024]: #14026
+#14124 := [monotonicity #14027 #14121]: #14123
+#14032 := (iff #13151 #14031)
+#14029 := (iff #3145 #14028)
+#14030 := [rewrite]: #14029
+#14033 := [monotonicity #14030]: #14032
+#14127 := [monotonicity #14033 #14124]: #14126
+#14130 := [monotonicity #13523 #14127]: #14129
+#14044 := (iff #13168 #14043)
+#14041 := (iff #3142 #14040)
+#14038 := (iff #3141 #14037)
+#14039 := [rewrite]: #14038
+#14035 := (iff #3140 #14034)
+#14036 := [rewrite]: #14035
+#14042 := [monotonicity #14036 #14039]: #14041
+#14045 := [monotonicity #14042]: #14044
+#14133 := [monotonicity #14045 #14130]: #14132
+#14054 := (iff #13177 #14053)
+#14051 := (iff #3138 #14050)
+#14048 := (iff #3137 #14046)
+#14049 := [rewrite]: #14048
+#14052 := [monotonicity #13514 #14049]: #14051
#14055 := [monotonicity #14052]: #14054
-#14058 := [monotonicity #14055]: #14057
-#14061 := [monotonicity #14058]: #14060
-#14064 := [monotonicity #14061]: #14063
-#13939 := (iff #13041 #13938)
-#13936 := (iff #12485 #12479)
-#13928 := (and true #12479)
-#13931 := (and true #13928)
-#13934 := (iff #13931 #12479)
-#13935 := [rewrite]: #13934
-#13932 := (iff #12485 #13931)
-#13929 := (iff #12482 #13928)
-#13924 := (iff #3231 true)
-#13919 := (forall (vars (?v0 S20)) (:pat #3229) true)
-#13922 := (iff #13919 true)
-#13923 := [elim-unused]: #13922
-#13920 := (iff #3231 #13919)
-#13917 := (iff #3230 true)
-#13918 := [rewrite]: #13917
-#13921 := [quant-intro #13918]: #13920
-#13925 := [trans #13921 #13923]: #13924
-#13930 := [monotonicity #13925]: #13929
-#13926 := (iff #3227 true)
-#13927 := [rewrite]: #13926
-#13933 := [monotonicity #13927 #13930]: #13932
-#13937 := [trans #13933 #13935]: #13936
-#13940 := [monotonicity #13937]: #13939
-#14067 := [monotonicity #13940 #14064]: #14066
-#14070 := [monotonicity #13940 #14067]: #14069
-#14073 := [monotonicity #13487 #14070]: #14072
-#14076 := [monotonicity #13487 #14073]: #14075
-#14079 := [monotonicity #13487 #14076]: #14078
-#14082 := [monotonicity #13487 #14079]: #14081
-#13956 := (iff #13097 #13955)
-#13953 := (iff #12217 #13950)
-#13947 := (and #13944 #12214)
-#13951 := (iff #13947 #13950)
-#13952 := [rewrite]: #13951
-#13948 := (iff #12217 #13947)
-#13945 := (iff #3151 #13944)
-#13946 := [rewrite]: #13945
-#13949 := [monotonicity #13946]: #13948
-#13954 := [trans #13949 #13952]: #13953
-#13957 := [monotonicity #13954]: #13956
-#14085 := [monotonicity #13957 #14082]: #14084
-#13990 := (iff #13106 #13989)
-#13987 := (iff #12211 #13986)
-#13984 := (iff #12206 #13981)
-#13975 := (or #13958 #13972)
-#13978 := (or #5712 #13975)
-#13982 := (iff #13978 #13981)
-#13983 := [rewrite]: #13982
-#13979 := (iff #12206 #13978)
-#13976 := (iff #12200 #13975)
-#13973 := (iff #3147 #13972)
-#13974 := [rewrite]: #13973
-#13968 := (iff #12199 #13958)
-#13960 := (not #13958)
-#13963 := (not #13960)
-#13966 := (iff #13963 #13958)
-#13967 := [rewrite]: #13966
-#13964 := (iff #12199 #13963)
-#13961 := (iff #3146 #13960)
-#13962 := [rewrite]: #13961
-#13965 := [monotonicity #13962]: #13964
-#13969 := [trans #13965 #13967]: #13968
-#13977 := [monotonicity #13969 #13974]: #13976
-#13980 := [monotonicity #5714 #13977]: #13979
-#13985 := [trans #13980 #13983]: #13984
-#13988 := [quant-intro #13985]: #13987
-#13991 := [monotonicity #13988]: #13990
-#14088 := [monotonicity #13991 #14085]: #14087
-#13996 := (iff #13115 #13995)
-#13993 := (iff #3145 #13992)
-#13994 := [rewrite]: #13993
-#13997 := [monotonicity #13994]: #13996
-#14091 := [monotonicity #13997 #14088]: #14090
-#14094 := [monotonicity #13487 #14091]: #14093
-#14008 := (iff #13132 #14007)
-#14005 := (iff #3142 #14004)
-#14002 := (iff #3141 #14001)
-#14003 := [rewrite]: #14002
-#13999 := (iff #3140 #13998)
-#14000 := [rewrite]: #13999
-#14006 := [monotonicity #14000 #14003]: #14005
-#14009 := [monotonicity #14006]: #14008
-#14097 := [monotonicity #14009 #14094]: #14096
-#14018 := (iff #13141 #14017)
-#14015 := (iff #3138 #14014)
-#14012 := (iff #3137 #14010)
-#14013 := [rewrite]: #14012
-#14016 := [monotonicity #13478 #14013]: #14015
-#14019 := [monotonicity #14016]: #14018
-#14100 := [monotonicity #14019 #14097]: #14099
-#14031 := (iff #13150 #14030)
-#14028 := (iff #3134 #14027)
-#14025 := (iff #3133 #14023)
-#14026 := [rewrite]: #14025
-#14021 := (iff #3132 #14020)
-#14022 := [rewrite]: #14021
-#14029 := [monotonicity #14022 #14026]: #14028
-#14032 := [monotonicity #14029]: #14031
-#14103 := [monotonicity #14032 #14100]: #14102
-#14042 := (iff #13159 #14041)
-#14039 := (iff #12193 #14036)
-#14037 := (iff #14033 #14036)
-#14038 := [rewrite]: #14037
-#14034 := (iff #12193 #14033)
-#13474 := (iff #3038 #13473)
-#13475 := [rewrite]: #13474
-#14035 := [monotonicity #13475]: #14034
-#14040 := [trans #14035 #14038]: #14039
-#14043 := [monotonicity #14040]: #14042
-#14106 := [monotonicity #14043 #14103]: #14105
-#14111 := [trans #14106 #14109]: #14110
-#14114 := [monotonicity #14035 #14111]: #14113
-#14119 := [trans #14114 #14117]: #14118
-#13470 := (iff #13171 #13469)
-#13467 := (iff #12188 #13466)
-#13464 := (iff #12183 #13461)
-#13455 := (or #13439 #13451)
-#13458 := (or #5712 #13455)
-#13462 := (iff #13458 #13461)
-#13463 := [rewrite]: #13462
-#13459 := (iff #12183 #13458)
-#13456 := (iff #12177 #13455)
-#13450 := (iff #3125 #13451)
-#13454 := [rewrite]: #13450
-#13448 := (iff #12176 #13439)
-#13440 := (not #13439)
-#13443 := (not #13440)
-#13446 := (iff #13443 #13439)
-#13447 := [rewrite]: #13446
-#13444 := (iff #12176 #13443)
-#13441 := (iff #3122 #13440)
-#13442 := [rewrite]: #13441
-#13445 := [monotonicity #13442]: #13444
-#13449 := [trans #13445 #13447]: #13448
-#13457 := [monotonicity #13449 #13454]: #13456
-#13460 := [monotonicity #5714 #13457]: #13459
-#13465 := [trans #13460 #13463]: #13464
-#13468 := [quant-intro #13465]: #13467
-#13471 := [monotonicity #13468]: #13470
-#14122 := [monotonicity #13471 #14119]: #14121
-#14125 := [monotonicity #13468 #14122]: #14124
-#13437 := (iff #13183 #13436)
-#13434 := (iff #3121 #13433)
-#13435 := [rewrite]: #13434
-#13438 := [monotonicity #13435]: #13437
-#14128 := [monotonicity #13438 #14125]: #14127
-#14131 := [monotonicity #13435 #14128]: #14130
-#13431 := (iff #13195 false)
-#12220 := (iff #3156 false)
-#12221 := [rewrite]: #12220
-#13429 := (iff #13195 #3156)
-#13427 := (iff #12173 true)
-#12532 := (and true true)
-#13422 := (and true #12532)
-#13425 := (iff #13422 true)
-#13426 := [rewrite]: #13425
-#13423 := (iff #12173 #13422)
-#13420 := (iff #12170 #12532)
-#13418 := (iff #3117 true)
-#13419 := [rewrite]: #13418
-#13416 := (iff #3116 true)
-#13417 := [rewrite]: #13416
-#13421 := [monotonicity #13417 #13419]: #13420
-#13424 := [monotonicity #13417 #13421]: #13423
-#13428 := [trans #13424 #13426]: #13427
-#13430 := [monotonicity #13428]: #13429
-#13432 := [trans #13430 #12221]: #13431
-#14134 := [monotonicity #13432 #14131]: #14133
-#14137 := [monotonicity #14134]: #14136
-#14140 := [monotonicity #14137]: #14139
-#14143 := [monotonicity #14140]: #14142
-#14146 := [monotonicity #14143]: #14145
-#14149 := [monotonicity #14146]: #14148
-#14154 := [trans #14149 #14152]: #14153
-#14157 := [monotonicity #14154]: #14156
-#14162 := [trans #14157 #14160]: #14161
-#14165 := [monotonicity #14162]: #14164
-#14168 := [monotonicity #14165]: #14167
-#14173 := [trans #14168 #14171]: #14172
+#14136 := [monotonicity #14055 #14133]: #14135
+#14067 := (iff #13186 #14066)
+#14064 := (iff #3134 #14063)
+#14061 := (iff #3133 #14059)
+#14062 := [rewrite]: #14061
+#14057 := (iff #3132 #14056)
+#14058 := [rewrite]: #14057
+#14065 := [monotonicity #14058 #14062]: #14064
+#14068 := [monotonicity #14065]: #14067
+#14139 := [monotonicity #14068 #14136]: #14138
+#14078 := (iff #13195 #14077)
+#14075 := (iff #12229 #14072)
+#14073 := (iff #14069 #14072)
+#14074 := [rewrite]: #14073
+#14070 := (iff #12229 #14069)
+#13510 := (iff #3038 #13509)
+#13511 := [rewrite]: #13510
+#14071 := [monotonicity #13511]: #14070
+#14076 := [trans #14071 #14074]: #14075
+#14079 := [monotonicity #14076]: #14078
+#14142 := [monotonicity #14079 #14139]: #14141
+#14147 := [trans #14142 #14145]: #14146
+#14150 := [monotonicity #14071 #14147]: #14149
+#14155 := [trans #14150 #14153]: #14154
+#13506 := (iff #13207 #13505)
+#13503 := (iff #12224 #13502)
+#13500 := (iff #12219 #13497)
+#13491 := (or #13475 #13487)
+#13494 := (or #5738 #13491)
+#13498 := (iff #13494 #13497)
+#13499 := [rewrite]: #13498
+#13495 := (iff #12219 #13494)
+#13492 := (iff #12213 #13491)
+#13486 := (iff #3125 #13487)
+#13490 := [rewrite]: #13486
+#13484 := (iff #12212 #13475)
+#13476 := (not #13475)
+#13479 := (not #13476)
+#13482 := (iff #13479 #13475)
+#13483 := [rewrite]: #13482
+#13480 := (iff #12212 #13479)
+#13477 := (iff #3122 #13476)
+#13478 := [rewrite]: #13477
+#13481 := [monotonicity #13478]: #13480
+#13485 := [trans #13481 #13483]: #13484
+#13493 := [monotonicity #13485 #13490]: #13492
+#13496 := [monotonicity #5740 #13493]: #13495
+#13501 := [trans #13496 #13499]: #13500
+#13504 := [quant-intro #13501]: #13503
+#13507 := [monotonicity #13504]: #13506
+#14158 := [monotonicity #13507 #14155]: #14157
+#14161 := [monotonicity #13504 #14158]: #14160
+#13473 := (iff #13219 #13472)
+#13470 := (iff #3121 #13469)
+#13471 := [rewrite]: #13470
+#13474 := [monotonicity #13471]: #13473
+#14164 := [monotonicity #13474 #14161]: #14163
+#14167 := [monotonicity #13471 #14164]: #14166
+#13467 := (iff #13231 false)
+#12256 := (iff #3156 false)
+#12257 := [rewrite]: #12256
+#13465 := (iff #13231 #3156)
+#13463 := (iff #12209 true)
+#12568 := (and true true)
+#13458 := (and true #12568)
+#13461 := (iff #13458 true)
+#13462 := [rewrite]: #13461
+#13459 := (iff #12209 #13458)
+#13456 := (iff #12206 #12568)
+#13454 := (iff #3117 true)
+#13455 := [rewrite]: #13454
+#13452 := (iff #3116 true)
+#13453 := [rewrite]: #13452
+#13457 := [monotonicity #13453 #13455]: #13456
+#13460 := [monotonicity #13453 #13457]: #13459
+#13464 := [trans #13460 #13462]: #13463
+#13466 := [monotonicity #13464]: #13465
+#13468 := [trans #13466 #12257]: #13467
+#14170 := [monotonicity #13468 #14167]: #14169
+#14173 := [monotonicity #14170]: #14172
#14176 := [monotonicity #14173]: #14175
#14179 := [monotonicity #14176]: #14178
-#13414 := (iff #13276 #13413)
-#13411 := (iff #3094 #13410)
-#13408 := (iff #3093 #13405)
-#13409 := [rewrite]: #13408
-#13402 := (iff #3092 #13403)
-#13404 := [rewrite]: #13402
-#13412 := [monotonicity #13404 #13409]: #13411
-#13415 := [monotonicity #13412]: #13414
-#14260 := [monotonicity #13415 #14179]: #14259
-#14263 := [monotonicity #14260]: #14262
-#14266 := [monotonicity #14263]: #14265
-#14269 := [monotonicity #14266]: #14268
-#14272 := [monotonicity #14269]: #14271
-#14190 := (iff #13321 #14189)
-#14187 := (iff #3075 #14186)
-#14184 := (iff #3074 #14180)
-#14185 := [rewrite]: #14184
-#14188 := [quant-intro #14185]: #14187
-#14191 := [monotonicity #14188]: #14190
-#14275 := [monotonicity #14191 #14272]: #14274
-#14278 := [monotonicity #14275]: #14277
-#14281 := [monotonicity #14278]: #14280
-#14196 := (iff #13348 #14195)
-#14193 := (iff #12100 #14192)
-#14194 := [rewrite]: #14193
-#14197 := [monotonicity #14194]: #14196
-#14284 := [monotonicity #14197 #14281]: #14283
-#14203 := (iff #13357 #13472)
-#14198 := (not #13473)
-#14201 := (iff #14198 #13472)
-#14202 := [rewrite]: #14201
-#14199 := (iff #13357 #14198)
-#14200 := [monotonicity #13475]: #14199
-#14204 := [trans #14200 #14202]: #14203
-#14287 := [monotonicity #14204 #14284]: #14286
-#14214 := (iff #13366 #14205)
-#14206 := (not #14205)
-#14209 := (not #14206)
-#14212 := (iff #14209 #14205)
-#14213 := [rewrite]: #14212
-#14210 := (iff #13366 #14209)
-#14207 := (iff #3037 #14206)
-#14208 := [rewrite]: #14207
-#14211 := [monotonicity #14208]: #14210
-#14215 := [trans #14211 #14213]: #14214
-#14290 := [monotonicity #14215 #14287]: #14289
-#14228 := (iff #13375 #14227)
-#14225 := (iff #3035 #14224)
-#14222 := (iff #3034 #14219)
-#14223 := [rewrite]: #14222
-#14216 := (iff #3033 #14217)
-#14218 := [rewrite]: #14216
-#14226 := [monotonicity #14218 #14223]: #14225
-#14229 := [monotonicity #14226]: #14228
-#14293 := [monotonicity #14229 #14290]: #14292
-#14242 := (iff #13384 #14241)
-#14239 := (iff #3031 #14238)
-#14236 := (iff #3030 #14233)
-#14237 := [rewrite]: #14236
-#14230 := (iff #3029 #14231)
-#14232 := [rewrite]: #14230
-#14240 := [monotonicity #14232 #14237]: #14239
-#14243 := [monotonicity #14240]: #14242
-#14296 := [monotonicity #14243 #14293]: #14295
-#14256 := (iff #13393 #14255)
-#14253 := (iff #3027 #14252)
-#14250 := (iff #3026 #14247)
-#14251 := [rewrite]: #14250
-#14244 := (iff #3025 #14245)
-#14246 := [rewrite]: #14244
-#14254 := [monotonicity #14246 #14251]: #14253
-#14257 := [monotonicity #14254]: #14256
-#14299 := [monotonicity #14257 #14296]: #14298
-#14304 := [trans #14299 #14302]: #14303
-#14307 := [monotonicity #14304]: #14306
-#13400 := (iff #3406 #13399)
-#13397 := (iff #3405 #13394)
-#13390 := (implies #3027 #13385)
+#14182 := [monotonicity #14179]: #14181
+#14185 := [monotonicity #14182]: #14184
+#14190 := [trans #14185 #14188]: #14189
+#14193 := [monotonicity #14190]: #14192
+#14198 := [trans #14193 #14196]: #14197
+#14201 := [monotonicity #14198]: #14200
+#14204 := [monotonicity #14201]: #14203
+#14209 := [trans #14204 #14207]: #14208
+#14212 := [monotonicity #14209]: #14211
+#14215 := [monotonicity #14212]: #14214
+#13450 := (iff #13312 #13449)
+#13447 := (iff #3094 #13446)
+#13444 := (iff #3093 #13441)
+#13445 := [rewrite]: #13444
+#13438 := (iff #3092 #13439)
+#13440 := [rewrite]: #13438
+#13448 := [monotonicity #13440 #13445]: #13447
+#13451 := [monotonicity #13448]: #13450
+#14296 := [monotonicity #13451 #14215]: #14295
+#14299 := [monotonicity #14296]: #14298
+#14302 := [monotonicity #14299]: #14301
+#14305 := [monotonicity #14302]: #14304
+#14308 := [monotonicity #14305]: #14307
+#14226 := (iff #13357 #14225)
+#14223 := (iff #3075 #14222)
+#14220 := (iff #3074 #14216)
+#14221 := [rewrite]: #14220
+#14224 := [quant-intro #14221]: #14223
+#14227 := [monotonicity #14224]: #14226
+#14311 := [monotonicity #14227 #14308]: #14310
+#14314 := [monotonicity #14311]: #14313
+#14317 := [monotonicity #14314]: #14316
+#14232 := (iff #13384 #14231)
+#14229 := (iff #12136 #14228)
+#14230 := [rewrite]: #14229
+#14233 := [monotonicity #14230]: #14232
+#14320 := [monotonicity #14233 #14317]: #14319
+#14239 := (iff #13393 #13508)
+#14234 := (not #13509)
+#14237 := (iff #14234 #13508)
+#14238 := [rewrite]: #14237
+#14235 := (iff #13393 #14234)
+#14236 := [monotonicity #13511]: #14235
+#14240 := [trans #14236 #14238]: #14239
+#14323 := [monotonicity #14240 #14320]: #14322
+#14250 := (iff #13402 #14241)
+#14242 := (not #14241)
+#14245 := (not #14242)
+#14248 := (iff #14245 #14241)
+#14249 := [rewrite]: #14248
+#14246 := (iff #13402 #14245)
+#14243 := (iff #3037 #14242)
+#14244 := [rewrite]: #14243
+#14247 := [monotonicity #14244]: #14246
+#14251 := [trans #14247 #14249]: #14250
+#14326 := [monotonicity #14251 #14323]: #14325
+#14264 := (iff #13411 #14263)
+#14261 := (iff #3035 #14260)
+#14258 := (iff #3034 #14255)
+#14259 := [rewrite]: #14258
+#14252 := (iff #3033 #14253)
+#14254 := [rewrite]: #14252
+#14262 := [monotonicity #14254 #14259]: #14261
+#14265 := [monotonicity #14262]: #14264
+#14329 := [monotonicity #14265 #14326]: #14328
+#14278 := (iff #13420 #14277)
+#14275 := (iff #3031 #14274)
+#14272 := (iff #3030 #14269)
+#14273 := [rewrite]: #14272
+#14266 := (iff #3029 #14267)
+#14268 := [rewrite]: #14266
+#14276 := [monotonicity #14268 #14273]: #14275
+#14279 := [monotonicity #14276]: #14278
+#14332 := [monotonicity #14279 #14329]: #14331
+#14292 := (iff #13429 #14291)
+#14289 := (iff #3027 #14288)
+#14286 := (iff #3026 #14283)
+#14287 := [rewrite]: #14286
+#14280 := (iff #3025 #14281)
+#14282 := [rewrite]: #14280
+#14290 := [monotonicity #14282 #14287]: #14289
+#14293 := [monotonicity #14290]: #14292
+#14335 := [monotonicity #14293 #14332]: #14334
+#14340 := [trans #14335 #14338]: #14339
+#14343 := [monotonicity #14340]: #14342
+#13436 := (iff #3406 #13435)
+#13433 := (iff #3405 #13430)
+#13426 := (implies #3027 #13421)
+#13431 := (iff #13426 #13430)
+#13432 := [rewrite]: #13431
+#13427 := (iff #3405 #13426)
+#13424 := (iff #3404 #13421)
+#13417 := (implies #3031 #13412)
+#13422 := (iff #13417 #13421)
+#13423 := [rewrite]: #13422
+#13418 := (iff #3404 #13417)
+#13415 := (iff #3403 #13412)
+#13408 := (implies #3035 #13403)
+#13413 := (iff #13408 #13412)
+#13414 := [rewrite]: #13413
+#13409 := (iff #3403 #13408)
+#13406 := (iff #3402 #13403)
+#13399 := (implies #3037 #13394)
+#13404 := (iff #13399 #13403)
+#13405 := [rewrite]: #13404
+#13400 := (iff #3402 #13399)
+#13397 := (iff #3401 #13394)
+#13390 := (implies #3038 #13385)
#13395 := (iff #13390 #13394)
#13396 := [rewrite]: #13395
-#13391 := (iff #3405 #13390)
-#13388 := (iff #3404 #13385)
-#13381 := (implies #3031 #13376)
+#13391 := (iff #3401 #13390)
+#13388 := (iff #3400 #13385)
+#13381 := (implies #12136 #13376)
#13386 := (iff #13381 #13385)
#13387 := [rewrite]: #13386
-#13382 := (iff #3404 #13381)
-#13379 := (iff #3403 #13376)
-#13372 := (implies #3035 #13367)
+#13382 := (iff #3400 #13381)
+#13379 := (iff #3399 #13376)
+#13372 := (implies #12139 #13367)
#13377 := (iff #13372 #13376)
#13378 := [rewrite]: #13377
-#13373 := (iff #3403 #13372)
-#13370 := (iff #3402 #13367)
-#13363 := (implies #3037 #13358)
+#13373 := (iff #3399 #13372)
+#13370 := (iff #3398 #13367)
+#13363 := (implies #12148 #13358)
#13368 := (iff #13363 #13367)
#13369 := [rewrite]: #13368
-#13364 := (iff #3402 #13363)
-#13361 := (iff #3401 #13358)
-#13354 := (implies #3038 #13349)
+#13364 := (iff #3398 #13363)
+#13361 := (iff #3397 #13358)
+#13354 := (implies #3075 #13349)
#13359 := (iff #13354 #13358)
#13360 := [rewrite]: #13359
-#13355 := (iff #3401 #13354)
-#13352 := (iff #3400 #13349)
-#13345 := (implies #12100 #13340)
+#13355 := (iff #3397 #13354)
+#13352 := (iff #3396 #13349)
+#13345 := (implies #12157 #13340)
#13350 := (iff #13345 #13349)
#13351 := [rewrite]: #13350
-#13346 := (iff #3400 #13345)
-#13343 := (iff #3399 #13340)
-#13336 := (implies #12103 #13331)
+#13346 := (iff #3396 #13345)
+#13343 := (iff #3395 #13340)
+#13336 := (implies #12160 #13331)
#13341 := (iff #13336 #13340)
#13342 := [rewrite]: #13341
-#13337 := (iff #3399 #13336)
-#13334 := (iff #3398 #13331)
-#13327 := (implies #12112 #13322)
+#13337 := (iff #3395 #13336)
+#13334 := (iff #3394 #13331)
+#13327 := (implies #3086 #13322)
#13332 := (iff #13327 #13331)
#13333 := [rewrite]: #13332
-#13328 := (iff #3398 #13327)
-#13325 := (iff #3397 #13322)
-#13318 := (implies #3075 #13313)
+#13328 := (iff #3394 #13327)
+#13325 := (iff #3393 #13322)
+#13318 := (implies #12174 #13313)
#13323 := (iff #13318 #13322)
#13324 := [rewrite]: #13323
-#13319 := (iff #3397 #13318)
-#13316 := (iff #3396 #13313)
-#13309 := (implies #12121 #13304)
+#13319 := (iff #3393 #13318)
+#13316 := (iff #3392 #13313)
+#13309 := (implies #3094 #13306)
#13314 := (iff #13309 #13313)
#13315 := [rewrite]: #13314
-#13310 := (iff #3396 #13309)
-#13307 := (iff #3395 #13304)
-#13300 := (implies #12124 #13295)
-#13305 := (iff #13300 #13304)
-#13306 := [rewrite]: #13305
-#13301 := (iff #3395 #13300)
-#13298 := (iff #3394 #13295)
-#13291 := (implies #3086 #13286)
-#13296 := (iff #13291 #13295)
-#13297 := [rewrite]: #13296
-#13292 := (iff #3394 #13291)
-#13289 := (iff #3393 #13286)
-#13282 := (implies #12138 #13277)
-#13287 := (iff #13282 #13286)
-#13288 := [rewrite]: #13287
-#13283 := (iff #3393 #13282)
-#13280 := (iff #3392 #13277)
-#13273 := (implies #3094 #13270)
+#13310 := (iff #3392 #13309)
+#13307 := (iff #3391 #13306)
+#13304 := (iff #3390 #13301)
+#13297 := (implies #12177 #13294)
+#13302 := (iff #13297 #13301)
+#13303 := [rewrite]: #13302
+#13298 := (iff #3390 #13297)
+#13295 := (iff #3389 #13294)
+#13292 := (iff #3388 #13289)
+#13285 := (implies #12186 #13282)
+#13290 := (iff #13285 #13289)
+#13291 := [rewrite]: #13290
+#13286 := (iff #3388 #13285)
+#13283 := (iff #3387 #13282)
+#13280 := (iff #3386 #13277)
+#13273 := (implies #12192 #13268)
#13278 := (iff #13273 #13277)
#13279 := [rewrite]: #13278
-#13274 := (iff #3392 #13273)
-#13271 := (iff #3391 #13270)
-#13268 := (iff #3390 #13265)
-#13261 := (implies #12141 #13258)
-#13266 := (iff #13261 #13265)
-#13267 := [rewrite]: #13266
-#13262 := (iff #3390 #13261)
-#13259 := (iff #3389 #13258)
-#13256 := (iff #3388 #13253)
-#13249 := (implies #12150 #13246)
-#13254 := (iff #13249 #13253)
-#13255 := [rewrite]: #13254
-#13250 := (iff #3388 #13249)
-#13247 := (iff #3387 #13246)
-#13244 := (iff #3386 #13241)
-#13237 := (implies #12156 #13232)
+#13274 := (iff #3386 #13273)
+#13271 := (iff #3385 #13268)
+#13264 := (implies #3109 #13259)
+#13269 := (iff #13264 #13268)
+#13270 := [rewrite]: #13269
+#13265 := (iff #3385 #13264)
+#13262 := (iff #3384 #13259)
+#13255 := (implies #12195 #13250)
+#13260 := (iff #13255 #13259)
+#13261 := [rewrite]: #13260
+#13256 := (iff #3384 #13255)
+#13253 := (iff #3383 #13250)
+#13246 := (implies #12198 #13241)
+#13251 := (iff #13246 #13250)
+#13252 := [rewrite]: #13251
+#13247 := (iff #3383 #13246)
+#13244 := (iff #3382 #13241)
+#13237 := (implies #12201 #13232)
#13242 := (iff #13237 #13241)
#13243 := [rewrite]: #13242
-#13238 := (iff #3386 #13237)
-#13235 := (iff #3385 #13232)
-#13228 := (implies #3109 #13223)
+#13238 := (iff #3382 #13237)
+#13235 := (iff #3381 #13232)
+#13228 := (implies #12209 #13225)
#13233 := (iff #13228 #13232)
#13234 := [rewrite]: #13233
-#13229 := (iff #3385 #13228)
-#13226 := (iff #3384 #13223)
-#13219 := (implies #12159 #13214)
-#13224 := (iff #13219 #13223)
-#13225 := [rewrite]: #13224
-#13220 := (iff #3384 #13219)
-#13217 := (iff #3383 #13214)
-#13210 := (implies #12162 #13205)
-#13215 := (iff #13210 #13214)
-#13216 := [rewrite]: #13215
-#13211 := (iff #3383 #13210)
-#13208 := (iff #3382 #13205)
-#13201 := (implies #12165 #13196)
-#13206 := (iff #13201 #13205)
-#13207 := [rewrite]: #13206
-#13202 := (iff #3382 #13201)
-#13199 := (iff #3381 #13196)
-#13192 := (implies #12173 #13189)
+#13229 := (iff #3381 #13228)
+#13226 := (iff #3380 #13225)
+#13223 := (iff #3379 #13220)
+#13216 := (implies #3121 #13213)
+#13221 := (iff #13216 #13220)
+#13222 := [rewrite]: #13221
+#13217 := (iff #3379 #13216)
+#13214 := (iff #3378 #13213)
+#13211 := (iff #3377 #13208)
+#13204 := (implies #12224 #13201)
+#13209 := (iff #13204 #13208)
+#13210 := [rewrite]: #13209
+#13205 := (iff #3377 #13204)
+#13202 := (iff #3376 #13201)
+#13199 := (iff #3375 #13196)
+#13192 := (implies #12229 #13187)
#13197 := (iff #13192 #13196)
#13198 := [rewrite]: #13197
-#13193 := (iff #3381 #13192)
-#13190 := (iff #3380 #13189)
-#13187 := (iff #3379 #13184)
-#13180 := (implies #3121 #13177)
-#13185 := (iff #13180 #13184)
-#13186 := [rewrite]: #13185
-#13181 := (iff #3379 #13180)
-#13178 := (iff #3378 #13177)
-#13175 := (iff #3377 #13172)
-#13168 := (implies #12188 #13165)
-#13173 := (iff #13168 #13172)
-#13174 := [rewrite]: #13173
-#13169 := (iff #3377 #13168)
-#13166 := (iff #3376 #13165)
-#13163 := (iff #3375 #13160)
-#13156 := (implies #12193 #13151)
-#13161 := (iff #13156 #13160)
+#13193 := (iff #3375 #13192)
+#13190 := (iff #3374 #13187)
+#13183 := (implies #3134 #13178)
+#13188 := (iff #13183 #13187)
+#13189 := [rewrite]: #13188
+#13184 := (iff #3374 #13183)
+#13181 := (iff #3373 #13178)
+#13174 := (implies #3138 #13169)
+#13179 := (iff #13174 #13178)
+#13180 := [rewrite]: #13179
+#13175 := (iff #3373 #13174)
+#13172 := (iff #3372 #13169)
+#13165 := (implies #3142 #13160)
+#13170 := (iff #13165 #13169)
+#13171 := [rewrite]: #13170
+#13166 := (iff #3372 #13165)
+#13163 := (iff #3371 #13160)
+#13157 := (implies #12232 #13152)
+#13161 := (iff #13157 #13160)
#13162 := [rewrite]: #13161
-#13157 := (iff #3375 #13156)
-#13154 := (iff #3374 #13151)
-#13147 := (implies #3134 #13142)
-#13152 := (iff #13147 #13151)
-#13153 := [rewrite]: #13152
-#13148 := (iff #3374 #13147)
-#13145 := (iff #3373 #13142)
-#13138 := (implies #3138 #13133)
-#13143 := (iff #13138 #13142)
-#13144 := [rewrite]: #13143
-#13139 := (iff #3373 #13138)
-#13136 := (iff #3372 #13133)
-#13129 := (implies #3142 #13124)
-#13134 := (iff #13129 #13133)
-#13135 := [rewrite]: #13134
-#13130 := (iff #3372 #13129)
-#13127 := (iff #3371 #13124)
-#13121 := (implies #12196 #13116)
-#13125 := (iff #13121 #13124)
-#13126 := [rewrite]: #13125
-#13122 := (iff #3371 #13121)
-#13119 := (iff #3370 #13116)
-#13112 := (implies #3145 #13107)
-#13117 := (iff #13112 #13116)
-#13118 := [rewrite]: #13117
-#13113 := (iff #3370 #13112)
-#13110 := (iff #3369 #13107)
-#13103 := (implies #12211 #13098)
-#13108 := (iff #13103 #13107)
-#13109 := [rewrite]: #13108
-#13104 := (iff #3369 #13103)
-#13101 := (iff #3368 #13098)
-#13094 := (implies #12217 #13089)
-#13099 := (iff #13094 #13098)
-#13100 := [rewrite]: #13099
-#13095 := (iff #3368 #13094)
-#13092 := (iff #3367 #13089)
-#13086 := (implies #12196 #13074)
-#13090 := (iff #13086 #13089)
-#13091 := [rewrite]: #13090
-#13087 := (iff #3367 #13086)
-#13084 := (iff #3366 #13074)
-#13079 := (and true #13074)
-#13082 := (iff #13079 #13074)
-#13083 := [rewrite]: #13082
-#13080 := (iff #3366 #13079)
-#13077 := (iff #3365 #13074)
-#13071 := (implies #12196 #13066)
-#13075 := (iff #13071 #13074)
-#13076 := [rewrite]: #13075
-#13072 := (iff #3365 #13071)
-#13069 := (iff #3364 #13066)
-#13063 := (implies #12196 #13058)
-#13067 := (iff #13063 #13066)
-#13068 := [rewrite]: #13067
-#13064 := (iff #3364 #13063)
-#13061 := (iff #3363 #13058)
-#13055 := (implies #12196 #13050)
-#13059 := (iff #13055 #13058)
-#13060 := [rewrite]: #13059
-#13056 := (iff #3363 #13055)
-#13053 := (iff #3362 #13050)
-#13047 := (implies #12485 #13042)
-#13051 := (iff #13047 #13050)
-#13052 := [rewrite]: #13051
-#13048 := (iff #3362 #13047)
-#13045 := (iff #3361 #13042)
-#13038 := (implies #12485 #13033)
-#13043 := (iff #13038 #13042)
-#13044 := [rewrite]: #13043
-#13039 := (iff #3361 #13038)
-#13036 := (iff #3360 #13033)
-#13030 := (implies #12228 #13025)
-#13034 := (iff #13030 #13033)
-#13035 := [rewrite]: #13034
-#13031 := (iff #3360 #13030)
-#13028 := (iff #3359 #13025)
-#13021 := (implies #12507 #13016)
+#13158 := (iff #3371 #13157)
+#13155 := (iff #3370 #13152)
+#13148 := (implies #3145 #13143)
+#13153 := (iff #13148 #13152)
+#13154 := [rewrite]: #13153
+#13149 := (iff #3370 #13148)
+#13146 := (iff #3369 #13143)
+#13139 := (implies #12247 #13134)
+#13144 := (iff #13139 #13143)
+#13145 := [rewrite]: #13144
+#13140 := (iff #3369 #13139)
+#13137 := (iff #3368 #13134)
+#13130 := (implies #12253 #13125)
+#13135 := (iff #13130 #13134)
+#13136 := [rewrite]: #13135
+#13131 := (iff #3368 #13130)
+#13128 := (iff #3367 #13125)
+#13122 := (implies #12232 #13110)
+#13126 := (iff #13122 #13125)
+#13127 := [rewrite]: #13126
+#13123 := (iff #3367 #13122)
+#13120 := (iff #3366 #13110)
+#13115 := (and true #13110)
+#13118 := (iff #13115 #13110)
+#13119 := [rewrite]: #13118
+#13116 := (iff #3366 #13115)
+#13113 := (iff #3365 #13110)
+#13107 := (implies #12232 #13102)
+#13111 := (iff #13107 #13110)
+#13112 := [rewrite]: #13111
+#13108 := (iff #3365 #13107)
+#13105 := (iff #3364 #13102)
+#13099 := (implies #12232 #13094)
+#13103 := (iff #13099 #13102)
+#13104 := [rewrite]: #13103
+#13100 := (iff #3364 #13099)
+#13097 := (iff #3363 #13094)
+#13091 := (implies #12232 #13086)
+#13095 := (iff #13091 #13094)
+#13096 := [rewrite]: #13095
+#13092 := (iff #3363 #13091)
+#13089 := (iff #3362 #13086)
+#13083 := (implies #12521 #13078)
+#13087 := (iff #13083 #13086)
+#13088 := [rewrite]: #13087
+#13084 := (iff #3362 #13083)
+#13081 := (iff #3361 #13078)
+#13074 := (implies #12521 #13069)
+#13079 := (iff #13074 #13078)
+#13080 := [rewrite]: #13079
+#13075 := (iff #3361 #13074)
+#13072 := (iff #3360 #13069)
+#13066 := (implies #12264 #13061)
+#13070 := (iff #13066 #13069)
+#13071 := [rewrite]: #13070
+#13067 := (iff #3360 #13066)
+#13064 := (iff #3359 #13061)
+#13057 := (implies #12543 #13052)
+#13062 := (iff #13057 #13061)
+#13063 := [rewrite]: #13062
+#13058 := (iff #3359 #13057)
+#13055 := (iff #3358 #13052)
+#13048 := (implies #12546 #13043)
+#13053 := (iff #13048 #13052)
+#13054 := [rewrite]: #13053
+#13049 := (iff #3358 #13048)
+#13046 := (iff #3357 #13043)
+#13039 := (implies #12549 #13034)
+#13044 := (iff #13039 #13043)
+#13045 := [rewrite]: #13044
+#13040 := (iff #3357 #13039)
+#13037 := (iff #3356 #13034)
+#13030 := (implies #12552 #13025)
+#13035 := (iff #13030 #13034)
+#13036 := [rewrite]: #13035
+#13031 := (iff #3356 #13030)
+#13028 := (iff #3355 #13025)
+#13021 := (implies #12561 #13009)
#13026 := (iff #13021 #13025)
#13027 := [rewrite]: #13026
-#13022 := (iff #3359 #13021)
-#13019 := (iff #3358 #13016)
-#13012 := (implies #12510 #13007)
-#13017 := (iff #13012 #13016)
+#13022 := (iff #3355 #13021)
+#13019 := (iff #3354 #13009)
+#13014 := (implies true #13009)
+#13017 := (iff #13014 #13009)
#13018 := [rewrite]: #13017
-#13013 := (iff #3358 #13012)
-#13010 := (iff #3357 #13007)
-#13003 := (implies #12513 #12998)
-#13008 := (iff #13003 #13007)
-#13009 := [rewrite]: #13008
-#13004 := (iff #3357 #13003)
-#13001 := (iff #3356 #12998)
-#12994 := (implies #12516 #12989)
-#12999 := (iff #12994 #12998)
+#13015 := (iff #3354 #13014)
+#13012 := (iff #3353 #13009)
+#13006 := (implies #12232 #13003)
+#13010 := (iff #13006 #13009)
+#13011 := [rewrite]: #13010
+#13007 := (iff #3353 #13006)
+#13004 := (iff #3352 #13003)
+#13001 := (iff #3351 #12998)
+#12995 := (implies #12232 #12990)
+#12999 := (iff #12995 #12998)
#13000 := [rewrite]: #12999
-#12995 := (iff #3356 #12994)
-#12992 := (iff #3355 #12989)
-#12985 := (implies #12525 #12973)
-#12990 := (iff #12985 #12989)
-#12991 := [rewrite]: #12990
-#12986 := (iff #3355 #12985)
-#12983 := (iff #3354 #12973)
-#12978 := (implies true #12973)
-#12981 := (iff #12978 #12973)
-#12982 := [rewrite]: #12981
-#12979 := (iff #3354 #12978)
-#12976 := (iff #3353 #12973)
-#12970 := (implies #12196 #12967)
+#12996 := (iff #3351 #12995)
+#12993 := (iff #3350 #12990)
+#12986 := (implies #3347 #12981)
+#12991 := (iff #12986 #12990)
+#12992 := [rewrite]: #12991
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+#12984 := (iff #3349 #12981)
+#12978 := (implies #12232 #12973)
+#12982 := (iff #12978 #12981)
+#12983 := [rewrite]: #12982
+#12979 := (iff #3349 #12978)
+#12976 := (iff #3348 #12973)
+#12970 := (implies #12232 #12394)
#12974 := (iff #12970 #12973)
#12975 := [rewrite]: #12974
-#12971 := (iff #3353 #12970)
-#12968 := (iff #3352 #12967)
-#12965 := (iff #3351 #12962)
-#12959 := (implies #12196 #12954)
-#12963 := (iff #12959 #12962)
-#12964 := [rewrite]: #12963
-#12960 := (iff #3351 #12959)
-#12957 := (iff #3350 #12954)
-#12950 := (implies #3347 #12945)
-#12955 := (iff #12950 #12954)
-#12956 := [rewrite]: #12955
-#12951 := (iff #3350 #12950)
-#12948 := (iff #3349 #12945)
-#12942 := (implies #12196 #12937)
-#12946 := (iff #12942 #12945)
-#12947 := [rewrite]: #12946
-#12943 := (iff #3349 #12942)
-#12940 := (iff #3348 #12937)
-#12934 := (implies #12196 #12358)
-#12938 := (iff #12934 #12937)
-#12939 := [rewrite]: #12938
-#12935 := (iff #3348 #12934)
-#12361 := (iff #3191 #12358)
-#12355 := (implies #12196 #12350)
+#12971 := (iff #3348 #12970)
+#12397 := (iff #3191 #12394)
+#12391 := (implies #12232 #12386)
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+#12396 := [rewrite]: #12395
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+#12389 := (iff #3190 #12386)
+#12383 := (implies #12232 #12380)
+#12387 := (iff #12383 #12386)
+#12388 := [rewrite]: #12387
+#12384 := (iff #3190 #12383)
+#12381 := (iff #3189 #12380)
+#12378 := (iff #3188 #12375)
+#12371 := (implies #10960 #12366)
+#12376 := (iff #12371 #12375)
+#12377 := [rewrite]: #12376
+#12372 := (iff #3188 #12371)
+#12369 := (iff #3187 #12366)
+#12363 := (implies #12232 #12358)
+#12367 := (iff #12363 #12366)
+#12368 := [rewrite]: #12367
+#12364 := (iff #3187 #12363)
+#12361 := (iff #3186 #12358)
+#12355 := (implies #12232 #12350)
#12359 := (iff #12355 #12358)
#12360 := [rewrite]: #12359
-#12356 := (iff #3191 #12355)
-#12353 := (iff #3190 #12350)
-#12347 := (implies #12196 #12344)
-#12351 := (iff #12347 #12350)
+#12356 := (iff #3186 #12355)
+#12353 := (iff #3185 #12350)
+#12346 := (implies #12232 #12341)
+#12351 := (iff #12346 #12350)
#12352 := [rewrite]: #12351
-#12348 := (iff #3190 #12347)
-#12345 := (iff #3189 #12344)
-#12342 := (iff #3188 #12339)
-#12335 := (implies #10924 #12330)
-#12340 := (iff #12335 #12339)
-#12341 := [rewrite]: #12340
-#12336 := (iff #3188 #12335)
-#12333 := (iff #3187 #12330)
-#12327 := (implies #12196 #12322)
-#12331 := (iff #12327 #12330)
-#12332 := [rewrite]: #12331
-#12328 := (iff #3187 #12327)
-#12325 := (iff #3186 #12322)
-#12319 := (implies #12196 #12314)
-#12323 := (iff #12319 #12322)
-#12324 := [rewrite]: #12323
-#12320 := (iff #3186 #12319)
-#12317 := (iff #3185 #12314)
-#12310 := (implies #12196 #12305)
+#12347 := (iff #3185 #12346)
+#12344 := (iff #3184 #12341)
+#12337 := (implies #12269 #12332)
+#12342 := (iff #12337 #12341)
+#12343 := [rewrite]: #12342
+#12338 := (iff #3184 #12337)
+#12335 := (iff #3183 #12332)
+#12328 := (implies #12272 #12323)
+#12333 := (iff #12328 #12332)
+#12334 := [rewrite]: #12333
+#12329 := (iff #3183 #12328)
+#12326 := (iff #3182 #12323)
+#12319 := (implies #12275 #12314)
+#12324 := (iff #12319 #12323)
+#12325 := [rewrite]: #12324
+#12320 := (iff #3182 #12319)
+#12317 := (iff #3181 #12314)
+#12310 := (implies #12278 #12307)
#12315 := (iff #12310 #12314)
#12316 := [rewrite]: #12315
-#12311 := (iff #3185 #12310)
-#12308 := (iff #3184 #12305)
-#12301 := (implies #12233 #12296)
-#12306 := (iff #12301 #12305)
-#12307 := [rewrite]: #12306
-#12302 := (iff #3184 #12301)
-#12299 := (iff #3183 #12296)
-#12292 := (implies #12236 #12287)
-#12297 := (iff #12292 #12296)
-#12298 := [rewrite]: #12297
-#12293 := (iff #3183 #12292)
-#12290 := (iff #3182 #12287)
-#12283 := (implies #12239 #12278)
-#12288 := (iff #12283 #12287)
-#12289 := [rewrite]: #12288
-#12284 := (iff #3182 #12283)
-#12281 := (iff #3181 #12278)
-#12274 := (implies #12242 #12271)
-#12279 := (iff #12274 #12278)
+#12311 := (iff #3181 #12310)
+#12308 := (iff #3180 #12307)
+#12305 := (iff #3179 #12302)
+#12298 := (implies #12293 #3177)
+#12303 := (iff #12298 #12302)
+#12304 := [rewrite]: #12303
+#12299 := (iff #3179 #12298)
+#12296 := (iff #3178 #3177)
+#12297 := [rewrite]: #12296
+#12294 := (iff #3172 #12293)
+#12291 := (iff #3171 #12288)
+#12285 := (implies #455 #12282)
+#12289 := (iff #12285 #12288)
+#12290 := [rewrite]: #12289
+#12286 := (iff #3171 #12285)
+#12283 := (iff #3170 #12282)
+#12284 := [rewrite]: #12283
+#12287 := [monotonicity #12284]: #12286
+#12292 := [trans #12287 #12290]: #12291
+#12295 := [quant-intro #12292]: #12294
+#12300 := [monotonicity #12295 #12297]: #12299
+#12306 := [trans #12300 #12304]: #12305
+#12309 := [monotonicity #12295 #12306]: #12308
+#12279 := (iff #3167 #12278)
#12280 := [rewrite]: #12279
-#12275 := (iff #3181 #12274)
-#12272 := (iff #3180 #12271)
-#12269 := (iff #3179 #12266)
-#12262 := (implies #12257 #3177)
-#12267 := (iff #12262 #12266)
-#12268 := [rewrite]: #12267
-#12263 := (iff #3179 #12262)
-#12260 := (iff #3178 #3177)
-#12261 := [rewrite]: #12260
-#12258 := (iff #3172 #12257)
-#12255 := (iff #3171 #12252)
-#12249 := (implies #455 #12246)
-#12253 := (iff #12249 #12252)
-#12254 := [rewrite]: #12253
-#12250 := (iff #3171 #12249)
-#12247 := (iff #3170 #12246)
-#12248 := [rewrite]: #12247
-#12251 := [monotonicity #12248]: #12250
-#12256 := [trans #12251 #12254]: #12255
-#12259 := [quant-intro #12256]: #12258
-#12264 := [monotonicity #12259 #12261]: #12263
-#12270 := [trans #12264 #12268]: #12269
-#12273 := [monotonicity #12259 #12270]: #12272
-#12243 := (iff #3167 #12242)
-#12244 := [rewrite]: #12243
-#12276 := [monotonicity #12244 #12273]: #12275
-#12282 := [trans #12276 #12280]: #12281
-#12240 := (iff #3165 #12239)
-#12241 := [rewrite]: #12240
-#12285 := [monotonicity #12241 #12282]: #12284
-#12291 := [trans #12285 #12289]: #12290
-#12237 := (iff #3163 #12236)
-#12238 := [rewrite]: #12237
-#12294 := [monotonicity #12238 #12291]: #12293
-#12300 := [trans #12294 #12298]: #12299
-#12234 := (iff #3161 #12233)
-#12235 := [rewrite]: #12234
-#12303 := [monotonicity #12235 #12300]: #12302
-#12309 := [trans #12303 #12307]: #12308
-#12197 := (iff #3144 #12196)
-#12198 := [rewrite]: #12197
-#12312 := [monotonicity #12198 #12309]: #12311
+#12312 := [monotonicity #12280 #12309]: #12311
#12318 := [trans #12312 #12316]: #12317
-#12321 := [monotonicity #12198 #12318]: #12320
-#12326 := [trans #12321 #12324]: #12325
-#12329 := [monotonicity #12198 #12326]: #12328
-#12334 := [trans #12329 #12332]: #12333
-#10926 := (iff #2542 #10924)
-#10927 := [rewrite]: #10926
-#12337 := [monotonicity #10927 #12334]: #12336
-#12343 := [trans #12337 #12341]: #12342
-#12346 := [monotonicity #10927 #12343]: #12345
-#12349 := [monotonicity #12198 #12346]: #12348
-#12354 := [trans #12349 #12352]: #12353
-#12357 := [monotonicity #12198 #12354]: #12356
+#12276 := (iff #3165 #12275)
+#12277 := [rewrite]: #12276
+#12321 := [monotonicity #12277 #12318]: #12320
+#12327 := [trans #12321 #12325]: #12326
+#12273 := (iff #3163 #12272)
+#12274 := [rewrite]: #12273
+#12330 := [monotonicity #12274 #12327]: #12329
+#12336 := [trans #12330 #12334]: #12335
+#12270 := (iff #3161 #12269)
+#12271 := [rewrite]: #12270
+#12339 := [monotonicity #12271 #12336]: #12338
+#12345 := [trans #12339 #12343]: #12344
+#12233 := (iff #3144 #12232)
+#12234 := [rewrite]: #12233
+#12348 := [monotonicity #12234 #12345]: #12347
+#12354 := [trans #12348 #12352]: #12353
+#12357 := [monotonicity #12234 #12354]: #12356
#12362 := [trans #12357 #12360]: #12361
-#12936 := [monotonicity #12198 #12362]: #12935
-#12941 := [trans #12936 #12939]: #12940
-#12944 := [monotonicity #12198 #12941]: #12943
-#12949 := [trans #12944 #12947]: #12948
-#12952 := [monotonicity #12949]: #12951
-#12958 := [trans #12952 #12956]: #12957
-#12961 := [monotonicity #12198 #12958]: #12960
-#12966 := [trans #12961 #12964]: #12965
-#12932 := (iff #3346 #12929)
-#12926 := (implies #12196 #12921)
+#12365 := [monotonicity #12234 #12362]: #12364
+#12370 := [trans #12365 #12368]: #12369
+#10962 := (iff #2542 #10960)
+#10963 := [rewrite]: #10962
+#12373 := [monotonicity #10963 #12370]: #12372
+#12379 := [trans #12373 #12377]: #12378
+#12382 := [monotonicity #10963 #12379]: #12381
+#12385 := [monotonicity #12234 #12382]: #12384
+#12390 := [trans #12385 #12388]: #12389
+#12393 := [monotonicity #12234 #12390]: #12392
+#12398 := [trans #12393 #12396]: #12397
+#12972 := [monotonicity #12234 #12398]: #12971
+#12977 := [trans #12972 #12975]: #12976
+#12980 := [monotonicity #12234 #12977]: #12979
+#12985 := [trans #12980 #12983]: #12984
+#12988 := [monotonicity #12985]: #12987
+#12994 := [trans #12988 #12992]: #12993
+#12997 := [monotonicity #12234 #12994]: #12996
+#13002 := [trans #12997 #13000]: #13001
+#12968 := (iff #3346 #12965)
+#12962 := (implies #12232 #12957)
+#12966 := (iff #12962 #12965)
+#12967 := [rewrite]: #12966
+#12963 := (iff #3346 #12962)
+#12960 := (iff #3345 #12957)
+#12953 := (implies #3256 #12948)
+#12958 := (iff #12953 #12957)
+#12959 := [rewrite]: #12958
+#12954 := (iff #3345 #12953)
+#12951 := (iff #3344 #12948)
+#12945 := (implies #12232 #12940)
+#12949 := (iff #12945 #12948)
+#12950 := [rewrite]: #12949
+#12946 := (iff #3344 #12945)
+#12943 := (iff #3343 #12940)
+#12937 := (implies #12232 #12934)
+#12941 := (iff #12937 #12940)
+#12942 := [rewrite]: #12941
+#12938 := (iff #3343 #12937)
+#12935 := (iff #3342 #12934)
+#12932 := (iff #3341 #12929)
+#12926 := (implies #12581 #12923)
#12930 := (iff #12926 #12929)
#12931 := [rewrite]: #12930
-#12927 := (iff #3346 #12926)
-#12924 := (iff #3345 #12921)
-#12917 := (implies #3256 #12912)
-#12922 := (iff #12917 #12921)
-#12923 := [rewrite]: #12922
-#12918 := (iff #3345 #12917)
-#12915 := (iff #3344 #12912)
-#12909 := (implies #12196 #12904)
-#12913 := (iff #12909 #12912)
-#12914 := [rewrite]: #12913
-#12910 := (iff #3344 #12909)
-#12907 := (iff #3343 #12904)
-#12901 := (implies #12196 #12898)
-#12905 := (iff #12901 #12904)
-#12906 := [rewrite]: #12905
-#12902 := (iff #3343 #12901)
-#12899 := (iff #3342 #12898)
-#12896 := (iff #3341 #12893)
-#12890 := (implies #12545 #12887)
-#12894 := (iff #12890 #12893)
-#12895 := [rewrite]: #12894
-#12891 := (iff #3341 #12890)
-#12888 := (iff #3340 #12887)
-#12885 := (iff #3339 #12882)
-#12879 := (implies #12551 #12874)
+#12927 := (iff #3341 #12926)
+#12924 := (iff #3340 #12923)
+#12921 := (iff #3339 #12918)
+#12915 := (implies #12587 #12910)
+#12919 := (iff #12915 #12918)
+#12920 := [rewrite]: #12919
+#12916 := (iff #3339 #12915)
+#12913 := (iff #3338 #12910)
+#12907 := (implies #12232 #12904)
+#12911 := (iff #12907 #12910)
+#12912 := [rewrite]: #12911
+#12908 := (iff #3338 #12907)
+#12905 := (iff #3337 #12904)
+#12902 := (iff #3336 #12899)
+#12896 := (implies #12232 #12891)
+#12900 := (iff #12896 #12899)
+#12901 := [rewrite]: #12900
+#12897 := (iff #3336 #12896)
+#12894 := (iff #3335 #12891)
+#12887 := (implies #3327 #12882)
+#12892 := (iff #12887 #12891)
+#12893 := [rewrite]: #12892
+#12888 := (iff #3335 #12887)
+#12885 := (iff #3334 #12882)
+#12879 := (implies #12232 #12874)
#12883 := (iff #12879 #12882)
#12884 := [rewrite]: #12883
-#12880 := (iff #3339 #12879)
-#12877 := (iff #3338 #12874)
-#12871 := (implies #12196 #12868)
+#12880 := (iff #3334 #12879)
+#12877 := (iff #3333 #12874)
+#12871 := (implies #12232 #12866)
#12875 := (iff #12871 #12874)
#12876 := [rewrite]: #12875
-#12872 := (iff #3338 #12871)
-#12869 := (iff #3337 #12868)
-#12866 := (iff #3336 #12863)
-#12860 := (implies #12196 #12855)
-#12864 := (iff #12860 #12863)
-#12865 := [rewrite]: #12864
-#12861 := (iff #3336 #12860)
-#12858 := (iff #3335 #12855)
-#12851 := (implies #3327 #12846)
-#12856 := (iff #12851 #12855)
-#12857 := [rewrite]: #12856
-#12852 := (iff #3335 #12851)
-#12849 := (iff #3334 #12846)
-#12843 := (implies #12196 #12838)
-#12847 := (iff #12843 #12846)
-#12848 := [rewrite]: #12847
-#12844 := (iff #3334 #12843)
-#12841 := (iff #3333 #12838)
-#12835 := (implies #12196 #12830)
-#12839 := (iff #12835 #12838)
-#12840 := [rewrite]: #12839
-#12836 := (iff #3333 #12835)
-#12833 := (iff #3332 #12830)
-#12827 := (implies #12196 #12822)
-#12831 := (iff #12827 #12830)
-#12832 := [rewrite]: #12831
-#12828 := (iff #3332 #12827)
-#12825 := (iff #3331 #12822)
-#12818 := (implies #12803 #12813)
-#12823 := (iff #12818 #12822)
-#12824 := [rewrite]: #12823
-#12819 := (iff #3331 #12818)
-#12816 := (iff #3330 #12813)
-#12809 := (implies #12806 #12687)
-#12814 := (iff #12809 #12813)
-#12815 := [rewrite]: #12814
-#12810 := (iff #3330 #12809)
-#12690 := (iff #3312 #12687)
-#12683 := (implies #3280 #12680)
-#12688 := (iff #12683 #12687)
-#12689 := [rewrite]: #12688
-#12684 := (iff #3312 #12683)
-#12681 := (iff #3311 #12680)
-#12678 := (iff #3310 #12675)
-#12671 := (implies #12580 #12666)
-#12676 := (iff #12671 #12675)
-#12677 := [rewrite]: #12676
-#12672 := (iff #3310 #12671)
-#12669 := (iff #3309 #12666)
-#12662 := (implies #12583 #12657)
-#12667 := (iff #12662 #12666)
-#12668 := [rewrite]: #12667
-#12663 := (iff #3309 #12662)
-#12660 := (iff #3308 #12657)
-#12653 := (implies #12586 #12648)
-#12658 := (iff #12653 #12657)
-#12659 := [rewrite]: #12658
-#12654 := (iff #3308 #12653)
-#12651 := (iff #3307 #12648)
-#12644 := (implies #12589 #12641)
-#12649 := (iff #12644 #12648)
-#12650 := [rewrite]: #12649
-#12645 := (iff #3307 #12644)
-#12642 := (iff #3306 #12641)
-#12639 := (iff #3305 #12636)
-#12632 := (implies #3291 #12629)
-#12637 := (iff #12632 #12636)
-#12638 := [rewrite]: #12637
-#12633 := (iff #3305 #12632)
-#12630 := (iff #3304 #12629)
-#12627 := (iff #3303 #12624)
-#12620 := (implies #12604 #12610)
-#12625 := (iff #12620 #12624)
-#12626 := [rewrite]: #12625
-#12621 := (iff #3303 #12620)
-#12618 := (iff #3302 #12610)
-#12613 := (and #12610 true)
-#12616 := (iff #12613 #12610)
-#12617 := [rewrite]: #12616
-#12614 := (iff #3302 #12613)
-#12611 := (iff #3301 #12610)
-#12608 := (iff #3300 #12607)
-#12609 := [rewrite]: #12608
-#12612 := [monotonicity #12609]: #12611
-#12615 := [monotonicity #12612]: #12614
-#12619 := [trans #12615 #12617]: #12618
-#12605 := (iff #3296 #12604)
-#12602 := (iff #3295 #12599)
-#12596 := (implies #455 #12593)
-#12600 := (iff #12596 #12599)
-#12601 := [rewrite]: #12600
-#12597 := (iff #3295 #12596)
-#12594 := (iff #3294 #12593)
-#12595 := [rewrite]: #12594
-#12598 := [monotonicity #12595]: #12597
-#12603 := [trans #12598 #12601]: #12602
-#12606 := [quant-intro #12603]: #12605
-#12622 := [monotonicity #12606 #12619]: #12621
-#12628 := [trans #12622 #12626]: #12627
-#12631 := [monotonicity #12606 #12628]: #12630
-#12634 := [monotonicity #12631]: #12633
-#12640 := [trans #12634 #12638]: #12639
-#12643 := [monotonicity #12640]: #12642
-#12590 := (iff #3290 #12589)
-#12591 := [rewrite]: #12590
-#12646 := [monotonicity #12591 #12643]: #12645
-#12652 := [trans #12646 #12650]: #12651
-#12587 := (iff #3288 #12586)
-#12588 := [rewrite]: #12587
-#12655 := [monotonicity #12588 #12652]: #12654
-#12661 := [trans #12655 #12659]: #12660
-#12584 := (iff #3286 #12583)
-#12572 := (= #3281 #12571)
-#12573 := [rewrite]: #12572
-#12585 := [monotonicity #12573]: #12584
-#12664 := [monotonicity #12585 #12661]: #12663
-#12670 := [trans #12664 #12668]: #12669
-#12581 := (iff #3284 #12580)
-#12578 := (iff #3283 #12577)
-#12579 := [monotonicity #12573]: #12578
-#12575 := (iff #3282 #12574)
-#12576 := [monotonicity #12573]: #12575
-#12582 := [monotonicity #12576 #12579]: #12581
-#12673 := [monotonicity #12582 #12670]: #12672
-#12679 := [trans #12673 #12677]: #12678
-#12682 := [monotonicity #12582 #12679]: #12681
-#12685 := [monotonicity #12682]: #12684
-#12691 := [trans #12685 #12689]: #12690
-#12807 := (iff #3329 #12806)
-#12808 := [rewrite]: #12807
-#12811 := [monotonicity #12808 #12691]: #12810
-#12817 := [trans #12811 #12815]: #12816
-#12804 := (iff #3328 #12803)
-#12805 := [rewrite]: #12804
-#12820 := [monotonicity #12805 #12817]: #12819
-#12826 := [trans #12820 #12824]: #12825
-#12829 := [monotonicity #12198 #12826]: #12828
-#12834 := [trans #12829 #12832]: #12833
-#12837 := [monotonicity #12198 #12834]: #12836
-#12842 := [trans #12837 #12840]: #12841
-#12845 := [monotonicity #12198 #12842]: #12844
-#12850 := [trans #12845 #12848]: #12849
-#12853 := [monotonicity #12850]: #12852
-#12859 := [trans #12853 #12857]: #12858
-#12862 := [monotonicity #12198 #12859]: #12861
-#12867 := [trans #12862 #12865]: #12866
-#12801 := (iff #3326 #12798)
-#12795 := (implies #12196 #12790)
-#12799 := (iff #12795 #12798)
-#12800 := [rewrite]: #12799
-#12796 := (iff #3326 #12795)
-#12793 := (iff #3325 #12790)
-#12786 := (implies #3267 #12781)
-#12791 := (iff #12786 #12790)
-#12792 := [rewrite]: #12791
-#12787 := (iff #3325 #12786)
-#12784 := (iff #3324 #12781)
-#12778 := (implies #12196 #12773)
-#12782 := (iff #12778 #12781)
-#12783 := [rewrite]: #12782
-#12779 := (iff #3324 #12778)
-#12776 := (iff #3323 #12773)
-#12770 := (implies #12196 #12767)
-#12774 := (iff #12770 #12773)
-#12775 := [rewrite]: #12774
-#12771 := (iff #3323 #12770)
-#12768 := (iff #3322 #12767)
-#12765 := (iff #3321 #12762)
-#12758 := (implies #12545 #12755)
-#12763 := (iff #12758 #12762)
-#12764 := [rewrite]: #12763
-#12759 := (iff #3321 #12758)
-#12756 := (iff #3320 #12755)
-#12753 := (iff #3319 #12750)
-#12746 := (implies #12551 #12741)
-#12751 := (iff #12746 #12750)
-#12752 := [rewrite]: #12751
-#12747 := (iff #3319 #12746)
-#12744 := (iff #3318 #12741)
-#12737 := (implies #12554 #12732)
-#12742 := (iff #12737 #12741)
-#12743 := [rewrite]: #12742
-#12738 := (iff #3318 #12737)
-#12735 := (iff #3317 #12732)
-#12728 := (implies #12557 #12723)
-#12733 := (iff #12728 #12732)
-#12734 := [rewrite]: #12733
-#12729 := (iff #3317 #12728)
-#12726 := (iff #3316 #12723)
-#12719 := (implies #12560 #12714)
+#12872 := (iff #3333 #12871)
+#12869 := (iff #3332 #12866)
+#12863 := (implies #12232 #12858)
+#12867 := (iff #12863 #12866)
+#12868 := [rewrite]: #12867
+#12864 := (iff #3332 #12863)
+#12861 := (iff #3331 #12858)
+#12854 := (implies #12839 #12849)
+#12859 := (iff #12854 #12858)
+#12860 := [rewrite]: #12859
+#12855 := (iff #3331 #12854)
+#12852 := (iff #3330 #12849)
+#12845 := (implies #12842 #12723)
+#12850 := (iff #12845 #12849)
+#12851 := [rewrite]: #12850
+#12846 := (iff #3330 #12845)
+#12726 := (iff #3312 #12723)
+#12719 := (implies #3280 #12716)
#12724 := (iff #12719 #12723)
#12725 := [rewrite]: #12724
-#12720 := (iff #3316 #12719)
-#12717 := (iff #3315 #12714)
-#12710 := (implies #3143 #12705)
-#12715 := (iff #12710 #12714)
-#12716 := [rewrite]: #12715
-#12711 := (iff #3315 #12710)
-#12708 := (iff #3314 #12705)
-#12701 := (implies #12565 #12696)
-#12706 := (iff #12701 #12705)
-#12707 := [rewrite]: #12706
-#12702 := (iff #3314 #12701)
-#12699 := (iff #3313 #12696)
-#12692 := (implies #12568 #12687)
-#12697 := (iff #12692 #12696)
-#12698 := [rewrite]: #12697
-#12693 := (iff #3313 #12692)
-#12569 := (iff #3278 #12568)
-#12570 := [rewrite]: #12569
-#12694 := [monotonicity #12570 #12691]: #12693
-#12700 := [trans #12694 #12698]: #12699
-#12566 := (iff #3276 #12565)
-#12567 := [rewrite]: #12566
-#12703 := [monotonicity #12567 #12700]: #12702
-#12709 := [trans #12703 #12707]: #12708
-#12563 := (iff #3274 #3143)
-#12564 := [rewrite]: #12563
-#12712 := [monotonicity #12564 #12709]: #12711
-#12718 := [trans #12712 #12716]: #12717
-#12561 := (iff #3273 #12560)
-#12562 := [rewrite]: #12561
-#12721 := [monotonicity #12562 #12718]: #12720
+#12720 := (iff #3312 #12719)
+#12717 := (iff #3311 #12716)
+#12714 := (iff #3310 #12711)
+#12707 := (implies #12616 #12702)
+#12712 := (iff #12707 #12711)
+#12713 := [rewrite]: #12712
+#12708 := (iff #3310 #12707)
+#12705 := (iff #3309 #12702)
+#12698 := (implies #12619 #12693)
+#12703 := (iff #12698 #12702)
+#12704 := [rewrite]: #12703
+#12699 := (iff #3309 #12698)
+#12696 := (iff #3308 #12693)
+#12689 := (implies #12622 #12684)
+#12694 := (iff #12689 #12693)
+#12695 := [rewrite]: #12694
+#12690 := (iff #3308 #12689)
+#12687 := (iff #3307 #12684)
+#12680 := (implies #12625 #12677)
+#12685 := (iff #12680 #12684)
+#12686 := [rewrite]: #12685
+#12681 := (iff #3307 #12680)
+#12678 := (iff #3306 #12677)
+#12675 := (iff #3305 #12672)
+#12668 := (implies #3291 #12665)
+#12673 := (iff #12668 #12672)
+#12674 := [rewrite]: #12673
+#12669 := (iff #3305 #12668)
+#12666 := (iff #3304 #12665)
+#12663 := (iff #3303 #12660)
+#12656 := (implies #12640 #12646)
+#12661 := (iff #12656 #12660)
+#12662 := [rewrite]: #12661
+#12657 := (iff #3303 #12656)
+#12654 := (iff #3302 #12646)
+#12649 := (and #12646 true)
+#12652 := (iff #12649 #12646)
+#12653 := [rewrite]: #12652
+#12650 := (iff #3302 #12649)
+#12647 := (iff #3301 #12646)
+#12644 := (iff #3300 #12643)
+#12645 := [rewrite]: #12644
+#12648 := [monotonicity #12645]: #12647
+#12651 := [monotonicity #12648]: #12650
+#12655 := [trans #12651 #12653]: #12654
+#12641 := (iff #3296 #12640)
+#12638 := (iff #3295 #12635)
+#12632 := (implies #455 #12629)
+#12636 := (iff #12632 #12635)
+#12637 := [rewrite]: #12636
+#12633 := (iff #3295 #12632)
+#12630 := (iff #3294 #12629)
+#12631 := [rewrite]: #12630
+#12634 := [monotonicity #12631]: #12633
+#12639 := [trans #12634 #12637]: #12638
+#12642 := [quant-intro #12639]: #12641
+#12658 := [monotonicity #12642 #12655]: #12657
+#12664 := [trans #12658 #12662]: #12663
+#12667 := [monotonicity #12642 #12664]: #12666
+#12670 := [monotonicity #12667]: #12669
+#12676 := [trans #12670 #12674]: #12675
+#12679 := [monotonicity #12676]: #12678
+#12626 := (iff #3290 #12625)
+#12627 := [rewrite]: #12626
+#12682 := [monotonicity #12627 #12679]: #12681
+#12688 := [trans #12682 #12686]: #12687
+#12623 := (iff #3288 #12622)
+#12624 := [rewrite]: #12623
+#12691 := [monotonicity #12624 #12688]: #12690
+#12697 := [trans #12691 #12695]: #12696
+#12620 := (iff #3286 #12619)
+#12608 := (= #3281 #12607)
+#12609 := [rewrite]: #12608
+#12621 := [monotonicity #12609]: #12620
+#12700 := [monotonicity #12621 #12697]: #12699
+#12706 := [trans #12700 #12704]: #12705
+#12617 := (iff #3284 #12616)
+#12614 := (iff #3283 #12613)
+#12615 := [monotonicity #12609]: #12614
+#12611 := (iff #3282 #12610)
+#12612 := [monotonicity #12609]: #12611
+#12618 := [monotonicity #12612 #12615]: #12617
+#12709 := [monotonicity #12618 #12706]: #12708
+#12715 := [trans #12709 #12713]: #12714
+#12718 := [monotonicity #12618 #12715]: #12717
+#12721 := [monotonicity #12718]: #12720
#12727 := [trans #12721 #12725]: #12726
-#12558 := (iff #3271 #12557)
-#12559 := [rewrite]: #12558
-#12730 := [monotonicity #12559 #12727]: #12729
+#12843 := (iff #3329 #12842)
+#12844 := [rewrite]: #12843
+#12847 := [monotonicity #12844 #12727]: #12846
+#12853 := [trans #12847 #12851]: #12852
+#12840 := (iff #3328 #12839)
+#12841 := [rewrite]: #12840
+#12856 := [monotonicity #12841 #12853]: #12855
+#12862 := [trans #12856 #12860]: #12861
+#12865 := [monotonicity #12234 #12862]: #12864
+#12870 := [trans #12865 #12868]: #12869
+#12873 := [monotonicity #12234 #12870]: #12872
+#12878 := [trans #12873 #12876]: #12877
+#12881 := [monotonicity #12234 #12878]: #12880
+#12886 := [trans #12881 #12884]: #12885
+#12889 := [monotonicity #12886]: #12888
+#12895 := [trans #12889 #12893]: #12894
+#12898 := [monotonicity #12234 #12895]: #12897
+#12903 := [trans #12898 #12901]: #12902
+#12837 := (iff #3326 #12834)
+#12831 := (implies #12232 #12826)
+#12835 := (iff #12831 #12834)
+#12836 := [rewrite]: #12835
+#12832 := (iff #3326 #12831)
+#12829 := (iff #3325 #12826)
+#12822 := (implies #3267 #12817)
+#12827 := (iff #12822 #12826)
+#12828 := [rewrite]: #12827
+#12823 := (iff #3325 #12822)
+#12820 := (iff #3324 #12817)
+#12814 := (implies #12232 #12809)
+#12818 := (iff #12814 #12817)
+#12819 := [rewrite]: #12818
+#12815 := (iff #3324 #12814)
+#12812 := (iff #3323 #12809)
+#12806 := (implies #12232 #12803)
+#12810 := (iff #12806 #12809)
+#12811 := [rewrite]: #12810
+#12807 := (iff #3323 #12806)
+#12804 := (iff #3322 #12803)
+#12801 := (iff #3321 #12798)
+#12794 := (implies #12581 #12791)
+#12799 := (iff #12794 #12798)
+#12800 := [rewrite]: #12799
+#12795 := (iff #3321 #12794)
+#12792 := (iff #3320 #12791)
+#12789 := (iff #3319 #12786)
+#12782 := (implies #12587 #12777)
+#12787 := (iff #12782 #12786)
+#12788 := [rewrite]: #12787
+#12783 := (iff #3319 #12782)
+#12780 := (iff #3318 #12777)
+#12773 := (implies #12590 #12768)
+#12778 := (iff #12773 #12777)
+#12779 := [rewrite]: #12778
+#12774 := (iff #3318 #12773)
+#12771 := (iff #3317 #12768)
+#12764 := (implies #12593 #12759)
+#12769 := (iff #12764 #12768)
+#12770 := [rewrite]: #12769
+#12765 := (iff #3317 #12764)
+#12762 := (iff #3316 #12759)
+#12755 := (implies #12596 #12750)
+#12760 := (iff #12755 #12759)
+#12761 := [rewrite]: #12760
+#12756 := (iff #3316 #12755)
+#12753 := (iff #3315 #12750)
+#12746 := (implies #3143 #12741)
+#12751 := (iff #12746 #12750)
+#12752 := [rewrite]: #12751
+#12747 := (iff #3315 #12746)
+#12744 := (iff #3314 #12741)
+#12737 := (implies #12601 #12732)
+#12742 := (iff #12737 #12741)
+#12743 := [rewrite]: #12742
+#12738 := (iff #3314 #12737)
+#12735 := (iff #3313 #12732)
+#12728 := (implies #12604 #12723)
+#12733 := (iff #12728 #12732)
+#12734 := [rewrite]: #12733
+#12729 := (iff #3313 #12728)
+#12605 := (iff #3278 #12604)
+#12606 := [rewrite]: #12605
+#12730 := [monotonicity #12606 #12727]: #12729
#12736 := [trans #12730 #12734]: #12735
-#12555 := (iff #3269 #12554)
-#12556 := [rewrite]: #12555
-#12739 := [monotonicity #12556 #12736]: #12738
+#12602 := (iff #3276 #12601)
+#12603 := [rewrite]: #12602
+#12739 := [monotonicity #12603 #12736]: #12738
#12745 := [trans #12739 #12743]: #12744
-#12552 := (iff #3265 #12551)
-#12549 := (iff #3264 #12548)
-#12550 := [rewrite]: #12549
-#12540 := (iff #3259 #12539)
-#12541 := [rewrite]: #12540
-#12553 := [monotonicity #12541 #12550]: #12552
-#12748 := [monotonicity #12553 #12745]: #12747
+#12599 := (iff #3274 #3143)
+#12600 := [rewrite]: #12599
+#12748 := [monotonicity #12600 #12745]: #12747
#12754 := [trans #12748 #12752]: #12753
-#12757 := [monotonicity #12553 #12754]: #12756
-#12546 := (iff #3262 #12545)
-#12543 := (iff #3261 #12542)
-#12544 := [rewrite]: #12543
-#12547 := [monotonicity #12541 #12544]: #12546
-#12760 := [monotonicity #12547 #12757]: #12759
-#12766 := [trans #12760 #12764]: #12765
-#12769 := [monotonicity #12547 #12766]: #12768
-#12772 := [monotonicity #12198 #12769]: #12771
-#12777 := [trans #12772 #12775]: #12776
-#12780 := [monotonicity #12198 #12777]: #12779
-#12785 := [trans #12780 #12783]: #12784
-#12788 := [monotonicity #12785]: #12787
-#12794 := [trans #12788 #12792]: #12793
-#12797 := [monotonicity #12198 #12794]: #12796
-#12802 := [trans #12797 #12800]: #12801
-#12870 := [monotonicity #12802 #12867]: #12869
-#12873 := [monotonicity #12198 #12870]: #12872
-#12878 := [trans #12873 #12876]: #12877
-#12881 := [monotonicity #12553 #12878]: #12880
-#12886 := [trans #12881 #12884]: #12885
-#12889 := [monotonicity #12553 #12886]: #12888
-#12892 := [monotonicity #12547 #12889]: #12891
-#12897 := [trans #12892 #12895]: #12896
-#12900 := [monotonicity #12547 #12897]: #12899
-#12903 := [monotonicity #12198 #12900]: #12902
-#12908 := [trans #12903 #12906]: #12907
-#12911 := [monotonicity #12198 #12908]: #12910
-#12916 := [trans #12911 #12914]: #12915
-#12919 := [monotonicity #12916]: #12918
-#12925 := [trans #12919 #12923]: #12924
-#12928 := [monotonicity #12198 #12925]: #12927
+#12597 := (iff #3273 #12596)
+#12598 := [rewrite]: #12597
+#12757 := [monotonicity #12598 #12754]: #12756
+#12763 := [trans #12757 #12761]: #12762
+#12594 := (iff #3271 #12593)
+#12595 := [rewrite]: #12594
+#12766 := [monotonicity #12595 #12763]: #12765
+#12772 := [trans #12766 #12770]: #12771
+#12591 := (iff #3269 #12590)
+#12592 := [rewrite]: #12591
+#12775 := [monotonicity #12592 #12772]: #12774
+#12781 := [trans #12775 #12779]: #12780
+#12588 := (iff #3265 #12587)
+#12585 := (iff #3264 #12584)
+#12586 := [rewrite]: #12585
+#12576 := (iff #3259 #12575)
+#12577 := [rewrite]: #12576
+#12589 := [monotonicity #12577 #12586]: #12588
+#12784 := [monotonicity #12589 #12781]: #12783
+#12790 := [trans #12784 #12788]: #12789
+#12793 := [monotonicity #12589 #12790]: #12792
+#12582 := (iff #3262 #12581)
+#12579 := (iff #3261 #12578)
+#12580 := [rewrite]: #12579
+#12583 := [monotonicity #12577 #12580]: #12582
+#12796 := [monotonicity #12583 #12793]: #12795
+#12802 := [trans #12796 #12800]: #12801
+#12805 := [monotonicity #12583 #12802]: #12804
+#12808 := [monotonicity #12234 #12805]: #12807
+#12813 := [trans #12808 #12811]: #12812
+#12816 := [monotonicity #12234 #12813]: #12815
+#12821 := [trans #12816 #12819]: #12820
+#12824 := [monotonicity #12821]: #12823
+#12830 := [trans #12824 #12828]: #12829
+#12833 := [monotonicity #12234 #12830]: #12832
+#12838 := [trans #12833 #12836]: #12837
+#12906 := [monotonicity #12838 #12903]: #12905
+#12909 := [monotonicity #12234 #12906]: #12908
+#12914 := [trans #12909 #12912]: #12913
+#12917 := [monotonicity #12589 #12914]: #12916
+#12922 := [trans #12917 #12920]: #12921
+#12925 := [monotonicity #12589 #12922]: #12924
+#12928 := [monotonicity #12583 #12925]: #12927
#12933 := [trans #12928 #12931]: #12932
-#12969 := [monotonicity #12933 #12966]: #12968
-#12972 := [monotonicity #12198 #12969]: #12971
-#12977 := [trans #12972 #12975]: #12976
-#12537 := (iff #3255 true)
-#12535 := (iff #12532 true)
-#12536 := [rewrite]: #12535
-#12533 := (iff #3255 #12532)
-#12530 := (iff #3254 true)
-#12531 := [rewrite]: #12530
-#12528 := (iff #3253 true)
-#12529 := [rewrite]: #12528
-#12534 := [monotonicity #12529 #12531]: #12533
-#12538 := [trans #12534 #12536]: #12537
-#12980 := [monotonicity #12538 #12977]: #12979
-#12984 := [trans #12980 #12982]: #12983
-#12526 := (iff #3252 #12525)
-#12523 := (iff #3251 #12522)
-#12524 := [rewrite]: #12523
-#12520 := (iff #3249 #12519)
-#12521 := [rewrite]: #12520
-#12527 := [monotonicity #12521 #12524]: #12526
-#12987 := [monotonicity #12527 #12984]: #12986
-#12993 := [trans #12987 #12991]: #12992
-#12517 := (iff #3247 #12516)
-#12518 := [rewrite]: #12517
-#12996 := [monotonicity #12518 #12993]: #12995
-#13002 := [trans #12996 #13000]: #13001
-#12514 := (iff #3245 #12513)
-#12515 := [rewrite]: #12514
-#13005 := [monotonicity #12515 #13002]: #13004
-#13011 := [trans #13005 #13009]: #13010
-#12511 := (iff #3243 #12510)
-#12512 := [rewrite]: #12511
-#13014 := [monotonicity #12512 #13011]: #13013
-#13020 := [trans #13014 #13018]: #13019
-#12508 := (iff #3241 #12507)
-#12509 := [rewrite]: #12508
-#13023 := [monotonicity #12509 #13020]: #13022
+#12936 := [monotonicity #12583 #12933]: #12935
+#12939 := [monotonicity #12234 #12936]: #12938
+#12944 := [trans #12939 #12942]: #12943
+#12947 := [monotonicity #12234 #12944]: #12946
+#12952 := [trans #12947 #12950]: #12951
+#12955 := [monotonicity #12952]: #12954
+#12961 := [trans #12955 #12959]: #12960
+#12964 := [monotonicity #12234 #12961]: #12963
+#12969 := [trans #12964 #12967]: #12968
+#13005 := [monotonicity #12969 #13002]: #13004
+#13008 := [monotonicity #12234 #13005]: #13007
+#13013 := [trans #13008 #13011]: #13012
+#12573 := (iff #3255 true)
+#12571 := (iff #12568 true)
+#12572 := [rewrite]: #12571
+#12569 := (iff #3255 #12568)
+#12566 := (iff #3254 true)
+#12567 := [rewrite]: #12566
+#12564 := (iff #3253 true)
+#12565 := [rewrite]: #12564
+#12570 := [monotonicity #12565 #12567]: #12569
+#12574 := [trans #12570 #12572]: #12573
+#13016 := [monotonicity #12574 #13013]: #13015
+#13020 := [trans #13016 #13018]: #13019
+#12562 := (iff #3252 #12561)
+#12559 := (iff #3251 #12558)
+#12560 := [rewrite]: #12559
+#12556 := (iff #3249 #12555)
+#12557 := [rewrite]: #12556
+#12563 := [monotonicity #12557 #12560]: #12562
+#13023 := [monotonicity #12563 #13020]: #13022
#13029 := [trans #13023 #13027]: #13028
-#12231 := (iff #3159 #12228)
-#12225 := (and #12222 #12109)
-#12229 := (iff #12225 #12228)
-#12230 := [rewrite]: #12229
-#12226 := (iff #3159 #12225)
-#12110 := (iff #3068 #12109)
-#12111 := [rewrite]: #12110
-#12223 := (iff #3158 #12222)
-#12224 := [rewrite]: #12223
-#12227 := [monotonicity #12224 #12111]: #12226
-#12232 := [trans #12227 #12230]: #12231
-#13032 := [monotonicity #12232 #13029]: #13031
-#13037 := [trans #13032 #13035]: #13036
-#12486 := (iff #3235 #12485)
-#12483 := (iff #3234 #12482)
-#12480 := (iff #3233 #12479)
-#12481 := [rewrite]: #12480
-#12484 := [monotonicity #12481]: #12483
-#12487 := [monotonicity #12484]: #12486
-#13040 := [monotonicity #12487 #13037]: #13039
-#13046 := [trans #13040 #13044]: #13045
-#12505 := (iff #3239 #12485)
-#12488 := (and true #12485)
-#12491 := (iff #12488 #12485)
-#12492 := [rewrite]: #12491
-#12503 := (iff #3239 #12488)
-#12501 := (iff #3238 #12485)
-#12499 := (iff #3238 #12488)
-#12497 := (iff #3237 #12485)
-#12495 := (iff #3237 #12488)
-#12493 := (iff #3236 #12485)
-#12489 := (iff #3236 #12488)
-#12477 := (iff #3226 true)
-#12472 := (forall (vars (?v0 S20)) (:pat #3222) true)
-#12475 := (iff #12472 true)
-#12476 := [elim-unused]: #12475
-#12473 := (iff #3226 #12472)
-#12470 := (iff #3225 true)
-#12422 := (= f1 #3210)
-#12434 := (implies #12422 #12422)
-#12437 := (iff #12434 true)
-#12438 := [rewrite]: #12437
-#12468 := (iff #3225 #12434)
-#12466 := (iff #3224 #12422)
-#12427 := (and true #12422)
-#12430 := (iff #12427 #12422)
-#12431 := [rewrite]: #12430
-#12464 := (iff #3224 #12427)
-#12423 := (iff #3211 #12422)
-#12424 := [rewrite]: #12423
-#12462 := (iff #3223 true)
-#12463 := [rewrite]: #12462
-#12465 := [monotonicity #12463 #12424]: #12464
-#12467 := [trans #12465 #12431]: #12466
-#12469 := [monotonicity #12424 #12467]: #12468
-#12471 := [trans #12469 #12438]: #12470
-#12474 := [quant-intro #12471]: #12473
-#12478 := [trans #12474 #12476]: #12477
-#12490 := [monotonicity #12478 #12487]: #12489
-#12494 := [trans #12490 #12492]: #12493
-#12460 := (iff #3219 true)
-#12415 := (forall (vars (?v0 S20)) (:pat #3199) true)
-#12418 := (iff #12415 true)
-#12419 := [elim-unused]: #12418
-#12458 := (iff #3219 #12415)
-#12456 := (iff #3218 true)
-#12454 := (iff #3218 #12434)
-#12452 := (iff #3217 #12422)
-#12450 := (iff #3217 #12427)
-#12448 := (iff #3216 true)
-#12449 := [rewrite]: #12448
-#12451 := [monotonicity #12449 #12424]: #12450
-#12453 := [trans #12451 #12431]: #12452
-#12455 := [monotonicity #12424 #12453]: #12454
-#12457 := [trans #12455 #12438]: #12456
-#12459 := [quant-intro #12457]: #12458
-#12461 := [trans #12459 #12419]: #12460
-#12496 := [monotonicity #12461 #12494]: #12495
-#12498 := [trans #12496 #12492]: #12497
-#12446 := (iff #3215 true)
-#12441 := (forall (vars (?v0 S20)) (:pat #3209) true)
-#12444 := (iff #12441 true)
-#12445 := [elim-unused]: #12444
-#12442 := (iff #3215 #12441)
-#12439 := (iff #3214 true)
-#12435 := (iff #3214 #12434)
-#12432 := (iff #3213 #12422)
-#12428 := (iff #3213 #12427)
-#12425 := (iff #3212 true)
-#12426 := [rewrite]: #12425
-#12429 := [monotonicity #12426 #12424]: #12428
-#12433 := [trans #12429 #12431]: #12432
-#12436 := [monotonicity #12424 #12433]: #12435
-#12440 := [trans #12436 #12438]: #12439
-#12443 := [quant-intro #12440]: #12442
-#12447 := [trans #12443 #12445]: #12446
-#12500 := [monotonicity #12447 #12498]: #12499
-#12502 := [trans #12500 #12492]: #12501
-#12420 := (iff #3206 true)
-#12416 := (iff #3206 #12415)
-#12413 := (iff #3205 true)
-#12402 := (= f273 #3202)
-#12405 := (not #12402)
-#12408 := (implies #12405 #12405)
-#12411 := (iff #12408 true)
-#12412 := [rewrite]: #12411
-#12409 := (iff #3205 #12408)
-#12406 := (iff #3204 #12405)
-#12403 := (iff #3203 #12402)
-#12404 := [rewrite]: #12403
-#12407 := [monotonicity #12404]: #12406
-#12410 := [monotonicity #12407 #12407]: #12409
-#12414 := [trans #12410 #12412]: #12413
-#12417 := [quant-intro #12414]: #12416
-#12421 := [trans #12417 #12419]: #12420
-#12504 := [monotonicity #12421 #12502]: #12503
-#12506 := [trans #12504 #12492]: #12505
-#13049 := [monotonicity #12506 #13046]: #13048
-#13054 := [trans #13049 #13052]: #13053
-#13057 := [monotonicity #12198 #13054]: #13056
-#13062 := [trans #13057 #13060]: #13061
-#13065 := [monotonicity #12198 #13062]: #13064
-#13070 := [trans #13065 #13068]: #13069
-#13073 := [monotonicity #12198 #13070]: #13072
-#13078 := [trans #13073 #13076]: #13077
-#12400 := (iff #3196 true)
-#12395 := (implies #12196 true)
-#12398 := (iff #12395 true)
-#12399 := [rewrite]: #12398
-#12396 := (iff #3196 #12395)
-#12393 := (iff #3195 true)
-#12367 := (or #12366 #12358)
-#12375 := (or #12313 #12367)
-#12383 := (or #12313 #12375)
-#12388 := (implies false #12383)
-#12391 := (iff #12388 true)
-#12392 := [rewrite]: #12391
-#12389 := (iff #3195 #12388)
-#12386 := (iff #3194 #12383)
-#12380 := (implies #12196 #12375)
-#12384 := (iff #12380 #12383)
-#12385 := [rewrite]: #12384
-#12381 := (iff #3194 #12380)
-#12378 := (iff #3193 #12375)
-#12372 := (implies #12196 #12367)
-#12376 := (iff #12372 #12375)
-#12377 := [rewrite]: #12376
-#12373 := (iff #3193 #12372)
-#12370 := (iff #3192 #12367)
-#12363 := (implies #12228 #12358)
-#12368 := (iff #12363 #12367)
-#12369 := [rewrite]: #12368
-#12364 := (iff #3192 #12363)
-#12365 := [monotonicity #12232 #12362]: #12364
-#12371 := [trans #12365 #12369]: #12370
-#12374 := [monotonicity #12198 #12371]: #12373
-#12379 := [trans #12374 #12377]: #12378
-#12382 := [monotonicity #12198 #12379]: #12381
-#12387 := [trans #12382 #12385]: #12386
-#12390 := [monotonicity #12221 #12387]: #12389
-#12394 := [trans #12390 #12392]: #12393
-#12397 := [monotonicity #12198 #12394]: #12396
-#12401 := [trans #12397 #12399]: #12400
-#13081 := [monotonicity #12401 #13078]: #13080
-#13085 := [trans #13081 #13083]: #13084
-#13088 := [monotonicity #12198 #13085]: #13087
-#13093 := [trans #13088 #13091]: #13092
-#12218 := (iff #3155 #12217)
-#12215 := (iff #3154 #12214)
-#12216 := [rewrite]: #12215
-#12219 := [monotonicity #12216]: #12218
-#13096 := [monotonicity #12219 #13093]: #13095
-#13102 := [trans #13096 #13100]: #13101
-#12212 := (iff #3150 #12211)
-#12209 := (iff #3149 #12206)
-#12203 := (implies #455 #12200)
-#12207 := (iff #12203 #12206)
-#12208 := [rewrite]: #12207
-#12204 := (iff #3149 #12203)
-#12201 := (iff #3148 #12200)
-#12202 := [rewrite]: #12201
-#12205 := [monotonicity #12202]: #12204
-#12210 := [trans #12205 #12208]: #12209
-#12213 := [quant-intro #12210]: #12212
-#13105 := [monotonicity #12213 #13102]: #13104
-#13111 := [trans #13105 #13109]: #13110
-#13114 := [monotonicity #13111]: #13113
-#13120 := [trans #13114 #13118]: #13119
-#13123 := [monotonicity #12198 #13120]: #13122
-#13128 := [trans #13123 #13126]: #13127
-#13131 := [monotonicity #13128]: #13130
-#13137 := [trans #13131 #13135]: #13136
-#13140 := [monotonicity #13137]: #13139
-#13146 := [trans #13140 #13144]: #13145
-#13149 := [monotonicity #13146]: #13148
-#13155 := [trans #13149 #13153]: #13154
-#12194 := (iff #3130 #12193)
-#12191 := (iff #3129 #3109)
-#12192 := [rewrite]: #12191
-#12195 := [monotonicity #12192]: #12194
-#13158 := [monotonicity #12195 #13155]: #13157
-#13164 := [trans #13158 #13162]: #13163
-#13167 := [monotonicity #12195 #13164]: #13166
-#12189 := (iff #3128 #12188)
-#12186 := (iff #3127 #12183)
-#12180 := (implies #455 #12177)
-#12184 := (iff #12180 #12183)
+#12553 := (iff #3247 #12552)
+#12554 := [rewrite]: #12553
+#13032 := [monotonicity #12554 #13029]: #13031
+#13038 := [trans #13032 #13036]: #13037
+#12550 := (iff #3245 #12549)
+#12551 := [rewrite]: #12550
+#13041 := [monotonicity #12551 #13038]: #13040
+#13047 := [trans #13041 #13045]: #13046
+#12547 := (iff #3243 #12546)
+#12548 := [rewrite]: #12547
+#13050 := [monotonicity #12548 #13047]: #13049
+#13056 := [trans #13050 #13054]: #13055
+#12544 := (iff #3241 #12543)
+#12545 := [rewrite]: #12544
+#13059 := [monotonicity #12545 #13056]: #13058
+#13065 := [trans #13059 #13063]: #13064
+#12267 := (iff #3159 #12264)
+#12261 := (and #12258 #12145)
+#12265 := (iff #12261 #12264)
+#12266 := [rewrite]: #12265
+#12262 := (iff #3159 #12261)
+#12146 := (iff #3068 #12145)
+#12147 := [rewrite]: #12146
+#12259 := (iff #3158 #12258)
+#12260 := [rewrite]: #12259
+#12263 := [monotonicity #12260 #12147]: #12262
+#12268 := [trans #12263 #12266]: #12267
+#13068 := [monotonicity #12268 #13065]: #13067
+#13073 := [trans #13068 #13071]: #13072
+#12522 := (iff #3235 #12521)
+#12519 := (iff #3234 #12518)
+#12516 := (iff #3233 #12515)
+#12517 := [rewrite]: #12516
+#12520 := [monotonicity #12517]: #12519
+#12523 := [monotonicity #12520]: #12522
+#13076 := [monotonicity #12523 #13073]: #13075
+#13082 := [trans #13076 #13080]: #13081
+#12541 := (iff #3239 #12521)
+#12524 := (and true #12521)
+#12527 := (iff #12524 #12521)
+#12528 := [rewrite]: #12527
+#12539 := (iff #3239 #12524)
+#12537 := (iff #3238 #12521)
+#12535 := (iff #3238 #12524)
+#12533 := (iff #3237 #12521)
+#12531 := (iff #3237 #12524)
+#12529 := (iff #3236 #12521)
+#12525 := (iff #3236 #12524)
+#12513 := (iff #3226 true)
+#12508 := (forall (vars (?v0 S20)) (:pat #3222) true)
+#12511 := (iff #12508 true)
+#12512 := [elim-unused]: #12511
+#12509 := (iff #3226 #12508)
+#12506 := (iff #3225 true)
+#12458 := (= f1 #3210)
+#12470 := (implies #12458 #12458)
+#12473 := (iff #12470 true)
+#12474 := [rewrite]: #12473
+#12504 := (iff #3225 #12470)
+#12502 := (iff #3224 #12458)
+#12463 := (and true #12458)
+#12466 := (iff #12463 #12458)
+#12467 := [rewrite]: #12466
+#12500 := (iff #3224 #12463)
+#12459 := (iff #3211 #12458)
+#12460 := [rewrite]: #12459
+#12498 := (iff #3223 true)
+#12499 := [rewrite]: #12498
+#12501 := [monotonicity #12499 #12460]: #12500
+#12503 := [trans #12501 #12467]: #12502
+#12505 := [monotonicity #12460 #12503]: #12504
+#12507 := [trans #12505 #12474]: #12506
+#12510 := [quant-intro #12507]: #12509
+#12514 := [trans #12510 #12512]: #12513
+#12526 := [monotonicity #12514 #12523]: #12525
+#12530 := [trans #12526 #12528]: #12529
+#12496 := (iff #3219 true)
+#12451 := (forall (vars (?v0 S20)) (:pat #3199) true)
+#12454 := (iff #12451 true)
+#12455 := [elim-unused]: #12454
+#12494 := (iff #3219 #12451)
+#12492 := (iff #3218 true)
+#12490 := (iff #3218 #12470)
+#12488 := (iff #3217 #12458)
+#12486 := (iff #3217 #12463)
+#12484 := (iff #3216 true)
+#12485 := [rewrite]: #12484
+#12487 := [monotonicity #12485 #12460]: #12486
+#12489 := [trans #12487 #12467]: #12488
+#12491 := [monotonicity #12460 #12489]: #12490
+#12493 := [trans #12491 #12474]: #12492
+#12495 := [quant-intro #12493]: #12494
+#12497 := [trans #12495 #12455]: #12496
+#12532 := [monotonicity #12497 #12530]: #12531
+#12534 := [trans #12532 #12528]: #12533
+#12482 := (iff #3215 true)
+#12477 := (forall (vars (?v0 S20)) (:pat #3209) true)
+#12480 := (iff #12477 true)
+#12481 := [elim-unused]: #12480
+#12478 := (iff #3215 #12477)
+#12475 := (iff #3214 true)
+#12471 := (iff #3214 #12470)
+#12468 := (iff #3213 #12458)
+#12464 := (iff #3213 #12463)
+#12461 := (iff #3212 true)
+#12462 := [rewrite]: #12461
+#12465 := [monotonicity #12462 #12460]: #12464
+#12469 := [trans #12465 #12467]: #12468
+#12472 := [monotonicity #12460 #12469]: #12471
+#12476 := [trans #12472 #12474]: #12475
+#12479 := [quant-intro #12476]: #12478
+#12483 := [trans #12479 #12481]: #12482
+#12536 := [monotonicity #12483 #12534]: #12535
+#12538 := [trans #12536 #12528]: #12537
+#12456 := (iff #3206 true)
+#12452 := (iff #3206 #12451)
+#12449 := (iff #3205 true)
+#12438 := (= f272 #3202)
+#12441 := (not #12438)
+#12444 := (implies #12441 #12441)
+#12447 := (iff #12444 true)
+#12448 := [rewrite]: #12447
+#12445 := (iff #3205 #12444)
+#12442 := (iff #3204 #12441)
+#12439 := (iff #3203 #12438)
+#12440 := [rewrite]: #12439
+#12443 := [monotonicity #12440]: #12442
+#12446 := [monotonicity #12443 #12443]: #12445
+#12450 := [trans #12446 #12448]: #12449
+#12453 := [quant-intro #12450]: #12452
+#12457 := [trans #12453 #12455]: #12456
+#12540 := [monotonicity #12457 #12538]: #12539
+#12542 := [trans #12540 #12528]: #12541
+#13085 := [monotonicity #12542 #13082]: #13084
+#13090 := [trans #13085 #13088]: #13089
+#13093 := [monotonicity #12234 #13090]: #13092
+#13098 := [trans #13093 #13096]: #13097
+#13101 := [monotonicity #12234 #13098]: #13100
+#13106 := [trans #13101 #13104]: #13105
+#13109 := [monotonicity #12234 #13106]: #13108
+#13114 := [trans #13109 #13112]: #13113
+#12436 := (iff #3196 true)
+#12431 := (implies #12232 true)
+#12434 := (iff #12431 true)
+#12435 := [rewrite]: #12434
+#12432 := (iff #3196 #12431)
+#12429 := (iff #3195 true)
+#12403 := (or #12402 #12394)
+#12411 := (or #12349 #12403)
+#12419 := (or #12349 #12411)
+#12424 := (implies false #12419)
+#12427 := (iff #12424 true)
+#12428 := [rewrite]: #12427
+#12425 := (iff #3195 #12424)
+#12422 := (iff #3194 #12419)
+#12416 := (implies #12232 #12411)
+#12420 := (iff #12416 #12419)
+#12421 := [rewrite]: #12420
+#12417 := (iff #3194 #12416)
+#12414 := (iff #3193 #12411)
+#12408 := (implies #12232 #12403)
+#12412 := (iff #12408 #12411)
+#12413 := [rewrite]: #12412
+#12409 := (iff #3193 #12408)
+#12406 := (iff #3192 #12403)
+#12399 := (implies #12264 #12394)
+#12404 := (iff #12399 #12403)
+#12405 := [rewrite]: #12404
+#12400 := (iff #3192 #12399)
+#12401 := [monotonicity #12268 #12398]: #12400
+#12407 := [trans #12401 #12405]: #12406
+#12410 := [monotonicity #12234 #12407]: #12409
+#12415 := [trans #12410 #12413]: #12414
+#12418 := [monotonicity #12234 #12415]: #12417
+#12423 := [trans #12418 #12421]: #12422
+#12426 := [monotonicity #12257 #12423]: #12425
+#12430 := [trans #12426 #12428]: #12429
+#12433 := [monotonicity #12234 #12430]: #12432
+#12437 := [trans #12433 #12435]: #12436
+#13117 := [monotonicity #12437 #13114]: #13116
+#13121 := [trans #13117 #13119]: #13120
+#13124 := [monotonicity #12234 #13121]: #13123
+#13129 := [trans #13124 #13127]: #13128
+#12254 := (iff #3155 #12253)
+#12251 := (iff #3154 #12250)
+#12252 := [rewrite]: #12251
+#12255 := [monotonicity #12252]: #12254
+#13132 := [monotonicity #12255 #13129]: #13131
+#13138 := [trans #13132 #13136]: #13137
+#12248 := (iff #3150 #12247)
+#12245 := (iff #3149 #12242)
+#12239 := (implies #455 #12236)
+#12243 := (iff #12239 #12242)
+#12244 := [rewrite]: #12243
+#12240 := (iff #3149 #12239)
+#12237 := (iff #3148 #12236)
+#12238 := [rewrite]: #12237
+#12241 := [monotonicity #12238]: #12240
+#12246 := [trans #12241 #12244]: #12245
+#12249 := [quant-intro #12246]: #12248
+#13141 := [monotonicity #12249 #13138]: #13140
+#13147 := [trans #13141 #13145]: #13146
+#13150 := [monotonicity #13147]: #13149
+#13156 := [trans #13150 #13154]: #13155
+#13159 := [monotonicity #12234 #13156]: #13158
+#13164 := [trans #13159 #13162]: #13163
+#13167 := [monotonicity #13164]: #13166
+#13173 := [trans #13167 #13171]: #13172
+#13176 := [monotonicity #13173]: #13175
+#13182 := [trans #13176 #13180]: #13181
+#13185 := [monotonicity #13182]: #13184
+#13191 := [trans #13185 #13189]: #13190
+#12230 := (iff #3130 #12229)
+#12227 := (iff #3129 #3109)
+#12228 := [rewrite]: #12227
+#12231 := [monotonicity #12228]: #12230
+#13194 := [monotonicity #12231 #13191]: #13193
+#13200 := [trans #13194 #13198]: #13199
+#13203 := [monotonicity #12231 #13200]: #13202
+#12225 := (iff #3128 #12224)
+#12222 := (iff #3127 #12219)
+#12216 := (implies #455 #12213)
+#12220 := (iff #12216 #12219)
+#12221 := [rewrite]: #12220
+#12217 := (iff #3127 #12216)
+#12214 := (iff #3126 #12213)
+#12215 := [rewrite]: #12214
+#12218 := [monotonicity #12215]: #12217
+#12223 := [trans #12218 #12221]: #12222
+#12226 := [quant-intro #12223]: #12225
+#13206 := [monotonicity #12226 #13203]: #13205
+#13212 := [trans #13206 #13210]: #13211
+#13215 := [monotonicity #12226 #13212]: #13214
+#13218 := [monotonicity #13215]: #13217
+#13224 := [trans #13218 #13222]: #13223
+#13227 := [monotonicity #13224]: #13226
+#12210 := (iff #3120 #12209)
+#12207 := (iff #3119 #12206)
+#12204 := (iff #3118 #3117)
+#12205 := [rewrite]: #12204
+#12208 := [monotonicity #12205]: #12207
+#12211 := [monotonicity #12208]: #12210
+#13230 := [monotonicity #12211 #13227]: #13229
+#13236 := [trans #13230 #13234]: #13235
+#12202 := (iff #3115 #12201)
+#12203 := [rewrite]: #12202
+#13239 := [monotonicity #12203 #13236]: #13238
+#13245 := [trans #13239 #13243]: #13244
+#12199 := (iff #3113 #12198)
+#12200 := [rewrite]: #12199
+#13248 := [monotonicity #12200 #13245]: #13247
+#13254 := [trans #13248 #13252]: #13253
+#12196 := (iff #3111 #12195)
+#12197 := [rewrite]: #12196
+#13257 := [monotonicity #12197 #13254]: #13256
+#13263 := [trans #13257 #13261]: #13262
+#13266 := [monotonicity #13263]: #13265
+#13272 := [trans #13266 #13270]: #13271
+#12193 := (iff #3106 #12192)
+#12190 := (iff #3105 #12189)
+#12191 := [rewrite]: #12190
+#12181 := (iff #3100 #12180)
+#12182 := [rewrite]: #12181
+#12194 := [monotonicity #12182 #12191]: #12193
+#13275 := [monotonicity #12194 #13272]: #13274
+#13281 := [trans #13275 #13279]: #13280
+#13284 := [monotonicity #12194 #13281]: #13283
+#12187 := (iff #3103 #12186)
+#12184 := (iff #3102 #12183)
#12185 := [rewrite]: #12184
-#12181 := (iff #3127 #12180)
-#12178 := (iff #3126 #12177)
+#12188 := [monotonicity #12182 #12185]: #12187
+#13287 := [monotonicity #12188 #13284]: #13286
+#13293 := [trans #13287 #13291]: #13292
+#13296 := [monotonicity #12188 #13293]: #13295
+#12178 := (iff #3097 #12177)
#12179 := [rewrite]: #12178
-#12182 := [monotonicity #12179]: #12181
-#12187 := [trans #12182 #12185]: #12186
-#12190 := [quant-intro #12187]: #12189
-#13170 := [monotonicity #12190 #13167]: #13169
-#13176 := [trans #13170 #13174]: #13175
-#13179 := [monotonicity #12190 #13176]: #13178
-#13182 := [monotonicity #13179]: #13181
-#13188 := [trans #13182 #13186]: #13187
-#13191 := [monotonicity #13188]: #13190
-#12174 := (iff #3120 #12173)
-#12171 := (iff #3119 #12170)
-#12168 := (iff #3118 #3117)
-#12169 := [rewrite]: #12168
-#12172 := [monotonicity #12169]: #12171
-#12175 := [monotonicity #12172]: #12174
-#13194 := [monotonicity #12175 #13191]: #13193
-#13200 := [trans #13194 #13198]: #13199
-#12166 := (iff #3115 #12165)
-#12167 := [rewrite]: #12166
-#13203 := [monotonicity #12167 #13200]: #13202
-#13209 := [trans #13203 #13207]: #13208
-#12163 := (iff #3113 #12162)
-#12164 := [rewrite]: #12163
-#13212 := [monotonicity #12164 #13209]: #13211
-#13218 := [trans #13212 #13216]: #13217
-#12160 := (iff #3111 #12159)
-#12161 := [rewrite]: #12160
-#13221 := [monotonicity #12161 #13218]: #13220
-#13227 := [trans #13221 #13225]: #13226
-#13230 := [monotonicity #13227]: #13229
-#13236 := [trans #13230 #13234]: #13235
-#12157 := (iff #3106 #12156)
-#12154 := (iff #3105 #12153)
-#12155 := [rewrite]: #12154
-#12145 := (iff #3100 #12144)
-#12146 := [rewrite]: #12145
-#12158 := [monotonicity #12146 #12155]: #12157
-#13239 := [monotonicity #12158 #13236]: #13238
-#13245 := [trans #13239 #13243]: #13244
-#13248 := [monotonicity #12158 #13245]: #13247
-#12151 := (iff #3103 #12150)
-#12148 := (iff #3102 #12147)
-#12149 := [rewrite]: #12148
-#12152 := [monotonicity #12146 #12149]: #12151
-#13251 := [monotonicity #12152 #13248]: #13250
-#13257 := [trans #13251 #13255]: #13256
-#13260 := [monotonicity #12152 #13257]: #13259
-#12142 := (iff #3097 #12141)
-#12143 := [rewrite]: #12142
-#13263 := [monotonicity #12143 #13260]: #13262
-#13269 := [trans #13263 #13267]: #13268
-#13272 := [monotonicity #12143 #13269]: #13271
-#13275 := [monotonicity #13272]: #13274
-#13281 := [trans #13275 #13279]: #13280
-#12139 := (iff #3091 #12138)
-#12136 := (iff #3090 #12133)
-#12130 := (iff #12127 false)
-#12134 := (iff #12130 #12133)
-#12135 := [rewrite]: #12134
-#12131 := (iff #3090 #12130)
-#12128 := (iff #3089 #12127)
-#12129 := [rewrite]: #12128
-#12132 := [monotonicity #12129]: #12131
-#12137 := [trans #12132 #12135]: #12136
-#12140 := [quant-intro #12137]: #12139
-#13284 := [monotonicity #12140 #13281]: #13283
-#13290 := [trans #13284 #13288]: #13289
-#13293 := [monotonicity #13290]: #13292
-#13299 := [trans #13293 #13297]: #13298
-#12125 := (iff #3083 #12124)
-#12126 := [rewrite]: #12125
-#13302 := [monotonicity #12126 #13299]: #13301
-#13308 := [trans #13302 #13306]: #13307
-#12122 := (iff #3081 #12121)
-#12119 := (iff #3080 #12118)
-#12120 := [rewrite]: #12119
-#12116 := (iff #3078 #12115)
-#12117 := [rewrite]: #12116
-#12123 := [monotonicity #12117 #12120]: #12122
-#13311 := [monotonicity #12123 #13308]: #13310
+#13299 := [monotonicity #12179 #13296]: #13298
+#13305 := [trans #13299 #13303]: #13304
+#13308 := [monotonicity #12179 #13305]: #13307
+#13311 := [monotonicity #13308]: #13310
#13317 := [trans #13311 #13315]: #13316
-#13320 := [monotonicity #13317]: #13319
+#12175 := (iff #3091 #12174)
+#12172 := (iff #3090 #12169)
+#12166 := (iff #12163 false)
+#12170 := (iff #12166 #12169)
+#12171 := [rewrite]: #12170
+#12167 := (iff #3090 #12166)
+#12164 := (iff #3089 #12163)
+#12165 := [rewrite]: #12164
+#12168 := [monotonicity #12165]: #12167
+#12173 := [trans #12168 #12171]: #12172
+#12176 := [quant-intro #12173]: #12175
+#13320 := [monotonicity #12176 #13317]: #13319
#13326 := [trans #13320 #13324]: #13325
-#12113 := (iff #3069 #12112)
-#12107 := (iff #3066 #12106)
-#12108 := [rewrite]: #12107
-#12114 := [monotonicity #12108 #12111]: #12113
-#13329 := [monotonicity #12114 #13326]: #13328
+#13329 := [monotonicity #13326]: #13328
#13335 := [trans #13329 #13333]: #13334
-#12104 := (iff #3064 #12103)
-#12105 := [rewrite]: #12104
-#13338 := [monotonicity #12105 #13335]: #13337
+#12161 := (iff #3083 #12160)
+#12162 := [rewrite]: #12161
+#13338 := [monotonicity #12162 #13335]: #13337
#13344 := [trans #13338 #13342]: #13343
-#12101 := (iff #3062 #12100)
-#12098 := (iff #3061 #12097)
-#12095 := (iff #3060 #12094)
-#12092 := (iff #3059 #12091)
-#12089 := (iff #3058 #12088)
-#12086 := (iff #3057 #12085)
-#12087 := [rewrite]: #12086
-#12083 := (iff #3055 #12082)
-#12080 := (iff #3054 #12079)
-#12081 := [rewrite]: #12080
-#12084 := [monotonicity #12081]: #12083
-#12090 := [monotonicity #12084 #12087]: #12089
-#12077 := (iff #3052 #12076)
-#12078 := [rewrite]: #12077
-#12093 := [monotonicity #12078 #12090]: #12092
-#12074 := (iff #3050 #12073)
-#12075 := [rewrite]: #12074
-#12096 := [monotonicity #12075 #12093]: #12095
-#12071 := (iff #3048 #12070)
-#12072 := [rewrite]: #12071
-#12099 := [monotonicity #12072 #12096]: #12098
-#12068 := (iff #3046 #12066)
-#12069 := [rewrite]: #12068
-#12102 := [monotonicity #12069 #12099]: #12101
-#13347 := [monotonicity #12102 #13344]: #13346
+#12158 := (iff #3081 #12157)
+#12155 := (iff #3080 #12154)
+#12156 := [rewrite]: #12155
+#12152 := (iff #3078 #12151)
+#12153 := [rewrite]: #12152
+#12159 := [monotonicity #12153 #12156]: #12158
+#13347 := [monotonicity #12159 #13344]: #13346
#13353 := [trans #13347 #13351]: #13352
#13356 := [monotonicity #13353]: #13355
#13362 := [trans #13356 #13360]: #13361
-#13365 := [monotonicity #13362]: #13364
+#12149 := (iff #3069 #12148)
+#12143 := (iff #3066 #12142)
+#12144 := [rewrite]: #12143
+#12150 := [monotonicity #12144 #12147]: #12149
+#13365 := [monotonicity #12150 #13362]: #13364
#13371 := [trans #13365 #13369]: #13370
-#13374 := [monotonicity #13371]: #13373
+#12140 := (iff #3064 #12139)
+#12141 := [rewrite]: #12140
+#13374 := [monotonicity #12141 #13371]: #13373
#13380 := [trans #13374 #13378]: #13379
-#13383 := [monotonicity #13380]: #13382
+#12137 := (iff #3062 #12136)
+#12134 := (iff #3061 #12133)
+#12131 := (iff #3060 #12130)
+#12128 := (iff #3059 #12127)
+#12125 := (iff #3058 #12124)
+#12122 := (iff #3057 #12121)
+#12123 := [rewrite]: #12122
+#12119 := (iff #3055 #12118)
+#12116 := (iff #3054 #12115)
+#12117 := [rewrite]: #12116
+#12120 := [monotonicity #12117]: #12119
+#12126 := [monotonicity #12120 #12123]: #12125
+#12113 := (iff #3052 #12112)
+#12114 := [rewrite]: #12113
+#12129 := [monotonicity #12114 #12126]: #12128
+#12110 := (iff #3050 #12109)
+#12111 := [rewrite]: #12110
+#12132 := [monotonicity #12111 #12129]: #12131
+#12107 := (iff #3048 #12106)
+#12108 := [rewrite]: #12107
+#12135 := [monotonicity #12108 #12132]: #12134
+#12104 := (iff #3046 #12102)
+#12105 := [rewrite]: #12104
+#12138 := [monotonicity #12105 #12135]: #12137
+#13383 := [monotonicity #12138 #13380]: #13382
#13389 := [trans #13383 #13387]: #13388
#13392 := [monotonicity #13389]: #13391
#13398 := [trans #13392 #13396]: #13397
#13401 := [monotonicity #13398]: #13400
-#14309 := [trans #13401 #14307]: #14308
-#12065 := [asserted]: #3406
-#14310 := [mp #12065 #14309]: #14305
-#14328 := [not-or-elim #14310]: #14192
-#14331 := [and-elim #14328]: #12073
-#275 := (:var 0 S18)
-#55 := (:var 1 S20)
-#2729 := (f59 #55 #275)
-#2730 := (pattern #2729)
-#11333 := (= f1 #2729)
-#11340 := (not #11333)
-#1302 := (f128 #55)
+#13407 := [trans #13401 #13405]: #13406
+#13410 := [monotonicity #13407]: #13409
+#13416 := [trans #13410 #13414]: #13415
+#13419 := [monotonicity #13416]: #13418
+#13425 := [trans #13419 #13423]: #13424
+#13428 := [monotonicity #13425]: #13427
+#13434 := [trans #13428 #13432]: #13433
+#13437 := [monotonicity #13434]: #13436
+#14345 := [trans #13437 #14343]: #14344
+#12101 := [asserted]: #3406
+#14346 := [mp #12101 #14345]: #14341
+#14364 := [not-or-elim #14346]: #14228
+#14367 := [and-elim #14364]: #12109
+#11376 := (not #11369)
+#1302 := (f127 #55)
#2732 := (f54 #275 #1302)
#2733 := (= #55 #2732)
-#11341 := (or #2733 #11340)
-#11346 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11341)
-#18246 := (~ #11346 #11346)
-#18244 := (~ #11341 #11341)
-#18245 := [refl]: #18244
-#18247 := [nnf-pos #18245]: #18246
-#2731 := (= #2729 f1)
+#11377 := (or #2733 #11376)
+#11382 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11377)
+#18282 := (~ #11382 #11382)
+#18280 := (~ #11377 #11377)
+#18281 := [refl]: #18280
+#18283 := [nnf-pos #18281]: #18282
#2734 := (implies #2731 #2733)
#2735 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #2734)
-#11347 := (iff #2735 #11346)
-#11344 := (iff #2734 #11341)
-#11337 := (implies #11333 #2733)
-#11342 := (iff #11337 #11341)
-#11343 := [rewrite]: #11342
-#11338 := (iff #2734 #11337)
-#11335 := (iff #2731 #11333)
-#11336 := [rewrite]: #11335
-#11339 := [monotonicity #11336]: #11338
-#11345 := [trans #11339 #11343]: #11344
-#11348 := [quant-intro #11345]: #11347
-#11332 := [asserted]: #2735
-#11351 := [mp #11332 #11348]: #11346
-#18248 := [mp~ #11351 #18247]: #11346
-#26145 := (not #12073)
-#26158 := (not #11346)
-#26159 := (or #26158 #26145 #26153)
-#26154 := (or #26153 #26145)
-#26160 := (or #26158 #26154)
-#26167 := (iff #26160 #26159)
-#26155 := (or #26145 #26153)
-#26162 := (or #26158 #26155)
-#26165 := (iff #26162 #26159)
-#26166 := [rewrite]: #26165
-#26163 := (iff #26160 #26162)
-#26156 := (iff #26154 #26155)
-#26157 := [rewrite]: #26156
-#26164 := [monotonicity #26157]: #26163
-#26168 := [trans #26164 #26166]: #26167
-#26161 := [quant-inst #3044 #3040]: #26160
-#26169 := [mp #26161 #26168]: #26159
-#28875 := [unit-resolution #26169 #18248 #14331]: #26153
-#26872 := [symm #28875]: #26866
-#26874 := [monotonicity #26872]: #26873
-#26876 := [trans #26874 #28878]: #26875
-#26910 := [monotonicity #26876]: #26909
-#26912 := [monotonicity #26910]: #26911
-#26914 := [symm #26912]: #26913
-#26899 := [monotonicity #26914]: #26897
-#14333 := [and-elim #14328]: #12082
-#26900 := [mp #14333 #26899]: #26915
-decl f208 :: (-> S19 S20 S20 S1)
-#26678 := (f208 f298 #26146 #26146)
-#26679 := (= f1 #26678)
-#26700 := (not #26679)
-#26680 := (f212 f298 #26146 #26146 f306)
-#26681 := (= f1 #26680)
-#26683 := (iff #26679 #26681)
+#11383 := (iff #2735 #11382)
+#11380 := (iff #2734 #11377)
+#11373 := (implies #11369 #2733)
+#11378 := (iff #11373 #11377)
+#11379 := [rewrite]: #11378
+#11374 := (iff #2734 #11373)
+#11375 := [monotonicity #11372]: #11374
+#11381 := [trans #11375 #11379]: #11380
+#11384 := [quant-intro #11381]: #11383
+#11368 := [asserted]: #2735
+#11387 := [mp #11368 #11384]: #11382
+#18284 := [mp~ #11387 #18283]: #11382
+#26181 := (not #12109)
+#26194 := (not #11382)
+#26195 := (or #26194 #26181 #26189)
+#26190 := (or #26189 #26181)
+#26196 := (or #26194 #26190)
+#26203 := (iff #26196 #26195)
+#26191 := (or #26181 #26189)
+#26198 := (or #26194 #26191)
+#26201 := (iff #26198 #26195)
+#26202 := [rewrite]: #26201
+#26199 := (iff #26196 #26198)
+#26192 := (iff #26190 #26191)
+#26193 := [rewrite]: #26192
+#26200 := [monotonicity #26193]: #26199
+#26204 := [trans #26200 #26202]: #26203
+#26197 := [quant-inst #3044 #3040]: #26196
+#26205 := [mp #26197 #26204]: #26195
+#28848 := [unit-resolution #26205 #18284 #14367]: #26189
+#28791 := [trans #28789 #28848]: #28790
+#28793 := [monotonicity #28791]: #28792
+#28796 := [symm #28793]: #28795
+#26777 := (= f1 #26776)
+decl f64 :: (-> S19 S20 S21)
+#26765 := (f64 f297 #26182)
+#26766 := (f26 #62 #26765)
+#26772 := (pattern #26766)
+decl f208 :: (-> S18 S1)
+#26586 := (f24 #26182)
+#26769 := (f208 #26586)
+#26770 := (= f1 #26769)
+#26767 := (= f1 #26766)
+#26768 := (not #26767)
+decl f158 :: (-> S20 S21 S1)
+decl f203 :: (-> S22 S21)
+decl f22 :: (-> S19 S20 S22)
+#26761 := (f22 f297 #26182)
+#26762 := (f203 #26761)
+#26763 := (f158 #62 #26762)
+#26764 := (= f1 #26763)
+#26782 := (or #26764 #26768 #26770)
+#26785 := (forall (vars (?v3 S20)) (:pat #26772) #26782)
+#26788 := (not #26785)
+#26778 := (not #26777)
+#26626 := (f38 f297 #26182)
+#26627 := (= f1 #26626)
+#26649 := (not #26627)
+#26791 := (or #26649 #26778 #26788)
+#26794 := (not #26791)
+decl f207 :: (-> S19 S20 S20 S1)
+#26714 := (f207 f297 #26182 #26182)
+#26715 := (= f1 #26714)
+#26716 := (f211 f297 #26182 #26182 f305)
+#26717 := (= f1 #26716)
+#26719 := (iff #26715 #26717)
#2299 := (:var 0 S31)
-#60 := (:var 2 S20)
#53 := (:var 3 S19)
-#2311 := (f212 #53 #60 #55 #2299)
+#2311 := (f211 #53 #60 #55 #2299)
#2312 := (pattern #2311)
-#2314 := (f208 #53 #60 #55)
-#10282 := (= f1 #2314)
-#10278 := (= f1 #2311)
-#10285 := (iff #10278 #10282)
-#10288 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10285)
-#17888 := (~ #10288 #10288)
-#17886 := (~ #10285 #10285)
-#17887 := [refl]: #17886
-#17889 := [nnf-pos #17887]: #17888
+#2314 := (f207 #53 #60 #55)
+#10318 := (= f1 #2314)
+#10314 := (= f1 #2311)
+#10321 := (iff #10314 #10318)
+#10324 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10321)
+#17924 := (~ #10324 #10324)
+#17922 := (~ #10321 #10321)
+#17923 := [refl]: #17922
+#17925 := [nnf-pos #17923]: #17924
#2315 := (= #2314 f1)
#2313 := (= #2311 f1)
#2316 := (iff #2313 #2315)
#2317 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #2316)
-#10289 := (iff #2317 #10288)
-#10286 := (iff #2316 #10285)
-#10283 := (iff #2315 #10282)
-#10284 := [rewrite]: #10283
-#10280 := (iff #2313 #10278)
-#10281 := [rewrite]: #10280
-#10287 := [monotonicity #10281 #10284]: #10286
-#10290 := [quant-intro #10287]: #10289
-#10277 := [asserted]: #2317
-#10293 := [mp #10277 #10290]: #10288
-#17890 := [mp~ #10293 #17889]: #10288
-#26698 := (not #10288)
-#26699 := (or #26698 #26683)
-#26682 := (iff #26681 #26679)
-#26701 := (or #26698 #26682)
-#26703 := (iff #26701 #26699)
-#26705 := (iff #26699 #26699)
-#26706 := [rewrite]: #26705
-#26684 := (iff #26682 #26683)
-#26685 := [rewrite]: #26684
-#26704 := [monotonicity #26685]: #26703
-#26686 := [trans #26704 #26706]: #26703
-#26702 := [quant-inst #3039 #26146 #26146 #3095]: #26701
-#26688 := [mp #26702 #26686]: #26699
-#26901 := [unit-resolution #26688 #17890]: #26683
-#26697 := (not #26681)
-#26908 := (iff #13264 #26697)
-#26906 := (iff #12141 #26681)
-#26904 := (iff #26681 #12141)
-#26903 := (= #26680 #3096)
-#26898 := [monotonicity #26872 #26872]: #26903
-#26905 := [monotonicity #26898]: #26904
-#26907 := [symm #26905]: #26906
-#26924 := [monotonicity #26907]: #26908
-#26902 := [hypothesis]: #13264
-#26925 := [mp #26902 #26924]: #26697
-#26689 := (not #26683)
-#26691 := (or #26689 #26700 #26681)
-#26692 := [def-axiom]: #26691
-#26926 := [unit-resolution #26692 #26925 #26901]: #26700
-#26784 := (f35 f298 #26146)
-#26785 := (= f1 #26784)
-#26930 := (= #3051 #26784)
-#26927 := (= #26784 #3051)
-#26928 := [monotonicity #26872]: #26927
-#26931 := [symm #26928]: #26930
-#14332 := [and-elim #14328]: #12076
-#26932 := [trans #14332 #26931]: #26785
-#26787 := (f59 #26146 #26550)
-#26788 := (= f1 #26787)
-#26923 := (= #3049 #26787)
-#26933 := (= #26787 #3049)
-#26921 := [monotonicity #26872 #26876]: #26933
-#26936 := [symm #26921]: #26923
-#26938 := [trans #14331 #26936]: #26788
-#26789 := (not #26788)
-#26786 := (not #26785)
-#26972 := (or #26679 #26786 #26789 #26795)
-#26562 := (f36 f298 #26146)
-#26790 := (= f37 #26562)
-#26941 := (= #3047 #26562)
-#26939 := (= #26562 #3047)
-#26937 := [monotonicity #26872]: #26939
-#26942 := [symm #26937]: #26941
-#14330 := [and-elim #14328]: #12070
-#26943 := [trans #14330 #26942]: #26790
-#26590 := (f38 f298 #26146)
-#26591 := (= f1 #26590)
-#26952 := (= #3045 #26590)
-#26944 := (= #26590 #3045)
-#26945 := [monotonicity #26872]: #26944
-#26953 := [symm #26945]: #26952
-#14329 := [and-elim #14328]: #12066
-#26965 := [trans #14329 #26953]: #26591
-#26551 := (f34 #26550)
-#26558 := (= f1 #26551)
-#26969 := (= #3056 #26551)
-#26966 := (= #26551 #3056)
-#26967 := [monotonicity #26876]: #26966
-#26970 := [symm #26967]: #26969
-#14334 := [and-elim #14328]: #12085
-#26971 := [trans #14334 #26970]: #26558
-#14313 := [not-or-elim #14310]: #12112
-#14315 := [and-elim #14313]: #12109
-#86 := (:var 1 S19)
-#2270 := (f208 #86 #62 #62)
+#10325 := (iff #2317 #10324)
+#10322 := (iff #2316 #10321)
+#10319 := (iff #2315 #10318)
+#10320 := [rewrite]: #10319
+#10316 := (iff #2313 #10314)
+#10317 := [rewrite]: #10316
+#10323 := [monotonicity #10317 #10320]: #10322
+#10326 := [quant-intro #10323]: #10325
+#10313 := [asserted]: #2317
+#10329 := [mp #10313 #10326]: #10324
+#17926 := [mp~ #10329 #17925]: #10324
+#26731 := (not #10324)
+#26749 := (or #26731 #26719)
+#26718 := (iff #26717 #26715)
+#26734 := (or #26731 #26718)
+#26738 := (iff #26734 #26749)
+#26739 := (iff #26749 #26749)
+#26740 := [rewrite]: #26739
+#26720 := (iff #26718 #26719)
+#26721 := [rewrite]: #26720
+#26735 := [monotonicity #26721]: #26738
+#26741 := [trans #26735 #26740]: #26738
+#26737 := [quant-inst #3039 #26182 #26182 #3095]: #26734
+#26742 := [mp #26737 #26741]: #26749
+#26937 := [unit-resolution #26742 #17926]: #26719
+#28782 := (= #3096 #26716)
+#26939 := (= #26716 #3096)
+#26934 := (= #26182 #3044)
+#26940 := [symm #28848]: #26934
+#26966 := [monotonicity #26940 #26940]: #26939
+#28799 := [symm #26966]: #28782
+#26828 := (f23 #26586)
+#26831 := (= f25 #26828)
+#26933 := (not #26831)
+#26947 := (iff #12118 #26933)
+#26950 := (iff #12115 #26831)
+#26948 := (iff #26831 #12115)
+#26960 := (= #26828 #3053)
+#26943 := (= #26586 #3040)
+#25117 := (f24 #3044)
+#28850 := (= #25117 #3040)
+#25120 := (= #3040 #25117)
+#25125 := (or #25064 #25120)
+#25126 := [quant-inst #3040 #3043]: #25125
+#28849 := [unit-resolution #25126 #23312]: #25120
+#28851 := [symm #28849]: #28850
+#26941 := (= #26586 #25117)
+#26942 := [monotonicity #26940]: #26941
+#26944 := [trans #26942 #28851]: #26943
+#26946 := [monotonicity #26944]: #26960
+#26949 := [monotonicity #26946]: #26948
+#26951 := [symm #26949]: #26950
+#26935 := [monotonicity #26951]: #26947
+#14369 := [and-elim #14364]: #12118
+#26936 := [mp #14369 #26935]: #26933
+#26736 := (not #26715)
+#26733 := (not #26717)
+#26958 := (iff #13300 #26733)
+#26969 := (iff #12177 #26717)
+#26967 := (iff #26717 #12177)
+#26968 := [monotonicity #26966]: #26967
+#26957 := [symm #26968]: #26969
+#26959 := [monotonicity #26957]: #26958
+#26938 := [hypothesis]: #13300
+#26972 := [mp #26938 #26959]: #26733
+#26722 := (not #26719)
+#26753 := (or #26722 #26736 #26717)
+#26754 := [def-axiom]: #26753
+#26974 := [unit-resolution #26754 #26972 #26937]: #26736
+#26820 := (f35 f297 #26182)
+#26821 := (= f1 #26820)
+#26965 := (= #3051 #26820)
+#26975 := (= #26820 #3051)
+#26963 := [monotonicity #26940]: #26975
+#26961 := [symm #26963]: #26965
+#14368 := [and-elim #14364]: #12112
+#26973 := [trans #14368 #26961]: #26821
+#26823 := (f59 #26182 #26586)
+#26824 := (= f1 #26823)
+#26978 := (= #3049 #26823)
+#26976 := (= #26823 #3049)
+#26962 := [monotonicity #26940 #26944]: #26976
+#26979 := [symm #26962]: #26978
+#26980 := [trans #14367 #26979]: #26824
+#26825 := (not #26824)
+#26822 := (not #26821)
+#27030 := (or #26715 #26822 #26825 #26831)
+#26598 := (f36 f297 #26182)
+#26826 := (= f37 #26598)
+#26989 := (= #3047 #26598)
+#26981 := (= #26598 #3047)
+#26987 := [monotonicity #26940]: #26981
+#27001 := [symm #26987]: #26989
+#14366 := [and-elim #14364]: #12106
+#27002 := [trans #14366 #27001]: #26826
+#27008 := (= #3045 #26626)
+#27003 := (= #26626 #3045)
+#27004 := [monotonicity #26940]: #27003
+#27009 := [symm #27004]: #27008
+#14365 := [and-elim #14364]: #12102
+#27010 := [trans #14365 #27009]: #26627
+#26587 := (f34 #26586)
+#26594 := (= f1 #26587)
+#27019 := (= #3056 #26587)
+#26996 := (= #26587 #3056)
+#26997 := [monotonicity #26944]: #26996
+#27020 := [symm #26997]: #27019
+#14370 := [and-elim #14364]: #12121
+#27029 := [trans #14370 #27020]: #26594
+#14349 := [not-or-elim #14346]: #12148
+#14351 := [and-elim #14349]: #12145
+#2270 := (f207 #86 #62 #62)
#2271 := (pattern #2270)
-#10154 := (= f1 #2270)
+#10190 := (= f1 #2270)
#269 := (f66 #86)
#4055 := (= f1 #269)
-#19445 := (not #4055)
-#186 := (f35 #86 #62)
-#3767 := (= f1 #186)
-#11261 := (not #3767)
-#65 := (f24 #62)
+#19481 := (not #4055)
#184 := (f59 #62 #65)
#3764 := (= f1 #184)
-#19319 := (not #3764)
-#182 := (f36 #86 #62)
-#3761 := (= f37 #182)
-#19318 := (not #3761)
+#19355 := (not #3764)
+#19354 := (not #3761)
#175 := (f38 #86 #62)
#3746 := (= f1 #175)
-#10874 := (not #3746)
+#10910 := (not #3746)
#110 := (f34 #65)
#3595 := (= f1 #110)
-#10933 := (not #3595)
-#66 := (f23 #65)
-#68 := (= #66 f25)
-#21878 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445 #10154)
-#21883 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21878)
-#91 := (not #68)
-#10169 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055)
-#10172 := (not #10169)
-#10178 := (or #10154 #10172)
-#10183 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10178)
-#21884 := (iff #10183 #21883)
-#21881 := (iff #10178 #21878)
-#21864 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445)
-#21875 := (or #10154 #21864)
-#21879 := (iff #21875 #21878)
-#21880 := [rewrite]: #21879
-#21876 := (iff #10178 #21875)
-#21873 := (iff #10172 #21864)
-#21865 := (not #21864)
-#21868 := (not #21865)
-#21871 := (iff #21868 #21864)
-#21872 := [rewrite]: #21871
-#21869 := (iff #10172 #21868)
-#21866 := (iff #10169 #21865)
-#21867 := [rewrite]: #21866
-#21870 := [monotonicity #21867]: #21869
-#21874 := [trans #21870 #21872]: #21873
-#21877 := [monotonicity #21874]: #21876
-#21882 := [trans #21877 #21880]: #21881
-#21885 := [quant-intro #21882]: #21884
-#17856 := (~ #10183 #10183)
-#17854 := (~ #10178 #10178)
-#17855 := [refl]: #17854
-#17857 := [nnf-pos #17855]: #17856
+#10969 := (not #3595)
+#21914 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481 #10190)
+#21919 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21914)
+#10205 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055)
+#10208 := (not #10205)
+#10214 := (or #10190 #10208)
+#10219 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10214)
+#21920 := (iff #10219 #21919)
+#21917 := (iff #10214 #21914)
+#21900 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481)
+#21911 := (or #10190 #21900)
+#21915 := (iff #21911 #21914)
+#21916 := [rewrite]: #21915
+#21912 := (iff #10214 #21911)
+#21909 := (iff #10208 #21900)
+#21901 := (not #21900)
+#21904 := (not #21901)
+#21907 := (iff #21904 #21900)
+#21908 := [rewrite]: #21907
+#21905 := (iff #10208 #21904)
+#21902 := (iff #10205 #21901)
+#21903 := [rewrite]: #21902
+#21906 := [monotonicity #21903]: #21905
+#21910 := [trans #21906 #21908]: #21909
+#21913 := [monotonicity #21910]: #21912
+#21918 := [trans #21913 #21916]: #21917
+#21921 := [quant-intro #21918]: #21920
+#17892 := (~ #10219 #10219)
+#17890 := (~ #10214 #10214)
+#17891 := [refl]: #17890
+#17893 := [nnf-pos #17891]: #17892
#2278 := (= #2270 f1)
#111 := (= #110 f1)
#2272 := (and #91 #111)
-#187 := (= #186 f1)
#2273 := (and #187 #2272)
#185 := (= #184 f1)
#2274 := (and #185 #2273)
-#183 := (= #182 f37)
#2275 := (and #183 #2274)
#176 := (= #175 f1)
#2276 := (and #176 #2275)
@@ -3227,2200 +4002,186 @@
#2277 := (and #271 #2276)
#2279 := (implies #2277 #2278)
#2280 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #2279)
-#10186 := (iff #2280 #10183)
-#10135 := (and #91 #3595)
-#10139 := (and #3767 #10135)
-#10142 := (and #3764 #10139)
-#10145 := (and #3761 #10142)
-#10148 := (and #3746 #10145)
-#10151 := (and #4055 #10148)
-#10160 := (not #10151)
-#10161 := (or #10160 #10154)
-#10166 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10161)
-#10184 := (iff #10166 #10183)
-#10181 := (iff #10161 #10178)
-#10175 := (or #10172 #10154)
-#10179 := (iff #10175 #10178)
-#10180 := [rewrite]: #10179
-#10176 := (iff #10161 #10175)
-#10173 := (iff #10160 #10172)
-#10170 := (iff #10151 #10169)
-#10171 := [rewrite]: #10170
-#10174 := [monotonicity #10171]: #10173
-#10177 := [monotonicity #10174]: #10176
-#10182 := [trans #10177 #10180]: #10181
-#10185 := [quant-intro #10182]: #10184
-#10167 := (iff #2280 #10166)
-#10164 := (iff #2279 #10161)
-#10157 := (implies #10151 #10154)
-#10162 := (iff #10157 #10161)
-#10163 := [rewrite]: #10162
-#10158 := (iff #2279 #10157)
-#10155 := (iff #2278 #10154)
-#10156 := [rewrite]: #10155
-#10152 := (iff #2277 #10151)
-#10149 := (iff #2276 #10148)
-#10146 := (iff #2275 #10145)
-#10143 := (iff #2274 #10142)
-#10140 := (iff #2273 #10139)
-#10137 := (iff #2272 #10135)
+#10222 := (iff #2280 #10219)
+#10171 := (and #91 #3595)
+#10175 := (and #3767 #10171)
+#10178 := (and #3764 #10175)
+#10181 := (and #3761 #10178)
+#10184 := (and #3746 #10181)
+#10187 := (and #4055 #10184)
+#10196 := (not #10187)
+#10197 := (or #10196 #10190)
+#10202 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10197)
+#10220 := (iff #10202 #10219)
+#10217 := (iff #10197 #10214)
+#10211 := (or #10208 #10190)
+#10215 := (iff #10211 #10214)
+#10216 := [rewrite]: #10215
+#10212 := (iff #10197 #10211)
+#10209 := (iff #10196 #10208)
+#10206 := (iff #10187 #10205)
+#10207 := [rewrite]: #10206
+#10210 := [monotonicity #10207]: #10209
+#10213 := [monotonicity #10210]: #10212
+#10218 := [trans #10213 #10216]: #10217
+#10221 := [quant-intro #10218]: #10220
+#10203 := (iff #2280 #10202)
+#10200 := (iff #2279 #10197)
+#10193 := (implies #10187 #10190)
+#10198 := (iff #10193 #10197)
+#10199 := [rewrite]: #10198
+#10194 := (iff #2279 #10193)
+#10191 := (iff #2278 #10190)
+#10192 := [rewrite]: #10191
+#10188 := (iff #2277 #10187)
+#10185 := (iff #2276 #10184)
+#10182 := (iff #2275 #10181)
+#10179 := (iff #2274 #10178)
+#10176 := (iff #2273 #10175)
+#10173 := (iff #2272 #10171)
#3596 := (iff #111 #3595)
#3597 := [rewrite]: #3596
-#10138 := [monotonicity #3597]: #10137
-#3768 := (iff #187 #3767)
-#3769 := [rewrite]: #3768
-#10141 := [monotonicity #3769 #10138]: #10140
+#10174 := [monotonicity #3597]: #10173
+#10177 := [monotonicity #3769 #10174]: #10176
#3765 := (iff #185 #3764)
#3766 := [rewrite]: #3765
-#10144 := [monotonicity #3766 #10141]: #10143
-#3762 := (iff #183 #3761)
-#3763 := [rewrite]: #3762
-#10147 := [monotonicity #3763 #10144]: #10146
+#10180 := [monotonicity #3766 #10177]: #10179
+#10183 := [monotonicity #3763 #10180]: #10182
#3748 := (iff #176 #3746)
#3749 := [rewrite]: #3748
-#10150 := [monotonicity #3749 #10147]: #10149
+#10186 := [monotonicity #3749 #10183]: #10185
#4057 := (iff #271 #4055)
#4058 := [rewrite]: #4057
-#10153 := [monotonicity #4058 #10150]: #10152
-#10159 := [monotonicity #10153 #10156]: #10158
-#10165 := [trans #10159 #10163]: #10164
-#10168 := [quant-intro #10165]: #10167
-#10187 := [trans #10168 #10185]: #10186
-#10134 := [asserted]: #2280
-#10188 := [mp #10134 #10187]: #10183
-#17858 := [mp~ #10188 #17857]: #10183
-#21886 := [mp #17858 #21885]: #21883
-#26791 := (not #26790)
-#26613 := (not #26591)
-#26559 := (not #26558)
-#24810 := (not #12109)
-#26766 := (not #21883)
-#26767 := (or #26766 #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795)
-#26793 := (= #26792 f25)
-#26794 := (or #26793 #26559 #26613 #26791 #26789 #26786 #24810 #26679)
-#26768 := (or #26766 #26794)
-#26774 := (iff #26768 #26767)
-#26801 := (or #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795)
-#26770 := (or #26766 #26801)
-#26772 := (iff #26770 #26767)
-#26773 := [rewrite]: #26772
-#26765 := (iff #26768 #26770)
-#26804 := (iff #26794 #26801)
-#26798 := (or #26795 #26559 #26613 #26791 #26789 #26786 #24810 #26679)
-#26802 := (iff #26798 #26801)
-#26803 := [rewrite]: #26802
-#26799 := (iff #26794 #26798)
-#26796 := (iff #26793 #26795)
-#26797 := [rewrite]: #26796
-#26800 := [monotonicity #26797]: #26799
-#26805 := [trans #26800 #26803]: #26804
-#26771 := [monotonicity #26805]: #26765
-#26775 := [trans #26771 #26773]: #26774
-#26769 := [quant-inst #3039 #26146]: #26768
-#26806 := [mp #26769 #26775]: #26767
-#26973 := [unit-resolution #26806 #21886 #14315 #26971 #26965 #26943]: #26972
-#26974 := [unit-resolution #26973 #26938 #26932 #26926 #26900]: false
-#26960 := [lemma #26974]: #12141
-#23566 := (or #13264 #23563)
-#22522 := (forall (vars (?v0 Int)) #22511)
-#22529 := (not #22522)
-#22507 := (forall (vars (?v0 Int)) #22502)
-#22528 := (not #22507)
-#22530 := (or #22528 #22529)
-#22531 := (not #22530)
-#22560 := (or #22531 #22557)
-#22566 := (not #22560)
-#22567 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #22566)
-#22568 := (not #22567)
-#22346 := (forall (vars (?v0 Int)) #22341)
-#22352 := (not #22346)
-#22353 := (or #22328 #22352)
-#22354 := (not #22353)
-#22383 := (or #22354 #22380)
-#22389 := (not #22383)
-#22390 := (or #13519 #22389)
-#22391 := (not #22390)
-#22396 := (or #13519 #22391)
-#22404 := (not #22396)
-#22405 := (or #12656 #22402 #18558 #22403 #13586 #18561 #22404)
-#22406 := (not #22405)
-#22411 := (or #18558 #18561 #22406)
-#22417 := (not #22411)
-#22454 := (or #12821 #12812 #22443 #13620 #22402 #13671 #22417)
-#22455 := (not #22454)
-#22418 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #22417)
-#22419 := (not #22418)
-#22424 := (or #18520 #18529 #22419)
-#22430 := (not #22424)
-#22431 := (or #18520 #18523 #22430)
-#22432 := (not #22431)
-#22437 := (or #18520 #18523 #22432)
-#22444 := (not #22437)
-#22445 := (or #22443 #13620 #13672 #22444)
-#22446 := (not #22445)
-#22460 := (or #22446 #22455)
-#22466 := (not #22460)
-#22467 := (or #18520 #18529 #22443 #13620 #22466)
-#22468 := (not #22467)
-#22473 := (or #18520 #18529 #22468)
-#22479 := (not #22473)
-#22480 := (or #18520 #18523 #22479)
-#22481 := (not #22480)
-#22486 := (or #18520 #18523 #22481)
-#22492 := (not #22486)
-#22493 := (or #22443 #13620 #13765 #22492)
-#22494 := (not #22493)
-#22573 := (or #22494 #22568)
-#22588 := (not #22573)
-#22323 := (forall (vars (?v0 Int)) #22318)
-#22584 := (not #22323)
-#22589 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #22584 #22588)
-#22590 := (not #22589)
-#22595 := (or #13231 #13472 #22590)
-#22602 := (not #22595)
-#22312 := (forall (vars (?v0 Int)) #22307)
-#22601 := (not #22312)
-#22603 := (or #22601 #22602)
-#22604 := (not #22603)
-#22609 := (or #22301 #22604)
-#22615 := (not #22609)
-#22616 := (or #13436 #22615)
-#22617 := (not #22616)
-#22622 := (or #13436 #22617)
-#22628 := (not #22622)
-#22629 := (or #13231 #18409 #18418 #13222 #13213 #13204 #22628)
-#22630 := (not #22629)
-#22635 := (or #18409 #18418 #22630)
-#22641 := (not #22635)
-#22642 := (or #18409 #18412 #22641)
-#22643 := (not #22642)
-#22648 := (or #18409 #18412 #22643)
-#22654 := (not #22648)
-#22655 := (or #13264 #22654)
-#22656 := (not #22655)
-#22661 := (or #13264 #22656)
-#23567 := (iff #22661 #23566)
-#23564 := (iff #22656 #23563)
-#23561 := (iff #22655 #23560)
-#23558 := (iff #22654 #23557)
-#23555 := (iff #22648 #23554)
-#23552 := (iff #22643 #23551)
-#23549 := (iff #22642 #23548)
-#23546 := (iff #22641 #23545)
-#23543 := (iff #22635 #23542)
-#23540 := (iff #22630 #23539)
-#23537 := (iff #22629 #23536)
-#23534 := (iff #22628 #23533)
-#23531 := (iff #22622 #23530)
-#23528 := (iff #22617 #23527)
-#23525 := (iff #22616 #23524)
-#23522 := (iff #22615 #23521)
-#23519 := (iff #22609 #23518)
-#23516 := (iff #22604 #23515)
-#23513 := (iff #22603 #23512)
-#23510 := (iff #22602 #23509)
-#23507 := (iff #22595 #23506)
-#23504 := (iff #22590 #23503)
-#23501 := (iff #22589 #23500)
-#23498 := (iff #22588 #23497)
-#23495 := (iff #22573 #23494)
-#23492 := (iff #22568 #23491)
-#23489 := (iff #22567 #23488)
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-#23562 := [monotonicity #23559]: #23561
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-#18743 := (~ #18742 #18741)
-#18738 := (not #15996)
-#18739 := (~ #18738 #18737)
-#18734 := (not #15993)
-#18735 := (~ #18734 #18733)
-#18730 := (not #15990)
-#18731 := (~ #18730 #18729)
-#18727 := (~ #18726 #18726)
-#18728 := [refl]: #18727
-#18732 := [nnf-neg #18728]: #18731
-#18723 := (not #15979)
-#18724 := (~ #18723 #15976)
-#18721 := (~ #15976 #15976)
-#18719 := (~ #15971 #15971)
-#18720 := [refl]: #18719
-#18722 := [nnf-pos #18720]: #18721
-#18725 := [nnf-neg #18722]: #18724
-#18736 := [nnf-neg #18725 #18732]: #18735
-#18715 := (~ #15979 #18714)
-#18716 := [sk]: #18715
-#18740 := [nnf-neg #18716 #18736]: #18739
-#18700 := (~ #13769 #13769)
-#18701 := [refl]: #18700
-#18491 := (~ #18490 #18490)
-#18492 := [refl]: #18491
-#18698 := (~ #18697 #18697)
-#18699 := [refl]: #18698
-#18695 := (~ #18694 #18694)
-#18696 := [refl]: #18695
-#18692 := (~ #18691 #18691)
-#18693 := [refl]: #18692
-#18689 := (~ #18688 #18688)
-#18690 := [refl]: #18689
-#18744 := [nnf-neg #18690 #18693 #18696 #18699 #18492 #18701 #18740]: #18743
-#18685 := (not #15963)
-#18686 := (~ #18685 #18684)
-#18681 := (not #15957)
-#18682 := (~ #18681 #18680)
-#18677 := (not #15954)
-#18678 := (~ #18677 #18676)
-#18673 := (not #15951)
-#18674 := (~ #18673 #18672)
-#18669 := (not #15948)
-#18670 := (~ #18669 #18668)
-#18665 := (not #15945)
-#18666 := (~ #18665 #18664)
-#18661 := (not #15940)
-#18662 := (~ #18661 #18660)
-#18629 := (not #15914)
-#18630 := (~ #18629 #18628)
-#18625 := (not #15909)
-#18626 := (~ #18625 #18624)
-#18622 := (~ #18621 #18621)
-#18623 := [refl]: #18622
-#18618 := (not #15897)
-#18619 := (~ #18618 #18617)
-#18614 := (not #15894)
-#18615 := (~ #18614 #18613)
-#18610 := (not #15891)
-#18611 := (~ #18610 #18609)
-#18606 := (not #15886)
-#18607 := (~ #18606 #18605)
-#18602 := (not #15880)
-#18603 := (~ #18602 #15877)
-#18600 := (~ #15877 #15877)
-#18598 := (~ #15872 #15872)
-#18599 := [refl]: #18598
-#18601 := [nnf-pos #18599]: #18600
-#18604 := [nnf-neg #18601]: #18603
-#18596 := (~ #18595 #18595)
-#18597 := [refl]: #18596
-#18608 := [nnf-neg #18597 #18604]: #18607
-#18591 := (~ #15880 #18590)
-#18592 := [sk]: #18591
-#18612 := [nnf-neg #18592 #18608]: #18611
-#18576 := (~ #18575 #18575)
-#18577 := [refl]: #18576
-#18616 := [nnf-neg #18577 #18612]: #18615
-#18573 := (~ #13519 #13519)
-#18574 := [refl]: #18573
-#18620 := [nnf-neg #18574 #18616]: #18619
-#18571 := (~ #18570 #18570)
-#18572 := [refl]: #18571
-#18568 := (~ #18567 #18567)
-#18569 := [refl]: #18568
-#18565 := (~ #18564 #18564)
-#18566 := [refl]: #18565
-#18627 := [nnf-neg #18566 #18569 #18572 #18620 #18623]: #18626
-#18562 := (~ #18561 #18561)
-#18563 := [refl]: #18562
-#18559 := (~ #18558 #18558)
-#18560 := [refl]: #18559
-#18631 := [nnf-neg #18560 #18563 #18627]: #18630
-#18658 := (~ #13677 #13677)
-#18659 := [refl]: #18658
-#18556 := (~ #18555 #18555)
-#18557 := [refl]: #18556
-#18656 := (~ #18655 #18655)
-#18657 := [refl]: #18656
-#18653 := (~ #18652 #18652)
-#18654 := [refl]: #18653
-#18663 := [nnf-neg #18654 #18657 #18492 #18557 #18659 #18631]: #18662
-#18649 := (not #15932)
-#18650 := (~ #18649 #18648)
-#18645 := (not #15926)
-#18646 := (~ #18645 #18644)
-#18641 := (not #15923)
-#18642 := (~ #18641 #18640)
-#18637 := (not #15920)
-#18638 := (~ #18637 #18636)
-#18633 := (not #15917)
-#18634 := (~ #18633 #18632)
-#18553 := (~ #18552 #18552)
-#18554 := [refl]: #18553
-#18550 := (~ #18549 #18549)
-#18551 := [refl]: #18550
-#18547 := (~ #18546 #18546)
-#18548 := [refl]: #18547
-#18544 := (~ #18543 #18543)
-#18545 := [refl]: #18544
-#18541 := (~ #18540 #18540)
-#18542 := [refl]: #18541
-#18538 := (~ #18537 #18537)
-#18539 := [refl]: #18538
-#18533 := (~ #18532 #18532)
-#18534 := [refl]: #18533
-#18635 := [nnf-neg #18534 #18539 #18542 #18545 #18548 #18551 #18554 #18557 #18631]: #18634
-#18530 := (~ #18529 #18529)
-#18531 := [refl]: #18530
-#18521 := (~ #18520 #18520)
-#18522 := [refl]: #18521
-#18639 := [nnf-neg #18522 #18531 #18635]: #18638
-#18527 := (~ #18526 #18526)
-#18528 := [refl]: #18527
-#18643 := [nnf-neg #18528 #18639]: #18642
-#18524 := (~ #18523 #18523)
-#18525 := [refl]: #18524
-#18647 := [nnf-neg #18522 #18525 #18643]: #18646
-#18535 := (~ #13671 #13671)
-#18536 := [refl]: #18535
-#18651 := [nnf-neg #18492 #18536 #18647]: #18650
-#18667 := [nnf-neg #18651 #18663]: #18666
-#18671 := [nnf-neg #18534 #18492 #18667]: #18670
-#18675 := [nnf-neg #18522 #18531 #18671]: #18674
-#18679 := [nnf-neg #18528 #18675]: #18678
-#18683 := [nnf-neg #18522 #18525 #18679]: #18682
-#18518 := (~ #13766 #13766)
-#18519 := [refl]: #18518
-#18687 := [nnf-neg #18492 #18519 #18683]: #18686
-#18748 := [nnf-neg #18687 #18744]: #18747
-#18516 := (~ #18515 #18515)
-#18517 := [refl]: #18516
-#18513 := (~ #18512 #18512)
-#18514 := [refl]: #18513
-#18510 := (~ #18509 #18509)
-#18511 := [refl]: #18510
-#18506 := (not #15806)
-#18507 := (~ #18506 #15803)
-#18504 := (~ #15803 #15803)
-#18502 := (~ #15798 #15798)
-#18503 := [refl]: #18502
-#18505 := [nnf-pos #18503]: #18504
-#18508 := [nnf-neg #18505]: #18507
-#18500 := (~ #18499 #18499)
-#18501 := [refl]: #18500
-#18497 := (~ #18496 #18496)
-#18498 := [refl]: #18497
-#18494 := (~ #18493 #18493)
-#18495 := [refl]: #18494
-#18488 := (~ #18487 #18487)
-#18489 := [refl]: #18488
-#18485 := (~ #18484 #18484)
-#18486 := [refl]: #18485
-#18482 := (~ #18481 #18481)
-#18483 := [refl]: #18482
-#18479 := (~ #18478 #18478)
-#18480 := [refl]: #18479
-#18476 := (~ #18475 #18475)
-#18477 := [refl]: #18476
-#18473 := (~ #18472 #18472)
-#18474 := [refl]: #18473
-#18470 := (~ #18469 #18469)
-#18471 := [refl]: #18470
-#18752 := [nnf-neg #18471 #18474 #18477 #18480 #18483 #18486 #18489 #18492 #18495 #18498 #18501 #18508 #18511 #18514 #18517 #18748]: #18751
-#18467 := (~ #14198 #14198)
-#18468 := [refl]: #18467
-#18465 := (~ #13231 #13231)
-#18466 := [refl]: #18465
-#18756 := [nnf-neg #18466 #18468 #18752]: #18755
-#18462 := (not #15792)
-#18463 := (~ #18462 #15789)
-#18460 := (~ #15789 #15789)
-#18458 := (~ #15784 #15784)
-#18459 := [refl]: #18458
-#18461 := [nnf-pos #18459]: #18460
-#18464 := [nnf-neg #18461]: #18463
-#18760 := [nnf-neg #18464 #18756]: #18759
-#18454 := (~ #15792 #18453)
-#18455 := [sk]: #18454
-#18764 := [nnf-neg #18455 #18760]: #18763
-#18439 := (~ #18438 #18438)
-#18440 := [refl]: #18439
-#18768 := [nnf-neg #18440 #18764]: #18767
-#18436 := (~ #13436 #13436)
-#18437 := [refl]: #18436
-#18772 := [nnf-neg #18437 #18768]: #18771
-#18434 := (~ #18433 #18433)
-#18435 := [refl]: #18434
-#18431 := (~ #18430 #18430)
-#18432 := [refl]: #18431
-#18428 := (~ #18427 #18427)
-#18429 := [refl]: #18428
-#18425 := (~ #18424 #18424)
-#18426 := [refl]: #18425
-#18422 := (~ #18421 #18421)
-#18423 := [refl]: #18422
-#18776 := [nnf-neg #18423 #18426 #18429 #18432 #18435 #18772]: #18775
-#18419 := (~ #18418 #18418)
-#18420 := [refl]: #18419
-#18410 := (~ #18409 #18409)
-#18411 := [refl]: #18410
-#18780 := [nnf-neg #18411 #18420 #18776]: #18779
-#18416 := (~ #18415 #18415)
-#18417 := [refl]: #18416
-#18784 := [nnf-neg #18417 #18780]: #18783
-#18413 := (~ #18412 #18412)
-#18414 := [refl]: #18413
-#18788 := [nnf-neg #18411 #18414 #18784]: #18787
-#18407 := (~ #18406 #18406)
-#18408 := [refl]: #18407
-#18792 := [nnf-neg #18408 #18788]: #18791
-#18404 := (~ #13264 #13264)
-#18405 := [refl]: #18404
-#18795 := [nnf-neg #18405 #18792]: #18794
-#15288 := (or #12304 #12295 #12286 #12277 #13485 #13766 #13852)
-#15293 := (and #13788 #15288)
-#15299 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13989 #13995 #14007 #14017 #14030 #14041 #15293)
-#15304 := (and #3109 #13473 #15299)
-#15307 := (or #13469 #15304)
-#15310 := (and #13466 #15307)
-#15313 := (or #13436 #15310)
-#15316 := (and #13433 #15313)
-#15319 := (or #13231 #13240 #13222 #13213 #13204 #15316)
-#15322 := (and #12144 #12153 #15319)
-#15325 := (or #13252 #15322)
-#15328 := (and #12144 #12147 #15325)
-#15331 := (or #13264 #15328)
-#15334 := (and #12141 #15331)
-#15337 := (not #15334)
-#16047 := (iff #15337 #16046)
-#16044 := (iff #15334 #16043)
-#16041 := (iff #15331 #16040)
-#16038 := (iff #15328 #16037)
-#16035 := (iff #15325 #16034)
-#16032 := (iff #15322 #16031)
-#16029 := (iff #15319 #16028)
-#16026 := (iff #15316 #16025)
-#16023 := (iff #15313 #16022)
-#16020 := (iff #15310 #16019)
-#16017 := (iff #15307 #16016)
-#16014 := (iff #15304 #16013)
-#16011 := (iff #15299 #16008)
-#16005 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #15806 #13995 #15823 #15840 #15857 #14041 #16002)
-#16009 := (iff #16005 #16008)
-#16010 := [rewrite]: #16009
-#16006 := (iff #15299 #16005)
-#16003 := (iff #15293 #16002)
-#16000 := (iff #15288 #15999)
-#15997 := (iff #13852 #15996)
-#15994 := (iff #13847 #15993)
-#15991 := (iff #13838 #15990)
-#15988 := (iff #13833 #15985)
-#15982 := (and #3173 #4202 #15183 #13795)
-#15986 := (iff #15982 #15985)
-#15987 := [rewrite]: #15986
-#15983 := (iff #13833 #15982)
-#15178 := (iff #4496 #15183)
-#15199 := -4294967295::Int
-#15191 := (+ -4294967295::Int #202)
-#15184 := (<= #15191 0::Int)
-#15180 := (iff #15184 #15183)
-#15181 := [rewrite]: #15180
-#15185 := (iff #4496 #15184)
-#15186 := (= #4495 #15191)
-#15192 := (+ #202 -4294967295::Int)
-#15188 := (= #15192 #15191)
-#15189 := [rewrite]: #15188
-#15193 := (= #4495 #15192)
-#15194 := (= #4494 -4294967295::Int)
-#15200 := (* -1::Int 4294967295::Int)
-#15196 := (= #15200 -4294967295::Int)
-#15197 := [rewrite]: #15196
-#15201 := (= #4494 #15200)
-#7601 := (= f88 4294967295::Int)
-#990 := 65536::Int
-#1365 := (* 65536::Int 65536::Int)
-#1370 := (- #1365 1::Int)
-#1371 := (= f88 #1370)
-#7602 := (iff #1371 #7601)
-#7599 := (= #1370 4294967295::Int)
-#1053 := 4294967296::Int
-#7592 := (- 4294967296::Int 1::Int)
-#7597 := (= #7592 4294967295::Int)
-#7598 := [rewrite]: #7597
-#7594 := (= #1370 #7592)
-#7563 := (= #1365 4294967296::Int)
-#7564 := [rewrite]: #7563
-#7595 := [monotonicity #7564]: #7594
-#7600 := [trans #7595 #7598]: #7599
-#7603 := [monotonicity #7600]: #7602
-#7591 := [asserted]: #1371
-#7606 := [mp #7591 #7603]: #7601
-#15198 := [monotonicity #7606]: #15201
-#15195 := [trans #15198 #15197]: #15194
-#15190 := [monotonicity #15195]: #15193
-#15187 := [trans #15190 #15189]: #15186
-#15182 := [monotonicity #15187]: #15185
-#15179 := [trans #15182 #15181]: #15178
-#15984 := [monotonicity #15179]: #15983
-#15989 := [trans #15984 #15987]: #15988
-#15992 := [quant-intro #15989]: #15991
-#15980 := (iff #13841 #15979)
-#15977 := (iff #13821 #15976)
-#15974 := (iff #13816 #15971)
-#15968 := (or #14425 #13793 #13807)
-#15972 := (iff #15968 #15971)
-#15973 := [rewrite]: #15972
-#15969 := (iff #13816 #15968)
-#14422 := (iff #5712 #14425)
-#14427 := (iff #4503 #14426)
-#14424 := [monotonicity #15179]: #14427
-#14423 := [monotonicity #14424]: #14422
-#15970 := [monotonicity #14423]: #15969
-#15975 := [trans #15970 #15973]: #15974
-#15978 := [quant-intro #15975]: #15977
-#15981 := [monotonicity #15978]: #15980
-#15995 := [monotonicity #15981 #15992]: #15994
-#15998 := [monotonicity #15978 #15995]: #15997
-#16001 := [monotonicity #15998]: #16000
-#15966 := (iff #13788 #15963)
-#15960 := (or #13485 #15957 #13765)
-#15964 := (iff #15960 #15963)
-#15965 := [rewrite]: #15964
-#15961 := (iff #13788 #15960)
-#15958 := (iff #13759 #15957)
-#15955 := (iff #13753 #15954)
-#15952 := (iff #13748 #15951)
-#15949 := (iff #13740 #15948)
-#15946 := (iff #13731 #15945)
-#15943 := (iff #13726 #15940)
-#15937 := (or #12821 #12812 #13485 #13494 #15914 #13671)
-#15941 := (iff #15937 #15940)
-#15942 := [rewrite]: #15941
-#15938 := (iff #13726 #15937)
-#15915 := (iff #13615 #15914)
-#15912 := (iff #13607 #15909)
-#15906 := (or #12656 #13511 #15897 #13586 #15903)
-#15910 := (iff #15906 #15909)
-#15911 := [rewrite]: #15910
-#15907 := (iff #13607 #15906)
-#15904 := (iff #13592 #15903)
-#15901 := (iff #13589 #15900)
-#15867 := (iff #13500 #15864)
-#15809 := (+ 4294967295::Int #13501)
-#15860 := (>= #15809 1::Int)
-#15865 := (iff #15860 #15864)
-#15866 := [rewrite]: #15865
-#15861 := (iff #13500 #15860)
-#15810 := (= #13502 #15809)
-#15811 := [monotonicity #7606]: #15810
-#15862 := [monotonicity #15811]: #15861
-#15868 := [trans #15862 #15866]: #15867
-#15902 := [monotonicity #15868]: #15901
-#15905 := [monotonicity #15902]: #15904
-#15898 := (iff #13579 #15897)
-#15895 := (iff #13576 #15894)
-#15892 := (iff #13573 #15891)
-#15889 := (iff #13570 #15886)
-#15883 := (or #15880 #13565)
-#15887 := (iff #15883 #15886)
-#15888 := [rewrite]: #15887
-#15884 := (iff #13570 #15883)
-#15881 := (iff #13553 #15880)
-#15878 := (iff #13550 #15877)
-#15875 := (iff #13545 #15872)
-#15869 := (or #14425 #13522 #13536)
-#15873 := (iff #15869 #15872)
-#15874 := [rewrite]: #15873
-#15870 := (iff #13545 #15869)
-#15871 := [monotonicity #14423]: #15870
-#15876 := [trans #15871 #15874]: #15875
-#15879 := [quant-intro #15876]: #15878
-#15882 := [monotonicity #15879]: #15881
-#15885 := [monotonicity #15882]: #15884
-#15890 := [trans #15885 #15888]: #15889
-#15893 := [monotonicity #15879 #15890]: #15892
-#15896 := [monotonicity #15893]: #15895
-#15899 := [monotonicity #15896]: #15898
-#15908 := [monotonicity #15899 #15905]: #15907
-#15913 := [trans #15908 #15911]: #15912
-#15916 := [monotonicity #15868 #15913]: #15915
-#15939 := [monotonicity #15916]: #15938
-#15944 := [trans #15939 #15942]: #15943
-#15935 := (iff #13696 #15932)
-#15929 := (or #13485 #15926 #13672)
-#15933 := (iff #15929 #15932)
-#15934 := [rewrite]: #15933
-#15930 := (iff #13696 #15929)
-#15927 := (iff #13666 #15926)
-#15924 := (iff #13660 #15923)
-#15921 := (iff #13655 #15920)
-#15918 := (iff #13647 #15917)
-#15919 := [monotonicity #15916]: #15918
-#15922 := [monotonicity #15919]: #15921
-#15925 := [monotonicity #15922]: #15924
-#15928 := [monotonicity #15925]: #15927
-#15931 := [monotonicity #15928]: #15930
-#15936 := [trans #15931 #15934]: #15935
-#15947 := [monotonicity #15936 #15944]: #15946
-#15950 := [monotonicity #15947]: #15949
-#15953 := [monotonicity #15950]: #15952
-#15956 := [monotonicity #15953]: #15955
-#15959 := [monotonicity #15956]: #15958
-#15962 := [monotonicity #15959]: #15961
-#15967 := [trans #15962 #15965]: #15966
-#16004 := [monotonicity #15967 #16001]: #16003
-#15858 := (iff #14030 #15857)
-#15855 := (iff #14027 #15854)
-#15852 := (iff #14023 #15849)
-#15843 := (+ 255::Int #13970)
-#15846 := (>= #15843 0::Int)
-#15850 := (iff #15846 #15849)
-#15851 := [rewrite]: #15850
-#15847 := (iff #14023 #15846)
-#15844 := (= #14024 #15843)
-#1375 := (= f90 255::Int)
-#7605 := [asserted]: #1375
-#15845 := [monotonicity #7605]: #15844
-#15848 := [monotonicity #15845]: #15847
-#15853 := [trans #15848 #15851]: #15852
-#15856 := [monotonicity #15853]: #15855
-#15859 := [monotonicity #15856]: #15858
-#15841 := (iff #14017 #15840)
-#15838 := (iff #14014 #15837)
-#15835 := (iff #14010 #15832)
-#15826 := (+ 4294967295::Int #13941)
-#15829 := (>= #15826 0::Int)
-#15833 := (iff #15829 #15832)
-#15834 := [rewrite]: #15833
-#15830 := (iff #14010 #15829)
-#15827 := (= #14011 #15826)
-#15828 := [monotonicity #7606]: #15827
-#15831 := [monotonicity #15828]: #15830
-#15836 := [trans #15831 #15834]: #15835
-#15839 := [monotonicity #15836]: #15838
-#15842 := [monotonicity #15839]: #15841
-#15824 := (iff #14007 #15823)
-#15821 := (iff #14004 #15820)
-#15818 := (iff #14001 #15815)
-#15812 := (>= #15809 0::Int)
-#15816 := (iff #15812 #15815)
-#15817 := [rewrite]: #15816
-#15813 := (iff #14001 #15812)
-#15814 := [monotonicity #15811]: #15813
-#15819 := [trans #15814 #15817]: #15818
-#15822 := [monotonicity #15819]: #15821
-#15825 := [monotonicity #15822]: #15824
-#15807 := (iff #13989 #15806)
-#15804 := (iff #13986 #15803)
-#15801 := (iff #13981 #15798)
-#15795 := (or #14425 #13958 #13972)
-#15799 := (iff #15795 #15798)
-#15800 := [rewrite]: #15799
-#15796 := (iff #13981 #15795)
-#15797 := [monotonicity #14423]: #15796
-#15802 := [trans #15797 #15800]: #15801
-#15805 := [quant-intro #15802]: #15804
-#15808 := [monotonicity #15805]: #15807
-#16007 := [monotonicity #15808 #15825 #15842 #15859 #16004]: #16006
-#16012 := [trans #16007 #16010]: #16011
-#16015 := [monotonicity #16012]: #16014
-#15793 := (iff #13469 #15792)
-#15790 := (iff #13466 #15789)
-#15787 := (iff #13461 #15784)
-#15781 := (or #14425 #13439 #13451)
-#15785 := (iff #15781 #15784)
-#15786 := [rewrite]: #15785
-#15782 := (iff #13461 #15781)
-#15783 := [monotonicity #14423]: #15782
-#15788 := [trans #15783 #15786]: #15787
-#15791 := [quant-intro #15788]: #15790
-#15794 := [monotonicity #15791]: #15793
-#16018 := [monotonicity #15794 #16015]: #16017
-#16021 := [monotonicity #15791 #16018]: #16020
-#16024 := [monotonicity #16021]: #16023
-#16027 := [monotonicity #16024]: #16026
-#16030 := [monotonicity #16027]: #16029
-#16033 := [monotonicity #16030]: #16032
-#16036 := [monotonicity #16033]: #16035
-#16039 := [monotonicity #16036]: #16038
-#16042 := [monotonicity #16039]: #16041
-#16045 := [monotonicity #16042]: #16044
-#16048 := [monotonicity #16045]: #16047
-#14325 := (not #14177)
-#15338 := (iff #14325 #15337)
-#15335 := (iff #14177 #15334)
-#15332 := (iff #14174 #15331)
-#15329 := (iff #14169 #15328)
-#15326 := (iff #14163 #15325)
-#15323 := (iff #14158 #15322)
-#15320 := (iff #14150 #15319)
-#15317 := (iff #14129 #15316)
-#15314 := (iff #14126 #15313)
-#15311 := (iff #14123 #15310)
-#15308 := (iff #14120 #15307)
-#15305 := (iff #14115 #15304)
-#15302 := (iff #14107 #15299)
-#15296 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #15293 #13955 #13989 #13995 #14007 #14017 #14030 #14041)
-#15300 := (iff #15296 #15299)
-#15301 := [rewrite]: #15300
-#15297 := (iff #14107 #15296)
-#15294 := (iff #13914 #15293)
-#15291 := (iff #13909 #15288)
-#15273 := (or #12304 #12295 #12286 #12277 #13485 #13852)
-#15285 := (or #13485 #13766 #15273)
-#15289 := (iff #15285 #15288)
-#15290 := [rewrite]: #15289
-#15286 := (iff #13909 #15285)
-#15283 := (iff #13884 #15273)
-#15278 := (and true #15273)
-#15281 := (iff #15278 #15273)
-#15282 := [rewrite]: #15281
-#15279 := (iff #13884 #15278)
-#15276 := (iff #13879 #15273)
-#15270 := (or false #12304 #12295 #12286 #12277 #13485 #13852)
-#15274 := (iff #15270 #15273)
-#15275 := [rewrite]: #15274
-#15271 := (iff #13879 #15270)
-#15268 := (iff #12338 false)
-#15266 := (iff #12338 #3156)
-#15004 := (iff #10924 true)
-#10923 := [asserted]: #2542
-#10930 := [mp #10923 #10927]: #10924
-#15005 := [iff-true #10930]: #15004
-#15267 := [monotonicity #15005]: #15266
-#15269 := [trans #15267 #12221]: #15268
-#15272 := [monotonicity #15269]: #15271
-#15277 := [trans #15272 #15275]: #15276
-#15280 := [monotonicity #15005 #15277]: #15279
-#15284 := [trans #15280 #15282]: #15283
-#15287 := [monotonicity #15284]: #15286
-#15292 := [trans #15287 #15290]: #15291
-#15295 := [monotonicity #15292]: #15294
-#15264 := (iff #12366 #15263)
-#15261 := (iff #12228 #12222)
-#15256 := (and true #12222)
-#15259 := (iff #15256 #12222)
-#15260 := [rewrite]: #15259
-#15257 := (iff #12228 #15256)
-#15240 := (iff #12109 true)
-#15241 := [iff-true #14315]: #15240
-#15258 := [monotonicity #15241]: #15257
-#15262 := [trans #15258 #15260]: #15261
-#15265 := [monotonicity #15262]: #15264
-#15298 := [monotonicity #15265 #15295]: #15297
-#15303 := [trans #15298 #15301]: #15302
-#15306 := [monotonicity #15303]: #15305
-#15309 := [monotonicity #15306]: #15308
-#15312 := [monotonicity #15309]: #15311
-#15315 := [monotonicity #15312]: #15314
-#15318 := [monotonicity #15315]: #15317
-#15321 := [monotonicity #15318]: #15320
-#15324 := [monotonicity #15321]: #15323
-#15327 := [monotonicity #15324]: #15326
-#15330 := [monotonicity #15327]: #15329
-#15333 := [monotonicity #15330]: #15332
-#15336 := [monotonicity #15333]: #15335
-#15339 := [monotonicity #15336]: #15338
-#14326 := [not-or-elim #14310]: #14325
-#15340 := [mp #14326 #15339]: #15337
-#16049 := [mp #15340 #16048]: #16046
-#18796 := [mp~ #16049 #18795]: #18793
-#18797 := [mp #18796 #19141]: #19139
-#22664 := [mp #18797 #22663]: #22661
-#23569 := [mp #22664 #23568]: #23566
-#29167 := [unit-resolution #23569 #26960]: #23563
-#24793 := (or #23560 #23554)
-#24794 := [def-axiom]: #24793
-#29168 := [unit-resolution #24794 #29167]: #23554
-#27003 := (f24 #3098)
-decl f156 :: (-> S18 S18)
-#24960 := (f156 #3040)
-#27004 := (= #24960 #27003)
-decl f39 :: (-> Int S20)
-#24797 := (f39 #3076)
-#27034 := (f128 #24797)
-decl f81 :: (-> Int Int Int)
-decl f151 :: (-> S18 Int)
-#27032 := (f151 #24960)
-#27033 := (f81 0::Int #27032)
-#27041 := (+ #27033 #27034)
-#27044 := (f54 #24960 #27041)
-#27233 := (f24 #27044)
-#27604 := (= #27233 #27003)
-#27600 := (= #27003 #27233)
-#27572 := (= #3098 #27044)
-#27028 := (f77 #24797 0::Int #24960)
-#27047 := (= #27028 #27044)
-#27050 := (not #27047)
-decl f150 :: (-> S20 S20 S1)
-#27029 := (f150 #27028 #24797)
-#27030 := (= f1 #27029)
-#27031 := (not #27030)
-#27056 := (or #27031 #27050)
-#27061 := (not #27056)
-#289 := (:var 1 Int)
-#1622 := (f77 #60 #289 #275)
-#1623 := (pattern #1622)
-#1624 := (f150 #1622 #60)
-#8354 := (= f1 #1624)
-#21196 := (not #8354)
-#1627 := (f151 #275)
-#1628 := (f81 #289 #1627)
-#1626 := (f128 #60)
-#1629 := (+ #1626 #1628)
-#1630 := (f54 #275 #1629)
-#1631 := (= #1622 #1630)
-#21195 := (not #1631)
-#21197 := (or #21195 #21196)
-#21198 := (not #21197)
-#21201 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21198)
-#8360 := (and #1631 #8354)
-#8365 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8360)
-#21202 := (iff #8365 #21201)
-#21199 := (iff #8360 #21198)
-#21200 := [rewrite]: #21199
-#21203 := [quant-intro #21200]: #21202
-#17329 := (~ #8365 #8365)
-#17327 := (~ #8360 #8360)
-#17328 := [refl]: #17327
-#17330 := [nnf-pos #17328]: #17329
-#1625 := (= #1624 f1)
-#1632 := (and #1625 #1631)
-#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632)
-#8366 := (iff #1633 #8365)
-#8363 := (iff #1632 #8360)
-#8357 := (and #8354 #1631)
-#8361 := (iff #8357 #8360)
-#8362 := [rewrite]: #8361
-#8358 := (iff #1632 #8357)
-#8355 := (iff #1625 #8354)
-#8356 := [rewrite]: #8355
-#8359 := [monotonicity #8356]: #8358
-#8364 := [trans #8359 #8362]: #8363
-#8367 := [quant-intro #8364]: #8366
-#8353 := [asserted]: #1633
-#8370 := [mp #8353 #8367]: #8365
-#17331 := [mp~ #8370 #17330]: #8365
-#21204 := [mp #17331 #21203]: #21201
-#27451 := (not #21201)
-#27452 := (or #27451 #27061)
-#27035 := (+ #27034 #27033)
-#27036 := (f54 #24960 #27035)
-#27037 := (= #27028 #27036)
-#27038 := (not #27037)
-#27039 := (or #27038 #27031)
-#27040 := (not #27039)
-#27453 := (or #27451 #27040)
-#27449 := (iff #27453 #27452)
-#27456 := (iff #27452 #27452)
-#27457 := [rewrite]: #27456
-#27062 := (iff #27040 #27061)
-#27059 := (iff #27039 #27056)
-#27053 := (or #27050 #27031)
-#27057 := (iff #27053 #27056)
-#27058 := [rewrite]: #27057
-#27054 := (iff #27039 #27053)
-#27051 := (iff #27038 #27050)
-#27048 := (iff #27037 #27047)
-#27045 := (= #27036 #27044)
-#27042 := (= #27035 #27041)
-#27043 := [rewrite]: #27042
-#27046 := [monotonicity #27043]: #27045
-#27049 := [monotonicity #27046]: #27048
-#27052 := [monotonicity #27049]: #27051
-#27055 := [monotonicity #27052]: #27054
-#27060 := [trans #27055 #27058]: #27059
-#27063 := [monotonicity #27060]: #27062
-#27455 := [monotonicity #27063]: #27449
-#27458 := [trans #27455 #27457]: #27449
-#27454 := [quant-inst #24797 #161 #24960]: #27453
-#27459 := [mp #27454 #27458]: #27452
-#27562 := [unit-resolution #27459 #21204]: #27061
-#27468 := (or #27056 #27047)
-#27466 := [def-axiom]: #27468
-#27568 := [unit-resolution #27466 #27562]: #27047
-#27570 := (= #3098 #27028)
-#24961 := (= f19 #24960)
-#1401 := (f136 #369 #202)
-#1638 := (pattern #1401)
-#1652 := (f156 #1401)
-#8415 := (= #369 #1652)
-#8419 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8415)
-#17359 := (~ #8419 #8419)
-#17357 := (~ #8415 #8415)
-#17358 := [refl]: #17357
-#17360 := [nnf-pos #17358]: #17359
-#1653 := (= #1652 #369)
-#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653)
-#8420 := (iff #1654 #8419)
-#8417 := (iff #1653 #8415)
-#8418 := [rewrite]: #8417
-#8421 := [quant-intro #8418]: #8420
-#8414 := [asserted]: #1654
-#8424 := [mp #8414 #8421]: #8419
-#17361 := [mp~ #8424 #17360]: #8419
-#24964 := (not #8419)
-#24965 := (or #24964 #24961)
-#24966 := [quant-inst #50 #3036]: #24965
-#28486 := [unit-resolution #24966 #17361]: #24961
-#24798 := (= #3042 #24797)
-#132 := (f40 #62)
-#23175 := (pattern #132)
-#133 := (f39 #132)
-#3682 := (= #62 #133)
-#23176 := (forall (vars (?v0 S20)) (:pat #23175) #3682)
-#3685 := (forall (vars (?v0 S20)) #3682)
-#23177 := (iff #3685 #23176)
-#23179 := (iff #23176 #23176)
-#23180 := [rewrite]: #23179
-#23178 := [rewrite]: #23177
-#23181 := [trans #23178 #23180]: #23177
-#16306 := (~ #3685 #3685)
-#16296 := (~ #3682 #3682)
-#16297 := [refl]: #16296
-#16362 := [nnf-pos #16297]: #16306
-#134 := (= #133 #62)
-#135 := (forall (vars (?v0 S20)) #134)
-#3686 := (iff #135 #3685)
-#3683 := (iff #134 #3682)
-#3684 := [rewrite]: #3683
-#3687 := [quant-intro #3684]: #3686
-#3681 := [asserted]: #135
-#3690 := [mp #3681 #3687]: #3685
-#16363 := [mp~ #3690 #16362]: #3685
-#23182 := [mp #16363 #23181]: #23176
-#24801 := (not #23176)
-#24802 := (or #24801 #24798)
-#24803 := [quant-inst #3042]: #24802
-#27569 := [unit-resolution #24803 #23182]: #24798
-#27571 := [monotonicity #27569 #28486]: #27570
-#27599 := [trans #27571 #27568]: #27572
-#27601 := [monotonicity #27599]: #27600
-#27591 := [symm #27601]: #27604
-#27234 := (= #24960 #27233)
-#27497 := (or #25028 #27234)
-#27503 := [quant-inst #24960 #27041]: #27497
-#27567 := [unit-resolution #27503 #23276]: #27234
-#27592 := [trans #27567 #27591]: #27004
-#27413 := (not #27004)
-#26977 := (f59 #3098 #24960)
-#26978 := (= f1 #26977)
-#27006 := (iff #26978 #27004)
-#1433 := (f24 #55)
-#9184 := (= #275 #1433)
-#11354 := (iff #9184 #11333)
-#23258 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11354)
-#11359 := (forall (vars (?v0 S20) (?v1 S18)) #11354)
-#23261 := (iff #11359 #23258)
-#23259 := (iff #11354 #11354)
-#23260 := [refl]: #23259
-#23262 := [quant-intro #23260]: #23261
-#18251 := (~ #11359 #11359)
-#18249 := (~ #11354 #11354)
-#18250 := [refl]: #18249
-#18252 := [nnf-pos #18250]: #18251
-#1939 := (= #1433 #275)
-#2736 := (iff #2731 #1939)
-#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736)
-#11360 := (iff #2737 #11359)
-#11357 := (iff #2736 #11354)
-#11350 := (iff #11333 #9184)
-#11355 := (iff #11350 #11354)
-#11356 := [rewrite]: #11355
-#11352 := (iff #2736 #11350)
-#9185 := (iff #1939 #9184)
-#9186 := [rewrite]: #9185
-#11353 := [monotonicity #11336 #9186]: #11352
-#11358 := [trans #11353 #11356]: #11357
-#11361 := [quant-intro #11358]: #11360
-#11349 := [asserted]: #2737
-#11364 := [mp #11349 #11361]: #11359
-#18253 := [mp~ #11364 #18252]: #11359
-#23263 := [mp #18253 #23262]: #23258
-#26174 := (not #23258)
-#27419 := (or #26174 #27006)
-#27005 := (iff #27004 #26978)
-#27420 := (or #26174 #27005)
-#27407 := (iff #27420 #27419)
-#27409 := (iff #27419 #27419)
-#27410 := [rewrite]: #27409
-#27007 := (iff #27005 #27006)
-#27008 := [rewrite]: #27007
-#27408 := [monotonicity #27008]: #27407
-#27411 := [trans #27408 #27410]: #27407
-#27405 := [quant-inst #3098 #24960]: #27420
-#27406 := [mp #27405 #27411]: #27419
-#27530 := [unit-resolution #27406 #23263]: #27006
-#26985 := (not #26978)
-#27563 := (iff #18409 #26985)
-#27535 := (iff #12144 #26978)
-#27533 := (iff #26978 #12144)
-#27526 := (= #26977 #3099)
-#28487 := (= #24960 f19)
-#28488 := [symm #28486]: #28487
-#27532 := [monotonicity #28488]: #27526
-#27534 := [monotonicity #27532]: #27533
-#27536 := [symm #27534]: #27535
-#27564 := [monotonicity #27536]: #27563
-#27531 := [hypothesis]: #18409
-#27565 := [mp #27531 #27564]: #26985
-#27412 := (not #27006)
-#27414 := (or #27412 #26978 #27413)
-#27415 := [def-axiom]: #27414
-#27566 := [unit-resolution #27415 #27565 #27530]: #27413
-#27590 := [unit-resolution #27566 #27592]: false
-#27593 := [lemma #27590]: #12144
-#27181 := (f54 #24960 #3043)
-#27182 := (f77 #27181 0::Int #24960)
-#27186 := (f35 f298 #27182)
-#27187 := (= f1 #27186)
-#27188 := (not #27187)
-#28139 := (iff #18412 #27188)
-#28109 := (iff #12147 #27187)
-#28136 := (iff #27187 #12147)
-#28133 := (= #27186 #3101)
-#27752 := (= #27182 #3098)
-#28494 := (= #27181 #3042)
-#28492 := (= #3043 f299)
-#25080 := (= f299 #3043)
-#2762 := (f128 #2761)
-#11409 := (= #202 #2762)
-#23265 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11409)
-#11413 := (forall (vars (?v0 S18) (?v1 Int)) #11409)
-#23268 := (iff #11413 #23265)
-#23266 := (iff #11409 #11409)
-#23267 := [refl]: #23266
-#23269 := [quant-intro #23267]: #23268
-#18266 := (~ #11413 #11413)
-#18264 := (~ #11409 #11409)
-#18265 := [refl]: #18264
-#18267 := [nnf-pos #18265]: #18266
-#2763 := (= #2762 #202)
-#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763)
-#11414 := (iff #2764 #11413)
-#11411 := (iff #2763 #11409)
-#11412 := [rewrite]: #11411
-#11415 := [quant-intro #11412]: #11414
-#11408 := [asserted]: #2764
-#11418 := [mp #11408 #11415]: #11413
-#18268 := [mp~ #11418 #18267]: #11413
-#23270 := [mp #18268 #23269]: #23265
-#25034 := (not #23265)
-#25085 := (or #25034 #25080)
-#25086 := [quant-inst #50 #3041]: #25085
-#28491 := [unit-resolution #25086 #23270]: #25080
-#28493 := [symm #28491]: #28492
-#28495 := [monotonicity #28488 #28493]: #28494
-#28135 := [monotonicity #28495 #28488]: #27752
-#27928 := [monotonicity #28135]: #28133
-#28137 := [monotonicity #27928]: #28136
-#28138 := [symm #28137]: #28109
-#28111 := [monotonicity #28138]: #28139
-#27751 := [hypothesis]: #18412
-#28112 := [mp #27751 #28111]: #27188
-decl f148 :: (-> S29 S1)
-#27183 := (f69 #3220 #27182)
-#27184 := (f148 #27183)
-#27185 := (= f1 #27184)
-#27198 := (or #27185 #27188)
-#27201 := (not #27198)
-decl f33 :: (-> S18 S1)
-#27194 := (f33 #24960)
-#27195 := (= f1 #27194)
-#2848 := (f33 f19)
-#28526 := (= #2848 #27194)
-#28523 := (= #27194 #2848)
-#28524 := [monotonicity #28488]: #28523
-#28527 := [symm #28524]: #28526
-#11588 := (= f1 #2848)
-#2849 := (= #2848 f1)
-#11590 := (iff #2849 #11588)
-#11591 := [rewrite]: #11590
-#11587 := [asserted]: #2849
-#11594 := [mp #11587 #11591]: #11588
-#28528 := [trans #11594 #28527]: #27195
-#27196 := (not #27195)
-#28357 := (or #27196 #27201)
-decl f26 :: (-> S20 S21 S1)
-decl f27 :: (-> S19 S20 S21)
-#26739 := (f27 f298 #26146)
-decl f155 :: (-> S18 Int)
-#24962 := (f155 #3040)
-#27102 := (f136 #24960 #24962)
-#27103 := (f54 #27102 #3043)
-#27191 := (f26 #27103 #26739)
-#27192 := (= f1 #27191)
-#26740 := (f26 #26146 #26739)
-#28128 := (= #26740 #27191)
-#28366 := (= #27191 #26740)
-#28055 := (= #27103 #26146)
-#28363 := (= #27103 #3044)
-#28152 := (= #27102 #3040)
-#28151 := (= #24962 f297)
-#24963 := (= f297 #24962)
-#1649 := (f155 #1401)
-#8408 := (= #202 #1649)
-#8411 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8408)
-#17354 := (~ #8411 #8411)
-#17352 := (~ #8408 #8408)
-#17353 := [refl]: #17352
-#17355 := [nnf-pos #17353]: #17354
-#1650 := (= #1649 #202)
-#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650)
-#8412 := (iff #1651 #8411)
-#8409 := (iff #1650 #8408)
-#8410 := [rewrite]: #8409
-#8413 := [quant-intro #8410]: #8412
-#8407 := [asserted]: #1651
-#8416 := [mp #8407 #8413]: #8411
-#17356 := [mp~ #8416 #17355]: #8411
-#24969 := (not #8411)
-#24970 := (or #24969 #24963)
-#24971 := [quant-inst #50 #3036]: #24970
-#28508 := [unit-resolution #24971 #17356]: #24963
-#27929 := [symm #28508]: #28151
-#28153 := [monotonicity #28488 #27929]: #28152
-#28364 := [monotonicity #28153]: #28363
-#28365 := [trans #28364 #28875]: #28055
-#28367 := [monotonicity #28365]: #28366
-#28129 := [symm #28367]: #28128
-#26741 := (= f1 #26740)
-decl f64 :: (-> S19 S20 S21)
-#26729 := (f64 f298 #26146)
-#26730 := (f26 #62 #26729)
-#26736 := (pattern #26730)
-decl f209 :: (-> S18 S1)
-#26733 := (f209 #26550)
-#26734 := (= f1 #26733)
-#26731 := (= f1 #26730)
-#26732 := (not #26731)
-decl f159 :: (-> S20 S21 S1)
-decl f204 :: (-> S22 S21)
-decl f22 :: (-> S19 S20 S22)
-#26725 := (f22 f298 #26146)
-#26726 := (f204 #26725)
-#26727 := (f159 #62 #26726)
-#26728 := (= f1 #26727)
-#26746 := (or #26728 #26732 #26734)
-#26749 := (forall (vars (?v3 S20)) (:pat #26736) #26746)
-#26752 := (not #26749)
-#26742 := (not #26741)
-#26755 := (or #26613 #26742 #26752)
-#26758 := (not #26755)
-#28107 := (= #3096 #26680)
-#28113 := [symm #26898]: #28107
-#28131 := [trans #26960 #28113]: #26681
-#26687 := (or #26689 #26679 #26697)
-#26690 := [def-axiom]: #26687
-#28108 := [unit-resolution #26690 #28131 #26901]: #26679
-#26761 := (or #26700 #26758)
+#10189 := [monotonicity #4058 #10186]: #10188
+#10195 := [monotonicity #10189 #10192]: #10194
+#10201 := [trans #10195 #10199]: #10200
+#10204 := [quant-intro #10201]: #10203
+#10223 := [trans #10204 #10221]: #10222
+#10170 := [asserted]: #2280
+#10224 := [mp #10170 #10223]: #10219
+#17894 := [mp~ #10224 #17893]: #10219
+#21922 := [mp #17894 #21921]: #21919
+#26827 := (not #26826)
+#26595 := (not #26594)
+#24846 := (not #12145)
+#26800 := (not #21919)
+#26802 := (or #26800 #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
+#26829 := (= #26828 f25)
+#26830 := (or #26829 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
+#26803 := (or #26800 #26830)
+#26843 := (iff #26803 #26802)
+#26837 := (or #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
+#26805 := (or #26800 #26837)
+#26847 := (iff #26805 #26802)
+#26848 := [rewrite]: #26847
+#26844 := (iff #26803 #26805)
+#26840 := (iff #26830 #26837)
+#26834 := (or #26831 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
+#26838 := (iff #26834 #26837)
+#26839 := [rewrite]: #26838
+#26835 := (iff #26830 #26834)
+#26832 := (iff #26829 #26831)
+#26833 := [rewrite]: #26832
+#26836 := [monotonicity #26833]: #26835
+#26841 := [trans #26836 #26839]: #26840
+#26846 := [monotonicity #26841]: #26844
+#26849 := [trans #26846 #26848]: #26843
+#26804 := [quant-inst #3039 #26182]: #26803
+#26845 := [mp #26804 #26849]: #26802
+#27031 := [unit-resolution #26845 #21922 #14351 #27029 #27010 #27002]: #27030
+#27032 := [unit-resolution #27031 #26980 #26973 #26974 #26936]: false
+#27033 := [lemma #27032]: #12177
+#28800 := [trans #27033 #28799]: #26717
+#26724 := (or #26722 #26715 #26733)
+#26751 := [def-axiom]: #26724
+#28801 := [unit-resolution #26751 #28800 #26937]: #26715
+#26797 := (or #26736 #26794)
#54 := (:var 2 S19)
-#2218 := (f208 #54 #55 #62)
+#2218 := (f207 #54 #55 #62)
#2281 := (pattern #2218)
#2282 := (f64 #53 #60)
#2283 := (f26 #62 #2282)
#2284 := (pattern #2283)
#2210 := (f22 #53 #55)
-#2290 := (f204 #2210)
-#2291 := (f159 #62 #2290)
-#10202 := (= f1 #2291)
-#10196 := (= f1 #2283)
-#21887 := (not #10196)
+#2290 := (f203 #2210)
+#2291 := (f158 #62 #2290)
+#10238 := (= f1 #2291)
+#10232 := (= f1 #2283)
+#21923 := (not #10232)
#1425 := (f24 #60)
-#2285 := (f209 #1425)
-#10190 := (= f1 #2285)
-#21902 := (or #10190 #21887 #10202)
-#21907 := (forall (vars (?v3 S20)) (:pat #2284) #21902)
-#21913 := (not #21907)
+#2285 := (f208 #1425)
+#10226 := (= f1 #2285)
+#21938 := (or #10226 #21923 #10238)
+#21943 := (forall (vars (?v3 S20)) (:pat #2284) #21938)
+#21949 := (not #21943)
#2197 := (f27 #54 #62)
#2198 := (f26 #55 #2197)
-#9890 := (= f1 #2198)
-#21722 := (not #9890)
+#9926 := (= f1 #2198)
+#21758 := (not #9926)
#221 := (f38 #54 #55)
#3873 := (= f1 #221)
-#10540 := (not #3873)
-#21914 := (or #10540 #21722 #21913)
-#21915 := (not #21914)
-#9938 := (= f1 #2218)
-#10226 := (not #9938)
-#21920 := (or #10226 #21915)
-#21923 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21920)
-#10193 := (not #10190)
-#10199 := (and #10193 #10196)
-#10208 := (not #10199)
-#10209 := (or #10208 #10202)
-#10214 := (forall (vars (?v3 S20)) (:pat #2284) #10209)
-#10235 := (and #3873 #9890 #10214)
-#10238 := (or #10226 #10235)
-#10241 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10238)
-#21924 := (iff #10241 #21923)
-#21921 := (iff #10238 #21920)
-#21918 := (iff #10235 #21915)
-#21910 := (and #3873 #9890 #21907)
-#21916 := (iff #21910 #21915)
-#21917 := [rewrite]: #21916
-#21911 := (iff #10235 #21910)
-#21908 := (iff #10214 #21907)
-#21905 := (iff #10209 #21902)
-#21888 := (or #10190 #21887)
-#21899 := (or #21888 #10202)
-#21903 := (iff #21899 #21902)
-#21904 := [rewrite]: #21903
-#21900 := (iff #10209 #21899)
-#21897 := (iff #10208 #21888)
-#21889 := (not #21888)
-#21892 := (not #21889)
-#21895 := (iff #21892 #21888)
-#21896 := [rewrite]: #21895
-#21893 := (iff #10208 #21892)
-#21890 := (iff #10199 #21889)
-#21891 := [rewrite]: #21890
-#21894 := [monotonicity #21891]: #21893
-#21898 := [trans #21894 #21896]: #21897
-#21901 := [monotonicity #21898]: #21900
-#21906 := [trans #21901 #21904]: #21905
-#21909 := [quant-intro #21906]: #21908
-#21912 := [monotonicity #21909]: #21911
-#21919 := [trans #21912 #21917]: #21918
-#21922 := [monotonicity #21919]: #21921
-#21925 := [quant-intro #21922]: #21924
-#17873 := (~ #10241 #10241)
-#17871 := (~ #10238 #10238)
-#17869 := (~ #10235 #10235)
-#17867 := (~ #10214 #10214)
-#17865 := (~ #10209 #10209)
-#17866 := [refl]: #17865
-#17868 := [nnf-pos #17866]: #17867
-#17863 := (~ #9890 #9890)
-#17864 := [refl]: #17863
-#17861 := (~ #3873 #3873)
-#17862 := [refl]: #17861
-#17870 := [monotonicity #17862 #17864 #17868]: #17869
-#17859 := (~ #10226 #10226)
-#17860 := [refl]: #17859
-#17872 := [monotonicity #17860 #17870]: #17871
-#17874 := [nnf-pos #17872]: #17873
+#10576 := (not #3873)
+#21950 := (or #10576 #21758 #21949)
+#21951 := (not #21950)
+#9974 := (= f1 #2218)
+#10262 := (not #9974)
+#21956 := (or #10262 #21951)
+#21959 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21956)
+#10229 := (not #10226)
+#10235 := (and #10229 #10232)
+#10244 := (not #10235)
+#10245 := (or #10244 #10238)
+#10250 := (forall (vars (?v3 S20)) (:pat #2284) #10245)
+#10271 := (and #3873 #9926 #10250)
+#10274 := (or #10262 #10271)
+#10277 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10274)
+#21960 := (iff #10277 #21959)
+#21957 := (iff #10274 #21956)
+#21954 := (iff #10271 #21951)
+#21946 := (and #3873 #9926 #21943)
+#21952 := (iff #21946 #21951)
+#21953 := [rewrite]: #21952
+#21947 := (iff #10271 #21946)
+#21944 := (iff #10250 #21943)
+#21941 := (iff #10245 #21938)
+#21924 := (or #10226 #21923)
+#21935 := (or #21924 #10238)
+#21939 := (iff #21935 #21938)
+#21940 := [rewrite]: #21939
+#21936 := (iff #10245 #21935)
+#21933 := (iff #10244 #21924)
+#21925 := (not #21924)
+#21928 := (not #21925)
+#21931 := (iff #21928 #21924)
+#21932 := [rewrite]: #21931
+#21929 := (iff #10244 #21928)
+#21926 := (iff #10235 #21925)
+#21927 := [rewrite]: #21926
+#21930 := [monotonicity #21927]: #21929
+#21934 := [trans #21930 #21932]: #21933
+#21937 := [monotonicity #21934]: #21936
+#21942 := [trans #21937 #21940]: #21941
+#21945 := [quant-intro #21942]: #21944
+#21948 := [monotonicity #21945]: #21947
+#21955 := [trans #21948 #21953]: #21954
+#21958 := [monotonicity #21955]: #21957
+#21961 := [quant-intro #21958]: #21960
+#17909 := (~ #10277 #10277)
+#17907 := (~ #10274 #10274)
+#17905 := (~ #10271 #10271)
+#17903 := (~ #10250 #10250)
+#17901 := (~ #10245 #10245)
+#17902 := [refl]: #17901
+#17904 := [nnf-pos #17902]: #17903
+#17899 := (~ #9926 #9926)
+#17900 := [refl]: #17899
+#17897 := (~ #3873 #3873)
+#17898 := [refl]: #17897
+#17906 := [monotonicity #17898 #17900 #17904]: #17905
+#17895 := (~ #10262 #10262)
+#17896 := [refl]: #17895
+#17908 := [monotonicity #17896 #17906]: #17907
+#17910 := [nnf-pos #17908]: #17909
#2292 := (= #2291 f1)
#2288 := (= #2283 f1)
#2286 := (= #2285 f1)
@@ -5435,110 +4196,154 @@
#2219 := (= #2218 f1)
#2297 := (implies #2219 #2296)
#2298 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #2297)
-#10244 := (iff #2298 #10241)
-#10217 := (and #3873 #10214)
-#10220 := (and #9890 #10217)
-#10227 := (or #10226 #10220)
-#10232 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10227)
-#10242 := (iff #10232 #10241)
-#10239 := (iff #10227 #10238)
-#10236 := (iff #10220 #10235)
-#10237 := [rewrite]: #10236
-#10240 := [monotonicity #10237]: #10239
-#10243 := [quant-intro #10240]: #10242
-#10233 := (iff #2298 #10232)
-#10230 := (iff #2297 #10227)
-#10223 := (implies #9938 #10220)
-#10228 := (iff #10223 #10227)
-#10229 := [rewrite]: #10228
-#10224 := (iff #2297 #10223)
-#10221 := (iff #2296 #10220)
-#10218 := (iff #2295 #10217)
-#10215 := (iff #2294 #10214)
-#10212 := (iff #2293 #10209)
-#10205 := (implies #10199 #10202)
-#10210 := (iff #10205 #10209)
-#10211 := [rewrite]: #10210
-#10206 := (iff #2293 #10205)
-#10203 := (iff #2292 #10202)
-#10204 := [rewrite]: #10203
-#10200 := (iff #2289 #10199)
-#10197 := (iff #2288 #10196)
-#10198 := [rewrite]: #10197
-#10194 := (iff #2287 #10193)
-#10191 := (iff #2286 #10190)
-#10192 := [rewrite]: #10191
-#10195 := [monotonicity #10192]: #10194
-#10201 := [monotonicity #10195 #10198]: #10200
-#10207 := [monotonicity #10201 #10204]: #10206
-#10213 := [trans #10207 #10211]: #10212
-#10216 := [quant-intro #10213]: #10215
+#10280 := (iff #2298 #10277)
+#10253 := (and #3873 #10250)
+#10256 := (and #9926 #10253)
+#10263 := (or #10262 #10256)
+#10268 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10263)
+#10278 := (iff #10268 #10277)
+#10275 := (iff #10263 #10274)
+#10272 := (iff #10256 #10271)
+#10273 := [rewrite]: #10272
+#10276 := [monotonicity #10273]: #10275
+#10279 := [quant-intro #10276]: #10278
+#10269 := (iff #2298 #10268)
+#10266 := (iff #2297 #10263)
+#10259 := (implies #9974 #10256)
+#10264 := (iff #10259 #10263)
+#10265 := [rewrite]: #10264
+#10260 := (iff #2297 #10259)
+#10257 := (iff #2296 #10256)
+#10254 := (iff #2295 #10253)
+#10251 := (iff #2294 #10250)
+#10248 := (iff #2293 #10245)
+#10241 := (implies #10235 #10238)
+#10246 := (iff #10241 #10245)
+#10247 := [rewrite]: #10246
+#10242 := (iff #2293 #10241)
+#10239 := (iff #2292 #10238)
+#10240 := [rewrite]: #10239
+#10236 := (iff #2289 #10235)
+#10233 := (iff #2288 #10232)
+#10234 := [rewrite]: #10233
+#10230 := (iff #2287 #10229)
+#10227 := (iff #2286 #10226)
+#10228 := [rewrite]: #10227
+#10231 := [monotonicity #10228]: #10230
+#10237 := [monotonicity #10231 #10234]: #10236
+#10243 := [monotonicity #10237 #10240]: #10242
+#10249 := [trans #10243 #10247]: #10248
+#10252 := [quant-intro #10249]: #10251
#3874 := (iff #225 #3873)
#3875 := [rewrite]: #3874
-#10219 := [monotonicity #3875 #10216]: #10218
-#9891 := (iff #2203 #9890)
-#9892 := [rewrite]: #9891
-#10222 := [monotonicity #9892 #10219]: #10221
-#9939 := (iff #2219 #9938)
-#9940 := [rewrite]: #9939
-#10225 := [monotonicity #9940 #10222]: #10224
-#10231 := [trans #10225 #10229]: #10230
-#10234 := [quant-intro #10231]: #10233
-#10245 := [trans #10234 #10243]: #10244
-#10189 := [asserted]: #2298
-#10246 := [mp #10189 #10245]: #10241
-#17875 := [mp~ #10246 #17874]: #10241
-#21926 := [mp #17875 #21925]: #21923
-#26714 := (not #21923)
-#26720 := (or #26714 #26700 #26758)
-#26735 := (or #26734 #26732 #26728)
-#26737 := (forall (vars (?v3 S20)) (:pat #26736) #26735)
-#26738 := (not #26737)
-#26743 := (or #26613 #26742 #26738)
-#26744 := (not #26743)
-#26745 := (or #26700 #26744)
-#26716 := (or #26714 #26745)
-#26810 := (iff #26716 #26720)
-#26722 := (or #26714 #26761)
-#26776 := (iff #26722 #26720)
-#26808 := [rewrite]: #26776
-#26723 := (iff #26716 #26722)
-#26762 := (iff #26745 #26761)
-#26759 := (iff #26744 #26758)
-#26756 := (iff #26743 #26755)
-#26753 := (iff #26738 #26752)
-#26750 := (iff #26737 #26749)
-#26747 := (iff #26735 #26746)
-#26748 := [rewrite]: #26747
-#26751 := [quant-intro #26748]: #26750
-#26754 := [monotonicity #26751]: #26753
-#26757 := [monotonicity #26754]: #26756
-#26760 := [monotonicity #26757]: #26759
-#26763 := [monotonicity #26760]: #26762
-#26724 := [monotonicity #26763]: #26723
-#26811 := [trans #26724 #26808]: #26810
-#26721 := [quant-inst #3039 #26146 #26146]: #26716
-#26812 := [mp #26721 #26811]: #26720
-#28140 := [unit-resolution #26812 #21926]: #26761
-#28132 := [unit-resolution #28140 #28108]: #26758
-#26809 := (or #26755 #26741)
-#26814 := [def-axiom]: #26809
-#28150 := [unit-resolution #26814 #28132]: #26741
-#28130 := [trans #28150 #28129]: #27192
-#27139 := (<= #24962 0::Int)
-#28353 := (not #27139)
-#14324 := [not-or-elim #14310]: #13473
-#27122 := (* -1::Int #24962)
-#27258 := (+ f297 #27122)
-#27259 := (<= #27258 0::Int)
-#28509 := (not #24963)
-#28510 := (or #28509 #27259)
-#28511 := [th-lemma arith triangle-eq]: #28510
-#28512 := [unit-resolution #28511 #28508]: #27259
-#28518 := (not #27259)
-#28354 := (or #28353 #13472 #28518)
-#28355 := [th-lemma arith assign-bounds -1 1]: #28354
-#28356 := [unit-resolution #28355 #28512 #14324]: #28353
+#10255 := [monotonicity #3875 #10252]: #10254
+#9927 := (iff #2203 #9926)
+#9928 := [rewrite]: #9927
+#10258 := [monotonicity #9928 #10255]: #10257
+#9975 := (iff #2219 #9974)
+#9976 := [rewrite]: #9975
+#10261 := [monotonicity #9976 #10258]: #10260
+#10267 := [trans #10261 #10265]: #10266
+#10270 := [quant-intro #10267]: #10269
+#10281 := [trans #10270 #10279]: #10280
+#10225 := [asserted]: #2298
+#10282 := [mp #10225 #10281]: #10277
+#17911 := [mp~ #10282 #17910]: #10277
+#21962 := [mp #17911 #21961]: #21959
+#26806 := (not #21959)
+#26801 := (or #26806 #26736 #26794)
+#26771 := (or #26770 #26768 #26764)
+#26773 := (forall (vars (?v3 S20)) (:pat #26772) #26771)
+#26774 := (not #26773)
+#26779 := (or #26649 #26778 #26774)
+#26780 := (not #26779)
+#26781 := (or #26736 #26780)
+#26758 := (or #26806 #26781)
+#26852 := (iff #26758 #26801)
+#26808 := (or #26806 #26797)
+#26811 := (iff #26808 #26801)
+#26850 := [rewrite]: #26811
+#26809 := (iff #26758 #26808)
+#26798 := (iff #26781 #26797)
+#26795 := (iff #26780 #26794)
+#26792 := (iff #26779 #26791)
+#26789 := (iff #26774 #26788)
+#26786 := (iff #26773 #26785)
+#26783 := (iff #26771 #26782)
+#26784 := [rewrite]: #26783
+#26787 := [quant-intro #26784]: #26786
+#26790 := [monotonicity #26787]: #26789
+#26793 := [monotonicity #26790]: #26792
+#26796 := [monotonicity #26793]: #26795
+#26799 := [monotonicity #26796]: #26798
+#26810 := [monotonicity #26799]: #26809
+#26853 := [trans #26810 #26850]: #26852
+#26807 := [quant-inst #3039 #26182 #26182]: #26758
+#26858 := [mp #26807 #26853]: #26801
+#28802 := [unit-resolution #26858 #21962]: #26797
+#28803 := [unit-resolution #28802 #28801]: #26794
+#26851 := (or #26791 #26777)
+#26863 := [def-axiom]: #26851
+#28804 := [unit-resolution #26863 #28803]: #26777
+#28797 := [trans #28804 #28796]: #27234
+#27235 := (not #27234)
+#27547 := (or #12183 #27235)
+#27223 := (f54 #24996 #3043)
+#27224 := (f77 #27223 0::Int #24996)
+#27228 := (f35 f297 #27224)
+#27229 := (= f1 #27228)
+#27230 := (not #27229)
+#27503 := (iff #18448 #27230)
+#27491 := (iff #12183 #27229)
+#27489 := (iff #27229 #12183)
+#27487 := (= #27228 #3101)
+#27486 := (= #27224 #3098)
+#28392 := (= #27223 #3042)
+#28393 := [monotonicity #28386 #28391]: #28392
+#27481 := [monotonicity #28393 #28386]: #27486
+#27488 := [monotonicity #27481]: #27487
+#27490 := [monotonicity #27488]: #27489
+#27502 := [symm #27490]: #27491
+#27511 := [monotonicity #27502]: #27503
+#27485 := [hypothesis]: #18448
+#27512 := [mp #27485 #27511]: #27230
+#27225 := (f69 #3220 #27224)
+#27226 := (f147 #27225)
+#27227 := (= f1 #27226)
+#27240 := (or #27227 #27230)
+#27243 := (not #27240)
+decl f33 :: (-> S18 S1)
+#27236 := (f33 #24996)
+#27237 := (= f1 #27236)
+#2848 := (f33 f19)
+#28424 := (= #2848 #27236)
+#28421 := (= #27236 #2848)
+#28422 := [monotonicity #28386]: #28421
+#28425 := [symm #28422]: #28424
+#11624 := (= f1 #2848)
+#2849 := (= #2848 f1)
+#11626 := (iff #2849 #11624)
+#11627 := [rewrite]: #11626
+#11623 := [asserted]: #2849
+#11630 := [mp #11623 #11627]: #11624
+#28426 := [trans #11630 #28425]: #27237
+#27238 := (not #27237)
+#27517 := (or #27238 #27243)
+#28427 := [hypothesis]: #27234
+#27181 := (<= #24998 0::Int)
+#27514 := (not #27181)
+#14360 := [not-or-elim #14346]: #13509
+#27164 := (* -1::Int #24998)
+#27273 := (+ f296 #27164)
+#27274 := (<= #27273 0::Int)
+#28407 := (not #24999)
+#28408 := (or #28407 #27274)
+#28409 := [th-lemma arith triangle-eq]: #28408
+#28410 := [unit-resolution #28409 #28406]: #27274
+#28416 := (not #27274)
+#27515 := (or #27514 #13508 #28416)
+#27510 := [th-lemma arith assign-bounds -1 1]: #27515
+#27516 := [unit-resolution #27510 #28410 #14360]: #27514
#279 := (f33 #275)
#805 := (:var 4 Int)
#2121 := (f54 #275 #805)
@@ -5548,67 +4353,67 @@
#1408 := (:var 3 S20)
#2119 := (f27 #1416 #1408)
#310 := (:var 2 Int)
-#2117 := (f136 #275 #310)
+#2117 := (f135 #275 #310)
#2118 := (f54 #2117 #805)
#2120 := (f26 #2118 #2119)
#2139 := (pattern #2120 #2138 #279)
#1590 := (f70 #1416)
#2136 := (f69 #1590 #2122)
#2137 := (pattern #2120 #2136 #279)
-#2142 := (f148 #2136)
-#9698 := (= f1 #2142)
+#2142 := (f147 #2136)
+#9734 := (= f1 #2142)
#2140 := (f35 #1416 #2122)
-#9695 := (= f1 #2140)
-#21632 := (not #9695)
-#21633 := (or #21632 #9698)
-#21634 := (not #21633)
-#9639 := (= f1 #2120)
-#21608 := (not #9639)
+#9731 := (= f1 #2140)
+#21668 := (not #9731)
+#21669 := (or #21668 #9734)
+#21670 := (not #21669)
+#9675 := (= f1 #2120)
+#21644 := (not #9675)
#2125 := (f66 #1416)
-#9636 := (= f1 #2125)
-#21607 := (not #9636)
+#9672 := (= f1 #2125)
+#21643 := (not #9672)
#4206 := (* -1::Int #310)
-#6244 := (+ #289 #4206)
-#6841 := (>= #6244 0::Int)
-#4448 := (>= #289 0::Int)
-#19545 := (not #4448)
+#6270 := (+ #289 #4206)
+#6867 := (>= #6270 0::Int)
+#4468 := (>= #289 0::Int)
+#19581 := (not #4468)
#4084 := (= f1 #279)
-#10425 := (not #4084)
-#21640 := (or #10425 #19545 #6841 #21607 #21608 #21634)
-#21645 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21640)
-#9701 := (not #9698)
-#9704 := (and #9695 #9701)
-#7898 := (not #6841)
-#9677 := (and #4084 #4448 #7898 #9636 #9639)
-#9682 := (not #9677)
-#9718 := (or #9682 #9704)
-#9721 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9718)
-#21646 := (iff #9721 #21645)
-#21643 := (iff #9718 #21640)
-#21609 := (or #10425 #19545 #6841 #21607 #21608)
-#21637 := (or #21609 #21634)
-#21641 := (iff #21637 #21640)
-#21642 := [rewrite]: #21641
-#21638 := (iff #9718 #21637)
-#21635 := (iff #9704 #21634)
-#21636 := [rewrite]: #21635
-#21618 := (iff #9682 #21609)
-#21610 := (not #21609)
-#21613 := (not #21610)
-#21616 := (iff #21613 #21609)
-#21617 := [rewrite]: #21616
-#21614 := (iff #9682 #21613)
-#21611 := (iff #9677 #21610)
-#21612 := [rewrite]: #21611
-#21615 := [monotonicity #21612]: #21614
-#21619 := [trans #21615 #21617]: #21618
-#21639 := [monotonicity #21619 #21636]: #21638
-#21644 := [trans #21639 #21642]: #21643
-#21647 := [quant-intro #21644]: #21646
-#17739 := (~ #9721 #9721)
-#17737 := (~ #9718 #9718)
-#17738 := [refl]: #17737
-#17740 := [nnf-pos #17738]: #17739
+#10461 := (not #4084)
+#21676 := (or #10461 #19581 #6867 #21643 #21644 #21670)
+#21681 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21676)
+#9737 := (not #9734)
+#9740 := (and #9731 #9737)
+#7934 := (not #6867)
+#9713 := (and #4084 #4468 #7934 #9672 #9675)
+#9718 := (not #9713)
+#9754 := (or #9718 #9740)
+#9757 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9754)
+#21682 := (iff #9757 #21681)
+#21679 := (iff #9754 #21676)
+#21645 := (or #10461 #19581 #6867 #21643 #21644)
+#21673 := (or #21645 #21670)
+#21677 := (iff #21673 #21676)
+#21678 := [rewrite]: #21677
+#21674 := (iff #9754 #21673)
+#21671 := (iff #9740 #21670)
+#21672 := [rewrite]: #21671
+#21654 := (iff #9718 #21645)
+#21646 := (not #21645)
+#21649 := (not #21646)
+#21652 := (iff #21649 #21645)
+#21653 := [rewrite]: #21652
+#21650 := (iff #9718 #21649)
+#21647 := (iff #9713 #21646)
+#21648 := [rewrite]: #21647
+#21651 := [monotonicity #21648]: #21650
+#21655 := [trans #21651 #21653]: #21654
+#21675 := [monotonicity #21655 #21672]: #21674
+#21680 := [trans #21675 #21678]: #21679
+#21683 := [quant-intro #21680]: #21682
+#17775 := (~ #9757 #9757)
+#17773 := (~ #9754 #9754)
+#17774 := [refl]: #17773
+#17776 := [nnf-pos #17774]: #17775
#2143 := (= #2142 f1)
#2144 := (not #2143)
#2141 := (= #2140 f1)
@@ -5624,476 +4429,242 @@
#2130 := (and #2126 #2129)
#2146 := (implies #2130 #2145)
#2147 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #2146)
-#9724 := (iff #2147 #9721)
-#9645 := (and #1478 #9639)
-#9650 := (and #4084 #9645)
-#9653 := (and #9636 #9650)
-#9659 := (not #9653)
-#9710 := (or #9659 #9704)
-#9715 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9710)
-#9722 := (iff #9715 #9721)
-#9719 := (iff #9710 #9718)
-#9683 := (iff #9659 #9682)
-#9680 := (iff #9653 #9677)
-#7901 := (and #4448 #7898)
-#9668 := (and #7901 #9639)
-#9671 := (and #4084 #9668)
-#9674 := (and #9636 #9671)
-#9678 := (iff #9674 #9677)
-#9679 := [rewrite]: #9678
-#9675 := (iff #9653 #9674)
-#9672 := (iff #9650 #9671)
-#9669 := (iff #9645 #9668)
-#7902 := (iff #1478 #7901)
-#7899 := (iff #1477 #7898)
-#7900 := [rewrite]: #7899
-#4447 := (iff #440 #4448)
-#4449 := [rewrite]: #4447
-#7903 := [monotonicity #4449 #7900]: #7902
-#9670 := [monotonicity #7903]: #9669
-#9673 := [monotonicity #9670]: #9672
-#9676 := [monotonicity #9673]: #9675
-#9681 := [trans #9676 #9679]: #9680
-#9684 := [monotonicity #9681]: #9683
-#9720 := [monotonicity #9684]: #9719
-#9723 := [quant-intro #9720]: #9722
-#9716 := (iff #2147 #9715)
-#9713 := (iff #2146 #9710)
-#9707 := (implies #9653 #9704)
-#9711 := (iff #9707 #9710)
-#9712 := [rewrite]: #9711
-#9708 := (iff #2146 #9707)
-#9705 := (iff #2145 #9704)
-#9702 := (iff #2144 #9701)
-#9699 := (iff #2143 #9698)
-#9700 := [rewrite]: #9699
-#9703 := [monotonicity #9700]: #9702
-#9696 := (iff #2141 #9695)
-#9697 := [rewrite]: #9696
-#9706 := [monotonicity #9697 #9703]: #9705
-#9654 := (iff #2130 #9653)
-#9651 := (iff #2129 #9650)
-#9648 := (iff #2128 #9645)
-#9642 := (and #9639 #1478)
-#9646 := (iff #9642 #9645)
-#9647 := [rewrite]: #9646
-#9643 := (iff #2128 #9642)
-#9640 := (iff #2127 #9639)
-#9641 := [rewrite]: #9640
-#9644 := [monotonicity #9641]: #9643
-#9649 := [trans #9644 #9647]: #9648
+#9760 := (iff #2147 #9757)
+#9681 := (and #1478 #9675)
+#9686 := (and #4084 #9681)
+#9689 := (and #9672 #9686)
+#9695 := (not #9689)
+#9746 := (or #9695 #9740)
+#9751 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9746)
+#9758 := (iff #9751 #9757)
+#9755 := (iff #9746 #9754)
+#9719 := (iff #9695 #9718)
+#9716 := (iff #9689 #9713)
+#7937 := (and #4468 #7934)
+#9704 := (and #7937 #9675)
+#9707 := (and #4084 #9704)
+#9710 := (and #9672 #9707)
+#9714 := (iff #9710 #9713)
+#9715 := [rewrite]: #9714
+#9711 := (iff #9689 #9710)
+#9708 := (iff #9686 #9707)
+#9705 := (iff #9681 #9704)
+#7938 := (iff #1478 #7937)
+#7935 := (iff #1477 #7934)
+#7936 := [rewrite]: #7935
+#4467 := (iff #440 #4468)
+#4469 := [rewrite]: #4467
+#7939 := [monotonicity #4469 #7936]: #7938
+#9706 := [monotonicity #7939]: #9705
+#9709 := [monotonicity #9706]: #9708
+#9712 := [monotonicity #9709]: #9711
+#9717 := [trans #9712 #9715]: #9716
+#9720 := [monotonicity #9717]: #9719
+#9756 := [monotonicity #9720]: #9755
+#9759 := [quant-intro #9756]: #9758
+#9752 := (iff #2147 #9751)
+#9749 := (iff #2146 #9746)
+#9743 := (implies #9689 #9740)
+#9747 := (iff #9743 #9746)
+#9748 := [rewrite]: #9747
+#9744 := (iff #2146 #9743)
+#9741 := (iff #2145 #9740)
+#9738 := (iff #2144 #9737)
+#9735 := (iff #2143 #9734)
+#9736 := [rewrite]: #9735
+#9739 := [monotonicity #9736]: #9738
+#9732 := (iff #2141 #9731)
+#9733 := [rewrite]: #9732
+#9742 := [monotonicity #9733 #9739]: #9741
+#9690 := (iff #2130 #9689)
+#9687 := (iff #2129 #9686)
+#9684 := (iff #2128 #9681)
+#9678 := (and #9675 #1478)
+#9682 := (iff #9678 #9681)
+#9683 := [rewrite]: #9682
+#9679 := (iff #2128 #9678)
+#9676 := (iff #2127 #9675)
+#9677 := [rewrite]: #9676
+#9680 := [monotonicity #9677]: #9679
+#9685 := [trans #9680 #9683]: #9684
#4085 := (iff #280 #4084)
#4086 := [rewrite]: #4085
-#9652 := [monotonicity #4086 #9649]: #9651
-#9637 := (iff #2126 #9636)
-#9638 := [rewrite]: #9637
-#9655 := [monotonicity #9638 #9652]: #9654
-#9709 := [monotonicity #9655 #9706]: #9708
-#9714 := [trans #9709 #9712]: #9713
-#9717 := [quant-intro #9714]: #9716
-#9725 := [trans #9717 #9723]: #9724
-#9694 := [asserted]: #2147
-#9726 := [mp #9694 #9725]: #9721
-#17741 := [mp~ #9726 #17740]: #9721
-#21648 := [mp #17741 #21647]: #21645
-#27193 := (not #27192)
-#27212 := (not #21645)
-#27669 := (or #27212 #24810 #27139 #27193 #27196 #27201)
-#27189 := (or #27188 #27185)
-#27190 := (not #27189)
-#27123 := (+ 0::Int #27122)
-#27124 := (>= #27123 0::Int)
-#27125 := (>= 0::Int 0::Int)
-#27126 := (not #27125)
-#27197 := (or #27196 #27126 #27124 #24810 #27193 #27190)
-#27664 := (or #27212 #27197)
-#27712 := (iff #27664 #27669)
-#27207 := (or #24810 #27139 #27193 #27196 #27201)
-#27671 := (or #27212 #27207)
-#27674 := (iff #27671 #27669)
-#27711 := [rewrite]: #27674
-#27672 := (iff #27664 #27671)
-#27210 := (iff #27197 #27207)
-#27204 := (or #27196 false #27139 #24810 #27193 #27201)
-#27208 := (iff #27204 #27207)
-#27209 := [rewrite]: #27208
-#27205 := (iff #27197 #27204)
-#27202 := (iff #27190 #27201)
-#27199 := (iff #27189 #27198)
-#27200 := [rewrite]: #27199
-#27203 := [monotonicity #27200]: #27202
-#27142 := (iff #27124 #27139)
-#27136 := (>= #27122 0::Int)
-#27140 := (iff #27136 #27139)
-#27141 := [rewrite]: #27140
-#27137 := (iff #27124 #27136)
-#27134 := (= #27123 #27122)
-#27135 := [rewrite]: #27134
-#27138 := [monotonicity #27135]: #27137
-#27143 := [trans #27138 #27141]: #27142
-#27132 := (iff #27126 false)
-#27130 := (iff #27126 #3156)
-#27128 := (iff #27125 true)
-#27129 := [rewrite]: #27128
-#27131 := [monotonicity #27129]: #27130
-#27133 := [trans #27131 #12221]: #27132
-#27206 := [monotonicity #27133 #27143 #27203]: #27205
-#27211 := [trans #27206 #27209]: #27210
-#27673 := [monotonicity #27211]: #27672
-#27713 := [trans #27673 #27711]: #27712
-#27670 := [quant-inst #3039 #3043 #26146 #24962 #161 #24960]: #27664
-#27714 := [mp #27670 #27713]: #27669
-#28373 := [unit-resolution #27714 #21648 #14315 #28356 #28130]: #28357
-#28352 := [unit-resolution #28373 #28528]: #27201
-#27717 := (or #27198 #27187)
-#27718 := [def-axiom]: #27717
-#28371 := [unit-resolution #27718 #28352 #28112]: false
-#28372 := [lemma #28371]: #12147
-#24789 := (or #23557 #18409 #18412 #23551)
-#24790 := [def-axiom]: #24789
-#29169 := [unit-resolution #24790 #28372 #27593 #29168]: #23551
-#24779 := (or #23548 #23542)
-#24780 := [def-axiom]: #24779
-#29170 := [unit-resolution #24780 #29169]: #23542
-decl f147 :: (-> S29 S20)
-#28602 := (f69 #3220 #27044)
-#28603 := (f147 #28602)
-#28607 := (f36 f298 #28603)
-#28608 := (= f37 #28607)
-decl f222 :: (-> S19 S20 S1)
-#28605 := (f222 f298 #28603)
-#28606 := (= f1 #28605)
-#28756 := (or #28606 #28608)
-#28740 := (not #28756)
-#28634 := (f148 #28602)
-#28635 := (= f1 #28634)
-#28636 := (not #28635)
-#28631 := (f38 f298 #28603)
-#28632 := (= f1 #28631)
-#28633 := (not #28632)
-#28750 := (or #28633 #28636)
-#28753 := (not #28750)
-#28639 := (f23 #27233)
-#28647 := (= f25 #28639)
-#28726 := (not #28647)
-#28619 := (f24 #28603)
-#28629 := (f23 #28619)
-#28630 := (= f25 #28629)
-#28745 := (or #28630 #28726 #28753 #28740)
-#28793 := (not #28745)
-#28624 := (f36 f298 #27044)
-#28625 := (= f37 #28624)
-#28623 := (f222 f298 #27044)
-#28616 := (= f1 #28623)
-#28595 := (or #28616 #28625)
-#28597 := (not #28595)
-#28706 := (or #28597 #28647)
-#28704 := (not #28706)
-#28796 := (or #28704 #28793)
-#28779 := (not #28796)
-#28643 := (f35 f298 #27044)
-#28644 := (= f1 #28643)
-#27803 := (= #3101 #28643)
-#27432 := (= #28643 #3101)
-#27430 := (= #27044 #3098)
-#27425 := (= #27028 #3098)
-#27426 := [symm #27571]: #27425
-#27382 := (= #27044 #27028)
-#27383 := [symm #27568]: #27382
-#27431 := [trans #27383 #27426]: #27430
-#27742 := [monotonicity #27431]: #27432
-#28586 := [symm #27742]: #27803
-#28587 := [trans #28372 #28586]: #28644
-#28649 := (not #28644)
-#28782 := (or #28649 #28779)
-#28784 := (not #28782)
-#28652 := (f79 f298 #27044)
-#28648 := (= f1 #28652)
-#28787 := (iff #28648 #28784)
-#2438 := (f79 #86 #62)
-#2439 := (pattern #2438)
-#324 := (f70 #86)
-#2441 := (f69 #324 #62)
-#2445 := (f147 #2441)
-#2456 := (f222 #86 #2445)
-#10660 := (= f1 #2456)
-#2454 := (f36 #86 #2445)
-#10657 := (= f37 #2454)
-#10663 := (or #10657 #10660)
-#22034 := (not #10663)
-#2450 := (f24 #2445)
-#2451 := (f23 #2450)
-#10651 := (= f25 #2451)
-#2446 := (f38 #86 #2445)
-#10642 := (= f1 #2446)
-#10645 := (not #10642)
-#2442 := (f148 #2441)
-#10636 := (= f1 #2442)
-#10639 := (not #10636)
-#10648 := (or #10639 #10645)
-#22033 := (not #10648)
-#22035 := (or #91 #22033 #10651 #22034)
-#22036 := (not #22035)
-#2462 := (f222 #86 #62)
-#10675 := (= f1 #2462)
-#10678 := (or #3761 #10675)
-#22028 := (not #10678)
-#22029 := (or #68 #22028)
-#22030 := (not #22029)
-#22039 := (or #22030 #22036)
-#22045 := (not #22039)
-#22046 := (or #11261 #22045)
-#22047 := (not #22046)
-#10632 := (= f1 #2438)
-#22052 := (iff #10632 #22047)
-#22055 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22052)
-#10654 := (not #10651)
-#10696 := (and #68 #10648 #10654 #10663)
-#10681 := (and #91 #10678)
-#10702 := (or #10681 #10696)
-#10707 := (and #3767 #10702)
-#10710 := (iff #10632 #10707)
-#10713 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10710)
-#22056 := (iff #10713 #22055)
-#22053 := (iff #10710 #22052)
-#22050 := (iff #10707 #22047)
-#22042 := (and #3767 #22039)
-#22048 := (iff #22042 #22047)
-#22049 := [rewrite]: #22048
-#22043 := (iff #10707 #22042)
-#22040 := (iff #10702 #22039)
-#22037 := (iff #10696 #22036)
-#22038 := [rewrite]: #22037
-#22031 := (iff #10681 #22030)
-#22032 := [rewrite]: #22031
-#22041 := [monotonicity #22032 #22038]: #22040
-#22044 := [monotonicity #22041]: #22043
-#22051 := [trans #22044 #22049]: #22050
-#22054 := [monotonicity #22051]: #22053
-#22057 := [quant-intro #22054]: #22056
-#17978 := (~ #10713 #10713)
-#17976 := (~ #10710 #10710)
-#17977 := [refl]: #17976
-#17979 := [nnf-pos #17977]: #17978
-#2463 := (= #2462 f1)
-#2464 := (or #183 #2463)
-#2465 := (and #91 #2464)
-#2457 := (= #2456 f1)
-#2455 := (= #2454 f37)
-#2458 := (or #2455 #2457)
-#2452 := (= #2451 f25)
-#2453 := (not #2452)
-#2459 := (and #2453 #2458)
-#2447 := (= #2446 f1)
-#2448 := (not #2447)
-#2443 := (= #2442 f1)
-#2444 := (not #2443)
-#2449 := (or #2444 #2448)
-#2460 := (and #2449 #2459)
-#2461 := (and #68 #2460)
-#2466 := (or #2461 #2465)
-#2467 := (and #187 #2466)
-#2440 := (= #2438 f1)
-#2468 := (iff #2440 #2467)
-#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468)
-#10716 := (iff #2469 #10713)
-#10666 := (and #10654 #10663)
-#10669 := (and #10648 #10666)
-#10672 := (and #68 #10669)
-#10684 := (or #10672 #10681)
-#10687 := (and #3767 #10684)
-#10690 := (iff #10632 #10687)
-#10693 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10690)
-#10714 := (iff #10693 #10713)
-#10711 := (iff #10690 #10710)
-#10708 := (iff #10687 #10707)
-#10705 := (iff #10684 #10702)
-#10699 := (or #10696 #10681)
-#10703 := (iff #10699 #10702)
-#10704 := [rewrite]: #10703
-#10700 := (iff #10684 #10699)
-#10697 := (iff #10672 #10696)
-#10698 := [rewrite]: #10697
-#10701 := [monotonicity #10698]: #10700
-#10706 := [trans #10701 #10704]: #10705
-#10709 := [monotonicity #10706]: #10708
-#10712 := [monotonicity #10709]: #10711
-#10715 := [quant-intro #10712]: #10714
-#10694 := (iff #2469 #10693)
-#10691 := (iff #2468 #10690)
-#10688 := (iff #2467 #10687)
-#10685 := (iff #2466 #10684)
-#10682 := (iff #2465 #10681)
-#10679 := (iff #2464 #10678)
-#10676 := (iff #2463 #10675)
-#10677 := [rewrite]: #10676
-#10680 := [monotonicity #3763 #10677]: #10679
-#10683 := [monotonicity #10680]: #10682
-#10673 := (iff #2461 #10672)
-#10670 := (iff #2460 #10669)
-#10667 := (iff #2459 #10666)
-#10664 := (iff #2458 #10663)
-#10661 := (iff #2457 #10660)
-#10662 := [rewrite]: #10661
-#10658 := (iff #2455 #10657)
-#10659 := [rewrite]: #10658
-#10665 := [monotonicity #10659 #10662]: #10664
-#10655 := (iff #2453 #10654)
-#10652 := (iff #2452 #10651)
-#10653 := [rewrite]: #10652
-#10656 := [monotonicity #10653]: #10655
-#10668 := [monotonicity #10656 #10665]: #10667
-#10649 := (iff #2449 #10648)
-#10646 := (iff #2448 #10645)
-#10643 := (iff #2447 #10642)
-#10644 := [rewrite]: #10643
-#10647 := [monotonicity #10644]: #10646
-#10640 := (iff #2444 #10639)
-#10637 := (iff #2443 #10636)
-#10638 := [rewrite]: #10637
-#10641 := [monotonicity #10638]: #10640
-#10650 := [monotonicity #10641 #10647]: #10649
-#10671 := [monotonicity #10650 #10668]: #10670
-#10674 := [monotonicity #10671]: #10673
-#10686 := [monotonicity #10674 #10683]: #10685
-#10689 := [monotonicity #3769 #10686]: #10688
-#10634 := (iff #2440 #10632)
-#10635 := [rewrite]: #10634
-#10692 := [monotonicity #10635 #10689]: #10691
-#10695 := [quant-intro #10692]: #10694
-#10717 := [trans #10695 #10715]: #10716
-#10631 := [asserted]: #2469
-#10718 := [mp #10631 #10717]: #10713
-#17980 := [mp~ #10718 #17979]: #10713
-#22058 := [mp #17980 #22057]: #22055
-#28805 := (not #22055)
-#28806 := (or #28805 #28787)
-#28609 := (or #28608 #28606)
-#28618 := (not #28609)
-#28637 := (or #28636 #28633)
-#28638 := (not #28637)
-#28617 := (= #28639 f25)
-#28620 := (not #28617)
-#28621 := (or #28620 #28638 #28630 #28618)
-#28622 := (not #28621)
-#28626 := (or #28625 #28616)
-#28627 := (not #28626)
-#28628 := (or #28617 #28627)
-#28640 := (not #28628)
-#28641 := (or #28640 #28622)
-#28642 := (not #28641)
-#28650 := (or #28649 #28642)
-#28651 := (not #28650)
-#28653 := (iff #28648 #28651)
-#28804 := (or #28805 #28653)
-#28808 := (iff #28804 #28806)
-#28826 := (iff #28806 #28806)
-#28827 := [rewrite]: #28826
-#28788 := (iff #28653 #28787)
-#28785 := (iff #28651 #28784)
-#28783 := (iff #28650 #28782)
-#28780 := (iff #28642 #28779)
-#28797 := (iff #28641 #28796)
-#28794 := (iff #28622 #28793)
-#28791 := (iff #28621 #28745)
-#28742 := (or #28726 #28753 #28630 #28740)
-#28746 := (iff #28742 #28745)
-#28747 := [rewrite]: #28746
-#28743 := (iff #28621 #28742)
-#28741 := (iff #28618 #28740)
-#28757 := (iff #28609 #28756)
-#28758 := [rewrite]: #28757
-#28739 := [monotonicity #28758]: #28741
-#28754 := (iff #28638 #28753)
-#28751 := (iff #28637 #28750)
-#28752 := [rewrite]: #28751
-#28755 := [monotonicity #28752]: #28754
-#28748 := (iff #28620 #28726)
-#28654 := (iff #28617 #28647)
-#28593 := [rewrite]: #28654
-#28749 := [monotonicity #28593]: #28748
-#28744 := [monotonicity #28749 #28755 #28739]: #28743
-#28792 := [trans #28744 #28747]: #28791
-#28795 := [monotonicity #28792]: #28794
-#28724 := (iff #28640 #28704)
-#28711 := (iff #28628 #28706)
-#28479 := (or #28647 #28597)
-#28707 := (iff #28479 #28706)
-#28710 := [rewrite]: #28707
-#28480 := (iff #28628 #28479)
-#28598 := (iff #28627 #28597)
-#28596 := (iff #28626 #28595)
-#28594 := [rewrite]: #28596
-#28468 := [monotonicity #28594]: #28598
-#28469 := [monotonicity #28593 #28468]: #28480
-#28703 := [trans #28469 #28710]: #28711
-#28725 := [monotonicity #28703]: #28724
-#28777 := [monotonicity #28725 #28795]: #28797
-#28781 := [monotonicity #28777]: #28780
-#28778 := [monotonicity #28781]: #28783
-#28786 := [monotonicity #28778]: #28785
-#28803 := [monotonicity #28786]: #28788
-#28809 := [monotonicity #28803]: #28808
-#28828 := [trans #28809 #28827]: #28808
-#28807 := [quant-inst #3039 #27044]: #28804
-#28829 := [mp #28807 #28828]: #28806
-#28588 := [unit-resolution #28829 #22058]: #28787
-#27354 := (not #28648)
-#28886 := (iff #18418 #27354)
-#28899 := (iff #12153 #28648)
-#28789 := (iff #28648 #12153)
-#28590 := (= #28652 #3104)
-#28591 := [monotonicity #27431]: #28590
-#28790 := [monotonicity #28591]: #28789
-#28900 := [symm #28790]: #28899
-#28887 := [monotonicity #28900]: #28886
-#28589 := [hypothesis]: #18418
-#28906 := [mp #28589 #28887]: #27354
-#27264 := (not #28787)
-#27352 := (or #27264 #28648 #28782)
-#27353 := [def-axiom]: #27352
-#28907 := [unit-resolution #27353 #28906 #28588]: #28782
-#27262 := (or #28784 #28649 #28779)
-#27263 := [def-axiom]: #27262
-#28908 := [unit-resolution #27263 #28907 #28587]: #28779
-#28841 := (not #28630)
-#29014 := (iff #12082 #28841)
-#29012 := (iff #12079 #28630)
-#29010 := (iff #28630 #12079)
-#29008 := (= #28629 #3053)
-#29006 := (= #28619 #3040)
-#29004 := (= #28619 #25081)
-#29002 := (= #28603 #3044)
-#29000 := (= #28603 #27103)
-#27104 := (f77 #27103 0::Int #24960)
-#27108 := (f69 #3220 #27104)
-#27114 := (f147 #27108)
-#28998 := (= #27114 #27103)
-#27115 := (= #27103 #27114)
-#27116 := (not #27115)
-#27112 := (f148 #27108)
-#27113 := (= f1 #27112)
-decl f78 :: (-> S29 S1)
-#27109 := (f78 #27108)
-#27110 := (= f1 #27109)
-#27111 := (not #27110)
-#27105 := (f35 f298 #27104)
-#27106 := (= f1 #27105)
-#27107 := (not #27106)
-#27144 := (or #27107 #27111 #27113 #27116)
-#27147 := (not #27144)
-#27119 := (f35 f298 #27103)
-#27120 := (= f1 #27119)
-#28912 := (= #3051 #27119)
-#28909 := (= #27119 #3051)
-#28910 := [monotonicity #28364]: #28909
-#28913 := [symm #28910]: #28912
-#28914 := [trans #14332 #28913]: #27120
-#27121 := (not #27120)
-#28915 := (or #27121 #27147)
+#9688 := [monotonicity #4086 #9685]: #9687
+#9673 := (iff #2126 #9672)
+#9674 := [rewrite]: #9673
+#9691 := [monotonicity #9674 #9688]: #9690
+#9745 := [monotonicity #9691 #9742]: #9744
+#9750 := [trans #9745 #9748]: #9749
+#9753 := [quant-intro #9750]: #9752
+#9761 := [trans #9753 #9759]: #9760
+#9730 := [asserted]: #2147
+#9762 := [mp #9730 #9761]: #9757
+#17777 := [mp~ #9762 #17776]: #9757
+#21684 := [mp #17777 #21683]: #21681
+#27254 := (not #21681)
+#27453 := (or #27254 #24846 #27181 #27235 #27238 #27243)
+#27231 := (or #27230 #27227)
+#27232 := (not #27231)
+#27165 := (+ 0::Int #27164)
+#27166 := (>= #27165 0::Int)
+#27167 := (>= 0::Int 0::Int)
+#27168 := (not #27167)
+#27239 := (or #27238 #27168 #27166 #24846 #27235 #27232)
+#27454 := (or #27254 #27239)
+#27466 := (iff #27454 #27453)
+#27249 := (or #24846 #27181 #27235 #27238 #27243)
+#27459 := (or #27254 #27249)
+#27464 := (iff #27459 #27453)
+#27465 := [rewrite]: #27464
+#27460 := (iff #27454 #27459)
+#27252 := (iff #27239 #27249)
+#27246 := (or #27238 false #27181 #24846 #27235 #27243)
+#27250 := (iff #27246 #27249)
+#27251 := [rewrite]: #27250
+#27247 := (iff #27239 #27246)
+#27244 := (iff #27232 #27243)
+#27241 := (iff #27231 #27240)
+#27242 := [rewrite]: #27241
+#27245 := [monotonicity #27242]: #27244
+#27184 := (iff #27166 #27181)
+#27178 := (>= #27164 0::Int)
+#27182 := (iff #27178 #27181)
+#27183 := [rewrite]: #27182
+#27179 := (iff #27166 #27178)
+#27176 := (= #27165 #27164)
+#27177 := [rewrite]: #27176
+#27180 := [monotonicity #27177]: #27179
+#27185 := [trans #27180 #27183]: #27184
+#27174 := (iff #27168 false)
+#27172 := (iff #27168 #3156)
+#27170 := (iff #27167 true)
+#27171 := [rewrite]: #27170
+#27173 := [monotonicity #27171]: #27172
+#27175 := [trans #27173 #12257]: #27174
+#27248 := [monotonicity #27175 #27185 #27245]: #27247
+#27253 := [trans #27248 #27251]: #27252
+#27461 := [monotonicity #27253]: #27460
+#27492 := [trans #27461 #27465]: #27466
+#27455 := [quant-inst #3039 #3043 #26182 #24998 #161 #24996]: #27454
+#27493 := [mp #27455 #27492]: #27453
+#27518 := [unit-resolution #27493 #21684 #14351 #27516 #28427]: #27517
+#27519 := [unit-resolution #27518 #28426]: #27243
+#27497 := (or #27240 #27229)
+#27482 := [def-axiom]: #27497
+#27520 := [unit-resolution #27482 #27519 #27512]: false
+#27548 := [lemma #27520]: #27547
+#28798 := [unit-resolution #27548 #28797]: #12183
+#28623 := (or #28377 #18448 #28443)
+#28624 := [def-axiom]: #28623
+#28817 := [unit-resolution #28624 #28798]: #28816
+#28818 := [unit-resolution #28817 #28780]: #28443
+#28615 := (or #28440 #28345)
+#28616 := [def-axiom]: #28615
+#28819 := [unit-resolution #28616 #28818]: #28345
+#28592 := (not #27227)
+#28835 := (iff #28592 #28148)
+#28832 := (iff #27227 #28147)
+#28814 := (= #27226 #28146)
+#28824 := (= #27225 #26985)
+#28825 := [monotonicity #27481]: #28824
+#28815 := [monotonicity #28825]: #28814
+#28834 := [monotonicity #28815]: #28832
+#28833 := [monotonicity #28834]: #28835
+#28821 := [unit-resolution #27493 #21684 #14351 #27516 #28797]: #27517
+#28822 := [unit-resolution #28821 #28426]: #27243
+#28593 := (or #27240 #28592)
+#28594 := [def-axiom]: #28593
+#28823 := [unit-resolution #28594 #28822]: #28592
+#28836 := [mp #28823 #28833]: #28148
+#28478 := (or #28326 #28147)
+#28484 := [def-axiom]: #28478
+#28837 := [unit-resolution #28484 #28836]: #28326
+#25501 := (f23 f19)
+#28366 := (= #25501 #27920)
+#27753 := (= #27920 #25501)
+#27686 := (= #27039 f19)
+#27684 := (= #25112 f19)
+#27685 := [symm #27139]: #27684
+#27369 := [hypothesis]: #27103
+#27370 := [unit-resolution #27749 #27369]: #27089
+#27416 := [trans #27409 #27370]: #27415
+#27681 := [trans #27416 #27414]: #27680
+#27683 := [monotonicity #27681]: #27682
+#27687 := [trans #27683 #27685]: #27686
+#27754 := [monotonicity #27687]: #27753
+#28467 := [symm #27754]: #28366
+#25502 := (= f25 #25501)
+#25509 := (iff #11624 #25502)
+#2363 := (pattern #279)
+#2902 := (f23 #275)
+#11803 := (= f25 #2902)
+#11807 := (iff #4084 #11803)
+#11810 := (forall (vars (?v0 S18)) (:pat #2363) #11807)
+#18402 := (~ #11810 #11810)
+#18400 := (~ #11807 #11807)
+#18401 := [refl]: #18400
+#18403 := [nnf-pos #18401]: #18402
+#2915 := (= #2902 f25)
+#2916 := (iff #280 #2915)
+#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916)
+#11811 := (iff #2917 #11810)
+#11808 := (iff #2916 #11807)
+#11805 := (iff #2915 #11803)
+#11806 := [rewrite]: #11805
+#11809 := [monotonicity #4086 #11806]: #11808
+#11812 := [quant-intro #11809]: #11811
+#11802 := [asserted]: #2917
+#11815 := [mp #11802 #11812]: #11810
+#18404 := [mp~ #11815 #18403]: #11810
+#25168 := (not #11810)
+#25512 := (or #25168 #25509)
+#25513 := [quant-inst #50]: #25512
+#28838 := [unit-resolution #25513 #18404]: #25509
+#25514 := (not #25509)
+#28839 := (or #25514 #25502)
+#25518 := (not #11624)
+#25519 := (or #25514 #25518 #25502)
+#25520 := [def-axiom]: #25519
+#28840 := [unit-resolution #25520 #11630]: #28839
+#28841 := [unit-resolution #28840 #28838]: #25502
+#28468 := [trans #28841 #28467]: #28266
+#28602 := (not #28097)
+#28934 := (iff #12118 #28602)
+#28932 := (iff #12115 #28097)
+#28930 := (iff #28097 #12115)
+#28928 := (= #28096 #3053)
+#28926 := (= #28095 #3040)
+#28924 := (= #28095 #25117)
+#28922 := (= #27775 #3044)
+#28920 := (= #27775 #27145)
+#27146 := (f77 #27145 0::Int #24996)
+#27150 := (f69 #3220 #27146)
+#27156 := (f146 #27150)
+#28918 := (= #27156 #27145)
+#27157 := (= #27145 #27156)
+#27158 := (not #27157)
+#27154 := (f147 #27150)
+#27155 := (= f1 #27154)
+#27151 := (f78 #27150)
+#27152 := (= f1 #27151)
+#27153 := (not #27152)
+#27147 := (f35 f297 #27146)
+#27148 := (= f1 #27147)
+#27149 := (not #27148)
+#27186 := (or #27149 #27153 #27155 #27158)
+#27189 := (not #27186)
+#27161 := (f35 f297 #27145)
+#27162 := (= f1 #27161)
+#28492 := (= #3051 #27161)
+#28489 := (= #27161 #3051)
+#28490 := [monotonicity #28789]: #28489
+#28872 := [symm #28490]: #28492
+#28873 := [trans #14368 #28872]: #27162
+#27163 := (not #27162)
+#28859 := (or #27163 #27189)
#319 := (:var 3 Int)
#353 := (:var 2 S18)
-#1513 := (f136 #353 #289)
+#1513 := (f135 #353 #289)
#1514 := (f54 #1513 #319)
#1510 := (f54 #353 #319)
#1511 := (f77 #1510 #202 #353)
@@ -6106,60 +4677,60 @@
#1515 := (pattern #1512 #1514)
#1521 := (f77 #1514 #202 #353)
#1530 := (f35 #74 #1521)
-#8059 := (= f1 #1530)
-#20972 := (not #8059)
+#8095 := (= f1 #1530)
+#21008 := (not #8095)
#1522 := (f69 #1516 #1521)
#1528 := (f78 #1522)
-#8056 := (= f1 #1528)
-#20971 := (not #8056)
-#1525 := (f148 #1522)
-#8050 := (= f1 #1525)
-#1523 := (f147 #1522)
-#8047 := (= #1514 #1523)
-#20970 := (not #8047)
-#20973 := (or #20970 #8050 #20971 #20972)
-#20974 := (not #20973)
+#8092 := (= f1 #1528)
+#21007 := (not #8092)
+#1525 := (f147 #1522)
+#8086 := (= f1 #1525)
+#1523 := (f146 #1522)
+#8083 := (= #1514 #1523)
+#21006 := (not #8083)
+#21009 := (or #21006 #8086 #21007 #21008)
+#21010 := (not #21009)
#1519 := (f35 #74 #1514)
-#8044 := (= f1 #1519)
-#8082 := (not #8044)
-#5372 := (* -1::Int #289)
-#6249 := (+ #202 #5372)
-#6250 := (>= #6249 0::Int)
-#20980 := (or #5104 #6250 #8082 #20974)
-#20985 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #20980)
-#8053 := (not #8050)
-#8091 := (and #8047 #8053 #8056 #8059)
-#7743 := (not #6250)
-#7746 := (and #4202 #7743)
-#7749 := (not #7746)
-#8100 := (or #7749 #8082 #8091)
-#8105 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8100)
-#20986 := (iff #8105 #20985)
-#20983 := (iff #8100 #20980)
-#20855 := (or #5104 #6250)
-#20977 := (or #20855 #8082 #20974)
-#20981 := (iff #20977 #20980)
-#20982 := [rewrite]: #20981
-#20978 := (iff #8100 #20977)
-#20975 := (iff #8091 #20974)
-#20976 := [rewrite]: #20975
-#20864 := (iff #7749 #20855)
-#20856 := (not #20855)
-#20859 := (not #20856)
-#20862 := (iff #20859 #20855)
-#20863 := [rewrite]: #20862
-#20860 := (iff #7749 #20859)
-#20857 := (iff #7746 #20856)
-#20858 := [rewrite]: #20857
-#20861 := [monotonicity #20858]: #20860
-#20865 := [trans #20861 #20863]: #20864
-#20979 := [monotonicity #20865 #20976]: #20978
-#20984 := [trans #20979 #20982]: #20983
-#20987 := [quant-intro #20984]: #20986
-#17104 := (~ #8105 #8105)
-#17102 := (~ #8100 #8100)
-#17103 := [refl]: #17102
-#17105 := [nnf-pos #17103]: #17104
+#8080 := (= f1 #1519)
+#8118 := (not #8080)
+#5395 := (* -1::Int #289)
+#6275 := (+ #202 #5395)
+#6276 := (>= #6275 0::Int)
+#21016 := (or #5124 #6276 #8118 #21010)
+#21021 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #21016)
+#8089 := (not #8086)
+#8127 := (and #8083 #8089 #8092 #8095)
+#7779 := (not #6276)
+#7782 := (and #4202 #7779)
+#7785 := (not #7782)
+#8136 := (or #7785 #8118 #8127)
+#8141 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8136)
+#21022 := (iff #8141 #21021)
+#21019 := (iff #8136 #21016)
+#20891 := (or #5124 #6276)
+#21013 := (or #20891 #8118 #21010)
+#21017 := (iff #21013 #21016)
+#21018 := [rewrite]: #21017
+#21014 := (iff #8136 #21013)
+#21011 := (iff #8127 #21010)
+#21012 := [rewrite]: #21011
+#20900 := (iff #7785 #20891)
+#20892 := (not #20891)
+#20895 := (not #20892)
+#20898 := (iff #20895 #20891)
+#20899 := [rewrite]: #20898
+#20896 := (iff #7785 #20895)
+#20893 := (iff #7782 #20892)
+#20894 := [rewrite]: #20893
+#20897 := [monotonicity #20894]: #20896
+#20901 := [trans #20897 #20899]: #20900
+#21015 := [monotonicity #20901 #21012]: #21014
+#21020 := [trans #21015 #21018]: #21019
+#21023 := [quant-intro #21020]: #21022
+#17140 := (~ #8141 #8141)
+#17138 := (~ #8136 #8136)
+#17139 := [refl]: #17138
+#17141 := [nnf-pos #17139]: #17140
#1531 := (= #1530 f1)
#1529 := (= #1528 f1)
#1532 := (and #1529 #1531)
@@ -6174,1602 +4745,3060 @@
#1520 := (= #1519 f1)
#1536 := (implies #1520 #1535)
#1537 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #1536)
-#8108 := (iff #1537 #8105)
-#8062 := (and #8056 #8059)
-#8065 := (and #8053 #8062)
-#8068 := (and #8047 #8065)
-#7713 := (not #1415)
-#8074 := (or #7713 #8068)
-#8083 := (or #8082 #8074)
-#8088 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8083)
-#8106 := (iff #8088 #8105)
-#8103 := (iff #8083 #8100)
-#8094 := (or #7749 #8091)
-#8097 := (or #8082 #8094)
-#8101 := (iff #8097 #8100)
-#8102 := [rewrite]: #8101
-#8098 := (iff #8083 #8097)
-#8095 := (iff #8074 #8094)
-#8092 := (iff #8068 #8091)
-#8093 := [rewrite]: #8092
-#7750 := (iff #7713 #7749)
-#7747 := (iff #1415 #7746)
-#7744 := (iff #1414 #7743)
-#7745 := [rewrite]: #7744
-#7748 := [monotonicity #4201 #7745]: #7747
-#7751 := [monotonicity #7748]: #7750
-#8096 := [monotonicity #7751 #8093]: #8095
-#8099 := [monotonicity #8096]: #8098
-#8104 := [trans #8099 #8102]: #8103
-#8107 := [quant-intro #8104]: #8106
-#8089 := (iff #1537 #8088)
-#8086 := (iff #1536 #8083)
-#8079 := (implies #8044 #8074)
-#8084 := (iff #8079 #8083)
+#8144 := (iff #1537 #8141)
+#8098 := (and #8092 #8095)
+#8101 := (and #8089 #8098)
+#8104 := (and #8083 #8101)
+#7749 := (not #1415)
+#8110 := (or #7749 #8104)
+#8119 := (or #8118 #8110)
+#8124 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8119)
+#8142 := (iff #8124 #8141)
+#8139 := (iff #8119 #8136)
+#8130 := (or #7785 #8127)
+#8133 := (or #8118 #8130)
+#8137 := (iff #8133 #8136)
+#8138 := [rewrite]: #8137
+#8134 := (iff #8119 #8133)
+#8131 := (iff #8110 #8130)
+#8128 := (iff #8104 #8127)
+#8129 := [rewrite]: #8128
+#7786 := (iff #7749 #7785)
+#7783 := (iff #1415 #7782)
+#7780 := (iff #1414 #7779)
+#7781 := [rewrite]: #7780
+#7784 := [monotonicity #4201 #7781]: #7783
+#7787 := [monotonicity #7784]: #7786
+#8132 := [monotonicity #7787 #8129]: #8131
+#8135 := [monotonicity #8132]: #8134
+#8140 := [trans #8135 #8138]: #8139
+#8143 := [quant-intro #8140]: #8142
+#8125 := (iff #1537 #8124)
+#8122 := (iff #1536 #8119)
+#8115 := (implies #8080 #8110)
+#8120 := (iff #8115 #8119)
+#8121 := [rewrite]: #8120
+#8116 := (iff #1536 #8115)
+#8113 := (iff #1535 #8110)
+#8107 := (implies #1415 #8104)
+#8111 := (iff #8107 #8110)
+#8112 := [rewrite]: #8111
+#8108 := (iff #1535 #8107)
+#8105 := (iff #1534 #8104)
+#8102 := (iff #1533 #8101)
+#8099 := (iff #1532 #8098)
+#8096 := (iff #1531 #8095)
+#8097 := [rewrite]: #8096
+#8093 := (iff #1529 #8092)
+#8094 := [rewrite]: #8093
+#8100 := [monotonicity #8094 #8097]: #8099
+#8090 := (iff #1527 #8089)
+#8087 := (iff #1526 #8086)
+#8088 := [rewrite]: #8087
+#8091 := [monotonicity #8088]: #8090
+#8103 := [monotonicity #8091 #8100]: #8102
+#8084 := (iff #1524 #8083)
#8085 := [rewrite]: #8084
-#8080 := (iff #1536 #8079)
-#8077 := (iff #1535 #8074)
-#8071 := (implies #1415 #8068)
-#8075 := (iff #8071 #8074)
-#8076 := [rewrite]: #8075
-#8072 := (iff #1535 #8071)
-#8069 := (iff #1534 #8068)
-#8066 := (iff #1533 #8065)
-#8063 := (iff #1532 #8062)
-#8060 := (iff #1531 #8059)
-#8061 := [rewrite]: #8060
-#8057 := (iff #1529 #8056)
-#8058 := [rewrite]: #8057
-#8064 := [monotonicity #8058 #8061]: #8063
-#8054 := (iff #1527 #8053)
-#8051 := (iff #1526 #8050)
-#8052 := [rewrite]: #8051
-#8055 := [monotonicity #8052]: #8054
-#8067 := [monotonicity #8055 #8064]: #8066
-#8048 := (iff #1524 #8047)
-#8049 := [rewrite]: #8048
-#8070 := [monotonicity #8049 #8067]: #8069
-#8073 := [monotonicity #8070]: #8072
-#8078 := [trans #8073 #8076]: #8077
-#8045 := (iff #1520 #8044)
-#8046 := [rewrite]: #8045
-#8081 := [monotonicity #8046 #8078]: #8080
-#8087 := [trans #8081 #8085]: #8086
-#8090 := [quant-intro #8087]: #8089
-#8109 := [trans #8090 #8107]: #8108
-#8043 := [asserted]: #1537
-#8110 := [mp #8043 #8109]: #8105
-#17106 := [mp~ #8110 #17105]: #8105
-#20988 := [mp #17106 #20987]: #20985
-#27726 := (not #20985)
-#27734 := (or #27726 #27121 #27139 #27147)
-#27117 := (or #27116 #27113 #27111 #27107)
-#27118 := (not #27117)
-#27127 := (or #27126 #27124 #27121 #27118)
-#27725 := (or #27726 #27127)
-#28114 := (iff #27725 #27734)
-#27153 := (or #27121 #27139 #27147)
-#27733 := (or #27726 #27153)
-#27738 := (iff #27733 #27734)
-#27739 := [rewrite]: #27738
-#27736 := (iff #27725 #27733)
-#27156 := (iff #27127 #27153)
-#27150 := (or false #27139 #27121 #27147)
-#27154 := (iff #27150 #27153)
-#27155 := [rewrite]: #27154
-#27151 := (iff #27127 #27150)
-#27148 := (iff #27118 #27147)
-#27145 := (iff #27117 #27144)
-#27146 := [rewrite]: #27145
-#27149 := [monotonicity #27146]: #27148
-#27152 := [monotonicity #27133 #27143 #27149]: #27151
-#27157 := [trans #27152 #27155]: #27156
-#27737 := [monotonicity #27157]: #27736
-#28134 := [trans #27737 #27739]: #28114
-#27735 := [quant-inst #3039 #3043 #24960 #24962 #161]: #27725
-#27527 := [mp #27735 #28134]: #27734
-#28916 := [unit-resolution #27527 #20988 #28356]: #28915
-#28917 := [unit-resolution #28916 #28914]: #27147
-#28369 := (or #27144 #27115)
-#28110 := [def-axiom]: #28369
-#28918 := [unit-resolution #28110 #28917]: #27115
-#28999 := [symm #28918]: #28998
-#28996 := (= #28603 #27114)
-#28994 := (= #28602 #27108)
-#26949 := (f69 #3220 #3098)
-#28992 := (= #26949 #27108)
-#28990 := (= #27108 #26949)
-#28986 := (= #27104 #3098)
-#26957 := (f128 #3098)
-#26986 := (f54 #24960 #26957)
-#28980 := (= #26986 #3098)
-#26987 := (= #3098 #26986)
-#28920 := (= #3099 #26977)
-#28921 := [symm #27532]: #28920
-#28922 := [trans #27593 #28921]: #26978
-#26989 := (or #26985 #26987)
-#27469 := (or #26158 #26985 #26987)
-#26988 := (or #26987 #26985)
-#27470 := (or #26158 #26988)
-#27635 := (iff #27470 #27469)
-#27506 := (or #26158 #26989)
-#27519 := (iff #27506 #27469)
-#27632 := [rewrite]: #27519
-#27507 := (iff #27470 #27506)
-#26990 := (iff #26988 #26989)
-#26991 := [rewrite]: #26990
-#27518 := [monotonicity #26991]: #27507
-#27636 := [trans #27518 #27632]: #27635
-#27505 := [quant-inst #3098 #24960]: #27470
-#27637 := [mp #27505 #27636]: #27469
-#28923 := [unit-resolution #27637 #18248]: #26989
-#28924 := [unit-resolution #28923 #28922]: #26987
-#28981 := [symm #28924]: #28980
-#28984 := (= #27104 #26986)
-#27307 := (f128 #26146)
-#27314 := (+ #27033 #27307)
-#27317 := (f54 #24960 #27314)
-#28978 := (= #27317 #26986)
-#28972 := (= #27314 #26957)
-#28970 := (= #26957 #27314)
-#28573 := (* -1::Int #27307)
-#28580 := (+ #24844 #28573)
-#28581 := (<= #28580 0::Int)
-#28579 := (= #24844 #27307)
-#28925 := (= #27307 #24844)
-#28926 := [monotonicity #26872]: #28925
-#28927 := [symm #28926]: #28579
-#28928 := (not #28579)
-#28929 := (or #28928 #28581)
-#28930 := [th-lemma arith triangle-eq]: #28929
-#28931 := [unit-resolution #28930 #28927]: #28581
-#28582 := (>= #28580 0::Int)
-#28932 := (or #28928 #28582)
-#28933 := [th-lemma arith triangle-eq]: #28932
-#28934 := [unit-resolution #28933 #28927]: #28582
-#27237 := (f128 #27044)
-#27241 := (* -1::Int #27237)
-#28542 := (+ #26957 #27241)
-#28543 := (<= #28542 0::Int)
-#28541 := (= #26957 #27237)
-#28935 := (= #27237 #26957)
-#28936 := [monotonicity #27431]: #28935
-#28937 := [symm #28936]: #28541
-#28938 := (not #28541)
-#28939 := (or #28938 #28543)
-#28940 := [th-lemma arith triangle-eq]: #28939
-#28941 := [unit-resolution #28940 #28937]: #28543
-#28544 := (>= #28542 0::Int)
-#28942 := (or #28938 #28544)
-#28943 := [th-lemma arith triangle-eq]: #28942
-#28944 := [unit-resolution #28943 #28937]: #28544
-#27710 := (* -1::Int #27034)
-#27716 := (+ #24844 #27710)
-#27719 := (<= #27716 0::Int)
-#27715 := (= #24844 #27034)
-#28952 := (= #3043 #27034)
-#28950 := (= #27034 #3043)
-#28945 := (= #24797 #3042)
-#28946 := [symm #27569]: #28945
-#28951 := [monotonicity #28946]: #28950
-#28953 := [symm #28951]: #28952
-#28948 := (= #24844 #3043)
-#25087 := (= #3043 #24844)
-#25092 := (or #25034 #25087)
-#25093 := [quant-inst #3040 #3043]: #25092
-#28947 := [unit-resolution #25093 #23270]: #25087
-#28949 := [symm #28947]: #28948
-#28954 := [trans #28949 #28953]: #27715
-#28955 := (not #27715)
-#28956 := (or #28955 #27719)
-#28957 := [th-lemma arith triangle-eq]: #28956
-#28958 := [unit-resolution #28957 #28954]: #27719
-#27720 := (>= #27716 0::Int)
-#28959 := (or #28955 #27720)
-#28960 := [th-lemma arith triangle-eq]: #28959
-#28961 := [unit-resolution #28960 #28954]: #27720
-#27242 := (+ #27034 #27241)
-#27243 := (+ #27033 #27242)
-#28409 := (<= #27243 0::Int)
-#27244 := (= #27243 0::Int)
-#28127 := (or #25034 #27244)
-#27238 := (= #27041 #27237)
-#28359 := (or #25034 #27238)
-#28461 := (iff #28359 #28127)
-#28464 := (iff #28127 #28127)
-#28465 := [rewrite]: #28464
-#27245 := (iff #27238 #27244)
-#27246 := [rewrite]: #27245
-#28358 := [monotonicity #27246]: #28461
-#28466 := [trans #28358 #28465]: #28461
-#28463 := [quant-inst #24960 #27041]: #28359
-#28467 := [mp #28463 #28466]: #28127
-#28962 := [unit-resolution #28467 #23270]: #27244
-#28963 := (not #27244)
-#28964 := (or #28963 #28409)
-#28965 := [th-lemma arith triangle-eq]: #28964
-#28966 := [unit-resolution #28965 #28962]: #28409
-#28540 := (>= #27243 0::Int)
-#28967 := (or #28963 #28540)
-#28968 := [th-lemma arith triangle-eq]: #28967
-#28969 := [unit-resolution #28968 #28962]: #28540
-#28971 := [th-lemma arith eq-propagate -1 -1 -1 -1 1 1 1 1 #28969 #28966 #28961 #28958 #28944 #28941 #28934 #28931]: #28970
-#28973 := [symm #28971]: #28972
-#28979 := [monotonicity #28973]: #28978
-#28982 := (= #27104 #27317)
-#27303 := (f77 #26146 0::Int #24960)
-#27320 := (= #27303 #27317)
-#27323 := (not #27320)
-#27304 := (f150 #27303 #26146)
-#27305 := (= f1 #27304)
-#27306 := (not #27305)
-#27329 := (or #27306 #27323)
-#27334 := (not #27329)
-#28552 := (or #27451 #27334)
-#27308 := (+ #27307 #27033)
-#27309 := (f54 #24960 #27308)
-#27310 := (= #27303 #27309)
-#27311 := (not #27310)
-#27312 := (or #27311 #27306)
-#27313 := (not #27312)
-#28553 := (or #27451 #27313)
-#28555 := (iff #28553 #28552)
-#28568 := (iff #28552 #28552)
-#28569 := [rewrite]: #28568
-#27335 := (iff #27313 #27334)
-#27332 := (iff #27312 #27329)
-#27326 := (or #27323 #27306)
-#27330 := (iff #27326 #27329)
-#27331 := [rewrite]: #27330
-#27327 := (iff #27312 #27326)
-#27324 := (iff #27311 #27323)
-#27321 := (iff #27310 #27320)
-#27318 := (= #27309 #27317)
-#27315 := (= #27308 #27314)
-#27316 := [rewrite]: #27315
-#27319 := [monotonicity #27316]: #27318
-#27322 := [monotonicity #27319]: #27321
-#27325 := [monotonicity #27322]: #27324
-#27328 := [monotonicity #27325]: #27327
-#27333 := [trans #27328 #27331]: #27332
-#27336 := [monotonicity #27333]: #27335
-#28556 := [monotonicity #27336]: #28555
-#28570 := [trans #28556 #28569]: #28555
-#28554 := [quant-inst #26146 #161 #24960]: #28553
-#28571 := [mp #28554 #28570]: #28552
-#28974 := [unit-resolution #28571 #21204]: #27334
-#28576 := (or #27329 #27320)
-#28577 := [def-axiom]: #28576
-#28975 := [unit-resolution #28577 #28974]: #27320
-#28976 := (= #27104 #27303)
-#28977 := [monotonicity #28365]: #28976
-#28983 := [trans #28977 #28975]: #28982
-#28985 := [trans #28983 #28979]: #28984
-#28987 := [trans #28985 #28981]: #28986
-#28991 := [monotonicity #28987]: #28990
-#28993 := [symm #28991]: #28992
-#28988 := (= #28602 #26949)
-#28989 := [monotonicity #27431]: #28988
-#28995 := [trans #28989 #28993]: #28994
-#28997 := [monotonicity #28995]: #28996
-#29001 := [trans #28997 #28999]: #29000
-#29003 := [trans #29001 #28364]: #29002
-#29005 := [monotonicity #29003]: #29004
-#29007 := [trans #29005 #28878]: #29006
-#29009 := [monotonicity #29007]: #29008
-#29011 := [monotonicity #29009]: #29010
-#29013 := [symm #29011]: #29012
-#29015 := [monotonicity #29013]: #29014
-#29016 := [mp #14333 #29015]: #28841
-#29020 := (= #3047 #28607)
-#29017 := (= #28607 #3047)
-#29018 := [monotonicity #29003]: #29017
-#29021 := [symm #29018]: #29020
-#29022 := [trans #14330 #29021]: #28608
-#28848 := (not #28608)
-#28849 := (or #28756 #28848)
-#28850 := [def-axiom]: #28849
-#29023 := [unit-resolution #28850 #29022]: #28756
-#25465 := (f23 f19)
-#29036 := (= #25465 #28639)
-#29032 := (= #28639 #25465)
-#29030 := (= #27233 f19)
-#29028 := (= #27233 #24960)
-#29029 := [symm #27567]: #29028
-#29031 := [trans #29029 #28488]: #29030
-#29033 := [monotonicity #29031]: #29032
-#29037 := [symm #29033]: #29036
-#25466 := (= f25 #25465)
-#25473 := (iff #11588 #25466)
-#2363 := (pattern #279)
-#2902 := (f23 #275)
-#11767 := (= f25 #2902)
-#11771 := (iff #4084 #11767)
-#11774 := (forall (vars (?v0 S18)) (:pat #2363) #11771)
-#18366 := (~ #11774 #11774)
-#18364 := (~ #11771 #11771)
-#18365 := [refl]: #18364
-#18367 := [nnf-pos #18365]: #18366
-#2915 := (= #2902 f25)
-#2916 := (iff #280 #2915)
-#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916)
-#11775 := (iff #2917 #11774)
-#11772 := (iff #2916 #11771)
-#11769 := (iff #2915 #11767)
-#11770 := [rewrite]: #11769
-#11773 := [monotonicity #4086 #11770]: #11772
-#11776 := [quant-intro #11773]: #11775
-#11766 := [asserted]: #2917
-#11779 := [mp #11766 #11776]: #11774
-#18368 := [mp~ #11779 #18367]: #11774
-#25132 := (not #11774)
-#25476 := (or #25132 #25473)
-#25477 := [quant-inst #50]: #25476
-#29024 := [unit-resolution #25477 #18368]: #25473
-#25478 := (not #25473)
-#29025 := (or #25478 #25466)
-#25482 := (not #11588)
-#25483 := (or #25478 #25482 #25466)
-#25484 := [def-axiom]: #25483
-#29026 := [unit-resolution #25484 #11594]: #29025
-#29027 := [unit-resolution #29026 #29024]: #25466
-#29038 := [trans #29027 #29037]: #28647
-#28125 := (not #27185)
-#29056 := (iff #28125 #28636)
-#29054 := (iff #27185 #28635)
-#29052 := (iff #28635 #27185)
-#29050 := (= #28634 #27184)
-#29048 := (= #28602 #27183)
-#29046 := (= #26949 #27183)
-#29044 := (= #27183 #26949)
-#29045 := [monotonicity #28135]: #29044
-#29047 := [symm #29045]: #29046
-#29049 := [trans #28989 #29047]: #29048
-#29051 := [monotonicity #29049]: #29050
-#29053 := [monotonicity #29051]: #29052
-#29055 := [symm #29053]: #29054
-#29057 := [monotonicity #29055]: #29056
-#28141 := (or #27198 #28125)
-#28142 := [def-axiom]: #28141
-#29043 := [unit-resolution #28142 #28352]: #28125
-#29058 := [mp #29043 #29057]: #28636
-#28824 := (or #28750 #28635)
-#28825 := [def-axiom]: #28824
-#29059 := [unit-resolution #28825 #29058]: #28750
-#28866 := (or #28793 #28630 #28726 #28753 #28740)
-#28867 := [def-axiom]: #28866
-#29060 := [unit-resolution #28867 #29059 #29038 #29023 #29016]: #28793
-#27098 := (or #28796 #28745)
-#27099 := [def-axiom]: #27098
-#29061 := [unit-resolution #27099 #29060 #28908]: false
-#29062 := [lemma #29061]: #12153
-#24773 := (or #23545 #18409 #18418 #23539)
+#8106 := [monotonicity #8085 #8103]: #8105
+#8109 := [monotonicity #8106]: #8108
+#8114 := [trans #8109 #8112]: #8113
+#8081 := (iff #1520 #8080)
+#8082 := [rewrite]: #8081
+#8117 := [monotonicity #8082 #8114]: #8116
+#8123 := [trans #8117 #8121]: #8122
+#8126 := [quant-intro #8123]: #8125
+#8145 := [trans #8126 #8143]: #8144
+#8079 := [asserted]: #1537
+#8146 := [mp #8079 #8145]: #8141
+#17142 := [mp~ #8146 #17141]: #8141
+#21024 := [mp #17142 #21023]: #21021
+#28639 := (not #21021)
+#28640 := (or #28639 #27163 #27181 #27189)
+#27159 := (or #27158 #27155 #27153 #27149)
+#27160 := (not #27159)
+#27169 := (or #27168 #27166 #27163 #27160)
+#28641 := (or #28639 #27169)
+#28648 := (iff #28641 #28640)
+#27195 := (or #27163 #27181 #27189)
+#28643 := (or #28639 #27195)
+#28646 := (iff #28643 #28640)
+#28647 := [rewrite]: #28646
+#28644 := (iff #28641 #28643)
+#27198 := (iff #27169 #27195)
+#27192 := (or false #27181 #27163 #27189)
+#27196 := (iff #27192 #27195)
+#27197 := [rewrite]: #27196
+#27193 := (iff #27169 #27192)
+#27190 := (iff #27160 #27189)
+#27187 := (iff #27159 #27186)
+#27188 := [rewrite]: #27187
+#27191 := [monotonicity #27188]: #27190
+#27194 := [monotonicity #27175 #27185 #27191]: #27193
+#27199 := [trans #27194 #27197]: #27198
+#28645 := [monotonicity #27199]: #28644
+#28649 := [trans #28645 #28647]: #28648
+#28642 := [quant-inst #3039 #3043 #24996 #24998 #161]: #28641
+#28650 := [mp #28642 #28649]: #28640
+#28860 := [unit-resolution #28650 #21024 #27516]: #28859
+#28879 := [unit-resolution #28860 #28873]: #27189
+#28589 := (or #27186 #27157)
+#28587 := [def-axiom]: #28589
+#28880 := [unit-resolution #28587 #28879]: #27157
+#28919 := [symm #28880]: #28918
+#28916 := (= #27775 #27156)
+#28914 := (= #26985 #27150)
+#28912 := (= #27150 #26985)
+#28910 := (= #27146 #3098)
+#28900 := (= #27064 #3098)
+#28901 := [symm #27409]: #28900
+#28908 := (= #27146 #27064)
+#28898 := (= #27086 #27064)
+#28899 := [symm #27370]: #28898
+#28906 := (= #27146 #27086)
+#28896 := (= #3042 #27086)
+#28897 := [symm #27414]: #28896
+#28904 := (= #27146 #3042)
+#27318 := (f127 #26182)
+#27332 := (f54 #24996 #27318)
+#28894 := (= #27332 #3042)
+#28888 := (= #27318 f298)
+#28886 := (= #27318 #3043)
+#28884 := (= #24880 #3043)
+#25123 := (= #3043 #24880)
+#25128 := (or #25070 #25123)
+#25129 := [quant-inst #3040 #3043]: #25128
+#28881 := [unit-resolution #25129 #23306]: #25123
+#28885 := [symm #28881]: #28884
+#28882 := (= #27318 #24880)
+#28883 := [monotonicity #26940]: #28882
+#28887 := [trans #28883 #28885]: #28886
+#28889 := [trans #28887 #28391]: #28888
+#28895 := [monotonicity #28386 #28889]: #28894
+#28902 := (= #27146 #27332)
+#27314 := (f77 #26182 0::Int #24996)
+#27335 := (= #27314 #27332)
+#27338 := (not #27335)
+#27315 := (f149 #27314 #26182)
+#27316 := (= f1 #27315)
+#27317 := (not #27316)
+#27344 := (or #27317 #27338)
+#27349 := (not #27344)
+#28722 := (or #27721 #27349)
+#27319 := (+ #27318 #27069)
+#27320 := (f54 #24996 #27319)
+#27321 := (= #27314 #27320)
+#27322 := (not #27321)
+#27323 := (or #27322 #27317)
+#27324 := (not #27323)
+#28764 := (or #27721 #27324)
+#28766 := (iff #28764 #28722)
+#28768 := (iff #28722 #28722)
+#28769 := [rewrite]: #28768
+#27350 := (iff #27324 #27349)
+#27347 := (iff #27323 #27344)
+#27341 := (or #27338 #27317)
+#27345 := (iff #27341 #27344)
+#27346 := [rewrite]: #27345
+#27342 := (iff #27323 #27341)
+#27339 := (iff #27322 #27338)
+#27336 := (iff #27321 #27335)
+#27333 := (= #27320 #27332)
+#27330 := (= #27319 #27318)
+#27325 := (+ #27318 0::Int)
+#27328 := (= #27325 #27318)
+#27329 := [rewrite]: #27328
+#27326 := (= #27319 #27325)
+#27327 := [monotonicity #27078]: #27326
+#27331 := [trans #27327 #27329]: #27330
+#27334 := [monotonicity #27331]: #27333
+#27337 := [monotonicity #27334]: #27336
+#27340 := [monotonicity #27337]: #27339
+#27343 := [monotonicity #27340]: #27342
+#27348 := [trans #27343 #27346]: #27347
+#27351 := [monotonicity #27348]: #27350
+#28767 := [monotonicity #27351]: #28766
+#28770 := [trans #28767 #28769]: #28766
+#28765 := [quant-inst #26182 #161 #24996]: #28764
+#28752 := [mp #28765 #28770]: #28722
+#28890 := [unit-resolution #28752 #21240]: #27349
+#28756 := (or #27344 #27335)
+#28757 := [def-axiom]: #28756
+#28891 := [unit-resolution #28757 #28890]: #27335
+#28892 := (= #27146 #27314)
+#28893 := [monotonicity #28791]: #28892
+#28903 := [trans #28893 #28891]: #28902
+#28905 := [trans #28903 #28895]: #28904
+#28907 := [trans #28905 #28897]: #28906
+#28909 := [trans #28907 #28899]: #28908
+#28911 := [trans #28909 #28901]: #28910
+#28913 := [monotonicity #28911]: #28912
+#28915 := [symm #28913]: #28914
+#28917 := [monotonicity #28915]: #28916
+#28921 := [trans #28917 #28919]: #28920
+#28923 := [trans #28921 #28789]: #28922
+#28925 := [monotonicity #28923]: #28924
+#28927 := [trans #28925 #28851]: #28926
+#28929 := [monotonicity #28927]: #28928
+#28931 := [monotonicity #28929]: #28930
+#28933 := [symm #28931]: #28932
+#28935 := [monotonicity #28933]: #28934
+#28936 := [mp #14369 #28935]: #28602
+#28940 := (= #3047 #27778)
+#28937 := (= #27778 #3047)
+#28938 := [monotonicity #28923]: #28937
+#28941 := [symm #28938]: #28940
+#28942 := [trans #14366 #28941]: #27786
+#28597 := (not #27786)
+#28598 := (or #28363 #28597)
+#28599 := [def-axiom]: #28598
+#28943 := [unit-resolution #28599 #28942]: #28363
+#28611 := (or #28437 #28097 #28322 #28340 #28365)
+#28612 := [def-axiom]: #28611
+#28944 := [unit-resolution #28612 #28943 #28936 #28468 #28837 #28819]: false
+#28946 := [lemma #28944]: #28945
+#29128 := [unit-resolution #28946 #28653]: #12189
+#23578 := (or #18445 #18454 #23575)
+#23581 := (not #23578)
+#23584 := (or #18445 #18448 #23581)
+#23587 := (not #23584)
+#23590 := (or #18445 #18448 #23587)
+#23593 := (not #23590)
+#23596 := (or #13300 #23593)
+#23599 := (not #23596)
+#23602 := (or #13300 #23599)
+#22558 := (forall (vars (?v0 Int)) #22547)
+#22565 := (not #22558)
+#22543 := (forall (vars (?v0 Int)) #22538)
+#22564 := (not #22543)
+#22566 := (or #22564 #22565)
+#22567 := (not #22566)
+#22596 := (or #22567 #22593)
+#22602 := (not #22596)
+#22603 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #22602)
+#22604 := (not #22603)
+#22382 := (forall (vars (?v0 Int)) #22377)
+#22388 := (not #22382)
+#22389 := (or #22364 #22388)
+#22390 := (not #22389)
+#22419 := (or #22390 #22416)
+#22425 := (not #22419)
+#22426 := (or #13555 #22425)
+#22427 := (not #22426)
+#22432 := (or #13555 #22427)
+#22440 := (not #22432)
+#22441 := (or #12692 #22438 #18594 #22439 #13622 #18597 #22440)
+#22442 := (not #22441)
+#22447 := (or #18594 #18597 #22442)
+#22453 := (not #22447)
+#22490 := (or #12857 #12848 #22479 #13656 #22438 #13707 #22453)
+#22491 := (not #22490)
+#22454 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #22453)
+#22455 := (not #22454)
+#22460 := (or #18556 #18565 #22455)
+#22466 := (not #22460)
+#22467 := (or #18556 #18559 #22466)
+#22468 := (not #22467)
+#22473 := (or #18556 #18559 #22468)
+#22480 := (not #22473)
+#22481 := (or #22479 #13656 #13708 #22480)
+#22482 := (not #22481)
+#22496 := (or #22482 #22491)
+#22502 := (not #22496)
+#22503 := (or #18556 #18565 #22479 #13656 #22502)
+#22504 := (not #22503)
+#22509 := (or #18556 #18565 #22504)
+#22515 := (not #22509)
+#22516 := (or #18556 #18559 #22515)
+#22517 := (not #22516)
+#22522 := (or #18556 #18559 #22517)
+#22528 := (not #22522)
+#22529 := (or #22479 #13656 #13801 #22528)
+#22530 := (not #22529)
+#22609 := (or #22530 #22604)
+#22624 := (not #22609)
+#22359 := (forall (vars (?v0 Int)) #22354)
+#22620 := (not #22359)
+#22625 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #22620 #22624)
+#22626 := (not #22625)
+#22631 := (or #13267 #13508 #22626)
+#22638 := (not #22631)
+#22348 := (forall (vars (?v0 Int)) #22343)
+#22637 := (not #22348)
+#22639 := (or #22637 #22638)
+#22640 := (not #22639)
+#22645 := (or #22337 #22640)
+#22651 := (not #22645)
+#22652 := (or #13472 #22651)
+#22653 := (not #22652)
+#22658 := (or #13472 #22653)
+#22664 := (not #22658)
+#22665 := (or #13267 #18445 #18454 #13258 #13249 #13240 #22664)
+#22666 := (not #22665)
+#22671 := (or #18445 #18454 #22666)
+#22677 := (not #22671)
+#22678 := (or #18445 #18448 #22677)
+#22679 := (not #22678)
+#22684 := (or #18445 #18448 #22679)
+#22690 := (not #22684)
+#22691 := (or #13300 #22690)
+#22692 := (not #22691)
+#22697 := (or #13300 #22692)
+#23603 := (iff #22697 #23602)
+#23600 := (iff #22692 #23599)
+#23597 := (iff #22691 #23596)
+#23594 := (iff #22690 #23593)
+#23591 := (iff #22684 #23590)
+#23588 := (iff #22679 #23587)
+#23585 := (iff #22678 #23584)
+#23582 := (iff #22677 #23581)
+#23579 := (iff #22671 #23578)
+#23576 := (iff #22666 #23575)
+#23573 := (iff #22665 #23572)
+#23570 := (iff #22664 #23569)
+#23567 := (iff #22658 #23566)
+#23564 := (iff #22653 #23563)
+#23561 := (iff #22652 #23560)
+#23558 := (iff #22651 #23557)
+#23555 := (iff #22645 #23554)
+#23552 := (iff #22640 #23551)
+#23549 := (iff #22639 #23548)
+#23546 := (iff #22638 #23545)
+#23543 := (iff #22631 #23542)
+#23540 := (iff #22626 #23539)
+#23537 := (iff #22625 #23536)
+#23534 := (iff #22624 #23533)
+#23531 := (iff #22609 #23530)
+#23528 := (iff #22604 #23527)
+#23525 := (iff #22603 #23524)
+#23522 := (iff #22602 #23521)
+#23519 := (iff #22596 #23518)
+#23516 := (iff #22567 #23515)
+#23513 := (iff #22566 #23512)
+#23510 := (iff #22565 #23509)
+#23507 := (iff #22558 #23504)
+#23505 := (iff #22547 #22547)
+#23506 := [refl]: #23505
+#23508 := [quant-intro #23506]: #23507
+#23511 := [monotonicity #23508]: #23510
+#23502 := (iff #22564 #23501)
+#23499 := (iff #22543 #23496)
+#23497 := (iff #22538 #22538)
+#23498 := [refl]: #23497
+#23500 := [quant-intro #23498]: #23499
+#23503 := [monotonicity #23500]: #23502
+#23514 := [monotonicity #23503 #23511]: #23513
+#23517 := [monotonicity #23514]: #23516
+#23520 := [monotonicity #23517]: #23519
+#23523 := [monotonicity #23520]: #23522
+#23526 := [monotonicity #23523]: #23525
+#23529 := [monotonicity #23526]: #23528
+#23494 := (iff #22530 #23493)
+#23491 := (iff #22529 #23490)
+#23488 := (iff #22528 #23487)
+#23485 := (iff #22522 #23484)
+#23482 := (iff #22517 #23481)
+#23479 := (iff #22516 #23478)
+#23476 := (iff #22515 #23475)
+#23473 := (iff #22509 #23472)
+#23470 := (iff #22504 #23469)
+#23467 := (iff #22503 #23466)
+#23464 := (iff #22502 #23463)
+#23461 := (iff #22496 #23460)
+#23458 := (iff #22491 #23457)
+#23455 := (iff #22490 #23454)
+#23422 := (iff #22453 #23421)
+#23419 := (iff #22447 #23418)
+#23416 := (iff #22442 #23415)
+#23413 := (iff #22441 #23412)
+#23410 := (iff #22440 #23409)
+#23407 := (iff #22432 #23406)
+#23404 := (iff #22427 #23403)
+#23401 := (iff #22426 #23400)
+#23398 := (iff #22425 #23397)
+#23395 := (iff #22419 #23394)
+#23392 := (iff #22390 #23391)
+#23389 := (iff #22389 #23388)
+#23386 := (iff #22388 #23385)
+#23383 := (iff #22382 #23380)
+#23381 := (iff #22377 #22377)
+#23382 := [refl]: #23381
+#23384 := [quant-intro #23382]: #23383
+#23387 := [monotonicity #23384]: #23386
+#23390 := [monotonicity #23387]: #23389
+#23393 := [monotonicity #23390]: #23392
+#23396 := [monotonicity #23393]: #23395
+#23399 := [monotonicity #23396]: #23398
+#23402 := [monotonicity #23399]: #23401
+#23405 := [monotonicity #23402]: #23404
+#23408 := [monotonicity #23405]: #23407
+#23411 := [monotonicity #23408]: #23410
+#23414 := [monotonicity #23411]: #23413
+#23417 := [monotonicity #23414]: #23416
+#23420 := [monotonicity #23417]: #23419
+#23423 := [monotonicity #23420]: #23422
+#23456 := [monotonicity #23423]: #23455
+#23459 := [monotonicity #23456]: #23458
+#23452 := (iff #22482 #23451)
+#23449 := (iff #22481 #23448)
+#23446 := (iff #22480 #23445)
+#23443 := (iff #22473 #23442)
+#23440 := (iff #22468 #23439)
+#23437 := (iff #22467 #23436)
+#23434 := (iff #22466 #23433)
+#23431 := (iff #22460 #23430)
+#23428 := (iff #22455 #23427)
+#23425 := (iff #22454 #23424)
+#23426 := [monotonicity #23423]: #23425
+#23429 := [monotonicity #23426]: #23428
+#23432 := [monotonicity #23429]: #23431
+#23435 := [monotonicity #23432]: #23434
+#23438 := [monotonicity #23435]: #23437
+#23441 := [monotonicity #23438]: #23440
+#23444 := [monotonicity #23441]: #23443
+#23447 := [monotonicity #23444]: #23446
+#23450 := [monotonicity #23447]: #23449
+#23453 := [monotonicity #23450]: #23452
+#23462 := [monotonicity #23453 #23459]: #23461
+#23465 := [monotonicity #23462]: #23464
+#23468 := [monotonicity #23465]: #23467
+#23471 := [monotonicity #23468]: #23470
+#23474 := [monotonicity #23471]: #23473
+#23477 := [monotonicity #23474]: #23476
+#23480 := [monotonicity #23477]: #23479
+#23483 := [monotonicity #23480]: #23482
+#23486 := [monotonicity #23483]: #23485
+#23489 := [monotonicity #23486]: #23488
+#23492 := [monotonicity #23489]: #23491
+#23495 := [monotonicity #23492]: #23494
+#23532 := [monotonicity #23495 #23529]: #23531
+#23535 := [monotonicity #23532]: #23534
+#23378 := (iff #22620 #23377)
+#23375 := (iff #22359 #23372)
+#23373 := (iff #22354 #22354)
+#23374 := [refl]: #23373
+#23376 := [quant-intro #23374]: #23375
+#23379 := [monotonicity #23376]: #23378
+#23538 := [monotonicity #23379 #23535]: #23537
+#23541 := [monotonicity #23538]: #23540
+#23544 := [monotonicity #23541]: #23543
+#23547 := [monotonicity #23544]: #23546
+#23370 := (iff #22637 #23369)
+#23367 := (iff #22348 #23364)
+#23365 := (iff #22343 #22343)
+#23366 := [refl]: #23365
+#23368 := [quant-intro #23366]: #23367
+#23371 := [monotonicity #23368]: #23370
+#23550 := [monotonicity #23371 #23547]: #23549
+#23553 := [monotonicity #23550]: #23552
+#23556 := [monotonicity #23553]: #23555
+#23559 := [monotonicity #23556]: #23558
+#23562 := [monotonicity #23559]: #23561
+#23565 := [monotonicity #23562]: #23564
+#23568 := [monotonicity #23565]: #23567
+#23571 := [monotonicity #23568]: #23570
+#23574 := [monotonicity #23571]: #23573
+#23577 := [monotonicity #23574]: #23576
+#23580 := [monotonicity #23577]: #23579
+#23583 := [monotonicity #23580]: #23582
+#23586 := [monotonicity #23583]: #23585
+#23589 := [monotonicity #23586]: #23588
+#23592 := [monotonicity #23589]: #23591
+#23595 := [monotonicity #23592]: #23594
+#23598 := [monotonicity #23595]: #23597
+#23601 := [monotonicity #23598]: #23600
+#23604 := [monotonicity #23601]: #23603
+#19096 := (and #18739 #18740)
+#19099 := (not #19096)
+#19102 := (or #19078 #19091 #19099)
+#19105 := (not #19102)
+#16021 := (and #3173 #4202 #13831 #15219)
+#18762 := (not #16021)
+#18765 := (forall (vars (?v0 Int)) #18762)
+#14462 := (and #4202 #15219)
+#14461 := (not #14462)
+#16007 := (or #13829 #13843 #14461)
+#16012 := (forall (vars (?v0 Int)) #16007)
+#18769 := (and #16012 #18765)
+#19111 := (or #18769 #19105)
+#19119 := (and #12269 #12272 #12275 #12278 #13513 #13516 #13801 #19111)
+#18948 := (and #18615 #18616)
+#18951 := (not #18948)
+#18954 := (or #18930 #18943 #18951)
+#18957 := (not #18954)
+#15908 := (or #13558 #13572 #14461)
+#15913 := (forall (vars (?v0 Int)) #15908)
+#18631 := (not #13601)
+#18641 := (and #18631 #15913)
+#18963 := (or #18641 #18957)
+#18968 := (and #13550 #18963)
+#18971 := (or #13555 #18968)
+#18979 := (and #12622 #13525 #13534 #13542 #13618 #15900 #18971)
+#18984 := (or #18594 #18597 #18979)
+#19024 := (and #12839 #12842 #13513 #13516 #13525 #13708 #18984)
+#18990 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #18984)
+#18995 := (or #18556 #18565 #18990)
+#19001 := (and #12575 #12578 #18995)
+#19006 := (or #18556 #18559 #19001)
+#19012 := (and #13513 #13516 #13707 #19006)
+#19029 := (or #19012 #19024)
+#19035 := (and #12575 #12584 #13513 #13516 #19029)
+#19040 := (or #18556 #18565 #19035)
+#19046 := (and #12575 #12578 #19040)
+#19051 := (or #18556 #18559 #19046)
+#19057 := (and #13513 #13516 #13802 #19051)
+#19124 := (or #19057 #19119)
+#15834 := (or #13994 #14008 #14461)
+#15839 := (forall (vars (?v0 Int)) #15834)
+#19130 := (and #3109 #12250 #12258 #12515 #12543 #12546 #12549 #12552 #12555 #12558 #13509 #13513 #13516 #13980 #14028 #14034 #14056 #15839 #15851 #15868 #15885 #19124)
+#19135 := (or #13267 #13508 #19130)
+#15820 := (or #13475 #13487 #14461)
+#15825 := (forall (vars (?v0 Int)) #15820)
+#19138 := (and #15825 #19135)
+#18851 := (and #18478 #18479)
+#18854 := (not #18851)
+#18860 := (or #18486 #18487 #18854)
+#18865 := (not #18860)
+#19141 := (or #18865 #19138)
+#19144 := (and #13469 #19141)
+#19147 := (or #13472 #19144)
+#19153 := (and #3109 #12180 #12189 #12195 #12198 #12201 #19147)
+#19158 := (or #18445 #18454 #19153)
+#19164 := (and #12180 #12183 #19158)
+#19169 := (or #18445 #18448 #19164)
+#19172 := (and #12177 #19169)
+#19175 := (or #13300 #19172)
+#22698 := (iff #19175 #22697)
+#22695 := (iff #19172 #22692)
+#22687 := (and #12177 #22684)
+#22693 := (iff #22687 #22692)
+#22694 := [rewrite]: #22693
+#22688 := (iff #19172 #22687)
+#22685 := (iff #19169 #22684)
+#22682 := (iff #19164 #22679)
+#22674 := (and #12180 #12183 #22671)
+#22680 := (iff #22674 #22679)
+#22681 := [rewrite]: #22680
+#22675 := (iff #19164 #22674)
+#22672 := (iff #19158 #22671)
+#22669 := (iff #19153 #22666)
+#22661 := (and #3109 #12180 #12189 #12195 #12198 #12201 #22658)
+#22667 := (iff #22661 #22666)
+#22668 := [rewrite]: #22667
+#22662 := (iff #19153 #22661)
+#22659 := (iff #19147 #22658)
+#22656 := (iff #19144 #22653)
+#22648 := (and #13469 #22645)
+#22654 := (iff #22648 #22653)
+#22655 := [rewrite]: #22654
+#22649 := (iff #19144 #22648)
+#22646 := (iff #19141 #22645)
+#22643 := (iff #19138 #22640)
+#22634 := (and #22348 #22631)
+#22641 := (iff #22634 #22640)
+#22642 := [rewrite]: #22641
+#22635 := (iff #19138 #22634)
+#22632 := (iff #19135 #22631)
+#22629 := (iff #19130 #22626)
+#22612 := (and #3109 #12250 #12258 #12515 #12543 #12546 #12549 #12552 #12555 #12558 #13509 #13513 #13516 #13980 #14028 #14034 #14056 #22359 #15851 #15868 #15885 #22609)
+#22627 := (iff #22612 #22626)
+#22628 := [rewrite]: #22627
+#22613 := (iff #19130 #22612)
+#22610 := (iff #19124 #22609)
+#22607 := (iff #19119 #22604)
+#22599 := (and #12269 #12272 #12275 #12278 #13513 #13516 #13801 #22596)
+#22605 := (iff #22599 #22604)
+#22606 := [rewrite]: #22605
+#22600 := (iff #19119 #22599)
+#22597 := (iff #19111 #22596)
+#22594 := (iff #19105 #22593)
+#22591 := (iff #19102 #22588)
+#22574 := (or #22572 #22573)
+#22585 := (or #19078 #19091 #22574)
+#22589 := (iff #22585 #22588)
+#22590 := [rewrite]: #22589
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+#18944 := (iff #18938 #18943)
+#18945 := [rewrite]: #18944
+#18939 := (iff #18622 #18938)
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+#18947 := [trans #18940 #18945]: #18946
+#18933 := (iff #18624 #18930)
+#18922 := (+ #13551 ?v0!14)
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+#18931 := (iff #18925 #18930)
+#18932 := [rewrite]: #18931
+#18926 := (iff #18624 #18925)
+#18923 := (= #18623 #18922)
+#18924 := [rewrite]: #18923
+#18927 := [monotonicity #18924]: #18926
+#18934 := [trans #18927 #18932]: #18933
+#18956 := [monotonicity #18934 #18947 #18953]: #18955
+#18959 := [monotonicity #18956]: #18958
+#18962 := [monotonicity #18959]: #18961
+#18967 := [trans #18962 #18965]: #18966
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+#18812 := [nnf-neg #18459 #18462 #18465 #18468 #18471 #18808]: #18811
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+#18452 := (~ #18451 #18451)
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+#18443 := (~ #18442 #18442)
+#18444 := [refl]: #18443
+#18828 := [nnf-neg #18444 #18824]: #18827
+#18440 := (~ #13300 #13300)
+#18441 := [refl]: #18440
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+#15324 := (or #12340 #12331 #12322 #12313 #13521 #13802 #13888)
+#15329 := (and #13824 #15324)
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+#15340 := (and #3109 #13509 #15335)
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+#16047 := (iff #15335 #16044)
+#16041 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #15842 #14031 #15859 #15876 #15893 #14077 #16038)
+#16045 := (iff #16041 #16044)
+#16046 := [rewrite]: #16045
+#16042 := (iff #15335 #16041)
+#16039 := (iff #15329 #16038)
+#16036 := (iff #15324 #16035)
+#16033 := (iff #13888 #16032)
+#16030 := (iff #13883 #16029)
+#16027 := (iff #13874 #16026)
+#16024 := (iff #13869 #16021)
+#16018 := (and #3173 #4202 #15219 #13831)
+#16022 := (iff #16018 #16021)
+#16023 := [rewrite]: #16022
+#16019 := (iff #13869 #16018)
+#15214 := (iff #4516 #15219)
+#15235 := -4294967295::Int
+#15227 := (+ -4294967295::Int #202)
+#15220 := (<= #15227 0::Int)
+#15216 := (iff #15220 #15219)
+#15217 := [rewrite]: #15216
+#15221 := (iff #4516 #15220)
+#15222 := (= #4515 #15227)
+#15228 := (+ #202 -4294967295::Int)
+#15224 := (= #15228 #15227)
+#15225 := [rewrite]: #15224
+#15229 := (= #4515 #15228)
+#15230 := (= #4514 -4294967295::Int)
+#15236 := (* -1::Int 4294967295::Int)
+#15232 := (= #15236 -4294967295::Int)
+#15233 := [rewrite]: #15232
+#15237 := (= #4514 #15236)
+#7637 := (= f87 4294967295::Int)
+#990 := 65536::Int
+#1365 := (* 65536::Int 65536::Int)
+#1370 := (- #1365 1::Int)
+#1371 := (= f87 #1370)
+#7638 := (iff #1371 #7637)
+#7635 := (= #1370 4294967295::Int)
+#1053 := 4294967296::Int
+#7628 := (- 4294967296::Int 1::Int)
+#7633 := (= #7628 4294967295::Int)
+#7634 := [rewrite]: #7633
+#7630 := (= #1370 #7628)
+#7599 := (= #1365 4294967296::Int)
+#7600 := [rewrite]: #7599
+#7631 := [monotonicity #7600]: #7630
+#7636 := [trans #7631 #7634]: #7635
+#7639 := [monotonicity #7636]: #7638
+#7627 := [asserted]: #1371
+#7642 := [mp #7627 #7639]: #7637
+#15234 := [monotonicity #7642]: #15237
+#15231 := [trans #15234 #15233]: #15230
+#15226 := [monotonicity #15231]: #15229
+#15223 := [trans #15226 #15225]: #15222
+#15218 := [monotonicity #15223]: #15221
+#15215 := [trans #15218 #15217]: #15214
+#16020 := [monotonicity #15215]: #16019
+#16025 := [trans #16020 #16023]: #16024
+#16028 := [quant-intro #16025]: #16027
+#16016 := (iff #13877 #16015)
+#16013 := (iff #13857 #16012)
+#16010 := (iff #13852 #16007)
+#16004 := (or #14461 #13829 #13843)
+#16008 := (iff #16004 #16007)
+#16009 := [rewrite]: #16008
+#16005 := (iff #13852 #16004)
+#14458 := (iff #5738 #14461)
+#14463 := (iff #4523 #14462)
+#14460 := [monotonicity #15215]: #14463
+#14459 := [monotonicity #14460]: #14458
+#16006 := [monotonicity #14459]: #16005
+#16011 := [trans #16006 #16009]: #16010
+#16014 := [quant-intro #16011]: #16013
+#16017 := [monotonicity #16014]: #16016
+#16031 := [monotonicity #16017 #16028]: #16030
+#16034 := [monotonicity #16014 #16031]: #16033
+#16037 := [monotonicity #16034]: #16036
+#16002 := (iff #13824 #15999)
+#15996 := (or #13521 #15993 #13801)
+#16000 := (iff #15996 #15999)
+#16001 := [rewrite]: #16000
+#15997 := (iff #13824 #15996)
+#15994 := (iff #13795 #15993)
+#15991 := (iff #13789 #15990)
+#15988 := (iff #13784 #15987)
+#15985 := (iff #13776 #15984)
+#15982 := (iff #13767 #15981)
+#15979 := (iff #13762 #15976)
+#15973 := (or #12857 #12848 #13521 #13530 #15950 #13707)
+#15977 := (iff #15973 #15976)
+#15978 := [rewrite]: #15977
+#15974 := (iff #13762 #15973)
+#15951 := (iff #13651 #15950)
+#15948 := (iff #13643 #15945)
+#15942 := (or #12692 #13547 #15933 #13622 #15939)
+#15946 := (iff #15942 #15945)
+#15947 := [rewrite]: #15946
+#15943 := (iff #13643 #15942)
+#15940 := (iff #13628 #15939)
+#15937 := (iff #13625 #15936)
+#15903 := (iff #13536 #15900)
+#15845 := (+ 4294967295::Int #13537)
+#15896 := (>= #15845 1::Int)
+#15901 := (iff #15896 #15900)
+#15902 := [rewrite]: #15901
+#15897 := (iff #13536 #15896)
+#15846 := (= #13538 #15845)
+#15847 := [monotonicity #7642]: #15846
+#15898 := [monotonicity #15847]: #15897
+#15904 := [trans #15898 #15902]: #15903
+#15938 := [monotonicity #15904]: #15937
+#15941 := [monotonicity #15938]: #15940
+#15934 := (iff #13615 #15933)
+#15931 := (iff #13612 #15930)
+#15928 := (iff #13609 #15927)
+#15925 := (iff #13606 #15922)
+#15919 := (or #15916 #13601)
+#15923 := (iff #15919 #15922)
+#15924 := [rewrite]: #15923
+#15920 := (iff #13606 #15919)
+#15917 := (iff #13589 #15916)
+#15914 := (iff #13586 #15913)
+#15911 := (iff #13581 #15908)
+#15905 := (or #14461 #13558 #13572)
+#15909 := (iff #15905 #15908)
+#15910 := [rewrite]: #15909
+#15906 := (iff #13581 #15905)
+#15907 := [monotonicity #14459]: #15906
+#15912 := [trans #15907 #15910]: #15911
+#15915 := [quant-intro #15912]: #15914
+#15918 := [monotonicity #15915]: #15917
+#15921 := [monotonicity #15918]: #15920
+#15926 := [trans #15921 #15924]: #15925
+#15929 := [monotonicity #15915 #15926]: #15928
+#15932 := [monotonicity #15929]: #15931
+#15935 := [monotonicity #15932]: #15934
+#15944 := [monotonicity #15935 #15941]: #15943
+#15949 := [trans #15944 #15947]: #15948
+#15952 := [monotonicity #15904 #15949]: #15951
+#15975 := [monotonicity #15952]: #15974
+#15980 := [trans #15975 #15978]: #15979
+#15971 := (iff #13732 #15968)
+#15965 := (or #13521 #15962 #13708)
+#15969 := (iff #15965 #15968)
+#15970 := [rewrite]: #15969
+#15966 := (iff #13732 #15965)
+#15963 := (iff #13702 #15962)
+#15960 := (iff #13696 #15959)
+#15957 := (iff #13691 #15956)
+#15954 := (iff #13683 #15953)
+#15955 := [monotonicity #15952]: #15954
+#15958 := [monotonicity #15955]: #15957
+#15961 := [monotonicity #15958]: #15960
+#15964 := [monotonicity #15961]: #15963
+#15967 := [monotonicity #15964]: #15966
+#15972 := [trans #15967 #15970]: #15971
+#15983 := [monotonicity #15972 #15980]: #15982
+#15986 := [monotonicity #15983]: #15985
+#15989 := [monotonicity #15986]: #15988
+#15992 := [monotonicity #15989]: #15991
+#15995 := [monotonicity #15992]: #15994
+#15998 := [monotonicity #15995]: #15997
+#16003 := [trans #15998 #16001]: #16002
+#16040 := [monotonicity #16003 #16037]: #16039
+#15894 := (iff #14066 #15893)
+#15891 := (iff #14063 #15890)
+#15888 := (iff #14059 #15885)
+#15879 := (+ 255::Int #14006)
+#15882 := (>= #15879 0::Int)
+#15886 := (iff #15882 #15885)
+#15887 := [rewrite]: #15886
+#15883 := (iff #14059 #15882)
+#15880 := (= #14060 #15879)
+#1375 := (= f89 255::Int)
+#7641 := [asserted]: #1375
+#15881 := [monotonicity #7641]: #15880
+#15884 := [monotonicity #15881]: #15883
+#15889 := [trans #15884 #15887]: #15888
+#15892 := [monotonicity #15889]: #15891
+#15895 := [monotonicity #15892]: #15894
+#15877 := (iff #14053 #15876)
+#15874 := (iff #14050 #15873)
+#15871 := (iff #14046 #15868)
+#15862 := (+ 4294967295::Int #13977)
+#15865 := (>= #15862 0::Int)
+#15869 := (iff #15865 #15868)
+#15870 := [rewrite]: #15869
+#15866 := (iff #14046 #15865)
+#15863 := (= #14047 #15862)
+#15864 := [monotonicity #7642]: #15863
+#15867 := [monotonicity #15864]: #15866
+#15872 := [trans #15867 #15870]: #15871
+#15875 := [monotonicity #15872]: #15874
+#15878 := [monotonicity #15875]: #15877
+#15860 := (iff #14043 #15859)
+#15857 := (iff #14040 #15856)
+#15854 := (iff #14037 #15851)
+#15848 := (>= #15845 0::Int)
+#15852 := (iff #15848 #15851)
+#15853 := [rewrite]: #15852
+#15849 := (iff #14037 #15848)
+#15850 := [monotonicity #15847]: #15849
+#15855 := [trans #15850 #15853]: #15854
+#15858 := [monotonicity #15855]: #15857
+#15861 := [monotonicity #15858]: #15860
+#15843 := (iff #14025 #15842)
+#15840 := (iff #14022 #15839)
+#15837 := (iff #14017 #15834)
+#15831 := (or #14461 #13994 #14008)
+#15835 := (iff #15831 #15834)
+#15836 := [rewrite]: #15835
+#15832 := (iff #14017 #15831)
+#15833 := [monotonicity #14459]: #15832
+#15838 := [trans #15833 #15836]: #15837
+#15841 := [quant-intro #15838]: #15840
+#15844 := [monotonicity #15841]: #15843
+#16043 := [monotonicity #15844 #15861 #15878 #15895 #16040]: #16042
+#16048 := [trans #16043 #16046]: #16047
+#16051 := [monotonicity #16048]: #16050
+#15829 := (iff #13505 #15828)
+#15826 := (iff #13502 #15825)
+#15823 := (iff #13497 #15820)
+#15817 := (or #14461 #13475 #13487)
+#15821 := (iff #15817 #15820)
+#15822 := [rewrite]: #15821
+#15818 := (iff #13497 #15817)
+#15819 := [monotonicity #14459]: #15818
+#15824 := [trans #15819 #15822]: #15823
+#15827 := [quant-intro #15824]: #15826
+#15830 := [monotonicity #15827]: #15829
+#16054 := [monotonicity #15830 #16051]: #16053
+#16057 := [monotonicity #15827 #16054]: #16056
+#16060 := [monotonicity #16057]: #16059
+#16063 := [monotonicity #16060]: #16062
+#16066 := [monotonicity #16063]: #16065
+#16069 := [monotonicity #16066]: #16068
+#16072 := [monotonicity #16069]: #16071
+#16075 := [monotonicity #16072]: #16074
+#16078 := [monotonicity #16075]: #16077
+#16081 := [monotonicity #16078]: #16080
+#16084 := [monotonicity #16081]: #16083
+#14361 := (not #14213)
+#15374 := (iff #14361 #15373)
+#15371 := (iff #14213 #15370)
+#15368 := (iff #14210 #15367)
+#15365 := (iff #14205 #15364)
+#15362 := (iff #14199 #15361)
+#15359 := (iff #14194 #15358)
+#15356 := (iff #14186 #15355)
+#15353 := (iff #14165 #15352)
+#15350 := (iff #14162 #15349)
+#15347 := (iff #14159 #15346)
+#15344 := (iff #14156 #15343)
+#15341 := (iff #14151 #15340)
+#15338 := (iff #14143 #15335)
+#15332 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #15329 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
+#15336 := (iff #15332 #15335)
+#15337 := [rewrite]: #15336
+#15333 := (iff #14143 #15332)
+#15330 := (iff #13950 #15329)
+#15327 := (iff #13945 #15324)
+#15309 := (or #12340 #12331 #12322 #12313 #13521 #13888)
+#15321 := (or #13521 #13802 #15309)
+#15325 := (iff #15321 #15324)
+#15326 := [rewrite]: #15325
+#15322 := (iff #13945 #15321)
+#15319 := (iff #13920 #15309)
+#15314 := (and true #15309)
+#15317 := (iff #15314 #15309)
+#15318 := [rewrite]: #15317
+#15315 := (iff #13920 #15314)
+#15312 := (iff #13915 #15309)
+#15306 := (or false #12340 #12331 #12322 #12313 #13521 #13888)
+#15310 := (iff #15306 #15309)
+#15311 := [rewrite]: #15310
+#15307 := (iff #13915 #15306)
+#15304 := (iff #12374 false)
+#15302 := (iff #12374 #3156)
+#15040 := (iff #10960 true)
+#10959 := [asserted]: #2542
+#10966 := [mp #10959 #10963]: #10960
+#15041 := [iff-true #10966]: #15040
+#15303 := [monotonicity #15041]: #15302
+#15305 := [trans #15303 #12257]: #15304
+#15308 := [monotonicity #15305]: #15307
+#15313 := [trans #15308 #15311]: #15312
+#15316 := [monotonicity #15041 #15313]: #15315
+#15320 := [trans #15316 #15318]: #15319
+#15323 := [monotonicity #15320]: #15322
+#15328 := [trans #15323 #15326]: #15327
+#15331 := [monotonicity #15328]: #15330
+#15300 := (iff #12402 #15299)
+#15297 := (iff #12264 #12258)
+#15292 := (and true #12258)
+#15295 := (iff #15292 #12258)
+#15296 := [rewrite]: #15295
+#15293 := (iff #12264 #15292)
+#15276 := (iff #12145 true)
+#15277 := [iff-true #14351]: #15276
+#15294 := [monotonicity #15277]: #15293
+#15298 := [trans #15294 #15296]: #15297
+#15301 := [monotonicity #15298]: #15300
+#15334 := [monotonicity #15301 #15331]: #15333
+#15339 := [trans #15334 #15337]: #15338
+#15342 := [monotonicity #15339]: #15341
+#15345 := [monotonicity #15342]: #15344
+#15348 := [monotonicity #15345]: #15347
+#15351 := [monotonicity #15348]: #15350
+#15354 := [monotonicity #15351]: #15353
+#15357 := [monotonicity #15354]: #15356
+#15360 := [monotonicity #15357]: #15359
+#15363 := [monotonicity #15360]: #15362
+#15366 := [monotonicity #15363]: #15365
+#15369 := [monotonicity #15366]: #15368
+#15372 := [monotonicity #15369]: #15371
+#15375 := [monotonicity #15372]: #15374
+#14362 := [not-or-elim #14346]: #14361
+#15376 := [mp #14362 #15375]: #15373
+#16085 := [mp #15376 #16084]: #16082
+#18832 := [mp~ #16085 #18831]: #18829
+#18833 := [mp #18832 #19177]: #19175
+#22700 := [mp #18833 #22699]: #22697
+#23605 := [mp #22700 #23604]: #23602
+#29129 := [unit-resolution #23605 #27033]: #23599
+#24829 := (or #23596 #23590)
+#24830 := [def-axiom]: #24829
+#29130 := [unit-resolution #24830 #29129]: #23590
+#24825 := (or #23593 #18445 #18448 #23587)
+#24826 := [def-axiom]: #24825
+#29134 := [unit-resolution #24826 #27642 #28798 #29130]: #23587
+#24815 := (or #23584 #23578)
+#24816 := [def-axiom]: #24815
+#29135 := [unit-resolution #24816 #29134]: #23578
+#24809 := (or #23581 #18445 #18454 #23575)
+#24810 := [def-axiom]: #24809
+#29136 := [unit-resolution #24810 #29135 #29128 #27642]: #23575
+#24787 := (or #23572 #3109)
+#24788 := [def-axiom]: #24787
+#29137 := [unit-resolution #24788 #29136]: #3109
+#24799 := (or #23572 #23566)
+#24800 := [def-axiom]: #24799
+#29663 := [unit-resolution #24800 #29136]: #23566
+#29664 := (or #23569 #23563)
+#27310 := [hypothesis]: #13472
+#27311 := [th-lemma arith farkas 1 1 #14360 #27310]: false
+#27312 := [lemma #27311]: #13469
+#24785 := (or #23569 #13472 #23563)
+#24786 := [def-axiom]: #24785
+#29665 := [unit-resolution #24786 #27312]: #29664
+#29666 := [unit-resolution #29665 #29663]: #23563
+#24777 := (or #23560 #23554)
+#24778 := [def-axiom]: #24777
+#29667 := [unit-resolution #24778 #29666]: #23554
+#27615 := (* -1::Int #3108)
+#27616 := (+ f306 #27615)
+#27617 := (>= #27616 0::Int)
+#29138 := (or #13267 #27617)
+#29139 := [th-lemma arith triangle-eq]: #29138
+#29140 := [unit-resolution #29139 #29137]: #27617
+#24455 := (not #18486)
+#29141 := [hypothesis]: #22337
+#24456 := (or #22332 #24455)
+#24457 := [def-axiom]: #24456
+#29142 := [unit-resolution #24457 #29141]: #24455
+#29102 := (+ #3108 #18484)
+#29104 := (>= #29102 0::Int)
+#29101 := (= #3108 #18483)
+#29149 := (= #18483 #3108)
+#29147 := (= #18482 #3098)
+#29145 := (= ?v0!13 0::Int)
+#24458 := (not #18487)
+#24459 := (or #22332 #24458)
+#24460 := [def-axiom]: #24459
+#29143 := [unit-resolution #24460 #29141]: #24458
+#24453 := (or #22332 #18479)
+#24454 := [def-axiom]: #24453
+#29144 := [unit-resolution #24454 #29141]: #18479
+#29146 := [th-lemma arith eq-propagate 0 0 #29144 #29143]: #29145
+#29148 := [monotonicity #29146]: #29147
+#29150 := [monotonicity #29148]: #29149
+#29151 := [symm #29150]: #29101
+#29152 := (not #29101)
+#29153 := (or #29152 #29104)
+#29154 := [th-lemma arith triangle-eq]: #29153
+#29155 := [unit-resolution #29154 #29151]: #29104
+#29156 := [th-lemma arith farkas 1 -1 1 #29155 #29142 #29140]: false
+#29157 := [lemma #29156]: #22332
+#24773 := (or #23557 #22337 #23551)
#24774 := [def-axiom]: #24773
-#29171 := [unit-resolution #24774 #29062 #27593 #29170]: #23539
-#24751 := (or #23536 #3109)
+#29668 := [unit-resolution #24774 #29157 #29667]: #23551
+#24765 := (or #23548 #23542)
+#24766 := [def-axiom]: #24765
+#29669 := [unit-resolution #24766 #29668]: #23542
+#29670 := (or #23545 #13267 #23539)
+#24761 := (or #23545 #13267 #13508 #23539)
+#24762 := [def-axiom]: #24761
+#29671 := [unit-resolution #24762 #14360]: #29670
+#29672 := [unit-resolution #29671 #29669 #29137]: #23539
+#24751 := (or #23536 #23530)
#24752 := [def-axiom]: #24751
-#29172 := [unit-resolution #24752 #29171]: #3109
-#29126 := (+ #3108 #18448)
-#29128 := (>= #29126 0::Int)
-#29125 := (= #3108 #18447)
-#29159 := (= #18447 #3108)
-#29157 := (= #18446 #3098)
-#29155 := (= ?v0!13 0::Int)
-#24422 := (not #18451)
-#29152 := [hypothesis]: #22301
-#24423 := (or #22296 #24422)
-#24424 := [def-axiom]: #24423
-#29153 := [unit-resolution #24424 #29152]: #24422
-#24417 := (or #22296 #18443)
-#24418 := [def-axiom]: #24417
-#29154 := [unit-resolution #24418 #29152]: #18443
-#29156 := [th-lemma arith eq-propagate 0 0 #29154 #29153]: #29155
-#29158 := [monotonicity #29156]: #29157
-#29160 := [monotonicity #29158]: #29159
-#29161 := [symm #29160]: #29125
-#29162 := (not #29125)
-#29163 := (or #29162 #29128)
-#29164 := [th-lemma arith triangle-eq]: #29163
-#29165 := [unit-resolution #29164 #29161]: #29128
-#24419 := (not #18450)
-#24420 := (or #22296 #24419)
-#24421 := [def-axiom]: #24420
-#29166 := [unit-resolution #24421 #29152]: #24419
-#27612 := (* -1::Int #3108)
-#27613 := (+ f307 #27612)
-#27614 := (>= #27613 0::Int)
-#29173 := (or #13231 #27614)
-#29174 := [th-lemma arith triangle-eq]: #29173
-#29175 := [unit-resolution #29174 #29172]: #27614
-#29176 := [th-lemma arith farkas 1 -1 1 #29175 #29166 #29165]: false
-#29177 := [lemma #29176]: #22296
-#24763 := (or #23536 #23530)
-#24764 := [def-axiom]: #24763
-#29735 := [unit-resolution #24764 #29171]: #23530
-#29073 := [hypothesis]: #13436
-#29074 := [th-lemma arith farkas 1 1 #14324 #29073]: false
-#29075 := [lemma #29074]: #13433
-#24749 := (or #23533 #13436 #23527)
+#30100 := [unit-resolution #24752 #29672]: #23530
+#24749 := (or #23536 #23372)
#24750 := [def-axiom]: #24749
-#29738 := [unit-resolution #24750 #29075 #29735]: #23527
-#24741 := (or #23524 #23518)
-#24742 := [def-axiom]: #24741
-#29739 := [unit-resolution #24742 #29738]: #23518
-#24737 := (or #23521 #22301 #23515)
-#24738 := [def-axiom]: #24737
-#29740 := [unit-resolution #24738 #29739 #29177]: #23515
-#24729 := (or #23512 #23506)
-#24730 := [def-axiom]: #24729
-#29741 := [unit-resolution #24730 #29740]: #23506
-#29742 := (or #23509 #13231 #23503)
-#24725 := (or #23509 #13231 #13472 #23503)
-#24726 := [def-axiom]: #24725
-#29743 := [unit-resolution #24726 #14324]: #29742
-#29744 := [unit-resolution #29743 #29741 #29172]: #23503
-#24699 := (or #23500 #13944)
+#30095 := [unit-resolution #24750 #29672]: #23372
+#24711 := (or #23536 #12250)
+#24712 := [def-axiom]: #24711
+#30101 := [unit-resolution #24712 #29672]: #12250
+#24745 := (or #23536 #15868)
+#24746 := [def-axiom]: #24745
+#30102 := [unit-resolution #24746 #29672]: #15868
+#24735 := (or #23536 #13980)
+#24736 := [def-axiom]: #24735
+#30103 := [unit-resolution #24736 #29672]: #13980
+#27607 := (f24 #27086)
+#27608 := (f77 #27086 f308 #27607)
+#27609 := (f136 #27608 #27086)
+#27690 := (>= #27609 0::Int)
+#24731 := (or #23536 #13513)
+#24732 := [def-axiom]: #24731
+#30104 := [unit-resolution #24732 #29672]: #13513
+#27706 := (* -1::Int #27609)
+#27779 := (+ f308 #27706)
+#27780 := (<= #27779 0::Int)
+#27610 := (= f308 #27609)
+#29180 := (f77 #24833 f308 #27122)
+#29181 := (f136 #29180 #24833)
+#30129 := (= #29181 #27609)
+#30127 := (= #27609 #29181)
+#30105 := (= #27086 #24833)
+#30109 := [trans #27414 #27140]: #30105
+#30124 := (= #27608 #29180)
+#30122 := (= #3152 #29180)
+#30120 := (= #29180 #3152)
+#30112 := (= #27122 f19)
+#30110 := (= #27122 #25112)
+#30111 := [monotonicity #27142]: #30110
+#30113 := [trans #30111 #27685]: #30112
+#30121 := [monotonicity #27142 #30113]: #30120
+#30123 := [symm #30121]: #30122
+#30118 := (= #27608 #3152)
+#30116 := (= #27607 f19)
+#30114 := (= #27607 #25112)
+#30115 := [monotonicity #27414]: #30114
+#30117 := [trans #30115 #27685]: #30116
+#30119 := [monotonicity #27414 #30117]: #30118
+#30125 := [trans #30119 #30123]: #30124
+#30128 := [monotonicity #30125 #30109]: #30127
+#30130 := [symm #30128]: #30129
+#29182 := (= f308 #29181)
+#29185 := (or #27129 #29182)
+#29186 := [quant-inst #24833 #3135]: #29185
+#30126 := [unit-resolution #29186 #17107]: #29182
+#30131 := [trans #30126 #30130]: #27610
+#28118 := (not #27610)
+#30132 := (or #28118 #27780)
+#30133 := [th-lemma arith triangle-eq]: #30132
+#30134 := [unit-resolution #30133 #30131]: #27780
+#30135 := (not #27780)
+#30136 := (or #27690 #22479 #30135)
+#30137 := [th-lemma arith assign-bounds -1 1]: #30136
+#30138 := [unit-resolution #30137 #30134 #30104]: #27690
+#27691 := (not #27690)
+#28143 := (or #23524 #27691 #13979 #22622 #22615 #23377)
+#27988 := (f77 #3042 #27609 f19)
+#27989 := (f121 f297 #27988)
+#27992 := (= f313 #27989)
+#28098 := (= #3153 #27989)
+#28111 := (= #27989 #3153)
+#28105 := (= #27988 #3152)
+#28103 := (= #27609 f308)
+#27613 := (or #27129 #27610)
+#27614 := [quant-inst #27086 #3135]: #27613
+#28102 := [unit-resolution #27614 #17107]: #27610
+#28104 := [symm #28102]: #28103
+#28106 := [monotonicity #28104]: #28105
+#28112 := [monotonicity #28106]: #28111
+#28113 := [symm #28112]: #28098
+#28114 := (= f313 #3153)
+#28107 := [hypothesis]: #12250
+#28108 := [hypothesis]: #23527
+#24691 := (or #23524 #12278)
+#24692 := [def-axiom]: #24691
+#28109 := [unit-resolution #24692 #28108]: #12278
+#28110 := [symm #28109]: #3167
+#28115 := [trans #28110 #28107]: #28114
+#28116 := [trans #28115 #28113]: #27992
+#27973 := (<= #27609 4294967295::Int)
+#28117 := [hypothesis]: #15868
+#27781 := (>= #27779 0::Int)
+#28119 := (or #28118 #27781)
+#28120 := [th-lemma arith triangle-eq]: #28119
+#28121 := [unit-resolution #28120 #28102]: #27781
+#28122 := (not #27781)
+#28123 := (or #27973 #22622 #28122)
+#28124 := [th-lemma arith assign-bounds -1 1]: #28123
+#28125 := [unit-resolution #28124 #28121 #28117]: #27973
+#28015 := (+ f296 #27706)
+#28016 := (<= #28015 0::Int)
+#28127 := (not #28016)
+#28126 := [hypothesis]: #13980
+#28128 := (or #28127 #13979 #28122)
+#28129 := [th-lemma arith assign-bounds -1 -1]: #28128
+#28130 := [unit-resolution #28129 #28121 #28126]: #28127
+#27995 := (not #27992)
+#27974 := (not #27973)
+#28140 := (or #27974 #27995 #28016)
+#28131 := [hypothesis]: #27690
+#24699 := (or #23524 #23518)
#24700 := [def-axiom]: #24699
-#29749 := [unit-resolution #24700 #29744]: #13944
-#24675 := (or #23500 #12214)
+#28132 := [unit-resolution #24700 #28108]: #23518
+#24697 := (or #23524 #13801)
+#24698 := [def-axiom]: #24697
+#28133 := [unit-resolution #24698 #28108]: #13801
+#28039 := [hypothesis]: #23372
+#27785 := (+ f307 #13841)
+#27788 := (<= #27785 0::Int)
+#28134 := (or #12313 #27788)
+#28135 := [th-lemma arith triangle-eq]: #28134
+#28136 := [unit-resolution #28135 #28109]: #27788
+#28044 := (not #27788)
+#28045 := (or #22588 #28044 #23377 #13802)
+#28032 := [hypothesis]: #27788
+#24674 := (not #19091)
+#28033 := [hypothesis]: #22593
+#24675 := (or #22588 #24674)
#24676 := [def-axiom]: #24675
-#29747 := [unit-resolution #24676 #29744]: #12214
-#28447 := (or #23418 #22328 #13943 #22579)
-#28422 := [hypothesis]: #22327
-#28434 := (= #3153 #3299)
-#28432 := (= #3299 #3153)
-#28428 := (= #3298 #3152)
-#24559 := (or #23418 #12806)
-#24560 := [def-axiom]: #24559
-#28426 := [unit-resolution #24560 #28423]: #12806
-#28427 := [symm #28426]: #3329
-#28429 := [monotonicity #28427]: #28428
-#28433 := [monotonicity #28429]: #28432
-#28435 := [symm #28433]: #28434
-#28436 := (= f316 #3153)
-#28062 := [hypothesis]: #12214
-#28431 := [symm #28430]: #3328
-#28437 := [trans #28431 #28062]: #28436
-#28438 := [trans #28437 #28435]: #12607
-#28081 := [hypothesis]: #13944
-#24554 := (+ f309 #13556)
-#24556 := (>= #24554 0::Int)
-#28439 := (or #12812 #24556)
-#28440 := [th-lemma arith triangle-eq]: #28439
-#28441 := [unit-resolution #28440 #28426]: #24556
-#28442 := (not #24556)
-#28443 := (or #13559 #13943 #28442)
-#28444 := [th-lemma arith assign-bounds -1 -1]: #28443
-#28445 := [unit-resolution #28444 #28441 #28081]: #13559
-#24433 := (or #22328 #22326 #13558)
-#24434 := [def-axiom]: #24433
-#28446 := [unit-resolution #24434 #28445 #28438 #28422]: false
-#28448 := [lemma #28446]: #28447
-#29589 := [unit-resolution #28448 #29747 #29749]: #29594
-#29595 := [unit-resolution #29589 #28423]: #22328
-#24435 := (or #23352 #22327)
-#24436 := [def-axiom]: #24435
-#29718 := [unit-resolution #24436 #29595]: #23352
-#24569 := (or #23418 #23382)
-#24570 := [def-axiom]: #24569
-#29771 := [unit-resolution #24570 #28423]: #23382
-#29795 := (or #23385 #23379)
-#24715 := (or #23500 #23494)
-#24716 := [def-axiom]: #24715
-#29745 := [unit-resolution #24716 #29744]: #23494
-#24713 := (or #23500 #23336)
-#24714 := [def-axiom]: #24713
-#29746 := [unit-resolution #24714 #29744]: #23336
-#24709 := (or #23500 #15832)
-#24710 := [def-axiom]: #24709
-#29748 := [unit-resolution #24710 #29744]: #15832
-decl f137 :: (-> S20 S20 Int)
-#27080 := (f24 #24797)
-#27605 := (f77 #24797 f309 #27080)
-#27606 := (f137 #27605 #24797)
-#27679 := (>= #27606 0::Int)
-#24695 := (or #23500 #13477)
-#24696 := [def-axiom]: #24695
-#29750 := [unit-resolution #24696 #29744]: #13477
-#27695 := (* -1::Int #27606)
-#27744 := (+ f309 #27695)
-#27745 := (<= #27744 0::Int)
-#27607 := (= f309 #27606)
-#1434 := (f77 #55 #202 #1433)
-#1435 := (pattern #1434)
-#1436 := (f137 #1434 #55)
-#7788 := (= #202 #1436)
-#7792 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7788)
-#17069 := (~ #7792 #7792)
-#17067 := (~ #7788 #7788)
-#17068 := [refl]: #17067
-#17070 := [nnf-pos #17068]: #17069
-#1437 := (= #1436 #202)
-#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437)
-#7793 := (iff #1438 #7792)
-#7790 := (iff #1437 #7788)
-#7791 := [rewrite]: #7790
-#7794 := [quant-intro #7791]: #7793
-#7787 := [asserted]: #1438
-#7797 := [mp #7787 #7794]: #7792
-#17071 := [mp~ #7797 #17070]: #7792
-#27087 := (not #7792)
-#27610 := (or #27087 #27607)
-#27611 := [quant-inst #24797 #3135]: #27610
-#28057 := [unit-resolution #27611 #17071]: #27607
-#28073 := (not #27607)
-#29751 := (or #28073 #27745)
-#29752 := [th-lemma arith triangle-eq]: #29751
-#29753 := [unit-resolution #29752 #28057]: #27745
-#29754 := (not #27745)
-#29755 := (or #27679 #22443 #29754)
-#29756 := [th-lemma arith assign-bounds -1 1]: #29755
-#29757 := [unit-resolution #29756 #29753 #29750]: #27679
-#27680 := (not #27679)
-#28098 := (or #23488 #27680 #13943 #22586 #22579 #23341)
-#27951 := (f77 #3042 #27606 f19)
-#27952 := (f122 f298 #27951)
-#27955 := (= f314 #27952)
-#28053 := (= #3153 #27952)
-#28066 := (= #27952 #3153)
-#28060 := (= #27951 #3152)
-#28058 := (= #27606 f309)
-#28059 := [symm #28057]: #28058
-#28061 := [monotonicity #28059]: #28060
-#28067 := [monotonicity #28061]: #28066
-#28068 := [symm #28067]: #28053
-#28069 := (= f314 #3153)
-#28063 := [hypothesis]: #23491
-#24655 := (or #23488 #12242)
+#28034 := [unit-resolution #24676 #28033]: #24674
+#27868 := (+ f307 #19089)
+#27869 := (>= #27868 0::Int)
+#27856 := (+ f309 #19076)
+#27857 := (<= #27856 0::Int)
+#28029 := (not #27857)
+#28023 := [hypothesis]: #13801
+#24671 := (not #19078)
+#24672 := (or #22588 #24671)
+#24673 := [def-axiom]: #24672
+#28035 := [unit-resolution #24673 #28033]: #24671
+#28030 := (or #28029 #19078 #13802)
+#28024 := [hypothesis]: #27857
+#28027 := [hypothesis]: #24671
+#28028 := [th-lemma arith farkas -1 1 1 #28027 #28024 #28023]: false
+#28031 := [lemma #28028]: #28030
+#28036 := [unit-resolution #28031 #28035 #28023]: #28029
+#28040 := (or #27857 #27869)
+#24669 := (or #22588 #18740)
+#24670 := [def-axiom]: #24669
+#28037 := [unit-resolution #24670 #28033]: #18740
+#24667 := (or #22588 #18739)
+#24668 := [def-axiom]: #24667
+#28038 := [unit-resolution #24668 #28033]: #18739
+#27882 := (or #23377 #22572 #22573 #27857 #27869)
+#27845 := (+ #18744 #14006)
+#27846 := (<= #27845 0::Int)
+#27847 := (+ ?v0!15 #13537)
+#27848 := (>= #27847 0::Int)
+#27849 := (or #22573 #27848 #27846 #22572)
+#27883 := (or #23377 #27849)
+#27890 := (iff #27883 #27882)
+#27877 := (or #22572 #22573 #27857 #27869)
+#27885 := (or #23377 #27877)
+#27888 := (iff #27885 #27882)
+#27889 := [rewrite]: #27888
+#27886 := (iff #27883 #27885)
+#27880 := (iff #27849 #27877)
+#27874 := (or #22573 #27857 #27869 #22572)
+#27878 := (iff #27874 #27877)
+#27879 := [rewrite]: #27878
+#27875 := (iff #27849 #27874)
+#27872 := (iff #27846 #27869)
+#27862 := (+ #14006 #18744)
+#27865 := (<= #27862 0::Int)
+#27870 := (iff #27865 #27869)
+#27871 := [rewrite]: #27870
+#27866 := (iff #27846 #27865)
+#27863 := (= #27845 #27862)
+#27864 := [rewrite]: #27863
+#27867 := [monotonicity #27864]: #27866
+#27873 := [trans #27867 #27871]: #27872
+#27860 := (iff #27848 #27857)
+#27850 := (+ #13537 ?v0!15)
+#27853 := (>= #27850 0::Int)
+#27858 := (iff #27853 #27857)
+#27859 := [rewrite]: #27858
+#27854 := (iff #27848 #27853)
+#27851 := (= #27847 #27850)
+#27852 := [rewrite]: #27851
+#27855 := [monotonicity #27852]: #27854
+#27861 := [trans #27855 #27859]: #27860
+#27876 := [monotonicity #27861 #27873]: #27875
+#27881 := [trans #27876 #27879]: #27880
+#27887 := [monotonicity #27881]: #27886
+#27891 := [trans #27887 #27889]: #27890
+#27884 := [quant-inst #18738]: #27883
+#27892 := [mp #27884 #27891]: #27882
+#28041 := [unit-resolution #27892 #28039 #28038 #28037]: #28040
+#28042 := [unit-resolution #28041 #28036]: #27869
+#28043 := [th-lemma arith farkas -1 1 1 #28042 #28034 #28032]: false
+#28046 := [lemma #28043]: #28045
+#28137 := [unit-resolution #28046 #28136 #28039 #28133]: #22588
+#24683 := (or #23521 #23515 #22593)
+#24684 := [def-axiom]: #24683
+#28138 := [unit-resolution #24684 #28137 #28132]: #23515
+#24663 := (or #23512 #23504)
+#24664 := [def-axiom]: #24663
+#28139 := [unit-resolution #24664 #28138]: #23504
+#28052 := (or #23509 #27691 #27974 #27995 #28016)
+#27979 := (+ #27609 #13442)
+#27980 := (>= #27979 0::Int)
+#27987 := (= #27989 f313)
+#27990 := (not #27987)
+#27991 := (or #27990 #27691 #27980 #27974)
+#28053 := (or #23509 #27991)
+#28060 := (iff #28053 #28052)
+#28047 := (or #27691 #27974 #27995 #28016)
+#28055 := (or #23509 #28047)
+#28058 := (iff #28055 #28052)
+#28059 := [rewrite]: #28058
+#28056 := (iff #28053 #28055)
+#28050 := (iff #27991 #28047)
+#27996 := (or #27995 #27691 #28016 #27974)
+#28048 := (iff #27996 #28047)
+#28049 := [rewrite]: #28048
+#27997 := (iff #27991 #27996)
+#28026 := (iff #27980 #28016)
+#28010 := (+ #13442 #27609)
+#28007 := (>= #28010 0::Int)
+#28017 := (iff #28007 #28016)
+#28025 := [rewrite]: #28017
+#28013 := (iff #27980 #28007)
+#28011 := (= #27979 #28010)
+#28012 := [rewrite]: #28011
+#28014 := [monotonicity #28012]: #28013
+#27928 := [trans #28014 #28025]: #28026
+#28008 := (iff #27990 #27995)
+#27993 := (iff #27987 #27992)
+#27994 := [rewrite]: #27993
+#28009 := [monotonicity #27994]: #28008
+#28020 := [monotonicity #28009 #27928]: #27997
+#28051 := [trans #28020 #28049]: #28050
+#28057 := [monotonicity #28051]: #28056
+#28061 := [trans #28057 #28059]: #28060
+#28054 := [quant-inst #27609]: #28053
+#28062 := [mp #28054 #28061]: #28052
+#28141 := [unit-resolution #28062 #28139 #28131]: #28140
+#28142 := [unit-resolution #28141 #28130 #28125 #28116]: false
+#28144 := [lemma #28142]: #28143
+#30139 := [unit-resolution #28144 #30138 #30103 #30102 #30101 #30095]: #23524
+#24707 := (or #23533 #23493 #23527)
+#24708 := [def-axiom]: #24707
+#30140 := [unit-resolution #24708 #30139 #30100]: #23493
+#24655 := (or #23490 #13802)
#24656 := [def-axiom]: #24655
-#28064 := [unit-resolution #24656 #28063]: #12242
-#28065 := [symm #28064]: #3167
-#28070 := [trans #28065 #28062]: #28069
-#28071 := [trans #28070 #28068]: #27955
-#27936 := (<= #27606 4294967295::Int)
-#28072 := [hypothesis]: #15832
-#27746 := (>= #27744 0::Int)
-#28074 := (or #28073 #27746)
-#28075 := [th-lemma arith triangle-eq]: #28074
-#28076 := [unit-resolution #28075 #28057]: #27746
-#28077 := (not #27746)
-#28078 := (or #27936 #22586 #28077)
-#28079 := [th-lemma arith assign-bounds -1 1]: #28078
-#28080 := [unit-resolution #28079 #28076 #28072]: #27936
-#27993 := (+ f297 #27695)
-#27994 := (<= #27993 0::Int)
-#28082 := (not #27994)
-#28083 := (or #28082 #13943 #28077)
-#28084 := [th-lemma arith assign-bounds -1 -1]: #28083
-#28085 := [unit-resolution #28084 #28076 #28081]: #28082
-#27958 := (not #27955)
-#27937 := (not #27936)
-#28095 := (or #27937 #27958 #27994)
-#28086 := [hypothesis]: #27679
-#24663 := (or #23488 #23482)
-#24664 := [def-axiom]: #24663
-#28087 := [unit-resolution #24664 #28063]: #23482
-#27749 := (+ f308 #13805)
-#27750 := (<= #27749 0::Int)
-#28088 := (or #12277 #27750)
-#28089 := [th-lemma arith triangle-eq]: #28088
-#28090 := [unit-resolution #28089 #28064]: #27750
-#27982 := [hypothesis]: #23336
-#24661 := (or #23488 #13765)
-#24662 := [def-axiom]: #24661
-#28091 := [unit-resolution #24662 #28063]: #13765
-#27973 := (not #27750)
-#27988 := (or #22552 #13766 #23341 #27973)
-#27976 := [hypothesis]: #13765
-#27820 := (+ f310 #19040)
-#27821 := (<= #27820 0::Int)
-#27832 := (+ f308 #19053)
-#27833 := (>= #27832 0::Int)
-#27972 := (not #27833)
-#27966 := [hypothesis]: #27750
-#24638 := (not #19055)
-#27977 := [hypothesis]: #22557
-#24639 := (or #22552 #24638)
+#30141 := [unit-resolution #24656 #30140]: #13802
+#30242 := (not #29585)
+#30243 := (or #30241 #28416 #30242 #13801)
+#30244 := [th-lemma arith assign-bounds 1 -1 -1]: #30243
+#30245 := [unit-resolution #30244 #28410 #30141 #30237]: #30241
+#29465 := (>= #29368 0::Int)
+#24733 := (or #23536 #13516)
+#24734 := [def-axiom]: #24733
+#29673 := [unit-resolution #24734 #29672]: #13516
+#29584 := (<= #29583 0::Int)
+#29676 := (or #29675 #29584)
+#29677 := [th-lemma arith triangle-eq]: #29676
+#29678 := [unit-resolution #29677 #29674]: #29584
+#29466 := (not #29465)
+#29679 := [hypothesis]: #29466
+#29680 := [th-lemma arith farkas 1 1 1 #29679 #29678 #29673]: false
+#29681 := [lemma #29680]: #29465
+#30247 := (or #29466 #29476 #29484)
+#29495 := (or #28639 #27163 #29466 #29476 #29484)
+#29461 := (or #29460 #29457 #29455 #29451)
+#29462 := (not #29461)
+#29463 := (+ #29368 #27164)
+#29464 := (>= #29463 0::Int)
+#29467 := (or #29466 #29464 #27163 #29462)
+#29496 := (or #28639 #29467)
+#29503 := (iff #29496 #29495)
+#29490 := (or #27163 #29466 #29476 #29484)
+#29498 := (or #28639 #29490)
+#29501 := (iff #29498 #29495)
+#29502 := [rewrite]: #29501
+#29499 := (iff #29496 #29498)
+#29493 := (iff #29467 #29490)
+#29487 := (or #29466 #29476 #27163 #29484)
+#29491 := (iff #29487 #29490)
+#29492 := [rewrite]: #29491
+#29488 := (iff #29467 #29487)
+#29485 := (iff #29462 #29484)
+#29482 := (iff #29461 #29481)
+#29483 := [rewrite]: #29482
+#29486 := [monotonicity #29483]: #29485
+#29479 := (iff #29464 #29476)
+#29468 := (+ #27164 #29368)
+#29471 := (>= #29468 0::Int)
+#29477 := (iff #29471 #29476)
+#29478 := [rewrite]: #29477
+#29472 := (iff #29464 #29471)
+#29469 := (= #29463 #29468)
+#29470 := [rewrite]: #29469
+#29473 := [monotonicity #29470]: #29472
+#29480 := [trans #29473 #29478]: #29479
+#29489 := [monotonicity #29480 #29486]: #29488
+#29494 := [trans #29489 #29492]: #29493
+#29500 := [monotonicity #29494]: #29499
+#29504 := [trans #29500 #29502]: #29503
+#29497 := [quant-inst #3039 #3043 #24996 #24998 #29368]: #29496
+#29505 := [mp #29497 #29504]: #29495
+#30248 := [unit-resolution #29505 #21024 #28873]: #30247
+#30249 := [unit-resolution #30248 #29681 #30245]: #29484
+#29513 := (or #29481 #29459)
+#29514 := [def-axiom]: #29513
+#30250 := [unit-resolution #29514 #30249]: #29459
+#30281 := [symm #30250]: #30280
+#30278 := (= #28494 #29458)
+#30276 := (= #27834 #29452)
+#30274 := (= #29452 #27834)
+#30272 := (= #29431 #3257)
+#28088 := (f127 #3257)
+#28199 := (f54 #24996 #28088)
+#30266 := (= #28199 #3257)
+#28200 := (= #3257 #28199)
+#28205 := (f59 #3257 #24996)
+#28206 := (= f1 #28205)
+#30252 := (= #3258 #28205)
+#29418 := (= #28205 #3258)
+#29419 := [monotonicity #28386]: #29418
+#30253 := [symm #29419]: #30252
+#28203 := (= #24996 #28202)
+#28182 := (* f309 #27068)
+#29340 := (+ #27070 #28182)
+#29341 := (f54 #24996 #29340)
+#29371 := (f24 #29341)
+#29443 := (= #29371 #28202)
+#29439 := (= #28202 #29371)
+#29437 := (= #3257 #29341)
+#29336 := (f77 #24833 f309 #24996)
+#29342 := (= #29336 #29341)
+#29343 := (not #29342)
+#29337 := (f149 #29336 #24833)
+#29338 := (= f1 #29337)
+#29339 := (not #29338)
+#29346 := (or #29339 #29343)
+#29349 := (not #29346)
+#29352 := (or #27721 #29349)
+#29344 := (or #29343 #29339)
+#29345 := (not #29344)
+#29353 := (or #27721 #29345)
+#29355 := (iff #29353 #29352)
+#29357 := (iff #29352 #29352)
+#29358 := [rewrite]: #29357
+#29350 := (iff #29345 #29349)
+#29347 := (iff #29344 #29346)
+#29348 := [rewrite]: #29347
+#29351 := [monotonicity #29348]: #29350
+#29356 := [monotonicity #29351]: #29355
+#29359 := [trans #29356 #29358]: #29355
+#29354 := [quant-inst #24833 #3139 #24996]: #29353
+#29360 := [mp #29354 #29359]: #29352
+#29429 := [unit-resolution #29360 #21240]: #29349
+#29363 := (or #29346 #29342)
+#29364 := [def-axiom]: #29363
+#29430 := [unit-resolution #29364 #29429]: #29342
+#29435 := (= #3257 #29336)
+#29433 := (= #29336 #3257)
+#29434 := [monotonicity #27142 #28386]: #29433
+#29436 := [symm #29434]: #29435
+#29438 := [trans #29436 #29430]: #29437
+#29440 := [monotonicity #29438]: #29439
+#29444 := [symm #29440]: #29443
+#29374 := (= #24996 #29371)
+#29379 := (or #25064 #29374)
+#29380 := [quant-inst #24996 #29340]: #29379
+#29428 := [unit-resolution #29380 #23312]: #29374
+#29445 := [trans #29428 #29444]: #28203
+#29320 := (not #28203)
+#28280 := (iff #28203 #28206)
+#29315 := (or #26210 #28280)
+#29316 := [quant-inst #3257 #24996]: #29315
+#29416 := [unit-resolution #29316 #23299]: #28280
+#28198 := (not #28206)
+#29424 := (iff #18556 #28198)
+#29422 := (iff #12575 #28206)
+#29420 := (iff #28206 #12575)
+#29421 := [monotonicity #29419]: #29420
+#29423 := [symm #29421]: #29422
+#29425 := [monotonicity #29423]: #29424
+#29417 := [hypothesis]: #18556
+#29426 := [mp #29417 #29425]: #28198
+#29317 := (not #28280)
+#29321 := (or #29317 #29320 #28206)
+#29322 := [def-axiom]: #29321
+#29427 := [unit-resolution #29322 #29426 #29416]: #29320
+#29446 := [unit-resolution #29427 #29445]: false
+#29447 := [lemma #29446]: #12575
+#30254 := [trans #29447 #30253]: #28206
+#28201 := (or #28200 #28198)
+#29376 := (or #26194 #28200 #28198)
+#29388 := (or #26194 #28201)
+#29387 := (iff #29388 #29376)
+#29390 := [rewrite]: #29387
+#29389 := [quant-inst #3257 #24996]: #29388
+#29391 := [mp #29389 #29390]: #29376
+#30255 := [unit-resolution #29391 #18284]: #28201
+#30256 := [unit-resolution #30255 #30254]: #28200
+#30267 := [symm #30256]: #30266
+#30270 := (= #29431 #28199)
+#29648 := (* #27068 #29368)
+#29651 := (+ #27318 #29648)
+#29654 := (f54 #24996 #29651)
+#30264 := (= #29654 #28199)
+#30258 := (= #29651 #28088)
+#30229 := (= #28088 #29651)
+#30230 := (* -1::Int #29651)
+#30231 := (+ #28088 #30230)
+#30232 := (<= #30231 0::Int)
+#29206 := (* -1::Int #27070)
+#29207 := (+ #24880 #29206)
+#29209 := (>= #29207 0::Int)
+#29205 := (= #24880 #27070)
+#30031 := (= #3043 #27070)
+#29986 := [symm #27275]: #30031
+#29987 := [trans #28885 #29986]: #29205
+#30032 := (not #29205)
+#30000 := (or #30032 #29209)
+#29997 := [th-lemma arith triangle-eq]: #30000
+#29984 := [unit-resolution #29997 #29987]: #29209
+#29700 := (* -1::Int #27318)
+#29701 := (+ #24880 #29700)
+#29702 := (<= #29701 0::Int)
+#29699 := (= #24880 #27318)
+#29989 := [symm #28883]: #29699
+#29990 := (not #29699)
+#29991 := (or #29990 #29702)
+#29992 := [th-lemma arith triangle-eq]: #29991
+#29993 := [unit-resolution #29992 #29989]: #29702
+#29377 := (f127 #29341)
+#29381 := (* -1::Int #29377)
+#29587 := (+ #28088 #29381)
+#29588 := (<= #29587 0::Int)
+#29586 := (= #28088 #29377)
+#30043 := (= #29377 #28088)
+#30035 := (= #29341 #3257)
+#30026 := (= #29341 #29336)
+#30034 := [symm #29430]: #30026
+#30042 := [trans #30034 #29434]: #30035
+#30041 := [monotonicity #30042]: #30043
+#30033 := [symm #30041]: #29586
+#30044 := (not #29586)
+#30045 := (or #30044 #29588)
+#30046 := [th-lemma arith triangle-eq]: #30045
+#30049 := [unit-resolution #30046 #30033]: #29588
+#29382 := (+ #28182 #29381)
+#29383 := (+ #27070 #29382)
+#29571 := (>= #29383 0::Int)
+#29384 := (= #29383 0::Int)
+#29559 := (or #25070 #29384)
+#29378 := (= #29340 #29377)
+#29560 := (or #25070 #29378)
+#29564 := (iff #29560 #29559)
+#29566 := (iff #29559 #29559)
+#29567 := [rewrite]: #29566
+#29385 := (iff #29378 #29384)
+#29386 := [rewrite]: #29385
+#29565 := [monotonicity #29386]: #29564
+#29568 := [trans #29565 #29567]: #29564
+#29563 := [quant-inst #24996 #29340]: #29560
+#29569 := [mp #29563 #29568]: #29559
+#30050 := [unit-resolution #29569 #23306]: #29384
+#30055 := (not #29384)
+#30058 := (or #30055 #29571)
+#30057 := [th-lemma arith triangle-eq]: #30058
+#30059 := [unit-resolution #30057 #30050]: #29571
+#29212 := (>= #27068 1::Int)
+#29210 := (= #27068 1::Int)
+#2998 := (f150 f19)
+#2999 := (= #2998 1::Int)
+#12057 := [asserted]: #2999
+#30060 := (= #27068 #2998)
+#30080 := [monotonicity #28386]: #30060
+#30081 := [trans #30080 #12057]: #29210
+#30082 := (not #29210)
+#30098 := (or #30082 #29212)
+#30099 := [th-lemma arith triangle-eq]: #30098
+#30056 := [unit-resolution #30099 #30081]: #29212
+#29211 := (<= #27068 1::Int)
+#30145 := (or #30082 #29211)
+#30146 := [th-lemma arith triangle-eq]: #30145
+#30147 := [unit-resolution #30146 #30081]: #29211
+#30028 := (not #29584)
+#30027 := (not #29702)
+#29999 := (not #29211)
+#29754 := (not #29212)
+#29998 := (not #29209)
+#29995 := (not #29571)
+#29994 := (not #29588)
+#30029 := (or #30232 #29994 #29995 #29998 #29754 #29999 #29754 #29999 #30027 #30028)
+#30030 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30029
+#30025 := [unit-resolution #30030 #30147 #30056 #30059 #29678 #30049 #29993 #29984]: #30232
+#30233 := (>= #30231 0::Int)
+#29208 := (<= #29207 0::Int)
+#30152 := (or #30032 #29208)
+#30153 := [th-lemma arith triangle-eq]: #30152
+#30154 := [unit-resolution #30153 #29987]: #29208
+#29703 := (>= #29701 0::Int)
+#30155 := (or #29990 #29703)
+#30156 := [th-lemma arith triangle-eq]: #30155
+#30157 := [unit-resolution #30156 #29989]: #29703
+#29589 := (>= #29587 0::Int)
+#30150 := (or #30044 #29589)
+#30151 := [th-lemma arith triangle-eq]: #30150
+#30148 := [unit-resolution #30151 #30033]: #29589
+#29570 := (<= #29383 0::Int)
+#30149 := (or #30055 #29570)
+#30158 := [th-lemma arith triangle-eq]: #30149
+#30159 := [unit-resolution #30158 #30050]: #29570
+#30162 := (not #29703)
+#30161 := (not #29208)
+#29784 := (not #29570)
+#30160 := (not #29589)
+#30163 := (or #30233 #30160 #29784 #30161 #29754 #29999 #29754 #29999 #30162 #30242)
+#30164 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30163
+#30165 := [unit-resolution #30164 #30147 #30056 #30159 #30237 #30148 #30157 #30154]: #30233
+#30169 := (not #30233)
+#30168 := (not #30232)
+#30178 := (or #30229 #30168 #30169)
+#30179 := [th-lemma arith triangle-eq]: #30178
+#30180 := [unit-resolution #30179 #30165 #30025]: #30229
+#30177 := [symm #30180]: #30258
+#30186 := [monotonicity #30177]: #30264
+#30268 := (= #29431 #29654)
+#29637 := (f77 #26182 #29368 #24996)
+#29657 := (= #29637 #29654)
+#29592 := (not #29657)
+#29638 := (f149 #29637 #26182)
+#29639 := (= f1 #29638)
+#29640 := (not #29639)
+#29597 := (or #29640 #29592)
+#29660 := (not #29597)
+#29684 := (or #27721 #29660)
+#29641 := (* #29368 #27068)
+#29642 := (+ #27318 #29641)
+#29643 := (f54 #24996 #29642)
+#29644 := (= #29637 #29643)
+#29645 := (not #29644)
+#29646 := (or #29645 #29640)
+#29647 := (not #29646)
+#29685 := (or #27721 #29647)
+#29687 := (iff #29685 #29684)
+#29689 := (iff #29684 #29684)
+#29690 := [rewrite]: #29689
+#29682 := (iff #29647 #29660)
+#29661 := (iff #29646 #29597)
+#29594 := (or #29592 #29640)
+#29598 := (iff #29594 #29597)
+#29599 := [rewrite]: #29598
+#29595 := (iff #29646 #29594)
+#29593 := (iff #29645 #29592)
+#29658 := (iff #29644 #29657)
+#29655 := (= #29643 #29654)
+#29652 := (= #29642 #29651)
+#29649 := (= #29641 #29648)
+#29650 := [rewrite]: #29649
+#29653 := [monotonicity #29650]: #29652
+#29656 := [monotonicity #29653]: #29655
+#29659 := [monotonicity #29656]: #29658
+#29591 := [monotonicity #29659]: #29593
+#29596 := [monotonicity #29591]: #29595
+#29662 := [trans #29596 #29599]: #29661
+#29683 := [monotonicity #29662]: #29682
+#29688 := [monotonicity #29683]: #29687
+#29691 := [trans #29688 #29690]: #29687
+#29686 := [quant-inst #26182 #29368 #24996]: #29685
+#29692 := [mp #29686 #29691]: #29684
+#30260 := [unit-resolution #29692 #21240]: #29660
+#29695 := (or #29597 #29657)
+#29696 := [def-axiom]: #29695
+#30261 := [unit-resolution #29696 #30260]: #29657
+#30262 := (= #29431 #29637)
+#30263 := [monotonicity #28791]: #30262
+#30269 := [trans #30263 #30261]: #30268
+#30187 := [trans #30269 #30186]: #30270
+#30188 := [trans #30187 #30267]: #30272
+#30189 := [monotonicity #30188]: #30274
+#30190 := [symm #30189]: #30276
+#30185 := [monotonicity #30190]: #30278
+#30191 := [trans #30185 #30281]: #30282
+#30192 := [trans #30191 #28789]: #30284
+#30194 := [monotonicity #30192]: #30193
+#30200 := [symm #30194]: #30199
+#30198 := [trans #14366 #30200]: #28498
+#29947 := (not #28498)
+#29948 := (or #28554 #29947)
+#29934 := [def-axiom]: #29948
+#30201 := [unit-resolution #29934 #30198]: #28554
+#30210 := (= #25501 #28512)
+#30212 := (= #28512 #25501)
+#30205 := (= #28202 f19)
+#30203 := (= #28202 #24996)
+#29392 := (or #29317 #28203 #28198)
+#29393 := [def-axiom]: #29392
+#30202 := [unit-resolution #29393 #30254 #29416]: #28203
+#30204 := [symm #30202]: #30203
+#30211 := [trans #30204 #28386]: #30205
+#30213 := [monotonicity #30211]: #30212
+#30216 := [symm #30213]: #30210
+#30217 := [trans #28841 #30216]: #28530
+#29890 := (not #28503)
+#30239 := (iff #12118 #29890)
+#30251 := (iff #12115 #28503)
+#30224 := (iff #28503 #12115)
+#30222 := (= #28502 #3053)
+#30220 := (= #28501 #3040)
+#30218 := (= #28501 #25117)
+#30219 := [monotonicity #30192]: #30218
+#30221 := [trans #30219 #28851]: #30220
+#30223 := [monotonicity #30221]: #30222
+#30288 := [monotonicity #30223]: #30224
+#30246 := [symm #30288]: #30251
+#30240 := [monotonicity #30246]: #30239
+#30238 := [mp #14369 #30240]: #29890
+#29517 := (f77 #27223 #29368 #24996)
+#29518 := (f69 #3220 #29517)
+#29519 := (f147 #29518)
+#29520 := (= f1 #29519)
+#29552 := (not #29520)
+#30315 := (iff #29552 #28509)
+#30313 := (iff #29520 #28508)
+#30311 := (iff #28508 #29520)
+#30309 := (= #28507 #29519)
+#30307 := (= #27834 #29518)
+#30305 := (= #29518 #27834)
+#30303 := (= #29517 #3257)
+#30301 := (= #29368 f309)
+#30302 := [symm #29674]: #30301
+#30304 := [monotonicity #28393 #30302 #28386]: #30303
+#30306 := [monotonicity #30304]: #30305
+#30308 := [symm #30306]: #30307
+#30310 := [monotonicity #30308]: #30309
+#30312 := [monotonicity #30310]: #30311
+#30314 := [symm #30312]: #30313
+#30316 := [monotonicity #30314]: #30315
+#29521 := (f35 f297 #29517)
+#29522 := (= f1 #29521)
+#29523 := (not #29522)
+#29527 := (or #29520 #29523)
+#29530 := (not #29527)
+#30297 := (or #29466 #29476 #29530)
+#29541 := (or #27254 #24846 #27235 #27238 #29466 #29476 #29530)
+#29524 := (or #29523 #29520)
+#29525 := (not #29524)
+#29526 := (or #27238 #29466 #29464 #24846 #27235 #29525)
+#29542 := (or #27254 #29526)
+#29549 := (iff #29542 #29541)
+#29536 := (or #24846 #27235 #27238 #29466 #29476 #29530)
+#29544 := (or #27254 #29536)
+#29547 := (iff #29544 #29541)
+#29548 := [rewrite]: #29547
+#29545 := (iff #29542 #29544)
+#29539 := (iff #29526 #29536)
+#29533 := (or #27238 #29466 #29476 #24846 #27235 #29530)
+#29537 := (iff #29533 #29536)
+#29538 := [rewrite]: #29537
+#29534 := (iff #29526 #29533)
+#29531 := (iff #29525 #29530)
+#29528 := (iff #29524 #29527)
+#29529 := [rewrite]: #29528
+#29532 := [monotonicity #29529]: #29531
+#29535 := [monotonicity #29480 #29532]: #29534
+#29540 := [trans #29535 #29538]: #29539
+#29546 := [monotonicity #29540]: #29545
+#29550 := [trans #29546 #29548]: #29549
+#29543 := [quant-inst #3039 #3043 #26182 #24998 #29368 #24996]: #29542
+#29551 := [mp #29543 #29550]: #29541
+#30298 := [unit-resolution #29551 #21684 #14351 #28797 #28426]: #30297
+#30299 := [unit-resolution #30298 #29681 #30245]: #29530
+#29553 := (or #29527 #29552)
+#29554 := [def-axiom]: #29553
+#30300 := [unit-resolution #29554 #30299]: #29552
+#30317 := [mp #30300 #30316]: #28509
+#29772 := (or #28548 #28508)
+#29773 := [def-axiom]: #29772
+#30318 := [unit-resolution #29773 #30317]: #28548
+#29907 := (or #28568 #28503 #28545 #28551 #28557)
+#29965 := [def-axiom]: #29907
+#30319 := [unit-resolution #29965 #30318 #30238 #30217 #30201 #30167]: false
+#30320 := [lemma #30319]: #28568
+#29805 := (or #28571 #28563)
+#29738 := [def-axiom]: #29805
+#30175 := [unit-resolution #29738 #30320]: #28571
+#28432 := (or #12578 #13656 #27235 #13801)
+#28375 := [hypothesis]: #13516
+#28210 := (f77 #27086 f309 #27607)
+#28211 := (f136 #28210 #27086)
+#28242 := (* -1::Int #28211)
+#28370 := (+ f309 #28242)
+#28371 := (<= #28370 0::Int)
+#28212 := (= f309 #28211)
+#28215 := (or #27129 #28212)
+#28216 := [quant-inst #27086 #3139]: #28215
+#28376 := [unit-resolution #28216 #17107]: #28212
+#28379 := (not #28212)
+#28380 := (or #28379 #28371)
+#28381 := [th-lemma arith triangle-eq]: #28380
+#28382 := [unit-resolution #28381 #28376]: #28371
+#28233 := (>= #28211 0::Int)
+#28234 := (not #28233)
+#28285 := (f77 #27223 #28211 #24996)
+#28289 := (f35 f297 #28285)
+#28290 := (= f1 #28289)
+#28291 := (not #28290)
+#28286 := (f69 #3220 #28285)
+#28287 := (f147 #28286)
+#28288 := (= f1 #28287)
+#28295 := (or #28288 #28291)
+#28402 := (iff #18559 #28291)
+#28400 := (iff #12578 #28290)
+#28398 := (iff #28290 #12578)
+#28396 := (= #28289 #3260)
+#28394 := (= #28285 #3257)
+#28387 := (= #28211 f309)
+#28388 := [symm #28376]: #28387
+#28395 := [monotonicity #28393 #28388 #28386]: #28394
+#28397 := [monotonicity #28395]: #28396
+#28399 := [monotonicity #28397]: #28398
+#28401 := [symm #28399]: #28400
+#28403 := [monotonicity #28401]: #28402
+#28383 := [hypothesis]: #18559
+#28404 := [mp #28383 #28403]: #28291
+#28323 := (or #28295 #28290)
+#28324 := [def-axiom]: #28323
+#28405 := [unit-resolution #28324 #28404]: #28295
+#28243 := (+ #24998 #28242)
+#28244 := (<= #28243 0::Int)
+#28415 := (not #28244)
+#28411 := [hypothesis]: #13802
+#28372 := (>= #28370 0::Int)
+#28412 := (or #28379 #28372)
+#28413 := [th-lemma arith triangle-eq]: #28412
+#28414 := [unit-resolution #28413 #28376]: #28372
+#28417 := (not #28372)
+#28418 := (or #28415 #28416 #28417 #13801)
+#28419 := [th-lemma arith assign-bounds 1 -1 -1]: #28418
+#28420 := [unit-resolution #28419 #28414 #28411 #28410]: #28415
+#28298 := (not #28295)
+#28428 := (or #28234 #28244 #28298)
+#28309 := (or #27254 #24846 #27235 #27238 #28234 #28244 #28298)
+#28292 := (or #28291 #28288)
+#28293 := (not #28292)
+#28231 := (+ #28211 #27164)
+#28232 := (>= #28231 0::Int)
+#28294 := (or #27238 #28234 #28232 #24846 #27235 #28293)
+#28310 := (or #27254 #28294)
+#28317 := (iff #28310 #28309)
+#28304 := (or #24846 #27235 #27238 #28234 #28244 #28298)
+#28312 := (or #27254 #28304)
+#28315 := (iff #28312 #28309)
+#28316 := [rewrite]: #28315
+#28313 := (iff #28310 #28312)
+#28307 := (iff #28294 #28304)
+#28301 := (or #27238 #28234 #28244 #24846 #27235 #28298)
+#28305 := (iff #28301 #28304)
+#28306 := [rewrite]: #28305
+#28302 := (iff #28294 #28301)
+#28299 := (iff #28293 #28298)
+#28296 := (iff #28292 #28295)
+#28297 := [rewrite]: #28296
+#28300 := [monotonicity #28297]: #28299
+#28247 := (iff #28232 #28244)
+#28236 := (+ #27164 #28211)
+#28239 := (>= #28236 0::Int)
+#28245 := (iff #28239 #28244)
+#28246 := [rewrite]: #28245
+#28240 := (iff #28232 #28239)
+#28237 := (= #28231 #28236)
+#28238 := [rewrite]: #28237
+#28241 := [monotonicity #28238]: #28240
+#28248 := [trans #28241 #28246]: #28247
+#28303 := [monotonicity #28248 #28300]: #28302
+#28308 := [trans #28303 #28306]: #28307
+#28314 := [monotonicity #28308]: #28313
+#28318 := [trans #28314 #28316]: #28317
+#28311 := [quant-inst #3039 #3043 #26182 #24998 #28211 #24996]: #28310
+#28319 := [mp #28311 #28318]: #28309
+#28429 := [unit-resolution #28319 #21684 #14351 #28427 #28426]: #28428
+#28430 := [unit-resolution #28429 #28420 #28405]: #28234
+#28431 := [th-lemma arith farkas 1 1 1 #28430 #28382 #28375]: false
+#28433 := [lemma #28431]: #28432
+#30142 := [unit-resolution #28433 #30141 #28797 #29673]: #12578
+#30170 := (or #28580 #18559 #28574)
+#30171 := [def-axiom]: #30170
+#30321 := [unit-resolution #30171 #30142 #30175]: #28580
+#29900 := (or #29899 #12584 #28577)
+#29898 := [def-axiom]: #29900
+#30323 := [unit-resolution #29898 #30321]: #30322
+#30324 := [unit-resolution #30323 #30215]: #12584
+#30424 := (+ f309 #18928)
+#30620 := (>= #30424 0::Int)
+#30702 := (not #30620)
+#30595 := (= f309 ?v0!14)
+#30648 := (not #30595)
+#30651 := [hypothesis]: #23457
+#24603 := (or #23454 #13708)
+#24604 := [def-axiom]: #24603
+#30652 := [unit-resolution #24604 #30651]: #13708
+#24587 := (+ f307 #13570)
+#24588 := (<= #24587 0::Int)
+#24593 := (or #23454 #12839)
+#24594 := [def-axiom]: #24593
+#30653 := [unit-resolution #24594 #30651]: #12839
+#30654 := (or #12857 #24588)
+#30655 := [th-lemma arith triangle-eq]: #30654
+#30656 := [unit-resolution #30655 #30653]: #24588
+#24484 := (not #18943)
+#30195 := [hypothesis]: #23421
+#24605 := (or #23454 #23418)
+#24606 := [def-axiom]: #24605
+#30176 := [unit-resolution #24606 #30195]: #23454
+#24549 := (or #23424 #23418)
+#24550 := [def-axiom]: #24549
+#30325 := [unit-resolution #24550 #30195]: #23424
+#30326 := (or #23433 #18565 #23427)
+#24559 := (or #23433 #18556 #18565 #23427)
+#24560 := [def-axiom]: #24559
+#30327 := [unit-resolution #24560 #29447]: #30326
+#30328 := [unit-resolution #30327 #30325 #30324]: #23433
+#29801 := (or #23430 #23457)
+#29776 := [hypothesis]: #23454
+#29777 := [hypothesis]: #23433
+#24555 := (or #23430 #12584)
+#24556 := [def-axiom]: #24555
+#29775 := [unit-resolution #24556 #29777]: #12584
+#29789 := (or #18565 #23469)
+#24657 := (or #23490 #23484)
+#24658 := [def-axiom]: #24657
+#29786 := [unit-resolution #24658 #30140]: #23484
+#27971 := (or #23472 #23487 #18559)
+#27967 := [hypothesis]: #12578
+#27968 := [hypothesis]: #23484
+#27930 := [hypothesis]: #23475
+#24627 := (or #23472 #12575)
+#24628 := [def-axiom]: #24627
+#27969 := [unit-resolution #24628 #27930]: #12575
+#24639 := (or #23478 #23472)
#24640 := [def-axiom]: #24639
-#27978 := [unit-resolution #24640 #27977]: #24638
-#27974 := (or #27972 #19055 #27973)
-#27967 := [hypothesis]: #24638
-#27970 := [hypothesis]: #27833
-#27971 := [th-lemma arith farkas -1 1 1 #27970 #27967 #27966]: false
-#27975 := [lemma #27971]: #27974
-#27979 := [unit-resolution #27975 #27978 #27966]: #27972
-#27983 := (or #27821 #27833)
-#24633 := (or #22552 #18704)
+#27964 := [unit-resolution #24640 #27930]: #23478
+#24649 := (or #23487 #18556 #18559 #23481)
+#24650 := [def-axiom]: #24649
+#27970 := [unit-resolution #24650 #27964 #27969 #27968 #27967]: false
+#27972 := [lemma #27970]: #27971
+#29787 := [unit-resolution #27972 #30142 #29786]: #23472
+#24633 := (or #23475 #18556 #18565 #23469)
#24634 := [def-axiom]: #24633
-#27980 := [unit-resolution #24634 #27977]: #18704
-#24631 := (or #22552 #18703)
-#24632 := [def-axiom]: #24631
-#27981 := [unit-resolution #24632 #27977]: #18703
-#27846 := (or #23341 #22536 #22537 #27821 #27833)
-#27809 := (+ #18708 #13970)
-#27810 := (<= #27809 0::Int)
-#27811 := (+ ?v0!15 #13501)
-#27812 := (>= #27811 0::Int)
-#27813 := (or #22537 #27812 #27810 #22536)
-#27847 := (or #23341 #27813)
-#27854 := (iff #27847 #27846)
-#27841 := (or #22536 #22537 #27821 #27833)
-#27849 := (or #23341 #27841)
-#27852 := (iff #27849 #27846)
-#27853 := [rewrite]: #27852
-#27850 := (iff #27847 #27849)
-#27844 := (iff #27813 #27841)
-#27838 := (or #22537 #27821 #27833 #22536)
-#27842 := (iff #27838 #27841)
-#27843 := [rewrite]: #27842
-#27839 := (iff #27813 #27838)
-#27836 := (iff #27810 #27833)
-#27826 := (+ #13970 #18708)
-#27829 := (<= #27826 0::Int)
-#27834 := (iff #27829 #27833)
-#27835 := [rewrite]: #27834
-#27830 := (iff #27810 #27829)
-#27827 := (= #27809 #27826)
-#27828 := [rewrite]: #27827
-#27831 := [monotonicity #27828]: #27830
-#27837 := [trans #27831 #27835]: #27836
-#27824 := (iff #27812 #27821)
-#27814 := (+ #13501 ?v0!15)
-#27817 := (>= #27814 0::Int)
-#27822 := (iff #27817 #27821)
-#27823 := [rewrite]: #27822
-#27818 := (iff #27812 #27817)
-#27815 := (= #27811 #27814)
-#27816 := [rewrite]: #27815
-#27819 := [monotonicity #27816]: #27818
-#27825 := [trans #27819 #27823]: #27824
-#27840 := [monotonicity #27825 #27837]: #27839
-#27845 := [trans #27840 #27843]: #27844
-#27851 := [monotonicity #27845]: #27850
-#27855 := [trans #27851 #27853]: #27854
-#27848 := [quant-inst #18702]: #27847
-#27856 := [mp #27848 #27855]: #27846
-#27984 := [unit-resolution #27856 #27982 #27981 #27980]: #27983
-#27985 := [unit-resolution #27984 #27979]: #27821
-#24635 := (not #19042)
-#24636 := (or #22552 #24635)
-#24637 := [def-axiom]: #24636
-#27986 := [unit-resolution #24637 #27977]: #24635
-#27987 := [th-lemma arith farkas -1 1 1 #27986 #27985 #27976]: false
-#27989 := [lemma #27987]: #27988
-#28092 := [unit-resolution #27989 #28091 #27982 #28090]: #22552
-#24647 := (or #23485 #23479 #22557)
-#24648 := [def-axiom]: #24647
-#28093 := [unit-resolution #24648 #28092 #28087]: #23479
-#24627 := (or #23476 #23468)
-#24628 := [def-axiom]: #24627
-#28094 := [unit-resolution #24628 #28093]: #23468
-#28007 := (or #23473 #27680 #27937 #27958 #27994)
-#27942 := (+ #27606 #13406)
-#27943 := (>= #27942 0::Int)
-#27950 := (= #27952 f314)
-#27953 := (not #27950)
-#27954 := (or #27953 #27680 #27943 #27937)
-#28008 := (or #23473 #27954)
-#28015 := (iff #28008 #28007)
-#28002 := (or #27680 #27937 #27958 #27994)
-#28010 := (or #23473 #28002)
-#28013 := (iff #28010 #28007)
-#28014 := [rewrite]: #28013
-#28011 := (iff #28008 #28010)
-#28005 := (iff #27954 #28002)
-#27999 := (or #27958 #27680 #27994 #27937)
-#28003 := (iff #27999 #28002)
-#28004 := [rewrite]: #28003
-#28000 := (iff #27954 #27999)
-#27997 := (iff #27943 #27994)
-#27959 := (+ #13406 #27606)
-#27990 := (>= #27959 0::Int)
-#27995 := (iff #27990 #27994)
-#27996 := [rewrite]: #27995
-#27991 := (iff #27943 #27990)
-#27960 := (= #27942 #27959)
-#27963 := [rewrite]: #27960
-#27992 := [monotonicity #27963]: #27991
-#27998 := [trans #27992 #27996]: #27997
-#27968 := (iff #27953 #27958)
-#27956 := (iff #27950 #27955)
-#27957 := [rewrite]: #27956
-#27969 := [monotonicity #27957]: #27968
-#28001 := [monotonicity #27969 #27998]: #28000
-#28006 := [trans #28001 #28004]: #28005
-#28012 := [monotonicity #28006]: #28011
-#28016 := [trans #28012 #28014]: #28015
-#28009 := [quant-inst #27606]: #28008
-#28017 := [mp #28009 #28016]: #28007
-#28096 := [unit-resolution #28017 #28094 #28086]: #28095
-#28097 := [unit-resolution #28096 #28085 #28080 #28071]: false
-#28099 := [lemma #28097]: #28098
-#29758 := [unit-resolution #28099 #29757 #29749 #29748 #29747 #29746]: #23488
-#24671 := (or #23497 #23457 #23491)
-#24672 := [def-axiom]: #24671
-#29759 := [unit-resolution #24672 #29758 #29745]: #23457
-#24619 := (or #23454 #13766)
-#24620 := [def-axiom]: #24619
-#29760 := [unit-resolution #24620 #29759]: #13766
-#28712 := (or #15864 #13765)
-#15775 := (<= f297 4294967295::Int)
-#15778 := (iff #13405 #15775)
-#15769 := (+ 4294967295::Int #13406)
-#15772 := (>= #15769 0::Int)
-#15776 := (iff #15772 #15775)
-#15777 := [rewrite]: #15776
-#15773 := (iff #13405 #15772)
-#15770 := (= #13407 #15769)
-#15771 := [monotonicity #7606]: #15770
-#15774 := [monotonicity #15771]: #15773
-#15779 := [trans #15774 #15777]: #15778
-#14321 := [not-or-elim #14310]: #13410
-#14323 := [and-elim #14321]: #13405
-#15780 := [mp #14323 #15779]: #15775
-#28513 := [hypothesis]: #13766
-#28701 := [hypothesis]: #18561
-#28702 := [th-lemma arith farkas -1 -1 1 #28701 #28513 #15780]: false
-#28713 := [lemma #28702]: #28712
-#29775 := [unit-resolution #28713 #29760]: #15864
-#24697 := (or #23500 #13480)
-#24698 := [def-axiom]: #24697
-#29674 := [unit-resolution #24698 #29744]: #13480
-#29789 := (or #13620 #13498)
-#29781 := [th-lemma arith farkas 1 1]: #29789
-#29770 := [unit-resolution #29781 #29674]: #13498
-#24493 := (or #23385 #18558 #18561 #23379)
-#24494 := [def-axiom]: #24493
-#29796 := [unit-resolution #24494 #29770 #29775]: #29795
-#29797 := [unit-resolution #29796 #29771]: #23379
-#24483 := (or #23376 #23370)
-#24484 := [def-axiom]: #24483
-#29798 := [unit-resolution #24484 #29797]: #23370
-#24428 := (>= #13583 -1::Int)
-#24479 := (or #23376 #13582)
-#24480 := [def-axiom]: #24479
-#29788 := [unit-resolution #24480 #29797]: #13582
-#29593 := (or #13586 #24428)
-#29608 := [th-lemma arith triangle-eq]: #29593
-#29883 := [unit-resolution #29608 #29788]: #24428
-#29763 := (not #24428)
-#29764 := (or #13514 #29763)
-#29734 := [hypothesis]: #24428
-#29761 := [hypothesis]: #13519
-#29762 := [th-lemma arith farkas -1 1 1 #29761 #29760 #29734]: false
-#29765 := [lemma #29762]: #29764
-#29611 := [unit-resolution #29765 #29883]: #13514
-#24469 := (or #23373 #13519 #23367)
+#29788 := [unit-resolution #24634 #29787]: #23472
+#29790 := [unit-resolution #29788 #29447]: #29789
+#29791 := [unit-resolution #29790 #29775]: #23469
+#24623 := (or #23466 #23460)
+#24624 := [def-axiom]: #24623
+#29792 := [unit-resolution #24624 #29791]: #23460
+#24565 := (or #23436 #23430)
+#24566 := [def-axiom]: #24565
+#29793 := [unit-resolution #24566 #29777]: #23436
+#29796 := (or #23445 #23439)
+#29794 := (or #23445 #18556 #23439)
+#24575 := (or #23445 #18556 #18559 #23439)
+#24576 := [def-axiom]: #24575
+#29795 := [unit-resolution #24576 #30142]: #29794
+#29797 := [unit-resolution #29795 #29447]: #29796
+#29798 := [unit-resolution #29797 #29793]: #23445
+#24583 := (or #23448 #23442)
+#24584 := [def-axiom]: #24583
+#29799 := [unit-resolution #24584 #29798]: #23448
+#24613 := (or #23463 #23451 #23457)
+#24614 := [def-axiom]: #24613
+#29800 := [unit-resolution #24614 #29799 #29792 #29776]: false
+#29802 := [lemma #29800]: #29801
+#30329 := [unit-resolution #29802 #30328 #30176]: false
+#30330 := [lemma #30329]: #23418
+#30607 := (or #23421 #23415)
+#15811 := (<= f296 4294967295::Int)
+#15814 := (iff #13441 #15811)
+#15805 := (+ 4294967295::Int #13442)
+#15808 := (>= #15805 0::Int)
+#15812 := (iff #15808 #15811)
+#15813 := [rewrite]: #15812
+#15809 := (iff #13441 #15808)
+#15806 := (= #13443 #15805)
+#15807 := [monotonicity #7642]: #15806
+#15810 := [monotonicity #15807]: #15809
+#15815 := [trans #15810 #15813]: #15814
+#14357 := [not-or-elim #14346]: #13446
+#14359 := [and-elim #14357]: #13441
+#15816 := [mp #14359 #15815]: #15811
+#29996 := [hypothesis]: #18597
+#29985 := [th-lemma arith farkas -1 -1 1 #30141 #29996 #15816]: false
+#29988 := [lemma #29985]: #15900
+#30605 := (or #23421 #18597 #23415)
+#30602 := (or #13656 #13534)
+#30603 := [th-lemma arith farkas 1 1]: #30602
+#30604 := [unit-resolution #30603 #29673]: #13534
+#24529 := (or #23421 #18594 #18597 #23415)
+#24530 := [def-axiom]: #24529
+#30606 := [unit-resolution #24530 #30604]: #30605
+#30608 := [unit-resolution #30606 #29988]: #30607
+#30609 := [unit-resolution #30608 #30330]: #23415
+#24519 := (or #23412 #23406)
+#24520 := [def-axiom]: #24519
+#30660 := [unit-resolution #24520 #30609]: #23406
+#24464 := (>= #13619 -1::Int)
+#24515 := (or #23412 #13618)
+#24516 := [def-axiom]: #24515
+#30610 := [unit-resolution #24516 #30609]: #13618
+#30611 := (or #13622 #24464)
+#30612 := [th-lemma arith triangle-eq]: #30611
+#30613 := [unit-resolution #30612 #30610]: #24464
+#29780 := (not #24464)
+#29781 := (or #29780 #13550)
+#29774 := [hypothesis]: #24464
+#29778 := [hypothesis]: #13555
+#29779 := [th-lemma arith farkas -1 1 1 #29778 #30141 #29774]: false
+#29782 := [lemma #29779]: #29781
+#30661 := [unit-resolution #29782 #30613]: #13550
+#24505 := (or #23409 #13555 #23403)
+#24506 := [def-axiom]: #24505
+#30662 := [unit-resolution #24506 #30661 #30660]: #23403
+#24497 := (or #23400 #23394)
+#24498 := [def-axiom]: #24497
+#30663 := [unit-resolution #24498 #30662]: #23394
+#24590 := (+ f308 #13592)
+#24592 := (>= #24590 0::Int)
+#24595 := (or #23454 #12842)
+#24596 := [def-axiom]: #24595
+#30664 := [unit-resolution #24596 #30651]: #12842
+#30665 := (or #12848 #24592)
+#30666 := [th-lemma arith triangle-eq]: #30665
+#30667 := [unit-resolution #30666 #30664]: #24592
+#30668 := (not #24592)
+#30671 := (or #13595 #30668)
+#30669 := (or #13595 #13979 #30668)
+#30670 := [th-lemma arith assign-bounds -1 -1]: #30669
+#30672 := [unit-resolution #30670 #30103]: #30671
+#30673 := [unit-resolution #30672 #30667]: #13595
+#30680 := (= #3153 #3299)
+#30678 := (= #3299 #3153)
+#30675 := (= #3298 #3152)
+#30674 := [symm #30664]: #3329
+#30676 := [monotonicity #30674]: #30675
+#30679 := [monotonicity #30676]: #30678
+#30681 := [symm #30679]: #30680
+#30682 := (= f315 #3153)
+#30677 := [symm #30653]: #3328
+#30683 := [trans #30677 #30101]: #30682
+#30684 := [trans #30683 #30681]: #12643
+#24469 := (or #22364 #22362 #13594)
#24470 := [def-axiom]: #24469
-#29612 := [unit-resolution #24470 #29611 #29798]: #23367
-#24461 := (or #23364 #23358)
-#24462 := [def-axiom]: #24461
-#29610 := [unit-resolution #24462 #29612]: #23358
-#24457 := (or #23361 #23355 #22380)
-#24458 := [def-axiom]: #24457
-#29766 := [unit-resolution #24458 #29610 #29718]: #22380
-#24449 := (or #22375 #24448)
-#24450 := [def-axiom]: #24449
-#29724 := [unit-resolution #24450 #29766]: #24448
-#30349 := (not #24552)
-#29599 := (or #30220 #18907 #30349)
-#29597 := [th-lemma arith assign-bounds -1 -1]: #29599
-#29598 := [unit-resolution #29597 #29724 #29590]: #30220
-#24443 := (or #22375 #18580)
-#24444 := [def-axiom]: #24443
-#29609 := [unit-resolution #24444 #29766]: #18580
-#24441 := (or #22375 #18579)
-#24442 := [def-axiom]: #24441
-#29607 := [unit-resolution #24442 #29766]: #18579
-#29528 := (not #29868)
-#30337 := (not #30332)
-#30348 := (not #30338)
-#24567 := (or #23418 #13672)
-#24568 := [def-axiom]: #24567
-#29677 := [unit-resolution #24568 #28423]: #13672
-#30350 := (or #30348 #18907 #30349 #13671)
-#30343 := [hypothesis]: #13672
-#30344 := [hypothesis]: #24552
-#30345 := [hypothesis]: #24448
-#30346 := [hypothesis]: #30338
-#30347 := [th-lemma arith farkas 1 -1 -1 1 #30346 #30345 #30344 #30343]: false
-#30351 := [lemma #30347]: #30350
-#29874 := [unit-resolution #30351 #29724 #29590 #29677]: #30348
-#30339 := (or #30337 #30338)
-#30340 := [th-lemma arith triangle-eq]: #30339
-#29875 := [unit-resolution #30340 #29874]: #30337
-#29596 := (or #29528 #30332)
-#30115 := (= #18584 #3266)
-#30117 := (= #18583 #3257)
-#30119 := (= ?v0!14 f310)
-#29952 := [hypothesis]: #29868
-#30116 := [symm #29952]: #30119
-#30118 := [monotonicity #30116]: #30117
-#30110 := [monotonicity #30118]: #30115
-#30120 := [symm #30110]: #30332
-#29943 := [hypothesis]: #30337
-#30077 := [unit-resolution #29943 #30120]: false
-#30080 := [lemma #30077]: #29596
-#29873 := [unit-resolution #30080 #29875]: #29528
-#29810 := (+ f310 #18892)
-#29634 := (>= #29810 0::Int)
-#24445 := (not #18894)
-#24446 := (or #22375 #24445)
-#24447 := [def-axiom]: #24446
-#29887 := [unit-resolution #24447 #29766]: #24445
-#29882 := (or #29634 #18894 #29763)
-#29717 := [th-lemma arith assign-bounds 1 1]: #29882
-#29618 := [unit-resolution #29717 #29887 #29883]: #29634
-#30414 := (not #29634)
-#30418 := (or #30414 #29868 #22359 #22360 #29823)
-#30217 := [hypothesis]: #29528
-#30226 := [hypothesis]: #29634
-#29811 := (<= #29810 0::Int)
-#30221 := [hypothesis]: #30220
-#30222 := [hypothesis]: #18580
-#30238 := [hypothesis]: #18579
-#29699 := (or #23341 #22359 #22360 #29811 #29823)
-#29799 := (+ #18584 #13970)
-#29800 := (<= #29799 0::Int)
-#29801 := (+ ?v0!14 #13501)
-#29802 := (>= #29801 0::Int)
-#29803 := (or #22360 #29802 #29800 #22359)
-#29936 := (or #23341 #29803)
-#30174 := (iff #29936 #29699)
-#29831 := (or #22359 #22360 #29811 #29823)
-#29867 := (or #23341 #29831)
-#30176 := (iff #29867 #29699)
-#30172 := [rewrite]: #30176
-#30161 := (iff #29936 #29867)
-#29834 := (iff #29803 #29831)
-#29828 := (or #22360 #29811 #29823 #22359)
-#29832 := (iff #29828 #29831)
-#29833 := [rewrite]: #29832
-#29829 := (iff #29803 #29828)
-#29826 := (iff #29800 #29823)
-#29816 := (+ #13970 #18584)
-#29819 := (<= #29816 0::Int)
-#29824 := (iff #29819 #29823)
-#29825 := [rewrite]: #29824
-#29820 := (iff #29800 #29819)
-#29817 := (= #29799 #29816)
-#29818 := [rewrite]: #29817
-#29821 := [monotonicity #29818]: #29820
-#29827 := [trans #29821 #29825]: #29826
-#29814 := (iff #29802 #29811)
-#29804 := (+ #13501 ?v0!14)
-#29807 := (>= #29804 0::Int)
-#29812 := (iff #29807 #29811)
-#29813 := [rewrite]: #29812
-#29808 := (iff #29802 #29807)
-#29805 := (= #29801 #29804)
-#29806 := [rewrite]: #29805
-#29809 := [monotonicity #29806]: #29808
-#29815 := [trans #29809 #29813]: #29814
-#29830 := [monotonicity #29815 #29827]: #29829
-#29835 := [trans #29830 #29833]: #29834
-#30170 := [monotonicity #29835]: #30161
-#30177 := [trans #30170 #30172]: #30174
-#29870 := [quant-inst #18578]: #29936
-#30173 := [mp #29870 #30177]: #29699
-#30239 := [unit-resolution #30173 #29746 #30238 #30222 #30221]: #29811
-#30413 := (not #29811)
-#30415 := (or #29868 #30413 #30414)
-#30416 := [th-lemma arith triangle-eq]: #30415
-#30417 := [unit-resolution #30416 #30239 #30226 #30217]: false
-#30419 := [lemma #30417]: #30418
-#29716 := [unit-resolution #30419 #29618 #29873 #29607 #29609 #29598]: false
-#29631 := [lemma #29716]: #23418
-#27798 := (f69 #3220 #3257)
-#28223 := (f147 #27798)
-#28228 := (f36 f298 #28223)
-#28229 := (= f37 #28228)
-#28224 := (f222 f298 #28223)
-#28227 := (= f1 #28224)
-#28285 := (or #28227 #28229)
-#28288 := (not #28285)
-#28238 := (f148 #27798)
-#28239 := (= f1 #28238)
-#28240 := (not #28239)
-#28235 := (f38 f298 #28223)
-#28236 := (= f1 #28235)
-#28237 := (not #28236)
-#28279 := (or #28237 #28240)
-#28282 := (not #28279)
-#28118 := (f24 #3257)
-#28243 := (f23 #28118)
-#28261 := (= f25 #28243)
-#28276 := (not #28261)
-#28232 := (f24 #28223)
-#28233 := (f23 #28232)
-#28234 := (= f25 #28233)
-#28294 := (or #28234 #28276 #28282 #28288)
-#28299 := (not #28294)
-#28250 := (f36 f298 #3257)
-#28251 := (= f37 #28250)
-#28248 := (f222 f298 #3257)
-#28249 := (= f1 #28248)
-#28264 := (or #28249 #28251)
-#28267 := (not #28264)
-#28270 := (or #28261 #28267)
-#28273 := (not #28270)
-#28302 := (or #28273 #28299)
-#28305 := (not #28302)
-#28308 := (or #18523 #28305)
-#28311 := (not #28308)
-#28314 := (iff #12548 #28311)
-#30431 := (not #28314)
-#30440 := [hypothesis]: #30431
-#29632 := (or #28805 #28314)
-#28230 := (or #28229 #28227)
-#28231 := (not #28230)
-#28241 := (or #28240 #28237)
-#28242 := (not #28241)
-#28244 := (= #28243 f25)
-#28245 := (not #28244)
-#28246 := (or #28245 #28242 #28234 #28231)
-#28247 := (not #28246)
-#28252 := (or #28251 #28249)
-#28253 := (not #28252)
-#28254 := (or #28244 #28253)
-#28255 := (not #28254)
-#28256 := (or #28255 #28247)
-#28257 := (not #28256)
-#28258 := (or #18523 #28257)
-#28259 := (not #28258)
-#28260 := (iff #12548 #28259)
-#29633 := (or #28805 #28260)
-#29715 := (iff #29633 #29632)
-#30083 := (iff #29632 #29632)
-#30081 := [rewrite]: #30083
-#28315 := (iff #28260 #28314)
-#28312 := (iff #28259 #28311)
-#28309 := (iff #28258 #28308)
-#28306 := (iff #28257 #28305)
-#28303 := (iff #28256 #28302)
-#28300 := (iff #28247 #28299)
-#28297 := (iff #28246 #28294)
-#28291 := (or #28276 #28282 #28234 #28288)
-#28295 := (iff #28291 #28294)
-#28296 := [rewrite]: #28295
-#28292 := (iff #28246 #28291)
-#28289 := (iff #28231 #28288)
-#28286 := (iff #28230 #28285)
-#28287 := [rewrite]: #28286
-#28290 := [monotonicity #28287]: #28289
-#28283 := (iff #28242 #28282)
-#28280 := (iff #28241 #28279)
-#28281 := [rewrite]: #28280
-#28284 := [monotonicity #28281]: #28283
-#28277 := (iff #28245 #28276)
-#28262 := (iff #28244 #28261)
-#28263 := [rewrite]: #28262
-#28278 := [monotonicity #28263]: #28277
-#28293 := [monotonicity #28278 #28284 #28290]: #28292
-#28298 := [trans #28293 #28296]: #28297
-#28301 := [monotonicity #28298]: #28300
-#28274 := (iff #28255 #28273)
-#28271 := (iff #28254 #28270)
-#28268 := (iff #28253 #28267)
-#28265 := (iff #28252 #28264)
-#28266 := [rewrite]: #28265
-#28269 := [monotonicity #28266]: #28268
-#28272 := [monotonicity #28263 #28269]: #28271
-#28275 := [monotonicity #28272]: #28274
-#28304 := [monotonicity #28275 #28301]: #28303
-#28307 := [monotonicity #28304]: #28306
-#28310 := [monotonicity #28307]: #28309
-#28313 := [monotonicity #28310]: #28312
-#28316 := [monotonicity #28313]: #28315
-#30082 := [monotonicity #28316]: #29715
-#30079 := [trans #30082 #30081]: #29715
-#29714 := [quant-inst #3039 #3257]: #29633
-#29698 := [mp #29714 #30079]: #29632
-#30441 := [unit-resolution #29698 #22058 #30440]: false
-#30442 := [lemma #30441]: #28314
-#30489 := (or #30431 #12548)
-#29869 := [hypothesis]: #28294
-#29937 := (= #3047 #28228)
-#29960 := (= #28228 #3047)
-#30333 := (= #28223 #3044)
-#30330 := (= #28223 #27103)
-#28220 := (f77 #24797 f310 #27080)
-#28221 := (f137 #28220 #24797)
-#28154 := (f77 #27103 #28221 #24960)
-#28159 := (f69 #3220 #28154)
-#28219 := (f147 #28159)
-#30328 := (= #28219 #27103)
-#28206 := (= #27103 #28219)
-#28217 := (f148 #28159)
-#28218 := (= f1 #28217)
-#28214 := (f78 #28159)
-#28215 := (= f1 #28214)
-#28216 := (not #28215)
-#28207 := (not #28206)
-#28149 := (f35 f298 #28154)
-#28157 := (= f1 #28149)
-#28158 := (not #28157)
-#28338 := (or #28158 #28207 #28216 #28218)
-#28341 := (not #28338)
-#28211 := (>= #28221 0::Int)
-#24703 := (or #23500 #13998)
-#24704 := [def-axiom]: #24703
-#30247 := [unit-resolution #24704 #29744]: #13998
-#28331 := (* -1::Int #28221)
-#28472 := (+ f310 #28331)
-#28473 := (<= #28472 0::Int)
-#28222 := (= f310 #28221)
-#28155 := (or #27087 #28222)
-#28156 := [quant-inst #24797 #3139]: #28155
-#28478 := [unit-resolution #28156 #17071]: #28222
-#28481 := (not #28222)
-#28482 := (or #28481 #28473)
-#28483 := [th-lemma arith triangle-eq]: #28482
-#28484 := [unit-resolution #28483 #28478]: #28473
-#30252 := (not #28473)
-#30253 := (or #28211 #22582 #30252)
-#30282 := [th-lemma arith assign-bounds 1 1]: #30253
-#30283 := [unit-resolution #30282 #28484 #30247]: #28211
-#28212 := (not #28211)
-#30281 := (or #28212 #28341)
-#28332 := (+ #24962 #28331)
-#28333 := (<= #28332 0::Int)
-#28517 := (not #28333)
-#28474 := (>= #28472 0::Int)
-#28514 := (or #28481 #28474)
-#28515 := [th-lemma arith triangle-eq]: #28514
-#28516 := [unit-resolution #28515 #28478]: #28474
-#28519 := (not #28474)
-#30285 := (or #28517 #28519 #13765)
-#28520 := (or #28517 #28518 #28519 #13765)
-#28521 := [th-lemma arith assign-bounds 1 -1 -1]: #28520
-#30258 := [unit-resolution #28521 #28512]: #30285
-#30286 := [unit-resolution #30258 #28516 #29760]: #28517
-#29476 := (or #27726 #27121 #28212 #28333 #28341)
-#28205 := (or #28207 #28218 #28216 #28158)
-#28208 := (not #28205)
-#28209 := (+ #28221 #27122)
-#28210 := (>= #28209 0::Int)
-#28213 := (or #28212 #28210 #27121 #28208)
-#29477 := (or #27726 #28213)
-#29484 := (iff #29477 #29476)
-#28347 := (or #27121 #28212 #28333 #28341)
-#29479 := (or #27726 #28347)
-#29482 := (iff #29479 #29476)
-#29483 := [rewrite]: #29482
-#29480 := (iff #29477 #29479)
-#28350 := (iff #28213 #28347)
-#28344 := (or #28212 #28333 #27121 #28341)
-#28348 := (iff #28344 #28347)
-#28349 := [rewrite]: #28348
-#28345 := (iff #28213 #28344)
-#28342 := (iff #28208 #28341)
-#28339 := (iff #28205 #28338)
-#28340 := [rewrite]: #28339
-#28343 := [monotonicity #28340]: #28342
-#28336 := (iff #28210 #28333)
-#28225 := (+ #27122 #28221)
-#28328 := (>= #28225 0::Int)
-#28334 := (iff #28328 #28333)
-#28335 := [rewrite]: #28334
-#28329 := (iff #28210 #28328)
-#28226 := (= #28209 #28225)
-#28327 := [rewrite]: #28226
-#28330 := [monotonicity #28327]: #28329
-#28337 := [trans #28330 #28335]: #28336
-#28346 := [monotonicity #28337 #28343]: #28345
-#28351 := [trans #28346 #28349]: #28350
-#29481 := [monotonicity #28351]: #29480
-#29485 := [trans #29481 #29483]: #29484
-#29478 := [quant-inst #3039 #3043 #24960 #24962 #28221]: #29477
-#29486 := [mp #29478 #29485]: #29476
-#30287 := [unit-resolution #29486 #20988 #30286 #28914]: #30281
-#30288 := [unit-resolution #30287 #30283]: #28341
-#29489 := (or #28338 #28206)
-#29490 := [def-axiom]: #29489
-#30257 := [unit-resolution #29490 #30288]: #28206
-#30329 := [symm #30257]: #30328
-#30326 := (= #28223 #28219)
-#30324 := (= #27798 #28159)
-#29979 := (= #28159 #27798)
-#29970 := (= #28154 #3257)
-#27807 := (f128 #3257)
-#28101 := (f54 #24960 #27807)
-#30319 := (= #28101 #3257)
-#28102 := (= #3257 #28101)
-#28047 := (f59 #3257 #24960)
-#28042 := (= f1 #28047)
-#30290 := (= #3258 #28047)
-#29430 := (= #28047 #3258)
-#29431 := [monotonicity #28488]: #29430
-#30291 := [symm #29431]: #30290
-#28119 := (= #24960 #28118)
-#28192 := (f81 f310 #27032)
-#28193 := (+ #27034 #28192)
-#28194 := (f54 #24960 #28193)
-#28449 := (f24 #28194)
-#29455 := (= #28449 #28118)
-#29451 := (= #28118 #28449)
-#29449 := (= #3257 #28194)
-#28188 := (f77 #24797 f310 #24960)
-#28195 := (= #28188 #28194)
-#28196 := (not #28195)
-#28189 := (f150 #28188 #24797)
-#28190 := (= f1 #28189)
-#28191 := (not #28190)
-#28199 := (or #28191 #28196)
-#28202 := (not #28199)
-#29398 := (or #27451 #28202)
-#28197 := (or #28196 #28191)
-#28198 := (not #28197)
-#29399 := (or #27451 #28198)
-#29401 := (iff #29399 #29398)
-#29403 := (iff #29398 #29398)
-#29404 := [rewrite]: #29403
-#28203 := (iff #28198 #28202)
-#28200 := (iff #28197 #28199)
-#28201 := [rewrite]: #28200
-#28204 := [monotonicity #28201]: #28203
-#29402 := [monotonicity #28204]: #29401
-#29405 := [trans #29402 #29404]: #29401
-#29400 := [quant-inst #24797 #3139 #24960]: #29399
-#29406 := [mp #29400 #29405]: #29398
-#29441 := [unit-resolution #29406 #21204]: #28202
-#29409 := (or #28199 #28195)
-#29410 := [def-axiom]: #29409
-#29442 := [unit-resolution #29410 #29441]: #28195
-#29447 := (= #3257 #28188)
-#29445 := (= #28188 #3257)
-#29446 := [monotonicity #28946 #28488]: #29445
-#29448 := [symm #29446]: #29447
-#29450 := [trans #29448 #29442]: #29449
-#29452 := [monotonicity #29450]: #29451
-#29456 := [symm #29452]: #29455
-#28450 := (= #24960 #28449)
-#29417 := (or #25028 #28450)
-#29418 := [quant-inst #24960 #28193]: #29417
-#29440 := [unit-resolution #29418 #23276]: #28450
-#29457 := [trans #29440 #29456]: #28119
-#29378 := (not #28119)
-#28121 := (iff #28042 #28119)
-#29368 := (or #26174 #28121)
-#28120 := (iff #28119 #28042)
-#29369 := (or #26174 #28120)
-#29371 := (iff #29369 #29368)
-#29373 := (iff #29368 #29368)
-#29374 := [rewrite]: #29373
-#28122 := (iff #28120 #28121)
-#28123 := [rewrite]: #28122
-#29372 := [monotonicity #28123]: #29371
-#29375 := [trans #29372 #29374]: #29371
-#29370 := [quant-inst #3257 #24960]: #29369
-#29376 := [mp #29370 #29375]: #29368
-#29428 := [unit-resolution #29376 #23263]: #28121
-#28100 := (not #28042)
-#29436 := (iff #18520 #28100)
-#29434 := (iff #12539 #28042)
-#29432 := (iff #28042 #12539)
-#29433 := [monotonicity #29431]: #29432
-#29435 := [symm #29433]: #29434
-#29437 := [monotonicity #29435]: #29436
-#29429 := [hypothesis]: #18520
-#29438 := [mp #29429 #29437]: #28100
-#29377 := (not #28121)
-#29379 := (or #29377 #28042 #29378)
-#29380 := [def-axiom]: #29379
-#29439 := [unit-resolution #29380 #29438 #29428]: #29378
-#29458 := [unit-resolution #29439 #29457]: false
-#29459 := [lemma #29458]: #12539
-#30299 := [trans #29459 #30291]: #28042
-#28104 := (or #28100 #28102)
-#29381 := (or #26158 #28100 #28102)
-#28103 := (or #28102 #28100)
-#29382 := (or #26158 #28103)
-#29424 := (iff #29382 #29381)
-#29413 := (or #26158 #28104)
-#29422 := (iff #29413 #29381)
-#29423 := [rewrite]: #29422
-#29420 := (iff #29382 #29413)
-#28105 := (iff #28103 #28104)
-#28106 := [rewrite]: #28105
-#29421 := [monotonicity #28106]: #29420
-#29425 := [trans #29421 #29423]: #29424
-#29419 := [quant-inst #3257 #24960]: #29382
-#29426 := [mp #29419 #29425]: #29381
-#30300 := [unit-resolution #29426 #18248]: #28104
-#30303 := [unit-resolution #30300 #30299]: #28102
-#30298 := [symm #30303]: #30319
-#30322 := (= #28154 #28101)
-#29661 := (f81 #28221 #27032)
-#29662 := (+ #27307 #29661)
-#29663 := (f54 #24960 #29662)
-#30312 := (= #29663 #28101)
-#30302 := (= #29662 #27807)
-#30237 := (= #27807 #29662)
-#30243 := (* -1::Int #29662)
-#30244 := (+ #27807 #30243)
-#30190 := (<= #30244 0::Int)
-#29586 := (* -1::Int #29661)
-#29526 := (+ #28192 #29586)
-#29527 := (<= #29526 0::Int)
-#29585 := (= #28192 #29661)
-#30240 := (= #29661 #28192)
-#28489 := (= #28221 f310)
-#28490 := [symm #28478]: #28489
-#30230 := [monotonicity #28490]: #30240
-#30355 := [symm #30230]: #29585
-#30289 := (not #29585)
-#30284 := (or #30289 #29527)
-#30363 := [th-lemma arith triangle-eq]: #30284
-#30364 := [unit-resolution #30363 #30355]: #29527
-#28451 := (f128 #28194)
-#28455 := (* -1::Int #28451)
-#29517 := (+ #27807 #28455)
-#29518 := (<= #29517 0::Int)
-#29516 := (= #27807 #28451)
-#30369 := (= #28451 #27807)
-#30367 := (= #28194 #3257)
-#30365 := (= #28194 #28188)
-#30366 := [symm #29442]: #30365
-#30368 := [trans #30366 #29446]: #30367
-#30370 := [monotonicity #30368]: #30369
-#30371 := [symm #30370]: #29516
-#30372 := (not #29516)
-#30373 := (or #30372 #29518)
-#30374 := [th-lemma arith triangle-eq]: #30373
-#30375 := [unit-resolution #30374 #30371]: #29518
-#28456 := (+ #28192 #28455)
-#28457 := (+ #27034 #28456)
-#29515 := (>= #28457 0::Int)
-#28458 := (= #28457 0::Int)
-#29503 := (or #25034 #28458)
-#28452 := (= #28193 #28451)
-#29504 := (or #25034 #28452)
-#29508 := (iff #29504 #29503)
-#29510 := (iff #29503 #29503)
-#29511 := [rewrite]: #29510
-#28459 := (iff #28452 #28458)
-#28460 := [rewrite]: #28459
-#29509 := [monotonicity #28460]: #29508
-#29512 := [trans #29509 #29511]: #29508
-#29507 := [quant-inst #24960 #28193]: #29504
-#29513 := [mp #29507 #29512]: #29503
-#30376 := [unit-resolution #29513 #23270]: #28458
-#30377 := (not #28458)
-#30378 := (or #30377 #29515)
-#30379 := [th-lemma arith triangle-eq]: #30378
-#30380 := [unit-resolution #30379 #30376]: #29515
-#30385 := (not #29527)
-#30384 := (not #28581)
-#30383 := (not #27720)
-#30382 := (not #29515)
-#30381 := (not #29518)
-#30386 := (or #30190 #30381 #30382 #30383 #30384 #30385)
-#30387 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30386
-#30388 := [unit-resolution #30387 #28931 #30380 #30375 #30364 #28961]: #30190
-#30245 := (>= #30244 0::Int)
-#29637 := (>= #29526 0::Int)
-#30389 := (or #30289 #29637)
-#30390 := [th-lemma arith triangle-eq]: #30389
-#30391 := [unit-resolution #30390 #30355]: #29637
-#29519 := (>= #29517 0::Int)
-#30392 := (or #30372 #29519)
-#30393 := [th-lemma arith triangle-eq]: #30392
-#30394 := [unit-resolution #30393 #30371]: #29519
-#29514 := (<= #28457 0::Int)
-#30395 := (or #30377 #29514)
-#30396 := [th-lemma arith triangle-eq]: #30395
-#30397 := [unit-resolution #30396 #30376]: #29514
-#30402 := (not #29637)
-#30401 := (not #28582)
-#30400 := (not #27719)
-#30399 := (not #29514)
-#30398 := (not #29519)
-#30403 := (or #30245 #30398 #30399 #30400 #30401 #30402)
-#30404 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30403
-#30405 := [unit-resolution #30404 #28934 #30397 #30394 #30391 #28958]: #30245
-#30407 := (not #30245)
-#30406 := (not #30190)
-#30408 := (or #30237 #30406 #30407)
-#30409 := [th-lemma arith triangle-eq]: #30408
-#30410 := [unit-resolution #30409 #30405 #30388]: #30237
-#29871 := [symm #30410]: #30302
-#29864 := [monotonicity #29871]: #30312
-#30320 := (= #28154 #29663)
-#29657 := (f77 #26146 #28221 #24960)
-#29664 := (= #29657 #29663)
-#29665 := (not #29664)
-#29658 := (f150 #29657 #26146)
-#29659 := (= f1 #29658)
-#29660 := (not #29659)
-#29668 := (or #29660 #29665)
-#29671 := (not #29668)
-#29559 := (or #27451 #29671)
-#29666 := (or #29665 #29660)
-#29667 := (not #29666)
-#29560 := (or #27451 #29667)
-#29562 := (iff #29560 #29559)
-#29564 := (iff #29559 #29559)
-#29578 := [rewrite]: #29564
-#29672 := (iff #29667 #29671)
-#29669 := (iff #29666 #29668)
-#29670 := [rewrite]: #29669
-#29673 := [monotonicity #29670]: #29672
-#29563 := [monotonicity #29673]: #29562
-#29579 := [trans #29563 #29578]: #29562
-#29561 := [quant-inst #26146 #28221 #24960]: #29560
-#29577 := [mp #29561 #29579]: #29559
-#30315 := [unit-resolution #29577 #21204]: #29671
-#29581 := (or #29668 #29664)
-#29582 := [def-axiom]: #29581
-#30316 := [unit-resolution #29582 #30315]: #29664
-#30301 := (= #28154 #29657)
-#30317 := [monotonicity #28365]: #30301
-#30321 := [trans #30317 #30316]: #30320
-#29872 := [trans #30321 #29864]: #30322
-#29955 := [trans #29872 #30298]: #29970
-#29956 := [monotonicity #29955]: #29979
-#29957 := [symm #29956]: #30324
-#29958 := [monotonicity #29957]: #30326
-#29959 := [trans #29958 #30329]: #30330
-#29954 := [trans #29959 #28364]: #30333
-#29934 := [monotonicity #29954]: #29960
-#29935 := [symm #29934]: #29937
-#29944 := [trans #14330 #29935]: #28229
-#29725 := (not #28229)
-#29773 := (or #28285 #29725)
-#29774 := [def-axiom]: #29773
-#29951 := [unit-resolution #29774 #29944]: #28285
-#29706 := (= #25465 #28243)
-#29679 := (= #28243 #25465)
-#29938 := (= #28118 f19)
-#29839 := (= #28118 #24960)
-#29427 := (or #29377 #28100 #28119)
-#29453 := [def-axiom]: #29427
-#29953 := [unit-resolution #29453 #30299 #29428]: #28119
-#29681 := [symm #29953]: #29839
-#29682 := [trans #29681 #28488]: #29938
-#29680 := [monotonicity #29682]: #29679
-#30114 := [symm #29680]: #29706
-#29708 := [trans #29027 #30114]: #28261
-#29794 := (not #28234)
-#29837 := (iff #12082 #29794)
-#30112 := (iff #12079 #28234)
-#29876 := (iff #28234 #12079)
-#29843 := (= #28233 #3053)
-#29844 := (= #28232 #3040)
-#29842 := (= #28232 #25081)
-#29707 := [monotonicity #29954]: #29842
-#29845 := [trans #29707 #28878]: #29844
-#29846 := [monotonicity #29845]: #29843
-#29836 := [monotonicity #29846]: #29876
-#30113 := [symm #29836]: #30112
-#29838 := [monotonicity #30113]: #29837
-#30111 := [mp #14333 #29838]: #29794
-#28374 := (f77 #27181 #28221 #24960)
-#28375 := (f69 #3220 #28374)
-#28376 := (f148 #28375)
-#28377 := (= f1 #28376)
-#29498 := (not #28377)
-#30162 := (iff #29498 #28240)
-#30093 := (iff #28377 #28239)
-#30146 := (iff #28239 #28377)
-#30141 := (= #28238 #28376)
-#30156 := (= #27798 #28375)
-#30096 := (= #28375 #27798)
-#28496 := (= #28374 #3257)
-#28497 := [monotonicity #28495 #28490 #28488]: #28496
-#30097 := [monotonicity #28497]: #30096
-#30142 := [symm #30097]: #30156
-#29981 := [monotonicity #30142]: #30141
-#30140 := [monotonicity #29981]: #30146
-#30157 := [symm #30140]: #30093
-#30171 := [monotonicity #30157]: #30162
-#28378 := (f35 f298 #28374)
-#28379 := (= f1 #28378)
-#28380 := (not #28379)
-#28384 := (or #28377 #28380)
-#28317 := (not #28384)
-#30144 := (or #28212 #28317)
-#28415 := (or #27212 #24810 #27193 #27196 #28212 #28333 #28317)
-#28381 := (or #28380 #28377)
-#28382 := (not #28381)
-#28383 := (or #27196 #28212 #28210 #24810 #27193 #28382)
-#28416 := (or #27212 #28383)
-#28407 := (iff #28416 #28415)
-#28323 := (or #24810 #27193 #27196 #28212 #28333 #28317)
-#28418 := (or #27212 #28323)
-#28405 := (iff #28418 #28415)
-#28406 := [rewrite]: #28405
-#28419 := (iff #28416 #28418)
-#28326 := (iff #28383 #28323)
-#28318 := (or #27196 #28212 #28333 #24810 #27193 #28317)
-#28324 := (iff #28318 #28323)
-#28325 := [rewrite]: #28324
-#28321 := (iff #28383 #28318)
-#28319 := (iff #28382 #28317)
-#28385 := (iff #28381 #28384)
-#28386 := [rewrite]: #28385
-#28320 := [monotonicity #28386]: #28319
-#28322 := [monotonicity #28337 #28320]: #28321
-#28414 := [trans #28322 #28325]: #28326
-#28404 := [monotonicity #28414]: #28419
-#28408 := [trans #28404 #28406]: #28407
-#28417 := [quant-inst #3039 #3043 #26146 #24962 #28221 #24960]: #28416
-#28403 := [mp #28417 #28408]: #28415
-#30145 := [unit-resolution #28403 #21648 #14315 #28130 #30286 #28528]: #30144
-#30138 := [unit-resolution #30145 #30283]: #28317
-#29499 := (or #28384 #29498)
-#29500 := [def-axiom]: #29499
-#30095 := [unit-resolution #29500 #30138]: #29498
-#30137 := [mp #30095 #30171]: #28240
-#29767 := (or #28279 #28239)
-#29768 := [def-axiom]: #29767
-#30094 := [unit-resolution #29768 #30137]: #28279
-#29524 := (or #28299 #28234 #28276 #28282 #28288)
-#29592 := [def-axiom]: #29524
-#30092 := [unit-resolution #29592 #30094 #30111 #29708 #29951 #29869]: false
-#30175 := [lemma #30092]: #28299
-#30421 := (or #28302 #28294)
-#30422 := [def-axiom]: #30421
-#30484 := [unit-resolution #30422 #30175]: #28302
-#28534 := (or #12542 #13620 #27193 #13765)
-#28477 := [hypothesis]: #13480
-#28504 := (iff #18523 #28380)
-#28502 := (iff #12542 #28379)
-#28500 := (iff #28379 #12542)
-#28498 := (= #28378 #3260)
-#28499 := [monotonicity #28497]: #28498
-#28501 := [monotonicity #28499]: #28500
-#28503 := [symm #28501]: #28502
-#28505 := [monotonicity #28503]: #28504
-#28485 := [hypothesis]: #18523
-#28506 := [mp #28485 #28505]: #28380
-#28412 := (or #28384 #28379)
-#28413 := [def-axiom]: #28412
-#28507 := [unit-resolution #28413 #28506]: #28384
-#28522 := [unit-resolution #28521 #28516 #28513 #28512]: #28517
-#28530 := (or #28212 #28333 #28317)
-#28529 := [hypothesis]: #27192
-#28531 := [unit-resolution #28403 #21648 #14315 #28529 #28528]: #28530
-#28532 := [unit-resolution #28531 #28522 #28507]: #28212
-#28533 := [th-lemma arith farkas 1 1 1 #28532 #28484 #28477]: false
-#28535 := [lemma #28533]: #28534
-#29600 := [unit-resolution #28535 #29760 #28130 #29674]: #12542
-#30429 := (or #28311 #18523 #28305)
-#30430 := [def-axiom]: #30429
-#30488 := [unit-resolution #30430 #29600 #30484]: #28311
-#30432 := (or #30431 #12548 #28308)
-#30433 := [def-axiom]: #30432
-#30490 := [unit-resolution #30433 #30488]: #30489
-#30491 := [unit-resolution #30490 #30442]: #12548
-#29604 := (or #18529 #23421 #23391)
-#27935 := [hypothesis]: #23418
-#27930 := [hypothesis]: #12548
-#29655 := (or #23406 #18529 #23421)
-#24621 := (or #23454 #23448)
-#24622 := [def-axiom]: #24621
-#29654 := [unit-resolution #24622 #29759]: #23448
-#27883 := (or #23406 #18520 #18529 #23421 #23451)
-#27931 := [hypothesis]: #12539
-#27894 := [hypothesis]: #23448
-#27932 := [hypothesis]: #23409
-#24535 := (or #23406 #12542)
+#30685 := [unit-resolution #24470 #30684 #30673]: #22364
+#24471 := (or #23388 #22363)
+#24472 := [def-axiom]: #24471
+#30686 := [unit-resolution #24472 #30685]: #23388
+#24493 := (or #23397 #23391 #22416)
+#24494 := [def-axiom]: #24493
+#30687 := [unit-resolution #24494 #30686 #30663]: #22416
+#24485 := (or #22411 #24484)
+#24486 := [def-axiom]: #24485
+#30688 := [unit-resolution #24486 #30687]: #24484
+#30632 := (not #24588)
+#30633 := (or #30631 #18943 #30632 #13707)
+#30626 := [hypothesis]: #13708
+#30627 := [hypothesis]: #24588
+#30628 := [hypothesis]: #24484
+#30629 := [hypothesis]: #30621
+#30630 := [th-lemma arith farkas 1 -1 -1 1 #30629 #30628 #30627 #30626]: false
+#30634 := [lemma #30630]: #30633
+#30689 := [unit-resolution #30634 #30688 #30656 #30652]: #30631
+#30625 := (or #30624 #30621)
+#30635 := [th-lemma arith triangle-eq]: #30625
+#30690 := [unit-resolution #30635 #30689]: #30624
+#30649 := (or #30648 #30591)
+#30644 := (= #18620 #3266)
+#30642 := (= #18619 #3257)
+#30640 := (= ?v0!14 f309)
+#30639 := [hypothesis]: #30595
+#30641 := [symm #30639]: #30640
+#30643 := [monotonicity #30641]: #30642
+#30645 := [monotonicity #30643]: #30644
+#30646 := [symm #30645]: #30591
+#30638 := [hypothesis]: #30624
+#30647 := [unit-resolution #30638 #30646]: false
+#30650 := [lemma #30647]: #30649
+#30691 := [unit-resolution #30650 #30690]: #30648
+#30705 := (or #30595 #30702)
+#30425 := (<= #30424 0::Int)
+#30436 := (+ f307 #18941)
+#30437 := (>= #30436 0::Int)
+#30692 := (not #30437)
+#30693 := (or #30692 #18943 #30632)
+#30694 := [th-lemma arith assign-bounds -1 -1]: #30693
+#30695 := [unit-resolution #30694 #30656 #30688]: #30692
+#30698 := (or #30425 #30437)
+#24479 := (or #22411 #18616)
+#24480 := [def-axiom]: #24479
+#30696 := [unit-resolution #24480 #30687]: #18616
+#24477 := (or #22411 #18615)
+#24478 := [def-axiom]: #24477
+#30697 := [unit-resolution #24478 #30687]: #18615
+#30450 := (or #23377 #22395 #22396 #30425 #30437)
+#30413 := (+ #18620 #14006)
+#30414 := (<= #30413 0::Int)
+#30415 := (+ ?v0!14 #13537)
+#30416 := (>= #30415 0::Int)
+#30417 := (or #22396 #30416 #30414 #22395)
+#30451 := (or #23377 #30417)
+#30458 := (iff #30451 #30450)
+#30445 := (or #22395 #22396 #30425 #30437)
+#30453 := (or #23377 #30445)
+#30456 := (iff #30453 #30450)
+#30457 := [rewrite]: #30456
+#30454 := (iff #30451 #30453)
+#30448 := (iff #30417 #30445)
+#30442 := (or #22396 #30425 #30437 #22395)
+#30446 := (iff #30442 #30445)
+#30447 := [rewrite]: #30446
+#30443 := (iff #30417 #30442)
+#30440 := (iff #30414 #30437)
+#30430 := (+ #14006 #18620)
+#30433 := (<= #30430 0::Int)
+#30438 := (iff #30433 #30437)
+#30439 := [rewrite]: #30438
+#30434 := (iff #30414 #30433)
+#30431 := (= #30413 #30430)
+#30432 := [rewrite]: #30431
+#30435 := [monotonicity #30432]: #30434
+#30441 := [trans #30435 #30439]: #30440
+#30428 := (iff #30416 #30425)
+#30418 := (+ #13537 ?v0!14)
+#30421 := (>= #30418 0::Int)
+#30426 := (iff #30421 #30425)
+#30427 := [rewrite]: #30426
+#30422 := (iff #30416 #30421)
+#30419 := (= #30415 #30418)
+#30420 := [rewrite]: #30419
+#30423 := [monotonicity #30420]: #30422
+#30429 := [trans #30423 #30427]: #30428
+#30444 := [monotonicity #30429 #30441]: #30443
+#30449 := [trans #30444 #30447]: #30448
+#30455 := [monotonicity #30449]: #30454
+#30459 := [trans #30455 #30457]: #30458
+#30452 := [quant-inst #18614]: #30451
+#30460 := [mp #30452 #30459]: #30450
+#30699 := [unit-resolution #30460 #30095 #30697 #30696]: #30698
+#30700 := [unit-resolution #30699 #30695]: #30425
+#30701 := (not #30425)
+#30703 := (or #30595 #30701 #30702)
+#30704 := [th-lemma arith triangle-eq]: #30703
+#30706 := [unit-resolution #30704 #30700]: #30705
+#30707 := [unit-resolution #30706 #30691]: #30702
+#24481 := (not #18930)
+#24482 := (or #22411 #24481)
+#24483 := [def-axiom]: #24482
+#30708 := [unit-resolution #24483 #30687]: #24481
+#30709 := [th-lemma arith farkas -1 -1 1 #30708 #30613 #30707]: false
+#30710 := [lemma #30709]: #23454
+#26725 := [unit-resolution #29802 #30710]: #23430
+#26728 := [unit-resolution #30327 #26725 #30324]: #23427
+#24541 := (or #23424 #12601)
+#24542 := [def-axiom]: #24541
+#30556 := [unit-resolution #24542 #26728]: #12601
+#24535 := (or #23424 #12590)
#24536 := [def-axiom]: #24535
-#27927 := [unit-resolution #24536 #27932]: #12542
-#24613 := (or #23451 #18520 #18523 #23445)
-#24614 := [def-axiom]: #24613
-#27933 := [unit-resolution #24614 #27927 #27894 #27931]: #23445
-#24603 := (or #23442 #23436)
-#24604 := [def-axiom]: #24603
-#27934 := [unit-resolution #24604 #27933]: #23436
-#24547 := (or #23412 #23406)
-#24548 := [def-axiom]: #24547
-#28043 := [unit-resolution #24548 #27932]: #23412
-#24577 := (or #23427 #23415 #23421)
-#24578 := [def-axiom]: #24577
-#28044 := [unit-resolution #24578 #28043 #27935]: #23427
-#24587 := (or #23430 #23424)
-#24588 := [def-axiom]: #24587
-#27884 := [unit-resolution #24588 #28044]: #23430
-#24597 := (or #23439 #18520 #18529 #23433)
-#24598 := [def-axiom]: #24597
-#27885 := [unit-resolution #24598 #27884 #27934 #27931 #27930]: false
-#27895 := [lemma #27885]: #27883
-#29684 := [unit-resolution #27895 #29459 #29654]: #29655
-#29685 := [unit-resolution #29684 #27930 #27935]: #23406
-#29686 := [hypothesis]: #23388
-#29687 := (or #23397 #18529 #23391)
-#24523 := (or #23397 #18520 #18529 #23391)
-#24524 := [def-axiom]: #24523
-#29688 := [unit-resolution #24524 #29459]: #29687
-#29675 := [unit-resolution #29688 #27930 #29686]: #23397
-#24529 := (or #23400 #23394)
-#24530 := [def-axiom]: #24529
-#29676 := [unit-resolution #24530 #29675]: #23400
-#29601 := (or #23409 #23403)
-#24539 := (or #23409 #18520 #18523 #23403)
-#24540 := [def-axiom]: #24539
-#29602 := [unit-resolution #24540 #29600 #29459]: #29601
-#29603 := [unit-resolution #29602 #29676 #29685]: false
-#29605 := [lemma #29603]: #29604
-#30492 := [unit-resolution #29605 #30491 #29631]: #23391
-#24505 := (or #23388 #12565)
-#24506 := [def-axiom]: #24505
-#30493 := [unit-resolution #24506 #30492]: #12565
-#24499 := (or #23388 #12554)
-#24500 := [def-axiom]: #24499
-#30494 := [unit-resolution #24500 #30492]: #12554
-#30495 := [trans #30494 #30493]: #30446
-#30496 := (not #30446)
-#30497 := (or #30496 #30448)
-#30498 := [th-lemma arith triangle-eq]: #30497
-#30499 := [unit-resolution #30498 #30495]: #30448
-#30501 := (or #18529 #23433)
-#28051 := (or #23436 #23451 #18523)
-#28115 := [hypothesis]: #12542
-#28116 := [hypothesis]: #23439
-#24591 := (or #23436 #12539)
-#24592 := [def-axiom]: #24591
-#28050 := [unit-resolution #24592 #28116]: #12539
-#28048 := [unit-resolution #24604 #28116]: #23442
-#28049 := [unit-resolution #24614 #28048 #28050 #27894 #28115]: false
-#28052 := [lemma #28049]: #28051
-#30500 := [unit-resolution #28052 #29600 #29654]: #23436
-#30502 := [unit-resolution #24598 #30500 #29459]: #30501
-#30503 := [unit-resolution #30502 #30491]: #23433
-#30504 := [unit-resolution #24588 #30503]: #23424
-#30505 := [unit-resolution #24578 #30504 #29631]: #23415
-#24545 := (or #23412 #13671)
-#24546 := [def-axiom]: #24545
-#30506 := [unit-resolution #24546 #30505]: #13671
-#30507 := (not #30448)
-#30508 := (or #24552 #30507 #13672)
-#30509 := [th-lemma arith assign-bounds 1 1]: #30508
-#30510 := [unit-resolution #30509 #30506 #30499]: #24552
-#24513 := (or #23388 #23382)
-#24514 := [def-axiom]: #24513
-#30511 := [unit-resolution #24514 #30492]: #23382
-#30512 := [unit-resolution #29796 #30511]: #23379
-#30513 := [unit-resolution #24484 #30512]: #23370
-#30514 := [unit-resolution #24480 #30512]: #13582
-#30515 := [unit-resolution #29608 #30514]: #24428
-#30516 := [unit-resolution #29765 #30515]: #13514
-#30517 := [unit-resolution #24470 #30516 #30513]: #23367
-#30518 := [unit-resolution #24462 #30517]: #23358
-#30527 := (= #3266 #3299)
-#30523 := (= #3299 #3266)
-#30521 := (= #3298 #3257)
-#24507 := (or #23388 #12568)
-#24508 := [def-axiom]: #24507
-#30519 := [unit-resolution #24508 #30492]: #12568
-#30520 := [symm #30519]: #3278
-#30522 := [monotonicity #30520]: #30521
-#30524 := [monotonicity #30522]: #30523
-#30528 := [symm #30524]: #30527
-#30529 := (= f316 #3266)
-#30526 := [symm #30494]: #3269
-#30525 := [symm #30493]: #3276
-#30530 := [trans #30525 #30526]: #30529
-#30531 := [trans #30530 #30528]: #12607
-#30443 := (+ f310 #13556)
-#30445 := (>= #30443 0::Int)
-#30532 := (or #12695 #30445)
-#30533 := [th-lemma arith triangle-eq]: #30532
-#30534 := [unit-resolution #30533 #30519]: #30445
-#30535 := (not #30445)
-#30536 := (or #13559 #13765 #30535)
-#30537 := [th-lemma arith assign-bounds -1 -1]: #30536
-#30538 := [unit-resolution #30537 #29760 #30534]: #13559
-#30539 := [unit-resolution #24434 #30538 #30531]: #22328
-#30540 := [unit-resolution #24436 #30539]: #23352
-#30541 := [unit-resolution #24458 #30540 #30518]: #22380
-#30542 := [unit-resolution #24450 #30541]: #24448
-#30543 := [unit-resolution #29597 #30542 #30510]: #30220
-#30544 := [unit-resolution #24444 #30541]: #18580
-#30545 := [unit-resolution #24442 #30541]: #18579
-#30546 := [unit-resolution #24447 #30541]: #24445
-#30547 := [unit-resolution #29717 #30546 #30515]: #29634
-#30548 := [unit-resolution #30419 #30547 #30545 #30544 #30543]: #29868
-#30549 := [unit-resolution #30080 #30548]: #30332
-#30550 := [unit-resolution #30340 #30549]: #30338
-[th-lemma arith farkas -1 -1 1 #30542 #30499 #30550]: false
+#30557 := [unit-resolution #24536 #26728]: #12590
+#30555 := [trans #30557 #30556]: #30343
+#30558 := (not #30343)
+#30559 := (or #30558 #30172)
+#30560 := [th-lemma arith triangle-eq]: #30559
+#30561 := [unit-resolution #30560 #30555]: #30172
+#30340 := (+ f309 #13592)
+#30342 := (>= #30340 0::Int)
+#24543 := (or #23424 #12604)
+#24544 := [def-axiom]: #24543
+#26729 := [unit-resolution #24544 #26728]: #12604
+#26730 := (or #12731 #30342)
+#30377 := [th-lemma arith triangle-eq]: #26730
+#30378 := [unit-resolution #30377 #26729]: #30342
+#30379 := [hypothesis]: #13594
+#30374 := [th-lemma arith farkas -1 1 1 #30379 #30378 #30141]: false
+#30380 := [lemma #30374]: #13595
+#30585 := (or #22364 #13594)
+#30575 := (= #3266 #3299)
+#30577 := (= #3299 #3266)
+#30563 := (= #3298 #3257)
+#30562 := [symm #26729]: #3278
+#30576 := [monotonicity #30562]: #30563
+#30578 := [monotonicity #30576]: #30577
+#30581 := [symm #30578]: #30575
+#30582 := (= f315 #3266)
+#30580 := [symm #30557]: #3269
+#30579 := [symm #30556]: #3276
+#30583 := [trans #30579 #30580]: #30582
+#30584 := [trans #30583 #30581]: #12643
+#30593 := [unit-resolution #24470 #30584]: #30585
+#30594 := [unit-resolution #30593 #30380]: #22364
+#30496 := [unit-resolution #24472 #30594]: #23388
+#30564 := [unit-resolution #24494 #30663]: #23394
+#30565 := [unit-resolution #30564 #30496]: #22416
+#30592 := [unit-resolution #24486 #30565]: #24484
+#30658 := (not #30172)
+#30659 := (or #30631 #18943 #30658)
+#30657 := [th-lemma arith assign-bounds -1 -1]: #30659
+#30711 := [unit-resolution #30657 #30592 #30561]: #30631
+#30712 := [unit-resolution #30635 #30711]: #30624
+#30713 := [unit-resolution #24483 #30565]: #24481
+#30714 := (or #30620 #18930 #29780)
+#30715 := [th-lemma arith assign-bounds -1 -1]: #30714
+#30716 := [unit-resolution #30715 #30713 #30613]: #30620
+#30724 := (or #30692 #18943)
+#30717 := [unit-resolution #29790 #30324]: #23469
+#30718 := [unit-resolution #24624 #30717]: #23460
+#30719 := [unit-resolution #24614 #30710 #30718]: #23451
+#24581 := (or #23448 #13707)
+#24582 := [def-axiom]: #24581
+#30720 := [unit-resolution #24582 #30719]: #13707
+#30721 := (or #24588 #30658 #13708)
+#30722 := [th-lemma arith assign-bounds 1 1]: #30721
+#30723 := [unit-resolution #30722 #30720 #30561]: #24588
+#30725 := [unit-resolution #30694 #30723]: #30724
+#30726 := [unit-resolution #30725 #30592]: #30692
+#30727 := [unit-resolution #24480 #30565]: #18616
+#30728 := [unit-resolution #24478 #30565]: #18615
+#30729 := [unit-resolution #30460 #30095 #30728 #30727 #30726]: #30425
+#30730 := [unit-resolution #30704 #30729 #30716]: #30595
+[unit-resolution #30650 #30730 #30712]: false
unsat
--- a/src/HOL/SMT_Examples/SMT_Examples.certs Mon Dec 20 09:06:37 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs Mon Dec 20 09:31:47 2010 +0100
@@ -7423,425 +7423,698 @@
#37 := [asserted]: #17
[mp #37 #73]: false
unsat
-f9ae47f5aef750f37ea2d9309845d7cf08946d8c 211 0
-#2 := false
-#12 := 0::Int
+75da1862a2fd162477f9d85292ff8ab2e18559e4 342 0
+#2 := false
+#21 := 0::Int
decl f3 :: Int
#8 := f3
-#122 := (<= f3 0::Int)
-#135 := (>= f3 0::Int)
-#136 := (not #135)
-#123 := (not #122)
-#146 := (or #123 #136)
-#195 := (not #146)
-#69 := -2::Int
-#65 := -1::Int
-#66 := (* -1::Int f3)
-#72 := (mod #66 -2::Int)
-#78 := (* -1::Int #72)
+#419 := (<= f3 0::Int)
+#446 := (>= f3 0::Int)
+#753 := (not #446)
+#409 := (not #419)
+#754 := (or #409 #753)
+#715 := (not #754)
#11 := 2::Int
-#21 := (mod f3 2::Int)
-#149 := (ite #146 #21 #78)
-#193 := (= #21 #149)
-#284 := (not #193)
-#14 := (= f3 0::Int)
-#152 := (ite #14 0::Int #149)
-#268 := (* -1::Int #152)
-#269 := (+ #21 #268)
-#270 := (<= #269 0::Int)
-#267 := (= #21 #152)
-#192 := (= #149 #152)
-#202 := (not #14)
-#191 := (= #152 0::Int)
-#209 := (not #191)
-#175 := (>= #152 0::Int)
-#178 := (not #175)
+#443 := (mod f3 2::Int)
+#113 := -1::Int
+#444 := (* -1::Int #443)
+decl f4 :: (-> Int Int Int)
+#12 := (f4 f3 2::Int)
+#445 := (+ #12 #444)
+#442 := (= #445 0::Int)
+#705 := (not #442)
+#717 := (>= #445 0::Int)
+#647 := (not #717)
+#654 := [hypothesis]: #717
+#689 := (>= #443 0::Int)
+#1 := true
+#65 := [true-axiom]: true
+#665 := (or false #689)
+#643 := [th-lemma arith]: #665
+#644 := [unit-resolution #643 #65]: #689
+#95 := (>= #12 0::Int)
+#98 := (not #95)
#9 := 1::Int
-#23 := (- 2::Int)
-#22 := (- f3)
-#24 := (mod #22 #23)
-#25 := (- #24)
-#16 := (< 0::Int 2::Int)
-#18 := (< f3 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int f3)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#26 := (ite #20 #21 #25)
-#27 := (ite #14 0::Int #26)
-#13 := (= 2::Int 0::Int)
-#28 := (ite #13 f3 #27)
-#29 := (* 2::Int #28)
-#30 := (+ #29 1::Int)
-#31 := (+ f3 #30)
+#13 := (* 2::Int #12)
+#14 := (+ #13 1::Int)
+#15 := (+ f3 #14)
#10 := (+ f3 1::Int)
-#32 := (<= #10 #31)
-#33 := (not #32)
-#183 := (iff #33 #178)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#83 := (ite #62 #21 #78)
-#86 := (ite #14 0::Int #83)
-#96 := (* 2::Int #86)
-#110 := (+ f3 #96)
-#111 := (+ 1::Int #110)
-#54 := (+ 1::Int f3)
-#116 := (<= #54 #111)
-#119 := (not #116)
-#181 := (iff #119 #178)
-#155 := (* 2::Int #152)
-#168 := (>= #155 0::Int)
-#172 := (not #168)
-#179 := (iff #172 #178)
-#176 := (iff #168 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#173 := (iff #119 #172)
-#170 := (iff #116 #168)
-#158 := (+ f3 #155)
-#161 := (+ 1::Int #158)
-#164 := (<= #54 #161)
-#167 := (iff #164 #168)
-#169 := [rewrite]: #167
-#165 := (iff #116 #164)
-#162 := (= #111 #161)
-#159 := (= #110 #158)
-#156 := (= #96 #155)
-#153 := (= #86 #152)
-#150 := (= #83 #149)
-#147 := (iff #62 #146)
-#144 := (iff #59 #136)
-#1 := true
-#139 := (and true #136)
-#142 := (iff #139 #136)
-#143 := [rewrite]: #142
-#140 := (iff #59 #139)
-#137 := (iff #18 #136)
+#16 := (<= #10 #15)
+#17 := (not #16)
+#103 := (iff #17 #98)
+#77 := (+ f3 #13)
+#78 := (+ 1::Int #77)
+#68 := (+ 1::Int f3)
+#83 := (<= #68 #78)
+#86 := (not #83)
+#101 := (iff #86 #98)
+#93 := (>= #13 0::Int)
+#89 := (not #93)
+#99 := (iff #89 #98)
+#96 := (iff #93 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#90 := (iff #86 #89)
+#91 := (iff #83 #93)
+#92 := [rewrite]: #91
+#94 := [monotonicity #92]: #90
+#102 := [trans #94 #100]: #101
+#87 := (iff #17 #86)
+#84 := (iff #16 #83)
+#81 := (= #15 #78)
+#71 := (+ 1::Int #13)
+#74 := (+ f3 #71)
+#79 := (= #74 #78)
+#80 := [rewrite]: #79
+#75 := (= #15 #74)
+#72 := (= #14 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#82 := [trans #76 #80]: #81
+#69 := (= #10 #68)
+#70 := [rewrite]: #69
+#85 := [monotonicity #70 #82]: #84
+#88 := [monotonicity #85]: #87
+#104 := [trans #88 #102]: #103
+#67 := [asserted]: #17
+#105 := [mp #67 #104]: #98
+#646 := [th-lemma arith farkas -1 1 1 #105 #644 #654]: false
+#648 := [lemma #646]: #647
+#660 := (or #705 #717)
+#661 := [th-lemma arith triangle-eq]: #660
+#662 := [unit-resolution #661 #648]: #705
+#637 := (or #715 #442)
+#741 := -2::Int
+#439 := (* -1::Int f3)
+#465 := (mod #439 -2::Int)
+#361 := (+ #12 #465)
+#460 := (= #361 0::Int)
+#739 := (ite #754 #442 #460)
+#763 := (= #12 0::Int)
+#764 := (= f3 0::Int)
+#450 := (ite #764 #763 #739)
+#19 := (:var 0 Int)
+#18 := (:var 1 Int)
+#39 := (f4 #18 #19)
+#775 := (pattern #39)
+#117 := (* -1::Int #19)
+#114 := (* -1::Int #18)
+#172 := (mod #114 #117)
+#287 := (+ #39 #172)
+#288 := (= #287 0::Int)
+#40 := (mod #18 #19)
+#284 := (* -1::Int #40)
+#285 := (+ #39 #284)
+#286 := (= #285 0::Int)
+#146 := (>= #18 0::Int)
+#139 := (<= #19 0::Int)
+#231 := (or #139 #146)
+#232 := (not #231)
+#135 := (<= #18 0::Int)
+#229 := (or #135 #139)
+#230 := (not #229)
+#235 := (or #230 #232)
+#289 := (ite #235 #286 #288)
+#283 := (= #39 0::Int)
+#22 := (= #18 0::Int)
+#290 := (ite #22 #283 #289)
+#282 := (= #18 #39)
+#23 := (= #19 0::Int)
+#291 := (ite #23 #282 #290)
+#776 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #775) #291)
+#294 := (forall (vars (?v0 Int) (?v1 Int)) #291)
+#779 := (iff #294 #776)
+#777 := (iff #291 #291)
+#778 := [refl]: #777
+#780 := [quant-intro #778]: #779
+#178 := (* -1::Int #172)
+#251 := (ite #235 #40 #178)
+#254 := (ite #22 0::Int #251)
+#257 := (ite #23 #18 #254)
+#260 := (= #39 #257)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#295 := (iff #263 #294)
+#292 := (iff #260 #291)
+#293 := [rewrite]: #292
+#296 := [quant-intro #293]: #295
+#147 := (not #146)
+#140 := (not #139)
+#150 := (and #140 #147)
+#136 := (not #135)
+#143 := (and #136 #140)
+#153 := (or #143 #150)
+#198 := (ite #153 #40 #178)
+#201 := (ite #22 0::Int #198)
+#204 := (ite #23 #18 #201)
+#207 := (= #39 #204)
+#210 := (forall (vars (?v0 Int) (?v1 Int)) #207)
+#264 := (iff #210 #263)
+#261 := (iff #207 #260)
+#258 := (= #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#236 := (iff #153 #235)
+#233 := (iff #150 #232)
+#234 := [rewrite]: #233
+#223 := (iff #143 #230)
+#224 := [rewrite]: #223
+#237 := [monotonicity #224 #234]: #236
+#253 := [monotonicity #237]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [monotonicity #259]: #261
+#265 := [quant-intro #262]: #264
+#221 := (~ #210 #210)
+#220 := (~ #207 #207)
+#217 := [refl]: #220
+#222 := [nnf-pos #217]: #221
+#33 := (- #19)
+#32 := (- #18)
+#41 := (mod #32 #33)
+#42 := (- #41)
+#26 := (< 0::Int #19)
+#28 := (< #18 0::Int)
+#29 := (and #28 #26)
+#25 := (< 0::Int #18)
+#27 := (and #25 #26)
+#30 := (or #27 #29)
+#43 := (ite #30 #40 #42)
+#44 := (ite #22 0::Int #43)
+#45 := (ite #23 #18 #44)
+#46 := (= #39 #45)
+#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
+#213 := (iff #47 #210)
+#107 := (and #26 #28)
+#110 := (or #27 #107)
+#183 := (ite #110 #40 #178)
+#186 := (ite #22 0::Int #183)
+#189 := (ite #23 #18 #186)
+#192 := (= #39 #189)
+#195 := (forall (vars (?v0 Int) (?v1 Int)) #192)
+#211 := (iff #195 #210)
+#208 := (iff #192 #207)
+#205 := (= #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#154 := (iff #110 #153)
+#151 := (iff #107 #150)
+#148 := (iff #28 #147)
+#149 := [rewrite]: #148
+#141 := (iff #26 #140)
+#142 := [rewrite]: #141
+#152 := [monotonicity #142 #149]: #151
+#144 := (iff #27 #143)
+#137 := (iff #25 #136)
#138 := [rewrite]: #137
-#126 := (iff #16 true)
-#127 := [rewrite]: #126
-#141 := [monotonicity #127 #138]: #140
-#145 := [trans #141 #143]: #144
-#133 := (iff #17 #123)
-#128 := (and #123 true)
-#131 := (iff #128 #123)
-#132 := [rewrite]: #131
-#129 := (iff #17 #128)
-#124 := (iff #15 #123)
-#125 := [rewrite]: #124
-#130 := [monotonicity #125 #127]: #129
-#134 := [trans #130 #132]: #133
-#148 := [monotonicity #134 #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#171 := [trans #166 #169]: #170
-#174 := [monotonicity #171]: #173
-#182 := [trans #174 #180]: #181
-#120 := (iff #33 #119)
-#117 := (iff #32 #116)
-#114 := (= #31 #111)
-#102 := (+ 1::Int #96)
-#107 := (+ f3 #102)
-#112 := (= #107 #111)
-#113 := [rewrite]: #112
-#108 := (= #31 #107)
-#105 := (= #30 #102)
-#99 := (+ #96 1::Int)
-#103 := (= #99 #102)
-#104 := [rewrite]: #103
-#100 := (= #30 #99)
-#97 := (= #29 #96)
-#94 := (= #28 #86)
-#89 := (ite false f3 #86)
-#92 := (= #89 #86)
-#93 := [rewrite]: #92
-#90 := (= #28 #89)
-#87 := (= #27 #86)
-#84 := (= #26 #83)
-#81 := (= #25 #78)
-#75 := (- #72)
-#79 := (= #75 #78)
-#80 := [rewrite]: #79
-#76 := (= #25 #75)
-#73 := (= #24 #72)
-#70 := (= #23 -2::Int)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#57 := (iff #13 false)
-#58 := [rewrite]: #57
-#91 := [monotonicity #58 #88]: #90
-#95 := [trans #91 #93]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#106 := [trans #101 #104]: #105
-#109 := [monotonicity #106]: #108
-#115 := [trans #109 #113]: #114
-#55 := (= #10 #54)
-#56 := [rewrite]: #55
-#118 := [monotonicity #56 #115]: #117
-#121 := [monotonicity #118]: #120
-#184 := [trans #121 #182]: #183
-#53 := [asserted]: #33
-#185 := [mp #53 #184]: #178
-#208 := [hypothesis]: #191
-#210 := (or #209 #175)
-#211 := [th-lemma arith triangle-eq]: #210
-#212 := [unit-resolution #211 #208 #185]: false
-#213 := [lemma #212]: #209
-#203 := (or #202 #191)
-#204 := [def-axiom]: #203
-#272 := [unit-resolution #204 #213]: #202
-#205 := (or #14 #192)
-#206 := [def-axiom]: #205
-#273 := [unit-resolution #206 #272]: #192
-#274 := [hypothesis]: #193
-#275 := [trans #274 #273]: #267
-#276 := (not #267)
-#277 := (or #276 #270)
-#278 := [th-lemma arith triangle-eq]: #277
-#279 := [unit-resolution #278 #275]: #270
-#239 := (>= #21 0::Int)
-#51 := [true-axiom]: true
-#280 := (or false #239)
-#281 := [th-lemma arith]: #280
-#282 := [unit-resolution #281 #51]: #239
-#283 := [th-lemma arith farkas -1 1 1 #282 #185 #279]: false
-#285 := [lemma #283]: #284
-#198 := (or #195 #193)
-#199 := [def-axiom]: #198
-#262 := [unit-resolution #199 #285]: #195
-#189 := (or #146 #122)
-#190 := [def-axiom]: #189
-#263 := [unit-resolution #190 #262]: #122
-#187 := (or #146 #135)
-#188 := [def-axiom]: #187
-#264 := [unit-resolution #188 #262]: #135
-#265 := (or #14 #123 #136)
-#266 := [th-lemma arith triangle-eq]: #265
-#237 := [unit-resolution #266 #272]: #146
-[unit-resolution #237 #264 #263]: false
-unsat
-a9554a5e9a99c006412b9165d7d1ec39d927f284 207 0
-#2 := false
-#10 := 0::Int
+#145 := [monotonicity #138 #142]: #144
+#155 := [monotonicity #145 #152]: #154
+#200 := [monotonicity #155]: #199
+#203 := [monotonicity #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [monotonicity #206]: #208
+#212 := [quant-intro #209]: #211
+#196 := (iff #47 #195)
+#193 := (iff #46 #192)
+#190 := (= #45 #189)
+#187 := (= #44 #186)
+#184 := (= #43 #183)
+#181 := (= #42 #178)
+#175 := (- #172)
+#179 := (= #175 #178)
+#180 := [rewrite]: #179
+#176 := (= #42 #175)
+#173 := (= #41 #172)
+#118 := (= #33 #117)
+#119 := [rewrite]: #118
+#115 := (= #32 #114)
+#116 := [rewrite]: #115
+#174 := [monotonicity #116 #119]: #173
+#177 := [monotonicity #174]: #176
+#182 := [trans #177 #180]: #181
+#111 := (iff #30 #110)
+#108 := (iff #29 #107)
+#109 := [rewrite]: #108
+#112 := [monotonicity #109]: #111
+#185 := [monotonicity #112 #182]: #184
+#188 := [monotonicity #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [monotonicity #191]: #193
+#197 := [quant-intro #194]: #196
+#214 := [trans #197 #212]: #213
+#171 := [asserted]: #47
+#215 := [mp #171 #214]: #210
+#218 := [mp~ #215 #222]: #210
+#266 := [mp #218 #265]: #263
+#297 := [mp #266 #296]: #294
+#781 := [mp #297 #780]: #776
+#734 := (not #776)
+#723 := (or #734 #450)
+#355 := (* -1::Int 2::Int)
+#440 := (mod #439 #355)
+#441 := (+ #12 #440)
+#432 := (= #441 0::Int)
+#425 := (<= 2::Int 0::Int)
+#760 := (or #425 #446)
+#762 := (not #760)
+#549 := (or #419 #425)
+#756 := (not #549)
+#430 := (or #756 #762)
+#431 := (ite #430 #442 #432)
+#765 := (ite #764 #763 #431)
+#766 := (= f3 #12)
+#761 := (= 2::Int 0::Int)
+#767 := (ite #761 #766 #765)
+#724 := (or #734 #767)
+#720 := (iff #724 #723)
+#726 := (iff #723 #723)
+#727 := [rewrite]: #726
+#733 := (iff #767 #450)
+#453 := (ite false #766 #450)
+#447 := (iff #453 #450)
+#729 := [rewrite]: #447
+#731 := (iff #767 #453)
+#451 := (iff #765 #450)
+#736 := (iff #431 #739)
+#461 := (iff #432 #460)
+#737 := (= #441 #361)
+#466 := (= #440 #465)
+#742 := (= #355 -2::Int)
+#464 := [rewrite]: #742
+#467 := [monotonicity #464]: #466
+#738 := [monotonicity #467]: #737
+#735 := [monotonicity #738]: #461
+#752 := (iff #430 #754)
+#393 := (iff #762 #753)
+#388 := (iff #760 #446)
+#747 := (or false #446)
+#744 := (iff #747 #446)
+#750 := [rewrite]: #744
+#748 := (iff #760 #747)
+#422 := (iff #425 false)
+#758 := [rewrite]: #422
+#749 := [monotonicity #758]: #748
+#751 := [trans #749 #750]: #388
+#394 := [monotonicity #751]: #393
+#745 := (iff #756 #409)
+#407 := (iff #549 #419)
+#418 := (or #419 false)
+#743 := (iff #418 #419)
+#406 := [rewrite]: #743
+#759 := (iff #549 #418)
+#402 := [monotonicity #758]: #759
+#408 := [trans #402 #406]: #407
+#746 := [monotonicity #408]: #745
+#755 := [monotonicity #746 #394]: #752
+#740 := [monotonicity #755 #735]: #736
+#452 := [monotonicity #740]: #451
+#757 := (iff #761 false)
+#417 := [rewrite]: #757
+#732 := [monotonicity #417 #452]: #731
+#730 := [trans #732 #729]: #733
+#721 := [monotonicity #730]: #720
+#722 := [trans #721 #727]: #720
+#725 := [quant-inst #8 #11]: #724
+#728 := [mp #725 #722]: #723
+#663 := [unit-resolution #728 #781]: #450
+#593 := (not #764)
+#592 := (not #450)
+#649 := (or #592 #593)
+#698 := (not #763)
+#664 := (or #698 #95)
+#688 := [th-lemma arith triangle-eq]: #664
+#682 := [unit-resolution #688 #105]: #698
+#552 := (or #592 #593 #763)
+#700 := [def-axiom]: #552
+#650 := [unit-resolution #700 #682]: #649
+#645 := [unit-resolution #650 #663]: #593
+#602 := (or #592 #764 #739)
+#697 := [def-axiom]: #602
+#651 := [unit-resolution #697 #645 #663]: #739
+#719 := (not #739)
+#548 := (or #719 #715 #442)
+#550 := [def-axiom]: #548
+#633 := [unit-resolution #550 #651]: #637
+#634 := [unit-resolution #633 #662]: #715
+#570 := (or #754 #419)
+#571 := [def-axiom]: #570
+#635 := [unit-resolution #571 #634]: #419
+#713 := (or #754 #446)
+#714 := [def-axiom]: #713
+#638 := [unit-resolution #714 #634]: #446
+#639 := (or #764 #409 #753)
+#640 := [th-lemma arith triangle-eq]: #639
+#641 := [unit-resolution #640 #645]: #754
+[unit-resolution #641 #638 #635]: false
+unsat
+3b8dfbe5d2104f714ba2e5d249bcf001c2c84dba 349 0
+#2 := false
+#20 := 0::Int
decl f3 :: Int
#8 := f3
-#112 := (<= f3 0::Int)
-#125 := (>= f3 0::Int)
-#126 := (not #125)
-#113 := (not #112)
-#136 := (or #113 #126)
-#184 := (not #136)
-#65 := -2::Int
-#61 := -1::Int
-#62 := (* -1::Int f3)
-#68 := (mod #62 -2::Int)
-#74 := (* -1::Int #68)
+#438 := (>= f3 0::Int)
+#758 := (<= f3 0::Int)
+#404 := (not #758)
+#747 := (not #438)
+#751 := (or #747 #404)
+#714 := (not #751)
#9 := 2::Int
-#19 := (mod f3 2::Int)
-#139 := (ite #136 #19 #74)
-#182 := (= #19 #139)
-#279 := (not #182)
-#251 := (>= #19 2::Int)
-#252 := (not #251)
+#439 := (mod f3 2::Int)
+#108 := -1::Int
+#440 := (* -1::Int #439)
+decl f4 :: (-> Int Int Int)
+#10 := (f4 f3 2::Int)
+#368 := (+ #10 #440)
+#441 := (= #368 0::Int)
+#587 := (not #441)
+#544 := (<= #368 0::Int)
+#647 := (not #544)
+#655 := (>= #439 2::Int)
+#656 := (not #655)
#1 := true
-#50 := [true-axiom]: true
-#267 := (or false #252)
-#268 := [th-lemma arith]: #267
-#269 := [unit-resolution #268 #50]: #252
-#12 := (= f3 0::Int)
-#142 := (ite #12 0::Int #139)
-#263 := (* -1::Int #142)
-#264 := (+ #19 #263)
-#266 := (>= #264 0::Int)
-#262 := (= #19 #142)
-#181 := (= #139 #142)
-#191 := (not #12)
-#180 := (= #142 0::Int)
-#204 := (not #180)
-#196 := (<= #142 0::Int)
-#198 := (not #196)
-#167 := (>= #142 2::Int)
-#29 := 3::Int
-#30 := (+ f3 3::Int)
-#21 := (- 2::Int)
-#20 := (- f3)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#14 := (< 0::Int 2::Int)
-#16 := (< f3 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int f3)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#25 := (ite #12 0::Int #24)
-#11 := (= 2::Int 0::Int)
-#26 := (ite #11 f3 #25)
-#27 := (+ #26 #26)
-#28 := (+ f3 #27)
-#31 := (< #28 #30)
-#32 := (not #31)
-#172 := (iff #32 #167)
-#103 := (+ 3::Int f3)
-#55 := (and #14 #16)
-#58 := (or #15 #55)
-#79 := (ite #58 #19 #74)
-#82 := (ite #12 0::Int #79)
-#95 := (* 2::Int #82)
-#100 := (+ f3 #95)
-#106 := (< #100 #103)
-#109 := (not #106)
-#170 := (iff #109 #167)
-#145 := (* 2::Int #142)
-#155 := (>= #145 3::Int)
-#168 := (iff #155 #167)
-#169 := [rewrite]: #168
-#165 := (iff #109 #155)
-#154 := (not #155)
-#160 := (not #154)
-#163 := (iff #160 #155)
-#164 := [rewrite]: #163
-#161 := (iff #109 #160)
-#158 := (iff #106 #154)
-#148 := (+ f3 #145)
-#151 := (< #148 #103)
-#156 := (iff #151 #154)
-#157 := [rewrite]: #156
-#152 := (iff #106 #151)
-#149 := (= #100 #148)
-#146 := (= #95 #145)
-#143 := (= #82 #142)
-#140 := (= #79 #139)
-#137 := (iff #58 #136)
-#134 := (iff #55 #126)
-#129 := (and true #126)
-#132 := (iff #129 #126)
+#64 := [true-axiom]: true
+#643 := (or false #656)
+#644 := [th-lemma arith]: #643
+#645 := [unit-resolution #644 #64]: #656
+#646 := [hypothesis]: #544
+#93 := (>= #10 2::Int)
+#13 := 3::Int
+#14 := (+ f3 3::Int)
+#11 := (+ #10 #10)
+#12 := (+ f3 #11)
+#15 := (< #12 #14)
+#16 := (not #15)
+#98 := (iff #16 #93)
+#73 := (+ 3::Int f3)
+#67 := (* 2::Int #10)
+#70 := (+ f3 #67)
+#76 := (< #70 #73)
+#79 := (not #76)
+#96 := (iff #79 #93)
+#86 := (>= #67 3::Int)
+#94 := (iff #86 #93)
+#95 := [rewrite]: #94
+#91 := (iff #79 #86)
+#84 := (not #86)
+#83 := (not #84)
+#89 := (iff #83 #86)
+#90 := [rewrite]: #89
+#87 := (iff #79 #83)
+#85 := (iff #76 #84)
+#82 := [rewrite]: #85
+#88 := [monotonicity #82]: #87
+#92 := [trans #88 #90]: #91
+#97 := [trans #92 #95]: #96
+#80 := (iff #16 #79)
+#77 := (iff #15 #76)
+#74 := (= #14 #73)
+#75 := [rewrite]: #74
+#71 := (= #12 #70)
+#68 := (= #11 #67)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#78 := [monotonicity #72 #75]: #77
+#81 := [monotonicity #78]: #80
+#99 := [trans #81 #97]: #98
+#66 := [asserted]: #16
+#100 := [mp #66 #99]: #93
+#641 := [th-lemma arith farkas -1 1 1 #100 #646 #645]: false
+#633 := [lemma #641]: #647
+#650 := (or #587 #544)
+#661 := [th-lemma arith triangle-eq]: #650
+#639 := [unit-resolution #661 #633]: #587
+#611 := (or #714 #441)
+#462 := -2::Int
+#435 := (* -1::Int f3)
+#733 := (mod #435 -2::Int)
+#457 := (+ #10 #733)
+#732 := (= #457 0::Int)
+#447 := (ite #751 #441 #732)
+#427 := (= #10 0::Int)
+#759 := (= f3 0::Int)
+#727 := (ite #759 #427 #447)
+#18 := (:var 0 Int)
+#17 := (:var 1 Int)
+#38 := (f4 #17 #18)
+#771 := (pattern #38)
+#112 := (* -1::Int #18)
+#109 := (* -1::Int #17)
+#167 := (mod #109 #112)
+#282 := (+ #38 #167)
+#283 := (= #282 0::Int)
+#39 := (mod #17 #18)
+#279 := (* -1::Int #39)
+#280 := (+ #38 #279)
+#281 := (= #280 0::Int)
+#141 := (>= #17 0::Int)
+#134 := (<= #18 0::Int)
+#226 := (or #134 #141)
+#227 := (not #226)
+#130 := (<= #17 0::Int)
+#224 := (or #130 #134)
+#225 := (not #224)
+#230 := (or #225 #227)
+#284 := (ite #230 #281 #283)
+#278 := (= #38 0::Int)
+#21 := (= #17 0::Int)
+#285 := (ite #21 #278 #284)
+#277 := (= #17 #38)
+#22 := (= #18 0::Int)
+#286 := (ite #22 #277 #285)
+#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #286)
+#289 := (forall (vars (?v0 Int) (?v1 Int)) #286)
+#775 := (iff #289 #772)
+#773 := (iff #286 #286)
+#774 := [refl]: #773
+#776 := [quant-intro #774]: #775
+#173 := (* -1::Int #167)
+#246 := (ite #230 #39 #173)
+#249 := (ite #21 0::Int #246)
+#252 := (ite #22 #17 #249)
+#255 := (= #38 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#290 := (iff #258 #289)
+#287 := (iff #255 #286)
+#288 := [rewrite]: #287
+#291 := [quant-intro #288]: #290
+#142 := (not #141)
+#135 := (not #134)
+#145 := (and #135 #142)
+#131 := (not #130)
+#138 := (and #131 #135)
+#148 := (or #138 #145)
+#193 := (ite #148 #39 #173)
+#196 := (ite #21 0::Int #193)
+#199 := (ite #22 #17 #196)
+#202 := (= #38 #199)
+#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
+#259 := (iff #205 #258)
+#256 := (iff #202 #255)
+#253 := (= #199 #252)
+#250 := (= #196 #249)
+#247 := (= #193 #246)
+#231 := (iff #148 #230)
+#228 := (iff #145 #227)
+#229 := [rewrite]: #228
+#218 := (iff #138 #225)
+#219 := [rewrite]: #218
+#232 := [monotonicity #219 #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#216 := (~ #205 #205)
+#215 := (~ #202 #202)
+#212 := [refl]: #215
+#217 := [nnf-pos #212]: #216
+#32 := (- #18)
+#31 := (- #17)
+#40 := (mod #31 #32)
+#41 := (- #40)
+#25 := (< 0::Int #18)
+#27 := (< #17 0::Int)
+#28 := (and #27 #25)
+#24 := (< 0::Int #17)
+#26 := (and #24 #25)
+#29 := (or #26 #28)
+#42 := (ite #29 #39 #41)
+#43 := (ite #21 0::Int #42)
+#44 := (ite #22 #17 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#208 := (iff #46 #205)
+#102 := (and #25 #27)
+#105 := (or #26 #102)
+#178 := (ite #105 #39 #173)
+#181 := (ite #21 0::Int #178)
+#184 := (ite #22 #17 #181)
+#187 := (= #38 #184)
+#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
+#206 := (iff #190 #205)
+#203 := (iff #187 #202)
+#200 := (= #184 #199)
+#197 := (= #181 #196)
+#194 := (= #178 #193)
+#149 := (iff #105 #148)
+#146 := (iff #102 #145)
+#143 := (iff #27 #142)
+#144 := [rewrite]: #143
+#136 := (iff #25 #135)
+#137 := [rewrite]: #136
+#147 := [monotonicity #137 #144]: #146
+#139 := (iff #26 #138)
+#132 := (iff #24 #131)
#133 := [rewrite]: #132
-#130 := (iff #55 #129)
-#127 := (iff #16 #126)
-#128 := [rewrite]: #127
-#116 := (iff #14 true)
-#117 := [rewrite]: #116
-#131 := [monotonicity #117 #128]: #130
-#135 := [trans #131 #133]: #134
-#123 := (iff #15 #113)
-#118 := (and #113 true)
-#121 := (iff #118 #113)
-#122 := [rewrite]: #121
-#119 := (iff #15 #118)
-#114 := (iff #13 #113)
-#115 := [rewrite]: #114
-#120 := [monotonicity #115 #117]: #119
-#124 := [trans #120 #122]: #123
-#138 := [monotonicity #124 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [monotonicity #150]: #152
-#159 := [trans #153 #157]: #158
-#162 := [monotonicity #159]: #161
-#166 := [trans #162 #164]: #165
-#171 := [trans #166 #169]: #170
-#110 := (iff #32 #109)
-#107 := (iff #31 #106)
-#104 := (= #30 #103)
-#105 := [rewrite]: #104
-#101 := (= #28 #100)
-#98 := (= #27 #95)
-#92 := (+ #82 #82)
-#96 := (= #92 #95)
-#97 := [rewrite]: #96
-#93 := (= #27 #92)
-#90 := (= #26 #82)
-#85 := (ite false f3 #82)
-#88 := (= #85 #82)
-#89 := [rewrite]: #88
-#86 := (= #26 #85)
-#83 := (= #25 #82)
-#80 := (= #24 #79)
-#77 := (= #23 #74)
-#71 := (- #68)
-#75 := (= #71 #74)
-#76 := [rewrite]: #75
-#72 := (= #23 #71)
-#69 := (= #22 #68)
-#66 := (= #21 -2::Int)
-#67 := [rewrite]: #66
-#63 := (= #20 #62)
-#64 := [rewrite]: #63
-#70 := [monotonicity #64 #67]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#81 := [monotonicity #60 #78]: #80
-#84 := [monotonicity #81]: #83
-#53 := (iff #11 false)
-#54 := [rewrite]: #53
-#87 := [monotonicity #54 #84]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #91 #91]: #93
-#99 := [trans #94 #97]: #98
-#102 := [monotonicity #99]: #101
-#108 := [monotonicity #102 #105]: #107
-#111 := [monotonicity #108]: #110
-#173 := [trans #111 #171]: #172
-#52 := [asserted]: #32
-#174 := [mp #52 #173]: #167
-#199 := (not #167)
-#200 := (or #198 #199)
-#201 := [th-lemma arith farkas 1 1]: #200
-#202 := [unit-resolution #201 #174]: #198
-#203 := [hypothesis]: #180
-#205 := (or #204 #196)
-#206 := [th-lemma arith triangle-eq]: #205
-#207 := [unit-resolution #206 #203 #202]: false
-#208 := [lemma #207]: #204
-#192 := (or #191 #180)
-#193 := [def-axiom]: #192
-#270 := [unit-resolution #193 #208]: #191
-#194 := (or #12 #181)
-#195 := [def-axiom]: #194
-#271 := [unit-resolution #195 #270]: #181
-#272 := [hypothesis]: #182
-#273 := [trans #272 #271]: #262
-#274 := (not #262)
-#275 := (or #274 #266)
-#276 := [th-lemma arith triangle-eq]: #275
-#277 := [unit-resolution #276 #273]: #266
-#278 := [th-lemma arith farkas -1 -1 1 #174 #277 #269]: false
-#280 := [lemma #278]: #279
-#187 := (or #184 #182)
-#188 := [def-axiom]: #187
-#257 := [unit-resolution #188 #280]: #184
-#178 := (or #136 #112)
-#179 := [def-axiom]: #178
-#258 := [unit-resolution #179 #257]: #112
-#176 := (or #136 #125)
-#177 := [def-axiom]: #176
-#259 := [unit-resolution #177 #257]: #125
-#260 := (or #12 #113 #126)
-#261 := [th-lemma arith triangle-eq]: #260
-#232 := [unit-resolution #261 #270]: #136
-[unit-resolution #232 #259 #258]: false
+#140 := [monotonicity #133 #137]: #139
+#150 := [monotonicity #140 #147]: #149
+#195 := [monotonicity #150]: #194
+#198 := [monotonicity #195]: #197
+#201 := [monotonicity #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [quant-intro #204]: #206
+#191 := (iff #46 #190)
+#188 := (iff #45 #187)
+#185 := (= #44 #184)
+#182 := (= #43 #181)
+#179 := (= #42 #178)
+#176 := (= #41 #173)
+#170 := (- #167)
+#174 := (= #170 #173)
+#175 := [rewrite]: #174
+#171 := (= #41 #170)
+#168 := (= #40 #167)
+#113 := (= #32 #112)
+#114 := [rewrite]: #113
+#110 := (= #31 #109)
+#111 := [rewrite]: #110
+#169 := [monotonicity #111 #114]: #168
+#172 := [monotonicity #169]: #171
+#177 := [trans #172 #175]: #176
+#106 := (iff #29 #105)
+#103 := (iff #28 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#180 := [monotonicity #107 #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [quant-intro #189]: #191
+#209 := [trans #192 #207]: #208
+#166 := [asserted]: #46
+#210 := [mp #166 #209]: #205
+#213 := [mp~ #210 #217]: #205
+#261 := [mp #213 #260]: #258
+#292 := [mp #261 #291]: #289
+#777 := [mp #292 #776]: #772
+#716 := (not #772)
+#717 := (or #716 #727)
+#350 := (* -1::Int 2::Int)
+#436 := (mod #435 #350)
+#437 := (+ #10 #436)
+#428 := (= #437 0::Int)
+#442 := (<= 2::Int 0::Int)
+#421 := (or #442 #438)
+#756 := (not #421)
+#415 := (or #758 #442)
+#545 := (not #415)
+#752 := (or #545 #756)
+#426 := (ite #752 #441 #428)
+#760 := (ite #759 #427 #426)
+#761 := (= f3 #10)
+#762 := (= 2::Int 0::Int)
+#757 := (ite #762 #761 #760)
+#722 := (or #716 #757)
+#718 := (iff #722 #717)
+#565 := (iff #717 #717)
+#566 := [rewrite]: #565
+#720 := (iff #757 #727)
+#725 := (ite false #761 #727)
+#730 := (iff #725 #727)
+#719 := [rewrite]: #730
+#729 := (iff #757 #725)
+#728 := (iff #760 #727)
+#448 := (iff #426 #447)
+#736 := (iff #428 #732)
+#731 := (= #437 #457)
+#734 := (= #436 #733)
+#463 := (= #350 -2::Int)
+#356 := [rewrite]: #463
+#456 := [monotonicity #356]: #734
+#735 := [monotonicity #456]: #731
+#446 := [monotonicity #735]: #736
+#460 := (iff #752 #751)
+#390 := (or #404 #747)
+#737 := (iff #390 #751)
+#738 := [rewrite]: #737
+#750 := (iff #752 #390)
+#749 := (iff #756 #747)
+#746 := (iff #421 #438)
+#742 := (or false #438)
+#745 := (iff #742 #438)
+#740 := [rewrite]: #745
+#743 := (iff #421 #742)
+#413 := (iff #442 false)
+#418 := [rewrite]: #413
+#744 := [monotonicity #418]: #743
+#384 := [trans #744 #740]: #746
+#389 := [monotonicity #384]: #749
+#405 := (iff #545 #404)
+#402 := (iff #415 #758)
+#754 := (or #758 false)
+#398 := (iff #754 #758)
+#739 := [rewrite]: #398
+#414 := (iff #415 #754)
+#755 := [monotonicity #418]: #414
+#403 := [trans #755 #739]: #402
+#741 := [monotonicity #403]: #405
+#748 := [monotonicity #741 #389]: #750
+#461 := [trans #748 #738]: #460
+#449 := [monotonicity #461 #446]: #448
+#443 := [monotonicity #449]: #728
+#763 := (iff #762 false)
+#753 := [rewrite]: #763
+#726 := [monotonicity #753 #443]: #729
+#721 := [trans #726 #719]: #720
+#724 := [monotonicity #721]: #718
+#567 := [trans #724 #566]: #718
+#723 := [quant-inst #8 #9]: #722
+#709 := [mp #723 #567]: #717
+#640 := [unit-resolution #709 #777]: #727
+#694 := (not #759)
+#693 := (not #727)
+#636 := (or #693 #694)
+#600 := (not #427)
+#710 := (<= #10 0::Int)
+#642 := (not #710)
+#672 := (not #93)
+#673 := (or #642 #672)
+#629 := [th-lemma arith farkas 1 1]: #673
+#630 := [unit-resolution #629 #100]: #642
+#631 := (or #600 #710)
+#634 := [th-lemma arith triangle-eq]: #631
+#635 := [unit-resolution #634 #630]: #600
+#697 := (or #693 #694 #427)
+#582 := [def-axiom]: #697
+#637 := [unit-resolution #582 #635]: #636
+#632 := [unit-resolution #637 #640]: #694
+#597 := (or #693 #759 #447)
+#599 := [def-axiom]: #597
+#638 := [unit-resolution #599 #632 #640]: #447
+#701 := (not #447)
+#703 := (or #701 #714 #441)
+#704 := [def-axiom]: #703
+#612 := [unit-resolution #704 #638]: #611
+#613 := [unit-resolution #612 #639]: #714
+#712 := (or #751 #438)
+#706 := [def-axiom]: #712
+#506 := [unit-resolution #706 #613]: #438
+#707 := (or #751 #758)
+#713 := [def-axiom]: #707
+#617 := [unit-resolution #713 #613]: #758
+#618 := (or #759 #404 #747)
+#619 := [th-lemma arith triangle-eq]: #618
+#624 := [unit-resolution #619 #632]: #390
+[unit-resolution #624 #617 #506]: false
unsat
cfa8a4e8b0964986b89eaf37e6038032e9b8b0d6 101 0
#2 := false
@@ -7945,783 +8218,936 @@
#123 := [th-lemma arith triangle-eq]: #122
[unit-resolution #123 #119 #112 #46]: false
unsat
-cf727a25fbaea6abf5a0d302bf954b4ffa92b324 777 0
-#2 := false
-#9 := 0::Int
-#30 := 4::Int
-decl f3 :: Int
-#11 := f3
-#546 := (div f3 4::Int)
-#208 := -4::Int
-#574 := (* -4::Int #546)
-#39 := (mod f3 4::Int)
-#107 := -1::Int
-#573 := (* -1::Int #39)
-#575 := (+ #573 #574)
-#576 := (+ f3 #575)
-#581 := (<= #576 0::Int)
-#572 := (= #576 0::Int)
-#1 := true
-#93 := [true-axiom]: true
-#721 := (or false #572)
-#722 := [th-lemma arith]: #721
-#723 := [unit-resolution #722 #93]: #572
-#724 := (not #572)
-#725 := (or #724 #581)
-#726 := [th-lemma arith triangle-eq]: #725
-#727 := [unit-resolution #726 #723]: #581
-#582 := (>= #576 0::Int)
-#728 := (or #724 #582)
-#729 := [th-lemma arith triangle-eq]: #728
-#730 := [unit-resolution #729 #723]: #582
-#600 := (>= #39 4::Int)
-#601 := (not #600)
-#731 := (or false #601)
-#732 := [th-lemma arith]: #731
-#733 := [unit-resolution #732 #93]: #601
-#47 := 3::Int
-#613 := (>= #39 3::Int)
-#872 := (= #39 3::Int)
-#108 := (* -1::Int f3)
-#211 := (mod #108 -4::Int)
-#217 := (* -1::Int #211)
-#258 := (>= f3 0::Int)
-#259 := (not #258)
-#245 := (<= f3 0::Int)
-#246 := (not #245)
-#269 := (or #246 #259)
-#272 := (ite #269 #39 #217)
-#32 := (= f3 0::Int)
-#275 := (ite #32 0::Int #272)
-#282 := (= #275 3::Int)
-#41 := (- 4::Int)
-#40 := (- f3)
-#42 := (mod #40 #41)
-#43 := (- #42)
-#34 := (< 0::Int 4::Int)
-#36 := (< f3 0::Int)
-#37 := (and #36 #34)
-#33 := (< 0::Int f3)
-#35 := (and #33 #34)
-#38 := (or #35 #37)
-#44 := (ite #38 #39 #43)
-#45 := (ite #32 0::Int #44)
-#31 := (= 4::Int 0::Int)
-#46 := (ite #31 f3 #45)
-#48 := (= #46 3::Int)
-#286 := (iff #48 #282)
-#200 := (and #34 #36)
-#203 := (or #35 #200)
-#222 := (ite #203 #39 #217)
-#197 := (= 0::Int f3)
-#225 := (ite #197 0::Int #222)
-#238 := (= 3::Int #225)
-#284 := (iff #238 #282)
-#278 := (= 3::Int #275)
-#281 := (iff #278 #282)
-#283 := [rewrite]: #281
-#279 := (iff #238 #278)
-#276 := (= #225 #275)
-#273 := (= #222 #272)
-#270 := (iff #203 #269)
-#267 := (iff #200 #259)
-#262 := (and true #259)
-#265 := (iff #262 #259)
-#266 := [rewrite]: #265
-#263 := (iff #200 #262)
-#260 := (iff #36 #259)
-#261 := [rewrite]: #260
-#249 := (iff #34 true)
-#250 := [rewrite]: #249
-#264 := [monotonicity #250 #261]: #263
-#268 := [trans #264 #266]: #267
-#256 := (iff #35 #246)
-#251 := (and #246 true)
-#254 := (iff #251 #246)
-#255 := [rewrite]: #254
-#252 := (iff #35 #251)
-#247 := (iff #33 #246)
-#248 := [rewrite]: #247
-#253 := [monotonicity #248 #250]: #252
-#257 := [trans #253 #255]: #256
-#271 := [monotonicity #257 #268]: #270
-#274 := [monotonicity #271]: #273
-#243 := (iff #197 #32)
-#244 := [rewrite]: #243
-#277 := [monotonicity #244 #274]: #276
-#280 := [monotonicity #277]: #279
-#285 := [trans #280 #283]: #284
-#241 := (iff #48 #238)
-#235 := (= #225 3::Int)
-#239 := (iff #235 #238)
-#240 := [rewrite]: #239
-#236 := (iff #48 #235)
-#233 := (= #46 #225)
-#228 := (ite false f3 #225)
-#231 := (= #228 #225)
-#232 := [rewrite]: #231
-#229 := (= #46 #228)
-#226 := (= #45 #225)
-#223 := (= #44 #222)
-#220 := (= #43 #217)
-#214 := (- #211)
-#218 := (= #214 #217)
-#219 := [rewrite]: #218
-#215 := (= #43 #214)
-#212 := (= #42 #211)
-#209 := (= #41 -4::Int)
-#210 := [rewrite]: #209
-#206 := (= #40 #108)
-#207 := [rewrite]: #206
-#213 := [monotonicity #207 #210]: #212
-#216 := [monotonicity #213]: #215
-#221 := [trans #216 #219]: #220
-#204 := (iff #38 #203)
-#201 := (iff #37 #200)
-#202 := [rewrite]: #201
-#205 := [monotonicity #202]: #204
-#224 := [monotonicity #205 #221]: #223
-#198 := (iff #32 #197)
-#199 := [rewrite]: #198
-#227 := [monotonicity #199 #224]: #226
-#195 := (iff #31 false)
-#196 := [rewrite]: #195
-#230 := [monotonicity #196 #227]: #229
-#234 := [trans #230 #232]: #233
-#237 := [monotonicity #234]: #236
-#242 := [trans #237 #240]: #241
-#287 := [trans #242 #285]: #286
-#194 := [asserted]: #48
-#288 := [mp #194 #287]: #282
-#883 := (= #39 #275)
-#495 := (= #272 #275)
-#509 := (not #32)
-#494 := (= #275 0::Int)
-#829 := (not #494)
-#608 := (= 3::Int 0::Int)
-#610 := (iff #608 false)
-#827 := [rewrite]: #610
-#606 := [hypothesis]: #494
-#607 := [symm #288]: #278
-#609 := [trans #607 #606]: #608
-#828 := [mp #609 #827]: false
-#830 := [lemma #828]: #829
-#510 := (or #509 #494)
-#511 := [def-axiom]: #510
-#831 := [unit-resolution #511 #830]: #509
-#512 := (or #32 #495)
-#513 := [def-axiom]: #512
-#881 := [unit-resolution #513 #831]: #495
-#496 := (= #39 #272)
-#502 := (not #269)
-#666 := [hypothesis]: #502
-#498 := (or #269 #245)
-#499 := [def-axiom]: #498
-#667 := [unit-resolution #499 #666]: #245
-#500 := (or #269 #258)
-#501 := [def-axiom]: #500
-#813 := [unit-resolution #501 #666]: #258
-#814 := (or #32 #246 #259)
-#832 := [th-lemma arith triangle-eq]: #814
-#865 := [unit-resolution #832 #813 #667 #831]: false
-#866 := [lemma #865]: #269
-#505 := (or #502 #496)
-#506 := [def-axiom]: #505
-#882 := [unit-resolution #506 #866]: #496
-#884 := [trans #882 #881]: #883
-#885 := [trans #884 #288]: #872
-#886 := (not #872)
-#887 := (or #886 #613)
-#888 := [th-lemma arith triangle-eq]: #887
-#889 := [unit-resolution #888 #885]: #613
-#8 := 2::Int
+742e212b0179422ed718ceb7818522f48622510c 930 0
+#2 := false
+#20 := 1::Int
+decl f3 :: (-> Int Int Int)
+#11 := 2::Int
+decl f5 :: Int
+#9 := f5
+#22 := (f3 f5 2::Int)
+#1103 := (<= #22 1::Int)
+#13 := 0::Int
+#574 := (mod f5 2::Int)
+#108 := -1::Int
+#575 := (* -1::Int #574)
+#576 := (+ #22 #575)
+#954 := (<= #576 0::Int)
+#577 := (= #576 0::Int)
decl f4 :: Int
-#12 := f4
-#13 := (+ f3 f4)
-#614 := (div #13 2::Int)
-#113 := -2::Int
-#632 := (* -2::Int #614)
-#21 := (mod #13 2::Int)
-#631 := (* -1::Int #21)
-#633 := (+ #631 #632)
-#634 := (+ f4 #633)
-#635 := (+ f3 #634)
-#639 := (<= #635 0::Int)
-#629 := (= #635 0::Int)
-#735 := (or false #629)
-#736 := [th-lemma arith]: #735
-#737 := [unit-resolution #736 #93]: #629
-#738 := (not #629)
-#739 := (or #738 #639)
-#740 := [th-lemma arith triangle-eq]: #739
-#741 := [unit-resolution #740 #737]: #639
-#640 := (>= #635 0::Int)
-#742 := (or #738 #640)
-#743 := [th-lemma arith triangle-eq]: #742
-#744 := [unit-resolution #743 #737]: #640
-#710 := (<= #21 0::Int)
-#709 := (= #21 0::Int)
-#109 := (* -1::Int f4)
-#110 := (+ #108 #109)
-#116 := (mod #110 -2::Int)
-#122 := (* -1::Int #116)
-#163 := (>= #13 0::Int)
-#164 := (not #163)
-#150 := (<= #13 0::Int)
-#151 := (not #150)
-#174 := (or #151 #164)
-#177 := (ite #174 #21 #122)
-#14 := (= #13 0::Int)
-#180 := (ite #14 0::Int #177)
-#187 := (= #180 0::Int)
-#23 := (- 2::Int)
-#22 := (- #13)
-#24 := (mod #22 #23)
-#25 := (- #24)
-#16 := (< 0::Int 2::Int)
-#18 := (< #13 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #13)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#26 := (ite #20 #21 #25)
-#27 := (ite #14 0::Int #26)
-#10 := (= 2::Int 0::Int)
-#28 := (ite #10 #13 #27)
-#29 := (= #28 0::Int)
-#191 := (iff #29 #187)
-#101 := (and #16 #18)
-#104 := (or #17 #101)
-#127 := (ite #104 #21 #122)
-#98 := (= 0::Int #13)
-#130 := (ite #98 0::Int #127)
-#143 := (= 0::Int #130)
-#189 := (iff #143 #187)
-#183 := (= 0::Int #180)
-#186 := (iff #183 #187)
-#188 := [rewrite]: #186
-#184 := (iff #143 #183)
-#181 := (= #130 #180)
-#178 := (= #127 #177)
-#175 := (iff #104 #174)
-#172 := (iff #101 #164)
-#167 := (and true #164)
-#170 := (iff #167 #164)
-#171 := [rewrite]: #170
-#168 := (iff #101 #167)
-#165 := (iff #18 #164)
-#166 := [rewrite]: #165
-#154 := (iff #16 true)
-#155 := [rewrite]: #154
-#169 := [monotonicity #155 #166]: #168
-#173 := [trans #169 #171]: #172
-#161 := (iff #17 #151)
-#156 := (and #151 true)
-#159 := (iff #156 #151)
-#160 := [rewrite]: #159
-#157 := (iff #17 #156)
-#152 := (iff #15 #151)
-#153 := [rewrite]: #152
-#158 := [monotonicity #153 #155]: #157
-#162 := [trans #158 #160]: #161
-#176 := [monotonicity #162 #173]: #175
-#179 := [monotonicity #176]: #178
-#148 := (iff #98 #14)
-#149 := [rewrite]: #148
-#182 := [monotonicity #149 #179]: #181
-#185 := [monotonicity #182]: #184
-#190 := [trans #185 #188]: #189
-#146 := (iff #29 #143)
-#140 := (= #130 0::Int)
-#144 := (iff #140 #143)
-#145 := [rewrite]: #144
-#141 := (iff #29 #140)
-#138 := (= #28 #130)
-#133 := (ite false #13 #130)
-#136 := (= #133 #130)
-#137 := [rewrite]: #136
-#134 := (= #28 #133)
-#131 := (= #27 #130)
-#128 := (= #26 #127)
-#125 := (= #25 #122)
-#119 := (- #116)
-#123 := (= #119 #122)
-#124 := [rewrite]: #123
-#120 := (= #25 #119)
-#117 := (= #24 #116)
-#114 := (= #23 -2::Int)
-#115 := [rewrite]: #114
-#111 := (= #22 #110)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#121 := [monotonicity #118]: #120
-#126 := [trans #121 #124]: #125
-#105 := (iff #20 #104)
-#102 := (iff #19 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103]: #105
-#129 := [monotonicity #106 #126]: #128
-#99 := (iff #14 #98)
-#100 := [rewrite]: #99
-#132 := [monotonicity #100 #129]: #131
-#96 := (iff #10 false)
-#97 := [rewrite]: #96
-#135 := [monotonicity #97 #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#147 := [trans #142 #145]: #146
-#192 := [trans #147 #190]: #191
-#95 := [asserted]: #29
-#193 := [mp #95 #192]: #187
-#757 := (= #21 #180)
-#475 := (= #177 #180)
-#489 := (not #14)
-#423 := (>= f4 0::Int)
-#424 := (not #423)
-#412 := (<= f4 0::Int)
-#413 := (not #412)
-#434 := (or #413 #424)
-#534 := (not #434)
-#58 := 1::Int
-#66 := (mod f4 2::Int)
-#834 := (>= #66 1::Int)
-#837 := (not #834)
-#904 := (= #66 1::Int)
-#957 := (not #904)
-#345 := (mod #109 -2::Int)
-#351 := (* -1::Int #345)
-#437 := (ite #434 #66 #351)
-#60 := (= f4 0::Int)
-#440 := (ite #60 0::Int #437)
-#447 := (= #440 1::Int)
-#468 := (not #447)
-#958 := (iff #468 #957)
-#955 := (iff #447 #904)
-#953 := (iff #904 #447)
-#951 := (= #66 #440)
-#527 := (= #437 #440)
-#541 := (not #60)
-#552 := [hypothesis]: #434
-#895 := (or #541 #534)
-#558 := [hypothesis]: #60
-#553 := (or #541 #412)
-#554 := [th-lemma arith triangle-eq]: #553
-#555 := [unit-resolution #554 #558]: #412
-#559 := (or #541 #423)
-#892 := [th-lemma arith triangle-eq]: #559
-#893 := [unit-resolution #892 #558]: #423
-#535 := (or #534 #413 #424)
-#536 := [def-axiom]: #535
-#894 := [unit-resolution #536 #893 #555 #552]: false
-#896 := [lemma #894]: #895
-#947 := [unit-resolution #896 #552]: #541
-#544 := (or #60 #527)
-#545 := [def-axiom]: #544
-#948 := [unit-resolution #545 #947]: #527
-#528 := (= #66 #437)
-#537 := (or #534 #528)
-#538 := [def-axiom]: #537
-#946 := [unit-resolution #538 #552]: #528
-#952 := [trans #946 #948]: #951
-#954 := [monotonicity #952]: #953
-#956 := [symm #954]: #955
-#959 := [monotonicity #956]: #958
-#299 := (mod #108 -2::Int)
-#305 := (* -1::Int #299)
-#52 := (mod f3 2::Int)
-#396 := (ite #269 #52 #305)
-#399 := (ite #32 0::Int #396)
-#406 := (= #399 1::Int)
-#708 := (>= #52 1::Int)
-#669 := (div f3 2::Int)
-#683 := (* -2::Int #669)
-#682 := (* -1::Int #52)
-#684 := (+ #682 #683)
-#685 := (+ f3 #684)
-#556 := (<= #685 0::Int)
-#681 := (= #685 0::Int)
-#551 := (or false #681)
-#560 := [th-lemma arith]: #551
-#561 := [unit-resolution #560 #93]: #681
-#874 := (not #681)
-#875 := (or #874 #556)
-#876 := [th-lemma arith triangle-eq]: #875
-#877 := [unit-resolution #876 #561]: #556
-#557 := (>= #685 0::Int)
-#878 := (or #874 #557)
-#879 := [th-lemma arith triangle-eq]: #878
-#880 := [unit-resolution #879 #561]: #557
-#716 := (not #708)
-#717 := [hypothesis]: #716
-#692 := (>= #52 0::Int)
-#718 := (or false #692)
-#719 := [th-lemma arith]: #718
-#720 := [unit-resolution #719 #93]: #692
-#890 := [th-lemma arith gcd-test 1/4 1/4 1/4 1/4 -1/4 -1/4 -1/4 -1/4 #889 #733 #730 #727 #720 #717 #880 #877]: false
-#891 := [lemma #890]: #708
-#938 := (or #406 #716)
-#515 := (= #396 #399)
-#524 := (or #32 #515)
-#525 := [def-axiom]: #524
-#936 := [unit-resolution #525 #831]: #515
-#516 := (= #52 #396)
-#518 := (or #502 #516)
-#519 := [def-axiom]: #518
-#937 := [unit-resolution #519 #866]: #516
-#785 := (not #516)
-#784 := (not #515)
-#803 := (or #406 #784 #785 #716)
-#690 := (= #52 1::Int)
-#707 := (<= #52 1::Int)
-#788 := (not #707)
-#789 := [hypothesis]: #788
-#698 := (>= #52 2::Int)
-#699 := (not #698)
-#790 := (or false #699)
-#791 := [th-lemma arith]: #790
-#792 := [unit-resolution #791 #93]: #699
-#793 := [th-lemma arith farkas 1 1 #792 #789]: false
-#794 := [lemma #793]: #707
-#797 := [hypothesis]: #708
-#798 := (or #690 #788 #716)
-#799 := [th-lemma arith triangle-eq]: #798
-#800 := [unit-resolution #799 #797 #794]: #690
-#780 := (= #399 #52)
-#778 := (= #396 #52)
-#774 := [hypothesis]: #516
-#779 := [symm #774]: #778
-#776 := (= #399 #396)
-#775 := [hypothesis]: #515
-#777 := [symm #775]: #776
-#781 := [trans #777 #779]: #780
-#801 := [trans #781 #800]: #406
-#467 := (not #406)
-#796 := [hypothesis]: #467
-#802 := [unit-resolution #796 #801]: false
-#804 := [lemma #802]: #803
-#939 := [unit-resolution #804 #937 #936]: #938
-#944 := [unit-resolution #939 #891]: #406
-#461 := (or #467 #468)
-#451 := (and #406 #447)
-#454 := (not #451)
-#472 := (iff #454 #461)
-#462 := (not #461)
-#463 := (not #462)
-#470 := (iff #463 #461)
-#471 := [rewrite]: #470
-#464 := (iff #454 #463)
-#465 := (iff #451 #462)
-#466 := [rewrite]: #465
-#469 := [monotonicity #466]: #464
-#473 := [trans #469 #471]: #472
-#67 := (- f4)
-#68 := (mod #67 #23)
-#69 := (- #68)
-#63 := (< f4 0::Int)
-#64 := (and #63 #16)
-#61 := (< 0::Int f4)
-#62 := (and #61 #16)
-#65 := (or #62 #64)
-#70 := (ite #65 #66 #69)
-#71 := (ite #60 0::Int #70)
-#72 := (ite #10 f4 #71)
-#73 := (= #72 1::Int)
-#53 := (mod #40 #23)
-#54 := (- #53)
-#50 := (and #36 #16)
-#49 := (and #33 #16)
-#51 := (or #49 #50)
-#55 := (ite #51 #52 #54)
-#56 := (ite #32 0::Int #55)
-#57 := (ite #10 f3 #56)
-#59 := (= #57 1::Int)
-#74 := (and #59 #73)
-#75 := (not #74)
-#457 := (iff #75 #454)
-#337 := (and #16 #63)
-#334 := (and #16 #61)
-#340 := (or #334 #337)
-#356 := (ite #340 #66 #351)
-#331 := (= 0::Int f4)
-#359 := (ite #331 0::Int #356)
-#372 := (= 1::Int #359)
-#293 := (and #16 #36)
-#290 := (and #16 #33)
-#296 := (or #290 #293)
-#310 := (ite #296 #52 #305)
-#313 := (ite #197 0::Int #310)
-#326 := (= 1::Int #313)
-#377 := (and #326 #372)
-#380 := (not #377)
-#455 := (iff #380 #454)
-#452 := (iff #377 #451)
-#449 := (iff #372 #447)
-#443 := (= 1::Int #440)
-#446 := (iff #443 #447)
-#448 := [rewrite]: #446
-#444 := (iff #372 #443)
-#441 := (= #359 #440)
-#438 := (= #356 #437)
-#435 := (iff #340 #434)
-#432 := (iff #337 #424)
-#427 := (and true #424)
-#430 := (iff #427 #424)
-#431 := [rewrite]: #430
-#428 := (iff #337 #427)
-#425 := (iff #63 #424)
-#426 := [rewrite]: #425
-#429 := [monotonicity #155 #426]: #428
-#433 := [trans #429 #431]: #432
-#421 := (iff #334 #413)
-#416 := (and true #413)
-#419 := (iff #416 #413)
-#420 := [rewrite]: #419
-#417 := (iff #334 #416)
-#414 := (iff #61 #413)
-#415 := [rewrite]: #414
-#418 := [monotonicity #155 #415]: #417
-#422 := [trans #418 #420]: #421
-#436 := [monotonicity #422 #433]: #435
+#8 := f4
+#10 := (+ f4 f5)
+#461 := (>= #10 0::Int)
+#778 := (= #10 0::Int)
+#458 := (mod #10 2::Int)
+#459 := (* -1::Int #458)
+#12 := (f3 #10 2::Int)
+#460 := (+ #12 #459)
+#457 := (= #460 0::Int)
+#715 := (not #457)
+#720 := (<= #460 0::Int)
+#1107 := [hypothesis]: #457
+#1108 := (or #715 #720)
+#1109 := [th-lemma arith triangle-eq]: #1108
+#1110 := [unit-resolution #1109 #1107]: #720
+#722 := (>= #460 0::Int)
+#1111 := (or #715 #722)
+#1322 := [th-lemma arith triangle-eq]: #1111
+#1323 := [unit-resolution #1322 #1107]: #722
+#1193 := (not #720)
+#1239 := (not #722)
+#1348 := (or #1239 #1193)
+#1112 := (div f5 2::Int)
+#476 := -2::Int
+#1125 := (* -2::Int #1112)
+#1126 := (+ #575 #1125)
+#1127 := (+ f5 #1126)
+#1124 := (= #1127 0::Int)
+#1161 := (not #1124)
+#1276 := [hypothesis]: #1161
+#1 := true
+#72 := [true-axiom]: true
+#1154 := (or false #1124)
+#1159 := [th-lemma arith]: #1154
+#1277 := [unit-resolution #1159 #72 #1276]: false
+#1278 := [lemma #1277]: #1124
+#1274 := (or #1161 #1239 #1193)
+#1134 := (>= #574 0::Int)
+#1157 := (or false #1134)
+#1158 := [th-lemma arith]: #1157
+#1151 := [unit-resolution #1158 #72]: #1134
+#1224 := (>= #1127 0::Int)
+#1246 := [hypothesis]: #1124
+#1247 := (or #1161 #1224)
+#1248 := [th-lemma arith triangle-eq]: #1247
+#1249 := [unit-resolution #1248 #1246]: #1224
+#17 := 3::Int
+#15 := 4::Int
+#16 := (f3 f4 4::Int)
+#568 := (>= #16 3::Int)
+#18 := (= #16 3::Int)
+#75 := [asserted]: #18
+#967 := (not #18)
+#993 := (or #967 #568)
+#994 := [th-lemma arith triangle-eq]: #993
+#995 := [unit-resolution #994 #75]: #568
+#865 := (div f4 4::Int)
+#663 := -4::Int
+#881 := (* -4::Int #865)
+#696 := (mod f4 4::Int)
+#698 := (* -1::Int #696)
+#882 := (+ #698 #881)
+#883 := (+ f4 #882)
+#889 := (>= #883 0::Int)
+#880 := (= #883 0::Int)
+#971 := (or false #880)
+#972 := [th-lemma arith]: #971
+#973 := [unit-resolution #972 #72]: #880
+#974 := (not #880)
+#996 := (or #974 #889)
+#997 := [th-lemma arith triangle-eq]: #996
+#998 := [unit-resolution #997 #973]: #889
+#560 := (>= #12 0::Int)
+#14 := (= #12 0::Int)
+#74 := [asserted]: #14
+#622 := (not #14)
+#1230 := (or #622 #560)
+#1231 := [th-lemma arith triangle-eq]: #1230
+#1232 := [unit-resolution #1231 #74]: #560
+#811 := (div #10 2::Int)
+#828 := (* -2::Int #811)
+#829 := (+ #459 #828)
+#830 := (+ f5 #829)
+#831 := (+ f4 #830)
+#1106 := (>= #831 0::Int)
+#826 := (= #831 0::Int)
+#1167 := (or false #826)
+#1168 := [th-lemma arith]: #1167
+#1169 := [unit-resolution #1168 #72]: #826
+#1180 := (not #826)
+#1233 := (or #1180 #1106)
+#1234 := [th-lemma arith triangle-eq]: #1233
+#1235 := [unit-resolution #1234 #1169]: #1106
+#708 := (+ #16 #698)
+#600 := (>= #708 0::Int)
+#709 := (= #708 0::Int)
+#482 := (* -1::Int f4)
+#660 := (mod #482 -4::Int)
+#648 := (+ #16 #660)
+#653 := (= #648 0::Int)
+#710 := (>= f4 0::Int)
+#669 := (not #710)
+#701 := (<= f4 0::Int)
+#670 := (not #701)
+#659 := (or #670 #669)
+#656 := (ite #659 #709 #653)
+#689 := (= f4 0::Int)
+#590 := (not #689)
+#688 := (= #16 0::Int)
+#595 := (not #688)
+#428 := (= 3::Int 0::Int)
+#430 := (iff #428 false)
+#419 := [rewrite]: #430
+#425 := [hypothesis]: #688
+#426 := (= 3::Int #16)
+#427 := [symm #75]: #426
+#429 := [trans #427 #425]: #428
+#431 := [mp #429 #419]: false
+#412 := [lemma #431]: #595
+#1027 := (or #590 #688)
+#630 := (ite #689 #688 #656)
+#27 := (:var 0 Int)
+#26 := (:var 1 Int)
+#46 := (f3 #26 #27)
+#790 := (pattern #46)
+#112 := (* -1::Int #27)
+#109 := (* -1::Int #26)
+#173 := (mod #109 #112)
+#302 := (+ #46 #173)
+#303 := (= #302 0::Int)
+#47 := (mod #26 #27)
+#299 := (* -1::Int #47)
+#300 := (+ #46 #299)
+#301 := (= #300 0::Int)
+#147 := (>= #26 0::Int)
+#140 := (<= #27 0::Int)
+#246 := (or #140 #147)
+#247 := (not #246)
+#136 := (<= #26 0::Int)
+#242 := (or #136 #140)
+#243 := (not #242)
+#250 := (or #243 #247)
+#304 := (ite #250 #301 #303)
+#298 := (= #46 0::Int)
+#29 := (= #26 0::Int)
+#305 := (ite #29 #298 #304)
+#297 := (= #26 #46)
+#30 := (= #27 0::Int)
+#306 := (ite #30 #297 #305)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #306)
+#309 := (forall (vars (?v0 Int) (?v1 Int)) #306)
+#794 := (iff #309 #791)
+#792 := (iff #306 #306)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#179 := (* -1::Int #173)
+#266 := (ite #250 #47 #179)
+#269 := (ite #29 0::Int #266)
+#272 := (ite #30 #26 #269)
+#275 := (= #46 #272)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#310 := (iff #278 #309)
+#307 := (iff #275 #306)
+#308 := [rewrite]: #307
+#311 := [quant-intro #308]: #310
+#148 := (not #147)
+#141 := (not #140)
+#151 := (and #141 #148)
+#137 := (not #136)
+#144 := (and #137 #141)
+#154 := (or #144 #151)
+#199 := (ite #154 #47 #179)
+#202 := (ite #29 0::Int #199)
+#205 := (ite #30 #26 #202)
+#208 := (= #46 #205)
+#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
+#279 := (iff #211 #278)
+#276 := (iff #208 #275)
+#273 := (= #205 #272)
+#270 := (= #202 #269)
+#267 := (= #199 #266)
+#251 := (iff #154 #250)
+#248 := (iff #151 #247)
+#249 := [rewrite]: #248
+#244 := (iff #144 #243)
+#245 := [rewrite]: #244
+#252 := [monotonicity #245 #249]: #251
+#268 := [monotonicity #252]: #267
+#271 := [monotonicity #268]: #270
+#274 := [monotonicity #271]: #273
+#277 := [monotonicity #274]: #276
+#280 := [quant-intro #277]: #279
+#221 := (~ #211 #211)
+#223 := (~ #208 #208)
+#220 := [refl]: #223
+#224 := [nnf-pos #220]: #221
+#40 := (- #27)
+#39 := (- #26)
+#48 := (mod #39 #40)
+#49 := (- #48)
+#33 := (< 0::Int #27)
+#35 := (< #26 0::Int)
+#36 := (and #35 #33)
+#32 := (< 0::Int #26)
+#34 := (and #32 #33)
+#37 := (or #34 #36)
+#50 := (ite #37 #47 #49)
+#51 := (ite #29 0::Int #50)
+#52 := (ite #30 #26 #51)
+#53 := (= #46 #52)
+#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
+#214 := (iff #54 #211)
+#102 := (and #33 #35)
+#105 := (or #34 #102)
+#184 := (ite #105 #47 #179)
+#93 := (= 0::Int #26)
+#187 := (ite #93 0::Int #184)
+#96 := (= 0::Int #27)
+#190 := (ite #96 #26 #187)
+#193 := (= #46 #190)
+#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
+#212 := (iff #196 #211)
+#209 := (iff #193 #208)
+#206 := (= #190 #205)
+#203 := (= #187 #202)
+#200 := (= #184 #199)
+#155 := (iff #105 #154)
+#152 := (iff #102 #151)
+#149 := (iff #35 #148)
+#150 := [rewrite]: #149
+#142 := (iff #33 #141)
+#143 := [rewrite]: #142
+#153 := [monotonicity #143 #150]: #152
+#145 := (iff #34 #144)
+#138 := (iff #32 #137)
+#139 := [rewrite]: #138
+#146 := [monotonicity #139 #143]: #145
+#156 := [monotonicity #146 #153]: #155
+#201 := [monotonicity #156]: #200
+#130 := (iff #93 #29)
+#131 := [rewrite]: #130
+#204 := [monotonicity #131 #201]: #203
+#132 := (iff #96 #30)
+#133 := [rewrite]: #132
+#207 := [monotonicity #133 #204]: #206
+#210 := [monotonicity #207]: #209
+#213 := [quant-intro #210]: #212
+#197 := (iff #54 #196)
+#194 := (iff #53 #193)
+#191 := (= #52 #190)
+#188 := (= #51 #187)
+#185 := (= #50 #184)
+#182 := (= #49 #179)
+#176 := (- #173)
+#180 := (= #176 #179)
+#181 := [rewrite]: #180
+#177 := (= #49 #176)
+#174 := (= #48 #173)
+#113 := (= #40 #112)
+#114 := [rewrite]: #113
+#110 := (= #39 #109)
+#111 := [rewrite]: #110
+#175 := [monotonicity #111 #114]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#106 := (iff #37 #105)
+#103 := (iff #36 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#186 := [monotonicity #107 #183]: #185
+#94 := (iff #29 #93)
+#95 := [rewrite]: #94
+#189 := [monotonicity #95 #186]: #188
+#97 := (iff #30 #96)
+#98 := [rewrite]: #97
+#192 := [monotonicity #98 #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [quant-intro #195]: #197
+#215 := [trans #198 #213]: #214
+#172 := [asserted]: #54
+#216 := [mp #172 #215]: #211
+#225 := [mp~ #216 #224]: #211
+#281 := [mp #225 #280]: #278
+#312 := [mp #281 #311]: #309
+#796 := [mp #312 #795]: #791
+#584 := (not #791)
+#641 := (or #584 #630)
+#718 := (* -1::Int 4::Int)
+#705 := (mod #482 #718)
+#707 := (+ #16 #705)
+#699 := (= #707 0::Int)
+#706 := (<= 4::Int 0::Int)
+#711 := (or #706 #710)
+#700 := (not #711)
+#702 := (or #701 #706)
+#703 := (not #702)
+#697 := (or #703 #700)
+#704 := (ite #697 #709 #699)
+#691 := (ite #689 #688 #704)
+#692 := (= f4 #16)
+#693 := (= 4::Int 0::Int)
+#694 := (ite #693 #692 #691)
+#644 := (or #584 #694)
+#646 := (iff #644 #641)
+#647 := (iff #641 #641)
+#627 := [rewrite]: #647
+#639 := (iff #694 #630)
+#525 := (ite false #692 #630)
+#638 := (iff #525 #630)
+#643 := [rewrite]: #638
+#636 := (iff #694 #525)
+#631 := (iff #691 #630)
+#651 := (iff #704 #656)
+#654 := (iff #699 #653)
+#649 := (= #707 #648)
+#666 := (= #705 #660)
+#664 := (= #718 -4::Int)
+#665 := [rewrite]: #664
+#652 := [monotonicity #665]: #666
+#650 := [monotonicity #652]: #649
+#655 := [monotonicity #650]: #654
+#661 := (iff #697 #659)
+#680 := (iff #700 #669)
+#678 := (iff #711 #710)
+#673 := (or false #710)
+#676 := (iff #673 #710)
+#677 := [rewrite]: #676
+#674 := (iff #711 #673)
+#681 := (iff #706 false)
+#682 := [rewrite]: #681
+#675 := [monotonicity #682]: #674
+#679 := [trans #675 #677]: #678
+#658 := [monotonicity #679]: #680
+#671 := (iff #703 #670)
+#667 := (iff #702 #701)
+#684 := (or #701 false)
+#683 := (iff #684 #701)
+#687 := [rewrite]: #683
+#685 := (iff #702 #684)
+#686 := [monotonicity #682]: #685
+#668 := [trans #686 #687]: #667
+#672 := [monotonicity #668]: #671
+#662 := [monotonicity #672 #658]: #661
+#657 := [monotonicity #662 #655]: #651
+#632 := [monotonicity #657]: #631
+#690 := (iff #693 false)
+#695 := [rewrite]: #690
+#637 := [monotonicity #695 #632]: #636
+#640 := [trans #637 #643]: #639
+#642 := [monotonicity #640]: #646
+#573 := [trans #642 #627]: #646
+#645 := [quant-inst #8 #15]: #644
+#628 := [mp #645 #573]: #641
+#1048 := [unit-resolution #628 #796]: #630
+#589 := (not #630)
+#591 := (or #589 #590 #688)
+#592 := [def-axiom]: #591
+#1047 := [unit-resolution #592 #1048]: #1027
+#1043 := [unit-resolution #1047 #412]: #590
+#957 := (or #689 #656)
+#593 := (or #589 #689 #656)
+#594 := [def-axiom]: #593
+#964 := [unit-resolution #594 #1048]: #957
+#1033 := [unit-resolution #964 #1043]: #656
+#635 := (not #659)
+#860 := [hypothesis]: #635
+#609 := (or #659 #701)
+#633 := [def-axiom]: #609
+#861 := [unit-resolution #633 #860]: #701
+#634 := (or #659 #710)
+#629 := [def-axiom]: #634
+#862 := [unit-resolution #629 #860]: #710
+#863 := (or #689 #670 #669)
+#864 := [th-lemma arith triangle-eq]: #863
+#913 := [unit-resolution #864 #862 #861 #1043]: false
+#914 := [lemma #913]: #659
+#611 := (not #656)
+#613 := (or #611 #635 #709)
+#614 := [def-axiom]: #613
+#1165 := [unit-resolution #614 #914 #1033]: #709
+#605 := (not #709)
+#1054 := (or #605 #600)
+#1055 := [th-lemma arith triangle-eq]: #1054
+#1236 := [unit-resolution #1055 #1165]: #600
+#1237 := [hypothesis]: #722
+#1170 := (* -1::Int #1112)
+#1035 := (* -2::Int #865)
+#1171 := (+ #1035 #1170)
+#1155 := (* -1::Int #811)
+#1172 := (+ #1155 #1171)
+#1173 := (+ #698 #1172)
+#1174 := (+ #459 #1173)
+#1175 := (+ #16 #1174)
+#1176 := (+ #12 #1175)
+#1177 := (+ f5 #1176)
+#1178 := (+ f4 #1177)
+#1179 := (>= #1178 2::Int)
+#1191 := (not #1179)
+#955 := (>= #576 0::Int)
+#1184 := [hypothesis]: #720
+#1240 := (or #577 #1239 #1193)
+#561 := (<= #16 3::Int)
+#968 := (or #967 #561)
+#966 := [th-lemma arith triangle-eq]: #968
+#970 := [unit-resolution #966 #75]: #561
+#888 := (<= #883 0::Int)
+#975 := (or #974 #888)
+#976 := [th-lemma arith triangle-eq]: #975
+#982 := [unit-resolution #976 #973]: #888
+#580 := (<= f5 0::Int)
+#556 := (= f5 0::Int)
+#1059 := (not #577)
+#1146 := [hypothesis]: #1059
+#1222 := (or #556 #577)
+#376 := (* -1::Int f5)
+#521 := (mod #376 -2::Int)
+#523 := (+ #22 #521)
+#508 := (= #523 0::Int)
+#546 := (not #580)
+#578 := (>= f5 0::Int)
+#526 := (not #578)
+#536 := (or #526 #546)
+#511 := (ite #536 #577 #508)
+#1066 := (not #556)
+#1207 := [hypothesis]: #1066
+#1201 := (or #556 #511)
+#555 := (= #22 0::Int)
+#514 := (ite #556 #555 #511)
+#382 := (or #584 #514)
+#370 := (* -1::Int 2::Int)
+#570 := (mod #376 #370)
+#571 := (+ #22 #570)
+#572 := (= #571 0::Int)
+#440 := (<= 2::Int 0::Int)
+#579 := (or #440 #578)
+#562 := (not #579)
+#550 := (or #580 #440)
+#551 := (not #550)
+#552 := (or #551 #562)
+#553 := (ite #552 #577 #572)
+#557 := (ite #556 #555 #553)
+#400 := (= f5 #22)
+#781 := (= 2::Int 0::Int)
+#558 := (ite #781 #400 #557)
+#383 := (or #584 #558)
+#371 := (iff #383 #382)
+#375 := (iff #382 #382)
+#797 := [rewrite]: #375
+#498 := (iff #558 #514)
+#517 := (ite false #400 #514)
+#495 := (iff #517 #514)
+#497 := [rewrite]: #495
+#506 := (iff #558 #517)
+#515 := (iff #557 #514)
+#512 := (iff #553 #511)
+#509 := (iff #572 #508)
+#505 := (= #571 #523)
+#522 := (= #570 #521)
+#750 := (= #370 -2::Int)
+#754 := [rewrite]: #750
+#520 := [monotonicity #754]: #522
+#507 := [monotonicity #520]: #505
+#510 := [monotonicity #507]: #509
+#533 := (iff #552 #536)
+#531 := (or #546 #526)
+#529 := (iff #531 #536)
+#532 := [rewrite]: #529
+#535 := (iff #552 #531)
+#527 := (iff #562 #526)
+#534 := (iff #579 #578)
+#540 := (or false #578)
+#539 := (iff #540 #578)
+#544 := [rewrite]: #539
+#542 := (iff #579 #540)
+#758 := (iff #440 false)
+#421 := [rewrite]: #758
+#543 := [monotonicity #421]: #542
+#524 := [trans #543 #544]: #534
+#530 := [monotonicity #524]: #527
+#549 := (iff #551 #546)
+#547 := (iff #550 #580)
+#554 := (or #580 false)
+#541 := (iff #554 #580)
+#545 := [rewrite]: #541
+#559 := (iff #550 #554)
+#538 := [monotonicity #421]: #559
+#548 := [trans #538 #545]: #547
+#537 := [monotonicity #548]: #549
+#528 := [monotonicity #537 #530]: #535
+#519 := [trans #528 #532]: #533
+#513 := [monotonicity #519 #510]: #512
+#516 := [monotonicity #513]: #515
+#782 := (iff #781 false)
+#772 := [rewrite]: #782
+#518 := [monotonicity #772 #516]: #506
+#499 := [trans #518 #497]: #498
+#372 := [monotonicity #499]: #371
+#798 := [trans #372 #797]: #371
+#384 := [quant-inst #9 #11]: #383
+#799 := [mp #384 #798]: #382
+#1156 := [unit-resolution #799 #796]: #514
+#1028 := (not #514)
+#1034 := (or #1028 #556 #511)
+#1070 := [def-axiom]: #1034
+#1202 := [unit-resolution #1070 #1156]: #1201
+#1208 := [unit-resolution #1202 #1207]: #511
+#1205 := (or #578 #577)
+#1147 := [hypothesis]: #526
+#388 := (or #536 #578)
+#389 := [def-axiom]: #388
+#1148 := [unit-resolution #389 #1147]: #536
+#1149 := (or #1066 #578)
+#1150 := [th-lemma arith triangle-eq]: #1149
+#1133 := [unit-resolution #1150 #1147]: #1066
+#1203 := [unit-resolution #1202 #1133]: #511
+#917 := (not #536)
+#836 := (not #511)
+#1025 := (or #836 #917 #577)
+#1026 := [def-axiom]: #1025
+#1204 := [unit-resolution #1026 #1203 #1148 #1146]: false
+#1206 := [lemma #1204]: #1205
+#1209 := [unit-resolution #1206 #1146]: #578
+#1217 := (or #556 #546 #526)
+#1218 := [th-lemma arith triangle-eq]: #1217
+#1219 := [unit-resolution #1218 #1207 #1209]: #546
+#915 := (or #536 #580)
+#916 := [def-axiom]: #915
+#1220 := [unit-resolution #916 #1219]: #536
+#1221 := [unit-resolution #1026 #1220 #1208 #1146]: false
+#1223 := [lemma #1221]: #1222
+#1226 := [unit-resolution #1223 #1146]: #556
+#1227 := (or #1066 #580)
+#1228 := [th-lemma arith triangle-eq]: #1227
+#1229 := [unit-resolution #1228 #1226]: #580
+#599 := (<= #12 0::Int)
+#1186 := (or #622 #599)
+#1187 := [th-lemma arith triangle-eq]: #1186
+#1188 := [unit-resolution #1187 #74]: #599
+#1105 := (<= #831 0::Int)
+#1181 := (or #1180 #1105)
+#1182 := [th-lemma arith triangle-eq]: #1181
+#1183 := [unit-resolution #1182 #1169]: #1105
+#569 := (<= #708 0::Int)
+#1050 := (or #605 #569)
+#1051 := [th-lemma arith triangle-eq]: #1050
+#1166 := [unit-resolution #1051 #1165]: #569
+#1238 := [th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #1237 #1184 #1236 #1166 #1235 #1183 #1232 #1188 #1209 #1229 #998 #982 #995 #970]: false
+#1241 := [lemma #1238]: #1240
+#1250 := [unit-resolution #1241 #1237 #1184]: #577
+#1251 := (or #1059 #955)
+#1252 := [th-lemma arith triangle-eq]: #1251
+#1253 := [unit-resolution #1252 #1250]: #955
+#1104 := (>= #22 1::Int)
+#1152 := (not #1104)
+#1254 := (or #1059 #954)
+#1255 := [th-lemma arith triangle-eq]: #1254
+#1256 := [unit-resolution #1255 #1250]: #954
+#1140 := (>= #574 2::Int)
+#1141 := (not #1140)
+#1257 := (or false #1141)
+#1258 := [th-lemma arith]: #1257
+#1259 := [unit-resolution #1258 #72]: #1141
+#1260 := (not #954)
+#1261 := (or #1103 #1140 #1260)
+#1262 := [th-lemma arith assign-bounds 1 1]: #1261
+#1263 := [unit-resolution #1262 #1259 #1256]: #1103
+#1266 := (not #1103)
+#1269 := (or #1266 #1152)
+#23 := (= #22 1::Int)
+#219 := (not #23)
+#19 := (f3 f4 2::Int)
+#21 := (= #19 1::Int)
+#1097 := (or #635 #21)
+#918 := (div f4 2::Int)
+#1036 := (* -1::Int #918)
+#1037 := (+ #1035 #1036)
+#1038 := (+ #698 #1037)
+#483 := (mod f4 2::Int)
+#484 := (* -1::Int #483)
+#1039 := (+ #484 #1038)
+#1040 := (+ #16 #1039)
+#1041 := (+ f4 #1040)
+#1042 := (>= #1041 2::Int)
+#1030 := (not #1042)
+#1045 := [hypothesis]: #659
+#1049 := [unit-resolution #614 #1045 #1033]: #709
+#1052 := [unit-resolution #1051 #1049]: #569
+#988 := (not #569)
+#1031 := (or #1030 #988)
+#940 := (>= #483 0::Int)
+#1023 := (or false #940)
+#1024 := [th-lemma arith]: #1023
+#1021 := [unit-resolution #1024 #72]: #940
+#983 := [hypothesis]: #569
+#931 := (* -2::Int #918)
+#932 := (+ #484 #931)
+#933 := (+ f4 #932)
+#938 := (<= #933 0::Int)
+#930 := (= #933 0::Int)
+#1011 := (or false #930)
+#1010 := [th-lemma arith]: #1011
+#1009 := [unit-resolution #1010 #72]: #930
+#958 := (not #930)
+#959 := (or #958 #938)
+#965 := [th-lemma arith triangle-eq]: #959
+#963 := [unit-resolution #965 #1009]: #938
+#1022 := [hypothesis]: #1042
+#1029 := [th-lemma arith farkas -1 2 -1 -1 -1 1 #970 #1022 #982 #963 #983 #1021]: false
+#1032 := [lemma #1029]: #1031
+#1053 := [unit-resolution #1032 #1052]: #1030
+#1056 := [unit-resolution #1055 #1049]: #600
+#939 := (>= #933 0::Int)
+#1064 := (or #958 #939)
+#1065 := [th-lemma arith triangle-eq]: #1064
+#1068 := [unit-resolution #1065 #1009]: #939
+#485 := (+ #19 #484)
+#385 := (>= #485 0::Int)
+#477 := (= #485 0::Int)
+#500 := (mod #482 -2::Int)
+#504 := (+ #19 #500)
+#491 := (= #504 0::Int)
+#478 := (ite #659 #477 #491)
+#464 := (= #19 0::Int)
+#420 := (ite #689 #464 #478)
+#411 := (or #584 #420)
+#493 := (mod #482 #370)
+#492 := (+ #19 #493)
+#494 := (= #492 0::Int)
+#469 := (or #440 #710)
+#470 := (not #469)
+#471 := (or #701 #440)
+#463 := (not #471)
+#472 := (or #463 #470)
+#473 := (ite #472 #477 #494)
+#474 := (ite #689 #464 #473)
+#441 := (= f4 #19)
+#443 := (ite #781 #441 #474)
+#386 := (or #584 #443)
+#391 := (iff #386 #411)
+#398 := (iff #411 #411)
+#399 := [rewrite]: #398
+#410 := (iff #443 #420)
+#413 := (ite false #441 #420)
+#406 := (iff #413 #420)
+#407 := [rewrite]: #406
+#416 := (iff #443 #413)
+#414 := (iff #474 #420)
+#488 := (iff #473 #478)
+#486 := (iff #494 #491)
+#489 := (= #492 #504)
+#503 := (= #493 #500)
+#496 := [monotonicity #754]: #503
+#490 := [monotonicity #496]: #489
+#487 := [monotonicity #490]: #486
+#501 := (iff #472 #659)
+#438 := (iff #470 #669)
+#453 := (iff #469 #710)
+#452 := (iff #469 #673)
+#442 := [monotonicity #421]: #452
+#436 := [trans #442 #677]: #453
#439 := [monotonicity #436]: #438
-#410 := (iff #331 #60)
-#411 := [rewrite]: #410
-#442 := [monotonicity #411 #439]: #441
-#445 := [monotonicity #442]: #444
-#450 := [trans #445 #448]: #449
-#408 := (iff #326 #406)
-#402 := (= 1::Int #399)
-#405 := (iff #402 #406)
-#407 := [rewrite]: #405
-#403 := (iff #326 #402)
-#400 := (= #313 #399)
-#397 := (= #310 #396)
-#394 := (iff #296 #269)
-#392 := (iff #293 #259)
-#390 := (iff #293 #262)
-#391 := [monotonicity #155 #261]: #390
-#393 := [trans #391 #266]: #392
-#388 := (iff #290 #246)
-#383 := (and true #246)
-#386 := (iff #383 #246)
-#387 := [rewrite]: #386
-#384 := (iff #290 #383)
-#385 := [monotonicity #155 #248]: #384
-#389 := [trans #385 #387]: #388
-#395 := [monotonicity #389 #393]: #394
-#398 := [monotonicity #395]: #397
-#401 := [monotonicity #244 #398]: #400
-#404 := [monotonicity #401]: #403
-#409 := [trans #404 #407]: #408
-#453 := [monotonicity #409 #450]: #452
-#456 := [monotonicity #453]: #455
-#381 := (iff #75 #380)
-#378 := (iff #74 #377)
-#375 := (iff #73 #372)
-#369 := (= #359 1::Int)
-#373 := (iff #369 #372)
-#374 := [rewrite]: #373
-#370 := (iff #73 #369)
-#367 := (= #72 #359)
-#362 := (ite false f4 #359)
-#365 := (= #362 #359)
-#366 := [rewrite]: #365
-#363 := (= #72 #362)
-#360 := (= #71 #359)
-#357 := (= #70 #356)
-#354 := (= #69 #351)
-#348 := (- #345)
-#352 := (= #348 #351)
-#353 := [rewrite]: #352
-#349 := (= #69 #348)
-#346 := (= #68 #345)
-#343 := (= #67 #109)
-#344 := [rewrite]: #343
-#347 := [monotonicity #344 #115]: #346
-#350 := [monotonicity #347]: #349
-#355 := [trans #350 #353]: #354
-#341 := (iff #65 #340)
-#338 := (iff #64 #337)
-#339 := [rewrite]: #338
-#335 := (iff #62 #334)
-#336 := [rewrite]: #335
-#342 := [monotonicity #336 #339]: #341
-#358 := [monotonicity #342 #355]: #357
-#332 := (iff #60 #331)
-#333 := [rewrite]: #332
-#361 := [monotonicity #333 #358]: #360
-#364 := [monotonicity #97 #361]: #363
-#368 := [trans #364 #366]: #367
-#371 := [monotonicity #368]: #370
-#376 := [trans #371 #374]: #375
-#329 := (iff #59 #326)
-#323 := (= #313 1::Int)
-#327 := (iff #323 #326)
-#328 := [rewrite]: #327
-#324 := (iff #59 #323)
-#321 := (= #57 #313)
-#316 := (ite false f3 #313)
-#319 := (= #316 #313)
-#320 := [rewrite]: #319
-#317 := (= #57 #316)
-#314 := (= #56 #313)
-#311 := (= #55 #310)
-#308 := (= #54 #305)
-#302 := (- #299)
-#306 := (= #302 #305)
-#307 := [rewrite]: #306
-#303 := (= #54 #302)
-#300 := (= #53 #299)
-#301 := [monotonicity #207 #115]: #300
-#304 := [monotonicity #301]: #303
-#309 := [trans #304 #307]: #308
-#297 := (iff #51 #296)
-#294 := (iff #50 #293)
-#295 := [rewrite]: #294
-#291 := (iff #49 #290)
-#292 := [rewrite]: #291
-#298 := [monotonicity #292 #295]: #297
-#312 := [monotonicity #298 #309]: #311
-#315 := [monotonicity #199 #312]: #314
-#318 := [monotonicity #97 #315]: #317
-#322 := [trans #318 #320]: #321
-#325 := [monotonicity #322]: #324
-#330 := [trans #325 #328]: #329
-#379 := [monotonicity #330 #376]: #378
-#382 := [monotonicity #379]: #381
-#458 := [trans #382 #456]: #457
-#289 := [asserted]: #75
-#459 := [mp #289 #458]: #454
-#474 := [mp #459 #473]: #461
-#945 := [unit-resolution #474 #944]: #468
-#960 := [mp #945 #959]: #957
-#963 := (or #904 #837)
-#833 := (<= #66 1::Int)
-#858 := (not #833)
-#859 := [hypothesis]: #858
-#821 := (>= #66 2::Int)
-#822 := (not #821)
-#860 := (or false #822)
-#861 := [th-lemma arith]: #860
-#862 := [unit-resolution #861 #93]: #822
-#863 := [th-lemma arith farkas 1 1 #862 #859]: false
-#864 := [lemma #863]: #833
-#961 := (or #904 #858 #837)
-#962 := [th-lemma arith triangle-eq]: #961
-#964 := [unit-resolution #962 #864]: #963
-#965 := [unit-resolution #964 #960]: #837
-#909 := (or #151 #834)
-#906 := [hypothesis]: #150
-#838 := [hypothesis]: #837
-#931 := (or #163 #834)
-#705 := (div f4 2::Int)
-#806 := (* -2::Int #705)
-#805 := (* -1::Int #66)
-#807 := (+ #805 #806)
-#808 := (+ f4 #807)
-#897 := (<= #808 0::Int)
-#795 := (= #808 0::Int)
-#911 := (or false #795)
-#913 := [th-lemma arith]: #911
-#914 := [unit-resolution #913 #93]: #795
-#915 := (not #795)
-#916 := (or #915 #897)
-#917 := [th-lemma arith triangle-eq]: #916
-#918 := [unit-resolution #917 #914]: #897
-#898 := (>= #808 0::Int)
-#919 := (or #915 #898)
-#920 := [th-lemma arith triangle-eq]: #919
-#921 := [unit-resolution #920 #914]: #898
-#815 := (>= #66 0::Int)
-#839 := (or false #815)
-#840 := [th-lemma arith]: #839
-#841 := [unit-resolution #840 #93]: #815
-#922 := [hypothesis]: #164
-#751 := (or #489 #163)
-#752 := [th-lemma arith triangle-eq]: #751
-#923 := [unit-resolution #752 #922]: #489
-#492 := (or #14 #475)
-#493 := [def-axiom]: #492
-#924 := [unit-resolution #493 #923]: #475
-#476 := (= #21 #177)
-#480 := (or #174 #163)
-#481 := [def-axiom]: #480
-#925 := [unit-resolution #481 #922]: #174
-#482 := (not #174)
-#485 := (or #482 #476)
-#486 := [def-axiom]: #485
-#926 := [unit-resolution #486 #925]: #476
-#927 := [trans #926 #924]: #757
-#928 := [trans #927 #193]: #709
-#760 := (not #709)
-#761 := (or #760 #710)
-#762 := [th-lemma arith triangle-eq]: #761
-#929 := [unit-resolution #762 #928]: #710
-#641 := (>= #21 0::Int)
-#764 := (or false #641)
-#765 := [th-lemma arith]: #764
-#766 := [unit-resolution #765 #93]: #641
-#930 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #766 #929 #744 #741 #889 #733 #730 #727 #841 #838 #921 #918]: false
-#932 := [lemma #930]: #931
-#907 := [unit-resolution #932 #838]: #163
-#908 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 1/2 1/2 1/2 1/2 #841 #838 #921 #918 #907 #906 #889 #733 #730 #727]: false
-#910 := [lemma #908]: #909
-#966 := [unit-resolution #910 #965]: #151
-#967 := (or #489 #150)
-#968 := [th-lemma arith triangle-eq]: #967
-#969 := [unit-resolution #968 #966]: #489
-#970 := [unit-resolution #493 #969]: #475
-#478 := (or #174 #150)
-#479 := [def-axiom]: #478
-#971 := [unit-resolution #479 #966]: #174
-#972 := [unit-resolution #486 #971]: #476
-#973 := [trans #972 #970]: #757
-#974 := [trans #973 #193]: #709
-#975 := [unit-resolution #762 #974]: #710
-#976 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 #841 #965 #921 #918 #889 #733 #730 #727 #766 #975 #744 #741]: false
-#977 := [lemma #976]: #534
-#532 := (or #434 #423)
-#533 := [def-axiom]: #532
-#836 := [unit-resolution #533 #977]: #423
-#845 := (or #434 #258)
-#769 := (not #613)
-#770 := (or #434 #769 #258)
-#734 := [hypothesis]: #613
-#745 := [hypothesis]: #259
-#746 := [hypothesis]: #534
-#530 := (or #434 #412)
-#531 := [def-axiom]: #530
-#747 := [unit-resolution #531 #746]: #412
-#748 := (or #164 #258 #413)
-#749 := [th-lemma arith assign-bounds -1 -1]: #748
-#750 := [unit-resolution #749 #747 #745]: #164
-#753 := [unit-resolution #752 #750]: #489
-#754 := [unit-resolution #493 #753]: #475
-#755 := [unit-resolution #481 #750]: #174
-#756 := [unit-resolution #486 #755]: #476
-#758 := [trans #756 #754]: #757
-#759 := [trans #758 #193]: #709
-#763 := [unit-resolution #762 #759]: #710
-#767 := [unit-resolution #533 #746]: #423
-#768 := [th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #767 #747 #766 #763 #744 #741 #734 #733 #730 #727]: false
-#771 := [lemma #768]: #770
-#846 := [unit-resolution #771 #889]: #845
-#847 := [unit-resolution #846 #977]: #258
-#503 := (or #502 #246 #259)
-#504 := [def-axiom]: #503
-#844 := [unit-resolution #504 #866]: #269
-#848 := [unit-resolution #844 #847]: #246
-#849 := (or #151 #424 #245)
-#850 := [th-lemma arith assign-bounds -1 -1]: #849
-#851 := [unit-resolution #850 #848 #836]: #151
-#842 := [unit-resolution #968 #851]: #489
-#843 := [unit-resolution #493 #842]: #475
-#852 := [unit-resolution #479 #851]: #174
-#853 := [unit-resolution #486 #852]: #476
-#854 := [trans #853 #843]: #757
-#855 := [trans #854 #193]: #709
-#856 := [unit-resolution #762 #855]: #710
-#857 := [unit-resolution #531 #977]: #412
-[th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #836 #857 #766 #856 #744 #741 #889 #733 #730 #727]: false
+#450 := (iff #463 #670)
+#448 := (iff #471 #701)
+#444 := (iff #471 #684)
+#435 := [monotonicity #421]: #444
+#449 := [trans #435 #687]: #448
+#451 := [monotonicity #449]: #450
+#502 := [monotonicity #451 #439]: #501
+#418 := [monotonicity #502 #487]: #488
+#415 := [monotonicity #418]: #414
+#404 := [monotonicity #772 #415]: #416
+#405 := [trans #404 #407]: #410
+#396 := [monotonicity #405]: #391
+#401 := [trans #396 #399]: #391
+#390 := [quant-inst #8 #11]: #386
+#397 := [mp #390 #401]: #411
+#1069 := [unit-resolution #397 #796]: #420
+#379 := (not #420)
+#1072 := (or #379 #478)
+#373 := (or #379 #689 #478)
+#374 := [def-axiom]: #373
+#1073 := [unit-resolution #374 #1043]: #1072
+#1074 := [unit-resolution #1073 #1069]: #478
+#392 := (not #478)
+#393 := (or #392 #635 #477)
+#394 := [def-axiom]: #393
+#1075 := [unit-resolution #394 #1045 #1074]: #477
+#380 := (not #477)
+#1076 := (or #380 #385)
+#1077 := [th-lemma arith triangle-eq]: #1076
+#1078 := [unit-resolution #1077 #1075]: #385
+#801 := (>= #19 1::Int)
+#1015 := (not #801)
+#800 := (<= #19 1::Int)
+#946 := (>= #483 2::Int)
+#947 := (not #946)
+#1079 := (or false #947)
+#1080 := [th-lemma arith]: #1079
+#1081 := [unit-resolution #1080 #72]: #947
+#402 := (<= #485 0::Int)
+#1082 := (or #380 #402)
+#1083 := [th-lemma arith triangle-eq]: #1082
+#1084 := [unit-resolution #1083 #1075]: #402
+#1085 := (not #402)
+#1086 := (or #800 #946 #1085)
+#1087 := [th-lemma arith assign-bounds 1 1]: #1086
+#1088 := [unit-resolution #1087 #1084 #1081]: #800
+#1090 := (not #800)
+#1093 := (or #1090 #1015)
+#218 := (not #21)
+#1089 := [hypothesis]: #218
+#1091 := (or #21 #1090 #1015)
+#1092 := [th-lemma arith triangle-eq]: #1091
+#1094 := [unit-resolution #1092 #1089]: #1093
+#1095 := [unit-resolution #1094 #1088]: #1015
+#1096 := [th-lemma arith farkas -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1 #995 #998 #1095 #1078 #1068 #1056 #1053]: false
+#1098 := [lemma #1096]: #1097
+#1264 := [unit-resolution #1098 #914]: #21
+#230 := (or #218 #219)
+#24 := (and #21 #23)
+#25 := (not #24)
+#239 := (iff #25 #230)
+#231 := (not #230)
+#234 := (not #231)
+#237 := (iff #234 #230)
+#238 := [rewrite]: #237
+#235 := (iff #25 #234)
+#232 := (iff #24 #231)
+#233 := [rewrite]: #232
+#236 := [monotonicity #233]: #235
+#240 := [trans #236 #238]: #239
+#76 := [asserted]: #25
+#241 := [mp #76 #240]: #230
+#1265 := [unit-resolution #241 #1264]: #219
+#1267 := (or #23 #1266 #1152)
+#1268 := [th-lemma arith triangle-eq]: #1267
+#1270 := [unit-resolution #1268 #1265]: #1269
+#1271 := [unit-resolution #1270 #1263]: #1152
+#1192 := (not #955)
+#1194 := (or #1191 #1192 #1193 #1104)
+#1153 := [hypothesis]: #1152
+#1132 := (<= #1127 0::Int)
+#1160 := [unit-resolution #1159 #72]: #1124
+#1162 := (or #1161 #1132)
+#1163 := [th-lemma arith triangle-eq]: #1162
+#1164 := [unit-resolution #1163 #1160]: #1132
+#1185 := [hypothesis]: #1179
+#1189 := [hypothesis]: #955
+#1190 := [th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1 #1189 #1188 #1185 #1184 #1183 #1166 #1164 #982 #970 #1153]: false
+#1195 := [lemma #1190]: #1194
+#1272 := [unit-resolution #1195 #1271 #1184 #1253]: #1191
+#1273 := [th-lemma arith farkas -2 1 1 1 1 1 1 1 1 #1272 #1237 #1236 #1235 #1232 #998 #995 #1249 #1151]: false
+#1275 := [lemma #1273]: #1274
+#1349 := [unit-resolution #1275 #1278]: #1348
+#1350 := [unit-resolution #1349 #1323 #1110]: false
+#1351 := [lemma #1350]: #715
+#1281 := (or #778 #457)
+#1225 := [hypothesis]: #715
+#752 := (+ #482 #376)
+#751 := (mod #752 -2::Int)
+#466 := (+ #12 #751)
+#746 := (= #466 0::Int)
+#770 := (not #461)
+#434 := (<= #10 0::Int)
+#764 := (not #434)
+#479 := (or #764 #770)
+#744 := (ite #479 #457 #746)
+#618 := (not #778)
+#802 := [hypothesis]: #618
+#1243 := (or #778 #744)
+#749 := (ite #778 #14 #744)
+#585 := (or #584 #749)
+#454 := (* -1::Int #10)
+#455 := (mod #454 #370)
+#456 := (+ #12 #455)
+#447 := (= #456 0::Int)
+#775 := (or #440 #461)
+#777 := (not #775)
+#564 := (or #434 #440)
+#771 := (not #564)
+#445 := (or #771 #777)
+#446 := (ite #445 #457 #447)
+#779 := (ite #778 #14 #446)
+#780 := (= #10 #12)
+#776 := (ite #781 #780 #779)
+#586 := (or #584 #776)
+#729 := (iff #586 #585)
+#731 := (iff #585 #585)
+#725 := [rewrite]: #731
+#737 := (iff #776 #749)
+#432 := (* -1::Int #12)
+#437 := (+ f5 #432)
+#773 := (+ f4 #437)
+#433 := (= #773 0::Int)
+#740 := (ite false #433 #749)
+#741 := (iff #740 #749)
+#742 := [rewrite]: #741
+#735 := (iff #776 #740)
+#738 := (iff #779 #749)
+#748 := (iff #446 #744)
+#747 := (iff #447 #746)
+#467 := (= #456 #466)
+#755 := (= #455 #751)
+#753 := (= #454 #752)
+#475 := [rewrite]: #753
+#465 := [monotonicity #475 #754]: #755
+#468 := [monotonicity #465]: #467
+#462 := [monotonicity #468]: #747
+#480 := (iff #445 #479)
+#756 := (iff #777 #770)
+#769 := (iff #775 #461)
+#403 := (or false #461)
+#408 := (iff #403 #461)
+#409 := [rewrite]: #408
+#766 := (iff #775 #403)
+#768 := [monotonicity #421]: #766
+#767 := [trans #768 #409]: #769
+#757 := [monotonicity #767]: #756
+#759 := (iff #771 #764)
+#762 := (iff #564 #434)
+#422 := (or #434 false)
+#760 := (iff #422 #434)
+#761 := [rewrite]: #760
+#423 := (iff #564 #422)
+#424 := [monotonicity #421]: #423
+#763 := [trans #424 #761]: #762
+#765 := [monotonicity #763]: #759
+#481 := [monotonicity #765 #757]: #480
+#745 := [monotonicity #481 #462]: #748
+#739 := [monotonicity #745]: #738
+#774 := (iff #780 #433)
+#417 := [rewrite]: #774
+#736 := [monotonicity #772 #417 #739]: #735
+#743 := [trans #736 #742]: #737
+#730 := [monotonicity #743]: #729
+#726 := [trans #730 #725]: #729
+#728 := [quant-inst #10 #11]: #586
+#732 := [mp #728 #726]: #585
+#1242 := [unit-resolution #732 #796]: #749
+#616 := (not #749)
+#620 := (or #616 #778 #744)
+#621 := [def-axiom]: #620
+#1244 := [unit-resolution #621 #1242]: #1243
+#1245 := [unit-resolution #1244 #802]: #744
+#809 := (or #479 #778)
+#565 := (not #479)
+#803 := [hypothesis]: #565
+#733 := (or #479 #434)
+#727 := [def-axiom]: #733
+#804 := [unit-resolution #727 #803]: #434
+#734 := (or #479 #461)
+#563 := [def-axiom]: #734
+#805 := [unit-resolution #563 #803]: #461
+#806 := (or #778 #764 #770)
+#807 := [th-lemma arith triangle-eq]: #806
+#808 := [unit-resolution #807 #805 #804 #802]: false
+#810 := [lemma #808]: #809
+#1279 := [unit-resolution #810 #802]: #479
+#724 := (not #744)
+#606 := (or #724 #565 #457)
+#607 := [def-axiom]: #606
+#1280 := [unit-resolution #607 #1279 #1245 #1225]: false
+#1282 := [lemma #1280]: #1281
+#1352 := [unit-resolution #1282 #1351]: #778
+#1353 := (or #618 #461)
+#1354 := [th-lemma arith triangle-eq]: #1353
+#1355 := [unit-resolution #1354 #1352]: #461
+#1356 := (or #618 #434)
+#1357 := [th-lemma arith triangle-eq]: #1356
+#1358 := [unit-resolution #1357 #1352]: #434
+#1346 := (or #577 #770 #764)
+#1295 := [hypothesis]: #434
+#1327 := (or #526 #764 #701)
+#1005 := [hypothesis]: #670
+#1289 := [hypothesis]: #578
+#1291 := [th-lemma arith farkas -1 1 1 #1295 #1289 #1005]: false
+#1328 := [lemma #1291]: #1327
+#1342 := [unit-resolution #1328 #1209 #1295]: #701
+#1343 := [unit-resolution #864 #1043]: #659
+#1344 := [unit-resolution #1343 #1342]: #669
+#1290 := [hypothesis]: #461
+#1345 := [th-lemma arith farkas -1 1 1 #1290 #1344 #1229]: false
+#1347 := [lemma #1345]: #1346
+#1359 := [unit-resolution #1347 #1358 #1355]: #577
+#1360 := [unit-resolution #1255 #1359]: #954
+#1361 := (or #1103 #1260)
+#1302 := [hypothesis]: #1140
+#1308 := [unit-resolution #1258 #72 #1302]: false
+#1321 := [lemma #1308]: #1141
+#1362 := [unit-resolution #1262 #1321]: #1361
+#1363 := [unit-resolution #1362 #1360]: #1103
+#1303 := (+ #698 #1171)
+#1326 := (+ #575 #1303)
+#1335 := (+ #16 #1326)
+#1336 := (+ f5 #1335)
+#1337 := (+ f4 #1336)
+#1338 := (>= #1337 2::Int)
+#1329 := (not #1338)
+#1330 := (or #1329 #764)
+#1294 := [unit-resolution #1163 #1278]: #1132
+#1310 := [hypothesis]: #1338
+#1309 := [th-lemma arith farkas 2 -1 -1 -1 -1 -1 1 #1310 #1295 #1166 #982 #970 #1294 #1151]: false
+#1331 := [lemma #1309]: #1330
+#1364 := [unit-resolution #1331 #1358]: #1329
+#1365 := [unit-resolution #1252 #1359]: #955
+#1340 := (or #1192 #1338 #770 #1104)
+#1332 := [unit-resolution #1248 #1278]: #1224
+#1325 := [th-lemma arith #1290 #1153 #1189 #1236 #998 #995 #1332]: #1338
+#1324 := [hypothesis]: #1329
+#1339 := [unit-resolution #1324 #1325]: false
+#1341 := [lemma #1339]: #1340
+#1366 := [unit-resolution #1341 #1365 #1355 #1364]: #1104
+[unit-resolution #1270 #1366 #1363]: false
unsat
c04d38458726eb1b2cafd52bd3881d6f8160666f 24 0
#2 := false
@@ -10061,318 +10487,288 @@
unsat
ERROR: line 11 column 83: invalid pattern.
-8aba3814871680009d1d0267516334493c303e78 175 0
-#2 := false
-#8 := 0::Int
-decl f4 :: Int
-#18 := f4
-#138 := (<= f4 0::Int)
-#139 := (not #138)
+8f616b17d0807409dc26bfdf9593c5fcd06fb7e7 1 0
+unsat
+3eb9cf11ee8774c9212c37c265e7552f3b8f24a9 75 0
+#2 := false
+#10 := 1::Int
decl f5 :: Int
-#20 := f5
-#134 := (<= f5 0::Int)
-#135 := (not #134)
-decl f3 :: (-> Int Int Int)
-#21 := (f3 f4 f5)
-#123 := (<= #21 0::Int)
-#155 := (or #123 #135 #138)
-#160 := (not #155)
-#23 := (< 0::Int f5)
-#22 := (< 0::Int #21)
-#24 := (implies #22 #23)
-#19 := (< 0::Int f4)
-#25 := (implies #19 #24)
-#26 := (not #25)
-#163 := (iff #26 #160)
-#107 := (not #22)
-#108 := (or #107 #23)
-#114 := (not #19)
-#115 := (or #114 #108)
-#120 := (not #115)
-#161 := (iff #120 #160)
-#158 := (iff #115 #155)
-#149 := (or #123 #135)
-#152 := (or #138 #149)
-#156 := (iff #152 #155)
-#157 := [rewrite]: #156
-#153 := (iff #115 #152)
-#150 := (iff #108 #149)
-#136 := (iff #23 #135)
-#137 := [rewrite]: #136
-#132 := (iff #107 #123)
-#124 := (not #123)
-#127 := (not #124)
-#130 := (iff #127 #123)
-#131 := [rewrite]: #130
-#128 := (iff #107 #127)
-#125 := (iff #22 #124)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#151 := [monotonicity #133 #137]: #150
-#147 := (iff #114 #138)
-#142 := (not #139)
-#145 := (iff #142 #138)
-#146 := [rewrite]: #145
-#143 := (iff #114 #142)
-#140 := (iff #19 #139)
-#141 := [rewrite]: #140
-#144 := [monotonicity #141]: #143
-#148 := [trans #144 #146]: #147
-#154 := [monotonicity #148 #151]: #153
-#159 := [trans #154 #157]: #158
-#162 := [monotonicity #159]: #161
-#121 := (iff #26 #120)
-#118 := (iff #25 #115)
-#111 := (implies #19 #108)
-#116 := (iff #111 #115)
-#117 := [rewrite]: #116
-#112 := (iff #25 #111)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#113 := [monotonicity #110]: #112
-#119 := [trans #113 #117]: #118
-#122 := [monotonicity #119]: #121
-#164 := [trans #122 #162]: #163
-#106 := [asserted]: #26
-#165 := [mp #106 #164]: #160
-#168 := [not-or-elim #165]: #139
-#167 := [not-or-elim #165]: #134
-#166 := [not-or-elim #165]: #124
-#10 := (:var 0 Int)
-#9 := (:var 1 Int)
-#11 := (f3 #9 #10)
-#647 := (pattern #11)
-#78 := (<= #11 0::Int)
-#74 := (<= #10 0::Int)
-#75 := (not #74)
-#63 := (<= #9 0::Int)
-#95 := (or #63 #75 #78)
-#648 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #647) #95)
-#100 := (forall (vars (?v0 Int) (?v1 Int)) #95)
-#651 := (iff #100 #648)
-#649 := (iff #95 #95)
-#650 := [refl]: #649
-#652 := [quant-intro #650]: #651
-#182 := (~ #100 #100)
-#180 := (~ #95 #95)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#14 := (< 0::Int #10)
-#13 := (< 0::Int #9)
-#15 := (implies #13 #14)
-#12 := (< 0::Int #11)
-#16 := (implies #12 #15)
-#17 := (forall (vars (?v0 Int) (?v1 Int)) #16)
-#103 := (iff #17 #100)
-#47 := (not #13)
-#48 := (or #47 #14)
-#54 := (not #12)
-#55 := (or #54 #48)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #55)
-#101 := (iff #60 #100)
-#98 := (iff #55 #95)
-#89 := (or #63 #75)
-#92 := (or #78 #89)
-#96 := (iff #92 #95)
-#97 := [rewrite]: #96
-#93 := (iff #55 #92)
-#90 := (iff #48 #89)
-#76 := (iff #14 #75)
-#77 := [rewrite]: #76
-#72 := (iff #47 #63)
-#64 := (not #63)
-#67 := (not #64)
-#70 := (iff #67 #63)
+#12 := f5
+#16 := (+ f5 1::Int)
+decl f3 :: Int
+#8 := f3
+#17 := (* f3 #16)
+decl f4 :: Int
+#9 := f4
+#15 := (* f3 f4)
+#18 := (+ #15 #17)
+#11 := (+ f4 1::Int)
+#13 := (+ #11 f5)
+#14 := (* f3 #13)
+#19 := (= #14 #18)
+#20 := (not #19)
+#93 := (iff #20 false)
+#1 := true
+#88 := (not true)
+#91 := (iff #88 false)
+#92 := [rewrite]: #91
+#89 := (iff #20 #88)
+#86 := (iff #19 true)
+#56 := (* f3 f5)
+#57 := (+ #15 #56)
+#58 := (+ f3 #57)
+#81 := (= #58 #58)
+#84 := (iff #81 true)
+#85 := [rewrite]: #84
+#82 := (iff #19 #81)
+#79 := (= #18 #58)
+#69 := (+ f3 #56)
+#74 := (+ #15 #69)
+#77 := (= #74 #58)
+#78 := [rewrite]: #77
+#75 := (= #18 #74)
+#72 := (= #17 #69)
+#63 := (+ 1::Int f5)
+#66 := (* f3 #63)
+#70 := (= #66 #69)
#71 := [rewrite]: #70
-#68 := (iff #47 #67)
-#65 := (iff #13 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#91 := [monotonicity #73 #77]: #90
-#87 := (iff #54 #78)
-#79 := (not #78)
-#82 := (not #79)
-#85 := (iff #82 #78)
-#86 := [rewrite]: #85
-#83 := (iff #54 #82)
-#80 := (iff #12 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#94 := [monotonicity #88 #91]: #93
-#99 := [trans #94 #97]: #98
-#102 := [quant-intro #99]: #101
-#61 := (iff #17 #60)
-#58 := (iff #16 #55)
-#51 := (implies #12 #48)
-#56 := (iff #51 #55)
-#57 := [rewrite]: #56
-#52 := (iff #16 #51)
-#49 := (iff #15 #48)
+#67 := (= #17 #66)
+#64 := (= #16 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#73 := [trans #68 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#61 := (= #14 #58)
+#47 := (+ f4 f5)
+#48 := (+ 1::Int #47)
+#53 := (* f3 #48)
+#59 := (= #53 #58)
+#60 := [rewrite]: #59
+#54 := (= #14 #53)
+#51 := (= #13 #48)
+#41 := (+ 1::Int f4)
+#44 := (+ #41 f5)
+#49 := (= #44 #48)
#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#59 := [trans #53 #57]: #58
-#62 := [quant-intro #59]: #61
-#104 := [trans #62 #102]: #103
-#46 := [asserted]: #17
-#105 := [mp #46 #104]: #100
-#170 := [mp~ #105 #183]: #100
-#653 := [mp #170 #652]: #648
-#319 := (not #648)
-#310 := (or #319 #123 #135 #138)
-#232 := (or #138 #135 #123)
-#321 := (or #319 #232)
-#639 := (iff #321 #310)
-#250 := (or #319 #155)
-#324 := (iff #250 #310)
-#303 := [rewrite]: #324
-#323 := (iff #321 #250)
-#317 := (iff #232 #155)
-#318 := [rewrite]: #317
-#320 := [monotonicity #318]: #323
-#641 := [trans #320 #303]: #639
-#322 := [quant-inst #18 #20]: #321
-#297 := [mp #322 #641]: #310
-[unit-resolution #297 #653 #166 #167 #168]: false
-unsat
-0db52837dc3c07a6a4d5ca34a945edf7aeac1fdf 136 0
-#2 := false
-#58 := 0::Int
-decl f3 :: (-> Int Int Int)
+#45 := (= #13 #44)
+#42 := (= #11 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [monotonicity #52]: #54
+#62 := [trans #55 #60]: #61
+#83 := [monotonicity #62 #80]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #87]: #89
+#94 := [trans #90 #92]: #93
+#40 := [asserted]: #20
+[mp #40 #94]: false
+unsat
+741a564e40e4b6610d1d47bdab19a223e004482a 62 0
+#2 := false
+decl f4 :: Real
+#10 := f4
+decl f3 :: Real
+#8 := f3
+#16 := 2::Real
+#17 := (* 2::Real f3)
+#18 := (* #17 f4)
+#9 := 1::Real
+#13 := (- 1::Real f4)
+#14 := (* f3 #13)
+#11 := (+ 1::Real f4)
+#12 := (* f3 #11)
+#15 := (- #12 #14)
+#19 := (= #15 #18)
+#20 := (not #19)
+#81 := (iff #20 false)
+#1 := true
+#76 := (not true)
+#79 := (iff #76 false)
+#80 := [rewrite]: #79
+#77 := (iff #20 #76)
+#74 := (iff #19 true)
+#41 := (* f3 f4)
+#63 := (* 2::Real #41)
+#69 := (= #63 #63)
+#72 := (iff #69 true)
+#73 := [rewrite]: #72
+#70 := (iff #19 #69)
+#67 := (= #18 #63)
+#68 := [rewrite]: #67
+#65 := (= #15 #63)
+#45 := -1::Real
+#53 := (* -1::Real #41)
+#54 := (+ f3 #53)
+#42 := (+ f3 #41)
+#59 := (- #42 #54)
+#62 := (= #59 #63)
+#64 := [rewrite]: #62
+#60 := (= #15 #59)
+#57 := (= #14 #54)
+#46 := (* -1::Real f4)
+#47 := (+ 1::Real #46)
+#50 := (* f3 #47)
+#55 := (= #50 #54)
+#56 := [rewrite]: #55
+#51 := (= #14 #50)
+#48 := (= #13 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#58 := [trans #52 #56]: #57
+#43 := (= #12 #42)
+#44 := [rewrite]: #43
+#61 := [monotonicity #44 #58]: #60
+#66 := [trans #61 #64]: #65
+#71 := [monotonicity #66 #68]: #70
+#75 := [trans #71 #73]: #74
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#40 := [asserted]: #20
+[mp #40 #82]: false
+unsat
+06d1bd5308956fb019ef1c09bf97c6326d872fd6 141 0
+#2 := false
decl f6 :: Int
-#22 := f6
-#20 := 1::Int
-#80 := (+ 1::Int f6)
-decl f4 :: Int
-#18 := f4
-#83 := (f3 f4 #80)
+#13 := f6
+decl f7 :: Int
+#17 := f7
decl f5 :: Int
-#19 := f5
-#71 := (+ f5 f6)
-#72 := (+ 1::Int #71)
-#77 := (f3 f4 #72)
-#53 := -1::Int
-#99 := (* -1::Int #77)
-#100 := (+ #99 #83)
-#25 := (f3 f4 f5)
-#101 := (+ #25 #100)
-#97 := (= #101 0::Int)
-#98 := (not #97)
-#26 := (+ f6 1::Int)
-#27 := (f3 f4 #26)
-#28 := (+ #25 #27)
-#21 := (+ f5 1::Int)
-#23 := (+ #21 f6)
-#24 := (f3 f4 #23)
-#29 := (= #24 #28)
-#30 := (not #29)
-#104 := (iff #30 #98)
-#86 := (+ #25 #83)
-#89 := (= #77 #86)
-#92 := (not #89)
-#102 := (iff #92 #98)
-#96 := (iff #89 #97)
-#95 := [rewrite]: #96
-#103 := [monotonicity #95]: #102
-#93 := (iff #30 #92)
-#90 := (iff #29 #89)
-#87 := (= #28 #86)
-#84 := (= #27 #83)
-#81 := (= #26 #80)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#88 := [monotonicity #85]: #87
-#78 := (= #24 #77)
-#75 := (= #23 #72)
-#52 := (+ 1::Int f5)
-#68 := (+ #52 f6)
-#73 := (= #68 #72)
-#74 := [rewrite]: #73
-#69 := (= #23 #68)
-#66 := (= #21 #52)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#91 := [monotonicity #79 #88]: #90
-#94 := [monotonicity #91]: #93
-#105 := [trans #94 #103]: #104
-#51 := [asserted]: #30
-#106 := [mp #51 #105]: #98
-#10 := (:var 0 Int)
-#8 := (:var 2 Int)
-#14 := (f3 #8 #10)
-#9 := (:var 1 Int)
-#13 := (f3 #8 #9)
-#582 := (pattern #13 #14)
-#55 := (* -1::Int #14)
-#54 := (* -1::Int #13)
+#12 := f5
+#28 := (+ f5 f7)
+#29 := (+ #28 f6)
+decl f4 :: Int
+#10 := f4
+#9 := 1::Int
+#11 := (+ 1::Int f4)
+#30 := (* #11 #29)
+#25 := (* f7 f4)
+#23 := (* #11 f7)
+#14 := (+ f5 f6)
+#20 := 2::Int
+#21 := (* 2::Int #11)
+#22 := (* #21 #14)
+#24 := (+ #22 #23)
+#26 := (+ #24 #25)
+decl f3 :: Int
+#8 := f3
+#27 := (+ f3 #26)
+#31 := (- #27 #30)
+#18 := (* f4 f7)
+#15 := (* #11 #14)
+#16 := (+ f3 #15)
+#19 := (+ #16 #18)
+#32 := (= #19 #31)
+#33 := (not #32)
+#157 := (iff #33 false)
+#1 := true
+#152 := (not true)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #33 #152)
+#150 := (iff #32 true)
+#55 := (* f4 f6)
+#54 := (* f4 f5)
#56 := (+ #54 #55)
-#11 := (+ #9 #10)
-#12 := (f3 #8 #11)
-#57 := (+ #12 #56)
-#59 := (= #57 0::Int)
-#583 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) (:pat #582) #59)
-#62 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #59)
-#586 := (iff #62 #583)
-#584 := (iff #59 #59)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#116 := (~ #62 #62)
-#114 := (~ #59 #59)
-#115 := [refl]: #114
-#117 := [nnf-pos #115]: #116
-#15 := (+ #13 #14)
-#16 := (= #12 #15)
-#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #16)
-#63 := (iff #17 #62)
-#60 := (iff #16 #59)
-#61 := [rewrite]: #60
-#64 := [quant-intro #61]: #63
-#50 := [asserted]: #17
-#65 := [mp #50 #64]: #62
-#108 := [mp~ #65 #117]: #62
-#588 := [mp #108 #587]: #583
-#560 := (not #583)
-#415 := (or #560 #97)
-#530 := (* -1::Int #83)
-#255 := (* -1::Int #25)
-#524 := (+ #255 #530)
-#525 := (+ f5 #80)
-#531 := (f3 f4 #525)
-#532 := (+ #531 #524)
-#526 := (= #532 0::Int)
-#417 := (or #560 #526)
-#411 := (iff #417 #415)
-#420 := (iff #415 #415)
-#421 := [rewrite]: #420
-#515 := (iff #526 #97)
-#522 := (+ #77 #530)
-#520 := (+ #255 #522)
-#366 := (= #520 0::Int)
-#511 := (iff #366 #97)
-#512 := [rewrite]: #511
-#514 := (iff #526 #366)
-#406 := (= #532 #520)
-#518 := (+ #77 #524)
-#523 := (= #518 #520)
-#405 := [rewrite]: #523
-#519 := (= #532 #518)
-#364 := (= #531 #77)
-#533 := (= #525 #72)
-#362 := [rewrite]: #533
-#365 := [monotonicity #362]: #364
-#521 := [monotonicity #365]: #519
-#407 := [trans #521 #405]: #406
-#416 := [monotonicity #407]: #514
-#400 := [trans #416 #512]: #515
-#419 := [monotonicity #400]: #411
-#422 := [trans #419 #421]: #411
-#418 := [quant-inst #18 #19 #80]: #417
-#423 := [mp #418 #422]: #415
-[unit-resolution #423 #588 #106]: false
+#67 := (+ #18 #56)
+#68 := (+ f6 #67)
+#69 := (+ f5 #68)
+#70 := (+ f3 #69)
+#144 := (= #70 #70)
+#148 := (iff #144 true)
+#149 := [rewrite]: #148
+#143 := (iff #32 #144)
+#146 := (= #31 #70)
+#131 := (+ f7 #67)
+#132 := (+ f6 #131)
+#133 := (+ f5 #132)
+#85 := (* 2::Int #55)
+#83 := (* 2::Int #54)
+#86 := (+ #83 #85)
+#112 := (* 2::Int #18)
+#113 := (+ #112 #86)
+#114 := (+ f7 #113)
+#84 := (* 2::Int f6)
+#115 := (+ #84 #114)
+#82 := (* 2::Int f5)
+#116 := (+ #82 #115)
+#121 := (+ f3 #116)
+#138 := (- #121 #133)
+#141 := (= #138 #70)
+#147 := [rewrite]: #141
+#139 := (= #31 #138)
+#136 := (= #30 #133)
+#124 := (+ f6 f7)
+#125 := (+ f5 #124)
+#128 := (* #11 #125)
+#134 := (= #128 #133)
+#135 := [rewrite]: #134
+#129 := (= #30 #128)
+#126 := (= #29 #125)
+#127 := [rewrite]: #126
+#130 := [monotonicity #127]: #129
+#137 := [trans #130 #135]: #136
+#122 := (= #27 #121)
+#119 := (= #26 #116)
+#99 := (+ #18 #86)
+#100 := (+ f7 #99)
+#101 := (+ #84 #100)
+#102 := (+ #82 #101)
+#109 := (+ #102 #18)
+#117 := (= #109 #116)
+#118 := [rewrite]: #117
+#110 := (= #26 #109)
+#107 := (= #25 #18)
+#108 := [rewrite]: #107
+#105 := (= #24 #102)
+#93 := (+ f7 #18)
+#87 := (+ #84 #86)
+#88 := (+ #82 #87)
+#96 := (+ #88 #93)
+#103 := (= #96 #102)
+#104 := [rewrite]: #103
+#97 := (= #24 #96)
+#94 := (= #23 #93)
+#95 := [rewrite]: #94
+#91 := (= #22 #88)
+#75 := (* 2::Int f4)
+#76 := (+ 2::Int #75)
+#79 := (* #76 #14)
+#89 := (= #79 #88)
+#90 := [rewrite]: #89
+#80 := (= #22 #79)
+#77 := (= #21 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#92 := [trans #81 #90]: #91
+#98 := [monotonicity #92 #95]: #97
+#106 := [trans #98 #104]: #105
+#111 := [monotonicity #106 #108]: #110
+#120 := [trans #111 #118]: #119
+#123 := [monotonicity #120]: #122
+#140 := [monotonicity #123 #137]: #139
+#145 := [trans #140 #147]: #146
+#73 := (= #19 #70)
+#57 := (+ f6 #56)
+#58 := (+ f5 #57)
+#61 := (+ f3 #58)
+#64 := (+ #61 #18)
+#71 := (= #64 #70)
+#72 := [rewrite]: #71
+#65 := (= #19 #64)
+#62 := (= #16 #61)
+#59 := (= #15 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63]: #65
+#74 := [trans #66 #72]: #73
+#142 := [monotonicity #74 #145]: #143
+#151 := [trans #142 #149]: #150
+#154 := [monotonicity #151]: #153
+#158 := [trans #154 #156]: #157
+#53 := [asserted]: #33
+[mp #53 #158]: false
unsat
13d222fc57300189e3c05b2df538ad53757b2feb 257 0
#2 := false
@@ -13934,7 +14330,7 @@
#105 := [asserted]: #29
[unit-resolution #105 #402]: false
unsat
-526684221798fda6e81b23523c37671c2fd01b49 1 0
+cbddab0a93fe2901d1f5dd30bb313d7532a1c531 1 0
unsat
a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0
#2 := false
--- a/src/HOL/SMT_Examples/SMT_Examples.thy Mon Dec 20 09:06:37 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy Mon Dec 20 09:31:47 2010 +0100
@@ -399,20 +399,19 @@
subsection {* Non-linear arithmetic over integers and reals *}
lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
- using zero_less_mult_pos
+ using [[smt_oracle=true]]
by smt
lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
- using right_distrib
by smt
lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
- sorry (* FIXME: Z3 could solve this directly *)
+ by smt
lemma
"(U::int) + (1 + p) * (b + e) + p * d =
U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)"
- sorry (* FIXME: Z3 could solve this directly *)
+ by smt
subsection {* Linear arithmetic for natural numbers *}
--- a/src/HOL/SMT_Examples/SMT_Tests.certs Mon Dec 20 09:06:37 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs Mon Dec 20 09:31:47 2010 +0100
@@ -12789,4479 +12789,9503 @@
#53 := [asserted]: #16
[mp #53 #71]: false
unsat
-611c41109aa958be031117f9c38a7deb95b567a0 72 0
+6610e16f7eb0fe91ddb9c3e14cbb3397d007ccfb 260 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 0::Int
-#20 := (f3 0::Int)
-#15 := (- 0::Int)
-#16 := (div #15 #15)
-#14 := (div 0::Int 0::Int)
-#11 := (< 0::Int 0::Int)
-#12 := (and #11 #11)
-#13 := (or #12 #12)
-#17 := (ite #13 #14 #16)
-#9 := (= 0::Int 0::Int)
-#10 := (or #9 #9)
-#18 := (ite #10 0::Int #17)
-#19 := (f3 #18)
-#21 := (= #19 #20)
-#22 := (not #21)
-#108 := (iff #22 false)
-#1 := true
-#103 := (not true)
-#106 := (iff #103 false)
-#107 := [rewrite]: #106
-#104 := (iff #22 #103)
-#101 := (iff #21 true)
-#96 := (= #20 #20)
-#99 := (iff #96 true)
-#100 := [rewrite]: #99
-#97 := (iff #21 #96)
-#93 := (= #18 0::Int)
-#88 := (ite true 0::Int #14)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #18 #88)
-#86 := (= #17 #14)
-#81 := (ite #11 #14 #14)
-#84 := (= #81 #14)
-#85 := [rewrite]: #84
-#82 := (= #17 #81)
-#79 := (= #16 #14)
-#77 := (= #15 0::Int)
-#78 := [rewrite]: #77
-#80 := [monotonicity #78 #78]: #79
-#75 := (iff #13 #11)
-#70 := (or #11 #11)
-#73 := (iff #70 #11)
-#74 := [rewrite]: #73
-#71 := (iff #13 #70)
-#68 := (iff #12 #11)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69 #69]: #71
-#76 := [trans #72 #74]: #75
-#83 := [monotonicity #76 #80]: #82
-#87 := [trans #83 #85]: #86
-#66 := (iff #10 true)
-#61 := (or true true)
-#64 := (iff #61 true)
-#65 := [rewrite]: #64
-#62 := (iff #10 #61)
-#59 := (iff #9 true)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60 #60]: #62
-#67 := [trans #63 #65]: #66
-#90 := [monotonicity #67 #87]: #89
-#94 := [trans #90 #92]: #93
-#95 := [monotonicity #94]: #21
-#98 := [monotonicity #95]: #97
-#102 := [trans #98 #100]: #101
-#105 := [monotonicity #102]: #104
-#109 := [trans #105 #107]: #108
-#58 := [asserted]: #22
-[mp #58 #109]: false
-unsat
-a1635dd4dd56e9245fc52a441cde335332b960ef 79 0
+#11 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := (f4 0::Int 0::Int)
+#10 := (f3 #9)
+#12 := (= #10 #11)
+#798 := (= #9 0::Int)
+#19 := (:var 0 Int)
+#30 := (:var 1 Int)
+#31 := (f4 #30 #19)
+#877 := (pattern #31)
+#179 := -1::Int
+#183 := (* -1::Int #19)
+#180 := (* -1::Int #30)
+#186 := (div #180 #183)
+#358 := (* -1::Int #186)
+#359 := (+ #31 #358)
+#360 := (= #359 0::Int)
+#41 := (div #30 #19)
+#355 := (* -1::Int #41)
+#356 := (+ #31 #355)
+#357 := (= #356 0::Int)
+#218 := (>= #30 0::Int)
+#211 := (<= #19 0::Int)
+#318 := (or #211 #218)
+#319 := (not #318)
+#207 := (<= #30 0::Int)
+#316 := (or #207 #211)
+#317 := (not #316)
+#322 := (or #317 #319)
+#361 := (ite #322 #357 #360)
+#354 := (= #31 0::Int)
+#33 := (= #19 0::Int)
+#32 := (= #30 0::Int)
+#34 := (or #32 #33)
+#362 := (ite #34 #354 #361)
+#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #362)
+#365 := (forall (vars (?v0 Int) (?v1 Int)) #362)
+#881 := (iff #365 #878)
+#879 := (iff #362 #362)
+#880 := [refl]: #879
+#882 := [quant-intro #880]: #881
+#325 := (ite #322 #41 #186)
+#328 := (ite #34 0::Int #325)
+#331 := (= #31 #328)
+#334 := (forall (vars (?v0 Int) (?v1 Int)) #331)
+#366 := (iff #334 #365)
+#363 := (iff #331 #362)
+#364 := [rewrite]: #363
+#367 := [quant-intro #364]: #366
+#219 := (not #218)
+#212 := (not #211)
+#222 := (and #212 #219)
+#208 := (not #207)
+#215 := (and #208 #212)
+#225 := (or #215 #222)
+#228 := (ite #225 #41 #186)
+#231 := (ite #34 0::Int #228)
+#234 := (= #31 #231)
+#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
+#335 := (iff #237 #334)
+#332 := (iff #234 #331)
+#329 := (= #231 #328)
+#326 := (= #228 #325)
+#323 := (iff #225 #322)
+#320 := (iff #222 #319)
+#321 := [rewrite]: #320
+#301 := (iff #215 #317)
+#302 := [rewrite]: #301
+#324 := [monotonicity #302 #321]: #323
+#327 := [monotonicity #324]: #326
+#330 := [monotonicity #327]: #329
+#333 := [monotonicity #330]: #332
+#336 := [quant-intro #333]: #335
+#297 := (~ #237 #237)
+#310 := (~ #234 #234)
+#311 := [refl]: #310
+#298 := [nnf-pos #311]: #297
+#43 := (- #19)
+#42 := (- #30)
+#44 := (div #42 #43)
+#36 := (< 0::Int #19)
+#38 := (< #30 0::Int)
+#39 := (and #38 #36)
+#35 := (< 0::Int #30)
+#37 := (and #35 #36)
+#40 := (or #37 #39)
+#45 := (ite #40 #41 #44)
+#46 := (ite #34 0::Int #45)
+#47 := (= #31 #46)
+#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
+#240 := (iff #48 #237)
+#173 := (and #36 #38)
+#176 := (or #37 #173)
+#189 := (ite #176 #41 #186)
+#167 := (= 0::Int #19)
+#164 := (= 0::Int #30)
+#170 := (or #164 #167)
+#192 := (ite #170 0::Int #189)
+#195 := (= #31 #192)
+#198 := (forall (vars (?v0 Int) (?v1 Int)) #195)
+#238 := (iff #198 #237)
+#235 := (iff #195 #234)
+#232 := (= #192 #231)
+#229 := (= #189 #228)
+#226 := (iff #176 #225)
+#223 := (iff #173 #222)
+#220 := (iff #38 #219)
+#221 := [rewrite]: #220
+#213 := (iff #36 #212)
+#214 := [rewrite]: #213
+#224 := [monotonicity #214 #221]: #223
+#216 := (iff #37 #215)
+#209 := (iff #35 #208)
+#210 := [rewrite]: #209
+#217 := [monotonicity #210 #214]: #216
+#227 := [monotonicity #217 #224]: #226
+#230 := [monotonicity #227]: #229
+#205 := (iff #170 #34)
+#203 := (iff #167 #33)
+#204 := [rewrite]: #203
+#201 := (iff #164 #32)
+#202 := [rewrite]: #201
+#206 := [monotonicity #202 #204]: #205
+#233 := [monotonicity #206 #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [quant-intro #236]: #238
+#199 := (iff #48 #198)
+#196 := (iff #47 #195)
+#193 := (= #46 #192)
+#190 := (= #45 #189)
+#187 := (= #44 #186)
+#184 := (= #43 #183)
+#185 := [rewrite]: #184
+#181 := (= #42 #180)
+#182 := [rewrite]: #181
+#188 := [monotonicity #182 #185]: #187
+#177 := (iff #40 #176)
+#174 := (iff #39 #173)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#191 := [monotonicity #178 #188]: #190
+#171 := (iff #34 #170)
+#168 := (iff #33 #167)
+#169 := [rewrite]: #168
+#165 := (iff #32 #164)
+#166 := [rewrite]: #165
+#172 := [monotonicity #166 #169]: #171
+#194 := [monotonicity #172 #191]: #193
+#197 := [monotonicity #194]: #196
+#200 := [quant-intro #197]: #199
+#241 := [trans #200 #239]: #240
+#163 := [asserted]: #48
+#242 := [mp #163 #241]: #237
+#312 := [mp~ #242 #298]: #237
+#337 := [mp #312 #336]: #334
+#368 := [mp #337 #367]: #365
+#883 := [mp #368 #882]: #878
+#755 := (not #878)
+#757 := (or #755 #798)
+#811 := (* -1::Int 0::Int)
+#812 := (div #811 #811)
+#813 := (* -1::Int #812)
+#808 := (+ #9 #813)
+#809 := (= #808 0::Int)
+#814 := (div 0::Int 0::Int)
+#815 := (* -1::Int #814)
+#810 := (+ #9 #815)
+#816 := (= #810 0::Int)
+#833 := (>= 0::Int 0::Int)
+#657 := (<= 0::Int 0::Int)
+#658 := (or #657 #833)
+#659 := (not #658)
+#801 := (or #657 #657)
+#802 := (not #801)
+#803 := (or #802 #659)
+#804 := (ite #803 #816 #809)
+#799 := (= 0::Int 0::Int)
+#805 := (or #799 #799)
+#806 := (ite #805 #798 #804)
+#758 := (or #755 #806)
+#756 := (iff #758 #757)
+#740 := (iff #757 #757)
+#741 := [rewrite]: #740
+#768 := (iff #806 #798)
+#1 := true
+#764 := (ite true #798 #816)
+#767 := (iff #764 #798)
+#763 := [rewrite]: #767
+#765 := (iff #806 #764)
+#761 := (iff #804 #816)
+#774 := (ite false #816 #816)
+#770 := (iff #774 #816)
+#777 := [rewrite]: #770
+#775 := (iff #804 #774)
+#784 := (iff #809 #816)
+#783 := (= #808 #810)
+#781 := (= #813 #815)
+#769 := (= #812 #814)
+#780 := (= #811 0::Int)
+#772 := [rewrite]: #780
+#771 := [monotonicity #772 #772]: #769
+#782 := [monotonicity #771]: #781
+#779 := [monotonicity #782]: #783
+#773 := [monotonicity #779]: #784
+#791 := (iff #803 false)
+#695 := (or false false)
+#790 := (iff #695 false)
+#787 := [rewrite]: #790
+#696 := (iff #803 #695)
+#693 := (iff #659 false)
+#481 := (not true)
+#840 := (iff #481 false)
+#843 := [rewrite]: #840
+#692 := (iff #659 #481)
+#689 := (iff #658 true)
+#636 := (or true true)
+#792 := (iff #636 true)
+#793 := [rewrite]: #792
+#789 := (iff #658 #636)
+#839 := (iff #833 true)
+#841 := [rewrite]: #839
+#794 := (iff #657 true)
+#797 := [rewrite]: #794
+#674 := [monotonicity #797 #841]: #789
+#691 := [trans #674 #793]: #689
+#685 := [monotonicity #691]: #692
+#694 := [trans #685 #843]: #693
+#785 := (iff #802 false)
+#788 := (iff #802 #481)
+#681 := (iff #801 true)
+#679 := (iff #801 #636)
+#680 := [monotonicity #797 #797]: #679
+#640 := [trans #680 #793]: #681
+#690 := [monotonicity #640]: #788
+#786 := [trans #690 #843]: #785
+#697 := [monotonicity #786 #694]: #696
+#778 := [trans #697 #787]: #791
+#776 := [monotonicity #778 #773]: #775
+#762 := [trans #776 #777]: #761
+#795 := (iff #805 true)
+#638 := (iff #805 #636)
+#800 := (iff #799 true)
+#807 := [rewrite]: #800
+#639 := [monotonicity #807 #807]: #638
+#796 := [trans #639 #793]: #795
+#766 := [monotonicity #796 #762]: #765
+#754 := [trans #766 #763]: #768
+#760 := [monotonicity #754]: #756
+#743 := [trans #760 #741]: #756
+#759 := [quant-inst #8 #8]: #758
+#744 := [mp #759 #743]: #757
+#746 := [unit-resolution #744 #883]: #798
+#747 := [monotonicity #746]: #12
+#13 := (not #12)
+#77 := [asserted]: #13
+[unit-resolution #77 #747]: false
+unsat
+3797d02b9c4cbb9f278d97dba12e1e356411933c 275 0
#2 := false
decl f3 :: (-> Int S2)
#10 := 0::Int
-#27 := (f3 0::Int)
-#22 := (- 0::Int)
-decl f4 :: (-> S2 Int)
-decl f5 :: S2
-#8 := f5
-#9 := (f4 f5)
-#21 := (- #9)
-#23 := (div #21 #22)
-#20 := (div #9 0::Int)
-#15 := (< 0::Int 0::Int)
-#17 := (< #9 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #9)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 0::Int 0::Int)
-#11 := (= #9 0::Int)
-#13 := (or #11 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (f3 #25)
-#28 := (= #26 #27)
-#29 := (not #28)
-#113 := (iff #29 false)
-#1 := true
-#108 := (not true)
-#111 := (iff #108 false)
-#112 := [rewrite]: #111
-#109 := (iff #29 #108)
-#106 := (iff #28 true)
-#101 := (= #27 #27)
-#104 := (iff #101 true)
-#105 := [rewrite]: #104
-#102 := (iff #28 #101)
-#98 := (= #25 0::Int)
-#81 := -1::Int
-#82 := (* -1::Int #9)
-#87 := (div #82 0::Int)
-#75 := (and #15 #17)
-#78 := (or #16 #75)
-#90 := (ite #78 #20 #87)
-#93 := (ite true 0::Int #90)
-#96 := (= #93 0::Int)
-#97 := [rewrite]: #96
-#94 := (= #25 #93)
-#91 := (= #24 #90)
-#88 := (= #23 #87)
-#85 := (= #22 0::Int)
-#86 := [rewrite]: #85
-#83 := (= #21 #82)
-#84 := [rewrite]: #83
-#89 := [monotonicity #84 #86]: #88
-#79 := (iff #19 #78)
-#76 := (iff #18 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#92 := [monotonicity #80 #89]: #91
-#73 := (iff #13 true)
-#68 := (or #11 true)
-#71 := (iff #68 true)
-#72 := [rewrite]: #71
-#69 := (iff #13 #68)
-#66 := (iff #12 true)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#95 := [monotonicity #74 #92]: #94
-#99 := [trans #95 #97]: #98
-#100 := [monotonicity #99]: #28
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#65 := [asserted]: #29
-[mp #65 #114]: false
-unsat
-e01bd2bd51de7fe522eece30b6126b14fb1617b9 81 0
+#13 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#11 := (f4 #9 0::Int)
+#12 := (f3 #11)
+#14 := (= #12 #13)
+#641 := (= #11 0::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#33 := (f4 #32 #21)
+#879 := (pattern #33)
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#188 := (div #182 #185)
+#360 := (* -1::Int #188)
+#361 := (+ #33 #360)
+#362 := (= #361 0::Int)
+#43 := (div #32 #21)
+#357 := (* -1::Int #43)
+#358 := (+ #33 #357)
+#359 := (= #358 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#363 := (ite #324 #359 #362)
+#356 := (= #33 0::Int)
+#35 := (= #21 0::Int)
+#34 := (= #32 0::Int)
+#36 := (or #34 #35)
+#364 := (ite #36 #356 #363)
+#880 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #879) #364)
+#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
+#883 := (iff #367 #880)
+#881 := (iff #364 #364)
+#882 := [refl]: #881
+#884 := [quant-intro #882]: #883
+#327 := (ite #324 #43 #188)
+#330 := (ite #36 0::Int #327)
+#333 := (= #33 #330)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#368 := (iff #336 #367)
+#365 := (iff #333 #364)
+#366 := [rewrite]: #365
+#369 := [quant-intro #366]: #368
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#230 := (ite #227 #43 #188)
+#233 := (ite #36 0::Int #230)
+#236 := (= #33 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#337 := (iff #239 #336)
+#334 := (iff #236 #333)
+#331 := (= #233 #330)
+#328 := (= #230 #327)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#329 := [monotonicity #326]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [quant-intro #335]: #337
+#299 := (~ #239 #239)
+#312 := (~ #236 #236)
+#313 := [refl]: #312
+#300 := [nnf-pos #313]: #299
+#45 := (- #21)
+#44 := (- #32)
+#46 := (div #44 #45)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#47 := (ite #42 #43 #46)
+#48 := (ite #36 0::Int #47)
+#49 := (= #33 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#242 := (iff #50 #239)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#191 := (ite #178 #43 #188)
+#169 := (= 0::Int #21)
+#166 := (= 0::Int #32)
+#172 := (or #166 #169)
+#194 := (ite #172 0::Int #191)
+#197 := (= #33 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#240 := (iff #200 #239)
+#237 := (iff #197 #236)
+#234 := (= #194 #233)
+#231 := (= #191 #230)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#232 := [monotonicity #229]: #231
+#207 := (iff #172 #36)
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#208 := [monotonicity #204 #206]: #207
+#235 := [monotonicity #208 #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#201 := (iff #50 #200)
+#198 := (iff #49 #197)
+#195 := (= #48 #194)
+#192 := (= #47 #191)
+#189 := (= #46 #188)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#190 := [monotonicity #184 #187]: #189
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#193 := [monotonicity #180 #190]: #192
+#173 := (iff #36 #172)
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#174 := [monotonicity #168 #171]: #173
+#196 := [monotonicity #174 #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
+#243 := [trans #202 #241]: #242
+#165 := [asserted]: #50
+#244 := [mp #165 #243]: #239
+#314 := [mp~ #244 #300]: #239
+#339 := [mp #314 #338]: #336
+#370 := [mp #339 #369]: #367
+#885 := [mp #370 #884]: #880
+#755 := (not #880)
+#733 := (or #755 #641)
+#816 := (* -1::Int 0::Int)
+#817 := (* -1::Int #9)
+#812 := (div #817 #816)
+#818 := (* -1::Int #812)
+#659 := (+ #11 #818)
+#660 := (= #659 0::Int)
+#661 := (div #9 0::Int)
+#803 := (* -1::Int #661)
+#804 := (+ #11 #803)
+#805 := (= #804 0::Int)
+#806 := (>= #9 0::Int)
+#800 := (<= 0::Int 0::Int)
+#801 := (or #800 #806)
+#807 := (not #801)
+#808 := (<= #9 0::Int)
+#802 := (or #808 #800)
+#809 := (not #802)
+#638 := (or #809 #807)
+#640 := (ite #638 #805 #660)
+#794 := (= 0::Int 0::Int)
+#795 := (= #9 0::Int)
+#797 := (or #795 #794)
+#798 := (ite #797 #641 #640)
+#734 := (or #755 #798)
+#737 := (iff #734 #733)
+#739 := (iff #733 #733)
+#740 := [rewrite]: #739
+#754 := (iff #798 #641)
+#766 := (div #817 0::Int)
+#769 := (* -1::Int #766)
+#756 := (+ #11 #769)
+#760 := (= #756 0::Int)
+#1 := true
+#749 := (ite true #641 #760)
+#752 := (iff #749 #641)
+#753 := [rewrite]: #752
+#750 := (iff #798 #749)
+#747 := (iff #640 #760)
+#762 := (ite false #805 #760)
+#745 := (iff #762 #760)
+#746 := [rewrite]: #745
+#742 := (iff #640 #762)
+#761 := (iff #660 #760)
+#757 := (= #659 #756)
+#765 := (= #818 #769)
+#767 := (= #812 #766)
+#763 := (= #816 0::Int)
+#764 := [rewrite]: #763
+#768 := [monotonicity #764]: #767
+#770 := [monotonicity #768]: #765
+#759 := [monotonicity #770]: #757
+#758 := [monotonicity #759]: #761
+#772 := (iff #638 false)
+#786 := (or false false)
+#777 := (iff #786 false)
+#778 := [rewrite]: #777
+#775 := (iff #638 #786)
+#785 := (iff #807 false)
+#831 := (not true)
+#555 := (iff #831 false)
+#556 := [rewrite]: #555
+#783 := (iff #807 #831)
+#771 := (iff #801 true)
+#789 := (or true #806)
+#782 := (iff #789 true)
+#774 := [rewrite]: #782
+#793 := (iff #801 #789)
+#788 := (iff #800 true)
+#791 := [rewrite]: #788
+#780 := [monotonicity #791]: #793
+#773 := [trans #780 #774]: #771
+#784 := [monotonicity #773]: #783
+#781 := [trans #784 #556]: #785
+#699 := (iff #809 false)
+#697 := (iff #809 #831)
+#695 := (iff #802 true)
+#676 := (or #808 true)
+#694 := (iff #676 true)
+#687 := [rewrite]: #694
+#691 := (iff #802 #676)
+#693 := [monotonicity #791]: #691
+#696 := [trans #693 #687]: #695
+#698 := [monotonicity #696]: #697
+#792 := [trans #698 #556]: #699
+#776 := [monotonicity #792 #781]: #775
+#779 := [trans #776 #778]: #772
+#743 := [monotonicity #779 #758]: #742
+#748 := [trans #743 #746]: #747
+#692 := (iff #797 true)
+#681 := (or #795 true)
+#642 := (iff #681 true)
+#790 := [rewrite]: #642
+#682 := (iff #797 #681)
+#796 := (iff #794 true)
+#799 := [rewrite]: #796
+#683 := [monotonicity #799]: #682
+#787 := [trans #683 #790]: #692
+#751 := [monotonicity #787 #748]: #750
+#744 := [trans #751 #753]: #754
+#738 := [monotonicity #744]: #737
+#735 := [trans #738 #740]: #737
+#736 := [quant-inst #9 #10]: #734
+#741 := [mp #736 #735]: #733
+#723 := [unit-resolution #741 #885]: #641
+#724 := [monotonicity #723]: #14
+#15 := (not #14)
+#79 := [asserted]: #15
+[unit-resolution #79 #724]: false
+unsat
+589d59789d263d5382384d3b16ffc9ff725b6206 297 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 0::Int
-#24 := (f3 0::Int)
-#10 := 1::Int
-#19 := (- 1::Int)
-#18 := (- 0::Int)
-#20 := (div #18 #19)
-#17 := (div 0::Int 1::Int)
-#14 := (< 0::Int 1::Int)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#21 := (ite #16 #17 #20)
-#11 := (= 1::Int 0::Int)
-#9 := (= 0::Int 0::Int)
-#12 := (or #9 #11)
-#22 := (ite #12 0::Int #21)
-#23 := (f3 #22)
-#25 := (= #23 #24)
-#26 := (not #25)
-#117 := (iff #26 false)
-#1 := true
-#112 := (not true)
-#115 := (iff #112 false)
-#116 := [rewrite]: #115
-#113 := (iff #26 #112)
-#110 := (iff #25 true)
-#105 := (= #24 #24)
-#108 := (iff #105 true)
-#109 := [rewrite]: #108
-#106 := (iff #25 #105)
-#102 := (= #22 0::Int)
-#97 := (ite true 0::Int 0::Int)
-#100 := (= #97 0::Int)
-#101 := [rewrite]: #100
-#98 := (= #22 #97)
-#95 := (= #21 0::Int)
-#90 := (ite #15 0::Int 0::Int)
-#93 := (= #90 0::Int)
-#94 := [rewrite]: #93
-#91 := (= #21 #90)
-#88 := (= #20 0::Int)
-#80 := -1::Int
-#83 := (div 0::Int -1::Int)
-#86 := (= #83 0::Int)
-#87 := [rewrite]: #86
-#84 := (= #20 #83)
-#81 := (= #19 -1::Int)
-#82 := [rewrite]: #81
-#78 := (= #18 0::Int)
-#79 := [rewrite]: #78
-#85 := [monotonicity #79 #82]: #84
-#89 := [trans #85 #87]: #88
-#76 := (= #17 0::Int)
-#77 := [rewrite]: #76
-#74 := (iff #16 #15)
-#75 := [rewrite]: #74
-#92 := [monotonicity #75 #77 #89]: #91
-#96 := [trans #92 #94]: #95
-#72 := (iff #12 true)
-#67 := (or true false)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #12 #67)
-#65 := (iff #11 false)
-#66 := [rewrite]: #65
-#63 := (iff #9 true)
-#64 := [rewrite]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#99 := [monotonicity #73 #96]: #98
-#103 := [trans #99 #101]: #102
-#104 := [monotonicity #103]: #25
-#107 := [monotonicity #104]: #106
-#111 := [trans #107 #109]: #110
-#114 := [monotonicity #111]: #113
-#118 := [trans #114 #116]: #117
-#62 := [asserted]: #26
-[mp #62 #118]: false
-unsat
-4d757130b0dc28fe958cf4c129cd34caadcedd08 82 0
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 1::Int
+#10 := (f4 0::Int 1::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#806 := (= #10 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#32 := (f4 #31 #20)
+#877 := (pattern #32)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#187 := (div #181 #184)
+#359 := (* -1::Int #187)
+#360 := (+ #32 #359)
+#361 := (= #360 0::Int)
+#42 := (div #31 #20)
+#356 := (* -1::Int #42)
+#357 := (+ #32 #356)
+#358 := (= #357 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#362 := (ite #323 #358 #361)
+#355 := (= #32 0::Int)
+#34 := (= #20 0::Int)
+#33 := (= #31 0::Int)
+#35 := (or #33 #34)
+#363 := (ite #35 #355 #362)
+#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363)
+#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
+#881 := (iff #366 #878)
+#879 := (iff #363 #363)
+#880 := [refl]: #879
+#882 := [quant-intro #880]: #881
+#326 := (ite #323 #42 #187)
+#329 := (ite #35 0::Int #326)
+#332 := (= #32 #329)
+#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
+#367 := (iff #335 #366)
+#364 := (iff #332 #363)
+#365 := [rewrite]: #364
+#368 := [quant-intro #365]: #367
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#229 := (ite #226 #42 #187)
+#232 := (ite #35 0::Int #229)
+#235 := (= #32 #232)
+#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
+#336 := (iff #238 #335)
+#333 := (iff #235 #332)
+#330 := (= #232 #329)
+#327 := (= #229 #326)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#328 := [monotonicity #325]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [quant-intro #334]: #336
+#298 := (~ #238 #238)
+#311 := (~ #235 #235)
+#312 := [refl]: #311
+#299 := [nnf-pos #312]: #298
+#44 := (- #20)
+#43 := (- #31)
+#45 := (div #43 #44)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#46 := (ite #41 #42 #45)
+#47 := (ite #35 0::Int #46)
+#48 := (= #32 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#241 := (iff #49 #238)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#190 := (ite #177 #42 #187)
+#168 := (= 0::Int #20)
+#165 := (= 0::Int #31)
+#171 := (or #165 #168)
+#193 := (ite #171 0::Int #190)
+#196 := (= #32 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#239 := (iff #199 #238)
+#236 := (iff #196 #235)
+#233 := (= #193 #232)
+#230 := (= #190 #229)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#231 := [monotonicity #228]: #230
+#206 := (iff #171 #35)
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#207 := [monotonicity #203 #205]: #206
+#234 := [monotonicity #207 #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [quant-intro #237]: #239
+#200 := (iff #49 #199)
+#197 := (iff #48 #196)
+#194 := (= #47 #193)
+#191 := (= #46 #190)
+#188 := (= #45 #187)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#189 := [monotonicity #183 #186]: #188
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#192 := [monotonicity #179 #189]: #191
+#172 := (iff #35 #171)
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#173 := [monotonicity #167 #170]: #172
+#195 := [monotonicity #173 #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
+#242 := [trans #201 #240]: #241
+#164 := [asserted]: #49
+#243 := [mp #164 #242]: #238
+#313 := [mp~ #243 #299]: #238
+#338 := [mp #313 #337]: #335
+#369 := [mp #338 #368]: #366
+#883 := [mp #369 #882]: #878
+#724 := (not #878)
+#730 := (or #724 #806)
+#812 := (* -1::Int 1::Int)
+#813 := (* -1::Int 0::Int)
+#808 := (div #813 #812)
+#809 := (* -1::Int #808)
+#814 := (+ #10 #809)
+#815 := (= #814 0::Int)
+#810 := (div 0::Int 1::Int)
+#816 := (* -1::Int #810)
+#657 := (+ #10 #816)
+#658 := (= #657 0::Int)
+#834 := (>= 0::Int 0::Int)
+#659 := (<= 1::Int 0::Int)
+#801 := (or #659 #834)
+#802 := (not #801)
+#803 := (<= 0::Int 0::Int)
+#804 := (or #803 #659)
+#798 := (not #804)
+#799 := (or #798 #802)
+#805 := (ite #799 #658 #815)
+#800 := (= 1::Int 0::Int)
+#807 := (= 0::Int 0::Int)
+#636 := (or #807 #800)
+#638 := (ite #636 #806 #805)
+#703 := (or #724 #638)
+#705 := (iff #703 #730)
+#709 := (iff #730 #730)
+#710 := [rewrite]: #709
+#728 := (iff #638 #806)
+#1 := true
+#721 := (ite true #806 #806)
+#726 := (iff #721 #806)
+#727 := [rewrite]: #726
+#722 := (iff #638 #721)
+#739 := (iff #805 #806)
+#735 := (ite false #806 #806)
+#738 := (iff #735 #806)
+#733 := [rewrite]: #738
+#736 := (iff #805 #735)
+#732 := (iff #815 #806)
+#753 := (= #814 #10)
+#766 := (+ #10 0::Int)
+#768 := (= #766 #10)
+#754 := [rewrite]: #768
+#752 := (= #814 #766)
+#750 := (= #809 0::Int)
+#761 := (= #813 0::Int)
+#762 := [rewrite]: #761
+#748 := (= #809 #813)
+#746 := (= #808 0::Int)
+#740 := (div 0::Int -1::Int)
+#744 := (= #740 0::Int)
+#745 := [rewrite]: #744
+#741 := (= #808 #740)
+#756 := (= #812 -1::Int)
+#760 := [rewrite]: #756
+#743 := [monotonicity #762 #760]: #741
+#747 := [trans #743 #745]: #746
+#749 := [monotonicity #747]: #748
+#751 := [trans #749 #762]: #750
+#742 := [monotonicity #751]: #752
+#731 := [trans #742 #754]: #753
+#734 := [monotonicity #731]: #732
+#758 := (iff #658 #806)
+#755 := (= #657 #10)
+#767 := (= #657 #766)
+#764 := (= #816 0::Int)
+#770 := (= #816 #813)
+#775 := (= #810 0::Int)
+#776 := [rewrite]: #775
+#777 := [monotonicity #776]: #770
+#765 := [trans #777 #762]: #764
+#763 := [monotonicity #765]: #767
+#757 := [trans #763 #754]: #755
+#759 := [monotonicity #757]: #758
+#773 := (iff #799 false)
+#781 := (or false false)
+#779 := (iff #781 false)
+#784 := [rewrite]: #779
+#782 := (iff #799 #781)
+#769 := (iff #802 false)
+#482 := (not true)
+#843 := (iff #482 false)
+#829 := [rewrite]: #843
+#780 := (iff #802 #482)
+#791 := (iff #801 true)
+#695 := (or false true)
+#790 := (iff #695 true)
+#787 := [rewrite]: #790
+#696 := (iff #801 #695)
+#841 := (iff #834 true)
+#481 := [rewrite]: #841
+#785 := (iff #659 false)
+#786 := [rewrite]: #785
+#697 := [monotonicity #786 #481]: #696
+#778 := [trans #697 #787]: #791
+#772 := [monotonicity #778]: #780
+#771 := [trans #772 #829]: #769
+#693 := (iff #798 false)
+#692 := (iff #798 #482)
+#689 := (iff #804 true)
+#796 := (or true false)
+#679 := (iff #796 true)
+#680 := [rewrite]: #679
+#789 := (iff #804 #796)
+#788 := (iff #803 true)
+#690 := [rewrite]: #788
+#674 := [monotonicity #690 #786]: #789
+#691 := [trans #674 #680]: #689
+#685 := [monotonicity #691]: #692
+#694 := [trans #685 #829]: #693
+#783 := [monotonicity #694 #771]: #782
+#774 := [trans #783 #784]: #773
+#737 := [monotonicity #774 #759 #734]: #736
+#725 := [trans #737 #733]: #739
+#681 := (iff #636 true)
+#794 := (iff #636 #796)
+#793 := (iff #800 false)
+#795 := [rewrite]: #793
+#639 := (iff #807 true)
+#792 := [rewrite]: #639
+#797 := [monotonicity #792 #795]: #794
+#640 := [trans #797 #680]: #681
+#723 := [monotonicity #640 #725]: #722
+#729 := [trans #723 #727]: #728
+#598 := [monotonicity #729]: #705
+#711 := [trans #598 #710]: #705
+#704 := [quant-inst #8 #9]: #703
+#716 := [mp #704 #711]: #730
+#713 := [unit-resolution #716 #883]: #806
+#714 := [monotonicity #713]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #714]: false
+unsat
+009cf27bd16a3881b93b6b7959195f72499a5829 300 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 1::Int
-#23 := (f3 1::Int)
-#18 := (- 1::Int)
-#19 := (div #18 #18)
-#17 := (div 1::Int 1::Int)
-#9 := 0::Int
-#12 := (< 0::Int 1::Int)
-#14 := (< 1::Int 0::Int)
-#15 := (and #14 #12)
-#13 := (and #12 #12)
-#16 := (or #13 #15)
-#20 := (ite #16 #17 #19)
-#10 := (= 1::Int 0::Int)
-#11 := (or #10 #10)
-#21 := (ite #11 0::Int #20)
-#22 := (f3 #21)
-#24 := (= #22 #23)
-#25 := (not #24)
-#118 := (iff #25 false)
-#1 := true
-#113 := (not true)
-#116 := (iff #113 false)
-#117 := [rewrite]: #116
-#114 := (iff #25 #113)
-#111 := (iff #24 true)
-#106 := (= #23 #23)
-#109 := (iff #106 true)
-#110 := [rewrite]: #109
-#107 := (iff #24 #106)
-#103 := (= #21 1::Int)
-#98 := (ite false 0::Int 1::Int)
-#101 := (= #98 1::Int)
-#102 := [rewrite]: #101
-#99 := (= #21 #98)
-#96 := (= #20 1::Int)
-#73 := (and #12 #14)
-#76 := (or #12 #73)
-#91 := (ite #76 1::Int 1::Int)
-#94 := (= #91 1::Int)
-#95 := [rewrite]: #94
-#92 := (= #20 #91)
-#89 := (= #19 1::Int)
-#81 := -1::Int
-#84 := (div -1::Int -1::Int)
-#87 := (= #84 1::Int)
-#88 := [rewrite]: #87
-#85 := (= #19 #84)
-#82 := (= #18 -1::Int)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83 #83]: #85
-#90 := [trans #86 #88]: #89
-#79 := (= #17 1::Int)
-#80 := [rewrite]: #79
-#77 := (iff #16 #76)
-#74 := (iff #15 #73)
-#75 := [rewrite]: #74
-#71 := (iff #13 #12)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#93 := [monotonicity #78 #80 #90]: #92
-#97 := [trans #93 #95]: #96
-#69 := (iff #11 false)
-#64 := (or false false)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #11 #64)
-#62 := (iff #10 false)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63 #63]: #65
-#70 := [trans #66 #68]: #69
-#100 := [monotonicity #70 #97]: #99
-#104 := [trans #100 #102]: #103
-#105 := [monotonicity #104]: #24
-#108 := [monotonicity #105]: #107
-#112 := [trans #108 #110]: #111
-#115 := [monotonicity #112]: #114
-#119 := [trans #115 #117]: #118
-#61 := [asserted]: #25
-[mp #61 #119]: false
-unsat
-5e55bd29247a2ea10048c10929dae98ba0bdec4e 89 0
+#11 := (f3 1::Int)
+decl f4 :: (-> Int Int Int)
+#9 := (f4 1::Int 1::Int)
+#10 := (f3 #9)
+#12 := (= #10 #11)
+#759 := (= #9 1::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#32 := (f4 #31 #20)
+#877 := (pattern #32)
+#19 := 0::Int
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#187 := (div #181 #184)
+#359 := (* -1::Int #187)
+#360 := (+ #32 #359)
+#361 := (= #360 0::Int)
+#42 := (div #31 #20)
+#356 := (* -1::Int #42)
+#357 := (+ #32 #356)
+#358 := (= #357 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#362 := (ite #323 #358 #361)
+#355 := (= #32 0::Int)
+#34 := (= #20 0::Int)
+#33 := (= #31 0::Int)
+#35 := (or #33 #34)
+#363 := (ite #35 #355 #362)
+#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363)
+#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
+#881 := (iff #366 #878)
+#879 := (iff #363 #363)
+#880 := [refl]: #879
+#882 := [quant-intro #880]: #881
+#326 := (ite #323 #42 #187)
+#329 := (ite #35 0::Int #326)
+#332 := (= #32 #329)
+#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
+#367 := (iff #335 #366)
+#364 := (iff #332 #363)
+#365 := [rewrite]: #364
+#368 := [quant-intro #365]: #367
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#229 := (ite #226 #42 #187)
+#232 := (ite #35 0::Int #229)
+#235 := (= #32 #232)
+#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
+#336 := (iff #238 #335)
+#333 := (iff #235 #332)
+#330 := (= #232 #329)
+#327 := (= #229 #326)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#328 := [monotonicity #325]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [quant-intro #334]: #336
+#298 := (~ #238 #238)
+#311 := (~ #235 #235)
+#312 := [refl]: #311
+#299 := [nnf-pos #312]: #298
+#44 := (- #20)
+#43 := (- #31)
+#45 := (div #43 #44)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#46 := (ite #41 #42 #45)
+#47 := (ite #35 0::Int #46)
+#48 := (= #32 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#241 := (iff #49 #238)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#190 := (ite #177 #42 #187)
+#168 := (= 0::Int #20)
+#165 := (= 0::Int #31)
+#171 := (or #165 #168)
+#193 := (ite #171 0::Int #190)
+#196 := (= #32 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#239 := (iff #199 #238)
+#236 := (iff #196 #235)
+#233 := (= #193 #232)
+#230 := (= #190 #229)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#231 := [monotonicity #228]: #230
+#206 := (iff #171 #35)
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#207 := [monotonicity #203 #205]: #206
+#234 := [monotonicity #207 #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [quant-intro #237]: #239
+#200 := (iff #49 #199)
+#197 := (iff #48 #196)
+#194 := (= #47 #193)
+#191 := (= #46 #190)
+#188 := (= #45 #187)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#189 := [monotonicity #183 #186]: #188
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#192 := [monotonicity #179 #189]: #191
+#172 := (iff #35 #171)
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#173 := [monotonicity #167 #170]: #172
+#195 := [monotonicity #173 #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
+#242 := [trans #201 #240]: #241
+#164 := [asserted]: #49
+#243 := [mp #164 #242]: #238
+#313 := [mp~ #243 #299]: #238
+#338 := [mp #313 #337]: #335
+#369 := [mp #338 #368]: #366
+#883 := [mp #369 #882]: #878
+#705 := (not #878)
+#598 := (or #705 #759)
+#813 := (* -1::Int 1::Int)
+#808 := (div #813 #813)
+#809 := (* -1::Int #808)
+#814 := (+ #9 #809)
+#815 := (= #814 0::Int)
+#810 := (div 1::Int 1::Int)
+#816 := (* -1::Int #810)
+#657 := (+ #9 #816)
+#658 := (= #657 0::Int)
+#834 := (>= 1::Int 0::Int)
+#659 := (<= 1::Int 0::Int)
+#801 := (or #659 #834)
+#802 := (not #801)
+#803 := (or #659 #659)
+#804 := (not #803)
+#798 := (or #804 #802)
+#799 := (ite #798 #658 #815)
+#805 := (= #9 0::Int)
+#806 := (= 1::Int 0::Int)
+#800 := (or #806 #806)
+#807 := (ite #800 #805 #799)
+#709 := (or #705 #807)
+#711 := (iff #709 #598)
+#712 := (iff #598 #598)
+#713 := [rewrite]: #712
+#703 := (iff #807 #759)
+#727 := (ite false #805 #759)
+#724 := (iff #727 #759)
+#730 := [rewrite]: #724
+#728 := (iff #807 #727)
+#723 := (iff #799 #759)
+#1 := true
+#733 := (ite true #759 #759)
+#721 := (iff #733 #759)
+#722 := [rewrite]: #721
+#739 := (iff #799 #733)
+#737 := (iff #815 #759)
+#766 := (+ -1::Int #9)
+#755 := (= #766 0::Int)
+#756 := (iff #755 #759)
+#760 := [rewrite]: #756
+#735 := (iff #815 #755)
+#732 := (= #814 #766)
+#762 := (+ #9 -1::Int)
+#767 := (= #762 #766)
+#763 := [rewrite]: #767
+#753 := (= #814 #762)
+#752 := (= #809 -1::Int)
+#776 := (= #813 -1::Int)
+#770 := [rewrite]: #776
+#750 := (= #809 #813)
+#748 := (= #808 1::Int)
+#743 := (div -1::Int -1::Int)
+#746 := (= #743 1::Int)
+#747 := [rewrite]: #746
+#744 := (= #808 #743)
+#745 := [monotonicity #770 #770]: #744
+#749 := [trans #745 #747]: #748
+#751 := [monotonicity #749]: #750
+#742 := [trans #751 #770]: #752
+#731 := [monotonicity #742]: #753
+#734 := [trans #731 #763]: #732
+#736 := [monotonicity #734]: #735
+#738 := [trans #736 #760]: #737
+#740 := (iff #658 #759)
+#757 := (iff #658 #755)
+#768 := (= #657 #766)
+#764 := (= #657 #762)
+#777 := (= #816 -1::Int)
+#774 := (= #816 #813)
+#784 := (= #810 1::Int)
+#773 := [rewrite]: #784
+#775 := [monotonicity #773]: #774
+#761 := [trans #775 #770]: #777
+#765 := [monotonicity #761]: #764
+#754 := [trans #765 #763]: #768
+#758 := [monotonicity #754]: #757
+#741 := [trans #758 #760]: #740
+#783 := (iff #798 true)
+#772 := (or true false)
+#781 := (iff #772 true)
+#782 := [rewrite]: #781
+#769 := (iff #798 #772)
+#778 := (iff #802 false)
+#482 := (not true)
+#843 := (iff #482 false)
+#829 := [rewrite]: #843
+#787 := (iff #802 #482)
+#697 := (iff #801 true)
+#685 := (or false true)
+#695 := (iff #685 true)
+#696 := [rewrite]: #695
+#693 := (iff #801 #685)
+#841 := (iff #834 true)
+#481 := [rewrite]: #841
+#679 := (iff #659 false)
+#680 := [rewrite]: #679
+#694 := [monotonicity #680 #481]: #693
+#790 := [trans #694 #696]: #697
+#791 := [monotonicity #790]: #787
+#780 := [trans #791 #829]: #778
+#691 := (iff #804 true)
+#785 := (not false)
+#674 := (iff #785 true)
+#689 := [rewrite]: #674
+#786 := (iff #804 #785)
+#788 := (iff #803 false)
+#639 := (or false false)
+#795 := (iff #639 false)
+#796 := [rewrite]: #795
+#681 := (iff #803 #639)
+#640 := [monotonicity #680 #680]: #681
+#690 := [trans #640 #796]: #788
+#789 := [monotonicity #690]: #786
+#692 := [trans #789 #689]: #691
+#771 := [monotonicity #692 #780]: #769
+#779 := [trans #771 #782]: #783
+#725 := [monotonicity #779 #741 #738]: #739
+#726 := [trans #725 #722]: #723
+#794 := (iff #800 false)
+#792 := (iff #800 #639)
+#636 := (iff #806 false)
+#638 := [rewrite]: #636
+#793 := [monotonicity #638 #638]: #792
+#797 := [trans #793 #796]: #794
+#729 := [monotonicity #797 #726]: #728
+#704 := [trans #729 #730]: #703
+#716 := [monotonicity #704]: #711
+#714 := [trans #716 #713]: #711
+#710 := [quant-inst #8 #8]: #709
+#717 := [mp #710 #714]: #598
+#715 := [unit-resolution #717 #883]: #759
+#720 := [monotonicity #715]: #12
+#13 := (not #12)
+#78 := [asserted]: #13
+[unit-resolution #78 #720]: false
+unsat
+ec9d2fe48d42e5d40fd0739c3491a43f0bf8c69d 311 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 3::Int
-#27 := (f3 3::Int)
-#11 := 1::Int
-#22 := (- 1::Int)
-#21 := (- 3::Int)
-#23 := (div #21 #22)
-#20 := (div 3::Int 1::Int)
-#9 := 0::Int
-#15 := (< 0::Int 1::Int)
-#17 := (< 3::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 3::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 1::Int 0::Int)
-#10 := (= 3::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (f3 #25)
-#28 := (= #26 #27)
-#29 := (not #28)
-#125 := (iff #29 false)
-#1 := true
-#120 := (not true)
-#123 := (iff #120 false)
-#124 := [rewrite]: #123
-#121 := (iff #29 #120)
-#118 := (iff #28 true)
-#113 := (= #27 #27)
-#116 := (iff #113 true)
-#117 := [rewrite]: #116
-#114 := (iff #28 #113)
-#110 := (= #25 3::Int)
-#105 := (ite false 0::Int 3::Int)
-#108 := (= #105 3::Int)
-#109 := [rewrite]: #108
-#106 := (= #25 #105)
-#103 := (= #24 3::Int)
-#77 := (and #15 #17)
-#80 := (or #16 #77)
-#98 := (ite #80 3::Int 3::Int)
-#101 := (= #98 3::Int)
-#102 := [rewrite]: #101
-#99 := (= #24 #98)
-#96 := (= #23 3::Int)
-#88 := -1::Int
-#85 := -3::Int
-#91 := (div -3::Int -1::Int)
-#94 := (= #91 3::Int)
-#95 := [rewrite]: #94
-#92 := (= #23 #91)
-#89 := (= #22 -1::Int)
+#12 := (f3 3::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 1::Int
+#10 := (f4 3::Int 1::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#747 := (= #10 3::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#33 := (f4 #32 #21)
+#878 := (pattern #33)
+#20 := 0::Int
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#188 := (div #182 #185)
+#360 := (* -1::Int #188)
+#361 := (+ #33 #360)
+#362 := (= #361 0::Int)
+#43 := (div #32 #21)
+#357 := (* -1::Int #43)
+#358 := (+ #33 #357)
+#359 := (= #358 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#363 := (ite #324 #359 #362)
+#356 := (= #33 0::Int)
+#35 := (= #21 0::Int)
+#34 := (= #32 0::Int)
+#36 := (or #34 #35)
+#364 := (ite #36 #356 #363)
+#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
+#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
+#882 := (iff #367 #879)
+#880 := (iff #364 #364)
+#881 := [refl]: #880
+#883 := [quant-intro #881]: #882
+#327 := (ite #324 #43 #188)
+#330 := (ite #36 0::Int #327)
+#333 := (= #33 #330)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#368 := (iff #336 #367)
+#365 := (iff #333 #364)
+#366 := [rewrite]: #365
+#369 := [quant-intro #366]: #368
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#230 := (ite #227 #43 #188)
+#233 := (ite #36 0::Int #230)
+#236 := (= #33 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#337 := (iff #239 #336)
+#334 := (iff #236 #333)
+#331 := (= #233 #330)
+#328 := (= #230 #327)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#329 := [monotonicity #326]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [quant-intro #335]: #337
+#299 := (~ #239 #239)
+#312 := (~ #236 #236)
+#313 := [refl]: #312
+#300 := [nnf-pos #313]: #299
+#45 := (- #21)
+#44 := (- #32)
+#46 := (div #44 #45)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#47 := (ite #42 #43 #46)
+#48 := (ite #36 0::Int #47)
+#49 := (= #33 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#242 := (iff #50 #239)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#191 := (ite #178 #43 #188)
+#169 := (= 0::Int #21)
+#166 := (= 0::Int #32)
+#172 := (or #166 #169)
+#194 := (ite #172 0::Int #191)
+#197 := (= #33 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#240 := (iff #200 #239)
+#237 := (iff #197 #236)
+#234 := (= #194 #233)
+#231 := (= #191 #230)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#232 := [monotonicity #229]: #231
+#207 := (iff #172 #36)
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#208 := [monotonicity #204 #206]: #207
+#235 := [monotonicity #208 #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#201 := (iff #50 #200)
+#198 := (iff #49 #197)
+#195 := (= #48 #194)
+#192 := (= #47 #191)
+#189 := (= #46 #188)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#190 := [monotonicity #184 #187]: #189
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#193 := [monotonicity #180 #190]: #192
+#173 := (iff #36 #172)
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#174 := [monotonicity #168 #171]: #173
+#196 := [monotonicity #174 #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
+#243 := [trans #202 #241]: #242
+#165 := [asserted]: #50
+#244 := [mp #165 #243]: #239
+#314 := [mp~ #244 #300]: #239
+#339 := [mp #314 #338]: #336
+#370 := [mp #339 #369]: #367
+#884 := [mp #370 #883]: #879
+#719 := (not #879)
+#720 := (or #719 #747)
+#814 := (* -1::Int 1::Int)
+#809 := (* -1::Int 3::Int)
+#810 := (div #809 #814)
+#815 := (* -1::Int #810)
+#816 := (+ #10 #815)
+#811 := (= #816 0::Int)
+#817 := (div 3::Int 1::Int)
+#658 := (* -1::Int #817)
+#659 := (+ #10 #658)
+#660 := (= #659 0::Int)
+#835 := (>= 3::Int 0::Int)
+#802 := (<= 1::Int 0::Int)
+#803 := (or #802 #835)
+#804 := (not #803)
+#805 := (<= 3::Int 0::Int)
+#799 := (or #805 #802)
+#800 := (not #799)
+#806 := (or #800 #804)
+#807 := (ite #806 #660 #811)
+#801 := (= #10 0::Int)
+#808 := (= 1::Int 0::Int)
+#637 := (= 3::Int 0::Int)
+#639 := (or #637 #808)
+#640 := (ite #639 #801 #807)
+#716 := (or #719 #640)
+#701 := (iff #716 #720)
+#702 := (iff #720 #720)
+#683 := [rewrite]: #702
+#715 := (iff #640 #747)
+#711 := (ite false #801 #747)
+#713 := (iff #711 #747)
+#714 := [rewrite]: #713
+#712 := (iff #640 #711)
+#599 := (iff #807 #747)
+#1 := true
+#725 := (ite true #747 #747)
+#705 := (iff #725 #747)
+#706 := [rewrite]: #705
+#731 := (iff #807 #725)
+#729 := (iff #811 #747)
+#767 := -3::Int
+#760 := (+ -3::Int #10)
+#744 := (= #760 0::Int)
+#748 := (iff #744 #747)
+#749 := [rewrite]: #748
+#727 := (iff #811 #744)
+#723 := (= #816 #760)
+#756 := (+ #10 -3::Int)
+#757 := (= #756 #760)
+#761 := [rewrite]: #757
+#726 := (= #816 #756)
+#734 := (= #815 -3::Int)
+#768 := (= #809 -3::Int)
+#764 := [rewrite]: #768
+#738 := (= #815 #809)
+#736 := (= #810 3::Int)
+#743 := (div -3::Int -1::Int)
+#733 := (= #743 3::Int)
+#735 := [rewrite]: #733
+#754 := (= #810 #743)
+#752 := (= #814 -1::Int)
+#753 := [rewrite]: #752
+#732 := [monotonicity #764 #753]: #754
+#737 := [trans #732 #735]: #736
+#739 := [monotonicity #737]: #738
+#740 := [trans #739 #764]: #734
+#722 := [monotonicity #740]: #726
+#724 := [trans #722 #761]: #723
+#728 := [monotonicity #724]: #727
+#730 := [trans #728 #749]: #729
+#750 := (iff #660 #747)
+#745 := (iff #660 #744)
+#741 := (= #659 #760)
+#758 := (= #659 #756)
+#769 := (= #658 -3::Int)
+#765 := (= #658 #809)
+#762 := (= #817 3::Int)
+#763 := [rewrite]: #762
+#766 := [monotonicity #763]: #765
+#755 := [trans #766 #764]: #769
+#759 := [monotonicity #755]: #758
+#742 := [trans #759 #761]: #741
+#746 := [monotonicity #742]: #745
+#751 := [trans #746 #749]: #750
+#771 := (iff #806 true)
+#785 := (or true false)
+#776 := (iff #785 true)
+#777 := [rewrite]: #776
+#774 := (iff #806 #785)
+#784 := (iff #804 false)
+#483 := (not true)
+#844 := (iff #483 false)
+#830 := [rewrite]: #844
+#782 := (iff #804 #483)
+#770 := (iff #803 true)
+#788 := (or false true)
+#781 := (iff #788 true)
+#773 := [rewrite]: #781
+#792 := (iff #803 #788)
+#842 := (iff #835 true)
+#482 := [rewrite]: #842
+#787 := (iff #802 false)
+#790 := [rewrite]: #787
+#779 := [monotonicity #790 #482]: #792
+#772 := [trans #779 #773]: #770
+#783 := [monotonicity #772]: #782
+#780 := [trans #783 #830]: #784
+#698 := (iff #800 true)
+#686 := (not false)
+#696 := (iff #686 true)
+#697 := [rewrite]: #696
+#694 := (iff #800 #686)
+#692 := (iff #799 false)
+#795 := (or false false)
+#681 := (iff #795 false)
+#682 := [rewrite]: #681
+#675 := (iff #799 #795)
+#691 := (iff #805 false)
+#786 := [rewrite]: #691
+#690 := [monotonicity #786 #790]: #675
+#693 := [trans #690 #682]: #692
+#695 := [monotonicity #693]: #694
+#791 := [trans #695 #697]: #698
+#775 := [monotonicity #791 #780]: #774
+#778 := [trans #775 #777]: #771
+#704 := [monotonicity #778 #751 #730]: #731
+#710 := [trans #704 #706]: #599
+#641 := (iff #639 false)
+#798 := (iff #639 #795)
+#796 := (iff #808 false)
+#797 := [rewrite]: #796
+#793 := (iff #637 false)
+#794 := [rewrite]: #793
+#680 := [monotonicity #794 #797]: #798
+#789 := [trans #680 #682]: #641
+#717 := [monotonicity #789 #710]: #712
+#718 := [trans #717 #714]: #715
+#647 := [monotonicity #718]: #701
+#707 := [trans #647 #683]: #701
+#721 := [quant-inst #8 #9]: #716
+#708 := [mp #721 #707]: #720
+#677 := [unit-resolution #708 #884]: #747
+#684 := [monotonicity #677]: #13
+#14 := (not #13)
+#79 := [asserted]: #14
+[unit-resolution #79 #684]: false
+unsat
+3563b0bf363f404d85eb515efc0ea6c63953194a 378 0
+#2 := false
+decl f3 :: (-> Int S2)
+decl f4 :: (-> Int Int Int)
+#10 := 1::Int
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#11 := (f4 #9 1::Int)
+#12 := (f3 #11)
+#80 := (= f6 #12)
+#451 := (f3 #9)
+#669 := (= #451 #12)
+#663 := (= #12 #451)
+#731 := (= #11 #9)
+#845 := (div #9 1::Int)
+#660 := (= #845 #9)
+#598 := (= #9 #845)
+#20 := 0::Int
+#188 := -1::Int
+#840 := (* -1::Int #845)
+#632 := (+ #9 #840)
+#638 := (<= #632 0::Int)
+#631 := (= #632 0::Int)
+#1 := true
+#77 := [true-axiom]: true
+#588 := (or false #631)
+#589 := [th-lemma arith]: #588
+#590 := [unit-resolution #589 #77]: #631
+#591 := (not #631)
+#592 := (or #591 #638)
+#593 := [th-lemma arith triangle-eq]: #592
+#594 := [unit-resolution #593 #590]: #638
+#481 := (>= #632 0::Int)
+#595 := (or #591 #481)
+#596 := [th-lemma arith triangle-eq]: #595
+#597 := [unit-resolution #596 #590]: #481
+#587 := [th-lemma arith eq-propagate 1 1 #597 #594]: #598
+#578 := [symm #587]: #660
+#604 := (= #11 #845)
+#846 := (+ #11 #840)
+#790 := (<= #846 0::Int)
+#484 := (= #846 0::Int)
+#562 := (= #9 0::Int)
+#776 := (not #562)
+#715 := (= 0::Int #9)
+#654 := [hypothesis]: #562
+#730 := [symm #654]: #715
+#560 := (= #11 0::Int)
+#709 := (or #776 #560)
+#514 := (* -1::Int #9)
+#644 := (div #514 -1::Int)
+#800 := (* -1::Int #644)
+#804 := (+ #11 #800)
+#687 := (= #804 0::Int)
+#850 := (<= #9 0::Int)
+#830 := (not #850)
+#847 := (>= #9 0::Int)
+#665 := (not #847)
+#812 := (or #665 #830)
+#648 := (ite #812 #484 #687)
+#793 := (ite #562 #560 #648)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#33 := (f4 #32 #21)
+#885 := (pattern #33)
+#192 := (* -1::Int #21)
+#189 := (* -1::Int #32)
+#195 := (div #189 #192)
+#367 := (* -1::Int #195)
+#368 := (+ #33 #367)
+#369 := (= #368 0::Int)
+#43 := (div #32 #21)
+#364 := (* -1::Int #43)
+#365 := (+ #33 #364)
+#366 := (= #365 0::Int)
+#227 := (>= #32 0::Int)
+#220 := (<= #21 0::Int)
+#327 := (or #220 #227)
+#328 := (not #327)
+#216 := (<= #32 0::Int)
+#325 := (or #216 #220)
+#326 := (not #325)
+#331 := (or #326 #328)
+#370 := (ite #331 #366 #369)
+#363 := (= #33 0::Int)
+#35 := (= #21 0::Int)
+#34 := (= #32 0::Int)
+#36 := (or #34 #35)
+#371 := (ite #36 #363 #370)
+#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #371)
+#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
+#889 := (iff #374 #886)
+#887 := (iff #371 #371)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#334 := (ite #331 #43 #195)
+#337 := (ite #36 0::Int #334)
+#340 := (= #33 #337)
+#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
+#375 := (iff #343 #374)
+#372 := (iff #340 #371)
+#373 := [rewrite]: #372
+#376 := [quant-intro #373]: #375
+#228 := (not #227)
+#221 := (not #220)
+#231 := (and #221 #228)
+#217 := (not #216)
+#224 := (and #217 #221)
+#234 := (or #224 #231)
+#237 := (ite #234 #43 #195)
+#240 := (ite #36 0::Int #237)
+#243 := (= #33 #240)
+#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
+#344 := (iff #246 #343)
+#341 := (iff #243 #340)
+#338 := (= #240 #337)
+#335 := (= #237 #334)
+#332 := (iff #234 #331)
+#329 := (iff #231 #328)
+#330 := [rewrite]: #329
+#310 := (iff #224 #326)
+#311 := [rewrite]: #310
+#333 := [monotonicity #311 #330]: #332
+#336 := [monotonicity #333]: #335
+#339 := [monotonicity #336]: #338
+#342 := [monotonicity #339]: #341
+#345 := [quant-intro #342]: #344
+#306 := (~ #246 #246)
+#319 := (~ #243 #243)
+#320 := [refl]: #319
+#307 := [nnf-pos #320]: #306
+#45 := (- #21)
+#44 := (- #32)
+#46 := (div #44 #45)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#47 := (ite #42 #43 #46)
+#48 := (ite #36 0::Int #47)
+#49 := (= #33 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#249 := (iff #50 #246)
+#182 := (and #38 #40)
+#185 := (or #39 #182)
+#198 := (ite #185 #43 #195)
+#176 := (= 0::Int #21)
+#173 := (= 0::Int #32)
+#179 := (or #173 #176)
+#201 := (ite #179 0::Int #198)
+#204 := (= #33 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#247 := (iff #207 #246)
+#244 := (iff #204 #243)
+#241 := (= #201 #240)
+#238 := (= #198 #237)
+#235 := (iff #185 #234)
+#232 := (iff #182 #231)
+#229 := (iff #40 #228)
+#230 := [rewrite]: #229
+#222 := (iff #38 #221)
+#223 := [rewrite]: #222
+#233 := [monotonicity #223 #230]: #232
+#225 := (iff #39 #224)
+#218 := (iff #37 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#236 := [monotonicity #226 #233]: #235
+#239 := [monotonicity #236]: #238
+#214 := (iff #179 #36)
+#212 := (iff #176 #35)
+#213 := [rewrite]: #212
+#210 := (iff #173 #34)
+#211 := [rewrite]: #210
+#215 := [monotonicity #211 #213]: #214
+#242 := [monotonicity #215 #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [quant-intro #245]: #247
+#208 := (iff #50 #207)
+#205 := (iff #49 #204)
+#202 := (= #48 #201)
+#199 := (= #47 #198)
+#196 := (= #46 #195)
+#193 := (= #45 #192)
+#194 := [rewrite]: #193
+#190 := (= #44 #189)
+#191 := [rewrite]: #190
+#197 := [monotonicity #191 #194]: #196
+#186 := (iff #42 #185)
+#183 := (iff #41 #182)
+#184 := [rewrite]: #183
+#187 := [monotonicity #184]: #186
+#200 := [monotonicity #187 #197]: #199
+#180 := (iff #36 #179)
+#177 := (iff #35 #176)
+#178 := [rewrite]: #177
+#174 := (iff #34 #173)
+#175 := [rewrite]: #174
+#181 := [monotonicity #175 #178]: #180
+#203 := [monotonicity #181 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#250 := [trans #209 #248]: #249
+#172 := [asserted]: #50
+#251 := [mp #172 #250]: #246
+#321 := [mp~ #251 #307]: #246
+#346 := [mp #321 #345]: #343
+#377 := [mp #346 #376]: #374
+#891 := [mp #377 #890]: #886
+#682 := (not #886)
+#697 := (or #682 #793)
+#854 := (* -1::Int 1::Int)
+#841 := (div #514 #854)
+#842 := (* -1::Int #841)
+#843 := (+ #11 #842)
+#844 := (= #843 0::Int)
+#849 := (<= 1::Int 0::Int)
+#489 := (or #849 #847)
+#490 := (not #489)
+#848 := (or #850 #849)
+#851 := (not #848)
+#837 := (or #851 #490)
+#838 := (ite #837 #484 #844)
+#561 := (= 1::Int 0::Int)
+#563 := (or #562 #561)
+#457 := (ite #563 #560 #838)
+#699 := (or #682 #457)
+#693 := (iff #699 #697)
+#702 := (iff #697 #697)
+#703 := [rewrite]: #702
+#794 := (iff #457 #793)
+#796 := (iff #838 #648)
+#688 := (iff #844 #687)
+#802 := (= #843 #804)
+#801 := (= #842 #800)
+#646 := (= #841 #644)
+#808 := (= #854 -1::Int)
+#815 := [rewrite]: #808
+#647 := [monotonicity #815]: #646
+#803 := [monotonicity #647]: #801
+#805 := [monotonicity #803]: #802
+#689 := [monotonicity #805]: #688
+#813 := (iff #837 #812)
+#809 := (or #830 #665)
+#806 := (iff #809 #812)
+#807 := [rewrite]: #806
+#810 := (iff #837 #809)
+#666 := (iff #490 #665)
+#818 := (iff #489 #847)
+#821 := (or false #847)
+#822 := (iff #821 #847)
+#823 := [rewrite]: #822
+#816 := (iff #489 #821)
+#547 := (iff #849 false)
+#548 := [rewrite]: #547
+#817 := [monotonicity #548]: #816
+#824 := [trans #817 #823]: #818
+#667 := [monotonicity #824]: #666
+#819 := (iff #851 #830)
+#829 := (iff #848 #850)
+#549 := (or #850 false)
+#543 := (iff #549 #850)
+#825 := [rewrite]: #543
+#827 := (iff #848 #549)
+#828 := [monotonicity #548]: #827
+#826 := [trans #828 #825]: #829
+#820 := [monotonicity #826]: #819
+#811 := [monotonicity #820 #667]: #810
+#814 := [trans #811 #807]: #813
+#698 := [monotonicity #814 #689]: #796
+#836 := (iff #563 #562)
+#556 := (or #562 false)
+#835 := (iff #556 #562)
+#832 := [rewrite]: #835
+#557 := (iff #563 #556)
+#833 := (iff #561 false)
+#834 := [rewrite]: #833
+#831 := [monotonicity #834]: #557
+#546 := [trans #831 #832]: #836
+#797 := [monotonicity #546 #698]: #794
+#701 := [monotonicity #797]: #693
+#704 := [trans #701 #703]: #693
+#700 := [quant-inst #9 #10]: #699
+#705 := [mp #700 #704]: #697
+#684 := [unit-resolution #705 #891]: #793
+#771 := (not #793)
+#762 := (or #771 #776 #560)
+#763 := [def-axiom]: #762
+#690 := [unit-resolution #763 #684]: #709
+#714 := [unit-resolution #690 #654]: #560
+#707 := [trans #714 #730]: #731
+#668 := [monotonicity #707]: #663
+#670 := [symm #668]: #669
+#535 := (= f6 #451)
+#15 := (:var 0 S2)
+#16 := (f5 #15)
+#864 := (pattern #16)
+#17 := (f3 #16)
+#87 := (= #15 #17)
+#865 := (forall (vars (?v0 S2)) (:pat #864) #87)
+#91 := (forall (vars (?v0 S2)) #87)
+#866 := (iff #91 #865)
+#868 := (iff #865 #865)
+#869 := [rewrite]: #868
+#867 := [rewrite]: #866
+#870 := [trans #867 #869]: #866
+#314 := (~ #91 #91)
+#312 := (~ #87 #87)
+#313 := [refl]: #312
+#315 := [nnf-pos #313]: #314
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S2)) #18)
+#92 := (iff #19 #91)
+#89 := (iff #18 #87)
#90 := [rewrite]: #89
-#86 := (= #21 -3::Int)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#97 := [trans #93 #95]: #96
-#83 := (= #20 3::Int)
-#84 := [rewrite]: #83
-#81 := (iff #19 #80)
-#78 := (iff #18 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#100 := [monotonicity #82 #84 #97]: #99
-#104 := [trans #100 #102]: #103
-#75 := (iff #13 false)
-#70 := (or false false)
-#73 := (iff #70 false)
-#74 := [rewrite]: #73
-#71 := (iff #13 #70)
-#68 := (iff #12 false)
-#69 := [rewrite]: #68
-#66 := (iff #10 false)
-#67 := [rewrite]: #66
-#72 := [monotonicity #67 #69]: #71
-#76 := [trans #72 #74]: #75
-#107 := [monotonicity #76 #104]: #106
-#111 := [trans #107 #109]: #110
-#112 := [monotonicity #111]: #28
-#115 := [monotonicity #112]: #114
-#119 := [trans #115 #117]: #118
-#122 := [monotonicity #119]: #121
-#126 := [trans #122 #124]: #125
-#65 := [asserted]: #29
-[mp #65 #126]: false
-unsat
-541d6fe80b1182e33d84e37f649671b9536f0b45 313 0
+#93 := [quant-intro #90]: #92
+#86 := [asserted]: #19
+#96 := [mp #86 #93]: #91
+#300 := [mp~ #96 #315]: #91
+#871 := [mp #300 #870]: #865
+#528 := (not #865)
+#539 := (or #528 #535)
+#540 := [quant-inst #8]: #539
+#662 := [unit-resolution #540 #871]: #535
+#671 := [trans #662 #670]: #80
+#83 := (not #80)
+#13 := (= #12 f6)
+#14 := (not #13)
+#84 := (iff #14 #83)
+#81 := (iff #13 #80)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#79 := [asserted]: #14
+#88 := [mp #79 #85]: #83
+#672 := [unit-resolution #88 #671]: false
+#673 := [lemma #672]: #776
+#706 := (or #562 #484)
+#780 := (not #812)
+#769 := (not #484)
+#710 := [hypothesis]: #769
+#716 := [hypothesis]: #776
+#691 := (or #562 #648)
+#765 := (or #771 #562 #648)
+#766 := [def-axiom]: #765
+#650 := [unit-resolution #766 #684]: #691
+#681 := [unit-resolution #650 #716]: #648
+#782 := (not #648)
+#783 := (or #782 #780 #484)
+#784 := [def-axiom]: #783
+#683 := [unit-resolution #784 #681 #710]: #780
+#786 := (or #812 #850)
+#788 := [def-axiom]: #786
+#685 := [unit-resolution #788 #683]: #850
+#795 := (or #812 #847)
+#799 := [def-axiom]: #795
+#692 := [unit-resolution #799 #683]: #847
+#694 := (or #562 #830 #665)
+#695 := [th-lemma arith triangle-eq]: #694
+#696 := [unit-resolution #695 #716 #692 #685]: false
+#686 := [lemma #696]: #706
+#610 := [unit-resolution #686 #673]: #484
+#613 := (or #769 #790)
+#614 := [th-lemma arith triangle-eq]: #613
+#600 := [unit-resolution #614 #610]: #790
+#791 := (>= #846 0::Int)
+#602 := (or #769 #791)
+#603 := [th-lemma arith triangle-eq]: #602
+#601 := [unit-resolution #603 #610]: #791
+#586 := [th-lemma arith eq-propagate 1 1 #601 #600]: #604
+#579 := [trans #586 #578]: #731
+#580 := [monotonicity #579]: #663
+#581 := [symm #580]: #669
+#582 := [trans #662 #581]: #80
+[unit-resolution #88 #582]: false
+unsat
+84bb282eead031ef4ff9718b6ca086d90bb4eefb 298 0
#2 := false
decl f3 :: (-> Int S2)
-#81 := -1::Int
+#8 := 0::Int
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 3::Int
+#10 := (f4 0::Int 3::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#806 := (= #10 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#32 := (f4 #31 #20)
+#878 := (pattern #32)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#187 := (div #181 #184)
+#359 := (* -1::Int #187)
+#360 := (+ #32 #359)
+#361 := (= #360 0::Int)
+#42 := (div #31 #20)
+#356 := (* -1::Int #42)
+#357 := (+ #32 #356)
+#358 := (= #357 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#362 := (ite #323 #358 #361)
+#355 := (= #32 0::Int)
+#34 := (= #20 0::Int)
+#33 := (= #31 0::Int)
+#35 := (or #33 #34)
+#363 := (ite #35 #355 #362)
+#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #363)
+#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
+#882 := (iff #366 #879)
+#880 := (iff #363 #363)
+#881 := [refl]: #880
+#883 := [quant-intro #881]: #882
+#326 := (ite #323 #42 #187)
+#329 := (ite #35 0::Int #326)
+#332 := (= #32 #329)
+#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
+#367 := (iff #335 #366)
+#364 := (iff #332 #363)
+#365 := [rewrite]: #364
+#368 := [quant-intro #365]: #367
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#229 := (ite #226 #42 #187)
+#232 := (ite #35 0::Int #229)
+#235 := (= #32 #232)
+#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
+#336 := (iff #238 #335)
+#333 := (iff #235 #332)
+#330 := (= #232 #329)
+#327 := (= #229 #326)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#328 := [monotonicity #325]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [quant-intro #334]: #336
+#298 := (~ #238 #238)
+#311 := (~ #235 #235)
+#312 := [refl]: #311
+#299 := [nnf-pos #312]: #298
+#44 := (- #20)
+#43 := (- #31)
+#45 := (div #43 #44)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#46 := (ite #41 #42 #45)
+#47 := (ite #35 0::Int #46)
+#48 := (= #32 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#241 := (iff #49 #238)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#190 := (ite #177 #42 #187)
+#168 := (= 0::Int #20)
+#165 := (= 0::Int #31)
+#171 := (or #165 #168)
+#193 := (ite #171 0::Int #190)
+#196 := (= #32 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#239 := (iff #199 #238)
+#236 := (iff #196 #235)
+#233 := (= #193 #232)
+#230 := (= #190 #229)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#231 := [monotonicity #228]: #230
+#206 := (iff #171 #35)
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#207 := [monotonicity #203 #205]: #206
+#234 := [monotonicity #207 #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [quant-intro #237]: #239
+#200 := (iff #49 #199)
+#197 := (iff #48 #196)
+#194 := (= #47 #193)
+#191 := (= #46 #190)
+#188 := (= #45 #187)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#189 := [monotonicity #183 #186]: #188
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#192 := [monotonicity #179 #189]: #191
+#172 := (iff #35 #171)
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#173 := [monotonicity #167 #170]: #172
+#195 := [monotonicity #173 #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
+#242 := [trans #201 #240]: #241
+#164 := [asserted]: #49
+#243 := [mp #164 #242]: #238
+#313 := [mp~ #243 #299]: #238
+#338 := [mp #313 #337]: #335
+#369 := [mp #338 #368]: #366
+#884 := [mp #369 #883]: #879
+#725 := (not #879)
+#731 := (or #725 #806)
+#812 := (* -1::Int 3::Int)
+#813 := (* -1::Int 0::Int)
+#814 := (div #813 #812)
+#809 := (* -1::Int #814)
+#810 := (+ #10 #809)
+#815 := (= #810 0::Int)
+#816 := (div 0::Int 3::Int)
+#811 := (* -1::Int #816)
+#817 := (+ #10 #811)
+#658 := (= #817 0::Int)
+#834 := (>= 0::Int 0::Int)
+#659 := (<= 3::Int 0::Int)
+#660 := (or #659 #834)
+#802 := (not #660)
+#803 := (<= 0::Int 0::Int)
+#804 := (or #803 #659)
+#805 := (not #804)
+#799 := (or #805 #802)
+#800 := (ite #799 #658 #815)
+#807 := (= 3::Int 0::Int)
+#801 := (= 0::Int 0::Int)
+#808 := (or #801 #807)
+#637 := (ite #808 #806 #800)
+#704 := (or #725 #637)
+#706 := (iff #704 #731)
+#710 := (iff #731 #731)
+#711 := [rewrite]: #710
+#729 := (iff #637 #806)
+#1 := true
+#722 := (ite true #806 #806)
+#727 := (iff #722 #806)
+#728 := [rewrite]: #727
+#723 := (iff #637 #722)
+#740 := (iff #800 #806)
+#736 := (ite false #806 #806)
+#739 := (iff #736 #806)
+#734 := [rewrite]: #739
+#737 := (iff #800 #736)
+#733 := (iff #815 #806)
+#754 := (= #810 #10)
+#766 := (+ #10 0::Int)
+#764 := (= #766 #10)
+#769 := [rewrite]: #764
+#753 := (= #810 #766)
+#751 := (= #809 0::Int)
+#778 := (= #813 0::Int)
+#762 := [rewrite]: #778
+#749 := (= #809 #813)
+#747 := (= #814 0::Int)
+#760 := -3::Int
+#741 := (div 0::Int -3::Int)
+#745 := (= #741 0::Int)
+#746 := [rewrite]: #745
+#742 := (= #814 #741)
+#757 := (= #812 -3::Int)
+#761 := [rewrite]: #757
+#744 := [monotonicity #762 #761]: #742
+#748 := [trans #744 #746]: #747
+#750 := [monotonicity #748]: #749
+#752 := [trans #750 #762]: #751
+#743 := [monotonicity #752]: #753
+#732 := [trans #743 #769]: #754
+#735 := [monotonicity #732]: #733
+#758 := (iff #658 #806)
+#755 := (= #817 #10)
+#767 := (= #817 #766)
+#763 := (= #811 0::Int)
+#777 := (= #811 #813)
+#775 := (= #816 0::Int)
+#776 := [rewrite]: #775
+#771 := [monotonicity #776]: #777
+#765 := [trans #771 #762]: #763
+#768 := [monotonicity #765]: #767
+#756 := [trans #768 #769]: #755
+#759 := [monotonicity #756]: #758
+#785 := (iff #799 false)
+#772 := (or false false)
+#784 := (iff #772 false)
+#780 := [rewrite]: #784
+#782 := (iff #799 #772)
+#773 := (iff #802 false)
+#482 := (not true)
+#841 := (iff #482 false)
+#844 := [rewrite]: #841
+#779 := (iff #802 #482)
+#788 := (iff #660 true)
+#695 := (or false true)
+#698 := (iff #695 true)
+#791 := [rewrite]: #698
+#696 := (iff #660 #695)
+#840 := (iff #834 true)
+#842 := [rewrite]: #840
+#691 := (iff #659 false)
+#786 := [rewrite]: #691
+#697 := [monotonicity #786 #842]: #696
+#792 := [trans #697 #791]: #788
+#781 := [monotonicity #792]: #779
+#770 := [trans #781 #844]: #773
+#686 := (iff #805 false)
+#692 := (iff #805 #482)
+#675 := (iff #804 true)
+#796 := (or true false)
+#798 := (iff #796 true)
+#680 := [rewrite]: #798
+#787 := (iff #804 #796)
+#641 := (iff #803 true)
+#789 := [rewrite]: #641
+#790 := [monotonicity #789 #786]: #787
+#690 := [trans #790 #680]: #675
+#693 := [monotonicity #690]: #692
+#694 := [trans #693 #844]: #686
+#783 := [monotonicity #694 #770]: #782
+#774 := [trans #783 #780]: #785
+#738 := [monotonicity #774 #759 #735]: #737
+#726 := [trans #738 #734]: #740
+#681 := (iff #808 true)
+#797 := (iff #808 #796)
+#793 := (iff #807 false)
+#794 := [rewrite]: #793
+#639 := (iff #801 true)
+#640 := [rewrite]: #639
+#795 := [monotonicity #640 #794]: #797
+#682 := [trans #795 #680]: #681
+#724 := [monotonicity #682 #726]: #723
+#730 := [trans #724 #728]: #729
+#599 := [monotonicity #730]: #706
+#712 := [trans #599 #711]: #706
+#705 := [quant-inst #8 #9]: #704
+#717 := [mp #705 #712]: #731
+#714 := [unit-resolution #717 #884]: #806
+#715 := [monotonicity #714]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #715]: false
+unsat
+753372d6275197bbef48a8ecc32b53d9fd3d1075 315 0
+#2 := false
+decl f3 :: (-> Int S2)
+#12 := 0::Int
+#13 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 3::Int
+#8 := 1::Int
+#10 := (f4 1::Int 3::Int)
+#11 := (f3 #10)
+#14 := (= #11 #13)
+#801 := (= #10 0::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#33 := (f4 #32 #21)
+#878 := (pattern #33)
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#188 := (div #182 #185)
+#360 := (* -1::Int #188)
+#361 := (+ #33 #360)
+#362 := (= #361 0::Int)
+#43 := (div #32 #21)
+#357 := (* -1::Int #43)
+#358 := (+ #33 #357)
+#359 := (= #358 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#363 := (ite #324 #359 #362)
+#356 := (= #33 0::Int)
+#35 := (= #21 0::Int)
+#34 := (= #32 0::Int)
+#36 := (or #34 #35)
+#364 := (ite #36 #356 #363)
+#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
+#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
+#882 := (iff #367 #879)
+#880 := (iff #364 #364)
+#881 := [refl]: #880
+#883 := [quant-intro #881]: #882
+#327 := (ite #324 #43 #188)
+#330 := (ite #36 0::Int #327)
+#333 := (= #33 #330)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#368 := (iff #336 #367)
+#365 := (iff #333 #364)
+#366 := [rewrite]: #365
+#369 := [quant-intro #366]: #368
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#230 := (ite #227 #43 #188)
+#233 := (ite #36 0::Int #230)
+#236 := (= #33 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#337 := (iff #239 #336)
+#334 := (iff #236 #333)
+#331 := (= #233 #330)
+#328 := (= #230 #327)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#329 := [monotonicity #326]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [quant-intro #335]: #337
+#299 := (~ #239 #239)
+#312 := (~ #236 #236)
+#313 := [refl]: #312
+#300 := [nnf-pos #313]: #299
+#45 := (- #21)
+#44 := (- #32)
+#46 := (div #44 #45)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#47 := (ite #42 #43 #46)
+#48 := (ite #36 0::Int #47)
+#49 := (= #33 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#242 := (iff #50 #239)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#191 := (ite #178 #43 #188)
+#169 := (= 0::Int #21)
+#166 := (= 0::Int #32)
+#172 := (or #166 #169)
+#194 := (ite #172 0::Int #191)
+#197 := (= #33 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#240 := (iff #200 #239)
+#237 := (iff #197 #236)
+#234 := (= #194 #233)
+#231 := (= #191 #230)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#232 := [monotonicity #229]: #231
+#207 := (iff #172 #36)
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#208 := [monotonicity #204 #206]: #207
+#235 := [monotonicity #208 #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#201 := (iff #50 #200)
+#198 := (iff #49 #197)
+#195 := (= #48 #194)
+#192 := (= #47 #191)
+#189 := (= #46 #188)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#190 := [monotonicity #184 #187]: #189
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#193 := [monotonicity #180 #190]: #192
+#173 := (iff #36 #172)
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#174 := [monotonicity #168 #171]: #173
+#196 := [monotonicity #174 #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
+#243 := [trans #202 #241]: #242
+#165 := [asserted]: #50
+#244 := [mp #165 #243]: #239
+#314 := [mp~ #244 #300]: #239
+#339 := [mp #314 #338]: #336
+#370 := [mp #339 #369]: #367
+#884 := [mp #370 #883]: #879
+#702 := (not #879)
+#683 := (or #702 #801)
+#813 := (* -1::Int 3::Int)
+#814 := (* -1::Int 1::Int)
+#809 := (div #814 #813)
+#810 := (* -1::Int #809)
+#815 := (+ #10 #810)
+#816 := (= #815 0::Int)
+#811 := (div 1::Int 3::Int)
+#817 := (* -1::Int #811)
+#658 := (+ #10 #817)
+#659 := (= #658 0::Int)
+#660 := (>= 1::Int 0::Int)
+#802 := (<= 3::Int 0::Int)
+#803 := (or #802 #660)
+#804 := (not #803)
+#805 := (<= 1::Int 0::Int)
+#799 := (or #805 #802)
+#800 := (not #799)
+#806 := (or #800 #804)
+#807 := (ite #806 #659 #816)
+#808 := (= 3::Int 0::Int)
+#637 := (= 1::Int 0::Int)
+#639 := (or #637 #808)
+#640 := (ite #639 #801 #807)
+#707 := (or #702 #640)
+#703 := (iff #707 #683)
+#677 := (iff #683 #683)
+#684 := [rewrite]: #677
+#701 := (iff #640 #801)
+#718 := (ite false #801 #801)
+#716 := (iff #718 #801)
+#721 := [rewrite]: #716
+#719 := (iff #640 #718)
+#714 := (iff #807 #801)
+#731 := (= #10 1::Int)
+#1 := true
+#710 := (ite true #801 #731)
+#717 := (iff #710 #801)
+#713 := [rewrite]: #717
+#711 := (iff #807 #710)
+#706 := (iff #816 #731)
+#722 := (+ -1::Int #10)
+#729 := (= #722 0::Int)
+#704 := (iff #729 #731)
+#705 := [rewrite]: #704
+#730 := (iff #816 #729)
+#727 := (= #815 #722)
+#734 := (+ #10 -1::Int)
+#723 := (= #734 #722)
+#724 := [rewrite]: #723
+#740 := (= #815 #734)
+#738 := (= #810 -1::Int)
+#747 := (= #814 -1::Int)
+#748 := [rewrite]: #747
+#736 := (= #810 #814)
+#733 := (= #809 1::Int)
+#749 := -3::Int
+#752 := (div -1::Int -3::Int)
+#754 := (= #752 1::Int)
+#732 := [rewrite]: #754
+#753 := (= #809 #752)
+#750 := (= #813 -3::Int)
+#751 := [rewrite]: #750
+#743 := [monotonicity #748 #751]: #753
+#735 := [trans #743 #732]: #733
+#737 := [monotonicity #735]: #736
+#739 := [trans #737 #748]: #738
+#726 := [monotonicity #739]: #740
+#728 := [trans #726 #724]: #727
+#725 := [monotonicity #728]: #730
+#599 := [trans #725 #705]: #706
+#745 := (iff #659 #801)
+#742 := (= #658 #10)
+#759 := (+ #10 0::Int)
+#761 := (= #759 #10)
+#741 := [rewrite]: #761
+#760 := (= #658 #759)
+#756 := (= #817 0::Int)
+#767 := (* -1::Int 0::Int)
+#769 := (= #767 0::Int)
+#755 := [rewrite]: #769
+#768 := (= #817 #767)
+#765 := (= #811 0::Int)
+#766 := [rewrite]: #765
+#764 := [monotonicity #766]: #768
+#758 := [trans #764 #755]: #756
+#757 := [monotonicity #758]: #760
+#744 := [trans #757 #741]: #742
+#746 := [monotonicity #744]: #745
+#762 := (iff #806 true)
+#775 := (or true false)
+#771 := (iff #775 true)
+#778 := [rewrite]: #771
+#776 := (iff #806 #775)
+#785 := (iff #804 false)
+#483 := (not true)
+#844 := (iff #483 false)
+#830 := [rewrite]: #844
+#784 := (iff #804 #483)
+#782 := (iff #803 true)
+#779 := (or false true)
+#770 := (iff #779 true)
+#772 := [rewrite]: #770
+#781 := (iff #803 #779)
+#788 := (iff #660 true)
+#792 := [rewrite]: #788
+#787 := (iff #802 false)
+#790 := [rewrite]: #787
+#773 := [monotonicity #790 #792]: #781
+#783 := [trans #773 #772]: #782
+#780 := [monotonicity #783]: #784
+#774 := [trans #780 #830]: #785
+#698 := (iff #800 true)
+#686 := (not false)
+#696 := (iff #686 true)
+#697 := [rewrite]: #696
+#694 := (iff #800 #686)
+#692 := (iff #799 false)
+#795 := (or false false)
+#681 := (iff #795 false)
+#682 := [rewrite]: #681
+#675 := (iff #799 #795)
+#691 := (iff #805 false)
+#786 := [rewrite]: #691
+#690 := [monotonicity #786 #790]: #675
+#693 := [trans #690 #682]: #692
+#695 := [monotonicity #693]: #694
+#791 := [trans #695 #697]: #698
+#777 := [monotonicity #791 #774]: #776
+#763 := [trans #777 #778]: #762
+#712 := [monotonicity #763 #746 #599]: #711
+#715 := [trans #712 #713]: #714
+#641 := (iff #639 false)
+#798 := (iff #639 #795)
+#796 := (iff #808 false)
+#797 := [rewrite]: #796
+#793 := (iff #637 false)
+#794 := [rewrite]: #793
+#680 := [monotonicity #794 #797]: #798
+#789 := [trans #680 #682]: #641
+#720 := [monotonicity #789 #715]: #719
+#647 := [trans #720 #721]: #701
+#709 := [monotonicity #647]: #703
+#643 := [trans #709 #684]: #703
+#708 := [quant-inst #8 #9]: #707
+#674 := [mp #708 #643]: #683
+#678 := [unit-resolution #674 #884]: #801
+#685 := [monotonicity #678]: #14
+#15 := (not #14)
+#79 := [asserted]: #15
+[unit-resolution #79 #685]: false
+unsat
+c4211064b5728b62240cb2d0bc31b06836a1e3c1 305 0
+#2 := false
+decl f3 :: (-> Int S2)
+#11 := 1::Int
+#12 := (f3 1::Int)
+decl f4 :: (-> Int Int Int)
+#8 := 3::Int
+#9 := (f4 3::Int 3::Int)
+#10 := (f3 #9)
+#13 := (= #10 #12)
+#742 := (= #9 1::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#33 := (f4 #32 #21)
+#878 := (pattern #33)
+#20 := 0::Int
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#188 := (div #182 #185)
+#360 := (* -1::Int #188)
+#361 := (+ #33 #360)
+#362 := (= #361 0::Int)
+#43 := (div #32 #21)
+#357 := (* -1::Int #43)
+#358 := (+ #33 #357)
+#359 := (= #358 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#363 := (ite #324 #359 #362)
+#356 := (= #33 0::Int)
+#35 := (= #21 0::Int)
+#34 := (= #32 0::Int)
+#36 := (or #34 #35)
+#364 := (ite #36 #356 #363)
+#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
+#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
+#882 := (iff #367 #879)
+#880 := (iff #364 #364)
+#881 := [refl]: #880
+#883 := [quant-intro #881]: #882
+#327 := (ite #324 #43 #188)
+#330 := (ite #36 0::Int #327)
+#333 := (= #33 #330)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#368 := (iff #336 #367)
+#365 := (iff #333 #364)
+#366 := [rewrite]: #365
+#369 := [quant-intro #366]: #368
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#230 := (ite #227 #43 #188)
+#233 := (ite #36 0::Int #230)
+#236 := (= #33 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#337 := (iff #239 #336)
+#334 := (iff #236 #333)
+#331 := (= #233 #330)
+#328 := (= #230 #327)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#329 := [monotonicity #326]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [quant-intro #335]: #337
+#299 := (~ #239 #239)
+#312 := (~ #236 #236)
+#313 := [refl]: #312
+#300 := [nnf-pos #313]: #299
+#45 := (- #21)
+#44 := (- #32)
+#46 := (div #44 #45)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#47 := (ite #42 #43 #46)
+#48 := (ite #36 0::Int #47)
+#49 := (= #33 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#242 := (iff #50 #239)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#191 := (ite #178 #43 #188)
+#169 := (= 0::Int #21)
+#166 := (= 0::Int #32)
+#172 := (or #166 #169)
+#194 := (ite #172 0::Int #191)
+#197 := (= #33 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#240 := (iff #200 #239)
+#237 := (iff #197 #236)
+#234 := (= #194 #233)
+#231 := (= #191 #230)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#232 := [monotonicity #229]: #231
+#207 := (iff #172 #36)
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#208 := [monotonicity #204 #206]: #207
+#235 := [monotonicity #208 #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#201 := (iff #50 #200)
+#198 := (iff #49 #197)
+#195 := (= #48 #194)
+#192 := (= #47 #191)
+#189 := (= #46 #188)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#190 := [monotonicity #184 #187]: #189
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#193 := [monotonicity #180 #190]: #192
+#173 := (iff #36 #172)
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#174 := [monotonicity #168 #171]: #173
+#196 := [monotonicity #174 #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
+#243 := [trans #202 #241]: #242
+#165 := [asserted]: #50
+#244 := [mp #165 #243]: #239
+#314 := [mp~ #244 #300]: #239
+#339 := [mp #314 #338]: #336
+#370 := [mp #339 #369]: #367
+#884 := [mp #370 #883]: #879
+#714 := (not #879)
+#715 := (or #714 #742)
+#814 := (* -1::Int 3::Int)
+#809 := (div #814 #814)
+#810 := (* -1::Int #809)
+#815 := (+ #9 #810)
+#816 := (= #815 0::Int)
+#811 := (div 3::Int 3::Int)
+#817 := (* -1::Int #811)
+#658 := (+ #9 #817)
+#659 := (= #658 0::Int)
+#660 := (>= 3::Int 0::Int)
+#802 := (<= 3::Int 0::Int)
+#803 := (or #802 #660)
+#804 := (not #803)
+#805 := (or #802 #802)
+#799 := (not #805)
+#800 := (or #799 #804)
+#806 := (ite #800 #659 #816)
+#807 := (= #9 0::Int)
+#801 := (= 3::Int 0::Int)
+#808 := (or #801 #801)
+#637 := (ite #808 #807 #806)
+#718 := (or #714 #637)
+#720 := (iff #718 #715)
+#721 := (iff #715 #715)
+#701 := [rewrite]: #721
+#717 := (iff #637 #742)
+#706 := (ite false #807 #742)
+#711 := (iff #706 #742)
+#712 := [rewrite]: #711
+#599 := (iff #637 #706)
+#704 := (iff #806 #742)
+#1 := true
+#728 := (ite true #742 #742)
+#725 := (iff #728 #742)
+#731 := [rewrite]: #725
+#729 := (iff #806 #728)
+#724 := (iff #816 #742)
+#755 := (+ -1::Int #9)
+#757 := (= #755 0::Int)
+#744 := (iff #757 #742)
+#745 := [rewrite]: #744
+#722 := (iff #816 #757)
+#740 := (= #815 #755)
+#768 := (+ #9 -1::Int)
+#756 := (= #768 #755)
+#758 := [rewrite]: #756
+#739 := (= #815 #768)
+#737 := (= #810 -1::Int)
+#771 := (* -1::Int 1::Int)
+#763 := (= #771 -1::Int)
+#765 := [rewrite]: #763
+#735 := (= #810 #771)
+#732 := (= #809 1::Int)
+#748 := -3::Int
+#751 := (div -3::Int -3::Int)
+#743 := (= #751 1::Int)
+#754 := [rewrite]: #743
+#752 := (= #809 #751)
+#749 := (= #814 -3::Int)
+#750 := [rewrite]: #749
+#753 := [monotonicity #750 #750]: #752
+#733 := [trans #753 #754]: #732
+#736 := [monotonicity #733]: #735
+#738 := [trans #736 #765]: #737
+#734 := [monotonicity #738]: #739
+#726 := [trans #734 #758]: #740
+#723 := [monotonicity #726]: #722
+#727 := [trans #723 #745]: #724
+#746 := (iff #659 #742)
+#761 := (iff #659 #757)
+#759 := (= #658 #755)
+#764 := (= #658 #768)
+#766 := (= #817 -1::Int)
+#778 := (= #817 #771)
+#776 := (= #811 1::Int)
+#777 := [rewrite]: #776
+#762 := [monotonicity #777]: #778
+#767 := [trans #762 #765]: #766
+#769 := [monotonicity #767]: #764
+#760 := [trans #769 #758]: #759
+#741 := [monotonicity #760]: #761
+#747 := [trans #741 #745]: #746
+#774 := (iff #800 true)
+#782 := (or true false)
+#780 := (iff #782 true)
+#785 := [rewrite]: #780
+#783 := (iff #800 #782)
+#770 := (iff #804 false)
+#483 := (not true)
+#844 := (iff #483 false)
+#830 := [rewrite]: #844
+#781 := (iff #804 #483)
+#792 := (iff #803 true)
+#696 := (or false true)
+#791 := (iff #696 true)
+#788 := [rewrite]: #791
+#697 := (iff #803 #696)
+#694 := (iff #660 true)
+#695 := [rewrite]: #694
+#681 := (iff #802 false)
+#682 := [rewrite]: #681
+#698 := [monotonicity #682 #695]: #697
+#779 := [trans #698 #788]: #792
+#773 := [monotonicity #779]: #781
+#772 := [trans #773 #830]: #770
+#693 := (iff #799 true)
+#787 := (not false)
+#690 := (iff #787 true)
+#692 := [rewrite]: #690
+#790 := (iff #799 #787)
+#691 := (iff #805 false)
+#793 := (or false false)
+#797 := (iff #793 false)
+#795 := [rewrite]: #797
+#641 := (iff #805 #793)
+#789 := [monotonicity #682 #682]: #641
+#786 := [trans #789 #795]: #691
+#675 := [monotonicity #786]: #790
+#686 := [trans #675 #692]: #693
+#784 := [monotonicity #686 #772]: #783
+#775 := [trans #784 #785]: #774
+#730 := [monotonicity #775 #747 #727]: #729
+#705 := [trans #730 #731]: #704
+#798 := (iff #808 false)
+#794 := (iff #808 #793)
+#639 := (iff #801 false)
+#640 := [rewrite]: #639
+#796 := [monotonicity #640 #640]: #794
+#680 := [trans #796 #795]: #798
+#710 := [monotonicity #680 #705]: #599
+#713 := [trans #710 #712]: #717
+#716 := [monotonicity #713]: #720
+#647 := [trans #716 #701]: #720
+#719 := [quant-inst #8 #8]: #718
+#702 := [mp #719 #647]: #715
+#708 := [unit-resolution #702 #884]: #742
+#703 := [monotonicity #708]: #13
+#14 := (not #13)
+#79 := [asserted]: #14
+[unit-resolution #79 #703]: false
+unsat
+c8c3466ffe36eb7d0f579df3f5c17ffb47bc161f 459 0
+#2 := false
+#19 := 0::Int
+#10 := 3::Int
decl f4 :: (-> S2 Int)
decl f5 :: S2
#8 := f5
#9 := (f4 f5)
-#82 := (* -1::Int #9)
-#87 := (div #82 -1::Int)
-#12 := 1::Int
-#21 := (div #9 1::Int)
-#10 := 0::Int
-#123 := (>= #9 0::Int)
-#124 := (not #123)
-#110 := (<= #9 0::Int)
-#111 := (not #110)
-#134 := (or #111 #124)
-#137 := (ite #134 #21 #87)
-#11 := (= #9 0::Int)
-#140 := (ite #11 0::Int #137)
-#143 := (f3 #140)
-#146 := (= f5 #143)
-#725 := (f3 #9)
-#688 := (= #725 #143)
-#691 := (= #143 #725)
-#411 := (= #140 #9)
-#602 := (= #9 #140)
-#510 := (* -1::Int #21)
-#663 := (+ #9 #510)
-#668 := (<= #663 0::Int)
-#509 := (= #663 0::Int)
-#1 := true
-#63 := [true-axiom]: true
-#653 := (or false #509)
-#654 := [th-lemma arith]: #653
-#650 := [unit-resolution #654 #63]: #509
-#655 := (not #509)
-#644 := (or #655 #668)
-#645 := [th-lemma arith triangle-eq]: #644
-#646 := [unit-resolution #645 #650]: #668
-#550 := (>= #663 0::Int)
-#647 := (or #655 #550)
-#641 := [th-lemma arith triangle-eq]: #647
-#648 := [unit-resolution #641 #650]: #550
-#643 := (* -1::Int #140)
-#640 := (+ #21 #643)
-#642 := (<= #640 0::Int)
-#651 := (= #21 #140)
-#398 := (= #137 #140)
-#389 := (not #11)
-#409 := (= 0::Int #9)
-#695 := [hypothesis]: #11
-#410 := [symm #695]: #409
-#313 := (= #140 0::Int)
-#390 := (or #389 #313)
-#722 := [def-axiom]: #390
-#699 := [unit-resolution #722 #695]: #313
-#412 := [trans #699 #410]: #411
-#406 := [monotonicity #412]: #691
-#692 := [symm #406]: #688
-#720 := (= f5 #725)
-#30 := (:var 0 S2)
-#31 := (f4 #30)
-#727 := (pattern #31)
-#32 := (f3 #31)
-#156 := (= #30 #32)
-#728 := (forall (vars (?v0 S2)) (:pat #727) #156)
-#159 := (forall (vars (?v0 S2)) #156)
-#729 := (iff #159 #728)
-#731 := (iff #728 #728)
-#732 := [rewrite]: #731
-#730 := [rewrite]: #729
-#733 := [trans #730 #732]: #729
-#253 := (~ #159 #159)
-#251 := (~ #156 #156)
-#252 := [refl]: #251
-#254 := [nnf-pos #252]: #253
-#33 := (= #32 #30)
-#34 := (forall (vars (?v0 S2)) #33)
-#160 := (iff #34 #159)
-#157 := (iff #33 #156)
-#158 := [rewrite]: #157
-#161 := [quant-intro #158]: #160
-#155 := [asserted]: #34
-#164 := [mp #155 #161]: #159
-#243 := [mp~ #164 #254]: #159
-#734 := [mp #243 #733]: #728
-#376 := (not #728)
-#381 := (or #376 #720)
-#717 := [quant-inst #8]: #381
-#690 := [unit-resolution #717 #734]: #720
-#689 := [trans #690 #692]: #146
-#149 := (not #146)
-#23 := (- 1::Int)
-#22 := (- #9)
-#24 := (div #22 #23)
-#16 := (< 0::Int 1::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= 1::Int 0::Int)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (f3 #26)
-#28 := (= #27 f5)
-#29 := (not #28)
-#152 := (iff #29 #149)
-#75 := (and #16 #18)
-#78 := (or #17 #75)
-#90 := (ite #78 #21 #87)
-#93 := (ite #11 0::Int #90)
-#96 := (f3 #93)
-#102 := (= f5 #96)
-#107 := (not #102)
-#150 := (iff #107 #149)
-#147 := (iff #102 #146)
-#144 := (= #96 #143)
-#141 := (= #93 #140)
-#138 := (= #90 #137)
-#135 := (iff #78 #134)
-#132 := (iff #75 #124)
-#127 := (and true #124)
-#130 := (iff #127 #124)
-#131 := [rewrite]: #130
-#128 := (iff #75 #127)
-#125 := (iff #18 #124)
-#126 := [rewrite]: #125
-#114 := (iff #16 true)
-#115 := [rewrite]: #114
-#129 := [monotonicity #115 #126]: #128
-#133 := [trans #129 #131]: #132
-#121 := (iff #17 #111)
-#116 := (and #111 true)
-#119 := (iff #116 #111)
-#120 := [rewrite]: #119
-#117 := (iff #17 #116)
-#112 := (iff #15 #111)
-#113 := [rewrite]: #112
-#118 := [monotonicity #113 #115]: #117
-#122 := [trans #118 #120]: #121
-#136 := [monotonicity #122 #133]: #135
+#807 := (mod #9 3::Int)
+#81 := -1::Int
+#753 := (* -1::Int #807)
+#523 := (div #9 3::Int)
+#549 := -3::Int
+#751 := (* -3::Int #523)
+#754 := (+ #751 #753)
+#755 := (+ #9 #754)
+#750 := (= #755 0::Int)
+#1 := true
+#76 := [true-axiom]: true
+#719 := (or false #750)
+#720 := [th-lemma arith]: #719
+#721 := [unit-resolution #720 #76]: #750
+#759 := (>= #755 0::Int)
+#662 := (not #759)
+#760 := (>= #807 0::Int)
+#664 := (or false #760)
+#665 := [th-lemma arith]: #664
+#670 := [unit-resolution #665 #76]: #760
+decl f3 :: (-> Int Int Int)
+#11 := (f3 #9 3::Int)
+#84 := (* -1::Int #11)
+#85 := (+ #9 #84)
+#83 := (>= #85 0::Int)
+#87 := (not #83)
+#12 := (<= #11 #9)
+#13 := (not #12)
+#88 := (iff #13 #87)
+#82 := (iff #12 #83)
+#86 := [rewrite]: #82
+#89 := [monotonicity #86]: #88
+#78 := [asserted]: #13
+#90 := [mp #78 #89]: #87
+#858 := (* -1::Int #523)
+#860 := (+ #11 #858)
+#689 := (<= #860 0::Int)
+#517 := (= #860 0::Int)
+#539 := (* -1::Int #9)
+#829 := (div #539 -3::Int)
+#827 := (* -1::Int #829)
+#832 := (+ #11 #827)
+#823 := (= #832 0::Int)
+#861 := (<= #9 0::Int)
+#491 := (not #861)
+#647 := (>= #9 0::Int)
+#565 := (not #647)
+#833 := (or #565 #491)
+#824 := (ite #833 #517 #823)
+#515 := (= #9 0::Int)
+#706 := (not #515)
+#817 := (<= #11 0::Int)
+#865 := (= #11 0::Int)
+#740 := [hypothesis]: #515
+#713 := (or #706 #865)
+#826 := (ite #515 #865 #824)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#32 := (f3 #31 #20)
+#887 := (pattern #32)
+#193 := (* -1::Int #20)
+#190 := (* -1::Int #31)
+#196 := (div #190 #193)
+#368 := (* -1::Int #196)
+#369 := (+ #32 #368)
+#370 := (= #369 0::Int)
+#42 := (div #31 #20)
+#365 := (* -1::Int #42)
+#366 := (+ #32 #365)
+#367 := (= #366 0::Int)
+#228 := (>= #31 0::Int)
+#221 := (<= #20 0::Int)
+#328 := (or #221 #228)
+#329 := (not #328)
+#217 := (<= #31 0::Int)
+#326 := (or #217 #221)
+#327 := (not #326)
+#332 := (or #327 #329)
+#371 := (ite #332 #367 #370)
+#364 := (= #32 0::Int)
+#34 := (= #20 0::Int)
+#33 := (= #31 0::Int)
+#35 := (or #33 #34)
+#372 := (ite #35 #364 #371)
+#888 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #887) #372)
+#375 := (forall (vars (?v0 Int) (?v1 Int)) #372)
+#891 := (iff #375 #888)
+#889 := (iff #372 #372)
+#890 := [refl]: #889
+#892 := [quant-intro #890]: #891
+#335 := (ite #332 #42 #196)
+#338 := (ite #35 0::Int #335)
+#341 := (= #32 #338)
+#344 := (forall (vars (?v0 Int) (?v1 Int)) #341)
+#376 := (iff #344 #375)
+#373 := (iff #341 #372)
+#374 := [rewrite]: #373
+#377 := [quant-intro #374]: #376
+#229 := (not #228)
+#222 := (not #221)
+#232 := (and #222 #229)
+#218 := (not #217)
+#225 := (and #218 #222)
+#235 := (or #225 #232)
+#238 := (ite #235 #42 #196)
+#241 := (ite #35 0::Int #238)
+#244 := (= #32 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#345 := (iff #247 #344)
+#342 := (iff #244 #341)
+#339 := (= #241 #338)
+#336 := (= #238 #335)
+#333 := (iff #235 #332)
+#330 := (iff #232 #329)
+#331 := [rewrite]: #330
+#311 := (iff #225 #327)
+#312 := [rewrite]: #311
+#334 := [monotonicity #312 #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [monotonicity #337]: #339
+#343 := [monotonicity #340]: #342
+#346 := [quant-intro #343]: #345
+#307 := (~ #247 #247)
+#320 := (~ #244 #244)
+#321 := [refl]: #320
+#308 := [nnf-pos #321]: #307
+#44 := (- #20)
+#43 := (- #31)
+#45 := (div #43 #44)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#46 := (ite #41 #42 #45)
+#47 := (ite #35 0::Int #46)
+#48 := (= #32 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#250 := (iff #49 #247)
+#184 := (and #37 #39)
+#187 := (or #38 #184)
+#199 := (ite #187 #42 #196)
+#178 := (= 0::Int #20)
+#175 := (= 0::Int #31)
+#181 := (or #175 #178)
+#202 := (ite #181 0::Int #199)
+#205 := (= #32 #202)
+#208 := (forall (vars (?v0 Int) (?v1 Int)) #205)
+#248 := (iff #208 #247)
+#245 := (iff #205 #244)
+#242 := (= #202 #241)
+#239 := (= #199 #238)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#230 := (iff #39 #229)
+#231 := [rewrite]: #230
+#223 := (iff #37 #222)
+#224 := [rewrite]: #223
+#234 := [monotonicity #224 #231]: #233
+#226 := (iff #38 #225)
+#219 := (iff #36 #218)
+#220 := [rewrite]: #219
+#227 := [monotonicity #220 #224]: #226
+#237 := [monotonicity #227 #234]: #236
+#240 := [monotonicity #237]: #239
+#215 := (iff #181 #35)
+#213 := (iff #178 #34)
+#214 := [rewrite]: #213
+#211 := (iff #175 #33)
+#212 := [rewrite]: #211
+#216 := [monotonicity #212 #214]: #215
+#243 := [monotonicity #216 #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#209 := (iff #49 #208)
+#206 := (iff #48 #205)
+#203 := (= #47 #202)
+#200 := (= #46 #199)
+#197 := (= #45 #196)
+#194 := (= #44 #193)
+#195 := [rewrite]: #194
+#191 := (= #43 #190)
+#192 := [rewrite]: #191
+#198 := [monotonicity #192 #195]: #197
+#188 := (iff #41 #187)
+#185 := (iff #40 #184)
+#186 := [rewrite]: #185
+#189 := [monotonicity #186]: #188
+#201 := [monotonicity #189 #198]: #200
+#182 := (iff #35 #181)
+#179 := (iff #34 #178)
+#180 := [rewrite]: #179
+#176 := (iff #33 #175)
+#177 := [rewrite]: #176
+#183 := [monotonicity #177 #180]: #182
+#204 := [monotonicity #183 #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [quant-intro #207]: #209
+#251 := [trans #210 #249]: #250
+#174 := [asserted]: #49
+#252 := [mp #174 #251]: #247
+#322 := [mp~ #252 #308]: #247
+#347 := [mp #322 #346]: #344
+#378 := [mp #347 #377]: #375
+#893 := [mp #378 #892]: #888
+#669 := (not #888)
+#811 := (or #669 #826)
+#538 := (* -1::Int 3::Int)
+#470 := (div #539 #538)
+#543 := (* -1::Int #470)
+#540 := (+ #11 #543)
+#544 := (= #540 0::Int)
+#854 := (<= 3::Int 0::Int)
+#528 := (or #854 #647)
+#529 := (not #528)
+#862 := (or #861 #854)
+#863 := (not #862)
+#864 := (or #863 #529)
+#859 := (ite #864 #517 #544)
+#855 := (= 3::Int 0::Int)
+#520 := (or #515 #855)
+#856 := (ite #520 #865 #859)
+#812 := (or #669 #856)
+#814 := (iff #812 #811)
+#809 := (iff #811 #811)
+#815 := [rewrite]: #809
+#667 := (iff #856 #826)
+#825 := (iff #859 #824)
+#818 := (iff #544 #823)
+#821 := (= #540 #832)
+#831 := (= #543 #827)
+#830 := (= #470 #829)
+#550 := (= #538 -3::Int)
+#551 := [rewrite]: #550
+#545 := [monotonicity #551]: #830
+#828 := [monotonicity #545]: #831
+#822 := [monotonicity #828]: #821
+#819 := [monotonicity #822]: #818
+#838 := (iff #864 #833)
+#836 := (or #491 #565)
+#837 := (iff #836 #833)
+#834 := [rewrite]: #837
+#558 := (iff #864 #836)
+#458 := (iff #529 #565)
+#563 := (iff #528 #647)
+#850 := (or false #647)
+#840 := (iff #850 #647)
+#562 := [rewrite]: #840
+#853 := (iff #528 #850)
+#844 := (iff #854 false)
+#845 := [rewrite]: #844
+#839 := [monotonicity #845]: #853
+#564 := [trans #839 #562]: #563
+#835 := [monotonicity #564]: #458
+#492 := (iff #863 #491)
+#849 := (iff #862 #861)
+#846 := (or #861 false)
+#848 := (iff #846 #861)
+#486 := [rewrite]: #848
+#847 := (iff #862 #846)
+#842 := [monotonicity #845]: #847
+#851 := [trans #842 #486]: #849
+#852 := [monotonicity #851]: #492
+#559 := [monotonicity #852 #835]: #558
+#548 := [trans #559 #834]: #838
+#820 := [monotonicity #548 #819]: #825
+#507 := (iff #520 #515)
+#500 := (or #515 false)
+#505 := (iff #500 #515)
+#506 := [rewrite]: #505
+#841 := (iff #520 #500)
+#516 := (iff #855 false)
+#857 := [rewrite]: #516
+#504 := [monotonicity #857]: #841
+#843 := [trans #504 #506]: #507
+#668 := [monotonicity #843 #820]: #667
+#808 := [monotonicity #668]: #814
+#816 := [trans #808 #815]: #814
+#813 := [quant-inst #9 #10]: #812
+#810 := [mp #813 #816]: #811
+#728 := [unit-resolution #810 #893]: #826
+#705 := (not #826)
+#707 := (or #705 #706 #865)
+#800 := [def-axiom]: #707
+#714 := [unit-resolution #800 #728]: #713
+#715 := [unit-resolution #714 #740]: #865
+#788 := (not #865)
+#608 := (or #788 #817)
+#758 := [th-lemma arith triangle-eq]: #608
+#674 := [unit-resolution #758 #715]: #817
+#675 := (or #706 #647)
+#676 := [th-lemma arith triangle-eq]: #675
+#677 := [unit-resolution #676 #740]: #647
+#678 := [th-lemma arith farkas -1 1 1 #677 #90 #674]: false
+#679 := [lemma #678]: #706
+#729 := (or #515 #824)
+#797 := (or #705 #515 #824)
+#801 := [def-axiom]: #797
+#725 := [unit-resolution #801 #728]: #729
+#651 := [unit-resolution #725 #679]: #824
+decl f6 :: (-> Int S2)
+#452 := (f6 #9)
+#791 := (f4 #452)
+#792 := (= #791 0::Int)
+#696 := (not #792)
+#697 := (iff #706 #696)
+#687 := (iff #515 #792)
+#683 := (iff #792 #515)
+#693 := (= #791 #9)
+#718 := (= #452 f5)
+#537 := (= f5 #452)
+#14 := (:var 0 S2)
+#15 := (f4 #14)
+#866 := (pattern #15)
+#16 := (f6 #15)
+#80 := (= #14 #16)
+#867 := (forall (vars (?v0 S2)) (:pat #866) #80)
+#93 := (forall (vars (?v0 S2)) #80)
+#868 := (iff #93 #867)
+#870 := (iff #867 #867)
+#871 := [rewrite]: #870
+#869 := [rewrite]: #868
+#872 := [trans #869 #871]: #868
+#315 := (~ #93 #93)
+#313 := (~ #80 #80)
+#314 := [refl]: #313
+#316 := [nnf-pos #314]: #315
+#17 := (= #16 #14)
+#18 := (forall (vars (?v0 S2)) #17)
+#94 := (iff #18 #93)
+#91 := (iff #17 #80)
+#92 := [rewrite]: #91
+#95 := [quant-intro #92]: #94
+#79 := [asserted]: #18
+#98 := [mp #79 #95]: #93
+#301 := [mp~ #98 #316]: #93
+#873 := [mp #301 #872]: #867
+#530 := (not #867)
+#541 := (or #530 #537)
+#542 := [quant-inst #8]: #541
+#712 := [unit-resolution #542 #873]: #537
+#686 := [symm #712]: #718
+#652 := [monotonicity #686]: #693
+#685 := [monotonicity #652]: #683
+#694 := [symm #685]: #687
+#698 := [monotonicity #694]: #697
+#653 := [mp #679 #698]: #696
+#789 := (or #647 #792)
+#22 := (f6 #20)
+#874 := (pattern #22)
+#114 := (>= #20 0::Int)
+#23 := (f4 #22)
+#28 := (= #23 0::Int)
+#163 := (or #28 #114)
+#881 := (forall (vars (?v0 Int)) (:pat #874) #163)
+#168 := (forall (vars (?v0 Int)) #163)
+#884 := (iff #168 #881)
+#882 := (iff #163 #163)
+#883 := [refl]: #882
+#885 := [quant-intro #883]: #884
+#305 := (~ #168 #168)
+#317 := (~ #163 #163)
+#318 := [refl]: #317
+#306 := [nnf-pos #318]: #305
+#27 := (< #20 0::Int)
+#29 := (implies #27 #28)
+#30 := (forall (vars (?v0 Int)) #29)
+#171 := (iff #30 #168)
+#134 := (= 0::Int #23)
+#140 := (not #27)
+#141 := (or #140 #134)
+#146 := (forall (vars (?v0 Int)) #141)
+#169 := (iff #146 #168)
+#166 := (iff #141 #163)
+#160 := (or #114 #28)
+#164 := (iff #160 #163)
+#165 := [rewrite]: #164
+#161 := (iff #141 #160)
+#158 := (iff #134 #28)
+#159 := [rewrite]: #158
+#156 := (iff #140 #114)
+#116 := (not #114)
+#151 := (not #116)
+#154 := (iff #151 #114)
+#155 := [rewrite]: #154
+#152 := (iff #140 #151)
+#149 := (iff #27 #116)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#157 := [trans #153 #155]: #156
+#162 := [monotonicity #157 #159]: #161
+#167 := [trans #162 #165]: #166
+#170 := [quant-intro #167]: #169
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#137 := (implies #27 #134)
+#142 := (iff #137 #141)
+#143 := [rewrite]: #142
+#138 := (iff #29 #137)
+#135 := (iff #28 #134)
+#136 := [rewrite]: #135
#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#108 := (iff #29 #107)
-#105 := (iff #28 #102)
-#99 := (= #96 f5)
-#103 := (iff #99 #102)
-#104 := [rewrite]: #103
-#100 := (iff #28 #99)
-#97 := (= #27 #96)
-#94 := (= #26 #93)
-#91 := (= #25 #90)
-#88 := (= #24 #87)
-#85 := (= #23 -1::Int)
-#86 := [rewrite]: #85
-#83 := (= #22 #82)
-#84 := [rewrite]: #83
-#89 := [monotonicity #84 #86]: #88
-#79 := (iff #20 #78)
-#76 := (iff #19 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#92 := [monotonicity #80 #89]: #91
-#73 := (iff #14 #11)
-#68 := (or #11 false)
-#71 := (iff #68 #11)
-#72 := [rewrite]: #71
-#69 := (iff #14 #68)
-#66 := (iff #13 false)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#95 := [monotonicity #74 #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#106 := [trans #101 #104]: #105
-#109 := [monotonicity #106]: #108
-#153 := [trans #109 #151]: #152
-#65 := [asserted]: #29
-#154 := [mp #65 #153]: #149
-#693 := [unit-resolution #154 #689]: false
-#682 := [lemma #693]: #389
-#723 := (or #11 #398)
-#724 := [def-axiom]: #723
-#632 := [unit-resolution #724 #682]: #398
-#314 := (= #21 #137)
-#708 := (f4 #725)
-#703 := (= #708 0::Int)
-#626 := (not #703)
-#628 := (iff #389 #626)
-#639 := (iff #11 #703)
-#638 := (iff #703 #11)
-#636 := (= #708 #9)
-#633 := (= #725 f5)
-#635 := [symm #690]: #633
-#637 := [monotonicity #635]: #636
-#634 := [monotonicity #637]: #638
-#625 := [symm #634]: #639
-#629 := [monotonicity #625]: #628
-#630 := [mp #682 #629]: #626
-#714 := (or #123 #703)
-#35 := (:var 0 Int)
-#37 := (f3 #35)
-#735 := (pattern #37)
-#180 := (>= #35 0::Int)
-#38 := (f4 #37)
-#43 := (= #38 0::Int)
-#229 := (or #43 #180)
-#742 := (forall (vars (?v0 Int)) (:pat #735) #229)
-#234 := (forall (vars (?v0 Int)) #229)
-#745 := (iff #234 #742)
-#743 := (iff #229 #229)
-#744 := [refl]: #743
-#746 := [quant-intro #744]: #745
-#247 := (~ #234 #234)
-#255 := (~ #229 #229)
-#256 := [refl]: #255
-#248 := [nnf-pos #256]: #247
-#42 := (< #35 0::Int)
-#44 := (implies #42 #43)
-#45 := (forall (vars (?v0 Int)) #44)
-#237 := (iff #45 #234)
-#200 := (= 0::Int #38)
-#206 := (not #42)
-#207 := (or #206 #200)
-#212 := (forall (vars (?v0 Int)) #207)
-#235 := (iff #212 #234)
-#232 := (iff #207 #229)
-#226 := (or #180 #43)
-#230 := (iff #226 #229)
-#231 := [rewrite]: #230
-#227 := (iff #207 #226)
-#224 := (iff #200 #43)
-#225 := [rewrite]: #224
-#222 := (iff #206 #180)
-#182 := (not #180)
-#217 := (not #182)
-#220 := (iff #217 #180)
-#221 := [rewrite]: #220
-#218 := (iff #206 #217)
-#215 := (iff #42 #182)
-#216 := [rewrite]: #215
-#219 := [monotonicity #216]: #218
-#223 := [trans #219 #221]: #222
-#228 := [monotonicity #223 #225]: #227
-#233 := [trans #228 #231]: #232
-#236 := [quant-intro #233]: #235
-#213 := (iff #45 #212)
-#210 := (iff #44 #207)
-#203 := (implies #42 #200)
-#208 := (iff #203 #207)
-#209 := [rewrite]: #208
-#204 := (iff #44 #203)
-#201 := (iff #43 #200)
-#202 := [rewrite]: #201
-#205 := [monotonicity #202]: #204
-#211 := [trans #205 #209]: #210
-#214 := [quant-intro #211]: #213
-#238 := [trans #214 #236]: #237
-#199 := [asserted]: #45
-#239 := [mp #199 #238]: #234
-#257 := [mp~ #239 #248]: #234
-#747 := [mp #257 #746]: #742
-#709 := (not #742)
-#423 := (or #709 #123 #703)
-#711 := (or #703 #123)
-#424 := (or #709 #711)
-#420 := (iff #424 #423)
-#426 := (or #709 #714)
-#697 := (iff #426 #423)
-#419 := [rewrite]: #697
-#320 := (iff #424 #426)
-#700 := (iff #711 #714)
-#701 := [rewrite]: #700
-#696 := [monotonicity #701]: #320
-#694 := [trans #696 #419]: #420
-#425 := [quant-inst #9]: #424
-#698 := [mp #425 #694]: #423
-#627 := [unit-resolution #698 #747]: #714
-#631 := [unit-resolution #627 #630]: #123
-#611 := (or #11 #111 #124)
-#612 := [th-lemma arith triangle-eq]: #611
-#614 := [unit-resolution #612 #682]: #134
-#615 := [unit-resolution #614 #631]: #111
-#400 := (or #134 #110)
-#391 := [def-axiom]: #400
-#616 := [unit-resolution #391 #615]: #134
-#404 := (not #134)
-#721 := (or #404 #314)
-#378 := [def-axiom]: #721
-#617 := [unit-resolution #378 #616]: #314
-#618 := [trans #617 #632]: #651
-#619 := (not #651)
-#620 := (or #619 #642)
-#621 := [th-lemma arith triangle-eq]: #620
-#622 := [unit-resolution #621 #618]: #642
-#652 := (>= #640 0::Int)
-#623 := (or #619 #652)
-#613 := [th-lemma arith triangle-eq]: #623
-#624 := [unit-resolution #613 #618]: #652
-#603 := [th-lemma arith eq-propagate 1 1 1 1 #624 #622 #648 #646]: #602
-#605 := [symm #603]: #411
-#606 := [monotonicity #605]: #691
-#607 := [symm #606]: #688
-#608 := [trans #690 #607]: #146
-[unit-resolution #154 #608]: false
-unsat
-527e5e3123950986e94b94da9ebd83dc07302cc9 81 0
+#145 := [trans #139 #143]: #144
+#148 := [quant-intro #145]: #147
+#172 := [trans #148 #170]: #171
+#133 := [asserted]: #30
+#173 := [mp #133 #172]: #168
+#319 := [mp~ #173 #306]: #168
+#886 := [mp #319 #885]: #881
+#784 := (not #881)
+#785 := (or #784 #647 #792)
+#793 := (or #792 #647)
+#786 := (or #784 #793)
+#776 := (iff #786 #785)
+#787 := (or #784 #789)
+#774 := (iff #787 #785)
+#775 := [rewrite]: #774
+#771 := (iff #786 #787)
+#794 := (iff #793 #789)
+#783 := [rewrite]: #794
+#772 := [monotonicity #783]: #771
+#777 := [trans #772 #775]: #776
+#780 := [quant-inst #9]: #786
+#773 := [mp #780 #777]: #785
+#688 := [unit-resolution #773 #886]: #789
+#654 := [unit-resolution #688 #653]: #647
+#655 := (or #515 #491 #565)
+#657 := [th-lemma arith triangle-eq]: #655
+#658 := [unit-resolution #657 #654 #679]: #491
+#802 := (or #833 #861)
+#803 := [def-axiom]: #802
+#659 := [unit-resolution #803 #658]: #833
+#805 := (not #833)
+#700 := (not #824)
+#795 := (or #700 #805 #517)
+#796 := [def-axiom]: #795
+#660 := [unit-resolution #796 #659 #651]: #517
+#699 := (not #517)
+#692 := (or #699 #689)
+#716 := [th-lemma arith triangle-eq]: #692
+#661 := [unit-resolution #716 #660]: #689
+#663 := (not #689)
+#645 := (not #760)
+#633 := (or #662 #565 #645 #663 #83)
+#634 := [th-lemma arith assign-bounds 2 1 3 3]: #633
+#635 := [unit-resolution #634 #654 #661 #90 #670]: #662
+#726 := (not #750)
+#722 := (or #726 #759)
+#723 := [th-lemma arith triangle-eq]: #722
+[unit-resolution #723 #635 #721]: false
+unsat
+f4adf2827c5540d070c2e622505c61938b50a2ed 636 0
+#2 := false
+decl f3 :: (-> Int S2)
+decl f4 :: (-> Int Int Int)
+#10 := 3::Int
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#11 := (f4 #9 3::Int)
+#12 := (f3 #11)
+#83 := (= f6 #12)
+#14 := 0::Int
+#15 := (f3 0::Int)
+#932 := (= #15 #12)
+#930 := (= #12 #15)
+#819 := (= #11 0::Int)
+#822 := (= #9 0::Int)
+#867 := (f5 #15)
+#866 := (= #867 0::Int)
+#24 := (:var 0 Int)
+#26 := (f3 #24)
+#890 := (pattern #26)
+#130 := (>= #24 0::Int)
+#131 := (not #130)
+#27 := (f5 #26)
+#112 := (= #24 #27)
+#137 := (or #112 #131)
+#891 := (forall (vars (?v0 Int)) (:pat #890) #137)
+#142 := (forall (vars (?v0 Int)) #137)
+#894 := (iff #142 #891)
+#892 := (iff #137 #137)
+#893 := [refl]: #892
+#895 := [quant-intro #893]: #894
+#319 := (~ #142 #142)
+#318 := (~ #137 #137)
+#315 := [refl]: #318
+#320 := [nnf-pos #315]: #319
+#28 := (= #27 #24)
+#25 := (<= 0::Int #24)
+#29 := (implies #25 #28)
+#30 := (forall (vars (?v0 Int)) #29)
+#145 := (iff #30 #142)
+#119 := (not #25)
+#120 := (or #119 #112)
+#125 := (forall (vars (?v0 Int)) #120)
+#143 := (iff #125 #142)
+#140 := (iff #120 #137)
+#134 := (or #131 #112)
+#138 := (iff #134 #137)
+#139 := [rewrite]: #138
+#135 := (iff #120 #134)
+#132 := (iff #119 #131)
+#128 := (iff #25 #130)
+#129 := [rewrite]: #128
+#133 := [monotonicity #129]: #132
+#136 := [monotonicity #133]: #135
+#141 := [trans #136 #139]: #140
+#144 := [quant-intro #141]: #143
+#126 := (iff #30 #125)
+#123 := (iff #29 #120)
+#116 := (implies #25 #112)
+#121 := (iff #116 #120)
+#122 := [rewrite]: #121
+#117 := (iff #29 #116)
+#114 := (iff #28 #112)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#124 := [trans #118 #122]: #123
+#127 := [quant-intro #124]: #126
+#146 := [trans #127 #144]: #145
+#111 := [asserted]: #30
+#147 := [mp #111 #146]: #142
+#316 := [mp~ #147 #320]: #142
+#896 := [mp #316 #895]: #891
+#880 := (not #891)
+#565 := (or #880 #866)
+#502 := (>= 0::Int 0::Int)
+#865 := (not #502)
+#507 := (= 0::Int #867)
+#508 := (or #507 #865)
+#566 := (or #880 #508)
+#845 := (iff #566 #565)
+#561 := (iff #565 #565)
+#843 := [rewrite]: #561
+#854 := (iff #508 #866)
+#574 := (or #866 false)
+#853 := (iff #574 #866)
+#850 := [rewrite]: #853
+#575 := (iff #508 #574)
+#851 := (iff #865 false)
+#1 := true
+#578 := (not true)
+#581 := (iff #578 false)
+#474 := [rewrite]: #581
+#579 := (iff #865 #578)
+#855 := (iff #502 true)
+#856 := [rewrite]: #855
+#580 := [monotonicity #856]: #579
+#852 := [trans #580 #474]: #851
+#868 := (iff #507 #866)
+#869 := [rewrite]: #868
+#849 := [monotonicity #869 #852]: #575
+#564 := [trans #849 #850]: #854
+#846 := [monotonicity #564]: #845
+#847 := [trans #846 #843]: #845
+#567 := [quant-inst #14]: #566
+#844 := [mp #567 #847]: #565
+#923 := [unit-resolution #844 #896]: #866
+#926 := (= #9 #867)
+#16 := (= f6 #15)
+#560 := (f3 #9)
+#918 := (= #560 #15)
+#473 := (= #15 #560)
+#471 := (= 0::Int #9)
+#544 := (f5 #12)
+#626 := (= #544 #9)
+#497 := (= #9 #544)
+#97 := (not #16)
+#570 := [hypothesis]: #97
+#555 := (or #83 #16)
+#98 := (iff #83 #97)
+#13 := (= #12 f6)
+#17 := (iff #13 #16)
+#18 := (not #17)
+#101 := (iff #18 #98)
+#89 := (iff #16 #83)
+#94 := (not #89)
+#99 := (iff #94 #98)
+#100 := [rewrite]: #99
+#95 := (iff #18 #94)
+#92 := (iff #17 #89)
+#86 := (iff #83 #16)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #17 #86)
+#84 := (iff #13 #83)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [monotonicity #93]: #95
+#102 := [trans #96 #100]: #101
+#82 := [asserted]: #18
+#105 := [mp #82 #102]: #98
+#468 := (not #98)
+#553 := (or #83 #16 #468)
+#554 := [def-axiom]: #553
+#546 := [unit-resolution #554 #105]: #555
+#562 := [unit-resolution #546 #570]: #83
+#498 := [monotonicity #562]: #497
+#477 := [symm #498]: #626
+#482 := (= 0::Int #544)
+#545 := (= #11 #544)
+#874 := (>= #11 0::Int)
+#557 := (not #83)
+#628 := (or #874 #557)
+#878 := (= #544 0::Int)
+#630 := (iff #878 #822)
+#623 := [hypothesis]: #83
+#625 := [symm #623]: #13
+#629 := [monotonicity #625]: #626
+#634 := [monotonicity #629]: #630
+#876 := (not #874)
+#647 := [hypothesis]: #876
+#532 := (or #874 #878)
+#32 := (= #27 0::Int)
+#178 := (or #32 #130)
+#897 := (forall (vars (?v0 Int)) (:pat #890) #178)
+#183 := (forall (vars (?v0 Int)) #178)
+#900 := (iff #183 #897)
+#898 := (iff #178 #178)
+#899 := [refl]: #898
+#901 := [quant-intro #899]: #900
+#321 := (~ #183 #183)
+#333 := (~ #178 #178)
+#334 := [refl]: #333
+#322 := [nnf-pos #334]: #321
+#31 := (< #24 0::Int)
+#33 := (implies #31 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#186 := (iff #34 #183)
+#149 := (= 0::Int #27)
+#155 := (not #31)
+#156 := (or #155 #149)
+#161 := (forall (vars (?v0 Int)) #156)
+#184 := (iff #161 #183)
+#181 := (iff #156 #178)
+#175 := (or #130 #32)
+#179 := (iff #175 #178)
+#180 := [rewrite]: #179
+#176 := (iff #156 #175)
+#173 := (iff #149 #32)
+#174 := [rewrite]: #173
+#171 := (iff #155 #130)
+#166 := (not #131)
+#169 := (iff #166 #130)
+#170 := [rewrite]: #169
+#167 := (iff #155 #166)
+#164 := (iff #31 #131)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#172 := [trans #168 #170]: #171
+#177 := [monotonicity #172 #174]: #176
+#182 := [trans #177 #180]: #181
+#185 := [quant-intro #182]: #184
+#162 := (iff #34 #161)
+#159 := (iff #33 #156)
+#152 := (implies #31 #149)
+#157 := (iff #152 #156)
+#158 := [rewrite]: #157
+#153 := (iff #33 #152)
+#150 := (iff #32 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#160 := [trans #154 #158]: #159
+#163 := [quant-intro #160]: #162
+#187 := [trans #163 #185]: #186
+#148 := [asserted]: #34
+#188 := [mp #148 #187]: #183
+#335 := [mp~ #188 #322]: #183
+#902 := [mp #335 #901]: #897
+#857 := (not #897)
+#520 := (or #857 #874 #878)
+#879 := (or #878 #874)
+#521 := (or #857 #879)
+#863 := (iff #521 #520)
+#523 := (or #857 #532)
+#861 := (iff #523 #520)
+#862 := [rewrite]: #861
+#859 := (iff #521 #523)
+#873 := (iff #879 #532)
+#516 := [rewrite]: #873
+#860 := [monotonicity #516]: #859
+#858 := [trans #860 #862]: #863
+#522 := [quant-inst #11]: #521
+#864 := [mp #522 #858]: #520
+#643 := [unit-resolution #864 #902]: #532
+#633 := [unit-resolution #643 #647]: #878
+#627 := [mp #633 #634]: #822
+#740 := (not #822)
+#746 := (not #819)
+#645 := (or #746 #874)
+#648 := [th-lemma arith triangle-eq]: #645
+#636 := [unit-resolution #648 #647]: #746
+#641 := (or #740 #819)
+#788 := -3::Int
+#205 := -1::Int
+#842 := (* -1::Int #9)
+#792 := (div #842 -3::Int)
+#794 := (* -1::Int #792)
+#783 := (+ #11 #794)
+#782 := (= #783 0::Int)
+#828 := (div #9 3::Int)
+#829 := (* -1::Int #828)
+#830 := (+ #11 #829)
+#824 := (= #830 0::Int)
+#833 := (<= #9 0::Int)
+#723 := (not #833)
+#825 := (>= #9 0::Int)
+#808 := (not #825)
+#801 := (or #808 #723)
+#767 := (ite #801 #824 #782)
+#771 := (ite #822 #819 #767)
+#35 := (:var 1 Int)
+#36 := (f4 #35 #24)
+#903 := (pattern #36)
+#209 := (* -1::Int #24)
+#206 := (* -1::Int #35)
+#212 := (div #206 #209)
+#384 := (* -1::Int #212)
+#385 := (+ #36 #384)
+#386 := (= #385 0::Int)
+#46 := (div #35 #24)
+#381 := (* -1::Int #46)
+#382 := (+ #36 #381)
+#383 := (= #382 0::Int)
+#244 := (>= #35 0::Int)
+#237 := (<= #24 0::Int)
+#344 := (or #237 #244)
+#345 := (not #344)
+#233 := (<= #35 0::Int)
+#342 := (or #233 #237)
+#343 := (not #342)
+#348 := (or #343 #345)
+#387 := (ite #348 #383 #386)
+#380 := (= #36 0::Int)
+#38 := (= #24 0::Int)
+#37 := (= #35 0::Int)
+#39 := (or #37 #38)
+#388 := (ite #39 #380 #387)
+#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #388)
+#391 := (forall (vars (?v0 Int) (?v1 Int)) #388)
+#907 := (iff #391 #904)
+#905 := (iff #388 #388)
+#906 := [refl]: #905
+#908 := [quant-intro #906]: #907
+#351 := (ite #348 #46 #212)
+#354 := (ite #39 0::Int #351)
+#357 := (= #36 #354)
+#360 := (forall (vars (?v0 Int) (?v1 Int)) #357)
+#392 := (iff #360 #391)
+#389 := (iff #357 #388)
+#390 := [rewrite]: #389
+#393 := [quant-intro #390]: #392
+#245 := (not #244)
+#238 := (not #237)
+#248 := (and #238 #245)
+#234 := (not #233)
+#241 := (and #234 #238)
+#251 := (or #241 #248)
+#254 := (ite #251 #46 #212)
+#257 := (ite #39 0::Int #254)
+#260 := (= #36 #257)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#361 := (iff #263 #360)
+#358 := (iff #260 #357)
+#355 := (= #257 #354)
+#352 := (= #254 #351)
+#349 := (iff #251 #348)
+#346 := (iff #248 #345)
+#347 := [rewrite]: #346
+#327 := (iff #241 #343)
+#328 := [rewrite]: #327
+#350 := [monotonicity #328 #347]: #349
+#353 := [monotonicity #350]: #352
+#356 := [monotonicity #353]: #355
+#359 := [monotonicity #356]: #358
+#362 := [quant-intro #359]: #361
+#323 := (~ #263 #263)
+#336 := (~ #260 #260)
+#337 := [refl]: #336
+#324 := [nnf-pos #337]: #323
+#48 := (- #24)
+#47 := (- #35)
+#49 := (div #47 #48)
+#41 := (< 0::Int #24)
+#43 := (< #35 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #35)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#50 := (ite #45 #46 #49)
+#51 := (ite #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#266 := (iff #53 #263)
+#199 := (and #41 #43)
+#202 := (or #42 #199)
+#215 := (ite #202 #46 #212)
+#193 := (= 0::Int #24)
+#190 := (= 0::Int #35)
+#196 := (or #190 #193)
+#218 := (ite #196 0::Int #215)
+#221 := (= #36 #218)
+#224 := (forall (vars (?v0 Int) (?v1 Int)) #221)
+#264 := (iff #224 #263)
+#261 := (iff #221 #260)
+#258 := (= #218 #257)
+#255 := (= #215 #254)
+#252 := (iff #202 #251)
+#249 := (iff #199 #248)
+#246 := (iff #43 #245)
+#247 := [rewrite]: #246
+#239 := (iff #41 #238)
+#240 := [rewrite]: #239
+#250 := [monotonicity #240 #247]: #249
+#242 := (iff #42 #241)
+#235 := (iff #40 #234)
+#236 := [rewrite]: #235
+#243 := [monotonicity #236 #240]: #242
+#253 := [monotonicity #243 #250]: #252
+#256 := [monotonicity #253]: #255
+#231 := (iff #196 #39)
+#229 := (iff #193 #38)
+#230 := [rewrite]: #229
+#227 := (iff #190 #37)
+#228 := [rewrite]: #227
+#232 := [monotonicity #228 #230]: #231
+#259 := [monotonicity #232 #256]: #258
+#262 := [monotonicity #259]: #261
+#265 := [quant-intro #262]: #264
+#225 := (iff #53 #224)
+#222 := (iff #52 #221)
+#219 := (= #51 #218)
+#216 := (= #50 #215)
+#213 := (= #49 #212)
+#210 := (= #48 #209)
+#211 := [rewrite]: #210
+#207 := (= #47 #206)
+#208 := [rewrite]: #207
+#214 := [monotonicity #208 #211]: #213
+#203 := (iff #45 #202)
+#200 := (iff #44 #199)
+#201 := [rewrite]: #200
+#204 := [monotonicity #201]: #203
+#217 := [monotonicity #204 #214]: #216
+#197 := (iff #39 #196)
+#194 := (iff #38 #193)
+#195 := [rewrite]: #194
+#191 := (iff #37 #190)
+#192 := [rewrite]: #191
+#198 := [monotonicity #192 #195]: #197
+#220 := [monotonicity #198 #217]: #219
+#223 := [monotonicity #220]: #222
+#226 := [quant-intro #223]: #225
+#267 := [trans #226 #265]: #266
+#189 := [asserted]: #53
+#268 := [mp #189 #267]: #263
+#338 := [mp~ #268 #324]: #263
+#363 := [mp #338 #362]: #360
+#394 := [mp #363 #393]: #391
+#909 := [mp #394 #908]: #904
+#774 := (not #904)
+#775 := (or #774 #771)
+#836 := (* -1::Int 3::Int)
+#683 := (div #842 #836)
+#684 := (* -1::Int #683)
+#685 := (+ #11 #684)
+#827 := (= #685 0::Int)
+#831 := (<= 3::Int 0::Int)
+#832 := (or #831 #825)
+#826 := (not #832)
+#662 := (or #833 #831)
+#664 := (not #662)
+#665 := (or #664 #826)
+#818 := (ite #665 #824 #827)
+#821 := (= 3::Int 0::Int)
+#820 := (or #822 #821)
+#823 := (ite #820 #819 #818)
+#776 := (or #774 #823)
+#778 := (iff #776 #775)
+#779 := (iff #775 #775)
+#757 := [rewrite]: #779
+#772 := (iff #823 #771)
+#769 := (iff #818 #767)
+#786 := (iff #827 #782)
+#784 := (= #685 #783)
+#780 := (= #684 #794)
+#793 := (= #683 #792)
+#790 := (= #836 -3::Int)
+#791 := [rewrite]: #790
+#789 := [monotonicity #791]: #793
+#781 := [monotonicity #789]: #780
+#785 := [monotonicity #781]: #784
+#766 := [monotonicity #785]: #786
+#803 := (iff #665 #801)
+#810 := (or #723 #808)
+#802 := (iff #810 #801)
+#796 := [rewrite]: #802
+#799 := (iff #665 #810)
+#809 := (iff #826 #808)
+#797 := (iff #832 #825)
+#817 := (or false #825)
+#798 := (iff #817 #825)
+#795 := [rewrite]: #798
+#804 := (iff #832 #817)
+#700 := (iff #831 false)
+#715 := [rewrite]: #700
+#806 := [monotonicity #715]: #804
+#807 := [trans #806 #795]: #797
+#805 := [monotonicity #807]: #809
+#816 := (iff #664 #723)
+#721 := (iff #662 #833)
+#717 := (or #833 false)
+#719 := (iff #717 #833)
+#720 := [rewrite]: #719
+#718 := (iff #662 #717)
+#711 := [monotonicity #715]: #718
+#722 := [trans #711 #720]: #721
+#813 := [monotonicity #722]: #816
+#800 := [monotonicity #813 #805]: #799
+#787 := [trans #800 #796]: #803
+#770 := [monotonicity #787 #766]: #769
+#812 := (iff #820 #822)
+#707 := (or #822 false)
+#716 := (iff #707 #822)
+#811 := [rewrite]: #716
+#666 := (iff #820 #707)
+#705 := (iff #821 false)
+#706 := [rewrite]: #705
+#814 := [monotonicity #706]: #666
+#815 := [trans #814 #811]: #812
+#773 := [monotonicity #815 #770]: #772
+#768 := [monotonicity #773]: #778
+#758 := [trans #768 #757]: #778
+#777 := [quant-inst #9 #10]: #776
+#760 := [mp #777 #758]: #775
+#639 := [unit-resolution #760 #909]: #771
+#739 := (not #771)
+#743 := (or #739 #740 #819)
+#744 := [def-axiom]: #743
+#642 := [unit-resolution #744 #639]: #641
+#638 := [unit-resolution #642 #636]: #740
+#635 := [unit-resolution #638 #627]: false
+#631 := [lemma #635]: #628
+#571 := [unit-resolution #631 #562]: #874
+#877 := (or #545 #876)
+#875 := (or #880 #545 #876)
+#881 := (or #880 #877)
+#531 := (iff #881 #875)
+#536 := [rewrite]: #531
+#871 := [quant-inst #11]: #881
+#872 := [mp #871 #536]: #875
+#572 := [unit-resolution #872 #896]: #877
+#563 := [unit-resolution #572 #571]: #545
+#480 := (= 0::Int #11)
+#637 := (* -1::Int #11)
+#640 := (+ #9 #637)
+#646 := (>= #640 0::Int)
+#658 := (= #9 #11)
+#500 := (= #544 #11)
+#496 := [symm #563]: #500
+#501 := [trans #498 #496]: #658
+#483 := (not #658)
+#487 := (or #483 #646)
+#488 := [th-lemma arith triangle-eq]: #487
+#491 := [unit-resolution #488 #501]: #646
+#492 := (not #646)
+#493 := (or #825 #876 #492)
+#485 := [th-lemma arith assign-bounds 1 1]: #493
+#494 := [unit-resolution #485 #571 #491]: #825
+#644 := (<= #640 0::Int)
+#478 := (or #483 #644)
+#475 := [th-lemma arith triangle-eq]: #478
+#476 := [unit-resolution #475 #501]: #644
+#512 := (not #644)
+#489 := (or #819 #512 #808 #876)
+#613 := (* -3::Int #828)
+#748 := (mod #9 3::Int)
+#612 := (* -1::Int #748)
+#614 := (+ #612 #613)
+#615 := (+ #9 #614)
+#611 := (= #615 0::Int)
+#80 := [true-axiom]: true
+#573 := (or false #611)
+#540 := [th-lemma arith]: #573
+#542 := [unit-resolution #540 #80]: #611
+#597 := (>= #615 0::Int)
+#513 := (not #597)
+#598 := (>= #748 0::Int)
+#543 := (or false #598)
+#534 := [th-lemma arith]: #543
+#547 := [unit-resolution #534 #80]: #598
+#761 := (<= #11 0::Int)
+#550 := (not #761)
+#548 := [hypothesis]: #874
+#549 := [hypothesis]: #746
+#551 := (or #819 #550 #876)
+#541 := [th-lemma arith triangle-eq]: #551
+#552 := [unit-resolution #541 #549 #548]: #550
+#535 := [hypothesis]: #644
+#749 := (<= #830 0::Int)
+#537 := [unit-resolution #642 #549]: #740
+#538 := (or #822 #767)
+#745 := (or #739 #822 #767)
+#741 := [def-axiom]: #745
+#517 := [unit-resolution #741 #639]: #538
+#519 := [unit-resolution #517 #537]: #767
+#524 := [hypothesis]: #825
+#525 := (or #822 #723 #808)
+#526 := [th-lemma arith triangle-eq]: #525
+#527 := [unit-resolution #526 #537 #524]: #723
+#764 := (or #801 #833)
+#759 := [def-axiom]: #764
+#528 := [unit-resolution #759 #527]: #801
+#765 := (not #801)
+#750 := (not #767)
+#756 := (or #750 #765 #824)
+#729 := [def-axiom]: #756
+#529 := [unit-resolution #729 #528 #519]: #824
+#624 := (not #824)
+#518 := (or #624 #749)
+#530 := [th-lemma arith triangle-eq]: #518
+#511 := [unit-resolution #530 #529]: #749
+#515 := (not #749)
+#514 := (not #598)
+#503 := (or #513 #514 #761 #512 #515)
+#505 := [th-lemma arith assign-bounds 1 2 1 3]: #503
+#506 := [unit-resolution #505 #511 #535 #552 #547]: #513
+#509 := (not #611)
+#504 := (or #509 #597)
+#510 := [th-lemma arith triangle-eq]: #504
+#484 := [unit-resolution #510 #506 #542]: false
+#490 := [lemma #484]: #489
+#479 := [unit-resolution #490 #476 #494 #571]: #819
+#481 := [symm #479]: #480
+#469 := [trans #481 #563]: #482
+#472 := [trans #469 #477]: #471
+#917 := [monotonicity #472]: #473
+#919 := [symm #917]: #918
+#539 := (= f6 #560)
+#19 := (:var 0 S2)
+#20 := (f5 #19)
+#882 := (pattern #20)
+#21 := (f3 #20)
+#104 := (= #19 #21)
+#883 := (forall (vars (?v0 S2)) (:pat #882) #104)
+#108 := (forall (vars (?v0 S2)) #104)
+#884 := (iff #108 #883)
+#886 := (iff #883 #883)
+#887 := [rewrite]: #886
+#885 := [rewrite]: #884
+#888 := [trans #885 #887]: #884
+#331 := (~ #108 #108)
+#329 := (~ #104 #104)
+#330 := [refl]: #329
+#332 := [nnf-pos #330]: #331
+#22 := (= #21 #19)
+#23 := (forall (vars (?v0 S2)) #22)
+#109 := (iff #23 #108)
+#106 := (iff #22 #104)
+#107 := [rewrite]: #106
+#110 := [quant-intro #107]: #109
+#103 := [asserted]: #23
+#113 := [mp #103 #110]: #108
+#317 := [mp~ #113 #332]: #108
+#889 := [mp #317 #888]: #883
+#533 := (not #883)
+#663 := (or #533 #539)
+#870 := [quant-inst #8]: #663
+#470 := [unit-resolution #870 #889]: #539
+#920 := [trans #470 #919]: #16
+#921 := [unit-resolution #570 #920]: false
+#922 := [lemma #921]: #16
+#927 := [monotonicity #922]: #926
+#928 := [trans #927 #923]: #822
+#929 := [unit-resolution #642 #928]: #819
+#931 := [monotonicity #929]: #930
+#933 := [symm #931]: #932
+#934 := [trans #922 #933]: #83
+#559 := (or #557 #97)
+#558 := (or #557 #97 #468)
+#486 := [def-axiom]: #558
+#556 := [unit-resolution #486 #105]: #559
+#495 := [unit-resolution #556 #922]: #557
+[unit-resolution #495 #934]: false
+unsat
+2e39fe3f9575e15a240203df63c5032154a66535 279 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 0::Int
-#24 := (f3 0::Int)
-#10 := 3::Int
-#19 := (- 3::Int)
-#18 := (- 0::Int)
-#20 := (div #18 #19)
-#17 := (div 0::Int 3::Int)
-#14 := (< 0::Int 3::Int)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#21 := (ite #16 #17 #20)
-#11 := (= 3::Int 0::Int)
-#9 := (= 0::Int 0::Int)
-#12 := (or #9 #11)
-#22 := (ite #12 0::Int #21)
-#23 := (f3 #22)
-#25 := (= #23 #24)
-#26 := (not #25)
-#117 := (iff #26 false)
-#1 := true
-#112 := (not true)
-#115 := (iff #112 false)
-#116 := [rewrite]: #115
-#113 := (iff #26 #112)
-#110 := (iff #25 true)
-#105 := (= #24 #24)
-#108 := (iff #105 true)
-#109 := [rewrite]: #108
-#106 := (iff #25 #105)
-#102 := (= #22 0::Int)
-#97 := (ite true 0::Int 0::Int)
-#100 := (= #97 0::Int)
-#101 := [rewrite]: #100
-#98 := (= #22 #97)
-#95 := (= #21 0::Int)
-#90 := (ite #15 0::Int 0::Int)
-#93 := (= #90 0::Int)
-#94 := [rewrite]: #93
-#91 := (= #21 #90)
-#88 := (= #20 0::Int)
-#80 := -3::Int
-#83 := (div 0::Int -3::Int)
-#86 := (= #83 0::Int)
-#87 := [rewrite]: #86
-#84 := (= #20 #83)
-#81 := (= #19 -3::Int)
-#82 := [rewrite]: #81
-#78 := (= #18 0::Int)
-#79 := [rewrite]: #78
-#85 := [monotonicity #79 #82]: #84
-#89 := [trans #85 #87]: #88
-#76 := (= #17 0::Int)
-#77 := [rewrite]: #76
-#74 := (iff #16 #15)
-#75 := [rewrite]: #74
-#92 := [monotonicity #75 #77 #89]: #91
-#96 := [trans #92 #94]: #95
-#72 := (iff #12 true)
-#67 := (or true false)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #12 #67)
-#65 := (iff #11 false)
-#66 := [rewrite]: #65
-#63 := (iff #9 true)
-#64 := [rewrite]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#99 := [monotonicity #73 #96]: #98
-#103 := [trans #99 #101]: #102
-#104 := [monotonicity #103]: #25
-#107 := [monotonicity #104]: #106
-#111 := [trans #107 #109]: #110
-#114 := [monotonicity #111]: #113
-#118 := [trans #114 #116]: #117
-#62 := [asserted]: #26
-[mp #62 #118]: false
-unsat
-b6bcc3a997f628b30a8c56db4557945cb134a0bb 135 0
+#11 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := (f4 0::Int 0::Int)
+#10 := (f3 #9)
+#12 := (= #10 #11)
+#804 := (= #9 0::Int)
+#19 := (:var 0 Int)
+#30 := (:var 1 Int)
+#49 := (f4 #30 #19)
+#884 := (pattern #49)
+#179 := -1::Int
+#183 := (* -1::Int #19)
+#180 := (* -1::Int #30)
+#244 := (mod #180 #183)
+#374 := (+ #49 #244)
+#375 := (= #374 0::Int)
+#50 := (mod #30 #19)
+#371 := (* -1::Int #50)
+#372 := (+ #49 #371)
+#373 := (= #372 0::Int)
+#218 := (>= #30 0::Int)
+#211 := (<= #19 0::Int)
+#318 := (or #211 #218)
+#319 := (not #318)
+#207 := (<= #30 0::Int)
+#316 := (or #207 #211)
+#317 := (not #316)
+#322 := (or #317 #319)
+#376 := (ite #322 #373 #375)
+#370 := (= #49 0::Int)
+#32 := (= #30 0::Int)
+#377 := (ite #32 #370 #376)
+#369 := (= #30 #49)
+#33 := (= #19 0::Int)
+#378 := (ite #33 #369 #377)
+#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #378)
+#381 := (forall (vars (?v0 Int) (?v1 Int)) #378)
+#888 := (iff #381 #885)
+#886 := (iff #378 #378)
+#887 := [refl]: #886
+#889 := [quant-intro #887]: #888
+#250 := (* -1::Int #244)
+#338 := (ite #322 #50 #250)
+#341 := (ite #32 0::Int #338)
+#344 := (ite #33 #30 #341)
+#347 := (= #49 #344)
+#350 := (forall (vars (?v0 Int) (?v1 Int)) #347)
+#382 := (iff #350 #381)
+#379 := (iff #347 #378)
+#380 := [rewrite]: #379
+#383 := [quant-intro #380]: #382
+#219 := (not #218)
+#212 := (not #211)
+#222 := (and #212 #219)
+#208 := (not #207)
+#215 := (and #208 #212)
+#225 := (or #215 #222)
+#270 := (ite #225 #50 #250)
+#273 := (ite #32 0::Int #270)
+#276 := (ite #33 #30 #273)
+#279 := (= #49 #276)
+#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
+#351 := (iff #282 #350)
+#348 := (iff #279 #347)
+#345 := (= #276 #344)
+#342 := (= #273 #341)
+#339 := (= #270 #338)
+#323 := (iff #225 #322)
+#320 := (iff #222 #319)
+#321 := [rewrite]: #320
+#301 := (iff #215 #317)
+#302 := [rewrite]: #301
+#324 := [monotonicity #302 #321]: #323
+#340 := [monotonicity #324]: #339
+#343 := [monotonicity #340]: #342
+#346 := [monotonicity #343]: #345
+#349 := [monotonicity #346]: #348
+#352 := [quant-intro #349]: #351
+#299 := (~ #282 #282)
+#313 := (~ #279 #279)
+#314 := [refl]: #313
+#300 := [nnf-pos #314]: #299
+#43 := (- #19)
+#42 := (- #30)
+#51 := (mod #42 #43)
+#52 := (- #51)
+#36 := (< 0::Int #19)
+#38 := (< #30 0::Int)
+#39 := (and #38 #36)
+#35 := (< 0::Int #30)
+#37 := (and #35 #36)
+#40 := (or #37 #39)
+#53 := (ite #40 #50 #52)
+#54 := (ite #32 0::Int #53)
+#55 := (ite #33 #30 #54)
+#56 := (= #49 #55)
+#57 := (forall (vars (?v0 Int) (?v1 Int)) #56)
+#285 := (iff #57 #282)
+#173 := (and #36 #38)
+#176 := (or #37 #173)
+#255 := (ite #176 #50 #250)
+#164 := (= 0::Int #30)
+#258 := (ite #164 0::Int #255)
+#167 := (= 0::Int #19)
+#261 := (ite #167 #30 #258)
+#264 := (= #49 #261)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#283 := (iff #267 #282)
+#280 := (iff #264 #279)
+#277 := (= #261 #276)
+#274 := (= #258 #273)
+#271 := (= #255 #270)
+#226 := (iff #176 #225)
+#223 := (iff #173 #222)
+#220 := (iff #38 #219)
+#221 := [rewrite]: #220
+#213 := (iff #36 #212)
+#214 := [rewrite]: #213
+#224 := [monotonicity #214 #221]: #223
+#216 := (iff #37 #215)
+#209 := (iff #35 #208)
+#210 := [rewrite]: #209
+#217 := [monotonicity #210 #214]: #216
+#227 := [monotonicity #217 #224]: #226
+#272 := [monotonicity #227]: #271
+#201 := (iff #164 #32)
+#202 := [rewrite]: #201
+#275 := [monotonicity #202 #272]: #274
+#203 := (iff #167 #33)
+#204 := [rewrite]: #203
+#278 := [monotonicity #204 #275]: #277
+#281 := [monotonicity #278]: #280
+#284 := [quant-intro #281]: #283
+#268 := (iff #57 #267)
+#265 := (iff #56 #264)
+#262 := (= #55 #261)
+#259 := (= #54 #258)
+#256 := (= #53 #255)
+#253 := (= #52 #250)
+#247 := (- #244)
+#251 := (= #247 #250)
+#252 := [rewrite]: #251
+#248 := (= #52 #247)
+#245 := (= #51 #244)
+#184 := (= #43 #183)
+#185 := [rewrite]: #184
+#181 := (= #42 #180)
+#182 := [rewrite]: #181
+#246 := [monotonicity #182 #185]: #245
+#249 := [monotonicity #246]: #248
+#254 := [trans #249 #252]: #253
+#177 := (iff #40 #176)
+#174 := (iff #39 #173)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#257 := [monotonicity #178 #254]: #256
+#165 := (iff #32 #164)
+#166 := [rewrite]: #165
+#260 := [monotonicity #166 #257]: #259
+#168 := (iff #33 #167)
+#169 := [rewrite]: #168
+#263 := [monotonicity #169 #260]: #262
+#266 := [monotonicity #263]: #265
+#269 := [quant-intro #266]: #268
+#286 := [trans #269 #284]: #285
+#243 := [asserted]: #57
+#287 := [mp #243 #286]: #282
+#315 := [mp~ #287 #300]: #282
+#353 := [mp #315 #352]: #350
+#384 := [mp #353 #383]: #381
+#890 := [mp #384 #889]: #885
+#760 := (not #885)
+#740 := (or #760 #804)
+#811 := (* -1::Int 0::Int)
+#812 := (mod #811 #811)
+#813 := (+ #9 #812)
+#808 := (= #813 0::Int)
+#809 := (mod 0::Int 0::Int)
+#814 := (* -1::Int #809)
+#815 := (+ #9 #814)
+#810 := (= #815 0::Int)
+#833 := (>= 0::Int 0::Int)
+#816 := (<= 0::Int 0::Int)
+#657 := (or #816 #833)
+#658 := (not #657)
+#659 := (or #816 #816)
+#801 := (not #659)
+#802 := (or #801 #658)
+#803 := (ite #802 #810 #808)
+#798 := (= 0::Int 0::Int)
+#799 := (ite #798 #804 #803)
+#805 := (= 0::Int #9)
+#806 := (ite #798 #805 #799)
+#741 := (or #760 #806)
+#744 := (iff #741 #740)
+#746 := (iff #740 #740)
+#747 := [rewrite]: #746
+#759 := (iff #806 #804)
+#1 := true
+#768 := (ite true #804 #804)
+#757 := (iff #768 #804)
+#758 := [rewrite]: #757
+#754 := (iff #806 #768)
+#767 := (iff #799 #804)
+#769 := (+ #9 #809)
+#782 := (= #769 0::Int)
+#761 := (ite true #804 #782)
+#765 := (iff #761 #804)
+#766 := [rewrite]: #765
+#762 := (iff #799 #761)
+#770 := (iff #803 #782)
+#784 := (ite false #810 #782)
+#775 := (iff #784 #782)
+#776 := [rewrite]: #775
+#773 := (iff #803 #784)
+#783 := (iff #808 #782)
+#771 := (= #813 #769)
+#780 := (= #812 #809)
+#791 := (= #811 0::Int)
+#778 := [rewrite]: #791
+#772 := [monotonicity #778 #778]: #780
+#781 := [monotonicity #772]: #771
+#779 := [monotonicity #781]: #783
+#790 := (iff #802 false)
+#693 := (or false false)
+#696 := (iff #693 false)
+#697 := [rewrite]: #696
+#694 := (iff #802 #693)
+#692 := (iff #658 false)
+#481 := (not true)
+#840 := (iff #481 false)
+#843 := [rewrite]: #840
+#689 := (iff #658 #481)
+#789 := (iff #657 true)
+#793 := (or true true)
+#794 := (iff #793 true)
+#797 := [rewrite]: #794
+#785 := (iff #657 #793)
+#839 := (iff #833 true)
+#841 := [rewrite]: #839
+#639 := (iff #816 true)
+#792 := [rewrite]: #639
+#786 := [monotonicity #792 #841]: #785
+#674 := [trans #786 #797]: #789
+#691 := [monotonicity #674]: #689
+#685 := [trans #691 #843]: #692
+#788 := (iff #801 false)
+#681 := (iff #801 #481)
+#679 := (iff #659 true)
+#795 := (iff #659 #793)
+#796 := [monotonicity #792 #792]: #795
+#680 := [trans #796 #797]: #679
+#640 := [monotonicity #680]: #681
+#690 := [trans #640 #843]: #788
+#695 := [monotonicity #690 #685]: #694
+#787 := [trans #695 #697]: #790
+#774 := [monotonicity #787 #779]: #773
+#777 := [trans #774 #776]: #770
+#800 := (iff #798 true)
+#807 := [rewrite]: #800
+#764 := [monotonicity #807 #777]: #762
+#763 := [trans #764 #766]: #767
+#636 := (iff #805 #804)
+#638 := [rewrite]: #636
+#755 := [monotonicity #807 #638 #763]: #754
+#756 := [trans #755 #758]: #759
+#745 := [monotonicity #756]: #744
+#748 := [trans #745 #747]: #744
+#743 := [quant-inst #8 #8]: #741
+#749 := [mp #743 #748]: #740
+#751 := [unit-resolution #749 #890]: #804
+#752 := [monotonicity #751]: #12
+#13 := (not #12)
+#77 := [asserted]: #13
+[unit-resolution #77 #752]: false
+unsat
+eaf623ea6157604982b5732ebda9f473145c7bd3 326 0
#2 := false
decl f3 :: (-> Int S2)
-#9 := 0::Int
-#27 := (f3 0::Int)
-#11 := 3::Int
-#22 := (- 3::Int)
-#8 := 1::Int
-#21 := (- 1::Int)
-#23 := (div #21 #22)
-#20 := (div 1::Int 3::Int)
-#15 := (< 0::Int 3::Int)
-#17 := (< 1::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 1::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 3::Int 0::Int)
-#10 := (= 1::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (f3 #25)
-#28 := (= #26 #27)
-#29 := (not #28)
-#171 := (iff #29 false)
-#77 := (and #15 #17)
-#80 := (or #16 #77)
-#98 := (ite #80 0::Int 1::Int)
-#108 := (f3 #98)
-#114 := (= #27 #108)
-#119 := (not #114)
-#169 := (iff #119 false)
-#1 := true
-#164 := (not true)
-#167 := (iff #164 false)
-#168 := [rewrite]: #167
-#165 := (iff #119 #164)
-#162 := (iff #114 true)
-#157 := (= #27 #27)
-#160 := (iff #157 true)
-#161 := [rewrite]: #160
-#158 := (iff #114 #157)
-#111 := (= #108 #27)
-#154 := (= #98 0::Int)
-#149 := (ite true 0::Int 1::Int)
-#152 := (= #149 0::Int)
-#153 := [rewrite]: #152
-#150 := (= #98 #149)
-#147 := (iff #80 true)
-#142 := (or true false)
-#145 := (iff #142 true)
-#146 := [rewrite]: #145
-#143 := (iff #80 #142)
-#140 := (iff #77 false)
-#135 := (and true false)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #77 #135)
-#133 := (iff #17 false)
-#134 := [rewrite]: #133
-#124 := (iff #15 true)
-#125 := [rewrite]: #124
-#137 := [monotonicity #125 #134]: #136
-#141 := [trans #137 #139]: #140
-#131 := (iff #16 true)
-#126 := (and true true)
-#129 := (iff #126 true)
-#130 := [rewrite]: #129
-#127 := (iff #16 #126)
-#122 := (iff #14 true)
-#123 := [rewrite]: #122
-#128 := [monotonicity #123 #125]: #127
-#132 := [trans #128 #130]: #131
-#144 := [monotonicity #132 #141]: #143
-#148 := [trans #144 #146]: #147
-#151 := [monotonicity #148]: #150
-#155 := [trans #151 #153]: #154
-#156 := [monotonicity #155]: #111
-#159 := [monotonicity #156]: #158
-#163 := [trans #159 #161]: #162
-#166 := [monotonicity #163]: #165
-#170 := [trans #166 #168]: #169
-#120 := (iff #29 #119)
-#117 := (iff #28 #114)
-#115 := (iff #111 #114)
-#116 := [rewrite]: #115
-#112 := (iff #28 #111)
-#109 := (= #26 #108)
-#106 := (= #25 #98)
-#101 := (ite false 0::Int #98)
-#104 := (= #101 #98)
-#105 := [rewrite]: #104
-#102 := (= #25 #101)
-#99 := (= #24 #98)
-#96 := (= #23 1::Int)
-#88 := -3::Int
-#85 := -1::Int
-#91 := (div -1::Int -3::Int)
-#94 := (= #91 1::Int)
-#95 := [rewrite]: #94
-#92 := (= #23 #91)
-#89 := (= #22 -3::Int)
-#90 := [rewrite]: #89
-#86 := (= #21 -1::Int)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#97 := [trans #93 #95]: #96
-#83 := (= #20 0::Int)
-#84 := [rewrite]: #83
-#81 := (iff #19 #80)
-#78 := (iff #18 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#100 := [monotonicity #82 #84 #97]: #99
-#75 := (iff #13 false)
-#70 := (or false false)
-#73 := (iff #70 false)
-#74 := [rewrite]: #73
-#71 := (iff #13 #70)
-#68 := (iff #12 false)
-#69 := [rewrite]: #68
-#66 := (iff #10 false)
-#67 := [rewrite]: #66
-#72 := [monotonicity #67 #69]: #71
-#76 := [trans #72 #74]: #75
-#103 := [monotonicity #76 #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#118 := [trans #113 #116]: #117
-#121 := [monotonicity #118]: #120
-#172 := [trans #121 #170]: #171
-#65 := [asserted]: #29
-[mp #65 #172]: false
-unsat
-ec979d4232e8803cddce0557ed6997ff67bffe05 83 0
+decl f4 :: (-> Int Int Int)
+#10 := 0::Int
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#11 := (f4 #9 0::Int)
+#12 := (f3 #11)
+#79 := (= f6 #12)
+#450 := (f3 #9)
+#785 := (= #450 #12)
+#784 := (= #12 #450)
+#781 := (= #11 #9)
+#831 := (= #9 #11)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f4 #31 #20)
+#892 := (pattern #50)
+#187 := -1::Int
+#191 := (* -1::Int #20)
+#188 := (* -1::Int #31)
+#252 := (mod #188 #191)
+#382 := (+ #50 #252)
+#383 := (= #382 0::Int)
+#51 := (mod #31 #20)
+#379 := (* -1::Int #51)
+#380 := (+ #50 #379)
+#381 := (= #380 0::Int)
+#226 := (>= #31 0::Int)
+#219 := (<= #20 0::Int)
+#326 := (or #219 #226)
+#327 := (not #326)
+#215 := (<= #31 0::Int)
+#324 := (or #215 #219)
+#325 := (not #324)
+#330 := (or #325 #327)
+#384 := (ite #330 #381 #383)
+#378 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#385 := (ite #33 #378 #384)
+#377 := (= #31 #50)
+#34 := (= #20 0::Int)
+#386 := (ite #34 #377 #385)
+#893 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #892) #386)
+#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
+#896 := (iff #389 #893)
+#894 := (iff #386 #386)
+#895 := [refl]: #894
+#897 := [quant-intro #895]: #896
+#258 := (* -1::Int #252)
+#346 := (ite #330 #51 #258)
+#349 := (ite #33 0::Int #346)
+#352 := (ite #34 #31 #349)
+#355 := (= #50 #352)
+#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
+#390 := (iff #358 #389)
+#387 := (iff #355 #386)
+#388 := [rewrite]: #387
+#391 := [quant-intro #388]: #390
+#227 := (not #226)
+#220 := (not #219)
+#230 := (and #220 #227)
+#216 := (not #215)
+#223 := (and #216 #220)
+#233 := (or #223 #230)
+#278 := (ite #233 #51 #258)
+#281 := (ite #33 0::Int #278)
+#284 := (ite #34 #31 #281)
+#287 := (= #50 #284)
+#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
+#359 := (iff #290 #358)
+#356 := (iff #287 #355)
+#353 := (= #284 #352)
+#350 := (= #281 #349)
+#347 := (= #278 #346)
+#331 := (iff #233 #330)
+#328 := (iff #230 #327)
+#329 := [rewrite]: #328
+#309 := (iff #223 #325)
+#310 := [rewrite]: #309
+#332 := [monotonicity #310 #329]: #331
+#348 := [monotonicity #332]: #347
+#351 := [monotonicity #348]: #350
+#354 := [monotonicity #351]: #353
+#357 := [monotonicity #354]: #356
+#360 := [quant-intro #357]: #359
+#307 := (~ #290 #290)
+#321 := (~ #287 #287)
+#322 := [refl]: #321
+#308 := [nnf-pos #322]: #307
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#293 := (iff #58 #290)
+#181 := (and #37 #39)
+#184 := (or #38 #181)
+#263 := (ite #184 #51 #258)
+#172 := (= 0::Int #31)
+#266 := (ite #172 0::Int #263)
+#175 := (= 0::Int #20)
+#269 := (ite #175 #31 #266)
+#272 := (= #50 #269)
+#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
+#291 := (iff #275 #290)
+#288 := (iff #272 #287)
+#285 := (= #269 #284)
+#282 := (= #266 #281)
+#279 := (= #263 #278)
+#234 := (iff #184 #233)
+#231 := (iff #181 #230)
+#228 := (iff #39 #227)
+#229 := [rewrite]: #228
+#221 := (iff #37 #220)
+#222 := [rewrite]: #221
+#232 := [monotonicity #222 #229]: #231
+#224 := (iff #38 #223)
+#217 := (iff #36 #216)
+#218 := [rewrite]: #217
+#225 := [monotonicity #218 #222]: #224
+#235 := [monotonicity #225 #232]: #234
+#280 := [monotonicity #235]: #279
+#209 := (iff #172 #33)
+#210 := [rewrite]: #209
+#283 := [monotonicity #210 #280]: #282
+#211 := (iff #175 #34)
+#212 := [rewrite]: #211
+#286 := [monotonicity #212 #283]: #285
+#289 := [monotonicity #286]: #288
+#292 := [quant-intro #289]: #291
+#276 := (iff #58 #275)
+#273 := (iff #57 #272)
+#270 := (= #56 #269)
+#267 := (= #55 #266)
+#264 := (= #54 #263)
+#261 := (= #53 #258)
+#255 := (- #252)
+#259 := (= #255 #258)
+#260 := [rewrite]: #259
+#256 := (= #53 #255)
+#253 := (= #52 #252)
+#192 := (= #44 #191)
+#193 := [rewrite]: #192
+#189 := (= #43 #188)
+#190 := [rewrite]: #189
+#254 := [monotonicity #190 #193]: #253
+#257 := [monotonicity #254]: #256
+#262 := [trans #257 #260]: #261
+#185 := (iff #41 #184)
+#182 := (iff #40 #181)
+#183 := [rewrite]: #182
+#186 := [monotonicity #183]: #185
+#265 := [monotonicity #186 #262]: #264
+#173 := (iff #33 #172)
+#174 := [rewrite]: #173
+#268 := [monotonicity #174 #265]: #267
+#176 := (iff #34 #175)
+#177 := [rewrite]: #176
+#271 := [monotonicity #177 #268]: #270
+#274 := [monotonicity #271]: #273
+#277 := [quant-intro #274]: #276
+#294 := [trans #277 #292]: #293
+#251 := [asserted]: #58
+#295 := [mp #251 #294]: #290
+#323 := [mp~ #295 #308]: #290
+#361 := [mp #323 #360]: #358
+#392 := [mp #361 #391]: #389
+#898 := [mp #392 #897]: #893
+#799 := (not #893)
+#786 := (or #799 #831)
+#840 := (* -1::Int 0::Int)
+#846 := (* -1::Int #9)
+#484 := (mod #846 #840)
+#847 := (+ #11 #484)
+#849 := (= #847 0::Int)
+#489 := (mod #9 0::Int)
+#490 := (* -1::Int #489)
+#850 := (+ #11 #490)
+#848 := (= #850 0::Int)
+#851 := (>= #9 0::Int)
+#837 := (<= 0::Int 0::Int)
+#838 := (or #837 #851)
+#560 := (not #838)
+#561 := (<= #9 0::Int)
+#562 := (or #561 #837)
+#563 := (not #562)
+#456 := (or #563 #560)
+#833 := (ite #456 #848 #849)
+#834 := (= #11 0::Int)
+#556 := (= #9 0::Int)
+#557 := (ite #556 #834 #833)
+#835 := (= 0::Int 0::Int)
+#832 := (ite #835 #831 #557)
+#788 := (or #799 #832)
+#777 := (iff #788 #786)
+#789 := (iff #786 #786)
+#790 := [rewrite]: #789
+#798 := (iff #832 #831)
+#801 := (mod #846 0::Int)
+#802 := (+ #11 #801)
+#688 := (= #802 0::Int)
+#699 := (ite #556 #834 #688)
+#1 := true
+#701 := (ite true #831 #699)
+#704 := (iff #701 #831)
+#705 := [rewrite]: #704
+#702 := (iff #832 #701)
+#700 := (iff #557 #699)
+#682 := (iff #833 #688)
+#796 := (ite false #848 #688)
+#794 := (iff #796 #688)
+#797 := [rewrite]: #794
+#698 := (iff #833 #796)
+#689 := (iff #849 #688)
+#805 := (= #847 #802)
+#803 := (= #484 #801)
+#647 := (= #840 0::Int)
+#800 := [rewrite]: #647
+#804 := [monotonicity #800]: #803
+#687 := [monotonicity #804]: #805
+#648 := [monotonicity #687]: #689
+#644 := (iff #456 false)
+#807 := (or false false)
+#808 := (iff #807 false)
+#815 := [rewrite]: #808
+#813 := (iff #456 #807)
+#812 := (iff #560 false)
+#830 := (not true)
+#821 := (iff #830 false)
+#816 := [rewrite]: #821
+#810 := (iff #560 #830)
+#667 := (iff #838 true)
+#823 := (or true #851)
+#665 := (iff #823 true)
+#666 := [rewrite]: #665
+#818 := (iff #838 #823)
+#547 := (iff #837 true)
+#548 := [rewrite]: #547
+#824 := [monotonicity #548]: #818
+#809 := [trans #824 #666]: #667
+#811 := [monotonicity #809]: #810
+#806 := [trans #811 #816]: #812
+#817 := (iff #563 false)
+#819 := (iff #563 #830)
+#829 := (iff #562 true)
+#549 := (or #561 true)
+#543 := (iff #549 true)
+#825 := [rewrite]: #543
+#827 := (iff #562 #549)
+#828 := [monotonicity #548]: #827
+#826 := [trans #828 #825]: #829
+#820 := [monotonicity #826]: #819
+#822 := [trans #820 #816]: #817
+#814 := [monotonicity #822 #806]: #813
+#646 := [trans #814 #815]: #644
+#793 := [monotonicity #646 #648]: #698
+#697 := [trans #793 #797]: #682
+#693 := [monotonicity #697]: #700
+#836 := (iff #835 true)
+#546 := [rewrite]: #836
+#703 := [monotonicity #546 #693]: #702
+#795 := [trans #703 #705]: #798
+#779 := [monotonicity #795]: #777
+#791 := [trans #779 #790]: #777
+#780 := [quant-inst #9 #10]: #788
+#787 := [mp #780 #791]: #786
+#792 := [unit-resolution #787 #898]: #831
+#782 := [symm #792]: #781
+#778 := [monotonicity #782]: #784
+#769 := [symm #778]: #785
+#535 := (= f6 #450)
+#15 := (:var 0 S2)
+#16 := (f5 #15)
+#864 := (pattern #16)
+#17 := (f3 #16)
+#86 := (= #15 #17)
+#865 := (forall (vars (?v0 S2)) (:pat #864) #86)
+#90 := (forall (vars (?v0 S2)) #86)
+#866 := (iff #90 #865)
+#868 := (iff #865 #865)
+#869 := [rewrite]: #868
+#867 := [rewrite]: #866
+#870 := [trans #867 #869]: #866
+#313 := (~ #90 #90)
+#311 := (~ #86 #86)
+#312 := [refl]: #311
+#314 := [nnf-pos #312]: #313
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S2)) #18)
+#91 := (iff #19 #90)
+#88 := (iff #18 #86)
+#89 := [rewrite]: #88
+#92 := [quant-intro #89]: #91
+#85 := [asserted]: #19
+#95 := [mp #85 #92]: #90
+#299 := [mp~ #95 #314]: #90
+#871 := [mp #299 #870]: #865
+#528 := (not #865)
+#539 := (or #528 #535)
+#540 := [quant-inst #8]: #539
+#783 := [unit-resolution #540 #871]: #535
+#770 := [trans #783 #769]: #79
+#82 := (not #79)
+#13 := (= #12 f6)
+#14 := (not #13)
+#83 := (iff #14 #82)
+#80 := (iff #13 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := [asserted]: #14
+#87 := [mp #78 #84]: #82
+[unit-resolution #87 #770]: false
+unsat
+acd2d715307b02a82f8d3d25d1935b122a84c3b3 309 0
+#2 := false
+decl f3 :: (-> Int S2)
+#8 := 0::Int
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 1::Int
+#10 := (f4 0::Int 1::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#805 := (= #10 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f4 #31 #20)
+#884 := (pattern #50)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#245 := (mod #181 #184)
+#375 := (+ #50 #245)
+#376 := (= #375 0::Int)
+#51 := (mod #31 #20)
+#372 := (* -1::Int #51)
+#373 := (+ #50 #372)
+#374 := (= #373 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#377 := (ite #323 #374 #376)
+#371 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#378 := (ite #33 #371 #377)
+#370 := (= #31 #50)
+#34 := (= #20 0::Int)
+#379 := (ite #34 #370 #378)
+#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379)
+#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
+#888 := (iff #382 #885)
+#886 := (iff #379 #379)
+#887 := [refl]: #886
+#889 := [quant-intro #887]: #888
+#251 := (* -1::Int #245)
+#339 := (ite #323 #51 #251)
+#342 := (ite #33 0::Int #339)
+#345 := (ite #34 #31 #342)
+#348 := (= #50 #345)
+#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
+#383 := (iff #351 #382)
+#380 := (iff #348 #379)
+#381 := [rewrite]: #380
+#384 := [quant-intro #381]: #383
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#271 := (ite #226 #51 #251)
+#274 := (ite #33 0::Int #271)
+#277 := (ite #34 #31 #274)
+#280 := (= #50 #277)
+#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
+#352 := (iff #283 #351)
+#349 := (iff #280 #348)
+#346 := (= #277 #345)
+#343 := (= #274 #342)
+#340 := (= #271 #339)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#341 := [monotonicity #325]: #340
+#344 := [monotonicity #341]: #343
+#347 := [monotonicity #344]: #346
+#350 := [monotonicity #347]: #349
+#353 := [quant-intro #350]: #352
+#300 := (~ #283 #283)
+#314 := (~ #280 #280)
+#315 := [refl]: #314
+#301 := [nnf-pos #315]: #300
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#286 := (iff #58 #283)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#256 := (ite #177 #51 #251)
+#165 := (= 0::Int #31)
+#259 := (ite #165 0::Int #256)
+#168 := (= 0::Int #20)
+#262 := (ite #168 #31 #259)
+#265 := (= #50 #262)
+#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
+#284 := (iff #268 #283)
+#281 := (iff #265 #280)
+#278 := (= #262 #277)
+#275 := (= #259 #274)
+#272 := (= #256 #271)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#273 := [monotonicity #228]: #272
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#276 := [monotonicity #203 #273]: #275
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#279 := [monotonicity #205 #276]: #278
+#282 := [monotonicity #279]: #281
+#285 := [quant-intro #282]: #284
+#269 := (iff #58 #268)
+#266 := (iff #57 #265)
+#263 := (= #56 #262)
+#260 := (= #55 #259)
+#257 := (= #54 #256)
+#254 := (= #53 #251)
+#248 := (- #245)
+#252 := (= #248 #251)
+#253 := [rewrite]: #252
+#249 := (= #53 #248)
+#246 := (= #52 #245)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#247 := [monotonicity #183 #186]: #246
+#250 := [monotonicity #247]: #249
+#255 := [trans #250 #253]: #254
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#258 := [monotonicity #179 #255]: #257
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#261 := [monotonicity #167 #258]: #260
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#264 := [monotonicity #170 #261]: #263
+#267 := [monotonicity #264]: #266
+#270 := [quant-intro #267]: #269
+#287 := [trans #270 #285]: #286
+#244 := [asserted]: #58
+#288 := [mp #244 #287]: #283
+#316 := [mp~ #288 #301]: #283
+#354 := [mp #316 #353]: #351
+#385 := [mp #354 #384]: #382
+#890 := [mp #385 #889]: #885
+#728 := (not #885)
+#729 := (or #728 #805)
+#812 := (* -1::Int 1::Int)
+#813 := (* -1::Int 0::Int)
+#808 := (mod #813 #812)
+#809 := (+ #10 #808)
+#814 := (= #809 0::Int)
+#815 := (mod 0::Int 1::Int)
+#810 := (* -1::Int #815)
+#816 := (+ #10 #810)
+#657 := (= #816 0::Int)
+#834 := (>= 0::Int 0::Int)
+#658 := (<= 1::Int 0::Int)
+#659 := (or #658 #834)
+#801 := (not #659)
+#802 := (<= 0::Int 0::Int)
+#803 := (or #802 #658)
+#804 := (not #803)
+#798 := (or #804 #801)
+#799 := (ite #798 #657 #814)
+#806 := (= 0::Int 0::Int)
+#800 := (ite #806 #805 #799)
+#807 := (= 0::Int #10)
+#636 := (= 1::Int 0::Int)
+#638 := (ite #636 #807 #800)
+#724 := (or #728 #638)
+#703 := (iff #724 #729)
+#705 := (iff #729 #729)
+#598 := [rewrite]: #705
+#726 := (iff #638 #805)
+#752 := (ite false #805 #805)
+#731 := (iff #752 #805)
+#732 := [rewrite]: #731
+#722 := (iff #638 #752)
+#725 := (iff #800 #805)
+#1 := true
+#736 := (ite true #805 #805)
+#733 := (iff #736 #805)
+#739 := [rewrite]: #733
+#737 := (iff #800 #736)
+#734 := (iff #799 #805)
+#742 := (iff #799 #752)
+#750 := (iff #814 #805)
+#748 := (= #809 #10)
+#764 := (+ #10 0::Int)
+#767 := (= #764 #10)
+#763 := [rewrite]: #767
+#746 := (= #809 #764)
+#744 := (= #808 0::Int)
+#756 := (mod 0::Int -1::Int)
+#741 := (= #756 0::Int)
+#743 := [rewrite]: #741
+#760 := (= #808 #756)
+#758 := (= #812 -1::Int)
+#759 := [rewrite]: #758
+#770 := (= #813 0::Int)
+#777 := [rewrite]: #770
+#740 := [monotonicity #777 #759]: #760
+#745 := [trans #740 #743]: #744
+#747 := [monotonicity #745]: #746
+#749 := [trans #747 #763]: #748
+#751 := [monotonicity #749]: #750
+#755 := (iff #657 #805)
+#768 := (= #816 #10)
+#765 := (= #816 #764)
+#761 := (= #810 0::Int)
+#775 := (= #810 #813)
+#773 := (= #815 0::Int)
+#774 := [rewrite]: #773
+#776 := [monotonicity #774]: #775
+#762 := [trans #776 #777]: #761
+#766 := [monotonicity #762]: #765
+#754 := [trans #766 #763]: #768
+#757 := [monotonicity #754]: #755
+#779 := (iff #798 false)
+#769 := (or false false)
+#782 := (iff #769 false)
+#783 := [rewrite]: #782
+#771 := (iff #798 #769)
+#780 := (iff #801 false)
+#482 := (not true)
+#843 := (iff #482 false)
+#829 := [rewrite]: #843
+#791 := (iff #801 #482)
+#790 := (iff #659 true)
+#693 := (or false true)
+#696 := (iff #693 true)
+#697 := [rewrite]: #696
+#694 := (iff #659 #693)
+#841 := (iff #834 true)
+#481 := [rewrite]: #841
+#680 := (iff #658 false)
+#681 := [rewrite]: #680
+#695 := [monotonicity #681 #481]: #694
+#787 := [trans #695 #697]: #790
+#778 := [monotonicity #787]: #791
+#772 := [trans #778 #829]: #780
+#692 := (iff #804 false)
+#689 := (iff #804 #482)
+#789 := (iff #803 true)
+#640 := (or true false)
+#785 := (iff #640 true)
+#786 := [rewrite]: #785
+#788 := (iff #803 #640)
+#797 := (iff #802 true)
+#679 := [rewrite]: #797
+#690 := [monotonicity #679 #681]: #788
+#674 := [trans #690 #786]: #789
+#691 := [monotonicity #674]: #689
+#685 := [trans #691 #829]: #692
+#781 := [monotonicity #685 #772]: #771
+#784 := [trans #781 #783]: #779
+#753 := [monotonicity #784 #757 #751]: #742
+#735 := [trans #753 #732]: #734
+#796 := (iff #806 true)
+#794 := [rewrite]: #796
+#738 := [monotonicity #794 #735]: #737
+#721 := [trans #738 #739]: #725
+#793 := (iff #807 #805)
+#795 := [rewrite]: #793
+#639 := (iff #636 false)
+#792 := [rewrite]: #639
+#723 := [monotonicity #792 #795 #721]: #722
+#727 := [trans #723 #732]: #726
+#704 := [monotonicity #727]: #703
+#709 := [trans #704 #598]: #703
+#730 := [quant-inst #8 #9]: #724
+#710 := [mp #730 #709]: #729
+#716 := [unit-resolution #710 #890]: #805
+#712 := [monotonicity #716]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #712]: false
+unsat
+a77f50b29c69935853b053858b12886e75a3e1af 310 0
#2 := false
decl f3 :: (-> Int S2)
-#23 := 1::Int
-#24 := (f3 1::Int)
-#8 := 3::Int
-#18 := (- 3::Int)
-#19 := (div #18 #18)
-#17 := (div 3::Int 3::Int)
-#9 := 0::Int
-#12 := (< 0::Int 3::Int)
-#14 := (< 3::Int 0::Int)
-#15 := (and #14 #12)
-#13 := (and #12 #12)
-#16 := (or #13 #15)
-#20 := (ite #16 #17 #19)
-#10 := (= 3::Int 0::Int)
-#11 := (or #10 #10)
-#21 := (ite #11 0::Int #20)
-#22 := (f3 #21)
-#25 := (= #22 #24)
-#26 := (not #25)
-#119 := (iff #26 false)
-#1 := true
-#114 := (not true)
-#117 := (iff #114 false)
-#118 := [rewrite]: #117
-#115 := (iff #26 #114)
-#112 := (iff #25 true)
-#107 := (= #24 #24)
-#110 := (iff #107 true)
-#111 := [rewrite]: #110
-#108 := (iff #25 #107)
-#104 := (= #21 1::Int)
-#99 := (ite false 0::Int 1::Int)
-#102 := (= #99 1::Int)
-#103 := [rewrite]: #102
-#100 := (= #21 #99)
-#97 := (= #20 1::Int)
-#74 := (and #12 #14)
-#77 := (or #12 #74)
-#92 := (ite #77 1::Int 1::Int)
-#95 := (= #92 1::Int)
-#96 := [rewrite]: #95
-#93 := (= #20 #92)
-#90 := (= #19 1::Int)
-#82 := -3::Int
-#85 := (div -3::Int -3::Int)
-#88 := (= #85 1::Int)
-#89 := [rewrite]: #88
-#86 := (= #19 #85)
-#83 := (= #18 -3::Int)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84 #84]: #86
-#91 := [trans #87 #89]: #90
-#80 := (= #17 1::Int)
-#81 := [rewrite]: #80
-#78 := (iff #16 #77)
-#75 := (iff #15 #74)
-#76 := [rewrite]: #75
-#72 := (iff #13 #12)
-#73 := [rewrite]: #72
-#79 := [monotonicity #73 #76]: #78
-#94 := [monotonicity #79 #81 #91]: #93
-#98 := [trans #94 #96]: #97
-#70 := (iff #11 false)
-#65 := (or false false)
-#68 := (iff #65 false)
-#69 := [rewrite]: #68
-#66 := (iff #11 #65)
-#63 := (iff #10 false)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64 #64]: #66
-#71 := [trans #67 #69]: #70
-#101 := [monotonicity #71 #98]: #100
-#105 := [trans #101 #103]: #104
-#106 := [monotonicity #105]: #25
-#109 := [monotonicity #106]: #108
-#113 := [trans #109 #111]: #112
-#116 := [monotonicity #113]: #115
-#120 := [trans #116 #118]: #119
-#62 := [asserted]: #26
-[mp #62 #120]: false
-unsat
-7e6d147ebdbd2ef1c1366775850a7558514783c8 299 0
-#2 := false
-#10 := 0::Int
-#12 := 3::Int
-decl f3 :: (-> S2 Int)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#402 := (mod #9 3::Int)
-#403 := (>= #402 0::Int)
-#1 := true
-#62 := [true-axiom]: true
-#663 := (or false #403)
-#664 := [th-lemma arith]: #663
-#662 := [unit-resolution #664 #62]: #403
-#84 := -3::Int
-#80 := -1::Int
-#81 := (* -1::Int #9)
-#87 := (div #81 -3::Int)
-#21 := (div #9 3::Int)
-#115 := (>= #9 0::Int)
-#116 := (not #115)
-#102 := (<= #9 0::Int)
-#103 := (not #102)
-#126 := (or #103 #116)
-#129 := (ite #126 #21 #87)
-#11 := (= #9 0::Int)
-#132 := (ite #11 0::Int #129)
-#139 := (* -1::Int #132)
-#140 := (+ #9 #139)
-#138 := (>= #140 0::Int)
-#145 := (not #138)
-#23 := (- 3::Int)
-#22 := (- #9)
-#24 := (div #22 #23)
-#16 := (< 0::Int 3::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= 3::Int 0::Int)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (<= #26 #9)
-#28 := (not #27)
-#148 := (iff #28 #145)
-#74 := (and #16 #18)
-#77 := (or #17 #74)
-#90 := (ite #77 #21 #87)
-#93 := (ite #11 0::Int #90)
-#96 := (<= #93 #9)
-#99 := (not #96)
-#146 := (iff #99 #145)
-#143 := (iff #96 #138)
-#135 := (<= #132 #9)
-#141 := (iff #135 #138)
-#142 := [rewrite]: #141
-#136 := (iff #96 #135)
-#133 := (= #93 #132)
-#130 := (= #90 #129)
-#127 := (iff #77 #126)
-#124 := (iff #74 #116)
-#119 := (and true #116)
-#122 := (iff #119 #116)
-#123 := [rewrite]: #122
-#120 := (iff #74 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#106 := (iff #16 true)
-#107 := [rewrite]: #106
-#121 := [monotonicity #107 #118]: #120
-#125 := [trans #121 #123]: #124
-#113 := (iff #17 #103)
-#108 := (and #103 true)
-#111 := (iff #108 #103)
-#112 := [rewrite]: #111
-#109 := (iff #17 #108)
-#104 := (iff #15 #103)
-#105 := [rewrite]: #104
-#110 := [monotonicity #105 #107]: #109
-#114 := [trans #110 #112]: #113
-#128 := [monotonicity #114 #125]: #127
-#131 := [monotonicity #128]: #130
-#134 := [monotonicity #131]: #133
-#137 := [monotonicity #134]: #136
-#144 := [trans #137 #142]: #143
-#147 := [monotonicity #144]: #146
-#100 := (iff #28 #99)
-#97 := (iff #27 #96)
-#94 := (= #26 #93)
-#91 := (= #25 #90)
-#88 := (= #24 #87)
-#85 := (= #23 -3::Int)
-#86 := [rewrite]: #85
-#82 := (= #22 #81)
-#83 := [rewrite]: #82
-#89 := [monotonicity #83 #86]: #88
-#78 := (iff #20 #77)
-#75 := (iff #19 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#92 := [monotonicity #79 #89]: #91
-#72 := (iff #14 #11)
-#67 := (or #11 false)
-#70 := (iff #67 #11)
-#71 := [rewrite]: #70
-#68 := (iff #14 #67)
-#65 := (iff #13 false)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#95 := [monotonicity #73 #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#149 := [trans #101 #147]: #148
-#64 := [asserted]: #28
-#150 := [mp #64 #149]: #145
-#507 := (+ #21 #139)
-#661 := (>= #507 0::Int)
-#506 := (= #21 #132)
-#395 := (= #129 #132)
-#712 := (not #11)
-#344 := (<= #132 0::Int)
-#309 := (= #132 0::Int)
-#709 := [hypothesis]: #11
-#386 := (or #712 #309)
-#387 := [def-axiom]: #386
-#349 := [unit-resolution #387 #709]: #309
-#350 := (not #309)
-#710 := (or #350 #344)
-#708 := [th-lemma arith triangle-eq]: #710
-#711 := [unit-resolution #708 #349]: #344
-#697 := (or #712 #115)
-#698 := [th-lemma arith triangle-eq]: #697
-#420 := [unit-resolution #698 #709]: #115
-#421 := [th-lemma arith farkas -1 1 1 #420 #150 #711]: false
-#422 := [lemma #421]: #712
-#719 := (or #11 #395)
-#720 := [def-axiom]: #719
-#665 := [unit-resolution #720 #422]: #395
-#310 := (= #21 #129)
-decl f5 :: (-> Int S2)
-#721 := (f5 #9)
-#717 := (f3 #721)
-#723 := (= #717 0::Int)
-#542 := (not #723)
-#557 := (iff #712 #542)
-#654 := (iff #11 #723)
-#558 := (iff #723 #11)
-#508 := (= #717 #9)
-#548 := (= #721 f4)
-#722 := (= f4 #721)
-#29 := (:var 0 S2)
-#30 := (f3 #29)
-#724 := (pattern #30)
-#31 := (f5 #30)
-#152 := (= #29 #31)
-#725 := (forall (vars (?v0 S2)) (:pat #724) #152)
-#155 := (forall (vars (?v0 S2)) #152)
-#726 := (iff #155 #725)
-#728 := (iff #725 #725)
+#11 := 0::Int
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#8 := 1::Int
+#9 := (f4 1::Int 1::Int)
+#10 := (f3 #9)
+#13 := (= #10 #12)
+#799 := (= #9 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f4 #31 #20)
+#884 := (pattern #50)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#245 := (mod #181 #184)
+#375 := (+ #50 #245)
+#376 := (= #375 0::Int)
+#51 := (mod #31 #20)
+#372 := (* -1::Int #51)
+#373 := (+ #50 #372)
+#374 := (= #373 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#377 := (ite #323 #374 #376)
+#371 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#378 := (ite #33 #371 #377)
+#370 := (= #31 #50)
+#34 := (= #20 0::Int)
+#379 := (ite #34 #370 #378)
+#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379)
+#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
+#888 := (iff #382 #885)
+#886 := (iff #379 #379)
+#887 := [refl]: #886
+#889 := [quant-intro #887]: #888
+#251 := (* -1::Int #245)
+#339 := (ite #323 #51 #251)
+#342 := (ite #33 0::Int #339)
+#345 := (ite #34 #31 #342)
+#348 := (= #50 #345)
+#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
+#383 := (iff #351 #382)
+#380 := (iff #348 #379)
+#381 := [rewrite]: #380
+#384 := [quant-intro #381]: #383
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#271 := (ite #226 #51 #251)
+#274 := (ite #33 0::Int #271)
+#277 := (ite #34 #31 #274)
+#280 := (= #50 #277)
+#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
+#352 := (iff #283 #351)
+#349 := (iff #280 #348)
+#346 := (= #277 #345)
+#343 := (= #274 #342)
+#340 := (= #271 #339)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#341 := [monotonicity #325]: #340
+#344 := [monotonicity #341]: #343
+#347 := [monotonicity #344]: #346
+#350 := [monotonicity #347]: #349
+#353 := [quant-intro #350]: #352
+#300 := (~ #283 #283)
+#314 := (~ #280 #280)
+#315 := [refl]: #314
+#301 := [nnf-pos #315]: #300
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#286 := (iff #58 #283)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#256 := (ite #177 #51 #251)
+#165 := (= 0::Int #31)
+#259 := (ite #165 0::Int #256)
+#168 := (= 0::Int #20)
+#262 := (ite #168 #31 #259)
+#265 := (= #50 #262)
+#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
+#284 := (iff #268 #283)
+#281 := (iff #265 #280)
+#278 := (= #262 #277)
+#275 := (= #259 #274)
+#272 := (= #256 #271)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#273 := [monotonicity #228]: #272
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#276 := [monotonicity #203 #273]: #275
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#279 := [monotonicity #205 #276]: #278
+#282 := [monotonicity #279]: #281
+#285 := [quant-intro #282]: #284
+#269 := (iff #58 #268)
+#266 := (iff #57 #265)
+#263 := (= #56 #262)
+#260 := (= #55 #259)
+#257 := (= #54 #256)
+#254 := (= #53 #251)
+#248 := (- #245)
+#252 := (= #248 #251)
+#253 := [rewrite]: #252
+#249 := (= #53 #248)
+#246 := (= #52 #245)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#247 := [monotonicity #183 #186]: #246
+#250 := [monotonicity #247]: #249
+#255 := [trans #250 #253]: #254
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#258 := [monotonicity #179 #255]: #257
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#261 := [monotonicity #167 #258]: #260
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#264 := [monotonicity #170 #261]: #263
+#267 := [monotonicity #264]: #266
+#270 := [quant-intro #267]: #269
+#287 := [trans #270 #285]: #286
+#244 := [asserted]: #58
+#288 := [mp #244 #287]: #283
+#316 := [mp~ #288 #301]: #283
+#354 := [mp #316 #353]: #351
+#385 := [mp #354 #384]: #382
+#890 := [mp #385 #889]: #885
+#703 := (not #885)
+#704 := (or #703 #799)
+#812 := (* -1::Int 1::Int)
+#813 := (mod #812 #812)
+#808 := (+ #9 #813)
+#809 := (= #808 0::Int)
+#814 := (mod 1::Int 1::Int)
+#815 := (* -1::Int #814)
+#810 := (+ #9 #815)
+#816 := (= #810 0::Int)
+#657 := (>= 1::Int 0::Int)
+#658 := (<= 1::Int 0::Int)
+#659 := (or #658 #657)
+#801 := (not #659)
+#802 := (or #658 #658)
+#803 := (not #802)
+#804 := (or #803 #801)
+#798 := (ite #804 #816 #809)
+#805 := (= 1::Int 0::Int)
+#806 := (ite #805 #799 #798)
+#800 := (= 1::Int #9)
+#807 := (ite #805 #800 #806)
+#705 := (or #703 #807)
+#709 := (iff #705 #704)
+#711 := (iff #704 #704)
+#716 := [rewrite]: #711
+#724 := (iff #807 #799)
+#792 := (= #9 1::Int)
+#723 := (ite false #792 #799)
+#728 := (iff #723 #799)
#729 := [rewrite]: #728
-#727 := [rewrite]: #726
-#730 := [trans #727 #729]: #726
-#249 := (~ #155 #155)
-#247 := (~ #152 #152)
-#248 := [refl]: #247
-#250 := [nnf-pos #248]: #249
-#32 := (= #31 #29)
-#33 := (forall (vars (?v0 S2)) #32)
-#156 := (iff #33 #155)
-#153 := (iff #32 #152)
-#154 := [rewrite]: #153
-#157 := [quant-intro #154]: #156
-#151 := [asserted]: #33
-#160 := [mp #151 #157]: #155
-#239 := [mp~ #160 #250]: #155
-#731 := [mp #239 #730]: #725
-#713 := (not #725)
-#373 := (or #713 #722)
-#378 := [quant-inst #8]: #373
-#547 := [unit-resolution #378 #731]: #722
-#549 := [symm #547]: #548
-#656 := [monotonicity #549]: #508
-#653 := [monotonicity #656]: #558
-#657 := [symm #653]: #654
-#559 := [monotonicity #657]: #557
-#560 := [mp #422 #559]: #542
-#374 := (or #115 #723)
-#34 := (:var 0 Int)
-#36 := (f5 #34)
-#732 := (pattern #36)
-#176 := (>= #34 0::Int)
-#37 := (f3 #36)
-#42 := (= #37 0::Int)
-#225 := (or #42 #176)
-#739 := (forall (vars (?v0 Int)) (:pat #732) #225)
-#230 := (forall (vars (?v0 Int)) #225)
-#742 := (iff #230 #739)
-#740 := (iff #225 #225)
-#741 := [refl]: #740
-#743 := [quant-intro #741]: #742
-#243 := (~ #230 #230)
-#251 := (~ #225 #225)
-#252 := [refl]: #251
-#244 := [nnf-pos #252]: #243
-#41 := (< #34 0::Int)
-#43 := (implies #41 #42)
-#44 := (forall (vars (?v0 Int)) #43)
-#233 := (iff #44 #230)
-#196 := (= 0::Int #37)
-#202 := (not #41)
-#203 := (or #202 #196)
-#208 := (forall (vars (?v0 Int)) #203)
-#231 := (iff #208 #230)
-#228 := (iff #203 #225)
-#222 := (or #176 #42)
-#226 := (iff #222 #225)
-#227 := [rewrite]: #226
-#223 := (iff #203 #222)
-#220 := (iff #196 #42)
-#221 := [rewrite]: #220
-#218 := (iff #202 #176)
-#178 := (not #176)
-#213 := (not #178)
-#216 := (iff #213 #176)
-#217 := [rewrite]: #216
-#214 := (iff #202 #213)
-#211 := (iff #41 #178)
-#212 := [rewrite]: #211
-#215 := [monotonicity #212]: #214
-#219 := [trans #215 #217]: #218
-#224 := [monotonicity #219 #221]: #223
-#229 := [trans #224 #227]: #228
-#232 := [quant-intro #229]: #231
-#209 := (iff #44 #208)
-#206 := (iff #43 #203)
-#199 := (implies #41 #196)
-#204 := (iff #199 #203)
-#205 := [rewrite]: #204
-#200 := (iff #43 #199)
-#197 := (iff #42 #196)
-#198 := [rewrite]: #197
-#201 := [monotonicity #198]: #200
-#207 := [trans #201 #205]: #206
-#210 := [quant-intro #207]: #209
-#234 := [trans #210 #232]: #233
-#195 := [asserted]: #44
-#235 := [mp #195 #234]: #230
-#253 := [mp~ #235 #244]: #230
-#744 := [mp #253 #743]: #739
-#699 := (not #739)
-#362 := (or #699 #115 #723)
-#714 := (or #723 #115)
-#363 := (or #699 #714)
-#705 := (iff #363 #362)
-#365 := (or #699 #374)
-#703 := (iff #365 #362)
-#704 := [rewrite]: #703
-#701 := (iff #363 #365)
-#715 := (iff #714 #374)
-#358 := [rewrite]: #715
-#702 := [monotonicity #358]: #701
-#700 := [trans #702 #704]: #705
-#364 := [quant-inst #9]: #363
-#706 := [mp #364 #700]: #362
-#553 := [unit-resolution #706 #744]: #374
-#561 := [unit-resolution #553 #560]: #115
-#562 := (or #11 #103 #116)
-#563 := [th-lemma arith triangle-eq]: #562
-#564 := [unit-resolution #563 #561 #422]: #103
-#397 := (or #126 #102)
-#388 := [def-axiom]: #397
-#565 := [unit-resolution #388 #564]: #126
-#328 := (not #126)
-#716 := (or #328 #310)
-#718 := [def-axiom]: #716
-#658 := [unit-resolution #718 #565]: #310
-#655 := [trans #658 #665]: #506
-#659 := (not #506)
-#646 := (or #659 #661)
-#648 := [th-lemma arith triangle-eq]: #646
-#640 := [unit-resolution #648 #655]: #661
-#696 := (* -1::Int #402)
-#692 := (* -3::Int #21)
-#406 := (+ #692 #696)
-#407 := (+ #9 #406)
-#688 := (>= #407 0::Int)
-#695 := (= #407 0::Int)
-#637 := (or false #695)
-#639 := [th-lemma arith]: #637
-#649 := [unit-resolution #639 #62]: #695
-#650 := (not #695)
-#651 := (or #650 #688)
-#647 := [th-lemma arith triangle-eq]: #651
-#652 := [unit-resolution #647 #649]: #688
-[th-lemma arith farkas 2 1 3 3 1 #561 #652 #640 #150 #662]: false
-unsat
-73ec717ba0bbdd95adecb13ea22d00aede55f061 489 0
+#726 := (iff #807 #723)
+#721 := (iff #806 #799)
+#737 := (ite false #799 #799)
+#739 := (iff #737 #799)
+#725 := [rewrite]: #739
+#738 := (iff #806 #737)
+#735 := (iff #798 #799)
+#1 := true
+#742 := (ite true #799 #799)
+#732 := (iff #742 #799)
+#734 := [rewrite]: #732
+#753 := (iff #798 #742)
+#751 := (iff #809 #799)
+#749 := (= #808 #9)
+#765 := (+ #9 0::Int)
+#763 := (= #765 #9)
+#768 := [rewrite]: #763
+#747 := (= #808 #765)
+#745 := (= #813 0::Int)
+#760 := (mod -1::Int -1::Int)
+#743 := (= #760 0::Int)
+#744 := [rewrite]: #743
+#740 := (= #813 #760)
+#759 := (= #812 -1::Int)
+#756 := [rewrite]: #759
+#741 := [monotonicity #756 #756]: #740
+#746 := [trans #741 #744]: #745
+#748 := [monotonicity #746]: #747
+#750 := [trans #748 #768]: #749
+#752 := [monotonicity #750]: #751
+#757 := (iff #816 #799)
+#754 := (= #810 #9)
+#766 := (= #810 #765)
+#762 := (= #815 0::Int)
+#775 := (* -1::Int 0::Int)
+#777 := (= #775 0::Int)
+#761 := [rewrite]: #777
+#776 := (= #815 #775)
+#773 := (= #814 0::Int)
+#774 := [rewrite]: #773
+#770 := [monotonicity #774]: #776
+#764 := [trans #770 #761]: #762
+#767 := [monotonicity #764]: #766
+#755 := [trans #767 #768]: #754
+#758 := [monotonicity #755]: #757
+#779 := (iff #804 true)
+#769 := (or true false)
+#782 := (iff #769 true)
+#783 := [rewrite]: #782
+#771 := (iff #804 #769)
+#780 := (iff #801 false)
+#482 := (not true)
+#843 := (iff #482 false)
+#829 := [rewrite]: #843
+#791 := (iff #801 #482)
+#790 := (iff #659 true)
+#693 := (or false true)
+#696 := (iff #693 true)
+#697 := [rewrite]: #696
+#694 := (iff #659 #693)
+#692 := (iff #657 true)
+#685 := [rewrite]: #692
+#795 := (iff #658 false)
+#796 := [rewrite]: #795
+#695 := [monotonicity #796 #685]: #694
+#787 := [trans #695 #697]: #790
+#778 := [monotonicity #787]: #791
+#772 := [trans #778 #829]: #780
+#689 := (iff #803 true)
+#690 := (not false)
+#789 := (iff #690 true)
+#674 := [rewrite]: #789
+#785 := (iff #803 #690)
+#640 := (iff #802 false)
+#794 := (or false false)
+#680 := (iff #794 false)
+#681 := [rewrite]: #680
+#797 := (iff #802 #794)
+#679 := [monotonicity #796 #796]: #797
+#788 := [trans #679 #681]: #640
+#786 := [monotonicity #788]: #785
+#691 := [trans #786 #674]: #689
+#781 := [monotonicity #691 #772]: #771
+#784 := [trans #781 #783]: #779
+#731 := [monotonicity #784 #758 #752]: #753
+#736 := [trans #731 #734]: #735
+#636 := (iff #805 false)
+#638 := [rewrite]: #636
+#733 := [monotonicity #638 #736]: #738
+#722 := [trans #733 #725]: #721
+#639 := (iff #800 #792)
+#793 := [rewrite]: #639
+#727 := [monotonicity #638 #793 #722]: #726
+#730 := [trans #727 #729]: #724
+#710 := [monotonicity #730]: #709
+#712 := [trans #710 #716]: #709
+#598 := [quant-inst #8 #8]: #705
+#713 := [mp #598 #712]: #704
+#717 := [unit-resolution #713 #890]: #799
+#718 := [monotonicity #717]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #718]: false
+unsat
+0b8020dc224bc16c2ca4d4c9672c839314b04736 321 0
#2 := false
decl f3 :: (-> Int S2)
-#10 := 0::Int
-#29 := (f3 0::Int)
-decl f5 :: S2
-#8 := f5
-#30 := (= f5 #29)
-decl f4 :: (-> S2 Int)
-#9 := (f4 f5)
-#385 := (f3 #9)
-#662 := (= #385 #29)
-#631 := (= #29 #385)
-#629 := (= 0::Int #9)
-#11 := (= #9 0::Int)
-#12 := 3::Int
-#429 := (mod #9 3::Int)
-#663 := (>= #429 0::Int)
-#1 := true
-#66 := [true-axiom]: true
-#624 := (or false #663)
-#619 := [th-lemma arith]: #624
-#625 := [unit-resolution #619 #66]: #663
-#88 := -3::Int
-#84 := -1::Int
-#85 := (* -1::Int #9)
-#91 := (div #85 -3::Int)
-#21 := (div #9 3::Int)
-#141 := (>= #9 0::Int)
-#142 := (not #141)
-#128 := (<= #9 0::Int)
-#129 := (not #128)
-#152 := (or #129 #142)
-#155 := (ite #152 #21 #91)
-#158 := (ite #11 0::Int #155)
-#628 := (* -1::Int #158)
-#634 := (+ #9 #628)
-#620 := (<= #634 0::Int)
-#633 := (= #9 #158)
-#161 := (f3 #158)
-#708 := (f4 #161)
-#577 := (= #708 #158)
-#703 := (= #158 #708)
-#706 := (>= #158 0::Int)
-#709 := (= #708 0::Int)
-#608 := (not #709)
-#739 := (not #11)
-#609 := (iff #739 #608)
-#611 := (iff #11 #709)
-#605 := (iff #709 #11)
-#493 := (= #708 #9)
-#598 := (= #161 f5)
-#164 := (= f5 #161)
-#664 := (= #29 #161)
-#675 := (= #161 #29)
-#336 := (= #158 0::Int)
-#729 := (f4 #29)
-#727 := (= #729 0::Int)
-#38 := (:var 0 Int)
-#40 := (f3 #38)
-#759 := (pattern #40)
-#203 := (>= #38 0::Int)
-#205 := (not #203)
-#41 := (f4 #40)
-#186 := (= #38 #41)
-#211 := (or #186 #205)
-#760 := (forall (vars (?v0 Int)) (:pat #759) #211)
-#216 := (forall (vars (?v0 Int)) #211)
-#763 := (iff #216 #760)
-#761 := (iff #211 #211)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#268 := (~ #216 #216)
-#267 := (~ #211 #211)
-#264 := [refl]: #267
-#269 := [nnf-pos #264]: #268
-#42 := (= #41 #38)
-#39 := (<= 0::Int #38)
-#43 := (implies #39 #42)
-#44 := (forall (vars (?v0 Int)) #43)
-#219 := (iff #44 #216)
-#193 := (not #39)
-#194 := (or #193 #186)
-#199 := (forall (vars (?v0 Int)) #194)
-#217 := (iff #199 #216)
-#214 := (iff #194 #211)
-#208 := (or #205 #186)
-#212 := (iff #208 #211)
+#12 := 0::Int
+#13 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 1::Int
+#8 := 3::Int
+#10 := (f4 3::Int 1::Int)
+#11 := (f3 #10)
+#14 := (= #11 #13)
+#807 := (= #10 0::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#51 := (f4 #32 #21)
+#885 := (pattern #51)
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#246 := (mod #182 #185)
+#376 := (+ #51 #246)
+#377 := (= #376 0::Int)
+#52 := (mod #32 #21)
+#373 := (* -1::Int #52)
+#374 := (+ #51 #373)
+#375 := (= #374 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#378 := (ite #324 #375 #377)
+#372 := (= #51 0::Int)
+#34 := (= #32 0::Int)
+#379 := (ite #34 #372 #378)
+#371 := (= #32 #51)
+#35 := (= #21 0::Int)
+#380 := (ite #35 #371 #379)
+#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380)
+#383 := (forall (vars (?v0 Int) (?v1 Int)) #380)
+#889 := (iff #383 #886)
+#887 := (iff #380 #380)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#252 := (* -1::Int #246)
+#340 := (ite #324 #52 #252)
+#343 := (ite #34 0::Int #340)
+#346 := (ite #35 #32 #343)
+#349 := (= #51 #346)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#384 := (iff #352 #383)
+#381 := (iff #349 #380)
+#382 := [rewrite]: #381
+#385 := [quant-intro #382]: #384
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#272 := (ite #227 #52 #252)
+#275 := (ite #34 0::Int #272)
+#278 := (ite #35 #32 #275)
+#281 := (= #51 #278)
+#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
+#353 := (iff #284 #352)
+#350 := (iff #281 #349)
+#347 := (= #278 #346)
+#344 := (= #275 #343)
+#341 := (= #272 #340)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#342 := [monotonicity #326]: #341
+#345 := [monotonicity #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [quant-intro #351]: #353
+#301 := (~ #284 #284)
+#315 := (~ #281 #281)
+#316 := [refl]: #315
+#302 := [nnf-pos #316]: #301
+#45 := (- #21)
+#44 := (- #32)
+#53 := (mod #44 #45)
+#54 := (- #53)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#55 := (ite #42 #52 #54)
+#56 := (ite #34 0::Int #55)
+#57 := (ite #35 #32 #56)
+#58 := (= #51 #57)
+#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
+#287 := (iff #59 #284)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#257 := (ite #178 #52 #252)
+#166 := (= 0::Int #32)
+#260 := (ite #166 0::Int #257)
+#169 := (= 0::Int #21)
+#263 := (ite #169 #32 #260)
+#266 := (= #51 #263)
+#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
+#285 := (iff #269 #284)
+#282 := (iff #266 #281)
+#279 := (= #263 #278)
+#276 := (= #260 #275)
+#273 := (= #257 #272)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#274 := [monotonicity #229]: #273
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#277 := [monotonicity #204 #274]: #276
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#280 := [monotonicity #206 #277]: #279
+#283 := [monotonicity #280]: #282
+#286 := [quant-intro #283]: #285
+#270 := (iff #59 #269)
+#267 := (iff #58 #266)
+#264 := (= #57 #263)
+#261 := (= #56 #260)
+#258 := (= #55 #257)
+#255 := (= #54 #252)
+#249 := (- #246)
+#253 := (= #249 #252)
+#254 := [rewrite]: #253
+#250 := (= #54 #249)
+#247 := (= #53 #246)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#248 := [monotonicity #184 #187]: #247
+#251 := [monotonicity #248]: #250
+#256 := [trans #251 #254]: #255
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#259 := [monotonicity #180 #256]: #258
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#262 := [monotonicity #168 #259]: #261
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#265 := [monotonicity #171 #262]: #264
+#268 := [monotonicity #265]: #267
+#271 := [quant-intro #268]: #270
+#288 := [trans #271 #286]: #287
+#245 := [asserted]: #59
+#289 := [mp #245 #288]: #284
+#317 := [mp~ #289 #302]: #284
+#355 := [mp #317 #354]: #352
+#386 := [mp #355 #385]: #383
+#891 := [mp #386 #890]: #886
+#715 := (not #886)
+#718 := (or #715 #807)
+#813 := (* -1::Int 1::Int)
+#814 := (* -1::Int 3::Int)
+#809 := (mod #814 #813)
+#810 := (+ #10 #809)
+#815 := (= #810 0::Int)
+#816 := (mod 3::Int 1::Int)
+#811 := (* -1::Int #816)
+#817 := (+ #10 #811)
+#658 := (= #817 0::Int)
+#659 := (>= 3::Int 0::Int)
+#660 := (<= 1::Int 0::Int)
+#802 := (or #660 #659)
+#803 := (not #802)
+#804 := (<= 3::Int 0::Int)
+#805 := (or #804 #660)
+#799 := (not #805)
+#800 := (or #799 #803)
+#806 := (ite #800 #658 #815)
+#801 := (= 3::Int 0::Int)
+#808 := (ite #801 #807 #806)
+#637 := (= 3::Int #10)
+#639 := (= 1::Int 0::Int)
+#640 := (ite #639 #637 #808)
+#719 := (or #715 #640)
+#716 := (iff #719 #718)
+#701 := (iff #718 #718)
+#647 := [rewrite]: #701
+#713 := (iff #640 #807)
+#797 := (= #10 3::Int)
+#599 := (ite false #797 #807)
+#712 := (iff #599 #807)
+#717 := [rewrite]: #712
+#710 := (iff #640 #599)
+#705 := (iff #808 #807)
+#729 := (ite false #807 #807)
+#731 := (iff #729 #807)
+#704 := [rewrite]: #731
+#730 := (iff #808 #729)
+#727 := (iff #806 #807)
+#1 := true
+#740 := (ite true #807 #807)
+#723 := (iff #740 #807)
+#724 := [rewrite]: #723
+#726 := (iff #806 #740)
+#739 := (iff #815 #807)
+#737 := (= #810 #10)
+#758 := (+ #10 0::Int)
+#757 := (= #758 #10)
+#761 := [rewrite]: #757
+#735 := (= #810 #758)
+#732 := (= #809 0::Int)
+#746 := -3::Int
+#751 := (mod -3::Int -1::Int)
+#743 := (= #751 0::Int)
+#754 := [rewrite]: #743
+#752 := (= #809 #751)
+#749 := (= #813 -1::Int)
+#750 := [rewrite]: #749
+#747 := (= #814 -3::Int)
+#748 := [rewrite]: #747
+#753 := [monotonicity #748 #750]: #752
+#733 := [trans #753 #754]: #732
+#736 := [monotonicity #733]: #735
+#738 := [trans #736 #761]: #737
+#734 := [monotonicity #738]: #739
+#744 := (iff #658 #807)
+#741 := (= #817 #10)
+#759 := (= #817 #758)
+#755 := (= #811 0::Int)
+#766 := (* -1::Int 0::Int)
+#764 := (= #766 0::Int)
+#769 := [rewrite]: #764
+#767 := (= #811 #766)
+#763 := (= #816 0::Int)
+#765 := [rewrite]: #763
+#768 := [monotonicity #765]: #767
+#756 := [trans #768 #769]: #755
+#760 := [monotonicity #756]: #759
+#742 := [trans #760 #761]: #741
+#745 := [monotonicity #742]: #744
+#778 := (iff #800 true)
+#774 := (or true false)
+#777 := (iff #774 true)
+#771 := [rewrite]: #777
+#775 := (iff #800 #774)
+#780 := (iff #803 false)
+#483 := (not true)
+#844 := (iff #483 false)
+#830 := [rewrite]: #844
+#783 := (iff #803 #483)
+#772 := (iff #802 true)
+#792 := (or false true)
+#773 := (iff #792 true)
+#770 := [rewrite]: #773
+#779 := (iff #802 #792)
+#791 := (iff #659 true)
+#788 := [rewrite]: #791
+#641 := (iff #660 false)
+#789 := [rewrite]: #641
+#781 := [monotonicity #789 #788]: #779
+#782 := [trans #781 #770]: #772
+#784 := [monotonicity #782]: #783
+#785 := [trans #784 #830]: #780
+#697 := (iff #799 true)
+#693 := (not false)
+#695 := (iff #693 true)
+#696 := [rewrite]: #695
+#686 := (iff #799 #693)
+#690 := (iff #805 false)
+#691 := (or false false)
+#790 := (iff #691 false)
+#675 := [rewrite]: #790
+#786 := (iff #805 #691)
+#681 := (iff #804 false)
+#682 := [rewrite]: #681
+#787 := [monotonicity #682 #789]: #786
+#692 := [trans #787 #675]: #690
+#694 := [monotonicity #692]: #686
+#698 := [trans #694 #696]: #697
+#776 := [monotonicity #698 #785]: #775
+#762 := [trans #776 #771]: #778
+#722 := [monotonicity #762 #745 #734]: #726
+#728 := [trans #722 #724]: #727
+#798 := (iff #801 false)
+#680 := [rewrite]: #798
+#725 := [monotonicity #680 #728]: #730
+#706 := [trans #725 #704]: #705
+#796 := (iff #637 #797)
+#795 := [rewrite]: #796
+#793 := (iff #639 false)
+#794 := [rewrite]: #793
+#711 := [monotonicity #794 #795 #706]: #710
+#714 := [trans #711 #717]: #713
+#721 := [monotonicity #714]: #716
+#702 := [trans #721 #647]: #716
+#720 := [quant-inst #8 #9]: #719
+#683 := [mp #720 #702]: #718
+#708 := [unit-resolution #683 #891]: #807
+#703 := [monotonicity #708]: #14
+#15 := (not #14)
+#79 := [asserted]: #15
+[unit-resolution #79 #703]: false
+unsat
+beef9b82cbe8a31ac2e4568749757bdaef5ecf77 324 0
+#2 := false
+#13 := 0::Int
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#812 := (>= #9 0::Int)
+#694 := (not #812)
+#801 := (= #9 0::Int)
+#661 := (<= #9 0::Int)
+#683 := (not #661)
+#755 := (or #683 #801 #694)
+#712 := (not #755)
+decl f4 :: (-> Int Int Int)
+#10 := 1::Int
+#11 := (f4 #9 1::Int)
+#800 := (= #11 0::Int)
+#702 := (not #800)
+decl f3 :: (-> Int S2)
+#14 := (f3 0::Int)
+#12 := (f3 #11)
+#15 := (= #12 #14)
+#685 := [hypothesis]: #800
+#644 := [monotonicity #685]: #15
+#16 := (not #15)
+#80 := [asserted]: #16
+#690 := [unit-resolution #80 #644]: false
+#700 := [lemma #690]: #702
+#701 := (or #712 #800)
+#182 := -1::Int
+#824 := (* -1::Int #9)
+#763 := (mod #824 -1::Int)
+#767 := (+ #11 #763)
+#765 := (= #767 0::Int)
+#736 := (ite #755 #800 #765)
+#22 := (:var 0 Int)
+#33 := (:var 1 Int)
+#52 := (f4 #33 #22)
+#886 := (pattern #52)
+#186 := (* -1::Int #22)
+#183 := (* -1::Int #33)
+#247 := (mod #183 #186)
+#377 := (+ #52 #247)
+#378 := (= #377 0::Int)
+#53 := (mod #33 #22)
+#374 := (* -1::Int #53)
+#375 := (+ #52 #374)
+#376 := (= #375 0::Int)
+#221 := (>= #33 0::Int)
+#214 := (<= #22 0::Int)
+#321 := (or #214 #221)
+#322 := (not #321)
+#210 := (<= #33 0::Int)
+#319 := (or #210 #214)
+#320 := (not #319)
+#325 := (or #320 #322)
+#379 := (ite #325 #376 #378)
+#373 := (= #52 0::Int)
+#35 := (= #33 0::Int)
+#380 := (ite #35 #373 #379)
+#372 := (= #33 #52)
+#36 := (= #22 0::Int)
+#381 := (ite #36 #372 #380)
+#887 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #886) #381)
+#384 := (forall (vars (?v0 Int) (?v1 Int)) #381)
+#890 := (iff #384 #887)
+#888 := (iff #381 #381)
+#889 := [refl]: #888
+#891 := [quant-intro #889]: #890
+#253 := (* -1::Int #247)
+#341 := (ite #325 #53 #253)
+#344 := (ite #35 0::Int #341)
+#347 := (ite #36 #33 #344)
+#350 := (= #52 #347)
+#353 := (forall (vars (?v0 Int) (?v1 Int)) #350)
+#385 := (iff #353 #384)
+#382 := (iff #350 #381)
+#383 := [rewrite]: #382
+#386 := [quant-intro #383]: #385
+#222 := (not #221)
+#215 := (not #214)
+#225 := (and #215 #222)
+#211 := (not #210)
+#218 := (and #211 #215)
+#228 := (or #218 #225)
+#273 := (ite #228 #53 #253)
+#276 := (ite #35 0::Int #273)
+#279 := (ite #36 #33 #276)
+#282 := (= #52 #279)
+#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
+#354 := (iff #285 #353)
+#351 := (iff #282 #350)
+#348 := (= #279 #347)
+#345 := (= #276 #344)
+#342 := (= #273 #341)
+#326 := (iff #228 #325)
+#323 := (iff #225 #322)
+#324 := [rewrite]: #323
+#304 := (iff #218 #320)
+#305 := [rewrite]: #304
+#327 := [monotonicity #305 #324]: #326
+#343 := [monotonicity #327]: #342
+#346 := [monotonicity #343]: #345
+#349 := [monotonicity #346]: #348
+#352 := [monotonicity #349]: #351
+#355 := [quant-intro #352]: #354
+#302 := (~ #285 #285)
+#316 := (~ #282 #282)
+#317 := [refl]: #316
+#303 := [nnf-pos #317]: #302
+#46 := (- #22)
+#45 := (- #33)
+#54 := (mod #45 #46)
+#55 := (- #54)
+#39 := (< 0::Int #22)
+#41 := (< #33 0::Int)
+#42 := (and #41 #39)
+#38 := (< 0::Int #33)
+#40 := (and #38 #39)
+#43 := (or #40 #42)
+#56 := (ite #43 #53 #55)
+#57 := (ite #35 0::Int #56)
+#58 := (ite #36 #33 #57)
+#59 := (= #52 #58)
+#60 := (forall (vars (?v0 Int) (?v1 Int)) #59)
+#288 := (iff #60 #285)
+#176 := (and #39 #41)
+#179 := (or #40 #176)
+#258 := (ite #179 #53 #253)
+#167 := (= 0::Int #33)
+#261 := (ite #167 0::Int #258)
+#170 := (= 0::Int #22)
+#264 := (ite #170 #33 #261)
+#267 := (= #52 #264)
+#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
+#286 := (iff #270 #285)
+#283 := (iff #267 #282)
+#280 := (= #264 #279)
+#277 := (= #261 #276)
+#274 := (= #258 #273)
+#229 := (iff #179 #228)
+#226 := (iff #176 #225)
+#223 := (iff #41 #222)
+#224 := [rewrite]: #223
+#216 := (iff #39 #215)
+#217 := [rewrite]: #216
+#227 := [monotonicity #217 #224]: #226
+#219 := (iff #40 #218)
+#212 := (iff #38 #211)
#213 := [rewrite]: #212
-#209 := (iff #194 #208)
-#206 := (iff #193 #205)
-#202 := (iff #39 #203)
-#204 := [rewrite]: #202
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#215 := [trans #210 #213]: #214
-#218 := [quant-intro #215]: #217
-#200 := (iff #44 #199)
-#197 := (iff #43 #194)
-#190 := (implies #39 #186)
-#195 := (iff #190 #194)
-#196 := [rewrite]: #195
-#191 := (iff #43 #190)
-#188 := (iff #42 #186)
-#189 := [rewrite]: #188
-#192 := [monotonicity #189]: #191
-#198 := [trans #192 #196]: #197
-#201 := [quant-intro #198]: #200
-#220 := [trans #201 #218]: #219
-#185 := [asserted]: #44
-#221 := [mp #185 #220]: #216
-#265 := [mp~ #221 #269]: #216
-#765 := [mp #265 #764]: #760
-#721 := (not #760)
-#443 := (or #721 #727)
-#389 := (>= 0::Int 0::Int)
-#390 := (not #389)
-#730 := (= 0::Int #729)
-#731 := (or #730 #390)
-#444 := (or #721 #731)
-#722 := (iff #444 #443)
-#723 := (iff #443 #443)
-#433 := [rewrite]: #723
-#343 := (iff #731 #727)
-#725 := (or #727 false)
-#449 := (iff #725 #727)
-#450 := [rewrite]: #449
-#447 := (iff #731 #725)
-#738 := (iff #390 false)
-#736 := (not true)
-#737 := (iff #736 false)
-#735 := [rewrite]: #737
-#376 := (iff #390 #736)
-#371 := (iff #389 true)
-#734 := [rewrite]: #371
-#377 := [monotonicity #734]: #376
-#724 := [trans #377 #735]: #738
-#732 := (iff #730 #727)
-#733 := [rewrite]: #732
-#448 := [monotonicity #733 #724]: #447
-#720 := [trans #448 #450]: #343
-#719 := [monotonicity #720]: #722
-#434 := [trans #719 #433]: #722
-#718 := [quant-inst #10]: #444
-#435 := [mp #718 #434]: #443
-#590 := [unit-resolution #435 #765]: #727
-#685 := (= #9 #729)
-#748 := (not #164)
-#588 := [hypothesis]: #748
-#401 := (or #30 #164)
-#122 := (not #30)
-#170 := (iff #122 #164)
-#23 := (- 3::Int)
-#22 := (- #9)
-#24 := (div #22 #23)
-#16 := (< 0::Int 3::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= 3::Int 0::Int)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (f3 #26)
-#28 := (= #27 f5)
-#31 := (iff #28 #30)
-#32 := (not #31)
-#175 := (iff #32 #170)
-#78 := (and #16 #18)
-#81 := (or #17 #78)
-#94 := (ite #81 #21 #91)
-#97 := (ite #11 0::Int #94)
-#100 := (f3 #97)
-#106 := (= f5 #100)
-#123 := (iff #106 #122)
-#173 := (iff #123 #170)
-#167 := (iff #164 #122)
-#171 := (iff #167 #170)
+#220 := [monotonicity #213 #217]: #219
+#230 := [monotonicity #220 #227]: #229
+#275 := [monotonicity #230]: #274
+#204 := (iff #167 #35)
+#205 := [rewrite]: #204
+#278 := [monotonicity #205 #275]: #277
+#206 := (iff #170 #36)
+#207 := [rewrite]: #206
+#281 := [monotonicity #207 #278]: #280
+#284 := [monotonicity #281]: #283
+#287 := [quant-intro #284]: #286
+#271 := (iff #60 #270)
+#268 := (iff #59 #267)
+#265 := (= #58 #264)
+#262 := (= #57 #261)
+#259 := (= #56 #258)
+#256 := (= #55 #253)
+#250 := (- #247)
+#254 := (= #250 #253)
+#255 := [rewrite]: #254
+#251 := (= #55 #250)
+#248 := (= #54 #247)
+#187 := (= #46 #186)
+#188 := [rewrite]: #187
+#184 := (= #45 #183)
+#185 := [rewrite]: #184
+#249 := [monotonicity #185 #188]: #248
+#252 := [monotonicity #249]: #251
+#257 := [trans #252 #255]: #256
+#180 := (iff #43 #179)
+#177 := (iff #42 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
+#260 := [monotonicity #181 #257]: #259
+#168 := (iff #35 #167)
+#169 := [rewrite]: #168
+#263 := [monotonicity #169 #260]: #262
+#171 := (iff #36 #170)
#172 := [rewrite]: #171
-#168 := (iff #123 #167)
-#165 := (iff #106 #164)
-#162 := (= #100 #161)
-#159 := (= #97 #158)
-#156 := (= #94 #155)
-#153 := (iff #81 #152)
-#150 := (iff #78 #142)
-#145 := (and true #142)
-#148 := (iff #145 #142)
-#149 := [rewrite]: #148
-#146 := (iff #78 #145)
-#143 := (iff #18 #142)
-#144 := [rewrite]: #143
-#132 := (iff #16 true)
-#133 := [rewrite]: #132
-#147 := [monotonicity #133 #144]: #146
-#151 := [trans #147 #149]: #150
-#139 := (iff #17 #129)
-#134 := (and #129 true)
-#137 := (iff #134 #129)
-#138 := [rewrite]: #137
-#135 := (iff #17 #134)
-#130 := (iff #15 #129)
-#131 := [rewrite]: #130
-#136 := [monotonicity #131 #133]: #135
-#140 := [trans #136 #138]: #139
-#154 := [monotonicity #140 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#174 := [trans #169 #172]: #173
-#126 := (iff #32 #123)
-#114 := (iff #30 #106)
-#119 := (not #114)
-#124 := (iff #119 #123)
-#125 := [rewrite]: #124
-#120 := (iff #32 #119)
-#117 := (iff #31 #114)
-#111 := (iff #106 #30)
-#115 := (iff #111 #114)
-#116 := [rewrite]: #115
-#112 := (iff #31 #111)
-#109 := (iff #28 #106)
-#103 := (= #100 f5)
-#107 := (iff #103 #106)
-#108 := [rewrite]: #107
-#104 := (iff #28 #103)
-#101 := (= #27 #100)
-#98 := (= #26 #97)
-#95 := (= #25 #94)
-#92 := (= #24 #91)
-#89 := (= #23 -3::Int)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#82 := (iff #20 #81)
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#96 := [monotonicity #83 #93]: #95
-#76 := (iff #14 #11)
-#71 := (or #11 false)
-#74 := (iff #71 #11)
-#75 := [rewrite]: #74
-#72 := (iff #14 #71)
-#69 := (iff #13 false)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#99 := [monotonicity #77 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#110 := [trans #105 #108]: #109
-#113 := [monotonicity #110]: #112
-#118 := [trans #113 #116]: #117
-#121 := [monotonicity #118]: #120
-#127 := [trans #121 #125]: #126
-#176 := [trans #127 #174]: #175
-#68 := [asserted]: #32
-#177 := [mp #68 #176]: #170
-#749 := (not #170)
-#405 := (or #30 #164 #749)
-#741 := [def-axiom]: #405
-#742 := [unit-resolution #741 #177]: #401
-#589 := [unit-resolution #742 #588]: #30
-#682 := [monotonicity #589]: #685
-#686 := [trans #682 #590]: #11
-#413 := (or #739 #336)
-#414 := [def-axiom]: #413
-#673 := [unit-resolution #414 #686]: #336
-#667 := [monotonicity #673]: #675
-#666 := [symm #667]: #664
-#676 := [trans #589 #666]: #164
-#677 := [unit-resolution #588 #676]: false
-#678 := [lemma #677]: #164
-#599 := [symm #678]: #598
-#604 := [monotonicity #599]: #493
-#606 := [monotonicity #604]: #605
-#607 := [symm #606]: #611
-#612 := [monotonicity #607]: #609
-#600 := [hypothesis]: #739
-#613 := [mp #600 #612]: #608
-#697 := (or #706 #709)
-#46 := (= #41 0::Int)
-#252 := (or #46 #203)
-#766 := (forall (vars (?v0 Int)) (:pat #759) #252)
-#257 := (forall (vars (?v0 Int)) #252)
-#769 := (iff #257 #766)
-#767 := (iff #252 #252)
-#768 := [refl]: #767
-#770 := [quant-intro #768]: #769
-#270 := (~ #257 #257)
-#278 := (~ #252 #252)
-#279 := [refl]: #278
-#271 := [nnf-pos #279]: #270
-#45 := (< #38 0::Int)
-#47 := (implies #45 #46)
-#48 := (forall (vars (?v0 Int)) #47)
-#260 := (iff #48 #257)
-#223 := (= 0::Int #41)
-#229 := (not #45)
-#230 := (or #229 #223)
-#235 := (forall (vars (?v0 Int)) #230)
-#258 := (iff #235 #257)
-#255 := (iff #230 #252)
-#249 := (or #203 #46)
-#253 := (iff #249 #252)
-#254 := [rewrite]: #253
-#250 := (iff #230 #249)
-#247 := (iff #223 #46)
-#248 := [rewrite]: #247
-#245 := (iff #229 #203)
-#240 := (not #205)
-#243 := (iff #240 #203)
-#244 := [rewrite]: #243
-#241 := (iff #229 #240)
-#238 := (iff #45 #205)
-#239 := [rewrite]: #238
-#242 := [monotonicity #239]: #241
-#246 := [trans #242 #244]: #245
-#251 := [monotonicity #246 #248]: #250
-#256 := [trans #251 #254]: #255
-#259 := [quant-intro #256]: #258
-#236 := (iff #48 #235)
-#233 := (iff #47 #230)
-#226 := (implies #45 #223)
-#231 := (iff #226 #230)
-#232 := [rewrite]: #231
-#227 := (iff #47 #226)
-#224 := (iff #46 #223)
-#225 := [rewrite]: #224
-#228 := [monotonicity #225]: #227
-#234 := [trans #228 #232]: #233
-#237 := [quant-intro #234]: #236
-#261 := [trans #237 #259]: #260
-#222 := [asserted]: #48
-#262 := [mp #222 #261]: #257
-#280 := [mp~ #262 #271]: #257
-#771 := [mp #280 #770]: #766
-#693 := (not #766)
-#694 := (or #693 #706 #709)
-#710 := (or #709 #706)
-#700 := (or #693 #710)
-#687 := (iff #700 #694)
-#695 := (or #693 #697)
-#533 := (iff #695 #694)
-#534 := [rewrite]: #533
-#702 := (iff #700 #695)
-#698 := (iff #710 #697)
-#699 := [rewrite]: #698
-#531 := [monotonicity #699]: #702
-#688 := [trans #531 #534]: #687
-#701 := [quant-inst #158]: #700
-#690 := [mp #701 #688]: #694
-#614 := [unit-resolution #690 #771]: #697
-#610 := [unit-resolution #614 #613]: #706
-#707 := (not #706)
-#704 := (or #703 #707)
-#705 := (or #721 #703 #707)
-#711 := (or #721 #704)
-#553 := (iff #711 #705)
-#554 := [rewrite]: #553
-#552 := [quant-inst #158]: #711
-#696 := [mp #552 #554]: #705
-#615 := [unit-resolution #696 #765]: #704
-#595 := [unit-resolution #615 #610]: #703
-#601 := [symm #595]: #577
-#541 := (= #9 #708)
-#596 := [symm #604]: #541
-#602 := [trans #596 #601]: #633
-#597 := (not #633)
-#603 := (or #597 #620)
-#571 := [th-lemma arith triangle-eq]: #603
-#578 := [unit-resolution #571 #602]: #620
-#618 := (+ #21 #628)
-#622 := (>= #618 0::Int)
-#617 := (= #21 #158)
-#422 := (= #155 #158)
-#746 := (or #11 #422)
-#747 := [def-axiom]: #746
-#537 := [unit-resolution #747 #600]: #422
-#337 := (= #21 #155)
-#691 := (f4 #385)
-#689 := (= #691 0::Int)
-#594 := (not #689)
-#549 := (iff #739 #594)
-#593 := (iff #11 #689)
-#582 := (iff #689 #11)
-#579 := (= #691 #9)
-#570 := (= #385 f5)
-#726 := (= f5 #385)
-#33 := (:var 0 S2)
-#34 := (f4 #33)
-#751 := (pattern #34)
-#35 := (f3 #34)
-#179 := (= #33 #35)
-#752 := (forall (vars (?v0 S2)) (:pat #751) #179)
-#182 := (forall (vars (?v0 S2)) #179)
-#753 := (iff #182 #752)
-#755 := (iff #752 #752)
-#756 := [rewrite]: #755
-#754 := [rewrite]: #753
-#757 := [trans #754 #756]: #753
-#276 := (~ #182 #182)
-#274 := (~ #179 #179)
-#275 := [refl]: #274
-#277 := [nnf-pos #275]: #276
-#36 := (= #35 #33)
-#37 := (forall (vars (?v0 S2)) #36)
-#183 := (iff #37 #182)
-#180 := (iff #36 #179)
-#181 := [rewrite]: #180
-#184 := [quant-intro #181]: #183
-#178 := [asserted]: #37
-#187 := [mp #178 #184]: #182
-#266 := [mp~ #187 #277]: #182
-#758 := [mp #266 #757]: #752
-#391 := (not #752)
-#392 := (or #391 #726)
-#728 := [quant-inst #8]: #392
-#568 := [unit-resolution #728 #758]: #726
-#572 := [symm #568]: #570
-#581 := [monotonicity #572]: #579
-#583 := [monotonicity #581]: #582
-#573 := [symm #583]: #593
-#550 := [monotonicity #573]: #549
-#555 := [mp #600 #550]: #594
-#574 := (or #141 #689)
-#535 := (or #693 #141 #689)
-#692 := (or #689 #141)
-#683 := (or #693 #692)
-#586 := (iff #683 #535)
-#680 := (or #693 #574)
-#569 := (iff #680 #535)
-#584 := [rewrite]: #569
-#681 := (iff #683 #680)
-#575 := (iff #692 #574)
-#576 := [rewrite]: #575
-#684 := [monotonicity #576]: #681
-#587 := [trans #684 #584]: #586
-#585 := [quant-inst #9]: #683
-#580 := [mp #585 #587]: #535
-#556 := [unit-resolution #580 #771]: #574
-#557 := [unit-resolution #556 #555]: #141
-#558 := (or #11 #129 #142)
-#559 := [th-lemma arith triangle-eq]: #558
-#560 := [unit-resolution #559 #600]: #152
-#561 := [unit-resolution #560 #557]: #129
-#424 := (or #152 #128)
-#415 := [def-axiom]: #424
-#562 := [unit-resolution #415 #561]: #152
-#355 := (not #152)
-#743 := (or #355 #337)
-#745 := [def-axiom]: #743
-#563 := [unit-resolution #745 #562]: #337
-#564 := [trans #563 #537]: #617
-#565 := (not #617)
-#566 := (or #565 #622)
-#551 := [th-lemma arith triangle-eq]: #566
-#567 := [unit-resolution #551 #564]: #622
-#656 := (* -1::Int #429)
-#672 := (* -3::Int #21)
-#657 := (+ #672 #656)
-#659 := (+ #9 #657)
-#658 := (>= #659 0::Int)
-#665 := (= #659 0::Int)
-#528 := (or false #665)
-#529 := [th-lemma arith]: #528
-#536 := [unit-resolution #529 #66]: #665
-#538 := (not #665)
-#539 := (or #538 #658)
-#540 := [th-lemma arith triangle-eq]: #539
-#542 := [unit-resolution #540 #536]: #658
-#543 := [th-lemma arith farkas 2 1 3 3 1 #561 #542 #567 #578 #625]: false
-#544 := [lemma #543]: #11
-#630 := [symm #544]: #629
-#632 := [monotonicity #630]: #631
-#616 := [symm #632]: #662
-#621 := [trans #568 #616]: #30
-#740 := (or #122 #748)
-#744 := (or #122 #748 #749)
-#750 := [def-axiom]: #744
-#400 := [unit-resolution #750 #177]: #740
-#627 := [unit-resolution #400 #678]: #122
-[unit-resolution #627 #621]: false
-unsat
-1f21dc1a1f14ef0634d3f8992746cd150b8c3799 78 0
+#266 := [monotonicity #172 #263]: #265
+#269 := [monotonicity #266]: #268
+#272 := [quant-intro #269]: #271
+#289 := [trans #272 #287]: #288
+#246 := [asserted]: #60
+#290 := [mp #246 #289]: #285
+#318 := [mp~ #290 #303]: #285
+#356 := [mp #318 #355]: #353
+#387 := [mp #356 #386]: #384
+#892 := [mp #387 #891]: #887
+#735 := (not #887)
+#741 := (or #735 #736)
+#820 := (* -1::Int 1::Int)
+#813 := (mod #824 #820)
+#814 := (+ #11 #813)
+#815 := (= #814 0::Int)
+#810 := (mod #9 1::Int)
+#811 := (* -1::Int #810)
+#816 := (+ #11 #811)
+#817 := (= #816 0::Int)
+#818 := (<= 1::Int 0::Int)
+#659 := (or #818 #812)
+#660 := (not #659)
+#803 := (or #661 #818)
+#804 := (not #803)
+#805 := (or #804 #660)
+#806 := (ite #805 #817 #815)
+#807 := (ite #801 #800 #806)
+#808 := (= #9 #11)
+#802 := (= 1::Int 0::Int)
+#809 := (ite #802 #808 #807)
+#727 := (or #735 #809)
+#724 := (iff #727 #741)
+#728 := (iff #741 #741)
+#729 := [rewrite]: #728
+#739 := (iff #809 #736)
+#696 := (or #683 #694)
+#742 := (or #696 #801)
+#743 := (ite #742 #800 #765)
+#737 := (iff #743 #736)
+#733 := (iff #742 #755)
+#734 := [rewrite]: #733
+#738 := [monotonicity #734]: #737
+#754 := (iff #809 #743)
+#749 := (ite false #808 #743)
+#752 := (iff #749 #743)
+#753 := [rewrite]: #752
+#750 := (iff #809 #749)
+#747 := (iff #807 #743)
+#757 := (ite #696 #800 #765)
+#761 := (ite #801 #800 #757)
+#745 := (iff #761 #743)
+#746 := [rewrite]: #745
+#758 := (iff #807 #761)
+#759 := (iff #806 #757)
+#770 := (iff #815 #765)
+#768 := (= #814 #767)
+#764 := (= #813 #763)
+#772 := (= #820 -1::Int)
+#779 := [rewrite]: #772
+#766 := [monotonicity #779]: #764
+#769 := [monotonicity #766]: #768
+#756 := [monotonicity #769]: #770
+#777 := (iff #817 #800)
+#775 := (= #816 #11)
+#783 := (+ #11 0::Int)
+#781 := (= #783 #11)
+#786 := [rewrite]: #781
+#784 := (= #816 #783)
+#771 := (= #811 0::Int)
+#789 := (* -1::Int 0::Int)
+#782 := (= #789 0::Int)
+#774 := [rewrite]: #782
+#793 := (= #811 #789)
+#699 := (= #810 0::Int)
+#792 := [rewrite]: #699
+#780 := [monotonicity #792]: #793
+#773 := [trans #780 #774]: #771
+#785 := [monotonicity #773]: #784
+#776 := [trans #785 #786]: #775
+#778 := [monotonicity #776]: #777
+#697 := (iff #805 #696)
+#687 := (iff #660 #694)
+#691 := (iff #659 #812)
+#692 := (or false #812)
+#791 := (iff #692 #812)
+#676 := [rewrite]: #791
+#787 := (iff #659 #692)
+#641 := (iff #818 false)
+#794 := [rewrite]: #641
+#788 := [monotonicity #794]: #787
+#693 := [trans #788 #676]: #691
+#695 := [monotonicity #693]: #687
+#642 := (iff #804 #683)
+#681 := (iff #803 #661)
+#795 := (or #661 false)
+#796 := (iff #795 #661)
+#799 := [rewrite]: #796
+#797 := (iff #803 #795)
+#798 := [monotonicity #794]: #797
+#682 := [trans #798 #799]: #681
+#790 := [monotonicity #682]: #642
+#698 := [monotonicity #790 #695]: #697
+#760 := [monotonicity #698 #778 #756]: #759
+#762 := [monotonicity #760]: #758
+#748 := [trans #762 #746]: #747
+#638 := (iff #802 false)
+#640 := [rewrite]: #638
+#751 := [monotonicity #640 #748]: #750
+#744 := [trans #751 #753]: #754
+#740 := [trans #744 #738]: #739
+#725 := [monotonicity #740]: #724
+#730 := [trans #725 #729]: #724
+#723 := [quant-inst #9 #10]: #727
+#731 := [mp #723 #730]: #741
+#680 := [unit-resolution #731 #892]: #736
+#719 := (not #736)
+#720 := (or #719 #712 #800)
+#721 := [def-axiom]: #720
+#656 := [unit-resolution #721 #680]: #701
+#657 := [unit-resolution #656 #700]: #712
+#600 := (or #755 #812)
+#711 := [def-axiom]: #600
+#662 := [unit-resolution #711 #657]: #812
+#726 := (or #755 #661)
+#732 := [def-axiom]: #726
+#663 := [unit-resolution #732 #657]: #661
+#705 := (not #801)
+#706 := (or #755 #705)
+#707 := [def-axiom]: #706
+#664 := [unit-resolution #707 #657]: #705
+#665 := (or #801 #683 #694)
+#666 := [th-lemma arith triangle-eq]: #665
+[unit-resolution #666 #664 #663 #662]: false
+unsat
+9fbefb874a9c8d1ffb3917c9db0286d637e8beaf 310 0
#2 := false
decl f3 :: (-> Int S2)
#8 := 0::Int
-#21 := (f3 0::Int)
-#14 := (- 0::Int)
-#15 := (mod #14 #14)
-#16 := (- #15)
-#13 := (mod 0::Int 0::Int)
-#10 := (< 0::Int 0::Int)
-#11 := (and #10 #10)
-#12 := (or #11 #11)
-#17 := (ite #12 #13 #16)
-#9 := (= 0::Int 0::Int)
-#18 := (ite #9 0::Int #17)
-#19 := (ite #9 0::Int #18)
-#20 := (f3 #19)
-#22 := (= #20 #21)
-#23 := (not #22)
-#114 := (iff #23 false)
-#1 := true
-#109 := (not true)
-#112 := (iff #109 false)
-#113 := [rewrite]: #112
-#110 := (iff #23 #109)
-#107 := (iff #22 true)
-#102 := (= #21 #21)
-#105 := (iff #102 true)
-#106 := [rewrite]: #105
-#103 := (iff #22 #102)
-#99 := (= #19 0::Int)
-#94 := (ite true 0::Int 0::Int)
-#97 := (= #94 0::Int)
-#98 := [rewrite]: #97
-#95 := (= #19 #94)
-#92 := (= #18 0::Int)
-#78 := -1::Int
-#79 := (* -1::Int #13)
-#84 := (ite #10 #13 #79)
-#87 := (ite true 0::Int #84)
-#90 := (= #87 0::Int)
-#91 := [rewrite]: #90
-#88 := (= #18 #87)
-#85 := (= #17 #84)
-#82 := (= #16 #79)
-#75 := (- #13)
-#80 := (= #75 #79)
-#81 := [rewrite]: #80
-#76 := (= #16 #75)
-#73 := (= #15 #13)
-#71 := (= #14 0::Int)
-#72 := [rewrite]: #71
-#74 := [monotonicity #72 #72]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#69 := (iff #12 #10)
-#64 := (or #10 #10)
-#67 := (iff #64 #10)
-#68 := [rewrite]: #67
-#65 := (iff #12 #64)
-#62 := (iff #11 #10)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63 #63]: #65
-#70 := [trans #66 #68]: #69
-#86 := [monotonicity #70 #83]: #85
-#60 := (iff #9 true)
-#61 := [rewrite]: #60
-#89 := [monotonicity #61 #86]: #88
-#93 := [trans #89 #91]: #92
-#96 := [monotonicity #61 #93]: #95
-#100 := [trans #96 #98]: #99
-#101 := [monotonicity #100]: #22
-#104 := [monotonicity #101]: #103
-#108 := [trans #104 #106]: #107
-#111 := [monotonicity #108]: #110
-#115 := [trans #111 #113]: #114
-#59 := [asserted]: #23
-[mp #59 #115]: false
-unsat
-18c694d062a2e495b90f6c40f36cef6e909d6c58 115 0
-#2 := false
-decl f4 :: (-> S2 Int)
-#30 := (:var 0 S2)
-#31 := (f4 #30)
-#695 := (pattern #31)
-decl f3 :: (-> Int S2)
-#32 := (f3 #31)
-#122 := (= #30 #32)
-#696 := (forall (vars (?v0 S2)) (:pat #695) #122)
-#126 := (forall (vars (?v0 S2)) #122)
-#697 := (iff #126 #696)
-#699 := (iff #696 #696)
-#700 := [rewrite]: #699
-#698 := [rewrite]: #697
-#701 := [trans #698 #700]: #697
-#220 := (~ #126 #126)
-#218 := (~ #122 #122)
-#219 := [refl]: #218
-#221 := [nnf-pos #219]: #220
-#33 := (= #32 #30)
-#34 := (forall (vars (?v0 S2)) #33)
-#127 := (iff #34 #126)
-#124 := (iff #33 #122)
-#125 := [rewrite]: #124
-#128 := [quant-intro #125]: #127
-#121 := [asserted]: #34
-#131 := [mp #121 #128]: #126
-#210 := [mp~ #131 #221]: #126
-#702 := [mp #210 #701]: #696
-decl f5 :: S2
-#10 := f5
-#11 := (f4 f5)
-#107 := (f3 #11)
-#113 := (= f5 #107)
-#118 := (not #113)
-#8 := 0::Int
-#21 := (- 0::Int)
-#20 := (- #11)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod #11 0::Int)
-#14 := (< 0::Int 0::Int)
-#16 := (< #11 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int #11)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= #11 0::Int)
-#25 := (ite #12 0::Int #24)
-#9 := (= 0::Int 0::Int)
-#26 := (ite #9 #11 #25)
-#27 := (f3 #26)
-#28 := (= #27 f5)
-#29 := (not #28)
-#119 := (iff #29 #118)
-#116 := (iff #28 #113)
-#110 := (= #107 f5)
-#114 := (iff #110 #113)
-#115 := [rewrite]: #114
-#111 := (iff #28 #110)
-#108 := (= #27 #107)
-#105 := (= #26 #11)
-#77 := -1::Int
-#78 := (* -1::Int #11)
-#83 := (mod #78 0::Int)
-#89 := (* -1::Int #83)
-#71 := (and #14 #16)
-#74 := (or #15 #71)
-#94 := (ite #74 #19 #89)
-#68 := (= 0::Int #11)
-#97 := (ite #68 0::Int #94)
-#1 := true
-#100 := (ite true #11 #97)
-#103 := (= #100 #11)
-#104 := [rewrite]: #103
-#101 := (= #26 #100)
-#98 := (= #25 #97)
-#95 := (= #24 #94)
-#92 := (= #23 #89)
-#86 := (- #83)
-#90 := (= #86 #89)
-#91 := [rewrite]: #90
-#87 := (= #23 #86)
-#84 := (= #22 #83)
-#81 := (= #21 0::Int)
-#82 := [rewrite]: #81
-#79 := (= #20 #78)
-#80 := [rewrite]: #79
-#85 := [monotonicity #80 #82]: #84
-#88 := [monotonicity #85]: #87
-#93 := [trans #88 #91]: #92
-#75 := (iff #18 #74)
-#72 := (iff #17 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#96 := [monotonicity #76 #93]: #95
-#69 := (iff #12 #68)
-#70 := [rewrite]: #69
-#99 := [monotonicity #70 #96]: #98
-#66 := (iff #9 true)
-#67 := [rewrite]: #66
-#102 := [monotonicity #67 #99]: #101
-#106 := [trans #102 #104]: #105
-#109 := [monotonicity #106]: #108
-#112 := [monotonicity #109]: #111
-#117 := [trans #112 #115]: #116
-#120 := [monotonicity #117]: #119
-#65 := [asserted]: #29
-#123 := [mp #65 #120]: #118
-#281 := (not #696)
-#367 := (or #281 #113)
-#368 := [quant-inst #10]: #367
-[unit-resolution #368 #123 #702]: false
-unsat
-2713378ea3e2d16536aee750f4c4dea73990d05c 86 0
-#2 := false
-decl f3 :: (-> Int S2)
-#9 := 0::Int
-#25 := (f3 0::Int)
-#8 := 1::Int
-#18 := (- 1::Int)
-#17 := (- 0::Int)
-#19 := (mod #17 #18)
-#20 := (- #19)
-#16 := (mod 0::Int 1::Int)
-#13 := (< 0::Int 1::Int)
-#12 := (< 0::Int 0::Int)
-#14 := (and #12 #13)
-#15 := (or #14 #14)
-#21 := (ite #15 #16 #20)
-#11 := (= 0::Int 0::Int)
-#22 := (ite #11 0::Int #21)
-#10 := (= 1::Int 0::Int)
-#23 := (ite #10 0::Int #22)
-#24 := (f3 #23)
-#26 := (= #24 #25)
-#27 := (not #26)
-#122 := (iff #27 false)
-#1 := true
-#117 := (not true)
-#120 := (iff #117 false)
-#121 := [rewrite]: #120
-#118 := (iff #27 #117)
-#115 := (iff #26 true)
-#110 := (= #25 #25)
-#113 := (iff #110 true)
-#114 := [rewrite]: #113
-#111 := (iff #26 #110)
-#107 := (= #23 0::Int)
-#102 := (ite false 0::Int 0::Int)
-#105 := (= #102 0::Int)
-#106 := [rewrite]: #105
-#103 := (= #23 #102)
-#100 := (= #22 0::Int)
-#95 := (ite true 0::Int 0::Int)
-#98 := (= #95 0::Int)
-#99 := [rewrite]: #98
-#96 := (= #22 #95)
-#93 := (= #21 0::Int)
-#88 := (ite #14 0::Int 0::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #21 #88)
-#86 := (= #20 0::Int)
-#72 := (= #17 0::Int)
-#73 := [rewrite]: #72
-#84 := (= #20 #17)
-#82 := (= #19 0::Int)
-#74 := -1::Int
-#77 := (mod 0::Int -1::Int)
-#80 := (= #77 0::Int)
-#81 := [rewrite]: #80
-#78 := (= #19 #77)
-#75 := (= #18 -1::Int)
-#76 := [rewrite]: #75
-#79 := [monotonicity #73 #76]: #78
-#83 := [trans #79 #81]: #82
-#85 := [monotonicity #83]: #84
-#87 := [trans #85 #73]: #86
-#70 := (= #16 0::Int)
-#71 := [rewrite]: #70
-#68 := (iff #15 #14)
-#69 := [rewrite]: #68
-#90 := [monotonicity #69 #71 #87]: #89
-#94 := [trans #90 #92]: #93
-#66 := (iff #11 true)
-#67 := [rewrite]: #66
-#97 := [monotonicity #67 #94]: #96
-#101 := [trans #97 #99]: #100
-#64 := (iff #10 false)
-#65 := [rewrite]: #64
-#104 := [monotonicity #65 #101]: #103
-#108 := [trans #104 #106]: #107
-#109 := [monotonicity #108]: #26
-#112 := [monotonicity #109]: #111
-#116 := [trans #112 #114]: #115
-#119 := [monotonicity #116]: #118
-#123 := [trans #119 #121]: #122
-#63 := [asserted]: #27
-[mp #63 #123]: false
-unsat
-a1075089dc52af4042f6a4669e72797d6209efe9 90 0
-#2 := false
-decl f3 :: (-> Int S2)
-#9 := 0::Int
-#24 := (f3 0::Int)
-#8 := 1::Int
-#17 := (- 1::Int)
-#18 := (mod #17 #17)
-#19 := (- #18)
-#16 := (mod 1::Int 1::Int)
-#11 := (< 0::Int 1::Int)
-#13 := (< 1::Int 0::Int)
-#14 := (and #13 #11)
-#12 := (and #11 #11)
-#15 := (or #12 #14)
-#20 := (ite #15 #16 #19)
-#10 := (= 1::Int 0::Int)
-#21 := (ite #10 0::Int #20)
-#22 := (ite #10 1::Int #21)
-#23 := (f3 #22)
-#25 := (= #23 #24)
-#26 := (not #25)
-#126 := (iff #26 false)
-#1 := true
-#121 := (not true)
-#124 := (iff #121 false)
-#125 := [rewrite]: #124
-#122 := (iff #26 #121)
-#119 := (iff #25 true)
-#114 := (= #24 #24)
-#117 := (iff #114 true)
-#118 := [rewrite]: #117
-#115 := (iff #25 #114)
-#111 := (= #22 0::Int)
-#106 := (ite false 1::Int 0::Int)
-#109 := (= #106 0::Int)
-#110 := [rewrite]: #109
-#107 := (= #22 #106)
-#104 := (= #21 0::Int)
-#99 := (ite false 0::Int 0::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #21 #99)
-#97 := (= #20 0::Int)
-#67 := (and #11 #13)
-#70 := (or #11 #67)
-#92 := (ite #70 0::Int 0::Int)
-#95 := (= #92 0::Int)
-#96 := [rewrite]: #95
-#93 := (= #20 #92)
-#90 := (= #19 0::Int)
-#85 := (- 0::Int)
-#88 := (= #85 0::Int)
-#89 := [rewrite]: #88
-#86 := (= #19 #85)
-#83 := (= #18 0::Int)
-#75 := -1::Int
-#78 := (mod -1::Int -1::Int)
-#81 := (= #78 0::Int)
-#82 := [rewrite]: #81
-#79 := (= #18 #78)
-#76 := (= #17 -1::Int)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77 #77]: #79
-#84 := [trans #80 #82]: #83
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#73 := (= #16 0::Int)
-#74 := [rewrite]: #73
-#71 := (iff #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#65 := (iff #12 #11)
-#66 := [rewrite]: #65
-#72 := [monotonicity #66 #69]: #71
-#94 := [monotonicity #72 #74 #91]: #93
-#98 := [trans #94 #96]: #97
-#63 := (iff #10 false)
-#64 := [rewrite]: #63
-#101 := [monotonicity #64 #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #64 #105]: #107
-#112 := [trans #108 #110]: #111
-#113 := [monotonicity #112]: #25
-#116 := [monotonicity #113]: #115
-#120 := [trans #116 #118]: #119
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#62 := [asserted]: #26
-[mp #62 #127]: false
-unsat
-63c9d4e9b322eec0fd3bd7dd16ba42cd509506b7 97 0
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 3::Int
+#10 := (f4 0::Int 3::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#800 := (= #10 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f4 #31 #20)
+#885 := (pattern #50)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#245 := (mod #181 #184)
+#375 := (+ #50 #245)
+#376 := (= #375 0::Int)
+#51 := (mod #31 #20)
+#372 := (* -1::Int #51)
+#373 := (+ #50 #372)
+#374 := (= #373 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#377 := (ite #323 #374 #376)
+#371 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#378 := (ite #33 #371 #377)
+#370 := (= #31 #50)
+#34 := (= #20 0::Int)
+#379 := (ite #34 #370 #378)
+#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379)
+#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
+#889 := (iff #382 #886)
+#887 := (iff #379 #379)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#251 := (* -1::Int #245)
+#339 := (ite #323 #51 #251)
+#342 := (ite #33 0::Int #339)
+#345 := (ite #34 #31 #342)
+#348 := (= #50 #345)
+#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
+#383 := (iff #351 #382)
+#380 := (iff #348 #379)
+#381 := [rewrite]: #380
+#384 := [quant-intro #381]: #383
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#271 := (ite #226 #51 #251)
+#274 := (ite #33 0::Int #271)
+#277 := (ite #34 #31 #274)
+#280 := (= #50 #277)
+#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
+#352 := (iff #283 #351)
+#349 := (iff #280 #348)
+#346 := (= #277 #345)
+#343 := (= #274 #342)
+#340 := (= #271 #339)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#341 := [monotonicity #325]: #340
+#344 := [monotonicity #341]: #343
+#347 := [monotonicity #344]: #346
+#350 := [monotonicity #347]: #349
+#353 := [quant-intro #350]: #352
+#300 := (~ #283 #283)
+#314 := (~ #280 #280)
+#315 := [refl]: #314
+#301 := [nnf-pos #315]: #300
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#286 := (iff #58 #283)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#256 := (ite #177 #51 #251)
+#165 := (= 0::Int #31)
+#259 := (ite #165 0::Int #256)
+#168 := (= 0::Int #20)
+#262 := (ite #168 #31 #259)
+#265 := (= #50 #262)
+#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
+#284 := (iff #268 #283)
+#281 := (iff #265 #280)
+#278 := (= #262 #277)
+#275 := (= #259 #274)
+#272 := (= #256 #271)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#273 := [monotonicity #228]: #272
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#276 := [monotonicity #203 #273]: #275
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#279 := [monotonicity #205 #276]: #278
+#282 := [monotonicity #279]: #281
+#285 := [quant-intro #282]: #284
+#269 := (iff #58 #268)
+#266 := (iff #57 #265)
+#263 := (= #56 #262)
+#260 := (= #55 #259)
+#257 := (= #54 #256)
+#254 := (= #53 #251)
+#248 := (- #245)
+#252 := (= #248 #251)
+#253 := [rewrite]: #252
+#249 := (= #53 #248)
+#246 := (= #52 #245)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#247 := [monotonicity #183 #186]: #246
+#250 := [monotonicity #247]: #249
+#255 := [trans #250 #253]: #254
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#258 := [monotonicity #179 #255]: #257
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#261 := [monotonicity #167 #258]: #260
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#264 := [monotonicity #170 #261]: #263
+#267 := [monotonicity #264]: #266
+#270 := [quant-intro #267]: #269
+#287 := [trans #270 #285]: #286
+#244 := [asserted]: #58
+#288 := [mp #244 #287]: #283
+#316 := [mp~ #288 #301]: #283
+#354 := [mp #316 #353]: #351
+#385 := [mp #354 #384]: #382
+#891 := [mp #385 #890]: #886
+#729 := (not #886)
+#730 := (or #729 #800)
+#812 := (* -1::Int 3::Int)
+#813 := (* -1::Int 0::Int)
+#814 := (mod #813 #812)
+#809 := (+ #10 #814)
+#810 := (= #809 0::Int)
+#815 := (mod 0::Int 3::Int)
+#816 := (* -1::Int #815)
+#811 := (+ #10 #816)
+#817 := (= #811 0::Int)
+#834 := (>= 0::Int 0::Int)
+#658 := (<= 3::Int 0::Int)
+#659 := (or #658 #834)
+#660 := (not #659)
+#802 := (<= 0::Int 0::Int)
+#803 := (or #802 #658)
+#804 := (not #803)
+#805 := (or #804 #660)
+#799 := (ite #805 #817 #810)
+#806 := (= 0::Int 0::Int)
+#807 := (ite #806 #800 #799)
+#801 := (= 0::Int #10)
+#808 := (= 3::Int 0::Int)
+#637 := (ite #808 #801 #807)
+#725 := (or #729 #637)
+#704 := (iff #725 #730)
+#706 := (iff #730 #730)
+#599 := [rewrite]: #706
+#727 := (iff #637 #800)
+#753 := (ite false #800 #800)
+#732 := (iff #753 #800)
+#733 := [rewrite]: #732
+#723 := (iff #637 #753)
+#726 := (iff #807 #800)
+#1 := true
+#737 := (ite true #800 #800)
+#734 := (iff #737 #800)
+#740 := [rewrite]: #734
+#738 := (iff #807 #737)
+#735 := (iff #799 #800)
+#743 := (iff #799 #753)
+#751 := (iff #810 #800)
+#749 := (= #809 #10)
+#763 := (+ #10 0::Int)
+#767 := (= #763 #10)
+#768 := [rewrite]: #767
+#747 := (= #809 #763)
+#745 := (= #814 0::Int)
+#758 := -3::Int
+#757 := (mod 0::Int -3::Int)
+#742 := (= #757 0::Int)
+#744 := [rewrite]: #742
+#761 := (= #814 #757)
+#759 := (= #812 -3::Int)
+#760 := [rewrite]: #759
+#777 := (= #813 0::Int)
+#771 := [rewrite]: #777
+#741 := [monotonicity #771 #760]: #761
+#746 := [trans #741 #744]: #745
+#748 := [monotonicity #746]: #747
+#750 := [trans #748 #768]: #749
+#752 := [monotonicity #750]: #751
+#755 := (iff #817 #800)
+#764 := (= #811 #10)
+#765 := (= #811 #763)
+#778 := (= #816 0::Int)
+#775 := (= #816 #813)
+#785 := (= #815 0::Int)
+#774 := [rewrite]: #785
+#776 := [monotonicity #774]: #775
+#762 := [trans #776 #771]: #778
+#766 := [monotonicity #762]: #765
+#769 := [trans #766 #768]: #764
+#756 := [monotonicity #769]: #755
+#784 := (iff #805 false)
+#773 := (or false false)
+#782 := (iff #773 false)
+#783 := [rewrite]: #782
+#770 := (iff #805 #773)
+#779 := (iff #660 false)
+#482 := (not true)
+#841 := (iff #482 false)
+#844 := [rewrite]: #841
+#788 := (iff #660 #482)
+#698 := (iff #659 true)
+#686 := (or false true)
+#696 := (iff #686 true)
+#697 := [rewrite]: #696
+#694 := (iff #659 #686)
+#840 := (iff #834 true)
+#842 := [rewrite]: #840
+#680 := (iff #658 false)
+#681 := [rewrite]: #680
+#695 := [monotonicity #681 #842]: #694
+#791 := [trans #695 #697]: #698
+#792 := [monotonicity #791]: #788
+#781 := [trans #792 #844]: #779
+#692 := (iff #804 false)
+#675 := (iff #804 #482)
+#787 := (iff #803 true)
+#682 := (or true false)
+#691 := (iff #682 true)
+#786 := [rewrite]: #691
+#641 := (iff #803 #682)
+#795 := (iff #802 true)
+#798 := [rewrite]: #795
+#789 := [monotonicity #798 #681]: #641
+#790 := [trans #789 #786]: #787
+#690 := [monotonicity #790]: #675
+#693 := [trans #690 #844]: #692
+#772 := [monotonicity #693 #781]: #770
+#780 := [trans #772 #783]: #784
+#754 := [monotonicity #780 #756 #752]: #743
+#736 := [trans #754 #733]: #735
+#796 := (iff #806 true)
+#797 := [rewrite]: #796
+#739 := [monotonicity #797 #736]: #738
+#722 := [trans #739 #740]: #726
+#793 := (iff #801 #800)
+#794 := [rewrite]: #793
+#639 := (iff #808 false)
+#640 := [rewrite]: #639
+#724 := [monotonicity #640 #794 #722]: #723
+#728 := [trans #724 #733]: #727
+#705 := [monotonicity #728]: #704
+#710 := [trans #705 #599]: #704
+#731 := [quant-inst #8 #9]: #725
+#711 := [mp #731 #710]: #730
+#717 := [unit-resolution #711 #891]: #800
+#713 := [monotonicity #717]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #713]: false
+unsat
+e4bde0ae05cc3d53da641b07fe2928d0ca73206a 336 0
#2 := false
decl f3 :: (-> Int S2)
-#9 := 0::Int
-#28 := (f3 0::Int)
#8 := 1::Int
-#21 := (- 1::Int)
-#11 := 3::Int
-#20 := (- 3::Int)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod 3::Int 1::Int)
-#14 := (< 0::Int 1::Int)
-#16 := (< 3::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 3::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= 3::Int 0::Int)
-#25 := (ite #12 0::Int #24)
-#10 := (= 1::Int 0::Int)
-#26 := (ite #10 3::Int #25)
-#27 := (f3 #26)
-#29 := (= #27 #28)
-#30 := (not #29)
-#133 := (iff #30 false)
-#1 := true
-#128 := (not true)
-#131 := (iff #128 false)
-#132 := [rewrite]: #131
-#129 := (iff #30 #128)
-#126 := (iff #29 true)
-#121 := (= #28 #28)
-#124 := (iff #121 true)
-#125 := [rewrite]: #124
-#122 := (iff #29 #121)
-#118 := (= #26 0::Int)
-#113 := (ite false 3::Int 0::Int)
-#116 := (= #113 0::Int)
-#117 := [rewrite]: #116
-#114 := (= #26 #113)
-#111 := (= #25 0::Int)
-#106 := (ite false 0::Int 0::Int)
-#109 := (= #106 0::Int)
-#110 := [rewrite]: #109
-#107 := (= #25 #106)
-#104 := (= #24 0::Int)
-#71 := (and #14 #16)
-#74 := (or #15 #71)
-#99 := (ite #74 0::Int 0::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #24 #99)
-#97 := (= #23 0::Int)
-#92 := (- 0::Int)
-#95 := (= #92 0::Int)
-#96 := [rewrite]: #95
-#93 := (= #23 #92)
-#90 := (= #22 0::Int)
-#82 := -1::Int
-#79 := -3::Int
-#85 := (mod -3::Int -1::Int)
-#88 := (= #85 0::Int)
-#89 := [rewrite]: #88
-#86 := (= #22 #85)
-#83 := (= #21 -1::Int)
-#84 := [rewrite]: #83
-#80 := (= #20 -3::Int)
-#81 := [rewrite]: #80
-#87 := [monotonicity #81 #84]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #91]: #93
-#98 := [trans #94 #96]: #97
-#77 := (= #19 0::Int)
-#78 := [rewrite]: #77
-#75 := (iff #18 #74)
-#72 := (iff #17 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#101 := [monotonicity #76 #78 #98]: #100
-#105 := [trans #101 #103]: #104
-#69 := (iff #12 false)
-#70 := [rewrite]: #69
-#108 := [monotonicity #70 #105]: #107
-#112 := [trans #108 #110]: #111
-#67 := (iff #10 false)
-#68 := [rewrite]: #67
-#115 := [monotonicity #68 #112]: #114
-#119 := [trans #115 #117]: #118
-#120 := [monotonicity #119]: #29
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#66 := [asserted]: #30
-[mp #66 #134]: false
-unsat
-baacef3aba2d9193028d7d390c9e488f80e40513 170 0
-#2 := false
-#9 := 0::Int
-decl f4 :: (-> S2 Int)
-decl f5 :: S2
-#11 := f5
-#12 := (f4 f5)
-#144 := (>= #12 0::Int)
-#145 := (not #144)
-#131 := (<= #12 0::Int)
-#132 := (not #131)
-#13 := (= #12 0::Int)
-#163 := (or #13 #132 #145)
-#429 := (not #163)
-#81 := -1::Int
-#82 := (* -1::Int #12)
-#87 := (mod #82 -1::Int)
-#93 := (* -1::Int #87)
-#168 := (ite #163 0::Int #93)
-#341 := (= #168 0::Int)
-#706 := (not #341)
-decl f3 :: (-> Int S2)
-#171 := (f3 #168)
-#29 := (f3 0::Int)
-#174 := (= #29 #171)
-#698 := (= #171 #29)
-#697 := [hypothesis]: #341
-#704 := [monotonicity #697]: #698
-#705 := [symm #704]: #174
-#177 := (not #174)
-#8 := 1::Int
-#22 := (- 1::Int)
-#21 := (- #12)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod #12 1::Int)
-#15 := (< 0::Int 1::Int)
-#17 := (< #12 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #12)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#26 := (ite #13 0::Int #25)
-#10 := (= 1::Int 0::Int)
-#27 := (ite #10 #12 #26)
-#28 := (f3 #27)
-#30 := (= #28 #29)
-#31 := (not #30)
-#180 := (iff #31 #177)
-#73 := (and #15 #17)
-#76 := (or #16 #73)
-#70 := (= 0::Int #12)
-#104 := (or #70 #76)
-#105 := (ite #104 0::Int #93)
-#117 := (f3 #105)
-#123 := (= #29 #117)
-#128 := (not #123)
-#178 := (iff #128 #177)
-#175 := (iff #123 #174)
-#172 := (= #117 #171)
-#169 := (= #105 #168)
-#166 := (iff #104 #163)
-#157 := (or #132 #145)
-#160 := (or #13 #157)
-#164 := (iff #160 #163)
-#165 := [rewrite]: #164
-#161 := (iff #104 #160)
-#158 := (iff #76 #157)
-#153 := (iff #73 #145)
-#1 := true
-#148 := (and true #145)
-#151 := (iff #148 #145)
-#152 := [rewrite]: #151
-#149 := (iff #73 #148)
-#146 := (iff #17 #145)
-#147 := [rewrite]: #146
-#135 := (iff #15 true)
-#136 := [rewrite]: #135
-#150 := [monotonicity #136 #147]: #149
-#154 := [trans #150 #152]: #153
-#142 := (iff #16 #132)
-#137 := (and #132 true)
-#140 := (iff #137 #132)
-#141 := [rewrite]: #140
-#138 := (iff #16 #137)
-#133 := (iff #14 #132)
-#134 := [rewrite]: #133
-#139 := [monotonicity #134 #136]: #138
-#143 := [trans #139 #141]: #142
-#159 := [monotonicity #143 #154]: #158
-#155 := (iff #70 #13)
-#156 := [rewrite]: #155
-#162 := [monotonicity #156 #159]: #161
-#167 := [trans #162 #165]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#129 := (iff #31 #128)
-#126 := (iff #30 #123)
-#120 := (= #117 #29)
-#124 := (iff #120 #123)
-#125 := [rewrite]: #124
-#121 := (iff #30 #120)
-#118 := (= #28 #117)
-#115 := (= #27 #105)
-#110 := (ite false #12 #105)
-#113 := (= #110 #105)
-#114 := [rewrite]: #113
-#111 := (= #27 #110)
-#108 := (= #26 #105)
-#98 := (ite #76 0::Int #93)
-#101 := (ite #70 0::Int #98)
-#106 := (= #101 #105)
-#107 := [rewrite]: #106
-#102 := (= #26 #101)
-#99 := (= #25 #98)
-#96 := (= #24 #93)
-#90 := (- #87)
-#94 := (= #90 #93)
-#95 := [rewrite]: #94
-#91 := (= #24 #90)
-#88 := (= #23 #87)
-#85 := (= #22 -1::Int)
-#86 := [rewrite]: #85
-#83 := (= #21 #82)
-#84 := [rewrite]: #83
-#89 := [monotonicity #84 #86]: #88
-#92 := [monotonicity #89]: #91
-#97 := [trans #92 #95]: #96
-#79 := (= #20 0::Int)
-#80 := [rewrite]: #79
-#77 := (iff #19 #76)
-#74 := (iff #18 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#100 := [monotonicity #78 #80 #97]: #99
-#71 := (iff #13 #70)
-#72 := [rewrite]: #71
-#103 := [monotonicity #72 #100]: #102
-#109 := [trans #103 #107]: #108
-#68 := (iff #10 false)
-#69 := [rewrite]: #68
-#112 := [monotonicity #69 #109]: #111
-#116 := [trans #112 #114]: #115
-#119 := [monotonicity #116]: #118
-#122 := [monotonicity #119]: #121
-#127 := [trans #122 #125]: #126
-#130 := [monotonicity #127]: #129
-#181 := [trans #130 #179]: #180
-#67 := [asserted]: #31
-#182 := [mp #67 #181]: #177
-#699 := [unit-resolution #182 #705]: false
-#535 := [lemma #699]: #706
-#747 := (or #429 #341)
-#749 := [def-axiom]: #747
-#658 := [unit-resolution #749 #535]: #429
-#431 := (or #163 #144)
-#432 := [def-axiom]: #431
-#655 := [unit-resolution #432 #658]: #144
-#419 := (or #163 #131)
-#430 := [def-axiom]: #419
-#659 := [unit-resolution #430 #658]: #131
-#342 := (not #13)
-#427 := (or #163 #342)
-#428 := [def-axiom]: #427
-#639 := [unit-resolution #428 #658]: #342
-#640 := [th-lemma arith triangle-eq]: #163
-[unit-resolution #640 #639 #659 #655]: false
-unsat
-52940ae1c337d10436c752f28c341997638bfaa6 86 0
+#12 := (f3 1::Int)
+decl f4 :: (-> Int Int Int)
+#9 := 3::Int
+#10 := (f4 1::Int 3::Int)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#797 := (= #10 1::Int)
+#21 := (:var 0 Int)
+#32 := (:var 1 Int)
+#51 := (f4 #32 #21)
+#885 := (pattern #51)
+#20 := 0::Int
+#181 := -1::Int
+#185 := (* -1::Int #21)
+#182 := (* -1::Int #32)
+#246 := (mod #182 #185)
+#376 := (+ #51 #246)
+#377 := (= #376 0::Int)
+#52 := (mod #32 #21)
+#373 := (* -1::Int #52)
+#374 := (+ #51 #373)
+#375 := (= #374 0::Int)
+#220 := (>= #32 0::Int)
+#213 := (<= #21 0::Int)
+#320 := (or #213 #220)
+#321 := (not #320)
+#209 := (<= #32 0::Int)
+#318 := (or #209 #213)
+#319 := (not #318)
+#324 := (or #319 #321)
+#378 := (ite #324 #375 #377)
+#372 := (= #51 0::Int)
+#34 := (= #32 0::Int)
+#379 := (ite #34 #372 #378)
+#371 := (= #32 #51)
+#35 := (= #21 0::Int)
+#380 := (ite #35 #371 #379)
+#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380)
+#383 := (forall (vars (?v0 Int) (?v1 Int)) #380)
+#889 := (iff #383 #886)
+#887 := (iff #380 #380)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#252 := (* -1::Int #246)
+#340 := (ite #324 #52 #252)
+#343 := (ite #34 0::Int #340)
+#346 := (ite #35 #32 #343)
+#349 := (= #51 #346)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#384 := (iff #352 #383)
+#381 := (iff #349 #380)
+#382 := [rewrite]: #381
+#385 := [quant-intro #382]: #384
+#221 := (not #220)
+#214 := (not #213)
+#224 := (and #214 #221)
+#210 := (not #209)
+#217 := (and #210 #214)
+#227 := (or #217 #224)
+#272 := (ite #227 #52 #252)
+#275 := (ite #34 0::Int #272)
+#278 := (ite #35 #32 #275)
+#281 := (= #51 #278)
+#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
+#353 := (iff #284 #352)
+#350 := (iff #281 #349)
+#347 := (= #278 #346)
+#344 := (= #275 #343)
+#341 := (= #272 #340)
+#325 := (iff #227 #324)
+#322 := (iff #224 #321)
+#323 := [rewrite]: #322
+#303 := (iff #217 #319)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304 #323]: #325
+#342 := [monotonicity #326]: #341
+#345 := [monotonicity #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [quant-intro #351]: #353
+#301 := (~ #284 #284)
+#315 := (~ #281 #281)
+#316 := [refl]: #315
+#302 := [nnf-pos #316]: #301
+#45 := (- #21)
+#44 := (- #32)
+#53 := (mod #44 #45)
+#54 := (- #53)
+#38 := (< 0::Int #21)
+#40 := (< #32 0::Int)
+#41 := (and #40 #38)
+#37 := (< 0::Int #32)
+#39 := (and #37 #38)
+#42 := (or #39 #41)
+#55 := (ite #42 #52 #54)
+#56 := (ite #34 0::Int #55)
+#57 := (ite #35 #32 #56)
+#58 := (= #51 #57)
+#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
+#287 := (iff #59 #284)
+#175 := (and #38 #40)
+#178 := (or #39 #175)
+#257 := (ite #178 #52 #252)
+#166 := (= 0::Int #32)
+#260 := (ite #166 0::Int #257)
+#169 := (= 0::Int #21)
+#263 := (ite #169 #32 #260)
+#266 := (= #51 #263)
+#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
+#285 := (iff #269 #284)
+#282 := (iff #266 #281)
+#279 := (= #263 #278)
+#276 := (= #260 #275)
+#273 := (= #257 #272)
+#228 := (iff #178 #227)
+#225 := (iff #175 #224)
+#222 := (iff #40 #221)
+#223 := [rewrite]: #222
+#215 := (iff #38 #214)
+#216 := [rewrite]: #215
+#226 := [monotonicity #216 #223]: #225
+#218 := (iff #39 #217)
+#211 := (iff #37 #210)
+#212 := [rewrite]: #211
+#219 := [monotonicity #212 #216]: #218
+#229 := [monotonicity #219 #226]: #228
+#274 := [monotonicity #229]: #273
+#203 := (iff #166 #34)
+#204 := [rewrite]: #203
+#277 := [monotonicity #204 #274]: #276
+#205 := (iff #169 #35)
+#206 := [rewrite]: #205
+#280 := [monotonicity #206 #277]: #279
+#283 := [monotonicity #280]: #282
+#286 := [quant-intro #283]: #285
+#270 := (iff #59 #269)
+#267 := (iff #58 #266)
+#264 := (= #57 #263)
+#261 := (= #56 #260)
+#258 := (= #55 #257)
+#255 := (= #54 #252)
+#249 := (- #246)
+#253 := (= #249 #252)
+#254 := [rewrite]: #253
+#250 := (= #54 #249)
+#247 := (= #53 #246)
+#186 := (= #45 #185)
+#187 := [rewrite]: #186
+#183 := (= #44 #182)
+#184 := [rewrite]: #183
+#248 := [monotonicity #184 #187]: #247
+#251 := [monotonicity #248]: #250
+#256 := [trans #251 #254]: #255
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#259 := [monotonicity #180 #256]: #258
+#167 := (iff #34 #166)
+#168 := [rewrite]: #167
+#262 := [monotonicity #168 #259]: #261
+#170 := (iff #35 #169)
+#171 := [rewrite]: #170
+#265 := [monotonicity #171 #262]: #264
+#268 := [monotonicity #265]: #267
+#271 := [quant-intro #268]: #270
+#288 := [trans #271 #286]: #287
+#245 := [asserted]: #59
+#289 := [mp #245 #288]: #284
+#317 := [mp~ #289 #302]: #284
+#355 := [mp #317 #354]: #352
+#386 := [mp #355 #385]: #383
+#891 := [mp #386 #890]: #886
+#709 := (not #886)
+#677 := (or #709 #797)
+#814 := (* -1::Int 3::Int)
+#809 := (* -1::Int 1::Int)
+#810 := (mod #809 #814)
+#815 := (+ #10 #810)
+#816 := (= #815 0::Int)
+#811 := (mod 1::Int 3::Int)
+#817 := (* -1::Int #811)
+#658 := (+ #10 #817)
+#659 := (= #658 0::Int)
+#835 := (>= 1::Int 0::Int)
+#660 := (<= 3::Int 0::Int)
+#802 := (or #660 #835)
+#803 := (not #802)
+#804 := (<= 1::Int 0::Int)
+#805 := (or #804 #660)
+#799 := (not #805)
+#800 := (or #799 #803)
+#806 := (ite #800 #659 #816)
+#807 := (= #10 0::Int)
+#801 := (= 1::Int 0::Int)
+#808 := (ite #801 #807 #806)
+#637 := (= 1::Int #10)
+#639 := (= 3::Int 0::Int)
+#640 := (ite #639 #637 #808)
+#684 := (or #709 #640)
+#674 := (iff #684 #677)
+#678 := (iff #677 #677)
+#685 := [rewrite]: #678
+#708 := (iff #640 #797)
+#701 := (ite false #797 #797)
+#683 := (iff #701 #797)
+#707 := [rewrite]: #683
+#647 := (iff #640 #701)
+#716 := (iff #808 #797)
+#714 := (ite false #807 #797)
+#719 := (iff #714 #797)
+#720 := [rewrite]: #719
+#715 := (iff #808 #714)
+#717 := (iff #806 #797)
+#729 := -2::Int
+#730 := (= #10 -2::Int)
+#1 := true
+#706 := (ite true #797 #730)
+#711 := (iff #706 #797)
+#712 := [rewrite]: #711
+#599 := (iff #806 #706)
+#704 := (iff #816 #730)
+#754 := 2::Int
+#734 := (+ 2::Int #10)
+#724 := (= #734 0::Int)
+#725 := (iff #724 #730)
+#731 := [rewrite]: #725
+#727 := (iff #816 #724)
+#722 := (= #815 #734)
+#737 := (+ #10 2::Int)
+#740 := (= #737 #734)
+#726 := [rewrite]: #740
+#738 := (= #815 #737)
+#735 := (= #810 2::Int)
+#749 := -3::Int
+#752 := (mod -1::Int -3::Int)
+#732 := (= #752 2::Int)
+#733 := [rewrite]: #732
+#753 := (= #810 #752)
+#750 := (= #814 -3::Int)
+#751 := [rewrite]: #750
+#766 := (= #809 -1::Int)
+#767 := [rewrite]: #766
+#743 := [monotonicity #767 #751]: #753
+#736 := [trans #743 #733]: #735
+#739 := [monotonicity #736]: #738
+#723 := [trans #739 #726]: #722
+#728 := [monotonicity #723]: #727
+#705 := [trans #728 #731]: #704
+#747 := (iff #659 #797)
+#758 := (+ -1::Int #10)
+#741 := (= #758 0::Int)
+#745 := (iff #741 #797)
+#746 := [rewrite]: #745
+#742 := (iff #659 #741)
+#757 := (= #658 #758)
+#769 := (+ #10 -1::Int)
+#759 := (= #769 #758)
+#760 := [rewrite]: #759
+#755 := (= #658 #769)
+#768 := (= #817 -1::Int)
+#763 := (= #817 #809)
+#778 := (= #811 1::Int)
+#762 := [rewrite]: #778
+#765 := [monotonicity #762]: #763
+#764 := [trans #765 #767]: #768
+#756 := [monotonicity #764]: #755
+#761 := [trans #756 #760]: #757
+#744 := [monotonicity #761]: #742
+#748 := [trans #744 #746]: #747
+#777 := (iff #800 true)
+#780 := (or true false)
+#775 := (iff #780 true)
+#776 := [rewrite]: #775
+#785 := (iff #800 #780)
+#783 := (iff #803 false)
+#483 := (not true)
+#844 := (iff #483 false)
+#830 := [rewrite]: #844
+#772 := (iff #803 #483)
+#773 := (iff #802 true)
+#791 := (or false true)
+#779 := (iff #791 true)
+#781 := [rewrite]: #779
+#788 := (iff #802 #791)
+#842 := (iff #835 true)
+#482 := [rewrite]: #842
+#641 := (iff #660 false)
+#789 := [rewrite]: #641
+#792 := [monotonicity #789 #482]: #788
+#770 := [trans #792 #781]: #773
+#782 := [monotonicity #770]: #772
+#784 := [trans #782 #830]: #783
+#697 := (iff #799 true)
+#693 := (not false)
+#695 := (iff #693 true)
+#696 := [rewrite]: #695
+#686 := (iff #799 #693)
+#690 := (iff #805 false)
+#691 := (or false false)
+#790 := (iff #691 false)
+#675 := [rewrite]: #790
+#786 := (iff #805 #691)
+#681 := (iff #804 false)
+#682 := [rewrite]: #681
+#787 := [monotonicity #682 #789]: #786
+#692 := [trans #787 #675]: #690
+#694 := [monotonicity #692]: #686
+#698 := [trans #694 #696]: #697
+#774 := [monotonicity #698 #784]: #785
+#771 := [trans #774 #776]: #777
+#710 := [monotonicity #771 #748 #705]: #599
+#713 := [trans #710 #712]: #717
+#798 := (iff #801 false)
+#680 := [rewrite]: #798
+#718 := [monotonicity #680 #713]: #715
+#721 := [trans #718 #720]: #716
+#796 := (iff #637 #797)
+#795 := [rewrite]: #796
+#793 := (iff #639 false)
+#794 := [rewrite]: #793
+#702 := [monotonicity #794 #795 #721]: #647
+#703 := [trans #702 #707]: #708
+#676 := [monotonicity #703]: #674
+#687 := [trans #676 #685]: #674
+#643 := [quant-inst #8 #9]: #684
+#688 := [mp #643 #687]: #677
+#679 := [unit-resolution #688 #891]: #797
+#700 := [monotonicity #679]: #13
+#14 := (not #13)
+#79 := [asserted]: #14
+[unit-resolution #79 #700]: false
+unsat
+1120ebc08fbef118a46bc94c7a17d1ff3c4dbb08 311 0
#2 := false
decl f3 :: (-> Int S2)
-#9 := 0::Int
-#25 := (f3 0::Int)
-#8 := 3::Int
-#18 := (- 3::Int)
-#17 := (- 0::Int)
-#19 := (mod #17 #18)
-#20 := (- #19)
-#16 := (mod 0::Int 3::Int)
-#13 := (< 0::Int 3::Int)
-#12 := (< 0::Int 0::Int)
-#14 := (and #12 #13)
-#15 := (or #14 #14)
-#21 := (ite #15 #16 #20)
-#11 := (= 0::Int 0::Int)
-#22 := (ite #11 0::Int #21)
-#10 := (= 3::Int 0::Int)
-#23 := (ite #10 0::Int #22)
-#24 := (f3 #23)
-#26 := (= #24 #25)
-#27 := (not #26)
-#122 := (iff #27 false)
-#1 := true
-#117 := (not true)
-#120 := (iff #117 false)
-#121 := [rewrite]: #120
-#118 := (iff #27 #117)
-#115 := (iff #26 true)
-#110 := (= #25 #25)
-#113 := (iff #110 true)
-#114 := [rewrite]: #113
-#111 := (iff #26 #110)
-#107 := (= #23 0::Int)
-#102 := (ite false 0::Int 0::Int)
-#105 := (= #102 0::Int)
-#106 := [rewrite]: #105
-#103 := (= #23 #102)
-#100 := (= #22 0::Int)
-#95 := (ite true 0::Int 0::Int)
-#98 := (= #95 0::Int)
-#99 := [rewrite]: #98
-#96 := (= #22 #95)
-#93 := (= #21 0::Int)
-#88 := (ite #14 0::Int 0::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #21 #88)
-#86 := (= #20 0::Int)
-#72 := (= #17 0::Int)
-#73 := [rewrite]: #72
-#84 := (= #20 #17)
-#82 := (= #19 0::Int)
-#74 := -3::Int
-#77 := (mod 0::Int -3::Int)
-#80 := (= #77 0::Int)
-#81 := [rewrite]: #80
-#78 := (= #19 #77)
-#75 := (= #18 -3::Int)
-#76 := [rewrite]: #75
-#79 := [monotonicity #73 #76]: #78
-#83 := [trans #79 #81]: #82
-#85 := [monotonicity #83]: #84
-#87 := [trans #85 #73]: #86
-#70 := (= #16 0::Int)
-#71 := [rewrite]: #70
-#68 := (iff #15 #14)
-#69 := [rewrite]: #68
-#90 := [monotonicity #69 #71 #87]: #89
-#94 := [trans #90 #92]: #93
-#66 := (iff #11 true)
-#67 := [rewrite]: #66
-#97 := [monotonicity #67 #94]: #96
-#101 := [trans #97 #99]: #100
-#64 := (iff #10 false)
-#65 := [rewrite]: #64
-#104 := [monotonicity #65 #101]: #103
-#108 := [trans #104 #106]: #107
-#109 := [monotonicity #108]: #26
-#112 := [monotonicity #109]: #111
-#116 := [trans #112 #114]: #115
-#119 := [monotonicity #116]: #118
-#123 := [trans #119 #121]: #122
-#63 := [asserted]: #27
-[mp #63 #123]: false
-unsat
-eea72e0b08b81263eac13f5c3a2599d4713d6590 145 0
-#2 := false
-decl f3 :: (-> Int S2)
-#11 := 1::Int
-#28 := (f3 1::Int)
+#11 := 0::Int
+#12 := (f3 0::Int)
+decl f4 :: (-> Int Int Int)
#8 := 3::Int
-#21 := (- 3::Int)
-#20 := (- 1::Int)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod 1::Int 3::Int)
-#9 := 0::Int
-#14 := (< 0::Int 3::Int)
-#16 := (< 1::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 1::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= 1::Int 0::Int)
-#25 := (ite #12 0::Int #24)
-#10 := (= 3::Int 0::Int)
-#26 := (ite #10 1::Int #25)
-#27 := (f3 #26)
-#29 := (= #27 #28)
-#30 := (not #29)
-#181 := (iff #30 false)
-#96 := -2::Int
-#71 := (and #14 #16)
-#74 := (or #15 #71)
-#101 := (ite #74 1::Int -2::Int)
-#118 := (f3 #101)
-#124 := (= #28 #118)
-#129 := (not #124)
-#179 := (iff #129 false)
-#1 := true
-#174 := (not true)
-#177 := (iff #174 false)
-#178 := [rewrite]: #177
-#175 := (iff #129 #174)
-#172 := (iff #124 true)
-#167 := (= #28 #28)
-#170 := (iff #167 true)
-#171 := [rewrite]: #170
-#168 := (iff #124 #167)
-#121 := (= #118 #28)
-#164 := (= #101 1::Int)
-#159 := (ite true 1::Int -2::Int)
-#162 := (= #159 1::Int)
-#163 := [rewrite]: #162
-#160 := (= #101 #159)
-#157 := (iff #74 true)
-#152 := (or true false)
-#155 := (iff #152 true)
-#156 := [rewrite]: #155
-#153 := (iff #74 #152)
-#150 := (iff #71 false)
-#145 := (and true false)
-#148 := (iff #145 false)
-#149 := [rewrite]: #148
-#146 := (iff #71 #145)
-#143 := (iff #16 false)
-#144 := [rewrite]: #143
-#134 := (iff #14 true)
-#135 := [rewrite]: #134
-#147 := [monotonicity #135 #144]: #146
-#151 := [trans #147 #149]: #150
-#141 := (iff #15 true)
-#136 := (and true true)
-#139 := (iff #136 true)
-#140 := [rewrite]: #139
-#137 := (iff #15 #136)
-#132 := (iff #13 true)
-#133 := [rewrite]: #132
-#138 := [monotonicity #133 #135]: #137
-#142 := [trans #138 #140]: #141
-#154 := [monotonicity #142 #151]: #153
-#158 := [trans #154 #156]: #157
-#161 := [monotonicity #158]: #160
-#165 := [trans #161 #163]: #164
-#166 := [monotonicity #165]: #121
-#169 := [monotonicity #166]: #168
-#173 := [trans #169 #171]: #172
-#176 := [monotonicity #173]: #175
-#180 := [trans #176 #178]: #179
-#130 := (iff #30 #129)
-#127 := (iff #29 #124)
-#125 := (iff #121 #124)
-#126 := [rewrite]: #125
-#122 := (iff #29 #121)
-#119 := (= #27 #118)
-#116 := (= #26 #101)
-#111 := (ite false 1::Int #101)
-#114 := (= #111 #101)
-#115 := [rewrite]: #114
-#112 := (= #26 #111)
-#109 := (= #25 #101)
-#104 := (ite false 0::Int #101)
-#107 := (= #104 #101)
-#108 := [rewrite]: #107
-#105 := (= #25 #104)
-#102 := (= #24 #101)
-#99 := (= #23 -2::Int)
-#88 := 2::Int
-#93 := (- 2::Int)
-#97 := (= #93 -2::Int)
-#98 := [rewrite]: #97
-#94 := (= #23 #93)
-#91 := (= #22 2::Int)
-#82 := -3::Int
-#79 := -1::Int
-#85 := (mod -1::Int -3::Int)
-#89 := (= #85 2::Int)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#83 := (= #21 -3::Int)
-#84 := [rewrite]: #83
-#80 := (= #20 -1::Int)
-#81 := [rewrite]: #80
-#87 := [monotonicity #81 #84]: #86
-#92 := [trans #87 #90]: #91
-#95 := [monotonicity #92]: #94
-#100 := [trans #95 #98]: #99
-#77 := (= #19 1::Int)
-#78 := [rewrite]: #77
-#75 := (iff #18 #74)
-#72 := (iff #17 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#103 := [monotonicity #76 #78 #100]: #102
-#69 := (iff #12 false)
-#70 := [rewrite]: #69
-#106 := [monotonicity #70 #103]: #105
-#110 := [trans #106 #108]: #109
-#67 := (iff #10 false)
-#68 := [rewrite]: #67
-#113 := [monotonicity #68 #110]: #112
-#117 := [trans #113 #115]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#128 := [trans #123 #126]: #127
-#131 := [monotonicity #128]: #130
-#182 := [trans #131 #180]: #181
-#66 := [asserted]: #30
-[mp #66 #182]: false
-unsat
-3921706a8683868f2784292da2026eadf56bd286 90 0
-#2 := false
-decl f3 :: (-> Int S2)
-#9 := 0::Int
-#24 := (f3 0::Int)
-#8 := 3::Int
-#17 := (- 3::Int)
-#18 := (mod #17 #17)
-#19 := (- #18)
-#16 := (mod 3::Int 3::Int)
-#11 := (< 0::Int 3::Int)
-#13 := (< 3::Int 0::Int)
-#14 := (and #13 #11)
-#12 := (and #11 #11)
-#15 := (or #12 #14)
-#20 := (ite #15 #16 #19)
-#10 := (= 3::Int 0::Int)
-#21 := (ite #10 0::Int #20)
-#22 := (ite #10 3::Int #21)
-#23 := (f3 #22)
-#25 := (= #23 #24)
-#26 := (not #25)
-#126 := (iff #26 false)
-#1 := true
-#121 := (not true)
-#124 := (iff #121 false)
-#125 := [rewrite]: #124
-#122 := (iff #26 #121)
-#119 := (iff #25 true)
-#114 := (= #24 #24)
-#117 := (iff #114 true)
-#118 := [rewrite]: #117
-#115 := (iff #25 #114)
-#111 := (= #22 0::Int)
-#106 := (ite false 3::Int 0::Int)
-#109 := (= #106 0::Int)
-#110 := [rewrite]: #109
-#107 := (= #22 #106)
-#104 := (= #21 0::Int)
-#99 := (ite false 0::Int 0::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #21 #99)
-#97 := (= #20 0::Int)
-#67 := (and #11 #13)
-#70 := (or #11 #67)
-#92 := (ite #70 0::Int 0::Int)
-#95 := (= #92 0::Int)
-#96 := [rewrite]: #95
-#93 := (= #20 #92)
-#90 := (= #19 0::Int)
-#85 := (- 0::Int)
-#88 := (= #85 0::Int)
+#9 := (f4 3::Int 3::Int)
+#10 := (f3 #9)
+#13 := (= #10 #12)
+#799 := (= #9 0::Int)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f4 #31 #20)
+#885 := (pattern #50)
+#180 := -1::Int
+#184 := (* -1::Int #20)
+#181 := (* -1::Int #31)
+#245 := (mod #181 #184)
+#375 := (+ #50 #245)
+#376 := (= #375 0::Int)
+#51 := (mod #31 #20)
+#372 := (* -1::Int #51)
+#373 := (+ #50 #372)
+#374 := (= #373 0::Int)
+#219 := (>= #31 0::Int)
+#212 := (<= #20 0::Int)
+#319 := (or #212 #219)
+#320 := (not #319)
+#208 := (<= #31 0::Int)
+#317 := (or #208 #212)
+#318 := (not #317)
+#323 := (or #318 #320)
+#377 := (ite #323 #374 #376)
+#371 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#378 := (ite #33 #371 #377)
+#370 := (= #31 #50)
+#34 := (= #20 0::Int)
+#379 := (ite #34 #370 #378)
+#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379)
+#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
+#889 := (iff #382 #886)
+#887 := (iff #379 #379)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#251 := (* -1::Int #245)
+#339 := (ite #323 #51 #251)
+#342 := (ite #33 0::Int #339)
+#345 := (ite #34 #31 #342)
+#348 := (= #50 #345)
+#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
+#383 := (iff #351 #382)
+#380 := (iff #348 #379)
+#381 := [rewrite]: #380
+#384 := [quant-intro #381]: #383
+#220 := (not #219)
+#213 := (not #212)
+#223 := (and #213 #220)
+#209 := (not #208)
+#216 := (and #209 #213)
+#226 := (or #216 #223)
+#271 := (ite #226 #51 #251)
+#274 := (ite #33 0::Int #271)
+#277 := (ite #34 #31 #274)
+#280 := (= #50 #277)
+#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
+#352 := (iff #283 #351)
+#349 := (iff #280 #348)
+#346 := (= #277 #345)
+#343 := (= #274 #342)
+#340 := (= #271 #339)
+#324 := (iff #226 #323)
+#321 := (iff #223 #320)
+#322 := [rewrite]: #321
+#302 := (iff #216 #318)
+#303 := [rewrite]: #302
+#325 := [monotonicity #303 #322]: #324
+#341 := [monotonicity #325]: #340
+#344 := [monotonicity #341]: #343
+#347 := [monotonicity #344]: #346
+#350 := [monotonicity #347]: #349
+#353 := [quant-intro #350]: #352
+#300 := (~ #283 #283)
+#314 := (~ #280 #280)
+#315 := [refl]: #314
+#301 := [nnf-pos #315]: #300
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#286 := (iff #58 #283)
+#174 := (and #37 #39)
+#177 := (or #38 #174)
+#256 := (ite #177 #51 #251)
+#165 := (= 0::Int #31)
+#259 := (ite #165 0::Int #256)
+#168 := (= 0::Int #20)
+#262 := (ite #168 #31 #259)
+#265 := (= #50 #262)
+#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
+#284 := (iff #268 #283)
+#281 := (iff #265 #280)
+#278 := (= #262 #277)
+#275 := (= #259 #274)
+#272 := (= #256 #271)
+#227 := (iff #177 #226)
+#224 := (iff #174 #223)
+#221 := (iff #39 #220)
+#222 := [rewrite]: #221
+#214 := (iff #37 #213)
+#215 := [rewrite]: #214
+#225 := [monotonicity #215 #222]: #224
+#217 := (iff #38 #216)
+#210 := (iff #36 #209)
+#211 := [rewrite]: #210
+#218 := [monotonicity #211 #215]: #217
+#228 := [monotonicity #218 #225]: #227
+#273 := [monotonicity #228]: #272
+#202 := (iff #165 #33)
+#203 := [rewrite]: #202
+#276 := [monotonicity #203 #273]: #275
+#204 := (iff #168 #34)
+#205 := [rewrite]: #204
+#279 := [monotonicity #205 #276]: #278
+#282 := [monotonicity #279]: #281
+#285 := [quant-intro #282]: #284
+#269 := (iff #58 #268)
+#266 := (iff #57 #265)
+#263 := (= #56 #262)
+#260 := (= #55 #259)
+#257 := (= #54 #256)
+#254 := (= #53 #251)
+#248 := (- #245)
+#252 := (= #248 #251)
+#253 := [rewrite]: #252
+#249 := (= #53 #248)
+#246 := (= #52 #245)
+#185 := (= #44 #184)
+#186 := [rewrite]: #185
+#182 := (= #43 #181)
+#183 := [rewrite]: #182
+#247 := [monotonicity #183 #186]: #246
+#250 := [monotonicity #247]: #249
+#255 := [trans #250 #253]: #254
+#178 := (iff #41 #177)
+#175 := (iff #40 #174)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#258 := [monotonicity #179 #255]: #257
+#166 := (iff #33 #165)
+#167 := [rewrite]: #166
+#261 := [monotonicity #167 #258]: #260
+#169 := (iff #34 #168)
+#170 := [rewrite]: #169
+#264 := [monotonicity #170 #261]: #263
+#267 := [monotonicity #264]: #266
+#270 := [quant-intro #267]: #269
+#287 := [trans #270 #285]: #286
+#244 := [asserted]: #58
+#288 := [mp #244 #287]: #283
+#316 := [mp~ #288 #301]: #283
+#354 := [mp #316 #353]: #351
+#385 := [mp #354 #384]: #382
+#891 := [mp #385 #890]: #886
+#704 := (not #886)
+#705 := (or #704 #799)
+#812 := (* -1::Int 3::Int)
+#813 := (mod #812 #812)
+#814 := (+ #9 #813)
+#809 := (= #814 0::Int)
+#810 := (mod 3::Int 3::Int)
+#815 := (* -1::Int #810)
+#816 := (+ #9 #815)
+#811 := (= #816 0::Int)
+#817 := (>= 3::Int 0::Int)
+#658 := (<= 3::Int 0::Int)
+#659 := (or #658 #817)
+#660 := (not #659)
+#802 := (or #658 #658)
+#803 := (not #802)
+#804 := (or #803 #660)
+#805 := (ite #804 #811 #809)
+#800 := (= 3::Int 0::Int)
+#806 := (ite #800 #799 #805)
+#807 := (= 3::Int #9)
+#801 := (ite #800 #807 #806)
+#706 := (or #704 #801)
+#710 := (iff #706 #705)
+#712 := (iff #705 #705)
+#717 := [rewrite]: #712
+#725 := (iff #801 #799)
+#640 := (= #9 3::Int)
+#724 := (ite false #640 #799)
+#729 := (iff #724 #799)
+#730 := [rewrite]: #729
+#727 := (iff #801 #724)
+#722 := (iff #806 #799)
+#738 := (ite false #799 #799)
+#740 := (iff #738 #799)
+#726 := [rewrite]: #740
+#739 := (iff #806 #738)
+#736 := (iff #805 #799)
+#1 := true
+#743 := (ite true #799 #799)
+#733 := (iff #743 #799)
+#735 := [rewrite]: #733
+#754 := (iff #805 #743)
+#752 := (iff #809 #799)
+#750 := (= #814 #9)
+#765 := (+ #9 0::Int)
+#768 := (= #765 #9)
+#764 := [rewrite]: #768
+#748 := (= #814 #765)
+#746 := (= #813 0::Int)
+#759 := -3::Int
+#761 := (mod -3::Int -3::Int)
+#744 := (= #761 0::Int)
+#745 := [rewrite]: #744
+#741 := (= #813 #761)
+#760 := (= #812 -3::Int)
+#757 := [rewrite]: #760
+#742 := [monotonicity #757 #757]: #741
+#747 := [trans #742 #745]: #746
+#749 := [monotonicity #747]: #748
+#751 := [trans #749 #764]: #750
+#753 := [monotonicity #751]: #752
+#756 := (iff #811 #799)
+#769 := (= #816 #9)
+#766 := (= #816 #765)
+#762 := (= #815 0::Int)
+#775 := (* -1::Int 0::Int)
+#771 := (= #775 0::Int)
+#778 := [rewrite]: #771
+#776 := (= #815 #775)
+#785 := (= #810 0::Int)
+#774 := [rewrite]: #785
+#777 := [monotonicity #774]: #776
+#763 := [trans #777 #778]: #762
+#767 := [monotonicity #763]: #766
+#755 := [trans #767 #764]: #769
+#758 := [monotonicity #755]: #756
+#784 := (iff #804 true)
+#773 := (or true false)
+#782 := (iff #773 true)
+#783 := [rewrite]: #782
+#770 := (iff #804 #773)
+#779 := (iff #660 false)
+#482 := (not true)
+#841 := (iff #482 false)
+#844 := [rewrite]: #841
+#788 := (iff #660 #482)
+#698 := (iff #659 true)
+#686 := (or false true)
+#696 := (iff #686 true)
+#697 := [rewrite]: #696
+#694 := (iff #659 #686)
+#692 := (iff #817 true)
+#693 := [rewrite]: #692
+#794 := (iff #658 false)
+#796 := [rewrite]: #794
+#695 := [monotonicity #796 #693]: #694
+#791 := [trans #695 #697]: #698
+#792 := [monotonicity #791]: #788
+#781 := [trans #792 #844]: #779
+#675 := (iff #803 true)
+#789 := (not false)
+#787 := (iff #789 true)
+#790 := [rewrite]: #787
+#691 := (iff #803 #789)
+#682 := (iff #802 false)
+#797 := (or false false)
+#680 := (iff #797 false)
+#681 := [rewrite]: #680
+#795 := (iff #802 #797)
+#798 := [monotonicity #796 #796]: #795
+#641 := [trans #798 #681]: #682
+#786 := [monotonicity #641]: #691
+#690 := [trans #786 #790]: #675
+#772 := [monotonicity #690 #781]: #770
+#780 := [trans #772 #783]: #784
+#732 := [monotonicity #780 #758 #753]: #754
+#737 := [trans #732 #735]: #736
+#808 := (iff #800 false)
+#637 := [rewrite]: #808
+#734 := [monotonicity #637 #737]: #739
+#723 := [trans #734 #726]: #722
+#639 := (iff #807 #640)
+#793 := [rewrite]: #639
+#728 := [monotonicity #637 #793 #723]: #727
+#731 := [trans #728 #730]: #725
+#711 := [monotonicity #731]: #710
+#713 := [trans #711 #717]: #710
+#599 := [quant-inst #8 #8]: #706
+#714 := [mp #599 #713]: #705
+#718 := [unit-resolution #714 #891]: #799
+#719 := [monotonicity #718]: #13
+#14 := (not #13)
+#78 := [asserted]: #14
+[unit-resolution #78 #719]: false
+unsat
+f05688f0b5f9f483f17f9e461ed5ff3d814bfbb3 452 0
+#2 := false
+#10 := 3::Int
+decl f4 :: (-> S2 Int)
+decl f5 :: S2
+#8 := f5
+#9 := (f4 f5)
+#547 := (mod #9 3::Int)
+#741 := (>= #547 3::Int)
+#742 := (not #741)
+#1 := true
+#76 := [true-axiom]: true
+#729 := (or false #742)
+#725 := [th-lemma arith]: #729
+#726 := [unit-resolution #725 #76]: #742
+#19 := 0::Int
+#192 := -1::Int
+#526 := (* -1::Int #547)
+decl f3 :: (-> Int Int Int)
+#11 := (f3 #9 3::Int)
+#861 := (+ #11 #526)
+#808 := (<= #861 0::Int)
+#863 := (= #861 0::Int)
+#561 := -3::Int
+#542 := (* -1::Int #9)
+#840 := (mod #542 -3::Int)
+#551 := (+ #11 #840)
+#554 := (= #551 0::Int)
+#532 := (<= #9 0::Int)
+#849 := (not #532)
+#520 := (>= #9 0::Int)
+#853 := (not #520)
+#567 := (or #853 #849)
+#548 := (ite #567 #863 #554)
+#862 := (= #11 0::Int)
+#868 := (= #9 0::Int)
+#831 := (ite #868 #862 #548)
+#20 := (:var 0 Int)
+#31 := (:var 1 Int)
+#50 := (f3 #31 #20)
+#897 := (pattern #50)
+#196 := (* -1::Int #20)
+#193 := (* -1::Int #31)
+#257 := (mod #193 #196)
+#387 := (+ #50 #257)
+#388 := (= #387 0::Int)
+#51 := (mod #31 #20)
+#384 := (* -1::Int #51)
+#385 := (+ #50 #384)
+#386 := (= #385 0::Int)
+#231 := (>= #31 0::Int)
+#224 := (<= #20 0::Int)
+#331 := (or #224 #231)
+#332 := (not #331)
+#220 := (<= #31 0::Int)
+#329 := (or #220 #224)
+#330 := (not #329)
+#335 := (or #330 #332)
+#389 := (ite #335 #386 #388)
+#383 := (= #50 0::Int)
+#33 := (= #31 0::Int)
+#390 := (ite #33 #383 #389)
+#382 := (= #31 #50)
+#34 := (= #20 0::Int)
+#391 := (ite #34 #382 #390)
+#898 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #897) #391)
+#394 := (forall (vars (?v0 Int) (?v1 Int)) #391)
+#901 := (iff #394 #898)
+#899 := (iff #391 #391)
+#900 := [refl]: #899
+#902 := [quant-intro #900]: #901
+#263 := (* -1::Int #257)
+#351 := (ite #335 #51 #263)
+#354 := (ite #33 0::Int #351)
+#357 := (ite #34 #31 #354)
+#360 := (= #50 #357)
+#363 := (forall (vars (?v0 Int) (?v1 Int)) #360)
+#395 := (iff #363 #394)
+#392 := (iff #360 #391)
+#393 := [rewrite]: #392
+#396 := [quant-intro #393]: #395
+#232 := (not #231)
+#225 := (not #224)
+#235 := (and #225 #232)
+#221 := (not #220)
+#228 := (and #221 #225)
+#238 := (or #228 #235)
+#283 := (ite #238 #51 #263)
+#286 := (ite #33 0::Int #283)
+#289 := (ite #34 #31 #286)
+#292 := (= #50 #289)
+#295 := (forall (vars (?v0 Int) (?v1 Int)) #292)
+#364 := (iff #295 #363)
+#361 := (iff #292 #360)
+#358 := (= #289 #357)
+#355 := (= #286 #354)
+#352 := (= #283 #351)
+#336 := (iff #238 #335)
+#333 := (iff #235 #332)
+#334 := [rewrite]: #333
+#314 := (iff #228 #330)
+#315 := [rewrite]: #314
+#337 := [monotonicity #315 #334]: #336
+#353 := [monotonicity #337]: #352
+#356 := [monotonicity #353]: #355
+#359 := [monotonicity #356]: #358
+#362 := [monotonicity #359]: #361
+#365 := [quant-intro #362]: #364
+#312 := (~ #295 #295)
+#326 := (~ #292 #292)
+#327 := [refl]: #326
+#313 := [nnf-pos #327]: #312
+#44 := (- #20)
+#43 := (- #31)
+#52 := (mod #43 #44)
+#53 := (- #52)
+#37 := (< 0::Int #20)
+#39 := (< #31 0::Int)
+#40 := (and #39 #37)
+#36 := (< 0::Int #31)
+#38 := (and #36 #37)
+#41 := (or #38 #40)
+#54 := (ite #41 #51 #53)
+#55 := (ite #33 0::Int #54)
+#56 := (ite #34 #31 #55)
+#57 := (= #50 #56)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
+#298 := (iff #58 #295)
+#186 := (and #37 #39)
+#189 := (or #38 #186)
+#268 := (ite #189 #51 #263)
+#177 := (= 0::Int #31)
+#271 := (ite #177 0::Int #268)
+#180 := (= 0::Int #20)
+#274 := (ite #180 #31 #271)
+#277 := (= #50 #274)
+#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
+#296 := (iff #280 #295)
+#293 := (iff #277 #292)
+#290 := (= #274 #289)
+#287 := (= #271 #286)
+#284 := (= #268 #283)
+#239 := (iff #189 #238)
+#236 := (iff #186 #235)
+#233 := (iff #39 #232)
+#234 := [rewrite]: #233
+#226 := (iff #37 #225)
+#227 := [rewrite]: #226
+#237 := [monotonicity #227 #234]: #236
+#229 := (iff #38 #228)
+#222 := (iff #36 #221)
+#223 := [rewrite]: #222
+#230 := [monotonicity #223 #227]: #229
+#240 := [monotonicity #230 #237]: #239
+#285 := [monotonicity #240]: #284
+#214 := (iff #177 #33)
+#215 := [rewrite]: #214
+#288 := [monotonicity #215 #285]: #287
+#216 := (iff #180 #34)
+#217 := [rewrite]: #216
+#291 := [monotonicity #217 #288]: #290
+#294 := [monotonicity #291]: #293
+#297 := [quant-intro #294]: #296
+#281 := (iff #58 #280)
+#278 := (iff #57 #277)
+#275 := (= #56 #274)
+#272 := (= #55 #271)
+#269 := (= #54 #268)
+#266 := (= #53 #263)
+#260 := (- #257)
+#264 := (= #260 #263)
+#265 := [rewrite]: #264
+#261 := (= #53 #260)
+#258 := (= #52 #257)
+#197 := (= #44 #196)
+#198 := [rewrite]: #197
+#194 := (= #43 #193)
+#195 := [rewrite]: #194
+#259 := [monotonicity #195 #198]: #258
+#262 := [monotonicity #259]: #261
+#267 := [trans #262 #265]: #266
+#190 := (iff #41 #189)
+#187 := (iff #40 #186)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#270 := [monotonicity #191 #267]: #269
+#178 := (iff #33 #177)
+#179 := [rewrite]: #178
+#273 := [monotonicity #179 #270]: #272
+#181 := (iff #34 #180)
+#182 := [rewrite]: #181
+#276 := [monotonicity #182 #273]: #275
+#279 := [monotonicity #276]: #278
+#282 := [quant-intro #279]: #281
+#299 := [trans #282 #297]: #298
+#256 := [asserted]: #58
+#300 := [mp #256 #299]: #295
+#328 := [mp~ #300 #313]: #295
+#366 := [mp #328 #365]: #363
+#397 := [mp #366 #396]: #394
+#903 := [mp #397 #902]: #898
+#829 := (not #898)
+#670 := (or #829 #831)
+#541 := (* -1::Int 3::Int)
+#473 := (mod #542 #541)
+#546 := (+ #11 #473)
+#543 := (= #546 0::Int)
+#650 := (<= 3::Int 0::Int)
+#857 := (or #650 #520)
+#531 := (not #857)
+#864 := (or #532 #650)
+#865 := (not #864)
+#866 := (or #865 #531)
+#867 := (ite #866 #863 #543)
+#858 := (ite #868 #862 #867)
+#518 := (= #9 #11)
+#523 := (= 3::Int 0::Int)
+#859 := (ite #523 #518 #858)
+#671 := (or #829 #859)
+#814 := (iff #671 #670)
+#816 := (iff #670 #670)
+#817 := [rewrite]: #816
+#828 := (iff #859 #831)
+#825 := (ite false #518 #831)
+#822 := (iff #825 #831)
+#827 := [rewrite]: #822
+#826 := (iff #859 #825)
+#835 := (iff #858 #831)
+#830 := (iff #867 #548)
+#832 := (iff #543 #554)
+#552 := (= #546 #551)
+#837 := (= #473 #840)
+#562 := (= #541 -3::Int)
+#836 := [rewrite]: #562
+#841 := [monotonicity #836]: #837
+#553 := [monotonicity #841]: #552
+#833 := [monotonicity #553]: #832
+#838 := (iff #866 #567)
+#843 := (or #849 #853)
+#568 := (iff #843 #567)
+#461 := [rewrite]: #568
+#565 := (iff #866 #843)
+#856 := (iff #531 #853)
+#495 := (iff #857 #520)
+#851 := (or false #520)
+#854 := (iff #851 #520)
+#494 := [rewrite]: #854
+#489 := (iff #857 #851)
+#503 := (iff #650 false)
+#844 := [rewrite]: #503
+#852 := [monotonicity #844]: #489
+#855 := [trans #852 #494]: #495
+#842 := [monotonicity #855]: #856
+#850 := (iff #865 #849)
+#847 := (iff #864 #532)
+#507 := (or #532 false)
+#510 := (iff #507 #532)
+#846 := [rewrite]: #510
+#508 := (iff #864 #507)
+#509 := [monotonicity #844]: #508
+#848 := [trans #509 #846]: #847
+#845 := [monotonicity #848]: #850
+#566 := [monotonicity #845 #842]: #565
+#839 := [trans #566 #461]: #838
+#834 := [monotonicity #839 #833]: #830
+#824 := [monotonicity #834]: #835
+#519 := (iff #523 false)
+#860 := [rewrite]: #519
+#821 := [monotonicity #860 #824]: #826
+#823 := [trans #821 #827]: #828
+#815 := [monotonicity #823]: #814
+#811 := [trans #815 #817]: #814
+#672 := [quant-inst #9 #10]: #671
+#812 := [mp #672 #811]: #670
+#727 := [unit-resolution #812 #903]: #831
+#705 := (not #868)
+#704 := (not #831)
+#714 := (or #704 #705)
+#709 := (not #862)
+#818 := (<= #11 0::Int)
+#730 := (not #818)
+#83 := (>= #11 3::Int)
+#12 := (< #11 3::Int)
+#13 := (not #12)
+#90 := (iff #13 #83)
+#81 := (not #83)
+#85 := (not #81)
+#88 := (iff #85 #83)
#89 := [rewrite]: #88
-#86 := (= #19 #85)
-#83 := (= #18 0::Int)
-#75 := -3::Int
-#78 := (mod -3::Int -3::Int)
-#81 := (= #78 0::Int)
-#82 := [rewrite]: #81
-#79 := (= #18 #78)
-#76 := (= #17 -3::Int)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77 #77]: #79
-#84 := [trans #80 #82]: #83
+#86 := (iff #13 #85)
+#82 := (iff #12 #81)
+#84 := [rewrite]: #82
#87 := [monotonicity #84]: #86
#91 := [trans #87 #89]: #90
-#73 := (= #16 0::Int)
-#74 := [rewrite]: #73
-#71 := (iff #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#65 := (iff #12 #11)
-#66 := [rewrite]: #65
-#72 := [monotonicity #66 #69]: #71
-#94 := [monotonicity #72 #74 #91]: #93
-#98 := [trans #94 #96]: #97
-#63 := (iff #10 false)
-#64 := [rewrite]: #63
-#101 := [monotonicity #64 #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #64 #105]: #107
+#78 := [asserted]: #13
+#92 := [mp #78 #91]: #83
+#731 := (or #730 #81)
+#732 := [th-lemma arith farkas 1 1]: #731
+#728 := [unit-resolution #732 #92]: #730
+#733 := (or #709 #818)
+#713 := [th-lemma arith triangle-eq]: #733
+#659 := [unit-resolution #713 #728]: #709
+#698 := (or #704 #705 #862)
+#706 := [def-axiom]: #698
+#695 := [unit-resolution #706 #659]: #714
+#719 := [unit-resolution #695 #727]: #705
+#707 := (or #704 #868 #548)
+#708 := [def-axiom]: #707
+#720 := [unit-resolution #708 #719 #727]: #548
+decl f6 :: (-> Int S2)
+#455 := (f6 #9)
+#791 := (f4 #455)
+#793 := (= #791 0::Int)
+#699 := (not #793)
+#700 := (iff #705 #699)
+#690 := (iff #868 #793)
+#686 := (iff #793 #868)
+#696 := (= #791 #9)
+#721 := (= #455 f5)
+#540 := (= f5 #455)
+#14 := (:var 0 S2)
+#15 := (f4 #14)
+#869 := (pattern #15)
+#16 := (f6 #15)
+#80 := (= #14 #16)
+#870 := (forall (vars (?v0 S2)) (:pat #869) #80)
+#95 := (forall (vars (?v0 S2)) #80)
+#871 := (iff #95 #870)
+#873 := (iff #870 #870)
+#874 := [rewrite]: #873
+#872 := [rewrite]: #871
+#875 := [trans #872 #874]: #871
+#318 := (~ #95 #95)
+#316 := (~ #80 #80)
+#317 := [refl]: #316
+#319 := [nnf-pos #317]: #318
+#17 := (= #16 #14)
+#18 := (forall (vars (?v0 S2)) #17)
+#96 := (iff #18 #95)
+#93 := (iff #17 #80)
+#94 := [rewrite]: #93
+#97 := [quant-intro #94]: #96
+#79 := [asserted]: #18
+#100 := [mp #79 #97]: #95
+#304 := [mp~ #100 #319]: #95
+#876 := [mp #304 #875]: #870
+#533 := (not #870)
+#544 := (or #533 #540)
+#545 := [quant-inst #8]: #544
+#715 := [unit-resolution #545 #876]: #540
+#689 := [symm #715]: #721
+#655 := [monotonicity #689]: #696
+#688 := [monotonicity #655]: #686
+#697 := [symm #688]: #690
+#701 := [monotonicity #697]: #700
+#711 := [mp #719 #701]: #699
+#782 := (or #520 #793)
+#22 := (f6 #20)
+#877 := (pattern #22)
+#117 := (>= #20 0::Int)
+#23 := (f4 #22)
+#28 := (= #23 0::Int)
+#165 := (or #28 #117)
+#884 := (forall (vars (?v0 Int)) (:pat #877) #165)
+#170 := (forall (vars (?v0 Int)) #165)
+#887 := (iff #170 #884)
+#885 := (iff #165 #165)
+#886 := [refl]: #885
+#888 := [quant-intro #886]: #887
+#308 := (~ #170 #170)
+#320 := (~ #165 #165)
+#321 := [refl]: #320
+#309 := [nnf-pos #321]: #308
+#27 := (< #20 0::Int)
+#29 := (implies #27 #28)
+#30 := (forall (vars (?v0 Int)) #29)
+#173 := (iff #30 #170)
+#136 := (= 0::Int #23)
+#142 := (not #27)
+#143 := (or #142 #136)
+#148 := (forall (vars (?v0 Int)) #143)
+#171 := (iff #148 #170)
+#168 := (iff #143 #165)
+#162 := (or #117 #28)
+#166 := (iff #162 #165)
+#167 := [rewrite]: #166
+#163 := (iff #143 #162)
+#160 := (iff #136 #28)
+#161 := [rewrite]: #160
+#158 := (iff #142 #117)
+#118 := (not #117)
+#153 := (not #118)
+#156 := (iff #153 #117)
+#157 := [rewrite]: #156
+#154 := (iff #142 #153)
+#151 := (iff #27 #118)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#159 := [trans #155 #157]: #158
+#164 := [monotonicity #159 #161]: #163
+#169 := [trans #164 #167]: #168
+#172 := [quant-intro #169]: #171
+#149 := (iff #30 #148)
+#146 := (iff #29 #143)
+#139 := (implies #27 #136)
+#144 := (iff #139 #143)
+#145 := [rewrite]: #144
+#140 := (iff #29 #139)
+#137 := (iff #28 #136)
+#138 := [rewrite]: #137
+#141 := [monotonicity #138]: #140
+#147 := [trans #141 #145]: #146
+#150 := [quant-intro #147]: #149
+#174 := [trans #150 #172]: #173
+#135 := [asserted]: #30
+#175 := [mp #135 #174]: #170
+#322 := [mp~ #175 #309]: #170
+#889 := [mp #322 #888]: #884
+#795 := (not #884)
+#796 := (or #795 #520 #793)
+#785 := (or #793 #520)
+#792 := (or #795 #785)
+#790 := (iff #792 #796)
+#786 := (or #795 #782)
+#789 := (iff #786 #796)
+#783 := [rewrite]: #789
+#787 := (iff #792 #786)
+#784 := (iff #785 #782)
+#794 := [rewrite]: #784
+#788 := [monotonicity #794]: #787
+#774 := [trans #788 #783]: #790
+#797 := [quant-inst #9]: #792
+#775 := [mp #797 #774]: #796
+#691 := [unit-resolution #775 #889]: #782
+#712 := [unit-resolution #691 #711]: #520
+#667 := (or #868 #849 #853)
+#668 := [th-lemma arith triangle-eq]: #667
+#673 := [unit-resolution #668 #719]: #843
+#674 := [unit-resolution #673 #712]: #849
+#649 := (or #567 #532)
+#651 := [def-axiom]: #649
+#675 := [unit-resolution #651 #674]: #567
+#652 := (not #567)
+#692 := (not #548)
+#693 := (or #692 #652 #863)
+#694 := [def-axiom]: #693
+#676 := [unit-resolution #694 #675 #720]: #863
+#703 := (not #863)
+#677 := (or #703 #808)
+#678 := [th-lemma arith triangle-eq]: #677
+#679 := [unit-resolution #678 #676]: #808
+[th-lemma arith farkas -1 1 1 #92 #679 #726]: false
+unsat
+318d5be50bbd50da7b7b7962a11c2c98ae8be85c 662 0
+#2 := false
+#10 := 3::Int
+decl f5 :: (-> S2 Int)
+decl f6 :: S2
+#8 := f6
+#9 := (f5 f6)
+#883 := (mod #9 3::Int)
+#706 := (>= #883 3::Int)
+#707 := (not #706)
+#1 := true
+#79 := [true-axiom]: true
+#666 := (or false #707)
+#667 := [th-lemma arith]: #666
+#669 := [unit-resolution #667 #79]: #707
+#104 := (>= #9 3::Int)
+#102 := (not #104)
+#619 := [hypothesis]: #102
+#22 := 0::Int
+#220 := -1::Int
+#881 := (* -1::Int #883)
+decl f4 :: (-> Int Int Int)
+#11 := (f4 #9 3::Int)
+#884 := (+ #11 #881)
+#824 := (<= #884 0::Int)
+#870 := (= #884 0::Int)
+#864 := (= #9 0::Int)
+#809 := (not #864)
+decl f3 :: (-> Int S2)
+#12 := (f3 #11)
+#82 := (= f6 #12)
+#572 := (not #82)
+#574 := (or #572 #104)
+#113 := (iff #82 #104)
+#14 := (< #9 3::Int)
+#13 := (= #12 f6)
+#15 := (iff #13 #14)
+#16 := (not #15)
+#116 := (iff #16 #113)
+#96 := (not #14)
+#97 := (iff #82 #96)
+#114 := (iff #97 #113)
+#111 := (iff #96 #104)
+#106 := (not #102)
+#109 := (iff #106 #104)
+#110 := [rewrite]: #109
+#107 := (iff #96 #106)
+#103 := (iff #14 #102)
+#105 := [rewrite]: #103
+#108 := [monotonicity #105]: #107
#112 := [trans #108 #110]: #111
-#113 := [monotonicity #112]: #25
-#116 := [monotonicity #113]: #115
-#120 := [trans #116 #118]: #119
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#62 := [asserted]: #26
-[mp #62 #127]: false
-unsat
-514d90db39c84cc7bf19d9cbc0eb437cde0db30b 305 0
-#2 := false
-#8 := 3::Int
-decl f3 :: (-> S2 Int)
-decl f4 :: S2
-#11 := f4
-#12 := (f3 f4)
-#20 := (mod #12 3::Int)
-#690 := (>= #20 3::Int)
-#691 := (not #690)
-#1 := true
-#63 := [true-axiom]: true
-#525 := (or false #691)
-#673 := [th-lemma arith]: #525
-#575 := [unit-resolution #673 #63]: #691
-#9 := 0::Int
-#81 := -3::Int
-#77 := -1::Int
-#78 := (* -1::Int #12)
-#84 := (mod #78 -3::Int)
-#90 := (* -1::Int #84)
-#129 := (>= #12 0::Int)
-#130 := (not #129)
-#116 := (<= #12 0::Int)
-#117 := (not #116)
-#140 := (or #117 #130)
-#143 := (ite #140 #20 #90)
-#13 := (= #12 0::Int)
-#146 := (ite #13 0::Int #143)
-#682 := (* -1::Int #146)
-#564 := (+ #20 #682)
-#566 := (>= #564 0::Int)
-#679 := (= #20 #146)
-#412 := (= #143 #146)
-#392 := (not #13)
-#326 := (= #146 0::Int)
-#727 := (not #326)
-#717 := (<= #146 0::Int)
-#361 := (not #717)
-#153 := (>= #146 3::Int)
-#22 := (- 3::Int)
-#21 := (- #12)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#15 := (< 0::Int 3::Int)
-#17 := (< #12 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #12)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#26 := (ite #13 0::Int #25)
-#10 := (= 3::Int 0::Int)
-#27 := (ite #10 #12 #26)
-#28 := (< #27 3::Int)
-#29 := (not #28)
-#165 := (iff #29 #153)
-#71 := (and #15 #17)
-#74 := (or #16 #71)
-#95 := (ite #74 #20 #90)
-#68 := (= 0::Int #12)
-#98 := (ite #68 0::Int #95)
-#108 := (< #98 3::Int)
-#111 := (not #108)
-#163 := (iff #111 #153)
-#152 := (not #153)
-#158 := (not #152)
-#161 := (iff #158 #153)
-#162 := [rewrite]: #161
-#159 := (iff #111 #158)
-#156 := (iff #108 #152)
-#149 := (< #146 3::Int)
-#154 := (iff #149 #152)
-#155 := [rewrite]: #154
-#150 := (iff #108 #149)
-#147 := (= #98 #146)
-#144 := (= #95 #143)
-#141 := (iff #74 #140)
-#138 := (iff #71 #130)
-#133 := (and true #130)
-#136 := (iff #133 #130)
-#137 := [rewrite]: #136
-#134 := (iff #71 #133)
-#131 := (iff #17 #130)
-#132 := [rewrite]: #131
-#120 := (iff #15 true)
-#121 := [rewrite]: #120
-#135 := [monotonicity #121 #132]: #134
-#139 := [trans #135 #137]: #138
-#127 := (iff #16 #117)
-#122 := (and #117 true)
-#125 := (iff #122 #117)
-#126 := [rewrite]: #125
-#123 := (iff #16 #122)
-#118 := (iff #14 #117)
-#119 := [rewrite]: #118
-#124 := [monotonicity #119 #121]: #123
-#128 := [trans #124 #126]: #127
-#142 := [monotonicity #128 #139]: #141
-#145 := [monotonicity #142]: #144
-#114 := (iff #68 #13)
-#115 := [rewrite]: #114
-#148 := [monotonicity #115 #145]: #147
-#151 := [monotonicity #148]: #150
-#157 := [trans #151 #155]: #156
-#160 := [monotonicity #157]: #159
-#164 := [trans #160 #162]: #163
-#112 := (iff #29 #111)
-#109 := (iff #28 #108)
-#106 := (= #27 #98)
-#101 := (ite false #12 #98)
-#104 := (= #101 #98)
-#105 := [rewrite]: #104
-#102 := (= #27 #101)
-#99 := (= #26 #98)
-#96 := (= #25 #95)
-#93 := (= #24 #90)
-#87 := (- #84)
-#91 := (= #87 #90)
-#92 := [rewrite]: #91
-#88 := (= #24 #87)
-#85 := (= #23 #84)
-#82 := (= #22 -3::Int)
-#83 := [rewrite]: #82
-#79 := (= #21 #78)
-#80 := [rewrite]: #79
-#86 := [monotonicity #80 #83]: #85
-#89 := [monotonicity #86]: #88
-#94 := [trans #89 #92]: #93
-#75 := (iff #19 #74)
-#72 := (iff #18 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#97 := [monotonicity #76 #94]: #96
-#69 := (iff #13 #68)
-#70 := [rewrite]: #69
-#100 := [monotonicity #70 #97]: #99
-#66 := (iff #10 false)
-#67 := [rewrite]: #66
-#103 := [monotonicity #67 #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#166 := [trans #113 #164]: #165
-#65 := [asserted]: #29
-#167 := [mp #65 #166]: #153
-#724 := (or #361 #152)
-#726 := [th-lemma arith farkas 1 1]: #724
-#366 := [unit-resolution #726 #167]: #361
-#367 := [hypothesis]: #326
-#725 := (or #727 #717)
-#728 := [th-lemma arith triangle-eq]: #725
-#714 := [unit-resolution #728 #367 #366]: false
-#715 := [lemma #714]: #727
-#522 := (or #392 #326)
-#729 := [def-axiom]: #522
-#670 := [unit-resolution #729 #715]: #392
-#403 := (or #13 #412)
-#404 := [def-axiom]: #403
-#671 := [unit-resolution #404 #670]: #412
-#327 := (= #20 #143)
-decl f5 :: (-> Int S2)
-#736 := (f5 #12)
-#738 := (f3 #736)
-#739 := (= #738 0::Int)
-#581 := (not #739)
-#582 := (iff #392 #581)
-#579 := (iff #13 #739)
-#570 := (iff #739 #13)
-#576 := (= #738 #12)
-#559 := (= #736 f4)
-#737 := (= f4 #736)
-#30 := (:var 0 S2)
-#31 := (f3 #30)
-#741 := (pattern #31)
-#32 := (f5 #31)
-#169 := (= #30 #32)
-#742 := (forall (vars (?v0 S2)) (:pat #741) #169)
-#172 := (forall (vars (?v0 S2)) #169)
-#743 := (iff #172 #742)
-#745 := (iff #742 #742)
-#746 := [rewrite]: #745
-#744 := [rewrite]: #743
-#747 := [trans #744 #746]: #743
-#266 := (~ #172 #172)
-#264 := (~ #169 #169)
-#265 := [refl]: #264
-#267 := [nnf-pos #265]: #266
-#33 := (= #32 #30)
-#34 := (forall (vars (?v0 S2)) #33)
-#173 := (iff #34 #172)
-#170 := (iff #33 #169)
-#171 := [rewrite]: #170
-#174 := [quant-intro #171]: #173
-#168 := [asserted]: #34
-#177 := [mp #168 #174]: #172
-#256 := [mp~ #177 #267]: #172
-#748 := [mp #256 #747]: #742
-#734 := (not #742)
-#740 := (or #734 #737)
-#730 := [quant-inst #11]: #740
-#674 := [unit-resolution #730 #748]: #737
-#574 := [symm #674]: #559
-#577 := [monotonicity #574]: #576
-#578 := [monotonicity #577]: #570
-#580 := [symm #578]: #579
-#675 := [monotonicity #580]: #582
-#672 := [mp #670 #675]: #581
-#395 := (or #129 #739)
-#35 := (:var 0 Int)
-#37 := (f5 #35)
-#749 := (pattern #37)
-#193 := (>= #35 0::Int)
-#38 := (f3 #37)
-#43 := (= #38 0::Int)
-#242 := (or #43 #193)
-#756 := (forall (vars (?v0 Int)) (:pat #749) #242)
-#247 := (forall (vars (?v0 Int)) #242)
-#759 := (iff #247 #756)
-#757 := (iff #242 #242)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#260 := (~ #247 #247)
-#268 := (~ #242 #242)
-#269 := [refl]: #268
-#261 := [nnf-pos #269]: #260
-#42 := (< #35 0::Int)
-#44 := (implies #42 #43)
-#45 := (forall (vars (?v0 Int)) #44)
-#250 := (iff #45 #247)
-#213 := (= 0::Int #38)
-#219 := (not #42)
-#220 := (or #219 #213)
-#225 := (forall (vars (?v0 Int)) #220)
-#248 := (iff #225 #247)
-#245 := (iff #220 #242)
-#239 := (or #193 #43)
-#243 := (iff #239 #242)
-#244 := [rewrite]: #243
-#240 := (iff #220 #239)
-#237 := (iff #213 #43)
-#238 := [rewrite]: #237
-#235 := (iff #219 #193)
-#195 := (not #193)
-#230 := (not #195)
-#233 := (iff #230 #193)
-#234 := [rewrite]: #233
-#231 := (iff #219 #230)
-#228 := (iff #42 #195)
-#229 := [rewrite]: #228
-#232 := [monotonicity #229]: #231
-#236 := [trans #232 #234]: #235
-#241 := [monotonicity #236 #238]: #240
-#246 := [trans #241 #244]: #245
-#249 := [quant-intro #246]: #248
-#226 := (iff #45 #225)
-#223 := (iff #44 #220)
-#216 := (implies #42 #213)
-#221 := (iff #216 #220)
-#222 := [rewrite]: #221
-#217 := (iff #44 #216)
-#214 := (iff #43 #213)
-#215 := [rewrite]: #214
-#218 := [monotonicity #215]: #217
-#224 := [trans #218 #222]: #223
-#227 := [quant-intro #224]: #226
-#251 := [trans #227 #249]: #250
-#212 := [asserted]: #45
-#252 := [mp #212 #251]: #247
-#270 := [mp~ #252 #261]: #247
-#761 := [mp #270 #760]: #756
-#732 := (not #756)
-#375 := (or #732 #129 #739)
-#390 := (or #739 #129)
-#716 := (or #732 #390)
-#720 := (iff #716 #375)
-#380 := (or #732 #395)
-#718 := (iff #380 #375)
-#719 := [rewrite]: #718
-#381 := (iff #716 #380)
-#731 := (iff #390 #395)
-#391 := [rewrite]: #731
-#382 := [monotonicity #391]: #381
-#721 := [trans #382 #719]: #720
-#379 := [quant-inst #12]: #716
-#722 := [mp #379 #721]: #375
-#676 := [unit-resolution #722 #761]: #395
-#663 := [unit-resolution #676 #672]: #129
-#665 := (or #13 #117 #130)
-#657 := [th-lemma arith triangle-eq]: #665
-#654 := [unit-resolution #657 #670]: #140
-#656 := [unit-resolution #654 #663]: #117
-#414 := (or #140 #116)
-#405 := [def-axiom]: #414
-#666 := [unit-resolution #405 #656]: #140
-#345 := (not #140)
-#419 := (or #345 #327)
-#398 := [def-axiom]: #419
-#667 := [unit-resolution #398 #666]: #327
-#668 := [trans #667 #671]: #679
-#664 := (not #679)
-#669 := (or #664 #566)
-#658 := [th-lemma arith triangle-eq]: #669
-#659 := [unit-resolution #658 #668]: #566
-[th-lemma arith farkas -1 -1 1 #167 #659 #575]: false
-unsat
-2855a1e15b1d7788a0afdba64d4d2bd112ea0f3b 560 0
-#2 := false
-#9 := 0::Int
-decl f4 :: (-> S2 Int)
-decl f5 :: S2
-#11 := f5
-#12 := (f4 f5)
-#141 := (<= #12 0::Int)
-#142 := (not #141)
-#8 := 3::Int
-#180 := (>= #12 3::Int)
-#654 := 1::Int
-#706 := (div #12 3::Int)
-#555 := -2::Int
-#565 := (* -2::Int #706)
-#20 := (mod #12 3::Int)
-#80 := -1::Int
-#603 := (* -1::Int #20)
-#566 := (+ #603 #565)
-#549 := (+ #12 #566)
-#567 := (>= #549 1::Int)
-#84 := -3::Int
-#605 := (* -3::Int #706)
-#606 := (+ #603 #605)
-#599 := (+ #12 #606)
-#704 := (>= #599 0::Int)
-#588 := (= #599 0::Int)
-#1 := true
-#66 := [true-axiom]: true
-#629 := (or false #588)
-#634 := [th-lemma arith]: #629
-#614 := [unit-resolution #634 #66]: #588
-#560 := (not #588)
-#582 := (or #560 #704)
-#583 := [th-lemma arith triangle-eq]: #582
-#584 := [unit-resolution #583 #614]: #704
-#658 := (+ #12 #603)
-#659 := (<= #658 0::Int)
-#540 := (not #659)
-#657 := (= #12 #20)
-#627 := (not #657)
-decl f3 :: (-> Int S2)
-#81 := (* -1::Int #12)
-#87 := (mod #81 -3::Int)
-#93 := (* -1::Int #87)
-#154 := (>= #12 0::Int)
-#155 := (not #154)
-#165 := (or #142 #155)
-#168 := (ite #165 #20 #93)
-#13 := (= #12 0::Int)
-#171 := (ite #13 0::Int #168)
-#174 := (f3 #171)
-#177 := (= f5 #174)
-#769 := (not #177)
-#181 := (not #180)
-#548 := [hypothesis]: #181
-#424 := (or #769 #180)
-#191 := (iff #177 #180)
-#30 := (< #12 3::Int)
-#22 := (- 3::Int)
-#21 := (- #12)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#15 := (< 0::Int 3::Int)
-#17 := (< #12 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #12)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#26 := (ite #13 0::Int #25)
-#10 := (= 3::Int 0::Int)
-#27 := (ite #10 #12 #26)
-#28 := (f3 #27)
-#29 := (= #28 f5)
-#31 := (iff #29 #30)
-#32 := (not #31)
-#194 := (iff #32 #191)
-#133 := (not #30)
-#74 := (and #15 #17)
-#77 := (or #16 #74)
-#98 := (ite #77 #20 #93)
-#71 := (= 0::Int #12)
-#101 := (ite #71 0::Int #98)
-#111 := (f3 #101)
-#117 := (= f5 #111)
-#134 := (iff #117 #133)
-#192 := (iff #134 #191)
-#189 := (iff #133 #180)
-#184 := (not #181)
-#187 := (iff #184 #180)
-#188 := [rewrite]: #187
-#185 := (iff #133 #184)
-#182 := (iff #30 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#190 := [trans #186 #188]: #189
-#178 := (iff #117 #177)
-#175 := (= #111 #174)
-#172 := (= #101 #171)
-#169 := (= #98 #168)
-#166 := (iff #77 #165)
-#163 := (iff #74 #155)
-#158 := (and true #155)
-#161 := (iff #158 #155)
-#162 := [rewrite]: #161
-#159 := (iff #74 #158)
-#156 := (iff #17 #155)
-#157 := [rewrite]: #156
-#145 := (iff #15 true)
-#146 := [rewrite]: #145
-#160 := [monotonicity #146 #157]: #159
-#164 := [trans #160 #162]: #163
-#152 := (iff #16 #142)
-#147 := (and #142 true)
-#150 := (iff #147 #142)
-#151 := [rewrite]: #150
-#148 := (iff #16 #147)
-#143 := (iff #14 #142)
+#115 := [monotonicity #112]: #114
+#100 := (iff #16 #97)
+#88 := (iff #14 #82)
+#93 := (not #88)
+#98 := (iff #93 #97)
+#99 := [rewrite]: #98
+#94 := (iff #16 #93)
+#91 := (iff #15 #88)
+#85 := (iff #82 #14)
+#89 := (iff #85 #88)
+#90 := [rewrite]: #89
+#86 := (iff #15 #85)
+#83 := (iff #13 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#92 := [trans #87 #90]: #91
+#95 := [monotonicity #92]: #94
+#101 := [trans #95 #99]: #100
+#117 := [trans #101 #115]: #116
+#81 := [asserted]: #16
+#118 := [mp #81 #117]: #113
+#483 := (not #113)
+#573 := (or #572 #104 #483)
+#501 := [def-axiom]: #573
+#571 := [unit-resolution #501 #118]: #574
+#636 := [unit-resolution #571 #619]: #572
+#753 := (or #809 #82)
+#575 := (f3 #9)
+#750 := (= #575 #12)
+#746 := (= #12 #575)
+#771 := (= #11 #9)
+#770 := (= 0::Int #9)
+#764 := [hypothesis]: #864
+#765 := [symm #764]: #770
+#590 := (= #11 0::Int)
+#767 := (or #809 #590)
+#840 := -3::Int
+#880 := (* -1::Int #9)
+#841 := (mod #880 -3::Int)
+#679 := (+ #11 #841)
+#834 := (= #679 0::Int)
+#871 := (>= #9 0::Int)
+#700 := (not #871)
+#596 := (<= #9 0::Int)
+#853 := (not #596)
+#844 := (or #853 #700)
+#835 := (ite #844 #870 #834)
+#721 := (ite #864 #590 #835)
+#23 := (:var 0 Int)
+#34 := (:var 1 Int)
+#53 := (f4 #34 #23)
+#925 := (pattern #53)
+#224 := (* -1::Int #23)
+#221 := (* -1::Int #34)
+#285 := (mod #221 #224)
+#415 := (+ #53 #285)
+#416 := (= #415 0::Int)
+#54 := (mod #34 #23)
+#412 := (* -1::Int #54)
+#413 := (+ #53 #412)
+#414 := (= #413 0::Int)
+#259 := (>= #34 0::Int)
+#252 := (<= #23 0::Int)
+#359 := (or #252 #259)
+#360 := (not #359)
+#248 := (<= #34 0::Int)
+#357 := (or #248 #252)
+#358 := (not #357)
+#363 := (or #358 #360)
+#417 := (ite #363 #414 #416)
+#411 := (= #53 0::Int)
+#36 := (= #34 0::Int)
+#418 := (ite #36 #411 #417)
+#410 := (= #34 #53)
+#37 := (= #23 0::Int)
+#419 := (ite #37 #410 #418)
+#926 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #925) #419)
+#422 := (forall (vars (?v0 Int) (?v1 Int)) #419)
+#929 := (iff #422 #926)
+#927 := (iff #419 #419)
+#928 := [refl]: #927
+#930 := [quant-intro #928]: #929
+#291 := (* -1::Int #285)
+#379 := (ite #363 #54 #291)
+#382 := (ite #36 0::Int #379)
+#385 := (ite #37 #34 #382)
+#388 := (= #53 #385)
+#391 := (forall (vars (?v0 Int) (?v1 Int)) #388)
+#423 := (iff #391 #422)
+#420 := (iff #388 #419)
+#421 := [rewrite]: #420
+#424 := [quant-intro #421]: #423
+#260 := (not #259)
+#253 := (not #252)
+#263 := (and #253 #260)
+#249 := (not #248)
+#256 := (and #249 #253)
+#266 := (or #256 #263)
+#311 := (ite #266 #54 #291)
+#314 := (ite #36 0::Int #311)
+#317 := (ite #37 #34 #314)
+#320 := (= #53 #317)
+#323 := (forall (vars (?v0 Int) (?v1 Int)) #320)
+#392 := (iff #323 #391)
+#389 := (iff #320 #388)
+#386 := (= #317 #385)
+#383 := (= #314 #382)
+#380 := (= #311 #379)
+#364 := (iff #266 #363)
+#361 := (iff #263 #360)
+#362 := [rewrite]: #361
+#342 := (iff #256 #358)
+#343 := [rewrite]: #342
+#365 := [monotonicity #343 #362]: #364
+#381 := [monotonicity #365]: #380
+#384 := [monotonicity #381]: #383
+#387 := [monotonicity #384]: #386
+#390 := [monotonicity #387]: #389
+#393 := [quant-intro #390]: #392
+#340 := (~ #323 #323)
+#354 := (~ #320 #320)
+#355 := [refl]: #354
+#341 := [nnf-pos #355]: #340
+#47 := (- #23)
+#46 := (- #34)
+#55 := (mod #46 #47)
+#56 := (- #55)
+#40 := (< 0::Int #23)
+#42 := (< #34 0::Int)
+#43 := (and #42 #40)
+#39 := (< 0::Int #34)
+#41 := (and #39 #40)
+#44 := (or #41 #43)
+#57 := (ite #44 #54 #56)
+#58 := (ite #36 0::Int #57)
+#59 := (ite #37 #34 #58)
+#60 := (= #53 #59)
+#61 := (forall (vars (?v0 Int) (?v1 Int)) #60)
+#326 := (iff #61 #323)
+#214 := (and #40 #42)
+#217 := (or #41 #214)
+#296 := (ite #217 #54 #291)
+#205 := (= 0::Int #34)
+#299 := (ite #205 0::Int #296)
+#208 := (= 0::Int #23)
+#302 := (ite #208 #34 #299)
+#305 := (= #53 #302)
+#308 := (forall (vars (?v0 Int) (?v1 Int)) #305)
+#324 := (iff #308 #323)
+#321 := (iff #305 #320)
+#318 := (= #302 #317)
+#315 := (= #299 #314)
+#312 := (= #296 #311)
+#267 := (iff #217 #266)
+#264 := (iff #214 #263)
+#261 := (iff #42 #260)
+#262 := [rewrite]: #261
+#254 := (iff #40 #253)
+#255 := [rewrite]: #254
+#265 := [monotonicity #255 #262]: #264
+#257 := (iff #41 #256)
+#250 := (iff #39 #249)
+#251 := [rewrite]: #250
+#258 := [monotonicity #251 #255]: #257
+#268 := [monotonicity #258 #265]: #267
+#313 := [monotonicity #268]: #312
+#242 := (iff #205 #36)
+#243 := [rewrite]: #242
+#316 := [monotonicity #243 #313]: #315
+#244 := (iff #208 #37)
+#245 := [rewrite]: #244
+#319 := [monotonicity #245 #316]: #318
+#322 := [monotonicity #319]: #321
+#325 := [quant-intro #322]: #324
+#309 := (iff #61 #308)
+#306 := (iff #60 #305)
+#303 := (= #59 #302)
+#300 := (= #58 #299)
+#297 := (= #57 #296)
+#294 := (= #56 #291)
+#288 := (- #285)
+#292 := (= #288 #291)
+#293 := [rewrite]: #292
+#289 := (= #56 #288)
+#286 := (= #55 #285)
+#225 := (= #47 #224)
+#226 := [rewrite]: #225
+#222 := (= #46 #221)
+#223 := [rewrite]: #222
+#287 := [monotonicity #223 #226]: #286
+#290 := [monotonicity #287]: #289
+#295 := [trans #290 #293]: #294
+#218 := (iff #44 #217)
+#215 := (iff #43 #214)
+#216 := [rewrite]: #215
+#219 := [monotonicity #216]: #218
+#298 := [monotonicity #219 #295]: #297
+#206 := (iff #36 #205)
+#207 := [rewrite]: #206
+#301 := [monotonicity #207 #298]: #300
+#209 := (iff #37 #208)
+#210 := [rewrite]: #209
+#304 := [monotonicity #210 #301]: #303
+#307 := [monotonicity #304]: #306
+#310 := [quant-intro #307]: #309
+#327 := [trans #310 #325]: #326
+#284 := [asserted]: #61
+#328 := [mp #284 #327]: #323
+#356 := [mp~ #328 #341]: #323
+#394 := [mp #356 #393]: #391
+#425 := [mp #394 #424]: #422
+#931 := [mp #425 #930]: #926
+#732 := (not #926)
+#733 := (or #732 #721)
+#517 := (* -1::Int 3::Int)
+#882 := (mod #880 #517)
+#522 := (+ #11 #882)
+#523 := (= #522 0::Int)
+#593 := (<= 3::Int 0::Int)
+#594 := (or #593 #871)
+#595 := (not #594)
+#489 := (or #596 #593)
+#866 := (not #489)
+#867 := (or #866 #595)
+#589 := (ite #867 #870 #523)
+#868 := (ite #864 #590 #589)
+#865 := (= #9 #11)
+#869 := (= 3::Int 0::Int)
+#579 := (ite #869 #865 #868)
+#726 := (or #732 #579)
+#735 := (iff #726 #733)
+#737 := (iff #733 #733)
+#738 := [rewrite]: #737
+#715 := (iff #579 #721)
+#829 := (ite false #865 #721)
+#827 := (iff #829 #721)
+#830 := [rewrite]: #827
+#731 := (iff #579 #829)
+#722 := (iff #868 #721)
+#838 := (iff #589 #835)
+#836 := (iff #523 #834)
+#680 := (= #522 #679)
+#848 := (= #882 #841)
+#846 := (= #517 -3::Int)
+#847 := [rewrite]: #846
+#677 := [monotonicity #847]: #848
+#833 := [monotonicity #677]: #680
+#837 := [monotonicity #833]: #836
+#845 := (iff #867 #844)
+#842 := (iff #595 #700)
+#698 := (iff #594 #871)
+#850 := (or false #871)
+#851 := (iff #850 #871)
+#857 := [rewrite]: #851
+#855 := (iff #594 #850)
+#582 := (iff #593 false)
+#860 := [rewrite]: #582
+#856 := [monotonicity #860]: #855
+#699 := [trans #856 #857]: #698
+#843 := [monotonicity #699]: #842
+#854 := (iff #866 #853)
+#863 := (iff #489 #596)
+#861 := (or #596 false)
+#862 := (iff #861 #596)
+#859 := [rewrite]: #862
+#576 := (iff #489 #861)
+#858 := [monotonicity #860]: #576
+#852 := [trans #858 #859]: #863
+#849 := [monotonicity #852]: #854
+#839 := [monotonicity #849 #843]: #845
+#720 := [monotonicity #839 #837]: #838
+#681 := [monotonicity #720]: #722
+#580 := (iff #869 false)
+#581 := [rewrite]: #580
+#826 := [monotonicity #581 #681]: #731
+#730 := [trans #826 #830]: #715
+#736 := [monotonicity #730]: #735
+#831 := [trans #736 #738]: #735
+#734 := [quant-inst #9 #10]: #726
+#828 := [mp #734 #831]: #733
+#794 := [unit-resolution #828 #931]: #721
+#804 := (not #721)
+#795 := (or #804 #809 #590)
+#796 := [def-axiom]: #795
+#768 := [unit-resolution #796 #794]: #767
+#769 := [unit-resolution #768 #764]: #590
+#744 := [trans #769 #765]: #771
+#639 := [monotonicity #744]: #746
+#751 := [symm #639]: #750
+#554 := (= f6 #575)
+#17 := (:var 0 S2)
+#18 := (f5 #17)
+#897 := (pattern #18)
+#19 := (f3 #18)
+#120 := (= #17 #19)
+#898 := (forall (vars (?v0 S2)) (:pat #897) #120)
+#123 := (forall (vars (?v0 S2)) #120)
+#899 := (iff #123 #898)
+#901 := (iff #898 #898)
+#902 := [rewrite]: #901
+#900 := [rewrite]: #899
+#903 := [trans #900 #902]: #899
+#346 := (~ #123 #123)
+#344 := (~ #120 #120)
+#345 := [refl]: #344
+#347 := [nnf-pos #345]: #346
+#20 := (= #19 #17)
+#21 := (forall (vars (?v0 S2)) #20)
+#124 := (iff #21 #123)
+#121 := (iff #20 #120)
+#122 := [rewrite]: #121
+#125 := [quant-intro #122]: #124
+#119 := [asserted]: #21
+#128 := [mp #119 #125]: #123
+#332 := [mp~ #128 #347]: #123
+#904 := [mp #332 #903]: #898
+#548 := (not #898)
+#678 := (or #548 #554)
+#885 := [quant-inst #8]: #678
+#745 := [unit-resolution #885 #904]: #554
+#752 := [trans #745 #751]: #82
+#763 := [hypothesis]: #572
+#757 := [unit-resolution #763 #752]: false
+#754 := [lemma #757]: #753
+#634 := [unit-resolution #754 #636]: #809
+#766 := (or #864 #870)
+#787 := [hypothesis]: #809
+#812 := (not #844)
+#802 := (not #870)
+#788 := [hypothesis]: #802
+#772 := (or #864 #835)
+#798 := (or #804 #864 #835)
+#799 := [def-axiom]: #798
+#773 := [unit-resolution #799 #794]: #772
+#775 := [unit-resolution #773 #787]: #835
+#815 := (not #835)
+#816 := (or #815 #812 #870)
+#817 := [def-axiom]: #816
+#776 := [unit-resolution #817 #775 #788]: #812
+#819 := (or #844 #596)
+#821 := [def-axiom]: #819
+#777 := [unit-resolution #821 #776]: #596
+#813 := (or #844 #871)
+#810 := [def-axiom]: #813
+#778 := [unit-resolution #810 #776]: #871
+#779 := (or #864 #853 #700)
+#774 := [th-lemma arith triangle-eq]: #779
+#780 := [unit-resolution #774 #778 #777 #787]: false
+#762 := [lemma #780]: #766
+#623 := [unit-resolution #762 #634]: #870
+#624 := (or #802 #824)
+#625 := [th-lemma arith triangle-eq]: #624
+#626 := [unit-resolution #625 #623]: #824
+#755 := (div #9 3::Int)
+#747 := (* -3::Int #755)
+#748 := (+ #747 #881)
+#743 := (+ #9 #748)
+#724 := (<= #743 0::Int)
+#723 := (= #743 0::Int)
+#670 := (or false #723)
+#671 := [th-lemma arith]: #670
+#514 := [unit-resolution #671 #79]: #723
+#672 := (not #723)
+#668 := (or #672 #724)
+#673 := [th-lemma arith triangle-eq]: #668
+#652 := [unit-resolution #673 #514]: #724
+#630 := 1::Int
+#621 := -2::Int
+#627 := (* -2::Int #755)
+#628 := (+ #627 #881)
+#629 := (+ #9 #628)
+#631 := (>= #629 1::Int)
+#682 := (* -1::Int #11)
+#684 := (+ #9 #682)
+#685 := (<= #684 0::Int)
+#614 := (not #685)
+#676 := (not #865)
+#694 := (or #676 #82)
+#688 := [hypothesis]: #865
+#689 := [symm #688]: #771
+#690 := [monotonicity #689]: #746
+#691 := [symm #690]: #750
+#692 := [trans #745 #691]: #82
+#693 := [unit-resolution #763 #692]: false
+#664 := [lemma #693]: #694
+#608 := [unit-resolution #664 #636]: #676
+#686 := (>= #684 0::Int)
+#665 := (>= #755 0::Int)
+#784 := (f5 #575)
+#785 := (= #784 0::Int)
+#600 := (not #785)
+#601 := (iff #809 #600)
+#599 := (iff #864 #785)
+#597 := (iff #785 #864)
+#604 := (= #784 #9)
+#607 := (= #575 f6)
+#606 := [symm #745]: #607
+#605 := [monotonicity #606]: #604
+#598 := [monotonicity #605]: #597
+#591 := [symm #598]: #599
+#592 := [monotonicity #591]: #601
+#602 := [mp #634 #592]: #600
+#786 := (or #785 #871)
+#25 := (f3 #23)
+#905 := (pattern #25)
+#145 := (>= #23 0::Int)
+#26 := (f5 #25)
+#31 := (= #26 0::Int)
+#193 := (or #31 #145)
+#912 := (forall (vars (?v0 Int)) (:pat #905) #193)
+#198 := (forall (vars (?v0 Int)) #193)
+#915 := (iff #198 #912)
+#913 := (iff #193 #193)
+#914 := [refl]: #913
+#916 := [quant-intro #914]: #915
+#336 := (~ #198 #198)
+#348 := (~ #193 #193)
+#349 := [refl]: #348
+#337 := [nnf-pos #349]: #336
+#30 := (< #23 0::Int)
+#32 := (implies #30 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#201 := (iff #33 #198)
+#164 := (= 0::Int #26)
+#170 := (not #30)
+#171 := (or #170 #164)
+#176 := (forall (vars (?v0 Int)) #171)
+#199 := (iff #176 #198)
+#196 := (iff #171 #193)
+#190 := (or #145 #31)
+#194 := (iff #190 #193)
+#195 := [rewrite]: #194
+#191 := (iff #171 #190)
+#188 := (iff #164 #31)
+#189 := [rewrite]: #188
+#186 := (iff #170 #145)
+#146 := (not #145)
+#181 := (not #146)
+#184 := (iff #181 #145)
+#185 := [rewrite]: #184
+#182 := (iff #170 #181)
+#179 := (iff #30 #146)
+#180 := [rewrite]: #179
+#183 := [monotonicity #180]: #182
+#187 := [trans #183 #185]: #186
+#192 := [monotonicity #187 #189]: #191
+#197 := [trans #192 #195]: #196
+#200 := [quant-intro #197]: #199
+#177 := (iff #33 #176)
+#174 := (iff #32 #171)
+#167 := (implies #30 #164)
+#172 := (iff #167 #171)
+#173 := [rewrite]: #172
+#168 := (iff #32 #167)
+#165 := (iff #31 #164)
+#166 := [rewrite]: #165
+#169 := [monotonicity #166]: #168
+#175 := [trans #169 #173]: #174
+#178 := [quant-intro #175]: #177
+#202 := [trans #178 #200]: #201
+#163 := [asserted]: #33
+#203 := [mp #163 #202]: #198
+#350 := [mp~ #203 #337]: #198
+#917 := [mp #350 #916]: #912
+#872 := (not #912)
+#789 := (or #872 #785 #871)
+#790 := (or #872 #786)
+#792 := (iff #790 #789)
+#793 := [rewrite]: #792
+#791 := [quant-inst #9]: #790
+#783 := [mp #791 #793]: #789
+#583 := [unit-resolution #783 #917]: #786
+#584 := [unit-resolution #583 #602]: #871
+#660 := (or #665 #700)
+#655 := (not #665)
+#659 := [hypothesis]: #655
+#661 := [hypothesis]: #871
+#662 := [th-lemma arith farkas 1 3 1 1 #661 #659 #652 #669]: false
+#663 := [lemma #662]: #660
+#585 := [unit-resolution #663 #584]: #665
+#648 := (not #824)
+#633 := (or #686 #648 #655)
+#656 := (not #686)
+#657 := [hypothesis]: #656
+#683 := (>= #743 0::Int)
+#642 := (or #672 #683)
+#650 := [th-lemma arith triangle-eq]: #642
+#643 := [unit-resolution #650 #514]: #683
+#646 := [hypothesis]: #665
+#654 := [hypothesis]: #824
+#647 := [th-lemma arith farkas 1 -3 -1 1 #654 #646 #643 #657]: false
+#635 := [lemma #647]: #633
+#577 := [unit-resolution #635 #626 #585]: #686
+#586 := (or #865 #614 #656)
+#587 := [th-lemma arith triangle-eq]: #586
+#578 := [unit-resolution #587 #577 #608]: #614
+#820 := (>= #884 0::Int)
+#588 := (or #802 #820)
+#555 := [th-lemma arith triangle-eq]: #588
+#557 := [unit-resolution #555 #623]: #820
+#610 := (not #820)
+#618 := (or #631 #610 #685)
+#609 := (not #631)
+#613 := [hypothesis]: #609
+#615 := [hypothesis]: #614
+#616 := [hypothesis]: #820
+#617 := [th-lemma arith farkas -2/3 -1/3 -1/3 1 #643 #616 #615 #613]: false
+#603 := [lemma #617]: #618
+#558 := [unit-resolution #603 #557 #578]: #631
+#889 := (>= #11 0::Int)
+#714 := (>= #883 0::Int)
+#549 := (or false #714)
+#562 := [th-lemma arith]: #549
+#563 := [unit-resolution #562 #79]: #714
+#564 := (not #714)
+#565 := (or #889 #564 #610)
+#566 := [th-lemma arith assign-bounds 1 1]: #565
+#556 := [unit-resolution #566 #557 #563]: #889
+#567 := [th-lemma arith farkas -1 -3 2 1 1 #556 #558 #652 #626 #619]: false
+#550 := [lemma #567]: #104
+#559 := (f5 #12)
+#560 := (= #11 #559)
+#521 := (iff #560 #865)
+#518 := (iff #771 #865)
+#520 := [commutativity]: #518
+#527 := (iff #560 #771)
+#528 := (= #559 #9)
+#570 := (or #82 #102)
+#568 := (or #82 #102 #483)
+#569 := [def-axiom]: #568
+#561 := [unit-resolution #569 #118]: #570
+#545 := [unit-resolution #561 #550]: #82
+#526 := [symm #545]: #13
+#529 := [monotonicity #526]: #528
+#530 := [monotonicity #529]: #527
+#524 := [trans #530 #520]: #521
+#552 := (or #853 #102)
+#553 := [th-lemma arith farkas 1 1]: #552
+#532 := [unit-resolution #553 #550]: #853
+#534 := (or #809 #596)
+#539 := [th-lemma arith triangle-eq]: #534
+#540 := [unit-resolution #539 #532]: #809
+#541 := [unit-resolution #762 #540]: #870
+#542 := [unit-resolution #555 #541]: #820
+#543 := [unit-resolution #566 #542 #563]: #889
+#891 := (not #889)
+#892 := (or #560 #891)
+#127 := (= #23 #26)
+#152 := (or #127 #146)
+#906 := (forall (vars (?v0 Int)) (:pat #905) #152)
+#157 := (forall (vars (?v0 Int)) #152)
+#909 := (iff #157 #906)
+#907 := (iff #152 #152)
+#908 := [refl]: #907
+#910 := [quant-intro #908]: #909
+#334 := (~ #157 #157)
+#333 := (~ #152 #152)
+#330 := [refl]: #333
+#335 := [nnf-pos #330]: #334
+#27 := (= #26 #23)
+#24 := (<= 0::Int #23)
+#28 := (implies #24 #27)
+#29 := (forall (vars (?v0 Int)) #28)
+#160 := (iff #29 #157)
+#134 := (not #24)
+#135 := (or #134 #127)
+#140 := (forall (vars (?v0 Int)) #135)
+#158 := (iff #140 #157)
+#155 := (iff #135 #152)
+#149 := (or #146 #127)
+#153 := (iff #149 #152)
+#154 := [rewrite]: #153
+#150 := (iff #135 #149)
+#147 := (iff #134 #146)
+#143 := (iff #24 #145)
#144 := [rewrite]: #143
-#149 := [monotonicity #144 #146]: #148
-#153 := [trans #149 #151]: #152
-#167 := [monotonicity #153 #164]: #166
-#170 := [monotonicity #167]: #169
-#139 := (iff #71 #13)
-#140 := [rewrite]: #139
-#173 := [monotonicity #140 #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#193 := [monotonicity #179 #190]: #192
-#137 := (iff #32 #134)
-#125 := (iff #30 #117)
-#130 := (not #125)
-#135 := (iff #130 #134)
-#136 := [rewrite]: #135
-#131 := (iff #32 #130)
-#128 := (iff #31 #125)
-#122 := (iff #117 #30)
-#126 := (iff #122 #125)
-#127 := [rewrite]: #126
-#123 := (iff #31 #122)
-#120 := (iff #29 #117)
-#114 := (= #111 f5)
-#118 := (iff #114 #117)
-#119 := [rewrite]: #118
-#115 := (iff #29 #114)
-#112 := (= #28 #111)
-#109 := (= #27 #101)
-#104 := (ite false #12 #101)
-#107 := (= #104 #101)
-#108 := [rewrite]: #107
-#105 := (= #27 #104)
-#102 := (= #26 #101)
-#99 := (= #25 #98)
-#96 := (= #24 #93)
-#90 := (- #87)
-#94 := (= #90 #93)
-#95 := [rewrite]: #94
-#91 := (= #24 #90)
-#88 := (= #23 #87)
-#85 := (= #22 -3::Int)
-#86 := [rewrite]: #85
-#82 := (= #21 #81)
-#83 := [rewrite]: #82
-#89 := [monotonicity #83 #86]: #88
-#92 := [monotonicity #89]: #91
-#97 := [trans #92 #95]: #96
-#78 := (iff #19 #77)
-#75 := (iff #18 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#100 := [monotonicity #79 #97]: #99
-#72 := (iff #13 #71)
-#73 := [rewrite]: #72
-#103 := [monotonicity #73 #100]: #102
-#69 := (iff #10 false)
-#70 := [rewrite]: #69
-#106 := [monotonicity #70 #103]: #105
-#110 := [trans #106 #108]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#121 := [trans #116 #119]: #120
-#124 := [monotonicity #121]: #123
-#129 := [trans #124 #127]: #128
-#132 := [monotonicity #129]: #131
-#138 := [trans #132 #136]: #137
-#195 := [trans #138 #193]: #194
-#68 := [asserted]: #32
-#196 := [mp #68 #195]: #191
-#765 := (not #191)
-#759 := (or #769 #180 #765)
-#419 := [def-axiom]: #759
-#760 := [unit-resolution #419 #196]: #424
-#528 := [unit-resolution #760 #548]: #769
-#628 := (or #627 #177)
-#420 := (f3 #12)
-#720 := (= #420 #174)
-#713 := (= #174 #420)
-#717 := (= #171 #12)
-#617 := (= #20 #12)
-#641 := [hypothesis]: #657
-#618 := [symm #641]: #617
-#619 := (= #171 #20)
-#638 := (= #168 #20)
-#356 := (= #20 #168)
-#733 := (f4 #420)
-#734 := (= #733 0::Int)
-#648 := (not #734)
-#421 := (not #13)
-#649 := (iff #421 #648)
-#645 := (iff #13 #734)
-#656 := (iff #734 #13)
-#665 := (= #733 #12)
-#663 := (= #420 f5)
-#761 := (= f5 #420)
-#33 := (:var 0 S2)
-#34 := (f4 #33)
-#770 := (pattern #34)
-#35 := (f3 #34)
-#198 := (= #33 #35)
-#771 := (forall (vars (?v0 S2)) (:pat #770) #198)
-#201 := (forall (vars (?v0 S2)) #198)
-#772 := (iff #201 #771)
-#774 := (iff #771 #771)
-#775 := [rewrite]: #774
-#773 := [rewrite]: #772
-#776 := [trans #773 #775]: #772
-#295 := (~ #201 #201)
-#293 := (~ #198 #198)
-#294 := [refl]: #293
-#296 := [nnf-pos #294]: #295
-#36 := (= #35 #33)
-#37 := (forall (vars (?v0 S2)) #36)
-#202 := (iff #37 #201)
-#199 := (iff #36 #198)
-#200 := [rewrite]: #199
-#203 := [quant-intro #200]: #202
-#197 := [asserted]: #37
-#206 := [mp #197 #203]: #201
-#285 := [mp~ #206 #296]: #201
-#777 := [mp #285 #776]: #771
-#408 := (not #771)
-#409 := (or #408 #761)
-#410 := [quant-inst #11]: #409
-#712 := [unit-resolution #410 #777]: #761
-#664 := [symm #712]: #663
-#666 := [monotonicity #664]: #665
-#667 := [monotonicity #666]: #656
-#646 := [symm #667]: #645
-#650 := [monotonicity #646]: #649
-#572 := [hypothesis]: #769
-#552 := (or #421 #177)
-#573 := [hypothesis]: #13
-#716 := [symm #573]: #71
-#355 := (= #171 0::Int)
-#551 := (or #421 #355)
-#758 := [def-axiom]: #551
-#715 := [unit-resolution #758 #573]: #355
-#718 := [trans #715 #716]: #717
-#719 := [monotonicity #718]: #713
-#714 := [symm #719]: #720
-#721 := [trans #712 #714]: #177
-#550 := [unit-resolution #572 #721]: false
-#553 := [lemma #550]: #552
-#661 := [unit-resolution #553 #572]: #421
-#651 := [mp #661 #650]: #648
-#731 := (or #154 #734)
-#38 := (:var 0 Int)
-#40 := (f3 #38)
-#778 := (pattern #40)
-#222 := (>= #38 0::Int)
-#41 := (f4 #40)
-#46 := (= #41 0::Int)
-#271 := (or #46 #222)
-#785 := (forall (vars (?v0 Int)) (:pat #778) #271)
-#276 := (forall (vars (?v0 Int)) #271)
-#788 := (iff #276 #785)
-#786 := (iff #271 #271)
-#787 := [refl]: #786
-#789 := [quant-intro #787]: #788
-#289 := (~ #276 #276)
-#297 := (~ #271 #271)
-#298 := [refl]: #297
-#290 := [nnf-pos #298]: #289
-#45 := (< #38 0::Int)
-#47 := (implies #45 #46)
-#48 := (forall (vars (?v0 Int)) #47)
-#279 := (iff #48 #276)
-#242 := (= 0::Int #41)
-#248 := (not #45)
-#249 := (or #248 #242)
-#254 := (forall (vars (?v0 Int)) #249)
-#277 := (iff #254 #276)
-#274 := (iff #249 #271)
-#268 := (or #222 #46)
-#272 := (iff #268 #271)
-#273 := [rewrite]: #272
-#269 := (iff #249 #268)
-#266 := (iff #242 #46)
-#267 := [rewrite]: #266
-#264 := (iff #248 #222)
-#224 := (not #222)
-#259 := (not #224)
-#262 := (iff #259 #222)
-#263 := [rewrite]: #262
-#260 := (iff #248 #259)
-#257 := (iff #45 #224)
-#258 := [rewrite]: #257
-#261 := [monotonicity #258]: #260
-#265 := [trans #261 #263]: #264
-#270 := [monotonicity #265 #267]: #269
-#275 := [trans #270 #273]: #274
-#278 := [quant-intro #275]: #277
-#255 := (iff #48 #254)
-#252 := (iff #47 #249)
-#245 := (implies #45 #242)
-#250 := (iff #245 #249)
-#251 := [rewrite]: #250
-#246 := (iff #47 #245)
-#243 := (iff #46 #242)
-#244 := [rewrite]: #243
-#247 := [monotonicity #244]: #246
-#253 := [trans #247 #251]: #252
-#256 := [quant-intro #253]: #255
-#280 := [trans #256 #278]: #279
-#241 := [asserted]: #48
-#281 := [mp #241 #280]: #276
-#299 := [mp~ #281 #290]: #276
-#790 := [mp #299 #789]: #785
-#739 := (not #785)
-#736 := (or #739 #154 #734)
-#449 := (or #734 #154)
-#725 := (or #739 #449)
-#724 := (iff #725 #736)
-#727 := (or #739 #731)
-#728 := (iff #727 #736)
-#729 := [rewrite]: #728
-#722 := (iff #725 #727)
-#735 := (iff #449 #731)
-#732 := [rewrite]: #735
-#723 := [monotonicity #732]: #722
-#730 := [trans #723 #729]: #724
-#726 := [quant-inst #12]: #725
-#571 := [mp #726 #730]: #736
-#652 := [unit-resolution #571 #790]: #731
-#647 := [unit-resolution #652 #651]: #154
-#653 := (or #13 #142 #155)
-#639 := [th-lemma arith triangle-eq]: #653
-#635 := [unit-resolution #639 #661]: #165
-#636 := [unit-resolution #635 #647]: #142
-#443 := (or #165 #141)
-#434 := [def-axiom]: #443
-#637 := [unit-resolution #434 #636]: #165
-#374 := (not #165)
-#448 := (or #374 #356)
-#427 := [def-axiom]: #448
-#640 := [unit-resolution #427 #637]: #356
-#644 := [symm #640]: #638
-#642 := (= #171 #168)
-#441 := (= #168 #171)
-#432 := (or #13 #441)
-#433 := [def-axiom]: #432
-#662 := [unit-resolution #433 #661]: #441
-#643 := [symm #662]: #642
-#512 := [trans #643 #644]: #619
-#623 := [trans #512 #618]: #717
-#624 := [monotonicity #623]: #713
-#625 := [symm #624]: #720
-#630 := [trans #712 #625]: #177
-#626 := [unit-resolution #572 #630]: false
-#631 := [lemma #626]: #628
-#546 := [unit-resolution #631 #528]: #627
-#660 := (>= #658 0::Int)
-#578 := (* -1::Int #706)
-#579 := (+ #603 #578)
-#580 := (+ #12 #579)
-#581 := (>= #580 0::Int)
-#545 := [unit-resolution #553 #528]: #421
-#541 := [mp #545 #650]: #648
-#532 := [unit-resolution #652 #541]: #154
-#534 := [unit-resolution #639 #545]: #165
-#535 := [unit-resolution #534 #532]: #142
-#570 := (or #581 #141)
-#574 := (not #581)
-#577 := [hypothesis]: #574
-#691 := (>= #20 3::Int)
-#675 := (not #691)
-#616 := (or false #675)
-#622 := [th-lemma arith]: #616
-#590 := [unit-resolution #622 #66]: #675
-#632 := [hypothesis]: #142
-#585 := [th-lemma arith farkas -2/3 2/3 -1/3 1 #632 #590 #584 #577]: false
-#586 := [lemma #585]: #570
-#533 := [unit-resolution #586 #535]: #581
-#575 := (or #574 #660)
-#568 := (not #660)
-#569 := [hypothesis]: #568
-#611 := (<= #599 0::Int)
-#615 := (or #560 #611)
-#596 := [th-lemma arith triangle-eq]: #615
-#620 := [unit-resolution #596 #614]: #611
-#592 := [hypothesis]: #581
-#613 := [th-lemma arith farkas -3/2 1/2 1 #592 #620 #569]: false
-#576 := [lemma #613]: #575
-#536 := [unit-resolution #576 #533]: #660
-#524 := (or #657 #540 #568)
-#527 := [th-lemma arith triangle-eq]: #524
-#529 := [unit-resolution #527 #536 #546]: #540
-#530 := [th-lemma arith #529 #584]: #567
-#562 := (not #567)
-#563 := (or #562 #180)
-#701 := (>= #20 0::Int)
-#558 := (or false #701)
-#559 := [th-lemma arith]: #558
-#557 := [unit-resolution #559 #66]: #701
-#547 := [hypothesis]: #567
-#561 := [th-lemma arith farkas -1 3 -2 1 #548 #547 #620 #557]: false
-#564 := [lemma #561]: #563
-#525 := [unit-resolution #564 #548]: #562
-#526 := [unit-resolution #525 #530]: false
-#531 := [lemma #526]: #180
-#501 := (or #181 #142)
-#502 := [th-lemma arith farkas 1 1]: #501
-#503 := [unit-resolution #502 #531]: #142
-#411 := (f4 #174)
-#747 := (= #171 #411)
-#491 := (not #747)
-#476 := (iff #627 #491)
-#490 := (iff #657 #747)
-#485 := (= #411 #171)
-#488 := (iff #485 #747)
-#489 := [commutativity]: #488
-#486 := (iff #657 #485)
-#671 := (= #20 #171)
-#521 := [hypothesis]: #421
-#500 := [unit-resolution #433 #521]: #441
-#504 := [unit-resolution #434 #503]: #165
-#493 := [unit-resolution #427 #504]: #356
-#505 := [trans #493 #500]: #671
-#482 := (= #12 #411)
-#517 := (= #411 #12)
-#513 := (= #174 f5)
-#768 := (or #177 #181)
-#766 := (or #177 #181 #765)
+#148 := [monotonicity #144]: #147
+#151 := [monotonicity #148]: #150
+#156 := [trans #151 #154]: #155
+#159 := [quant-intro #156]: #158
+#141 := (iff #29 #140)
+#138 := (iff #28 #135)
+#131 := (implies #24 #127)
+#136 := (iff #131 #135)
+#137 := [rewrite]: #136
+#132 := (iff #28 #131)
+#129 := (iff #27 #127)
+#130 := [rewrite]: #129
+#133 := [monotonicity #130]: #132
+#139 := [trans #133 #137]: #138
+#142 := [quant-intro #139]: #141
+#161 := [trans #142 #159]: #160
+#126 := [asserted]: #29
+#162 := [mp #126 #161]: #157
+#331 := [mp~ #162 #335]: #157
+#911 := [mp #331 #910]: #906
+#895 := (not #906)
+#890 := (or #895 #560 #891)
+#896 := (or #895 #892)
+#546 := (iff #896 #890)
+#551 := [rewrite]: #546
+#886 := [quant-inst #11]: #896
+#887 := [mp #886 #551]: #890
+#544 := [unit-resolution #887 #911]: #892
+#533 := [unit-resolution #544 #543]: #560
+#519 := [mp #533 #524]: #865
+#525 := (or #676 #685)
+#499 := [th-lemma arith triangle-eq]: #525
+#504 := [unit-resolution #499 #519]: #685
+#505 := [unit-resolution #625 #541]: #824
+[th-lemma arith farkas 1 1 -1 1 #505 #504 #550 #669]: false
+unsat
+bf4ed7a0c67dc55dd17034c099d4eaab353230e6 827 0
+#2 := false
+decl f4 :: (-> Int S2)
+decl f7 :: (-> Int Int Int)
+#10 := 1::Int
+decl f6 :: (-> S2 Int)
+decl f3 :: S2
+#8 := f3
+#9 := (f6 f3)
+#13 := (f7 #9 1::Int)
+decl f5 :: (-> Int Int Int)
+#11 := (f5 #9 1::Int)
+#85 := (+ #11 #13)
+#88 := (f4 #85)
+#91 := (= f3 #88)
+#552 := (f6 #88)
+#470 := (f4 #552)
+#983 := (= #470 #88)
+#473 := (= #88 #470)
+#18 := (:var 0 S2)
+#19 := (f6 #18)
+#875 := (pattern #19)
+#20 := (f4 #19)
+#98 := (= #18 #20)
+#876 := (forall (vars (?v0 S2)) (:pat #875) #98)
+#102 := (forall (vars (?v0 S2)) #98)
+#877 := (iff #102 #876)
+#879 := (iff #876 #876)
+#880 := [rewrite]: #879
+#878 := [rewrite]: #877
+#881 := [trans #878 #880]: #877
+#325 := (~ #102 #102)
+#323 := (~ #98 #98)
+#324 := [refl]: #323
+#326 := [nnf-pos #324]: #325
+#21 := (= #20 #18)
+#22 := (forall (vars (?v0 S2)) #21)
+#103 := (iff #22 #102)
+#100 := (iff #21 #98)
+#101 := [rewrite]: #100
+#104 := [quant-intro #101]: #103
+#97 := [asserted]: #22
+#107 := [mp #97 #104]: #102
+#311 := [mp~ #107 #326]: #102
+#882 := [mp #311 #881]: #876
+#539 := (not #876)
+#931 := (or #539 #473)
+#932 := [quant-inst #88]: #931
+#978 := [unit-resolution #932 #882]: #473
+#984 := [symm #978]: #983
+#985 := (= f3 #470)
+#462 := (f4 #9)
+#981 := (= #462 #470)
+#979 := (= #470 #462)
+#976 := (= #552 #9)
+#23 := 0::Int
+#974 := (= 0::Int #9)
+#847 := (= #9 0::Int)
+#935 := (= #462 #88)
+#933 := (= #9 #85)
+#916 := (= #11 #85)
+#670 := (<= #13 0::Int)
+#757 := (= #13 0::Int)
+#844 := (<= #9 0::Int)
+#676 := (not #844)
+#572 := (>= #9 0::Int)
+#825 := (not #572)
+#718 := (or #825 #676 #847)
+#494 := [hypothesis]: #825
+#630 := (f6 #462)
+#633 := (= #630 0::Int)
+#510 := (iff #633 #847)
+#530 := (= #630 #9)
+#480 := (= #9 #630)
+#546 := (= f3 #462)
+#550 := (or #539 #546)
+#551 := [quant-inst #8]: #550
+#534 := [unit-resolution #551 #882]: #546
+#481 := [monotonicity #534]: #480
+#484 := [symm #481]: #530
+#485 := [monotonicity #484]: #510
+#639 := (or #572 #633)
+#24 := (:var 0 Int)
+#26 := (f4 #24)
+#883 := (pattern #26)
+#124 := (>= #24 0::Int)
+#27 := (f6 #26)
+#32 := (= #27 0::Int)
+#172 := (or #32 #124)
+#890 := (forall (vars (?v0 Int)) (:pat #883) #172)
+#177 := (forall (vars (?v0 Int)) #172)
+#893 := (iff #177 #890)
+#891 := (iff #172 #172)
+#892 := [refl]: #891
+#894 := [quant-intro #892]: #893
+#315 := (~ #177 #177)
+#327 := (~ #172 #172)
+#328 := [refl]: #327
+#316 := [nnf-pos #328]: #315
+#31 := (< #24 0::Int)
+#33 := (implies #31 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#180 := (iff #34 #177)
+#143 := (= 0::Int #27)
+#149 := (not #31)
+#150 := (or #149 #143)
+#155 := (forall (vars (?v0 Int)) #150)
+#178 := (iff #155 #177)
+#175 := (iff #150 #172)
+#169 := (or #124 #32)
+#173 := (iff #169 #172)
+#174 := [rewrite]: #173
+#170 := (iff #150 #169)
+#167 := (iff #143 #32)
+#168 := [rewrite]: #167
+#165 := (iff #149 #124)
+#125 := (not #124)
+#160 := (not #125)
+#163 := (iff #160 #124)
+#164 := [rewrite]: #163
+#161 := (iff #149 #160)
+#158 := (iff #31 #125)
+#159 := [rewrite]: #158
+#162 := [monotonicity #159]: #161
+#166 := [trans #162 #164]: #165
+#171 := [monotonicity #166 #168]: #170
+#176 := [trans #171 #174]: #175
+#179 := [quant-intro #176]: #178
+#156 := (iff #34 #155)
+#153 := (iff #33 #150)
+#146 := (implies #31 #143)
+#151 := (iff #146 #150)
+#152 := [rewrite]: #151
+#147 := (iff #33 #146)
+#144 := (iff #32 #143)
+#145 := [rewrite]: #144
+#148 := [monotonicity #145]: #147
+#154 := [trans #148 #152]: #153
+#157 := [quant-intro #154]: #156
+#181 := [trans #157 #179]: #180
+#142 := [asserted]: #34
+#182 := [mp #142 #181]: #177
+#329 := [mp~ #182 #316]: #177
+#895 := [mp #329 #894]: #890
+#853 := (not #890)
+#641 := (or #853 #572 #633)
+#637 := (or #633 #572)
+#629 := (or #853 #637)
+#616 := (iff #629 #641)
+#634 := (or #853 #639)
+#636 := (iff #634 #641)
+#626 := [rewrite]: #636
+#635 := (iff #629 #634)
+#640 := (iff #637 #639)
+#638 := [rewrite]: #640
+#631 := [monotonicity #638]: #635
+#618 := [trans #631 #626]: #616
+#632 := [quant-inst #9]: #629
+#619 := [mp #632 #618]: #641
+#511 := [unit-resolution #619 #895]: #639
+#477 := [unit-resolution #511 #494]: #633
+#486 := [mp #477 #485]: #847
+#763 := (not #847)
+#479 := (or #763 #572)
+#487 := [th-lemma arith triangle-eq]: #479
+#472 := [unit-resolution #487 #486 #494]: false
+#469 := [lemma #472]: #572
+#474 := [hypothesis]: #763
+#504 := (or #847 #676 #825)
+#506 := [th-lemma arith triangle-eq]: #504
+#475 := [unit-resolution #506 #474 #469]: #676
+#662 := (or #718 #844)
+#663 := [def-axiom]: #662
+#463 := [unit-resolution #663 #475]: #718
+#667 := (not #718)
+#466 := (or #667 #757)
+#199 := -1::Int
+#852 := (* -1::Int #9)
+#784 := (mod #852 -1::Int)
+#736 := (+ #13 #784)
+#734 := (= #736 0::Int)
+#679 := (ite #718 #757 #734)
+#35 := (:var 1 Int)
+#54 := (f7 #35 #24)
+#903 := (pattern #54)
+#203 := (* -1::Int #24)
+#200 := (* -1::Int #35)
+#264 := (mod #200 #203)
+#394 := (+ #54 #264)
+#395 := (= #394 0::Int)
+#55 := (mod #35 #24)
+#391 := (* -1::Int #55)
+#392 := (+ #54 #391)
+#393 := (= #392 0::Int)
+#238 := (>= #35 0::Int)
+#231 := (<= #24 0::Int)
+#338 := (or #231 #238)
+#339 := (not #338)
+#227 := (<= #35 0::Int)
+#336 := (or #227 #231)
+#337 := (not #336)
+#342 := (or #337 #339)
+#396 := (ite #342 #393 #395)
+#390 := (= #54 0::Int)
+#37 := (= #35 0::Int)
+#397 := (ite #37 #390 #396)
+#389 := (= #35 #54)
+#38 := (= #24 0::Int)
+#398 := (ite #38 #389 #397)
+#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #398)
+#401 := (forall (vars (?v0 Int) (?v1 Int)) #398)
+#907 := (iff #401 #904)
+#905 := (iff #398 #398)
+#906 := [refl]: #905
+#908 := [quant-intro #906]: #907
+#270 := (* -1::Int #264)
+#358 := (ite #342 #55 #270)
+#361 := (ite #37 0::Int #358)
+#364 := (ite #38 #35 #361)
+#367 := (= #54 #364)
+#370 := (forall (vars (?v0 Int) (?v1 Int)) #367)
+#402 := (iff #370 #401)
+#399 := (iff #367 #398)
+#400 := [rewrite]: #399
+#403 := [quant-intro #400]: #402
+#239 := (not #238)
+#232 := (not #231)
+#242 := (and #232 #239)
+#228 := (not #227)
+#235 := (and #228 #232)
+#245 := (or #235 #242)
+#290 := (ite #245 #55 #270)
+#293 := (ite #37 0::Int #290)
+#296 := (ite #38 #35 #293)
+#299 := (= #54 #296)
+#302 := (forall (vars (?v0 Int) (?v1 Int)) #299)
+#371 := (iff #302 #370)
+#368 := (iff #299 #367)
+#365 := (= #296 #364)
+#362 := (= #293 #361)
+#359 := (= #290 #358)
+#343 := (iff #245 #342)
+#340 := (iff #242 #339)
+#341 := [rewrite]: #340
+#321 := (iff #235 #337)
+#322 := [rewrite]: #321
+#344 := [monotonicity #322 #341]: #343
+#360 := [monotonicity #344]: #359
+#363 := [monotonicity #360]: #362
+#366 := [monotonicity #363]: #365
+#369 := [monotonicity #366]: #368
+#372 := [quant-intro #369]: #371
+#319 := (~ #302 #302)
+#333 := (~ #299 #299)
+#334 := [refl]: #333
+#320 := [nnf-pos #334]: #319
+#48 := (- #24)
+#47 := (- #35)
+#56 := (mod #47 #48)
+#57 := (- #56)
+#41 := (< 0::Int #24)
+#43 := (< #35 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #35)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#58 := (ite #45 #55 #57)
+#59 := (ite #37 0::Int #58)
+#60 := (ite #38 #35 #59)
+#61 := (= #54 #60)
+#62 := (forall (vars (?v0 Int) (?v1 Int)) #61)
+#305 := (iff #62 #302)
+#193 := (and #41 #43)
+#196 := (or #42 #193)
+#275 := (ite #196 #55 #270)
+#184 := (= 0::Int #35)
+#278 := (ite #184 0::Int #275)
+#187 := (= 0::Int #24)
+#281 := (ite #187 #35 #278)
+#284 := (= #54 #281)
+#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
+#303 := (iff #287 #302)
+#300 := (iff #284 #299)
+#297 := (= #281 #296)
+#294 := (= #278 #293)
+#291 := (= #275 #290)
+#246 := (iff #196 #245)
+#243 := (iff #193 #242)
+#240 := (iff #43 #239)
+#241 := [rewrite]: #240
+#233 := (iff #41 #232)
+#234 := [rewrite]: #233
+#244 := [monotonicity #234 #241]: #243
+#236 := (iff #42 #235)
+#229 := (iff #40 #228)
+#230 := [rewrite]: #229
+#237 := [monotonicity #230 #234]: #236
+#247 := [monotonicity #237 #244]: #246
+#292 := [monotonicity #247]: #291
+#221 := (iff #184 #37)
+#222 := [rewrite]: #221
+#295 := [monotonicity #222 #292]: #294
+#223 := (iff #187 #38)
+#224 := [rewrite]: #223
+#298 := [monotonicity #224 #295]: #297
+#301 := [monotonicity #298]: #300
+#304 := [quant-intro #301]: #303
+#288 := (iff #62 #287)
+#285 := (iff #61 #284)
+#282 := (= #60 #281)
+#279 := (= #59 #278)
+#276 := (= #58 #275)
+#273 := (= #57 #270)
+#267 := (- #264)
+#271 := (= #267 #270)
+#272 := [rewrite]: #271
+#268 := (= #57 #267)
+#265 := (= #56 #264)
+#204 := (= #48 #203)
+#205 := [rewrite]: #204
+#201 := (= #47 #200)
+#202 := [rewrite]: #201
+#266 := [monotonicity #202 #205]: #265
+#269 := [monotonicity #266]: #268
+#274 := [trans #269 #272]: #273
+#197 := (iff #45 #196)
+#194 := (iff #44 #193)
+#195 := [rewrite]: #194
+#198 := [monotonicity #195]: #197
+#277 := [monotonicity #198 #274]: #276
+#185 := (iff #37 #184)
+#186 := [rewrite]: #185
+#280 := [monotonicity #186 #277]: #279
+#188 := (iff #38 #187)
+#189 := [rewrite]: #188
+#283 := [monotonicity #189 #280]: #282
+#286 := [monotonicity #283]: #285
+#289 := [quant-intro #286]: #288
+#306 := [trans #289 #304]: #305
+#263 := [asserted]: #62
+#307 := [mp #263 #306]: #302
+#335 := [mp~ #307 #320]: #302
+#373 := [mp #335 #372]: #370
+#404 := [mp #373 #403]: #401
+#909 := [mp #404 #908]: #904
+#684 := (not #904)
+#685 := (or #684 #679)
+#516 := (* -1::Int 1::Int)
+#772 := (mod #852 #516)
+#750 := (+ #13 #772)
+#751 := (= #750 0::Int)
+#780 := (mod #9 1::Int)
+#753 := (* -1::Int #780)
+#754 := (+ #13 #753)
+#755 := (= #754 0::Int)
+#573 := (<= 1::Int 0::Int)
+#574 := (or #573 #572)
+#468 := (not #574)
+#845 := (or #844 #573)
+#567 := (not #845)
+#568 := (or #567 #468)
+#756 := (ite #568 #755 #751)
+#752 := (ite #847 #757 #756)
+#758 := (= #9 #13)
+#843 := (= 1::Int 0::Int)
+#744 := (ite #843 #758 #752)
+#686 := (or #684 #744)
+#688 := (iff #686 #685)
+#690 := (iff #685 #685)
+#675 := [rewrite]: #690
+#682 := (iff #744 #679)
+#811 := (or #825 #676)
+#727 := (or #811 #847)
+#695 := (ite #727 #757 #734)
+#680 := (iff #695 #679)
+#673 := (iff #727 #718)
+#674 := [rewrite]: #673
+#681 := [monotonicity #674]: #680
+#717 := (iff #744 #695)
+#696 := (ite false #758 #695)
+#706 := (iff #696 #695)
+#707 := [rewrite]: #706
+#703 := (iff #744 #696)
+#692 := (iff #752 #695)
+#665 := (ite #811 #757 #734)
+#725 := (ite #847 #757 #665)
+#702 := (iff #725 #695)
+#661 := [rewrite]: #702
+#726 := (iff #752 #725)
+#720 := (iff #756 #665)
+#739 := (iff #751 #734)
+#737 := (= #750 #736)
+#732 := (= #772 #784)
+#816 := (= #516 -1::Int)
+#698 := [rewrite]: #816
+#733 := [monotonicity #698]: #732
+#738 := [monotonicity #733]: #737
+#719 := [monotonicity #738]: #739
+#735 := (iff #755 #757)
+#729 := (= #754 #13)
+#722 := (+ #13 0::Int)
+#617 := (= #722 #13)
+#728 := [rewrite]: #617
+#723 := (= #754 #722)
+#743 := (= #753 0::Int)
+#742 := (* -1::Int 0::Int)
+#747 := (= #742 0::Int)
+#748 := [rewrite]: #747
+#745 := (= #753 #742)
+#740 := (= #780 0::Int)
+#741 := [rewrite]: #740
+#746 := [monotonicity #741]: #745
+#749 := [trans #746 #748]: #743
+#724 := [monotonicity #749]: #723
+#730 := [trans #724 #728]: #729
+#731 := [monotonicity #730]: #735
+#815 := (iff #568 #811)
+#655 := (or #676 #825)
+#812 := (iff #655 #811)
+#814 := [rewrite]: #812
+#657 := (iff #568 #655)
+#819 := (iff #468 #825)
+#818 := (iff #574 #572)
+#820 := (or false #572)
+#823 := (iff #820 #572)
+#817 := [rewrite]: #823
+#821 := (iff #574 #820)
+#830 := (iff #573 false)
+#831 := [rewrite]: #830
+#822 := [monotonicity #831]: #821
+#824 := [trans #822 #817]: #818
+#826 := [monotonicity #824]: #819
+#677 := (iff #567 #676)
+#829 := (iff #845 #844)
+#832 := (or #844 false)
+#833 := (iff #832 #844)
+#834 := [rewrite]: #833
+#827 := (iff #845 #832)
+#828 := [monotonicity #831]: #827
+#835 := [trans #828 #834]: #829
+#678 := [monotonicity #835]: #677
+#658 := [monotonicity #678 #826]: #657
+#813 := [trans #658 #814]: #815
+#701 := [monotonicity #813 #731 #719]: #720
+#721 := [monotonicity #701]: #726
+#694 := [trans #721 #661]: #692
+#559 := (iff #843 false)
+#560 := [rewrite]: #559
+#705 := [monotonicity #560 #694]: #703
+#697 := [trans #705 #707]: #717
+#683 := [trans #697 #681]: #682
+#689 := [monotonicity #683]: #688
+#691 := [trans #689 #675]: #688
+#687 := [quant-inst #9 #10]: #686
+#652 := [mp #687 #691]: #685
+#465 := [unit-resolution #652 #909]: #679
+#642 := (not #679)
+#643 := (or #642 #667 #757)
+#644 := [def-axiom]: #643
+#464 := [unit-resolution #644 #465]: #466
+#467 := [unit-resolution #464 #463]: #757
+#648 := (not #757)
+#910 := (or #648 #670)
+#911 := [th-lemma arith triangle-eq]: #910
+#912 := [unit-resolution #911 #467]: #670
+#671 := (>= #13 0::Int)
+#913 := (or #648 #671)
+#914 := [th-lemma arith triangle-eq]: #913
+#915 := [unit-resolution #914 #467]: #671
+#917 := [th-lemma arith eq-propagate -1 -1 #915 #912]: #916
+#929 := (= #9 #11)
+#862 := (div #9 1::Int)
+#848 := (* -1::Int #862)
+#849 := (+ #11 #848)
+#781 := (<= #849 0::Int)
+#571 := (= #849 0::Int)
+#793 := (or #811 #844)
+#794 := [def-axiom]: #793
+#918 := [unit-resolution #794 #475]: #811
+#699 := (div #852 -1::Int)
+#807 := (* -1::Int #699)
+#805 := (+ #11 #807)
+#708 := (= #805 0::Int)
+#704 := (ite #811 #571 #708)
+#542 := (or #847 #704)
+#846 := (= #11 0::Int)
+#714 := (ite #847 #846 #704)
+#36 := (f5 #35 #24)
+#896 := (pattern #36)
+#206 := (div #200 #203)
+#378 := (* -1::Int #206)
+#379 := (+ #36 #378)
+#380 := (= #379 0::Int)
+#46 := (div #35 #24)
+#375 := (* -1::Int #46)
+#376 := (+ #36 #375)
+#377 := (= #376 0::Int)
+#381 := (ite #342 #377 #380)
+#374 := (= #36 0::Int)
+#39 := (or #37 #38)
+#382 := (ite #39 #374 #381)
+#897 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #896) #382)
+#385 := (forall (vars (?v0 Int) (?v1 Int)) #382)
+#900 := (iff #385 #897)
+#898 := (iff #382 #382)
+#899 := [refl]: #898
+#901 := [quant-intro #899]: #900
+#345 := (ite #342 #46 #206)
+#348 := (ite #39 0::Int #345)
+#351 := (= #36 #348)
+#354 := (forall (vars (?v0 Int) (?v1 Int)) #351)
+#386 := (iff #354 #385)
+#383 := (iff #351 #382)
+#384 := [rewrite]: #383
+#387 := [quant-intro #384]: #386
+#248 := (ite #245 #46 #206)
+#251 := (ite #39 0::Int #248)
+#254 := (= #36 #251)
+#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
+#355 := (iff #257 #354)
+#352 := (iff #254 #351)
+#349 := (= #251 #348)
+#346 := (= #248 #345)
+#347 := [monotonicity #344]: #346
+#350 := [monotonicity #347]: #349
+#353 := [monotonicity #350]: #352
+#356 := [quant-intro #353]: #355
+#317 := (~ #257 #257)
+#330 := (~ #254 #254)
+#331 := [refl]: #330
+#318 := [nnf-pos #331]: #317
+#49 := (div #47 #48)
+#50 := (ite #45 #46 #49)
+#51 := (ite #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#260 := (iff #53 #257)
+#209 := (ite #196 #46 #206)
+#190 := (or #184 #187)
+#212 := (ite #190 0::Int #209)
+#215 := (= #36 #212)
+#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
+#258 := (iff #218 #257)
+#255 := (iff #215 #254)
+#252 := (= #212 #251)
+#249 := (= #209 #248)
+#250 := [monotonicity #247]: #249
+#225 := (iff #190 #39)
+#226 := [monotonicity #222 #224]: #225
+#253 := [monotonicity #226 #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [quant-intro #256]: #258
+#219 := (iff #53 #218)
+#216 := (iff #52 #215)
+#213 := (= #51 #212)
+#210 := (= #50 #209)
+#207 := (= #49 #206)
+#208 := [monotonicity #202 #205]: #207
+#211 := [monotonicity #198 #208]: #210
+#191 := (iff #39 #190)
+#192 := [monotonicity #186 #189]: #191
+#214 := [monotonicity #192 #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [quant-intro #217]: #219
+#261 := [trans #220 #259]: #260
+#183 := [asserted]: #53
+#262 := [mp #183 #261]: #257
+#332 := [mp~ #262 #318]: #257
+#357 := [mp #332 #356]: #354
+#388 := [mp #357 #387]: #385
+#902 := [mp #388 #901]: #897
+#809 := (not #897)
+#806 := (or #809 #714)
+#500 := (div #852 #516)
+#501 := (* -1::Int #500)
+#861 := (+ #11 #501)
+#859 := (= #861 0::Int)
+#842 := (ite #568 #571 #859)
+#557 := (or #847 #843)
+#558 := (ite #557 #846 #842)
+#810 := (or #809 #558)
+#799 := (iff #810 #806)
+#788 := (iff #806 #806)
+#790 := [rewrite]: #788
+#715 := (iff #558 #714)
+#712 := (iff #842 #704)
+#710 := (iff #859 #708)
+#808 := (= #861 #805)
+#709 := (= #501 #807)
+#700 := (= #500 #699)
+#659 := [monotonicity #698]: #700
+#804 := [monotonicity #659]: #709
+#693 := [monotonicity #804]: #808
+#711 := [monotonicity #693]: #710
+#713 := [monotonicity #813 #711]: #712
+#837 := (iff #557 #847)
+#838 := (or #847 false)
+#836 := (iff #838 #847)
+#840 := [rewrite]: #836
+#839 := (iff #557 #838)
+#554 := [monotonicity #560]: #839
+#841 := [trans #554 #840]: #837
+#716 := [monotonicity #841 #713]: #715
+#791 := [monotonicity #716]: #799
+#800 := [trans #791 #790]: #799
+#797 := [quant-inst #9 #10]: #810
+#801 := [mp #797 #800]: #806
+#536 := [unit-resolution #801 #902]: #714
+#762 := (not #714)
+#766 := (or #762 #847 #704)
#767 := [def-axiom]: #766
-#763 := [unit-resolution #767 #196]: #768
-#511 := [unit-resolution #763 #531]: #177
-#514 := [symm #511]: #513
-#518 := [monotonicity #514]: #517
-#484 := [symm #518]: #482
-#487 := [monotonicity #484 #505]: #486
-#483 := [trans #487 #489]: #490
-#477 := [monotonicity #483]: #476
-#494 := (or #540 #181 #691)
-#495 := [th-lemma arith assign-bounds -1 1]: #494
-#496 := [unit-resolution #495 #590 #531]: #540
-#497 := (or #627 #659)
-#498 := [th-lemma arith triangle-eq]: #497
-#499 := [unit-resolution #498 #496]: #627
-#478 := [mp #499 #477]: #491
-#404 := (>= #171 0::Int)
-#466 := (= #411 0::Int)
-#519 := (not #466)
-#520 := (iff #421 #519)
-#523 := (iff #13 #466)
-#522 := (iff #466 #13)
-#515 := [monotonicity #518]: #522
-#516 := [symm #515]: #523
-#506 := [monotonicity #516]: #520
-#508 := [mp #521 #506]: #519
-#468 := (or #404 #466)
-#740 := (or #739 #404 #466)
-#467 := (or #466 #404)
-#462 := (or #739 #467)
-#453 := (iff #462 #740)
-#737 := (or #739 #468)
-#742 := (iff #737 #740)
-#452 := [rewrite]: #742
-#741 := (iff #462 #737)
-#469 := (iff #467 #468)
-#362 := [rewrite]: #469
-#738 := [monotonicity #362]: #741
-#454 := [trans #738 #452]: #453
-#463 := [quant-inst #171]: #462
-#455 := [mp #463 #454]: #740
-#509 := [unit-resolution #455 #790]: #468
-#507 := [unit-resolution #509 #508]: #404
-#745 := (not #404)
-#749 := (or #745 #747)
-#205 := (= #38 #41)
-#230 := (or #205 #224)
-#779 := (forall (vars (?v0 Int)) (:pat #778) #230)
-#235 := (forall (vars (?v0 Int)) #230)
-#782 := (iff #235 #779)
-#780 := (iff #230 #230)
-#781 := [refl]: #780
-#783 := [quant-intro #781]: #782
-#287 := (~ #235 #235)
-#286 := (~ #230 #230)
-#283 := [refl]: #286
-#288 := [nnf-pos #283]: #287
-#42 := (= #41 #38)
-#39 := (<= 0::Int #38)
-#43 := (implies #39 #42)
-#44 := (forall (vars (?v0 Int)) #43)
-#238 := (iff #44 #235)
-#212 := (not #39)
-#213 := (or #212 #205)
-#218 := (forall (vars (?v0 Int)) #213)
-#236 := (iff #218 #235)
-#233 := (iff #213 #230)
-#227 := (or #224 #205)
-#231 := (iff #227 #230)
-#232 := [rewrite]: #231
-#228 := (iff #213 #227)
-#225 := (iff #212 #224)
-#221 := (iff #39 #222)
-#223 := [rewrite]: #221
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#234 := [trans #229 #232]: #233
-#237 := [quant-intro #234]: #236
-#219 := (iff #44 #218)
-#216 := (iff #43 #213)
-#209 := (implies #39 #205)
-#214 := (iff #209 #213)
-#215 := [rewrite]: #214
-#210 := (iff #43 #209)
-#207 := (iff #42 #205)
-#208 := [rewrite]: #207
-#211 := [monotonicity #208]: #210
-#217 := [trans #211 #215]: #216
-#220 := [quant-intro #217]: #219
-#239 := [trans #220 #237]: #238
-#204 := [asserted]: #44
-#240 := [mp #204 #239]: #235
-#284 := [mp~ #240 #288]: #235
-#784 := [mp #284 #783]: #779
-#746 := (not #779)
-#752 := (or #746 #745 #747)
-#748 := (or #747 #745)
-#390 := (or #746 #748)
-#757 := (iff #390 #752)
-#755 := (or #746 #749)
-#756 := (iff #755 #752)
-#754 := [rewrite]: #756
-#395 := (iff #390 #755)
-#750 := (iff #748 #749)
-#751 := [rewrite]: #750
-#396 := [monotonicity #751]: #395
-#743 := [trans #396 #754]: #757
-#753 := [quant-inst #171]: #390
-#744 := [mp #753 #743]: #752
-#510 := [unit-resolution #744 #784]: #749
-#492 := [unit-resolution #510 #507]: #747
-#480 := [unit-resolution #492 #478]: false
-#479 := [lemma #480]: #13
-#681 := (or #421 #141)
-#677 := [th-lemma arith triangle-eq]: #681
-[unit-resolution #677 #479 #503]: false
-unsat
-a73683b8b391e3ad74189bec3a2bead06af3f8bd 414 0
-#2 := false
-#10 := 0::Int
-decl f5 :: (-> S2 Int)
-decl f3 :: S2
-#8 := f3
-#9 := (f5 f3)
-#168 := (>= #9 0::Int)
-#169 := (not #168)
-#155 := (<= #9 0::Int)
-#156 := (not #155)
-#11 := (= #9 0::Int)
-#191 := (or #11 #156 #169)
-#776 := (not #191)
+#543 := [unit-resolution #767 #536]: #542
+#919 := [unit-resolution #543 #474]: #704
+#795 := (not #811)
+#782 := (not #704)
+#787 := (or #782 #795 #571)
+#773 := [def-axiom]: #787
+#920 := [unit-resolution #773 #919 #918]: #571
+#777 := (not #571)
+#921 := (or #777 #781)
+#922 := [th-lemma arith triangle-eq]: #921
+#923 := [unit-resolution #922 #920]: #781
+#783 := (>= #849 0::Int)
+#498 := (or #777 #783)
+#499 := [th-lemma arith triangle-eq]: #498
+#924 := [unit-resolution #499 #920]: #783
+#606 := (+ #9 #848)
+#610 := (<= #606 0::Int)
+#605 := (= #606 0::Int)
+#1 := true
+#80 := [true-axiom]: true
+#563 := (or false #605)
+#555 := [th-lemma arith]: #563
+#564 := [unit-resolution #555 #80]: #605
+#488 := (not #605)
+#490 := (or #488 #610)
+#491 := [th-lemma arith triangle-eq]: #490
+#925 := [unit-resolution #491 #564]: #610
+#587 := (>= #606 0::Int)
+#926 := (or #488 #587)
+#927 := [th-lemma arith triangle-eq]: #926
+#928 := [unit-resolution #927 #564]: #587
+#930 := [th-lemma arith eq-propagate 1 1 -1 -1 #928 #925 #924 #923]: #929
+#934 := [trans #930 #917]: #933
+#936 := [monotonicity #934]: #935
+#937 := [trans #534 #936]: #91
+#94 := (not #91)
+#12 := (* #11 1::Int)
+#14 := (+ #12 #13)
+#15 := (f4 #14)
+#16 := (= f3 #15)
+#17 := (not #16)
+#95 := (iff #17 #94)
+#92 := (iff #16 #91)
+#89 := (= #15 #88)
+#86 := (= #14 #85)
+#83 := (= #12 #11)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#90 := [monotonicity #87]: #89
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93]: #95
+#82 := [asserted]: #17
+#99 := [mp #82 #96]: #94
+#938 := [unit-resolution #99 #937]: false
+#939 := [lemma #938]: #847
+#975 := [symm #939]: #974
+#514 := (= #552 0::Int)
+#860 := (>= #552 0::Int)
+#664 := (or #718 #763)
+#666 := [def-axiom]: #664
+#471 := [unit-resolution #666 #939]: #718
+#476 := [unit-resolution #464 #471]: #757
+#940 := [unit-resolution #914 #476]: #671
+#798 := (>= #11 0::Int)
+#497 := (not #610)
+#565 := (not #798)
+#556 := [hypothesis]: #565
+#768 := (not #846)
+#566 := (or #768 #798)
+#533 := [th-lemma arith triangle-eq]: #566
+#535 := [unit-resolution #533 #556]: #768
+#527 := (or #763 #846)
+#764 := (or #762 #763 #846)
+#765 := [def-axiom]: #764
+#540 := [unit-resolution #765 #536]: #527
+#541 := [unit-resolution #540 #535]: #763
+#544 := [unit-resolution #543 #541]: #704
+#519 := (not #633)
+#520 := (iff #763 #519)
+#517 := (iff #847 #633)
+#545 := (= #462 f3)
+#528 := [symm #534]: #545
+#531 := [monotonicity #528]: #530
+#512 := [monotonicity #531]: #510
+#518 := [symm #512]: #517
+#521 := [monotonicity #518]: #520
+#522 := [mp #541 #521]: #519
+#523 := [unit-resolution #511 #522]: #572
+#507 := [unit-resolution #506 #541]: #655
+#505 := [unit-resolution #507 #523]: #676
+#508 := [unit-resolution #794 #505]: #811
+#496 := [unit-resolution #773 #508 #544]: #571
+#502 := [unit-resolution #499 #496]: #783
+#503 := (not #783)
+#478 := (or #497 #825 #798 #503)
+#482 := [th-lemma arith assign-bounds 1 1 -1]: #478
+#483 := [unit-resolution #482 #523 #502 #556]: #497
+#493 := [unit-resolution #491 #483 #564]: false
+#489 := [lemma #493]: #798
+#532 := (* -1::Int #552)
+#867 := (+ #13 #532)
+#869 := (+ #11 #867)
+#850 := (<= #869 0::Int)
+#526 := (= #869 0::Int)
+#547 := (>= #85 0::Int)
+#941 := (not #671)
+#942 := (or #547 #565 #941)
+#943 := [th-lemma arith assign-bounds -1 -1]: #942
+#944 := [unit-resolution #943 #940 #489]: #547
+#548 := (not #547)
+#537 := (or #526 #548)
+#106 := (= #24 #27)
+#131 := (or #106 #125)
+#884 := (forall (vars (?v0 Int)) (:pat #883) #131)
+#136 := (forall (vars (?v0 Int)) #131)
+#887 := (iff #136 #884)
+#885 := (iff #131 #131)
+#886 := [refl]: #885
+#888 := [quant-intro #886]: #887
+#313 := (~ #136 #136)
+#312 := (~ #131 #131)
+#309 := [refl]: #312
+#314 := [nnf-pos #309]: #313
+#28 := (= #27 #24)
+#25 := (<= 0::Int #24)
+#29 := (implies #25 #28)
+#30 := (forall (vars (?v0 Int)) #29)
+#139 := (iff #30 #136)
+#113 := (not #25)
+#114 := (or #113 #106)
+#119 := (forall (vars (?v0 Int)) #114)
+#137 := (iff #119 #136)
+#134 := (iff #114 #131)
+#128 := (or #125 #106)
+#132 := (iff #128 #131)
+#133 := [rewrite]: #132
+#129 := (iff #114 #128)
+#126 := (iff #113 #125)
+#122 := (iff #25 #124)
+#123 := [rewrite]: #122
+#127 := [monotonicity #123]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#138 := [quant-intro #135]: #137
+#120 := (iff #30 #119)
+#117 := (iff #29 #114)
+#110 := (implies #25 #106)
+#115 := (iff #110 #114)
+#116 := [rewrite]: #115
+#111 := (iff #29 #110)
+#108 := (iff #28 #106)
+#109 := [rewrite]: #108
+#112 := [monotonicity #109]: #111
+#118 := [trans #112 #116]: #117
+#121 := [quant-intro #118]: #120
+#140 := [trans #121 #138]: #139
+#105 := [asserted]: #30
+#141 := [mp #105 #140]: #136
+#310 := [mp~ #141 #314]: #136
+#889 := [mp #310 #888]: #884
+#871 := (not #884)
+#872 := (or #871 #526 #548)
+#549 := (= #85 #552)
+#553 := (or #549 #548)
+#873 := (or #871 #553)
+#525 := (iff #873 #872)
+#874 := (or #871 #537)
+#529 := (iff #874 #872)
+#865 := [rewrite]: #529
+#864 := (iff #873 #874)
+#538 := (iff #553 #537)
+#656 := (iff #549 #526)
+#863 := [rewrite]: #656
+#870 := [monotonicity #863]: #538
+#524 := [monotonicity #870]: #864
+#866 := [trans #524 #865]: #525
+#868 := [quant-inst #85]: #873
+#509 := [mp #868 #866]: #872
+#945 := [unit-resolution #509 #889]: #537
+#946 := [unit-resolution #945 #944]: #526
+#947 := (not #526)
+#948 := (or #947 #850)
+#949 := [th-lemma arith triangle-eq]: #948
+#950 := [unit-resolution #949 #946]: #850
+#951 := (not #850)
+#952 := (or #860 #941 #951 #565)
+#953 := [th-lemma arith assign-bounds -1 1 -1]: #952
+#954 := [unit-resolution #953 #950 #489 #940]: #860
+#858 := (<= #552 0::Int)
+#955 := [unit-resolution #911 #476]: #670
+#802 := (<= #11 0::Int)
+#956 := [unit-resolution #540 #939]: #846
+#957 := (or #768 #802)
+#958 := [th-lemma arith triangle-eq]: #957
+#959 := [unit-resolution #958 #956]: #802
+#513 := (>= #869 0::Int)
+#960 := (or #947 #513)
+#961 := [th-lemma arith triangle-eq]: #960
+#962 := [unit-resolution #961 #946]: #513
+#965 := (not #802)
+#964 := (not #513)
+#963 := (not #670)
+#966 := (or #858 #963 #964 #965)
+#967 := [th-lemma arith assign-bounds -1 1 -1]: #966
+#968 := [unit-resolution #967 #962 #959 #955]: #858
+#970 := (not #860)
+#969 := (not #858)
+#971 := (or #514 #969 #970)
+#972 := [th-lemma arith triangle-eq]: #971
+#973 := [unit-resolution #972 #968 #954]: #514
+#977 := [trans #973 #975]: #976
+#980 := [monotonicity #977]: #979
+#982 := [symm #980]: #981
+#986 := [trans #534 #982]: #985
+#987 := [trans #986 #984]: #91
+[unit-resolution #99 #987]: false
+unsat
+14ea837cc40eb6dd6a11b7a7e54b897ec75d15ed 873 0
+#2 := false
decl f4 :: (-> Int S2)
-#89 := -1::Int
-#90 := (* -1::Int #9)
-#113 := (mod #90 -1::Int)
-#119 := (* -1::Int #113)
-#196 := (ite #191 0::Int #119)
-#95 := (div #90 -1::Int)
-#12 := 1::Int
-#21 := (div #9 1::Int)
-#179 := (or #156 #169)
-#182 := (ite #179 #21 #95)
-#185 := (ite #11 0::Int #182)
-#199 := (+ #185 #196)
-#202 := (f4 #199)
-#205 := (= f3 #202)
-#426 := (f4 #9)
-#715 := (= #426 #202)
-#718 := (= #202 #426)
-#610 := (= #199 #9)
-#628 := (= #185 #9)
-#614 := (= #9 #185)
-#706 := (* -1::Int #21)
-#700 := (+ #9 #706)
-#695 := (<= #700 0::Int)
-#705 := (= #700 0::Int)
-#1 := true
-#71 := [true-axiom]: true
-#665 := (or false #705)
-#666 := [th-lemma arith]: #665
-#667 := [unit-resolution #666 #71]: #705
-#668 := (not #705)
-#663 := (or #668 #695)
-#669 := [th-lemma arith triangle-eq]: #663
-#655 := [unit-resolution #669 #667]: #695
-#696 := (>= #700 0::Int)
-#651 := (or #668 #696)
-#652 := [th-lemma arith triangle-eq]: #651
-#653 := [unit-resolution #652 #667]: #696
-#683 := (* -1::Int #185)
-#661 := (+ #21 #683)
-#662 := (<= #661 0::Int)
-#672 := (= #21 #185)
-#457 := (= #182 #185)
-#567 := (not #11)
-#735 := (<= #196 0::Int)
-#782 := (= #196 0::Int)
-#656 := [hypothesis]: #191
-#420 := (or #776 #782)
-#761 := [def-axiom]: #420
-#657 := [unit-resolution #761 #656]: #782
-#658 := (not #782)
-#659 := (or #658 #735)
-#654 := [th-lemma arith triangle-eq]: #659
-#660 := [unit-resolution #654 #657]: #735
-#736 := (>= #196 0::Int)
-#633 := (or #658 #736)
-#634 := [th-lemma arith triangle-eq]: #633
-#635 := [unit-resolution #634 #657]: #736
-#621 := (not #735)
-#619 := (not #736)
-#622 := (or #567 #619 #621)
-#726 := (= 0::Int #9)
-#730 := [hypothesis]: #11
-#724 := [symm #730]: #726
-#727 := (= #199 0::Int)
-#372 := (= #185 0::Int)
-#774 := (or #567 #372)
-#448 := [def-axiom]: #774
-#737 := [unit-resolution #448 #730]: #372
-#723 := (= #199 #185)
-#569 := (= #185 #199)
-#566 := [hypothesis]: #735
-#568 := [hypothesis]: #736
-#722 := [th-lemma arith eq-propagate -1 -1 #568 #566]: #569
-#725 := [symm #722]: #723
-#609 := [trans #725 #737]: #727
-#611 := [trans #609 #724]: #610
-#620 := [monotonicity #611]: #718
-#716 := [symm #620]: #715
-#427 := (= f3 #426)
-#38 := (:var 0 S2)
-#39 := (f5 #38)
-#786 := (pattern #39)
-#40 := (f4 #39)
-#215 := (= #38 #40)
-#787 := (forall (vars (?v0 S2)) (:pat #786) #215)
-#218 := (forall (vars (?v0 S2)) #215)
-#788 := (iff #218 #787)
-#790 := (iff #787 #787)
-#791 := [rewrite]: #790
-#789 := [rewrite]: #788
-#792 := [trans #789 #791]: #788
-#312 := (~ #218 #218)
-#310 := (~ #215 #215)
-#311 := [refl]: #310
-#313 := [nnf-pos #311]: #312
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#219 := (iff #42 #218)
-#216 := (iff #41 #215)
-#217 := [rewrite]: #216
-#220 := [quant-intro #217]: #219
-#214 := [asserted]: #42
-#223 := [mp #214 #220]: #218
-#302 := [mp~ #223 #313]: #218
-#793 := [mp #302 #792]: #787
-#765 := (not #787)
-#766 := (or #765 #427)
-#767 := [quant-inst #8]: #766
-#570 := [unit-resolution #767 #793]: #427
-#719 := [trans #570 #716]: #205
-#208 := (not #205)
-#23 := (- 1::Int)
-#22 := (- #9)
-#29 := (mod #22 #23)
-#30 := (- #29)
-#28 := (mod #9 1::Int)
-#16 := (< 0::Int 1::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#31 := (ite #20 #28 #30)
-#32 := (ite #11 0::Int #31)
-#13 := (= 1::Int 0::Int)
-#33 := (ite #13 #9 #32)
-#24 := (div #22 #23)
-#25 := (ite #20 #21 #24)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (* #26 1::Int)
-#34 := (+ #27 #33)
-#35 := (f4 #34)
-#36 := (= f3 #35)
-#37 := (not #36)
-#211 := (iff #37 #208)
-#83 := (and #16 #18)
-#86 := (or #17 #83)
-#130 := (or #11 #86)
-#131 := (ite #130 0::Int #119)
-#98 := (ite #86 #21 #95)
-#101 := (ite #11 0::Int #98)
-#143 := (+ #101 #131)
-#146 := (f4 #143)
-#149 := (= f3 #146)
-#152 := (not #149)
-#209 := (iff #152 #208)
-#206 := (iff #149 #205)
-#203 := (= #146 #202)
-#200 := (= #143 #199)
-#197 := (= #131 #196)
-#194 := (iff #130 #191)
-#188 := (or #11 #179)
-#192 := (iff #188 #191)
-#193 := [rewrite]: #192
-#189 := (iff #130 #188)
-#180 := (iff #86 #179)
-#177 := (iff #83 #169)
-#172 := (and true #169)
-#175 := (iff #172 #169)
-#176 := [rewrite]: #175
-#173 := (iff #83 #172)
-#170 := (iff #18 #169)
-#171 := [rewrite]: #170
-#159 := (iff #16 true)
+decl f7 :: (-> Int Int Int)
+#10 := 3::Int
+decl f6 :: (-> S2 Int)
+decl f3 :: S2
+#8 := f3
+#9 := (f6 f3)
+#13 := (f7 #9 3::Int)
+decl f5 :: (-> Int Int Int)
+#11 := (f5 #9 3::Int)
+#83 := (* 3::Int #11)
+#86 := (+ #83 #13)
+#89 := (f4 #86)
+#92 := (= f3 #89)
+#463 := (f4 #9)
+#1031 := (= #463 #89)
+#1029 := (= #89 #463)
+#1027 := (= #86 #9)
+#23 := 0::Int
+#1023 := (= 0::Int #9)
+#832 := (= #9 0::Int)
+#481 := (f6 #89)
+#554 := (= #86 #481)
+#943 := (not #554)
+#844 := (div #9 3::Int)
+#200 := -1::Int
+#848 := (* -1::Int #844)
+#845 := (+ #11 #848)
+#781 := (<= #845 0::Int)
+#849 := (= #845 0::Int)
+#840 := (<= #9 0::Int)
+#828 := (not #840)
+#559 := (>= #9 0::Int)
+#700 := (not #559)
+#806 := (or #700 #828)
+#594 := [hypothesis]: #700
+#671 := (f6 #463)
+#672 := (= #671 0::Int)
+#535 := (iff #672 #832)
+#558 := (= #671 #9)
+#596 := (= #9 #671)
+#548 := (= f3 #463)
+#18 := (:var 0 S2)
+#19 := (f6 #18)
+#877 := (pattern #19)
+#20 := (f4 #19)
+#99 := (= #18 #20)
+#878 := (forall (vars (?v0 S2)) (:pat #877) #99)
+#103 := (forall (vars (?v0 S2)) #99)
+#879 := (iff #103 #878)
+#881 := (iff #878 #878)
+#882 := [rewrite]: #881
+#880 := [rewrite]: #879
+#883 := [trans #880 #882]: #879
+#326 := (~ #103 #103)
+#324 := (~ #99 #99)
+#325 := [refl]: #324
+#327 := [nnf-pos #325]: #326
+#21 := (= #20 #18)
+#22 := (forall (vars (?v0 S2)) #21)
+#104 := (iff #22 #103)
+#101 := (iff #21 #99)
+#102 := [rewrite]: #101
+#105 := [quant-intro #102]: #104
+#98 := [asserted]: #22
+#108 := [mp #98 #105]: #103
+#312 := [mp~ #108 #327]: #103
+#884 := [mp #312 #883]: #878
+#541 := (not #878)
+#552 := (or #541 #548)
+#553 := [quant-inst #8]: #552
+#557 := [unit-resolution #553 #884]: #548
+#597 := [monotonicity #557]: #596
+#590 := [symm #597]: #558
+#498 := [monotonicity #590]: #535
+#656 := (or #559 #672)
+#24 := (:var 0 Int)
+#26 := (f4 #24)
+#885 := (pattern #26)
+#125 := (>= #24 0::Int)
+#27 := (f6 #26)
+#32 := (= #27 0::Int)
+#173 := (or #32 #125)
+#892 := (forall (vars (?v0 Int)) (:pat #885) #173)
+#178 := (forall (vars (?v0 Int)) #173)
+#895 := (iff #178 #892)
+#893 := (iff #173 #173)
+#894 := [refl]: #893
+#896 := [quant-intro #894]: #895
+#316 := (~ #178 #178)
+#328 := (~ #173 #173)
+#329 := [refl]: #328
+#317 := [nnf-pos #329]: #316
+#31 := (< #24 0::Int)
+#33 := (implies #31 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#181 := (iff #34 #178)
+#144 := (= 0::Int #27)
+#150 := (not #31)
+#151 := (or #150 #144)
+#156 := (forall (vars (?v0 Int)) #151)
+#179 := (iff #156 #178)
+#176 := (iff #151 #173)
+#170 := (or #125 #32)
+#174 := (iff #170 #173)
+#175 := [rewrite]: #174
+#171 := (iff #151 #170)
+#168 := (iff #144 #32)
+#169 := [rewrite]: #168
+#166 := (iff #150 #125)
+#126 := (not #125)
+#161 := (not #126)
+#164 := (iff #161 #125)
+#165 := [rewrite]: #164
+#162 := (iff #150 #161)
+#159 := (iff #31 #126)
#160 := [rewrite]: #159
-#174 := [monotonicity #160 #171]: #173
-#178 := [trans #174 #176]: #177
-#166 := (iff #17 #156)
-#161 := (and #156 true)
-#164 := (iff #161 #156)
-#165 := [rewrite]: #164
-#162 := (iff #17 #161)
-#157 := (iff #15 #156)
-#158 := [rewrite]: #157
-#163 := [monotonicity #158 #160]: #162
+#163 := [monotonicity #160]: #162
#167 := [trans #163 #165]: #166
-#181 := [monotonicity #167 #178]: #180
-#190 := [monotonicity #181]: #189
-#195 := [trans #190 #193]: #194
-#198 := [monotonicity #195]: #197
-#186 := (= #101 #185)
-#183 := (= #98 #182)
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#201 := [monotonicity #187 #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#153 := (iff #37 #152)
-#150 := (iff #36 #149)
-#147 := (= #35 #146)
-#144 := (= #34 #143)
-#141 := (= #33 #131)
-#136 := (ite false #9 #131)
-#139 := (= #136 #131)
-#140 := [rewrite]: #139
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#124 := (ite #86 0::Int #119)
-#127 := (ite #11 0::Int #124)
-#132 := (= #127 #131)
-#133 := [rewrite]: #132
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#122 := (= #30 #119)
-#116 := (- #113)
-#120 := (= #116 #119)
-#121 := [rewrite]: #120
-#117 := (= #30 #116)
-#114 := (= #29 #113)
-#93 := (= #23 -1::Int)
-#94 := [rewrite]: #93
-#91 := (= #22 #90)
-#92 := [rewrite]: #91
-#115 := [monotonicity #92 #94]: #114
-#118 := [monotonicity #115]: #117
-#123 := [trans #118 #121]: #122
-#111 := (= #28 0::Int)
-#112 := [rewrite]: #111
-#87 := (iff #20 #86)
-#84 := (iff #19 #83)
+#172 := [monotonicity #167 #169]: #171
+#177 := [trans #172 #175]: #176
+#180 := [quant-intro #177]: #179
+#157 := (iff #34 #156)
+#154 := (iff #33 #151)
+#147 := (implies #31 #144)
+#152 := (iff #147 #151)
+#153 := [rewrite]: #152
+#148 := (iff #33 #147)
+#145 := (iff #32 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#155 := [trans #149 #153]: #154
+#158 := [quant-intro #155]: #157
+#182 := [trans #158 #180]: #181
+#143 := [asserted]: #34
+#183 := [mp #143 #182]: #178
+#330 := [mp~ #183 #317]: #178
+#897 := [mp #330 #896]: #892
+#859 := (not #892)
+#645 := (or #859 #559 #672)
+#673 := (or #672 #559)
+#646 := (or #859 #673)
+#648 := (iff #646 #645)
+#649 := (or #859 #656)
+#494 := (iff #649 #645)
+#652 := [rewrite]: #494
+#650 := (iff #646 #649)
+#674 := (iff #673 #656)
+#644 := [rewrite]: #674
+#651 := [monotonicity #644]: #650
+#653 := [trans #651 #652]: #648
+#647 := [quant-inst #9]: #646
+#632 := [mp #647 #653]: #645
+#546 := [unit-resolution #632 #897]: #656
+#595 := [unit-resolution #546 #594]: #672
+#500 := [mp #595 #498]: #832
+#755 := (not #832)
+#501 := (or #755 #559)
+#504 := [th-lemma arith triangle-eq]: #501
+#499 := [unit-resolution #504 #500 #594]: false
+#505 := [lemma #499]: #559
+#480 := [hypothesis]: #755
+#547 := (or #832 #828 #700)
+#530 := [th-lemma arith triangle-eq]: #547
+#489 := [unit-resolution #530 #480 #505]: #828
+#775 := (or #806 #840)
+#776 := [def-axiom]: #775
+#488 := [unit-resolution #776 #489]: #806
+#712 := -3::Int
+#469 := (* -1::Int #9)
+#714 := (div #469 -3::Int)
+#717 := (* -1::Int #714)
+#808 := (+ #11 #717)
+#801 := (= #808 0::Int)
+#792 := (ite #806 #849 #801)
+#563 := (or #832 #792)
+#839 := (= #11 0::Int)
+#804 := (ite #832 #839 #792)
+#35 := (:var 1 Int)
+#36 := (f5 #35 #24)
+#898 := (pattern #36)
+#204 := (* -1::Int #24)
+#201 := (* -1::Int #35)
+#207 := (div #201 #204)
+#379 := (* -1::Int #207)
+#380 := (+ #36 #379)
+#381 := (= #380 0::Int)
+#46 := (div #35 #24)
+#376 := (* -1::Int #46)
+#377 := (+ #36 #376)
+#378 := (= #377 0::Int)
+#239 := (>= #35 0::Int)
+#232 := (<= #24 0::Int)
+#339 := (or #232 #239)
+#340 := (not #339)
+#228 := (<= #35 0::Int)
+#337 := (or #228 #232)
+#338 := (not #337)
+#343 := (or #338 #340)
+#382 := (ite #343 #378 #381)
+#375 := (= #36 0::Int)
+#38 := (= #24 0::Int)
+#37 := (= #35 0::Int)
+#39 := (or #37 #38)
+#383 := (ite #39 #375 #382)
+#899 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #898) #383)
+#386 := (forall (vars (?v0 Int) (?v1 Int)) #383)
+#902 := (iff #386 #899)
+#900 := (iff #383 #383)
+#901 := [refl]: #900
+#903 := [quant-intro #901]: #902
+#346 := (ite #343 #46 #207)
+#349 := (ite #39 0::Int #346)
+#352 := (= #36 #349)
+#355 := (forall (vars (?v0 Int) (?v1 Int)) #352)
+#387 := (iff #355 #386)
+#384 := (iff #352 #383)
+#385 := [rewrite]: #384
+#388 := [quant-intro #385]: #387
+#240 := (not #239)
+#233 := (not #232)
+#243 := (and #233 #240)
+#229 := (not #228)
+#236 := (and #229 #233)
+#246 := (or #236 #243)
+#249 := (ite #246 #46 #207)
+#252 := (ite #39 0::Int #249)
+#255 := (= #36 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#356 := (iff #258 #355)
+#353 := (iff #255 #352)
+#350 := (= #252 #349)
+#347 := (= #249 #346)
+#344 := (iff #246 #343)
+#341 := (iff #243 #340)
+#342 := [rewrite]: #341
+#322 := (iff #236 #338)
+#323 := [rewrite]: #322
+#345 := [monotonicity #323 #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [monotonicity #351]: #353
+#357 := [quant-intro #354]: #356
+#318 := (~ #258 #258)
+#331 := (~ #255 #255)
+#332 := [refl]: #331
+#319 := [nnf-pos #332]: #318
+#48 := (- #24)
+#47 := (- #35)
+#49 := (div #47 #48)
+#41 := (< 0::Int #24)
+#43 := (< #35 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #35)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#50 := (ite #45 #46 #49)
+#51 := (ite #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#261 := (iff #53 #258)
+#194 := (and #41 #43)
+#197 := (or #42 #194)
+#210 := (ite #197 #46 #207)
+#188 := (= 0::Int #24)
+#185 := (= 0::Int #35)
+#191 := (or #185 #188)
+#213 := (ite #191 0::Int #210)
+#216 := (= #36 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#259 := (iff #219 #258)
+#256 := (iff #216 #255)
+#253 := (= #213 #252)
+#250 := (= #210 #249)
+#247 := (iff #197 #246)
+#244 := (iff #194 #243)
+#241 := (iff #43 #240)
+#242 := [rewrite]: #241
+#234 := (iff #41 #233)
+#235 := [rewrite]: #234
+#245 := [monotonicity #235 #242]: #244
+#237 := (iff #42 #236)
+#230 := (iff #40 #229)
+#231 := [rewrite]: #230
+#238 := [monotonicity #231 #235]: #237
+#248 := [monotonicity #238 #245]: #247
+#251 := [monotonicity #248]: #250
+#226 := (iff #191 #39)
+#224 := (iff #188 #38)
+#225 := [rewrite]: #224
+#222 := (iff #185 #37)
+#223 := [rewrite]: #222
+#227 := [monotonicity #223 #225]: #226
+#254 := [monotonicity #227 #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#220 := (iff #53 #219)
+#217 := (iff #52 #216)
+#214 := (= #51 #213)
+#211 := (= #50 #210)
+#208 := (= #49 #207)
+#205 := (= #48 #204)
+#206 := [rewrite]: #205
+#202 := (= #47 #201)
+#203 := [rewrite]: #202
+#209 := [monotonicity #203 #206]: #208
+#198 := (iff #45 #197)
+#195 := (iff #44 #194)
+#196 := [rewrite]: #195
+#199 := [monotonicity #196]: #198
+#212 := [monotonicity #199 #209]: #211
+#192 := (iff #39 #191)
+#189 := (iff #38 #188)
+#190 := [rewrite]: #189
+#186 := (iff #37 #185)
+#187 := [rewrite]: #186
+#193 := [monotonicity #187 #190]: #192
+#215 := [monotonicity #193 #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#262 := [trans #221 #260]: #261
+#184 := [asserted]: #53
+#263 := [mp #184 #262]: #258
+#333 := [mp~ #263 #319]: #258
+#358 := [mp #333 #357]: #355
+#389 := [mp #358 #388]: #386
+#904 := [mp #389 #903]: #899
+#794 := (not #899)
+#795 := (or #794 #804)
+#576 := (* -1::Int 3::Int)
+#846 := (div #469 #576)
+#847 := (* -1::Int #846)
+#569 := (+ #11 #847)
+#570 := (= #569 0::Int)
+#560 := (<= 3::Int 0::Int)
+#561 := (or #560 #559)
+#562 := (not #561)
+#841 := (or #840 #560)
+#556 := (not #841)
+#838 := (or #556 #562)
+#842 := (ite #838 #849 #570)
+#843 := (= 3::Int 0::Int)
+#833 := (or #832 #843)
+#834 := (ite #833 #839 #842)
+#796 := (or #794 #834)
+#791 := (iff #796 #795)
+#782 := (iff #795 #795)
+#783 := [rewrite]: #782
+#800 := (iff #834 #804)
+#802 := (iff #842 #792)
+#793 := (iff #570 #801)
+#812 := (= #569 #808)
+#718 := (= #847 #717)
+#715 := (= #846 #714)
+#713 := (= #576 -3::Int)
+#706 := [rewrite]: #713
+#716 := [monotonicity #706]: #715
+#811 := [monotonicity #716]: #718
+#799 := [monotonicity #811]: #812
+#790 := [monotonicity #799]: #793
+#695 := (iff #838 #806)
+#661 := (or #828 #700)
+#807 := (iff #661 #806)
+#810 := [rewrite]: #807
+#809 := (iff #838 #661)
+#701 := (iff #562 #700)
+#815 := (iff #561 #559)
+#660 := (or false #559)
+#816 := (iff #660 #559)
+#817 := [rewrite]: #816
+#813 := (iff #561 #660)
+#822 := (iff #560 false)
+#823 := [rewrite]: #822
+#814 := [monotonicity #823]: #813
+#818 := [trans #814 #817]: #815
+#702 := [monotonicity #818]: #701
+#657 := (iff #556 #828)
+#827 := (iff #841 #840)
+#824 := (or #840 false)
+#820 := (iff #824 #840)
+#826 := [rewrite]: #820
+#825 := (iff #841 #824)
+#819 := [monotonicity #823]: #825
+#821 := [trans #819 #826]: #827
+#659 := [monotonicity #821]: #657
+#711 := [monotonicity #659 #702]: #809
+#710 := [trans #711 #810]: #695
+#803 := [monotonicity #710 #790]: #802
+#679 := (iff #833 #832)
+#835 := (or #832 false)
+#837 := (iff #835 #832)
+#678 := [rewrite]: #837
+#836 := (iff #833 #835)
+#829 := (iff #843 false)
+#830 := [rewrite]: #829
+#831 := [monotonicity #830]: #836
+#680 := [trans #831 #678]: #679
+#805 := [monotonicity #680 #803]: #800
+#798 := [monotonicity #805]: #791
+#785 := [trans #798 #783]: #791
+#797 := [quant-inst #9 #10]: #796
+#786 := [mp #797 #785]: #795
+#580 := [unit-resolution #786 #904]: #804
+#753 := (not #804)
+#758 := (or #753 #832 #792)
+#759 := [def-axiom]: #758
+#564 := [unit-resolution #759 #580]: #563
+#473 := [unit-resolution #564 #480]: #792
+#778 := (not #806)
+#766 := (not #792)
+#767 := (or #766 #778 #849)
+#768 := [def-axiom]: #767
+#470 := [unit-resolution #768 #473 #488]: #849
+#771 := (not #849)
+#471 := (or #771 #781)
+#946 := [th-lemma arith triangle-eq]: #471
+#947 := [unit-resolution #946 #470]: #781
+#777 := (mod #9 3::Int)
+#749 := (* -1::Int #777)
+#750 := (+ #13 #749)
+#675 := (<= #750 0::Int)
+#745 := (= #750 0::Int)
+#762 := (mod #469 -3::Int)
+#732 := (+ #13 #762)
+#734 := (= #732 0::Int)
+#739 := (ite #806 #745 #734)
+#949 := (or #832 #739)
+#724 := (= #13 0::Int)
+#741 := (ite #832 #724 #739)
+#54 := (f7 #35 #24)
+#905 := (pattern #54)
+#265 := (mod #201 #204)
+#395 := (+ #54 #265)
+#396 := (= #395 0::Int)
+#55 := (mod #35 #24)
+#392 := (* -1::Int #55)
+#393 := (+ #54 #392)
+#394 := (= #393 0::Int)
+#397 := (ite #343 #394 #396)
+#391 := (= #54 0::Int)
+#398 := (ite #37 #391 #397)
+#390 := (= #35 #54)
+#399 := (ite #38 #390 #398)
+#906 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #905) #399)
+#402 := (forall (vars (?v0 Int) (?v1 Int)) #399)
+#909 := (iff #402 #906)
+#907 := (iff #399 #399)
+#908 := [refl]: #907
+#910 := [quant-intro #908]: #909
+#271 := (* -1::Int #265)
+#359 := (ite #343 #55 #271)
+#362 := (ite #37 0::Int #359)
+#365 := (ite #38 #35 #362)
+#368 := (= #54 #365)
+#371 := (forall (vars (?v0 Int) (?v1 Int)) #368)
+#403 := (iff #371 #402)
+#400 := (iff #368 #399)
+#401 := [rewrite]: #400
+#404 := [quant-intro #401]: #403
+#291 := (ite #246 #55 #271)
+#294 := (ite #37 0::Int #291)
+#297 := (ite #38 #35 #294)
+#300 := (= #54 #297)
+#303 := (forall (vars (?v0 Int) (?v1 Int)) #300)
+#372 := (iff #303 #371)
+#369 := (iff #300 #368)
+#366 := (= #297 #365)
+#363 := (= #294 #362)
+#360 := (= #291 #359)
+#361 := [monotonicity #345]: #360
+#364 := [monotonicity #361]: #363
+#367 := [monotonicity #364]: #366
+#370 := [monotonicity #367]: #369
+#373 := [quant-intro #370]: #372
+#320 := (~ #303 #303)
+#334 := (~ #300 #300)
+#335 := [refl]: #334
+#321 := [nnf-pos #335]: #320
+#56 := (mod #47 #48)
+#57 := (- #56)
+#58 := (ite #45 #55 #57)
+#59 := (ite #37 0::Int #58)
+#60 := (ite #38 #35 #59)
+#61 := (= #54 #60)
+#62 := (forall (vars (?v0 Int) (?v1 Int)) #61)
+#306 := (iff #62 #303)
+#276 := (ite #197 #55 #271)
+#279 := (ite #185 0::Int #276)
+#282 := (ite #188 #35 #279)
+#285 := (= #54 #282)
+#288 := (forall (vars (?v0 Int) (?v1 Int)) #285)
+#304 := (iff #288 #303)
+#301 := (iff #285 #300)
+#298 := (= #282 #297)
+#295 := (= #279 #294)
+#292 := (= #276 #291)
+#293 := [monotonicity #248]: #292
+#296 := [monotonicity #223 #293]: #295
+#299 := [monotonicity #225 #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [quant-intro #302]: #304
+#289 := (iff #62 #288)
+#286 := (iff #61 #285)
+#283 := (= #60 #282)
+#280 := (= #59 #279)
+#277 := (= #58 #276)
+#274 := (= #57 #271)
+#268 := (- #265)
+#272 := (= #268 #271)
+#273 := [rewrite]: #272
+#269 := (= #57 #268)
+#266 := (= #56 #265)
+#267 := [monotonicity #203 #206]: #266
+#270 := [monotonicity #267]: #269
+#275 := [trans #270 #273]: #274
+#278 := [monotonicity #199 #275]: #277
+#281 := [monotonicity #187 #278]: #280
+#284 := [monotonicity #190 #281]: #283
+#287 := [monotonicity #284]: #286
+#290 := [quant-intro #287]: #289
+#307 := [trans #290 #305]: #306
+#264 := [asserted]: #62
+#308 := [mp #264 #307]: #303
+#336 := [mp~ #308 #321]: #303
+#374 := [mp #336 #373]: #371
+#405 := [mp #374 #404]: #402
+#911 := [mp #405 #910]: #906
+#704 := (not #906)
+#663 := (or #704 #741)
+#744 := (mod #469 #576)
+#747 := (+ #13 #744)
+#748 := (= #747 0::Int)
+#751 := (ite #838 #745 #748)
+#725 := (ite #832 #724 #751)
+#726 := (= #9 #13)
+#619 := (ite #843 #726 #725)
+#694 := (or #704 #619)
+#698 := (iff #694 #663)
+#707 := (iff #663 #663)
+#708 := [rewrite]: #707
+#729 := (iff #619 #741)
+#722 := (ite false #726 #741)
+#728 := (iff #722 #741)
+#723 := [rewrite]: #728
+#703 := (iff #619 #722)
+#721 := (iff #725 #741)
+#740 := (iff #751 #739)
+#735 := (iff #748 #734)
+#737 := (= #747 #732)
+#730 := (= #744 #762)
+#731 := [monotonicity #706]: #730
+#733 := [monotonicity #731]: #737
+#738 := [monotonicity #733]: #735
+#736 := [monotonicity #710 #738]: #740
+#667 := [monotonicity #736]: #721
+#727 := [monotonicity #830 #667]: #703
+#697 := [trans #727 #723]: #729
+#705 := [monotonicity #697]: #698
+#709 := [trans #705 #708]: #698
+#696 := [quant-inst #9 #10]: #694
+#719 := [mp #696 #709]: #663
+#948 := [unit-resolution #719 #911]: #741
+#693 := (not #741)
+#662 := (or #693 #832 #739)
+#664 := [def-axiom]: #662
+#950 := [unit-resolution #664 #948]: #949
+#951 := [unit-resolution #950 #480]: #739
+#683 := (not #739)
+#684 := (or #683 #778 #745)
+#685 := [def-axiom]: #684
+#952 := [unit-resolution #685 #951 #488]: #745
+#688 := (not #745)
+#953 := (or #688 #675)
+#954 := [th-lemma arith triangle-eq]: #953
+#955 := [unit-resolution #954 #952]: #675
+#761 := (>= #845 0::Int)
+#519 := (or #771 #761)
+#520 := [th-lemma arith triangle-eq]: #519
+#956 := [unit-resolution #520 #470]: #761
+#676 := (>= #750 0::Int)
+#957 := (or #688 #676)
+#958 := [th-lemma arith triangle-eq]: #957
+#959 := [unit-resolution #958 #952]: #676
+#916 := (not #781)
+#917 := (not #675)
+#523 := (not #761)
+#924 := (not #676)
+#944 := (or #943 #924 #523 #917 #916)
+#493 := (f4 #481)
+#937 := (= #493 #89)
+#495 := (= #89 #493)
+#478 := (or #541 #495)
+#482 := [quant-inst #89]: #478
+#466 := [unit-resolution #482 #884]: #495
+#938 := [symm #466]: #937
+#939 := (= f3 #493)
+#935 := (= #463 #493)
+#933 := (= #9 #481)
+#467 := [hypothesis]: #554
+#475 := (= #9 #86)
+#476 := (* -1::Int #86)
+#472 := (+ #9 #476)
+#464 := (>= #472 0::Int)
+#465 := [hypothesis]: #781
+#621 := (* -3::Int #844)
+#624 := (+ #749 #621)
+#625 := (+ #9 #624)
+#627 := (>= #625 0::Int)
+#620 := (= #625 0::Int)
+#1 := true
+#80 := [true-axiom]: true
+#598 := (or false #620)
+#583 := [th-lemma arith]: #598
+#584 := [unit-resolution #583 #80]: #620
+#506 := (not #620)
+#468 := (or #506 #627)
+#912 := [th-lemma arith triangle-eq]: #468
+#913 := [unit-resolution #912 #584]: #627
+#914 := [hypothesis]: #675
+#915 := (not #627)
+#918 := (or #464 #915 #916 #917)
+#919 := [th-lemma arith assign-bounds -1 3 1]: #918
+#920 := [unit-resolution #919 #914 #913 #465]: #464
+#477 := (<= #472 0::Int)
+#921 := [hypothesis]: #761
+#626 := (<= #625 0::Int)
+#508 := (or #506 #626)
+#509 := [th-lemma arith triangle-eq]: #508
+#922 := [unit-resolution #509 #584]: #626
+#923 := [hypothesis]: #676
+#522 := (not #626)
+#925 := (or #477 #522 #523 #924)
+#926 := [th-lemma arith assign-bounds -1 3 1]: #925
+#927 := [unit-resolution #926 #923 #922 #921]: #477
+#929 := (not #464)
+#928 := (not #477)
+#930 := (or #475 #928 #929)
+#931 := [th-lemma arith triangle-eq]: #930
+#932 := [unit-resolution #931 #927 #920]: #475
+#934 := [trans #932 #467]: #933
+#936 := [monotonicity #934]: #935
+#940 := [trans #557 #936]: #939
+#941 := [trans #940 #938]: #92
+#95 := (not #92)
+#12 := (* #11 3::Int)
+#14 := (+ #12 #13)
+#15 := (f4 #14)
+#16 := (= f3 #15)
+#17 := (not #16)
+#96 := (iff #17 #95)
+#93 := (iff #16 #92)
+#90 := (= #15 #89)
+#87 := (= #14 #86)
+#84 := (= #12 #83)
#85 := [rewrite]: #84
#88 := [monotonicity #85]: #87
-#126 := [monotonicity #88 #112 #123]: #125
-#129 := [monotonicity #126]: #128
-#135 := [trans #129 #133]: #134
-#74 := (iff #13 false)
-#75 := [rewrite]: #74
-#138 := [monotonicity #75 #135]: #137
-#142 := [trans #138 #140]: #141
-#109 := (= #27 #101)
-#104 := (* #101 1::Int)
-#107 := (= #104 #101)
-#108 := [rewrite]: #107
-#105 := (= #27 #104)
-#102 := (= #26 #101)
-#99 := (= #25 #98)
-#96 := (= #24 #95)
-#97 := [monotonicity #92 #94]: #96
-#100 := [monotonicity #88 #97]: #99
-#81 := (iff #14 #11)
-#76 := (or #11 false)
-#79 := (iff #76 #11)
-#80 := [rewrite]: #79
-#77 := (iff #14 #76)
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#103 := [monotonicity #82 #100]: #102
-#106 := [monotonicity #103]: #105
-#110 := [trans #106 #108]: #109
-#145 := [monotonicity #110 #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#212 := [trans #154 #210]: #211
-#73 := [asserted]: #37
-#213 := [mp #73 #212]: #208
-#604 := [unit-resolution #213 #719]: false
-#615 := [lemma #604]: #622
-#528 := [unit-resolution #615 #635 #660]: #567
-#449 := (or #11 #457)
-#781 := [def-axiom]: #449
-#639 := [unit-resolution #781 #528]: #457
-#373 := (= #21 #182)
-#471 := (f5 #426)
-#749 := (= #471 0::Int)
-#649 := (not #749)
-#645 := (iff #567 #649)
-#647 := (iff #11 #749)
-#643 := (iff #749 #11)
-#646 := (= #471 #9)
-#640 := (= #426 f3)
-#641 := [symm #570]: #640
-#642 := [monotonicity #641]: #646
-#644 := [monotonicity #642]: #643
-#648 := [symm #644]: #647
-#650 := [monotonicity #648]: #645
-#630 := [mp #528 #650]: #649
-#739 := (or #168 #749)
-#43 := (:var 0 Int)
-#45 := (f4 #43)
-#794 := (pattern #45)
-#239 := (>= #43 0::Int)
-#46 := (f5 #45)
-#51 := (= #46 0::Int)
-#288 := (or #51 #239)
-#801 := (forall (vars (?v0 Int)) (:pat #794) #288)
-#293 := (forall (vars (?v0 Int)) #288)
-#804 := (iff #293 #801)
-#802 := (iff #288 #288)
-#803 := [refl]: #802
-#805 := [quant-intro #803]: #804
-#306 := (~ #293 #293)
-#314 := (~ #288 #288)
-#315 := [refl]: #314
-#307 := [nnf-pos #315]: #306
-#50 := (< #43 0::Int)
-#52 := (implies #50 #51)
-#53 := (forall (vars (?v0 Int)) #52)
-#296 := (iff #53 #293)
-#259 := (= 0::Int #46)
-#265 := (not #50)
-#266 := (or #265 #259)
-#271 := (forall (vars (?v0 Int)) #266)
-#294 := (iff #271 #293)
-#291 := (iff #266 #288)
-#285 := (or #239 #51)
-#289 := (iff #285 #288)
-#290 := [rewrite]: #289
-#286 := (iff #266 #285)
-#283 := (iff #259 #51)
-#284 := [rewrite]: #283
-#281 := (iff #265 #239)
-#241 := (not #239)
-#276 := (not #241)
-#279 := (iff #276 #239)
-#280 := [rewrite]: #279
-#277 := (iff #265 #276)
-#274 := (iff #50 #241)
-#275 := [rewrite]: #274
-#278 := [monotonicity #275]: #277
-#282 := [trans #278 #280]: #281
-#287 := [monotonicity #282 #284]: #286
-#292 := [trans #287 #290]: #291
-#295 := [quant-intro #292]: #294
-#272 := (iff #53 #271)
-#269 := (iff #52 #266)
-#262 := (implies #50 #259)
-#267 := (iff #262 #266)
-#268 := [rewrite]: #267
-#263 := (iff #52 #262)
-#260 := (iff #51 #259)
-#261 := [rewrite]: #260
-#264 := [monotonicity #261]: #263
-#270 := [trans #264 #268]: #269
-#273 := [quant-intro #270]: #272
-#297 := [trans #273 #295]: #296
-#258 := [asserted]: #53
-#298 := [mp #258 #297]: #293
-#316 := [mp~ #298 #307]: #293
-#806 := [mp #316 #805]: #801
-#750 := (not #801)
-#740 := (or #750 #168 #749)
-#738 := (or #749 #168)
-#746 := (or #750 #738)
-#734 := (iff #746 #740)
-#588 := (or #750 #739)
-#732 := (iff #588 #740)
-#733 := [rewrite]: #732
-#589 := (iff #746 #588)
-#744 := (iff #738 #739)
-#745 := [rewrite]: #744
-#731 := [monotonicity #745]: #589
-#728 := [trans #731 #733]: #734
-#587 := [quant-inst #9]: #746
-#729 := [mp #587 #728]: #740
-#576 := [unit-resolution #729 #806]: #739
-#631 := [unit-resolution #576 #630]: #168
-#436 := (or #776 #11 #156 #169)
-#777 := [def-axiom]: #436
-#612 := [unit-resolution #777 #631 #528 #656]: #156
-#459 := (or #179 #155)
-#450 := [def-axiom]: #459
-#636 := [unit-resolution #450 #612]: #179
-#463 := (not #179)
-#443 := (or #463 #373)
-#778 := [def-axiom]: #443
-#637 := [unit-resolution #778 #636]: #373
-#632 := [trans #637 #639]: #672
-#638 := (not #672)
-#606 := (or #638 #662)
-#613 := [th-lemma arith triangle-eq]: #606
-#572 := [unit-resolution #613 #632]: #662
-#664 := (>= #661 0::Int)
-#603 := (or #638 #664)
-#605 := [th-lemma arith triangle-eq]: #603
-#607 := [unit-resolution #605 #632]: #664
-#616 := [th-lemma arith eq-propagate 1 1 1 1 #607 #572 #653 #655]: #614
-#608 := [symm #616]: #628
-#617 := [th-lemma arith eq-propagate -1 -1 #635 #660]: #569
-#618 := [symm #617]: #723
-#629 := [trans #618 #608]: #610
-#584 := [monotonicity #629]: #718
-#585 := [symm #584]: #715
-#590 := [trans #570 #585]: #205
-#591 := [unit-resolution #213 #590]: false
-#592 := [lemma #591]: #776
-#435 := (or #191 #168)
-#440 := [def-axiom]: #435
-#533 := [unit-resolution #440 #592]: #168
-#785 := (or #191 #155)
-#775 := [def-axiom]: #785
-#534 := [unit-resolution #775 #592]: #155
-#784 := (or #191 #567)
-#779 := [def-axiom]: #784
-#538 := [unit-resolution #779 #592]: #567
-#531 := [th-lemma arith triangle-eq]: #191
-[unit-resolution #531 #538 #534 #533]: false
-unsat
-9915a65ab7888a474bcd2f001f0a80c1938cedba 411 0
-#2 := false
-decl f4 :: (-> Int S2)
-#93 := -3::Int
-decl f5 :: (-> S2 Int)
-decl f3 :: S2
-#8 := f3
-#9 := (f5 f3)
-#89 := -1::Int
-#90 := (* -1::Int #9)
-#113 := (mod #90 -3::Int)
-#119 := (* -1::Int #113)
-#12 := 3::Int
-#28 := (mod #9 3::Int)
-#10 := 0::Int
-#162 := (>= #9 0::Int)
-#163 := (not #162)
-#149 := (<= #9 0::Int)
-#150 := (not #149)
-#173 := (or #150 #163)
-#185 := (ite #173 #28 #119)
-#11 := (= #9 0::Int)
-#188 := (ite #11 0::Int #185)
-#96 := (div #90 -3::Int)
-#21 := (div #9 3::Int)
-#176 := (ite #173 #21 #96)
-#179 := (ite #11 0::Int #176)
-#182 := (* 3::Int #179)
-#191 := (+ #182 #188)
-#194 := (f4 #191)
-#197 := (= f3 #194)
-#413 := (f4 #9)
-#714 := (= #413 #194)
-#713 := (= #194 #413)
-#618 := (= #191 #9)
-#579 := (= #9 #191)
-#693 := (* -1::Int #28)
-#699 := (* -3::Int #21)
-#700 := (+ #699 #693)
-#684 := (+ #9 #700)
-#688 := (<= #684 0::Int)
-#698 := (= #684 0::Int)
-#1 := true
-#71 := [true-axiom]: true
-#630 := (or false #698)
-#625 := [th-lemma arith]: #630
-#631 := [unit-resolution #625 #71]: #698
-#599 := (not #698)
-#606 := (or #599 #688)
-#565 := [th-lemma arith triangle-eq]: #606
-#596 := [unit-resolution #565 #631]: #688
-#689 := (>= #684 0::Int)
-#584 := (or #599 #689)
-#585 := [th-lemma arith triangle-eq]: #584
-#588 := [unit-resolution #585 #631]: #689
-#660 := (* -1::Int #179)
-#661 := (+ #21 #660)
-#656 := (<= #661 0::Int)
-#659 := (= #21 #179)
-#450 := (= #176 #179)
-#430 := (not #11)
-#616 := (= 0::Int #9)
-#716 := [hypothesis]: #11
-#617 := [symm #716]: #616
-#615 := (= #191 0::Int)
-#562 := (<= #188 0::Int)
-#774 := (= #188 0::Int)
-#433 := (or #430 #774)
-#769 := [def-axiom]: #433
-#718 := [unit-resolution #769 #716]: #774
-#719 := (not #774)
-#717 := (or #719 #562)
-#720 := [th-lemma arith triangle-eq]: #717
-#602 := [unit-resolution #720 #718]: #562
-#715 := (>= #188 0::Int)
-#603 := (or #719 #715)
-#604 := [th-lemma arith triangle-eq]: #603
-#563 := [unit-resolution #604 #718]: #715
-#559 := (<= #179 0::Int)
-#364 := (= #179 0::Int)
-#560 := (or #430 #364)
-#767 := [def-axiom]: #560
-#711 := [unit-resolution #767 #716]: #364
-#613 := (not #364)
-#708 := (or #613 #559)
-#709 := [th-lemma arith triangle-eq]: #708
-#712 := [unit-resolution #709 #711]: #559
-#561 := (>= #179 0::Int)
-#597 := (or #613 #561)
-#612 := [th-lemma arith triangle-eq]: #597
-#614 := [unit-resolution #612 #711]: #561
-#608 := [th-lemma arith eq-propagate -3 -3 -1 -1 #614 #712 #563 #602]: #615
-#619 := [trans #608 #617]: #618
-#710 := [monotonicity #619]: #713
-#701 := [symm #710]: #714
-#754 := (= f3 #413)
-#38 := (:var 0 S2)
-#39 := (f5 #38)
-#779 := (pattern #39)
-#40 := (f4 #39)
-#207 := (= #38 #40)
-#780 := (forall (vars (?v0 S2)) (:pat #779) #207)
-#210 := (forall (vars (?v0 S2)) #207)
-#781 := (iff #210 #780)
-#783 := (iff #780 #780)
-#784 := [rewrite]: #783
-#782 := [rewrite]: #781
-#785 := [trans #782 #784]: #781
-#304 := (~ #210 #210)
-#302 := (~ #207 #207)
-#303 := [refl]: #302
-#305 := [nnf-pos #303]: #304
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#211 := (iff #42 #210)
-#208 := (iff #41 #207)
-#209 := [rewrite]: #208
-#212 := [quant-intro #209]: #211
-#206 := [asserted]: #42
-#215 := [mp #206 #212]: #210
-#294 := [mp~ #215 #305]: #210
-#786 := [mp #294 #785]: #780
-#419 := (not #780)
-#420 := (or #419 #754)
-#756 := [quant-inst #8]: #420
-#620 := [unit-resolution #756 #786]: #754
-#703 := [trans #620 #701]: #197
-#200 := (not #197)
-#23 := (- 3::Int)
-#22 := (- #9)
-#29 := (mod #22 #23)
-#30 := (- #29)
-#16 := (< 0::Int 3::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#31 := (ite #20 #28 #30)
-#32 := (ite #11 0::Int #31)
-#13 := (= 3::Int 0::Int)
-#33 := (ite #13 #9 #32)
-#24 := (div #22 #23)
-#25 := (ite #20 #21 #24)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (* #26 3::Int)
-#34 := (+ #27 #33)
-#35 := (f4 #34)
-#36 := (= f3 #35)
-#37 := (not #36)
-#203 := (iff #37 #200)
-#83 := (and #16 #18)
-#86 := (or #17 #83)
-#124 := (ite #86 #28 #119)
-#127 := (ite #11 0::Int #124)
-#99 := (ite #86 #21 #96)
-#102 := (ite #11 0::Int #99)
-#108 := (* 3::Int #102)
-#137 := (+ #108 #127)
-#140 := (f4 #137)
-#143 := (= f3 #140)
-#146 := (not #143)
-#201 := (iff #146 #200)
-#198 := (iff #143 #197)
-#195 := (= #140 #194)
-#192 := (= #137 #191)
-#189 := (= #127 #188)
-#186 := (= #124 #185)
-#174 := (iff #86 #173)
-#171 := (iff #83 #163)
-#166 := (and true #163)
-#169 := (iff #166 #163)
-#170 := [rewrite]: #169
-#167 := (iff #83 #166)
-#164 := (iff #18 #163)
-#165 := [rewrite]: #164
-#153 := (iff #16 true)
-#154 := [rewrite]: #153
-#168 := [monotonicity #154 #165]: #167
-#172 := [trans #168 #170]: #171
-#160 := (iff #17 #150)
-#155 := (and #150 true)
-#158 := (iff #155 #150)
-#159 := [rewrite]: #158
-#156 := (iff #17 #155)
-#151 := (iff #15 #150)
-#152 := [rewrite]: #151
-#157 := [monotonicity #152 #154]: #156
-#161 := [trans #157 #159]: #160
-#175 := [monotonicity #161 #172]: #174
-#187 := [monotonicity #175]: #186
-#190 := [monotonicity #187]: #189
-#183 := (= #108 #182)
-#180 := (= #102 #179)
-#177 := (= #99 #176)
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#193 := [monotonicity #184 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#147 := (iff #37 #146)
-#144 := (iff #36 #143)
-#141 := (= #35 #140)
-#138 := (= #34 #137)
-#135 := (= #33 #127)
-#130 := (ite false #9 #127)
-#133 := (= #130 #127)
+#91 := [monotonicity #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#82 := [asserted]: #17
+#100 := [mp #82 #97]: #95
+#942 := [unit-resolution #100 #941]: false
+#945 := [lemma #942]: #944
+#960 := [unit-resolution #945 #959 #956 #955 #947]: #943
+#555 := (* -1::Int #481)
+#486 := (+ #86 #555)
+#487 := (<= #486 0::Int)
+#534 := (+ #13 #555)
+#869 := (+ #83 #534)
+#518 := (<= #869 0::Int)
+#871 := (= #869 0::Int)
+#549 := (>= #86 0::Int)
+#788 := (>= #11 0::Int)
+#600 := (>= #777 3::Int)
+#612 := (not #600)
+#585 := (or false #612)
+#587 := [th-lemma arith]: #585
+#586 := [unit-resolution #587 #80]: #612
+#588 := (not #788)
+#577 := [hypothesis]: #588
+#754 := (not #839)
+#578 := (or #754 #788)
+#579 := [th-lemma arith triangle-eq]: #578
+#571 := [unit-resolution #579 #577]: #754
+#581 := (or #755 #839)
+#756 := (or #753 #755 #839)
+#757 := [def-axiom]: #756
+#572 := [unit-resolution #757 #580]: #581
+#582 := [unit-resolution #572 #571]: #755
+#565 := [unit-resolution #564 #582]: #792
+#542 := (not #672)
+#543 := (iff #755 #542)
+#538 := (iff #832 #672)
+#566 := (= #463 f3)
+#567 := [symm #557]: #566
+#568 := [monotonicity #567]: #558
+#537 := [monotonicity #568]: #535
+#529 := [symm #537]: #538
+#544 := [monotonicity #529]: #543
+#545 := [mp #582 #544]: #542
+#536 := [unit-resolution #546 #545]: #559
+#532 := [unit-resolution #530 #582]: #661
+#533 := [unit-resolution #532 #536]: #828
+#512 := [unit-resolution #776 #533]: #806
+#514 := [unit-resolution #768 #512 #565]: #849
+#521 := [unit-resolution #520 #514]: #761
+#524 := (or #522 #700 #600 #788 #523)
+#513 := [th-lemma arith assign-bounds 1 1 3 -3]: #524
+#525 := [unit-resolution #513 #536 #521 #577 #586]: #522
+#507 := [unit-resolution #509 #525 #584]: false
+#510 := [lemma #507]: #788
+#720 := (>= #13 0::Int)
+#613 := (>= #777 0::Int)
+#961 := (or false #613)
+#962 := [th-lemma arith]: #961
+#963 := [unit-resolution #962 #80]: #613
+#964 := (not #613)
+#965 := (or #720 #964 #924)
+#966 := [th-lemma arith assign-bounds 1 1]: #965
+#967 := [unit-resolution #966 #959 #963]: #720
+#968 := (not #720)
+#969 := (or #549 #968 #588)
+#970 := [th-lemma arith assign-bounds 1 3]: #969
+#971 := [unit-resolution #970 #967 #510]: #549
+#550 := (not #549)
+#872 := (or #550 #871)
+#107 := (= #24 #27)
+#132 := (or #107 #126)
+#886 := (forall (vars (?v0 Int)) (:pat #885) #132)
+#137 := (forall (vars (?v0 Int)) #132)
+#889 := (iff #137 #886)
+#887 := (iff #132 #132)
+#888 := [refl]: #887
+#890 := [quant-intro #888]: #889
+#314 := (~ #137 #137)
+#313 := (~ #132 #132)
+#310 := [refl]: #313
+#315 := [nnf-pos #310]: #314
+#28 := (= #27 #24)
+#25 := (<= 0::Int #24)
+#29 := (implies #25 #28)
+#30 := (forall (vars (?v0 Int)) #29)
+#140 := (iff #30 #137)
+#114 := (not #25)
+#115 := (or #114 #107)
+#120 := (forall (vars (?v0 Int)) #115)
+#138 := (iff #120 #137)
+#135 := (iff #115 #132)
+#129 := (or #126 #107)
+#133 := (iff #129 #132)
#134 := [rewrite]: #133
-#131 := (= #33 #130)
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#122 := (= #30 #119)
-#116 := (- #113)
-#120 := (= #116 #119)
-#121 := [rewrite]: #120
-#117 := (= #30 #116)
-#114 := (= #29 #113)
-#94 := (= #23 -3::Int)
-#95 := [rewrite]: #94
-#91 := (= #22 #90)
-#92 := [rewrite]: #91
-#115 := [monotonicity #92 #95]: #114
-#118 := [monotonicity #115]: #117
-#123 := [trans #118 #121]: #122
-#87 := (iff #20 #86)
-#84 := (iff #19 #83)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#126 := [monotonicity #88 #123]: #125
-#129 := [monotonicity #126]: #128
-#74 := (iff #13 false)
-#75 := [rewrite]: #74
-#132 := [monotonicity #75 #129]: #131
-#136 := [trans #132 #134]: #135
-#111 := (= #27 #108)
-#105 := (* #102 3::Int)
-#109 := (= #105 #108)
+#130 := (iff #115 #129)
+#127 := (iff #114 #126)
+#123 := (iff #25 #125)
+#124 := [rewrite]: #123
+#128 := [monotonicity #124]: #127
+#131 := [monotonicity #128]: #130
+#136 := [trans #131 #134]: #135
+#139 := [quant-intro #136]: #138
+#121 := (iff #30 #120)
+#118 := (iff #29 #115)
+#111 := (implies #25 #107)
+#116 := (iff #111 #115)
+#117 := [rewrite]: #116
+#112 := (iff #29 #111)
+#109 := (iff #28 #107)
#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#103 := (= #26 #102)
-#100 := (= #25 #99)
-#97 := (= #24 #96)
-#98 := [monotonicity #92 #95]: #97
-#101 := [monotonicity #88 #98]: #100
-#81 := (iff #14 #11)
-#76 := (or #11 false)
-#79 := (iff #76 #11)
-#80 := [rewrite]: #79
-#77 := (iff #14 #76)
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#104 := [monotonicity #82 #101]: #103
-#107 := [monotonicity #104]: #106
-#112 := [trans #107 #110]: #111
-#139 := [monotonicity #112 #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#204 := [trans #148 #202]: #203
-#73 := [asserted]: #37
-#205 := [mp #73 #204]: #200
-#695 := [unit-resolution #205 #703]: false
-#692 := [lemma #695]: #430
-#441 := (or #11 #450)
-#442 := [def-axiom]: #441
-#598 := [unit-resolution #442 #692]: #450
-#365 := (= #21 #176)
-#737 := (f5 #413)
-#738 := (= #737 0::Int)
-#632 := (not #738)
-#633 := (iff #430 #632)
-#628 := (iff #11 #738)
-#626 := (iff #738 #11)
-#647 := (= #737 #9)
-#651 := (= #413 f3)
-#652 := [symm #620]: #651
-#653 := [monotonicity #652]: #647
-#627 := [monotonicity #653]: #626
-#521 := [symm #627]: #628
-#634 := [monotonicity #521]: #633
-#639 := [mp #692 #634]: #632
-#739 := (or #162 #738)
-#43 := (:var 0 Int)
-#45 := (f4 #43)
-#787 := (pattern #45)
-#231 := (>= #43 0::Int)
-#46 := (f5 #45)
-#51 := (= #46 0::Int)
-#280 := (or #51 #231)
-#794 := (forall (vars (?v0 Int)) (:pat #787) #280)
-#285 := (forall (vars (?v0 Int)) #280)
-#797 := (iff #285 #794)
-#795 := (iff #280 #280)
-#796 := [refl]: #795
-#798 := [quant-intro #796]: #797
-#298 := (~ #285 #285)
-#306 := (~ #280 #280)
-#307 := [refl]: #306
-#299 := [nnf-pos #307]: #298
-#50 := (< #43 0::Int)
-#52 := (implies #50 #51)
-#53 := (forall (vars (?v0 Int)) #52)
-#288 := (iff #53 #285)
-#251 := (= 0::Int #46)
-#257 := (not #50)
-#258 := (or #257 #251)
-#263 := (forall (vars (?v0 Int)) #258)
-#286 := (iff #263 #285)
-#283 := (iff #258 #280)
-#277 := (or #231 #51)
-#281 := (iff #277 #280)
-#282 := [rewrite]: #281
-#278 := (iff #258 #277)
-#275 := (iff #251 #51)
-#276 := [rewrite]: #275
-#273 := (iff #257 #231)
-#233 := (not #231)
-#268 := (not #233)
-#271 := (iff #268 #231)
-#272 := [rewrite]: #271
-#269 := (iff #257 #268)
-#266 := (iff #50 #233)
-#267 := [rewrite]: #266
-#270 := [monotonicity #267]: #269
-#274 := [trans #270 #272]: #273
-#279 := [monotonicity #274 #276]: #278
-#284 := [trans #279 #282]: #283
-#287 := [quant-intro #284]: #286
-#264 := (iff #53 #263)
-#261 := (iff #52 #258)
-#254 := (implies #50 #251)
-#259 := (iff #254 #258)
-#260 := [rewrite]: #259
-#255 := (iff #52 #254)
-#252 := (iff #51 #251)
-#253 := [rewrite]: #252
-#256 := [monotonicity #253]: #255
-#262 := [trans #256 #260]: #261
-#265 := [quant-intro #262]: #264
-#289 := [trans #265 #287]: #288
-#250 := [asserted]: #53
-#290 := [mp #250 #289]: #285
-#308 := [mp~ #290 #299]: #285
-#799 := [mp #308 #798]: #794
-#463 := (not #794)
-#582 := (or #463 #162 #738)
-#733 := (or #738 #162)
-#724 := (or #463 #733)
-#729 := (iff #724 #582)
-#726 := (or #463 #739)
-#722 := (iff #726 #582)
-#728 := [rewrite]: #722
-#727 := (iff #724 #726)
-#580 := (iff #733 #739)
-#581 := [rewrite]: #580
-#721 := [monotonicity #581]: #727
-#723 := [trans #721 #728]: #729
-#725 := [quant-inst #9]: #724
-#730 := [mp #725 #723]: #582
-#635 := [unit-resolution #730 #799]: #739
-#636 := [unit-resolution #635 #639]: #162
-#637 := (or #11 #150 #163)
-#640 := [th-lemma arith triangle-eq]: #637
-#641 := [unit-resolution #640 #692]: #173
-#642 := [unit-resolution #641 #636]: #150
-#452 := (or #173 #149)
-#443 := [def-axiom]: #452
-#638 := [unit-resolution #443 #642]: #173
-#383 := (not #173)
-#457 := (or #383 #365)
-#436 := [def-axiom]: #457
-#600 := [unit-resolution #436 #638]: #365
-#607 := [trans #600 #598]: #659
-#609 := (not #659)
-#610 := (or #609 #656)
-#611 := [th-lemma arith triangle-eq]: #610
-#621 := [unit-resolution #611 #607]: #656
-#662 := (>= #661 0::Int)
-#589 := (or #609 #662)
-#590 := [th-lemma arith triangle-eq]: #589
-#591 := [unit-resolution #590 #607]: #662
-#644 := (* -1::Int #188)
-#645 := (+ #28 #644)
-#646 := (<= #645 0::Int)
-#648 := (= #28 #188)
-#775 := (= #185 #188)
-#429 := (or #11 #775)
-#770 := [def-axiom]: #429
-#650 := [unit-resolution #770 #692]: #775
-#776 := (= #28 #185)
-#772 := (or #383 #776)
-#778 := [def-axiom]: #772
-#643 := [unit-resolution #778 #638]: #776
-#623 := [trans #643 #650]: #648
-#569 := (not #648)
-#624 := (or #569 #646)
-#605 := [th-lemma arith triangle-eq]: #624
-#629 := [unit-resolution #605 #623]: #646
-#649 := (>= #645 0::Int)
-#592 := (or #569 #649)
-#593 := [th-lemma arith triangle-eq]: #592
-#594 := [unit-resolution #593 #623]: #649
-#595 := [th-lemma arith eq-propagate 1 1 3 3 1 1 #594 #629 #591 #621 #588 #596]: #579
-#556 := [symm #595]: #618
-#557 := [monotonicity #556]: #713
-#564 := [symm #557]: #714
-#566 := [trans #620 #564]: #197
-[unit-resolution #205 #566]: false
+#113 := [monotonicity #110]: #112
+#119 := [trans #113 #117]: #118
+#122 := [quant-intro #119]: #121
+#141 := [trans #122 #139]: #140
+#106 := [asserted]: #30
+#142 := [mp #106 #141]: #137
+#311 := [mp~ #142 #315]: #137
+#891 := [mp #311 #890]: #886
+#876 := (not #886)
+#866 := (or #876 #550 #871)
+#551 := (or #554 #550)
+#526 := (or #876 #551)
+#515 := (iff #526 #866)
+#867 := (or #876 #872)
+#511 := (iff #867 #866)
+#852 := [rewrite]: #511
+#527 := (iff #526 #867)
+#875 := (iff #551 #872)
+#865 := (or #871 #550)
+#873 := (iff #865 #872)
+#874 := [rewrite]: #873
+#539 := (iff #551 #865)
+#528 := (iff #554 #871)
+#658 := [rewrite]: #528
+#540 := [monotonicity #658]: #539
+#870 := [trans #540 #874]: #875
+#868 := [monotonicity #870]: #527
+#516 := [trans #868 #852]: #515
+#531 := [quant-inst #86]: #526
+#517 := [mp #531 #516]: #866
+#972 := [unit-resolution #517 #891]: #872
+#973 := [unit-resolution #972 #971]: #871
+#974 := (not #871)
+#975 := (or #974 #518)
+#976 := [th-lemma arith triangle-eq]: #975
+#977 := [unit-resolution #976 #973]: #518
+#978 := (not #518)
+#979 := (or #487 #978)
+#980 := [th-lemma arith assign-bounds -1]: #979
+#981 := [unit-resolution #980 #977]: #487
+#474 := (>= #486 0::Int)
+#854 := (>= #869 0::Int)
+#982 := (or #974 #854)
+#983 := [th-lemma arith triangle-eq]: #982
+#984 := [unit-resolution #983 #973]: #854
+#985 := (not #854)
+#986 := (or #474 #985)
+#987 := [th-lemma arith assign-bounds -1]: #986
+#988 := [unit-resolution #987 #984]: #474
+#990 := (not #474)
+#989 := (not #487)
+#991 := (or #554 #989 #990)
+#992 := [th-lemma arith triangle-eq]: #991
+#993 := [unit-resolution #992 #988 #981 #960]: false
+#994 := [lemma #993]: #832
+#1024 := [symm #994]: #1023
+#1025 := (= #86 0::Int)
+#855 := (= #481 0::Int)
+#575 := (>= #481 0::Int)
+#479 := (or #755 #724)
+#654 := (or #693 #755 #724)
+#655 := [def-axiom]: #654
+#484 := [unit-resolution #655 #948]: #479
+#485 := [unit-resolution #484 #994]: #724
+#665 := (not #724)
+#490 := (or #665 #720)
+#492 := [th-lemma arith triangle-eq]: #490
+#995 := [unit-resolution #492 #485]: #720
+#996 := [unit-resolution #970 #995 #510]: #549
+#997 := [unit-resolution #972 #996]: #871
+#998 := [unit-resolution #976 #997]: #518
+#999 := (or #575 #968 #978 #588)
+#1000 := [th-lemma arith assign-bounds 1 1 3]: #999
+#1001 := [unit-resolution #1000 #998 #510 #995]: #575
+#574 := (<= #481 0::Int)
+#699 := (<= #13 0::Int)
+#1002 := (or #665 #699)
+#1003 := [th-lemma arith triangle-eq]: #1002
+#1004 := [unit-resolution #1003 #485]: #699
+#787 := (<= #11 0::Int)
+#1005 := [unit-resolution #572 #994]: #839
+#1006 := (or #754 #787)
+#1007 := [th-lemma arith triangle-eq]: #1006
+#1008 := [unit-resolution #1007 #1005]: #787
+#1009 := [unit-resolution #983 #997]: #854
+#1011 := (not #787)
+#1010 := (not #699)
+#1012 := (or #574 #1010 #985 #1011)
+#1013 := [th-lemma arith assign-bounds -1 1 -3]: #1012
+#1014 := [unit-resolution #1013 #1009 #1008 #1004]: #574
+#1016 := (not #575)
+#1015 := (not #574)
+#1017 := (or #855 #1015 #1016)
+#1018 := [th-lemma arith triangle-eq]: #1017
+#1019 := [unit-resolution #1018 #1014 #1001]: #855
+#1020 := [unit-resolution #980 #998]: #487
+#1021 := [unit-resolution #987 #1009]: #474
+#1022 := [unit-resolution #992 #1021 #1020]: #554
+#1026 := [trans #1022 #1019]: #1025
+#1028 := [trans #1026 #1024]: #1027
+#1030 := [monotonicity #1028]: #1029
+#1032 := [symm #1030]: #1031
+#1033 := [trans #557 #1032]: #92
+[unit-resolution #100 #1033]: false
unsat
34a7ceb02d535a80474ebf3499258caaaf0b3c6d 74 0
#2 := false
@@ -21415,6734 +26439,16909 @@
#33 := [asserted]: #13
[mp #33 #49]: false
unsat
-c3a19f1e9eadfa9e1e60ed3204d9afca1d3962d0 64 0
-#2 := false
+9ce15ee2c485c15c28a4c003e8c335d04c1523a1 254 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#13 := (:var 0 Int)
+#12 := (:var 1 Int)
+#14 := (f3 #12 #13)
+#749 := (pattern #14)
#8 := 0::Int
-#15 := (- 0::Int)
-#16 := (div #15 #15)
-#14 := (div 0::Int 0::Int)
-#11 := (< 0::Int 0::Int)
-#12 := (and #11 #11)
-#13 := (or #12 #12)
-#17 := (ite #13 #14 #16)
-#9 := (= 0::Int 0::Int)
-#10 := (or #9 #9)
-#18 := (ite #10 0::Int #17)
-#19 := (= #18 0::Int)
-#20 := (not #19)
-#85 := (iff #20 false)
-#1 := true
-#80 := (not true)
-#83 := (iff #80 false)
-#84 := [rewrite]: #83
-#81 := (iff #20 #80)
-#78 := (iff #19 true)
-#41 := (iff #9 true)
-#42 := [rewrite]: #41
-#76 := (iff #19 #9)
-#70 := (ite true 0::Int #14)
-#73 := (= #70 0::Int)
+#87 := -1::Int
+#91 := (* -1::Int #13)
+#88 := (* -1::Int #12)
+#94 := (div #88 #91)
+#251 := (* -1::Int #94)
+#252 := (+ #14 #251)
+#253 := (= #252 0::Int)
+#24 := (div #12 #13)
+#248 := (* -1::Int #24)
+#249 := (+ #14 #248)
+#250 := (= #249 0::Int)
+#126 := (>= #12 0::Int)
+#119 := (<= #13 0::Int)
+#211 := (or #119 #126)
+#212 := (not #211)
+#115 := (<= #12 0::Int)
+#209 := (or #115 #119)
+#210 := (not #209)
+#215 := (or #210 #212)
+#254 := (ite #215 #250 #253)
+#247 := (= #14 0::Int)
+#16 := (= #13 0::Int)
+#15 := (= #12 0::Int)
+#17 := (or #15 #16)
+#255 := (ite #17 #247 #254)
+#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #255)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#753 := (iff #258 #750)
+#751 := (iff #255 #255)
+#752 := [refl]: #751
+#754 := [quant-intro #752]: #753
+#218 := (ite #215 #24 #94)
+#221 := (ite #17 0::Int #218)
+#224 := (= #14 #221)
+#227 := (forall (vars (?v0 Int) (?v1 Int)) #224)
+#259 := (iff #227 #258)
+#256 := (iff #224 #255)
+#257 := [rewrite]: #256
+#260 := [quant-intro #257]: #259
+#127 := (not #126)
+#120 := (not #119)
+#130 := (and #120 #127)
+#116 := (not #115)
+#123 := (and #116 #120)
+#133 := (or #123 #130)
+#136 := (ite #133 #24 #94)
+#139 := (ite #17 0::Int #136)
+#142 := (= #14 #139)
+#145 := (forall (vars (?v0 Int) (?v1 Int)) #142)
+#228 := (iff #145 #227)
+#225 := (iff #142 #224)
+#222 := (= #139 #221)
+#219 := (= #136 #218)
+#216 := (iff #133 #215)
+#213 := (iff #130 #212)
+#214 := [rewrite]: #213
+#203 := (iff #123 #210)
+#204 := [rewrite]: #203
+#217 := [monotonicity #204 #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [quant-intro #226]: #228
+#207 := (~ #145 #145)
+#205 := (~ #142 #142)
+#206 := [refl]: #205
+#208 := [nnf-pos #206]: #207
+#26 := (- #13)
+#25 := (- #12)
+#27 := (div #25 #26)
+#19 := (< 0::Int #13)
+#21 := (< #12 0::Int)
+#22 := (and #21 #19)
+#18 := (< 0::Int #12)
+#20 := (and #18 #19)
+#23 := (or #20 #22)
+#28 := (ite #23 #24 #27)
+#29 := (ite #17 0::Int #28)
+#30 := (= #14 #29)
+#31 := (forall (vars (?v0 Int) (?v1 Int)) #30)
+#148 := (iff #31 #145)
+#81 := (and #19 #21)
+#84 := (or #20 #81)
+#97 := (ite #84 #24 #94)
+#75 := (= 0::Int #13)
+#72 := (= 0::Int #12)
+#78 := (or #72 #75)
+#100 := (ite #78 0::Int #97)
+#103 := (= #14 #100)
+#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
+#146 := (iff #106 #145)
+#143 := (iff #103 #142)
+#140 := (= #100 #139)
+#137 := (= #97 #136)
+#134 := (iff #84 #133)
+#131 := (iff #81 #130)
+#128 := (iff #21 #127)
+#129 := [rewrite]: #128
+#121 := (iff #19 #120)
+#122 := [rewrite]: #121
+#132 := [monotonicity #122 #129]: #131
+#124 := (iff #20 #123)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#125 := [monotonicity #118 #122]: #124
+#135 := [monotonicity #125 #132]: #134
+#138 := [monotonicity #135]: #137
+#113 := (iff #78 #17)
+#111 := (iff #75 #16)
+#112 := [rewrite]: #111
+#109 := (iff #72 #15)
+#110 := [rewrite]: #109
+#114 := [monotonicity #110 #112]: #113
+#141 := [monotonicity #114 #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [quant-intro #144]: #146
+#107 := (iff #31 #106)
+#104 := (iff #30 #103)
+#101 := (= #29 #100)
+#98 := (= #28 #97)
+#95 := (= #27 #94)
+#92 := (= #26 #91)
+#93 := [rewrite]: #92
+#89 := (= #25 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90 #93]: #95
+#85 := (iff #23 #84)
+#82 := (iff #22 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#99 := [monotonicity #86 #96]: #98
+#79 := (iff #17 #78)
+#76 := (iff #16 #75)
+#77 := [rewrite]: #76
+#73 := (iff #15 #72)
#74 := [rewrite]: #73
-#71 := (= #18 #70)
-#68 := (= #17 #14)
-#63 := (ite #11 #14 #14)
-#66 := (= #63 #14)
-#67 := [rewrite]: #66
-#64 := (= #17 #63)
-#61 := (= #16 #14)
-#59 := (= #15 0::Int)
-#60 := [rewrite]: #59
-#62 := [monotonicity #60 #60]: #61
-#57 := (iff #13 #11)
-#52 := (or #11 #11)
-#55 := (iff #52 #11)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#50 := (iff #12 #11)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51 #51]: #53
-#58 := [trans #54 #56]: #57
-#65 := [monotonicity #58 #62]: #64
-#69 := [trans #65 #67]: #68
-#48 := (iff #10 true)
-#43 := (or true true)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #10 #43)
-#45 := [monotonicity #42 #42]: #44
-#49 := [trans #45 #47]: #48
-#72 := [monotonicity #49 #69]: #71
-#75 := [trans #72 #74]: #19
-#77 := [monotonicity #75]: #76
-#79 := [trans #77 #42]: #78
-#82 := [monotonicity #79]: #81
-#86 := [trans #82 #84]: #85
-#40 := [asserted]: #20
-[mp #40 #86]: false
-unsat
-c39d13f4d2f865f3613c6b94cb5e51281b48ea9a 69 0
-#2 := false
-#9 := 0::Int
-#21 := (- 0::Int)
-decl f3 :: Int
-#8 := f3
-#20 := (- f3)
-#22 := (div #20 #21)
-#19 := (div f3 0::Int)
-#14 := (< 0::Int 0::Int)
-#16 := (< f3 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int f3)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#23 := (ite #18 #19 #22)
-#11 := (= 0::Int 0::Int)
-#10 := (= f3 0::Int)
-#12 := (or #10 #11)
-#24 := (ite #12 0::Int #23)
-#25 := (= #24 0::Int)
-#26 := (not #25)
-#89 := (iff #26 false)
-#1 := true
-#84 := (not true)
-#87 := (iff #84 false)
-#88 := [rewrite]: #87
-#85 := (iff #26 #84)
-#82 := (iff #25 true)
-#47 := (iff #11 true)
-#48 := [rewrite]: #47
-#80 := (iff #25 #11)
-#62 := -1::Int
-#63 := (* -1::Int f3)
-#68 := (div #63 0::Int)
-#56 := (and #14 #16)
-#59 := (or #15 #56)
-#71 := (ite #59 #19 #68)
-#74 := (ite true 0::Int #71)
-#77 := (= #74 0::Int)
-#78 := [rewrite]: #77
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#69 := (= #22 #68)
-#66 := (= #21 0::Int)
-#67 := [rewrite]: #66
-#64 := (= #20 #63)
-#65 := [rewrite]: #64
-#70 := [monotonicity #65 #67]: #69
-#60 := (iff #18 #59)
-#57 := (iff #17 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#73 := [monotonicity #61 #70]: #72
-#54 := (iff #12 true)
-#49 := (or #10 true)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #12 #49)
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#76 := [monotonicity #55 #73]: #75
-#79 := [trans #76 #78]: #25
-#81 := [monotonicity #79]: #80
-#83 := [trans #81 #48]: #82
-#86 := [monotonicity #83]: #85
-#90 := [trans #86 #88]: #89
-#46 := [asserted]: #26
-[mp #46 #90]: false
-unsat
-bea53353954aa4070bfc4dfeef54e3441dcd8b82 73 0
-#2 := false
-#8 := 0::Int
-#10 := 1::Int
-#19 := (- 1::Int)
-#18 := (- 0::Int)
-#20 := (div #18 #19)
-#17 := (div 0::Int 1::Int)
-#14 := (< 0::Int 1::Int)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#21 := (ite #16 #17 #20)
-#11 := (= 1::Int 0::Int)
-#9 := (= 0::Int 0::Int)
-#12 := (or #9 #11)
-#22 := (ite #12 0::Int #21)
-#23 := (= #22 0::Int)
-#24 := (not #23)
-#94 := (iff #24 false)
-#1 := true
-#89 := (not true)
-#92 := (iff #89 false)
-#93 := [rewrite]: #92
-#90 := (iff #24 #89)
-#87 := (iff #23 true)
-#45 := (iff #9 true)
-#46 := [rewrite]: #45
-#85 := (iff #23 #9)
-#79 := (ite true 0::Int 0::Int)
-#82 := (= #79 0::Int)
-#83 := [rewrite]: #82
-#80 := (= #22 #79)
-#77 := (= #21 0::Int)
-#72 := (ite #15 0::Int 0::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #21 #72)
-#70 := (= #20 0::Int)
-#62 := -1::Int
-#65 := (div 0::Int -1::Int)
-#68 := (= #65 0::Int)
-#69 := [rewrite]: #68
-#66 := (= #20 #65)
-#63 := (= #19 -1::Int)
-#64 := [rewrite]: #63
-#60 := (= #18 0::Int)
-#61 := [rewrite]: #60
-#67 := [monotonicity #61 #64]: #66
-#71 := [trans #67 #69]: #70
-#58 := (= #17 0::Int)
-#59 := [rewrite]: #58
-#56 := (iff #16 #15)
-#57 := [rewrite]: #56
-#74 := [monotonicity #57 #59 #71]: #73
-#78 := [trans #74 #76]: #77
-#54 := (iff #12 true)
-#49 := (or true false)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #12 #49)
-#47 := (iff #11 false)
-#48 := [rewrite]: #47
-#51 := [monotonicity #46 #48]: #50
-#55 := [trans #51 #53]: #54
-#81 := [monotonicity #55 #78]: #80
-#84 := [trans #81 #83]: #23
-#86 := [monotonicity #84]: #85
-#88 := [trans #86 #46]: #87
-#91 := [monotonicity #88]: #90
-#95 := [trans #91 #93]: #94
-#44 := [asserted]: #24
-[mp #44 #95]: false
-unsat
-9f6a38ce629880be5bf8c7f73c6606884657520c 77 0
-#2 := false
-#8 := 1::Int
-#18 := (- 1::Int)
-#19 := (div #18 #18)
-#17 := (div 1::Int 1::Int)
+#80 := [monotonicity #74 #77]: #79
+#102 := [monotonicity #80 #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [quant-intro #105]: #107
+#149 := [trans #108 #147]: #148
+#71 := [asserted]: #31
+#150 := [mp #71 #149]: #145
+#199 := [mp~ #150 #208]: #145
+#230 := [mp #199 #229]: #227
+#261 := [mp #230 #260]: #258
+#755 := [mp #261 #754]: #750
+#9 := (f3 0::Int 0::Int)
+#10 := (= #9 0::Int)
+#11 := (not #10)
+#60 := [asserted]: #11
+#707 := (not #750)
+#708 := (or #707 #10)
+#335 := (* -1::Int 0::Int)
+#420 := (div #335 #335)
+#421 := (* -1::Int #420)
+#422 := (+ #9 #421)
+#413 := (= #422 0::Int)
+#424 := (div 0::Int 0::Int)
+#425 := (* -1::Int #424)
+#353 := (+ #9 #425)
+#426 := (= #353 0::Int)
+#423 := (>= 0::Int 0::Int)
+#427 := (<= 0::Int 0::Int)
+#406 := (or #427 #423)
+#741 := (not #406)
+#743 := (or #427 #427)
+#400 := (not #743)
+#530 := (or #400 #741)
+#737 := (ite #530 #426 #413)
+#411 := (= 0::Int 0::Int)
+#412 := (or #411 #411)
+#744 := (ite #412 #10 #737)
+#703 := (or #707 #744)
+#550 := (iff #703 #708)
+#552 := (iff #708 #708)
+#694 := [rewrite]: #552
+#701 := (iff #744 #10)
+#1 := true
+#711 := (ite true #10 #426)
+#705 := (iff #711 #10)
+#706 := [rewrite]: #705
+#715 := (iff #744 #711)
+#710 := (iff #737 #426)
+#433 := (ite false #426 #426)
+#713 := (iff #433 #426)
+#428 := [rewrite]: #713
+#434 := (iff #737 #433)
+#431 := (iff #413 #426)
+#717 := (= #422 #353)
+#716 := (= #421 #425)
+#441 := (= #420 #424)
+#718 := (= #335 0::Int)
+#719 := [rewrite]: #718
+#442 := [monotonicity #719 #719]: #441
+#720 := [monotonicity #442]: #716
+#721 := [monotonicity #720]: #717
+#432 := [monotonicity #721]: #431
+#448 := (iff #530 false)
+#722 := (or false false)
+#446 := (iff #722 false)
+#447 := [rewrite]: #446
+#723 := (iff #530 #722)
+#733 := (iff #741 false)
+#389 := (not true)
+#727 := (iff #389 false)
+#728 := [rewrite]: #727
+#375 := (iff #741 #389)
+#734 := (iff #406 true)
+#747 := (or true true)
+#738 := (iff #747 true)
+#398 := [rewrite]: #738
+#369 := (iff #406 #747)
+#725 := (iff #423 true)
+#731 := [rewrite]: #725
+#399 := (iff #427 true)
+#740 := [rewrite]: #399
+#732 := [monotonicity #740 #731]: #369
+#374 := [trans #732 #398]: #734
+#735 := [monotonicity #374]: #375
+#736 := [trans #735 #728]: #733
+#729 := (iff #400 false)
+#390 := (iff #400 #389)
+#387 := (iff #743 true)
+#383 := (iff #743 #747)
+#724 := [monotonicity #740 #740]: #383
+#388 := [trans #724 #398]: #387
+#726 := [monotonicity #388]: #390
+#730 := [trans #726 #728]: #729
+#445 := [monotonicity #730 #736]: #723
+#341 := [trans #445 #447]: #448
+#712 := [monotonicity #341 #432]: #434
+#714 := [trans #712 #428]: #710
+#403 := (iff #412 true)
+#742 := (iff #412 #747)
+#745 := (iff #411 true)
+#746 := [rewrite]: #745
+#748 := [monotonicity #746 #746]: #742
+#739 := [trans #748 #398]: #403
+#704 := [monotonicity #739 #714]: #715
+#702 := [trans #704 #706]: #701
+#551 := [monotonicity #702]: #550
+#695 := [trans #551 #694]: #550
+#709 := [quant-inst #8 #8]: #703
+#696 := [mp #709 #695]: #708
+[unit-resolution #696 #60 #755]: false
+unsat
+8c864635f2131bf56f7aae6736c04969e8015d95 267 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#750 := (pattern #15)
#9 := 0::Int
-#12 := (< 0::Int 1::Int)
-#14 := (< 1::Int 0::Int)
-#15 := (and #14 #12)
-#13 := (and #12 #12)
-#16 := (or #13 #15)
-#20 := (ite #16 #17 #19)
-#10 := (= 1::Int 0::Int)
-#11 := (or #10 #10)
-#21 := (ite #11 0::Int #20)
-#22 := (= #21 1::Int)
-#23 := (not #22)
-#98 := (iff #23 false)
-#1 := true
-#93 := (not true)
-#96 := (iff #93 false)
-#97 := [rewrite]: #96
-#94 := (iff #23 #93)
-#91 := (iff #22 true)
-#86 := (= 1::Int 1::Int)
-#89 := (iff #86 true)
-#90 := [rewrite]: #89
-#87 := (iff #22 #86)
-#80 := (ite false 0::Int 1::Int)
-#83 := (= #80 1::Int)
-#84 := [rewrite]: #83
-#81 := (= #21 #80)
-#78 := (= #20 1::Int)
-#55 := (and #12 #14)
-#58 := (or #12 #55)
-#73 := (ite #58 1::Int 1::Int)
-#76 := (= #73 1::Int)
-#77 := [rewrite]: #76
-#74 := (= #20 #73)
-#71 := (= #19 1::Int)
-#63 := -1::Int
-#66 := (div -1::Int -1::Int)
-#69 := (= #66 1::Int)
-#70 := [rewrite]: #69
-#67 := (= #19 #66)
-#64 := (= #18 -1::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65 #65]: #67
-#72 := [trans #68 #70]: #71
-#61 := (= #17 1::Int)
-#62 := [rewrite]: #61
-#59 := (iff #16 #58)
-#56 := (iff #15 #55)
-#57 := [rewrite]: #56
-#53 := (iff #13 #12)
-#54 := [rewrite]: #53
-#60 := [monotonicity #54 #57]: #59
-#75 := [monotonicity #60 #62 #72]: #74
-#79 := [trans #75 #77]: #78
-#51 := (iff #11 false)
-#46 := (or false false)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #11 #46)
-#44 := (iff #10 false)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45 #45]: #47
-#52 := [trans #48 #50]: #51
-#82 := [monotonicity #52 #79]: #81
-#85 := [trans #82 #84]: #22
-#88 := [monotonicity #85]: #87
-#92 := [trans #88 #90]: #91
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#43 := [asserted]: #23
-[mp #43 #99]: false
-unsat
-519fa461c6409fb549ed180638c452bbb592389a 84 0
-#2 := false
-#8 := 3::Int
-#11 := 1::Int
-#22 := (- 1::Int)
-#21 := (- 3::Int)
-#23 := (div #21 #22)
-#20 := (div 3::Int 1::Int)
-#9 := 0::Int
-#15 := (< 0::Int 1::Int)
-#17 := (< 3::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 3::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 1::Int 0::Int)
-#10 := (= 3::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (= #25 3::Int)
-#27 := (not #26)
-#105 := (iff #27 false)
-#1 := true
-#100 := (not true)
-#103 := (iff #100 false)
-#104 := [rewrite]: #103
-#101 := (iff #27 #100)
-#98 := (iff #26 true)
-#93 := (= 3::Int 3::Int)
-#96 := (iff #93 true)
-#97 := [rewrite]: #96
-#94 := (iff #26 #93)
-#87 := (ite false 0::Int 3::Int)
-#90 := (= #87 3::Int)
+#88 := -1::Int
+#92 := (* -1::Int #14)
+#89 := (* -1::Int #13)
+#95 := (div #89 #92)
+#252 := (* -1::Int #95)
+#253 := (+ #15 #252)
+#254 := (= #253 0::Int)
+#25 := (div #13 #14)
+#249 := (* -1::Int #25)
+#250 := (+ #15 #249)
+#251 := (= #250 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#255 := (ite #216 #251 #254)
+#248 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#16 := (= #13 0::Int)
+#18 := (or #16 #17)
+#256 := (ite #18 #248 #255)
+#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#754 := (iff #259 #751)
+#752 := (iff #256 #256)
+#753 := [refl]: #752
+#755 := [quant-intro #753]: #754
+#219 := (ite #216 #25 #95)
+#222 := (ite #18 0::Int #219)
+#225 := (= #15 #222)
+#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#137 := (ite #134 #25 #95)
+#140 := (ite #18 0::Int #137)
+#143 := (= #15 #140)
+#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
+#229 := (iff #146 #228)
+#226 := (iff #143 #225)
+#223 := (= #140 #222)
+#220 := (= #137 #219)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#208 := (~ #146 #146)
+#206 := (~ #143 #143)
+#207 := [refl]: #206
+#209 := [nnf-pos #207]: #208
+#27 := (- #14)
+#26 := (- #13)
+#28 := (div #26 #27)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#29 := (ite #24 #25 #28)
+#30 := (ite #18 0::Int #29)
+#31 := (= #15 #30)
+#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
+#149 := (iff #32 #146)
+#82 := (and #20 #22)
+#85 := (or #21 #82)
+#98 := (ite #85 #25 #95)
+#76 := (= 0::Int #14)
+#73 := (= 0::Int #13)
+#79 := (or #73 #76)
+#101 := (ite #79 0::Int #98)
+#104 := (= #15 #101)
+#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
+#147 := (iff #107 #146)
+#144 := (iff #104 #143)
+#141 := (= #101 #140)
+#138 := (= #98 #137)
+#135 := (iff #85 #134)
+#132 := (iff #82 #131)
+#129 := (iff #22 #128)
+#130 := [rewrite]: #129
+#122 := (iff #20 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #21 #124)
+#118 := (iff #19 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#139 := [monotonicity #136]: #138
+#114 := (iff #79 #18)
+#112 := (iff #76 #17)
+#113 := [rewrite]: #112
+#110 := (iff #73 #16)
+#111 := [rewrite]: #110
+#115 := [monotonicity #111 #113]: #114
+#142 := [monotonicity #115 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#108 := (iff #32 #107)
+#105 := (iff #31 #104)
+#102 := (= #30 #101)
+#99 := (= #29 #98)
+#96 := (= #28 #95)
+#93 := (= #27 #92)
+#94 := [rewrite]: #93
+#90 := (= #26 #89)
#91 := [rewrite]: #90
-#88 := (= #25 #87)
-#85 := (= #24 3::Int)
-#59 := (and #15 #17)
-#62 := (or #16 #59)
-#80 := (ite #62 3::Int 3::Int)
-#83 := (= #80 3::Int)
+#97 := [monotonicity #91 #94]: #96
+#86 := (iff #24 #85)
+#83 := (iff #23 #82)
#84 := [rewrite]: #83
-#81 := (= #24 #80)
-#78 := (= #23 3::Int)
-#70 := -1::Int
-#67 := -3::Int
-#73 := (div -3::Int -1::Int)
-#76 := (= #73 3::Int)
-#77 := [rewrite]: #76
-#74 := (= #23 #73)
-#71 := (= #22 -1::Int)
-#72 := [rewrite]: #71
-#68 := (= #21 -3::Int)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#79 := [trans #75 #77]: #78
-#65 := (= #20 3::Int)
-#66 := [rewrite]: #65
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#82 := [monotonicity #64 #66 #79]: #81
-#86 := [trans #82 #84]: #85
-#57 := (iff #13 false)
-#52 := (or false false)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#50 := (iff #12 false)
-#51 := [rewrite]: #50
-#48 := (iff #10 false)
-#49 := [rewrite]: #48
-#54 := [monotonicity #49 #51]: #53
-#58 := [trans #54 #56]: #57
-#89 := [monotonicity #58 #86]: #88
-#92 := [trans #89 #91]: #26
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#102 := [monotonicity #99]: #101
-#106 := [trans #102 #104]: #105
-#47 := [asserted]: #27
-[mp #47 #106]: false
-unsat
-8d9d1f916dc7c49723b00373e1ef641d98863a50 174 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#8 := f3
-#89 := (<= f3 0::Int)
-#102 := (>= f3 0::Int)
-#103 := (not #102)
-#90 := (not #89)
-#113 := (or #90 #103)
-#140 := (not #113)
-#63 := -1::Int
-#64 := (* -1::Int f3)
-#69 := (div #64 -1::Int)
-#11 := 1::Int
-#20 := (div f3 1::Int)
-#116 := (ite #113 #20 #69)
-#138 := (= #20 #116)
-#246 := (not #138)
-#10 := (= f3 0::Int)
-#119 := (ite #10 0::Int #116)
-#122 := (= f3 #119)
-#137 := (= #116 #119)
-#149 := (not #10)
-#136 := (= #119 0::Int)
-#163 := (iff #136 #122)
-#161 := (iff #122 #136)
-#156 := (= 0::Int #119)
-#159 := (iff #156 #136)
-#160 := [commutativity]: #159
-#157 := (iff #122 #156)
-#154 := [hypothesis]: #10
-#158 := [monotonicity #154]: #157
-#162 := [trans #158 #160]: #161
-#164 := [symm #162]: #163
-#150 := (or #149 #136)
-#151 := [def-axiom]: #150
-#155 := [unit-resolution #151 #154]: #136
-#165 := [mp #155 #164]: #122
-#125 := (not #122)
-#22 := (- 1::Int)
-#21 := (- f3)
-#23 := (div #21 #22)
-#15 := (< 0::Int 1::Int)
-#17 := (< f3 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int f3)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 1::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (= #25 f3)
-#27 := (not #26)
-#128 := (iff #27 #125)
-#57 := (and #15 #17)
-#60 := (or #16 #57)
-#72 := (ite #60 #20 #69)
-#75 := (ite #10 0::Int #72)
-#81 := (= f3 #75)
-#86 := (not #81)
-#126 := (iff #86 #125)
-#123 := (iff #81 #122)
-#120 := (= #75 #119)
-#117 := (= #72 #116)
-#114 := (iff #60 #113)
-#111 := (iff #57 #103)
-#1 := true
-#106 := (and true #103)
-#109 := (iff #106 #103)
-#110 := [rewrite]: #109
-#107 := (iff #57 #106)
-#104 := (iff #17 #103)
-#105 := [rewrite]: #104
-#93 := (iff #15 true)
+#87 := [monotonicity #84]: #86
+#100 := [monotonicity #87 #97]: #99
+#80 := (iff #18 #79)
+#77 := (iff #17 #76)
+#78 := [rewrite]: #77
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#81 := [monotonicity #75 #78]: #80
+#103 := [monotonicity #81 #100]: #102
+#106 := [monotonicity #103]: #105
+#109 := [quant-intro #106]: #108
+#150 := [trans #109 #148]: #149
+#72 := [asserted]: #32
+#151 := [mp #72 #150]: #146
+#200 := [mp~ #151 #209]: #146
+#231 := [mp #200 #230]: #228
+#262 := [mp #231 #261]: #259
+#756 := [mp #262 #755]: #751
+decl f4 :: Int
+#8 := f4
+#10 := (f3 f4 0::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#692 := (not #751)
+#693 := (or #692 #11)
+#336 := (* -1::Int 0::Int)
+#421 := (* -1::Int f4)
+#422 := (div #421 #336)
+#423 := (* -1::Int #422)
+#414 := (+ #10 #423)
+#425 := (= #414 0::Int)
+#426 := (div f4 0::Int)
+#354 := (* -1::Int #426)
+#427 := (+ #10 #354)
+#424 := (= #427 0::Int)
+#428 := (>= f4 0::Int)
+#407 := (<= 0::Int 0::Int)
+#742 := (or #407 #428)
+#744 := (not #742)
+#401 := (<= f4 0::Int)
+#531 := (or #401 #407)
+#738 := (not #531)
+#412 := (or #738 #744)
+#413 := (ite #412 #424 #425)
+#745 := (= 0::Int 0::Int)
+#746 := (= f4 0::Int)
+#747 := (or #746 #745)
+#748 := (ite #747 #11 #413)
+#699 := (or #692 #748)
+#694 := (iff #699 #693)
+#530 := (iff #693 #693)
+#532 := [rewrite]: #530
+#697 := (iff #748 #11)
+#433 := (div #421 0::Int)
+#713 := (* -1::Int #433)
+#711 := (+ #10 #713)
+#716 := (= #711 0::Int)
+#1 := true
+#551 := (ite true #11 #716)
+#695 := (iff #551 #11)
+#696 := [rewrite]: #695
+#552 := (iff #748 #551)
+#704 := (iff #413 #716)
+#707 := (ite false #424 #716)
+#708 := (iff #707 #716)
+#709 := [rewrite]: #708
+#702 := (iff #413 #707)
+#705 := (iff #425 #716)
+#715 := (= #414 #711)
+#714 := (= #423 #713)
+#434 := (= #422 #433)
+#722 := (= #336 0::Int)
+#432 := [rewrite]: #722
+#435 := [monotonicity #432]: #434
+#429 := [monotonicity #435]: #714
+#712 := [monotonicity #429]: #715
+#706 := [monotonicity #712]: #705
+#721 := (iff #412 false)
+#719 := (or false false)
+#443 := (iff #719 false)
+#717 := [rewrite]: #443
+#720 := (iff #412 #719)
+#449 := (iff #744 false)
+#731 := (not true)
+#370 := (iff #731 false)
+#733 := [rewrite]: #370
+#447 := (iff #744 #731)
+#724 := (iff #742 true)
+#376 := (or true #428)
+#737 := (iff #376 true)
+#723 := [rewrite]: #737
+#736 := (iff #742 #376)
+#725 := (iff #407 true)
+#388 := [rewrite]: #725
+#734 := [monotonicity #388]: #736
+#446 := [trans #734 #723]: #724
+#448 := [monotonicity #446]: #447
+#342 := [trans #448 #733]: #449
+#735 := (iff #738 false)
+#726 := (iff #738 #731)
+#729 := (iff #531 true)
+#389 := (or #401 true)
+#727 := (iff #389 true)
+#728 := [rewrite]: #727
+#390 := (iff #531 #389)
+#391 := [monotonicity #388]: #390
+#730 := [trans #391 #728]: #729
+#732 := [monotonicity #730]: #726
+#375 := [trans #732 #733]: #735
+#442 := [monotonicity #375 #342]: #720
+#718 := [trans #442 #717]: #721
+#703 := [monotonicity #718 #706]: #702
+#710 := [trans #703 #709]: #704
+#741 := (iff #747 true)
+#739 := (or #746 true)
+#740 := (iff #739 true)
+#400 := [rewrite]: #740
+#399 := (iff #747 #739)
+#743 := (iff #745 true)
+#749 := [rewrite]: #743
+#404 := [monotonicity #749]: #399
+#384 := [trans #404 #400]: #741
+#553 := [monotonicity #384 #710]: #552
+#698 := [trans #553 #696]: #697
+#701 := [monotonicity #698]: #694
+#533 := [trans #701 #532]: #694
+#700 := [quant-inst #8 #9]: #699
+#686 := [mp #700 #533]: #693
+[unit-resolution #686 #61 #756]: false
+unsat
+5b04feaa787b42fcdecf376c99ee15421d3ebc84 291 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#749 := (pattern #15)
+#8 := 0::Int
+#88 := -1::Int
+#92 := (* -1::Int #14)
+#89 := (* -1::Int #13)
+#95 := (div #89 #92)
+#252 := (* -1::Int #95)
+#253 := (+ #15 #252)
+#254 := (= #253 0::Int)
+#25 := (div #13 #14)
+#249 := (* -1::Int #25)
+#250 := (+ #15 #249)
+#251 := (= #250 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#255 := (ite #216 #251 #254)
+#248 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#16 := (= #13 0::Int)
+#18 := (or #16 #17)
+#256 := (ite #18 #248 #255)
+#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#753 := (iff #259 #750)
+#751 := (iff #256 #256)
+#752 := [refl]: #751
+#754 := [quant-intro #752]: #753
+#219 := (ite #216 #25 #95)
+#222 := (ite #18 0::Int #219)
+#225 := (= #15 #222)
+#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#137 := (ite #134 #25 #95)
+#140 := (ite #18 0::Int #137)
+#143 := (= #15 #140)
+#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
+#229 := (iff #146 #228)
+#226 := (iff #143 #225)
+#223 := (= #140 #222)
+#220 := (= #137 #219)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#208 := (~ #146 #146)
+#206 := (~ #143 #143)
+#207 := [refl]: #206
+#209 := [nnf-pos #207]: #208
+#27 := (- #14)
+#26 := (- #13)
+#28 := (div #26 #27)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#29 := (ite #24 #25 #28)
+#30 := (ite #18 0::Int #29)
+#31 := (= #15 #30)
+#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
+#149 := (iff #32 #146)
+#82 := (and #20 #22)
+#85 := (or #21 #82)
+#98 := (ite #85 #25 #95)
+#76 := (= 0::Int #14)
+#73 := (= 0::Int #13)
+#79 := (or #73 #76)
+#101 := (ite #79 0::Int #98)
+#104 := (= #15 #101)
+#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
+#147 := (iff #107 #146)
+#144 := (iff #104 #143)
+#141 := (= #101 #140)
+#138 := (= #98 #137)
+#135 := (iff #85 #134)
+#132 := (iff #82 #131)
+#129 := (iff #22 #128)
+#130 := [rewrite]: #129
+#122 := (iff #20 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #21 #124)
+#118 := (iff #19 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#139 := [monotonicity #136]: #138
+#114 := (iff #79 #18)
+#112 := (iff #76 #17)
+#113 := [rewrite]: #112
+#110 := (iff #73 #16)
+#111 := [rewrite]: #110
+#115 := [monotonicity #111 #113]: #114
+#142 := [monotonicity #115 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#108 := (iff #32 #107)
+#105 := (iff #31 #104)
+#102 := (= #30 #101)
+#99 := (= #29 #98)
+#96 := (= #28 #95)
+#93 := (= #27 #92)
#94 := [rewrite]: #93
-#108 := [monotonicity #94 #105]: #107
-#112 := [trans #108 #110]: #111
-#100 := (iff #16 #90)
-#95 := (and #90 true)
-#98 := (iff #95 #90)
-#99 := [rewrite]: #98
-#96 := (iff #16 #95)
-#91 := (iff #14 #90)
-#92 := [rewrite]: #91
-#97 := [monotonicity #92 #94]: #96
-#101 := [trans #97 #99]: #100
-#115 := [monotonicity #101 #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [monotonicity #118]: #120
+#90 := (= #26 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#86 := (iff #24 #85)
+#83 := (iff #23 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#100 := [monotonicity #87 #97]: #99
+#80 := (iff #18 #79)
+#77 := (iff #17 #76)
+#78 := [rewrite]: #77
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#81 := [monotonicity #75 #78]: #80
+#103 := [monotonicity #81 #100]: #102
+#106 := [monotonicity #103]: #105
+#109 := [quant-intro #106]: #108
+#150 := [trans #109 #148]: #149
+#72 := [asserted]: #32
+#151 := [mp #72 #150]: #146
+#200 := [mp~ #151 #209]: #146
+#231 := [mp #200 #230]: #228
+#262 := [mp #231 #261]: #259
+#755 := [mp #262 #754]: #750
+#9 := 1::Int
+#10 := (f3 0::Int 1::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#584 := (not #750)
+#585 := (or #584 #11)
+#336 := (* -1::Int 1::Int)
+#420 := (* -1::Int 0::Int)
+#421 := (div #420 #336)
+#422 := (* -1::Int #421)
+#413 := (+ #10 #422)
+#424 := (= #413 0::Int)
+#425 := (div 0::Int 1::Int)
+#426 := (* -1::Int #425)
+#423 := (+ #10 #426)
+#427 := (= #423 0::Int)
+#406 := (>= 0::Int 0::Int)
+#741 := (<= 1::Int 0::Int)
+#743 := (or #741 #406)
+#400 := (not #743)
+#530 := (<= 0::Int 0::Int)
+#737 := (or #530 #741)
+#411 := (not #737)
+#412 := (or #411 #400)
+#744 := (ite #412 #427 #424)
+#745 := (= 1::Int 0::Int)
+#746 := (= 0::Int 0::Int)
+#747 := (or #746 #745)
+#742 := (ite #747 #11 #744)
+#578 := (or #584 #742)
+#587 := (iff #578 #585)
+#589 := (iff #585 #585)
+#590 := [rewrite]: #589
+#567 := (iff #742 #11)
+#1 := true
+#681 := (ite true #11 #11)
+#679 := (iff #681 #11)
+#682 := [rewrite]: #679
+#583 := (iff #742 #681)
+#574 := (iff #744 #11)
+#689 := (ite false #11 #11)
+#572 := (iff #689 #11)
+#573 := [rewrite]: #572
+#687 := (iff #744 #689)
+#686 := (iff #424 #11)
+#532 := (= #413 #10)
+#704 := (+ #10 0::Int)
+#701 := (= #704 #10)
+#702 := [rewrite]: #701
+#529 := (= #413 #704)
+#693 := (= #422 0::Int)
+#710 := (= #420 0::Int)
+#714 := [rewrite]: #710
+#698 := (= #422 #420)
+#691 := (= #421 0::Int)
+#552 := (div 0::Int -1::Int)
+#696 := (= #552 0::Int)
+#697 := [rewrite]: #696
+#694 := (= #421 #552)
+#550 := (= #336 -1::Int)
+#551 := [rewrite]: #550
+#695 := [monotonicity #714 #551]: #694
+#692 := [trans #695 #697]: #691
+#699 := [monotonicity #692]: #698
+#700 := [trans #699 #714]: #693
+#531 := [monotonicity #700]: #529
+#685 := [trans #531 #702]: #532
+#688 := [monotonicity #685]: #686
+#703 := (iff #427 #11)
+#707 := (= #423 #10)
+#705 := (= #423 #704)
+#711 := (= #426 0::Int)
+#713 := (= #426 #420)
+#434 := (= #425 0::Int)
+#712 := [rewrite]: #434
+#428 := [monotonicity #712]: #713
+#715 := [trans #428 #714]: #711
+#706 := [monotonicity #715]: #705
+#708 := [trans #706 #702]: #707
+#709 := [monotonicity #708]: #703
+#432 := (iff #412 false)
+#716 := (or false false)
+#721 := (iff #716 false)
+#431 := [rewrite]: #721
+#720 := (iff #412 #716)
+#441 := (iff #400 false)
+#731 := (not true)
+#734 := (iff #731 false)
+#374 := [rewrite]: #734
+#718 := (iff #400 #731)
+#448 := (iff #743 true)
+#722 := (or false true)
+#446 := (iff #722 true)
+#447 := [rewrite]: #446
+#723 := (iff #743 #722)
+#733 := (iff #406 true)
+#736 := [rewrite]: #733
+#726 := (iff #741 false)
+#727 := [rewrite]: #726
+#445 := [monotonicity #727 #736]: #723
+#342 := [trans #445 #447]: #448
+#719 := [monotonicity #342]: #718
+#442 := [trans #719 #374]: #441
+#375 := (iff #411 false)
+#369 := (iff #411 #731)
+#730 := (iff #737 true)
+#739 := (or true false)
+#383 := (iff #739 true)
+#724 := [rewrite]: #383
+#728 := (iff #737 #739)
+#389 := (iff #530 true)
+#390 := [rewrite]: #389
+#729 := [monotonicity #390 #727]: #728
+#725 := [trans #729 #724]: #730
+#732 := [monotonicity #725]: #369
+#735 := [trans #732 #374]: #375
+#717 := [monotonicity #735 #442]: #720
+#433 := [trans #717 #431]: #432
+#690 := [monotonicity #433 #709 #688]: #687
+#533 := [trans #690 #573]: #574
+#387 := (iff #747 true)
+#399 := (iff #747 #739)
+#398 := (iff #745 false)
+#403 := [rewrite]: #398
+#748 := (iff #746 true)
+#738 := [rewrite]: #748
+#740 := [monotonicity #738 #403]: #399
+#388 := [trans #740 #724]: #387
+#678 := [monotonicity #388 #533]: #583
+#582 := [trans #678 #682]: #567
+#588 := [monotonicity #582]: #587
+#683 := [trans #588 #590]: #587
+#586 := [quant-inst #8 #9]: #578
+#680 := [mp #586 #683]: #585
+[unit-resolution #680 #61 #755]: false
+unsat
+ca32959e06f9134641deb61724af7aaee2701280 279 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#13 := (:var 0 Int)
+#12 := (:var 1 Int)
+#14 := (f3 #12 #13)
+#734 := (pattern #14)
+#15 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #13)
+#80 := (* -1::Int #12)
+#86 := (div #80 #83)
+#237 := (* -1::Int #86)
+#238 := (+ #14 #237)
+#239 := (= #238 0::Int)
+#25 := (div #12 #13)
+#234 := (* -1::Int #25)
+#235 := (+ #14 #234)
+#236 := (= #235 0::Int)
+#112 := (>= #12 0::Int)
+#105 := (<= #13 0::Int)
+#197 := (or #105 #112)
+#198 := (not #197)
+#101 := (<= #12 0::Int)
+#195 := (or #101 #105)
+#196 := (not #195)
+#201 := (or #196 #198)
+#240 := (ite #201 #236 #239)
+#233 := (= #14 0::Int)
+#17 := (= #13 0::Int)
+#16 := (= #12 0::Int)
+#18 := (or #16 #17)
+#241 := (ite #18 #233 #240)
+#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #241)
+#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
+#738 := (iff #244 #735)
+#736 := (iff #241 #241)
+#737 := [refl]: #736
+#739 := [quant-intro #737]: #738
+#204 := (ite #201 #25 #86)
+#207 := (ite #18 0::Int #204)
+#210 := (= #14 #207)
+#213 := (forall (vars (?v0 Int) (?v1 Int)) #210)
+#245 := (iff #213 #244)
+#242 := (iff #210 #241)
+#243 := [rewrite]: #242
+#246 := [quant-intro #243]: #245
+#113 := (not #112)
+#106 := (not #105)
+#116 := (and #106 #113)
+#102 := (not #101)
+#109 := (and #102 #106)
+#119 := (or #109 #116)
+#122 := (ite #119 #25 #86)
+#125 := (ite #18 0::Int #122)
+#128 := (= #14 #125)
+#131 := (forall (vars (?v0 Int) (?v1 Int)) #128)
+#214 := (iff #131 #213)
+#211 := (iff #128 #210)
+#208 := (= #125 #207)
+#205 := (= #122 #204)
+#202 := (iff #119 #201)
+#199 := (iff #116 #198)
+#200 := [rewrite]: #199
+#189 := (iff #109 #196)
+#190 := [rewrite]: #189
+#203 := [monotonicity #190 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [quant-intro #212]: #214
+#193 := (~ #131 #131)
+#191 := (~ #128 #128)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#27 := (- #13)
+#26 := (- #12)
+#28 := (div #26 #27)
+#20 := (< 0::Int #13)
+#22 := (< #12 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #12)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#29 := (ite #24 #25 #28)
+#30 := (ite #18 0::Int #29)
+#31 := (= #14 #30)
+#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
+#134 := (iff #32 #131)
+#73 := (and #20 #22)
+#76 := (or #21 #73)
+#89 := (ite #76 #25 #86)
+#92 := (ite #18 0::Int #89)
+#95 := (= #14 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#132 := (iff #98 #131)
+#129 := (iff #95 #128)
+#126 := (= #92 #125)
+#123 := (= #89 #122)
+#120 := (iff #76 #119)
+#117 := (iff #73 #116)
+#114 := (iff #22 #113)
+#115 := [rewrite]: #114
+#107 := (iff #20 #106)
+#108 := [rewrite]: #107
+#118 := [monotonicity #108 #115]: #117
+#110 := (iff #21 #109)
+#103 := (iff #19 #102)
+#104 := [rewrite]: #103
+#111 := [monotonicity #104 #108]: #110
+#121 := [monotonicity #111 #118]: #120
#124 := [monotonicity #121]: #123
#127 := [monotonicity #124]: #126
-#87 := (iff #27 #86)
-#84 := (iff #26 #81)
-#78 := (= #75 f3)
-#82 := (iff #78 #81)
-#83 := [rewrite]: #82
-#79 := (iff #26 #78)
-#76 := (= #25 #75)
-#73 := (= #24 #72)
-#70 := (= #23 #69)
-#67 := (= #22 -1::Int)
-#68 := [rewrite]: #67
-#65 := (= #21 #64)
-#66 := [rewrite]: #65
-#71 := [monotonicity #66 #68]: #70
-#61 := (iff #19 #60)
-#58 := (iff #18 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#74 := [monotonicity #62 #71]: #73
-#55 := (iff #13 #10)
-#50 := (or #10 false)
-#53 := (iff #50 #10)
-#54 := [rewrite]: #53
-#51 := (iff #13 #50)
-#48 := (iff #12 false)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#77 := [monotonicity #56 #74]: #76
-#80 := [monotonicity #77]: #79
-#85 := [trans #80 #83]: #84
-#88 := [monotonicity #85]: #87
-#129 := [trans #88 #127]: #128
-#47 := [asserted]: #27
-#130 := [mp #47 #129]: #125
-#166 := [unit-resolution #130 #165]: false
-#167 := [lemma #166]: #149
-#152 := (or #10 #137)
-#153 := [def-axiom]: #152
-#225 := [unit-resolution #153 #167]: #137
-#242 := (= f3 #116)
-#226 := [hypothesis]: #138
-#224 := (= f3 #20)
-#191 := (* -1::Int #20)
-#192 := (+ f3 #191)
-#197 := (<= #192 0::Int)
-#190 := (= #192 0::Int)
-#45 := [true-axiom]: true
-#227 := (or false #190)
-#228 := [th-lemma arith]: #227
-#229 := [unit-resolution #228 #45]: #190
-#230 := (not #190)
-#231 := (or #230 #197)
-#232 := [th-lemma arith triangle-eq]: #231
-#233 := [unit-resolution #232 #229]: #197
-#198 := (>= #192 0::Int)
-#234 := (or #230 #198)
-#235 := [th-lemma arith triangle-eq]: #234
-#236 := [unit-resolution #235 #229]: #198
-#238 := (not #198)
-#237 := (not #197)
-#239 := (or #224 #237 #238)
-#240 := [th-lemma arith triangle-eq]: #239
-#241 := [unit-resolution #240 #236 #233]: #224
-#243 := [trans #241 #226]: #242
-#244 := [trans #243 #225]: #122
-#245 := [unit-resolution #130 #244]: false
-#247 := [lemma #245]: #246
-#145 := (or #140 #138)
-#146 := [def-axiom]: #145
-#221 := [unit-resolution #146 #247]: #140
-#134 := (or #113 #89)
-#135 := [def-axiom]: #134
-#222 := [unit-resolution #135 #221]: #89
-#132 := (or #113 #102)
-#133 := [def-axiom]: #132
-#223 := [unit-resolution #133 #221]: #102
-#248 := (or #10 #90 #103)
-#249 := [th-lemma arith triangle-eq]: #248
-#250 := [unit-resolution #249 #167]: #113
-[unit-resolution #250 #223 #222]: false
-unsat
-7116e1ffcf5d8f75fc236e1967d4dc10ce43d95d 102 0
-#2 := false
-#8 := 0::Int
-#10 := 1::Int
-#11 := (- 1::Int)
-#20 := (- #11)
-#19 := (- 0::Int)
-#21 := (div #19 #20)
-#18 := (div 0::Int #11)
-#15 := (< 0::Int #11)
-#14 := (< 0::Int 0::Int)
-#16 := (and #14 #15)
-#17 := (or #16 #16)
-#22 := (ite #17 #18 #21)
-#12 := (= #11 0::Int)
-#9 := (= 0::Int 0::Int)
-#13 := (or #9 #12)
-#23 := (ite #13 0::Int #22)
-#24 := (= #23 0::Int)
-#25 := (not #24)
-#123 := (iff #25 false)
-#1 := true
-#118 := (not true)
-#121 := (iff #118 false)
-#122 := [rewrite]: #121
-#119 := (iff #25 #118)
-#116 := (iff #24 true)
-#46 := (iff #9 true)
-#47 := [rewrite]: #46
-#114 := (iff #24 #9)
-#108 := (ite true 0::Int 0::Int)
-#111 := (= #108 0::Int)
-#112 := [rewrite]: #111
-#109 := (= #23 #108)
-#106 := (= #22 0::Int)
-#48 := -1::Int
-#65 := (< 0::Int -1::Int)
-#68 := (and #14 #65)
-#101 := (ite #68 0::Int 0::Int)
-#104 := (= #101 0::Int)
-#105 := [rewrite]: #104
-#102 := (= #22 #101)
-#99 := (= #21 0::Int)
-#94 := (div 0::Int 1::Int)
-#97 := (= #94 0::Int)
-#98 := [rewrite]: #97
-#95 := (= #21 #94)
-#92 := (= #20 1::Int)
-#87 := (- -1::Int)
-#90 := (= #87 1::Int)
-#91 := [rewrite]: #90
-#88 := (= #20 #87)
-#49 := (= #11 -1::Int)
-#50 := [rewrite]: #49
-#89 := [monotonicity #50]: #88
-#93 := [trans #89 #91]: #92
-#85 := (= #19 0::Int)
-#86 := [rewrite]: #85
-#96 := [monotonicity #86 #93]: #95
-#100 := [trans #96 #98]: #99
-#83 := (= #18 0::Int)
-#78 := (div 0::Int -1::Int)
-#81 := (= #78 0::Int)
+#130 := [monotonicity #127]: #129
+#133 := [quant-intro #130]: #132
+#99 := (iff #32 #98)
+#96 := (iff #31 #95)
+#93 := (= #30 #92)
+#90 := (= #29 #89)
+#87 := (= #28 #86)
+#84 := (= #27 #83)
+#85 := [rewrite]: #84
+#81 := (= #26 #80)
#82 := [rewrite]: #81
-#79 := (= #18 #78)
-#80 := [monotonicity #50]: #79
-#84 := [trans #80 #82]: #83
-#76 := (iff #17 #68)
-#71 := (or #68 #68)
-#74 := (iff #71 #68)
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #24 #76)
+#74 := (iff #23 #73)
#75 := [rewrite]: #74
-#72 := (iff #17 #71)
-#69 := (iff #16 #68)
-#66 := (iff #15 #65)
-#67 := [monotonicity #50]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70 #70]: #72
-#77 := [trans #73 #75]: #76
-#103 := [monotonicity #77 #84 #100]: #102
-#107 := [trans #103 #105]: #106
-#63 := (iff #13 true)
-#58 := (or true false)
-#61 := (iff #58 true)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#56 := (iff #12 false)
-#51 := (= -1::Int 0::Int)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #47 #57]: #59
-#64 := [trans #60 #62]: #63
-#110 := [monotonicity #64 #107]: #109
-#113 := [trans #110 #112]: #24
-#115 := [monotonicity #113]: #114
-#117 := [trans #115 #47]: #116
-#120 := [monotonicity #117]: #119
-#124 := [trans #120 #122]: #123
-#45 := [asserted]: #25
-[mp #45 #124]: false
-unsat
-5c9ec68cb5c6bc2336555bc99c13f0ecae2167b7 104 0
-#2 := false
+#78 := [monotonicity #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#135 := [trans #100 #133]: #134
+#72 := [asserted]: #32
+#136 := [mp #72 #135]: #131
+#185 := [mp~ #136 #194]: #131
+#216 := [mp #185 #215]: #213
+#247 := [mp #216 #246]: #244
+#740 := [mp #247 #739]: #735
#8 := 1::Int
-#11 := (- 1::Int)
-#21 := (- #11)
-#22 := (div #11 #21)
-#20 := (div 1::Int #11)
-#9 := 0::Int
-#15 := (< 0::Int #11)
-#17 := (< 1::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 1::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#23 := (ite #19 #20 #22)
+#9 := (f3 1::Int 1::Int)
+#10 := (= #9 1::Int)
+#11 := (not #10)
+#61 := [asserted]: #11
+#571 := (not #735)
+#572 := (or #571 #10)
+#321 := (* -1::Int 1::Int)
+#405 := (div #321 #321)
+#406 := (* -1::Int #405)
+#407 := (+ #9 #406)
+#398 := (= #407 0::Int)
+#409 := (div 1::Int 1::Int)
+#410 := (* -1::Int #409)
+#411 := (+ #9 #410)
+#408 := (= #411 0::Int)
+#412 := (>= 1::Int 0::Int)
+#391 := (<= 1::Int 0::Int)
+#726 := (or #391 #412)
+#728 := (not #726)
+#385 := (or #391 #391)
+#515 := (not #385)
+#722 := (or #515 #728)
+#396 := (ite #722 #408 #398)
+#397 := (= #9 0::Int)
+#729 := (= 1::Int 0::Int)
+#730 := (or #729 #729)
+#731 := (ite #730 #397 #396)
+#573 := (or #571 #731)
+#575 := (iff #573 #572)
+#665 := (iff #572 #572)
+#669 := [rewrite]: #665
+#570 := (iff #731 #10)
+#664 := (ite false #397 #10)
+#567 := (iff #664 #10)
+#569 := [rewrite]: #567
+#667 := (iff #731 #664)
+#568 := (iff #396 #10)
+#1 := true
+#557 := (ite true #10 #10)
+#518 := (iff #557 #10)
+#666 := [rewrite]: #518
+#558 := (iff #396 #557)
+#672 := (iff #398 #10)
+#689 := (+ -1::Int #9)
+#692 := (= #689 0::Int)
+#694 := (iff #692 #10)
+#535 := [rewrite]: #694
+#673 := (iff #398 #692)
+#670 := (= #407 #689)
+#699 := (+ #9 -1::Int)
+#690 := (= #699 #689)
+#691 := [rewrite]: #690
+#516 := (= #407 #699)
+#685 := (= #406 -1::Int)
+#697 := (= #321 -1::Int)
+#698 := [rewrite]: #697
+#684 := (= #406 #321)
+#677 := (= #405 1::Int)
+#679 := (div -1::Int -1::Int)
+#682 := (= #679 1::Int)
+#676 := [rewrite]: #682
+#680 := (= #405 #679)
+#681 := [monotonicity #698 #698]: #680
+#683 := [trans #681 #676]: #677
+#678 := [monotonicity #683]: #684
+#514 := [trans #678 #698]: #685
+#517 := [monotonicity #514]: #516
+#671 := [trans #517 #691]: #670
+#674 := [monotonicity #671]: #673
+#675 := [trans #674 #535]: #672
+#536 := (iff #408 #10)
+#693 := (iff #408 #692)
+#686 := (= #411 #689)
+#696 := (= #411 #699)
+#413 := (= #410 -1::Int)
+#418 := (= #410 #321)
+#416 := (= #409 1::Int)
+#417 := [rewrite]: #416
+#419 := [monotonicity #417]: #418
+#695 := [trans #419 #698]: #413
+#700 := [monotonicity #695]: #696
+#687 := [trans #700 #691]: #686
+#688 := [monotonicity #687]: #693
+#537 := [trans #688 #535]: #536
+#702 := (iff #722 true)
+#704 := (or true false)
+#701 := (iff #704 true)
+#705 := [rewrite]: #701
+#426 := (iff #722 #704)
+#327 := (iff #728 false)
+#708 := (not true)
+#432 := (iff #708 false)
+#433 := [rewrite]: #432
+#430 := (iff #728 #708)
+#721 := (iff #726 true)
+#719 := (or false true)
+#720 := (iff #719 true)
+#718 := [rewrite]: #720
+#359 := (iff #726 #719)
+#354 := (iff #412 true)
+#717 := [rewrite]: #354
+#368 := (iff #391 false)
+#709 := [rewrite]: #368
+#360 := [monotonicity #709 #717]: #359
+#707 := [trans #360 #718]: #721
+#431 := [monotonicity #707]: #430
+#703 := [trans #431 #433]: #327
+#710 := (iff #515 true)
+#711 := (not false)
+#714 := (iff #711 true)
+#715 := [rewrite]: #714
+#712 := (iff #515 #711)
+#374 := (iff #385 false)
+#733 := (or false false)
+#388 := (iff #733 false)
+#724 := [rewrite]: #388
+#372 := (iff #385 #733)
+#373 := [monotonicity #709 #709]: #372
+#375 := [trans #373 #724]: #374
+#713 := [monotonicity #375]: #712
+#716 := [trans #713 #715]: #710
+#427 := [monotonicity #716 #703]: #426
+#706 := [trans #427 #705]: #702
+#559 := [monotonicity #706 #537 #675]: #558
+#663 := [trans #559 #666]: #568
+#384 := (iff #730 false)
+#723 := (iff #730 #733)
+#732 := (iff #729 false)
+#727 := [rewrite]: #732
+#383 := [monotonicity #727 #727]: #723
+#725 := [trans #383 #724]: #384
+#552 := [monotonicity #725 #663]: #667
+#563 := [trans #552 #569]: #570
+#668 := [monotonicity #563]: #575
+#656 := [trans #668 #669]: #575
+#574 := [quant-inst #8 #8]: #573
+#658 := [mp #574 #656]: #572
+[unit-resolution #658 #61 #740]: false
+unsat
+4e490baf730f7c2e9689bb8a2892f4f8f052ba53 290 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#735 := (pattern #15)
+#16 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #14)
+#81 := (* -1::Int #13)
+#87 := (div #81 #84)
+#238 := (* -1::Int #87)
+#239 := (+ #15 #238)
+#240 := (= #239 0::Int)
+#26 := (div #13 #14)
+#235 := (* -1::Int #26)
+#236 := (+ #15 #235)
+#237 := (= #236 0::Int)
+#113 := (>= #13 0::Int)
+#106 := (<= #14 0::Int)
+#198 := (or #106 #113)
+#199 := (not #198)
+#102 := (<= #13 0::Int)
+#196 := (or #102 #106)
+#197 := (not #196)
+#202 := (or #197 #199)
+#241 := (ite #202 #237 #240)
+#234 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#17 := (= #13 0::Int)
+#19 := (or #17 #18)
+#242 := (ite #19 #234 #241)
+#736 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #735) #242)
+#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
+#739 := (iff #245 #736)
+#737 := (iff #242 #242)
+#738 := [refl]: #737
+#740 := [quant-intro #738]: #739
+#205 := (ite #202 #26 #87)
+#208 := (ite #19 0::Int #205)
+#211 := (= #15 #208)
+#214 := (forall (vars (?v0 Int) (?v1 Int)) #211)
+#246 := (iff #214 #245)
+#243 := (iff #211 #242)
+#244 := [rewrite]: #243
+#247 := [quant-intro #244]: #246
+#114 := (not #113)
+#107 := (not #106)
+#117 := (and #107 #114)
+#103 := (not #102)
+#110 := (and #103 #107)
+#120 := (or #110 #117)
+#123 := (ite #120 #26 #87)
+#126 := (ite #19 0::Int #123)
+#129 := (= #15 #126)
+#132 := (forall (vars (?v0 Int) (?v1 Int)) #129)
+#215 := (iff #132 #214)
+#212 := (iff #129 #211)
+#209 := (= #126 #208)
+#206 := (= #123 #205)
+#203 := (iff #120 #202)
+#200 := (iff #117 #199)
+#201 := [rewrite]: #200
+#190 := (iff #110 #197)
+#191 := [rewrite]: #190
+#204 := [monotonicity #191 #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [monotonicity #207]: #209
+#213 := [monotonicity #210]: #212
+#216 := [quant-intro #213]: #215
+#194 := (~ #132 #132)
+#192 := (~ #129 #129)
+#193 := [refl]: #192
+#195 := [nnf-pos #193]: #194
+#28 := (- #14)
+#27 := (- #13)
+#29 := (div #27 #28)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #15 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#135 := (iff #33 #132)
+#74 := (and #21 #23)
+#77 := (or #22 #74)
+#90 := (ite #77 #26 #87)
+#93 := (ite #19 0::Int #90)
+#96 := (= #15 #93)
+#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
+#133 := (iff #99 #132)
+#130 := (iff #96 #129)
+#127 := (= #93 #126)
+#124 := (= #90 #123)
+#121 := (iff #77 #120)
+#118 := (iff #74 #117)
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#108 := (iff #21 #107)
+#109 := [rewrite]: #108
+#119 := [monotonicity #109 #116]: #118
+#111 := (iff #22 #110)
+#104 := (iff #20 #103)
+#105 := [rewrite]: #104
+#112 := [monotonicity #105 #109]: #111
+#122 := [monotonicity #112 #119]: #121
+#125 := [monotonicity #122]: #124
+#128 := [monotonicity #125]: #127
+#131 := [monotonicity #128]: #130
+#134 := [quant-intro #131]: #133
+#100 := (iff #33 #99)
+#97 := (iff #32 #96)
+#94 := (= #31 #93)
+#91 := (= #30 #90)
+#88 := (= #29 #87)
+#85 := (= #28 #84)
+#86 := [rewrite]: #85
+#82 := (= #27 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #25 #77)
+#75 := (iff #24 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [quant-intro #98]: #100
+#136 := [trans #101 #134]: #135
+#73 := [asserted]: #33
+#137 := [mp #73 #136]: #132
+#186 := [mp~ #137 #195]: #132
+#217 := [mp #186 #216]: #214
+#248 := [mp #217 #247]: #245
+#741 := [mp #248 #740]: #736
+#8 := 3::Int
+#9 := 1::Int
+#10 := (f3 3::Int 1::Int)
+#11 := (= #10 3::Int)
+#12 := (not #11)
+#62 := [asserted]: #12
+#651 := (not #736)
+#648 := (or #651 #11)
+#322 := (* -1::Int 1::Int)
+#406 := (* -1::Int 3::Int)
+#407 := (div #406 #322)
+#408 := (* -1::Int #407)
+#399 := (+ #10 #408)
+#410 := (= #399 0::Int)
+#411 := (div 3::Int 1::Int)
+#412 := (* -1::Int #411)
+#409 := (+ #10 #412)
+#413 := (= #409 0::Int)
+#392 := (>= 3::Int 0::Int)
+#727 := (<= 1::Int 0::Int)
+#729 := (or #727 #392)
+#386 := (not #729)
+#516 := (<= 3::Int 0::Int)
+#723 := (or #516 #727)
+#397 := (not #723)
+#398 := (or #397 #386)
+#730 := (ite #398 #413 #410)
+#731 := (= #10 0::Int)
+#732 := (= 1::Int 0::Int)
+#733 := (= 3::Int 0::Int)
+#728 := (or #733 #732)
+#734 := (ite #728 #731 #730)
+#650 := (or #651 #734)
+#661 := (iff #650 #648)
+#658 := (iff #648 #648)
+#663 := [rewrite]: #658
+#657 := (iff #734 #11)
+#575 := (ite false #731 #11)
+#666 := (iff #575 #11)
+#670 := [rewrite]: #666
+#576 := (iff #734 #575)
+#573 := (iff #730 #11)
+#1 := true
+#568 := (ite true #11 #11)
+#564 := (iff #568 #11)
+#572 := [rewrite]: #564
+#570 := (iff #730 #568)
+#668 := (iff #410 #11)
+#690 := -3::Int
+#695 := (+ -3::Int #10)
+#681 := (= #695 0::Int)
+#677 := (iff #681 #11)
+#678 := [rewrite]: #677
+#664 := (iff #410 #681)
+#667 := (= #399 #695)
+#693 := (+ #10 -3::Int)
+#536 := (= #693 #695)
+#537 := [rewrite]: #536
+#560 := (= #399 #693)
+#558 := (= #408 -3::Int)
+#691 := (= #406 -3::Int)
+#692 := [rewrite]: #691
+#673 := (= #408 #406)
+#674 := (= #407 3::Int)
+#515 := (div -3::Int -1::Int)
+#671 := (= #515 3::Int)
+#672 := [rewrite]: #671
+#517 := (= #407 #515)
+#679 := (= #322 -1::Int)
+#686 := [rewrite]: #679
+#518 := [monotonicity #692 #686]: #517
+#675 := [trans #518 #672]: #674
+#676 := [monotonicity #675]: #673
+#559 := [trans #676 #692]: #558
+#519 := [monotonicity #559]: #560
+#569 := [trans #519 #537]: #667
+#665 := [monotonicity #569]: #664
+#553 := [trans #665 #678]: #668
+#684 := (iff #413 #11)
+#682 := (iff #413 #681)
+#538 := (= #409 #695)
+#694 := (= #409 #693)
+#687 := (= #412 -3::Int)
+#697 := (= #412 #406)
+#696 := (= #411 3::Int)
+#700 := [rewrite]: #696
+#701 := [monotonicity #700]: #697
+#688 := [trans #701 #692]: #687
+#689 := [monotonicity #688]: #694
+#680 := [trans #689 #537]: #538
+#683 := [monotonicity #680]: #682
+#685 := [trans #683 #678]: #684
+#699 := (iff #398 true)
+#417 := (or true false)
+#420 := (iff #417 true)
+#698 := [rewrite]: #420
+#418 := (iff #398 #417)
+#703 := (iff #386 false)
+#705 := (not true)
+#702 := (iff #705 false)
+#706 := [rewrite]: #702
+#427 := (iff #386 #705)
+#328 := (iff #729 true)
+#709 := (or false true)
+#433 := (iff #709 true)
+#434 := [rewrite]: #433
+#431 := (iff #729 #709)
+#722 := (iff #392 true)
+#708 := [rewrite]: #722
+#713 := (iff #727 false)
+#714 := [rewrite]: #713
+#432 := [monotonicity #714 #708]: #431
+#704 := [trans #432 #434]: #328
+#428 := [monotonicity #704]: #427
+#707 := [trans #428 #706]: #703
+#721 := (iff #397 true)
+#355 := (not false)
+#360 := (iff #355 true)
+#361 := [rewrite]: #360
+#718 := (iff #397 #355)
+#711 := (iff #723 false)
+#385 := (or false false)
+#710 := (iff #385 false)
+#373 := [rewrite]: #710
+#715 := (iff #723 #385)
+#376 := (iff #516 false)
+#712 := [rewrite]: #376
+#716 := [monotonicity #712 #714]: #715
+#717 := [trans #716 #373]: #711
+#720 := [monotonicity #717]: #718
+#719 := [trans #720 #361]: #721
+#419 := [monotonicity #719 #707]: #418
+#414 := [trans #419 #698]: #699
+#571 := [monotonicity #414 #685 #553]: #570
+#574 := [trans #571 #572]: #573
+#374 := (iff #728 false)
+#726 := (iff #728 #385)
+#389 := (iff #732 false)
+#725 := [rewrite]: #389
+#724 := (iff #733 false)
+#384 := [rewrite]: #724
+#369 := [monotonicity #384 #725]: #726
+#375 := [trans #369 #373]: #374
+#669 := [monotonicity #375 #574]: #576
+#659 := [trans #669 #670]: #657
+#662 := [monotonicity #659]: #661
+#652 := [trans #662 #663]: #661
+#660 := [quant-inst #8 #9]: #650
+#653 := [mp #660 #652]: #648
+[unit-resolution #653 #62 #741]: false
+unsat
+3af8b375b2f7758b71c609be3059c3c3f068c4d0 327 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#9 := 1::Int
+decl f4 :: Int
+#8 := f4
+#10 := (f3 f4 1::Int)
+#63 := (= f4 #10)
+#16 := 0::Int
+#728 := (= #10 0::Int)
+#543 := (iff #728 #63)
+#541 := (iff #63 #728)
+#536 := (= 0::Int #10)
+#539 := (iff #536 #728)
+#540 := [commutativity]: #539
+#537 := (iff #63 #536)
+#730 := (= f4 0::Int)
+#408 := (div f4 1::Int)
+#77 := -1::Int
+#409 := (* -1::Int #408)
+#406 := (+ #10 #409)
+#410 := (= #406 0::Int)
+#516 := (not #410)
+#552 := (= #408 #10)
+#590 := (= #10 #408)
+#515 := (<= #406 0::Int)
+#474 := [hypothesis]: #410
+#585 := (or #516 #515)
+#586 := [th-lemma arith triangle-eq]: #585
+#587 := [unit-resolution #586 #474]: #515
+#668 := (>= #406 0::Int)
+#592 := (or #516 #668)
+#588 := [th-lemma arith triangle-eq]: #592
+#589 := [unit-resolution #588 #474]: #668
+#593 := [th-lemma arith eq-propagate 1 1 #589 #587]: #590
+#559 := [symm #593]: #552
+#578 := (= f4 #408)
+#621 := (+ f4 #409)
+#626 := (<= #621 0::Int)
+#620 := (= #621 0::Int)
+#1 := true
+#60 := [true-axiom]: true
+#594 := (or false #620)
+#595 := [th-lemma arith]: #594
+#591 := [unit-resolution #595 #60]: #620
+#596 := (not #620)
+#576 := (or #596 #626)
+#522 := [th-lemma arith triangle-eq]: #576
+#577 := [unit-resolution #522 #591]: #626
+#627 := (>= #621 0::Int)
+#558 := (or #596 #627)
+#582 := [th-lemma arith triangle-eq]: #558
+#583 := [unit-resolution #582 #591]: #627
+#584 := [th-lemma arith eq-propagate 1 1 #583 #577]: #578
+#518 := [trans #584 #559]: #63
+#66 := (not #63)
+#11 := (= #10 f4)
+#12 := (not #11)
+#67 := (iff #12 #66)
+#64 := (iff #11 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#62 := [asserted]: #12
+#71 := [mp #62 #68]: #66
+#549 := [unit-resolution #71 #518]: false
+#551 := [lemma #549]: #516
+#403 := (* -1::Int f4)
+#704 := (div #403 -1::Int)
+#416 := (* -1::Int #704)
+#696 := (+ #10 #416)
+#697 := (= #696 0::Int)
+#513 := (<= f4 0::Int)
+#714 := (not #513)
+#389 := (>= f4 0::Int)
+#706 := (not #389)
+#701 := (or #706 #714)
+#687 := (ite #701 #410 #697)
+#565 := (not #730)
+#657 := [hypothesis]: #565
+#560 := (or #730 #687)
+#684 := (ite #730 #728 #687)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#732 := (pattern #15)
+#81 := (* -1::Int #14)
+#78 := (* -1::Int #13)
+#84 := (div #78 #81)
+#235 := (* -1::Int #84)
+#236 := (+ #15 #235)
+#237 := (= #236 0::Int)
+#26 := (div #13 #14)
+#232 := (* -1::Int #26)
+#233 := (+ #15 #232)
+#234 := (= #233 0::Int)
+#110 := (>= #13 0::Int)
+#103 := (<= #14 0::Int)
+#195 := (or #103 #110)
+#196 := (not #195)
+#99 := (<= #13 0::Int)
+#193 := (or #99 #103)
+#194 := (not #193)
+#199 := (or #194 #196)
+#238 := (ite #199 #234 #237)
+#231 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#17 := (= #13 0::Int)
+#19 := (or #17 #18)
+#239 := (ite #19 #231 #238)
+#733 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #732) #239)
+#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
+#736 := (iff #242 #733)
+#734 := (iff #239 #239)
+#735 := [refl]: #734
+#737 := [quant-intro #735]: #736
+#202 := (ite #199 #26 #84)
+#205 := (ite #19 0::Int #202)
+#208 := (= #15 #205)
+#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
+#243 := (iff #211 #242)
+#240 := (iff #208 #239)
+#241 := [rewrite]: #240
+#244 := [quant-intro #241]: #243
+#111 := (not #110)
+#104 := (not #103)
+#114 := (and #104 #111)
+#100 := (not #99)
+#107 := (and #100 #104)
+#117 := (or #107 #114)
+#120 := (ite #117 #26 #84)
+#123 := (ite #19 0::Int #120)
+#126 := (= #15 #123)
+#129 := (forall (vars (?v0 Int) (?v1 Int)) #126)
+#212 := (iff #129 #211)
+#209 := (iff #126 #208)
+#206 := (= #123 #205)
+#203 := (= #120 #202)
+#200 := (iff #117 #199)
+#197 := (iff #114 #196)
+#198 := [rewrite]: #197
+#187 := (iff #107 #194)
+#188 := [rewrite]: #187
+#201 := [monotonicity #188 #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [monotonicity #207]: #209
+#213 := [quant-intro #210]: #212
+#191 := (~ #129 #129)
+#189 := (~ #126 #126)
+#190 := [refl]: #189
+#192 := [nnf-pos #190]: #191
+#28 := (- #14)
+#27 := (- #13)
+#29 := (div #27 #28)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #15 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#132 := (iff #33 #129)
+#70 := (and #21 #23)
+#74 := (or #22 #70)
+#87 := (ite #74 #26 #84)
+#90 := (ite #19 0::Int #87)
+#93 := (= #15 #90)
+#96 := (forall (vars (?v0 Int) (?v1 Int)) #93)
+#130 := (iff #96 #129)
+#127 := (iff #93 #126)
+#124 := (= #90 #123)
+#121 := (= #87 #120)
+#118 := (iff #74 #117)
+#115 := (iff #70 #114)
+#112 := (iff #23 #111)
+#113 := [rewrite]: #112
+#105 := (iff #21 #104)
+#106 := [rewrite]: #105
+#116 := [monotonicity #106 #113]: #115
+#108 := (iff #22 #107)
+#101 := (iff #20 #100)
+#102 := [rewrite]: #101
+#109 := [monotonicity #102 #106]: #108
+#119 := [monotonicity #109 #116]: #118
+#122 := [monotonicity #119]: #121
+#125 := [monotonicity #122]: #124
+#128 := [monotonicity #125]: #127
+#131 := [quant-intro #128]: #130
+#97 := (iff #33 #96)
+#94 := (iff #32 #93)
+#91 := (= #31 #90)
+#88 := (= #30 #87)
+#85 := (= #29 #84)
+#82 := (= #28 #81)
+#83 := [rewrite]: #82
+#79 := (= #27 #78)
+#80 := [rewrite]: #79
+#86 := [monotonicity #80 #83]: #85
+#75 := (iff #25 #74)
+#72 := (iff #24 #70)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#89 := [monotonicity #76 #86]: #88
+#92 := [monotonicity #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [quant-intro #95]: #97
+#133 := [trans #98 #131]: #132
+#69 := [asserted]: #33
+#134 := [mp #69 #133]: #129
+#183 := [mp~ #134 #192]: #129
+#214 := [mp #183 #213]: #211
+#245 := [mp #214 #244]: #242
+#738 := [mp #245 #737]: #733
+#691 := (not #733)
+#686 := (or #691 #684)
+#319 := (* -1::Int 1::Int)
+#404 := (div #403 #319)
+#405 := (* -1::Int #404)
+#396 := (+ #10 #405)
+#407 := (= #396 0::Int)
+#724 := (<= 1::Int 0::Int)
+#726 := (or #724 #389)
+#383 := (not #726)
+#720 := (or #513 #724)
+#394 := (not #720)
+#395 := (or #394 #383)
+#727 := (ite #395 #410 #407)
+#729 := (= 1::Int 0::Int)
+#725 := (or #730 #729)
+#731 := (ite #725 #728 #727)
+#692 := (or #691 #731)
+#534 := (iff #692 #686)
+#677 := (iff #686 #686)
+#678 := [rewrite]: #677
+#685 := (iff #731 #684)
+#688 := (iff #727 #687)
+#694 := (iff #407 #697)
+#411 := (= #396 #696)
+#417 := (= #405 #416)
+#414 := (= #404 #704)
+#703 := (= #319 -1::Int)
+#700 := [rewrite]: #703
+#415 := [monotonicity #700]: #414
+#695 := [monotonicity #415]: #417
+#693 := [monotonicity #695]: #411
+#698 := [monotonicity #693]: #694
+#425 := (iff #395 #701)
+#430 := (or #714 #706)
+#702 := (iff #430 #701)
+#424 := [rewrite]: #702
+#431 := (iff #395 #430)
+#428 := (iff #383 #706)
+#719 := (iff #726 #389)
+#717 := (or false #389)
+#718 := (iff #717 #389)
+#716 := [rewrite]: #718
+#357 := (iff #726 #717)
+#371 := (iff #724 false)
+#372 := [rewrite]: #371
+#358 := [monotonicity #372]: #357
+#705 := [trans #358 #716]: #719
+#429 := [monotonicity #705]: #428
+#352 := (iff #394 #714)
+#713 := (iff #720 #513)
+#373 := (or #513 false)
+#711 := (iff #373 #513)
+#712 := [rewrite]: #711
+#709 := (iff #720 #373)
+#710 := [monotonicity #372]: #709
+#708 := [trans #710 #712]: #713
+#715 := [monotonicity #708]: #352
+#325 := [monotonicity #715 #429]: #431
+#699 := [trans #325 #424]: #425
+#689 := [monotonicity #699 #698]: #688
+#707 := (iff #725 #730)
+#386 := (or #730 false)
+#723 := (iff #386 #730)
+#366 := [rewrite]: #723
+#722 := (iff #725 #386)
+#721 := (iff #729 false)
+#381 := [rewrite]: #721
+#382 := [monotonicity #381]: #722
+#370 := [trans #382 #366]: #707
+#690 := [monotonicity #370 #689]: #685
+#535 := [monotonicity #690]: #534
+#679 := [trans #535 #678]: #534
+#533 := [quant-inst #8 #9]: #692
+#680 := [mp #533 #679]: #686
+#553 := [unit-resolution #680 #738]: #684
+#550 := (not #684)
+#561 := (or #550 #730 #687)
+#569 := [def-axiom]: #561
+#562 := [unit-resolution #569 #553]: #560
+#563 := [unit-resolution #562 #657]: #687
+#649 := (or #701 #730)
+#676 := (not #701)
+#648 := [hypothesis]: #676
+#674 := (or #701 #389)
+#675 := [def-axiom]: #674
+#645 := [unit-resolution #675 #648]: #389
+#681 := (or #701 #513)
+#682 := [def-axiom]: #681
+#647 := [unit-resolution #682 #648]: #513
+#658 := (or #730 #714 #706)
+#659 := [th-lemma arith triangle-eq]: #658
+#655 := [unit-resolution #659 #657]: #430
+#660 := [unit-resolution #655 #647 #645]: false
+#650 := [lemma #660]: #649
+#564 := [unit-resolution #650 #657]: #701
+#670 := (not #687)
+#673 := (or #670 #676 #410)
+#555 := [def-axiom]: #673
+#574 := [unit-resolution #555 #564 #563 #551]: false
+#554 := [lemma #574]: #730
+#538 := [monotonicity #554]: #537
+#542 := [trans #538 #540]: #541
+#544 := [symm #542]: #543
+#575 := (or #565 #728)
+#567 := (or #550 #565 #728)
+#568 := [def-axiom]: #567
+#530 := [unit-resolution #568 #553]: #575
+#531 := [unit-resolution #530 #554]: #728
+#545 := [mp #531 #544]: #63
+[unit-resolution #71 #545]: false
+unsat
+6a8ee4256f7c15262363d462bd2dccb9364bb175 316 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#764 := (pattern #16)
+#8 := 0::Int
+#63 := -1::Int
+#107 := (* -1::Int #15)
+#104 := (* -1::Int #14)
+#110 := (div #104 #107)
+#267 := (* -1::Int #110)
+#268 := (+ #16 #267)
+#269 := (= #268 0::Int)
+#26 := (div #14 #15)
+#264 := (* -1::Int #26)
+#265 := (+ #16 #264)
+#266 := (= #265 0::Int)
+#142 := (>= #14 0::Int)
+#135 := (<= #15 0::Int)
+#227 := (or #135 #142)
+#228 := (not #227)
+#131 := (<= #14 0::Int)
+#225 := (or #131 #135)
+#226 := (not #225)
+#231 := (or #226 #228)
+#270 := (ite #231 #266 #269)
+#263 := (= #16 0::Int)
+#18 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#19 := (or #17 #18)
+#271 := (ite #19 #263 #270)
+#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #271)
+#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
+#768 := (iff #274 #765)
+#766 := (iff #271 #271)
+#767 := [refl]: #766
+#769 := [quant-intro #767]: #768
+#234 := (ite #231 #26 #110)
+#237 := (ite #19 0::Int #234)
+#240 := (= #16 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#275 := (iff #243 #274)
+#272 := (iff #240 #271)
+#273 := [rewrite]: #272
+#276 := [quant-intro #273]: #275
+#143 := (not #142)
+#136 := (not #135)
+#146 := (and #136 #143)
+#132 := (not #131)
+#139 := (and #132 #136)
+#149 := (or #139 #146)
+#152 := (ite #149 #26 #110)
+#155 := (ite #19 0::Int #152)
+#158 := (= #16 #155)
+#161 := (forall (vars (?v0 Int) (?v1 Int)) #158)
+#244 := (iff #161 #243)
+#241 := (iff #158 #240)
+#238 := (= #155 #237)
+#235 := (= #152 #234)
+#232 := (iff #149 #231)
+#229 := (iff #146 #228)
+#230 := [rewrite]: #229
+#219 := (iff #139 #226)
+#220 := [rewrite]: #219
+#233 := [monotonicity #220 #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
+#223 := (~ #161 #161)
+#221 := (~ #158 #158)
+#222 := [refl]: #221
+#224 := [nnf-pos #222]: #223
+#28 := (- #15)
+#27 := (- #14)
+#29 := (div #27 #28)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #16 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#164 := (iff #33 #161)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#113 := (ite #101 #26 #110)
+#92 := (= 0::Int #15)
+#89 := (= 0::Int #14)
+#95 := (or #89 #92)
+#116 := (ite #95 0::Int #113)
+#119 := (= #16 #116)
+#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
+#162 := (iff #122 #161)
+#159 := (iff #119 #158)
+#156 := (= #116 #155)
+#153 := (= #113 #152)
+#150 := (iff #101 #149)
+#147 := (iff #98 #146)
+#144 := (iff #23 #143)
+#145 := [rewrite]: #144
+#137 := (iff #21 #136)
+#138 := [rewrite]: #137
+#148 := [monotonicity #138 #145]: #147
+#140 := (iff #22 #139)
+#133 := (iff #20 #132)
+#134 := [rewrite]: #133
+#141 := [monotonicity #134 #138]: #140
+#151 := [monotonicity #141 #148]: #150
+#154 := [monotonicity #151]: #153
+#129 := (iff #95 #19)
+#127 := (iff #92 #18)
+#128 := [rewrite]: #127
+#125 := (iff #89 #17)
+#126 := [rewrite]: #125
+#130 := [monotonicity #126 #128]: #129
+#157 := [monotonicity #130 #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [quant-intro #160]: #162
+#123 := (iff #33 #122)
+#120 := (iff #32 #119)
+#117 := (= #31 #116)
+#114 := (= #30 #113)
+#111 := (= #29 #110)
+#108 := (= #28 #107)
+#109 := [rewrite]: #108
+#105 := (= #27 #104)
+#106 := [rewrite]: #105
+#112 := [monotonicity #106 #109]: #111
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#115 := [monotonicity #103 #112]: #114
+#96 := (iff #19 #95)
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#118 := [monotonicity #97 #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [quant-intro #121]: #123
+#165 := [trans #124 #163]: #164
+#88 := [asserted]: #33
+#166 := [mp #88 #165]: #161
+#215 := [mp~ #166 #224]: #161
+#246 := [mp #215 #245]: #243
+#277 := [mp #246 #276]: #274
+#770 := [mp #277 #769]: #765
+#66 := (f3 0::Int -1::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := 1::Int
+#10 := (- 1::Int)
+#11 := (f3 0::Int #10)
#12 := (= #11 0::Int)
-#10 := (= 1::Int 0::Int)
-#13 := (or #10 #12)
-#24 := (ite #13 0::Int #23)
-#25 := (= #24 #11)
-#26 := (not #25)
-#125 := (iff #26 false)
-#1 := true
-#120 := (not true)
-#123 := (iff #120 false)
-#124 := [rewrite]: #123
-#121 := (iff #26 #120)
-#118 := (iff #25 true)
-#49 := -1::Int
-#113 := (= -1::Int -1::Int)
-#116 := (iff #113 true)
-#117 := [rewrite]: #116
-#114 := (iff #25 #113)
-#50 := (= #11 -1::Int)
-#51 := [rewrite]: #50
-#111 := (= #24 -1::Int)
-#106 := (ite false 0::Int -1::Int)
-#109 := (= #106 -1::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #11 #66)
+#64 := (= #10 -1::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#599 := (not #765)
+#600 := (or #599 #69)
+#351 := (* -1::Int -1::Int)
+#435 := (* -1::Int 0::Int)
+#436 := (div #435 #351)
+#437 := (* -1::Int #436)
+#428 := (+ #66 #437)
+#439 := (= #428 0::Int)
+#440 := (div 0::Int -1::Int)
+#441 := (* -1::Int #440)
+#438 := (+ #66 #441)
+#442 := (= #438 0::Int)
+#421 := (>= 0::Int 0::Int)
+#756 := (<= -1::Int 0::Int)
+#758 := (or #756 #421)
+#415 := (not #758)
+#545 := (<= 0::Int 0::Int)
+#752 := (or #545 #756)
+#426 := (not #752)
+#427 := (or #426 #415)
+#759 := (ite #427 #442 #439)
+#760 := (= -1::Int 0::Int)
+#761 := (= 0::Int 0::Int)
+#762 := (or #761 #760)
+#757 := (ite #762 #69 #759)
+#593 := (or #599 #757)
+#602 := (iff #593 #600)
+#604 := (iff #600 #600)
+#605 := [rewrite]: #604
+#582 := (iff #757 #69)
+#1 := true
+#696 := (ite true #69 #69)
+#694 := (iff #696 #69)
+#697 := [rewrite]: #694
+#598 := (iff #757 #696)
+#589 := (iff #759 #69)
+#704 := (ite false #69 #69)
+#587 := (iff #704 #69)
+#588 := [rewrite]: #587
+#702 := (iff #759 #704)
+#701 := (iff #439 #69)
+#547 := (= #428 #66)
+#719 := (+ #66 0::Int)
+#716 := (= #719 #66)
+#717 := [rewrite]: #716
+#544 := (= #428 #719)
+#708 := (= #437 0::Int)
+#725 := (= #435 0::Int)
+#729 := [rewrite]: #725
+#713 := (= #437 #435)
+#706 := (= #436 0::Int)
+#567 := (div 0::Int 1::Int)
+#711 := (= #567 0::Int)
+#712 := [rewrite]: #711
+#709 := (= #436 #567)
+#565 := (= #351 1::Int)
+#566 := [rewrite]: #565
+#710 := [monotonicity #729 #566]: #709
+#707 := [trans #710 #712]: #706
+#714 := [monotonicity #707]: #713
+#715 := [trans #714 #729]: #708
+#546 := [monotonicity #715]: #544
+#700 := [trans #546 #717]: #547
+#703 := [monotonicity #700]: #701
+#718 := (iff #442 #69)
+#722 := (= #438 #66)
+#720 := (= #438 #719)
+#726 := (= #441 0::Int)
+#728 := (= #441 #435)
+#449 := (= #440 0::Int)
+#727 := [rewrite]: #449
+#443 := [monotonicity #727]: #728
+#730 := [trans #443 #729]: #726
+#721 := [monotonicity #730]: #720
+#723 := [trans #721 #717]: #722
+#724 := [monotonicity #723]: #718
+#447 := (iff #427 false)
+#731 := (or false false)
+#736 := (iff #731 false)
+#446 := [rewrite]: #736
+#735 := (iff #427 #731)
+#456 := (iff #415 false)
+#749 := (not true)
+#750 := (iff #749 false)
+#748 := [rewrite]: #750
+#733 := (iff #415 #749)
+#463 := (iff #758 true)
+#743 := (or true true)
+#740 := (iff #743 true)
+#746 := [rewrite]: #740
+#461 := (iff #758 #743)
+#738 := (iff #421 true)
+#460 := [rewrite]: #738
+#741 := (iff #756 true)
+#742 := [rewrite]: #741
+#462 := [monotonicity #742 #460]: #461
+#357 := [trans #462 #746]: #463
+#734 := [monotonicity #357]: #733
+#457 := [trans #734 #748]: #456
+#751 := (iff #426 false)
+#389 := (iff #426 #749)
+#384 := (iff #752 true)
+#744 := (iff #752 #743)
+#404 := (iff #545 true)
+#405 := [rewrite]: #404
+#745 := [monotonicity #405 #742]: #744
+#747 := [trans #745 #746]: #384
+#390 := [monotonicity #747]: #389
+#737 := [trans #390 #748]: #751
+#732 := [monotonicity #737 #457]: #735
+#448 := [trans #732 #446]: #447
+#705 := [monotonicity #448 #724 #703]: #702
+#548 := [trans #705 #588]: #589
+#402 := (iff #762 true)
+#754 := (or true false)
+#398 := (iff #754 true)
+#739 := [rewrite]: #398
+#414 := (iff #762 #754)
+#413 := (iff #760 false)
+#418 := [rewrite]: #413
+#763 := (iff #761 true)
+#753 := [rewrite]: #763
+#755 := [monotonicity #753 #418]: #414
+#403 := [trans #755 #739]: #402
+#693 := [monotonicity #403 #548]: #598
+#597 := [trans #693 #697]: #582
+#603 := [monotonicity #597]: #602
+#698 := [trans #603 #605]: #602
+#601 := [quant-inst #8 #63]: #593
+#695 := [mp #601 #698]: #600
+[unit-resolution #695 #87 #770]: false
+unsat
+beaa0a62fe76b86ad510bf8c2d69fe2ce8dbdc5f 310 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#749 := (pattern #15)
+#16 := 0::Int
+#63 := -1::Int
+#98 := (* -1::Int #14)
+#95 := (* -1::Int #13)
+#101 := (div #95 #98)
+#252 := (* -1::Int #101)
+#253 := (+ #15 #252)
+#254 := (= #253 0::Int)
+#26 := (div #13 #14)
+#249 := (* -1::Int #26)
+#250 := (+ #15 #249)
+#251 := (= #250 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#255 := (ite #216 #251 #254)
+#248 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#17 := (= #13 0::Int)
+#19 := (or #17 #18)
+#256 := (ite #19 #248 #255)
+#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#753 := (iff #259 #750)
+#751 := (iff #256 #256)
+#752 := [refl]: #751
+#754 := [quant-intro #752]: #753
+#219 := (ite #216 #26 #101)
+#222 := (ite #19 0::Int #219)
+#225 := (= #15 #222)
+#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#137 := (ite #134 #26 #101)
+#140 := (ite #19 0::Int #137)
+#143 := (= #15 #140)
+#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
+#229 := (iff #146 #228)
+#226 := (iff #143 #225)
+#223 := (= #140 #222)
+#220 := (= #137 #219)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#208 := (~ #146 #146)
+#206 := (~ #143 #143)
+#207 := [refl]: #206
+#209 := [nnf-pos #207]: #208
+#28 := (- #14)
+#27 := (- #13)
+#29 := (div #27 #28)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #15 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#149 := (iff #33 #146)
+#89 := (and #21 #23)
+#92 := (or #22 #89)
+#104 := (ite #92 #26 #101)
+#107 := (ite #19 0::Int #104)
+#110 := (= #15 #107)
+#113 := (forall (vars (?v0 Int) (?v1 Int)) #110)
+#147 := (iff #113 #146)
+#144 := (iff #110 #143)
+#141 := (= #107 #140)
+#138 := (= #104 #137)
+#135 := (iff #92 #134)
+#132 := (iff #89 #131)
+#129 := (iff #23 #128)
+#130 := [rewrite]: #129
+#122 := (iff #21 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #22 #124)
+#118 := (iff #20 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#114 := (iff #33 #113)
+#111 := (iff #32 #110)
+#108 := (= #31 #107)
+#105 := (= #30 #104)
+#102 := (= #29 #101)
+#99 := (= #28 #98)
+#100 := [rewrite]: #99
+#96 := (= #27 #95)
+#97 := [rewrite]: #96
+#103 := [monotonicity #97 #100]: #102
+#93 := (iff #25 #92)
+#90 := (iff #24 #89)
+#91 := [rewrite]: #90
+#94 := [monotonicity #91]: #93
+#106 := [monotonicity #94 #103]: #105
+#109 := [monotonicity #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [quant-intro #112]: #114
+#150 := [trans #115 #148]: #149
+#88 := [asserted]: #33
+#151 := [mp #88 #150]: #146
+#200 := [mp~ #151 #209]: #146
+#231 := [mp #200 #230]: #228
+#262 := [mp #231 #261]: #259
+#755 := [mp #262 #754]: #750
+#8 := 1::Int
+#66 := (f3 1::Int -1::Int)
+#69 := (= #66 -1::Int)
+#82 := (not #69)
+#9 := (- 1::Int)
+#10 := (f3 1::Int #9)
+#11 := (= #10 #9)
+#12 := (not #11)
+#85 := (iff #12 #82)
+#72 := (= -1::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #12 #77)
+#75 := (iff #11 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #11 #69)
+#64 := (= #9 -1::Int)
+#65 := [rewrite]: #64
+#67 := (= #10 #66)
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68 #65]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #12
+#87 := [mp #62 #86]: #82
+#680 := (not #750)
+#684 := (or #680 #69)
+#336 := (* -1::Int -1::Int)
+#420 := (* -1::Int 1::Int)
+#421 := (div #420 #336)
+#422 := (* -1::Int #421)
+#413 := (+ #66 #422)
+#424 := (= #413 0::Int)
+#425 := (div 1::Int -1::Int)
+#426 := (* -1::Int #425)
+#423 := (+ #66 #426)
+#427 := (= #423 0::Int)
+#406 := (>= 1::Int 0::Int)
+#741 := (<= -1::Int 0::Int)
+#743 := (or #741 #406)
+#400 := (not #743)
+#530 := (<= 1::Int 0::Int)
+#737 := (or #530 #741)
+#411 := (not #737)
+#412 := (or #411 #400)
+#744 := (ite #412 #427 #424)
+#745 := (= #66 0::Int)
+#746 := (= -1::Int 0::Int)
+#747 := (= 1::Int 0::Int)
+#742 := (or #747 #746)
+#748 := (ite #742 #745 #744)
+#671 := (or #680 #748)
+#665 := (iff #671 #684)
+#664 := (iff #684 #684)
+#674 := [rewrite]: #664
+#590 := (iff #748 #69)
+#578 := (ite false #745 #69)
+#588 := (iff #578 #69)
+#589 := [rewrite]: #588
+#586 := (iff #748 #578)
+#584 := (iff #744 #69)
+#678 := (ite false #69 #69)
+#567 := (iff #678 #69)
+#582 := [rewrite]: #567
+#679 := (iff #744 #678)
+#681 := (iff #424 #69)
+#702 := (+ 1::Int #66)
+#550 := (= #702 0::Int)
+#694 := (iff #550 #69)
+#695 := [rewrite]: #694
+#574 := (iff #424 #550)
+#572 := (= #413 #702)
+#705 := (+ #66 1::Int)
+#707 := (= #705 #702)
+#708 := [rewrite]: #707
+#687 := (= #413 #705)
+#688 := (= #422 1::Int)
+#714 := (= #336 1::Int)
+#711 := [rewrite]: #714
+#685 := (= #422 #336)
+#531 := (= #421 -1::Int)
+#698 := (div -1::Int 1::Int)
+#700 := (= #698 -1::Int)
+#529 := [rewrite]: #700
+#699 := (= #421 #698)
+#691 := (= #420 -1::Int)
+#692 := [rewrite]: #691
+#693 := [monotonicity #692 #711]: #699
+#532 := [trans #693 #529]: #531
+#686 := [monotonicity #532]: #685
+#689 := [trans #686 #711]: #688
+#690 := [monotonicity #689]: #687
+#573 := [trans #690 #708]: #572
+#533 := [monotonicity #573]: #574
+#583 := [trans #533 #695]: #681
+#696 := (iff #427 #69)
+#551 := (iff #427 #550)
+#703 := (= #423 #702)
+#706 := (= #423 #705)
+#715 := (= #426 1::Int)
+#428 := (= #426 #336)
+#712 := (= #425 -1::Int)
+#713 := [rewrite]: #712
+#710 := [monotonicity #713]: #428
+#704 := [trans #710 #711]: #715
+#701 := [monotonicity #704]: #706
+#709 := [trans #701 #708]: #703
+#552 := [monotonicity #709]: #551
+#697 := [trans #552 #695]: #696
+#433 := (iff #412 false)
+#399 := (or false false)
+#724 := (iff #399 false)
+#387 := [rewrite]: #724
+#431 := (iff #412 #399)
+#717 := (iff #400 false)
+#1 := true
+#374 := (not true)
+#733 := (iff #374 false)
+#736 := [rewrite]: #733
+#716 := (iff #400 #374)
+#441 := (iff #743 true)
+#447 := (or true true)
+#718 := (iff #447 true)
+#719 := [rewrite]: #718
+#448 := (iff #743 #447)
+#445 := (iff #406 true)
+#446 := [rewrite]: #445
+#727 := (iff #741 true)
+#728 := [rewrite]: #727
+#342 := [monotonicity #728 #446]: #448
+#442 := [trans #342 #719]: #441
+#720 := [monotonicity #442]: #716
+#721 := [trans #720 #736]: #717
+#722 := (iff #411 false)
+#375 := (iff #411 #374)
+#732 := (iff #737 true)
+#729 := (or false true)
+#731 := (iff #729 true)
+#369 := [rewrite]: #731
+#730 := (iff #737 #729)
+#390 := (iff #530 false)
+#726 := [rewrite]: #390
+#725 := [monotonicity #726 #728]: #730
+#734 := [trans #725 #369]: #732
+#735 := [monotonicity #734]: #375
+#723 := [trans #735 #736]: #722
+#432 := [monotonicity #723 #721]: #431
+#434 := [trans #432 #387]: #433
+#682 := [monotonicity #434 #697 #583]: #679
+#585 := [trans #682 #582]: #584
+#388 := (iff #742 false)
+#740 := (iff #742 #399)
+#403 := (iff #746 false)
+#739 := [rewrite]: #403
+#738 := (iff #747 false)
+#398 := [rewrite]: #738
+#383 := [monotonicity #398 #739]: #740
+#389 := [trans #383 #387]: #388
+#587 := [monotonicity #389 #585]: #586
+#683 := [trans #587 #589]: #590
+#662 := [monotonicity #683]: #665
+#675 := [trans #662 #674]: #665
+#673 := [quant-inst #8 #63]: #671
+#676 := [mp #673 #675]: #684
+[unit-resolution #676 #87 #755]: false
+unsat
+d7870bb48e209893f272c06c1d45c5a7c1765225 306 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#17 := (f3 #15 #16)
+#742 := (pattern #17)
+#18 := 0::Int
+#65 := -1::Int
+#91 := (* -1::Int #16)
+#88 := (* -1::Int #15)
+#94 := (div #88 #91)
+#245 := (* -1::Int #94)
+#246 := (+ #17 #245)
+#247 := (= #246 0::Int)
+#28 := (div #15 #16)
+#242 := (* -1::Int #28)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
+#120 := (>= #15 0::Int)
+#113 := (<= #16 0::Int)
+#205 := (or #113 #120)
+#206 := (not #205)
+#109 := (<= #15 0::Int)
+#203 := (or #109 #113)
+#204 := (not #203)
+#209 := (or #204 #206)
+#248 := (ite #209 #244 #247)
+#241 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#249 := (ite #21 #241 #248)
+#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#746 := (iff #252 #743)
+#744 := (iff #249 #249)
+#745 := [refl]: #744
+#747 := [quant-intro #745]: #746
+#212 := (ite #209 #28 #94)
+#215 := (ite #21 0::Int #212)
+#218 := (= #17 #215)
+#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
+#253 := (iff #221 #252)
+#250 := (iff #218 #249)
+#251 := [rewrite]: #250
+#254 := [quant-intro #251]: #253
+#121 := (not #120)
+#114 := (not #113)
+#124 := (and #114 #121)
+#110 := (not #109)
+#117 := (and #110 #114)
+#127 := (or #117 #124)
+#130 := (ite #127 #28 #94)
+#133 := (ite #21 0::Int #130)
+#136 := (= #17 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#216 := (= #133 #215)
+#213 := (= #130 #212)
+#210 := (iff #127 #209)
+#207 := (iff #124 #206)
+#208 := [rewrite]: #207
+#197 := (iff #117 #204)
+#198 := [rewrite]: #197
+#211 := [monotonicity #198 #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [quant-intro #220]: #222
+#201 := (~ #139 #139)
+#199 := (~ #136 #136)
+#200 := [refl]: #199
+#202 := [nnf-pos #200]: #201
+#30 := (- #16)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#142 := (iff #35 #139)
+#81 := (and #23 #25)
+#85 := (or #24 #81)
+#97 := (ite #85 #28 #94)
+#100 := (ite #21 0::Int #97)
+#103 := (= #17 #100)
+#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
+#140 := (iff #106 #139)
+#137 := (iff #103 #136)
+#134 := (= #100 #133)
+#131 := (= #97 #130)
+#128 := (iff #85 #127)
+#125 := (iff #81 #124)
+#122 := (iff #25 #121)
+#123 := [rewrite]: #122
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#126 := [monotonicity #116 #123]: #125
+#118 := (iff #24 #117)
+#111 := (iff #22 #110)
+#112 := [rewrite]: #111
+#119 := [monotonicity #112 #116]: #118
+#129 := [monotonicity #119 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#107 := (iff #35 #106)
+#104 := (iff #34 #103)
+#101 := (= #33 #100)
+#98 := (= #32 #97)
+#95 := (= #31 #94)
+#92 := (= #30 #91)
+#93 := [rewrite]: #92
+#89 := (= #29 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90 #93]: #95
+#86 := (iff #27 #85)
+#83 := (iff #26 #81)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#99 := [monotonicity #87 #96]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [quant-intro #105]: #107
+#143 := [trans #108 #141]: #142
+#80 := [asserted]: #35
+#144 := [mp #80 #143]: #139
+#193 := [mp~ #144 #202]: #139
+#224 := [mp #193 #223]: #221
+#255 := [mp #224 #254]: #252
+#748 := [mp #255 #747]: #743
+#71 := -3::Int
+#8 := 3::Int
+#68 := (f3 3::Int -1::Int)
+#74 := (= #68 -3::Int)
+#77 := (not #74)
+#12 := (- 3::Int)
+#9 := 1::Int
+#10 := (- 1::Int)
+#11 := (f3 3::Int #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#78 := (iff #14 #77)
+#75 := (iff #13 #74)
+#72 := (= #12 -3::Int)
+#73 := [rewrite]: #72
+#69 := (= #11 #68)
+#66 := (= #10 -1::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [monotonicity #70 #73]: #75
+#79 := [monotonicity #76]: #78
+#64 := [asserted]: #14
+#82 := [mp #64 #79]: #77
+#666 := (not #743)
+#658 := (or #666 #74)
+#329 := (* -1::Int -1::Int)
+#413 := (* -1::Int 3::Int)
+#414 := (div #413 #329)
+#415 := (* -1::Int #414)
+#406 := (+ #68 #415)
+#417 := (= #406 0::Int)
+#418 := (div 3::Int -1::Int)
+#419 := (* -1::Int #418)
+#416 := (+ #68 #419)
+#420 := (= #416 0::Int)
+#399 := (>= 3::Int 0::Int)
+#734 := (<= -1::Int 0::Int)
+#736 := (or #734 #399)
+#393 := (not #736)
+#523 := (<= 3::Int 0::Int)
+#730 := (or #523 #734)
+#404 := (not #730)
+#405 := (or #404 #393)
+#737 := (ite #405 #420 #417)
+#738 := (= #68 0::Int)
+#739 := (= -1::Int 0::Int)
+#740 := (= 3::Int 0::Int)
+#735 := (or #740 #739)
+#741 := (ite #735 #738 #737)
+#655 := (or #666 #741)
+#667 := (iff #655 #658)
+#669 := (iff #658 #658)
+#665 := [rewrite]: #669
+#677 := (iff #741 #74)
+#581 := (ite false #738 #74)
+#676 := (iff #581 #74)
+#673 := [rewrite]: #676
+#582 := (iff #741 #581)
+#579 := (iff #737 #74)
+#560 := (ite false #74 #74)
+#578 := (iff #560 #74)
+#571 := [rewrite]: #578
+#575 := (iff #737 #560)
+#672 := (iff #417 #74)
+#700 := (+ 3::Int #68)
+#544 := (= #700 0::Int)
+#688 := (iff #544 #74)
+#689 := [rewrite]: #688
+#576 := (iff #417 #544)
+#526 := (= #406 #700)
+#699 := (+ #68 3::Int)
+#701 := (= #699 #700)
+#696 := [rewrite]: #701
+#566 := (= #406 #699)
+#683 := (= #415 3::Int)
+#421 := (* -1::Int -3::Int)
+#704 := (= #421 3::Int)
+#708 := [rewrite]: #704
+#682 := (= #415 #421)
+#679 := (= #414 -3::Int)
+#693 := (div -3::Int 1::Int)
+#525 := (= #693 -3::Int)
+#678 := [rewrite]: #525
+#522 := (= #414 #693)
+#692 := (= #329 1::Int)
+#686 := [rewrite]: #692
+#685 := (= #413 -3::Int)
+#691 := [rewrite]: #685
+#524 := [monotonicity #691 #686]: #522
+#681 := [trans #524 #678]: #679
+#680 := [monotonicity #681]: #682
+#565 := [trans #680 #708]: #683
+#567 := [monotonicity #565]: #566
+#674 := [trans #567 #696]: #526
+#671 := [monotonicity #674]: #576
+#675 := [trans #671 #689]: #672
+#690 := (iff #420 #74)
+#545 := (iff #420 #544)
+#702 := (= #416 #700)
+#694 := (= #416 #699)
+#697 := (= #419 3::Int)
+#703 := (= #419 #421)
+#705 := (= #418 -3::Int)
+#706 := [rewrite]: #705
+#707 := [monotonicity #706]: #703
+#698 := [trans #707 #708]: #697
+#695 := [monotonicity #698]: #694
+#543 := [trans #695 #696]: #702
+#687 := [monotonicity #543]: #545
+#684 := [trans #687 #689]: #690
+#426 := (iff #405 false)
+#392 := (or false false)
+#717 := (iff #392 false)
+#380 := [rewrite]: #717
+#424 := (iff #405 #392)
+#710 := (iff #393 false)
+#1 := true
+#367 := (not true)
+#726 := (iff #367 false)
+#729 := [rewrite]: #726
+#709 := (iff #393 #367)
+#434 := (iff #736 true)
+#440 := (or true true)
+#711 := (iff #440 true)
+#712 := [rewrite]: #711
+#441 := (iff #736 #440)
+#438 := (iff #399 true)
+#439 := [rewrite]: #438
+#720 := (iff #734 true)
+#721 := [rewrite]: #720
+#335 := [monotonicity #721 #439]: #441
+#435 := [trans #335 #712]: #434
+#713 := [monotonicity #435]: #709
+#714 := [trans #713 #729]: #710
+#715 := (iff #404 false)
+#368 := (iff #404 #367)
+#725 := (iff #730 true)
+#722 := (or false true)
+#724 := (iff #722 true)
+#362 := [rewrite]: #724
+#723 := (iff #730 #722)
+#383 := (iff #523 false)
+#719 := [rewrite]: #383
+#718 := [monotonicity #719 #721]: #723
+#727 := [trans #718 #362]: #725
+#728 := [monotonicity #727]: #368
+#716 := [trans #728 #729]: #715
+#425 := [monotonicity #716 #714]: #424
+#427 := [trans #425 #380]: #426
+#577 := [monotonicity #427 #684 #675]: #575
+#580 := [trans #577 #571]: #579
+#381 := (iff #735 false)
+#733 := (iff #735 #392)
+#396 := (iff #739 false)
+#732 := [rewrite]: #396
+#731 := (iff #740 false)
+#391 := [rewrite]: #731
+#376 := [monotonicity #391 #732]: #733
+#382 := [trans #376 #380]: #381
+#583 := [monotonicity #382 #580]: #582
+#664 := [trans #583 #673]: #677
+#668 := [monotonicity #664]: #667
+#670 := [trans #668 #665]: #667
+#657 := [quant-inst #8 #65]: #655
+#659 := [mp #657 #670]: #658
+[unit-resolution #659 #82 #748]: false
+unsat
+5ee37b7887579207f198e2d96f811691f176d723 350 0
+#2 := false
+#18 := 0::Int
+#9 := 1::Int
+decl f4 :: Int
+#8 := f4
+#65 := -1::Int
+#71 := (* -1::Int f4)
+#714 := (div #71 1::Int)
+#712 := (* -1::Int #714)
+decl f3 :: (-> Int Int Int)
+#68 := (f3 f4 -1::Int)
+#717 := (+ #68 #712)
+#691 := (<= #717 0::Int)
+#708 := (= #717 0::Int)
+#744 := (= f4 0::Int)
+#574 := (not #744)
+#739 := (<= f4 0::Int)
+#615 := [hypothesis]: #744
+#595 := (or #574 #739)
+#541 := [th-lemma arith triangle-eq]: #595
+#596 := [unit-resolution #541 #615]: #739
+#80 := (+ f4 #68)
+#338 := (<= #80 0::Int)
+#577 := (not #338)
+#422 := (>= #80 0::Int)
+#743 := (>= f4 0::Int)
+#684 := (not #708)
+#689 := (>= #717 0::Int)
+#621 := (not #689)
+#630 := (not #422)
+#631 := [hypothesis]: #630
+#622 := (or #621 #422)
+#629 := [hypothesis]: #689
+#665 := (+ f4 #714)
+#662 := (>= #665 0::Int)
+#672 := (= #665 0::Int)
+#1 := true
+#62 := [true-axiom]: true
+#632 := (or false #672)
+#633 := [th-lemma arith]: #632
+#628 := [unit-resolution #633 #62]: #672
+#634 := (not #672)
+#620 := (or #634 #662)
+#616 := [th-lemma arith triangle-eq]: #620
+#617 := [unit-resolution #616 #628]: #662
+#618 := [th-lemma arith farkas 1 -1 1 #617 #631 #629]: false
+#623 := [lemma #618]: #622
+#661 := [unit-resolution #623 #631]: #621
+#624 := (or #684 #689)
+#619 := [th-lemma arith triangle-eq]: #624
+#625 := [unit-resolution #619 #661]: #684
+#599 := (or #744 #708)
+#748 := (= #68 0::Int)
+#696 := (ite #744 #748 #708)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#17 := (f3 #15 #16)
+#751 := (pattern #17)
+#100 := (* -1::Int #16)
+#97 := (* -1::Int #15)
+#103 := (div #97 #100)
+#254 := (* -1::Int #103)
+#255 := (+ #17 #254)
+#256 := (= #255 0::Int)
+#28 := (div #15 #16)
+#251 := (* -1::Int #28)
+#252 := (+ #17 #251)
+#253 := (= #252 0::Int)
+#129 := (>= #15 0::Int)
+#122 := (<= #16 0::Int)
+#214 := (or #122 #129)
+#215 := (not #214)
+#118 := (<= #15 0::Int)
+#212 := (or #118 #122)
+#213 := (not #212)
+#218 := (or #213 #215)
+#257 := (ite #218 #253 #256)
+#250 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#258 := (ite #21 #250 #257)
+#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258)
+#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
+#755 := (iff #261 #752)
+#753 := (iff #258 #258)
+#754 := [refl]: #753
+#756 := [quant-intro #754]: #755
+#221 := (ite #218 #28 #103)
+#224 := (ite #21 0::Int #221)
+#227 := (= #17 #224)
+#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
+#262 := (iff #230 #261)
+#259 := (iff #227 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#130 := (not #129)
+#123 := (not #122)
+#133 := (and #123 #130)
+#119 := (not #118)
+#126 := (and #119 #123)
+#136 := (or #126 #133)
+#139 := (ite #136 #28 #103)
+#142 := (ite #21 0::Int #139)
+#145 := (= #17 #142)
+#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
+#231 := (iff #148 #230)
+#228 := (iff #145 #227)
+#225 := (= #142 #224)
+#222 := (= #139 #221)
+#219 := (iff #136 #218)
+#216 := (iff #133 #215)
+#217 := [rewrite]: #216
+#206 := (iff #126 #213)
+#207 := [rewrite]: #206
+#220 := [monotonicity #207 #217]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#210 := (~ #148 #148)
+#208 := (~ #145 #145)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#30 := (- #16)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#151 := (iff #35 #148)
+#91 := (and #23 #25)
+#94 := (or #24 #91)
+#106 := (ite #94 #28 #103)
+#109 := (ite #21 0::Int #106)
+#112 := (= #17 #109)
+#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
+#149 := (iff #115 #148)
+#146 := (iff #112 #145)
+#143 := (= #109 #142)
+#140 := (= #106 #139)
+#137 := (iff #94 #136)
+#134 := (iff #91 #133)
+#131 := (iff #25 #130)
+#132 := [rewrite]: #131
+#124 := (iff #23 #123)
+#125 := [rewrite]: #124
+#135 := [monotonicity #125 #132]: #134
+#127 := (iff #24 #126)
+#120 := (iff #22 #119)
+#121 := [rewrite]: #120
+#128 := [monotonicity #121 #125]: #127
+#138 := [monotonicity #128 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#116 := (iff #35 #115)
+#113 := (iff #34 #112)
+#110 := (= #33 #109)
+#107 := (= #32 #106)
+#104 := (= #31 #103)
+#101 := (= #30 #100)
+#102 := [rewrite]: #101
+#98 := (= #29 #97)
+#99 := [rewrite]: #98
+#105 := [monotonicity #99 #102]: #104
+#95 := (iff #27 #94)
+#92 := (iff #26 #91)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#108 := [monotonicity #96 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [quant-intro #114]: #116
+#152 := [trans #117 #150]: #151
+#90 := [asserted]: #35
+#153 := [mp #90 #152]: #148
+#202 := [mp~ #153 #211]: #148
+#233 := [mp #202 #232]: #230
+#264 := [mp #233 #263]: #261
+#757 := [mp #264 #756]: #752
+#699 := (not #752)
+#693 := (or #699 #696)
+#423 := (* -1::Int -1::Int)
+#424 := (div #71 #423)
+#415 := (* -1::Int #424)
+#426 := (+ #68 #415)
+#427 := (= #426 0::Int)
+#428 := (div f4 -1::Int)
+#425 := (* -1::Int #428)
+#429 := (+ #68 #425)
+#408 := (= #429 0::Int)
+#745 := (<= -1::Int 0::Int)
+#402 := (or #745 #743)
+#532 := (not #402)
+#413 := (or #739 #745)
+#414 := (not #413)
+#746 := (or #414 #532)
+#747 := (ite #746 #408 #427)
+#749 := (= -1::Int 0::Int)
+#750 := (or #744 #749)
+#740 := (ite #750 #748 #747)
+#694 := (or #699 #740)
+#701 := (iff #694 #693)
+#702 := (iff #693 #693)
+#531 := [rewrite]: #702
+#697 := (iff #740 #696)
+#553 := (iff #747 #708)
+#709 := (ite false #408 #708)
+#711 := (iff #709 #708)
+#552 := [rewrite]: #711
+#710 := (iff #747 #709)
+#703 := (iff #427 #708)
+#706 := (= #426 #717)
+#716 := (= #415 #712)
+#715 := (= #424 #714)
+#435 := (= #423 1::Int)
+#436 := [rewrite]: #435
+#430 := [monotonicity #436]: #715
+#713 := [monotonicity #430]: #716
+#707 := [monotonicity #713]: #706
+#704 := [monotonicity #707]: #703
+#433 := (iff #746 false)
+#444 := (or false false)
+#719 := (iff #444 false)
+#723 := [rewrite]: #719
+#718 := (iff #746 #444)
+#721 := (iff #532 false)
+#371 := (not true)
+#376 := (iff #371 false)
+#377 := [rewrite]: #376
+#344 := (iff #532 #371)
+#449 := (iff #402 true)
+#738 := (or true #743)
+#447 := (iff #738 true)
+#448 := [rewrite]: #447
+#724 := (iff #402 #738)
+#391 := (iff #745 true)
+#392 := [rewrite]: #391
+#725 := [monotonicity #392]: #724
+#450 := [trans #725 #448]: #449
+#720 := [monotonicity #450]: #344
+#443 := [trans #720 #377]: #721
+#737 := (iff #414 false)
+#734 := (iff #414 #371)
+#727 := (iff #413 true)
+#728 := (or #739 true)
+#731 := (iff #728 true)
+#732 := [rewrite]: #731
+#729 := (iff #413 #728)
+#730 := [monotonicity #392]: #729
+#733 := [trans #730 #732]: #727
+#736 := [monotonicity #733]: #734
+#735 := [trans #736 #377]: #737
+#722 := [monotonicity #735 #443]: #718
+#434 := [trans #722 #723]: #433
+#705 := [monotonicity #434 #704]: #710
+#554 := [trans #705 #552]: #553
+#389 := (iff #750 #744)
+#741 := (or #744 false)
+#385 := (iff #741 #744)
+#726 := [rewrite]: #385
+#401 := (iff #750 #741)
+#400 := (iff #749 false)
+#405 := [rewrite]: #400
+#742 := [monotonicity #405]: #401
+#390 := [trans #742 #726]: #389
+#698 := [monotonicity #390 #554]: #697
+#695 := [monotonicity #698]: #701
+#533 := [trans #695 #531]: #701
+#700 := [quant-inst #8 #65]: #694
+#534 := [mp #700 #533]: #693
+#598 := [unit-resolution #534 #757]: #696
+#692 := (not #696)
+#535 := (or #692 #744 #708)
+#683 := [def-axiom]: #535
+#600 := [unit-resolution #683 #598]: #599
+#493 := [unit-resolution #600 #625]: #744
+#604 := (or #574 #743)
+#605 := [th-lemma arith triangle-eq]: #604
+#606 := [unit-resolution #605 #493]: #743
+#688 := (>= #68 0::Int)
+#611 := (or #574 #748)
+#575 := (or #692 #574 #748)
+#576 := [def-axiom]: #575
+#607 := [unit-resolution #576 #598]: #611
+#608 := [unit-resolution #607 #493]: #748
+#585 := (not #748)
+#609 := (or #585 #688)
+#612 := [th-lemma arith triangle-eq]: #609
+#613 := [unit-resolution #612 #608]: #688
+#614 := [th-lemma arith farkas 1 -1 1 #613 #631 #606]: false
+#610 := [lemma #614]: #422
+#597 := (or #577 #630)
+#81 := (= #80 0::Int)
+#84 := (not #81)
+#12 := (- f4)
+#10 := (- 1::Int)
+#11 := (f3 f4 #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#87 := (iff #14 #84)
+#74 := (= #68 #71)
+#77 := (not #74)
+#85 := (iff #77 #84)
+#82 := (iff #74 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#78 := (iff #14 #77)
+#75 := (iff #13 #74)
+#72 := (= #12 #71)
+#73 := [rewrite]: #72
+#69 := (= #11 #68)
+#66 := (= #10 -1::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [monotonicity #70 #73]: #75
+#79 := [monotonicity #76]: #78
+#88 := [trans #79 #86]: #87
+#64 := [asserted]: #14
+#89 := [mp #64 #88]: #84
+#601 := (or #81 #577 #630)
+#602 := [th-lemma arith triangle-eq]: #601
+#603 := [unit-resolution #602 #89]: #597
+#571 := [unit-resolution #603 #610]: #577
+#687 := (<= #68 0::Int)
+#578 := [unit-resolution #607 #615]: #748
+#537 := (or #585 #687)
+#568 := [th-lemma arith triangle-eq]: #537
+#570 := [unit-resolution #568 #578]: #687
+#572 := [th-lemma arith farkas 1 -1 1 #570 #571 #596]: false
+#579 := [lemma #572]: #574
+#582 := [unit-resolution #600 #579]: #708
+#583 := (or #684 #691)
+#593 := [th-lemma arith triangle-eq]: #583
+#573 := [unit-resolution #593 #582]: #691
+#581 := (<= #665 0::Int)
+#594 := (or #634 #581)
+#549 := [th-lemma arith triangle-eq]: #594
+#550 := [unit-resolution #549 #628]: #581
+[th-lemma arith farkas 1 -1 1 #550 #571 #573]: false
+unsat
+8db711c99a743e7c5b35063fc01bbf7e9119b29e 292 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#750 := (pattern #15)
+#8 := 0::Int
+#88 := -1::Int
+#92 := (* -1::Int #14)
+#89 := (* -1::Int #13)
+#95 := (div #89 #92)
+#252 := (* -1::Int #95)
+#253 := (+ #15 #252)
+#254 := (= #253 0::Int)
+#25 := (div #13 #14)
+#249 := (* -1::Int #25)
+#250 := (+ #15 #249)
+#251 := (= #250 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#255 := (ite #216 #251 #254)
+#248 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#16 := (= #13 0::Int)
+#18 := (or #16 #17)
+#256 := (ite #18 #248 #255)
+#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#754 := (iff #259 #751)
+#752 := (iff #256 #256)
+#753 := [refl]: #752
+#755 := [quant-intro #753]: #754
+#219 := (ite #216 #25 #95)
+#222 := (ite #18 0::Int #219)
+#225 := (= #15 #222)
+#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#137 := (ite #134 #25 #95)
+#140 := (ite #18 0::Int #137)
+#143 := (= #15 #140)
+#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
+#229 := (iff #146 #228)
+#226 := (iff #143 #225)
+#223 := (= #140 #222)
+#220 := (= #137 #219)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#208 := (~ #146 #146)
+#206 := (~ #143 #143)
+#207 := [refl]: #206
+#209 := [nnf-pos #207]: #208
+#27 := (- #14)
+#26 := (- #13)
+#28 := (div #26 #27)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#29 := (ite #24 #25 #28)
+#30 := (ite #18 0::Int #29)
+#31 := (= #15 #30)
+#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
+#149 := (iff #32 #146)
+#82 := (and #20 #22)
+#85 := (or #21 #82)
+#98 := (ite #85 #25 #95)
+#76 := (= 0::Int #14)
+#73 := (= 0::Int #13)
+#79 := (or #73 #76)
+#101 := (ite #79 0::Int #98)
+#104 := (= #15 #101)
+#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
+#147 := (iff #107 #146)
+#144 := (iff #104 #143)
+#141 := (= #101 #140)
+#138 := (= #98 #137)
+#135 := (iff #85 #134)
+#132 := (iff #82 #131)
+#129 := (iff #22 #128)
+#130 := [rewrite]: #129
+#122 := (iff #20 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #21 #124)
+#118 := (iff #19 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#139 := [monotonicity #136]: #138
+#114 := (iff #79 #18)
+#112 := (iff #76 #17)
+#113 := [rewrite]: #112
+#110 := (iff #73 #16)
+#111 := [rewrite]: #110
+#115 := [monotonicity #111 #113]: #114
+#142 := [monotonicity #115 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#108 := (iff #32 #107)
+#105 := (iff #31 #104)
+#102 := (= #30 #101)
+#99 := (= #29 #98)
+#96 := (= #28 #95)
+#93 := (= #27 #92)
+#94 := [rewrite]: #93
+#90 := (= #26 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#86 := (iff #24 #85)
+#83 := (iff #23 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#100 := [monotonicity #87 #97]: #99
+#80 := (iff #18 #79)
+#77 := (iff #17 #76)
+#78 := [rewrite]: #77
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#81 := [monotonicity #75 #78]: #80
+#103 := [monotonicity #81 #100]: #102
+#106 := [monotonicity #103]: #105
+#109 := [quant-intro #106]: #108
+#150 := [trans #109 #148]: #149
+#72 := [asserted]: #32
+#151 := [mp #72 #150]: #146
+#200 := [mp~ #151 #209]: #146
+#231 := [mp #200 #230]: #228
+#262 := [mp #231 #261]: #259
+#756 := [mp #262 #755]: #751
+#9 := 3::Int
+#10 := (f3 0::Int 3::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#585 := (not #751)
+#586 := (or #585 #11)
+#336 := (* -1::Int 3::Int)
+#421 := (* -1::Int 0::Int)
+#422 := (div #421 #336)
+#423 := (* -1::Int #422)
+#414 := (+ #10 #423)
+#425 := (= #414 0::Int)
+#426 := (div 0::Int 3::Int)
+#354 := (* -1::Int #426)
+#427 := (+ #10 #354)
+#424 := (= #427 0::Int)
+#428 := (>= 0::Int 0::Int)
+#407 := (<= 3::Int 0::Int)
+#742 := (or #407 #428)
+#744 := (not #742)
+#401 := (<= 0::Int 0::Int)
+#531 := (or #401 #407)
+#738 := (not #531)
+#412 := (or #738 #744)
+#413 := (ite #412 #424 #425)
+#745 := (= 3::Int 0::Int)
+#746 := (= 0::Int 0::Int)
+#747 := (or #746 #745)
+#748 := (ite #747 #11 #413)
+#579 := (or #585 #748)
+#588 := (iff #579 #586)
+#590 := (iff #586 #586)
+#591 := [rewrite]: #590
+#568 := (iff #748 #11)
+#1 := true
+#682 := (ite true #11 #11)
+#680 := (iff #682 #11)
+#683 := [rewrite]: #680
+#584 := (iff #748 #682)
+#575 := (iff #413 #11)
+#690 := (ite false #11 #11)
+#573 := (iff #690 #11)
+#574 := [rewrite]: #573
+#688 := (iff #413 #690)
+#687 := (iff #425 #11)
+#533 := (= #414 #10)
+#716 := (+ #10 0::Int)
+#707 := (= #716 #10)
+#702 := [rewrite]: #707
+#530 := (= #414 #716)
+#694 := (= #423 0::Int)
+#429 := (= #421 0::Int)
+#711 := [rewrite]: #429
+#699 := (= #423 #421)
+#692 := (= #422 0::Int)
+#710 := -3::Int
+#553 := (div 0::Int -3::Int)
+#697 := (= #553 0::Int)
+#698 := [rewrite]: #697
+#695 := (= #422 #553)
+#551 := (= #336 -3::Int)
+#552 := [rewrite]: #551
+#696 := [monotonicity #711 #552]: #695
+#693 := [trans #696 #698]: #692
+#700 := [monotonicity #693]: #699
+#701 := [trans #700 #711]: #694
+#532 := [monotonicity #701]: #530
+#686 := [trans #532 #702]: #533
+#689 := [monotonicity #686]: #687
+#709 := (iff #424 #11)
+#703 := (= #427 #10)
+#705 := (= #427 #716)
+#715 := (= #354 0::Int)
+#713 := (= #354 #421)
+#434 := (= #426 0::Int)
+#435 := [rewrite]: #434
+#714 := [monotonicity #435]: #713
+#712 := [trans #714 #711]: #715
+#706 := [monotonicity #712]: #705
+#708 := [trans #706 #702]: #703
+#704 := [monotonicity #708]: #709
+#432 := (iff #412 false)
+#443 := (or false false)
+#718 := (iff #443 false)
+#722 := [rewrite]: #718
+#717 := (iff #412 #443)
+#720 := (iff #744 false)
+#726 := (not true)
+#733 := (iff #726 false)
+#735 := [rewrite]: #733
+#342 := (iff #744 #726)
+#448 := (iff #742 true)
+#737 := (or false true)
+#446 := (iff #737 true)
+#447 := [rewrite]: #446
+#723 := (iff #742 #737)
+#736 := (iff #428 true)
+#734 := [rewrite]: #736
+#391 := (iff #407 false)
+#727 := [rewrite]: #391
+#724 := [monotonicity #727 #734]: #723
+#449 := [trans #724 #447]: #448
+#719 := [monotonicity #449]: #342
+#442 := [trans #719 #735]: #720
+#375 := (iff #738 false)
+#732 := (iff #738 #726)
+#730 := (iff #531 true)
+#404 := (or true false)
+#741 := (iff #404 true)
+#384 := [rewrite]: #741
+#728 := (iff #531 #404)
+#389 := (iff #401 true)
+#390 := [rewrite]: #389
+#729 := [monotonicity #390 #727]: #728
+#731 := [trans #729 #384]: #730
+#370 := [monotonicity #731]: #732
+#376 := [trans #370 #735]: #375
+#721 := [monotonicity #376 #442]: #717
+#433 := [trans #721 #722]: #432
+#691 := [monotonicity #433 #704 #689]: #688
+#534 := [trans #691 #574]: #575
+#725 := (iff #747 true)
+#740 := (iff #747 #404)
+#739 := (iff #745 false)
+#399 := [rewrite]: #739
+#743 := (iff #746 true)
+#749 := [rewrite]: #743
+#400 := [monotonicity #749 #399]: #740
+#388 := [trans #400 #384]: #725
+#679 := [monotonicity #388 #534]: #584
+#583 := [trans #679 #683]: #568
+#589 := [monotonicity #583]: #588
+#684 := [trans #589 #591]: #588
+#587 := [quant-inst #8 #9]: #579
+#681 := [mp #587 #684]: #586
+[unit-resolution #681 #61 #756]: false
+unsat
+6aeb136b7e9b0d9bd350f376d5db91cb7cdd5fa1 317 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#766 := (pattern #16)
+#8 := 0::Int
+#104 := -1::Int
+#108 := (* -1::Int #15)
+#105 := (* -1::Int #14)
+#111 := (div #105 #108)
+#268 := (* -1::Int #111)
+#269 := (+ #16 #268)
+#270 := (= #269 0::Int)
+#26 := (div #14 #15)
+#265 := (* -1::Int #26)
+#266 := (+ #16 #265)
+#267 := (= #266 0::Int)
+#143 := (>= #14 0::Int)
+#136 := (<= #15 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #14 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#271 := (ite #232 #267 #270)
+#264 := (= #16 0::Int)
+#18 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#19 := (or #17 #18)
+#272 := (ite #19 #264 #271)
+#767 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #766) #272)
+#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
+#770 := (iff #275 #767)
+#768 := (iff #272 #272)
+#769 := [refl]: #768
+#771 := [quant-intro #769]: #770
+#235 := (ite #232 #26 #111)
+#238 := (ite #19 0::Int #235)
+#241 := (= #16 #238)
+#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
+#276 := (iff #244 #275)
+#273 := (iff #241 #272)
+#274 := [rewrite]: #273
+#277 := [quant-intro #274]: #276
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#153 := (ite #150 #26 #111)
+#156 := (ite #19 0::Int #153)
+#159 := (= #16 #156)
+#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
+#245 := (iff #162 #244)
+#242 := (iff #159 #241)
+#239 := (= #156 #238)
+#236 := (= #153 #235)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [quant-intro #243]: #245
+#224 := (~ #162 #162)
+#222 := (~ #159 #159)
+#223 := [refl]: #222
+#225 := [nnf-pos #223]: #224
+#28 := (- #15)
+#27 := (- #14)
+#29 := (div #27 #28)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #16 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#165 := (iff #33 #162)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#114 := (ite #101 #26 #111)
+#92 := (= 0::Int #15)
+#89 := (= 0::Int #14)
+#95 := (or #89 #92)
+#117 := (ite #95 0::Int #114)
+#120 := (= #16 #117)
+#123 := (forall (vars (?v0 Int) (?v1 Int)) #120)
+#163 := (iff #123 #162)
+#160 := (iff #120 #159)
+#157 := (= #117 #156)
+#154 := (= #114 #153)
+#151 := (iff #101 #150)
+#148 := (iff #98 #147)
+#145 := (iff #23 #144)
+#146 := [rewrite]: #145
+#138 := (iff #21 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #22 #140)
+#134 := (iff #20 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#155 := [monotonicity #152]: #154
+#130 := (iff #95 #19)
+#128 := (iff #92 #18)
+#129 := [rewrite]: #128
+#126 := (iff #89 #17)
+#127 := [rewrite]: #126
+#131 := [monotonicity #127 #129]: #130
+#158 := [monotonicity #131 #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#124 := (iff #33 #123)
+#121 := (iff #32 #120)
+#118 := (= #31 #117)
+#115 := (= #30 #114)
+#112 := (= #29 #111)
+#109 := (= #28 #108)
#110 := [rewrite]: #109
-#107 := (= #24 #106)
-#104 := (= #23 -1::Int)
-#66 := (< 0::Int -1::Int)
-#72 := (and #17 #66)
-#69 := (and #14 #66)
-#75 := (or #69 #72)
-#99 := (ite #75 -1::Int -1::Int)
-#102 := (= #99 -1::Int)
-#103 := [rewrite]: #102
-#100 := (= #23 #99)
-#97 := (= #22 -1::Int)
-#92 := (div -1::Int 1::Int)
-#95 := (= #92 -1::Int)
+#106 := (= #27 #105)
+#107 := [rewrite]: #106
+#113 := [monotonicity #107 #110]: #112
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#116 := [monotonicity #103 #113]: #115
+#96 := (iff #19 #95)
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#119 := [monotonicity #97 #116]: #118
+#122 := [monotonicity #119]: #121
+#125 := [quant-intro #122]: #124
+#166 := [trans #125 #164]: #165
+#88 := [asserted]: #33
+#167 := [mp #88 #166]: #162
+#216 := [mp~ #167 #225]: #162
+#247 := [mp #216 #246]: #244
+#278 := [mp #247 #277]: #275
+#772 := [mp #278 #771]: #767
+#63 := -3::Int
+#66 := (f3 0::Int -3::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 0::Int #10)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #11 #66)
+#64 := (= #10 -3::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#599 := (not #767)
+#601 := (or #599 #69)
+#352 := (* -1::Int -3::Int)
+#437 := (* -1::Int 0::Int)
+#438 := (div #437 #352)
+#439 := (* -1::Int #438)
+#430 := (+ #66 #439)
+#441 := (= #430 0::Int)
+#442 := (div 0::Int -3::Int)
+#370 := (* -1::Int #442)
+#443 := (+ #66 #370)
+#440 := (= #443 0::Int)
+#444 := (>= 0::Int 0::Int)
+#423 := (<= -3::Int 0::Int)
+#758 := (or #423 #444)
+#760 := (not #758)
+#417 := (<= 0::Int 0::Int)
+#547 := (or #417 #423)
+#754 := (not #547)
+#428 := (or #754 #760)
+#429 := (ite #428 #440 #441)
+#761 := (= -3::Int 0::Int)
+#762 := (= 0::Int 0::Int)
+#763 := (or #762 #761)
+#764 := (ite #763 #69 #429)
+#602 := (or #599 #764)
+#603 := (iff #602 #601)
+#605 := (iff #601 #601)
+#606 := [rewrite]: #605
+#699 := (iff #764 #69)
+#1 := true
+#550 := (ite true #69 #69)
+#695 := (iff #550 #69)
+#696 := [rewrite]: #695
+#698 := (iff #764 #550)
+#590 := (iff #429 #69)
+#705 := (ite false #69 #69)
+#707 := (iff #705 #69)
+#589 := [rewrite]: #707
+#706 := (iff #429 #705)
+#702 := (iff #441 #69)
+#548 := (= #430 #66)
+#732 := (+ #66 0::Int)
+#723 := (= #732 #66)
+#718 := [rewrite]: #723
+#717 := (= #430 #732)
+#716 := (= #439 0::Int)
+#445 := (= #437 0::Int)
+#727 := [rewrite]: #445
+#709 := (= #439 #437)
+#714 := (= #438 0::Int)
+#568 := (div 0::Int 3::Int)
+#712 := (= #568 0::Int)
+#713 := [rewrite]: #712
+#569 := (= #438 #568)
+#726 := (= #352 3::Int)
+#567 := [rewrite]: #726
+#711 := [monotonicity #727 #567]: #569
+#708 := [trans #711 #713]: #714
+#715 := [monotonicity #708]: #709
+#710 := [trans #715 #727]: #716
+#546 := [monotonicity #710]: #717
+#549 := [trans #546 #718]: #548
+#703 := [monotonicity #549]: #702
+#725 := (iff #440 #69)
+#719 := (= #443 #66)
+#721 := (= #443 #732)
+#731 := (= #370 0::Int)
+#729 := (= #370 #437)
+#450 := (= #442 0::Int)
+#451 := [rewrite]: #450
+#730 := [monotonicity #451]: #729
+#728 := [trans #730 #727]: #731
+#722 := [monotonicity #728]: #721
+#724 := [trans #722 #718]: #719
+#720 := [monotonicity #724]: #725
+#448 := (iff #428 false)
+#459 := (or false false)
+#734 := (iff #459 false)
+#738 := [rewrite]: #734
+#733 := (iff #428 #459)
+#736 := (iff #760 false)
+#749 := (not true)
+#392 := (iff #749 false)
+#752 := [rewrite]: #392
+#358 := (iff #760 #749)
+#464 := (iff #758 true)
+#744 := (or true true)
+#747 := (iff #744 true)
+#742 := [rewrite]: #747
+#462 := (iff #758 #744)
+#739 := (iff #444 true)
+#740 := [rewrite]: #739
+#407 := (iff #423 true)
+#743 := [rewrite]: #407
+#463 := [monotonicity #743 #740]: #462
+#465 := [trans #463 #742]: #464
+#735 := [monotonicity #465]: #358
+#458 := [trans #735 #752]: #736
+#750 := (iff #754 false)
+#751 := (iff #754 #749)
+#748 := (iff #547 true)
+#745 := (iff #547 #744)
+#405 := (iff #417 true)
+#406 := [rewrite]: #405
+#746 := [monotonicity #406 #743]: #745
+#386 := [trans #746 #742]: #748
+#391 := [monotonicity #386]: #751
+#753 := [trans #391 #752]: #750
+#737 := [monotonicity #753 #458]: #733
+#449 := [trans #737 #738]: #448
+#704 := [monotonicity #449 #720 #703]: #706
+#591 := [trans #704 #589]: #590
+#741 := (iff #763 true)
+#420 := (or true false)
+#757 := (iff #420 true)
+#400 := [rewrite]: #757
+#756 := (iff #763 #420)
+#755 := (iff #761 false)
+#415 := [rewrite]: #755
+#759 := (iff #762 true)
+#765 := [rewrite]: #759
+#416 := [monotonicity #765 #415]: #756
+#404 := [trans #416 #400]: #741
+#600 := [monotonicity #404 #591]: #698
+#584 := [trans #600 #696]: #699
+#604 := [monotonicity #584]: #603
+#607 := [trans #604 #606]: #603
+#595 := [quant-inst #8 #63]: #602
+#700 := [mp #595 #607]: #601
+[unit-resolution #700 #87 #772]: false
+unsat
+a6a62a3b765435aa1a5f654ae0aa2e6502518a55 309 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#740 := (pattern #16)
+#11 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #15)
+#80 := (* -1::Int #14)
+#86 := (div #80 #83)
+#243 := (* -1::Int #86)
+#244 := (+ #16 #243)
+#245 := (= #244 0::Int)
+#26 := (div #14 #15)
+#240 := (* -1::Int #26)
+#241 := (+ #16 #240)
+#242 := (= #241 0::Int)
+#118 := (>= #14 0::Int)
+#111 := (<= #15 0::Int)
+#203 := (or #111 #118)
+#204 := (not #203)
+#107 := (<= #14 0::Int)
+#201 := (or #107 #111)
+#202 := (not #201)
+#207 := (or #202 #204)
+#246 := (ite #207 #242 #245)
+#239 := (= #16 0::Int)
+#18 := (= #15 0::Int)
+#17 := (= #14 0::Int)
+#19 := (or #17 #18)
+#247 := (ite #19 #239 #246)
+#741 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #740) #247)
+#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
+#744 := (iff #250 #741)
+#742 := (iff #247 #247)
+#743 := [refl]: #742
+#745 := [quant-intro #743]: #744
+#210 := (ite #207 #26 #86)
+#213 := (ite #19 0::Int #210)
+#216 := (= #16 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#251 := (iff #219 #250)
+#248 := (iff #216 #247)
+#249 := [rewrite]: #248
+#252 := [quant-intro #249]: #251
+#119 := (not #118)
+#112 := (not #111)
+#122 := (and #112 #119)
+#108 := (not #107)
+#115 := (and #108 #112)
+#125 := (or #115 #122)
+#128 := (ite #125 #26 #86)
+#131 := (ite #19 0::Int #128)
+#134 := (= #16 #131)
+#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
+#220 := (iff #137 #219)
+#217 := (iff #134 #216)
+#214 := (= #131 #213)
+#211 := (= #128 #210)
+#208 := (iff #125 #207)
+#205 := (iff #122 #204)
+#206 := [rewrite]: #205
+#195 := (iff #115 #202)
+#196 := [rewrite]: #195
+#209 := [monotonicity #196 #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#199 := (~ #137 #137)
+#197 := (~ #134 #134)
+#198 := [refl]: #197
+#200 := [nnf-pos #198]: #199
+#28 := (- #15)
+#27 := (- #14)
+#29 := (div #27 #28)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #16 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#140 := (iff #33 #137)
+#73 := (and #21 #23)
+#76 := (or #22 #73)
+#89 := (ite #76 #26 #86)
+#67 := (= 0::Int #15)
+#64 := (= 0::Int #14)
+#70 := (or #64 #67)
+#92 := (ite #70 0::Int #89)
+#95 := (= #16 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#138 := (iff #98 #137)
+#135 := (iff #95 #134)
+#132 := (= #92 #131)
+#129 := (= #89 #128)
+#126 := (iff #76 #125)
+#123 := (iff #73 #122)
+#120 := (iff #23 #119)
+#121 := [rewrite]: #120
+#113 := (iff #21 #112)
+#114 := [rewrite]: #113
+#124 := [monotonicity #114 #121]: #123
+#116 := (iff #22 #115)
+#109 := (iff #20 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#127 := [monotonicity #117 #124]: #126
+#130 := [monotonicity #127]: #129
+#105 := (iff #70 #19)
+#103 := (iff #67 #18)
+#104 := [rewrite]: #103
+#101 := (iff #64 #17)
+#102 := [rewrite]: #101
+#106 := [monotonicity #102 #104]: #105
+#133 := [monotonicity #106 #130]: #132
+#136 := [monotonicity #133]: #135
+#139 := [quant-intro #136]: #138
+#99 := (iff #33 #98)
+#96 := (iff #32 #95)
+#93 := (= #31 #92)
+#90 := (= #30 #89)
+#87 := (= #29 #86)
+#84 := (= #28 #83)
+#85 := [rewrite]: #84
+#81 := (= #27 #80)
+#82 := [rewrite]: #81
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #25 #76)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#71 := (iff #19 #70)
+#68 := (iff #18 #67)
+#69 := [rewrite]: #68
+#65 := (iff #17 #64)
+#66 := [rewrite]: #65
+#72 := [monotonicity #66 #69]: #71
+#94 := [monotonicity #72 #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#141 := [trans #100 #139]: #140
+#63 := [asserted]: #33
+#142 := [mp #63 #141]: #137
+#191 := [mp~ #142 #200]: #137
+#222 := [mp #191 #221]: #219
+#253 := [mp #222 #252]: #250
+#746 := [mp #253 #745]: #741
+#9 := 3::Int
+#8 := 1::Int
+#10 := (f3 1::Int 3::Int)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#62 := [asserted]: #13
+#666 := (not #741)
+#667 := (or #666 #12)
+#327 := (* -1::Int 3::Int)
+#411 := (* -1::Int 1::Int)
+#412 := (div #411 #327)
+#413 := (* -1::Int #412)
+#404 := (+ #10 #413)
+#415 := (= #404 0::Int)
+#416 := (div 1::Int 3::Int)
+#417 := (* -1::Int #416)
+#414 := (+ #10 #417)
+#418 := (= #414 0::Int)
+#397 := (>= 1::Int 0::Int)
+#732 := (<= 3::Int 0::Int)
+#734 := (or #732 #397)
+#391 := (not #734)
+#521 := (<= 1::Int 0::Int)
+#728 := (or #521 #732)
+#402 := (not #728)
+#403 := (or #402 #391)
+#735 := (ite #403 #418 #415)
+#736 := (= 3::Int 0::Int)
+#737 := (= 1::Int 0::Int)
+#738 := (or #737 #736)
+#733 := (ite #738 #12 #735)
+#663 := (or #666 #733)
+#657 := (iff #663 #667)
+#659 := (iff #667 #667)
+#660 := [rewrite]: #659
+#655 := (iff #733 #12)
+#675 := (ite false #12 #12)
+#656 := (iff #675 #12)
+#653 := [rewrite]: #656
+#662 := (iff #733 #675)
+#674 := (iff #735 #12)
+#558 := (= #10 1::Int)
+#1 := true
+#577 := (ite true #12 #558)
+#580 := (iff #577 #12)
+#581 := [rewrite]: #580
+#578 := (iff #735 #577)
+#576 := (iff #415 #558)
+#564 := (+ -1::Int #10)
+#669 := (= #564 0::Int)
+#573 := (iff #669 #558)
+#575 := [rewrite]: #573
+#670 := (iff #415 #669)
+#672 := (= #404 #564)
+#678 := (+ #10 -1::Int)
+#565 := (= #678 #564)
+#524 := [rewrite]: #565
+#681 := (= #404 #678)
+#679 := (= #413 -1::Int)
+#686 := (= #411 -1::Int)
+#687 := [rewrite]: #686
+#676 := (= #413 #411)
+#522 := (= #412 1::Int)
+#688 := -3::Int
+#689 := (div -1::Int -3::Int)
+#691 := (= #689 1::Int)
+#520 := [rewrite]: #691
+#690 := (= #412 #689)
+#682 := (= #327 -3::Int)
+#683 := [rewrite]: #682
+#684 := [monotonicity #687 #683]: #690
+#523 := [trans #684 #520]: #522
+#677 := [monotonicity #523]: #676
+#680 := [trans #677 #687]: #679
+#563 := [monotonicity #680]: #681
+#574 := [trans #563 #524]: #672
+#673 := [monotonicity #574]: #670
+#569 := [trans #673 #575]: #576
+#543 := (iff #418 #12)
+#541 := (= #414 #10)
+#693 := (+ #10 0::Int)
+#694 := (= #693 #10)
+#700 := [rewrite]: #694
+#698 := (= #414 #693)
+#697 := (= #417 0::Int)
+#705 := (* -1::Int 0::Int)
+#695 := (= #705 0::Int)
+#696 := [rewrite]: #695
+#702 := (= #417 #705)
+#419 := (= #416 0::Int)
+#701 := [rewrite]: #419
+#706 := [monotonicity #701]: #702
+#692 := [trans #706 #696]: #697
+#699 := [monotonicity #692]: #698
+#542 := [trans #699 #700]: #541
+#685 := [monotonicity #542]: #543
+#703 := (iff #403 true)
+#712 := (or true false)
+#424 := (iff #712 true)
+#425 := [rewrite]: #424
+#422 := (iff #403 #712)
+#711 := (iff #391 false)
+#709 := (not true)
+#433 := (iff #709 false)
+#707 := [rewrite]: #433
+#710 := (iff #391 #709)
+#439 := (iff #734 true)
+#713 := (or false true)
+#437 := (iff #713 true)
+#438 := [rewrite]: #437
+#714 := (iff #734 #713)
+#724 := (iff #397 true)
+#727 := [rewrite]: #724
+#717 := (iff #732 false)
+#718 := [rewrite]: #717
+#436 := [monotonicity #718 #727]: #714
+#333 := [trans #436 #438]: #439
+#432 := [monotonicity #333]: #710
+#708 := [trans #432 #707]: #711
+#366 := (iff #402 true)
+#722 := (not false)
+#725 := (iff #722 true)
+#365 := [rewrite]: #725
+#360 := (iff #402 #722)
+#721 := (iff #728 false)
+#730 := (or false false)
+#374 := (iff #730 false)
+#715 := [rewrite]: #374
+#719 := (iff #728 #730)
+#380 := (iff #521 false)
+#381 := [rewrite]: #380
+#720 := [monotonicity #381 #718]: #719
+#716 := [trans #720 #715]: #721
+#723 := [monotonicity #716]: #360
+#726 := [trans #723 #365]: #366
+#423 := [monotonicity #726 #708]: #422
+#704 := [trans #423 #425]: #703
+#579 := [monotonicity #704 #685 #569]: #578
+#671 := [trans #579 #581]: #674
+#378 := (iff #738 false)
+#390 := (iff #738 #730)
+#389 := (iff #736 false)
+#394 := [rewrite]: #389
+#739 := (iff #737 false)
+#729 := [rewrite]: #739
+#731 := [monotonicity #729 #394]: #390
+#379 := [trans #731 #715]: #378
+#664 := [monotonicity #379 #671]: #662
+#665 := [trans #664 #653]: #655
+#658 := [monotonicity #665]: #657
+#654 := [trans #658 #660]: #657
+#668 := [quant-inst #8 #9]: #663
+#661 := [mp #668 #654]: #667
+[unit-resolution #661 #62 #746]: false
+unsat
+e8bc05d54be641b4942beaff512e603a9cfaa4dd 284 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#15 := (f3 #13 #14)
+#725 := (pattern #15)
+#16 := 0::Int
+#70 := -1::Int
+#74 := (* -1::Int #14)
+#71 := (* -1::Int #13)
+#77 := (div #71 #74)
+#228 := (* -1::Int #77)
+#229 := (+ #15 #228)
+#230 := (= #229 0::Int)
+#26 := (div #13 #14)
+#225 := (* -1::Int #26)
+#226 := (+ #15 #225)
+#227 := (= #226 0::Int)
+#103 := (>= #13 0::Int)
+#96 := (<= #14 0::Int)
+#188 := (or #96 #103)
+#189 := (not #188)
+#92 := (<= #13 0::Int)
+#186 := (or #92 #96)
+#187 := (not #186)
+#192 := (or #187 #189)
+#231 := (ite #192 #227 #230)
+#224 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#17 := (= #13 0::Int)
+#19 := (or #17 #18)
+#232 := (ite #19 #224 #231)
+#726 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #725) #232)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#729 := (iff #235 #726)
+#727 := (iff #232 #232)
+#728 := [refl]: #727
+#730 := [quant-intro #728]: #729
+#195 := (ite #192 #26 #77)
+#198 := (ite #19 0::Int #195)
+#201 := (= #15 #198)
+#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
+#236 := (iff #204 #235)
+#233 := (iff #201 #232)
+#234 := [rewrite]: #233
+#237 := [quant-intro #234]: #236
+#104 := (not #103)
+#97 := (not #96)
+#107 := (and #97 #104)
+#93 := (not #92)
+#100 := (and #93 #97)
+#110 := (or #100 #107)
+#113 := (ite #110 #26 #77)
+#116 := (ite #19 0::Int #113)
+#119 := (= #15 #116)
+#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
+#205 := (iff #122 #204)
+#202 := (iff #119 #201)
+#199 := (= #116 #198)
+#196 := (= #113 #195)
+#193 := (iff #110 #192)
+#190 := (iff #107 #189)
+#191 := [rewrite]: #190
+#180 := (iff #100 #187)
+#181 := [rewrite]: #180
+#194 := [monotonicity #181 #191]: #193
+#197 := [monotonicity #194]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [quant-intro #203]: #205
+#184 := (~ #122 #122)
+#182 := (~ #119 #119)
+#183 := [refl]: #182
+#185 := [nnf-pos #183]: #184
+#28 := (- #14)
+#27 := (- #13)
+#29 := (div #27 #28)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (ite #25 #26 #29)
+#31 := (ite #19 0::Int #30)
+#32 := (= #15 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#125 := (iff #33 #122)
+#64 := (and #21 #23)
+#67 := (or #22 #64)
+#80 := (ite #67 #26 #77)
+#83 := (ite #19 0::Int #80)
+#86 := (= #15 #83)
+#89 := (forall (vars (?v0 Int) (?v1 Int)) #86)
+#123 := (iff #89 #122)
+#120 := (iff #86 #119)
+#117 := (= #83 #116)
+#114 := (= #80 #113)
+#111 := (iff #67 #110)
+#108 := (iff #64 #107)
+#105 := (iff #23 #104)
+#106 := [rewrite]: #105
+#98 := (iff #21 #97)
+#99 := [rewrite]: #98
+#109 := [monotonicity #99 #106]: #108
+#101 := (iff #22 #100)
+#94 := (iff #20 #93)
+#95 := [rewrite]: #94
+#102 := [monotonicity #95 #99]: #101
+#112 := [monotonicity #102 #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [quant-intro #121]: #123
+#90 := (iff #33 #89)
+#87 := (iff #32 #86)
+#84 := (= #31 #83)
+#81 := (= #30 #80)
+#78 := (= #29 #77)
+#75 := (= #28 #74)
+#76 := [rewrite]: #75
+#72 := (= #27 #71)
+#73 := [rewrite]: #72
+#79 := [monotonicity #73 #76]: #78
+#68 := (iff #25 #67)
+#65 := (iff #24 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#82 := [monotonicity #69 #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [monotonicity #85]: #87
+#91 := [quant-intro #88]: #90
+#126 := [trans #91 #124]: #125
+#63 := [asserted]: #33
+#127 := [mp #63 #126]: #122
+#176 := [mp~ #127 #185]: #122
+#207 := [mp #176 #206]: #204
+#238 := [mp #207 #237]: #235
+#731 := [mp #238 #730]: #726
+#10 := 1::Int
+#8 := 3::Int
+#9 := (f3 3::Int 3::Int)
+#11 := (= #9 1::Int)
+#12 := (not #11)
+#62 := [asserted]: #12
+#566 := (not #726)
+#659 := (or #566 #11)
+#312 := (* -1::Int 3::Int)
+#396 := (div #312 #312)
+#397 := (* -1::Int #396)
+#398 := (+ #9 #397)
+#389 := (= #398 0::Int)
+#400 := (div 3::Int 3::Int)
+#401 := (* -1::Int #400)
+#402 := (+ #9 #401)
+#399 := (= #402 0::Int)
+#403 := (>= 3::Int 0::Int)
+#382 := (<= 3::Int 0::Int)
+#717 := (or #382 #403)
+#719 := (not #717)
+#376 := (or #382 #382)
+#506 := (not #376)
+#713 := (or #506 #719)
+#387 := (ite #713 #399 #389)
+#388 := (= #9 0::Int)
+#720 := (= 3::Int 0::Int)
+#721 := (or #720 #720)
+#722 := (ite #721 #388 #387)
+#656 := (or #566 #722)
+#647 := (iff #656 #659)
+#641 := (iff #659 #659)
+#638 := [rewrite]: #641
+#564 := (iff #722 #11)
+#560 := (ite false #388 #11)
+#562 := (iff #560 #11)
+#563 := [rewrite]: #562
+#561 := (iff #722 #560)
+#543 := (iff #387 #11)
+#1 := true
+#657 := (ite true #11 #11)
+#655 := (iff #657 #11)
+#658 := [rewrite]: #655
+#559 := (iff #387 #657)
+#550 := (iff #389 #11)
+#681 := (+ -1::Int #9)
+#684 := (= #681 0::Int)
+#526 := (iff #684 #11)
+#527 := [rewrite]: #526
+#548 := (iff #389 #684)
+#663 := (= #398 #681)
+#687 := (+ #9 -1::Int)
+#682 := (= #687 #681)
+#677 := [rewrite]: #682
+#664 := (= #398 #687)
+#661 := (= #397 -1::Int)
+#409 := (* -1::Int 1::Int)
+#689 := (= #409 -1::Int)
+#404 := [rewrite]: #689
+#507 := (= #397 #409)
+#676 := (= #396 1::Int)
+#671 := -3::Int
+#667 := (div -3::Int -3::Int)
+#675 := (= #667 1::Int)
+#669 := [rewrite]: #675
+#668 := (= #396 #667)
+#672 := (= #312 -3::Int)
+#673 := [rewrite]: #672
+#674 := [monotonicity #673 #673]: #668
+#505 := [trans #674 #669]: #676
+#508 := [monotonicity #505]: #507
+#662 := [trans #508 #404]: #661
+#665 := [monotonicity #662]: #664
+#666 := [trans #665 #677]: #663
+#549 := [monotonicity #666]: #548
+#509 := [trans #549 #527]: #550
+#528 := (iff #399 #11)
+#679 := (iff #399 #684)
+#678 := (= #402 #681)
+#691 := (= #402 #687)
+#686 := (= #401 -1::Int)
+#410 := (= #401 #409)
+#407 := (= #400 1::Int)
+#408 := [rewrite]: #407
+#688 := [monotonicity #408]: #410
+#690 := [trans #688 #404]: #686
+#680 := [monotonicity #690]: #691
+#683 := [trans #680 #677]: #678
+#685 := [monotonicity #683]: #679
+#670 := [trans #685 #527]: #528
+#693 := (iff #713 true)
+#695 := (or true false)
+#692 := (iff #695 true)
+#696 := [rewrite]: #692
+#417 := (iff #713 #695)
+#318 := (iff #719 false)
+#699 := (not true)
+#423 := (iff #699 false)
+#424 := [rewrite]: #423
+#421 := (iff #719 #699)
+#712 := (iff #717 true)
+#710 := (or false true)
+#711 := (iff #710 true)
+#709 := [rewrite]: #711
+#350 := (iff #717 #710)
+#345 := (iff #403 true)
+#708 := [rewrite]: #345
+#359 := (iff #382 false)
+#700 := [rewrite]: #359
+#351 := [monotonicity #700 #708]: #350
+#698 := [trans #351 #709]: #712
+#422 := [monotonicity #698]: #421
+#694 := [trans #422 #424]: #318
+#701 := (iff #506 true)
+#702 := (not false)
+#705 := (iff #702 true)
+#706 := [rewrite]: #705
+#703 := (iff #506 #702)
+#365 := (iff #376 false)
+#724 := (or false false)
+#379 := (iff #724 false)
+#715 := [rewrite]: #379
+#363 := (iff #376 #724)
+#364 := [monotonicity #700 #700]: #363
+#366 := [trans #364 #715]: #365
+#704 := [monotonicity #366]: #703
+#707 := [trans #704 #706]: #701
+#418 := [monotonicity #707 #694]: #417
+#697 := [trans #418 #696]: #693
+#654 := [monotonicity #697 #670 #509]: #559
+#558 := [trans #654 #658]: #543
+#375 := (iff #721 false)
+#714 := (iff #721 #724)
+#723 := (iff #720 false)
+#718 := [rewrite]: #723
+#374 := [monotonicity #718 #718]: #714
+#716 := [trans #374 #715]: #375
+#554 := [monotonicity #716 #558]: #561
+#565 := [trans #554 #563]: #564
+#649 := [monotonicity #565]: #647
+#640 := [trans #649 #638]: #647
+#660 := [quant-inst #8 #8]: #656
+#650 := [mp #660 #640]: #659
+[unit-resolution #650 #62 #731]: false
+unsat
+e5eddbef23d1553e8639810f42b39c3055238ad5 308 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#726 := (pattern #16)
+#17 := 0::Int
+#71 := -1::Int
+#75 := (* -1::Int #15)
+#72 := (* -1::Int #14)
+#78 := (div #72 #75)
+#229 := (* -1::Int #78)
+#230 := (+ #16 #229)
+#231 := (= #230 0::Int)
+#27 := (div #14 #15)
+#226 := (* -1::Int #27)
+#227 := (+ #16 #226)
+#228 := (= #227 0::Int)
+#104 := (>= #14 0::Int)
+#97 := (<= #15 0::Int)
+#189 := (or #97 #104)
+#190 := (not #189)
+#93 := (<= #14 0::Int)
+#187 := (or #93 #97)
+#188 := (not #187)
+#193 := (or #188 #190)
+#232 := (ite #193 #228 #231)
+#225 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#20 := (or #18 #19)
+#233 := (ite #20 #225 #232)
+#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #233)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#730 := (iff #236 #727)
+#728 := (iff #233 #233)
+#729 := [refl]: #728
+#731 := [quant-intro #729]: #730
+#196 := (ite #193 #27 #78)
+#199 := (ite #20 0::Int #196)
+#202 := (= #16 #199)
+#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
+#237 := (iff #205 #236)
+#234 := (iff #202 #233)
+#235 := [rewrite]: #234
+#238 := [quant-intro #235]: #237
+#105 := (not #104)
+#98 := (not #97)
+#108 := (and #98 #105)
+#94 := (not #93)
+#101 := (and #94 #98)
+#111 := (or #101 #108)
+#114 := (ite #111 #27 #78)
+#117 := (ite #20 0::Int #114)
+#120 := (= #16 #117)
+#123 := (forall (vars (?v0 Int) (?v1 Int)) #120)
+#206 := (iff #123 #205)
+#203 := (iff #120 #202)
+#200 := (= #117 #199)
+#197 := (= #114 #196)
+#194 := (iff #111 #193)
+#191 := (iff #108 #190)
+#192 := [rewrite]: #191
+#181 := (iff #101 #188)
+#182 := [rewrite]: #181
+#195 := [monotonicity #182 #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [monotonicity #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [quant-intro #204]: #206
+#185 := (~ #123 #123)
+#183 := (~ #120 #120)
+#184 := [refl]: #183
+#186 := [nnf-pos #184]: #185
+#29 := (- #15)
+#28 := (- #14)
+#30 := (div #28 #29)
+#22 := (< 0::Int #15)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (ite #26 #27 #30)
+#32 := (ite #20 0::Int #31)
+#33 := (= #16 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#126 := (iff #34 #123)
+#65 := (and #22 #24)
+#68 := (or #23 #65)
+#81 := (ite #68 #27 #78)
+#84 := (ite #20 0::Int #81)
+#87 := (= #16 #84)
+#90 := (forall (vars (?v0 Int) (?v1 Int)) #87)
+#124 := (iff #90 #123)
+#121 := (iff #87 #120)
+#118 := (= #84 #117)
+#115 := (= #81 #114)
+#112 := (iff #68 #111)
+#109 := (iff #65 #108)
+#106 := (iff #24 #105)
+#107 := [rewrite]: #106
+#99 := (iff #22 #98)
+#100 := [rewrite]: #99
+#110 := [monotonicity #100 #107]: #109
+#102 := (iff #23 #101)
+#95 := (iff #21 #94)
#96 := [rewrite]: #95
-#93 := (= #22 #92)
-#90 := (= #21 1::Int)
-#85 := (- -1::Int)
-#88 := (= #85 1::Int)
-#89 := [rewrite]: #88
-#86 := (= #21 #85)
-#87 := [monotonicity #51]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #51 #91]: #93
-#98 := [trans #94 #96]: #97
-#83 := (= #20 -1::Int)
-#78 := (div 1::Int -1::Int)
-#81 := (= #78 -1::Int)
-#82 := [rewrite]: #81
-#79 := (= #20 #78)
-#80 := [monotonicity #51]: #79
-#84 := [trans #80 #82]: #83
-#76 := (iff #19 #75)
-#73 := (iff #18 #72)
-#67 := (iff #15 #66)
-#68 := [monotonicity #51]: #67
-#74 := [monotonicity #68]: #73
-#70 := (iff #16 #69)
-#71 := [monotonicity #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#101 := [monotonicity #77 #84 #98]: #100
-#105 := [trans #101 #103]: #104
-#64 := (iff #13 false)
-#59 := (or false false)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #13 #59)
-#57 := (iff #12 false)
-#52 := (= -1::Int 0::Int)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #12 #52)
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#47 := (iff #10 false)
-#48 := [rewrite]: #47
-#61 := [monotonicity #48 #58]: #60
-#65 := [trans #61 #63]: #64
-#108 := [monotonicity #65 #105]: #107
-#112 := [trans #108 #110]: #111
-#115 := [monotonicity #112 #51]: #114
-#119 := [trans #115 #117]: #118
+#103 := [monotonicity #96 #100]: #102
+#113 := [monotonicity #103 #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
#122 := [monotonicity #119]: #121
-#126 := [trans #122 #124]: #125
-#46 := [asserted]: #26
-[mp #46 #126]: false
-unsat
-a8c1cb5f3abdb5b9970e52ea21ab71e754348560 109 0
-#2 := false
+#125 := [quant-intro #122]: #124
+#91 := (iff #34 #90)
+#88 := (iff #33 #87)
+#85 := (= #32 #84)
+#82 := (= #31 #81)
+#79 := (= #30 #78)
+#76 := (= #29 #75)
+#77 := [rewrite]: #76
+#73 := (= #28 #72)
+#74 := [rewrite]: #73
+#80 := [monotonicity #74 #77]: #79
+#69 := (iff #26 #68)
+#66 := (iff #25 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#83 := [monotonicity #70 #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [monotonicity #86]: #88
+#92 := [quant-intro #89]: #91
+#127 := [trans #92 #125]: #126
+#64 := [asserted]: #34
+#128 := [mp #64 #127]: #123
+#177 := [mp~ #128 #186]: #123
+#208 := [mp #177 #207]: #205
+#239 := [mp #208 #238]: #236
+#732 := [mp #239 #731]: #727
+#11 := 1::Int
+#9 := 3::Int
+#8 := 5::Int
+#10 := (f3 5::Int 3::Int)
+#12 := (= #10 1::Int)
+#13 := (not #12)
+#63 := [asserted]: #13
+#635 := (not #727)
+#636 := (or #635 #12)
+#313 := (* -1::Int 3::Int)
+#397 := (* -1::Int 5::Int)
+#398 := (div #397 #313)
+#399 := (* -1::Int #398)
+#390 := (+ #10 #399)
+#401 := (= #390 0::Int)
+#402 := (div 5::Int 3::Int)
+#403 := (* -1::Int #402)
+#400 := (+ #10 #403)
+#404 := (= #400 0::Int)
+#383 := (>= 5::Int 0::Int)
+#718 := (<= 3::Int 0::Int)
+#720 := (or #718 #383)
+#377 := (not #720)
+#507 := (<= 5::Int 0::Int)
+#714 := (or #507 #718)
+#388 := (not #714)
+#389 := (or #388 #377)
+#721 := (ite #389 #404 #401)
+#722 := (= #10 0::Int)
+#723 := (= 3::Int 0::Int)
+#724 := (= 5::Int 0::Int)
+#719 := (or #724 #723)
+#725 := (ite #719 #722 #721)
+#637 := (or #635 #725)
+#638 := (iff #637 #636)
+#625 := (iff #636 #636)
+#627 := [rewrite]: #625
+#632 := (iff #725 #12)
+#645 := (ite false #722 #12)
+#647 := (iff #645 #12)
+#631 := [rewrite]: #647
+#646 := (iff #725 #645)
+#643 := (iff #721 #12)
+#664 := 2::Int
+#648 := (= #10 2::Int)
+#1 := true
+#651 := (ite true #12 #648)
+#649 := (iff #651 #12)
+#654 := [rewrite]: #649
+#652 := (iff #721 #651)
+#639 := (iff #401 #648)
+#655 := -2::Int
+#563 := (+ -2::Int #10)
+#660 := (= #563 0::Int)
+#650 := (iff #660 #648)
+#642 := [rewrite]: #650
+#657 := (iff #401 #660)
+#566 := (= #390 #563)
+#561 := (+ #10 -2::Int)
+#564 := (= #561 #563)
+#565 := [rewrite]: #564
+#562 := (= #390 #561)
+#544 := (= #399 -2::Int)
+#510 := (* -1::Int 2::Int)
+#656 := (= #510 -2::Int)
+#659 := [rewrite]: #656
+#658 := (= #399 #510)
+#550 := (= #398 2::Int)
+#508 := -3::Int
+#670 := -5::Int
+#663 := (div -5::Int -3::Int)
+#667 := (= #663 2::Int)
+#549 := [rewrite]: #667
+#665 := (= #398 #663)
+#509 := (= #313 -3::Int)
+#662 := [rewrite]: #509
+#677 := (= #397 -5::Int)
+#506 := [rewrite]: #677
+#666 := [monotonicity #506 #662]: #665
+#551 := [trans #666 #549]: #550
+#560 := [monotonicity #551]: #658
+#559 := [trans #560 #659]: #544
+#555 := [monotonicity #559]: #562
+#567 := [trans #555 #565]: #566
+#661 := [monotonicity #567]: #657
+#641 := [trans #661 #642]: #639
+#675 := (iff #404 #12)
+#686 := (+ -1::Int #10)
+#672 := (= #686 0::Int)
+#668 := (iff #672 #12)
+#669 := [rewrite]: #668
+#673 := (iff #404 #672)
+#529 := (= #400 #686)
+#684 := (+ #10 -1::Int)
+#527 := (= #684 #686)
+#528 := [rewrite]: #527
+#685 := (= #400 #684)
+#678 := (= #403 -1::Int)
+#688 := (* -1::Int 1::Int)
+#682 := (= #688 -1::Int)
+#683 := [rewrite]: #682
+#692 := (= #403 #688)
+#687 := (= #402 1::Int)
+#691 := [rewrite]: #687
+#681 := [monotonicity #691]: #692
+#679 := [trans #681 #683]: #678
+#680 := [monotonicity #679]: #685
+#671 := [trans #680 #528]: #529
+#674 := [monotonicity #671]: #673
+#676 := [trans #674 #669]: #675
+#690 := (iff #389 true)
+#408 := (or true false)
+#411 := (iff #408 true)
+#689 := [rewrite]: #411
+#409 := (iff #389 #408)
+#694 := (iff #377 false)
+#696 := (not true)
+#693 := (iff #696 false)
+#697 := [rewrite]: #693
+#418 := (iff #377 #696)
+#319 := (iff #720 true)
+#700 := (or false true)
+#424 := (iff #700 true)
+#425 := [rewrite]: #424
+#422 := (iff #720 #700)
+#713 := (iff #383 true)
+#699 := [rewrite]: #713
+#704 := (iff #718 false)
+#705 := [rewrite]: #704
+#423 := [monotonicity #705 #699]: #422
+#695 := [trans #423 #425]: #319
+#419 := [monotonicity #695]: #418
+#698 := [trans #419 #697]: #694
+#712 := (iff #388 true)
+#346 := (not false)
+#351 := (iff #346 true)
+#352 := [rewrite]: #351
+#709 := (iff #388 #346)
+#702 := (iff #714 false)
+#376 := (or false false)
+#701 := (iff #376 false)
+#364 := [rewrite]: #701
+#706 := (iff #714 #376)
+#367 := (iff #507 false)
+#703 := [rewrite]: #367
+#707 := [monotonicity #703 #705]: #706
+#708 := [trans #707 #364]: #702
+#711 := [monotonicity #708]: #709
+#710 := [trans #711 #352]: #712
+#410 := [monotonicity #710 #698]: #409
+#405 := [trans #410 #689]: #690
+#653 := [monotonicity #405 #676 #641]: #652
+#644 := [trans #653 #654]: #643
+#365 := (iff #719 false)
+#717 := (iff #719 #376)
+#380 := (iff #723 false)
+#716 := [rewrite]: #380
+#715 := (iff #724 false)
+#375 := [rewrite]: #715
+#360 := [monotonicity #375 #716]: #717
+#366 := [trans #360 #364]: #365
+#640 := [monotonicity #366 #644]: #646
+#634 := [trans #640 #631]: #632
+#624 := [monotonicity #634]: #638
+#628 := [trans #624 #627]: #638
+#633 := [quant-inst #8 #9]: #637
+#629 := [mp #633 #628]: #636
+[unit-resolution #629 #63 #732]: false
+unsat
+191c033321d69fed907f76825c4e08dd5071fdbf 307 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#17 := (f3 #15 #16)
+#742 := (pattern #17)
+#18 := 0::Int
+#71 := -1::Int
+#91 := (* -1::Int #16)
+#88 := (* -1::Int #15)
+#94 := (div #88 #91)
+#245 := (* -1::Int #94)
+#246 := (+ #17 #245)
+#247 := (= #246 0::Int)
+#28 := (div #15 #16)
+#242 := (* -1::Int #28)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
+#120 := (>= #15 0::Int)
+#113 := (<= #16 0::Int)
+#205 := (or #113 #120)
+#206 := (not #205)
+#109 := (<= #15 0::Int)
+#203 := (or #109 #113)
+#204 := (not #203)
+#209 := (or #204 #206)
+#248 := (ite #209 #244 #247)
+#241 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#249 := (ite #21 #241 #248)
+#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#746 := (iff #252 #743)
+#744 := (iff #249 #249)
+#745 := [refl]: #744
+#747 := [quant-intro #745]: #746
+#212 := (ite #209 #28 #94)
+#215 := (ite #21 0::Int #212)
+#218 := (= #17 #215)
+#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
+#253 := (iff #221 #252)
+#250 := (iff #218 #249)
+#251 := [rewrite]: #250
+#254 := [quant-intro #251]: #253
+#121 := (not #120)
+#114 := (not #113)
+#124 := (and #114 #121)
+#110 := (not #109)
+#117 := (and #110 #114)
+#127 := (or #117 #124)
+#130 := (ite #127 #28 #94)
+#133 := (ite #21 0::Int #130)
+#136 := (= #17 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#216 := (= #133 #215)
+#213 := (= #130 #212)
+#210 := (iff #127 #209)
+#207 := (iff #124 #206)
+#208 := [rewrite]: #207
+#197 := (iff #117 #204)
+#198 := [rewrite]: #197
+#211 := [monotonicity #198 #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [quant-intro #220]: #222
+#201 := (~ #139 #139)
+#199 := (~ #136 #136)
+#200 := [refl]: #199
+#202 := [nnf-pos #200]: #201
+#30 := (- #16)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#142 := (iff #35 #139)
+#81 := (and #23 #25)
+#85 := (or #24 #81)
+#97 := (ite #85 #28 #94)
+#100 := (ite #21 0::Int #97)
+#103 := (= #17 #100)
+#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
+#140 := (iff #106 #139)
+#137 := (iff #103 #136)
+#134 := (= #100 #133)
+#131 := (= #97 #130)
+#128 := (iff #85 #127)
+#125 := (iff #81 #124)
+#122 := (iff #25 #121)
+#123 := [rewrite]: #122
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#126 := [monotonicity #116 #123]: #125
+#118 := (iff #24 #117)
+#111 := (iff #22 #110)
+#112 := [rewrite]: #111
+#119 := [monotonicity #112 #116]: #118
+#129 := [monotonicity #119 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#107 := (iff #35 #106)
+#104 := (iff #34 #103)
+#101 := (= #33 #100)
+#98 := (= #32 #97)
+#95 := (= #31 #94)
+#92 := (= #30 #91)
+#93 := [rewrite]: #92
+#89 := (= #29 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90 #93]: #95
+#86 := (iff #27 #85)
+#83 := (iff #26 #81)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#99 := [monotonicity #87 #96]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [quant-intro #105]: #107
+#143 := [trans #108 #141]: #142
+#80 := [asserted]: #35
+#144 := [mp #80 #143]: #139
+#193 := [mp~ #144 #202]: #139
+#224 := [mp #193 #223]: #221
+#255 := [mp #224 #254]: #252
+#748 := [mp #255 #747]: #743
+#65 := -3::Int
+#8 := 1::Int
+#68 := (f3 1::Int -3::Int)
+#74 := (= #68 -1::Int)
+#77 := (not #74)
+#12 := (- 1::Int)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 1::Int #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#78 := (iff #14 #77)
+#75 := (iff #13 #74)
+#72 := (= #12 -1::Int)
+#73 := [rewrite]: #72
+#69 := (= #11 #68)
+#66 := (= #10 -3::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [monotonicity #70 #73]: #75
+#79 := [monotonicity #76]: #78
+#64 := [asserted]: #14
+#82 := [mp #64 #79]: #77
+#658 := (not #743)
+#655 := (or #658 #74)
+#329 := (* -1::Int -3::Int)
+#413 := (* -1::Int 1::Int)
+#414 := (div #413 #329)
+#415 := (* -1::Int #414)
+#406 := (+ #68 #415)
+#417 := (= #406 0::Int)
+#418 := (div 1::Int -3::Int)
+#419 := (* -1::Int #418)
+#416 := (+ #68 #419)
+#420 := (= #416 0::Int)
+#399 := (>= 1::Int 0::Int)
+#734 := (<= -3::Int 0::Int)
+#736 := (or #734 #399)
+#393 := (not #736)
+#523 := (<= 1::Int 0::Int)
+#730 := (or #523 #734)
+#404 := (not #730)
+#405 := (or #404 #393)
+#737 := (ite #405 #420 #417)
+#738 := (= #68 0::Int)
+#739 := (= -3::Int 0::Int)
+#740 := (= 1::Int 0::Int)
+#735 := (or #740 #739)
+#741 := (ite #735 #738 #737)
+#657 := (or #658 #741)
+#668 := (iff #657 #655)
+#665 := (iff #655 #655)
+#670 := [rewrite]: #665
+#664 := (iff #741 #74)
+#571 := (ite false #738 #74)
+#581 := (iff #571 #74)
+#582 := [rewrite]: #581
+#673 := (iff #741 #571)
+#583 := (iff #737 #74)
+#579 := (iff #737 #571)
+#577 := (iff #417 #74)
+#566 := (+ 1::Int #68)
+#671 := (= #566 0::Int)
+#560 := (iff #671 #74)
+#575 := [rewrite]: #560
+#672 := (iff #417 #671)
+#674 := (= #406 #566)
+#680 := (+ #68 1::Int)
+#567 := (= #680 #566)
+#526 := [rewrite]: #567
+#683 := (= #406 #680)
+#681 := (= #415 1::Int)
+#522 := (* -1::Int -1::Int)
+#678 := (= #522 1::Int)
+#679 := [rewrite]: #678
+#524 := (= #415 #522)
+#686 := (= #414 -1::Int)
+#690 := (div -1::Int 3::Int)
+#691 := (= #690 -1::Int)
+#692 := [rewrite]: #691
+#684 := (= #414 #690)
+#688 := (= #329 3::Int)
+#689 := [rewrite]: #688
+#545 := (= #413 -1::Int)
+#687 := [rewrite]: #545
+#685 := [monotonicity #687 #689]: #684
+#693 := [trans #685 #692]: #686
+#525 := [monotonicity #693]: #524
+#682 := [trans #525 #679]: #681
+#565 := [monotonicity #682]: #683
+#576 := [trans #565 #526]: #674
+#675 := [monotonicity #576]: #672
+#578 := [trans #675 #575]: #577
+#543 := (iff #420 #738)
+#696 := (= #416 #68)
+#699 := (+ #68 0::Int)
+#700 := (= #699 #68)
+#701 := [rewrite]: #700
+#694 := (= #416 #699)
+#697 := (= #419 0::Int)
+#421 := (* -1::Int 0::Int)
+#704 := (= #421 0::Int)
+#708 := [rewrite]: #704
+#703 := (= #419 #421)
+#705 := (= #418 0::Int)
+#706 := [rewrite]: #705
+#707 := [monotonicity #706]: #703
+#698 := [trans #707 #708]: #697
+#695 := [monotonicity #698]: #694
+#702 := [trans #695 #701]: #696
+#544 := [monotonicity #702]: #543
+#426 := (iff #405 false)
+#392 := (or false false)
+#717 := (iff #392 false)
+#380 := [rewrite]: #717
+#424 := (iff #405 #392)
+#710 := (iff #393 false)
+#1 := true
+#367 := (not true)
+#726 := (iff #367 false)
+#729 := [rewrite]: #726
+#709 := (iff #393 #367)
+#434 := (iff #736 true)
+#440 := (or true true)
+#711 := (iff #440 true)
+#712 := [rewrite]: #711
+#441 := (iff #736 #440)
+#438 := (iff #399 true)
+#439 := [rewrite]: #438
+#720 := (iff #734 true)
+#721 := [rewrite]: #720
+#335 := [monotonicity #721 #439]: #441
+#435 := [trans #335 #712]: #434
+#713 := [monotonicity #435]: #709
+#714 := [trans #713 #729]: #710
+#715 := (iff #404 false)
+#368 := (iff #404 #367)
+#725 := (iff #730 true)
+#722 := (or false true)
+#724 := (iff #722 true)
+#362 := [rewrite]: #724
+#723 := (iff #730 #722)
+#383 := (iff #523 false)
+#719 := [rewrite]: #383
+#718 := [monotonicity #719 #721]: #723
+#727 := [trans #718 #362]: #725
+#728 := [monotonicity #727]: #368
+#716 := [trans #728 #729]: #715
+#425 := [monotonicity #716 #714]: #424
+#427 := [trans #425 #380]: #426
+#580 := [monotonicity #427 #544 #578]: #579
+#676 := [trans #580 #582]: #583
+#381 := (iff #735 false)
+#733 := (iff #735 #392)
+#396 := (iff #739 false)
+#732 := [rewrite]: #396
+#731 := (iff #740 false)
+#391 := [rewrite]: #731
+#376 := [monotonicity #391 #732]: #733
+#382 := [trans #376 #380]: #381
+#677 := [monotonicity #382 #676]: #673
+#666 := [trans #677 #582]: #664
+#669 := [monotonicity #666]: #668
+#659 := [trans #669 #670]: #668
+#667 := [quant-inst #8 #65]: #657
+#660 := [mp #667 #659]: #655
+[unit-resolution #660 #82 #748]: false
+unsat
+5ac842dfccd0a130b836d32f5bc0e4f0b730d4cf 306 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#17 := (f3 #15 #16)
+#742 := (pattern #17)
+#18 := 0::Int
+#71 := -1::Int
+#91 := (* -1::Int #16)
+#88 := (* -1::Int #15)
+#94 := (div #88 #91)
+#245 := (* -1::Int #94)
+#246 := (+ #17 #245)
+#247 := (= #246 0::Int)
+#28 := (div #15 #16)
+#242 := (* -1::Int #28)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
+#120 := (>= #15 0::Int)
+#113 := (<= #16 0::Int)
+#205 := (or #113 #120)
+#206 := (not #205)
+#109 := (<= #15 0::Int)
+#203 := (or #109 #113)
+#204 := (not #203)
+#209 := (or #204 #206)
+#248 := (ite #209 #244 #247)
+#241 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#249 := (ite #21 #241 #248)
+#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#746 := (iff #252 #743)
+#744 := (iff #249 #249)
+#745 := [refl]: #744
+#747 := [quant-intro #745]: #746
+#212 := (ite #209 #28 #94)
+#215 := (ite #21 0::Int #212)
+#218 := (= #17 #215)
+#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
+#253 := (iff #221 #252)
+#250 := (iff #218 #249)
+#251 := [rewrite]: #250
+#254 := [quant-intro #251]: #253
+#121 := (not #120)
+#114 := (not #113)
+#124 := (and #114 #121)
+#110 := (not #109)
+#117 := (and #110 #114)
+#127 := (or #117 #124)
+#130 := (ite #127 #28 #94)
+#133 := (ite #21 0::Int #130)
+#136 := (= #17 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#216 := (= #133 #215)
+#213 := (= #130 #212)
+#210 := (iff #127 #209)
+#207 := (iff #124 #206)
+#208 := [rewrite]: #207
+#197 := (iff #117 #204)
+#198 := [rewrite]: #197
+#211 := [monotonicity #198 #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [quant-intro #220]: #222
+#201 := (~ #139 #139)
+#199 := (~ #136 #136)
+#200 := [refl]: #199
+#202 := [nnf-pos #200]: #201
+#30 := (- #16)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#142 := (iff #35 #139)
+#81 := (and #23 #25)
+#85 := (or #24 #81)
+#97 := (ite #85 #28 #94)
+#100 := (ite #21 0::Int #97)
+#103 := (= #17 #100)
+#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
+#140 := (iff #106 #139)
+#137 := (iff #103 #136)
+#134 := (= #100 #133)
+#131 := (= #97 #130)
+#128 := (iff #85 #127)
+#125 := (iff #81 #124)
+#122 := (iff #25 #121)
+#123 := [rewrite]: #122
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#126 := [monotonicity #116 #123]: #125
+#118 := (iff #24 #117)
+#111 := (iff #22 #110)
+#112 := [rewrite]: #111
+#119 := [monotonicity #112 #116]: #118
+#129 := [monotonicity #119 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#107 := (iff #35 #106)
+#104 := (iff #34 #103)
+#101 := (= #33 #100)
+#98 := (= #32 #97)
+#95 := (= #31 #94)
+#92 := (= #30 #91)
+#93 := [rewrite]: #92
+#89 := (= #29 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90 #93]: #95
+#86 := (iff #27 #85)
+#83 := (iff #26 #81)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#99 := [monotonicity #87 #96]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [quant-intro #105]: #107
+#143 := [trans #108 #141]: #142
+#80 := [asserted]: #35
+#144 := [mp #80 #143]: #139
+#193 := [mp~ #144 #202]: #139
+#224 := [mp #193 #223]: #221
+#255 := [mp #224 #254]: #252
+#748 := [mp #255 #747]: #743
+#65 := -3::Int
#8 := 3::Int
-#22 := (- 3::Int)
+#68 := (f3 3::Int -3::Int)
+#74 := (= #68 -1::Int)
+#77 := (not #74)
#11 := 1::Int
#12 := (- 1::Int)
-#23 := (- #12)
-#24 := (div #22 #23)
-#21 := (div 3::Int #12)
-#9 := 0::Int
-#16 := (< 0::Int #12)
-#18 := (< 3::Int 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int 3::Int)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= #12 0::Int)
-#10 := (= 3::Int 0::Int)
-#14 := (or #10 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (= #26 #22)
-#28 := (not #27)
-#130 := (iff #28 false)
-#1 := true
-#125 := (not true)
-#128 := (iff #125 false)
-#129 := [rewrite]: #128
-#126 := (iff #28 #125)
-#123 := (iff #27 true)
-#83 := -3::Int
-#118 := (= -3::Int -3::Int)
-#121 := (iff #118 true)
-#122 := [rewrite]: #121
-#119 := (iff #27 #118)
-#88 := (= #22 -3::Int)
-#89 := [rewrite]: #88
-#116 := (= #26 -3::Int)
-#111 := (ite false 0::Int -3::Int)
-#114 := (= #111 -3::Int)
-#115 := [rewrite]: #114
-#112 := (= #26 #111)
-#109 := (= #25 -3::Int)
-#51 := -1::Int
-#68 := (< 0::Int -1::Int)
-#74 := (and #18 #68)
-#71 := (and #15 #68)
-#77 := (or #71 #74)
-#104 := (ite #77 -3::Int -3::Int)
-#107 := (= #104 -3::Int)
-#108 := [rewrite]: #107
-#105 := (= #25 #104)
-#102 := (= #24 -3::Int)
-#97 := (div -3::Int 1::Int)
-#100 := (= #97 -3::Int)
-#101 := [rewrite]: #100
-#98 := (= #24 #97)
-#95 := (= #23 1::Int)
-#90 := (- -1::Int)
-#93 := (= #90 1::Int)
-#94 := [rewrite]: #93
-#91 := (= #23 #90)
-#52 := (= #12 -1::Int)
-#53 := [rewrite]: #52
-#92 := [monotonicity #53]: #91
-#96 := [trans #92 #94]: #95
-#99 := [monotonicity #89 #96]: #98
-#103 := [trans #99 #101]: #102
-#86 := (= #21 -3::Int)
-#80 := (div 3::Int -1::Int)
-#84 := (= #80 -3::Int)
+#9 := (- 3::Int)
+#10 := (f3 3::Int #9)
+#13 := (= #10 #12)
+#14 := (not #13)
+#78 := (iff #14 #77)
+#75 := (iff #13 #74)
+#72 := (= #12 -1::Int)
+#73 := [rewrite]: #72
+#69 := (= #10 #68)
+#66 := (= #9 -3::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [monotonicity #70 #73]: #75
+#79 := [monotonicity #76]: #78
+#64 := [asserted]: #14
+#82 := [mp #64 #79]: #77
+#666 := (not #743)
+#658 := (or #666 #74)
+#329 := (* -1::Int -3::Int)
+#413 := (* -1::Int 3::Int)
+#414 := (div #413 #329)
+#415 := (* -1::Int #414)
+#406 := (+ #68 #415)
+#417 := (= #406 0::Int)
+#418 := (div 3::Int -3::Int)
+#419 := (* -1::Int #418)
+#416 := (+ #68 #419)
+#420 := (= #416 0::Int)
+#399 := (>= 3::Int 0::Int)
+#734 := (<= -3::Int 0::Int)
+#736 := (or #734 #399)
+#393 := (not #736)
+#523 := (<= 3::Int 0::Int)
+#730 := (or #523 #734)
+#404 := (not #730)
+#405 := (or #404 #393)
+#737 := (ite #405 #420 #417)
+#738 := (= #68 0::Int)
+#739 := (= -3::Int 0::Int)
+#740 := (= 3::Int 0::Int)
+#735 := (or #740 #739)
+#741 := (ite #735 #738 #737)
+#655 := (or #666 #741)
+#667 := (iff #655 #658)
+#669 := (iff #658 #658)
+#665 := [rewrite]: #669
+#677 := (iff #741 #74)
+#581 := (ite false #738 #74)
+#676 := (iff #581 #74)
+#673 := [rewrite]: #676
+#582 := (iff #741 #581)
+#579 := (iff #737 #74)
+#560 := (ite false #74 #74)
+#578 := (iff #560 #74)
+#571 := [rewrite]: #578
+#575 := (iff #737 #560)
+#672 := (iff #417 #74)
+#700 := (+ 1::Int #68)
+#544 := (= #700 0::Int)
+#688 := (iff #544 #74)
+#689 := [rewrite]: #688
+#576 := (iff #417 #544)
+#526 := (= #406 #700)
+#699 := (+ #68 1::Int)
+#701 := (= #699 #700)
+#696 := [rewrite]: #701
+#566 := (= #406 #699)
+#683 := (= #415 1::Int)
+#421 := (* -1::Int -1::Int)
+#704 := (= #421 1::Int)
+#708 := [rewrite]: #704
+#682 := (= #415 #421)
+#679 := (= #414 -1::Int)
+#693 := (div -3::Int 3::Int)
+#525 := (= #693 -1::Int)
+#678 := [rewrite]: #525
+#522 := (= #414 #693)
+#692 := (= #329 3::Int)
+#686 := [rewrite]: #692
+#685 := (= #413 -3::Int)
+#691 := [rewrite]: #685
+#524 := [monotonicity #691 #686]: #522
+#681 := [trans #524 #678]: #679
+#680 := [monotonicity #681]: #682
+#565 := [trans #680 #708]: #683
+#567 := [monotonicity #565]: #566
+#674 := [trans #567 #696]: #526
+#671 := [monotonicity #674]: #576
+#675 := [trans #671 #689]: #672
+#690 := (iff #420 #74)
+#545 := (iff #420 #544)
+#702 := (= #416 #700)
+#694 := (= #416 #699)
+#697 := (= #419 1::Int)
+#703 := (= #419 #421)
+#705 := (= #418 -1::Int)
+#706 := [rewrite]: #705
+#707 := [monotonicity #706]: #703
+#698 := [trans #707 #708]: #697
+#695 := [monotonicity #698]: #694
+#543 := [trans #695 #696]: #702
+#687 := [monotonicity #543]: #545
+#684 := [trans #687 #689]: #690
+#426 := (iff #405 false)
+#392 := (or false false)
+#717 := (iff #392 false)
+#380 := [rewrite]: #717
+#424 := (iff #405 #392)
+#710 := (iff #393 false)
+#1 := true
+#367 := (not true)
+#726 := (iff #367 false)
+#729 := [rewrite]: #726
+#709 := (iff #393 #367)
+#434 := (iff #736 true)
+#440 := (or true true)
+#711 := (iff #440 true)
+#712 := [rewrite]: #711
+#441 := (iff #736 #440)
+#438 := (iff #399 true)
+#439 := [rewrite]: #438
+#720 := (iff #734 true)
+#721 := [rewrite]: #720
+#335 := [monotonicity #721 #439]: #441
+#435 := [trans #335 #712]: #434
+#713 := [monotonicity #435]: #709
+#714 := [trans #713 #729]: #710
+#715 := (iff #404 false)
+#368 := (iff #404 #367)
+#725 := (iff #730 true)
+#722 := (or false true)
+#724 := (iff #722 true)
+#362 := [rewrite]: #724
+#723 := (iff #730 #722)
+#383 := (iff #523 false)
+#719 := [rewrite]: #383
+#718 := [monotonicity #719 #721]: #723
+#727 := [trans #718 #362]: #725
+#728 := [monotonicity #727]: #368
+#716 := [trans #728 #729]: #715
+#425 := [monotonicity #716 #714]: #424
+#427 := [trans #425 #380]: #426
+#577 := [monotonicity #427 #684 #675]: #575
+#580 := [trans #577 #571]: #579
+#381 := (iff #735 false)
+#733 := (iff #735 #392)
+#396 := (iff #739 false)
+#732 := [rewrite]: #396
+#731 := (iff #740 false)
+#391 := [rewrite]: #731
+#376 := [monotonicity #391 #732]: #733
+#382 := [trans #376 #380]: #381
+#583 := [monotonicity #382 #580]: #582
+#664 := [trans #583 #673]: #677
+#668 := [monotonicity #664]: #667
+#670 := [trans #668 #665]: #667
+#657 := [quant-inst #8 #65]: #655
+#659 := [mp #657 #670]: #658
+[unit-resolution #659 #82 #748]: false
+unsat
+ff5c5d19f29597667640ddc4ac233d7f220d9f19 321 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#18 := (f3 #16 #17)
+#745 := (pattern #18)
+#19 := 0::Int
+#89 := -1::Int
+#93 := (* -1::Int #17)
+#90 := (* -1::Int #16)
+#96 := (div #90 #93)
+#247 := (* -1::Int #96)
+#248 := (+ #18 #247)
+#249 := (= #248 0::Int)
+#29 := (div #16 #17)
+#244 := (* -1::Int #29)
+#245 := (+ #18 #244)
+#246 := (= #245 0::Int)
+#122 := (>= #16 0::Int)
+#115 := (<= #17 0::Int)
+#207 := (or #115 #122)
+#208 := (not #207)
+#111 := (<= #16 0::Int)
+#205 := (or #111 #115)
+#206 := (not #205)
+#211 := (or #206 #208)
+#250 := (ite #211 #246 #249)
+#243 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#22 := (or #20 #21)
+#251 := (ite #22 #243 #250)
+#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251)
+#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
+#749 := (iff #254 #746)
+#747 := (iff #251 #251)
+#748 := [refl]: #747
+#750 := [quant-intro #748]: #749
+#214 := (ite #211 #29 #96)
+#217 := (ite #22 0::Int #214)
+#220 := (= #18 #217)
+#223 := (forall (vars (?v0 Int) (?v1 Int)) #220)
+#255 := (iff #223 #254)
+#252 := (iff #220 #251)
+#253 := [rewrite]: #252
+#256 := [quant-intro #253]: #255
+#123 := (not #122)
+#116 := (not #115)
+#126 := (and #116 #123)
+#112 := (not #111)
+#119 := (and #112 #116)
+#129 := (or #119 #126)
+#132 := (ite #129 #29 #96)
+#135 := (ite #22 0::Int #132)
+#138 := (= #18 #135)
+#141 := (forall (vars (?v0 Int) (?v1 Int)) #138)
+#224 := (iff #141 #223)
+#221 := (iff #138 #220)
+#218 := (= #135 #217)
+#215 := (= #132 #214)
+#212 := (iff #129 #211)
+#209 := (iff #126 #208)
+#210 := [rewrite]: #209
+#199 := (iff #119 #206)
+#200 := [rewrite]: #199
+#213 := [monotonicity #200 #210]: #212
+#216 := [monotonicity #213]: #215
+#219 := [monotonicity #216]: #218
+#222 := [monotonicity #219]: #221
+#225 := [quant-intro #222]: #224
+#203 := (~ #141 #141)
+#201 := (~ #138 #138)
+#202 := [refl]: #201
+#204 := [nnf-pos #202]: #203
+#31 := (- #17)
+#30 := (- #16)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (ite #28 #29 #32)
+#34 := (ite #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#144 := (iff #36 #141)
+#82 := (and #24 #26)
+#86 := (or #25 #82)
+#99 := (ite #86 #29 #96)
+#102 := (ite #22 0::Int #99)
+#105 := (= #18 #102)
+#108 := (forall (vars (?v0 Int) (?v1 Int)) #105)
+#142 := (iff #108 #141)
+#139 := (iff #105 #138)
+#136 := (= #102 #135)
+#133 := (= #99 #132)
+#130 := (iff #86 #129)
+#127 := (iff #82 #126)
+#124 := (iff #26 #123)
+#125 := [rewrite]: #124
+#117 := (iff #24 #116)
+#118 := [rewrite]: #117
+#128 := [monotonicity #118 #125]: #127
+#120 := (iff #25 #119)
+#113 := (iff #23 #112)
+#114 := [rewrite]: #113
+#121 := [monotonicity #114 #118]: #120
+#131 := [monotonicity #121 #128]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [quant-intro #140]: #142
+#109 := (iff #36 #108)
+#106 := (iff #35 #105)
+#103 := (= #34 #102)
+#100 := (= #33 #99)
+#97 := (= #32 #96)
+#94 := (= #31 #93)
+#95 := [rewrite]: #94
+#91 := (= #30 #90)
+#92 := [rewrite]: #91
+#98 := [monotonicity #92 #95]: #97
+#87 := (iff #28 #86)
+#84 := (iff #27 #82)
#85 := [rewrite]: #84
-#81 := (= #21 #80)
-#82 := [monotonicity #53]: #81
-#87 := [trans #82 #85]: #86
-#78 := (iff #20 #77)
-#75 := (iff #19 #74)
-#69 := (iff #16 #68)
-#70 := [monotonicity #53]: #69
-#76 := [monotonicity #70]: #75
-#72 := (iff #17 #71)
-#73 := [monotonicity #70]: #72
-#79 := [monotonicity #73 #76]: #78
-#106 := [monotonicity #79 #87 #103]: #105
-#110 := [trans #106 #108]: #109
-#66 := (iff #14 false)
-#61 := (or false false)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #14 #61)
-#59 := (iff #13 false)
-#54 := (= -1::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #13 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#63 := [monotonicity #50 #60]: #62
-#67 := [trans #63 #65]: #66
-#113 := [monotonicity #67 #110]: #112
-#117 := [trans #113 #115]: #116
-#120 := [monotonicity #117 #89]: #119
-#124 := [trans #120 #122]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#48 := [asserted]: #28
-[mp #48 #131]: false
-unsat
-99124c49e46379cd9d9cbc824f6c48eaad703212 215 0
-#2 := false
-#9 := 0::Int
-#11 := 1::Int
-decl f3 :: Int
-#8 := f3
-#49 := -1::Int
-#81 := (* -1::Int f3)
-#91 := (div #81 1::Int)
-#10 := (= f3 0::Int)
-#149 := (ite #10 0::Int #91)
-#157 := (+ f3 #149)
-#177 := (>= #157 0::Int)
-#274 := (not #177)
-#255 := [hypothesis]: #177
-#176 := (<= #157 0::Int)
-#251 := (* -1::Int #149)
-#252 := (+ #91 #251)
-#254 := (>= #252 0::Int)
-#173 := (= #91 #149)
-#175 := (not #10)
-#156 := (= #157 0::Int)
-#172 := (= #149 0::Int)
-#180 := [hypothesis]: #10
-#170 := (or #175 #172)
-#171 := [def-axiom]: #170
-#181 := [unit-resolution #171 #180]: #172
-#190 := (= #157 #149)
-#188 := (= #149 #157)
-#111 := (<= f3 0::Int)
-#182 := (or #175 #111)
-#183 := [th-lemma arith triangle-eq]: #182
-#184 := [unit-resolution #183 #180]: #111
-#124 := (>= f3 0::Int)
-#185 := (or #175 #124)
-#186 := [th-lemma arith triangle-eq]: #185
-#187 := [unit-resolution #186 #180]: #124
-#189 := [th-lemma arith eq-propagate 1 1 #187 #184]: #188
-#191 := [symm #189]: #190
-#192 := [trans #191 #181]: #156
-#161 := (not #156)
-#22 := (- f3)
-#12 := (- 1::Int)
-#23 := (- #12)
-#24 := (div #22 #23)
-#21 := (div f3 #12)
-#16 := (< 0::Int #12)
-#18 := (< f3 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int f3)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= #12 0::Int)
-#14 := (or #10 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (= #26 #22)
-#28 := (not #27)
-#164 := (iff #28 #161)
-#78 := (div f3 -1::Int)
-#66 := (< 0::Int -1::Int)
-#72 := (and #18 #66)
-#69 := (and #15 #66)
-#75 := (or #69 #72)
-#94 := (ite #75 #78 #91)
-#97 := (ite #10 0::Int #94)
-#103 := (= #81 #97)
-#108 := (not #103)
-#162 := (iff #108 #161)
-#159 := (iff #103 #156)
-#152 := (= #81 #149)
-#155 := (iff #152 #156)
-#158 := [rewrite]: #155
-#153 := (iff #103 #152)
-#150 := (= #97 #149)
-#147 := (= #94 #91)
-#142 := (ite false #78 #91)
-#145 := (= #142 #91)
-#146 := [rewrite]: #145
-#143 := (= #94 #142)
-#140 := (iff #75 false)
-#135 := (or false false)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #75 #135)
-#133 := (iff #72 false)
-#125 := (not #124)
-#128 := (and #125 false)
-#131 := (iff #128 false)
-#132 := [rewrite]: #131
-#129 := (iff #72 #128)
-#115 := (iff #66 false)
-#116 := [rewrite]: #115
-#126 := (iff #18 #125)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127 #116]: #129
-#134 := [trans #130 #132]: #133
-#122 := (iff #69 false)
-#112 := (not #111)
-#117 := (and #112 false)
-#120 := (iff #117 false)
-#121 := [rewrite]: #120
-#118 := (iff #69 #117)
-#113 := (iff #15 #112)
-#114 := [rewrite]: #113
-#119 := [monotonicity #114 #116]: #118
-#123 := [trans #119 #121]: #122
-#137 := [monotonicity #123 #134]: #136
-#141 := [trans #137 #139]: #140
-#144 := [monotonicity #141]: #143
-#148 := [trans #144 #146]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#160 := [trans #154 #158]: #159
-#163 := [monotonicity #160]: #162
-#109 := (iff #28 #108)
-#106 := (iff #27 #103)
-#100 := (= #97 #81)
-#104 := (iff #100 #103)
-#105 := [rewrite]: #104
-#101 := (iff #27 #100)
-#82 := (= #22 #81)
-#83 := [rewrite]: #82
-#98 := (= #26 #97)
-#95 := (= #25 #94)
-#92 := (= #24 #91)
-#89 := (= #23 1::Int)
-#84 := (- -1::Int)
-#87 := (= #84 1::Int)
-#88 := [rewrite]: #87
-#85 := (= #23 #84)
-#50 := (= #12 -1::Int)
-#51 := [rewrite]: #50
-#86 := [monotonicity #51]: #85
-#90 := [trans #86 #88]: #89
-#93 := [monotonicity #83 #90]: #92
-#79 := (= #21 #78)
-#80 := [monotonicity #51]: #79
-#76 := (iff #20 #75)
-#73 := (iff #19 #72)
-#67 := (iff #16 #66)
-#68 := [monotonicity #51]: #67
-#74 := [monotonicity #68]: #73
-#70 := (iff #17 #69)
+#88 := [monotonicity #85]: #87
+#101 := [monotonicity #88 #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#110 := [quant-intro #107]: #109
+#145 := [trans #110 #143]: #144
+#81 := [asserted]: #36
+#146 := [mp #81 #145]: #141
+#195 := [mp~ #146 #204]: #141
+#226 := [mp #195 #225]: #223
+#257 := [mp #226 #256]: #254
+#751 := [mp #257 #750]: #746
+#72 := -2::Int
+#66 := -3::Int
+#8 := 5::Int
+#69 := (f3 5::Int -3::Int)
+#75 := (= #69 -2::Int)
+#78 := (not #75)
+#12 := 2::Int
+#13 := (- 2::Int)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 5::Int #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#79 := (iff #15 #78)
+#76 := (iff #14 #75)
+#73 := (= #13 -2::Int)
+#74 := [rewrite]: #73
+#70 := (= #11 #69)
+#67 := (= #10 -3::Int)
+#68 := [rewrite]: #67
#71 := [monotonicity #68]: #70
#77 := [monotonicity #71 #74]: #76
-#96 := [monotonicity #77 #80 #93]: #95
-#64 := (iff #14 #10)
-#59 := (or #10 false)
-#62 := (iff #59 #10)
-#63 := [rewrite]: #62
-#60 := (iff #14 #59)
-#57 := (iff #13 false)
-#52 := (= -1::Int 0::Int)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#99 := [monotonicity #65 #96]: #98
-#102 := [monotonicity #99 #83]: #101
-#107 := [trans #102 #105]: #106
+#80 := [monotonicity #77]: #79
+#65 := [asserted]: #15
+#83 := [mp #65 #80]: #78
+#665 := (not #746)
+#659 := (or #665 #75)
+#331 := (* -1::Int -3::Int)
+#416 := (* -1::Int 5::Int)
+#417 := (div #416 #331)
+#418 := (* -1::Int #417)
+#409 := (+ #69 #418)
+#420 := (= #409 0::Int)
+#421 := (div 5::Int -3::Int)
+#349 := (* -1::Int #421)
+#422 := (+ #69 #349)
+#419 := (= #422 0::Int)
+#423 := (>= 5::Int 0::Int)
+#402 := (<= -3::Int 0::Int)
+#737 := (or #402 #423)
+#739 := (not #737)
+#396 := (<= 5::Int 0::Int)
+#526 := (or #396 #402)
+#733 := (not #526)
+#407 := (or #733 #739)
+#408 := (ite #407 #419 #420)
+#740 := (= #69 0::Int)
+#741 := (= -3::Int 0::Int)
+#742 := (= 5::Int 0::Int)
+#743 := (or #742 #741)
+#738 := (ite #743 #740 #408)
+#666 := (or #665 #738)
+#651 := (iff #666 #659)
+#654 := (iff #659 #659)
+#655 := [rewrite]: #654
+#663 := (iff #738 #75)
+#671 := (ite false #740 #75)
+#673 := (iff #671 #75)
+#662 := [rewrite]: #673
+#672 := (iff #738 #671)
+#660 := (iff #408 #75)
+#691 := (= #69 -1::Int)
+#680 := (ite false #691 #75)
+#661 := (iff #680 #75)
+#658 := [rewrite]: #661
+#667 := (iff #408 #680)
+#679 := (iff #420 #75)
+#563 := (+ 2::Int #69)
+#582 := (= #563 0::Int)
+#585 := (iff #582 #75)
+#586 := [rewrite]: #585
+#583 := (iff #420 #582)
+#581 := (= #409 #563)
+#674 := (+ #69 2::Int)
+#578 := (= #674 #563)
+#580 := [rewrite]: #578
+#675 := (= #409 #674)
+#677 := (= #418 2::Int)
+#686 := (* -1::Int -2::Int)
+#570 := (= #686 2::Int)
+#529 := [rewrite]: #570
+#568 := (= #418 #686)
+#685 := (= #417 -2::Int)
+#694 := -5::Int
+#527 := (div -5::Int 3::Int)
+#682 := (= #527 -2::Int)
+#684 := [rewrite]: #682
+#528 := (= #417 #527)
+#696 := (= #331 3::Int)
+#525 := [rewrite]: #696
+#695 := (= #416 -5::Int)
+#689 := [rewrite]: #695
+#681 := [monotonicity #689 #525]: #528
+#683 := [trans #681 #684]: #685
+#569 := [monotonicity #683]: #568
+#579 := [trans #569 #529]: #677
+#678 := [monotonicity #579]: #675
+#574 := [trans #678 #580]: #581
+#584 := [monotonicity #574]: #583
+#676 := [trans #584 #586]: #679
+#687 := (iff #419 #691)
+#710 := 1::Int
+#703 := (+ 1::Int #69)
+#547 := (= #703 0::Int)
+#692 := (iff #547 #691)
+#693 := [rewrite]: #692
+#548 := (iff #419 #547)
+#705 := (= #422 #703)
+#702 := (+ #69 1::Int)
+#704 := (= #702 #703)
+#699 := [rewrite]: #704
+#697 := (= #422 #702)
+#700 := (= #349 1::Int)
+#709 := (* -1::Int -1::Int)
+#707 := (= #709 1::Int)
+#711 := [rewrite]: #707
+#424 := (= #349 #709)
+#430 := (= #421 -1::Int)
+#708 := [rewrite]: #430
+#706 := [monotonicity #708]: #424
+#701 := [trans #706 #711]: #700
+#698 := [monotonicity #701]: #697
+#546 := [trans #698 #699]: #705
+#690 := [monotonicity #546]: #548
+#688 := [trans #690 #693]: #687
+#428 := (iff #407 false)
+#735 := (or false false)
+#379 := (iff #735 false)
+#720 := [rewrite]: #379
+#717 := (iff #407 #735)
+#716 := (iff #739 false)
+#1 := true
+#730 := (not true)
+#731 := (iff #730 false)
+#729 := [rewrite]: #731
+#438 := (iff #739 #730)
+#715 := (iff #737 true)
+#442 := (or true true)
+#337 := (iff #442 true)
+#714 := [rewrite]: #337
+#443 := (iff #737 #442)
+#719 := (iff #423 true)
+#441 := [rewrite]: #719
+#722 := (iff #402 true)
+#723 := [rewrite]: #722
+#444 := [monotonicity #723 #441]: #443
+#437 := [trans #444 #714]: #715
+#712 := [monotonicity #437]: #438
+#713 := [trans #712 #729]: #716
+#732 := (iff #733 false)
+#370 := (iff #733 #730)
+#365 := (iff #526 true)
+#724 := (or false true)
+#721 := (iff #724 true)
+#727 := [rewrite]: #721
+#725 := (iff #526 #724)
+#385 := (iff #396 false)
+#386 := [rewrite]: #385
+#726 := [monotonicity #386 #723]: #725
+#728 := [trans #726 #727]: #365
+#371 := [monotonicity #728]: #370
+#718 := [trans #371 #729]: #732
+#427 := [monotonicity #718 #713]: #717
+#429 := [trans #427 #720]: #428
+#669 := [monotonicity #429 #688 #676]: #667
+#670 := [trans #669 #658]: #660
+#383 := (iff #743 false)
+#395 := (iff #743 #735)
+#394 := (iff #741 false)
+#399 := [rewrite]: #394
+#744 := (iff #742 false)
+#734 := [rewrite]: #744
+#736 := [monotonicity #734 #399]: #395
+#384 := [trans #736 #720]: #383
+#668 := [monotonicity #384 #670]: #672
+#664 := [trans #668 #662]: #663
+#653 := [monotonicity #664]: #651
+#656 := [trans #653 #655]: #651
+#650 := [quant-inst #8 #66]: #666
+#652 := [mp #650 #656]: #659
+[unit-resolution #652 #83 #751]: false
+unsat
+3b09e93d3eb1701446a8a6f0f64071b3ee25d56a 319 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#750 := (pattern #16)
+#17 := 0::Int
+#64 := -1::Int
+#99 := (* -1::Int #15)
+#96 := (* -1::Int #14)
+#102 := (div #96 #99)
+#253 := (* -1::Int #102)
+#254 := (+ #16 #253)
+#255 := (= #254 0::Int)
+#27 := (div #14 #15)
+#250 := (* -1::Int #27)
+#251 := (+ #16 #250)
+#252 := (= #251 0::Int)
+#128 := (>= #14 0::Int)
+#121 := (<= #15 0::Int)
+#213 := (or #121 #128)
+#214 := (not #213)
+#117 := (<= #14 0::Int)
+#211 := (or #117 #121)
+#212 := (not #211)
+#217 := (or #212 #214)
+#256 := (ite #217 #252 #255)
+#249 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#20 := (or #18 #19)
+#257 := (ite #20 #249 #256)
+#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #257)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#754 := (iff #260 #751)
+#752 := (iff #257 #257)
+#753 := [refl]: #752
+#755 := [quant-intro #753]: #754
+#220 := (ite #217 #27 #102)
+#223 := (ite #20 0::Int #220)
+#226 := (= #16 #223)
+#229 := (forall (vars (?v0 Int) (?v1 Int)) #226)
+#261 := (iff #229 #260)
+#258 := (iff #226 #257)
+#259 := [rewrite]: #258
+#262 := [quant-intro #259]: #261
+#129 := (not #128)
+#122 := (not #121)
+#132 := (and #122 #129)
+#118 := (not #117)
+#125 := (and #118 #122)
+#135 := (or #125 #132)
+#138 := (ite #135 #27 #102)
+#141 := (ite #20 0::Int #138)
+#144 := (= #16 #141)
+#147 := (forall (vars (?v0 Int) (?v1 Int)) #144)
+#230 := (iff #147 #229)
+#227 := (iff #144 #226)
+#224 := (= #141 #223)
+#221 := (= #138 #220)
+#218 := (iff #135 #217)
+#215 := (iff #132 #214)
+#216 := [rewrite]: #215
+#205 := (iff #125 #212)
+#206 := [rewrite]: #205
+#219 := [monotonicity #206 #216]: #218
+#222 := [monotonicity #219]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [quant-intro #228]: #230
+#209 := (~ #147 #147)
+#207 := (~ #144 #144)
+#208 := [refl]: #207
+#210 := [nnf-pos #208]: #209
+#29 := (- #15)
+#28 := (- #14)
+#30 := (div #28 #29)
+#22 := (< 0::Int #15)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (ite #26 #27 #30)
+#32 := (ite #20 0::Int #31)
+#33 := (= #16 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#150 := (iff #34 #147)
+#90 := (and #22 #24)
+#93 := (or #23 #90)
+#105 := (ite #93 #27 #102)
+#108 := (ite #20 0::Int #105)
+#111 := (= #16 #108)
+#114 := (forall (vars (?v0 Int) (?v1 Int)) #111)
+#148 := (iff #114 #147)
+#145 := (iff #111 #144)
+#142 := (= #108 #141)
+#139 := (= #105 #138)
+#136 := (iff #93 #135)
+#133 := (iff #90 #132)
+#130 := (iff #24 #129)
+#131 := [rewrite]: #130
+#123 := (iff #22 #122)
+#124 := [rewrite]: #123
+#134 := [monotonicity #124 #131]: #133
+#126 := (iff #23 #125)
+#119 := (iff #21 #118)
+#120 := [rewrite]: #119
+#127 := [monotonicity #120 #124]: #126
+#137 := [monotonicity #127 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#115 := (iff #34 #114)
+#112 := (iff #33 #111)
+#109 := (= #32 #108)
+#106 := (= #31 #105)
+#103 := (= #30 #102)
+#100 := (= #29 #99)
+#101 := [rewrite]: #100
+#97 := (= #28 #96)
+#98 := [rewrite]: #97
+#104 := [monotonicity #98 #101]: #103
+#94 := (iff #26 #93)
+#91 := (iff #25 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#107 := [monotonicity #95 #104]: #106
#110 := [monotonicity #107]: #109
-#165 := [trans #110 #163]: #164
-#48 := [asserted]: #28
-#166 := [mp #48 #165]: #161
-#193 := [unit-resolution #166 #192]: false
-#194 := [lemma #193]: #175
-#168 := (or #10 #173)
-#169 := [def-axiom]: #168
-#256 := [unit-resolution #169 #194]: #173
-#257 := (not #173)
-#258 := (or #257 #254)
-#259 := [th-lemma arith triangle-eq]: #258
-#260 := [unit-resolution #259 #256]: #254
-#218 := (+ f3 #91)
-#224 := (<= #218 0::Int)
-#219 := (= #218 0::Int)
-#1 := true
-#46 := [true-axiom]: true
-#261 := (or false #219)
-#262 := [th-lemma arith]: #261
-#263 := [unit-resolution #262 #46]: #219
-#264 := (not #219)
-#265 := (or #264 #224)
-#266 := [th-lemma arith triangle-eq]: #265
-#267 := [unit-resolution #266 #263]: #224
-#269 := (not #224)
-#268 := (not #254)
-#270 := (or #176 #268 #269)
-#271 := [th-lemma arith assign-bounds 1 -1]: #270
-#272 := [unit-resolution #271 #267 #260]: #176
-#273 := (not #176)
-#277 := (or #273 #274)
-#275 := (or #156 #273 #274)
-#276 := [th-lemma arith triangle-eq]: #275
-#278 := [unit-resolution #276 #166]: #277
-#279 := [unit-resolution #278 #272 #255]: false
-#280 := [lemma #279]: #274
-#253 := (<= #252 0::Int)
-#281 := (or #257 #253)
-#282 := [th-lemma arith triangle-eq]: #281
-#283 := [unit-resolution #282 #256]: #253
-#225 := (>= #218 0::Int)
-#284 := (or #264 #225)
-#285 := [th-lemma arith triangle-eq]: #284
-#286 := [unit-resolution #285 #263]: #225
-#288 := (not #225)
-#287 := (not #253)
-#289 := (or #177 #287 #288)
-#290 := [th-lemma arith assign-bounds 1 -1]: #289
-#291 := [unit-resolution #290 #286 #283]: #177
-[unit-resolution #291 #280]: false
-unsat
-530d84b9b60629031058dc22de3bbb66e9dd68b7 73 0
-#2 := false
-#8 := 0::Int
+#113 := [monotonicity #110]: #112
+#116 := [quant-intro #113]: #115
+#151 := [trans #116 #149]: #150
+#89 := [asserted]: #34
+#152 := [mp #89 #151]: #147
+#201 := [mp~ #152 #210]: #147
+#232 := [mp #201 #231]: #229
+#263 := [mp #232 #262]: #260
+#756 := [mp #263 #755]: #751
#10 := 3::Int
-#19 := (- 3::Int)
-#18 := (- 0::Int)
-#20 := (div #18 #19)
-#17 := (div 0::Int 3::Int)
-#14 := (< 0::Int 3::Int)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#21 := (ite #16 #17 #20)
-#11 := (= 3::Int 0::Int)
-#9 := (= 0::Int 0::Int)
-#12 := (or #9 #11)
-#22 := (ite #12 0::Int #21)
-#23 := (= #22 0::Int)
-#24 := (not #23)
-#94 := (iff #24 false)
-#1 := true
-#89 := (not true)
-#92 := (iff #89 false)
+#67 := (f3 -1::Int 3::Int)
+#70 := (= #67 -1::Int)
+#83 := (not #70)
+#8 := 1::Int
+#9 := (- 1::Int)
+#11 := (f3 #9 3::Int)
+#12 := (= #11 #9)
+#13 := (not #12)
+#86 := (iff #13 #83)
+#73 := (= -1::Int #67)
+#78 := (not #73)
+#84 := (iff #78 #83)
+#81 := (iff #73 #70)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#79 := (iff #13 #78)
+#76 := (iff #12 #73)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #12 #70)
+#65 := (= #9 -1::Int)
+#66 := [rewrite]: #65
+#68 := (= #11 #67)
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69 #66]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#87 := [trans #80 #85]: #86
+#63 := [asserted]: #13
+#88 := [mp #63 #87]: #83
+#676 := (not #751)
+#677 := (or #676 #70)
+#337 := (* -1::Int 3::Int)
+#421 := (* -1::Int -1::Int)
+#422 := (div #421 #337)
+#423 := (* -1::Int #422)
+#414 := (+ #67 #423)
+#425 := (= #414 0::Int)
+#426 := (div -1::Int 3::Int)
+#427 := (* -1::Int #426)
+#424 := (+ #67 #427)
+#428 := (= #424 0::Int)
+#407 := (>= -1::Int 0::Int)
+#742 := (<= 3::Int 0::Int)
+#744 := (or #742 #407)
+#401 := (not #744)
+#531 := (<= -1::Int 0::Int)
+#738 := (or #531 #742)
+#412 := (not #738)
+#413 := (or #412 #401)
+#745 := (ite #413 #428 #425)
+#746 := (= #67 0::Int)
+#747 := (= 3::Int 0::Int)
+#748 := (= -1::Int 0::Int)
+#743 := (or #748 #747)
+#749 := (ite #743 #746 #745)
+#673 := (or #676 #749)
+#667 := (iff #673 #677)
+#669 := (iff #677 #677)
+#670 := [rewrite]: #669
+#665 := (iff #749 #70)
+#685 := (ite false #746 #70)
+#666 := (iff #685 #70)
+#663 := [rewrite]: #666
+#672 := (iff #749 #685)
+#684 := (iff #745 #70)
+#1 := true
+#587 := (ite true #70 #746)
+#590 := (iff #587 #70)
+#591 := [rewrite]: #590
+#588 := (iff #745 #587)
+#586 := (iff #425 #746)
+#583 := (= #414 #67)
+#584 := (+ #67 0::Int)
+#683 := (= #584 #67)
+#568 := [rewrite]: #683
+#679 := (= #414 #584)
+#534 := (= #423 0::Int)
+#688 := (* -1::Int 0::Int)
+#574 := (= #688 0::Int)
+#575 := [rewrite]: #574
+#691 := (= #423 #688)
+#689 := (= #422 0::Int)
+#700 := -3::Int
+#530 := (div 1::Int -3::Int)
+#686 := (= #530 0::Int)
+#687 := [rewrite]: #686
+#532 := (= #422 #530)
+#694 := (= #337 -3::Int)
+#701 := [rewrite]: #694
+#705 := (= #421 1::Int)
+#706 := [rewrite]: #705
+#533 := [monotonicity #706 #701]: #532
+#690 := [trans #533 #687]: #689
+#573 := [monotonicity #690]: #691
+#682 := [trans #573 #575]: #534
+#680 := [monotonicity #682]: #679
+#585 := [trans #680 #568]: #583
+#579 := [monotonicity #585]: #586
+#693 := (iff #428 #70)
+#704 := (+ 1::Int #67)
+#695 := (= #704 0::Int)
+#698 := (iff #695 #70)
+#692 := [rewrite]: #698
+#696 := (iff #428 #695)
+#552 := (= #424 #704)
+#703 := (+ #67 1::Int)
+#710 := (= #703 #704)
+#551 := [rewrite]: #710
+#708 := (= #424 #703)
+#707 := (= #427 1::Int)
+#712 := (= #427 #421)
+#711 := (= #426 -1::Int)
+#715 := [rewrite]: #711
+#716 := [monotonicity #715]: #712
+#702 := [trans #716 #706]: #707
+#709 := [monotonicity #702]: #708
+#553 := [trans #709 #551]: #552
+#697 := [monotonicity #553]: #696
+#699 := [trans #697 #692]: #693
+#714 := (iff #413 true)
+#432 := (or false true)
+#435 := (iff #432 true)
+#713 := [rewrite]: #435
+#433 := (iff #413 #432)
+#718 := (iff #401 true)
+#720 := (not false)
+#717 := (iff #720 true)
+#721 := [rewrite]: #717
+#442 := (iff #401 #720)
+#343 := (iff #744 false)
+#400 := (or false false)
+#725 := (iff #400 false)
+#388 := [rewrite]: #725
+#448 := (iff #744 #400)
+#446 := (iff #407 false)
+#447 := [rewrite]: #446
+#728 := (iff #742 false)
+#729 := [rewrite]: #728
+#449 := [monotonicity #729 #447]: #448
+#719 := [trans #449 #388]: #343
+#443 := [monotonicity #719]: #442
+#722 := [trans #443 #721]: #718
+#723 := (iff #412 false)
+#375 := (not true)
+#734 := (iff #375 false)
+#737 := [rewrite]: #734
+#376 := (iff #412 #375)
+#733 := (iff #738 true)
+#730 := (or true false)
+#732 := (iff #730 true)
+#370 := [rewrite]: #732
+#731 := (iff #738 #730)
+#391 := (iff #531 true)
+#727 := [rewrite]: #391
+#726 := [monotonicity #727 #729]: #731
+#735 := [trans #726 #370]: #733
+#736 := [monotonicity #735]: #376
+#724 := [trans #736 #737]: #723
+#434 := [monotonicity #724 #722]: #433
+#429 := [trans #434 #713]: #714
+#589 := [monotonicity #429 #699 #579]: #588
+#681 := [trans #589 #591]: #684
+#389 := (iff #743 false)
+#741 := (iff #743 #400)
+#404 := (iff #747 false)
+#740 := [rewrite]: #404
+#739 := (iff #748 false)
+#399 := [rewrite]: #739
+#384 := [monotonicity #399 #740]: #741
+#390 := [trans #384 #388]: #389
+#674 := [monotonicity #390 #681]: #672
+#675 := [trans #674 #663]: #665
+#668 := [monotonicity #675]: #667
+#664 := [trans #668 #670]: #667
+#678 := [quant-inst #64 #10]: #673
+#671 := [mp #678 #664]: #677
+[unit-resolution #671 #88 #756]: false
+unsat
+896650ef8f75fd8ef47b1c1a736049dce2114a91 309 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#17 := (f3 #15 #16)
+#742 := (pattern #17)
+#18 := 0::Int
+#71 := -1::Int
+#91 := (* -1::Int #16)
+#88 := (* -1::Int #15)
+#94 := (div #88 #91)
+#245 := (* -1::Int #94)
+#246 := (+ #17 #245)
+#247 := (= #246 0::Int)
+#28 := (div #15 #16)
+#242 := (* -1::Int #28)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
+#120 := (>= #15 0::Int)
+#113 := (<= #16 0::Int)
+#205 := (or #113 #120)
+#206 := (not #205)
+#109 := (<= #15 0::Int)
+#203 := (or #109 #113)
+#204 := (not #203)
+#209 := (or #204 #206)
+#248 := (ite #209 #244 #247)
+#241 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#249 := (ite #21 #241 #248)
+#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#746 := (iff #252 #743)
+#744 := (iff #249 #249)
+#745 := [refl]: #744
+#747 := [quant-intro #745]: #746
+#212 := (ite #209 #28 #94)
+#215 := (ite #21 0::Int #212)
+#218 := (= #17 #215)
+#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
+#253 := (iff #221 #252)
+#250 := (iff #218 #249)
+#251 := [rewrite]: #250
+#254 := [quant-intro #251]: #253
+#121 := (not #120)
+#114 := (not #113)
+#124 := (and #114 #121)
+#110 := (not #109)
+#117 := (and #110 #114)
+#127 := (or #117 #124)
+#130 := (ite #127 #28 #94)
+#133 := (ite #21 0::Int #130)
+#136 := (= #17 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#216 := (= #133 #215)
+#213 := (= #130 #212)
+#210 := (iff #127 #209)
+#207 := (iff #124 #206)
+#208 := [rewrite]: #207
+#197 := (iff #117 #204)
+#198 := [rewrite]: #197
+#211 := [monotonicity #198 #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [quant-intro #220]: #222
+#201 := (~ #139 #139)
+#199 := (~ #136 #136)
+#200 := [refl]: #199
+#202 := [nnf-pos #200]: #201
+#30 := (- #16)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#142 := (iff #35 #139)
+#81 := (and #23 #25)
+#85 := (or #24 #81)
+#97 := (ite #85 #28 #94)
+#100 := (ite #21 0::Int #97)
+#103 := (= #17 #100)
+#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
+#140 := (iff #106 #139)
+#137 := (iff #103 #136)
+#134 := (= #100 #133)
+#131 := (= #97 #130)
+#128 := (iff #85 #127)
+#125 := (iff #81 #124)
+#122 := (iff #25 #121)
+#123 := [rewrite]: #122
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#126 := [monotonicity #116 #123]: #125
+#118 := (iff #24 #117)
+#111 := (iff #22 #110)
+#112 := [rewrite]: #111
+#119 := [monotonicity #112 #116]: #118
+#129 := [monotonicity #119 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#107 := (iff #35 #106)
+#104 := (iff #34 #103)
+#101 := (= #33 #100)
+#98 := (= #32 #97)
+#95 := (= #31 #94)
+#92 := (= #30 #91)
#93 := [rewrite]: #92
-#90 := (iff #24 #89)
-#87 := (iff #23 true)
-#45 := (iff #9 true)
-#46 := [rewrite]: #45
-#85 := (iff #23 #9)
-#79 := (ite true 0::Int 0::Int)
-#82 := (= #79 0::Int)
-#83 := [rewrite]: #82
-#80 := (= #22 #79)
-#77 := (= #21 0::Int)
-#72 := (ite #15 0::Int 0::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #21 #72)
-#70 := (= #20 0::Int)
-#62 := -3::Int
-#65 := (div 0::Int -3::Int)
-#68 := (= #65 0::Int)
-#69 := [rewrite]: #68
-#66 := (= #20 #65)
-#63 := (= #19 -3::Int)
-#64 := [rewrite]: #63
-#60 := (= #18 0::Int)
-#61 := [rewrite]: #60
-#67 := [monotonicity #61 #64]: #66
-#71 := [trans #67 #69]: #70
-#58 := (= #17 0::Int)
-#59 := [rewrite]: #58
-#56 := (iff #16 #15)
-#57 := [rewrite]: #56
-#74 := [monotonicity #57 #59 #71]: #73
-#78 := [trans #74 #76]: #77
-#54 := (iff #12 true)
-#49 := (or true false)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #12 #49)
-#47 := (iff #11 false)
-#48 := [rewrite]: #47
-#51 := [monotonicity #46 #48]: #50
-#55 := [trans #51 #53]: #54
-#81 := [monotonicity #55 #78]: #80
-#84 := [trans #81 #83]: #23
-#86 := [monotonicity #84]: #85
-#88 := [trans #86 #46]: #87
-#91 := [monotonicity #88]: #90
-#95 := [trans #91 #93]: #94
-#44 := [asserted]: #24
-[mp #44 #95]: false
-unsat
-99c1933dfc0f818aac1f7a0114d4293293e0a0a1 102 0
-#2 := false
-#8 := 0::Int
+#89 := (= #29 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90 #93]: #95
+#86 := (iff #27 #85)
+#83 := (iff #26 #81)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#99 := [monotonicity #87 #96]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [quant-intro #105]: #107
+#143 := [trans #108 #141]: #142
+#80 := [asserted]: #35
+#144 := [mp #80 #143]: #139
+#193 := [mp~ #144 #202]: #139
+#224 := [mp #193 #223]: #221
+#255 := [mp #224 #254]: #252
+#748 := [mp #255 #747]: #743
+#8 := 3::Int
+#65 := -3::Int
+#68 := (f3 -3::Int 3::Int)
+#74 := (= #68 -1::Int)
+#77 := (not #74)
+#11 := 1::Int
+#12 := (- 1::Int)
+#9 := (- 3::Int)
+#10 := (f3 #9 3::Int)
+#13 := (= #10 #12)
+#14 := (not #13)
+#78 := (iff #14 #77)
+#75 := (iff #13 #74)
+#72 := (= #12 -1::Int)
+#73 := [rewrite]: #72
+#69 := (= #10 #68)
+#66 := (= #9 -3::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [monotonicity #70 #73]: #75
+#79 := [monotonicity #76]: #78
+#64 := [asserted]: #14
+#82 := [mp #64 #79]: #77
+#657 := (not #743)
+#667 := (or #657 #74)
+#329 := (* -1::Int 3::Int)
+#413 := (* -1::Int -3::Int)
+#414 := (div #413 #329)
+#415 := (* -1::Int #414)
+#406 := (+ #68 #415)
+#417 := (= #406 0::Int)
+#418 := (div -3::Int 3::Int)
+#419 := (* -1::Int #418)
+#416 := (+ #68 #419)
+#420 := (= #416 0::Int)
+#399 := (>= -3::Int 0::Int)
+#734 := (<= 3::Int 0::Int)
+#736 := (or #734 #399)
+#393 := (not #736)
+#523 := (<= -3::Int 0::Int)
+#730 := (or #523 #734)
+#404 := (not #730)
+#405 := (or #404 #393)
+#737 := (ite #405 #420 #417)
+#738 := (= #68 0::Int)
+#739 := (= 3::Int 0::Int)
+#740 := (= -3::Int 0::Int)
+#735 := (or #740 #739)
+#741 := (ite #735 #738 #737)
+#668 := (or #657 #741)
+#665 := (iff #668 #667)
+#659 := (iff #667 #667)
+#660 := [rewrite]: #659
+#658 := (iff #741 #74)
+#676 := (ite false #738 #74)
+#664 := (iff #676 #74)
+#666 := [rewrite]: #664
+#673 := (iff #741 #676)
+#582 := (iff #737 #74)
+#1 := true
+#578 := (ite true #74 #74)
+#580 := (iff #578 #74)
+#581 := [rewrite]: #580
+#571 := (iff #737 #578)
+#575 := (iff #417 #74)
+#702 := (+ 1::Int #68)
+#688 := (= #702 0::Int)
+#684 := (iff #688 #74)
+#685 := [rewrite]: #684
+#675 := (iff #417 #688)
+#671 := (= #406 #702)
+#700 := (+ #68 1::Int)
+#543 := (= #700 #702)
+#544 := [rewrite]: #543
+#674 := (= #406 #700)
+#567 := (= #415 1::Int)
+#704 := (* -1::Int -1::Int)
+#698 := (= #704 1::Int)
+#699 := [rewrite]: #698
+#565 := (= #415 #704)
+#680 := (= #414 -1::Int)
+#525 := (div 3::Int -3::Int)
+#681 := (= #525 -1::Int)
+#682 := [rewrite]: #681
+#678 := (= #414 #525)
+#522 := (= #329 -3::Int)
+#524 := [rewrite]: #522
+#686 := (= #413 3::Int)
+#693 := [rewrite]: #686
+#679 := [monotonicity #693 #524]: #678
+#683 := [trans #679 #682]: #680
+#566 := [monotonicity #683]: #565
+#526 := [trans #566 #699]: #567
+#576 := [monotonicity #526]: #674
+#672 := [trans #576 #544]: #671
+#560 := [monotonicity #672]: #675
+#577 := [trans #560 #685]: #575
+#691 := (iff #420 #74)
+#689 := (iff #420 #688)
+#545 := (= #416 #702)
+#701 := (= #416 #700)
+#694 := (= #419 1::Int)
+#708 := (= #419 #704)
+#703 := (= #418 -1::Int)
+#707 := [rewrite]: #703
+#697 := [monotonicity #707]: #708
+#695 := [trans #697 #699]: #694
+#696 := [monotonicity #695]: #701
+#687 := [trans #696 #544]: #545
+#690 := [monotonicity #687]: #689
+#692 := [trans #690 #685]: #691
+#706 := (iff #405 true)
+#424 := (or false true)
+#427 := (iff #424 true)
+#705 := [rewrite]: #427
+#425 := (iff #405 #424)
+#710 := (iff #393 true)
+#712 := (not false)
+#709 := (iff #712 true)
+#713 := [rewrite]: #709
+#434 := (iff #393 #712)
+#335 := (iff #736 false)
+#392 := (or false false)
+#717 := (iff #392 false)
+#380 := [rewrite]: #717
+#440 := (iff #736 #392)
+#438 := (iff #399 false)
+#439 := [rewrite]: #438
+#720 := (iff #734 false)
+#721 := [rewrite]: #720
+#441 := [monotonicity #721 #439]: #440
+#711 := [trans #441 #380]: #335
+#435 := [monotonicity #711]: #434
+#714 := [trans #435 #713]: #710
+#715 := (iff #404 false)
+#367 := (not true)
+#726 := (iff #367 false)
+#729 := [rewrite]: #726
+#368 := (iff #404 #367)
+#725 := (iff #730 true)
+#722 := (or true false)
+#724 := (iff #722 true)
+#362 := [rewrite]: #724
+#723 := (iff #730 #722)
+#383 := (iff #523 true)
+#719 := [rewrite]: #383
+#718 := [monotonicity #719 #721]: #723
+#727 := [trans #718 #362]: #725
+#728 := [monotonicity #727]: #368
+#716 := [trans #728 #729]: #715
+#426 := [monotonicity #716 #714]: #425
+#421 := [trans #426 #705]: #706
+#579 := [monotonicity #421 #692 #577]: #571
+#583 := [trans #579 #581]: #582
+#381 := (iff #735 false)
+#733 := (iff #735 #392)
+#396 := (iff #739 false)
+#732 := [rewrite]: #396
+#731 := (iff #740 false)
+#391 := [rewrite]: #731
+#376 := [monotonicity #391 #732]: #733
+#382 := [trans #376 #380]: #381
+#677 := [monotonicity #382 #583]: #673
+#655 := [trans #677 #666]: #658
+#670 := [monotonicity #655]: #665
+#661 := [trans #670 #660]: #665
+#669 := [quant-inst #65 #8]: #668
+#662 := [mp #669 #661]: #667
+[unit-resolution #662 #82 #748]: false
+unsat
+5e9e5ffc31aa8934508da0815460298eed868a8c 324 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#18 := (f3 #16 #17)
+#745 := (pattern #18)
+#19 := 0::Int
+#89 := -1::Int
+#93 := (* -1::Int #17)
+#90 := (* -1::Int #16)
+#96 := (div #90 #93)
+#247 := (* -1::Int #96)
+#248 := (+ #18 #247)
+#249 := (= #248 0::Int)
+#29 := (div #16 #17)
+#244 := (* -1::Int #29)
+#245 := (+ #18 #244)
+#246 := (= #245 0::Int)
+#122 := (>= #16 0::Int)
+#115 := (<= #17 0::Int)
+#207 := (or #115 #122)
+#208 := (not #207)
+#111 := (<= #16 0::Int)
+#205 := (or #111 #115)
+#206 := (not #205)
+#211 := (or #206 #208)
+#250 := (ite #211 #246 #249)
+#243 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#22 := (or #20 #21)
+#251 := (ite #22 #243 #250)
+#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251)
+#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
+#749 := (iff #254 #746)
+#747 := (iff #251 #251)
+#748 := [refl]: #747
+#750 := [quant-intro #748]: #749
+#214 := (ite #211 #29 #96)
+#217 := (ite #22 0::Int #214)
+#220 := (= #18 #217)
+#223 := (forall (vars (?v0 Int) (?v1 Int)) #220)
+#255 := (iff #223 #254)
+#252 := (iff #220 #251)
+#253 := [rewrite]: #252
+#256 := [quant-intro #253]: #255
+#123 := (not #122)
+#116 := (not #115)
+#126 := (and #116 #123)
+#112 := (not #111)
+#119 := (and #112 #116)
+#129 := (or #119 #126)
+#132 := (ite #129 #29 #96)
+#135 := (ite #22 0::Int #132)
+#138 := (= #18 #135)
+#141 := (forall (vars (?v0 Int) (?v1 Int)) #138)
+#224 := (iff #141 #223)
+#221 := (iff #138 #220)
+#218 := (= #135 #217)
+#215 := (= #132 #214)
+#212 := (iff #129 #211)
+#209 := (iff #126 #208)
+#210 := [rewrite]: #209
+#199 := (iff #119 #206)
+#200 := [rewrite]: #199
+#213 := [monotonicity #200 #210]: #212
+#216 := [monotonicity #213]: #215
+#219 := [monotonicity #216]: #218
+#222 := [monotonicity #219]: #221
+#225 := [quant-intro #222]: #224
+#203 := (~ #141 #141)
+#201 := (~ #138 #138)
+#202 := [refl]: #201
+#204 := [nnf-pos #202]: #203
+#31 := (- #17)
+#30 := (- #16)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (ite #28 #29 #32)
+#34 := (ite #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#144 := (iff #36 #141)
+#82 := (and #24 #26)
+#86 := (or #25 #82)
+#99 := (ite #86 #29 #96)
+#102 := (ite #22 0::Int #99)
+#105 := (= #18 #102)
+#108 := (forall (vars (?v0 Int) (?v1 Int)) #105)
+#142 := (iff #108 #141)
+#139 := (iff #105 #138)
+#136 := (= #102 #135)
+#133 := (= #99 #132)
+#130 := (iff #86 #129)
+#127 := (iff #82 #126)
+#124 := (iff #26 #123)
+#125 := [rewrite]: #124
+#117 := (iff #24 #116)
+#118 := [rewrite]: #117
+#128 := [monotonicity #118 #125]: #127
+#120 := (iff #25 #119)
+#113 := (iff #23 #112)
+#114 := [rewrite]: #113
+#121 := [monotonicity #114 #118]: #120
+#131 := [monotonicity #121 #128]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [quant-intro #140]: #142
+#109 := (iff #36 #108)
+#106 := (iff #35 #105)
+#103 := (= #34 #102)
+#100 := (= #33 #99)
+#97 := (= #32 #96)
+#94 := (= #31 #93)
+#95 := [rewrite]: #94
+#91 := (= #30 #90)
+#92 := [rewrite]: #91
+#98 := [monotonicity #92 #95]: #97
+#87 := (iff #28 #86)
+#84 := (iff #27 #82)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#101 := [monotonicity #88 #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#110 := [quant-intro #107]: #109
+#145 := [trans #110 #143]: #144
+#81 := [asserted]: #36
+#146 := [mp #81 #145]: #141
+#195 := [mp~ #146 #204]: #141
+#226 := [mp #195 #225]: #223
+#257 := [mp #226 #256]: #254
+#751 := [mp #257 #750]: #746
+#72 := -2::Int
+#10 := 3::Int
+#66 := -5::Int
+#69 := (f3 -5::Int 3::Int)
+#75 := (= #69 -2::Int)
+#78 := (not #75)
+#12 := 2::Int
+#13 := (- 2::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#11 := (f3 #9 3::Int)
+#14 := (= #11 #13)
+#15 := (not #14)
+#79 := (iff #15 #78)
+#76 := (iff #14 #75)
+#73 := (= #13 -2::Int)
+#74 := [rewrite]: #73
+#70 := (= #11 #69)
+#67 := (= #9 -5::Int)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#80 := [monotonicity #77]: #79
+#65 := [asserted]: #15
+#83 := [mp #65 #80]: #78
+#650 := (not #746)
+#651 := (or #650 #75)
+#331 := (* -1::Int 3::Int)
+#416 := (* -1::Int -5::Int)
+#417 := (div #416 #331)
+#418 := (* -1::Int #417)
+#409 := (+ #69 #418)
+#420 := (= #409 0::Int)
+#421 := (div -5::Int 3::Int)
+#349 := (* -1::Int #421)
+#422 := (+ #69 #349)
+#419 := (= #422 0::Int)
+#423 := (>= -5::Int 0::Int)
+#402 := (<= 3::Int 0::Int)
+#737 := (or #402 #423)
+#739 := (not #737)
+#396 := (<= -5::Int 0::Int)
+#526 := (or #396 #402)
+#733 := (not #526)
+#407 := (or #733 #739)
+#408 := (ite #407 #419 #420)
+#740 := (= #69 0::Int)
+#741 := (= 3::Int 0::Int)
+#742 := (= -5::Int 0::Int)
+#743 := (or #742 #741)
+#738 := (ite #743 #740 #408)
+#653 := (or #650 #738)
+#655 := (iff #653 #651)
+#652 := (iff #651 #651)
+#657 := [rewrite]: #652
+#659 := (iff #738 #75)
+#673 := (ite false #740 #75)
+#664 := (iff #673 #75)
+#665 := [rewrite]: #664
+#662 := (iff #738 #673)
+#672 := (iff #408 #75)
+#679 := (= #69 -1::Int)
+#1 := true
+#661 := (ite true #75 #679)
+#670 := (iff #661 #75)
+#671 := [rewrite]: #670
+#658 := (iff #408 #661)
+#667 := (iff #420 #679)
+#529 := 1::Int
+#580 := (+ 1::Int #69)
+#584 := (= #580 0::Int)
+#676 := (iff #584 #679)
+#680 := [rewrite]: #676
+#585 := (iff #420 #584)
+#582 := (= #409 #580)
+#678 := (+ #69 1::Int)
+#581 := (= #678 #580)
+#574 := [rewrite]: #581
+#563 := (= #409 #678)
+#674 := (= #418 1::Int)
+#568 := (* -1::Int -1::Int)
+#677 := (= #568 1::Int)
+#579 := [rewrite]: #677
+#569 := (= #418 #568)
+#683 := (= #417 -1::Int)
+#696 := -3::Int
+#528 := (div 5::Int -3::Int)
+#684 := (= #528 -1::Int)
+#685 := [rewrite]: #684
+#681 := (= #417 #528)
+#525 := (= #331 -3::Int)
+#527 := [rewrite]: #525
+#695 := (= #416 5::Int)
+#689 := [rewrite]: #695
+#682 := [monotonicity #689 #527]: #681
+#686 := [trans #682 #685]: #683
+#570 := [monotonicity #686]: #569
+#675 := [trans #570 #579]: #674
+#578 := [monotonicity #675]: #563
+#583 := [trans #578 #574]: #582
+#586 := [monotonicity #583]: #585
+#669 := [trans #586 #680]: #667
+#688 := (iff #419 #75)
+#699 := (+ 2::Int #69)
+#690 := (= #699 0::Int)
+#693 := (iff #690 #75)
+#687 := [rewrite]: #693
+#691 := (iff #419 #690)
+#547 := (= #422 #699)
+#698 := (+ #69 2::Int)
+#705 := (= #698 #699)
+#546 := [rewrite]: #705
+#703 := (= #422 #698)
+#702 := (= #349 2::Int)
+#710 := (* -1::Int -2::Int)
+#700 := (= #710 2::Int)
+#701 := [rewrite]: #700
+#707 := (= #349 #710)
+#424 := (= #421 -2::Int)
+#706 := [rewrite]: #424
+#711 := [monotonicity #706]: #707
+#697 := [trans #711 #701]: #702
+#704 := [monotonicity #697]: #703
+#548 := [trans #704 #546]: #547
+#692 := [monotonicity #548]: #691
+#694 := [trans #692 #687]: #688
+#708 := (iff #407 true)
+#717 := (or false true)
+#429 := (iff #717 true)
+#430 := [rewrite]: #429
+#427 := (iff #407 #717)
+#716 := (iff #739 true)
+#714 := (not false)
+#438 := (iff #714 true)
+#712 := [rewrite]: #438
+#715 := (iff #739 #714)
+#444 := (iff #737 false)
+#735 := (or false false)
+#379 := (iff #735 false)
+#720 := [rewrite]: #379
+#442 := (iff #737 #735)
+#719 := (iff #423 false)
+#441 := [rewrite]: #719
+#722 := (iff #402 false)
+#723 := [rewrite]: #722
+#443 := [monotonicity #723 #441]: #442
+#337 := [trans #443 #720]: #444
+#437 := [monotonicity #337]: #715
+#713 := [trans #437 #712]: #716
+#732 := (iff #733 false)
+#730 := (not true)
+#731 := (iff #730 false)
+#729 := [rewrite]: #731
+#370 := (iff #733 #730)
+#365 := (iff #526 true)
+#724 := (or true false)
+#721 := (iff #724 true)
+#727 := [rewrite]: #721
+#725 := (iff #526 #724)
+#385 := (iff #396 true)
+#386 := [rewrite]: #385
+#726 := [monotonicity #386 #723]: #725
+#728 := [trans #726 #727]: #365
+#371 := [monotonicity #728]: #370
+#718 := [trans #371 #729]: #732
+#428 := [monotonicity #718 #713]: #427
+#709 := [trans #428 #430]: #708
+#660 := [monotonicity #709 #694 #669]: #658
+#668 := [trans #660 #671]: #672
+#383 := (iff #743 false)
+#395 := (iff #743 #735)
+#394 := (iff #741 false)
+#399 := [rewrite]: #394
+#744 := (iff #742 false)
+#734 := [rewrite]: #744
+#736 := [monotonicity #734 #399]: #395
+#384 := [trans #736 #720]: #383
+#663 := [monotonicity #384 #668]: #662
+#666 := [trans #663 #665]: #659
+#656 := [monotonicity #666]: #655
+#643 := [trans #656 #657]: #655
+#654 := [quant-inst #66 #10]: #653
+#644 := [mp #654 #643]: #651
+[unit-resolution #644 #83 #751]: false
+unsat
+7de568581f12c6417657495045816e0055a747d5 337 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#18 := (f3 #16 #17)
+#769 := (pattern #18)
+#13 := 0::Int
+#65 := -1::Int
+#112 := (* -1::Int #17)
+#109 := (* -1::Int #16)
+#115 := (div #109 #112)
+#272 := (* -1::Int #115)
+#273 := (+ #18 #272)
+#274 := (= #273 0::Int)
+#28 := (div #16 #17)
+#269 := (* -1::Int #28)
+#270 := (+ #18 #269)
+#271 := (= #270 0::Int)
+#147 := (>= #16 0::Int)
+#140 := (<= #17 0::Int)
+#232 := (or #140 #147)
+#233 := (not #232)
+#136 := (<= #16 0::Int)
+#230 := (or #136 #140)
+#231 := (not #230)
+#236 := (or #231 #233)
+#275 := (ite #236 #271 #274)
+#268 := (= #18 0::Int)
+#20 := (= #17 0::Int)
+#19 := (= #16 0::Int)
+#21 := (or #19 #20)
+#276 := (ite #21 #268 #275)
+#770 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #769) #276)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#773 := (iff #279 #770)
+#771 := (iff #276 #276)
+#772 := [refl]: #771
+#774 := [quant-intro #772]: #773
+#239 := (ite #236 #28 #115)
+#242 := (ite #21 0::Int #239)
+#245 := (= #18 #242)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#280 := (iff #248 #279)
+#277 := (iff #245 #276)
+#278 := [rewrite]: #277
+#281 := [quant-intro #278]: #280
+#148 := (not #147)
+#141 := (not #140)
+#151 := (and #141 #148)
+#137 := (not #136)
+#144 := (and #137 #141)
+#154 := (or #144 #151)
+#157 := (ite #154 #28 #115)
+#160 := (ite #21 0::Int #157)
+#163 := (= #18 #160)
+#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
+#249 := (iff #166 #248)
+#246 := (iff #163 #245)
+#243 := (= #160 #242)
+#240 := (= #157 #239)
+#237 := (iff #154 #236)
+#234 := (iff #151 #233)
+#235 := [rewrite]: #234
+#224 := (iff #144 #231)
+#225 := [rewrite]: #224
+#238 := [monotonicity #225 #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#228 := (~ #166 #166)
+#226 := (~ #163 #163)
+#227 := [refl]: #226
+#229 := [nnf-pos #227]: #228
+#30 := (- #17)
+#29 := (- #16)
+#31 := (div #29 #30)
+#23 := (< 0::Int #17)
+#25 := (< #16 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #16)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (ite #27 #28 #31)
+#33 := (ite #21 0::Int #32)
+#34 := (= #18 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#169 := (iff #35 #166)
+#103 := (and #23 #25)
+#106 := (or #24 #103)
+#118 := (ite #106 #28 #115)
+#97 := (= 0::Int #17)
+#94 := (= 0::Int #16)
+#100 := (or #94 #97)
+#121 := (ite #100 0::Int #118)
+#124 := (= #18 #121)
+#127 := (forall (vars (?v0 Int) (?v1 Int)) #124)
+#167 := (iff #127 #166)
+#164 := (iff #124 #163)
+#161 := (= #121 #160)
+#158 := (= #118 #157)
+#155 := (iff #106 #154)
+#152 := (iff #103 #151)
+#149 := (iff #25 #148)
+#150 := [rewrite]: #149
+#142 := (iff #23 #141)
+#143 := [rewrite]: #142
+#153 := [monotonicity #143 #150]: #152
+#145 := (iff #24 #144)
+#138 := (iff #22 #137)
+#139 := [rewrite]: #138
+#146 := [monotonicity #139 #143]: #145
+#156 := [monotonicity #146 #153]: #155
+#159 := [monotonicity #156]: #158
+#134 := (iff #100 #21)
+#132 := (iff #97 #20)
+#133 := [rewrite]: #132
+#130 := (iff #94 #19)
+#131 := [rewrite]: #130
+#135 := [monotonicity #131 #133]: #134
+#162 := [monotonicity #135 #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#128 := (iff #35 #127)
+#125 := (iff #34 #124)
+#122 := (= #33 #121)
+#119 := (= #32 #118)
+#116 := (= #31 #115)
+#113 := (= #30 #112)
+#114 := [rewrite]: #113
+#110 := (= #29 #109)
+#111 := [rewrite]: #110
+#117 := [monotonicity #111 #114]: #116
+#107 := (iff #27 #106)
+#104 := (iff #26 #103)
+#105 := [rewrite]: #104
+#108 := [monotonicity #105]: #107
+#120 := [monotonicity #108 #117]: #119
+#101 := (iff #21 #100)
+#98 := (iff #20 #97)
+#99 := [rewrite]: #98
+#95 := (iff #19 #94)
+#96 := [rewrite]: #95
+#102 := [monotonicity #96 #99]: #101
+#123 := [monotonicity #102 #120]: #122
+#126 := [monotonicity #123]: #125
+#129 := [quant-intro #126]: #128
+#170 := [trans #129 #168]: #169
+#93 := [asserted]: #35
+#171 := [mp #93 #170]: #166
+#220 := [mp~ #171 #229]: #166
+#251 := [mp #220 #250]: #248
+#282 := [mp #251 #281]: #279
+#775 := [mp #282 #774]: #770
+#68 := -3::Int
+#71 := (f3 -1::Int -3::Int)
+#74 := (= #71 0::Int)
+#87 := (not #74)
#10 := 3::Int
#11 := (- 3::Int)
-#20 := (- #11)
-#19 := (- 0::Int)
-#21 := (div #19 #20)
-#18 := (div 0::Int #11)
-#15 := (< 0::Int #11)
-#14 := (< 0::Int 0::Int)
-#16 := (and #14 #15)
-#17 := (or #16 #16)
-#22 := (ite #17 #18 #21)
-#12 := (= #11 0::Int)
-#9 := (= 0::Int 0::Int)
-#13 := (or #9 #12)
-#23 := (ite #13 0::Int #22)
-#24 := (= #23 0::Int)
-#25 := (not #24)
-#123 := (iff #25 false)
-#1 := true
-#118 := (not true)
-#121 := (iff #118 false)
-#122 := [rewrite]: #121
-#119 := (iff #25 #118)
-#116 := (iff #24 true)
-#46 := (iff #9 true)
-#47 := [rewrite]: #46
-#114 := (iff #24 #9)
-#108 := (ite true 0::Int 0::Int)
-#111 := (= #108 0::Int)
-#112 := [rewrite]: #111
-#109 := (= #23 #108)
-#106 := (= #22 0::Int)
-#48 := -3::Int
-#65 := (< 0::Int -3::Int)
-#68 := (and #14 #65)
-#101 := (ite #68 0::Int 0::Int)
-#104 := (= #101 0::Int)
-#105 := [rewrite]: #104
-#102 := (= #22 #101)
-#99 := (= #21 0::Int)
-#94 := (div 0::Int 3::Int)
-#97 := (= #94 0::Int)
-#98 := [rewrite]: #97
-#95 := (= #21 #94)
-#92 := (= #20 3::Int)
-#87 := (- -3::Int)
-#90 := (= #87 3::Int)
-#91 := [rewrite]: #90
-#88 := (= #20 #87)
-#49 := (= #11 -3::Int)
-#50 := [rewrite]: #49
-#89 := [monotonicity #50]: #88
-#93 := [trans #89 #91]: #92
-#85 := (= #19 0::Int)
+#8 := 1::Int
+#9 := (- 1::Int)
+#12 := (f3 #9 #11)
+#14 := (= #12 0::Int)
+#15 := (not #14)
+#90 := (iff #15 #87)
+#77 := (= 0::Int #71)
+#82 := (not #77)
+#88 := (iff #82 #87)
+#85 := (iff #77 #74)
#86 := [rewrite]: #85
-#96 := [monotonicity #86 #93]: #95
-#100 := [trans #96 #98]: #99
-#83 := (= #18 0::Int)
-#78 := (div 0::Int -3::Int)
-#81 := (= #78 0::Int)
+#89 := [monotonicity #86]: #88
+#83 := (iff #15 #82)
+#80 := (iff #14 #77)
+#78 := (iff #74 #77)
+#79 := [rewrite]: #78
+#75 := (iff #14 #74)
+#72 := (= #12 #71)
+#69 := (= #11 -3::Int)
+#70 := [rewrite]: #69
+#66 := (= #9 -1::Int)
+#67 := [rewrite]: #66
+#73 := [monotonicity #67 #70]: #72
+#76 := [monotonicity #73]: #75
+#81 := [trans #76 #79]: #80
+#84 := [monotonicity #81]: #83
+#91 := [trans #84 #89]: #90
+#64 := [asserted]: #15
+#92 := [mp #64 #91]: #87
+#694 := (not #770)
+#695 := (or #694 #74)
+#356 := (* -1::Int -3::Int)
+#440 := (* -1::Int -1::Int)
+#441 := (div #440 #356)
+#442 := (* -1::Int #441)
+#433 := (+ #71 #442)
+#444 := (= #433 0::Int)
+#445 := (div -1::Int -3::Int)
+#446 := (* -1::Int #445)
+#443 := (+ #71 #446)
+#447 := (= #443 0::Int)
+#426 := (>= -1::Int 0::Int)
+#761 := (<= -3::Int 0::Int)
+#763 := (or #761 #426)
+#420 := (not #763)
+#550 := (<= -1::Int 0::Int)
+#757 := (or #550 #761)
+#431 := (not #757)
+#432 := (or #431 #420)
+#764 := (ite #432 #447 #444)
+#765 := (= -3::Int 0::Int)
+#766 := (= -1::Int 0::Int)
+#767 := (or #766 #765)
+#762 := (ite #767 #74 #764)
+#696 := (or #694 #762)
+#697 := (iff #696 #695)
+#687 := (iff #695 #695)
+#688 := [rewrite]: #687
+#682 := (iff #762 #74)
+#700 := (ite false #74 #74)
+#693 := (iff #700 #74)
+#685 := [rewrite]: #693
+#704 := (iff #762 #700)
+#610 := (iff #764 #74)
+#714 := (= #71 1::Int)
+#598 := (ite false #714 #74)
+#608 := (iff #598 #74)
+#609 := [rewrite]: #608
+#606 := (iff #764 #598)
+#604 := (iff #444 #74)
+#587 := (= #433 #71)
+#701 := (+ #71 0::Int)
+#699 := (= #701 #71)
+#702 := [rewrite]: #699
+#603 := (= #433 #701)
+#594 := (= #442 0::Int)
+#709 := (* -1::Int 0::Int)
+#592 := (= #709 0::Int)
+#593 := [rewrite]: #592
+#707 := (= #442 #709)
+#706 := (= #441 0::Int)
+#720 := (div 1::Int 3::Int)
+#552 := (= #720 0::Int)
+#705 := [rewrite]: #552
+#549 := (= #441 #720)
+#719 := (= #356 3::Int)
+#713 := [rewrite]: #719
+#712 := (= #440 1::Int)
+#718 := [rewrite]: #712
+#551 := [monotonicity #718 #713]: #549
+#708 := [trans #551 #705]: #706
+#710 := [monotonicity #708]: #707
+#553 := [trans #710 #593]: #594
+#698 := [monotonicity #553]: #603
+#602 := [trans #698 #702]: #587
+#605 := [monotonicity #602]: #604
+#717 := (iff #447 #714)
+#722 := (+ -1::Int #71)
+#570 := (= #722 0::Int)
+#715 := (iff #570 #714)
+#716 := [rewrite]: #715
+#571 := (iff #447 #570)
+#723 := (= #443 #722)
+#725 := (+ #71 -1::Int)
+#727 := (= #725 #722)
+#728 := [rewrite]: #727
+#726 := (= #443 #725)
+#735 := (= #446 -1::Int)
+#733 := (* -1::Int 1::Int)
+#734 := (= #733 -1::Int)
+#731 := [rewrite]: #734
+#448 := (= #446 #733)
+#454 := (= #445 1::Int)
+#732 := [rewrite]: #454
+#730 := [monotonicity #732]: #448
+#724 := [trans #730 #731]: #735
+#721 := [monotonicity #724]: #726
+#729 := [trans #721 #728]: #723
+#572 := [monotonicity #729]: #571
+#711 := [trans #572 #716]: #717
+#452 := (iff #432 false)
+#759 := (or false false)
+#403 := (iff #759 false)
+#744 := [rewrite]: #403
+#741 := (iff #432 #759)
+#740 := (iff #420 false)
+#1 := true
+#754 := (not true)
+#755 := (iff #754 false)
+#753 := [rewrite]: #755
+#462 := (iff #420 #754)
+#739 := (iff #763 true)
+#466 := (or true false)
+#362 := (iff #466 true)
+#738 := [rewrite]: #362
+#467 := (iff #763 #466)
+#743 := (iff #426 false)
+#465 := [rewrite]: #743
+#746 := (iff #761 true)
+#747 := [rewrite]: #746
+#468 := [monotonicity #747 #465]: #467
+#461 := [trans #468 #738]: #739
+#736 := [monotonicity #461]: #462
+#737 := [trans #736 #753]: #740
+#756 := (iff #431 false)
+#394 := (iff #431 #754)
+#389 := (iff #757 true)
+#748 := (or true true)
+#745 := (iff #748 true)
+#751 := [rewrite]: #745
+#749 := (iff #757 #748)
+#409 := (iff #550 true)
+#410 := [rewrite]: #409
+#750 := [monotonicity #410 #747]: #749
+#752 := [trans #750 #751]: #389
+#395 := [monotonicity #752]: #394
+#742 := [trans #395 #753]: #756
+#451 := [monotonicity #742 #737]: #741
+#453 := [trans #451 #744]: #452
+#607 := [monotonicity #453 #711 #605]: #606
+#703 := [trans #607 #609]: #610
+#407 := (iff #767 false)
+#419 := (iff #767 #759)
+#418 := (iff #765 false)
+#423 := [rewrite]: #418
+#768 := (iff #766 false)
+#758 := [rewrite]: #768
+#760 := [monotonicity #758 #423]: #419
+#408 := [trans #760 #744]: #407
+#691 := [monotonicity #408 #703]: #704
+#684 := [trans #691 #685]: #682
+#686 := [monotonicity #684]: #697
+#689 := [trans #686 #688]: #697
+#692 := [quant-inst #65 #68]: #696
+#683 := [mp #692 #689]: #695
+[unit-resolution #683 #92 #775]: false
+unsat
+67c5769d49bd3d505a24355d203b30bb2a6d4f8d 306 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#16 := (f3 #14 #15)
+#751 := (pattern #16)
+#17 := 0::Int
+#96 := -1::Int
+#100 := (* -1::Int #15)
+#97 := (* -1::Int #14)
+#103 := (div #97 #100)
+#254 := (* -1::Int #103)
+#255 := (+ #16 #254)
+#256 := (= #255 0::Int)
+#27 := (div #14 #15)
+#251 := (* -1::Int #27)
+#252 := (+ #16 #251)
+#253 := (= #252 0::Int)
+#129 := (>= #14 0::Int)
+#122 := (<= #15 0::Int)
+#214 := (or #122 #129)
+#215 := (not #214)
+#118 := (<= #14 0::Int)
+#212 := (or #118 #122)
+#213 := (not #212)
+#218 := (or #213 #215)
+#257 := (ite #218 #253 #256)
+#250 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#18 := (= #14 0::Int)
+#20 := (or #18 #19)
+#258 := (ite #20 #250 #257)
+#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258)
+#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
+#755 := (iff #261 #752)
+#753 := (iff #258 #258)
+#754 := [refl]: #753
+#756 := [quant-intro #754]: #755
+#221 := (ite #218 #27 #103)
+#224 := (ite #20 0::Int #221)
+#227 := (= #16 #224)
+#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
+#262 := (iff #230 #261)
+#259 := (iff #227 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#130 := (not #129)
+#123 := (not #122)
+#133 := (and #123 #130)
+#119 := (not #118)
+#126 := (and #119 #123)
+#136 := (or #126 #133)
+#139 := (ite #136 #27 #103)
+#142 := (ite #20 0::Int #139)
+#145 := (= #16 #142)
+#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
+#231 := (iff #148 #230)
+#228 := (iff #145 #227)
+#225 := (= #142 #224)
+#222 := (= #139 #221)
+#219 := (iff #136 #218)
+#216 := (iff #133 #215)
+#217 := [rewrite]: #216
+#206 := (iff #126 #213)
+#207 := [rewrite]: #206
+#220 := [monotonicity #207 #217]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#210 := (~ #148 #148)
+#208 := (~ #145 #145)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#29 := (- #15)
+#28 := (- #14)
+#30 := (div #28 #29)
+#22 := (< 0::Int #15)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (ite #26 #27 #30)
+#32 := (ite #20 0::Int #31)
+#33 := (= #16 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#151 := (iff #34 #148)
+#90 := (and #22 #24)
+#93 := (or #23 #90)
+#106 := (ite #93 #27 #103)
+#109 := (ite #20 0::Int #106)
+#112 := (= #16 #109)
+#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
+#149 := (iff #115 #148)
+#146 := (iff #112 #145)
+#143 := (= #109 #142)
+#140 := (= #106 #139)
+#137 := (iff #93 #136)
+#134 := (iff #90 #133)
+#131 := (iff #24 #130)
+#132 := [rewrite]: #131
+#124 := (iff #22 #123)
+#125 := [rewrite]: #124
+#135 := [monotonicity #125 #132]: #134
+#127 := (iff #23 #126)
+#120 := (iff #21 #119)
+#121 := [rewrite]: #120
+#128 := [monotonicity #121 #125]: #127
+#138 := [monotonicity #128 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#116 := (iff #34 #115)
+#113 := (iff #33 #112)
+#110 := (= #32 #109)
+#107 := (= #31 #106)
+#104 := (= #30 #103)
+#101 := (= #29 #100)
+#102 := [rewrite]: #101
+#98 := (= #28 #97)
+#99 := [rewrite]: #98
+#105 := [monotonicity #99 #102]: #104
+#94 := (iff #26 #93)
+#91 := (iff #25 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#108 := [monotonicity #95 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [quant-intro #114]: #116
+#152 := [trans #117 #150]: #151
+#89 := [asserted]: #34
+#153 := [mp #89 #152]: #148
+#202 := [mp~ #153 #211]: #148
+#233 := [mp #202 #232]: #230
+#264 := [mp #233 #263]: #261
+#757 := [mp #264 #756]: #752
+#11 := 1::Int
+#64 := -3::Int
+#67 := (f3 -3::Int -3::Int)
+#70 := (= #67 1::Int)
+#83 := (not #70)
+#8 := 3::Int
+#9 := (- 3::Int)
+#10 := (f3 #9 #9)
+#12 := (= #10 1::Int)
+#13 := (not #12)
+#86 := (iff #13 #83)
+#73 := (= 1::Int #67)
+#78 := (not #73)
+#84 := (iff #78 #83)
+#81 := (iff #73 #70)
#82 := [rewrite]: #81
-#79 := (= #18 #78)
-#80 := [monotonicity #50]: #79
-#84 := [trans #80 #82]: #83
-#76 := (iff #17 #68)
-#71 := (or #68 #68)
-#74 := (iff #71 #68)
+#85 := [monotonicity #82]: #84
+#79 := (iff #13 #78)
+#76 := (iff #12 #73)
+#74 := (iff #70 #73)
#75 := [rewrite]: #74
-#72 := (iff #17 #71)
-#69 := (iff #16 #68)
-#66 := (iff #15 #65)
-#67 := [monotonicity #50]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70 #70]: #72
-#77 := [trans #73 #75]: #76
-#103 := [monotonicity #77 #84 #100]: #102
-#107 := [trans #103 #105]: #106
-#63 := (iff #13 true)
-#58 := (or true false)
-#61 := (iff #58 true)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#56 := (iff #12 false)
-#51 := (= -3::Int 0::Int)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #47 #57]: #59
-#64 := [trans #60 #62]: #63
-#110 := [monotonicity #64 #107]: #109
-#113 := [trans #110 #112]: #24
-#115 := [monotonicity #113]: #114
-#117 := [trans #115 #47]: #116
-#120 := [monotonicity #117]: #119
-#124 := [trans #120 #122]: #123
-#45 := [asserted]: #25
-[mp #45 #124]: false
-unsat
-9d138480c7d61fdc258e935f0608d147c435d8d1 113 0
-#2 := false
-#9 := 0::Int
-#11 := 3::Int
-#22 := (- 3::Int)
-#8 := 1::Int
-#21 := (- 1::Int)
-#23 := (div #21 #22)
-#20 := (div 1::Int 3::Int)
-#15 := (< 0::Int 3::Int)
-#17 := (< 1::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 1::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 3::Int 0::Int)
-#10 := (= 1::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (= #25 0::Int)
-#27 := (not #26)
-#134 := (iff #27 false)
-#59 := (and #15 #17)
-#62 := (or #16 #59)
-#97 := (not #62)
-#132 := (iff #97 false)
-#1 := true
-#127 := (not true)
-#130 := (iff #127 false)
-#131 := [rewrite]: #130
-#128 := (iff #97 #127)
-#125 := (iff #62 true)
-#120 := (or true false)
-#123 := (iff #120 true)
-#124 := [rewrite]: #123
-#121 := (iff #62 #120)
-#118 := (iff #59 false)
-#113 := (and true false)
-#116 := (iff #113 false)
-#117 := [rewrite]: #116
-#114 := (iff #59 #113)
-#111 := (iff #17 false)
-#112 := [rewrite]: #111
-#102 := (iff #15 true)
-#103 := [rewrite]: #102
-#115 := [monotonicity #103 #112]: #114
-#119 := [trans #115 #117]: #118
-#109 := (iff #16 true)
-#104 := (and true true)
-#107 := (iff #104 true)
-#108 := [rewrite]: #107
-#105 := (iff #16 #104)
-#100 := (iff #14 true)
-#101 := [rewrite]: #100
-#106 := [monotonicity #101 #103]: #105
-#110 := [trans #106 #108]: #109
-#122 := [monotonicity #110 #119]: #121
-#126 := [trans #122 #124]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#98 := (iff #27 #97)
-#95 := (iff #26 #62)
-#80 := (ite #62 0::Int 1::Int)
-#90 := (= #80 0::Int)
-#93 := (iff #90 #62)
-#94 := [rewrite]: #93
-#91 := (iff #26 #90)
-#88 := (= #25 #80)
-#83 := (ite false 0::Int #80)
-#86 := (= #83 #80)
-#87 := [rewrite]: #86
-#84 := (= #25 #83)
-#81 := (= #24 #80)
-#78 := (= #23 1::Int)
-#70 := -3::Int
-#67 := -1::Int
-#73 := (div -1::Int -3::Int)
-#76 := (= #73 1::Int)
-#77 := [rewrite]: #76
-#74 := (= #23 #73)
-#71 := (= #22 -3::Int)
-#72 := [rewrite]: #71
-#68 := (= #21 -1::Int)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#79 := [trans #75 #77]: #78
-#65 := (= #20 0::Int)
-#66 := [rewrite]: #65
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#82 := [monotonicity #64 #66 #79]: #81
-#57 := (iff #13 false)
-#52 := (or false false)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#50 := (iff #12 false)
-#51 := [rewrite]: #50
-#48 := (iff #10 false)
-#49 := [rewrite]: #48
-#54 := [monotonicity #49 #51]: #53
-#58 := [trans #54 #56]: #57
-#85 := [monotonicity #58 #82]: #84
-#89 := [trans #85 #87]: #88
-#92 := [monotonicity #89]: #91
-#96 := [trans #92 #94]: #95
-#99 := [monotonicity #96]: #98
-#135 := [trans #99 #133]: #134
-#47 := [asserted]: #27
-[mp #47 #135]: false
-unsat
-59082baebee56f4a9740d0c291f81d87438f8452 78 0
-#2 := false
-#22 := 1::Int
-#8 := 3::Int
-#18 := (- 3::Int)
-#19 := (div #18 #18)
-#17 := (div 3::Int 3::Int)
-#9 := 0::Int
-#12 := (< 0::Int 3::Int)
-#14 := (< 3::Int 0::Int)
-#15 := (and #14 #12)
-#13 := (and #12 #12)
-#16 := (or #13 #15)
-#20 := (ite #16 #17 #19)
-#10 := (= 3::Int 0::Int)
-#11 := (or #10 #10)
-#21 := (ite #11 0::Int #20)
-#23 := (= #21 1::Int)
-#24 := (not #23)
-#99 := (iff #24 false)
-#1 := true
-#94 := (not true)
-#97 := (iff #94 false)
-#98 := [rewrite]: #97
-#95 := (iff #24 #94)
-#92 := (iff #23 true)
-#87 := (= 1::Int 1::Int)
-#90 := (iff #87 true)
-#91 := [rewrite]: #90
-#88 := (iff #23 #87)
-#81 := (ite false 0::Int 1::Int)
-#84 := (= #81 1::Int)
-#85 := [rewrite]: #84
-#82 := (= #21 #81)
-#79 := (= #20 1::Int)
-#56 := (and #12 #14)
-#59 := (or #12 #56)
-#74 := (ite #59 1::Int 1::Int)
-#77 := (= #74 1::Int)
-#78 := [rewrite]: #77
-#75 := (= #20 #74)
-#72 := (= #19 1::Int)
-#64 := -3::Int
-#67 := (div -3::Int -3::Int)
-#70 := (= #67 1::Int)
-#71 := [rewrite]: #70
-#68 := (= #19 #67)
-#65 := (= #18 -3::Int)
+#71 := (iff #12 #70)
+#68 := (= #10 #67)
+#65 := (= #9 -3::Int)
#66 := [rewrite]: #65
#69 := [monotonicity #66 #66]: #68
-#73 := [trans #69 #71]: #72
-#62 := (= #17 1::Int)
-#63 := [rewrite]: #62
-#60 := (iff #16 #59)
-#57 := (iff #15 #56)
-#58 := [rewrite]: #57
-#54 := (iff #13 #12)
-#55 := [rewrite]: #54
-#61 := [monotonicity #55 #58]: #60
-#76 := [monotonicity #61 #63 #73]: #75
-#80 := [trans #76 #78]: #79
-#52 := (iff #11 false)
-#47 := (or false false)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #11 #47)
-#45 := (iff #10 false)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46 #46]: #48
-#53 := [trans #49 #51]: #52
-#83 := [monotonicity #53 #80]: #82
-#86 := [trans #83 #85]: #23
-#89 := [monotonicity #86]: #88
-#93 := [trans #89 #91]: #92
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#44 := [asserted]: #24
-[mp #44 #100]: false
-unsat
-b2dbf88881de745f35b3193199fcda41f7406d84 115 0
-#2 := false
-#26 := 1::Int
-#11 := 3::Int
-#22 := (- 3::Int)
-#8 := 5::Int
-#21 := (- 5::Int)
-#23 := (div #21 #22)
-#20 := (div 5::Int 3::Int)
-#9 := 0::Int
-#15 := (< 0::Int 3::Int)
-#17 := (< 5::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 5::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#24 := (ite #19 #20 #23)
-#12 := (= 3::Int 0::Int)
-#10 := (= 5::Int 0::Int)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#27 := (= #25 1::Int)
-#28 := (not #27)
-#136 := (iff #28 false)
-#60 := (and #15 #17)
-#63 := (or #16 #60)
-#99 := (not #63)
-#134 := (iff #99 false)
-#1 := true
-#129 := (not true)
-#132 := (iff #129 false)
-#133 := [rewrite]: #132
-#130 := (iff #99 #129)
-#127 := (iff #63 true)
-#122 := (or true false)
-#125 := (iff #122 true)
-#126 := [rewrite]: #125
-#123 := (iff #63 #122)
-#120 := (iff #60 false)
-#115 := (and true false)
-#118 := (iff #115 false)
-#119 := [rewrite]: #118
-#116 := (iff #60 #115)
-#113 := (iff #17 false)
-#114 := [rewrite]: #113
-#104 := (iff #15 true)
-#105 := [rewrite]: #104
-#117 := [monotonicity #105 #114]: #116
-#121 := [trans #117 #119]: #120
-#111 := (iff #16 true)
-#106 := (and true true)
-#109 := (iff #106 true)
-#110 := [rewrite]: #109
-#107 := (iff #16 #106)
-#102 := (iff #14 true)
-#103 := [rewrite]: #102
-#108 := [monotonicity #103 #105]: #107
-#112 := [trans #108 #110]: #111
-#124 := [monotonicity #112 #121]: #123
-#128 := [trans #124 #126]: #127
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#100 := (iff #28 #99)
-#97 := (iff #27 #63)
-#77 := 2::Int
-#82 := (ite #63 1::Int 2::Int)
-#92 := (= #82 1::Int)
-#95 := (iff #92 #63)
-#96 := [rewrite]: #95
-#93 := (iff #27 #92)
-#90 := (= #25 #82)
-#85 := (ite false 0::Int #82)
-#88 := (= #85 #82)
-#89 := [rewrite]: #88
-#86 := (= #25 #85)
-#83 := (= #24 #82)
-#80 := (= #23 2::Int)
-#71 := -3::Int
-#68 := -5::Int
-#74 := (div -5::Int -3::Int)
-#78 := (= #74 2::Int)
-#79 := [rewrite]: #78
-#75 := (= #23 #74)
-#72 := (= #22 -3::Int)
-#73 := [rewrite]: #72
-#69 := (= #21 -5::Int)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#81 := [trans #76 #79]: #80
-#66 := (= #20 1::Int)
-#67 := [rewrite]: #66
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#84 := [monotonicity #65 #67 #81]: #83
-#58 := (iff #13 false)
-#53 := (or false false)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #13 #53)
-#51 := (iff #12 false)
-#52 := [rewrite]: #51
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#55 := [monotonicity #50 #52]: #54
-#59 := [trans #55 #57]: #58
-#87 := [monotonicity #59 #84]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #91]: #93
-#98 := [trans #94 #96]: #97
-#101 := [monotonicity #98]: #100
-#137 := [trans #101 #135]: #136
-#48 := [asserted]: #28
-[mp #48 #137]: false
-unsat
-e8c50ca8f2d03b633ebd301c60837eeba13d5124 132 0
-#2 := false
-#8 := 1::Int
-#22 := (- 1::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#23 := (- #12)
-#24 := (div #22 #23)
-#21 := (div 1::Int #12)
-#9 := 0::Int
-#16 := (< 0::Int #12)
-#18 := (< 1::Int 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int 1::Int)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= #12 0::Int)
-#10 := (= 1::Int 0::Int)
-#14 := (or #10 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (= #26 #22)
-#28 := (not #27)
-#153 := (iff #28 false)
-#51 := -3::Int
-#68 := (< 0::Int -3::Int)
-#74 := (and #18 #68)
-#71 := (and #15 #68)
-#77 := (or #71 #74)
-#151 := (iff #77 false)
-#61 := (or false false)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#149 := (iff #77 #61)
-#147 := (iff #74 false)
-#142 := (and false false)
-#145 := (iff #142 false)
-#146 := [rewrite]: #145
-#143 := (iff #74 #142)
-#131 := (iff #68 false)
-#132 := [rewrite]: #131
-#140 := (iff #18 false)
-#141 := [rewrite]: #140
-#144 := [monotonicity #141 #132]: #143
-#148 := [trans #144 #146]: #147
-#138 := (iff #71 false)
-#1 := true
-#133 := (and true false)
-#136 := (iff #133 false)
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#87 := [trans #80 #85]: #86
+#63 := [asserted]: #13
+#88 := [mp #63 #87]: #83
+#588 := (not #752)
+#589 := (or #588 #70)
+#338 := (* -1::Int -3::Int)
+#422 := (div #338 #338)
+#423 := (* -1::Int #422)
+#424 := (+ #67 #423)
+#415 := (= #424 0::Int)
+#426 := (div -3::Int -3::Int)
+#427 := (* -1::Int #426)
+#428 := (+ #67 #427)
+#425 := (= #428 0::Int)
+#429 := (>= -3::Int 0::Int)
+#408 := (<= -3::Int 0::Int)
+#743 := (or #408 #429)
+#745 := (not #743)
+#402 := (or #408 #408)
+#532 := (not #402)
+#739 := (or #532 #745)
+#413 := (ite #739 #425 #415)
+#414 := (= #67 0::Int)
+#746 := (= -3::Int 0::Int)
+#747 := (or #746 #746)
+#748 := (ite #747 #414 #413)
+#590 := (or #588 #748)
+#592 := (iff #590 #589)
+#682 := (iff #589 #589)
+#686 := [rewrite]: #682
+#587 := (iff #748 #70)
+#681 := (ite false #414 #70)
+#584 := (iff #681 #70)
+#586 := [rewrite]: #584
+#684 := (iff #748 #681)
+#585 := (iff #413 #70)
+#574 := (ite false #70 #70)
+#535 := (iff #574 #70)
+#683 := [rewrite]: #535
+#575 := (iff #413 #574)
+#689 := (iff #415 #70)
+#713 := (+ -1::Int #67)
+#703 := (= #713 0::Int)
+#710 := (iff #703 #70)
+#705 := [rewrite]: #710
+#690 := (iff #415 #703)
+#687 := (= #424 #713)
+#430 := (+ #67 -1::Int)
+#717 := (= #430 #713)
+#706 := [rewrite]: #717
+#533 := (= #424 #430)
+#702 := (= #423 -1::Int)
+#723 := (* -1::Int 1::Int)
+#435 := (= #723 -1::Int)
+#436 := [rewrite]: #435
+#701 := (= #423 #723)
+#694 := (= #422 1::Int)
+#696 := (div 3::Int 3::Int)
+#699 := (= #696 1::Int)
+#693 := [rewrite]: #699
+#697 := (= #422 #696)
+#553 := (= #338 3::Int)
+#554 := [rewrite]: #553
+#698 := [monotonicity #554 #554]: #697
+#700 := [trans #698 #693]: #694
+#695 := [monotonicity #700]: #701
+#531 := [trans #695 #436]: #702
+#534 := [monotonicity #531]: #533
+#688 := [trans #534 #706]: #687
+#691 := [monotonicity #688]: #690
+#692 := [trans #691 #705]: #689
+#711 := (iff #425 #70)
+#704 := (iff #425 #703)
+#707 := (= #428 #713)
+#712 := (= #428 #430)
+#714 := (= #427 -1::Int)
+#433 := (= #427 #723)
+#722 := (= #426 1::Int)
+#719 := [rewrite]: #722
+#434 := [monotonicity #719]: #433
+#715 := [trans #434 #436]: #714
+#716 := [monotonicity #715]: #712
+#708 := [trans #716 #706]: #707
+#709 := [monotonicity #708]: #704
+#552 := [trans #709 #705]: #711
+#444 := (iff #739 false)
+#750 := (or false false)
+#405 := (iff #750 false)
+#741 := [rewrite]: #405
+#721 := (iff #739 #750)
+#344 := (iff #745 false)
+#1 := true
+#731 := (not true)
+#733 := (iff #731 false)
+#371 := [rewrite]: #733
+#449 := (iff #745 #731)
+#447 := (iff #743 true)
+#737 := (or true false)
+#724 := (iff #737 true)
+#725 := [rewrite]: #724
+#735 := (iff #743 #737)
+#376 := (iff #429 false)
+#377 := [rewrite]: #376
+#385 := (iff #408 true)
+#726 := [rewrite]: #385
+#738 := [monotonicity #726 #377]: #735
+#448 := [trans #738 #725]: #447
+#450 := [monotonicity #448]: #449
+#720 := [trans #450 #371]: #344
+#734 := (iff #532 false)
+#732 := (iff #532 #731)
+#729 := (iff #402 true)
+#389 := (or true true)
+#392 := (iff #389 true)
+#728 := [rewrite]: #392
+#390 := (iff #402 #389)
+#391 := [monotonicity #726 #726]: #390
+#730 := [trans #391 #728]: #729
+#727 := [monotonicity #730]: #732
+#736 := [trans #727 #371]: #734
+#443 := [monotonicity #736 #720]: #721
+#718 := [trans #443 #741]: #444
+#576 := [monotonicity #718 #552 #692]: #575
+#680 := [trans #576 #683]: #585
+#401 := (iff #747 false)
+#740 := (iff #747 #750)
+#749 := (iff #746 false)
+#744 := [rewrite]: #749
+#400 := [monotonicity #744 #744]: #740
+#742 := [trans #400 #741]: #401
+#569 := [monotonicity #742 #680]: #684
+#580 := [trans #569 #586]: #587
+#685 := [monotonicity #580]: #592
+#673 := [trans #685 #686]: #592
+#591 := [quant-inst #64 #64]: #590
+#675 := [mp #591 #673]: #589
+[unit-resolution #675 #88 #757]: false
+unsat
+602bd1c64454e63be2273eaf718ba5b3413f9555 333 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#18 := (f3 #16 #17)
+#756 := (pattern #18)
+#19 := 0::Int
+#101 := -1::Int
+#105 := (* -1::Int #17)
+#102 := (* -1::Int #16)
+#108 := (div #102 #105)
+#259 := (* -1::Int #108)
+#260 := (+ #18 #259)
+#261 := (= #260 0::Int)
+#29 := (div #16 #17)
+#256 := (* -1::Int #29)
+#257 := (+ #18 #256)
+#258 := (= #257 0::Int)
+#134 := (>= #16 0::Int)
+#127 := (<= #17 0::Int)
+#219 := (or #127 #134)
+#220 := (not #219)
+#123 := (<= #16 0::Int)
+#217 := (or #123 #127)
+#218 := (not #217)
+#223 := (or #218 #220)
+#262 := (ite #223 #258 #261)
+#255 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#22 := (or #20 #21)
+#263 := (ite #22 #255 #262)
+#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #223 #29 #108)
+#229 := (ite #22 0::Int #226)
+#232 := (= #18 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#135 := (not #134)
+#128 := (not #127)
+#138 := (and #128 #135)
+#124 := (not #123)
+#131 := (and #124 #128)
+#141 := (or #131 #138)
+#144 := (ite #141 #29 #108)
+#147 := (ite #22 0::Int #144)
+#150 := (= #18 #147)
+#153 := (forall (vars (?v0 Int) (?v1 Int)) #150)
+#236 := (iff #153 #235)
+#233 := (iff #150 #232)
+#230 := (= #147 #229)
+#227 := (= #144 #226)
+#224 := (iff #141 #223)
+#221 := (iff #138 #220)
+#222 := [rewrite]: #221
+#211 := (iff #131 #218)
+#212 := [rewrite]: #211
+#225 := [monotonicity #212 #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#215 := (~ #153 #153)
+#213 := (~ #150 #150)
+#214 := [refl]: #213
+#216 := [nnf-pos #214]: #215
+#31 := (- #17)
+#30 := (- #16)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (ite #28 #29 #32)
+#34 := (ite #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#156 := (iff #36 #153)
+#95 := (and #24 #26)
+#98 := (or #25 #95)
+#111 := (ite #98 #29 #108)
+#114 := (ite #22 0::Int #111)
+#117 := (= #18 #114)
+#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
+#154 := (iff #120 #153)
+#151 := (iff #117 #150)
+#148 := (= #114 #147)
+#145 := (= #111 #144)
+#142 := (iff #98 #141)
+#139 := (iff #95 #138)
+#136 := (iff #26 #135)
#137 := [rewrite]: #136
-#134 := (iff #71 #133)
-#129 := (iff #15 true)
+#129 := (iff #24 #128)
#130 := [rewrite]: #129
-#135 := [monotonicity #130 #132]: #134
-#139 := [trans #135 #137]: #138
-#150 := [monotonicity #139 #148]: #149
-#152 := [trans #150 #65]: #151
-#127 := (iff #28 #77)
-#117 := (not #77)
-#122 := (not #117)
-#125 := (iff #122 #77)
+#140 := [monotonicity #130 #137]: #139
+#132 := (iff #25 #131)
+#125 := (iff #23 #124)
#126 := [rewrite]: #125
-#123 := (iff #28 #122)
-#120 := (iff #27 #117)
-#87 := -1::Int
-#104 := (ite #77 0::Int -1::Int)
-#114 := (= #104 -1::Int)
-#118 := (iff #114 #117)
-#119 := [rewrite]: #118
-#115 := (iff #27 #114)
-#88 := (= #22 -1::Int)
-#89 := [rewrite]: #88
-#112 := (= #26 #104)
-#107 := (ite false 0::Int #104)
-#110 := (= #107 #104)
-#111 := [rewrite]: #110
-#108 := (= #26 #107)
-#105 := (= #25 #104)
-#102 := (= #24 -1::Int)
-#97 := (div -1::Int 3::Int)
-#100 := (= #97 -1::Int)
-#101 := [rewrite]: #100
-#98 := (= #24 #97)
-#95 := (= #23 3::Int)
-#90 := (- -3::Int)
-#93 := (= #90 3::Int)
-#94 := [rewrite]: #93
-#91 := (= #23 #90)
-#52 := (= #12 -3::Int)
-#53 := [rewrite]: #52
-#92 := [monotonicity #53]: #91
-#96 := [trans #92 #94]: #95
-#99 := [monotonicity #89 #96]: #98
-#103 := [trans #99 #101]: #102
-#85 := (= #21 0::Int)
-#80 := (div 1::Int -3::Int)
-#83 := (= #80 0::Int)
-#84 := [rewrite]: #83
-#81 := (= #21 #80)
-#82 := [monotonicity #53]: #81
-#86 := [trans #82 #84]: #85
-#78 := (iff #20 #77)
-#75 := (iff #19 #74)
-#69 := (iff #16 #68)
-#70 := [monotonicity #53]: #69
-#76 := [monotonicity #70]: #75
-#72 := (iff #17 #71)
-#73 := [monotonicity #70]: #72
-#79 := [monotonicity #73 #76]: #78
-#106 := [monotonicity #79 #86 #103]: #105
-#66 := (iff #14 false)
-#62 := (iff #14 #61)
-#59 := (iff #13 false)
-#54 := (= -3::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #13 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#63 := [monotonicity #50 #60]: #62
-#67 := [trans #63 #65]: #66
-#109 := [monotonicity #67 #106]: #108
-#113 := [trans #109 #111]: #112
-#116 := [monotonicity #113 #89]: #115
-#121 := [trans #116 #119]: #120
-#124 := [monotonicity #121]: #123
-#128 := [trans #124 #126]: #127
-#154 := [trans #128 #152]: #153
-#48 := [asserted]: #28
-[mp #48 #154]: false
-unsat
-e161cbc5766adb3a07b2f61822dd61195f3dd163 109 0
-#2 := false
-#25 := 1::Int
-#26 := (- 1::Int)
-#8 := 3::Int
-#11 := (- 3::Int)
-#21 := (- #11)
-#22 := (div #11 #21)
-#20 := (div 3::Int #11)
-#9 := 0::Int
-#15 := (< 0::Int #11)
-#17 := (< 3::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 3::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#23 := (ite #19 #20 #22)
-#12 := (= #11 0::Int)
-#10 := (= 3::Int 0::Int)
-#13 := (or #10 #12)
-#24 := (ite #13 0::Int #23)
-#27 := (= #24 #26)
-#28 := (not #27)
-#130 := (iff #28 false)
-#1 := true
-#125 := (not true)
-#128 := (iff #125 false)
-#129 := [rewrite]: #128
-#126 := (iff #28 #125)
-#123 := (iff #27 true)
-#83 := -1::Int
-#118 := (= -1::Int -1::Int)
-#121 := (iff #118 true)
-#122 := [rewrite]: #121
-#119 := (iff #27 #118)
-#116 := (= #26 -1::Int)
-#117 := [rewrite]: #116
-#114 := (= #24 -1::Int)
-#109 := (ite false 0::Int -1::Int)
-#112 := (= #109 -1::Int)
-#113 := [rewrite]: #112
-#110 := (= #24 #109)
-#107 := (= #23 -1::Int)
-#51 := -3::Int
-#68 := (< 0::Int -3::Int)
-#74 := (and #17 #68)
-#71 := (and #14 #68)
-#77 := (or #71 #74)
-#102 := (ite #77 -1::Int -1::Int)
-#105 := (= #102 -1::Int)
-#106 := [rewrite]: #105
-#103 := (= #23 #102)
-#100 := (= #22 -1::Int)
-#95 := (div -3::Int 3::Int)
-#98 := (= #95 -1::Int)
-#99 := [rewrite]: #98
-#96 := (= #22 #95)
-#93 := (= #21 3::Int)
-#88 := (- -3::Int)
-#91 := (= #88 3::Int)
-#92 := [rewrite]: #91
-#89 := (= #21 #88)
-#52 := (= #11 -3::Int)
-#53 := [rewrite]: #52
-#90 := [monotonicity #53]: #89
-#94 := [trans #90 #92]: #93
-#97 := [monotonicity #53 #94]: #96
-#101 := [trans #97 #99]: #100
-#86 := (= #20 -1::Int)
-#80 := (div 3::Int -3::Int)
-#84 := (= #80 -1::Int)
-#85 := [rewrite]: #84
-#81 := (= #20 #80)
-#82 := [monotonicity #53]: #81
-#87 := [trans #82 #85]: #86
-#78 := (iff #19 #77)
-#75 := (iff #18 #74)
-#69 := (iff #15 #68)
-#70 := [monotonicity #53]: #69
-#76 := [monotonicity #70]: #75
-#72 := (iff #16 #71)
-#73 := [monotonicity #70]: #72
-#79 := [monotonicity #73 #76]: #78
-#104 := [monotonicity #79 #87 #101]: #103
-#108 := [trans #104 #106]: #107
-#66 := (iff #13 false)
-#61 := (or false false)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #13 #61)
-#59 := (iff #12 false)
-#54 := (= -3::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #12 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#63 := [monotonicity #50 #60]: #62
-#67 := [trans #63 #65]: #66
-#111 := [monotonicity #67 #108]: #110
-#115 := [trans #111 #113]: #114
-#120 := [monotonicity #115 #117]: #119
-#124 := [trans #120 #122]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#48 := [asserted]: #28
-[mp #48 #131]: false
-unsat
-17920425f93d8549a15817d71271ba90ab0e16ae 138 0
-#2 := false
-#27 := 2::Int
-#28 := (- 2::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#23 := (- #12)
-#8 := 5::Int
-#22 := (- 5::Int)
-#24 := (div #22 #23)
-#21 := (div 5::Int #12)
-#9 := 0::Int
-#16 := (< 0::Int #12)
-#18 := (< 5::Int 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int 5::Int)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= #12 0::Int)
-#10 := (= 5::Int 0::Int)
-#14 := (or #10 #13)
-#26 := (ite #14 0::Int #25)
-#29 := (= #26 #28)
-#30 := (not #29)
-#159 := (iff #30 false)
-#53 := -3::Int
-#70 := (< 0::Int -3::Int)
-#76 := (and #18 #70)
-#73 := (and #15 #70)
-#79 := (or #73 #76)
-#157 := (iff #79 false)
-#63 := (or false false)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#155 := (iff #79 #63)
-#153 := (iff #76 false)
-#148 := (and false false)
-#151 := (iff #148 false)
-#152 := [rewrite]: #151
-#149 := (iff #76 #148)
-#137 := (iff #70 false)
-#138 := [rewrite]: #137
-#146 := (iff #18 false)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147 #138]: #149
-#154 := [trans #150 #152]: #153
-#144 := (iff #73 false)
-#1 := true
-#139 := (and true false)
-#142 := (iff #139 false)
-#143 := [rewrite]: #142
-#140 := (iff #73 #139)
-#135 := (iff #15 true)
-#136 := [rewrite]: #135
-#141 := [monotonicity #136 #138]: #140
-#145 := [trans #141 #143]: #144
-#156 := [monotonicity #145 #154]: #155
-#158 := [trans #156 #67]: #157
-#133 := (iff #30 #79)
-#123 := (not #79)
-#128 := (not #123)
-#131 := (iff #128 #79)
-#132 := [rewrite]: #131
-#129 := (iff #30 #128)
-#126 := (iff #29 #123)
-#103 := -2::Int
-#85 := -1::Int
-#108 := (ite #79 -1::Int -2::Int)
-#120 := (= #108 -2::Int)
-#124 := (iff #120 #123)
-#125 := [rewrite]: #124
-#121 := (iff #29 #120)
-#118 := (= #28 -2::Int)
-#119 := [rewrite]: #118
-#116 := (= #26 #108)
-#111 := (ite false 0::Int #108)
-#114 := (= #111 #108)
-#115 := [rewrite]: #114
-#112 := (= #26 #111)
-#109 := (= #25 #108)
-#106 := (= #24 -2::Int)
-#90 := -5::Int
-#100 := (div -5::Int 3::Int)
-#104 := (= #100 -2::Int)
-#105 := [rewrite]: #104
-#101 := (= #24 #100)
-#98 := (= #23 3::Int)
-#93 := (- -3::Int)
-#96 := (= #93 3::Int)
+#133 := [monotonicity #126 #130]: #132
+#143 := [monotonicity #133 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#155 := [quant-intro #152]: #154
+#121 := (iff #36 #120)
+#118 := (iff #35 #117)
+#115 := (= #34 #114)
+#112 := (= #33 #111)
+#109 := (= #32 #108)
+#106 := (= #31 #105)
+#107 := [rewrite]: #106
+#103 := (= #30 #102)
+#104 := [rewrite]: #103
+#110 := [monotonicity #104 #107]: #109
+#99 := (iff #28 #98)
+#96 := (iff #27 #95)
#97 := [rewrite]: #96
-#94 := (= #23 #93)
-#54 := (= #12 -3::Int)
-#55 := [rewrite]: #54
-#95 := [monotonicity #55]: #94
-#99 := [trans #95 #97]: #98
-#91 := (= #22 -5::Int)
-#92 := [rewrite]: #91
-#102 := [monotonicity #92 #99]: #101
-#107 := [trans #102 #105]: #106
-#88 := (= #21 -1::Int)
-#82 := (div 5::Int -3::Int)
-#86 := (= #82 -1::Int)
-#87 := [rewrite]: #86
-#83 := (= #21 #82)
-#84 := [monotonicity #55]: #83
-#89 := [trans #84 #87]: #88
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#71 := (iff #16 #70)
-#72 := [monotonicity #55]: #71
-#78 := [monotonicity #72]: #77
-#74 := (iff #17 #73)
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#110 := [monotonicity #81 #89 #107]: #109
-#68 := (iff #14 false)
-#64 := (iff #14 #63)
-#61 := (iff #13 false)
-#56 := (= -3::Int 0::Int)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #13 #56)
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#51 := (iff #10 false)
-#52 := [rewrite]: #51
-#65 := [monotonicity #52 #62]: #64
-#69 := [trans #65 #67]: #68
-#113 := [monotonicity #69 #110]: #112
-#117 := [trans #113 #115]: #116
-#122 := [monotonicity #117 #119]: #121
-#127 := [trans #122 #125]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#160 := [trans #134 #158]: #159
-#50 := [asserted]: #30
-[mp #50 #160]: false
-unsat
-a358eed5b14d12c6db4e25a50a2df755d735c9b5 150 0
-#2 := false
-#8 := 1::Int
-#9 := (- 1::Int)
-#12 := 3::Int
-#23 := (- 3::Int)
-#22 := (- #9)
-#24 := (div #22 #23)
-#21 := (div #9 3::Int)
-#10 := 0::Int
-#16 := (< 0::Int 3::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= 3::Int 0::Int)
-#11 := (= #9 0::Int)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#27 := (= #26 #9)
-#28 := (not #27)
-#171 := (iff #28 false)
-#49 := -1::Int
-#79 := (< -1::Int 0::Int)
-#85 := (and #16 #79)
-#68 := (< 0::Int -1::Int)
-#74 := (and #16 #68)
-#90 := (or #74 #85)
-#134 := (not #90)
-#169 := (iff #134 false)
-#1 := true
-#164 := (not true)
-#167 := (iff #164 false)
-#168 := [rewrite]: #167
-#165 := (iff #134 #164)
-#162 := (iff #90 true)
-#157 := (or false true)
-#160 := (iff #157 true)
-#161 := [rewrite]: #160
-#158 := (iff #90 #157)
-#155 := (iff #85 true)
-#150 := (and true true)
-#153 := (iff #150 true)
-#154 := [rewrite]: #153
-#151 := (iff #85 #150)
-#148 := (iff #79 true)
-#149 := [rewrite]: #148
-#137 := (iff #16 true)
-#138 := [rewrite]: #137
-#152 := [monotonicity #138 #149]: #151
-#156 := [trans #152 #154]: #155
-#146 := (iff #74 false)
-#141 := (and true false)
-#144 := (iff #141 false)
-#145 := [rewrite]: #144
-#142 := (iff #74 #141)
-#139 := (iff #68 false)
-#140 := [rewrite]: #139
-#143 := [monotonicity #138 #140]: #142
-#147 := [trans #143 #145]: #146
-#159 := [monotonicity #147 #156]: #158
-#163 := [trans #159 #161]: #162
-#166 := [monotonicity #163]: #165
-#170 := [trans #166 #168]: #169
-#135 := (iff #28 #134)
-#132 := (iff #27 #90)
-#117 := (ite #90 -1::Int 0::Int)
-#127 := (= #117 -1::Int)
-#130 := (iff #127 #90)
-#131 := [rewrite]: #130
-#128 := (iff #27 #127)
-#50 := (= #9 -1::Int)
-#51 := [rewrite]: #50
-#125 := (= #26 #117)
-#120 := (ite false 0::Int #117)
-#123 := (= #120 #117)
-#124 := [rewrite]: #123
-#121 := (= #26 #120)
-#118 := (= #25 #117)
-#115 := (= #24 0::Int)
-#107 := -3::Int
-#110 := (div 1::Int -3::Int)
-#113 := (= #110 0::Int)
-#114 := [rewrite]: #113
-#111 := (= #24 #110)
-#108 := (= #23 -3::Int)
-#109 := [rewrite]: #108
-#105 := (= #22 1::Int)
-#100 := (- -1::Int)
-#103 := (= #100 1::Int)
-#104 := [rewrite]: #103
-#101 := (= #22 #100)
-#102 := [monotonicity #51]: #101
-#106 := [trans #102 #104]: #105
-#112 := [monotonicity #106 #109]: #111
-#116 := [trans #112 #114]: #115
-#98 := (= #21 -1::Int)
-#93 := (div -1::Int 3::Int)
-#96 := (= #93 -1::Int)
-#97 := [rewrite]: #96
-#94 := (= #21 #93)
-#95 := [monotonicity #51]: #94
-#99 := [trans #95 #97]: #98
-#91 := (iff #20 #90)
-#88 := (iff #19 #85)
-#82 := (and #79 #16)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #19 #82)
-#80 := (iff #18 #79)
-#81 := [monotonicity #51]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#77 := (iff #17 #74)
-#71 := (and #68 #16)
-#75 := (iff #71 #74)
-#76 := [rewrite]: #75
-#72 := (iff #17 #71)
-#69 := (iff #15 #68)
-#70 := [monotonicity #51]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#92 := [monotonicity #78 #89]: #91
-#119 := [monotonicity #92 #99 #116]: #118
-#66 := (iff #14 false)
-#61 := (or false false)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #14 #61)
-#59 := (iff #13 false)
-#60 := [rewrite]: #59
-#57 := (iff #11 false)
-#52 := (= -1::Int 0::Int)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #11 #52)
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#63 := [monotonicity #58 #60]: #62
-#67 := [trans #63 #65]: #66
-#122 := [monotonicity #67 #119]: #121
-#126 := [trans #122 #124]: #125
-#129 := [monotonicity #126 #51]: #128
-#133 := [trans #129 #131]: #132
-#136 := [monotonicity #133]: #135
-#172 := [trans #136 #170]: #171
-#48 := [asserted]: #28
-[mp #48 #172]: false
-unsat
-282152f210622b67ee14b9ad0372daa57d1c2fe0 122 0
-#2 := false
-#25 := 1::Int
-#26 := (- 1::Int)
-#8 := 3::Int
-#9 := (- 3::Int)
-#21 := (- #9)
-#22 := (div #21 #9)
-#20 := (div #9 3::Int)
-#10 := 0::Int
-#15 := (< 0::Int 3::Int)
-#17 := (< #9 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #9)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#23 := (ite #19 #20 #22)
-#12 := (= 3::Int 0::Int)
-#11 := (= #9 0::Int)
-#13 := (or #11 #12)
-#24 := (ite #13 0::Int #23)
-#27 := (= #24 #26)
-#28 := (not #27)
-#143 := (iff #28 false)
-#1 := true
-#138 := (not true)
-#141 := (iff #138 false)
-#142 := [rewrite]: #141
-#139 := (iff #28 #138)
-#136 := (iff #27 true)
-#96 := -1::Int
-#131 := (= -1::Int -1::Int)
-#134 := (iff #131 true)
-#135 := [rewrite]: #134
-#132 := (iff #27 #131)
-#129 := (= #26 -1::Int)
-#130 := [rewrite]: #129
-#127 := (= #24 -1::Int)
-#122 := (ite false 0::Int -1::Int)
-#125 := (= #122 -1::Int)
-#126 := [rewrite]: #125
-#123 := (= #24 #122)
-#120 := (= #23 -1::Int)
-#49 := -3::Int
-#79 := (< -3::Int 0::Int)
-#85 := (and #15 #79)
-#68 := (< 0::Int -3::Int)
-#74 := (and #15 #68)
-#90 := (or #74 #85)
-#115 := (ite #90 -1::Int -1::Int)
-#118 := (= #115 -1::Int)
-#119 := [rewrite]: #118
-#116 := (= #23 #115)
-#113 := (= #22 -1::Int)
-#108 := (div 3::Int -3::Int)
-#111 := (= #108 -1::Int)
-#112 := [rewrite]: #111
-#109 := (= #22 #108)
-#50 := (= #9 -3::Int)
-#51 := [rewrite]: #50
-#106 := (= #21 3::Int)
-#101 := (- -3::Int)
-#104 := (= #101 3::Int)
-#105 := [rewrite]: #104
-#102 := (= #21 #101)
-#103 := [monotonicity #51]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107 #51]: #109
-#114 := [trans #110 #112]: #113
-#99 := (= #20 -1::Int)
-#93 := (div -3::Int 3::Int)
-#97 := (= #93 -1::Int)
-#98 := [rewrite]: #97
-#94 := (= #20 #93)
-#95 := [monotonicity #51]: #94
-#100 := [trans #95 #98]: #99
-#91 := (iff #19 #90)
-#88 := (iff #18 #85)
-#82 := (and #79 #15)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #18 #82)
-#80 := (iff #17 #79)
-#81 := [monotonicity #51]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#77 := (iff #16 #74)
-#71 := (and #68 #15)
-#75 := (iff #71 #74)
-#76 := [rewrite]: #75
-#72 := (iff #16 #71)
-#69 := (iff #14 #68)
-#70 := [monotonicity #51]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#92 := [monotonicity #78 #89]: #91
-#117 := [monotonicity #92 #100 #114]: #116
-#121 := [trans #117 #119]: #120
-#66 := (iff #13 false)
-#61 := (or false false)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #13 #61)
-#59 := (iff #12 false)
-#60 := [rewrite]: #59
-#57 := (iff #11 false)
-#52 := (= -3::Int 0::Int)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #11 #52)
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#63 := [monotonicity #58 #60]: #62
-#67 := [trans #63 #65]: #66
-#124 := [monotonicity #67 #121]: #123
-#128 := [trans #124 #126]: #127
-#133 := [monotonicity #128 #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #137]: #139
-#144 := [trans #140 #142]: #143
-#48 := [asserted]: #28
-[mp #48 #144]: false
-unsat
-09bd21e8184625daa5375adf22f60c439ab0cf17 156 0
-#2 := false
-#27 := 2::Int
-#28 := (- 2::Int)
-#12 := 3::Int
-#23 := (- 3::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#22 := (- #9)
-#24 := (div #22 #23)
-#21 := (div #9 3::Int)
-#10 := 0::Int
-#16 := (< 0::Int 3::Int)
-#18 := (< #9 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #9)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#13 := (= 3::Int 0::Int)
-#11 := (= #9 0::Int)
-#14 := (or #11 #13)
-#26 := (ite #14 0::Int #25)
-#29 := (= #26 #28)
-#30 := (not #29)
-#177 := (iff #30 false)
-#51 := -5::Int
-#81 := (< -5::Int 0::Int)
-#87 := (and #16 #81)
-#70 := (< 0::Int -5::Int)
-#76 := (and #16 #70)
-#92 := (or #76 #87)
-#140 := (not #92)
-#175 := (iff #140 false)
-#1 := true
-#170 := (not true)
-#173 := (iff #170 false)
-#174 := [rewrite]: #173
-#171 := (iff #140 #170)
-#168 := (iff #92 true)
-#163 := (or false true)
-#166 := (iff #163 true)
-#167 := [rewrite]: #166
-#164 := (iff #92 #163)
-#161 := (iff #87 true)
-#156 := (and true true)
-#159 := (iff #156 true)
-#160 := [rewrite]: #159
-#157 := (iff #87 #156)
-#154 := (iff #81 true)
-#155 := [rewrite]: #154
-#143 := (iff #16 true)
-#144 := [rewrite]: #143
-#158 := [monotonicity #144 #155]: #157
-#162 := [trans #158 #160]: #161
-#152 := (iff #76 false)
-#147 := (and true false)
-#150 := (iff #147 false)
-#151 := [rewrite]: #150
-#148 := (iff #76 #147)
-#145 := (iff #70 false)
-#146 := [rewrite]: #145
-#149 := [monotonicity #144 #146]: #148
-#153 := [trans #149 #151]: #152
-#165 := [monotonicity #153 #162]: #164
-#169 := [trans #165 #167]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#141 := (iff #30 #140)
-#138 := (iff #29 #92)
-#98 := -2::Int
-#116 := -1::Int
-#121 := (ite #92 -2::Int -1::Int)
-#133 := (= #121 -2::Int)
-#136 := (iff #133 #92)
-#137 := [rewrite]: #136
-#134 := (iff #29 #133)
-#131 := (= #28 -2::Int)
-#132 := [rewrite]: #131
-#129 := (= #26 #121)
-#124 := (ite false 0::Int #121)
-#127 := (= #124 #121)
-#128 := [rewrite]: #127
-#125 := (= #26 #124)
-#122 := (= #25 #121)
-#119 := (= #24 -1::Int)
-#110 := -3::Int
-#113 := (div 5::Int -3::Int)
-#117 := (= #113 -1::Int)
-#118 := [rewrite]: #117
-#114 := (= #24 #113)
-#111 := (= #23 -3::Int)
-#112 := [rewrite]: #111
-#108 := (= #22 5::Int)
-#103 := (- -5::Int)
-#106 := (= #103 5::Int)
-#107 := [rewrite]: #106
-#104 := (= #22 #103)
-#52 := (= #9 -5::Int)
-#53 := [rewrite]: #52
-#105 := [monotonicity #53]: #104
-#109 := [trans #105 #107]: #108
-#115 := [monotonicity #109 #112]: #114
-#120 := [trans #115 #118]: #119
-#101 := (= #21 -2::Int)
-#95 := (div -5::Int 3::Int)
-#99 := (= #95 -2::Int)
-#100 := [rewrite]: #99
-#96 := (= #21 #95)
-#97 := [monotonicity #53]: #96
-#102 := [trans #97 #100]: #101
-#93 := (iff #20 #92)
-#90 := (iff #19 #87)
-#84 := (and #81 #16)
-#88 := (iff #84 #87)
-#89 := [rewrite]: #88
-#85 := (iff #19 #84)
-#82 := (iff #18 #81)
-#83 := [monotonicity #53]: #82
-#86 := [monotonicity #83]: #85
-#91 := [trans #86 #89]: #90
-#79 := (iff #17 #76)
-#73 := (and #70 #16)
-#77 := (iff #73 #76)
-#78 := [rewrite]: #77
-#74 := (iff #17 #73)
-#71 := (iff #15 #70)
-#72 := [monotonicity #53]: #71
-#75 := [monotonicity #72]: #74
-#80 := [trans #75 #78]: #79
-#94 := [monotonicity #80 #91]: #93
-#123 := [monotonicity #94 #102 #120]: #122
-#68 := (iff #14 false)
-#63 := (or false false)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #14 #63)
-#61 := (iff #13 false)
-#62 := [rewrite]: #61
-#59 := (iff #11 false)
-#54 := (= -5::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #11 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#65 := [monotonicity #60 #62]: #64
-#69 := [trans #65 #67]: #68
-#126 := [monotonicity #69 #123]: #125
-#130 := [trans #126 #128]: #129
-#135 := [monotonicity #130 #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#178 := [trans #142 #176]: #177
-#50 := [asserted]: #30
-[mp #50 #178]: false
-unsat
-75a498a3ae15008c6ba6962bb8ff41e876585e27 156 0
-#2 := false
-#10 := 0::Int
-#12 := 3::Int
-#13 := (- 3::Int)
-#24 := (- #13)
-#8 := 1::Int
-#9 := (- 1::Int)
-#23 := (- #9)
-#25 := (div #23 #24)
-#22 := (div #9 #13)
-#17 := (< 0::Int #13)
-#19 := (< #9 0::Int)
-#20 := (and #19 #17)
-#16 := (< 0::Int #9)
-#18 := (and #16 #17)
-#21 := (or #18 #20)
-#26 := (ite #21 #22 #25)
-#14 := (= #13 0::Int)
-#11 := (= #9 0::Int)
-#15 := (or #11 #14)
-#27 := (ite #15 0::Int #26)
-#28 := (= #27 0::Int)
-#29 := (not #28)
-#177 := (iff #29 false)
-#50 := -1::Int
-#86 := (< -1::Int 0::Int)
-#60 := -3::Int
-#80 := (< 0::Int -3::Int)
-#92 := (and #80 #86)
-#77 := (< 0::Int -1::Int)
-#83 := (and #77 #80)
-#97 := (or #83 #92)
-#175 := (iff #97 false)
-#70 := (or false false)
-#73 := (iff #70 false)
-#74 := [rewrite]: #73
-#173 := (iff #97 #70)
-#171 := (iff #92 false)
-#1 := true
-#166 := (and false true)
-#169 := (iff #166 false)
-#170 := [rewrite]: #169
-#167 := (iff #92 #166)
-#164 := (iff #86 true)
-#165 := [rewrite]: #164
-#155 := (iff #80 false)
-#156 := [rewrite]: #155
-#168 := [monotonicity #156 #165]: #167
-#172 := [trans #168 #170]: #171
-#162 := (iff #83 false)
-#157 := (and false false)
-#160 := (iff #157 false)
-#161 := [rewrite]: #160
-#158 := (iff #83 #157)
-#153 := (iff #77 false)
-#154 := [rewrite]: #153
-#159 := [monotonicity #154 #156]: #158
-#163 := [trans #159 #161]: #162
-#174 := [monotonicity #163 #172]: #173
-#176 := [trans #174 #74]: #175
-#151 := (iff #29 #97)
-#141 := (not #97)
-#146 := (not #141)
-#149 := (iff #146 #97)
-#150 := [rewrite]: #149
-#147 := (iff #29 #146)
-#144 := (iff #28 #141)
-#128 := (ite #97 1::Int 0::Int)
-#138 := (= #128 0::Int)
-#142 := (iff #138 #141)
-#143 := [rewrite]: #142
-#139 := (iff #28 #138)
-#136 := (= #27 #128)
-#131 := (ite false 0::Int #128)
-#134 := (= #131 #128)
-#135 := [rewrite]: #134
-#132 := (= #27 #131)
-#129 := (= #26 #128)
-#126 := (= #25 0::Int)
-#121 := (div 1::Int 3::Int)
-#124 := (= #121 0::Int)
-#125 := [rewrite]: #124
-#122 := (= #25 #121)
-#119 := (= #24 3::Int)
-#114 := (- -3::Int)
-#117 := (= #114 3::Int)
-#118 := [rewrite]: #117
-#115 := (= #24 #114)
-#61 := (= #13 -3::Int)
-#62 := [rewrite]: #61
-#116 := [monotonicity #62]: #115
-#120 := [trans #116 #118]: #119
-#112 := (= #23 1::Int)
-#107 := (- -1::Int)
-#110 := (= #107 1::Int)
-#111 := [rewrite]: #110
-#108 := (= #23 #107)
-#51 := (= #9 -1::Int)
-#52 := [rewrite]: #51
-#109 := [monotonicity #52]: #108
-#113 := [trans #109 #111]: #112
-#123 := [monotonicity #113 #120]: #122
-#127 := [trans #123 #125]: #126
-#105 := (= #22 1::Int)
-#100 := (div -1::Int -3::Int)
-#103 := (= #100 1::Int)
-#104 := [rewrite]: #103
-#101 := (= #22 #100)
-#102 := [monotonicity #52 #62]: #101
-#106 := [trans #102 #104]: #105
-#98 := (iff #21 #97)
-#95 := (iff #20 #92)
-#89 := (and #86 #80)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #20 #89)
-#81 := (iff #17 #80)
-#82 := [monotonicity #62]: #81
-#87 := (iff #19 #86)
-#88 := [monotonicity #52]: #87
-#91 := [monotonicity #88 #82]: #90
-#96 := [trans #91 #94]: #95
-#84 := (iff #18 #83)
-#78 := (iff #16 #77)
-#79 := [monotonicity #52]: #78
-#85 := [monotonicity #79 #82]: #84
-#99 := [monotonicity #85 #96]: #98
-#130 := [monotonicity #99 #106 #127]: #129
-#75 := (iff #15 false)
-#71 := (iff #15 #70)
-#68 := (iff #14 false)
-#63 := (= -3::Int 0::Int)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #14 #63)
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#58 := (iff #11 false)
-#53 := (= -1::Int 0::Int)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #11 #53)
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#72 := [monotonicity #59 #69]: #71
-#76 := [trans #72 #74]: #75
-#133 := [monotonicity #76 #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #137]: #139
-#145 := [trans #140 #143]: #144
-#148 := [monotonicity #145]: #147
-#152 := [trans #148 #150]: #151
-#178 := [trans #152 #176]: #177
-#49 := [asserted]: #29
-[mp #49 #178]: false
-unsat
-b0f55b14153bd1415b180d8eb26a6650d8024f22 112 0
-#2 := false
-#23 := 1::Int
-#8 := 3::Int
-#9 := (- 3::Int)
-#19 := (- #9)
-#20 := (div #19 #19)
-#18 := (div #9 #9)
-#10 := 0::Int
-#13 := (< 0::Int #9)
-#15 := (< #9 0::Int)
-#16 := (and #15 #13)
-#14 := (and #13 #13)
-#17 := (or #14 #16)
-#21 := (ite #17 #18 #20)
-#11 := (= #9 0::Int)
-#12 := (or #11 #11)
-#22 := (ite #12 0::Int #21)
-#24 := (= #22 1::Int)
-#25 := (not #24)
-#133 := (iff #25 false)
-#1 := true
-#128 := (not true)
-#131 := (iff #128 false)
-#132 := [rewrite]: #131
-#129 := (iff #25 #128)
-#126 := (iff #24 true)
-#121 := (= 1::Int 1::Int)
-#124 := (iff #121 true)
-#125 := [rewrite]: #124
-#122 := (iff #24 #121)
-#115 := (ite false 0::Int 1::Int)
-#118 := (= #115 1::Int)
-#119 := [rewrite]: #118
-#116 := (= #22 #115)
-#113 := (= #21 1::Int)
-#46 := -3::Int
-#73 := (< -3::Int 0::Int)
-#63 := (< 0::Int -3::Int)
-#79 := (and #63 #73)
-#84 := (or #63 #79)
-#108 := (ite #84 1::Int 1::Int)
-#111 := (= #108 1::Int)
-#112 := [rewrite]: #111
-#109 := (= #21 #108)
-#106 := (= #20 1::Int)
-#101 := (div 3::Int 3::Int)
-#104 := (= #101 1::Int)
-#105 := [rewrite]: #104
-#102 := (= #20 #101)
-#99 := (= #19 3::Int)
-#94 := (- -3::Int)
-#97 := (= #94 3::Int)
-#98 := [rewrite]: #97
-#95 := (= #19 #94)
-#47 := (= #9 -3::Int)
-#48 := [rewrite]: #47
-#96 := [monotonicity #48]: #95
-#100 := [trans #96 #98]: #99
-#103 := [monotonicity #100 #100]: #102
-#107 := [trans #103 #105]: #106
-#92 := (= #18 1::Int)
-#87 := (div -3::Int -3::Int)
-#90 := (= #87 1::Int)
-#91 := [rewrite]: #90
-#88 := (= #18 #87)
-#89 := [monotonicity #48 #48]: #88
-#93 := [trans #89 #91]: #92
-#85 := (iff #17 #84)
-#82 := (iff #16 #79)
-#76 := (and #73 #63)
-#80 := (iff #76 #79)
-#81 := [rewrite]: #80
-#77 := (iff #16 #76)
-#64 := (iff #13 #63)
-#65 := [monotonicity #48]: #64
-#74 := (iff #15 #73)
-#75 := [monotonicity #48]: #74
-#78 := [monotonicity #75 #65]: #77
-#83 := [trans #78 #81]: #82
-#71 := (iff #14 #63)
-#66 := (and #63 #63)
-#69 := (iff #66 #63)
-#70 := [rewrite]: #69
-#67 := (iff #14 #66)
-#68 := [monotonicity #65 #65]: #67
-#72 := [trans #68 #70]: #71
-#86 := [monotonicity #72 #83]: #85
-#110 := [monotonicity #86 #93 #107]: #109
-#114 := [trans #110 #112]: #113
-#61 := (iff #12 false)
-#56 := (or false false)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #12 #56)
-#54 := (iff #11 false)
-#49 := (= -3::Int 0::Int)
-#52 := (iff #49 false)
-#53 := [rewrite]: #52
-#50 := (iff #11 #49)
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55 #55]: #57
-#62 := [trans #58 #60]: #61
-#117 := [monotonicity #62 #114]: #116
-#120 := [trans #117 #119]: #24
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#45 := [asserted]: #25
-[mp #45 #134]: false
-unsat
-cebc167e67bf5c5c55d952431648797ef2d30dde 158 0
-#2 := false
-#28 := 1::Int
-#12 := 3::Int
-#13 := (- 3::Int)
-#24 := (- #13)
+#100 := [monotonicity #97]: #99
+#113 := [monotonicity #100 #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#157 := [trans #122 #155]: #156
+#94 := [asserted]: #36
+#158 := [mp #94 #157]: #153
+#207 := [mp~ #158 #216]: #153
+#238 := [mp #207 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#13 := 1::Int
+#69 := -3::Int
+#66 := -5::Int
+#72 := (f3 -5::Int -3::Int)
+#75 := (= #72 1::Int)
+#88 := (not #75)
+#10 := 3::Int
+#11 := (- 3::Int)
#8 := 5::Int
#9 := (- 5::Int)
-#23 := (- #9)
-#25 := (div #23 #24)
-#22 := (div #9 #13)
-#10 := 0::Int
-#17 := (< 0::Int #13)
-#19 := (< #9 0::Int)
-#20 := (and #19 #17)
-#16 := (< 0::Int #9)
-#18 := (and #16 #17)
-#21 := (or #18 #20)
-#26 := (ite #21 #22 #25)
-#14 := (= #13 0::Int)
-#11 := (= #9 0::Int)
-#15 := (or #11 #14)
-#27 := (ite #15 0::Int #26)
-#29 := (= #27 1::Int)
-#30 := (not #29)
-#179 := (iff #30 false)
-#51 := -5::Int
-#87 := (< -5::Int 0::Int)
-#61 := -3::Int
-#81 := (< 0::Int -3::Int)
-#93 := (and #81 #87)
-#78 := (< 0::Int -5::Int)
-#84 := (and #78 #81)
-#98 := (or #84 #93)
-#177 := (iff #98 false)
-#71 := (or false false)
-#74 := (iff #71 false)
-#75 := [rewrite]: #74
-#175 := (iff #98 #71)
-#173 := (iff #93 false)
-#1 := true
-#168 := (and false true)
-#171 := (iff #168 false)
-#172 := [rewrite]: #171
-#169 := (iff #93 #168)
-#166 := (iff #87 true)
-#167 := [rewrite]: #166
-#157 := (iff #81 false)
-#158 := [rewrite]: #157
-#170 := [monotonicity #158 #167]: #169
-#174 := [trans #170 #172]: #173
-#164 := (iff #84 false)
-#159 := (and false false)
-#162 := (iff #159 false)
-#163 := [rewrite]: #162
-#160 := (iff #84 #159)
-#155 := (iff #78 false)
-#156 := [rewrite]: #155
-#161 := [monotonicity #156 #158]: #160
-#165 := [trans #161 #163]: #164
-#176 := [monotonicity #165 #174]: #175
-#178 := [trans #176 #75]: #177
-#153 := (iff #30 #98)
-#143 := (not #98)
-#148 := (not #143)
-#151 := (iff #148 #98)
-#152 := [rewrite]: #151
-#149 := (iff #30 #148)
-#146 := (iff #29 #143)
-#104 := 2::Int
-#130 := (ite #98 2::Int 1::Int)
-#140 := (= #130 1::Int)
-#144 := (iff #140 #143)
-#145 := [rewrite]: #144
-#141 := (iff #29 #140)
-#138 := (= #27 #130)
-#133 := (ite false 0::Int #130)
-#136 := (= #133 #130)
-#137 := [rewrite]: #136
-#134 := (= #27 #133)
-#131 := (= #26 #130)
-#128 := (= #25 1::Int)
-#123 := (div 5::Int 3::Int)
-#126 := (= #123 1::Int)
-#127 := [rewrite]: #126
-#124 := (= #25 #123)
-#121 := (= #24 3::Int)
-#116 := (- -3::Int)
-#119 := (= #116 3::Int)
-#120 := [rewrite]: #119
-#117 := (= #24 #116)
-#62 := (= #13 -3::Int)
-#63 := [rewrite]: #62
-#118 := [monotonicity #63]: #117
-#122 := [trans #118 #120]: #121
-#114 := (= #23 5::Int)
-#109 := (- -5::Int)
-#112 := (= #109 5::Int)
-#113 := [rewrite]: #112
-#110 := (= #23 #109)
-#52 := (= #9 -5::Int)
-#53 := [rewrite]: #52
-#111 := [monotonicity #53]: #110
-#115 := [trans #111 #113]: #114
-#125 := [monotonicity #115 #122]: #124
-#129 := [trans #125 #127]: #128
-#107 := (= #22 2::Int)
-#101 := (div -5::Int -3::Int)
-#105 := (= #101 2::Int)
-#106 := [rewrite]: #105
-#102 := (= #22 #101)
-#103 := [monotonicity #53 #63]: #102
-#108 := [trans #103 #106]: #107
-#99 := (iff #21 #98)
-#96 := (iff #20 #93)
-#90 := (and #87 #81)
-#94 := (iff #90 #93)
-#95 := [rewrite]: #94
-#91 := (iff #20 #90)
-#82 := (iff #17 #81)
-#83 := [monotonicity #63]: #82
-#88 := (iff #19 #87)
-#89 := [monotonicity #53]: #88
-#92 := [monotonicity #89 #83]: #91
-#97 := [trans #92 #95]: #96
-#85 := (iff #18 #84)
-#79 := (iff #16 #78)
-#80 := [monotonicity #53]: #79
-#86 := [monotonicity #80 #83]: #85
-#100 := [monotonicity #86 #97]: #99
-#132 := [monotonicity #100 #108 #129]: #131
-#76 := (iff #15 false)
-#72 := (iff #15 #71)
-#69 := (iff #14 false)
-#64 := (= -3::Int 0::Int)
-#67 := (iff #64 false)
+#12 := (f3 #9 #11)
+#14 := (= #12 1::Int)
+#15 := (not #14)
+#91 := (iff #15 #88)
+#78 := (= 1::Int #72)
+#83 := (not #78)
+#89 := (iff #83 #88)
+#86 := (iff #78 #75)
+#87 := [rewrite]: #86
+#90 := [monotonicity #87]: #89
+#84 := (iff #15 #83)
+#81 := (iff #14 #78)
+#79 := (iff #75 #78)
+#80 := [rewrite]: #79
+#76 := (iff #14 #75)
+#73 := (= #12 #72)
+#70 := (= #11 -3::Int)
+#71 := [rewrite]: #70
+#67 := (= #9 -5::Int)
#68 := [rewrite]: #67
-#65 := (iff #14 #64)
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#59 := (iff #11 false)
-#54 := (= -5::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #11 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#73 := [monotonicity #60 #70]: #72
-#77 := [trans #73 #75]: #76
-#135 := [monotonicity #77 #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#147 := [trans #142 #145]: #146
-#150 := [monotonicity #147]: #149
-#154 := [trans #150 #152]: #153
-#180 := [trans #154 #178]: #179
-#50 := [asserted]: #30
-[mp #50 #180]: false
-unsat
-cb26d273f6e817a53bda9b00a467150cd5bc2594 70 0
-#2 := false
-#8 := 0::Int
-#14 := (- 0::Int)
-#15 := (mod #14 #14)
-#16 := (- #15)
-#13 := (mod 0::Int 0::Int)
-#10 := (< 0::Int 0::Int)
-#11 := (and #10 #10)
-#12 := (or #11 #11)
-#17 := (ite #12 #13 #16)
-#9 := (= 0::Int 0::Int)
-#18 := (ite #9 0::Int #17)
-#19 := (ite #9 0::Int #18)
-#20 := (= #19 0::Int)
-#21 := (not #20)
-#91 := (iff #21 false)
-#1 := true
-#86 := (not true)
-#89 := (iff #86 false)
-#90 := [rewrite]: #89
-#87 := (iff #21 #86)
-#84 := (iff #20 true)
-#42 := (iff #9 true)
-#43 := [rewrite]: #42
-#82 := (iff #20 #9)
-#76 := (ite true 0::Int 0::Int)
-#79 := (= #76 0::Int)
-#80 := [rewrite]: #79
-#77 := (= #19 #76)
-#74 := (= #18 0::Int)
-#60 := -1::Int
-#61 := (* -1::Int #13)
-#66 := (ite #10 #13 #61)
-#69 := (ite true 0::Int #66)
-#72 := (= #69 0::Int)
-#73 := [rewrite]: #72
-#70 := (= #18 #69)
-#67 := (= #17 #66)
-#64 := (= #16 #61)
-#57 := (- #13)
-#62 := (= #57 #61)
-#63 := [rewrite]: #62
-#58 := (= #16 #57)
-#55 := (= #15 #13)
-#53 := (= #14 0::Int)
-#54 := [rewrite]: #53
-#56 := [monotonicity #54 #54]: #55
-#59 := [monotonicity #56]: #58
-#65 := [trans #59 #63]: #64
-#51 := (iff #12 #10)
-#46 := (or #10 #10)
-#49 := (iff #46 #10)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 #10)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45 #45]: #47
-#52 := [trans #48 #50]: #51
-#68 := [monotonicity #52 #65]: #67
-#71 := [monotonicity #43 #68]: #70
-#75 := [trans #71 #73]: #74
-#78 := [monotonicity #43 #75]: #77
-#81 := [trans #78 #80]: #20
-#83 := [monotonicity #81]: #82
-#85 := [trans #83 #43]: #84
-#88 := [monotonicity #85]: #87
-#92 := [trans #88 #90]: #91
-#41 := [asserted]: #21
-[mp #41 #92]: false
-unsat
-1ec64b4c0435485d0864f4fb378fed079f553a7b 80 0
-#2 := false
-decl f3 :: Int
-#10 := f3
+#74 := [monotonicity #68 #71]: #73
+#77 := [monotonicity #74]: #76
+#82 := [trans #77 #80]: #81
+#85 := [monotonicity #82]: #84
+#92 := [trans #85 #90]: #91
+#65 := [asserted]: #15
+#93 := [mp #65 #92]: #88
+#670 := (not #757)
+#677 := (or #670 #75)
+#343 := (* -1::Int -3::Int)
+#427 := (* -1::Int -5::Int)
+#428 := (div #427 #343)
+#429 := (* -1::Int #428)
+#420 := (+ #72 #429)
+#431 := (= #420 0::Int)
+#432 := (div -5::Int -3::Int)
+#433 := (* -1::Int #432)
+#430 := (+ #72 #433)
+#434 := (= #430 0::Int)
+#413 := (>= -5::Int 0::Int)
+#748 := (<= -3::Int 0::Int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (<= -5::Int 0::Int)
+#744 := (or #537 #748)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #72 0::Int)
+#753 := (= -3::Int 0::Int)
+#754 := (= -5::Int 0::Int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#661 := (or #670 #755)
+#664 := (iff #661 #677)
+#666 := (iff #677 #677)
+#667 := [rewrite]: #666
+#675 := (iff #755 #75)
+#683 := (ite false #752 #75)
+#673 := (iff #683 #75)
+#674 := [rewrite]: #673
+#679 := (iff #755 #683)
+#681 := (iff #751 #75)
+#719 := 2::Int
+#704 := (= #72 2::Int)
+#678 := (ite false #704 #75)
+#669 := (iff #678 #75)
+#671 := [rewrite]: #669
+#680 := (iff #751 #678)
+#687 := (iff #431 #75)
+#589 := (+ -1::Int #72)
+#594 := (= #589 0::Int)
+#597 := (iff #594 #75)
+#690 := [rewrite]: #597
+#595 := (iff #431 #594)
+#585 := (= #420 #589)
+#686 := (+ #72 -1::Int)
+#591 := (= #686 #589)
+#592 := [rewrite]: #591
+#689 := (= #420 #686)
+#590 := (= #429 -1::Int)
+#579 := (* -1::Int 1::Int)
+#540 := (= #579 -1::Int)
+#688 := [rewrite]: #540
+#580 := (= #429 #579)
+#694 := (= #428 1::Int)
+#539 := (div 5::Int 3::Int)
+#695 := (= #539 1::Int)
+#696 := [rewrite]: #695
+#692 := (= #428 #539)
+#536 := (= #343 3::Int)
+#538 := [rewrite]: #536
+#700 := (= #427 5::Int)
+#707 := [rewrite]: #700
+#693 := [monotonicity #707 #538]: #692
+#697 := [trans #693 #696]: #694
+#581 := [monotonicity #697]: #580
+#685 := [trans #581 #688]: #590
+#574 := [monotonicity #685]: #689
+#593 := [trans #574 #592]: #585
+#596 := [monotonicity #593]: #595
+#691 := [trans #596 #690]: #687
+#705 := (iff #434 #704)
+#722 := -2::Int
+#710 := (+ -2::Int #72)
+#701 := (= #710 0::Int)
+#698 := (iff #701 #704)
+#699 := [rewrite]: #698
+#702 := (iff #434 #701)
+#558 := (= #430 #710)
+#709 := (+ #72 -2::Int)
+#716 := (= #709 #710)
+#557 := [rewrite]: #716
+#714 := (= #430 #709)
+#713 := (= #433 -2::Int)
+#717 := (* -1::Int 2::Int)
+#711 := (= #717 -2::Int)
+#712 := [rewrite]: #711
+#721 := (= #433 #717)
+#720 := (= #432 2::Int)
+#435 := [rewrite]: #720
+#718 := [monotonicity #435]: #721
+#708 := [trans #718 #712]: #713
+#715 := [monotonicity #708]: #714
+#559 := [trans #715 #557]: #558
+#703 := [monotonicity #559]: #702
+#706 := [trans #703 #699]: #705
+#440 := (iff #419 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#438 := (iff #419 #406)
+#724 := (iff #407 false)
+#1 := true
+#381 := (not true)
+#740 := (iff #381 false)
+#743 := [rewrite]: #740
+#723 := (iff #407 #381)
+#448 := (iff #750 true)
+#454 := (or true false)
+#725 := (iff #454 true)
+#726 := [rewrite]: #725
+#455 := (iff #750 #454)
+#452 := (iff #413 false)
+#453 := [rewrite]: #452
+#734 := (iff #748 true)
+#735 := [rewrite]: #734
+#349 := [monotonicity #735 #453]: #455
+#449 := [trans #349 #726]: #448
+#727 := [monotonicity #449]: #723
+#728 := [trans #727 #743]: #724
+#729 := (iff #418 false)
+#382 := (iff #418 #381)
+#739 := (iff #744 true)
+#736 := (or true true)
+#738 := (iff #736 true)
+#376 := [rewrite]: #738
+#737 := (iff #744 #736)
+#397 := (iff #537 true)
+#733 := [rewrite]: #397
+#732 := [monotonicity #733 #735]: #737
+#741 := [trans #732 #376]: #739
+#742 := [monotonicity #741]: #382
+#730 := [trans #742 #743]: #729
+#439 := [monotonicity #730 #728]: #438
+#441 := [trans #439 #394]: #440
+#672 := [monotonicity #441 #706 #691]: #680
+#682 := [trans #672 #671]: #681
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#684 := [monotonicity #396 #682]: #679
+#676 := [trans #684 #674]: #675
+#665 := [monotonicity #676]: #664
+#663 := [trans #665 #667]: #664
+#662 := [quant-inst #66 #69]: #661
+#668 := [mp #662 #663]: #677
+[unit-resolution #668 #93 #762]: false
+unsat
+9d955d673529089780c55958aa0742a5b1471d68 273 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#13 := (:var 0 Int)
+#12 := (:var 1 Int)
+#32 := (f3 #12 #13)
+#756 := (pattern #32)
#8 := 0::Int
-#20 := (- 0::Int)
-#19 := (- f3)
-#21 := (mod #19 #20)
-#22 := (- #21)
-#18 := (mod f3 0::Int)
-#13 := (< 0::Int 0::Int)
-#15 := (< f3 0::Int)
-#16 := (and #15 #13)
-#12 := (< 0::Int f3)
-#14 := (and #12 #13)
-#17 := (or #14 #16)
-#23 := (ite #17 #18 #22)
-#11 := (= f3 0::Int)
-#24 := (ite #11 0::Int #23)
-#9 := (= 0::Int 0::Int)
-#25 := (ite #9 f3 #24)
-#26 := (= #25 f3)
-#27 := (not #26)
-#100 := (iff #27 false)
-#1 := true
-#95 := (not true)
-#98 := (iff #95 false)
-#99 := [rewrite]: #98
-#96 := (iff #27 #95)
-#93 := (iff #26 true)
-#88 := (= f3 f3)
-#91 := (iff #88 true)
-#92 := [rewrite]: #91
-#89 := (iff #26 #88)
-#59 := -1::Int
-#60 := (* -1::Int f3)
-#65 := (mod #60 0::Int)
-#71 := (* -1::Int #65)
-#53 := (and #13 #15)
-#56 := (or #14 #53)
-#76 := (ite #56 #18 #71)
-#50 := (= 0::Int f3)
-#79 := (ite #50 0::Int #76)
-#82 := (ite true f3 #79)
-#85 := (= #82 f3)
-#86 := [rewrite]: #85
-#83 := (= #25 #82)
-#80 := (= #24 #79)
-#77 := (= #23 #76)
-#74 := (= #22 #71)
-#68 := (- #65)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#66 := (= #21 #65)
-#63 := (= #20 0::Int)
-#64 := [rewrite]: #63
-#61 := (= #19 #60)
-#62 := [rewrite]: #61
-#67 := [monotonicity #62 #64]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#57 := (iff #17 #56)
-#54 := (iff #16 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#78 := [monotonicity #58 #75]: #77
-#51 := (iff #11 #50)
-#52 := [rewrite]: #51
-#81 := [monotonicity #52 #78]: #80
-#48 := (iff #9 true)
-#49 := [rewrite]: #48
-#84 := [monotonicity #49 #81]: #83
-#87 := [trans #84 #86]: #26
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#97 := [monotonicity #94]: #96
-#101 := [trans #97 #99]: #100
-#47 := [asserted]: #27
-[mp #47 #101]: false
-unsat
-57af3178bd4bde4a26173de026e5de08dfc9faa6 78 0
-#2 := false
-#9 := 0::Int
-#8 := 1::Int
-#18 := (- 1::Int)
-#17 := (- 0::Int)
-#19 := (mod #17 #18)
-#20 := (- #19)
-#16 := (mod 0::Int 1::Int)
-#13 := (< 0::Int 1::Int)
-#12 := (< 0::Int 0::Int)
-#14 := (and #12 #13)
-#15 := (or #14 #14)
-#21 := (ite #15 #16 #20)
-#11 := (= 0::Int 0::Int)
-#22 := (ite #11 0::Int #21)
-#10 := (= 1::Int 0::Int)
-#23 := (ite #10 0::Int #22)
-#24 := (= #23 0::Int)
-#25 := (not #24)
-#99 := (iff #25 false)
-#1 := true
-#94 := (not true)
-#97 := (iff #94 false)
-#98 := [rewrite]: #97
-#95 := (iff #25 #94)
-#92 := (iff #24 true)
-#48 := (iff #11 true)
-#49 := [rewrite]: #48
-#90 := (iff #24 #11)
-#84 := (ite false 0::Int 0::Int)
-#87 := (= #84 0::Int)
-#88 := [rewrite]: #87
-#85 := (= #23 #84)
-#82 := (= #22 0::Int)
-#77 := (ite true 0::Int 0::Int)
-#80 := (= #77 0::Int)
-#81 := [rewrite]: #80
-#78 := (= #22 #77)
-#75 := (= #21 0::Int)
-#70 := (ite #14 0::Int 0::Int)
-#73 := (= #70 0::Int)
+#87 := -1::Int
+#91 := (* -1::Int #13)
+#88 := (* -1::Int #12)
+#152 := (mod #88 #91)
+#267 := (+ #32 #152)
+#268 := (= #267 0::Int)
+#33 := (mod #12 #13)
+#264 := (* -1::Int #33)
+#265 := (+ #32 #264)
+#266 := (= #265 0::Int)
+#126 := (>= #12 0::Int)
+#119 := (<= #13 0::Int)
+#211 := (or #119 #126)
+#212 := (not #211)
+#115 := (<= #12 0::Int)
+#209 := (or #115 #119)
+#210 := (not #209)
+#215 := (or #210 #212)
+#269 := (ite #215 #266 #268)
+#263 := (= #32 0::Int)
+#15 := (= #12 0::Int)
+#270 := (ite #15 #263 #269)
+#262 := (= #12 #32)
+#16 := (= #13 0::Int)
+#271 := (ite #16 #262 #270)
+#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271)
+#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
+#760 := (iff #274 #757)
+#758 := (iff #271 #271)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#158 := (* -1::Int #152)
+#231 := (ite #215 #33 #158)
+#234 := (ite #15 0::Int #231)
+#237 := (ite #16 #12 #234)
+#240 := (= #32 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#275 := (iff #243 #274)
+#272 := (iff #240 #271)
+#273 := [rewrite]: #272
+#276 := [quant-intro #273]: #275
+#127 := (not #126)
+#120 := (not #119)
+#130 := (and #120 #127)
+#116 := (not #115)
+#123 := (and #116 #120)
+#133 := (or #123 #130)
+#178 := (ite #133 #33 #158)
+#181 := (ite #15 0::Int #178)
+#184 := (ite #16 #12 #181)
+#187 := (= #32 #184)
+#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
+#244 := (iff #190 #243)
+#241 := (iff #187 #240)
+#238 := (= #184 #237)
+#235 := (= #181 #234)
+#232 := (= #178 #231)
+#216 := (iff #133 #215)
+#213 := (iff #130 #212)
+#214 := [rewrite]: #213
+#203 := (iff #123 #210)
+#204 := [rewrite]: #203
+#217 := [monotonicity #204 #214]: #216
+#233 := [monotonicity #217]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
+#201 := (~ #190 #190)
+#200 := (~ #187 #187)
+#197 := [refl]: #200
+#202 := [nnf-pos #197]: #201
+#26 := (- #13)
+#25 := (- #12)
+#34 := (mod #25 #26)
+#35 := (- #34)
+#19 := (< 0::Int #13)
+#21 := (< #12 0::Int)
+#22 := (and #21 #19)
+#18 := (< 0::Int #12)
+#20 := (and #18 #19)
+#23 := (or #20 #22)
+#36 := (ite #23 #33 #35)
+#37 := (ite #15 0::Int #36)
+#38 := (ite #16 #12 #37)
+#39 := (= #32 #38)
+#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
+#193 := (iff #40 #190)
+#81 := (and #19 #21)
+#84 := (or #20 #81)
+#163 := (ite #84 #33 #158)
+#72 := (= 0::Int #12)
+#166 := (ite #72 0::Int #163)
+#75 := (= 0::Int #13)
+#169 := (ite #75 #12 #166)
+#172 := (= #32 #169)
+#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
+#191 := (iff #175 #190)
+#188 := (iff #172 #187)
+#185 := (= #169 #184)
+#182 := (= #166 #181)
+#179 := (= #163 #178)
+#134 := (iff #84 #133)
+#131 := (iff #81 #130)
+#128 := (iff #21 #127)
+#129 := [rewrite]: #128
+#121 := (iff #19 #120)
+#122 := [rewrite]: #121
+#132 := [monotonicity #122 #129]: #131
+#124 := (iff #20 #123)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#125 := [monotonicity #118 #122]: #124
+#135 := [monotonicity #125 #132]: #134
+#180 := [monotonicity #135]: #179
+#109 := (iff #72 #15)
+#110 := [rewrite]: #109
+#183 := [monotonicity #110 #180]: #182
+#111 := (iff #75 #16)
+#112 := [rewrite]: #111
+#186 := [monotonicity #112 #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [quant-intro #189]: #191
+#176 := (iff #40 #175)
+#173 := (iff #39 #172)
+#170 := (= #38 #169)
+#167 := (= #37 #166)
+#164 := (= #36 #163)
+#161 := (= #35 #158)
+#155 := (- #152)
+#159 := (= #155 #158)
+#160 := [rewrite]: #159
+#156 := (= #35 #155)
+#153 := (= #34 #152)
+#92 := (= #26 #91)
+#93 := [rewrite]: #92
+#89 := (= #25 #88)
+#90 := [rewrite]: #89
+#154 := [monotonicity #90 #93]: #153
+#157 := [monotonicity #154]: #156
+#162 := [trans #157 #160]: #161
+#85 := (iff #23 #84)
+#82 := (iff #22 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#165 := [monotonicity #86 #162]: #164
+#73 := (iff #15 #72)
#74 := [rewrite]: #73
-#71 := (= #21 #70)
-#68 := (= #20 0::Int)
-#54 := (= #17 0::Int)
-#55 := [rewrite]: #54
-#66 := (= #20 #17)
-#64 := (= #19 0::Int)
-#56 := -1::Int
-#59 := (mod 0::Int -1::Int)
-#62 := (= #59 0::Int)
-#63 := [rewrite]: #62
-#60 := (= #19 #59)
-#57 := (= #18 -1::Int)
-#58 := [rewrite]: #57
-#61 := [monotonicity #55 #58]: #60
-#65 := [trans #61 #63]: #64
-#67 := [monotonicity #65]: #66
-#69 := [trans #67 #55]: #68
-#52 := (= #16 0::Int)
-#53 := [rewrite]: #52
-#50 := (iff #15 #14)
-#51 := [rewrite]: #50
-#72 := [monotonicity #51 #53 #69]: #71
-#76 := [trans #72 #74]: #75
-#79 := [monotonicity #49 #76]: #78
-#83 := [trans #79 #81]: #82
-#46 := (iff #10 false)
-#47 := [rewrite]: #46
-#86 := [monotonicity #47 #83]: #85
-#89 := [trans #86 #88]: #24
-#91 := [monotonicity #89]: #90
-#93 := [trans #91 #49]: #92
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#45 := [asserted]: #25
-[mp #45 #100]: false
-unsat
-1f0751610d262907ec6f1f51ed51a6cd0992f6da 85 0
-#2 := false
-#9 := 0::Int
-#8 := 1::Int
-#17 := (- 1::Int)
-#18 := (mod #17 #17)
-#19 := (- #18)
-#16 := (mod 1::Int 1::Int)
-#11 := (< 0::Int 1::Int)
-#13 := (< 1::Int 0::Int)
-#14 := (and #13 #11)
-#12 := (and #11 #11)
-#15 := (or #12 #14)
-#20 := (ite #15 #16 #19)
-#10 := (= 1::Int 0::Int)
-#21 := (ite #10 0::Int #20)
-#22 := (ite #10 1::Int #21)
-#23 := (= #22 0::Int)
-#24 := (not #23)
-#106 := (iff #24 false)
-#1 := true
-#101 := (not true)
-#104 := (iff #101 false)
-#105 := [rewrite]: #104
-#102 := (iff #24 #101)
-#99 := (iff #23 true)
-#94 := (= 0::Int 0::Int)
-#97 := (iff #94 true)
-#98 := [rewrite]: #97
-#95 := (iff #23 #94)
-#88 := (ite false 1::Int 0::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #22 #88)
-#86 := (= #21 0::Int)
-#81 := (ite false 0::Int 0::Int)
-#84 := (= #81 0::Int)
-#85 := [rewrite]: #84
-#82 := (= #21 #81)
-#79 := (= #20 0::Int)
-#49 := (and #11 #13)
-#52 := (or #11 #49)
-#74 := (ite #52 0::Int 0::Int)
-#77 := (= #74 0::Int)
-#78 := [rewrite]: #77
-#75 := (= #20 #74)
-#72 := (= #19 0::Int)
-#67 := (- 0::Int)
-#70 := (= #67 0::Int)
-#71 := [rewrite]: #70
-#68 := (= #19 #67)
-#65 := (= #18 0::Int)
-#57 := -1::Int
-#60 := (mod -1::Int -1::Int)
-#63 := (= #60 0::Int)
-#64 := [rewrite]: #63
-#61 := (= #18 #60)
-#58 := (= #17 -1::Int)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59 #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#55 := (= #16 0::Int)
-#56 := [rewrite]: #55
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#47 := (iff #12 #11)
-#48 := [rewrite]: #47
-#54 := [monotonicity #48 #51]: #53
-#76 := [monotonicity #54 #56 #73]: #75
-#80 := [trans #76 #78]: #79
-#45 := (iff #10 false)
-#46 := [rewrite]: #45
-#83 := [monotonicity #46 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #46 #87]: #89
-#93 := [trans #90 #92]: #23
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#44 := [asserted]: #24
-[mp #44 #107]: false
-unsat
-da01481f3f884bcc8fb68943f21adbedb119b252 92 0
-#2 := false
+#168 := [monotonicity #74 #165]: #167
+#76 := (iff #16 #75)
+#77 := [rewrite]: #76
+#171 := [monotonicity #77 #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [quant-intro #174]: #176
+#194 := [trans #177 #192]: #193
+#151 := [asserted]: #40
+#195 := [mp #151 #194]: #190
+#198 := [mp~ #195 #202]: #190
+#246 := [mp #198 #245]: #243
+#277 := [mp #246 #276]: #274
+#762 := [mp #277 #761]: #757
+#9 := (f3 0::Int 0::Int)
+#10 := (= #9 0::Int)
+#11 := (not #10)
+#60 := [asserted]: #11
+#703 := (not #757)
+#709 := (or #703 #10)
+#335 := (* -1::Int 0::Int)
+#420 := (mod #335 #335)
+#421 := (+ #9 #420)
+#422 := (= #421 0::Int)
+#413 := (mod 0::Int 0::Int)
+#424 := (* -1::Int #413)
+#425 := (+ #9 #424)
+#353 := (= #425 0::Int)
+#426 := (>= 0::Int 0::Int)
+#423 := (<= 0::Int 0::Int)
+#427 := (or #423 #426)
+#406 := (not #427)
+#741 := (or #423 #423)
+#743 := (not #741)
+#400 := (or #743 #406)
+#530 := (ite #400 #353 #422)
+#737 := (= 0::Int 0::Int)
+#411 := (ite #737 #10 #530)
+#61 := (= 0::Int #9)
+#412 := (ite #737 #61 #411)
+#550 := (or #703 #412)
+#552 := (iff #550 #709)
+#695 := (iff #709 #709)
+#696 := [rewrite]: #695
+#707 := (iff #412 #10)
+#1 := true
+#704 := (ite true #10 #10)
+#701 := (iff #704 #10)
+#702 := [rewrite]: #701
+#705 := (iff #412 #704)
+#711 := (iff #411 #10)
+#341 := (+ #9 #413)
+#441 := (= #341 0::Int)
+#712 := (ite true #10 #441)
+#710 := (iff #712 #10)
+#714 := [rewrite]: #710
+#713 := (iff #411 #712)
+#433 := (iff #530 #441)
+#720 := (ite false #353 #441)
+#431 := (iff #720 #441)
+#432 := [rewrite]: #431
+#717 := (iff #530 #720)
+#442 := (iff #422 #441)
+#718 := (= #421 #341)
+#447 := (= #420 #413)
+#445 := (= #335 0::Int)
+#446 := [rewrite]: #445
+#448 := [monotonicity #446 #446]: #447
+#719 := [monotonicity #448]: #718
+#716 := [monotonicity #719]: #442
+#722 := (iff #400 false)
+#374 := (or false false)
+#733 := (iff #374 false)
+#736 := [rewrite]: #733
+#375 := (iff #400 #374)
+#732 := (iff #406 false)
+#740 := (not true)
+#387 := (iff #740 false)
+#388 := [rewrite]: #387
+#731 := (iff #406 #740)
+#730 := (iff #427 true)
+#742 := (or true true)
+#398 := (iff #742 true)
+#403 := [rewrite]: #398
+#728 := (iff #427 #742)
+#726 := (iff #426 true)
+#727 := [rewrite]: #726
+#746 := (iff #423 true)
+#747 := [rewrite]: #746
+#729 := [monotonicity #747 #727]: #728
+#725 := [trans #729 #403]: #730
+#369 := [monotonicity #725]: #731
+#734 := [trans #369 #388]: #732
+#389 := (iff #743 false)
+#383 := (iff #743 #740)
+#739 := (iff #741 true)
+#748 := (iff #741 #742)
+#738 := [monotonicity #747 #747]: #748
+#399 := [trans #738 #403]: #739
+#724 := [monotonicity #399]: #383
+#390 := [trans #724 #388]: #389
+#735 := [monotonicity #390 #734]: #375
+#723 := [trans #735 #736]: #722
+#721 := [monotonicity #723 #716]: #717
+#434 := [trans #721 #432]: #433
+#744 := (iff #737 true)
+#745 := [rewrite]: #744
+#428 := [monotonicity #745 #434]: #713
+#715 := [trans #428 #714]: #711
+#67 := (iff #61 #10)
+#68 := [rewrite]: #67
+#706 := [monotonicity #745 #68 #715]: #705
+#708 := [trans #706 #702]: #707
+#694 := [monotonicity #708]: #552
+#697 := [trans #694 #696]: #552
+#551 := [quant-inst #8 #8]: #550
+#691 := [mp #551 #697]: #709
+[unit-resolution #691 #60 #762]: false
+unsat
+ea8997dddba0ea4cee2a7011c7fb001434f88f23 281 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#33 := (f3 #13 #14)
+#754 := (pattern #33)
#9 := 0::Int
+#85 := -1::Int
+#89 := (* -1::Int #14)
+#86 := (* -1::Int #13)
+#150 := (mod #86 #89)
+#265 := (+ #33 #150)
+#266 := (= #265 0::Int)
+#34 := (mod #13 #14)
+#262 := (* -1::Int #34)
+#263 := (+ #33 #262)
+#264 := (= #263 0::Int)
+#124 := (>= #13 0::Int)
+#117 := (<= #14 0::Int)
+#209 := (or #117 #124)
+#210 := (not #209)
+#113 := (<= #13 0::Int)
+#207 := (or #113 #117)
+#208 := (not #207)
+#213 := (or #208 #210)
+#267 := (ite #213 #264 #266)
+#261 := (= #33 0::Int)
+#16 := (= #13 0::Int)
+#268 := (ite #16 #261 #267)
+#260 := (= #13 #33)
+#17 := (= #14 0::Int)
+#269 := (ite #17 #260 #268)
+#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #269)
+#272 := (forall (vars (?v0 Int) (?v1 Int)) #269)
+#758 := (iff #272 #755)
+#756 := (iff #269 #269)
+#757 := [refl]: #756
+#759 := [quant-intro #757]: #758
+#156 := (* -1::Int #150)
+#229 := (ite #213 #34 #156)
+#232 := (ite #16 0::Int #229)
+#235 := (ite #17 #13 #232)
+#238 := (= #33 #235)
+#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
+#273 := (iff #241 #272)
+#270 := (iff #238 #269)
+#271 := [rewrite]: #270
+#274 := [quant-intro #271]: #273
+#125 := (not #124)
+#118 := (not #117)
+#128 := (and #118 #125)
+#114 := (not #113)
+#121 := (and #114 #118)
+#131 := (or #121 #128)
+#176 := (ite #131 #34 #156)
+#179 := (ite #16 0::Int #176)
+#182 := (ite #17 #13 #179)
+#185 := (= #33 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#242 := (iff #188 #241)
+#239 := (iff #185 #238)
+#236 := (= #182 #235)
+#233 := (= #179 #232)
+#230 := (= #176 #229)
+#214 := (iff #131 #213)
+#211 := (iff #128 #210)
+#212 := [rewrite]: #211
+#201 := (iff #121 #208)
+#202 := [rewrite]: #201
+#215 := [monotonicity #202 #212]: #214
+#231 := [monotonicity #215]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [quant-intro #240]: #242
+#199 := (~ #188 #188)
+#198 := (~ #185 #185)
+#195 := [refl]: #198
+#200 := [nnf-pos #195]: #199
+#27 := (- #14)
+#26 := (- #13)
+#35 := (mod #26 #27)
+#36 := (- #35)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#37 := (ite #24 #34 #36)
+#38 := (ite #16 0::Int #37)
+#39 := (ite #17 #13 #38)
+#40 := (= #33 #39)
+#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
+#191 := (iff #41 #188)
+#79 := (and #20 #22)
+#82 := (or #21 #79)
+#161 := (ite #82 #34 #156)
+#69 := (= 0::Int #13)
+#164 := (ite #69 0::Int #161)
+#73 := (= 0::Int #14)
+#167 := (ite #73 #13 #164)
+#170 := (= #33 #167)
+#173 := (forall (vars (?v0 Int) (?v1 Int)) #170)
+#189 := (iff #173 #188)
+#186 := (iff #170 #185)
+#183 := (= #167 #182)
+#180 := (= #164 #179)
+#177 := (= #161 #176)
+#132 := (iff #82 #131)
+#129 := (iff #79 #128)
+#126 := (iff #22 #125)
+#127 := [rewrite]: #126
+#119 := (iff #20 #118)
+#120 := [rewrite]: #119
+#130 := [monotonicity #120 #127]: #129
+#122 := (iff #21 #121)
+#115 := (iff #19 #114)
+#116 := [rewrite]: #115
+#123 := [monotonicity #116 #120]: #122
+#133 := [monotonicity #123 #130]: #132
+#178 := [monotonicity #133]: #177
+#107 := (iff #69 #16)
+#108 := [rewrite]: #107
+#181 := [monotonicity #108 #178]: #180
+#109 := (iff #73 #17)
+#110 := [rewrite]: #109
+#184 := [monotonicity #110 #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
+#174 := (iff #41 #173)
+#171 := (iff #40 #170)
+#168 := (= #39 #167)
+#165 := (= #38 #164)
+#162 := (= #37 #161)
+#159 := (= #36 #156)
+#153 := (- #150)
+#157 := (= #153 #156)
+#158 := [rewrite]: #157
+#154 := (= #36 #153)
+#151 := (= #35 #150)
+#90 := (= #27 #89)
+#91 := [rewrite]: #90
+#87 := (= #26 #86)
+#88 := [rewrite]: #87
+#152 := [monotonicity #88 #91]: #151
+#155 := [monotonicity #152]: #154
+#160 := [trans #155 #158]: #159
+#83 := (iff #24 #82)
+#80 := (iff #23 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#163 := [monotonicity #84 #160]: #162
+#71 := (iff #16 #69)
+#72 := [rewrite]: #71
+#166 := [monotonicity #72 #163]: #165
+#74 := (iff #17 #73)
+#75 := [rewrite]: #74
+#169 := [monotonicity #75 #166]: #168
+#172 := [monotonicity #169]: #171
+#175 := [quant-intro #172]: #174
+#192 := [trans #175 #190]: #191
+#149 := [asserted]: #41
+#193 := [mp #149 #192]: #188
+#196 := [mp~ #193 #200]: #188
+#244 := [mp #196 #243]: #241
+#275 := [mp #244 #274]: #272
+#760 := [mp #275 #759]: #755
+decl f4 :: Int
+#8 := f4
+#10 := (f3 f4 0::Int)
+#62 := (= f4 #10)
+#65 := (not #62)
+#11 := (= #10 f4)
+#12 := (not #11)
+#66 := (iff #12 #65)
+#63 := (iff #11 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#61 := [asserted]: #12
+#70 := [mp #61 #67]: #65
+#548 := (not #755)
+#549 := (or #548 #62)
+#333 := (* -1::Int 0::Int)
+#418 := (* -1::Int f4)
+#419 := (mod #418 #333)
+#420 := (+ #10 #419)
+#411 := (= #420 0::Int)
+#422 := (mod f4 0::Int)
+#423 := (* -1::Int #422)
+#351 := (+ #10 #423)
+#424 := (= #351 0::Int)
+#421 := (>= f4 0::Int)
+#425 := (<= 0::Int 0::Int)
+#404 := (or #425 #421)
+#739 := (not #404)
+#741 := (<= f4 0::Int)
+#398 := (or #741 #425)
+#528 := (not #398)
+#735 := (or #528 #739)
+#409 := (ite #735 #424 #411)
+#410 := (= #10 0::Int)
+#742 := (= f4 0::Int)
+#743 := (ite #742 #410 #409)
+#744 := (= 0::Int 0::Int)
+#745 := (ite #744 #62 #743)
+#550 := (or #548 #745)
+#693 := (iff #550 #549)
+#695 := (iff #549 #549)
+#689 := [rewrite]: #695
+#701 := (iff #745 #62)
+#439 := (mod #418 0::Int)
+#718 := (+ #10 #439)
+#429 := (= #718 0::Int)
+#713 := (ite #742 #410 #429)
+#1 := true
+#704 := (ite true #62 #713)
+#705 := (iff #704 #62)
+#706 := [rewrite]: #705
+#699 := (iff #745 #704)
+#702 := (iff #743 #713)
+#712 := (iff #409 #429)
+#432 := (ite false #424 #429)
+#426 := (iff #432 #429)
+#708 := [rewrite]: #426
+#710 := (iff #409 #432)
+#430 := (iff #411 #429)
+#715 := (= #420 #718)
+#440 := (= #419 #439)
+#716 := (= #333 0::Int)
+#717 := [rewrite]: #716
+#714 := [monotonicity #717]: #440
+#719 := [monotonicity #714]: #715
+#431 := [monotonicity #719]: #430
+#446 := (iff #735 false)
+#720 := (or false false)
+#444 := (iff #720 false)
+#445 := [rewrite]: #444
+#721 := (iff #735 #720)
+#731 := (iff #739 false)
+#386 := (not true)
+#724 := (iff #386 false)
+#725 := [rewrite]: #724
+#373 := (iff #739 #386)
+#732 := (iff #404 true)
+#728 := (or true #421)
+#367 := (iff #728 true)
+#730 := [rewrite]: #367
+#723 := (iff #404 #728)
+#736 := (iff #425 true)
+#396 := [rewrite]: #736
+#729 := [monotonicity #396]: #723
+#372 := [trans #729 #730]: #732
+#733 := [monotonicity #372]: #373
+#734 := [trans #733 #725]: #731
+#726 := (iff #528 false)
+#387 := (iff #528 #386)
+#722 := (iff #398 true)
+#401 := (or #741 true)
+#738 := (iff #401 true)
+#381 := [rewrite]: #738
+#737 := (iff #398 #401)
+#397 := [monotonicity #396]: #737
+#385 := [trans #397 #381]: #722
+#388 := [monotonicity #385]: #387
+#727 := [trans #388 #725]: #726
+#443 := [monotonicity #727 #734]: #721
+#339 := [trans #443 #445]: #446
+#711 := [monotonicity #339 #431]: #710
+#709 := [trans #711 #708]: #712
+#703 := [monotonicity #709]: #702
+#740 := (iff #744 true)
+#746 := [rewrite]: #740
+#700 := [monotonicity #746 #703]: #699
+#707 := [trans #700 #706]: #701
+#694 := [monotonicity #707]: #693
+#690 := [trans #694 #689]: #693
+#692 := [quant-inst #8 #9]: #550
+#696 := [mp #692 #690]: #549
+[unit-resolution #696 #70 #760]: false
+unsat
+b2456294470b5bb8cf71e8629c4adcc89dacf753 303 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#33 := (f3 #13 #14)
+#756 := (pattern #33)
+#8 := 0::Int
+#88 := -1::Int
+#92 := (* -1::Int #14)
+#89 := (* -1::Int #13)
+#153 := (mod #89 #92)
+#268 := (+ #33 #153)
+#269 := (= #268 0::Int)
+#34 := (mod #13 #14)
+#265 := (* -1::Int #34)
+#266 := (+ #33 #265)
+#267 := (= #266 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#270 := (ite #216 #267 #269)
+#264 := (= #33 0::Int)
+#16 := (= #13 0::Int)
+#271 := (ite #16 #264 #270)
+#263 := (= #13 #33)
+#17 := (= #14 0::Int)
+#272 := (ite #17 #263 #271)
+#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #272)
+#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
+#760 := (iff #275 #757)
+#758 := (iff #272 #272)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#159 := (* -1::Int #153)
+#232 := (ite #216 #34 #159)
+#235 := (ite #16 0::Int #232)
+#238 := (ite #17 #13 #235)
+#241 := (= #33 #238)
+#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
+#276 := (iff #244 #275)
+#273 := (iff #241 #272)
+#274 := [rewrite]: #273
+#277 := [quant-intro #274]: #276
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#179 := (ite #134 #34 #159)
+#182 := (ite #16 0::Int #179)
+#185 := (ite #17 #13 #182)
+#188 := (= #33 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#245 := (iff #191 #244)
+#242 := (iff #188 #241)
+#239 := (= #185 #238)
+#236 := (= #182 #235)
+#233 := (= #179 #232)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#234 := [monotonicity #218]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [quant-intro #243]: #245
+#202 := (~ #191 #191)
+#201 := (~ #188 #188)
+#198 := [refl]: #201
+#203 := [nnf-pos #198]: #202
+#27 := (- #14)
+#26 := (- #13)
+#35 := (mod #26 #27)
+#36 := (- #35)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#37 := (ite #24 #34 #36)
+#38 := (ite #16 0::Int #37)
+#39 := (ite #17 #13 #38)
+#40 := (= #33 #39)
+#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
+#194 := (iff #41 #191)
+#82 := (and #20 #22)
+#85 := (or #21 #82)
+#164 := (ite #85 #34 #159)
+#73 := (= 0::Int #13)
+#167 := (ite #73 0::Int #164)
+#76 := (= 0::Int #14)
+#170 := (ite #76 #13 #167)
+#173 := (= #33 #170)
+#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
+#192 := (iff #176 #191)
+#189 := (iff #173 #188)
+#186 := (= #170 #185)
+#183 := (= #167 #182)
+#180 := (= #164 #179)
+#135 := (iff #85 #134)
+#132 := (iff #82 #131)
+#129 := (iff #22 #128)
+#130 := [rewrite]: #129
+#122 := (iff #20 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #21 #124)
+#118 := (iff #19 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#181 := [monotonicity #136]: #180
+#110 := (iff #73 #16)
+#111 := [rewrite]: #110
+#184 := [monotonicity #111 #181]: #183
+#112 := (iff #76 #17)
+#113 := [rewrite]: #112
+#187 := [monotonicity #113 #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
+#177 := (iff #41 #176)
+#174 := (iff #40 #173)
+#171 := (= #39 #170)
+#168 := (= #38 #167)
+#165 := (= #37 #164)
+#162 := (= #36 #159)
+#156 := (- #153)
+#160 := (= #156 #159)
+#161 := [rewrite]: #160
+#157 := (= #36 #156)
+#154 := (= #35 #153)
+#93 := (= #27 #92)
+#94 := [rewrite]: #93
+#90 := (= #26 #89)
+#91 := [rewrite]: #90
+#155 := [monotonicity #91 #94]: #154
+#158 := [monotonicity #155]: #157
+#163 := [trans #158 #161]: #162
+#86 := (iff #24 #85)
+#83 := (iff #23 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#166 := [monotonicity #87 #163]: #165
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#169 := [monotonicity #75 #166]: #168
+#77 := (iff #17 #76)
+#78 := [rewrite]: #77
+#172 := [monotonicity #78 #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [quant-intro #175]: #177
+#195 := [trans #178 #193]: #194
+#152 := [asserted]: #41
+#196 := [mp #152 #195]: #191
+#199 := [mp~ #196 #203]: #191
+#247 := [mp #199 #246]: #244
+#278 := [mp #247 #277]: #275
+#762 := [mp #278 #761]: #757
+#9 := 1::Int
+#10 := (f3 0::Int 1::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#678 := (not #757)
+#679 := (or #678 #11)
+#336 := (* -1::Int 1::Int)
+#420 := (* -1::Int 0::Int)
+#421 := (mod #420 #336)
+#422 := (+ #10 #421)
+#413 := (= #422 0::Int)
+#424 := (mod 0::Int 1::Int)
+#425 := (* -1::Int #424)
+#426 := (+ #10 #425)
+#423 := (= #426 0::Int)
+#427 := (>= 0::Int 0::Int)
+#406 := (<= 1::Int 0::Int)
+#741 := (or #406 #427)
+#743 := (not #741)
+#400 := (<= 0::Int 0::Int)
+#530 := (or #400 #406)
+#737 := (not #530)
+#411 := (or #737 #743)
+#412 := (ite #411 #423 #413)
+#744 := (= 0::Int 0::Int)
+#745 := (ite #744 #11 #412)
+#62 := (= 0::Int #10)
+#746 := (= 1::Int 0::Int)
+#747 := (ite #746 #62 #745)
+#682 := (or #678 #747)
+#582 := (iff #682 #679)
+#585 := (iff #679 #679)
+#578 := [rewrite]: #585
+#681 := (iff #747 #11)
+#699 := (ite false #11 #11)
+#529 := (iff #699 #11)
+#531 := [rewrite]: #529
+#574 := (iff #747 #699)
+#572 := (iff #745 #11)
+#1 := true
+#686 := (ite true #11 #11)
+#687 := (iff #686 #11)
+#690 := [rewrite]: #687
+#688 := (iff #745 #686)
+#532 := (iff #412 #11)
+#693 := (iff #412 #699)
+#692 := (iff #413 #11)
+#697 := (= #422 #10)
+#428 := (+ #10 0::Int)
+#711 := (= #428 #10)
+#715 := [rewrite]: #711
+#695 := (= #422 #428)
+#552 := (= #421 0::Int)
+#708 := (mod 0::Int -1::Int)
+#550 := (= #708 0::Int)
+#551 := [rewrite]: #550
+#703 := (= #421 #708)
+#702 := (= #336 -1::Int)
+#707 := [rewrite]: #702
+#433 := (= #420 0::Int)
+#434 := [rewrite]: #433
+#709 := [monotonicity #434 #707]: #703
+#694 := [trans #709 #551]: #552
+#696 := [monotonicity #694]: #695
+#691 := [trans #696 #715]: #697
+#698 := [monotonicity #691]: #692
+#706 := (iff #423 #11)
+#704 := (= #426 #10)
+#710 := (= #426 #428)
+#712 := (= #425 0::Int)
+#431 := (= #425 #420)
+#717 := (= #424 0::Int)
+#721 := [rewrite]: #717
+#432 := [monotonicity #721]: #431
+#713 := [trans #432 #434]: #712
+#714 := [monotonicity #713]: #710
+#705 := [trans #714 #715]: #704
+#701 := [monotonicity #705]: #706
+#716 := (iff #411 false)
+#342 := (or false false)
+#441 := (iff #342 false)
+#442 := [rewrite]: #441
+#718 := (iff #411 #342)
+#447 := (iff #743 false)
+#727 := (not true)
+#730 := (iff #727 false)
+#725 := [rewrite]: #730
+#445 := (iff #743 #727)
+#722 := (iff #741 true)
+#374 := (or false true)
+#733 := (iff #374 true)
+#736 := [rewrite]: #733
+#375 := (iff #741 #374)
+#732 := (iff #427 true)
+#734 := [rewrite]: #732
+#399 := (iff #406 false)
+#740 := [rewrite]: #399
+#735 := [monotonicity #740 #734]: #375
+#723 := [trans #735 #736]: #722
+#446 := [monotonicity #723]: #445
+#448 := [trans #446 #725]: #447
+#731 := (iff #737 false)
+#728 := (iff #737 #727)
+#390 := (iff #530 true)
+#383 := (or true false)
+#388 := (iff #383 true)
+#389 := [rewrite]: #388
+#724 := (iff #530 #383)
+#403 := (iff #400 true)
+#739 := [rewrite]: #403
+#387 := [monotonicity #739 #740]: #724
+#726 := [trans #387 #389]: #390
+#729 := [monotonicity #726]: #728
+#369 := [trans #729 #725]: #731
+#719 := [monotonicity #369 #448]: #718
+#720 := [trans #719 #442]: #716
+#700 := [monotonicity #720 #701 #698]: #693
+#685 := [trans #700 #531]: #532
+#738 := (iff #744 true)
+#398 := [rewrite]: #738
+#689 := [monotonicity #398 #685]: #688
+#573 := [trans #689 #690]: #572
+#68 := (iff #62 #11)
+#69 := [rewrite]: #68
+#742 := (iff #746 false)
+#748 := [rewrite]: #742
+#533 := [monotonicity #748 #69 #573]: #574
+#583 := [trans #533 #531]: #681
+#584 := [monotonicity #583]: #582
+#586 := [trans #584 #578]: #582
+#567 := [quant-inst #8 #9]: #682
+#587 := [mp #567 #586]: #679
+[unit-resolution #587 #61 #762]: false
+unsat
+e9db2756594c83e73847951deaad9e2f60acdae2 304 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#33 := (f3 #13 #14)
+#746 := (pattern #33)
+#10 := 0::Int
+#78 := -1::Int
+#82 := (* -1::Int #14)
+#79 := (* -1::Int #13)
+#143 := (mod #79 #82)
+#258 := (+ #33 #143)
+#259 := (= #258 0::Int)
+#34 := (mod #13 #14)
+#255 := (* -1::Int #34)
+#256 := (+ #33 #255)
+#257 := (= #256 0::Int)
+#117 := (>= #13 0::Int)
+#110 := (<= #14 0::Int)
+#202 := (or #110 #117)
+#203 := (not #202)
+#106 := (<= #13 0::Int)
+#200 := (or #106 #110)
+#201 := (not #200)
+#206 := (or #201 #203)
+#260 := (ite #206 #257 #259)
+#254 := (= #33 0::Int)
+#16 := (= #13 0::Int)
+#261 := (ite #16 #254 #260)
+#253 := (= #13 #33)
+#17 := (= #14 0::Int)
+#262 := (ite #17 #253 #261)
+#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#750 := (iff #265 #747)
+#748 := (iff #262 #262)
+#749 := [refl]: #748
+#751 := [quant-intro #749]: #750
+#149 := (* -1::Int #143)
+#222 := (ite #206 #34 #149)
+#225 := (ite #16 0::Int #222)
+#228 := (ite #17 #13 #225)
+#231 := (= #33 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #34 #149)
+#172 := (ite #16 0::Int #169)
+#175 := (ite #17 #13 #172)
+#178 := (= #33 #175)
+#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
+#235 := (iff #181 #234)
+#232 := (iff #178 #231)
+#229 := (= #175 #228)
+#226 := (= #172 #225)
+#223 := (= #169 #222)
+#207 := (iff #124 #206)
+#204 := (iff #121 #203)
+#205 := [rewrite]: #204
+#194 := (iff #114 #201)
+#195 := [rewrite]: #194
+#208 := [monotonicity #195 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#192 := (~ #181 #181)
+#191 := (~ #178 #178)
+#188 := [refl]: #191
+#193 := [nnf-pos #188]: #192
+#27 := (- #14)
+#26 := (- #13)
+#35 := (mod #26 #27)
+#36 := (- #35)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#37 := (ite #24 #34 #36)
+#38 := (ite #16 0::Int #37)
+#39 := (ite #17 #13 #38)
+#40 := (= #33 #39)
+#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
+#184 := (iff #41 #181)
+#72 := (and #20 #22)
+#75 := (or #21 #72)
+#154 := (ite #75 #34 #149)
+#63 := (= 0::Int #13)
+#157 := (ite #63 0::Int #154)
+#66 := (= 0::Int #14)
+#160 := (ite #66 #13 #157)
+#163 := (= #33 #160)
+#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #75 #124)
+#122 := (iff #72 #121)
+#119 := (iff #22 #118)
+#120 := [rewrite]: #119
+#112 := (iff #20 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #21 #114)
+#108 := (iff #19 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#100 := (iff #63 #16)
+#101 := [rewrite]: #100
+#174 := [monotonicity #101 #171]: #173
+#102 := (iff #66 #17)
+#103 := [rewrite]: #102
+#177 := [monotonicity #103 #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #41 #166)
+#164 := (iff #40 #163)
+#161 := (= #39 #160)
+#158 := (= #38 #157)
+#155 := (= #37 #154)
+#152 := (= #36 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #36 #146)
+#144 := (= #35 #143)
+#83 := (= #27 #82)
+#84 := [rewrite]: #83
+#80 := (= #26 #79)
+#81 := [rewrite]: #80
+#145 := [monotonicity #81 #84]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#76 := (iff #24 #75)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#156 := [monotonicity #77 #153]: #155
+#64 := (iff #16 #63)
+#65 := [rewrite]: #64
+#159 := [monotonicity #65 #156]: #158
+#67 := (iff #17 #66)
+#68 := [rewrite]: #67
+#162 := [monotonicity #68 #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #41
+#186 := [mp #142 #185]: #181
+#189 := [mp~ #186 #193]: #181
+#237 := [mp #189 #236]: #234
+#268 := [mp #237 #267]: #265
+#752 := [mp #268 #751]: #747
#8 := 1::Int
-#21 := (- 1::Int)
-#11 := 3::Int
-#20 := (- 3::Int)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod 3::Int 1::Int)
-#14 := (< 0::Int 1::Int)
-#16 := (< 3::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 3::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= 3::Int 0::Int)
-#25 := (ite #12 0::Int #24)
-#10 := (= 1::Int 0::Int)
-#26 := (ite #10 3::Int #25)
-#27 := (= #26 0::Int)
-#28 := (not #27)
-#113 := (iff #28 false)
-#1 := true
-#108 := (not true)
-#111 := (iff #108 false)
-#112 := [rewrite]: #111
-#109 := (iff #28 #108)
-#106 := (iff #27 true)
-#101 := (= 0::Int 0::Int)
-#104 := (iff #101 true)
-#105 := [rewrite]: #104
-#102 := (iff #27 #101)
-#95 := (ite false 3::Int 0::Int)
-#98 := (= #95 0::Int)
-#99 := [rewrite]: #98
-#96 := (= #26 #95)
-#93 := (= #25 0::Int)
-#88 := (ite false 0::Int 0::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #25 #88)
-#86 := (= #24 0::Int)
-#53 := (and #14 #16)
-#56 := (or #15 #53)
-#81 := (ite #56 0::Int 0::Int)
-#84 := (= #81 0::Int)
+#9 := (f3 1::Int 1::Int)
+#11 := (= #9 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#572 := (not #747)
+#574 := (or #572 #11)
+#326 := (* -1::Int 1::Int)
+#410 := (mod #326 #326)
+#411 := (+ #9 #410)
+#412 := (= #411 0::Int)
+#403 := (mod 1::Int 1::Int)
+#414 := (* -1::Int #403)
+#415 := (+ #9 #414)
+#416 := (= #415 0::Int)
+#413 := (>= 1::Int 0::Int)
+#417 := (<= 1::Int 0::Int)
+#396 := (or #417 #413)
+#731 := (not #396)
+#733 := (or #417 #417)
+#390 := (not #733)
+#520 := (or #390 #731)
+#727 := (ite #520 #416 #412)
+#401 := (= 1::Int 0::Int)
+#402 := (ite #401 #11 #727)
+#734 := (= 1::Int #9)
+#735 := (ite #401 #734 #402)
+#575 := (or #572 #735)
+#576 := (iff #575 #574)
+#578 := (iff #574 #574)
+#579 := [rewrite]: #578
+#672 := (iff #735 #11)
+#738 := (= #9 1::Int)
+#523 := (ite false #738 #11)
+#668 := (iff #523 #11)
+#669 := [rewrite]: #668
+#671 := (iff #735 #523)
+#563 := (iff #402 #11)
+#678 := (ite false #11 #11)
+#680 := (iff #678 #11)
+#562 := [rewrite]: #680
+#679 := (iff #402 #678)
+#675 := (iff #727 #11)
+#1 := true
+#683 := (ite true #11 #11)
+#521 := (iff #683 #11)
+#522 := [rewrite]: #521
+#690 := (iff #727 #683)
+#688 := (iff #412 #11)
+#681 := (= #411 #9)
+#700 := (+ #9 0::Int)
+#705 := (= #700 #9)
+#694 := [rewrite]: #705
+#686 := (= #411 #700)
+#684 := (= #410 0::Int)
+#693 := (mod -1::Int -1::Int)
+#541 := (= #693 0::Int)
+#542 := [rewrite]: #541
+#699 := (= #410 #693)
+#697 := (= #326 -1::Int)
+#698 := [rewrite]: #697
+#540 := [monotonicity #698 #698]: #699
+#685 := [trans #540 #542]: #684
+#687 := [monotonicity #685]: #686
+#682 := [trans #687 #694]: #681
+#689 := [monotonicity #682]: #688
+#691 := (iff #416 #11)
+#695 := (= #415 #9)
+#704 := (= #415 #700)
+#703 := (= #414 0::Int)
+#421 := (* -1::Int 0::Int)
+#424 := (= #421 0::Int)
+#702 := [rewrite]: #424
+#422 := (= #414 #421)
+#707 := (= #403 0::Int)
+#711 := [rewrite]: #707
+#423 := [monotonicity #711]: #422
+#418 := [trans #423 #702]: #703
+#701 := [monotonicity #418]: #704
+#696 := [trans #701 #694]: #695
+#692 := [monotonicity #696]: #691
+#706 := (iff #520 true)
+#332 := (or true false)
+#431 := (iff #332 true)
+#432 := [rewrite]: #431
+#708 := (iff #520 #332)
+#437 := (iff #731 false)
+#726 := (not true)
+#435 := (iff #726 false)
+#436 := [rewrite]: #435
+#712 := (iff #731 #726)
+#725 := (iff #396 true)
+#359 := (or false true)
+#364 := (iff #359 true)
+#365 := [rewrite]: #364
+#722 := (iff #396 #359)
+#715 := (iff #413 true)
+#721 := [rewrite]: #715
+#388 := (iff #417 false)
+#393 := [rewrite]: #388
+#724 := [monotonicity #393 #721]: #722
+#723 := [trans #724 #365]: #725
+#713 := [monotonicity #723]: #712
+#438 := [trans #713 #436]: #437
+#719 := (iff #390 true)
+#379 := (not false)
+#717 := (iff #379 true)
+#718 := [rewrite]: #717
+#380 := (iff #390 #379)
+#377 := (iff #733 false)
+#729 := (or false false)
+#373 := (iff #729 false)
+#714 := [rewrite]: #373
+#389 := (iff #733 #729)
+#730 := [monotonicity #393 #393]: #389
+#378 := [trans #730 #714]: #377
+#716 := [monotonicity #378]: #380
+#720 := [trans #716 #718]: #719
+#709 := [monotonicity #720 #438]: #708
+#710 := [trans #709 #432]: #706
+#519 := [monotonicity #710 #692 #689]: #690
+#676 := [trans #519 #522]: #675
+#736 := (iff #401 false)
+#737 := [rewrite]: #736
+#677 := [monotonicity #737 #676]: #679
+#564 := [trans #677 #562]: #563
+#732 := (iff #734 #738)
+#728 := [rewrite]: #732
+#573 := [monotonicity #737 #728 #564]: #671
+#557 := [trans #573 #669]: #672
+#577 := [monotonicity #557]: #576
+#580 := [trans #577 #579]: #576
+#568 := [quant-inst #8 #8]: #575
+#673 := [mp #568 #580]: #574
+[unit-resolution #673 #61 #752]: false
+unsat
+5a27e28e4534905d80bae8170a2a6b87f8d4215e 315 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#747 := (pattern #34)
+#11 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #15)
+#80 := (* -1::Int #14)
+#144 := (mod #80 #83)
+#259 := (+ #34 #144)
+#260 := (= #259 0::Int)
+#35 := (mod #14 #15)
+#256 := (* -1::Int #35)
+#257 := (+ #34 #256)
+#258 := (= #257 0::Int)
+#118 := (>= #14 0::Int)
+#111 := (<= #15 0::Int)
+#203 := (or #111 #118)
+#204 := (not #203)
+#107 := (<= #14 0::Int)
+#201 := (or #107 #111)
+#202 := (not #201)
+#207 := (or #202 #204)
+#261 := (ite #207 #258 #260)
+#255 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#262 := (ite #17 #255 #261)
+#254 := (= #14 #34)
+#18 := (= #15 0::Int)
+#263 := (ite #18 #254 #262)
+#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#751 := (iff #266 #748)
+#749 := (iff #263 #263)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#150 := (* -1::Int #144)
+#223 := (ite #207 #35 #150)
+#226 := (ite #17 0::Int #223)
+#229 := (ite #18 #14 #226)
+#232 := (= #34 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#119 := (not #118)
+#112 := (not #111)
+#122 := (and #112 #119)
+#108 := (not #107)
+#115 := (and #108 #112)
+#125 := (or #115 #122)
+#170 := (ite #125 #35 #150)
+#173 := (ite #17 0::Int #170)
+#176 := (ite #18 #14 #173)
+#179 := (= #34 #176)
+#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
+#236 := (iff #182 #235)
+#233 := (iff #179 #232)
+#230 := (= #176 #229)
+#227 := (= #173 #226)
+#224 := (= #170 #223)
+#208 := (iff #125 #207)
+#205 := (iff #122 #204)
+#206 := [rewrite]: #205
+#195 := (iff #115 #202)
+#196 := [rewrite]: #195
+#209 := [monotonicity #196 #206]: #208
+#225 := [monotonicity #209]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#193 := (~ #182 #182)
+#192 := (~ #179 #179)
+#189 := [refl]: #192
+#194 := [nnf-pos #189]: #193
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#185 := (iff #42 #182)
+#73 := (and #21 #23)
+#76 := (or #22 #73)
+#155 := (ite #76 #35 #150)
+#64 := (= 0::Int #14)
+#158 := (ite #64 0::Int #155)
+#67 := (= 0::Int #15)
+#161 := (ite #67 #14 #158)
+#164 := (= #34 #161)
+#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
+#183 := (iff #167 #182)
+#180 := (iff #164 #179)
+#177 := (= #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#126 := (iff #76 #125)
+#123 := (iff #73 #122)
+#120 := (iff #23 #119)
+#121 := [rewrite]: #120
+#113 := (iff #21 #112)
+#114 := [rewrite]: #113
+#124 := [monotonicity #114 #121]: #123
+#116 := (iff #22 #115)
+#109 := (iff #20 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#127 := [monotonicity #117 #124]: #126
+#172 := [monotonicity #127]: #171
+#101 := (iff #64 #17)
+#102 := [rewrite]: #101
+#175 := [monotonicity #102 #172]: #174
+#103 := (iff #67 #18)
+#104 := [rewrite]: #103
+#178 := [monotonicity #104 #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [quant-intro #181]: #183
+#168 := (iff #42 #167)
+#165 := (iff #41 #164)
+#162 := (= #40 #161)
+#159 := (= #39 #158)
+#156 := (= #38 #155)
+#153 := (= #37 #150)
+#147 := (- #144)
+#151 := (= #147 #150)
+#152 := [rewrite]: #151
+#148 := (= #37 #147)
+#145 := (= #36 #144)
+#84 := (= #28 #83)
#85 := [rewrite]: #84
-#82 := (= #24 #81)
-#79 := (= #23 0::Int)
-#74 := (- 0::Int)
-#77 := (= #74 0::Int)
-#78 := [rewrite]: #77
-#75 := (= #23 #74)
-#72 := (= #22 0::Int)
-#64 := -1::Int
-#61 := -3::Int
-#67 := (mod -3::Int -1::Int)
-#70 := (= #67 0::Int)
-#71 := [rewrite]: #70
-#68 := (= #22 #67)
-#65 := (= #21 -1::Int)
+#81 := (= #27 #80)
+#82 := [rewrite]: #81
+#146 := [monotonicity #82 #85]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#77 := (iff #25 #76)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#157 := [monotonicity #78 #154]: #156
+#65 := (iff #17 #64)
#66 := [rewrite]: #65
-#62 := (= #20 -3::Int)
-#63 := [rewrite]: #62
-#69 := [monotonicity #63 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#59 := (= #19 0::Int)
-#60 := [rewrite]: #59
-#57 := (iff #18 #56)
-#54 := (iff #17 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#83 := [monotonicity #58 #60 #80]: #82
-#87 := [trans #83 #85]: #86
-#51 := (iff #12 false)
-#52 := [rewrite]: #51
-#90 := [monotonicity #52 #87]: #89
-#94 := [trans #90 #92]: #93
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#97 := [monotonicity #50 #94]: #96
-#100 := [trans #97 #99]: #27
+#160 := [monotonicity #66 #157]: #159
+#68 := (iff #18 #67)
+#69 := [rewrite]: #68
+#163 := [monotonicity #69 #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#186 := [trans #169 #184]: #185
+#143 := [asserted]: #42
+#187 := [mp #143 #186]: #182
+#190 := [mp~ #187 #194]: #182
+#238 := [mp #190 #237]: #235
+#269 := [mp #238 #268]: #266
+#753 := [mp #269 #752]: #748
+#9 := 1::Int
+#8 := 3::Int
+#10 := (f3 3::Int 1::Int)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#62 := [asserted]: #13
+#671 := (not #748)
+#675 := (or #671 #12)
+#327 := (* -1::Int 1::Int)
+#411 := (* -1::Int 3::Int)
+#412 := (mod #411 #327)
+#413 := (+ #10 #412)
+#404 := (= #413 0::Int)
+#415 := (mod 3::Int 1::Int)
+#416 := (* -1::Int #415)
+#417 := (+ #10 #416)
+#414 := (= #417 0::Int)
+#418 := (>= 3::Int 0::Int)
+#397 := (<= 1::Int 0::Int)
+#732 := (or #397 #418)
+#734 := (not #732)
+#391 := (<= 3::Int 0::Int)
+#521 := (or #391 #397)
+#728 := (not #521)
+#402 := (or #728 #734)
+#403 := (ite #402 #414 #404)
+#735 := (= 3::Int 0::Int)
+#736 := (ite #735 #12 #403)
+#737 := (= 3::Int #10)
+#738 := (= 1::Int 0::Int)
+#733 := (ite #738 #737 #736)
+#662 := (or #671 #733)
+#656 := (iff #662 #675)
+#655 := (iff #675 #675)
+#665 := [rewrite]: #655
+#581 := (iff #733 #12)
+#394 := (= #10 3::Int)
+#569 := (ite false #394 #12)
+#579 := (iff #569 #12)
+#580 := [rewrite]: #579
+#577 := (iff #733 #569)
+#575 := (iff #736 #12)
+#669 := (ite false #12 #12)
+#558 := (iff #669 #12)
+#573 := [rewrite]: #558
+#670 := (iff #736 #669)
+#672 := (iff #403 #12)
+#1 := true
+#681 := (ite true #12 #12)
+#565 := (iff #681 #12)
+#524 := [rewrite]: #565
+#563 := (iff #403 #681)
+#680 := (iff #404 #12)
+#677 := (= #413 #10)
+#692 := (+ #10 0::Int)
+#699 := (= #692 #10)
+#694 := [rewrite]: #699
+#523 := (= #413 #692)
+#520 := (= #412 0::Int)
+#685 := -3::Int
+#683 := (mod -3::Int -1::Int)
+#684 := (= #683 0::Int)
+#691 := [rewrite]: #684
+#689 := (= #412 #683)
+#688 := (= #327 -1::Int)
+#682 := [rewrite]: #688
+#686 := (= #411 -3::Int)
+#687 := [rewrite]: #686
+#690 := [monotonicity #687 #682]: #689
+#522 := [trans #690 #691]: #520
+#676 := [monotonicity #522]: #523
+#679 := [trans #676 #694]: #677
+#678 := [monotonicity #679]: #680
+#542 := (iff #414 #12)
+#700 := (= #417 #10)
+#693 := (= #417 #692)
+#696 := (= #416 0::Int)
+#701 := (* -1::Int 0::Int)
+#706 := (= #701 0::Int)
+#695 := [rewrite]: #706
+#705 := (= #416 #701)
+#704 := (= #415 0::Int)
+#419 := [rewrite]: #704
+#702 := [monotonicity #419]: #705
+#697 := [trans #702 #695]: #696
+#698 := [monotonicity #697]: #693
+#541 := [trans #698 #694]: #700
+#543 := [monotonicity #541]: #542
+#425 := (iff #402 true)
+#708 := (or true false)
+#423 := (iff #708 true)
+#424 := [rewrite]: #423
+#712 := (iff #402 #708)
+#707 := (iff #734 false)
+#333 := (not true)
+#432 := (iff #333 false)
+#433 := [rewrite]: #432
+#709 := (iff #734 #333)
+#438 := (iff #732 true)
+#727 := (or false true)
+#436 := (iff #727 true)
+#437 := [rewrite]: #436
+#713 := (iff #732 #727)
+#726 := (iff #418 true)
+#724 := [rewrite]: #726
+#378 := (iff #397 false)
+#379 := [rewrite]: #378
+#714 := [monotonicity #379 #724]: #713
+#439 := [trans #714 #437]: #438
+#710 := [monotonicity #439]: #709
+#711 := [trans #710 #433]: #707
+#365 := (iff #728 true)
+#716 := (not false)
+#723 := (iff #716 true)
+#725 := [rewrite]: #723
+#722 := (iff #728 #716)
+#720 := (iff #521 false)
+#380 := (or false false)
+#718 := (iff #380 false)
+#719 := [rewrite]: #718
+#381 := (iff #521 #380)
+#374 := (iff #391 false)
+#715 := [rewrite]: #374
+#717 := [monotonicity #715 #379]: #381
+#721 := [trans #717 #719]: #720
+#360 := [monotonicity #721]: #722
+#366 := [trans #360 #725]: #365
+#422 := [monotonicity #366 #711]: #712
+#703 := [trans #422 #424]: #425
+#564 := [monotonicity #703 #543 #678]: #563
+#574 := [trans #564 #524]: #672
+#390 := (iff #735 false)
+#731 := [rewrite]: #390
+#673 := [monotonicity #731 #574]: #670
+#576 := [trans #673 #573]: #575
+#389 := (iff #737 #394)
+#730 := [rewrite]: #389
+#739 := (iff #738 false)
+#729 := [rewrite]: #739
+#578 := [monotonicity #729 #730 #576]: #577
+#674 := [trans #578 #580]: #581
+#653 := [monotonicity #674]: #656
+#666 := [trans #653 #665]: #656
+#664 := [quant-inst #8 #9]: #662
+#667 := [mp #664 #666]: #675
+[unit-resolution #667 #62 #753]: false
+unsat
+1b99f23affb0dadf3316102e865176c5efc38d4f 313 0
+#2 := false
+#11 := 0::Int
+decl f4 :: Int
+#8 := f4
+#735 := (= f4 0::Int)
+#576 := (not #735)
+#418 := (>= f4 0::Int)
+#723 := (not #418)
+#391 := (<= f4 0::Int)
+#380 := (not #391)
+#691 := (or #380 #723 #735)
+#578 := (not #691)
+#79 := -1::Int
+#411 := (* -1::Int f4)
+#703 := (mod #411 -1::Int)
+decl f3 :: (-> Int Int Int)
+#9 := 1::Int
+#10 := (f3 f4 1::Int)
+#701 := (+ #10 #703)
+#706 := (= #701 0::Int)
+#12 := (= #10 0::Int)
+#523 := (ite #691 #12 #706)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#747 := (pattern #34)
+#83 := (* -1::Int #15)
+#80 := (* -1::Int #14)
+#144 := (mod #80 #83)
+#259 := (+ #34 #144)
+#260 := (= #259 0::Int)
+#35 := (mod #14 #15)
+#256 := (* -1::Int #35)
+#257 := (+ #34 #256)
+#258 := (= #257 0::Int)
+#118 := (>= #14 0::Int)
+#111 := (<= #15 0::Int)
+#203 := (or #111 #118)
+#204 := (not #203)
+#107 := (<= #14 0::Int)
+#201 := (or #107 #111)
+#202 := (not #201)
+#207 := (or #202 #204)
+#261 := (ite #207 #258 #260)
+#255 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#262 := (ite #17 #255 #261)
+#254 := (= #14 #34)
+#18 := (= #15 0::Int)
+#263 := (ite #18 #254 #262)
+#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#751 := (iff #266 #748)
+#749 := (iff #263 #263)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#150 := (* -1::Int #144)
+#223 := (ite #207 #35 #150)
+#226 := (ite #17 0::Int #223)
+#229 := (ite #18 #14 #226)
+#232 := (= #34 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#119 := (not #118)
+#112 := (not #111)
+#122 := (and #112 #119)
+#108 := (not #107)
+#115 := (and #108 #112)
+#125 := (or #115 #122)
+#170 := (ite #125 #35 #150)
+#173 := (ite #17 0::Int #170)
+#176 := (ite #18 #14 #173)
+#179 := (= #34 #176)
+#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
+#236 := (iff #182 #235)
+#233 := (iff #179 #232)
+#230 := (= #176 #229)
+#227 := (= #173 #226)
+#224 := (= #170 #223)
+#208 := (iff #125 #207)
+#205 := (iff #122 #204)
+#206 := [rewrite]: #205
+#195 := (iff #115 #202)
+#196 := [rewrite]: #195
+#209 := [monotonicity #196 #206]: #208
+#225 := [monotonicity #209]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#193 := (~ #182 #182)
+#192 := (~ #179 #179)
+#189 := [refl]: #192
+#194 := [nnf-pos #189]: #193
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#185 := (iff #42 #182)
+#73 := (and #21 #23)
+#76 := (or #22 #73)
+#155 := (ite #76 #35 #150)
+#64 := (= 0::Int #14)
+#158 := (ite #64 0::Int #155)
+#67 := (= 0::Int #15)
+#161 := (ite #67 #14 #158)
+#164 := (= #34 #161)
+#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
+#183 := (iff #167 #182)
+#180 := (iff #164 #179)
+#177 := (= #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#126 := (iff #76 #125)
+#123 := (iff #73 #122)
+#120 := (iff #23 #119)
+#121 := [rewrite]: #120
+#113 := (iff #21 #112)
+#114 := [rewrite]: #113
+#124 := [monotonicity #114 #121]: #123
+#116 := (iff #22 #115)
+#109 := (iff #20 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#127 := [monotonicity #117 #124]: #126
+#172 := [monotonicity #127]: #171
+#101 := (iff #64 #17)
+#102 := [rewrite]: #101
+#175 := [monotonicity #102 #172]: #174
+#103 := (iff #67 #18)
+#104 := [rewrite]: #103
+#178 := [monotonicity #104 #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [quant-intro #181]: #183
+#168 := (iff #42 #167)
+#165 := (iff #41 #164)
+#162 := (= #40 #161)
+#159 := (= #39 #158)
+#156 := (= #38 #155)
+#153 := (= #37 #150)
+#147 := (- #144)
+#151 := (= #147 #150)
+#152 := [rewrite]: #151
+#148 := (= #37 #147)
+#145 := (= #36 #144)
+#84 := (= #28 #83)
+#85 := [rewrite]: #84
+#81 := (= #27 #80)
+#82 := [rewrite]: #81
+#146 := [monotonicity #82 #85]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#77 := (iff #25 #76)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#157 := [monotonicity #78 #154]: #156
+#65 := (iff #17 #64)
+#66 := [rewrite]: #65
+#160 := [monotonicity #66 #157]: #159
+#68 := (iff #18 #67)
+#69 := [rewrite]: #68
+#163 := [monotonicity #69 #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#186 := [trans #169 #184]: #185
+#143 := [asserted]: #42
+#187 := [mp #143 #186]: #182
+#190 := [mp~ #187 #194]: #182
+#238 := [mp #190 #237]: #235
+#269 := [mp #238 #268]: #266
+#753 := [mp #269 #752]: #748
+#678 := (not #748)
+#681 := (or #678 #523)
+#327 := (* -1::Int 1::Int)
+#412 := (mod #411 #327)
+#413 := (+ #10 #412)
+#404 := (= #413 0::Int)
+#415 := (mod f4 1::Int)
+#416 := (* -1::Int #415)
+#417 := (+ #10 #416)
+#414 := (= #417 0::Int)
+#397 := (<= 1::Int 0::Int)
+#732 := (or #397 #418)
+#734 := (not #732)
+#521 := (or #391 #397)
+#728 := (not #521)
+#402 := (or #728 #734)
+#403 := (ite #402 #414 #404)
+#736 := (ite #735 #12 #403)
+#737 := (= f4 #10)
+#738 := (= 1::Int 0::Int)
+#733 := (ite #738 #737 #736)
+#563 := (or #678 #733)
+#565 := (iff #563 #681)
+#672 := (iff #681 #681)
+#574 := [rewrite]: #672
+#679 := (iff #733 #523)
+#366 := (or #380 #723)
+#700 := (or #366 #735)
+#541 := (ite #700 #12 #706)
+#676 := (iff #541 #523)
+#520 := (iff #700 #691)
+#522 := [rewrite]: #520
+#677 := [monotonicity #522]: #676
+#690 := (iff #733 #541)
+#687 := (ite false #737 #541)
+#683 := (iff #687 #541)
+#689 := [rewrite]: #683
+#688 := (iff #733 #687)
+#685 := (iff #736 #541)
+#697 := (ite #366 #12 #706)
+#698 := (ite #735 #12 #697)
+#542 := (iff #698 #541)
+#543 := [rewrite]: #542
+#699 := (iff #736 #698)
+#692 := (iff #403 #697)
+#695 := (iff #404 #706)
+#705 := (= #413 #701)
+#704 := (= #412 #703)
+#424 := (= #327 -1::Int)
+#425 := [rewrite]: #424
+#419 := [monotonicity #425]: #704
+#702 := [monotonicity #419]: #705
+#696 := [monotonicity #702]: #695
+#422 := (iff #414 #12)
+#708 := (= #417 #10)
+#710 := (+ #10 0::Int)
+#707 := (= #710 #10)
+#711 := [rewrite]: #707
+#432 := (= #417 #710)
+#333 := (= #416 0::Int)
+#714 := (* -1::Int 0::Int)
+#438 := (= #714 0::Int)
+#439 := [rewrite]: #438
+#436 := (= #416 #714)
+#727 := (= #415 0::Int)
+#713 := [rewrite]: #727
+#437 := [monotonicity #713]: #436
+#709 := [trans #437 #439]: #333
+#433 := [monotonicity #709]: #432
+#712 := [trans #433 #711]: #708
+#423 := [monotonicity #712]: #422
+#726 := (iff #402 #366)
+#725 := (iff #734 #723)
+#722 := (iff #732 #418)
+#718 := (or false #418)
+#721 := (iff #718 #418)
+#716 := [rewrite]: #721
+#719 := (iff #732 #718)
+#389 := (iff #397 false)
+#394 := [rewrite]: #389
+#720 := [monotonicity #394]: #719
+#360 := [trans #720 #716]: #722
+#365 := [monotonicity #360]: #725
+#381 := (iff #728 #380)
+#378 := (iff #521 #391)
+#730 := (or #391 false)
+#374 := (iff #730 #391)
+#715 := [rewrite]: #374
+#390 := (iff #521 #730)
+#731 := [monotonicity #394]: #390
+#379 := [trans #731 #715]: #378
+#717 := [monotonicity #379]: #381
+#724 := [monotonicity #717 #365]: #726
+#693 := [monotonicity #724 #423 #696]: #692
+#694 := [monotonicity #693]: #699
+#686 := [trans #694 #543]: #685
+#739 := (iff #738 false)
+#729 := [rewrite]: #739
+#682 := [monotonicity #729 #686]: #688
+#684 := [trans #682 #689]: #690
+#680 := [trans #684 #677]: #679
+#524 := [monotonicity #680]: #565
+#669 := [trans #524 #574]: #565
+#564 := [quant-inst #8 #9]: #563
+#670 := [mp #564 #669]: #681
+#663 := [unit-resolution #670 #753]: #523
+#671 := (not #523)
+#668 := (or #671 #578)
+#13 := (not #12)
+#62 := [asserted]: #13
+#675 := (or #671 #578 #12)
+#662 := [def-axiom]: #675
+#657 := [unit-resolution #662 #62]: #668
+#658 := [unit-resolution #657 #663]: #578
+#569 := (or #691 #576)
+#577 := [def-axiom]: #569
+#659 := [unit-resolution #577 #658]: #576
+#673 := (or #691 #391)
+#558 := [def-axiom]: #673
+#660 := [unit-resolution #558 #658]: #391
+#573 := (or #691 #418)
+#575 := [def-axiom]: #573
+#654 := [unit-resolution #575 #658]: #418
+#661 := (or #735 #380 #723)
+#645 := [th-lemma arith triangle-eq]: #661
+[unit-resolution #645 #654 #660 #659]: false
+unsat
+b6f64755653a305b62fdd8df3fd24f1d40f3cc04 322 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#771 := (pattern #34)
+#8 := 0::Int
+#63 := -1::Int
+#107 := (* -1::Int #15)
+#104 := (* -1::Int #14)
+#168 := (mod #104 #107)
+#283 := (+ #34 #168)
+#284 := (= #283 0::Int)
+#35 := (mod #14 #15)
+#280 := (* -1::Int #35)
+#281 := (+ #34 #280)
+#282 := (= #281 0::Int)
+#142 := (>= #14 0::Int)
+#135 := (<= #15 0::Int)
+#227 := (or #135 #142)
+#228 := (not #227)
+#131 := (<= #14 0::Int)
+#225 := (or #131 #135)
+#226 := (not #225)
+#231 := (or #226 #228)
+#285 := (ite #231 #282 #284)
+#279 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#286 := (ite #17 #279 #285)
+#278 := (= #14 #34)
+#18 := (= #15 0::Int)
+#287 := (ite #18 #278 #286)
+#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287)
+#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
+#775 := (iff #290 #772)
+#773 := (iff #287 #287)
+#774 := [refl]: #773
+#776 := [quant-intro #774]: #775
+#174 := (* -1::Int #168)
+#247 := (ite #231 #35 #174)
+#250 := (ite #17 0::Int #247)
+#253 := (ite #18 #14 #250)
+#256 := (= #34 #253)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#291 := (iff #259 #290)
+#288 := (iff #256 #287)
+#289 := [rewrite]: #288
+#292 := [quant-intro #289]: #291
+#143 := (not #142)
+#136 := (not #135)
+#146 := (and #136 #143)
+#132 := (not #131)
+#139 := (and #132 #136)
+#149 := (or #139 #146)
+#194 := (ite #149 #35 #174)
+#197 := (ite #17 0::Int #194)
+#200 := (ite #18 #14 #197)
+#203 := (= #34 #200)
+#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
+#260 := (iff #206 #259)
+#257 := (iff #203 #256)
+#254 := (= #200 #253)
+#251 := (= #197 #250)
+#248 := (= #194 #247)
+#232 := (iff #149 #231)
+#229 := (iff #146 #228)
+#230 := [rewrite]: #229
+#219 := (iff #139 #226)
+#220 := [rewrite]: #219
+#233 := [monotonicity #220 #230]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [quant-intro #258]: #260
+#217 := (~ #206 #206)
+#216 := (~ #203 #203)
+#213 := [refl]: #216
+#218 := [nnf-pos #213]: #217
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#209 := (iff #42 #206)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#179 := (ite #101 #35 #174)
+#89 := (= 0::Int #14)
+#182 := (ite #89 0::Int #179)
+#92 := (= 0::Int #15)
+#185 := (ite #92 #14 #182)
+#188 := (= #34 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#207 := (iff #191 #206)
+#204 := (iff #188 #203)
+#201 := (= #185 #200)
+#198 := (= #182 #197)
+#195 := (= #179 #194)
+#150 := (iff #101 #149)
+#147 := (iff #98 #146)
+#144 := (iff #23 #143)
+#145 := [rewrite]: #144
+#137 := (iff #21 #136)
+#138 := [rewrite]: #137
+#148 := [monotonicity #138 #145]: #147
+#140 := (iff #22 #139)
+#133 := (iff #20 #132)
+#134 := [rewrite]: #133
+#141 := [monotonicity #134 #138]: #140
+#151 := [monotonicity #141 #148]: #150
+#196 := [monotonicity #151]: #195
+#125 := (iff #89 #17)
+#126 := [rewrite]: #125
+#199 := [monotonicity #126 #196]: #198
+#127 := (iff #92 #18)
+#128 := [rewrite]: #127
+#202 := [monotonicity #128 #199]: #201
+#205 := [monotonicity #202]: #204
+#208 := [quant-intro #205]: #207
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#186 := (= #40 #185)
+#183 := (= #39 #182)
+#180 := (= #38 #179)
+#177 := (= #37 #174)
+#171 := (- #168)
+#175 := (= #171 #174)
+#176 := [rewrite]: #175
+#172 := (= #37 #171)
+#169 := (= #36 #168)
+#108 := (= #28 #107)
+#109 := [rewrite]: #108
+#105 := (= #27 #104)
+#106 := [rewrite]: #105
+#170 := [monotonicity #106 #109]: #169
+#173 := [monotonicity #170]: #172
+#178 := [trans #173 #176]: #177
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#48 := [asserted]: #28
-[mp #48 #114]: false
-unsat
-eb6e7e04e393e3fdf7579776e17a2526d7e7757f 156 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#11 := f3
-#122 := (>= f3 0::Int)
-#123 := (not #122)
-#109 := (<= f3 0::Int)
-#110 := (not #109)
-#12 := (= f3 0::Int)
-#141 := (or #12 #110 #123)
-#172 := (not #141)
-#62 := -1::Int
-#63 := (* -1::Int f3)
-#68 := (mod #63 -1::Int)
-#74 := (* -1::Int #68)
-#146 := (ite #141 0::Int #74)
-#153 := (= #146 0::Int)
-#157 := (not #153)
-#8 := 1::Int
-#21 := (- 1::Int)
-#20 := (- f3)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod f3 1::Int)
-#14 := (< 0::Int 1::Int)
-#16 := (< f3 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int f3)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#25 := (ite #12 0::Int #24)
-#10 := (= 1::Int 0::Int)
-#26 := (ite #10 f3 #25)
-#27 := (= #26 0::Int)
-#28 := (not #27)
-#160 := (iff #28 #157)
-#54 := (and #14 #16)
-#57 := (or #15 #54)
-#51 := (= 0::Int f3)
-#85 := (or #51 #57)
-#86 := (ite #85 0::Int #74)
-#101 := (= 0::Int #86)
-#106 := (not #101)
-#158 := (iff #106 #157)
-#155 := (iff #101 #153)
-#149 := (= 0::Int #146)
-#152 := (iff #149 #153)
-#154 := [rewrite]: #152
+#181 := [monotonicity #103 #178]: #180
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#184 := [monotonicity #91 #181]: #183
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#187 := [monotonicity #94 #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
+#210 := [trans #193 #208]: #209
+#167 := [asserted]: #42
+#211 := [mp #167 #210]: #206
+#214 := [mp~ #211 #218]: #206
+#262 := [mp #214 #261]: #259
+#293 := [mp #262 #292]: #290
+#777 := [mp #293 #776]: #772
+#66 := (f3 0::Int -1::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := 1::Int
+#10 := (- 1::Int)
+#11 := (f3 0::Int #10)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #11 #66)
+#64 := (= #10 -1::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#548 := (not #772)
+#696 := (or #548 #69)
+#351 := (* -1::Int -1::Int)
+#435 := (* -1::Int 0::Int)
+#436 := (mod #435 #351)
+#437 := (+ #66 #436)
+#428 := (= #437 0::Int)
+#439 := (mod 0::Int -1::Int)
+#440 := (* -1::Int #439)
+#441 := (+ #66 #440)
+#438 := (= #441 0::Int)
+#442 := (>= 0::Int 0::Int)
+#421 := (<= -1::Int 0::Int)
+#756 := (or #421 #442)
+#758 := (not #756)
+#415 := (<= 0::Int 0::Int)
+#545 := (or #415 #421)
+#752 := (not #545)
+#426 := (or #752 #758)
+#427 := (ite #426 #438 #428)
+#759 := (= 0::Int 0::Int)
+#760 := (ite #759 #69 #427)
+#761 := (= -1::Int 0::Int)
+#762 := (ite #761 #72 #760)
+#598 := (or #548 #762)
+#694 := (iff #598 #696)
+#582 := (iff #696 #696)
+#597 := [rewrite]: #582
+#588 := (iff #762 #69)
+#706 := (ite false #69 #69)
+#714 := (iff #706 #69)
+#708 := [rewrite]: #714
+#705 := (iff #762 #706)
+#704 := (iff #760 #69)
+#1 := true
+#546 := (ite true #69 #69)
+#701 := (iff #546 #69)
+#703 := [rewrite]: #701
+#547 := (iff #760 #546)
+#715 := (iff #427 #69)
+#707 := (iff #427 #706)
+#711 := (iff #428 #69)
+#709 := (= #437 #66)
+#449 := (+ #66 0::Int)
+#443 := (= #449 #66)
+#725 := [rewrite]: #443
+#566 := (= #437 #449)
+#724 := (= #436 0::Int)
+#716 := (mod 0::Int 1::Int)
+#723 := (= #716 0::Int)
+#718 := [rewrite]: #723
+#717 := (= #436 #716)
+#720 := (= #351 1::Int)
+#721 := [rewrite]: #720
+#736 := (= #435 0::Int)
+#446 := [rewrite]: #736
+#722 := [monotonicity #446 #721]: #717
+#565 := [trans #722 #718]: #724
+#567 := [monotonicity #565]: #566
+#710 := [trans #567 #725]: #709
+#712 := [monotonicity #710]: #711
+#730 := (iff #438 #69)
+#729 := (= #441 #66)
+#727 := (= #441 #449)
+#447 := (= #440 0::Int)
+#735 := (= #440 #435)
+#457 := (= #439 0::Int)
+#731 := [rewrite]: #457
+#732 := [monotonicity #731]: #735
+#448 := [trans #732 #446]: #447
+#728 := [monotonicity #448]: #727
+#726 := [trans #728 #725]: #729
+#719 := [monotonicity #726]: #730
+#734 := (iff #426 false)
+#461 := (or false false)
+#357 := (iff #461 false)
+#733 := [rewrite]: #357
+#462 := (iff #426 #461)
+#738 := (iff #758 false)
+#742 := (not true)
+#745 := (iff #742 false)
+#740 := [rewrite]: #745
+#751 := (iff #758 #742)
+#750 := (iff #756 true)
+#398 := (or true true)
+#403 := (iff #398 true)
+#404 := [rewrite]: #403
+#389 := (iff #756 #398)
+#747 := (iff #442 true)
+#749 := [rewrite]: #747
+#414 := (iff #421 true)
+#755 := [rewrite]: #414
+#390 := [monotonicity #755 #749]: #389
+#748 := [trans #390 #404]: #750
+#737 := [monotonicity #748]: #751
+#460 := [trans #737 #740]: #738
+#746 := (iff #752 false)
+#743 := (iff #752 #742)
+#405 := (iff #545 true)
+#739 := (iff #545 #398)
+#418 := (iff #415 true)
+#754 := [rewrite]: #418
+#402 := [monotonicity #754 #755]: #739
+#741 := [trans #402 #404]: #405
+#744 := [monotonicity #741]: #743
+#384 := [trans #744 #740]: #746
+#463 := [monotonicity #384 #460]: #462
+#456 := [trans #463 #733]: #734
+#713 := [monotonicity #456 #719 #712]: #707
+#544 := [trans #713 #708]: #715
+#753 := (iff #759 true)
+#413 := [rewrite]: #753
+#700 := [monotonicity #413 #544]: #547
+#702 := [trans #700 #703]: #704
+#757 := (iff #761 false)
+#763 := [rewrite]: #757
+#587 := [monotonicity #763 #81 #702]: #705
+#589 := [trans #587 #708]: #588
+#697 := [monotonicity #589]: #694
+#599 := [trans #697 #597]: #694
+#693 := [quant-inst #8 #63]: #598
+#600 := [mp #693 #599]: #696
+[unit-resolution #600 #87 #777]: false
+unsat
+7554e53ad4bbf50aa6cebedfca61c8a301b15856 332 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#771 := (pattern #34)
+#11 := 0::Int
+#63 := -1::Int
+#107 := (* -1::Int #15)
+#104 := (* -1::Int #14)
+#168 := (mod #104 #107)
+#283 := (+ #34 #168)
+#284 := (= #283 0::Int)
+#35 := (mod #14 #15)
+#280 := (* -1::Int #35)
+#281 := (+ #34 #280)
+#282 := (= #281 0::Int)
+#142 := (>= #14 0::Int)
+#135 := (<= #15 0::Int)
+#227 := (or #135 #142)
+#228 := (not #227)
+#131 := (<= #14 0::Int)
+#225 := (or #131 #135)
+#226 := (not #225)
+#231 := (or #226 #228)
+#285 := (ite #231 #282 #284)
+#279 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#286 := (ite #17 #279 #285)
+#278 := (= #14 #34)
+#18 := (= #15 0::Int)
+#287 := (ite #18 #278 #286)
+#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287)
+#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
+#775 := (iff #290 #772)
+#773 := (iff #287 #287)
+#774 := [refl]: #773
+#776 := [quant-intro #774]: #775
+#174 := (* -1::Int #168)
+#247 := (ite #231 #35 #174)
+#250 := (ite #17 0::Int #247)
+#253 := (ite #18 #14 #250)
+#256 := (= #34 #253)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#291 := (iff #259 #290)
+#288 := (iff #256 #287)
+#289 := [rewrite]: #288
+#292 := [quant-intro #289]: #291
+#143 := (not #142)
+#136 := (not #135)
+#146 := (and #136 #143)
+#132 := (not #131)
+#139 := (and #132 #136)
+#149 := (or #139 #146)
+#194 := (ite #149 #35 #174)
+#197 := (ite #17 0::Int #194)
+#200 := (ite #18 #14 #197)
+#203 := (= #34 #200)
+#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
+#260 := (iff #206 #259)
+#257 := (iff #203 #256)
+#254 := (= #200 #253)
+#251 := (= #197 #250)
+#248 := (= #194 #247)
+#232 := (iff #149 #231)
+#229 := (iff #146 #228)
+#230 := [rewrite]: #229
+#219 := (iff #139 #226)
+#220 := [rewrite]: #219
+#233 := [monotonicity #220 #230]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [quant-intro #258]: #260
+#217 := (~ #206 #206)
+#216 := (~ #203 #203)
+#213 := [refl]: #216
+#218 := [nnf-pos #213]: #217
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#209 := (iff #42 #206)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#179 := (ite #101 #35 #174)
+#89 := (= 0::Int #14)
+#182 := (ite #89 0::Int #179)
+#92 := (= 0::Int #15)
+#185 := (ite #92 #14 #182)
+#188 := (= #34 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#207 := (iff #191 #206)
+#204 := (iff #188 #203)
+#201 := (= #185 #200)
+#198 := (= #182 #197)
+#195 := (= #179 #194)
#150 := (iff #101 #149)
-#147 := (= #86 #146)
-#144 := (iff #85 #141)
-#135 := (or #110 #123)
-#138 := (or #12 #135)
-#142 := (iff #138 #141)
-#143 := [rewrite]: #142
-#139 := (iff #85 #138)
-#136 := (iff #57 #135)
-#131 := (iff #54 #123)
-#1 := true
-#126 := (and true #123)
-#129 := (iff #126 #123)
-#130 := [rewrite]: #129
-#127 := (iff #54 #126)
-#124 := (iff #16 #123)
-#125 := [rewrite]: #124
-#113 := (iff #14 true)
-#114 := [rewrite]: #113
-#128 := [monotonicity #114 #125]: #127
-#132 := [trans #128 #130]: #131
-#120 := (iff #15 #110)
-#115 := (and #110 true)
-#118 := (iff #115 #110)
-#119 := [rewrite]: #118
-#116 := (iff #15 #115)
-#111 := (iff #13 #110)
-#112 := [rewrite]: #111
-#117 := [monotonicity #112 #114]: #116
-#121 := [trans #117 #119]: #120
-#137 := [monotonicity #121 #132]: #136
-#133 := (iff #51 #12)
+#147 := (iff #98 #146)
+#144 := (iff #23 #143)
+#145 := [rewrite]: #144
+#137 := (iff #21 #136)
+#138 := [rewrite]: #137
+#148 := [monotonicity #138 #145]: #147
+#140 := (iff #22 #139)
+#133 := (iff #20 #132)
#134 := [rewrite]: #133
-#140 := [monotonicity #134 #137]: #139
-#145 := [trans #140 #143]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [monotonicity #156]: #158
-#107 := (iff #28 #106)
-#104 := (iff #27 #101)
-#98 := (= #86 0::Int)
-#102 := (iff #98 #101)
-#103 := [rewrite]: #102
-#99 := (iff #27 #98)
-#96 := (= #26 #86)
-#91 := (ite false f3 #86)
-#94 := (= #91 #86)
-#95 := [rewrite]: #94
-#92 := (= #26 #91)
-#89 := (= #25 #86)
-#79 := (ite #57 0::Int #74)
-#82 := (ite #51 0::Int #79)
-#87 := (= #82 #86)
-#88 := [rewrite]: #87
-#83 := (= #25 #82)
-#80 := (= #24 #79)
-#77 := (= #23 #74)
-#71 := (- #68)
-#75 := (= #71 #74)
-#76 := [rewrite]: #75
-#72 := (= #23 #71)
-#69 := (= #22 #68)
-#66 := (= #21 -1::Int)
-#67 := [rewrite]: #66
-#64 := (= #20 #63)
+#141 := [monotonicity #134 #138]: #140
+#151 := [monotonicity #141 #148]: #150
+#196 := [monotonicity #151]: #195
+#125 := (iff #89 #17)
+#126 := [rewrite]: #125
+#199 := [monotonicity #126 #196]: #198
+#127 := (iff #92 #18)
+#128 := [rewrite]: #127
+#202 := [monotonicity #128 #199]: #201
+#205 := [monotonicity #202]: #204
+#208 := [quant-intro #205]: #207
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#186 := (= #40 #185)
+#183 := (= #39 #182)
+#180 := (= #38 #179)
+#177 := (= #37 #174)
+#171 := (- #168)
+#175 := (= #171 #174)
+#176 := [rewrite]: #175
+#172 := (= #37 #171)
+#169 := (= #36 #168)
+#108 := (= #28 #107)
+#109 := [rewrite]: #108
+#105 := (= #27 #104)
+#106 := [rewrite]: #105
+#170 := [monotonicity #106 #109]: #169
+#173 := [monotonicity #170]: #172
+#178 := [trans #173 #176]: #177
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#181 := [monotonicity #103 #178]: #180
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#184 := [monotonicity #91 #181]: #183
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#187 := [monotonicity #94 #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
+#210 := [trans #193 #208]: #209
+#167 := [asserted]: #42
+#211 := [mp #167 #210]: #206
+#214 := [mp~ #211 #218]: #206
+#262 := [mp #214 #261]: #259
+#293 := [mp #262 #292]: #290
+#777 := [mp #293 #776]: #772
+#8 := 1::Int
+#66 := (f3 1::Int -1::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := (- 1::Int)
+#10 := (f3 1::Int #9)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #10 #66)
+#64 := (= #9 -1::Int)
#65 := [rewrite]: #64
-#70 := [monotonicity #65 #67]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#60 := (= #19 0::Int)
-#61 := [rewrite]: #60
-#58 := (iff #18 #57)
-#55 := (iff #17 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#81 := [monotonicity #59 #61 #78]: #80
-#52 := (iff #12 #51)
-#53 := [rewrite]: #52
-#84 := [monotonicity #53 #81]: #83
-#90 := [trans #84 #88]: #89
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#93 := [monotonicity #50 #90]: #92
-#97 := [trans #93 #95]: #96
-#100 := [monotonicity #97]: #99
-#105 := [trans #100 #103]: #104
-#108 := [monotonicity #105]: #107
-#161 := [trans #108 #159]: #160
-#48 := [asserted]: #28
-#162 := [mp #48 #161]: #157
-#175 := (or #172 #153)
-#176 := [def-axiom]: #175
-#233 := [unit-resolution #176 #162]: #172
-#164 := (or #141 #122)
-#165 := [def-axiom]: #164
-#234 := [unit-resolution #165 #233]: #122
-#166 := (or #141 #109)
-#167 := [def-axiom]: #166
-#235 := [unit-resolution #167 #233]: #109
-#169 := (not #12)
-#170 := (or #141 #169)
-#171 := [def-axiom]: #170
-#236 := [unit-resolution #171 #233]: #169
-#237 := [th-lemma arith triangle-eq]: #141
-[unit-resolution #237 #236 #235 #234]: false
-unsat
-106013bb1f998104836223245ab92e3b99397a07 107 0
-#2 := false
-#10 := 0::Int
-#8 := 1::Int
-#9 := (- 1::Int)
-#19 := (- #9)
-#18 := (- 0::Int)
-#20 := (mod #18 #19)
-#21 := (- #20)
-#17 := (mod 0::Int #9)
-#14 := (< 0::Int #9)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#22 := (ite #16 #17 #21)
-#12 := (= 0::Int 0::Int)
-#23 := (ite #12 0::Int #22)
-#11 := (= #9 0::Int)
-#24 := (ite #11 0::Int #23)
-#25 := (= #24 0::Int)
-#26 := (not #25)
-#128 := (iff #26 false)
-#1 := true
-#123 := (not true)
-#126 := (iff #123 false)
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#593 := (not #772)
+#601 := (or #593 #69)
+#351 := (* -1::Int -1::Int)
+#435 := (* -1::Int 1::Int)
+#436 := (mod #435 #351)
+#437 := (+ #66 #436)
+#428 := (= #437 0::Int)
+#439 := (mod 1::Int -1::Int)
+#440 := (* -1::Int #439)
+#441 := (+ #66 #440)
+#438 := (= #441 0::Int)
+#442 := (>= 1::Int 0::Int)
+#421 := (<= -1::Int 0::Int)
+#756 := (or #421 #442)
+#758 := (not #756)
+#415 := (<= 1::Int 0::Int)
+#545 := (or #415 #421)
+#752 := (not #545)
+#426 := (or #752 #758)
+#427 := (ite #426 #438 #428)
+#759 := (= 1::Int 0::Int)
+#760 := (ite #759 #69 #427)
+#761 := (= 1::Int #66)
+#762 := (= -1::Int 0::Int)
+#757 := (ite #762 #761 #760)
+#602 := (or #593 #757)
+#604 := (iff #602 #601)
+#698 := (iff #601 #601)
+#695 := [rewrite]: #698
+#599 := (iff #757 #69)
+#418 := (= #66 1::Int)
+#693 := (ite false #418 #69)
+#582 := (iff #693 #69)
+#597 := [rewrite]: #582
+#694 := (iff #757 #693)
+#696 := (iff #760 #69)
+#701 := (ite false #69 #69)
+#702 := (iff #701 #69)
+#705 := [rewrite]: #702
+#589 := (iff #760 #701)
+#587 := (iff #427 #69)
+#703 := (iff #427 #701)
+#547 := (iff #428 #69)
+#544 := (= #437 #66)
+#719 := (+ #66 0::Int)
+#716 := (= #719 #66)
+#717 := [rewrite]: #716
+#708 := (= #437 #719)
+#713 := (= #436 0::Int)
+#710 := (mod -1::Int 1::Int)
+#706 := (= #710 0::Int)
+#707 := [rewrite]: #706
+#711 := (= #436 #710)
+#567 := (= #351 1::Int)
+#709 := [rewrite]: #567
+#565 := (= #435 -1::Int)
+#566 := [rewrite]: #565
+#712 := [monotonicity #566 #709]: #711
+#714 := [trans #712 #707]: #713
+#715 := [monotonicity #714]: #708
+#546 := [trans #715 #717]: #544
+#700 := [monotonicity #546]: #547
+#718 := (iff #438 #69)
+#722 := (= #441 #66)
+#720 := (= #441 #719)
+#726 := (= #440 0::Int)
+#727 := (* -1::Int 0::Int)
+#725 := (= #727 0::Int)
+#729 := [rewrite]: #725
+#728 := (= #440 #727)
+#448 := (= #439 0::Int)
+#449 := [rewrite]: #448
+#443 := [monotonicity #449]: #728
+#730 := [trans #443 #729]: #726
+#721 := [monotonicity #730]: #720
+#723 := [trans #721 #717]: #722
+#724 := [monotonicity #723]: #718
+#446 := (iff #426 false)
+#457 := (or false false)
+#732 := (iff #457 false)
+#736 := [rewrite]: #732
+#731 := (iff #426 #457)
+#734 := (iff #758 false)
+#1 := true
+#740 := (not true)
+#747 := (iff #740 false)
+#749 := [rewrite]: #747
+#357 := (iff #758 #740)
+#462 := (iff #756 true)
+#751 := (or true true)
+#460 := (iff #751 true)
+#461 := [rewrite]: #460
+#737 := (iff #756 #751)
+#750 := (iff #442 true)
+#748 := [rewrite]: #750
+#402 := (iff #421 true)
+#403 := [rewrite]: #402
+#738 := [monotonicity #403 #748]: #737
+#463 := [trans #738 #461]: #462
+#733 := [monotonicity #463]: #357
+#456 := [trans #733 #749]: #734
+#389 := (iff #752 false)
+#746 := (iff #752 #740)
+#744 := (iff #545 true)
+#404 := (or false true)
+#742 := (iff #404 true)
+#743 := [rewrite]: #742
+#405 := (iff #545 #404)
+#398 := (iff #415 false)
+#739 := [rewrite]: #398
+#741 := [monotonicity #739 #403]: #405
+#745 := [trans #741 #743]: #744
+#384 := [monotonicity #745]: #746
+#390 := [trans #384 #749]: #389
+#735 := [monotonicity #390 #456]: #731
+#447 := [trans #735 #736]: #446
+#704 := [monotonicity #447 #724 #700]: #703
+#588 := [trans #704 #705]: #587
+#414 := (iff #759 false)
+#755 := [rewrite]: #414
+#548 := [monotonicity #755 #588]: #589
+#598 := [trans #548 #705]: #696
+#413 := (iff #761 #418)
+#754 := [rewrite]: #413
+#763 := (iff #762 false)
+#753 := [rewrite]: #763
+#697 := [monotonicity #753 #754 #598]: #694
+#600 := [trans #697 #597]: #599
+#605 := [monotonicity #600]: #604
+#699 := [trans #605 #695]: #604
+#603 := [quant-inst #8 #63]: #602
+#686 := [mp #603 #699]: #601
+[unit-resolution #686 #87 #777]: false
+unsat
+768cdc3a48375ab653481018d34501c9146cb16e 334 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#35 := (f3 #15 #16)
+#772 := (pattern #35)
+#12 := 0::Int
+#64 := -1::Int
+#108 := (* -1::Int #16)
+#105 := (* -1::Int #15)
+#169 := (mod #105 #108)
+#284 := (+ #35 #169)
+#285 := (= #284 0::Int)
+#36 := (mod #15 #16)
+#281 := (* -1::Int #36)
+#282 := (+ #35 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #15 0::Int)
+#136 := (<= #16 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #15 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #35 0::Int)
+#18 := (= #15 0::Int)
+#287 := (ite #18 #280 #286)
+#279 := (= #15 #35)
+#19 := (= #16 0::Int)
+#288 := (ite #19 #279 #287)
+#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#776 := (iff #291 #773)
+#774 := (iff #288 #288)
+#775 := [refl]: #774
+#777 := [quant-intro #775]: #776
+#175 := (* -1::Int #169)
+#248 := (ite #232 #36 #175)
+#251 := (ite #18 0::Int #248)
+#254 := (ite #19 #15 #251)
+#257 := (= #35 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #36 #175)
+#198 := (ite #18 0::Int #195)
+#201 := (ite #19 #15 #198)
+#204 := (= #35 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#29 := (- #16)
+#28 := (- #15)
+#37 := (mod #28 #29)
+#38 := (- #37)
+#22 := (< 0::Int #16)
+#24 := (< #15 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #15)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#39 := (ite #26 #36 #38)
+#40 := (ite #18 0::Int #39)
+#41 := (ite #19 #15 #40)
+#42 := (= #35 #41)
+#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
+#210 := (iff #43 #207)
+#99 := (and #22 #24)
+#102 := (or #23 #99)
+#180 := (ite #102 #36 #175)
+#90 := (= 0::Int #15)
+#183 := (ite #90 0::Int #180)
+#93 := (= 0::Int #16)
+#186 := (ite #93 #15 #183)
+#189 := (= #35 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #102 #150)
+#148 := (iff #99 #147)
+#145 := (iff #24 #144)
+#146 := [rewrite]: #145
+#138 := (iff #22 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #23 #140)
+#134 := (iff #21 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #90 #18)
#127 := [rewrite]: #126
-#124 := (iff #26 #123)
-#121 := (iff #25 true)
-#57 := (iff #12 true)
-#58 := [rewrite]: #57
-#119 := (iff #25 #12)
-#113 := (ite false 0::Int 0::Int)
-#116 := (= #113 0::Int)
-#117 := [rewrite]: #116
-#114 := (= #24 #113)
-#111 := (= #23 0::Int)
-#106 := (ite true 0::Int 0::Int)
-#109 := (= #106 0::Int)
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #93 #19)
+#129 := [rewrite]: #128
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #43 #192)
+#190 := (iff #42 #189)
+#187 := (= #41 #186)
+#184 := (= #40 #183)
+#181 := (= #39 #180)
+#178 := (= #38 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #38 #172)
+#170 := (= #37 #169)
+#109 := (= #29 #108)
+#110 := [rewrite]: #109
+#106 := (= #28 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#103 := (iff #26 #102)
+#100 := (iff #25 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#182 := [monotonicity #104 #179]: #181
+#91 := (iff #18 #90)
+#92 := [rewrite]: #91
+#185 := [monotonicity #92 #182]: #184
+#94 := (iff #19 #93)
+#95 := [rewrite]: #94
+#188 := [monotonicity #95 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #43
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#778 := [mp #294 #777]: #773
+#8 := 3::Int
+#67 := (f3 3::Int -1::Int)
+#70 := (= #67 0::Int)
+#83 := (not #70)
+#9 := 1::Int
+#10 := (- 1::Int)
+#11 := (f3 3::Int #10)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#86 := (iff #14 #83)
+#73 := (= 0::Int #67)
+#78 := (not #73)
+#84 := (iff #78 #83)
+#81 := (iff #73 #70)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#79 := (iff #14 #78)
+#76 := (iff #13 #73)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #13 #70)
+#68 := (= #11 #67)
+#65 := (= #10 -1::Int)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#87 := [trans #80 #85]: #86
+#63 := [asserted]: #14
+#88 := [mp #63 #87]: #83
+#602 := (not #773)
+#603 := (or #602 #70)
+#352 := (* -1::Int -1::Int)
+#436 := (* -1::Int 3::Int)
+#437 := (mod #436 #352)
+#438 := (+ #67 #437)
+#429 := (= #438 0::Int)
+#440 := (mod 3::Int -1::Int)
+#441 := (* -1::Int #440)
+#442 := (+ #67 #441)
+#439 := (= #442 0::Int)
+#443 := (>= 3::Int 0::Int)
+#422 := (<= -1::Int 0::Int)
+#757 := (or #422 #443)
+#759 := (not #757)
+#416 := (<= 3::Int 0::Int)
+#546 := (or #416 #422)
+#753 := (not #546)
+#427 := (or #753 #759)
+#428 := (ite #427 #439 #429)
+#760 := (= 3::Int 0::Int)
+#761 := (ite #760 #70 #428)
+#762 := (= 3::Int #67)
+#763 := (= -1::Int 0::Int)
+#758 := (ite #763 #762 #761)
+#604 := (or #602 #758)
+#606 := (iff #604 #603)
+#696 := (iff #603 #603)
+#700 := [rewrite]: #696
+#601 := (iff #758 #70)
+#419 := (= #67 3::Int)
+#695 := (ite false #419 #70)
+#598 := (iff #695 #70)
+#600 := [rewrite]: #598
+#698 := (iff #758 #695)
+#599 := (iff #761 #70)
+#704 := (ite false #70 #70)
+#706 := (iff #704 #70)
+#588 := [rewrite]: #706
+#549 := (iff #761 #704)
+#589 := (iff #428 #70)
+#705 := (iff #428 #704)
+#701 := (iff #429 #70)
+#547 := (= #438 #67)
+#720 := (+ #67 0::Int)
+#717 := (= #720 #67)
+#718 := [rewrite]: #717
+#716 := (= #438 #720)
+#715 := (= #437 0::Int)
+#566 := -3::Int
+#712 := (mod -3::Int 1::Int)
+#708 := (= #712 0::Int)
+#714 := [rewrite]: #708
+#713 := (= #437 #712)
+#710 := (= #352 1::Int)
+#711 := [rewrite]: #710
+#567 := (= #436 -3::Int)
+#568 := [rewrite]: #567
+#707 := [monotonicity #568 #711]: #713
+#709 := [trans #707 #714]: #715
+#545 := [monotonicity #709]: #716
+#548 := [trans #545 #718]: #547
+#702 := [monotonicity #548]: #701
+#719 := (iff #439 #70)
+#723 := (= #442 #67)
+#721 := (= #442 #720)
+#727 := (= #441 0::Int)
+#728 := (* -1::Int 0::Int)
+#726 := (= #728 0::Int)
+#730 := [rewrite]: #726
+#729 := (= #441 #728)
+#449 := (= #440 0::Int)
+#450 := [rewrite]: #449
+#444 := [monotonicity #450]: #729
+#731 := [trans #444 #730]: #727
+#722 := [monotonicity #731]: #721
+#724 := [trans #722 #718]: #723
+#725 := [monotonicity #724]: #719
+#447 := (iff #427 false)
+#458 := (or false false)
+#733 := (iff #458 false)
+#737 := [rewrite]: #733
+#732 := (iff #427 #458)
+#735 := (iff #759 false)
+#1 := true
+#741 := (not true)
+#748 := (iff #741 false)
+#750 := [rewrite]: #748
+#358 := (iff #759 #741)
+#463 := (iff #757 true)
+#752 := (or true true)
+#461 := (iff #752 true)
+#462 := [rewrite]: #461
+#738 := (iff #757 #752)
+#751 := (iff #443 true)
+#749 := [rewrite]: #751
+#403 := (iff #422 true)
+#404 := [rewrite]: #403
+#739 := [monotonicity #404 #749]: #738
+#464 := [trans #739 #462]: #463
+#734 := [monotonicity #464]: #358
+#457 := [trans #734 #750]: #735
+#390 := (iff #753 false)
+#747 := (iff #753 #741)
+#745 := (iff #546 true)
+#405 := (or false true)
+#743 := (iff #405 true)
+#744 := [rewrite]: #743
+#406 := (iff #546 #405)
+#399 := (iff #416 false)
+#740 := [rewrite]: #399
+#742 := [monotonicity #740 #404]: #406
+#746 := [trans #742 #744]: #745
+#385 := [monotonicity #746]: #747
+#391 := [trans #385 #750]: #390
+#736 := [monotonicity #391 #457]: #732
+#448 := [trans #736 #737]: #447
+#703 := [monotonicity #448 #725 #702]: #705
+#590 := [trans #703 #588]: #589
+#415 := (iff #760 false)
+#756 := [rewrite]: #415
+#697 := [monotonicity #756 #590]: #549
+#694 := [trans #697 #588]: #599
+#414 := (iff #762 #419)
+#755 := [rewrite]: #414
+#764 := (iff #763 false)
+#754 := [rewrite]: #764
+#583 := [monotonicity #754 #755 #694]: #698
+#594 := [trans #583 #600]: #601
+#699 := [monotonicity #594]: #606
+#687 := [trans #699 #700]: #606
+#605 := [quant-inst #8 #64]: #604
+#689 := [mp #605 #687]: #603
+[unit-resolution #689 #88 #778]: false
+unsat
+d313c8803fd67ab7c81ae803664ddc96f0a1cd58 311 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#35 := (f3 #15 #16)
+#772 := (pattern #35)
+#12 := 0::Int
+#64 := -1::Int
+#108 := (* -1::Int #16)
+#105 := (* -1::Int #15)
+#169 := (mod #105 #108)
+#284 := (+ #35 #169)
+#285 := (= #284 0::Int)
+#36 := (mod #15 #16)
+#281 := (* -1::Int #36)
+#282 := (+ #35 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #15 0::Int)
+#136 := (<= #16 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #15 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #35 0::Int)
+#18 := (= #15 0::Int)
+#287 := (ite #18 #280 #286)
+#279 := (= #15 #35)
+#19 := (= #16 0::Int)
+#288 := (ite #19 #279 #287)
+#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#776 := (iff #291 #773)
+#774 := (iff #288 #288)
+#775 := [refl]: #774
+#777 := [quant-intro #775]: #776
+#175 := (* -1::Int #169)
+#248 := (ite #232 #36 #175)
+#251 := (ite #18 0::Int #248)
+#254 := (ite #19 #15 #251)
+#257 := (= #35 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #36 #175)
+#198 := (ite #18 0::Int #195)
+#201 := (ite #19 #15 #198)
+#204 := (= #35 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#29 := (- #16)
+#28 := (- #15)
+#37 := (mod #28 #29)
+#38 := (- #37)
+#22 := (< 0::Int #16)
+#24 := (< #15 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #15)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#39 := (ite #26 #36 #38)
+#40 := (ite #18 0::Int #39)
+#41 := (ite #19 #15 #40)
+#42 := (= #35 #41)
+#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
+#210 := (iff #43 #207)
+#99 := (and #22 #24)
+#102 := (or #23 #99)
+#180 := (ite #102 #36 #175)
+#90 := (= 0::Int #15)
+#183 := (ite #90 0::Int #180)
+#93 := (= 0::Int #16)
+#186 := (ite #93 #15 #183)
+#189 := (= #35 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #102 #150)
+#148 := (iff #99 #147)
+#145 := (iff #24 #144)
+#146 := [rewrite]: #145
+#138 := (iff #22 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #23 #140)
+#134 := (iff #21 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #90 #18)
+#127 := [rewrite]: #126
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #93 #19)
+#129 := [rewrite]: #128
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #43 #192)
+#190 := (iff #42 #189)
+#187 := (= #41 #186)
+#184 := (= #40 #183)
+#181 := (= #39 #180)
+#178 := (= #38 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #38 #172)
+#170 := (= #37 #169)
+#109 := (= #29 #108)
#110 := [rewrite]: #109
-#107 := (= #23 #106)
-#104 := (= #22 0::Int)
-#47 := -1::Int
-#59 := (< 0::Int -1::Int)
-#62 := (and #13 #59)
-#99 := (ite #62 0::Int 0::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #22 #99)
-#97 := (= #21 0::Int)
-#79 := (= #18 0::Int)
-#80 := [rewrite]: #79
-#95 := (= #21 #18)
-#93 := (= #20 0::Int)
-#88 := (mod 0::Int 1::Int)
-#91 := (= #88 0::Int)
+#106 := (= #28 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#103 := (iff #26 #102)
+#100 := (iff #25 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#182 := [monotonicity #104 #179]: #181
+#91 := (iff #18 #90)
#92 := [rewrite]: #91
-#89 := (= #20 #88)
-#86 := (= #19 1::Int)
-#81 := (- -1::Int)
-#84 := (= #81 1::Int)
-#85 := [rewrite]: #84
-#82 := (= #19 #81)
-#48 := (= #9 -1::Int)
-#49 := [rewrite]: #48
-#83 := [monotonicity #49]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #80 #87]: #89
-#94 := [trans #90 #92]: #93
-#96 := [monotonicity #94]: #95
-#98 := [trans #96 #80]: #97
-#77 := (= #17 0::Int)
-#72 := (mod 0::Int -1::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #17 #72)
-#74 := [monotonicity #49]: #73
-#78 := [trans #74 #76]: #77
-#70 := (iff #16 #62)
-#65 := (or #62 #62)
-#68 := (iff #65 #62)
+#185 := [monotonicity #92 #182]: #184
+#94 := (iff #19 #93)
+#95 := [rewrite]: #94
+#188 := [monotonicity #95 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #43
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#778 := [mp #294 #777]: #773
+decl f4 :: Int
+#8 := f4
+#67 := (f3 f4 -1::Int)
+#70 := (= #67 0::Int)
+#83 := (not #70)
+#9 := 1::Int
+#10 := (- 1::Int)
+#11 := (f3 f4 #10)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#86 := (iff #14 #83)
+#73 := (= 0::Int #67)
+#78 := (not #73)
+#84 := (iff #78 #83)
+#81 := (iff #73 #70)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#79 := (iff #14 #78)
+#76 := (iff #13 #73)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #13 #70)
+#68 := (= #11 #67)
+#65 := (= #10 -1::Int)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#87 := [trans #80 #85]: #86
+#63 := [asserted]: #14
+#88 := [mp #63 #87]: #83
+#716 := (not #773)
+#545 := (or #716 #70)
+#352 := (* -1::Int -1::Int)
+#436 := (* -1::Int f4)
+#437 := (mod #436 #352)
+#438 := (+ #67 #437)
+#429 := (= #438 0::Int)
+#440 := (mod f4 -1::Int)
+#441 := (* -1::Int #440)
+#442 := (+ #67 #441)
+#439 := (= #442 0::Int)
+#443 := (>= f4 0::Int)
+#422 := (<= -1::Int 0::Int)
+#757 := (or #422 #443)
+#759 := (not #757)
+#416 := (<= f4 0::Int)
+#546 := (or #416 #422)
+#753 := (not #546)
+#427 := (or #753 #759)
+#428 := (ite #427 #439 #429)
+#760 := (= f4 0::Int)
+#761 := (ite #760 #70 #428)
+#762 := (= f4 #67)
+#763 := (= -1::Int 0::Int)
+#758 := (ite #763 #762 #761)
+#547 := (or #716 #758)
+#701 := (iff #547 #545)
+#704 := (iff #545 #545)
+#705 := [rewrite]: #704
+#715 := (iff #758 #70)
+#712 := (ite false #762 #70)
+#708 := (iff #712 #70)
+#714 := [rewrite]: #708
+#713 := (iff #758 #712)
+#710 := (iff #761 #70)
+#719 := (ite #760 #70 #70)
+#567 := (iff #719 #70)
+#568 := [rewrite]: #567
+#725 := (iff #761 #719)
+#723 := (iff #428 #70)
+#720 := (ite false #439 #70)
+#717 := (iff #720 #70)
+#718 := [rewrite]: #717
+#721 := (iff #428 #720)
+#727 := (iff #429 #70)
+#726 := (= #438 #67)
+#449 := (+ #67 0::Int)
+#729 := (= #449 #67)
+#444 := [rewrite]: #729
+#450 := (= #438 #449)
+#447 := (= #437 0::Int)
+#458 := (mod #436 1::Int)
+#733 := (= #458 0::Int)
+#737 := [rewrite]: #733
+#732 := (= #437 #458)
+#735 := (= #352 1::Int)
+#457 := [rewrite]: #735
+#736 := [monotonicity #457]: #732
+#448 := [trans #736 #737]: #447
+#728 := [monotonicity #448]: #450
+#730 := [trans #728 #444]: #726
+#731 := [monotonicity #730]: #727
+#358 := (iff #427 false)
+#739 := (or false false)
+#463 := (iff #739 false)
+#464 := [rewrite]: #463
+#461 := (iff #427 #739)
+#752 := (iff #759 false)
+#1 := true
+#405 := (not true)
+#743 := (iff #405 false)
+#744 := [rewrite]: #743
+#751 := (iff #759 #405)
+#390 := (iff #757 true)
+#741 := (or true #443)
+#748 := (iff #741 true)
+#750 := [rewrite]: #748
+#747 := (iff #757 #741)
+#414 := (iff #422 true)
+#419 := [rewrite]: #414
+#385 := [monotonicity #419]: #747
+#391 := [trans #385 #750]: #390
+#749 := [monotonicity #391]: #751
+#738 := [trans #749 #744]: #752
+#745 := (iff #753 false)
+#406 := (iff #753 #405)
+#403 := (iff #546 true)
+#755 := (or #416 true)
+#399 := (iff #755 true)
+#740 := [rewrite]: #399
+#415 := (iff #546 #755)
+#756 := [monotonicity #419]: #415
+#404 := [trans #756 #740]: #403
+#742 := [monotonicity #404]: #406
+#746 := [trans #742 #744]: #745
+#462 := [monotonicity #746 #738]: #461
+#734 := [trans #462 #464]: #358
+#722 := [monotonicity #734 #731]: #721
+#724 := [trans #722 #718]: #723
+#566 := [monotonicity #724]: #725
+#711 := [trans #566 #568]: #710
+#764 := (iff #763 false)
+#754 := [rewrite]: #764
+#707 := [monotonicity #754 #711]: #713
+#709 := [trans #707 #714]: #715
+#702 := [monotonicity #709]: #701
+#703 := [trans #702 #705]: #701
+#548 := [quant-inst #8 #64]: #547
+#706 := [mp #548 #703]: #545
+[unit-resolution #706 #88 #778]: false
+unsat
+4e6d1a0d0e4d1e5ccd22f2801665c723ffc6cafc 304 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#33 := (f3 #13 #14)
+#757 := (pattern #33)
+#8 := 0::Int
+#88 := -1::Int
+#92 := (* -1::Int #14)
+#89 := (* -1::Int #13)
+#153 := (mod #89 #92)
+#268 := (+ #33 #153)
+#269 := (= #268 0::Int)
+#34 := (mod #13 #14)
+#265 := (* -1::Int #34)
+#266 := (+ #33 #265)
+#267 := (= #266 0::Int)
+#127 := (>= #13 0::Int)
+#120 := (<= #14 0::Int)
+#212 := (or #120 #127)
+#213 := (not #212)
+#116 := (<= #13 0::Int)
+#210 := (or #116 #120)
+#211 := (not #210)
+#216 := (or #211 #213)
+#270 := (ite #216 #267 #269)
+#264 := (= #33 0::Int)
+#16 := (= #13 0::Int)
+#271 := (ite #16 #264 #270)
+#263 := (= #13 #33)
+#17 := (= #14 0::Int)
+#272 := (ite #17 #263 #271)
+#758 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #757) #272)
+#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
+#761 := (iff #275 #758)
+#759 := (iff #272 #272)
+#760 := [refl]: #759
+#762 := [quant-intro #760]: #761
+#159 := (* -1::Int #153)
+#232 := (ite #216 #34 #159)
+#235 := (ite #16 0::Int #232)
+#238 := (ite #17 #13 #235)
+#241 := (= #33 #238)
+#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
+#276 := (iff #244 #275)
+#273 := (iff #241 #272)
+#274 := [rewrite]: #273
+#277 := [quant-intro #274]: #276
+#128 := (not #127)
+#121 := (not #120)
+#131 := (and #121 #128)
+#117 := (not #116)
+#124 := (and #117 #121)
+#134 := (or #124 #131)
+#179 := (ite #134 #34 #159)
+#182 := (ite #16 0::Int #179)
+#185 := (ite #17 #13 #182)
+#188 := (= #33 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#245 := (iff #191 #244)
+#242 := (iff #188 #241)
+#239 := (= #185 #238)
+#236 := (= #182 #235)
+#233 := (= #179 #232)
+#217 := (iff #134 #216)
+#214 := (iff #131 #213)
+#215 := [rewrite]: #214
+#204 := (iff #124 #211)
+#205 := [rewrite]: #204
+#218 := [monotonicity #205 #215]: #217
+#234 := [monotonicity #218]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [quant-intro #243]: #245
+#202 := (~ #191 #191)
+#201 := (~ #188 #188)
+#198 := [refl]: #201
+#203 := [nnf-pos #198]: #202
+#27 := (- #14)
+#26 := (- #13)
+#35 := (mod #26 #27)
+#36 := (- #35)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#37 := (ite #24 #34 #36)
+#38 := (ite #16 0::Int #37)
+#39 := (ite #17 #13 #38)
+#40 := (= #33 #39)
+#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
+#194 := (iff #41 #191)
+#82 := (and #20 #22)
+#85 := (or #21 #82)
+#164 := (ite #85 #34 #159)
+#73 := (= 0::Int #13)
+#167 := (ite #73 0::Int #164)
+#76 := (= 0::Int #14)
+#170 := (ite #76 #13 #167)
+#173 := (= #33 #170)
+#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
+#192 := (iff #176 #191)
+#189 := (iff #173 #188)
+#186 := (= #170 #185)
+#183 := (= #167 #182)
+#180 := (= #164 #179)
+#135 := (iff #85 #134)
+#132 := (iff #82 #131)
+#129 := (iff #22 #128)
+#130 := [rewrite]: #129
+#122 := (iff #20 #121)
+#123 := [rewrite]: #122
+#133 := [monotonicity #123 #130]: #132
+#125 := (iff #21 #124)
+#118 := (iff #19 #117)
+#119 := [rewrite]: #118
+#126 := [monotonicity #119 #123]: #125
+#136 := [monotonicity #126 #133]: #135
+#181 := [monotonicity #136]: #180
+#110 := (iff #73 #16)
+#111 := [rewrite]: #110
+#184 := [monotonicity #111 #181]: #183
+#112 := (iff #76 #17)
+#113 := [rewrite]: #112
+#187 := [monotonicity #113 #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
+#177 := (iff #41 #176)
+#174 := (iff #40 #173)
+#171 := (= #39 #170)
+#168 := (= #38 #167)
+#165 := (= #37 #164)
+#162 := (= #36 #159)
+#156 := (- #153)
+#160 := (= #156 #159)
+#161 := [rewrite]: #160
+#157 := (= #36 #156)
+#154 := (= #35 #153)
+#93 := (= #27 #92)
+#94 := [rewrite]: #93
+#90 := (= #26 #89)
+#91 := [rewrite]: #90
+#155 := [monotonicity #91 #94]: #154
+#158 := [monotonicity #155]: #157
+#163 := [trans #158 #161]: #162
+#86 := (iff #24 #85)
+#83 := (iff #23 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#166 := [monotonicity #87 #163]: #165
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#169 := [monotonicity #75 #166]: #168
+#77 := (iff #17 #76)
+#78 := [rewrite]: #77
+#172 := [monotonicity #78 #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [quant-intro #175]: #177
+#195 := [trans #178 #193]: #194
+#152 := [asserted]: #41
+#196 := [mp #152 #195]: #191
+#199 := [mp~ #196 #203]: #191
+#247 := [mp #199 #246]: #244
+#278 := [mp #247 #277]: #275
+#763 := [mp #278 #762]: #758
+#9 := 3::Int
+#10 := (f3 0::Int 3::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#679 := (not #758)
+#680 := (or #679 #11)
+#336 := (* -1::Int 3::Int)
+#421 := (* -1::Int 0::Int)
+#422 := (mod #421 #336)
+#423 := (+ #10 #422)
+#414 := (= #423 0::Int)
+#425 := (mod 0::Int 3::Int)
+#426 := (* -1::Int #425)
+#354 := (+ #10 #426)
+#427 := (= #354 0::Int)
+#424 := (>= 0::Int 0::Int)
+#428 := (<= 3::Int 0::Int)
+#407 := (or #428 #424)
+#742 := (not #407)
+#744 := (<= 0::Int 0::Int)
+#401 := (or #744 #428)
+#531 := (not #401)
+#738 := (or #531 #742)
+#412 := (ite #738 #427 #414)
+#413 := (= 0::Int 0::Int)
+#745 := (ite #413 #11 #412)
+#62 := (= 0::Int #10)
+#746 := (= 3::Int 0::Int)
+#747 := (ite #746 #62 #745)
+#683 := (or #679 #747)
+#583 := (iff #683 #680)
+#586 := (iff #680 #680)
+#579 := [rewrite]: #586
+#682 := (iff #747 #11)
+#700 := (ite false #11 #11)
+#530 := (iff #700 #11)
+#532 := [rewrite]: #530
+#575 := (iff #747 #700)
+#573 := (iff #745 #11)
+#1 := true
+#687 := (ite true #11 #11)
+#688 := (iff #687 #11)
+#691 := [rewrite]: #688
+#689 := (iff #745 #687)
+#533 := (iff #412 #11)
+#694 := (iff #412 #700)
+#693 := (iff #414 #11)
+#698 := (= #423 #10)
+#714 := (+ #10 0::Int)
+#715 := (= #714 #10)
+#712 := [rewrite]: #715
+#696 := (= #423 #714)
+#553 := (= #422 0::Int)
+#702 := -3::Int
+#709 := (mod 0::Int -3::Int)
+#551 := (= #709 0::Int)
+#552 := [rewrite]: #551
+#704 := (= #422 #709)
+#703 := (= #336 -3::Int)
+#708 := [rewrite]: #703
+#433 := (= #421 0::Int)
+#434 := [rewrite]: #433
+#710 := [monotonicity #434 #708]: #704
+#695 := [trans #710 #552]: #553
+#697 := [monotonicity #695]: #696
+#692 := [trans #697 #712]: #698
+#699 := [monotonicity #692]: #693
+#706 := (iff #427 #11)
+#716 := (= #354 #10)
+#429 := (= #354 #714)
+#435 := (= #426 0::Int)
+#722 := (= #426 #421)
+#721 := (= #425 0::Int)
+#718 := [rewrite]: #721
+#432 := [monotonicity #718]: #722
+#713 := [trans #432 #434]: #435
+#711 := [monotonicity #713]: #429
+#705 := [trans #711 #712]: #716
+#707 := [monotonicity #705]: #706
+#443 := (iff #738 false)
+#449 := (or false false)
+#720 := (iff #449 false)
+#442 := [rewrite]: #720
+#342 := (iff #738 #449)
+#447 := (iff #742 false)
+#727 := (not true)
+#730 := (iff #727 false)
+#731 := [rewrite]: #730
+#724 := (iff #742 #727)
+#737 := (iff #407 true)
+#735 := (or false true)
+#736 := (iff #735 true)
+#734 := [rewrite]: #736
+#375 := (iff #407 #735)
+#370 := (iff #424 true)
+#733 := [rewrite]: #370
+#740 := (iff #428 false)
+#400 := [rewrite]: #740
+#376 := [monotonicity #400 #733]: #375
+#723 := [trans #376 #734]: #737
+#446 := [monotonicity #723]: #724
+#448 := [trans #446 #731]: #447
+#726 := (iff #531 false)
+#728 := (iff #531 #727)
+#390 := (iff #401 true)
+#741 := (or true false)
+#388 := (iff #741 true)
+#389 := [rewrite]: #388
+#384 := (iff #401 #741)
+#399 := (iff #744 true)
+#404 := [rewrite]: #399
+#725 := [monotonicity #404 #400]: #384
+#391 := [trans #725 #389]: #390
+#729 := [monotonicity #391]: #728
+#732 := [trans #729 #731]: #726
+#719 := [monotonicity #732 #448]: #342
+#717 := [trans #719 #442]: #443
+#701 := [monotonicity #717 #707 #699]: #694
+#686 := [trans #701 #532]: #533
+#749 := (iff #413 true)
+#739 := [rewrite]: #749
+#690 := [monotonicity #739 #686]: #689
+#574 := [trans #690 #691]: #573
+#68 := (iff #62 #11)
#69 := [rewrite]: #68
-#66 := (iff #16 #65)
-#63 := (iff #15 #62)
-#60 := (iff #14 #59)
-#61 := [monotonicity #49]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64 #64]: #66
-#71 := [trans #67 #69]: #70
-#101 := [monotonicity #71 #78 #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #58 #105]: #107
-#112 := [trans #108 #110]: #111
-#55 := (iff #11 false)
-#50 := (= -1::Int 0::Int)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #11 #50)
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#115 := [monotonicity #56 #112]: #114
-#118 := [trans #115 #117]: #25
-#120 := [monotonicity #118]: #119
-#122 := [trans #120 #58]: #121
-#125 := [monotonicity #122]: #124
-#129 := [trans #125 #127]: #128
-#46 := [asserted]: #26
-[mp #46 #129]: false
-unsat
-8d5198a1caadbe07ee33787baa9fbc0f66546c9a 111 0
-#2 := false
-#10 := 0::Int
+#748 := (iff #746 false)
+#743 := [rewrite]: #748
+#534 := [monotonicity #743 #69 #574]: #575
+#584 := [trans #534 #532]: #682
+#585 := [monotonicity #584]: #583
+#587 := [trans #585 #579]: #583
+#568 := [quant-inst #8 #9]: #683
+#588 := [mp #568 #587]: #680
+[unit-resolution #588 #61 #763]: false
+unsat
+8c07fa0d73a756ba84d0fe9fed90f7b86f2beac8 323 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#773 := (pattern #34)
+#8 := 0::Int
+#104 := -1::Int
+#108 := (* -1::Int #15)
+#105 := (* -1::Int #14)
+#169 := (mod #105 #108)
+#284 := (+ #34 #169)
+#285 := (= #284 0::Int)
+#35 := (mod #14 #15)
+#281 := (* -1::Int #35)
+#282 := (+ #34 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #14 0::Int)
+#136 := (<= #15 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #14 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#287 := (ite #17 #280 #286)
+#279 := (= #14 #34)
+#18 := (= #15 0::Int)
+#288 := (ite #18 #279 #287)
+#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#777 := (iff #291 #774)
+#775 := (iff #288 #288)
+#776 := [refl]: #775
+#778 := [quant-intro #776]: #777
+#175 := (* -1::Int #169)
+#248 := (ite #232 #35 #175)
+#251 := (ite #17 0::Int #248)
+#254 := (ite #18 #14 #251)
+#257 := (= #34 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #35 #175)
+#198 := (ite #17 0::Int #195)
+#201 := (ite #18 #14 #198)
+#204 := (= #34 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#210 := (iff #42 #207)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#180 := (ite #101 #35 #175)
+#89 := (= 0::Int #14)
+#183 := (ite #89 0::Int #180)
+#92 := (= 0::Int #15)
+#186 := (ite #92 #14 #183)
+#189 := (= #34 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #101 #150)
+#148 := (iff #98 #147)
+#145 := (iff #23 #144)
+#146 := [rewrite]: #145
+#138 := (iff #21 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #22 #140)
+#134 := (iff #20 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #89 #17)
+#127 := [rewrite]: #126
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #92 #18)
+#129 := [rewrite]: #128
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#187 := (= #40 #186)
+#184 := (= #39 #183)
+#181 := (= #38 #180)
+#178 := (= #37 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #37 #172)
+#170 := (= #36 #169)
+#109 := (= #28 #108)
+#110 := [rewrite]: #109
+#106 := (= #27 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#182 := [monotonicity #103 #179]: #181
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#185 := [monotonicity #91 #182]: #184
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#188 := [monotonicity #94 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #42
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#779 := [mp #294 #778]: #774
+#63 := -3::Int
+#66 := (f3 0::Int -3::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 0::Int #10)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #11 #66)
+#64 := (= #10 -3::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#591 := (not #774)
+#550 := (or #591 #69)
+#352 := (* -1::Int -3::Int)
+#437 := (* -1::Int 0::Int)
+#438 := (mod #437 #352)
+#439 := (+ #66 #438)
+#430 := (= #439 0::Int)
+#441 := (mod 0::Int -3::Int)
+#442 := (* -1::Int #441)
+#370 := (+ #66 #442)
+#443 := (= #370 0::Int)
+#440 := (>= 0::Int 0::Int)
+#444 := (<= -3::Int 0::Int)
+#423 := (or #444 #440)
+#758 := (not #423)
+#760 := (<= 0::Int 0::Int)
+#417 := (or #760 #444)
+#547 := (not #417)
+#754 := (or #547 #758)
+#428 := (ite #754 #443 #430)
+#429 := (= 0::Int 0::Int)
+#761 := (ite #429 #69 #428)
+#762 := (= -3::Int 0::Int)
+#763 := (ite #762 #72 #761)
+#698 := (or #591 #763)
+#695 := (iff #698 #550)
+#699 := (iff #550 #550)
+#584 := [rewrite]: #699
+#589 := (iff #763 #69)
+#714 := (ite false #69 #69)
+#715 := (iff #714 #69)
+#716 := [rewrite]: #715
+#704 := (iff #763 #714)
+#705 := (iff #761 #69)
+#1 := true
+#546 := (ite true #69 #69)
+#702 := (iff #546 #69)
+#703 := [rewrite]: #702
+#548 := (iff #761 #546)
+#710 := (iff #428 #69)
+#708 := (iff #428 #714)
+#712 := (iff #430 #69)
+#569 := (= #439 #66)
+#450 := (+ #66 0::Int)
+#730 := (= #450 #66)
+#445 := [rewrite]: #730
+#567 := (= #439 #450)
+#720 := (= #438 0::Int)
+#723 := (mod 0::Int 3::Int)
+#724 := (= #723 0::Int)
+#725 := [rewrite]: #724
+#718 := (= #438 #723)
+#721 := (= #352 3::Int)
+#722 := [rewrite]: #721
+#734 := (= #437 0::Int)
+#738 := [rewrite]: #734
+#719 := [monotonicity #738 #722]: #718
+#726 := [trans #719 #725]: #720
+#568 := [monotonicity #726]: #567
+#711 := [trans #568 #445]: #569
+#713 := [monotonicity #711]: #712
+#728 := (iff #443 #69)
+#727 := (= #370 #66)
+#451 := (= #370 #450)
+#448 := (= #442 0::Int)
+#733 := (= #442 #437)
+#458 := (= #441 0::Int)
+#459 := [rewrite]: #458
+#737 := [monotonicity #459]: #733
+#449 := [trans #737 #738]: #448
+#729 := [monotonicity #449]: #451
+#731 := [trans #729 #445]: #727
+#732 := [monotonicity #731]: #728
+#735 := (iff #754 false)
+#462 := (or false false)
+#465 := (iff #462 false)
+#358 := [rewrite]: #465
+#463 := (iff #754 #462)
+#739 := (iff #758 false)
+#743 := (not true)
+#746 := (iff #743 false)
+#747 := [rewrite]: #746
+#750 := (iff #758 #743)
+#392 := (iff #423 true)
+#757 := (or true true)
+#404 := (iff #757 true)
+#405 := [rewrite]: #404
+#751 := (iff #423 #757)
+#386 := (iff #440 true)
+#749 := [rewrite]: #386
+#756 := (iff #444 true)
+#416 := [rewrite]: #756
+#391 := [monotonicity #416 #749]: #751
+#752 := [trans #391 #405]: #392
+#753 := [monotonicity #752]: #750
+#740 := [trans #753 #747]: #739
+#742 := (iff #547 false)
+#744 := (iff #547 #743)
+#406 := (iff #417 true)
+#400 := (iff #417 #757)
+#415 := (iff #760 true)
+#420 := [rewrite]: #415
+#741 := [monotonicity #420 #416]: #400
+#407 := [trans #741 #405]: #406
+#745 := [monotonicity #407]: #744
+#748 := [trans #745 #747]: #742
+#464 := [monotonicity #748 #740]: #463
+#736 := [trans #464 #358]: #735
+#709 := [monotonicity #736 #732 #713]: #708
+#717 := [trans #709 #716]: #710
+#765 := (iff #429 true)
+#755 := [rewrite]: #765
+#549 := [monotonicity #755 #717]: #548
+#706 := [trans #549 #703]: #705
+#764 := (iff #762 false)
+#759 := [rewrite]: #764
+#707 := [monotonicity #759 #81 #706]: #704
+#590 := [trans #707 #716]: #589
+#696 := [monotonicity #590]: #695
+#599 := [trans #696 #584]: #695
+#600 := [quant-inst #8 #63]: #698
+#601 := [mp #600 #599]: #550
+[unit-resolution #601 #87 #779]: false
+unsat
+4b125b55545fc1a8ed3851433e86bbecb0071f7b 320 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#34 := (f3 #13 #14)
+#742 := (pattern #34)
+#16 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #14)
+#81 := (* -1::Int #13)
+#139 := (mod #81 #84)
+#254 := (+ #34 #139)
+#255 := (= #254 0::Int)
+#35 := (mod #13 #14)
+#251 := (* -1::Int #35)
+#252 := (+ #34 #251)
+#253 := (= #252 0::Int)
+#113 := (>= #13 0::Int)
+#106 := (<= #14 0::Int)
+#198 := (or #106 #113)
+#199 := (not #198)
+#102 := (<= #13 0::Int)
+#196 := (or #102 #106)
+#197 := (not #196)
+#202 := (or #197 #199)
+#256 := (ite #202 #253 #255)
+#250 := (= #34 0::Int)
+#17 := (= #13 0::Int)
+#257 := (ite #17 #250 #256)
+#249 := (= #13 #34)
+#18 := (= #14 0::Int)
+#258 := (ite #18 #249 #257)
+#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #258)
+#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
+#746 := (iff #261 #743)
+#744 := (iff #258 #258)
+#745 := [refl]: #744
+#747 := [quant-intro #745]: #746
+#145 := (* -1::Int #139)
+#218 := (ite #202 #35 #145)
+#221 := (ite #17 0::Int #218)
+#224 := (ite #18 #13 #221)
+#227 := (= #34 #224)
+#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
+#262 := (iff #230 #261)
+#259 := (iff #227 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#114 := (not #113)
+#107 := (not #106)
+#117 := (and #107 #114)
+#103 := (not #102)
+#110 := (and #103 #107)
+#120 := (or #110 #117)
+#165 := (ite #120 #35 #145)
+#168 := (ite #17 0::Int #165)
+#171 := (ite #18 #13 #168)
+#174 := (= #34 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#231 := (iff #177 #230)
+#228 := (iff #174 #227)
+#225 := (= #171 #224)
+#222 := (= #168 #221)
+#219 := (= #165 #218)
+#203 := (iff #120 #202)
+#200 := (iff #117 #199)
+#201 := [rewrite]: #200
+#190 := (iff #110 #197)
+#191 := [rewrite]: #190
+#204 := [monotonicity #191 #201]: #203
+#220 := [monotonicity #204]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#188 := (~ #177 #177)
+#187 := (~ #174 #174)
+#184 := [refl]: #187
+#189 := [nnf-pos #184]: #188
+#28 := (- #14)
+#27 := (- #13)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #13 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#180 := (iff #42 #177)
+#74 := (and #21 #23)
+#77 := (or #22 #74)
+#150 := (ite #77 #35 #145)
+#153 := (ite #17 0::Int #150)
+#156 := (ite #18 #13 #153)
+#159 := (= #34 #156)
+#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
+#178 := (iff #162 #177)
+#175 := (iff #159 #174)
+#172 := (= #156 #171)
+#169 := (= #153 #168)
+#166 := (= #150 #165)
+#121 := (iff #77 #120)
+#118 := (iff #74 #117)
+#115 := (iff #23 #114)
+#116 := [rewrite]: #115
+#108 := (iff #21 #107)
+#109 := [rewrite]: #108
+#119 := [monotonicity #109 #116]: #118
+#111 := (iff #22 #110)
+#104 := (iff #20 #103)
+#105 := [rewrite]: #104
+#112 := [monotonicity #105 #109]: #111
+#122 := [monotonicity #112 #119]: #121
+#167 := [monotonicity #122]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#163 := (iff #42 #162)
+#160 := (iff #41 #159)
+#157 := (= #40 #156)
+#154 := (= #39 #153)
+#151 := (= #38 #150)
+#148 := (= #37 #145)
+#142 := (- #139)
+#146 := (= #142 #145)
+#147 := [rewrite]: #146
+#143 := (= #37 #142)
+#140 := (= #36 #139)
+#85 := (= #28 #84)
+#86 := [rewrite]: #85
+#82 := (= #27 #81)
+#83 := [rewrite]: #82
+#141 := [monotonicity #83 #86]: #140
+#144 := [monotonicity #141]: #143
+#149 := [trans #144 #147]: #148
+#78 := (iff #25 #77)
+#75 := (iff #24 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#152 := [monotonicity #79 #149]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#181 := [trans #164 #179]: #180
+#138 := [asserted]: #42
+#182 := [mp #138 #181]: #177
+#185 := [mp~ #182 #189]: #177
+#233 := [mp #185 #232]: #230
+#264 := [mp #233 #263]: #261
+#748 := [mp #264 #747]: #743
#8 := 1::Int
-#9 := (- 1::Int)
-#20 := (- #9)
-#21 := (mod #9 #20)
-#22 := (- #21)
-#19 := (mod 1::Int #9)
-#14 := (< 0::Int #9)
-#16 := (< 1::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 1::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#23 := (ite #18 #19 #22)
-#12 := (= 1::Int 0::Int)
-#24 := (ite #12 0::Int #23)
+#9 := 3::Int
+#10 := (f3 1::Int 3::Int)
+#11 := (= #10 1::Int)
+#12 := (not #11)
+#62 := [asserted]: #12
+#652 := (not #743)
+#653 := (or #652 #11)
+#322 := (* -1::Int 3::Int)
+#406 := (* -1::Int 1::Int)
+#407 := (mod #406 #322)
+#408 := (+ #10 #407)
+#399 := (= #408 0::Int)
+#410 := (mod 1::Int 3::Int)
+#411 := (* -1::Int #410)
+#412 := (+ #10 #411)
+#409 := (= #412 0::Int)
+#413 := (>= 1::Int 0::Int)
+#392 := (<= 3::Int 0::Int)
+#727 := (or #392 #413)
+#729 := (not #727)
+#386 := (<= 1::Int 0::Int)
+#516 := (or #386 #392)
+#723 := (not #516)
+#397 := (or #723 #729)
+#398 := (ite #397 #409 #399)
+#730 := (= #10 0::Int)
+#731 := (= 1::Int 0::Int)
+#732 := (ite #731 #730 #398)
+#63 := (= 1::Int #10)
+#733 := (= 3::Int 0::Int)
+#728 := (ite #733 #63 #732)
+#654 := (or #652 #728)
+#649 := (iff #654 #653)
+#640 := (iff #653 #653)
+#641 := [rewrite]: #640
+#658 := (iff #728 #11)
+#648 := (ite false #11 #11)
+#661 := (iff #648 #11)
+#662 := [rewrite]: #661
+#650 := (iff #728 #648)
+#659 := (iff #732 #11)
+#576 := (ite false #730 #11)
+#670 := (iff #576 #11)
+#657 := [rewrite]: #670
+#669 := (iff #732 #576)
+#574 := (iff #398 #11)
+#569 := -2::Int
+#664 := (= #10 -2::Int)
+#1 := true
+#570 := (ite true #11 #664)
+#572 := (iff #570 #11)
+#573 := [rewrite]: #572
+#571 := (iff #398 #570)
+#553 := (iff #399 #664)
+#679 := 2::Int
+#675 := (+ 2::Int #10)
+#560 := (= #675 0::Int)
+#665 := (iff #560 #664)
+#668 := [rewrite]: #665
+#519 := (iff #399 #560)
+#558 := (= #408 #675)
+#671 := (+ #10 2::Int)
+#673 := (= #671 #675)
+#676 := [rewrite]: #673
+#672 := (= #408 #671)
+#517 := (= #407 2::Int)
+#682 := -3::Int
+#678 := (mod -1::Int -3::Int)
+#686 := (= #678 2::Int)
+#515 := [rewrite]: #686
+#684 := (= #407 #678)
+#683 := (= #322 -3::Int)
+#677 := [rewrite]: #683
+#414 := (= #406 -1::Int)
+#696 := [rewrite]: #414
+#685 := [monotonicity #696 #677]: #684
+#518 := [trans #685 #515]: #517
+#674 := [monotonicity #518]: #672
+#559 := [trans #674 #676]: #558
+#667 := [monotonicity #559]: #519
+#568 := [trans #667 #668]: #553
+#680 := (iff #409 #11)
+#692 := (+ -1::Int #10)
+#689 := (= #692 0::Int)
+#537 := (iff #689 #11)
+#538 := [rewrite]: #537
+#695 := (iff #409 #689)
+#693 := (= #412 #692)
+#701 := (+ #10 -1::Int)
+#687 := (= #701 #692)
+#688 := [rewrite]: #687
+#690 := (= #412 #701)
+#700 := (= #411 -1::Int)
+#698 := (= #411 #406)
+#419 := (= #410 1::Int)
+#420 := [rewrite]: #419
+#699 := [monotonicity #420]: #698
+#697 := [trans #699 #696]: #700
+#691 := [monotonicity #697]: #690
+#694 := [trans #691 #688]: #693
+#536 := [monotonicity #694]: #695
+#681 := [trans #536 #538]: #680
+#417 := (iff #397 true)
+#428 := (or true false)
+#703 := (iff #428 true)
+#707 := [rewrite]: #703
+#702 := (iff #397 #428)
+#705 := (iff #729 false)
+#432 := (not true)
+#328 := (iff #432 false)
+#704 := [rewrite]: #328
+#433 := (iff #729 #432)
+#709 := (iff #727 true)
+#361 := (or false true)
+#722 := (iff #361 true)
+#708 := [rewrite]: #722
+#721 := (iff #727 #361)
+#720 := (iff #413 true)
+#360 := [rewrite]: #720
+#726 := (iff #392 false)
+#369 := [rewrite]: #726
+#719 := [monotonicity #369 #360]: #721
+#431 := [trans #719 #708]: #709
+#434 := [monotonicity #431]: #433
+#427 := [trans #434 #704]: #705
+#355 := (iff #723 true)
+#714 := (not false)
+#711 := (iff #714 true)
+#717 := [rewrite]: #711
+#715 := (iff #723 #714)
+#712 := (iff #516 false)
+#710 := (or false false)
+#375 := (iff #710 false)
+#376 := [rewrite]: #375
+#373 := (iff #516 #710)
+#725 := (iff #386 false)
+#385 := [rewrite]: #725
+#374 := [monotonicity #385 #369]: #373
+#713 := [trans #374 #376]: #712
+#716 := [monotonicity #713]: #715
+#718 := [trans #716 #717]: #355
+#706 := [monotonicity #718 #427]: #702
+#418 := [trans #706 #707]: #417
+#564 := [monotonicity #418 #681 #568]: #571
+#575 := [trans #564 #573]: #574
+#384 := (iff #731 false)
+#389 := [rewrite]: #384
+#666 := [monotonicity #389 #575]: #669
+#651 := [trans #666 #657]: #659
+#69 := (iff #63 #11)
+#70 := [rewrite]: #69
+#734 := (iff #733 false)
+#724 := [rewrite]: #734
+#660 := [monotonicity #724 #70 #651]: #650
+#663 := [trans #660 #662]: #658
+#656 := [monotonicity #663]: #649
+#643 := [trans #656 #641]: #649
+#655 := [quant-inst #8 #9]: #654
+#644 := [mp #655 #643]: #653
+[unit-resolution #644 #62 #748]: false
+unsat
+8af900968418033d3c8752b20b45c64c00fb3744 305 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#33 := (f3 #13 #14)
+#747 := (pattern #33)
+#10 := 0::Int
+#78 := -1::Int
+#82 := (* -1::Int #14)
+#79 := (* -1::Int #13)
+#143 := (mod #79 #82)
+#258 := (+ #33 #143)
+#259 := (= #258 0::Int)
+#34 := (mod #13 #14)
+#255 := (* -1::Int #34)
+#256 := (+ #33 #255)
+#257 := (= #256 0::Int)
+#117 := (>= #13 0::Int)
+#110 := (<= #14 0::Int)
+#202 := (or #110 #117)
+#203 := (not #202)
+#106 := (<= #13 0::Int)
+#200 := (or #106 #110)
+#201 := (not #200)
+#206 := (or #201 #203)
+#260 := (ite #206 #257 #259)
+#254 := (= #33 0::Int)
+#16 := (= #13 0::Int)
+#261 := (ite #16 #254 #260)
+#253 := (= #13 #33)
+#17 := (= #14 0::Int)
+#262 := (ite #17 #253 #261)
+#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#751 := (iff #265 #748)
+#749 := (iff #262 #262)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#149 := (* -1::Int #143)
+#222 := (ite #206 #34 #149)
+#225 := (ite #16 0::Int #222)
+#228 := (ite #17 #13 #225)
+#231 := (= #33 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #34 #149)
+#172 := (ite #16 0::Int #169)
+#175 := (ite #17 #13 #172)
+#178 := (= #33 #175)
+#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
+#235 := (iff #181 #234)
+#232 := (iff #178 #231)
+#229 := (= #175 #228)
+#226 := (= #172 #225)
+#223 := (= #169 #222)
+#207 := (iff #124 #206)
+#204 := (iff #121 #203)
+#205 := [rewrite]: #204
+#194 := (iff #114 #201)
+#195 := [rewrite]: #194
+#208 := [monotonicity #195 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#192 := (~ #181 #181)
+#191 := (~ #178 #178)
+#188 := [refl]: #191
+#193 := [nnf-pos #188]: #192
+#27 := (- #14)
+#26 := (- #13)
+#35 := (mod #26 #27)
+#36 := (- #35)
+#20 := (< 0::Int #14)
+#22 := (< #13 0::Int)
+#23 := (and #22 #20)
+#19 := (< 0::Int #13)
+#21 := (and #19 #20)
+#24 := (or #21 #23)
+#37 := (ite #24 #34 #36)
+#38 := (ite #16 0::Int #37)
+#39 := (ite #17 #13 #38)
+#40 := (= #33 #39)
+#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
+#184 := (iff #41 #181)
+#72 := (and #20 #22)
+#75 := (or #21 #72)
+#154 := (ite #75 #34 #149)
+#63 := (= 0::Int #13)
+#157 := (ite #63 0::Int #154)
+#66 := (= 0::Int #14)
+#160 := (ite #66 #13 #157)
+#163 := (= #33 #160)
+#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #75 #124)
+#122 := (iff #72 #121)
+#119 := (iff #22 #118)
+#120 := [rewrite]: #119
+#112 := (iff #20 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #21 #114)
+#108 := (iff #19 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#100 := (iff #63 #16)
+#101 := [rewrite]: #100
+#174 := [monotonicity #101 #171]: #173
+#102 := (iff #66 #17)
+#103 := [rewrite]: #102
+#177 := [monotonicity #103 #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #41 #166)
+#164 := (iff #40 #163)
+#161 := (= #39 #160)
+#158 := (= #38 #157)
+#155 := (= #37 #154)
+#152 := (= #36 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #36 #146)
+#144 := (= #35 #143)
+#83 := (= #27 #82)
+#84 := [rewrite]: #83
+#80 := (= #26 #79)
+#81 := [rewrite]: #80
+#145 := [monotonicity #81 #84]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#76 := (iff #24 #75)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#156 := [monotonicity #77 #153]: #155
+#64 := (iff #16 #63)
+#65 := [rewrite]: #64
+#159 := [monotonicity #65 #156]: #158
+#67 := (iff #17 #66)
+#68 := [rewrite]: #67
+#162 := [monotonicity #68 #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #41
+#186 := [mp #142 #185]: #181
+#189 := [mp~ #186 #193]: #181
+#237 := [mp #189 #236]: #234
+#268 := [mp #237 #267]: #265
+#753 := [mp #268 #752]: #748
+#8 := 3::Int
+#9 := (f3 3::Int 3::Int)
#11 := (= #9 0::Int)
-#25 := (ite #11 1::Int #24)
-#26 := (= #25 0::Int)
-#27 := (not #26)
-#132 := (iff #27 false)
-#1 := true
-#127 := (not true)
-#130 := (iff #127 false)
-#131 := [rewrite]: #130
-#128 := (iff #27 #127)
-#125 := (iff #26 true)
-#120 := (= 0::Int 0::Int)
-#123 := (iff #120 true)
-#124 := [rewrite]: #123
-#121 := (iff #26 #120)
-#114 := (ite false 1::Int 0::Int)
-#117 := (= #114 0::Int)
+#12 := (not #11)
+#61 := [asserted]: #12
+#573 := (not #748)
+#575 := (or #573 #11)
+#326 := (* -1::Int 3::Int)
+#411 := (mod #326 #326)
+#412 := (+ #9 #411)
+#413 := (= #412 0::Int)
+#404 := (mod 3::Int 3::Int)
+#415 := (* -1::Int #404)
+#416 := (+ #9 #415)
+#344 := (= #416 0::Int)
+#417 := (>= 3::Int 0::Int)
+#414 := (<= 3::Int 0::Int)
+#418 := (or #414 #417)
+#397 := (not #418)
+#732 := (or #414 #414)
+#734 := (not #732)
+#391 := (or #734 #397)
+#521 := (ite #391 #344 #413)
+#728 := (= 3::Int 0::Int)
+#402 := (ite #728 #11 #521)
+#403 := (= 3::Int #9)
+#735 := (ite #728 #403 #402)
+#576 := (or #573 #735)
+#577 := (iff #576 #575)
+#579 := (iff #575 #575)
+#580 := [rewrite]: #579
+#673 := (iff #735 #11)
+#733 := (= #9 3::Int)
+#524 := (ite false #733 #11)
+#669 := (iff #524 #11)
+#670 := [rewrite]: #669
+#672 := (iff #735 #524)
+#564 := (iff #402 #11)
+#679 := (ite false #11 #11)
+#681 := (iff #679 #11)
+#563 := [rewrite]: #681
+#680 := (iff #402 #679)
+#676 := (iff #521 #11)
+#1 := true
+#684 := (ite true #11 #11)
+#522 := (iff #684 #11)
+#523 := [rewrite]: #522
+#691 := (iff #521 #684)
+#689 := (iff #413 #11)
+#682 := (= #412 #9)
+#419 := (+ #9 0::Int)
+#702 := (= #419 #9)
+#706 := [rewrite]: #702
+#687 := (= #412 #419)
+#685 := (= #411 0::Int)
+#693 := -3::Int
+#694 := (mod -3::Int -3::Int)
+#542 := (= #694 0::Int)
+#543 := [rewrite]: #542
+#700 := (= #411 #694)
+#698 := (= #326 -3::Int)
+#699 := [rewrite]: #698
+#541 := [monotonicity #699 #699]: #700
+#686 := [trans #541 #543]: #685
+#688 := [monotonicity #686]: #687
+#683 := [trans #688 #706]: #682
+#690 := [monotonicity #683]: #689
+#697 := (iff #344 #11)
+#695 := (= #416 #9)
+#701 := (= #416 #419)
+#703 := (= #415 0::Int)
+#712 := (* -1::Int 0::Int)
+#424 := (= #712 0::Int)
+#425 := [rewrite]: #424
+#422 := (= #415 #712)
+#711 := (= #404 0::Int)
+#708 := [rewrite]: #711
+#423 := [monotonicity #708]: #422
+#704 := [trans #423 #425]: #703
+#705 := [monotonicity #704]: #701
+#696 := [trans #705 #706]: #695
+#692 := [monotonicity #696]: #697
+#433 := (iff #391 true)
+#439 := (or true false)
+#710 := (iff #439 true)
+#432 := [rewrite]: #710
+#332 := (iff #391 #439)
+#437 := (iff #397 false)
+#724 := (not true)
+#714 := (iff #724 false)
+#436 := [rewrite]: #714
+#727 := (iff #397 #724)
+#366 := (iff #418 true)
+#722 := (or false true)
+#725 := (iff #722 true)
+#365 := [rewrite]: #725
+#360 := (iff #418 #722)
+#721 := (iff #417 true)
+#716 := [rewrite]: #721
+#729 := (iff #414 false)
+#389 := [rewrite]: #729
+#723 := [monotonicity #389 #716]: #360
+#726 := [trans #723 #365]: #366
+#713 := [monotonicity #726]: #727
+#438 := [trans #713 #436]: #437
+#719 := (iff #734 true)
+#379 := (not false)
+#717 := (iff #379 true)
+#718 := [rewrite]: #717
+#380 := (iff #734 #379)
+#715 := (iff #732 false)
+#394 := (or false false)
+#731 := (iff #394 false)
+#374 := [rewrite]: #731
+#730 := (iff #732 #394)
+#390 := [monotonicity #389 #389]: #730
+#378 := [trans #390 #374]: #715
+#381 := [monotonicity #378]: #380
+#720 := [trans #381 #718]: #719
+#709 := [monotonicity #720 #438]: #332
+#707 := [trans #709 #432]: #433
+#520 := [monotonicity #707 #692 #690]: #691
+#677 := [trans #520 #523]: #676
+#736 := (iff #728 false)
+#737 := [rewrite]: #736
+#678 := [monotonicity #737 #677]: #680
+#565 := [trans #678 #563]: #564
+#738 := (iff #403 #733)
+#739 := [rewrite]: #738
+#574 := [monotonicity #737 #739 #565]: #672
+#558 := [trans #574 #670]: #673
+#578 := [monotonicity #558]: #577
+#581 := [trans #578 #580]: #577
+#569 := [quant-inst #8 #8]: #576
+#674 := [mp #569 #581]: #575
+[unit-resolution #674 #61 #753]: false
+unsat
+e06ff93350d55c82e0187108fc1a1d48234a7767 326 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#35 := (f3 #14 #15)
+#734 := (pattern #35)
+#17 := 0::Int
+#71 := -1::Int
+#75 := (* -1::Int #15)
+#72 := (* -1::Int #14)
+#130 := (mod #72 #75)
+#245 := (+ #35 #130)
+#246 := (= #245 0::Int)
+#36 := (mod #14 #15)
+#242 := (* -1::Int #36)
+#243 := (+ #35 #242)
+#244 := (= #243 0::Int)
+#104 := (>= #14 0::Int)
+#97 := (<= #15 0::Int)
+#189 := (or #97 #104)
+#190 := (not #189)
+#93 := (<= #14 0::Int)
+#187 := (or #93 #97)
+#188 := (not #187)
+#193 := (or #188 #190)
+#247 := (ite #193 #244 #246)
+#241 := (= #35 0::Int)
+#18 := (= #14 0::Int)
+#248 := (ite #18 #241 #247)
+#240 := (= #14 #35)
+#19 := (= #15 0::Int)
+#249 := (ite #19 #240 #248)
+#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #249)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#738 := (iff #252 #735)
+#736 := (iff #249 #249)
+#737 := [refl]: #736
+#739 := [quant-intro #737]: #738
+#136 := (* -1::Int #130)
+#209 := (ite #193 #36 #136)
+#212 := (ite #18 0::Int #209)
+#215 := (ite #19 #14 #212)
+#218 := (= #35 #215)
+#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
+#253 := (iff #221 #252)
+#250 := (iff #218 #249)
+#251 := [rewrite]: #250
+#254 := [quant-intro #251]: #253
+#105 := (not #104)
+#98 := (not #97)
+#108 := (and #98 #105)
+#94 := (not #93)
+#101 := (and #94 #98)
+#111 := (or #101 #108)
+#156 := (ite #111 #36 #136)
+#159 := (ite #18 0::Int #156)
+#162 := (ite #19 #14 #159)
+#165 := (= #35 #162)
+#168 := (forall (vars (?v0 Int) (?v1 Int)) #165)
+#222 := (iff #168 #221)
+#219 := (iff #165 #218)
+#216 := (= #162 #215)
+#213 := (= #159 #212)
+#210 := (= #156 #209)
+#194 := (iff #111 #193)
+#191 := (iff #108 #190)
+#192 := [rewrite]: #191
+#181 := (iff #101 #188)
+#182 := [rewrite]: #181
+#195 := [monotonicity #182 #192]: #194
+#211 := [monotonicity #195]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#223 := [quant-intro #220]: #222
+#179 := (~ #168 #168)
+#178 := (~ #165 #165)
+#175 := [refl]: #178
+#180 := [nnf-pos #175]: #179
+#29 := (- #15)
+#28 := (- #14)
+#37 := (mod #28 #29)
+#38 := (- #37)
+#22 := (< 0::Int #15)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#39 := (ite #26 #36 #38)
+#40 := (ite #18 0::Int #39)
+#41 := (ite #19 #14 #40)
+#42 := (= #35 #41)
+#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
+#171 := (iff #43 #168)
+#65 := (and #22 #24)
+#68 := (or #23 #65)
+#141 := (ite #68 #36 #136)
+#144 := (ite #18 0::Int #141)
+#147 := (ite #19 #14 #144)
+#150 := (= #35 #147)
+#153 := (forall (vars (?v0 Int) (?v1 Int)) #150)
+#169 := (iff #153 #168)
+#166 := (iff #150 #165)
+#163 := (= #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#112 := (iff #68 #111)
+#109 := (iff #65 #108)
+#106 := (iff #24 #105)
+#107 := [rewrite]: #106
+#99 := (iff #22 #98)
+#100 := [rewrite]: #99
+#110 := [monotonicity #100 #107]: #109
+#102 := (iff #23 #101)
+#95 := (iff #21 #94)
+#96 := [rewrite]: #95
+#103 := [monotonicity #96 #100]: #102
+#113 := [monotonicity #103 #110]: #112
+#158 := [monotonicity #113]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [quant-intro #167]: #169
+#154 := (iff #43 #153)
+#151 := (iff #42 #150)
+#148 := (= #41 #147)
+#145 := (= #40 #144)
+#142 := (= #39 #141)
+#139 := (= #38 #136)
+#133 := (- #130)
+#137 := (= #133 #136)
+#138 := [rewrite]: #137
+#134 := (= #38 #133)
+#131 := (= #37 #130)
+#76 := (= #29 #75)
+#77 := [rewrite]: #76
+#73 := (= #28 #72)
+#74 := [rewrite]: #73
+#132 := [monotonicity #74 #77]: #131
+#135 := [monotonicity #132]: #134
+#140 := [trans #135 #138]: #139
+#69 := (iff #26 #68)
+#66 := (iff #25 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#143 := [monotonicity #70 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#155 := [quant-intro #152]: #154
+#172 := [trans #155 #170]: #171
+#129 := [asserted]: #43
+#173 := [mp #129 #172]: #168
+#176 := [mp~ #173 #180]: #168
+#224 := [mp #176 #223]: #221
+#255 := [mp #224 #254]: #252
+#740 := [mp #255 #739]: #735
+#11 := 2::Int
+#9 := 3::Int
+#8 := 5::Int
+#10 := (f3 5::Int 3::Int)
+#12 := (= #10 2::Int)
+#13 := (not #12)
+#63 := [asserted]: #13
+#633 := (not #735)
+#635 := (or #633 #12)
+#313 := (* -1::Int 3::Int)
+#398 := (* -1::Int 5::Int)
+#399 := (mod #398 #313)
+#400 := (+ #10 #399)
+#391 := (= #400 0::Int)
+#402 := (mod 5::Int 3::Int)
+#403 := (* -1::Int #402)
+#331 := (+ #10 #403)
+#404 := (= #331 0::Int)
+#401 := (>= 5::Int 0::Int)
+#405 := (<= 3::Int 0::Int)
+#384 := (or #405 #401)
+#719 := (not #384)
+#721 := (<= 5::Int 0::Int)
+#378 := (or #721 #405)
+#508 := (not #378)
+#715 := (or #508 #719)
+#389 := (ite #715 #404 #391)
+#390 := (= #10 0::Int)
+#722 := (= 5::Int 0::Int)
+#723 := (ite #722 #390 #389)
+#724 := (= 5::Int #10)
+#725 := (= 3::Int 0::Int)
+#720 := (ite #725 #724 #723)
+#636 := (or #633 #720)
+#638 := (iff #636 #635)
+#639 := (iff #635 #635)
+#625 := [rewrite]: #639
+#648 := (iff #720 #12)
+#381 := (= #10 5::Int)
+#644 := (ite false #381 #12)
+#647 := (iff #644 #12)
+#641 := [rewrite]: #647
+#645 := (iff #720 #644)
+#650 := (iff #723 #12)
+#640 := (ite false #390 #12)
+#653 := (iff #640 #12)
+#654 := [rewrite]: #653
+#642 := (iff #723 #640)
+#651 := (iff #389 #12)
+#556 := (= #10 -1::Int)
+#1 := true
+#568 := (ite true #12 #556)
+#662 := (iff #568 #12)
+#649 := [rewrite]: #662
+#661 := (iff #389 #568)
+#566 := (iff #391 #556)
+#667 := 1::Int
+#561 := (+ 1::Int #10)
+#560 := (= #561 0::Int)
+#564 := (iff #560 #556)
+#565 := [rewrite]: #564
+#562 := (iff #391 #560)
+#660 := (= #400 #561)
+#552 := (+ #10 1::Int)
+#656 := (= #552 #561)
+#657 := [rewrite]: #656
+#511 := (= #400 #552)
+#550 := (= #399 1::Int)
+#507 := -3::Int
+#677 := -5::Int
+#663 := (mod -5::Int -3::Int)
+#665 := (= #663 1::Int)
+#668 := [rewrite]: #665
+#664 := (= #399 #663)
+#509 := (= #313 -3::Int)
+#510 := [rewrite]: #509
+#671 := (= #398 -5::Int)
+#678 := [rewrite]: #671
+#666 := [monotonicity #678 #510]: #664
+#551 := [trans #666 #668]: #550
+#659 := [monotonicity #551]: #511
+#545 := [trans #659 #657]: #660
+#563 := [monotonicity #545]: #562
+#567 := [trans #563 #565]: #566
+#670 := (iff #404 #12)
+#693 := -2::Int
+#681 := (+ -2::Int #10)
+#672 := (= #681 0::Int)
+#675 := (iff #672 #12)
+#669 := [rewrite]: #675
+#673 := (iff #404 #672)
+#529 := (= #331 #681)
+#680 := (+ #10 -2::Int)
+#687 := (= #680 #681)
+#528 := [rewrite]: #687
+#685 := (= #331 #680)
+#684 := (= #403 -2::Int)
+#688 := (* -1::Int 2::Int)
+#682 := (= #688 -2::Int)
+#683 := [rewrite]: #682
+#692 := (= #403 #688)
+#691 := (= #402 2::Int)
+#406 := [rewrite]: #691
+#689 := [monotonicity #406]: #692
+#679 := [trans #689 #683]: #684
+#686 := [monotonicity #679]: #685
+#530 := [trans #686 #528]: #529
+#674 := [monotonicity #530]: #673
+#676 := [trans #674 #669]: #670
+#412 := (iff #715 true)
+#695 := (or true false)
+#410 := (iff #695 true)
+#411 := [rewrite]: #410
+#699 := (iff #715 #695)
+#694 := (iff #719 false)
+#319 := (not true)
+#419 := (iff #319 false)
+#420 := [rewrite]: #419
+#696 := (iff #719 #319)
+#425 := (iff #384 true)
+#714 := (or false true)
+#423 := (iff #714 true)
+#424 := [rewrite]: #423
+#700 := (iff #384 #714)
+#713 := (iff #401 true)
+#711 := [rewrite]: #713
+#365 := (iff #405 false)
+#366 := [rewrite]: #365
+#701 := [monotonicity #366 #711]: #700
+#426 := [trans #701 #424]: #425
+#697 := [monotonicity #426]: #696
+#698 := [trans #697 #420]: #694
+#352 := (iff #508 true)
+#703 := (not false)
+#710 := (iff #703 true)
+#712 := [rewrite]: #710
+#709 := (iff #508 #703)
+#707 := (iff #378 false)
+#367 := (or false false)
+#705 := (iff #367 false)
+#706 := [rewrite]: #705
+#368 := (iff #378 #367)
+#361 := (iff #721 false)
+#702 := [rewrite]: #361
+#704 := [monotonicity #702 #366]: #368
+#708 := [trans #704 #706]: #707
+#347 := [monotonicity #708]: #709
+#353 := [trans #347 #712]: #352
+#409 := [monotonicity #353 #698]: #699
+#690 := [trans #409 #411]: #412
+#658 := [monotonicity #690 #676 #567]: #661
+#643 := [trans #658 #649]: #651
+#377 := (iff #722 false)
+#718 := [rewrite]: #377
+#652 := [monotonicity #718 #643]: #642
+#655 := [trans #652 #654]: #650
+#376 := (iff #724 #381)
+#717 := [rewrite]: #376
+#726 := (iff #725 false)
+#716 := [rewrite]: #726
+#646 := [monotonicity #716 #717 #655]: #645
+#632 := [trans #646 #641]: #648
+#634 := [monotonicity #632]: #638
+#626 := [trans #634 #625]: #638
+#637 := [quant-inst #8 #9]: #636
+#628 := [mp #637 #626]: #635
+[unit-resolution #628 #63 #740]: false
+unsat
+216c9ba1da8ff35ffdfffd11994f68f93a59b859 330 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#37 := (f3 #16 #17)
+#751 := (pattern #37)
+#19 := 0::Int
+#89 := -1::Int
+#93 := (* -1::Int #17)
+#90 := (* -1::Int #16)
+#148 := (mod #90 #93)
+#263 := (+ #37 #148)
+#264 := (= #263 0::Int)
+#38 := (mod #16 #17)
+#260 := (* -1::Int #38)
+#261 := (+ #37 #260)
+#262 := (= #261 0::Int)
+#122 := (>= #16 0::Int)
+#115 := (<= #17 0::Int)
+#207 := (or #115 #122)
+#208 := (not #207)
+#111 := (<= #16 0::Int)
+#205 := (or #111 #115)
+#206 := (not #205)
+#211 := (or #206 #208)
+#265 := (ite #211 #262 #264)
+#259 := (= #37 0::Int)
+#20 := (= #16 0::Int)
+#266 := (ite #20 #259 #265)
+#258 := (= #16 #37)
+#21 := (= #17 0::Int)
+#267 := (ite #21 #258 #266)
+#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #267)
+#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
+#755 := (iff #270 #752)
+#753 := (iff #267 #267)
+#754 := [refl]: #753
+#756 := [quant-intro #754]: #755
+#154 := (* -1::Int #148)
+#227 := (ite #211 #38 #154)
+#230 := (ite #20 0::Int #227)
+#233 := (ite #21 #16 #230)
+#236 := (= #37 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#271 := (iff #239 #270)
+#268 := (iff #236 #267)
+#269 := [rewrite]: #268
+#272 := [quant-intro #269]: #271
+#123 := (not #122)
+#116 := (not #115)
+#126 := (and #116 #123)
+#112 := (not #111)
+#119 := (and #112 #116)
+#129 := (or #119 #126)
+#174 := (ite #129 #38 #154)
+#177 := (ite #20 0::Int #174)
+#180 := (ite #21 #16 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#240 := (iff #186 #239)
+#237 := (iff #183 #236)
+#234 := (= #180 #233)
+#231 := (= #177 #230)
+#228 := (= #174 #227)
+#212 := (iff #129 #211)
+#209 := (iff #126 #208)
+#210 := [rewrite]: #209
+#199 := (iff #119 #206)
+#200 := [rewrite]: #199
+#213 := [monotonicity #200 #210]: #212
+#229 := [monotonicity #213]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#197 := (~ #186 #186)
+#196 := (~ #183 #183)
+#193 := [refl]: #196
+#198 := [nnf-pos #193]: #197
+#31 := (- #17)
+#30 := (- #16)
+#39 := (mod #30 #31)
+#40 := (- #39)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#41 := (ite #28 #38 #40)
+#42 := (ite #20 0::Int #41)
+#43 := (ite #21 #16 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#189 := (iff #45 #186)
+#82 := (and #24 #26)
+#86 := (or #25 #82)
+#159 := (ite #86 #38 #154)
+#162 := (ite #20 0::Int #159)
+#165 := (ite #21 #16 #162)
+#168 := (= #37 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#187 := (iff #171 #186)
+#184 := (iff #168 #183)
+#181 := (= #165 #180)
+#178 := (= #162 #177)
+#175 := (= #159 #174)
+#130 := (iff #86 #129)
+#127 := (iff #82 #126)
+#124 := (iff #26 #123)
+#125 := [rewrite]: #124
+#117 := (iff #24 #116)
#118 := [rewrite]: #117
-#115 := (= #25 #114)
-#112 := (= #24 0::Int)
-#107 := (ite false 0::Int 0::Int)
-#110 := (= #107 0::Int)
-#111 := [rewrite]: #110
-#108 := (= #24 #107)
-#105 := (= #23 0::Int)
-#48 := -1::Int
-#60 := (< 0::Int -1::Int)
-#66 := (and #16 #60)
-#63 := (and #13 #60)
-#69 := (or #63 #66)
-#100 := (ite #69 0::Int 0::Int)
-#103 := (= #100 0::Int)
-#104 := [rewrite]: #103
-#101 := (= #23 #100)
-#98 := (= #22 0::Int)
-#93 := (- 0::Int)
-#96 := (= #93 0::Int)
-#97 := [rewrite]: #96
-#94 := (= #22 #93)
-#91 := (= #21 0::Int)
-#86 := (mod -1::Int 1::Int)
-#89 := (= #86 0::Int)
-#90 := [rewrite]: #89
-#87 := (= #21 #86)
-#84 := (= #20 1::Int)
-#79 := (- -1::Int)
-#82 := (= #79 1::Int)
-#83 := [rewrite]: #82
-#80 := (= #20 #79)
-#49 := (= #9 -1::Int)
-#50 := [rewrite]: #49
-#81 := [monotonicity #50]: #80
-#85 := [trans #81 #83]: #84
-#88 := [monotonicity #50 #85]: #87
-#92 := [trans #88 #90]: #91
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#77 := (= #19 0::Int)
-#72 := (mod 1::Int -1::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #19 #72)
-#74 := [monotonicity #50]: #73
-#78 := [trans #74 #76]: #77
-#70 := (iff #18 #69)
-#67 := (iff #17 #66)
-#61 := (iff #14 #60)
-#62 := [monotonicity #50]: #61
-#68 := [monotonicity #62]: #67
-#64 := (iff #15 #63)
-#65 := [monotonicity #62]: #64
-#71 := [monotonicity #65 #68]: #70
-#102 := [monotonicity #71 #78 #99]: #101
-#106 := [trans #102 #104]: #105
-#58 := (iff #12 false)
-#59 := [rewrite]: #58
-#109 := [monotonicity #59 #106]: #108
-#113 := [trans #109 #111]: #112
-#56 := (iff #11 false)
-#51 := (= -1::Int 0::Int)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #11 #51)
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#116 := [monotonicity #57 #113]: #115
-#119 := [trans #116 #118]: #26
-#122 := [monotonicity #119]: #121
-#126 := [trans #122 #124]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#47 := [asserted]: #27
-[mp #47 #133]: false
-unsat
-3e5306453747f88fb9407b2be361e50903b04cbd 116 0
-#2 := false
-#10 := 0::Int
+#128 := [monotonicity #118 #125]: #127
+#120 := (iff #25 #119)
+#113 := (iff #23 #112)
+#114 := [rewrite]: #113
+#121 := [monotonicity #114 #118]: #120
+#131 := [monotonicity #121 #128]: #130
+#176 := [monotonicity #131]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
+#172 := (iff #45 #171)
+#169 := (iff #44 #168)
+#166 := (= #43 #165)
+#163 := (= #42 #162)
+#160 := (= #41 #159)
+#157 := (= #40 #154)
+#151 := (- #148)
+#155 := (= #151 #154)
+#156 := [rewrite]: #155
+#152 := (= #40 #151)
+#149 := (= #39 #148)
+#94 := (= #31 #93)
+#95 := [rewrite]: #94
+#91 := (= #30 #90)
+#92 := [rewrite]: #91
+#150 := [monotonicity #92 #95]: #149
+#153 := [monotonicity #150]: #152
+#158 := [trans #153 #156]: #157
+#87 := (iff #28 #86)
+#84 := (iff #27 #82)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#161 := [monotonicity #88 #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#190 := [trans #173 #188]: #189
+#147 := [asserted]: #45
+#191 := [mp #147 #190]: #186
+#194 := [mp~ #191 #198]: #186
+#242 := [mp #194 #241]: #239
+#273 := [mp #242 #272]: #270
+#757 := [mp #273 #756]: #752
+#72 := -2::Int
+#66 := -3::Int
+#8 := 1::Int
+#69 := (f3 1::Int -3::Int)
+#75 := (= #69 -2::Int)
+#78 := (not #75)
+#12 := 2::Int
+#13 := (- 2::Int)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 1::Int #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#79 := (iff #15 #78)
+#76 := (iff #14 #75)
+#73 := (= #13 -2::Int)
+#74 := [rewrite]: #73
+#70 := (= #11 #69)
+#67 := (= #10 -3::Int)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#80 := [monotonicity #77]: #79
+#65 := [asserted]: #15
+#83 := [mp #65 #80]: #78
+#659 := (not #752)
+#669 := (or #659 #75)
+#331 := (* -1::Int -3::Int)
+#415 := (* -1::Int 1::Int)
+#416 := (mod #415 #331)
+#417 := (+ #69 #416)
+#408 := (= #417 0::Int)
+#419 := (mod 1::Int -3::Int)
+#420 := (* -1::Int #419)
+#421 := (+ #69 #420)
+#418 := (= #421 0::Int)
+#422 := (>= 1::Int 0::Int)
+#401 := (<= -3::Int 0::Int)
+#736 := (or #401 #422)
+#738 := (not #736)
+#395 := (<= 1::Int 0::Int)
+#525 := (or #395 #401)
+#732 := (not #525)
+#406 := (or #732 #738)
+#407 := (ite #406 #418 #408)
+#739 := (= #69 0::Int)
+#740 := (= 1::Int 0::Int)
+#741 := (ite #740 #739 #407)
+#742 := (= 1::Int #69)
+#737 := (= -3::Int 0::Int)
+#743 := (ite #737 #742 #741)
+#670 := (or #659 #743)
+#667 := (iff #670 #669)
+#661 := (iff #669 #669)
+#662 := [rewrite]: #661
+#660 := (iff #743 #75)
+#734 := (= #69 1::Int)
+#677 := (ite false #734 #75)
+#579 := (iff #677 #75)
+#580 := [rewrite]: #579
+#666 := (iff #743 #677)
+#675 := (iff #741 #75)
+#582 := (ite false #739 #75)
+#585 := (iff #582 #75)
+#678 := [rewrite]: #585
+#583 := (iff #741 #582)
+#573 := (iff #407 #75)
+#562 := (iff #407 #677)
+#673 := (iff #408 #75)
+#683 := (+ 2::Int #69)
+#568 := (= #683 0::Int)
+#676 := (iff #568 #75)
+#578 := [rewrite]: #676
+#569 := (iff #408 #568)
+#685 := (= #417 #683)
+#527 := (+ #69 2::Int)
+#684 := (= #527 #683)
+#682 := [rewrite]: #684
+#680 := (= #417 #527)
+#524 := (= #416 2::Int)
+#687 := (mod -1::Int 3::Int)
+#688 := (= #687 2::Int)
+#695 := [rewrite]: #688
+#693 := (= #416 #687)
+#692 := (= #331 3::Int)
+#686 := [rewrite]: #692
+#705 := (= #415 -1::Int)
+#709 := [rewrite]: #705
+#694 := [monotonicity #709 #686]: #693
+#526 := [trans #694 #695]: #524
+#681 := [monotonicity #526]: #680
+#567 := [trans #681 #682]: #685
+#528 := [monotonicity #567]: #569
+#674 := [trans #528 #578]: #673
+#690 := (iff #418 #734)
+#696 := (+ -1::Int #69)
+#704 := (= #696 0::Int)
+#547 := (iff #704 #734)
+#689 := [rewrite]: #547
+#545 := (iff #418 #704)
+#703 := (= #421 #696)
+#699 := (+ #69 -1::Int)
+#697 := (= #699 #696)
+#702 := [rewrite]: #697
+#700 := (= #421 #699)
+#706 := (= #420 -1::Int)
+#708 := (= #420 #415)
+#429 := (= #419 1::Int)
+#707 := [rewrite]: #429
+#423 := [monotonicity #707]: #708
+#710 := [trans #423 #709]: #706
+#701 := [monotonicity #710]: #700
+#698 := [trans #701 #702]: #703
+#546 := [monotonicity #698]: #545
+#691 := [trans #546 #689]: #690
+#427 := (iff #406 false)
+#711 := (or false false)
+#716 := (iff #711 false)
+#426 := [rewrite]: #716
+#715 := (iff #406 #711)
+#436 := (iff #738 false)
+#1 := true
+#726 := (not true)
+#729 := (iff #726 false)
+#369 := [rewrite]: #729
+#713 := (iff #738 #726)
+#443 := (iff #736 true)
+#717 := (or true true)
+#441 := (iff #717 true)
+#442 := [rewrite]: #441
+#718 := (iff #736 #717)
+#728 := (iff #422 true)
+#731 := [rewrite]: #728
+#383 := (iff #401 true)
+#384 := [rewrite]: #383
+#440 := [monotonicity #384 #731]: #718
+#337 := [trans #440 #442]: #443
+#714 := [monotonicity #337]: #713
+#437 := [trans #714 #369]: #436
+#370 := (iff #732 false)
+#364 := (iff #732 #726)
+#725 := (iff #525 true)
+#385 := (or false true)
+#723 := (iff #385 true)
+#724 := [rewrite]: #723
+#721 := (iff #525 #385)
+#719 := (iff #395 false)
+#382 := [rewrite]: #719
+#722 := [monotonicity #382 #384]: #721
+#720 := [trans #722 #724]: #725
+#727 := [monotonicity #720]: #364
+#730 := [trans #727 #369]: #370
+#712 := [monotonicity #730 #437]: #715
+#428 := [trans #712 #426]: #427
+#577 := [monotonicity #428 #691 #674]: #562
+#581 := [trans #577 #580]: #573
+#735 := (iff #740 false)
+#378 := [rewrite]: #735
+#584 := [monotonicity #378 #581]: #583
+#679 := [trans #584 #678]: #675
+#398 := (iff #742 #734)
+#394 := [rewrite]: #398
+#733 := (iff #737 false)
+#393 := [rewrite]: #733
+#668 := [monotonicity #393 #394 #679]: #666
+#657 := [trans #668 #580]: #660
+#672 := [monotonicity #657]: #667
+#663 := [trans #672 #662]: #667
+#671 := [quant-inst #8 #66]: #670
+#664 := [mp #671 #663]: #669
+[unit-resolution #664 #83 #757]: false
+unsat
+e4d7746f48f3d604f4d6994a010e44b10b471dbd 333 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#773 := (pattern #34)
+#11 := 0::Int
+#104 := -1::Int
+#108 := (* -1::Int #15)
+#105 := (* -1::Int #14)
+#169 := (mod #105 #108)
+#284 := (+ #34 #169)
+#285 := (= #284 0::Int)
+#35 := (mod #14 #15)
+#281 := (* -1::Int #35)
+#282 := (+ #34 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #14 0::Int)
+#136 := (<= #15 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #14 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#287 := (ite #17 #280 #286)
+#279 := (= #14 #34)
+#18 := (= #15 0::Int)
+#288 := (ite #18 #279 #287)
+#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#777 := (iff #291 #774)
+#775 := (iff #288 #288)
+#776 := [refl]: #775
+#778 := [quant-intro #776]: #777
+#175 := (* -1::Int #169)
+#248 := (ite #232 #35 #175)
+#251 := (ite #17 0::Int #248)
+#254 := (ite #18 #14 #251)
+#257 := (= #34 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #35 #175)
+#198 := (ite #17 0::Int #195)
+#201 := (ite #18 #14 #198)
+#204 := (= #34 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#210 := (iff #42 #207)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#180 := (ite #101 #35 #175)
+#89 := (= 0::Int #14)
+#183 := (ite #89 0::Int #180)
+#92 := (= 0::Int #15)
+#186 := (ite #92 #14 #183)
+#189 := (= #34 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #101 #150)
+#148 := (iff #98 #147)
+#145 := (iff #23 #144)
+#146 := [rewrite]: #145
+#138 := (iff #21 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #22 #140)
+#134 := (iff #20 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #89 #17)
+#127 := [rewrite]: #126
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #92 #18)
+#129 := [rewrite]: #128
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#187 := (= #40 #186)
+#184 := (= #39 #183)
+#181 := (= #38 #180)
+#178 := (= #37 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #37 #172)
+#170 := (= #36 #169)
+#109 := (= #28 #108)
+#110 := [rewrite]: #109
+#106 := (= #27 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#182 := [monotonicity #103 #179]: #181
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#185 := [monotonicity #91 #182]: #184
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#188 := [monotonicity #94 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #42
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#779 := [mp #294 #778]: #774
+#63 := -3::Int
+#8 := 3::Int
+#66 := (f3 3::Int -3::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := (- 3::Int)
+#10 := (f3 3::Int #9)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #10 #66)
+#64 := (= #9 -3::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#602 := (not #774)
+#595 := (or #602 #69)
+#352 := (* -1::Int -3::Int)
+#437 := (* -1::Int 3::Int)
+#438 := (mod #437 #352)
+#439 := (+ #66 #438)
+#430 := (= #439 0::Int)
+#441 := (mod 3::Int -3::Int)
+#442 := (* -1::Int #441)
+#370 := (+ #66 #442)
+#443 := (= #370 0::Int)
+#440 := (>= 3::Int 0::Int)
+#444 := (<= -3::Int 0::Int)
+#423 := (or #444 #440)
+#758 := (not #423)
+#760 := (<= 3::Int 0::Int)
+#417 := (or #760 #444)
+#547 := (not #417)
+#754 := (or #547 #758)
+#428 := (ite #754 #443 #430)
+#429 := (= 3::Int 0::Int)
+#761 := (ite #429 #69 #428)
+#762 := (= 3::Int #66)
+#763 := (= -3::Int 0::Int)
+#764 := (ite #763 #762 #761)
+#603 := (or #602 #764)
+#605 := (iff #603 #595)
+#607 := (iff #595 #595)
+#700 := [rewrite]: #607
+#599 := (iff #764 #69)
+#415 := (= #66 3::Int)
+#600 := (ite false #415 #69)
+#699 := (iff #600 #69)
+#584 := [rewrite]: #699
+#695 := (iff #764 #600)
+#550 := (iff #761 #69)
+#702 := (ite false #69 #69)
+#706 := (iff #702 #69)
+#704 := [rewrite]: #706
+#590 := (iff #761 #702)
+#707 := (iff #428 #69)
+#703 := (iff #428 #702)
+#548 := (iff #430 #69)
+#717 := (= #439 #66)
+#732 := (+ #66 0::Int)
+#723 := (= #732 #66)
+#718 := [rewrite]: #723
+#716 := (= #439 #732)
+#709 := (= #438 0::Int)
+#711 := (mod -3::Int 3::Int)
+#714 := (= #711 0::Int)
+#708 := [rewrite]: #714
+#712 := (= #438 #711)
+#568 := (= #352 3::Int)
+#569 := [rewrite]: #568
+#726 := (= #437 -3::Int)
+#567 := [rewrite]: #726
+#713 := [monotonicity #567 #569]: #712
+#715 := [trans #713 #708]: #709
+#710 := [monotonicity #715]: #716
+#546 := [trans #710 #718]: #717
+#549 := [monotonicity #546]: #548
+#725 := (iff #443 #69)
+#719 := (= #370 #66)
+#721 := (= #370 #732)
+#731 := (= #442 0::Int)
+#451 := (* -1::Int 0::Int)
+#445 := (= #451 0::Int)
+#727 := [rewrite]: #445
+#729 := (= #442 #451)
+#449 := (= #441 0::Int)
+#450 := [rewrite]: #449
+#730 := [monotonicity #450]: #729
+#728 := [trans #730 #727]: #731
+#722 := [monotonicity #728]: #721
+#724 := [trans #722 #718]: #719
+#720 := [monotonicity #724]: #725
+#738 := (iff #754 false)
+#458 := (or false false)
+#737 := (iff #458 false)
+#734 := [rewrite]: #737
+#459 := (iff #754 #458)
+#735 := (iff #758 false)
+#1 := true
+#747 := (not true)
+#386 := (iff #747 false)
+#749 := [rewrite]: #386
+#465 := (iff #758 #747)
+#463 := (iff #423 true)
+#750 := (or true true)
+#740 := (iff #750 true)
+#462 := [rewrite]: #740
+#753 := (iff #423 #750)
+#392 := (iff #440 true)
+#752 := [rewrite]: #392
+#741 := (iff #444 true)
+#404 := [rewrite]: #741
+#739 := [monotonicity #404 #752]: #753
+#464 := [trans #739 #462]: #463
+#358 := [monotonicity #464]: #465
+#736 := [trans #358 #749]: #735
+#751 := (iff #547 false)
+#742 := (iff #547 #747)
+#745 := (iff #417 true)
+#405 := (or false true)
+#743 := (iff #405 true)
+#744 := [rewrite]: #743
+#406 := (iff #417 #405)
+#757 := (iff #760 false)
+#400 := [rewrite]: #757
+#407 := [monotonicity #400 #404]: #406
+#746 := [trans #407 #744]: #745
+#748 := [monotonicity #746]: #742
+#391 := [trans #748 #749]: #751
+#733 := [monotonicity #391 #736]: #459
+#448 := [trans #733 #734]: #738
+#705 := [monotonicity #448 #720 #549]: #703
+#589 := [trans #705 #704]: #707
+#756 := (iff #429 false)
+#416 := [rewrite]: #756
+#591 := [monotonicity #416 #589]: #590
+#698 := [trans #591 #704]: #550
+#755 := (iff #762 #415)
+#420 := [rewrite]: #755
+#759 := (iff #763 false)
+#765 := [rewrite]: #759
+#696 := [monotonicity #765 #420 #698]: #695
+#601 := [trans #696 #584]: #599
+#606 := [monotonicity #601]: #605
+#697 := [trans #606 #700]: #605
+#604 := [quant-inst #8 #63]: #603
+#701 := [mp #604 #697]: #595
+[unit-resolution #701 #87 #779]: false
+unsat
+62dc22cc0a1f11a224be0520d214fcdfef9b8378 339 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#37 := (f3 #16 #17)
+#750 := (pattern #37)
+#19 := 0::Int
+#72 := -1::Int
+#92 := (* -1::Int #17)
+#89 := (* -1::Int #16)
+#147 := (mod #89 #92)
+#262 := (+ #37 #147)
+#263 := (= #262 0::Int)
+#38 := (mod #16 #17)
+#259 := (* -1::Int #38)
+#260 := (+ #37 #259)
+#261 := (= #260 0::Int)
+#121 := (>= #16 0::Int)
+#114 := (<= #17 0::Int)
+#206 := (or #114 #121)
+#207 := (not #206)
+#110 := (<= #16 0::Int)
+#204 := (or #110 #114)
+#205 := (not #204)
+#210 := (or #205 #207)
+#264 := (ite #210 #261 #263)
+#258 := (= #37 0::Int)
+#20 := (= #16 0::Int)
+#265 := (ite #20 #258 #264)
+#257 := (= #16 #37)
+#21 := (= #17 0::Int)
+#266 := (ite #21 #257 #265)
+#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #266)
+#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
+#754 := (iff #269 #751)
+#752 := (iff #266 #266)
+#753 := [refl]: #752
+#755 := [quant-intro #753]: #754
+#153 := (* -1::Int #147)
+#226 := (ite #210 #38 #153)
+#229 := (ite #20 0::Int #226)
+#232 := (ite #21 #16 #229)
+#235 := (= #37 #232)
+#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
+#270 := (iff #238 #269)
+#267 := (iff #235 #266)
+#268 := [rewrite]: #267
+#271 := [quant-intro #268]: #270
+#122 := (not #121)
+#115 := (not #114)
+#125 := (and #115 #122)
+#111 := (not #110)
+#118 := (and #111 #115)
+#128 := (or #118 #125)
+#173 := (ite #128 #38 #153)
+#176 := (ite #20 0::Int #173)
+#179 := (ite #21 #16 #176)
+#182 := (= #37 #179)
+#185 := (forall (vars (?v0 Int) (?v1 Int)) #182)
+#239 := (iff #185 #238)
+#236 := (iff #182 #235)
+#233 := (= #179 #232)
+#230 := (= #176 #229)
+#227 := (= #173 #226)
+#211 := (iff #128 #210)
+#208 := (iff #125 #207)
+#209 := [rewrite]: #208
+#198 := (iff #118 #205)
+#199 := [rewrite]: #198
+#212 := [monotonicity #199 #209]: #211
+#228 := [monotonicity #212]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [quant-intro #237]: #239
+#196 := (~ #185 #185)
+#195 := (~ #182 #182)
+#192 := [refl]: #195
+#197 := [nnf-pos #192]: #196
+#31 := (- #17)
+#30 := (- #16)
+#39 := (mod #30 #31)
+#40 := (- #39)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#41 := (ite #28 #38 #40)
+#42 := (ite #20 0::Int #41)
+#43 := (ite #21 #16 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#188 := (iff #45 #185)
+#82 := (and #24 #26)
+#86 := (or #25 #82)
+#158 := (ite #86 #38 #153)
+#161 := (ite #20 0::Int #158)
+#164 := (ite #21 #16 #161)
+#167 := (= #37 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#186 := (iff #170 #185)
+#183 := (iff #167 #182)
+#180 := (= #164 #179)
+#177 := (= #161 #176)
+#174 := (= #158 #173)
+#129 := (iff #86 #128)
+#126 := (iff #82 #125)
+#123 := (iff #26 #122)
+#124 := [rewrite]: #123
+#116 := (iff #24 #115)
+#117 := [rewrite]: #116
+#127 := [monotonicity #117 #124]: #126
+#119 := (iff #25 #118)
+#112 := (iff #23 #111)
+#113 := [rewrite]: #112
+#120 := [monotonicity #113 #117]: #119
+#130 := [monotonicity #120 #127]: #129
+#175 := [monotonicity #130]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [quant-intro #184]: #186
+#171 := (iff #45 #170)
+#168 := (iff #44 #167)
+#165 := (= #43 #164)
+#162 := (= #42 #161)
+#159 := (= #41 #158)
+#156 := (= #40 #153)
+#150 := (- #147)
+#154 := (= #150 #153)
+#155 := [rewrite]: #154
+#151 := (= #40 #150)
+#148 := (= #39 #147)
+#93 := (= #31 #92)
+#94 := [rewrite]: #93
+#90 := (= #30 #89)
+#91 := [rewrite]: #90
+#149 := [monotonicity #91 #94]: #148
+#152 := [monotonicity #149]: #151
+#157 := [trans #152 #155]: #156
+#87 := (iff #28 #86)
+#84 := (iff #27 #82)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#160 := [monotonicity #88 #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
+#189 := [trans #172 #187]: #188
+#146 := [asserted]: #45
+#190 := [mp #146 #189]: #185
+#193 := [mp~ #190 #197]: #185
+#241 := [mp #193 #240]: #238
+#272 := [mp #241 #271]: #269
+#756 := [mp #272 #755]: #751
+#66 := -3::Int
+#8 := 5::Int
+#69 := (f3 5::Int -3::Int)
+#75 := (= #69 -1::Int)
+#78 := (not #75)
+#12 := 1::Int
+#13 := (- 1::Int)
+#9 := 3::Int
+#10 := (- 3::Int)
+#11 := (f3 5::Int #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#79 := (iff #15 #78)
+#76 := (iff #14 #75)
+#73 := (= #13 -1::Int)
+#74 := [rewrite]: #73
+#70 := (= #11 #69)
+#67 := (= #10 -3::Int)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#80 := [monotonicity #77]: #79
+#65 := [asserted]: #15
+#83 := [mp #65 #80]: #78
+#657 := (not #751)
+#664 := (or #657 #75)
+#330 := (* -1::Int -3::Int)
+#414 := (* -1::Int 5::Int)
+#415 := (mod #414 #330)
+#416 := (+ #69 #415)
+#407 := (= #416 0::Int)
+#418 := (mod 5::Int -3::Int)
+#419 := (* -1::Int #418)
+#420 := (+ #69 #419)
+#417 := (= #420 0::Int)
+#421 := (>= 5::Int 0::Int)
+#400 := (<= -3::Int 0::Int)
+#735 := (or #400 #421)
+#737 := (not #735)
+#394 := (<= 5::Int 0::Int)
+#524 := (or #394 #400)
+#731 := (not #524)
+#405 := (or #731 #737)
+#406 := (ite #405 #417 #407)
+#738 := (= #69 0::Int)
+#739 := (= 5::Int 0::Int)
+#740 := (ite #739 #738 #406)
+#741 := (= 5::Int #69)
+#736 := (= -3::Int 0::Int)
+#742 := (ite #736 #741 #740)
+#648 := (or #657 #742)
+#651 := (iff #648 #664)
+#653 := (iff #664 #664)
+#654 := [rewrite]: #653
+#662 := (iff #742 #75)
+#733 := (= #69 5::Int)
+#670 := (ite false #733 #75)
+#660 := (iff #670 #75)
+#661 := [rewrite]: #660
+#666 := (iff #742 #670)
+#668 := (iff #740 #75)
+#665 := (ite false #738 #75)
+#656 := (iff #665 #75)
+#658 := [rewrite]: #656
+#667 := (iff #740 #665)
+#674 := (iff #406 #75)
+#428 := 2::Int
+#690 := (= #69 2::Int)
+#581 := (ite false #690 #75)
+#584 := (iff #581 #75)
+#677 := [rewrite]: #584
+#582 := (iff #406 #581)
+#572 := (iff #407 #75)
+#527 := (+ 1::Int #69)
+#676 := (= #527 0::Int)
+#578 := (iff #676 #75)
+#579 := [rewrite]: #578
+#561 := (iff #407 #676)
+#672 := (= #416 #527)
+#566 := (+ #69 1::Int)
+#675 := (= #566 #527)
+#577 := [rewrite]: #675
+#567 := (= #416 #566)
+#681 := (= #415 1::Int)
+#693 := -5::Int
+#526 := (mod -5::Int 3::Int)
+#682 := (= #526 1::Int)
+#683 := [rewrite]: #682
+#679 := (= #415 #526)
+#523 := (= #330 3::Int)
+#525 := [rewrite]: #523
+#687 := (= #414 -5::Int)
+#694 := [rewrite]: #687
+#680 := [monotonicity #694 #525]: #679
+#684 := [trans #680 #683]: #681
+#568 := [monotonicity #684]: #567
+#673 := [trans #568 #577]: #672
+#576 := [monotonicity #673]: #561
+#580 := [trans #576 #579]: #572
+#686 := (iff #417 #690)
+#705 := -2::Int
+#702 := (+ -2::Int #69)
+#546 := (= #702 0::Int)
+#691 := (iff #546 #690)
+#685 := [rewrite]: #691
+#688 := (iff #417 #546)
+#544 := (= #420 #702)
+#695 := (+ #69 -2::Int)
+#697 := (= #695 #702)
+#703 := [rewrite]: #697
+#696 := (= #420 #695)
+#699 := (= #419 -2::Int)
+#422 := (* -1::Int 2::Int)
+#709 := (= #422 -2::Int)
+#698 := [rewrite]: #709
+#704 := (= #419 #422)
+#706 := (= #418 2::Int)
+#707 := [rewrite]: #706
+#708 := [monotonicity #707]: #704
+#700 := [trans #708 #698]: #699
+#701 := [monotonicity #700]: #696
+#545 := [trans #701 #703]: #544
+#689 := [monotonicity #545]: #688
+#692 := [trans #689 #685]: #686
+#426 := (iff #405 false)
+#710 := (or false false)
+#715 := (iff #710 false)
+#425 := [rewrite]: #715
+#714 := (iff #405 #710)
+#435 := (iff #737 false)
+#1 := true
+#725 := (not true)
+#728 := (iff #725 false)
+#368 := [rewrite]: #728
+#712 := (iff #737 #725)
+#442 := (iff #735 true)
+#716 := (or true true)
+#440 := (iff #716 true)
+#441 := [rewrite]: #440
+#717 := (iff #735 #716)
+#727 := (iff #421 true)
+#730 := [rewrite]: #727
+#382 := (iff #400 true)
+#383 := [rewrite]: #382
+#439 := [monotonicity #383 #730]: #717
+#336 := [trans #439 #441]: #442
+#713 := [monotonicity #336]: #712
+#436 := [trans #713 #368]: #435
+#369 := (iff #731 false)
+#363 := (iff #731 #725)
+#724 := (iff #524 true)
+#384 := (or false true)
+#722 := (iff #384 true)
+#723 := [rewrite]: #722
+#720 := (iff #524 #384)
+#718 := (iff #394 false)
+#381 := [rewrite]: #718
+#721 := [monotonicity #381 #383]: #720
+#719 := [trans #721 #723]: #724
+#726 := [monotonicity #719]: #363
+#729 := [trans #726 #368]: #369
+#711 := [monotonicity #729 #436]: #714
+#427 := [trans #711 #425]: #426
+#583 := [monotonicity #427 #692 #580]: #582
+#678 := [trans #583 #677]: #674
+#734 := (iff #739 false)
+#377 := [rewrite]: #734
+#659 := [monotonicity #377 #678]: #667
+#669 := [trans #659 #658]: #668
+#397 := (iff #741 #733)
+#393 := [rewrite]: #397
+#732 := (iff #736 false)
+#392 := [rewrite]: #732
+#671 := [monotonicity #392 #393 #669]: #666
+#663 := [trans #671 #661]: #662
+#652 := [monotonicity #663]: #651
+#650 := [trans #652 #654]: #651
+#649 := [quant-inst #8 #66]: #648
+#655 := [mp #649 #650]: #664
+[unit-resolution #655 #83 #756]: false
+unsat
+5d7ad299834cafeb0e7528443dd40353cb086137 348 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#36 := (f3 #15 #16)
+#758 := (pattern #36)
+#18 := 0::Int
+#65 := -1::Int
+#100 := (* -1::Int #16)
+#97 := (* -1::Int #15)
+#155 := (mod #97 #100)
+#270 := (+ #36 #155)
+#271 := (= #270 0::Int)
+#37 := (mod #15 #16)
+#267 := (* -1::Int #37)
+#268 := (+ #36 #267)
+#269 := (= #268 0::Int)
+#129 := (>= #15 0::Int)
+#122 := (<= #16 0::Int)
+#214 := (or #122 #129)
+#215 := (not #214)
+#118 := (<= #15 0::Int)
+#212 := (or #118 #122)
+#213 := (not #212)
+#218 := (or #213 #215)
+#272 := (ite #218 #269 #271)
+#266 := (= #36 0::Int)
+#19 := (= #15 0::Int)
+#273 := (ite #19 #266 #272)
+#265 := (= #15 #36)
+#20 := (= #16 0::Int)
+#274 := (ite #20 #265 #273)
+#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #274)
+#277 := (forall (vars (?v0 Int) (?v1 Int)) #274)
+#762 := (iff #277 #759)
+#760 := (iff #274 #274)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#161 := (* -1::Int #155)
+#234 := (ite #218 #37 #161)
+#237 := (ite #19 0::Int #234)
+#240 := (ite #20 #15 #237)
+#243 := (= #36 #240)
+#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
+#278 := (iff #246 #277)
+#275 := (iff #243 #274)
+#276 := [rewrite]: #275
+#279 := [quant-intro #276]: #278
+#130 := (not #129)
+#123 := (not #122)
+#133 := (and #123 #130)
+#119 := (not #118)
+#126 := (and #119 #123)
+#136 := (or #126 #133)
+#181 := (ite #136 #37 #161)
+#184 := (ite #19 0::Int #181)
+#187 := (ite #20 #15 #184)
+#190 := (= #36 #187)
+#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
+#247 := (iff #193 #246)
+#244 := (iff #190 #243)
+#241 := (= #187 #240)
+#238 := (= #184 #237)
+#235 := (= #181 #234)
+#219 := (iff #136 #218)
+#216 := (iff #133 #215)
+#217 := [rewrite]: #216
+#206 := (iff #126 #213)
+#207 := [rewrite]: #206
+#220 := [monotonicity #207 #217]: #219
+#236 := [monotonicity #220]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [quant-intro #245]: #247
+#204 := (~ #193 #193)
+#203 := (~ #190 #190)
+#200 := [refl]: #203
+#205 := [nnf-pos #200]: #204
+#30 := (- #16)
+#29 := (- #15)
+#38 := (mod #29 #30)
+#39 := (- #38)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#40 := (ite #27 #37 #39)
+#41 := (ite #19 0::Int #40)
+#42 := (ite #20 #15 #41)
+#43 := (= #36 #42)
+#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
+#196 := (iff #44 #193)
+#91 := (and #23 #25)
+#94 := (or #24 #91)
+#166 := (ite #94 #37 #161)
+#169 := (ite #19 0::Int #166)
+#172 := (ite #20 #15 #169)
+#175 := (= #36 #172)
+#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
+#194 := (iff #178 #193)
+#191 := (iff #175 #190)
+#188 := (= #172 #187)
+#185 := (= #169 #184)
+#182 := (= #166 #181)
+#137 := (iff #94 #136)
+#134 := (iff #91 #133)
+#131 := (iff #25 #130)
+#132 := [rewrite]: #131
+#124 := (iff #23 #123)
+#125 := [rewrite]: #124
+#135 := [monotonicity #125 #132]: #134
+#127 := (iff #24 #126)
+#120 := (iff #22 #119)
+#121 := [rewrite]: #120
+#128 := [monotonicity #121 #125]: #127
+#138 := [monotonicity #128 #135]: #137
+#183 := [monotonicity #138]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [quant-intro #192]: #194
+#179 := (iff #44 #178)
+#176 := (iff #43 #175)
+#173 := (= #42 #172)
+#170 := (= #41 #169)
+#167 := (= #40 #166)
+#164 := (= #39 #161)
+#158 := (- #155)
+#162 := (= #158 #161)
+#163 := [rewrite]: #162
+#159 := (= #39 #158)
+#156 := (= #38 #155)
+#101 := (= #30 #100)
+#102 := [rewrite]: #101
+#98 := (= #29 #97)
+#99 := [rewrite]: #98
+#157 := [monotonicity #99 #102]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#95 := (iff #27 #94)
+#92 := (iff #26 #91)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#168 := [monotonicity #96 #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [quant-intro #177]: #179
+#197 := [trans #180 #195]: #196
+#154 := [asserted]: #44
+#198 := [mp #154 #197]: #193
+#201 := [mp~ #198 #205]: #193
+#249 := [mp #201 #248]: #246
+#280 := [mp #249 #279]: #277
+#764 := [mp #280 #763]: #759
+#12 := 2::Int
+#10 := 3::Int
+#68 := (f3 -1::Int 3::Int)
+#71 := (= #68 2::Int)
+#84 := (not #71)
#8 := 1::Int
#9 := (- 1::Int)
-#22 := (- #9)
-#12 := 3::Int
-#21 := (- 3::Int)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod 3::Int #9)
-#15 := (< 0::Int #9)
-#17 := (< 3::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 3::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= 3::Int 0::Int)
-#26 := (ite #13 0::Int #25)
-#11 := (= #9 0::Int)
-#27 := (ite #11 3::Int #26)
-#28 := (= #27 0::Int)
-#29 := (not #28)
-#137 := (iff #29 false)
-#1 := true
-#132 := (not true)
-#135 := (iff #132 false)
-#136 := [rewrite]: #135
-#133 := (iff #29 #132)
-#130 := (iff #28 true)
-#125 := (= 0::Int 0::Int)
-#128 := (iff #125 true)
+#11 := (f3 #9 3::Int)
+#13 := (= #11 2::Int)
+#14 := (not #13)
+#87 := (iff #14 #84)
+#74 := (= 2::Int #68)
+#79 := (not #74)
+#85 := (iff #79 #84)
+#82 := (iff #74 #71)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#80 := (iff #14 #79)
+#77 := (iff #13 #74)
+#75 := (iff #71 #74)
+#76 := [rewrite]: #75
+#72 := (iff #13 #71)
+#69 := (= #11 #68)
+#66 := (= #9 -1::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#81 := [monotonicity #78]: #80
+#88 := [trans #81 #86]: #87
+#64 := [asserted]: #14
+#89 := [mp #64 #88]: #84
+#672 := (not #759)
+#656 := (or #672 #71)
+#338 := (* -1::Int 3::Int)
+#422 := (* -1::Int -1::Int)
+#423 := (mod #422 #338)
+#424 := (+ #68 #423)
+#415 := (= #424 0::Int)
+#426 := (mod -1::Int 3::Int)
+#427 := (* -1::Int #426)
+#428 := (+ #68 #427)
+#425 := (= #428 0::Int)
+#429 := (>= -1::Int 0::Int)
+#408 := (<= 3::Int 0::Int)
+#743 := (or #408 #429)
+#745 := (not #743)
+#402 := (<= -1::Int 0::Int)
+#532 := (or #402 #408)
+#739 := (not #532)
+#413 := (or #739 #745)
+#414 := (ite #413 #425 #415)
+#746 := (= #68 0::Int)
+#747 := (= -1::Int 0::Int)
+#748 := (ite #747 #746 #414)
+#749 := (= -1::Int #68)
+#744 := (= 3::Int 0::Int)
+#750 := (ite #744 #749 #748)
+#657 := (or #672 #750)
+#660 := (iff #657 #656)
+#662 := (iff #656 #656)
+#658 := [rewrite]: #662
+#671 := (iff #750 #71)
+#741 := (= #68 -1::Int)
+#674 := (ite false #741 #71)
+#669 := (iff #674 #71)
+#670 := [rewrite]: #669
+#679 := (iff #750 #674)
+#677 := (iff #748 #71)
+#675 := (ite false #746 #71)
+#666 := (iff #675 #71)
+#676 := [rewrite]: #666
+#667 := (iff #748 #675)
+#686 := (iff #414 #71)
+#1 := true
+#590 := (ite true #71 #741)
+#685 := (iff #590 #71)
+#682 := [rewrite]: #685
+#591 := (iff #414 #590)
+#588 := (iff #415 #741)
+#683 := (+ 1::Int #68)
+#569 := (= #683 0::Int)
+#587 := (iff #569 #741)
+#580 := [rewrite]: #587
+#584 := (iff #415 #569)
+#681 := (= #424 #683)
+#575 := (+ #68 1::Int)
+#585 := (= #575 #683)
+#680 := [rewrite]: #585
+#576 := (= #424 #575)
+#692 := (= #423 1::Int)
+#531 := -3::Int
+#687 := (mod 1::Int -3::Int)
+#691 := (= #687 1::Int)
+#689 := [rewrite]: #691
+#688 := (= #423 #687)
+#533 := (= #338 -3::Int)
+#534 := [rewrite]: #533
+#695 := (= #422 1::Int)
+#702 := [rewrite]: #695
+#690 := [monotonicity #702 #534]: #688
+#574 := [trans #690 #689]: #692
+#535 := [monotonicity #574]: #576
+#684 := [trans #535 #680]: #681
+#586 := [monotonicity #684]: #584
+#589 := [trans #586 #580]: #588
+#700 := (iff #425 #71)
+#706 := -2::Int
+#711 := (+ -2::Int #68)
+#697 := (= #711 0::Int)
+#693 := (iff #697 #71)
+#694 := [rewrite]: #693
+#698 := (iff #425 #697)
+#554 := (= #428 #711)
+#709 := (+ #68 -2::Int)
+#552 := (= #709 #711)
+#553 := [rewrite]: #552
+#710 := (= #428 #709)
+#703 := (= #427 -2::Int)
+#716 := (* -1::Int 2::Int)
+#707 := (= #716 -2::Int)
+#708 := [rewrite]: #707
+#713 := (= #427 #716)
+#430 := (= #426 2::Int)
+#712 := [rewrite]: #430
+#717 := [monotonicity #712]: #713
+#704 := [trans #717 #708]: #703
+#705 := [monotonicity #704]: #710
+#696 := [trans #705 #553]: #554
+#699 := [monotonicity #696]: #698
+#701 := [trans #699 #694]: #700
+#714 := (iff #413 true)
+#723 := (or false true)
+#435 := (iff #723 true)
+#436 := [rewrite]: #435
+#433 := (iff #413 #723)
+#722 := (iff #745 true)
+#720 := (not false)
+#444 := (iff #720 true)
+#718 := [rewrite]: #444
+#721 := (iff #745 #720)
+#450 := (iff #743 false)
+#724 := (or false false)
+#448 := (iff #724 false)
+#449 := [rewrite]: #448
+#725 := (iff #743 #724)
+#735 := (iff #429 false)
+#738 := [rewrite]: #735
+#390 := (iff #408 false)
+#391 := [rewrite]: #390
+#447 := [monotonicity #391 #738]: #725
+#344 := [trans #447 #449]: #450
+#443 := [monotonicity #344]: #721
+#719 := [trans #443 #718]: #722
+#377 := (iff #739 false)
+#733 := (not true)
+#736 := (iff #733 false)
+#376 := [rewrite]: #736
+#371 := (iff #739 #733)
+#732 := (iff #532 true)
+#392 := (or true false)
+#730 := (iff #392 true)
+#731 := [rewrite]: #730
+#728 := (iff #532 #392)
+#726 := (iff #402 true)
+#389 := [rewrite]: #726
+#729 := [monotonicity #389 #391]: #728
+#727 := [trans #729 #731]: #732
+#734 := [monotonicity #727]: #371
+#737 := [trans #734 #376]: #377
+#434 := [monotonicity #737 #719]: #433
+#715 := [trans #434 #436]: #714
+#592 := [monotonicity #715 #701 #589]: #591
+#673 := [trans #592 #682]: #686
+#742 := (iff #747 false)
+#385 := [rewrite]: #742
+#664 := [monotonicity #385 #673]: #667
+#678 := [trans #664 #676]: #677
+#405 := (iff #749 #741)
+#401 := [rewrite]: #405
+#740 := (iff #744 false)
+#400 := [rewrite]: #740
+#668 := [monotonicity #400 #401 #678]: #679
+#665 := [trans #668 #670]: #671
+#661 := [monotonicity #665]: #660
+#663 := [trans #661 #658]: #660
+#659 := [quant-inst #65 #10]: #657
+#649 := [mp #659 #663]: #656
+[unit-resolution #649 #89 #764]: false
+unsat
+513cb6376361794229c618f4dacebc2dcd3ef34a 339 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#773 := (pattern #34)
+#11 := 0::Int
+#104 := -1::Int
+#108 := (* -1::Int #15)
+#105 := (* -1::Int #14)
+#169 := (mod #105 #108)
+#284 := (+ #34 #169)
+#285 := (= #284 0::Int)
+#35 := (mod #14 #15)
+#281 := (* -1::Int #35)
+#282 := (+ #34 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #14 0::Int)
+#136 := (<= #15 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #14 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#287 := (ite #17 #280 #286)
+#279 := (= #14 #34)
+#18 := (= #15 0::Int)
+#288 := (ite #18 #279 #287)
+#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#777 := (iff #291 #774)
+#775 := (iff #288 #288)
+#776 := [refl]: #775
+#778 := [quant-intro #776]: #777
+#175 := (* -1::Int #169)
+#248 := (ite #232 #35 #175)
+#251 := (ite #17 0::Int #248)
+#254 := (ite #18 #14 #251)
+#257 := (= #34 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #35 #175)
+#198 := (ite #17 0::Int #195)
+#201 := (ite #18 #14 #198)
+#204 := (= #34 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#210 := (iff #42 #207)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#180 := (ite #101 #35 #175)
+#89 := (= 0::Int #14)
+#183 := (ite #89 0::Int #180)
+#92 := (= 0::Int #15)
+#186 := (ite #92 #14 #183)
+#189 := (= #34 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #101 #150)
+#148 := (iff #98 #147)
+#145 := (iff #23 #144)
+#146 := [rewrite]: #145
+#138 := (iff #21 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #22 #140)
+#134 := (iff #20 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #89 #17)
+#127 := [rewrite]: #126
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #92 #18)
#129 := [rewrite]: #128
-#126 := (iff #28 #125)
-#119 := (ite false 3::Int 0::Int)
-#122 := (= #119 0::Int)
-#123 := [rewrite]: #122
-#120 := (= #27 #119)
-#117 := (= #26 0::Int)
-#112 := (ite false 0::Int 0::Int)
-#115 := (= #112 0::Int)
-#116 := [rewrite]: #115
-#113 := (= #26 #112)
-#110 := (= #25 0::Int)
-#50 := -1::Int
-#62 := (< 0::Int -1::Int)
-#68 := (and #17 #62)
-#65 := (and #14 #62)
-#71 := (or #65 #68)
-#105 := (ite #71 0::Int 0::Int)
-#108 := (= #105 0::Int)
-#109 := [rewrite]: #108
-#106 := (= #25 #105)
-#103 := (= #24 0::Int)
-#98 := (- 0::Int)
-#101 := (= #98 0::Int)
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#187 := (= #40 #186)
+#184 := (= #39 #183)
+#181 := (= #38 #180)
+#178 := (= #37 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #37 #172)
+#170 := (= #36 #169)
+#109 := (= #28 #108)
+#110 := [rewrite]: #109
+#106 := (= #27 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#182 := [monotonicity #103 #179]: #181
+#90 := (iff #17 #89)
+#91 := [rewrite]: #90
+#185 := [monotonicity #91 #182]: #184
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#188 := [monotonicity #94 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #42
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#779 := [mp #294 #778]: #774
+#8 := 3::Int
+#63 := -3::Int
+#66 := (f3 -3::Int 3::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
+#9 := (- 3::Int)
+#10 := (f3 #9 3::Int)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #12 #69)
+#67 := (= #10 #66)
+#64 := (= #9 -3::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#607 := (not #774)
+#700 := (or #607 #69)
+#352 := (* -1::Int 3::Int)
+#437 := (* -1::Int -3::Int)
+#438 := (mod #437 #352)
+#439 := (+ #66 #438)
+#430 := (= #439 0::Int)
+#441 := (mod -3::Int 3::Int)
+#442 := (* -1::Int #441)
+#370 := (+ #66 #442)
+#443 := (= #370 0::Int)
+#440 := (>= -3::Int 0::Int)
+#444 := (<= 3::Int 0::Int)
+#423 := (or #444 #440)
+#758 := (not #423)
+#760 := (<= -3::Int 0::Int)
+#417 := (or #760 #444)
+#547 := (not #417)
+#754 := (or #547 #758)
+#428 := (ite #754 #443 #430)
+#429 := (= -3::Int 0::Int)
+#761 := (ite #429 #69 #428)
+#762 := (= -3::Int #66)
+#763 := (= 3::Int 0::Int)
+#764 := (ite #763 #762 #761)
+#697 := (or #607 #764)
+#688 := (iff #697 #700)
+#682 := (iff #700 #700)
+#679 := [rewrite]: #682
+#605 := (iff #764 #69)
+#415 := (= #66 -3::Int)
+#601 := (ite false #415 #69)
+#603 := (iff #601 #69)
+#604 := [rewrite]: #603
+#602 := (iff #764 #601)
+#584 := (iff #761 #69)
+#698 := (ite false #69 #69)
+#696 := (iff #698 #69)
+#699 := [rewrite]: #696
+#600 := (iff #761 #698)
+#591 := (iff #428 #69)
+#1 := true
+#706 := (ite true #69 #69)
+#589 := (iff #706 #69)
+#590 := [rewrite]: #589
+#704 := (iff #428 #706)
+#703 := (iff #430 #69)
+#549 := (= #439 #66)
+#723 := (+ #66 0::Int)
+#724 := (= #723 #66)
+#725 := [rewrite]: #724
+#546 := (= #439 #723)
+#710 := (= #438 0::Int)
+#714 := (mod 3::Int -3::Int)
+#715 := (= #714 0::Int)
+#716 := [rewrite]: #715
+#708 := (= #438 #714)
+#712 := (= #352 -3::Int)
+#713 := [rewrite]: #712
+#569 := (= #437 3::Int)
+#711 := [rewrite]: #569
+#709 := [monotonicity #711 #713]: #708
+#717 := [trans #709 #716]: #710
+#548 := [monotonicity #717]: #546
+#702 := [trans #548 #725]: #549
+#705 := [monotonicity #702]: #703
+#567 := (iff #443 #69)
+#720 := (= #370 #66)
+#718 := (= #370 #723)
+#721 := (= #442 0::Int)
+#445 := (* -1::Int 0::Int)
+#728 := (= #445 0::Int)
+#732 := [rewrite]: #728
+#727 := (= #442 #445)
+#729 := (= #441 0::Int)
+#730 := [rewrite]: #729
+#731 := [monotonicity #730]: #727
+#722 := [trans #731 #732]: #721
+#719 := [monotonicity #722]: #718
+#726 := [trans #719 #725]: #720
+#568 := [monotonicity #726]: #567
+#450 := (iff #754 true)
+#737 := (or false true)
+#448 := (iff #737 true)
+#449 := [rewrite]: #448
+#734 := (iff #754 #737)
+#459 := (iff #758 true)
+#465 := (not false)
+#736 := (iff #465 true)
+#458 := [rewrite]: #736
+#358 := (iff #758 #465)
+#463 := (iff #423 false)
+#750 := (or false false)
+#740 := (iff #750 false)
+#462 := [rewrite]: #740
+#753 := (iff #423 #750)
+#392 := (iff #440 false)
+#752 := [rewrite]: #392
+#741 := (iff #444 false)
+#404 := [rewrite]: #741
+#739 := [monotonicity #404 #752]: #753
+#464 := [trans #739 #462]: #463
+#735 := [monotonicity #464]: #358
+#733 := [trans #735 #458]: #459
+#751 := (iff #547 false)
+#747 := (not true)
+#386 := (iff #747 false)
+#749 := [rewrite]: #386
+#742 := (iff #547 #747)
+#745 := (iff #417 true)
+#405 := (or true false)
+#743 := (iff #405 true)
+#744 := [rewrite]: #743
+#406 := (iff #417 #405)
+#757 := (iff #760 true)
+#400 := [rewrite]: #757
+#407 := [monotonicity #400 #404]: #406
+#746 := [trans #407 #744]: #745
+#748 := [monotonicity #746]: #742
+#391 := [trans #748 #749]: #751
+#738 := [monotonicity #391 #733]: #734
+#451 := [trans #738 #449]: #450
+#707 := [monotonicity #451 #568 #705]: #704
+#550 := [trans #707 #590]: #591
+#756 := (iff #429 false)
+#416 := [rewrite]: #756
+#695 := [monotonicity #416 #550]: #600
+#599 := [trans #695 #699]: #584
+#755 := (iff #762 #415)
+#420 := [rewrite]: #755
+#759 := (iff #763 false)
+#765 := [rewrite]: #759
+#595 := [monotonicity #765 #420 #599]: #602
+#606 := [trans #595 #604]: #605
+#690 := [monotonicity #606]: #688
+#681 := [trans #690 #679]: #688
+#701 := [quant-inst #63 #8]: #697
+#691 := [mp #701 #681]: #700
+[unit-resolution #691 #87 #779]: false
+unsat
+117ddb585bc1c6246f02758b44ec466b148da99c 351 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#36 := (f3 #15 #16)
+#759 := (pattern #36)
+#18 := 0::Int
+#97 := -1::Int
+#101 := (* -1::Int #16)
+#98 := (* -1::Int #15)
+#156 := (mod #98 #101)
+#271 := (+ #36 #156)
+#272 := (= #271 0::Int)
+#37 := (mod #15 #16)
+#268 := (* -1::Int #37)
+#269 := (+ #36 #268)
+#270 := (= #269 0::Int)
+#130 := (>= #15 0::Int)
+#123 := (<= #16 0::Int)
+#215 := (or #123 #130)
+#216 := (not #215)
+#119 := (<= #15 0::Int)
+#213 := (or #119 #123)
+#214 := (not #213)
+#219 := (or #214 #216)
+#273 := (ite #219 #270 #272)
+#267 := (= #36 0::Int)
+#19 := (= #15 0::Int)
+#274 := (ite #19 #267 #273)
+#266 := (= #15 #36)
+#20 := (= #16 0::Int)
+#275 := (ite #20 #266 #274)
+#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#763 := (iff #278 #760)
+#761 := (iff #275 #275)
+#762 := [refl]: #761
+#764 := [quant-intro #762]: #763
+#162 := (* -1::Int #156)
+#235 := (ite #219 #37 #162)
+#238 := (ite #19 0::Int #235)
+#241 := (ite #20 #15 #238)
+#244 := (= #36 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#131 := (not #130)
+#124 := (not #123)
+#134 := (and #124 #131)
+#120 := (not #119)
+#127 := (and #120 #124)
+#137 := (or #127 #134)
+#182 := (ite #137 #37 #162)
+#185 := (ite #19 0::Int #182)
+#188 := (ite #20 #15 #185)
+#191 := (= #36 #188)
+#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
+#248 := (iff #194 #247)
+#245 := (iff #191 #244)
+#242 := (= #188 #241)
+#239 := (= #185 #238)
+#236 := (= #182 #235)
+#220 := (iff #137 #219)
+#217 := (iff #134 #216)
+#218 := [rewrite]: #217
+#207 := (iff #127 #214)
+#208 := [rewrite]: #207
+#221 := [monotonicity #208 #218]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#205 := (~ #194 #194)
+#204 := (~ #191 #191)
+#201 := [refl]: #204
+#206 := [nnf-pos #201]: #205
+#30 := (- #16)
+#29 := (- #15)
+#38 := (mod #29 #30)
+#39 := (- #38)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#40 := (ite #27 #37 #39)
+#41 := (ite #19 0::Int #40)
+#42 := (ite #20 #15 #41)
+#43 := (= #36 #42)
+#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
+#197 := (iff #44 #194)
+#91 := (and #23 #25)
+#94 := (or #24 #91)
+#167 := (ite #94 #37 #162)
+#170 := (ite #19 0::Int #167)
+#173 := (ite #20 #15 #170)
+#176 := (= #36 #173)
+#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
+#195 := (iff #179 #194)
+#192 := (iff #176 #191)
+#189 := (= #173 #188)
+#186 := (= #170 #185)
+#183 := (= #167 #182)
+#138 := (iff #94 #137)
+#135 := (iff #91 #134)
+#132 := (iff #25 #131)
+#133 := [rewrite]: #132
+#125 := (iff #23 #124)
+#126 := [rewrite]: #125
+#136 := [monotonicity #126 #133]: #135
+#128 := (iff #24 #127)
+#121 := (iff #22 #120)
+#122 := [rewrite]: #121
+#129 := [monotonicity #122 #126]: #128
+#139 := [monotonicity #129 #136]: #138
+#184 := [monotonicity #139]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [monotonicity #190]: #192
+#196 := [quant-intro #193]: #195
+#180 := (iff #44 #179)
+#177 := (iff #43 #176)
+#174 := (= #42 #173)
+#171 := (= #41 #170)
+#168 := (= #40 #167)
+#165 := (= #39 #162)
+#159 := (- #156)
+#163 := (= #159 #162)
+#164 := [rewrite]: #163
+#160 := (= #39 #159)
+#157 := (= #38 #156)
+#102 := (= #30 #101)
+#103 := [rewrite]: #102
+#99 := (= #29 #98)
+#100 := [rewrite]: #99
+#158 := [monotonicity #100 #103]: #157
+#161 := [monotonicity #158]: #160
+#166 := [trans #161 #164]: #165
+#95 := (iff #27 #94)
+#92 := (iff #26 #91)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#169 := [monotonicity #96 #166]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#198 := [trans #181 #196]: #197
+#155 := [asserted]: #44
+#199 := [mp #155 #198]: #194
+#202 := [mp~ #199 #206]: #194
+#250 := [mp #202 #249]: #247
+#281 := [mp #250 #280]: #278
+#765 := [mp #281 #764]: #760
+#12 := 1::Int
+#10 := 3::Int
+#65 := -5::Int
+#68 := (f3 -5::Int 3::Int)
+#71 := (= #68 1::Int)
+#84 := (not #71)
+#8 := 5::Int
+#9 := (- 5::Int)
+#11 := (f3 #9 3::Int)
+#13 := (= #11 1::Int)
+#14 := (not #13)
+#87 := (iff #14 #84)
+#74 := (= 1::Int #68)
+#79 := (not #74)
+#85 := (iff #79 #84)
+#82 := (iff #74 #71)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#80 := (iff #14 #79)
+#77 := (iff #13 #74)
+#75 := (iff #71 #74)
+#76 := [rewrite]: #75
+#72 := (iff #13 #71)
+#69 := (= #11 #68)
+#66 := (= #9 -5::Int)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#81 := [monotonicity #78]: #80
+#88 := [trans #81 #86]: #87
+#64 := [asserted]: #14
+#89 := [mp #64 #88]: #84
+#658 := (not #760)
+#660 := (or #658 #71)
+#339 := (* -1::Int 3::Int)
+#423 := (* -1::Int -5::Int)
+#424 := (mod #423 #339)
+#425 := (+ #68 #424)
+#416 := (= #425 0::Int)
+#427 := (mod -5::Int 3::Int)
+#428 := (* -1::Int #427)
+#429 := (+ #68 #428)
+#426 := (= #429 0::Int)
+#430 := (>= -5::Int 0::Int)
+#409 := (<= 3::Int 0::Int)
+#744 := (or #409 #430)
+#746 := (not #744)
+#403 := (<= -5::Int 0::Int)
+#533 := (or #403 #409)
+#740 := (not #533)
+#414 := (or #740 #746)
+#415 := (ite #414 #426 #416)
+#747 := (= #68 0::Int)
+#748 := (= -5::Int 0::Int)
+#749 := (ite #748 #747 #415)
+#750 := (= -5::Int #68)
+#745 := (= 3::Int 0::Int)
+#751 := (ite #745 #750 #749)
+#661 := (or #658 #751)
+#663 := (iff #661 #660)
+#664 := (iff #660 #660)
+#650 := [rewrite]: #664
+#673 := (iff #751 #71)
+#742 := (= #68 -5::Int)
+#669 := (ite false #742 #71)
+#672 := (iff #669 #71)
+#666 := [rewrite]: #672
+#670 := (iff #751 #669)
+#675 := (iff #749 #71)
+#665 := (ite false #747 #71)
+#678 := (iff #665 #71)
+#679 := [rewrite]: #678
+#667 := (iff #749 #665)
+#676 := (iff #415 #71)
+#588 := -2::Int
+#581 := (= #68 -2::Int)
+#1 := true
+#593 := (ite true #71 #581)
+#687 := (iff #593 #71)
+#674 := [rewrite]: #687
+#686 := (iff #415 #593)
+#591 := (iff #416 #581)
+#691 := 2::Int
+#684 := (+ 2::Int #68)
+#570 := (= #684 0::Int)
+#589 := (iff #570 #581)
+#590 := [rewrite]: #589
+#585 := (iff #416 #570)
+#682 := (= #425 #684)
+#576 := (+ #68 2::Int)
+#586 := (= #576 #684)
+#681 := [rewrite]: #586
+#577 := (= #425 #576)
+#693 := (= #424 2::Int)
+#703 := -3::Int
+#535 := (mod 5::Int -3::Int)
+#692 := (= #535 2::Int)
+#690 := [rewrite]: #692
+#688 := (= #424 #535)
+#532 := (= #339 -3::Int)
+#534 := [rewrite]: #532
+#702 := (= #423 5::Int)
+#696 := [rewrite]: #702
+#689 := [monotonicity #696 #534]: #688
+#575 := [trans #689 #690]: #693
+#536 := [monotonicity #575]: #577
+#685 := [trans #536 #681]: #682
+#587 := [monotonicity #685]: #585
+#592 := [trans #587 #590]: #591
+#695 := (iff #426 #71)
+#706 := (+ -1::Int #68)
+#697 := (= #706 0::Int)
+#700 := (iff #697 #71)
+#694 := [rewrite]: #700
+#698 := (iff #426 #697)
+#554 := (= #429 #706)
+#705 := (+ #68 -1::Int)
+#712 := (= #705 #706)
+#553 := [rewrite]: #712
+#710 := (= #429 #705)
+#709 := (= #428 -1::Int)
+#717 := (* -1::Int 1::Int)
+#707 := (= #717 -1::Int)
+#708 := [rewrite]: #707
+#714 := (= #428 #717)
+#431 := (= #427 1::Int)
+#713 := [rewrite]: #431
+#718 := [monotonicity #713]: #714
+#704 := [trans #718 #708]: #709
+#711 := [monotonicity #704]: #710
+#555 := [trans #711 #553]: #554
+#699 := [monotonicity #555]: #698
+#701 := [trans #699 #694]: #695
+#715 := (iff #414 true)
+#724 := (or false true)
+#436 := (iff #724 true)
+#437 := [rewrite]: #436
+#434 := (iff #414 #724)
+#723 := (iff #746 true)
+#721 := (not false)
+#445 := (iff #721 true)
+#719 := [rewrite]: #445
+#722 := (iff #746 #721)
+#451 := (iff #744 false)
+#725 := (or false false)
+#449 := (iff #725 false)
+#450 := [rewrite]: #449
+#726 := (iff #744 #725)
+#736 := (iff #430 false)
+#739 := [rewrite]: #736
+#391 := (iff #409 false)
+#392 := [rewrite]: #391
+#448 := [monotonicity #392 #739]: #726
+#345 := [trans #448 #450]: #451
+#444 := [monotonicity #345]: #722
+#720 := [trans #444 #719]: #723
+#378 := (iff #740 false)
+#734 := (not true)
+#737 := (iff #734 false)
+#377 := [rewrite]: #737
+#372 := (iff #740 #734)
+#733 := (iff #533 true)
+#393 := (or true false)
+#731 := (iff #393 true)
+#732 := [rewrite]: #731
+#729 := (iff #533 #393)
+#727 := (iff #403 true)
+#390 := [rewrite]: #727
+#730 := [monotonicity #390 #392]: #729
+#728 := [trans #730 #732]: #733
+#735 := [monotonicity #728]: #372
+#738 := [trans #735 #377]: #378
+#435 := [monotonicity #738 #720]: #434
+#716 := [trans #435 #437]: #715
+#683 := [monotonicity #716 #701 #592]: #686
+#668 := [trans #683 #674]: #676
+#743 := (iff #748 false)
+#386 := [rewrite]: #743
+#677 := [monotonicity #386 #668]: #667
+#680 := [trans #677 #679]: #675
+#406 := (iff #750 #742)
+#402 := [rewrite]: #406
+#741 := (iff #745 false)
+#401 := [rewrite]: #741
+#671 := [monotonicity #401 #402 #680]: #670
+#657 := [trans #671 #666]: #673
+#659 := [monotonicity #657]: #663
+#651 := [trans #659 #650]: #663
+#662 := [quant-inst #65 #10]: #661
+#653 := [mp #662 #651]: #660
+[unit-resolution #653 #89 #765]: false
+unsat
+e49f7307606e8c00bbcb83b5fb72cc73d56a411b 345 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#36 := (f3 #15 #16)
+#761 := (pattern #36)
+#18 := 0::Int
+#65 := -1::Int
+#103 := (* -1::Int #16)
+#100 := (* -1::Int #15)
+#158 := (mod #100 #103)
+#273 := (+ #36 #158)
+#274 := (= #273 0::Int)
+#37 := (mod #15 #16)
+#270 := (* -1::Int #37)
+#271 := (+ #36 #270)
+#272 := (= #271 0::Int)
+#132 := (>= #15 0::Int)
+#125 := (<= #16 0::Int)
+#217 := (or #125 #132)
+#218 := (not #217)
+#121 := (<= #15 0::Int)
+#215 := (or #121 #125)
+#216 := (not #215)
+#221 := (or #216 #218)
+#275 := (ite #221 #272 #274)
+#269 := (= #36 0::Int)
+#19 := (= #15 0::Int)
+#276 := (ite #19 #269 #275)
+#268 := (= #15 #36)
+#20 := (= #16 0::Int)
+#277 := (ite #20 #268 #276)
+#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #277)
+#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
+#765 := (iff #280 #762)
+#763 := (iff #277 #277)
+#764 := [refl]: #763
+#766 := [quant-intro #764]: #765
+#164 := (* -1::Int #158)
+#237 := (ite #221 #37 #164)
+#240 := (ite #19 0::Int #237)
+#243 := (ite #20 #15 #240)
+#246 := (= #36 #243)
+#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
+#281 := (iff #249 #280)
+#278 := (iff #246 #277)
+#279 := [rewrite]: #278
+#282 := [quant-intro #279]: #281
+#133 := (not #132)
+#126 := (not #125)
+#136 := (and #126 #133)
+#122 := (not #121)
+#129 := (and #122 #126)
+#139 := (or #129 #136)
+#184 := (ite #139 #37 #164)
+#187 := (ite #19 0::Int #184)
+#190 := (ite #20 #15 #187)
+#193 := (= #36 #190)
+#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
+#250 := (iff #196 #249)
+#247 := (iff #193 #246)
+#244 := (= #190 #243)
+#241 := (= #187 #240)
+#238 := (= #184 #237)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#220 := [rewrite]: #219
+#209 := (iff #129 #216)
+#210 := [rewrite]: #209
+#223 := [monotonicity #210 #220]: #222
+#239 := [monotonicity #223]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [monotonicity #245]: #247
+#251 := [quant-intro #248]: #250
+#207 := (~ #196 #196)
+#206 := (~ #193 #193)
+#203 := [refl]: #206
+#208 := [nnf-pos #203]: #207
+#30 := (- #16)
+#29 := (- #15)
+#38 := (mod #29 #30)
+#39 := (- #38)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#40 := (ite #27 #37 #39)
+#41 := (ite #19 0::Int #40)
+#42 := (ite #20 #15 #41)
+#43 := (= #36 #42)
+#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
+#199 := (iff #44 #196)
+#94 := (and #23 #25)
+#97 := (or #24 #94)
+#169 := (ite #97 #37 #164)
+#172 := (ite #19 0::Int #169)
+#175 := (ite #20 #15 #172)
+#178 := (= #36 #175)
+#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
+#197 := (iff #181 #196)
+#194 := (iff #178 #193)
+#191 := (= #175 #190)
+#188 := (= #172 #187)
+#185 := (= #169 #184)
+#140 := (iff #97 #139)
+#137 := (iff #94 #136)
+#134 := (iff #25 #133)
+#135 := [rewrite]: #134
+#127 := (iff #23 #126)
+#128 := [rewrite]: #127
+#138 := [monotonicity #128 #135]: #137
+#130 := (iff #24 #129)
+#123 := (iff #22 #122)
+#124 := [rewrite]: #123
+#131 := [monotonicity #124 #128]: #130
+#141 := [monotonicity #131 #138]: #140
+#186 := [monotonicity #141]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [quant-intro #195]: #197
+#182 := (iff #44 #181)
+#179 := (iff #43 #178)
+#176 := (= #42 #175)
+#173 := (= #41 #172)
+#170 := (= #40 #169)
+#167 := (= #39 #164)
+#161 := (- #158)
+#165 := (= #161 #164)
+#166 := [rewrite]: #165
+#162 := (= #39 #161)
+#159 := (= #38 #158)
+#104 := (= #30 #103)
+#105 := [rewrite]: #104
+#101 := (= #29 #100)
#102 := [rewrite]: #101
-#99 := (= #24 #98)
-#96 := (= #23 0::Int)
-#81 := -3::Int
-#91 := (mod -3::Int 1::Int)
-#94 := (= #91 0::Int)
-#95 := [rewrite]: #94
-#92 := (= #23 #91)
-#89 := (= #22 1::Int)
-#84 := (- -1::Int)
-#87 := (= #84 1::Int)
-#88 := [rewrite]: #87
-#85 := (= #22 #84)
-#51 := (= #9 -1::Int)
-#52 := [rewrite]: #51
-#86 := [monotonicity #52]: #85
-#90 := [trans #86 #88]: #89
-#82 := (= #21 -3::Int)
-#83 := [rewrite]: #82
-#93 := [monotonicity #83 #90]: #92
-#97 := [trans #93 #95]: #96
-#100 := [monotonicity #97]: #99
-#104 := [trans #100 #102]: #103
-#79 := (= #20 0::Int)
-#74 := (mod 3::Int -1::Int)
-#77 := (= #74 0::Int)
-#78 := [rewrite]: #77
-#75 := (= #20 #74)
-#76 := [monotonicity #52]: #75
-#80 := [trans #76 #78]: #79
-#72 := (iff #19 #71)
-#69 := (iff #18 #68)
-#63 := (iff #15 #62)
-#64 := [monotonicity #52]: #63
-#70 := [monotonicity #64]: #69
-#66 := (iff #16 #65)
-#67 := [monotonicity #64]: #66
-#73 := [monotonicity #67 #70]: #72
-#107 := [monotonicity #73 #80 #104]: #106
-#111 := [trans #107 #109]: #110
-#60 := (iff #13 false)
-#61 := [rewrite]: #60
-#114 := [monotonicity #61 #111]: #113
-#118 := [trans #114 #116]: #117
-#58 := (iff #11 false)
-#53 := (= -1::Int 0::Int)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #11 #53)
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#121 := [monotonicity #59 #118]: #120
-#124 := [trans #121 #123]: #28
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#134 := [monotonicity #131]: #133
-#138 := [trans #134 #136]: #137
-#49 := [asserted]: #29
-[mp #49 #138]: false
-unsat
-56a38afd92c36cbda7ea0320ace529eafcdd0527 180 0
-#2 := false
-#10 := 0::Int
+#160 := [monotonicity #102 #105]: #159
+#163 := [monotonicity #160]: #162
+#168 := [trans #163 #166]: #167
+#98 := (iff #27 #97)
+#95 := (iff #26 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#171 := [monotonicity #99 #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#200 := [trans #183 #198]: #199
+#157 := [asserted]: #44
+#201 := [mp #157 #200]: #196
+#204 := [mp~ #201 #208]: #196
+#252 := [mp #204 #251]: #249
+#283 := [mp #252 #282]: #280
+#767 := [mp #283 #766]: #762
+#68 := -3::Int
+#71 := (f3 -1::Int -3::Int)
+#74 := (= #71 -1::Int)
+#87 := (not #74)
#8 := 1::Int
#9 := (- 1::Int)
-#22 := (- #9)
-decl f3 :: Int
-#12 := f3
-#21 := (- f3)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod f3 #9)
-#15 := (< 0::Int #9)
-#17 := (< f3 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int f3)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= f3 0::Int)
-#26 := (ite #13 0::Int #25)
-#11 := (= #9 0::Int)
-#27 := (ite #11 f3 #26)
-#28 := (= #27 0::Int)
-#29 := (not #28)
-#200 := (iff #29 false)
-#50 := -1::Int
-#75 := (mod f3 -1::Int)
-#63 := (< 0::Int -1::Int)
-#69 := (and #17 #63)
-#66 := (and #14 #63)
-#72 := (or #66 #69)
-#108 := (not #72)
-#60 := (= 0::Int f3)
-#109 := (or #60 #108)
-#110 := (ite #109 0::Int #75)
-#125 := (= 0::Int #110)
-#130 := (not #125)
-#198 := (iff #130 false)
-#1 := true
-#193 := (not true)
-#196 := (iff #193 false)
-#197 := [rewrite]: #196
-#194 := (iff #130 #193)
-#191 := (iff #125 true)
-#186 := (= 0::Int 0::Int)
-#189 := (iff #186 true)
-#190 := [rewrite]: #189
-#187 := (iff #125 #186)
-#122 := (= #110 0::Int)
-#180 := (ite true 0::Int #75)
-#183 := (= #180 0::Int)
-#184 := [rewrite]: #183
-#181 := (= #110 #180)
-#178 := (iff #109 true)
-#173 := (or #13 true)
-#176 := (iff #173 true)
-#177 := [rewrite]: #176
-#174 := (iff #109 #173)
-#171 := (iff #108 true)
-#166 := (not false)
-#169 := (iff #166 true)
-#170 := [rewrite]: #169
-#167 := (iff #108 #166)
-#164 := (iff #72 false)
-#159 := (or false false)
-#162 := (iff #159 false)
-#163 := [rewrite]: #162
-#160 := (iff #72 #159)
-#157 := (iff #69 false)
-#148 := (>= f3 0::Int)
-#149 := (not #148)
-#152 := (and #149 false)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #69 #152)
-#139 := (iff #63 false)
-#140 := [rewrite]: #139
-#150 := (iff #17 #149)
-#151 := [rewrite]: #150
-#154 := [monotonicity #151 #140]: #153
-#158 := [trans #154 #156]: #157
-#146 := (iff #66 false)
-#135 := (<= f3 0::Int)
-#136 := (not #135)
-#141 := (and #136 false)
-#144 := (iff #141 false)
-#145 := [rewrite]: #144
-#142 := (iff #66 #141)
-#137 := (iff #14 #136)
-#138 := [rewrite]: #137
-#143 := [monotonicity #138 #140]: #142
-#147 := [trans #143 #145]: #146
-#161 := [monotonicity #147 #158]: #160
-#165 := [trans #161 #163]: #164
-#168 := [monotonicity #165]: #167
-#172 := [trans #168 #170]: #171
-#133 := (iff #60 #13)
-#134 := [rewrite]: #133
-#175 := [monotonicity #134 #172]: #174
-#179 := [trans #175 #177]: #178
-#182 := [monotonicity #179]: #181
-#185 := [trans #182 #184]: #122
-#188 := [monotonicity #185]: #187
-#192 := [trans #188 #190]: #191
-#195 := [monotonicity #192]: #194
-#199 := [trans #195 #197]: #198
-#131 := (iff #29 #130)
-#128 := (iff #28 #125)
-#126 := (iff #122 #125)
-#127 := [rewrite]: #126
-#123 := (iff #28 #122)
-#120 := (= #27 #110)
-#115 := (ite false f3 #110)
-#118 := (= #115 #110)
-#119 := [rewrite]: #118
-#116 := (= #27 #115)
-#113 := (= #26 #110)
-#102 := (ite #72 #75 0::Int)
-#105 := (ite #60 0::Int #102)
-#111 := (= #105 #110)
-#112 := [rewrite]: #111
-#106 := (= #26 #105)
-#103 := (= #25 #102)
-#100 := (= #24 0::Int)
-#95 := (- 0::Int)
-#98 := (= #95 0::Int)
-#99 := [rewrite]: #98
-#96 := (= #24 #95)
-#93 := (= #23 0::Int)
-#78 := (* -1::Int f3)
-#88 := (mod #78 1::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #23 #88)
-#86 := (= #22 1::Int)
-#81 := (- -1::Int)
-#84 := (= #81 1::Int)
-#85 := [rewrite]: #84
-#82 := (= #22 #81)
-#51 := (= #9 -1::Int)
-#52 := [rewrite]: #51
-#83 := [monotonicity #52]: #82
-#87 := [trans #83 #85]: #86
-#79 := (= #21 #78)
-#80 := [rewrite]: #79
-#90 := [monotonicity #80 #87]: #89
-#94 := [trans #90 #92]: #93
-#97 := [monotonicity #94]: #96
-#101 := [trans #97 #99]: #100
-#76 := (= #20 #75)
-#77 := [monotonicity #52]: #76
-#73 := (iff #19 #72)
-#70 := (iff #18 #69)
-#64 := (iff #15 #63)
-#65 := [monotonicity #52]: #64
-#71 := [monotonicity #65]: #70
-#67 := (iff #16 #66)
-#68 := [monotonicity #65]: #67
-#74 := [monotonicity #68 #71]: #73
-#104 := [monotonicity #74 #77 #101]: #103
-#61 := (iff #13 #60)
-#62 := [rewrite]: #61
-#107 := [monotonicity #62 #104]: #106
-#114 := [trans #107 #112]: #113
-#58 := (iff #11 false)
-#53 := (= -1::Int 0::Int)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #11 #53)
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#117 := [monotonicity #59 #114]: #116
-#121 := [trans #117 #119]: #120
-#124 := [monotonicity #121]: #123
-#129 := [trans #124 #127]: #128
-#132 := [monotonicity #129]: #131
-#201 := [trans #132 #199]: #200
-#49 := [asserted]: #29
-[mp #49 #201]: false
-unsat
-aaecefccca197f785d6ec165e82f88f0ae2f4e23 78 0
-#2 := false
-#9 := 0::Int
-#8 := 3::Int
-#18 := (- 3::Int)
-#17 := (- 0::Int)
-#19 := (mod #17 #18)
-#20 := (- #19)
-#16 := (mod 0::Int 3::Int)
-#13 := (< 0::Int 3::Int)
-#12 := (< 0::Int 0::Int)
-#14 := (and #12 #13)
-#15 := (or #14 #14)
-#21 := (ite #15 #16 #20)
-#11 := (= 0::Int 0::Int)
-#22 := (ite #11 0::Int #21)
-#10 := (= 3::Int 0::Int)
-#23 := (ite #10 0::Int #22)
-#24 := (= #23 0::Int)
-#25 := (not #24)
-#99 := (iff #25 false)
-#1 := true
-#94 := (not true)
-#97 := (iff #94 false)
-#98 := [rewrite]: #97
-#95 := (iff #25 #94)
-#92 := (iff #24 true)
-#48 := (iff #11 true)
-#49 := [rewrite]: #48
-#90 := (iff #24 #11)
-#84 := (ite false 0::Int 0::Int)
-#87 := (= #84 0::Int)
-#88 := [rewrite]: #87
-#85 := (= #23 #84)
-#82 := (= #22 0::Int)
-#77 := (ite true 0::Int 0::Int)
-#80 := (= #77 0::Int)
-#81 := [rewrite]: #80
-#78 := (= #22 #77)
-#75 := (= #21 0::Int)
-#70 := (ite #14 0::Int 0::Int)
-#73 := (= #70 0::Int)
-#74 := [rewrite]: #73
-#71 := (= #21 #70)
-#68 := (= #20 0::Int)
-#54 := (= #17 0::Int)
-#55 := [rewrite]: #54
-#66 := (= #20 #17)
-#64 := (= #19 0::Int)
-#56 := -3::Int
-#59 := (mod 0::Int -3::Int)
-#62 := (= #59 0::Int)
-#63 := [rewrite]: #62
-#60 := (= #19 #59)
-#57 := (= #18 -3::Int)
-#58 := [rewrite]: #57
-#61 := [monotonicity #55 #58]: #60
-#65 := [trans #61 #63]: #64
-#67 := [monotonicity #65]: #66
-#69 := [trans #67 #55]: #68
-#52 := (= #16 0::Int)
-#53 := [rewrite]: #52
-#50 := (iff #15 #14)
-#51 := [rewrite]: #50
-#72 := [monotonicity #51 #53 #69]: #71
-#76 := [trans #72 #74]: #75
-#79 := [monotonicity #49 #76]: #78
-#83 := [trans #79 #81]: #82
-#46 := (iff #10 false)
-#47 := [rewrite]: #46
-#86 := [monotonicity #47 #83]: #85
-#89 := [trans #86 #88]: #24
-#91 := [monotonicity #89]: #90
-#93 := [trans #91 #49]: #92
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#45 := [asserted]: #25
-[mp #45 #100]: false
-unsat
-000d5a08395f518246c54a195994fc62266f45ed 107 0
-#2 := false
-#10 := 0::Int
-#8 := 3::Int
-#9 := (- 3::Int)
-#19 := (- #9)
-#18 := (- 0::Int)
-#20 := (mod #18 #19)
-#21 := (- #20)
-#17 := (mod 0::Int #9)
-#14 := (< 0::Int #9)
-#13 := (< 0::Int 0::Int)
-#15 := (and #13 #14)
-#16 := (or #15 #15)
-#22 := (ite #16 #17 #21)
-#12 := (= 0::Int 0::Int)
-#23 := (ite #12 0::Int #22)
-#11 := (= #9 0::Int)
-#24 := (ite #11 0::Int #23)
-#25 := (= #24 0::Int)
-#26 := (not #25)
-#128 := (iff #26 false)
-#1 := true
-#123 := (not true)
-#126 := (iff #123 false)
-#127 := [rewrite]: #126
-#124 := (iff #26 #123)
-#121 := (iff #25 true)
-#57 := (iff #12 true)
-#58 := [rewrite]: #57
-#119 := (iff #25 #12)
-#113 := (ite false 0::Int 0::Int)
-#116 := (= #113 0::Int)
-#117 := [rewrite]: #116
-#114 := (= #24 #113)
-#111 := (= #23 0::Int)
-#106 := (ite true 0::Int 0::Int)
-#109 := (= #106 0::Int)
-#110 := [rewrite]: #109
-#107 := (= #23 #106)
-#104 := (= #22 0::Int)
-#47 := -3::Int
-#59 := (< 0::Int -3::Int)
-#62 := (and #13 #59)
-#99 := (ite #62 0::Int 0::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #22 #99)
-#97 := (= #21 0::Int)
-#79 := (= #18 0::Int)
-#80 := [rewrite]: #79
-#95 := (= #21 #18)
-#93 := (= #20 0::Int)
-#88 := (mod 0::Int 3::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #20 #88)
-#86 := (= #19 3::Int)
-#81 := (- -3::Int)
-#84 := (= #81 3::Int)
-#85 := [rewrite]: #84
-#82 := (= #19 #81)
-#48 := (= #9 -3::Int)
-#49 := [rewrite]: #48
-#83 := [monotonicity #49]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #80 #87]: #89
-#94 := [trans #90 #92]: #93
-#96 := [monotonicity #94]: #95
-#98 := [trans #96 #80]: #97
-#77 := (= #17 0::Int)
-#72 := (mod 0::Int -3::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #17 #72)
-#74 := [monotonicity #49]: #73
-#78 := [trans #74 #76]: #77
-#70 := (iff #16 #62)
-#65 := (or #62 #62)
-#68 := (iff #65 #62)
-#69 := [rewrite]: #68
-#66 := (iff #16 #65)
-#63 := (iff #15 #62)
-#60 := (iff #14 #59)
-#61 := [monotonicity #49]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64 #64]: #66
-#71 := [trans #67 #69]: #70
-#101 := [monotonicity #71 #78 #98]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #58 #105]: #107
-#112 := [trans #108 #110]: #111
-#55 := (iff #11 false)
-#50 := (= -3::Int 0::Int)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #11 #50)
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#115 := [monotonicity #56 #112]: #114
-#118 := [trans #115 #117]: #25
-#120 := [monotonicity #118]: #119
-#122 := [trans #120 #58]: #121
-#125 := [monotonicity #122]: #124
-#129 := [trans #125 #127]: #128
-#46 := [asserted]: #26
-[mp #46 #129]: false
-unsat
-54496e8e1bdde41302d50e03b35540e70008eccf 123 0
-#2 := false
-#11 := 1::Int
-#8 := 3::Int
-#21 := (- 3::Int)
-#20 := (- 1::Int)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod 1::Int 3::Int)
-#9 := 0::Int
-#14 := (< 0::Int 3::Int)
-#16 := (< 1::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 1::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= 1::Int 0::Int)
-#25 := (ite #12 0::Int #24)
-#10 := (= 3::Int 0::Int)
-#26 := (ite #10 1::Int #25)
-#27 := (= #26 1::Int)
-#28 := (not #27)
-#144 := (iff #28 false)
-#53 := (and #14 #16)
-#56 := (or #15 #53)
-#107 := (not #56)
-#142 := (iff #107 false)
-#1 := true
-#137 := (not true)
-#140 := (iff #137 false)
-#141 := [rewrite]: #140
-#138 := (iff #107 #137)
-#135 := (iff #56 true)
-#130 := (or true false)
-#133 := (iff #130 true)
-#134 := [rewrite]: #133
-#131 := (iff #56 #130)
-#128 := (iff #53 false)
-#123 := (and true false)
-#126 := (iff #123 false)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
+#13 := (= #12 #9)
+#14 := (not #13)
+#90 := (iff #14 #87)
+#77 := (= -1::Int #71)
+#82 := (not #77)
+#88 := (iff #82 #87)
+#85 := (iff #77 #74)
+#86 := [rewrite]: #85
+#89 := [monotonicity #86]: #88
+#83 := (iff #14 #82)
+#80 := (iff #13 #77)
+#78 := (iff #74 #77)
+#79 := [rewrite]: #78
+#75 := (iff #13 #74)
+#66 := (= #9 -1::Int)
+#67 := [rewrite]: #66
+#72 := (= #12 #71)
+#69 := (= #11 -3::Int)
+#70 := [rewrite]: #69
+#73 := [monotonicity #67 #70]: #72
+#76 := [monotonicity #73 #67]: #75
+#81 := [trans #76 #79]: #80
+#84 := [monotonicity #81]: #83
+#91 := [trans #84 #89]: #90
+#64 := [asserted]: #14
+#92 := [mp #64 #91]: #87
+#682 := (not #762)
+#671 := (or #682 #74)
+#341 := (* -1::Int -3::Int)
+#425 := (* -1::Int -1::Int)
+#426 := (mod #425 #341)
+#427 := (+ #71 #426)
+#418 := (= #427 0::Int)
+#429 := (mod -1::Int -3::Int)
+#430 := (* -1::Int #429)
+#431 := (+ #71 #430)
+#428 := (= #431 0::Int)
+#432 := (>= -1::Int 0::Int)
+#411 := (<= -3::Int 0::Int)
+#746 := (or #411 #432)
+#748 := (not #746)
+#405 := (<= -1::Int 0::Int)
+#535 := (or #405 #411)
+#742 := (not #535)
+#416 := (or #742 #748)
+#417 := (ite #416 #428 #418)
+#749 := (= #71 0::Int)
+#750 := (= -1::Int 0::Int)
+#751 := (ite #750 #749 #417)
+#752 := (= -3::Int 0::Int)
+#747 := (ite #752 #77 #751)
+#672 := (or #682 #747)
+#674 := (iff #672 #671)
+#675 := (iff #671 #671)
+#659 := [rewrite]: #675
+#681 := (iff #747 #74)
+#670 := (ite false #74 #74)
+#679 := (iff #670 #74)
+#680 := [rewrite]: #679
+#667 := (iff #747 #670)
+#676 := (iff #751 #74)
+#594 := (ite false #749 #74)
+#685 := (iff #594 #74)
+#689 := [rewrite]: #685
+#595 := (iff #751 #594)
+#592 := (iff #417 #74)
+#726 := 2::Int
+#556 := (= #71 2::Int)
+#587 := (ite false #556 #74)
+#583 := (iff #587 #74)
+#591 := [rewrite]: #583
+#589 := (iff #417 #587)
+#687 := (iff #418 #74)
+#692 := (+ 1::Int #71)
+#538 := (= #692 0::Int)
+#683 := (iff #538 #74)
+#684 := [rewrite]: #683
+#686 := (iff #418 #538)
+#578 := (= #427 #692)
+#691 := (+ #71 1::Int)
+#695 := (= #691 #692)
+#577 := [rewrite]: #695
+#693 := (= #427 #691)
+#537 := (= #426 1::Int)
+#704 := (mod 1::Int 3::Int)
+#534 := (= #704 1::Int)
+#536 := [rewrite]: #534
+#698 := (= #426 #704)
+#697 := (= #341 3::Int)
+#703 := [rewrite]: #697
+#702 := (= #425 1::Int)
+#696 := [rewrite]: #702
+#705 := [monotonicity #696 #703]: #698
+#690 := [trans #705 #536]: #537
+#694 := [monotonicity #690]: #693
+#579 := [trans #694 #577]: #578
+#588 := [monotonicity #579]: #686
+#572 := [trans #588 #684]: #687
+#700 := (iff #428 #556)
+#718 := -2::Int
+#711 := (+ -2::Int #71)
+#708 := (= #711 0::Int)
+#557 := (iff #708 #556)
+#699 := [rewrite]: #557
+#714 := (iff #428 #708)
+#712 := (= #431 #711)
+#720 := (+ #71 -2::Int)
+#706 := (= #720 #711)
+#707 := [rewrite]: #706
+#709 := (= #431 #720)
+#719 := (= #430 -2::Int)
+#438 := (* -1::Int 2::Int)
+#433 := (= #438 -2::Int)
+#715 := [rewrite]: #433
+#439 := (= #430 #438)
+#436 := (= #429 2::Int)
+#437 := [rewrite]: #436
+#717 := [monotonicity #437]: #439
+#716 := [trans #717 #715]: #719
+#710 := [monotonicity #716]: #709
+#713 := [trans #710 #707]: #712
+#555 := [monotonicity #713]: #714
+#701 := [trans #555 #699]: #700
+#725 := (iff #416 false)
+#723 := (or false false)
+#447 := (iff #723 false)
+#721 := [rewrite]: #447
+#724 := (iff #416 #723)
+#453 := (iff #748 false)
+#1 := true
+#733 := (not true)
+#730 := (iff #733 false)
+#736 := [rewrite]: #730
+#451 := (iff #748 #733)
+#728 := (iff #746 true)
+#380 := (or true false)
+#741 := (iff #380 true)
+#727 := [rewrite]: #741
+#740 := (iff #746 #380)
+#739 := (iff #432 false)
+#379 := [rewrite]: #739
+#745 := (iff #411 true)
+#388 := [rewrite]: #745
+#738 := [monotonicity #388 #379]: #740
+#450 := [trans #738 #727]: #728
+#452 := [monotonicity #450]: #451
+#347 := [trans #452 #736]: #453
+#374 := (iff #742 false)
+#734 := (iff #742 #733)
+#731 := (iff #535 true)
+#729 := (or true true)
+#394 := (iff #729 true)
+#395 := [rewrite]: #394
+#392 := (iff #535 #729)
+#744 := (iff #405 true)
+#404 := [rewrite]: #744
+#393 := [monotonicity #404 #388]: #392
+#732 := [trans #393 #395]: #731
+#735 := [monotonicity #732]: #734
+#737 := [trans #735 #736]: #374
+#446 := [monotonicity #737 #347]: #724
+#722 := [trans #446 #721]: #725
+#590 := [monotonicity #722 #701 #572]: #589
+#593 := [trans #590 #591]: #592
+#403 := (iff #750 false)
+#408 := [rewrite]: #403
+#688 := [monotonicity #408 #593]: #595
+#678 := [trans #688 #689]: #676
+#753 := (iff #752 false)
+#743 := [rewrite]: #753
+#669 := [monotonicity #743 #86 #678]: #667
+#677 := [trans #669 #680]: #681
+#668 := [monotonicity #677]: #674
+#660 := [trans #668 #659]: #674
+#673 := [quant-inst #65 #68]: #672
+#662 := [mp #673 #660]: #671
+[unit-resolution #662 #92 #767]: false
+unsat
+a8f315f795d8dc3da5b76a3fe9d6ebfef481af33 324 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#15 := (:var 0 Int)
+#14 := (:var 1 Int)
+#34 := (f3 #14 #15)
+#773 := (pattern #34)
+#11 := 0::Int
+#104 := -1::Int
+#108 := (* -1::Int #15)
+#105 := (* -1::Int #14)
+#169 := (mod #105 #108)
+#284 := (+ #34 #169)
+#285 := (= #284 0::Int)
+#35 := (mod #14 #15)
+#281 := (* -1::Int #35)
+#282 := (+ #34 #281)
+#283 := (= #282 0::Int)
+#143 := (>= #14 0::Int)
+#136 := (<= #15 0::Int)
+#228 := (or #136 #143)
+#229 := (not #228)
+#132 := (<= #14 0::Int)
+#226 := (or #132 #136)
+#227 := (not #226)
+#232 := (or #227 #229)
+#286 := (ite #232 #283 #285)
+#280 := (= #34 0::Int)
+#17 := (= #14 0::Int)
+#287 := (ite #17 #280 #286)
+#279 := (= #14 #34)
+#18 := (= #15 0::Int)
+#288 := (ite #18 #279 #287)
+#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
+#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
+#777 := (iff #291 #774)
+#775 := (iff #288 #288)
+#776 := [refl]: #775
+#778 := [quant-intro #776]: #777
+#175 := (* -1::Int #169)
+#248 := (ite #232 #35 #175)
+#251 := (ite #17 0::Int #248)
+#254 := (ite #18 #14 #251)
+#257 := (= #34 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#292 := (iff #260 #291)
+#289 := (iff #257 #288)
+#290 := [rewrite]: #289
+#293 := [quant-intro #290]: #292
+#144 := (not #143)
+#137 := (not #136)
+#147 := (and #137 #144)
+#133 := (not #132)
+#140 := (and #133 #137)
+#150 := (or #140 #147)
+#195 := (ite #150 #35 #175)
+#198 := (ite #17 0::Int #195)
+#201 := (ite #18 #14 #198)
+#204 := (= #34 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#261 := (iff #207 #260)
+#258 := (iff #204 #257)
+#255 := (= #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#233 := (iff #150 #232)
+#230 := (iff #147 #229)
+#231 := [rewrite]: #230
+#220 := (iff #140 #227)
+#221 := [rewrite]: #220
+#234 := [monotonicity #221 #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
+#218 := (~ #207 #207)
+#217 := (~ #204 #204)
+#214 := [refl]: #217
+#219 := [nnf-pos #214]: #218
+#28 := (- #15)
+#27 := (- #14)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #15)
+#23 := (< #14 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #14)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #14 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#210 := (iff #42 #207)
+#98 := (and #21 #23)
+#101 := (or #22 #98)
+#180 := (ite #101 #35 #175)
+#89 := (= 0::Int #14)
+#183 := (ite #89 0::Int #180)
+#92 := (= 0::Int #15)
+#186 := (ite #92 #14 #183)
+#189 := (= #34 #186)
+#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
+#208 := (iff #192 #207)
+#205 := (iff #189 #204)
+#202 := (= #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#151 := (iff #101 #150)
+#148 := (iff #98 #147)
+#145 := (iff #23 #144)
+#146 := [rewrite]: #145
+#138 := (iff #21 #137)
+#139 := [rewrite]: #138
+#149 := [monotonicity #139 #146]: #148
+#141 := (iff #22 #140)
+#134 := (iff #20 #133)
+#135 := [rewrite]: #134
+#142 := [monotonicity #135 #139]: #141
+#152 := [monotonicity #142 #149]: #151
+#197 := [monotonicity #152]: #196
+#126 := (iff #89 #17)
#127 := [rewrite]: #126
-#124 := (iff #53 #123)
-#121 := (iff #16 false)
-#122 := [rewrite]: #121
-#112 := (iff #14 true)
-#113 := [rewrite]: #112
-#125 := [monotonicity #113 #122]: #124
-#129 := [trans #125 #127]: #128
-#119 := (iff #15 true)
-#114 := (and true true)
-#117 := (iff #114 true)
-#118 := [rewrite]: #117
-#115 := (iff #15 #114)
-#110 := (iff #13 true)
-#111 := [rewrite]: #110
-#116 := [monotonicity #111 #113]: #115
-#120 := [trans #116 #118]: #119
-#132 := [monotonicity #120 #129]: #131
-#136 := [trans #132 #134]: #135
-#139 := [monotonicity #136]: #138
-#143 := [trans #139 #141]: #142
-#108 := (iff #28 #107)
-#105 := (iff #27 #56)
-#78 := -2::Int
-#83 := (ite #56 1::Int -2::Int)
-#100 := (= #83 1::Int)
-#103 := (iff #100 #56)
-#104 := [rewrite]: #103
-#101 := (iff #27 #100)
-#98 := (= #26 #83)
-#93 := (ite false 1::Int #83)
-#96 := (= #93 #83)
-#97 := [rewrite]: #96
-#94 := (= #26 #93)
-#91 := (= #25 #83)
-#86 := (ite false 0::Int #83)
-#89 := (= #86 #83)
-#90 := [rewrite]: #89
-#87 := (= #25 #86)
-#84 := (= #24 #83)
-#81 := (= #23 -2::Int)
-#70 := 2::Int
-#75 := (- 2::Int)
-#79 := (= #75 -2::Int)
-#80 := [rewrite]: #79
-#76 := (= #23 #75)
-#73 := (= #22 2::Int)
-#64 := -3::Int
-#61 := -1::Int
-#67 := (mod -1::Int -3::Int)
-#71 := (= #67 2::Int)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#65 := (= #21 -3::Int)
-#66 := [rewrite]: #65
-#62 := (= #20 -1::Int)
-#63 := [rewrite]: #62
-#69 := [monotonicity #63 #66]: #68
-#74 := [trans #69 #72]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#59 := (= #19 1::Int)
-#60 := [rewrite]: #59
-#57 := (iff #18 #56)
-#54 := (iff #17 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#85 := [monotonicity #58 #60 #82]: #84
-#51 := (iff #12 false)
-#52 := [rewrite]: #51
-#88 := [monotonicity #52 #85]: #87
-#92 := [trans #88 #90]: #91
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#95 := [monotonicity #50 #92]: #94
-#99 := [trans #95 #97]: #98
-#102 := [monotonicity #99]: #101
-#106 := [trans #102 #104]: #105
-#109 := [monotonicity #106]: #108
-#145 := [trans #109 #143]: #144
-#48 := [asserted]: #28
-[mp #48 #145]: false
-unsat
-2e12b506bd838c7a91cf9b35f04a675da557e17b 85 0
-#2 := false
-#9 := 0::Int
-#8 := 3::Int
-#17 := (- 3::Int)
-#18 := (mod #17 #17)
-#19 := (- #18)
-#16 := (mod 3::Int 3::Int)
-#11 := (< 0::Int 3::Int)
-#13 := (< 3::Int 0::Int)
-#14 := (and #13 #11)
-#12 := (and #11 #11)
-#15 := (or #12 #14)
-#20 := (ite #15 #16 #19)
-#10 := (= 3::Int 0::Int)
-#21 := (ite #10 0::Int #20)
-#22 := (ite #10 3::Int #21)
-#23 := (= #22 0::Int)
-#24 := (not #23)
-#106 := (iff #24 false)
-#1 := true
-#101 := (not true)
-#104 := (iff #101 false)
-#105 := [rewrite]: #104
-#102 := (iff #24 #101)
-#99 := (iff #23 true)
-#94 := (= 0::Int 0::Int)
-#97 := (iff #94 true)
-#98 := [rewrite]: #97
-#95 := (iff #23 #94)
-#88 := (ite false 3::Int 0::Int)
-#91 := (= #88 0::Int)
-#92 := [rewrite]: #91
-#89 := (= #22 #88)
-#86 := (= #21 0::Int)
-#81 := (ite false 0::Int 0::Int)
-#84 := (= #81 0::Int)
-#85 := [rewrite]: #84
-#82 := (= #21 #81)
-#79 := (= #20 0::Int)
-#49 := (and #11 #13)
-#52 := (or #11 #49)
-#74 := (ite #52 0::Int 0::Int)
-#77 := (= #74 0::Int)
-#78 := [rewrite]: #77
-#75 := (= #20 #74)
-#72 := (= #19 0::Int)
-#67 := (- 0::Int)
-#70 := (= #67 0::Int)
-#71 := [rewrite]: #70
-#68 := (= #19 #67)
-#65 := (= #18 0::Int)
-#57 := -3::Int
-#60 := (mod -3::Int -3::Int)
-#63 := (= #60 0::Int)
-#64 := [rewrite]: #63
-#61 := (= #18 #60)
-#58 := (= #17 -3::Int)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59 #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#55 := (= #16 0::Int)
-#56 := [rewrite]: #55
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#47 := (iff #12 #11)
-#48 := [rewrite]: #47
-#54 := [monotonicity #48 #51]: #53
-#76 := [monotonicity #54 #56 #73]: #75
-#80 := [trans #76 #78]: #79
-#45 := (iff #10 false)
-#46 := [rewrite]: #45
-#83 := [monotonicity #46 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #46 #87]: #89
-#93 := [trans #90 #92]: #23
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
+#200 := [monotonicity #127 #197]: #199
+#128 := (iff #92 #18)
+#129 := [rewrite]: #128
+#203 := [monotonicity #129 #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#187 := (= #40 #186)
+#184 := (= #39 #183)
+#181 := (= #38 #180)
+#178 := (= #37 #175)
+#172 := (- #169)
+#176 := (= #172 #175)
+#177 := [rewrite]: #176
+#173 := (= #37 #172)
+#170 := (= #36 #169)
+#109 := (= #28 #108)
+#110 := [rewrite]: #109
+#106 := (= #27 #105)
+#107 := [rewrite]: #106
+#171 := [monotonicity #107 #110]: #170
+#174 := [monotonicity #171]: #173
+#179 := [trans #174 #177]: #178
+#102 := (iff #25 #101)
+#99 := (iff #24 #98)
+#100 := [rewrite]: #99
#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#44 := [asserted]: #24
-[mp #44 #107]: false
-unsat
-a185dd1db6f642a5e7d15c4c9072da159f55df2d 124 0
-#2 := false
-#27 := 2::Int
-#8 := 3::Int
-#21 := (- 3::Int)
-#11 := 5::Int
-#20 := (- 5::Int)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#19 := (mod 5::Int 3::Int)
-#9 := 0::Int
-#14 := (< 0::Int 3::Int)
-#16 := (< 5::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 5::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#12 := (= 5::Int 0::Int)
-#25 := (ite #12 0::Int #24)
-#10 := (= 3::Int 0::Int)
-#26 := (ite #10 5::Int #25)
-#28 := (= #26 2::Int)
-#29 := (not #28)
-#145 := (iff #29 false)
-#54 := (and #14 #16)
-#57 := (or #15 #54)
-#108 := (not #57)
-#143 := (iff #108 false)
-#1 := true
-#138 := (not true)
-#141 := (iff #138 false)
-#142 := [rewrite]: #141
-#139 := (iff #108 #138)
-#136 := (iff #57 true)
-#131 := (or true false)
-#134 := (iff #131 true)
-#135 := [rewrite]: #134
-#132 := (iff #57 #131)
-#129 := (iff #54 false)
-#124 := (and true false)
-#127 := (iff #124 false)
-#128 := [rewrite]: #127
-#125 := (iff #54 #124)
-#122 := (iff #16 false)
-#123 := [rewrite]: #122
-#113 := (iff #14 true)
-#114 := [rewrite]: #113
-#126 := [monotonicity #114 #123]: #125
-#130 := [trans #126 #128]: #129
-#120 := (iff #15 true)
-#115 := (and true true)
-#118 := (iff #115 true)
-#119 := [rewrite]: #118
-#116 := (iff #15 #115)
-#111 := (iff #13 true)
-#112 := [rewrite]: #111
-#117 := [monotonicity #112 #114]: #116
-#121 := [trans #117 #119]: #120
-#133 := [monotonicity #121 #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #137]: #139
-#144 := [trans #140 #142]: #143
-#109 := (iff #29 #108)
-#106 := (iff #28 #57)
-#79 := -1::Int
-#84 := (ite #57 2::Int -1::Int)
-#101 := (= #84 2::Int)
-#104 := (iff #101 #57)
-#105 := [rewrite]: #104
-#102 := (iff #28 #101)
-#99 := (= #26 #84)
-#94 := (ite false 5::Int #84)
-#97 := (= #94 #84)
-#98 := [rewrite]: #97
-#95 := (= #26 #94)
-#92 := (= #25 #84)
-#87 := (ite false 0::Int #84)
-#90 := (= #87 #84)
+#182 := [monotonicity #103 #179]: #181
+#90 := (iff #17 #89)
#91 := [rewrite]: #90
-#88 := (= #25 #87)
-#85 := (= #24 #84)
-#82 := (= #23 -1::Int)
-#71 := 1::Int
-#76 := (- 1::Int)
-#80 := (= #76 -1::Int)
-#81 := [rewrite]: #80
-#77 := (= #23 #76)
-#74 := (= #22 1::Int)
-#65 := -3::Int
-#62 := -5::Int
-#68 := (mod -5::Int -3::Int)
-#72 := (= #68 1::Int)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#66 := (= #21 -3::Int)
-#67 := [rewrite]: #66
-#63 := (= #20 -5::Int)
-#64 := [rewrite]: #63
-#70 := [monotonicity #64 #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#83 := [trans #78 #81]: #82
-#60 := (= #19 2::Int)
-#61 := [rewrite]: #60
-#58 := (iff #18 #57)
-#55 := (iff #17 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#86 := [monotonicity #59 #61 #83]: #85
-#52 := (iff #12 false)
-#53 := [rewrite]: #52
-#89 := [monotonicity #53 #86]: #88
-#93 := [trans #89 #91]: #92
-#50 := (iff #10 false)
-#51 := [rewrite]: #50
-#96 := [monotonicity #51 #93]: #95
-#100 := [trans #96 #98]: #99
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#146 := [trans #110 #144]: #145
-#49 := [asserted]: #29
-[mp #49 #146]: false
-unsat
-7d327b19e01666c9f9c62ef0af0f737663d19d70 145 0
-#2 := false
-#28 := 2::Int
-#29 := (- 2::Int)
-#8 := 3::Int
-#9 := (- 3::Int)
-#22 := (- #9)
-#12 := 1::Int
-#21 := (- 1::Int)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod 1::Int #9)
-#10 := 0::Int
-#15 := (< 0::Int #9)
-#17 := (< 1::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 1::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= 1::Int 0::Int)
-#26 := (ite #13 0::Int #25)
-#11 := (= #9 0::Int)
-#27 := (ite #11 1::Int #26)
-#30 := (= #27 #29)
-#31 := (not #30)
-#166 := (iff #31 false)
-#52 := -3::Int
-#64 := (< 0::Int -3::Int)
-#70 := (and #17 #64)
-#67 := (and #14 #64)
-#73 := (or #67 #70)
-#164 := (iff #73 false)
-#159 := (or false false)
-#162 := (iff #159 false)
-#163 := [rewrite]: #162
-#160 := (iff #73 #159)
-#157 := (iff #70 false)
-#152 := (and false false)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #70 #152)
-#141 := (iff #64 false)
-#142 := [rewrite]: #141
-#150 := (iff #17 false)
-#151 := [rewrite]: #150
-#154 := [monotonicity #151 #142]: #153
-#158 := [trans #154 #156]: #157
-#148 := (iff #67 false)
-#1 := true
-#143 := (and true false)
-#146 := (iff #143 false)
-#147 := [rewrite]: #146
-#144 := (iff #67 #143)
-#139 := (iff #14 true)
-#140 := [rewrite]: #139
-#145 := [monotonicity #140 #142]: #144
-#149 := [trans #145 #147]: #148
-#161 := [monotonicity #149 #158]: #160
-#165 := [trans #161 #163]: #164
-#137 := (iff #31 #73)
-#127 := (not #73)
-#132 := (not #127)
-#135 := (iff #132 #73)
-#136 := [rewrite]: #135
-#133 := (iff #31 #132)
-#130 := (iff #30 #127)
-#102 := -2::Int
-#107 := (ite #73 1::Int -2::Int)
-#124 := (= #107 -2::Int)
-#128 := (iff #124 #127)
-#129 := [rewrite]: #128
-#125 := (iff #30 #124)
-#103 := (= #29 -2::Int)
-#104 := [rewrite]: #103
-#122 := (= #27 #107)
-#117 := (ite false 1::Int #107)
-#120 := (= #117 #107)
-#121 := [rewrite]: #120
-#118 := (= #27 #117)
-#115 := (= #26 #107)
-#110 := (ite false 0::Int #107)
-#113 := (= #110 #107)
-#114 := [rewrite]: #113
-#111 := (= #26 #110)
-#108 := (= #25 #107)
-#105 := (= #24 -2::Int)
-#100 := (= #24 #29)
-#98 := (= #23 2::Int)
-#83 := -1::Int
-#93 := (mod -1::Int 3::Int)
-#96 := (= #93 2::Int)
-#97 := [rewrite]: #96
-#94 := (= #23 #93)
-#91 := (= #22 3::Int)
-#86 := (- -3::Int)
-#89 := (= #86 3::Int)
-#90 := [rewrite]: #89
-#87 := (= #22 #86)
-#53 := (= #9 -3::Int)
-#54 := [rewrite]: #53
-#88 := [monotonicity #54]: #87
-#92 := [trans #88 #90]: #91
-#84 := (= #21 -1::Int)
-#85 := [rewrite]: #84
-#95 := [monotonicity #85 #92]: #94
-#99 := [trans #95 #97]: #98
-#101 := [monotonicity #99]: #100
-#106 := [trans #101 #104]: #105
-#81 := (= #20 1::Int)
-#76 := (mod 1::Int -3::Int)
-#79 := (= #76 1::Int)
-#80 := [rewrite]: #79
-#77 := (= #20 #76)
-#78 := [monotonicity #54]: #77
-#82 := [trans #78 #80]: #81
-#74 := (iff #19 #73)
-#71 := (iff #18 #70)
-#65 := (iff #15 #64)
-#66 := [monotonicity #54]: #65
-#72 := [monotonicity #66]: #71
-#68 := (iff #16 #67)
-#69 := [monotonicity #66]: #68
-#75 := [monotonicity #69 #72]: #74
-#109 := [monotonicity #75 #82 #106]: #108
-#62 := (iff #13 false)
-#63 := [rewrite]: #62
-#112 := [monotonicity #63 #109]: #111
-#116 := [trans #112 #114]: #115
-#60 := (iff #11 false)
-#55 := (= -3::Int 0::Int)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #11 #55)
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#119 := [monotonicity #61 #116]: #118
-#123 := [trans #119 #121]: #122
-#126 := [monotonicity #123 #104]: #125
-#131 := [trans #126 #129]: #130
-#134 := [monotonicity #131]: #133
-#138 := [trans #134 #136]: #137
-#167 := [trans #138 #165]: #166
-#51 := [asserted]: #31
-[mp #51 #167]: false
-unsat
-82d6113024911b407663ddeabeafc31ab21bb4b0 111 0
-#2 := false
-#10 := 0::Int
+#185 := [monotonicity #91 #182]: #184
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#188 := [monotonicity #94 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [quant-intro #191]: #193
+#211 := [trans #194 #209]: #210
+#168 := [asserted]: #42
+#212 := [mp #168 #211]: #207
+#215 := [mp~ #212 #219]: #207
+#263 := [mp #215 #262]: #260
+#294 := [mp #263 #293]: #291
+#779 := [mp #294 #778]: #774
+#63 := -3::Int
+#66 := (f3 -3::Int -3::Int)
+#69 := (= #66 0::Int)
+#82 := (not #69)
#8 := 3::Int
#9 := (- 3::Int)
-#20 := (- #9)
-#21 := (mod #9 #20)
-#22 := (- #21)
-#19 := (mod 3::Int #9)
-#14 := (< 0::Int #9)
-#16 := (< 3::Int 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int 3::Int)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#23 := (ite #18 #19 #22)
-#12 := (= 3::Int 0::Int)
-#24 := (ite #12 0::Int #23)
-#11 := (= #9 0::Int)
-#25 := (ite #11 3::Int #24)
-#26 := (= #25 0::Int)
-#27 := (not #26)
-#132 := (iff #27 false)
-#1 := true
-#127 := (not true)
-#130 := (iff #127 false)
-#131 := [rewrite]: #130
-#128 := (iff #27 #127)
-#125 := (iff #26 true)
-#120 := (= 0::Int 0::Int)
-#123 := (iff #120 true)
-#124 := [rewrite]: #123
-#121 := (iff #26 #120)
-#114 := (ite false 3::Int 0::Int)
-#117 := (= #114 0::Int)
-#118 := [rewrite]: #117
-#115 := (= #25 #114)
-#112 := (= #24 0::Int)
-#107 := (ite false 0::Int 0::Int)
-#110 := (= #107 0::Int)
-#111 := [rewrite]: #110
-#108 := (= #24 #107)
-#105 := (= #23 0::Int)
-#48 := -3::Int
-#60 := (< 0::Int -3::Int)
-#66 := (and #16 #60)
-#63 := (and #13 #60)
-#69 := (or #63 #66)
-#100 := (ite #69 0::Int 0::Int)
-#103 := (= #100 0::Int)
-#104 := [rewrite]: #103
-#101 := (= #23 #100)
-#98 := (= #22 0::Int)
-#93 := (- 0::Int)
-#96 := (= #93 0::Int)
-#97 := [rewrite]: #96
-#94 := (= #22 #93)
-#91 := (= #21 0::Int)
-#86 := (mod -3::Int 3::Int)
-#89 := (= #86 0::Int)
-#90 := [rewrite]: #89
-#87 := (= #21 #86)
-#84 := (= #20 3::Int)
-#79 := (- -3::Int)
-#82 := (= #79 3::Int)
-#83 := [rewrite]: #82
-#80 := (= #20 #79)
-#49 := (= #9 -3::Int)
-#50 := [rewrite]: #49
-#81 := [monotonicity #50]: #80
-#85 := [trans #81 #83]: #84
-#88 := [monotonicity #50 #85]: #87
-#92 := [trans #88 #90]: #91
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#77 := (= #19 0::Int)
-#72 := (mod 3::Int -3::Int)
-#75 := (= #72 0::Int)
-#76 := [rewrite]: #75
-#73 := (= #19 #72)
-#74 := [monotonicity #50]: #73
-#78 := [trans #74 #76]: #77
-#70 := (iff #18 #69)
-#67 := (iff #17 #66)
-#61 := (iff #14 #60)
-#62 := [monotonicity #50]: #61
-#68 := [monotonicity #62]: #67
-#64 := (iff #15 #63)
-#65 := [monotonicity #62]: #64
-#71 := [monotonicity #65 #68]: #70
-#102 := [monotonicity #71 #78 #99]: #101
-#106 := [trans #102 #104]: #105
-#58 := (iff #12 false)
-#59 := [rewrite]: #58
-#109 := [monotonicity #59 #106]: #108
-#113 := [trans #109 #111]: #112
-#56 := (iff #11 false)
-#51 := (= -3::Int 0::Int)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #11 #51)
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#116 := [monotonicity #57 #113]: #115
-#119 := [trans #116 #118]: #26
-#122 := [monotonicity #119]: #121
-#126 := [trans #122 #124]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#47 := [asserted]: #27
-[mp #47 #133]: false
-unsat
-c4214ad6df5eccc4b53bd004dab0150c7519b10c 146 0
-#2 := false
-#28 := 1::Int
-#29 := (- 1::Int)
-#8 := 3::Int
-#9 := (- 3::Int)
-#22 := (- #9)
-#12 := 5::Int
-#21 := (- 5::Int)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod 5::Int #9)
-#10 := 0::Int
-#15 := (< 0::Int #9)
-#17 := (< 5::Int 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int 5::Int)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= 5::Int 0::Int)
-#26 := (ite #13 0::Int #25)
-#11 := (= #9 0::Int)
-#27 := (ite #11 5::Int #26)
-#30 := (= #27 #29)
-#31 := (not #30)
-#167 := (iff #31 false)
-#52 := -3::Int
-#64 := (< 0::Int -3::Int)
-#70 := (and #17 #64)
-#67 := (and #14 #64)
-#73 := (or #67 #70)
-#165 := (iff #73 false)
-#160 := (or false false)
-#163 := (iff #160 false)
-#164 := [rewrite]: #163
-#161 := (iff #73 #160)
-#158 := (iff #70 false)
-#153 := (and false false)
-#156 := (iff #153 false)
-#157 := [rewrite]: #156
-#154 := (iff #70 #153)
-#142 := (iff #64 false)
-#143 := [rewrite]: #142
-#151 := (iff #17 false)
-#152 := [rewrite]: #151
-#155 := [monotonicity #152 #143]: #154
-#159 := [trans #155 #157]: #158
-#149 := (iff #67 false)
-#1 := true
-#144 := (and true false)
-#147 := (iff #144 false)
-#148 := [rewrite]: #147
-#145 := (iff #67 #144)
-#140 := (iff #14 true)
-#141 := [rewrite]: #140
-#146 := [monotonicity #141 #143]: #145
-#150 := [trans #146 #148]: #149
-#162 := [monotonicity #150 #159]: #161
-#166 := [trans #162 #164]: #165
-#138 := (iff #31 #73)
-#128 := (not #73)
-#133 := (not #128)
-#136 := (iff #133 #73)
-#137 := [rewrite]: #136
-#134 := (iff #31 #133)
-#131 := (iff #30 #128)
-#103 := -1::Int
-#79 := 2::Int
-#108 := (ite #73 2::Int -1::Int)
-#125 := (= #108 -1::Int)
-#129 := (iff #125 #128)
-#130 := [rewrite]: #129
-#126 := (iff #30 #125)
-#104 := (= #29 -1::Int)
-#105 := [rewrite]: #104
-#123 := (= #27 #108)
-#118 := (ite false 5::Int #108)
-#121 := (= #118 #108)
-#122 := [rewrite]: #121
-#119 := (= #27 #118)
-#116 := (= #26 #108)
-#111 := (ite false 0::Int #108)
-#114 := (= #111 #108)
-#115 := [rewrite]: #114
-#112 := (= #26 #111)
-#109 := (= #25 #108)
-#106 := (= #24 -1::Int)
-#101 := (= #24 #29)
-#99 := (= #23 1::Int)
-#84 := -5::Int
-#94 := (mod -5::Int 3::Int)
-#97 := (= #94 1::Int)
-#98 := [rewrite]: #97
-#95 := (= #23 #94)
-#92 := (= #22 3::Int)
-#87 := (- -3::Int)
-#90 := (= #87 3::Int)
-#91 := [rewrite]: #90
-#88 := (= #22 #87)
-#53 := (= #9 -3::Int)
-#54 := [rewrite]: #53
-#89 := [monotonicity #54]: #88
-#93 := [trans #89 #91]: #92
-#85 := (= #21 -5::Int)
-#86 := [rewrite]: #85
-#96 := [monotonicity #86 #93]: #95
-#100 := [trans #96 #98]: #99
-#102 := [monotonicity #100]: #101
-#107 := [trans #102 #105]: #106
-#82 := (= #20 2::Int)
-#76 := (mod 5::Int -3::Int)
-#80 := (= #76 2::Int)
+#10 := (f3 #9 #9)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#85 := (iff #13 #82)
+#72 := (= 0::Int #66)
+#77 := (not #72)
+#83 := (iff #77 #82)
+#80 := (iff #72 #69)
#81 := [rewrite]: #80
-#77 := (= #20 #76)
-#78 := [monotonicity #54]: #77
-#83 := [trans #78 #81]: #82
-#74 := (iff #19 #73)
-#71 := (iff #18 #70)
-#65 := (iff #15 #64)
-#66 := [monotonicity #54]: #65
-#72 := [monotonicity #66]: #71
-#68 := (iff #16 #67)
-#69 := [monotonicity #66]: #68
-#75 := [monotonicity #69 #72]: #74
-#110 := [monotonicity #75 #83 #107]: #109
-#62 := (iff #13 false)
-#63 := [rewrite]: #62
-#113 := [monotonicity #63 #110]: #112
-#117 := [trans #113 #115]: #116
-#60 := (iff #11 false)
-#55 := (= -3::Int 0::Int)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #11 #55)
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#120 := [monotonicity #61 #117]: #119
-#124 := [trans #120 #122]: #123
-#127 := [monotonicity #124 #105]: #126
-#132 := [trans #127 #130]: #131
-#135 := [monotonicity #132]: #134
-#139 := [trans #135 #137]: #138
-#168 := [trans #139 #166]: #167
-#51 := [asserted]: #31
-[mp #51 #168]: false
-unsat
-fac742ba4b7a09666d1c5cd8a1a25074910c56cc 156 0
-#2 := false
-#28 := 2::Int
-#8 := 3::Int
-#22 := (- 3::Int)
-#11 := 1::Int
-#12 := (- 1::Int)
-#21 := (- #12)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod #12 3::Int)
-#9 := 0::Int
-#15 := (< 0::Int 3::Int)
-#17 := (< #12 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #12)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= #12 0::Int)
-#26 := (ite #13 0::Int #25)
-#10 := (= 3::Int 0::Int)
-#27 := (ite #10 #12 #26)
-#29 := (= #27 2::Int)
-#30 := (not #29)
-#177 := (iff #30 false)
-#53 := -1::Int
-#74 := (< -1::Int 0::Int)
-#80 := (and #15 #74)
-#63 := (< 0::Int -1::Int)
-#69 := (and #15 #63)
-#85 := (or #69 #80)
-#140 := (not #85)
-#175 := (iff #140 false)
-#1 := true
-#170 := (not true)
-#173 := (iff #170 false)
-#174 := [rewrite]: #173
-#171 := (iff #140 #170)
-#168 := (iff #85 true)
-#163 := (or false true)
-#166 := (iff #163 true)
-#167 := [rewrite]: #166
-#164 := (iff #85 #163)
-#161 := (iff #80 true)
-#156 := (and true true)
-#159 := (iff #156 true)
-#160 := [rewrite]: #159
-#157 := (iff #80 #156)
-#154 := (iff #74 true)
-#155 := [rewrite]: #154
-#143 := (iff #15 true)
-#144 := [rewrite]: #143
-#158 := [monotonicity #144 #155]: #157
-#162 := [trans #158 #160]: #161
-#152 := (iff #69 false)
-#147 := (and true false)
-#150 := (iff #147 false)
-#151 := [rewrite]: #150
-#148 := (iff #69 #147)
-#145 := (iff #63 false)
-#146 := [rewrite]: #145
-#149 := [monotonicity #144 #146]: #148
-#153 := [trans #149 #151]: #152
-#165 := [monotonicity #153 #162]: #164
-#169 := [trans #165 #167]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#141 := (iff #30 #140)
-#138 := (iff #29 #85)
-#116 := (ite #85 2::Int -1::Int)
-#133 := (= #116 2::Int)
-#136 := (iff #133 #85)
-#137 := [rewrite]: #136
-#134 := (iff #29 #133)
-#131 := (= #27 #116)
-#126 := (ite false -1::Int #116)
-#129 := (= #126 #116)
-#130 := [rewrite]: #129
-#127 := (= #27 #126)
-#124 := (= #26 #116)
-#119 := (ite false 0::Int #116)
-#122 := (= #119 #116)
-#123 := [rewrite]: #122
-#120 := (= #26 #119)
-#117 := (= #25 #116)
-#114 := (= #24 -1::Int)
-#54 := (= #12 -1::Int)
-#55 := [rewrite]: #54
-#112 := (= #24 #12)
-#110 := (= #23 1::Int)
-#102 := -3::Int
-#105 := (mod 1::Int -3::Int)
-#108 := (= #105 1::Int)
-#109 := [rewrite]: #108
-#106 := (= #23 #105)
-#103 := (= #22 -3::Int)
-#104 := [rewrite]: #103
-#100 := (= #21 1::Int)
-#95 := (- -1::Int)
-#98 := (= #95 1::Int)
-#99 := [rewrite]: #98
-#96 := (= #21 #95)
-#97 := [monotonicity #55]: #96
-#101 := [trans #97 #99]: #100
-#107 := [monotonicity #101 #104]: #106
-#111 := [trans #107 #109]: #110
-#113 := [monotonicity #111]: #112
-#115 := [trans #113 #55]: #114
-#93 := (= #20 2::Int)
-#88 := (mod -1::Int 3::Int)
-#91 := (= #88 2::Int)
-#92 := [rewrite]: #91
-#89 := (= #20 #88)
-#90 := [monotonicity #55]: #89
-#94 := [trans #90 #92]: #93
-#86 := (iff #19 #85)
-#83 := (iff #18 #80)
-#77 := (and #74 #15)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #18 #77)
-#75 := (iff #17 #74)
-#76 := [monotonicity #55]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#72 := (iff #16 #69)
-#66 := (and #63 #15)
-#70 := (iff #66 #69)
-#71 := [rewrite]: #70
-#67 := (iff #16 #66)
-#64 := (iff #14 #63)
-#65 := [monotonicity #55]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#87 := [monotonicity #73 #84]: #86
-#118 := [monotonicity #87 #94 #115]: #117
-#61 := (iff #13 false)
-#56 := (= -1::Int 0::Int)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #13 #56)
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#121 := [monotonicity #62 #118]: #120
-#125 := [trans #121 #123]: #124
-#51 := (iff #10 false)
-#52 := [rewrite]: #51
-#128 := [monotonicity #52 #55 #125]: #127
-#132 := [trans #128 #130]: #131
-#135 := [monotonicity #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#178 := [trans #142 #176]: #177
-#50 := [asserted]: #30
-[mp #50 #178]: false
-unsat
-c22b2f1ee044330de34ce6ed88bd5a128a3b12e5 124 0
-#2 := false
-#9 := 0::Int
-#8 := 3::Int
-#11 := (- 3::Int)
-#20 := (- #11)
-#21 := (mod #20 #11)
-#22 := (- #21)
-#19 := (mod #11 3::Int)
-#14 := (< 0::Int 3::Int)
-#16 := (< #11 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int #11)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#23 := (ite #18 #19 #22)
-#12 := (= #11 0::Int)
-#24 := (ite #12 0::Int #23)
-#10 := (= 3::Int 0::Int)
-#25 := (ite #10 #11 #24)
-#26 := (= #25 0::Int)
-#27 := (not #26)
-#145 := (iff #27 false)
-#1 := true
-#140 := (not true)
-#143 := (iff #140 false)
-#144 := [rewrite]: #143
-#141 := (iff #27 #140)
-#138 := (iff #26 true)
-#133 := (= 0::Int 0::Int)
-#136 := (iff #133 true)
-#137 := [rewrite]: #136
-#134 := (iff #26 #133)
-#50 := -3::Int
-#127 := (ite false -3::Int 0::Int)
-#130 := (= #127 0::Int)
-#131 := [rewrite]: #130
-#128 := (= #25 #127)
-#125 := (= #24 0::Int)
-#120 := (ite false 0::Int 0::Int)
-#123 := (= #120 0::Int)
-#124 := [rewrite]: #123
-#121 := (= #24 #120)
-#118 := (= #23 0::Int)
-#71 := (< -3::Int 0::Int)
-#77 := (and #14 #71)
-#60 := (< 0::Int -3::Int)
-#66 := (and #14 #60)
-#82 := (or #66 #77)
-#113 := (ite #82 0::Int 0::Int)
-#116 := (= #113 0::Int)
-#117 := [rewrite]: #116
-#114 := (= #23 #113)
-#111 := (= #22 0::Int)
-#106 := (- 0::Int)
-#109 := (= #106 0::Int)
-#110 := [rewrite]: #109
-#107 := (= #22 #106)
-#104 := (= #21 0::Int)
-#99 := (mod 3::Int -3::Int)
-#102 := (= #99 0::Int)
-#103 := [rewrite]: #102
-#100 := (= #21 #99)
-#51 := (= #11 -3::Int)
-#52 := [rewrite]: #51
-#97 := (= #20 3::Int)
-#92 := (- -3::Int)
-#95 := (= #92 3::Int)
-#96 := [rewrite]: #95
-#93 := (= #20 #92)
-#94 := [monotonicity #52]: #93
-#98 := [trans #94 #96]: #97
-#101 := [monotonicity #98 #52]: #100
-#105 := [trans #101 #103]: #104
-#108 := [monotonicity #105]: #107
-#112 := [trans #108 #110]: #111
-#90 := (= #19 0::Int)
-#85 := (mod -3::Int 3::Int)
-#88 := (= #85 0::Int)
-#89 := [rewrite]: #88
-#86 := (= #19 #85)
-#87 := [monotonicity #52]: #86
-#91 := [trans #87 #89]: #90
-#83 := (iff #18 #82)
-#80 := (iff #17 #77)
-#74 := (and #71 #14)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #17 #74)
-#72 := (iff #16 #71)
-#73 := [monotonicity #52]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#69 := (iff #15 #66)
-#63 := (and #60 #14)
-#67 := (iff #63 #66)
-#68 := [rewrite]: #67
-#64 := (iff #15 #63)
-#61 := (iff #13 #60)
-#62 := [monotonicity #52]: #61
-#65 := [monotonicity #62]: #64
-#70 := [trans #65 #68]: #69
-#84 := [monotonicity #70 #81]: #83
-#115 := [monotonicity #84 #91 #112]: #114
-#119 := [trans #115 #117]: #118
-#58 := (iff #12 false)
-#53 := (= -3::Int 0::Int)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #12 #53)
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#122 := [monotonicity #59 #119]: #121
-#126 := [trans #122 #124]: #125
-#48 := (iff #10 false)
-#49 := [rewrite]: #48
-#129 := [monotonicity #49 #52 #126]: #128
-#132 := [trans #129 #131]: #26
-#135 := [monotonicity #132]: #134
-#139 := [trans #135 #137]: #138
-#142 := [monotonicity #139]: #141
-#146 := [trans #142 #144]: #145
-#47 := [asserted]: #27
-[mp #47 #146]: false
-unsat
-1702a8956e7405182723d9b7e49a559e524180e5 161 0
-#2 := false
-#28 := 1::Int
-#8 := 3::Int
-#22 := (- 3::Int)
-#11 := 5::Int
-#12 := (- 5::Int)
-#21 := (- #12)
-#23 := (mod #21 #22)
-#24 := (- #23)
-#20 := (mod #12 3::Int)
-#9 := 0::Int
-#15 := (< 0::Int 3::Int)
-#17 := (< #12 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int #12)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#25 := (ite #19 #20 #24)
-#13 := (= #12 0::Int)
-#26 := (ite #13 0::Int #25)
-#10 := (= 3::Int 0::Int)
-#27 := (ite #10 #12 #26)
-#29 := (= #27 1::Int)
-#30 := (not #29)
-#182 := (iff #30 false)
-#53 := -5::Int
-#74 := (< -5::Int 0::Int)
-#80 := (and #15 #74)
-#63 := (< 0::Int -5::Int)
-#69 := (and #15 #63)
-#85 := (or #69 #80)
-#145 := (not #85)
-#180 := (iff #145 false)
-#1 := true
-#175 := (not true)
-#178 := (iff #175 false)
-#179 := [rewrite]: #178
-#176 := (iff #145 #175)
-#173 := (iff #85 true)
-#168 := (or false true)
-#171 := (iff #168 true)
-#172 := [rewrite]: #171
-#169 := (iff #85 #168)
-#166 := (iff #80 true)
-#161 := (and true true)
-#164 := (iff #161 true)
-#165 := [rewrite]: #164
-#162 := (iff #80 #161)
-#159 := (iff #74 true)
-#160 := [rewrite]: #159
-#148 := (iff #15 true)
-#149 := [rewrite]: #148
-#163 := [monotonicity #149 #160]: #162
-#167 := [trans #163 #165]: #166
-#157 := (iff #69 false)
-#152 := (and true false)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #69 #152)
-#150 := (iff #63 false)
-#151 := [rewrite]: #150
-#154 := [monotonicity #149 #151]: #153
-#158 := [trans #154 #156]: #157
-#170 := [monotonicity #158 #167]: #169
-#174 := [trans #170 #172]: #173
-#177 := [monotonicity #174]: #176
-#181 := [trans #177 #179]: #180
-#146 := (iff #30 #145)
-#143 := (iff #29 #85)
-#116 := -2::Int
-#121 := (ite #85 1::Int -2::Int)
-#138 := (= #121 1::Int)
-#141 := (iff #138 #85)
-#142 := [rewrite]: #141
-#139 := (iff #29 #138)
-#136 := (= #27 #121)
-#131 := (ite false -5::Int #121)
-#134 := (= #131 #121)
-#135 := [rewrite]: #134
-#132 := (= #27 #131)
-#129 := (= #26 #121)
-#124 := (ite false 0::Int #121)
-#127 := (= #124 #121)
-#128 := [rewrite]: #127
-#125 := (= #26 #124)
-#122 := (= #25 #121)
-#119 := (= #24 -2::Int)
-#108 := 2::Int
-#113 := (- 2::Int)
-#117 := (= #113 -2::Int)
-#118 := [rewrite]: #117
-#114 := (= #24 #113)
-#111 := (= #23 2::Int)
-#102 := -3::Int
-#105 := (mod 5::Int -3::Int)
-#109 := (= #105 2::Int)
-#110 := [rewrite]: #109
-#106 := (= #23 #105)
-#103 := (= #22 -3::Int)
-#104 := [rewrite]: #103
-#100 := (= #21 5::Int)
-#95 := (- -5::Int)
-#98 := (= #95 5::Int)
-#99 := [rewrite]: #98
-#96 := (= #21 #95)
-#54 := (= #12 -5::Int)
-#55 := [rewrite]: #54
-#97 := [monotonicity #55]: #96
-#101 := [trans #97 #99]: #100
-#107 := [monotonicity #101 #104]: #106
-#112 := [trans #107 #110]: #111
-#115 := [monotonicity #112]: #114
-#120 := [trans #115 #118]: #119
-#93 := (= #20 1::Int)
-#88 := (mod -5::Int 3::Int)
-#91 := (= #88 1::Int)
-#92 := [rewrite]: #91
-#89 := (= #20 #88)
-#90 := [monotonicity #55]: #89
-#94 := [trans #90 #92]: #93
-#86 := (iff #19 #85)
-#83 := (iff #18 #80)
-#77 := (and #74 #15)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #18 #77)
-#75 := (iff #17 #74)
-#76 := [monotonicity #55]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#72 := (iff #16 #69)
-#66 := (and #63 #15)
-#70 := (iff #66 #69)
-#71 := [rewrite]: #70
-#67 := (iff #16 #66)
-#64 := (iff #14 #63)
-#65 := [monotonicity #55]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#87 := [monotonicity #73 #84]: #86
-#123 := [monotonicity #87 #94 #120]: #122
-#61 := (iff #13 false)
-#56 := (= -5::Int 0::Int)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #13 #56)
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#126 := [monotonicity #62 #123]: #125
-#130 := [trans #126 #128]: #129
-#51 := (iff #10 false)
-#52 := [rewrite]: #51
-#133 := [monotonicity #52 #55 #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #137]: #139
-#144 := [trans #140 #142]: #143
-#147 := [monotonicity #144]: #146
-#183 := [trans #147 #181]: #182
-#50 := [asserted]: #30
-[mp #50 #183]: false
-unsat
-1974063c697470ee08048aa93c91e77e8294ad37 165 0
-#2 := false
-#12 := 1::Int
-#13 := (- 1::Int)
-#8 := 3::Int
-#9 := (- 3::Int)
-#23 := (- #9)
-#22 := (- #13)
-#24 := (mod #22 #23)
-#25 := (- #24)
-#21 := (mod #13 #9)
-#10 := 0::Int
-#16 := (< 0::Int #9)
-#18 := (< #13 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #13)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#26 := (ite #20 #21 #25)
-#14 := (= #13 0::Int)
-#27 := (ite #14 0::Int #26)
-#11 := (= #9 0::Int)
-#28 := (ite #11 #13 #27)
-#29 := (= #28 #13)
-#30 := (not #29)
-#186 := (iff #30 false)
-#61 := -1::Int
-#80 := (< -1::Int 0::Int)
-#51 := -3::Int
-#74 := (< 0::Int -3::Int)
-#86 := (and #74 #80)
-#71 := (< 0::Int -1::Int)
-#77 := (and #71 #74)
-#91 := (or #77 #86)
-#184 := (iff #91 false)
-#179 := (or false false)
-#182 := (iff #179 false)
-#183 := [rewrite]: #182
-#180 := (iff #91 #179)
-#177 := (iff #86 false)
-#1 := true
-#172 := (and false true)
-#175 := (iff #172 false)
-#176 := [rewrite]: #175
-#173 := (iff #86 #172)
-#170 := (iff #80 true)
-#171 := [rewrite]: #170
-#161 := (iff #74 false)
-#162 := [rewrite]: #161
-#174 := [monotonicity #162 #171]: #173
-#178 := [trans #174 #176]: #177
-#168 := (iff #77 false)
-#163 := (and false false)
-#166 := (iff #163 false)
-#167 := [rewrite]: #166
-#164 := (iff #77 #163)
-#159 := (iff #71 false)
-#160 := [rewrite]: #159
-#165 := [monotonicity #160 #162]: #164
-#169 := [trans #165 #167]: #168
-#181 := [monotonicity #169 #178]: #180
-#185 := [trans #181 #183]: #184
-#157 := (iff #30 #91)
-#147 := (not #91)
-#152 := (not #147)
-#155 := (iff #152 #91)
-#156 := [rewrite]: #155
-#153 := (iff #30 #152)
-#150 := (iff #29 #147)
-#97 := 2::Int
-#127 := (ite #91 2::Int -1::Int)
-#144 := (= #127 -1::Int)
-#148 := (iff #144 #147)
-#149 := [rewrite]: #148
-#145 := (iff #29 #144)
-#62 := (= #13 -1::Int)
-#63 := [rewrite]: #62
-#142 := (= #28 #127)
-#137 := (ite false -1::Int #127)
-#140 := (= #137 #127)
-#141 := [rewrite]: #140
-#138 := (= #28 #137)
-#135 := (= #27 #127)
-#130 := (ite false 0::Int #127)
-#133 := (= #130 #127)
-#134 := [rewrite]: #133
-#131 := (= #27 #130)
-#128 := (= #26 #127)
-#125 := (= #25 -1::Int)
-#123 := (= #25 #13)
-#121 := (= #24 1::Int)
-#116 := (mod 1::Int 3::Int)
-#119 := (= #116 1::Int)
-#120 := [rewrite]: #119
-#117 := (= #24 #116)
-#114 := (= #23 3::Int)
-#109 := (- -3::Int)
-#112 := (= #109 3::Int)
-#113 := [rewrite]: #112
-#110 := (= #23 #109)
-#52 := (= #9 -3::Int)
-#53 := [rewrite]: #52
-#111 := [monotonicity #53]: #110
-#115 := [trans #111 #113]: #114
-#107 := (= #22 1::Int)
-#102 := (- -1::Int)
-#105 := (= #102 1::Int)
-#106 := [rewrite]: #105
-#103 := (= #22 #102)
-#104 := [monotonicity #63]: #103
-#108 := [trans #104 #106]: #107
-#118 := [monotonicity #108 #115]: #117
-#122 := [trans #118 #120]: #121
-#124 := [monotonicity #122]: #123
-#126 := [trans #124 #63]: #125
-#100 := (= #21 2::Int)
-#94 := (mod -1::Int -3::Int)
-#98 := (= #94 2::Int)
-#99 := [rewrite]: #98
-#95 := (= #21 #94)
-#96 := [monotonicity #63 #53]: #95
-#101 := [trans #96 #99]: #100
-#92 := (iff #20 #91)
-#89 := (iff #19 #86)
-#83 := (and #80 #74)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #19 #83)
-#75 := (iff #16 #74)
-#76 := [monotonicity #53]: #75
-#81 := (iff #18 #80)
-#82 := [monotonicity #63]: #81
-#85 := [monotonicity #82 #76]: #84
-#90 := [trans #85 #88]: #89
-#78 := (iff #17 #77)
-#72 := (iff #15 #71)
-#73 := [monotonicity #63]: #72
-#79 := [monotonicity #73 #76]: #78
-#93 := [monotonicity #79 #90]: #92
-#129 := [monotonicity #93 #101 #126]: #128
-#69 := (iff #14 false)
-#64 := (= -1::Int 0::Int)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #14 #64)
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#132 := [monotonicity #70 #129]: #131
-#136 := [trans #132 #134]: #135
-#59 := (iff #11 false)
-#54 := (= -3::Int 0::Int)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #11 #54)
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#139 := [monotonicity #60 #63 #136]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143 #63]: #145
-#151 := [trans #146 #149]: #150
-#154 := [monotonicity #151]: #153
-#158 := [trans #154 #156]: #157
-#187 := [trans #158 #185]: #186
-#50 := [asserted]: #30
-[mp #50 #187]: false
-unsat
-230992a84e85c41a4507e3a0c4b596203478f52c 119 0
-#2 := false
-#10 := 0::Int
-#8 := 3::Int
-#9 := (- 3::Int)
-#18 := (- #9)
-#19 := (mod #18 #18)
-#20 := (- #19)
-#17 := (mod #9 #9)
-#12 := (< 0::Int #9)
-#14 := (< #9 0::Int)
-#15 := (and #14 #12)
-#13 := (and #12 #12)
-#16 := (or #13 #15)
-#21 := (ite #16 #17 #20)
-#11 := (= #9 0::Int)
-#22 := (ite #11 0::Int #21)
-#23 := (ite #11 #9 #22)
-#24 := (= #23 0::Int)
-#25 := (not #24)
-#140 := (iff #25 false)
-#1 := true
-#135 := (not true)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #25 #135)
-#133 := (iff #24 true)
-#128 := (= 0::Int 0::Int)
-#131 := (iff #128 true)
-#132 := [rewrite]: #131
-#129 := (iff #24 #128)
-#46 := -3::Int
-#122 := (ite false -3::Int 0::Int)
-#125 := (= #122 0::Int)
-#126 := [rewrite]: #125
-#123 := (= #23 #122)
-#120 := (= #22 0::Int)
-#115 := (ite false 0::Int 0::Int)
-#118 := (= #115 0::Int)
-#119 := [rewrite]: #118
-#116 := (= #22 #115)
-#113 := (= #21 0::Int)
-#66 := (< -3::Int 0::Int)
-#56 := (< 0::Int -3::Int)
-#72 := (and #56 #66)
-#77 := (or #56 #72)
-#108 := (ite #77 0::Int 0::Int)
-#111 := (= #108 0::Int)
-#112 := [rewrite]: #111
-#109 := (= #21 #108)
-#106 := (= #20 0::Int)
-#101 := (- 0::Int)
-#104 := (= #101 0::Int)
-#105 := [rewrite]: #104
-#102 := (= #20 #101)
-#99 := (= #19 0::Int)
-#94 := (mod 3::Int 3::Int)
-#97 := (= #94 0::Int)
-#98 := [rewrite]: #97
-#95 := (= #19 #94)
-#92 := (= #18 3::Int)
-#87 := (- -3::Int)
-#90 := (= #87 3::Int)
-#91 := [rewrite]: #90
-#88 := (= #18 #87)
-#47 := (= #9 -3::Int)
-#48 := [rewrite]: #47
-#89 := [monotonicity #48]: #88
-#93 := [trans #89 #91]: #92
-#96 := [monotonicity #93 #93]: #95
-#100 := [trans #96 #98]: #99
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#85 := (= #17 0::Int)
-#80 := (mod -3::Int -3::Int)
-#83 := (= #80 0::Int)
-#84 := [rewrite]: #83
-#81 := (= #17 #80)
-#82 := [monotonicity #48 #48]: #81
-#86 := [trans #82 #84]: #85
-#78 := (iff #16 #77)
-#75 := (iff #15 #72)
-#69 := (and #66 #56)
+#84 := [monotonicity #81]: #83
+#78 := (iff #13 #77)
+#75 := (iff #12 #72)
#73 := (iff #69 #72)
#74 := [rewrite]: #73
-#70 := (iff #15 #69)
-#57 := (iff #12 #56)
-#58 := [monotonicity #48]: #57
-#67 := (iff #14 #66)
-#68 := [monotonicity #48]: #67
-#71 := [monotonicity #68 #58]: #70
-#76 := [trans #71 #74]: #75
-#64 := (iff #13 #56)
-#59 := (and #56 #56)
-#62 := (iff #59 #56)
-#63 := [rewrite]: #62
-#60 := (iff #13 #59)
-#61 := [monotonicity #58 #58]: #60
-#65 := [trans #61 #63]: #64
-#79 := [monotonicity #65 #76]: #78
-#110 := [monotonicity #79 #86 #107]: #109
-#114 := [trans #110 #112]: #113
-#54 := (iff #11 false)
-#49 := (= -3::Int 0::Int)
-#52 := (iff #49 false)
-#53 := [rewrite]: #52
-#50 := (iff #11 #49)
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#117 := [monotonicity #55 #114]: #116
-#121 := [trans #117 #119]: #120
-#124 := [monotonicity #55 #48 #121]: #123
-#127 := [trans #124 #126]: #24
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134]: #136
-#141 := [trans #137 #139]: #140
-#45 := [asserted]: #25
-[mp #45 #141]: false
-unsat
-41d81c01f2d4595c3188777c9ff27286d543d121 170 0
-#2 := false
-#29 := 2::Int
-#30 := (- 2::Int)
-#8 := 3::Int
-#9 := (- 3::Int)
-#23 := (- #9)
-#12 := 5::Int
-#13 := (- 5::Int)
-#22 := (- #13)
-#24 := (mod #22 #23)
-#25 := (- #24)
-#21 := (mod #13 #9)
-#10 := 0::Int
-#16 := (< 0::Int #9)
-#18 := (< #13 0::Int)
-#19 := (and #18 #16)
-#15 := (< 0::Int #13)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#26 := (ite #20 #21 #25)
-#14 := (= #13 0::Int)
-#27 := (ite #14 0::Int #26)
-#11 := (= #9 0::Int)
-#28 := (ite #11 #13 #27)
-#31 := (= #28 #30)
-#32 := (not #31)
-#191 := (iff #32 false)
-#63 := -5::Int
-#82 := (< -5::Int 0::Int)
-#53 := -3::Int
-#76 := (< 0::Int -3::Int)
-#88 := (and #76 #82)
-#73 := (< 0::Int -5::Int)
-#79 := (and #73 #76)
-#93 := (or #79 #88)
-#189 := (iff #93 false)
-#184 := (or false false)
-#187 := (iff #184 false)
-#188 := [rewrite]: #187
-#185 := (iff #93 #184)
-#182 := (iff #88 false)
-#1 := true
-#177 := (and false true)
-#180 := (iff #177 false)
-#181 := [rewrite]: #180
-#178 := (iff #88 #177)
-#175 := (iff #82 true)
-#176 := [rewrite]: #175
-#166 := (iff #76 false)
-#167 := [rewrite]: #166
-#179 := [monotonicity #167 #176]: #178
-#183 := [trans #179 #181]: #182
-#173 := (iff #79 false)
-#168 := (and false false)
-#171 := (iff #168 false)
-#172 := [rewrite]: #171
-#169 := (iff #79 #168)
-#164 := (iff #73 false)
-#165 := [rewrite]: #164
-#170 := [monotonicity #165 #167]: #169
-#174 := [trans #170 #172]: #173
-#186 := [monotonicity #174 #183]: #185
-#190 := [trans #186 #188]: #189
-#162 := (iff #32 #93)
-#152 := (not #93)
-#157 := (not #152)
-#160 := (iff #157 #93)
-#161 := [rewrite]: #160
-#158 := (iff #32 #157)
-#155 := (iff #31 #152)
-#127 := -2::Int
-#99 := 1::Int
-#132 := (ite #93 1::Int -2::Int)
-#149 := (= #132 -2::Int)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #31 #149)
-#128 := (= #30 -2::Int)
-#129 := [rewrite]: #128
-#147 := (= #28 #132)
-#142 := (ite false -5::Int #132)
-#145 := (= #142 #132)
-#146 := [rewrite]: #145
-#143 := (= #28 #142)
-#140 := (= #27 #132)
-#135 := (ite false 0::Int #132)
-#138 := (= #135 #132)
-#139 := [rewrite]: #138
-#136 := (= #27 #135)
-#133 := (= #26 #132)
-#130 := (= #25 -2::Int)
-#125 := (= #25 #30)
-#123 := (= #24 2::Int)
-#118 := (mod 5::Int 3::Int)
-#121 := (= #118 2::Int)
-#122 := [rewrite]: #121
-#119 := (= #24 #118)
-#116 := (= #23 3::Int)
-#111 := (- -3::Int)
-#114 := (= #111 3::Int)
-#115 := [rewrite]: #114
-#112 := (= #23 #111)
-#54 := (= #9 -3::Int)
-#55 := [rewrite]: #54
-#113 := [monotonicity #55]: #112
-#117 := [trans #113 #115]: #116
-#109 := (= #22 5::Int)
-#104 := (- -5::Int)
-#107 := (= #104 5::Int)
-#108 := [rewrite]: #107
-#105 := (= #22 #104)
-#64 := (= #13 -5::Int)
-#65 := [rewrite]: #64
-#106 := [monotonicity #65]: #105
-#110 := [trans #106 #108]: #109
-#120 := [monotonicity #110 #117]: #119
-#124 := [trans #120 #122]: #123
-#126 := [monotonicity #124]: #125
-#131 := [trans #126 #129]: #130
-#102 := (= #21 1::Int)
-#96 := (mod -5::Int -3::Int)
-#100 := (= #96 1::Int)
-#101 := [rewrite]: #100
-#97 := (= #21 #96)
-#98 := [monotonicity #65 #55]: #97
-#103 := [trans #98 #101]: #102
-#94 := (iff #20 #93)
-#91 := (iff #19 #88)
-#85 := (and #82 #76)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #19 #85)
-#77 := (iff #16 #76)
-#78 := [monotonicity #55]: #77
-#83 := (iff #18 #82)
-#84 := [monotonicity #65]: #83
-#87 := [monotonicity #84 #78]: #86
-#92 := [trans #87 #90]: #91
-#80 := (iff #17 #79)
-#74 := (iff #15 #73)
-#75 := [monotonicity #65]: #74
-#81 := [monotonicity #75 #78]: #80
-#95 := [monotonicity #81 #92]: #94
-#134 := [monotonicity #95 #103 #131]: #133
-#71 := (iff #14 false)
-#66 := (= -5::Int 0::Int)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #14 #66)
-#68 := [monotonicity #65]: #67
-#72 := [trans #68 #70]: #71
-#137 := [monotonicity #72 #134]: #136
-#141 := [trans #137 #139]: #140
-#61 := (iff #11 false)
-#56 := (= -3::Int 0::Int)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #11 #56)
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#144 := [monotonicity #62 #65 #141]: #143
-#148 := [trans #144 #146]: #147
-#151 := [monotonicity #148 #129]: #150
-#156 := [trans #151 #154]: #155
-#159 := [monotonicity #156]: #158
-#163 := [trans #159 #161]: #162
-#192 := [trans #163 #190]: #191
-#52 := [asserted]: #32
-[mp #52 #192]: false
-unsat
-37d641fb0d3f5af8883d250eb08e7f4e580b8a49 182 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#11 := f3
-#99 := (<= f3 0::Int)
-#112 := (>= f3 0::Int)
-#113 := (not #112)
-#100 := (not #99)
-#123 := (or #100 #113)
-#160 := (not #123)
-#64 := -3::Int
-#60 := -1::Int
-#61 := (* -1::Int f3)
-#67 := (mod #61 -3::Int)
-#73 := (* -1::Int #67)
-#8 := 3::Int
-#19 := (mod f3 3::Int)
-#126 := (ite #123 #19 #73)
-#158 := (= #19 #126)
-#254 := (not #158)
-#226 := (>= #19 3::Int)
-#227 := (not #226)
-#1 := true
-#46 := [true-axiom]: true
-#242 := (or false #227)
-#243 := [th-lemma arith]: #242
-#244 := [unit-resolution #243 #46]: #227
-#12 := (= f3 0::Int)
-#129 := (ite #12 0::Int #126)
-#238 := (* -1::Int #129)
-#239 := (+ #19 #238)
-#241 := (>= #239 0::Int)
-#237 := (= #19 #129)
-#157 := (= #126 #129)
-#167 := (not #12)
-#156 := (= #129 0::Int)
-#179 := (not #156)
-#172 := (<= #129 0::Int)
-#174 := (not #172)
-#136 := (>= #129 3::Int)
-#21 := (- 3::Int)
-#20 := (- f3)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#14 := (< 0::Int 3::Int)
-#16 := (< f3 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int f3)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#25 := (ite #12 0::Int #24)
-#10 := (= 3::Int 0::Int)
-#26 := (ite #10 f3 #25)
-#27 := (< #26 3::Int)
-#28 := (not #27)
-#148 := (iff #28 #136)
-#54 := (and #14 #16)
-#57 := (or #15 #54)
-#78 := (ite #57 #19 #73)
-#51 := (= 0::Int f3)
-#81 := (ite #51 0::Int #78)
-#91 := (< #81 3::Int)
-#94 := (not #91)
-#146 := (iff #94 #136)
-#135 := (not #136)
-#141 := (not #135)
-#144 := (iff #141 #136)
-#145 := [rewrite]: #144
-#142 := (iff #94 #141)
-#139 := (iff #91 #135)
-#132 := (< #129 3::Int)
-#137 := (iff #132 #135)
-#138 := [rewrite]: #137
-#133 := (iff #91 #132)
-#130 := (= #81 #129)
-#127 := (= #78 #126)
-#124 := (iff #57 #123)
-#121 := (iff #54 #113)
-#116 := (and true #113)
-#119 := (iff #116 #113)
-#120 := [rewrite]: #119
-#117 := (iff #54 #116)
-#114 := (iff #16 #113)
-#115 := [rewrite]: #114
-#103 := (iff #14 true)
-#104 := [rewrite]: #103
-#118 := [monotonicity #104 #115]: #117
-#122 := [trans #118 #120]: #121
-#110 := (iff #15 #100)
-#105 := (and #100 true)
-#108 := (iff #105 #100)
-#109 := [rewrite]: #108
-#106 := (iff #15 #105)
-#101 := (iff #13 #100)
-#102 := [rewrite]: #101
-#107 := [monotonicity #102 #104]: #106
-#111 := [trans #107 #109]: #110
-#125 := [monotonicity #111 #122]: #124
-#128 := [monotonicity #125]: #127
-#97 := (iff #51 #12)
-#98 := [rewrite]: #97
-#131 := [monotonicity #98 #128]: #130
-#134 := [monotonicity #131]: #133
-#140 := [trans #134 #138]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#95 := (iff #28 #94)
-#92 := (iff #27 #91)
-#89 := (= #26 #81)
-#84 := (ite false f3 #81)
-#87 := (= #84 #81)
-#88 := [rewrite]: #87
-#85 := (= #26 #84)
-#82 := (= #25 #81)
-#79 := (= #24 #78)
-#76 := (= #23 #73)
-#70 := (- #67)
-#74 := (= #70 #73)
-#75 := [rewrite]: #74
-#71 := (= #23 #70)
-#68 := (= #22 #67)
-#65 := (= #21 -3::Int)
-#66 := [rewrite]: #65
-#62 := (= #20 #61)
-#63 := [rewrite]: #62
-#69 := [monotonicity #63 #66]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#58 := (iff #18 #57)
-#55 := (iff #17 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#80 := [monotonicity #59 #77]: #79
-#52 := (iff #12 #51)
-#53 := [rewrite]: #52
-#83 := [monotonicity #53 #80]: #82
-#49 := (iff #10 false)
-#50 := [rewrite]: #49
-#86 := [monotonicity #50 #83]: #85
-#90 := [trans #86 #88]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#149 := [trans #96 #147]: #148
-#48 := [asserted]: #28
-#150 := [mp #48 #149]: #136
-#175 := (or #174 #135)
-#176 := [th-lemma arith farkas 1 1]: #175
-#177 := [unit-resolution #176 #150]: #174
-#178 := [hypothesis]: #156
-#180 := (or #179 #172)
-#181 := [th-lemma arith triangle-eq]: #180
-#182 := [unit-resolution #181 #178 #177]: false
-#183 := [lemma #182]: #179
-#168 := (or #167 #156)
-#169 := [def-axiom]: #168
-#245 := [unit-resolution #169 #183]: #167
-#170 := (or #12 #157)
-#171 := [def-axiom]: #170
-#246 := [unit-resolution #171 #245]: #157
-#247 := [hypothesis]: #158
-#248 := [trans #247 #246]: #237
-#249 := (not #237)
-#250 := (or #249 #241)
-#251 := [th-lemma arith triangle-eq]: #250
-#252 := [unit-resolution #251 #248]: #241
-#253 := [th-lemma arith farkas -1 -1 1 #150 #252 #244]: false
-#255 := [lemma #253]: #254
-#163 := (or #160 #158)
-#164 := [def-axiom]: #163
-#232 := [unit-resolution #164 #255]: #160
-#154 := (or #123 #99)
-#155 := [def-axiom]: #154
-#233 := [unit-resolution #155 #232]: #99
-#152 := (or #123 #112)
-#153 := [def-axiom]: #152
-#234 := [unit-resolution #153 #232]: #112
-#235 := (or #12 #100 #113)
-#236 := [th-lemma arith triangle-eq]: #235
-#207 := [unit-resolution #236 #245]: #123
-[unit-resolution #207 #234 #233]: false
-unsat
-fcd3f8cba75d0af01f63efd762505b1dda18b530 187 0
-#2 := false
-#8 := 3::Int
-decl f3 :: Int
-#11 := f3
-#19 := (mod f3 3::Int)
-#233 := (>= #19 3::Int)
-#234 := (not #233)
-#1 := true
-#48 := [true-axiom]: true
-#248 := (or false #234)
-#249 := [th-lemma arith]: #248
-#250 := [unit-resolution #249 #48]: #234
-#9 := 0::Int
-#62 := -1::Int
-#206 := (* -1::Int #19)
-#245 := (+ f3 #206)
-#246 := (<= #245 0::Int)
-#244 := (= f3 #19)
-#66 := -3::Int
-#63 := (* -1::Int f3)
-#69 := (mod #63 -3::Int)
-#75 := (* -1::Int #69)
-#132 := (>= f3 0::Int)
-#133 := (not #132)
-#119 := (<= f3 0::Int)
-#120 := (not #119)
-#143 := (or #120 #133)
-#146 := (ite #143 #19 #75)
-#262 := (= #146 #19)
-#178 := (= #19 #146)
-#113 := (>= f3 3::Int)
-#12 := (= f3 0::Int)
-#149 := (ite #12 0::Int #146)
-#152 := (= f3 #149)
-#155 := (not #152)
-#114 := (not #113)
-#158 := (or #114 #155)
-#161 := (not #158)
-#28 := (< f3 3::Int)
-#21 := (- 3::Int)
-#20 := (- f3)
-#22 := (mod #20 #21)
-#23 := (- #22)
-#14 := (< 0::Int 3::Int)
-#16 := (< f3 0::Int)
-#17 := (and #16 #14)
-#13 := (< 0::Int f3)
-#15 := (and #13 #14)
-#18 := (or #15 #17)
-#24 := (ite #18 #19 #23)
-#25 := (ite #12 0::Int #24)
-#10 := (= 3::Int 0::Int)
-#26 := (ite #10 f3 #25)
-#27 := (= #26 f3)
-#29 := (implies #27 #28)
-#30 := (not #29)
-#164 := (iff #30 #161)
-#56 := (and #14 #16)
-#59 := (or #15 #56)
-#80 := (ite #59 #19 #75)
-#53 := (= 0::Int f3)
-#83 := (ite #53 0::Int #80)
-#96 := (= f3 #83)
-#104 := (not #96)
-#105 := (or #28 #104)
-#110 := (not #105)
-#162 := (iff #110 #161)
-#159 := (iff #105 #158)
-#156 := (iff #104 #155)
-#153 := (iff #96 #152)
-#150 := (= #83 #149)
-#147 := (= #80 #146)
-#144 := (iff #59 #143)
-#141 := (iff #56 #133)
-#136 := (and true #133)
-#139 := (iff #136 #133)
-#140 := [rewrite]: #139
-#137 := (iff #56 #136)
-#134 := (iff #16 #133)
-#135 := [rewrite]: #134
-#123 := (iff #14 true)
-#124 := [rewrite]: #123
-#138 := [monotonicity #124 #135]: #137
-#142 := [trans #138 #140]: #141
-#130 := (iff #15 #120)
-#125 := (and #120 true)
-#128 := (iff #125 #120)
-#129 := [rewrite]: #128
-#126 := (iff #15 #125)
-#121 := (iff #13 #120)
-#122 := [rewrite]: #121
-#127 := [monotonicity #122 #124]: #126
-#131 := [trans #127 #129]: #130
-#145 := [monotonicity #131 #142]: #144
-#148 := [monotonicity #145]: #147
-#117 := (iff #53 #12)
-#118 := [rewrite]: #117
-#151 := [monotonicity #118 #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#115 := (iff #28 #114)
-#116 := [rewrite]: #115
-#160 := [monotonicity #116 #157]: #159
-#163 := [monotonicity #160]: #162
-#111 := (iff #30 #110)
-#108 := (iff #29 #105)
-#101 := (implies #96 #28)
-#106 := (iff #101 #105)
-#107 := [rewrite]: #106
-#102 := (iff #29 #101)
-#99 := (iff #27 #96)
-#93 := (= #83 f3)
-#97 := (iff #93 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#91 := (= #26 #83)
-#86 := (ite false f3 #83)
-#89 := (= #86 #83)
-#90 := [rewrite]: #89
-#87 := (= #26 #86)
-#84 := (= #25 #83)
-#81 := (= #24 #80)
-#78 := (= #23 #75)
-#72 := (- #69)
-#76 := (= #72 #75)
-#77 := [rewrite]: #76
-#73 := (= #23 #72)
-#70 := (= #22 #69)
-#67 := (= #21 -3::Int)
-#68 := [rewrite]: #67
-#64 := (= #20 #63)
+#70 := (iff #12 #69)
+#67 := (= #10 #66)
+#64 := (= #9 -3::Int)
#65 := [rewrite]: #64
-#71 := [monotonicity #65 #68]: #70
-#74 := [monotonicity #71]: #73
-#79 := [trans #74 #77]: #78
-#60 := (iff #18 #59)
-#57 := (iff #17 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#82 := [monotonicity #61 #79]: #81
-#54 := (iff #12 #53)
-#55 := [rewrite]: #54
-#85 := [monotonicity #55 #82]: #84
-#51 := (iff #10 false)
-#52 := [rewrite]: #51
-#88 := [monotonicity #52 #85]: #87
-#92 := [trans #88 #90]: #91
-#95 := [monotonicity #92]: #94
-#100 := [trans #95 #98]: #99
-#103 := [monotonicity #100]: #102
-#109 := [trans #103 #107]: #108
-#112 := [monotonicity #109]: #111
-#165 := [trans #112 #163]: #164
-#50 := [asserted]: #30
-#166 := [mp #50 #165]: #161
-#167 := [not-or-elim #166]: #113
-#251 := (or #120 #114)
-#252 := [th-lemma arith farkas 1 1]: #251
-#253 := [unit-resolution #252 #167]: #120
-#174 := (or #143 #119)
-#175 := [def-axiom]: #174
-#258 := [unit-resolution #175 #253]: #143
-#170 := (not #143)
-#181 := (or #170 #178)
-#182 := [def-axiom]: #181
-#259 := [unit-resolution #182 #258]: #178
-#263 := [symm #259]: #262
-#264 := (= f3 #146)
-#260 := (= #149 #146)
-#177 := (= #146 #149)
-#185 := (not #12)
-#254 := (or #185 #119)
-#255 := [th-lemma arith triangle-eq]: #254
-#256 := [unit-resolution #255 #253]: #185
-#188 := (or #12 #177)
-#189 := [def-axiom]: #188
-#257 := [unit-resolution #189 #256]: #177
-#261 := [symm #257]: #260
-#168 := [not-or-elim #166]: #152
-#265 := [trans #168 #261]: #264
-#266 := [trans #265 #263]: #244
-#267 := (not #244)
-#268 := (or #267 #246)
-#269 := [th-lemma arith triangle-eq]: #268
-#270 := [unit-resolution #269 #266]: #246
-[th-lemma arith farkas -1 1 1 #167 #270 #250]: false
-unsat
-b0d0143b1d623c3b7e34600e7103453eafcbef9f 326 0
-#2 := false
-#9 := 0::Int
-#71 := -1::Int
-decl f3 :: Int
-#8 := f3
-#72 := (* -1::Int f3)
-#95 := (mod #72 -1::Int)
-#101 := (* -1::Int #95)
-#147 := (>= f3 0::Int)
-#148 := (not #147)
-#134 := (<= f3 0::Int)
-#135 := (not #134)
-#10 := (= f3 0::Int)
-#170 := (or #10 #135 #148)
-#175 := (ite #170 0::Int #101)
-#288 := (<= #175 0::Int)
-#220 := (= #175 0::Int)
-#215 := (not #10)
-#228 := (not #170)
-#375 := [hypothesis]: #228
-#222 := (or #170 #215)
-#223 := [def-axiom]: #222
-#376 := [unit-resolution #223 #375]: #215
-#226 := (or #170 #147)
-#227 := [def-axiom]: #226
-#377 := [unit-resolution #227 #375]: #147
-#378 := (or #10 #148)
-#185 := (* -1::Int #175)
-#77 := (div #72 -1::Int)
-#11 := 1::Int
-#20 := (div f3 1::Int)
-#158 := (or #135 #148)
-#161 := (ite #158 #20 #77)
-#164 := (ite #10 0::Int #161)
-#184 := (* -1::Int #164)
-#186 := (+ #184 #185)
-#187 := (+ f3 #186)
-#236 := (>= #187 0::Int)
-#291 := (+ #20 #184)
-#293 := (>= #291 0::Int)
-#290 := (= #20 #164)
-#205 := (= #161 #164)
-#294 := [hypothesis]: #135
-#295 := (or #215 #134)
-#296 := [th-lemma arith triangle-eq]: #295
-#297 := [unit-resolution #296 #294]: #215
-#218 := (or #10 #205)
-#219 := [def-axiom]: #218
-#298 := [unit-resolution #219 #297]: #205
-#206 := (= #20 #161)
-#202 := (or #158 #134)
-#203 := [def-axiom]: #202
-#299 := [unit-resolution #203 #294]: #158
-#208 := (not #158)
-#211 := (or #208 #206)
-#212 := [def-axiom]: #211
-#300 := [unit-resolution #212 #299]: #206
-#301 := [trans #300 #298]: #290
-#302 := (not #290)
-#303 := (or #302 #293)
-#304 := [th-lemma arith triangle-eq]: #303
-#305 := [unit-resolution #304 #301]: #293
-#224 := (or #170 #134)
-#225 := [def-axiom]: #224
-#306 := [unit-resolution #225 #294]: #170
-#231 := (or #228 #220)
-#232 := [def-axiom]: #231
-#307 := [unit-resolution #232 #306]: #220
-#308 := (not #220)
-#309 := (or #308 #288)
-#310 := [th-lemma arith triangle-eq]: #309
-#311 := [unit-resolution #310 #307]: #288
-#258 := (* -1::Int #20)
-#259 := (+ f3 #258)
-#265 := (>= #259 0::Int)
-#257 := (= #259 0::Int)
-#1 := true
-#53 := [true-axiom]: true
-#312 := (or false #257)
-#313 := [th-lemma arith]: #312
-#314 := [unit-resolution #313 #53]: #257
-#315 := (not #257)
-#316 := (or #315 #265)
-#317 := [th-lemma arith triangle-eq]: #316
-#318 := [unit-resolution #317 #314]: #265
-#321 := (not #265)
-#320 := (not #293)
-#319 := (not #288)
-#322 := (or #236 #319 #320 #321)
-#323 := [th-lemma arith assign-bounds 1 -1 -1]: #322
-#324 := [unit-resolution #323 #318 #311 #305]: #236
-#235 := (<= #187 0::Int)
-#292 := (<= #291 0::Int)
-#325 := (or #302 #292)
-#326 := [th-lemma arith triangle-eq]: #325
-#327 := [unit-resolution #326 #301]: #292
-#289 := (>= #175 0::Int)
-#328 := (or #308 #289)
-#329 := [th-lemma arith triangle-eq]: #328
-#330 := [unit-resolution #329 #307]: #289
-#264 := (<= #259 0::Int)
-#331 := (or #315 #264)
-#332 := [th-lemma arith triangle-eq]: #331
-#333 := [unit-resolution #332 #314]: #264
-#336 := (not #264)
-#335 := (not #292)
-#334 := (not #289)
-#337 := (or #235 #334 #335 #336)
-#338 := [th-lemma arith assign-bounds 1 -1 -1]: #337
-#339 := [unit-resolution #338 #333 #330 #327]: #235
-#341 := (not #236)
-#340 := (not #235)
-#344 := (or #340 #341)
-#188 := (= #187 0::Int)
-#193 := (not #188)
-#22 := (- 1::Int)
-#21 := (- f3)
-#28 := (mod #21 #22)
-#29 := (- #28)
-#27 := (mod f3 1::Int)
-#15 := (< 0::Int 1::Int)
-#17 := (< f3 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int f3)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#30 := (ite #19 #27 #29)
-#31 := (ite #10 0::Int #30)
-#12 := (= 1::Int 0::Int)
-#32 := (ite #12 f3 #31)
-#23 := (div #21 #22)
-#24 := (ite #19 #20 #23)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (* #25 1::Int)
-#33 := (+ #26 #32)
-#34 := (= f3 #33)
-#35 := (not #34)
-#196 := (iff #35 #193)
-#65 := (and #15 #17)
-#68 := (or #16 #65)
-#112 := (or #10 #68)
-#113 := (ite #112 0::Int #101)
-#80 := (ite #68 #20 #77)
-#83 := (ite #10 0::Int #80)
-#125 := (+ #83 #113)
-#128 := (= f3 #125)
-#131 := (not #128)
-#194 := (iff #131 #193)
-#191 := (iff #128 #188)
-#178 := (+ #164 #175)
-#181 := (= f3 #178)
-#189 := (iff #181 #188)
-#190 := [rewrite]: #189
-#182 := (iff #128 #181)
-#179 := (= #125 #178)
-#176 := (= #113 #175)
-#173 := (iff #112 #170)
-#167 := (or #10 #158)
-#171 := (iff #167 #170)
-#172 := [rewrite]: #171
-#168 := (iff #112 #167)
-#159 := (iff #68 #158)
-#156 := (iff #65 #148)
-#151 := (and true #148)
-#154 := (iff #151 #148)
-#155 := [rewrite]: #154
-#152 := (iff #65 #151)
-#149 := (iff #17 #148)
-#150 := [rewrite]: #149
-#138 := (iff #15 true)
-#139 := [rewrite]: #138
-#153 := [monotonicity #139 #150]: #152
-#157 := [trans #153 #155]: #156
-#145 := (iff #16 #135)
-#140 := (and #135 true)
-#143 := (iff #140 #135)
-#144 := [rewrite]: #143
-#141 := (iff #16 #140)
-#136 := (iff #14 #135)
-#137 := [rewrite]: #136
-#142 := [monotonicity #137 #139]: #141
-#146 := [trans #142 #144]: #145
-#160 := [monotonicity #146 #157]: #159
-#169 := [monotonicity #160]: #168
-#174 := [trans #169 #172]: #173
-#177 := [monotonicity #174]: #176
-#165 := (= #83 #164)
-#162 := (= #80 #161)
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#180 := [monotonicity #166 #177]: #179
-#183 := [monotonicity #180]: #182
-#192 := [trans #183 #190]: #191
-#195 := [monotonicity #192]: #194
-#132 := (iff #35 #131)
-#129 := (iff #34 #128)
-#126 := (= #33 #125)
-#123 := (= #32 #113)
-#118 := (ite false f3 #113)
-#121 := (= #118 #113)
+#68 := [monotonicity #65 #65]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [monotonicity #76]: #78
+#86 := [trans #79 #84]: #85
+#62 := [asserted]: #13
+#87 := [mp #62 #86]: #82
+#550 := (not #774)
+#698 := (or #550 #69)
+#352 := (* -1::Int -3::Int)
+#437 := (mod #352 #352)
+#438 := (+ #66 #437)
+#439 := (= #438 0::Int)
+#430 := (mod -3::Int -3::Int)
+#441 := (* -1::Int #430)
+#442 := (+ #66 #441)
+#370 := (= #442 0::Int)
+#443 := (>= -3::Int 0::Int)
+#440 := (<= -3::Int 0::Int)
+#444 := (or #440 #443)
+#423 := (not #444)
+#758 := (or #440 #440)
+#760 := (not #758)
+#417 := (or #760 #423)
+#547 := (ite #417 #370 #439)
+#754 := (= -3::Int 0::Int)
+#428 := (ite #754 #69 #547)
+#429 := (= -3::Int #66)
+#761 := (ite #754 #429 #428)
+#600 := (or #550 #761)
+#696 := (iff #600 #698)
+#584 := (iff #698 #698)
+#599 := [rewrite]: #584
+#590 := (iff #761 #69)
+#759 := (= #66 -3::Int)
+#705 := (ite false #759 #69)
+#707 := (iff #705 #69)
+#589 := [rewrite]: #707
+#706 := (iff #761 #705)
+#702 := (iff #428 #69)
+#708 := (ite false #69 #69)
+#716 := (iff #708 #69)
+#710 := [rewrite]: #716
+#548 := (iff #428 #708)
+#717 := (iff #547 #69)
+#709 := (iff #547 #708)
+#713 := (iff #439 #69)
+#711 := (= #438 #66)
+#451 := (+ #66 0::Int)
+#445 := (= #451 #66)
+#727 := [rewrite]: #445
+#568 := (= #438 #451)
+#726 := (= #437 0::Int)
+#718 := (mod 3::Int 3::Int)
+#725 := (= #718 0::Int)
+#720 := [rewrite]: #725
+#719 := (= #437 #718)
+#722 := (= #352 3::Int)
+#723 := [rewrite]: #722
+#724 := [monotonicity #723 #723]: #719
+#567 := [trans #724 #720]: #726
+#569 := [monotonicity #567]: #568
+#712 := [trans #569 #727]: #711
+#714 := [monotonicity #712]: #713
+#732 := (iff #370 #69)
+#731 := (= #442 #66)
+#729 := (= #442 #451)
+#449 := (= #441 0::Int)
+#733 := (* -1::Int 0::Int)
+#738 := (= #733 0::Int)
+#448 := [rewrite]: #738
+#737 := (= #441 #733)
+#458 := (= #430 0::Int)
+#459 := [rewrite]: #458
+#734 := [monotonicity #459]: #737
+#450 := [trans #734 #448]: #449
+#730 := [monotonicity #450]: #729
+#728 := [trans #730 #727]: #731
+#721 := [monotonicity #728]: #732
+#735 := (iff #417 false)
+#462 := (or false false)
+#465 := (iff #462 false)
+#358 := [rewrite]: #465
+#463 := (iff #417 #462)
+#739 := (iff #423 false)
+#1 := true
+#405 := (not true)
+#743 := (iff #405 false)
+#744 := [rewrite]: #743
+#750 := (iff #423 #405)
+#392 := (iff #444 true)
+#748 := (or true false)
+#751 := (iff #748 true)
+#391 := [rewrite]: #751
+#386 := (iff #444 #748)
+#747 := (iff #443 false)
+#742 := [rewrite]: #747
+#755 := (iff #440 true)
+#415 := [rewrite]: #755
+#749 := [monotonicity #415 #742]: #386
+#752 := [trans #749 #391]: #392
+#753 := [monotonicity #752]: #750
+#740 := [trans #753 #744]: #739
+#745 := (iff #760 false)
+#406 := (iff #760 #405)
+#741 := (iff #758 true)
+#420 := (or true true)
+#757 := (iff #420 true)
+#400 := [rewrite]: #757
+#756 := (iff #758 #420)
+#416 := [monotonicity #415 #415]: #756
+#404 := [trans #416 #400]: #741
+#407 := [monotonicity #404]: #406
+#746 := [trans #407 #744]: #745
+#464 := [monotonicity #746 #740]: #463
+#736 := [trans #464 #358]: #735
+#715 := [monotonicity #736 #721 #714]: #709
+#546 := [trans #715 #710]: #717
+#762 := (iff #754 false)
+#763 := [rewrite]: #762
+#549 := [monotonicity #763 #546]: #548
+#703 := [trans #549 #710]: #702
+#764 := (iff #429 #759)
+#765 := [rewrite]: #764
+#704 := [monotonicity #763 #765 #703]: #706
+#591 := [trans #704 #589]: #590
+#699 := [monotonicity #591]: #696
+#601 := [trans #699 #599]: #696
+#695 := [quant-inst #63 #63]: #600
+#602 := [mp #695 #601]: #698
+[unit-resolution #602 #87 #779]: false
+unsat
+ab60a5d229f921e05cbaa6708d883c31816e3a4a 342 0
+#2 := false
+decl f3 :: (-> Int Int Int)
+#18 := (:var 0 Int)
+#17 := (:var 1 Int)
+#38 := (f3 #17 #18)
+#756 := (pattern #38)
+#20 := 0::Int
+#93 := -1::Int
+#97 := (* -1::Int #18)
+#94 := (* -1::Int #17)
+#152 := (mod #94 #97)
+#267 := (+ #38 #152)
+#268 := (= #267 0::Int)
+#39 := (mod #17 #18)
+#264 := (* -1::Int #39)
+#265 := (+ #38 #264)
+#266 := (= #265 0::Int)
+#126 := (>= #17 0::Int)
+#119 := (<= #18 0::Int)
+#211 := (or #119 #126)
+#212 := (not #211)
+#115 := (<= #17 0::Int)
+#209 := (or #115 #119)
+#210 := (not #209)
+#215 := (or #210 #212)
+#269 := (ite #215 #266 #268)
+#263 := (= #38 0::Int)
+#21 := (= #17 0::Int)
+#270 := (ite #21 #263 #269)
+#262 := (= #17 #38)
+#22 := (= #18 0::Int)
+#271 := (ite #22 #262 #270)
+#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271)
+#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
+#760 := (iff #274 #757)
+#758 := (iff #271 #271)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#158 := (* -1::Int #152)
+#231 := (ite #215 #39 #158)
+#234 := (ite #21 0::Int #231)
+#237 := (ite #22 #17 #234)
+#240 := (= #38 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#275 := (iff #243 #274)
+#272 := (iff #240 #271)
+#273 := [rewrite]: #272
+#276 := [quant-intro #273]: #275
+#127 := (not #126)
+#120 := (not #119)
+#130 := (and #120 #127)
+#116 := (not #115)
+#123 := (and #116 #120)
+#133 := (or #123 #130)
+#178 := (ite #133 #39 #158)
+#181 := (ite #21 0::Int #178)
+#184 := (ite #22 #17 #181)
+#187 := (= #38 #184)
+#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
+#244 := (iff #190 #243)
+#241 := (iff #187 #240)
+#238 := (= #184 #237)
+#235 := (= #181 #234)
+#232 := (= #178 #231)
+#216 := (iff #133 #215)
+#213 := (iff #130 #212)
+#214 := [rewrite]: #213
+#203 := (iff #123 #210)
+#204 := [rewrite]: #203
+#217 := [monotonicity #204 #214]: #216
+#233 := [monotonicity #217]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
+#201 := (~ #190 #190)
+#200 := (~ #187 #187)
+#197 := [refl]: #200
+#202 := [nnf-pos #197]: #201
+#32 := (- #18)
+#31 := (- #17)
+#40 := (mod #31 #32)
+#41 := (- #40)
+#25 := (< 0::Int #18)
+#27 := (< #17 0::Int)
+#28 := (and #27 #25)
+#24 := (< 0::Int #17)
+#26 := (and #24 #25)
+#29 := (or #26 #28)
+#42 := (ite #29 #39 #41)
+#43 := (ite #21 0::Int #42)
+#44 := (ite #22 #17 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#193 := (iff #46 #190)
+#86 := (and #25 #27)
+#90 := (or #26 #86)
+#163 := (ite #90 #39 #158)
+#166 := (ite #21 0::Int #163)
+#169 := (ite #22 #17 #166)
+#172 := (= #38 #169)
+#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
+#191 := (iff #175 #190)
+#188 := (iff #172 #187)
+#185 := (= #169 #184)
+#182 := (= #166 #181)
+#179 := (= #163 #178)
+#134 := (iff #90 #133)
+#131 := (iff #86 #130)
+#128 := (iff #27 #127)
+#129 := [rewrite]: #128
+#121 := (iff #25 #120)
#122 := [rewrite]: #121
-#119 := (= #32 #118)
-#116 := (= #31 #113)
-#106 := (ite #68 0::Int #101)
-#109 := (ite #10 0::Int #106)
-#114 := (= #109 #113)
-#115 := [rewrite]: #114
-#110 := (= #31 #109)
-#107 := (= #30 #106)
-#104 := (= #29 #101)
-#98 := (- #95)
-#102 := (= #98 #101)
-#103 := [rewrite]: #102
-#99 := (= #29 #98)
-#96 := (= #28 #95)
-#75 := (= #22 -1::Int)
-#76 := [rewrite]: #75
-#73 := (= #21 #72)
-#74 := [rewrite]: #73
-#97 := [monotonicity #74 #76]: #96
-#100 := [monotonicity #97]: #99
-#105 := [trans #100 #103]: #104
-#93 := (= #27 0::Int)
-#94 := [rewrite]: #93
-#69 := (iff #19 #68)
-#66 := (iff #18 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#108 := [monotonicity #70 #94 #105]: #107
-#111 := [monotonicity #108]: #110
-#117 := [trans #111 #115]: #116
-#56 := (iff #12 false)
-#57 := [rewrite]: #56
-#120 := [monotonicity #57 #117]: #119
-#124 := [trans #120 #122]: #123
-#91 := (= #26 #83)
-#86 := (* #83 1::Int)
-#89 := (= #86 #83)
-#90 := [rewrite]: #89
-#87 := (= #26 #86)
-#84 := (= #25 #83)
-#81 := (= #24 #80)
-#78 := (= #23 #77)
-#79 := [monotonicity #74 #76]: #78
-#82 := [monotonicity #70 #79]: #81
-#63 := (iff #13 #10)
-#58 := (or #10 false)
-#61 := (iff #58 #10)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#85 := [monotonicity #64 #82]: #84
-#88 := [monotonicity #85]: #87
-#92 := [trans #88 #90]: #91
-#127 := [monotonicity #92 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#197 := [trans #133 #195]: #196
-#55 := [asserted]: #35
-#198 := [mp #55 #197]: #193
-#342 := (or #188 #340 #341)
-#343 := [th-lemma arith triangle-eq]: #342
-#345 := [unit-resolution #343 #198]: #344
-#346 := [unit-resolution #345 #339 #324]: false
-#347 := [lemma #346]: #134
-#363 := [th-lemma arith triangle-eq]: #170
-#379 := [unit-resolution #363 #347]: #378
-#380 := [unit-resolution #379 #377 #376]: false
-#381 := [lemma #380]: #170
-#390 := [unit-resolution #232 #381]: #220
-#391 := [unit-resolution #310 #390]: #288
-#382 := (<= #164 0::Int)
-#204 := (= #164 0::Int)
-#383 := [hypothesis]: #147
-#384 := [unit-resolution #379 #383]: #10
-#216 := (or #215 #204)
-#217 := [def-axiom]: #216
-#385 := [unit-resolution #217 #384]: #204
-#355 := (not #204)
-#386 := (or #355 #382)
-#387 := [th-lemma arith triangle-eq]: #386
-#388 := [unit-resolution #387 #385]: #382
-#359 := [hypothesis]: #340
-#361 := (or #215 #235)
-#350 := [hypothesis]: #10
-#351 := [unit-resolution #223 #350]: #170
-#352 := [unit-resolution #232 #351]: #220
-#353 := [unit-resolution #329 #352]: #289
-#349 := (>= #164 0::Int)
-#354 := [unit-resolution #217 #350]: #204
-#356 := (or #355 #349)
-#357 := [th-lemma arith triangle-eq]: #356
-#358 := [unit-resolution #357 #354]: #349
-#360 := [th-lemma arith farkas 1 1 -1 1 #359 #358 #347 #353]: false
-#362 := [lemma #360]: #361
-#348 := [unit-resolution #362 #359]: #215
-#364 := [unit-resolution #363 #348 #347]: #148
-#365 := [unit-resolution #227 #364]: #170
-#366 := [unit-resolution #232 #365]: #220
-#367 := [unit-resolution #329 #366]: #289
-#368 := [unit-resolution #219 #348]: #205
-#200 := (or #158 #147)
-#201 := [def-axiom]: #200
-#369 := [unit-resolution #201 #364]: #158
-#370 := [unit-resolution #212 #369]: #206
-#371 := [trans #370 #368]: #290
-#372 := [unit-resolution #326 #371]: #292
-#373 := [unit-resolution #338 #333 #372 #359 #367]: false
-#374 := [lemma #373]: #235
-#389 := [unit-resolution #345 #374]: #341
-#392 := [th-lemma arith farkas 1 1 -1 1 #391 #389 #383 #388]: false
-#393 := [lemma #392]: #148
-#394 := (or #215 #147)
-#395 := [th-lemma arith triangle-eq]: #394
-#396 := [unit-resolution #395 #393]: #215
-#397 := [unit-resolution #219 #396]: #205
-#398 := [unit-resolution #201 #393]: #158
-#399 := [unit-resolution #212 #398]: #206
-#400 := [trans #399 #397]: #290
-#401 := [unit-resolution #304 #400]: #293
-#402 := (or #319 #320 #321)
-#403 := [unit-resolution #323 #389]: #402
-[unit-resolution #403 #318 #401 #391]: false
-unsat
-31fe1e25557ea7df409ade184e44a23cd64eda4c 308 0
-#2 := false
-#9 := 0::Int
-#75 := -3::Int
-decl f3 :: Int
-#8 := f3
-#71 := -1::Int
-#72 := (* -1::Int f3)
-#95 := (mod #72 -3::Int)
-#101 := (* -1::Int #95)
-#11 := 3::Int
-#27 := (mod f3 3::Int)
-#141 := (>= f3 0::Int)
-#142 := (not #141)
-#128 := (<= f3 0::Int)
-#129 := (not #128)
-#152 := (or #129 #142)
-#164 := (ite #152 #27 #101)
-#10 := (= f3 0::Int)
-#167 := (ite #10 0::Int #164)
-#177 := (* -1::Int #167)
-#321 := (+ #27 #177)
-#358 := (>= #321 0::Int)
-#320 := (= #27 #167)
-#213 := (= #164 #167)
-#207 := (not #10)
-#78 := (div #72 -3::Int)
-#20 := (div f3 3::Int)
-#155 := (ite #152 #20 #78)
-#158 := (ite #10 0::Int #155)
-#176 := (* -3::Int #158)
-#178 := (+ #176 #177)
-#179 := (+ f3 #178)
-#225 := (>= #179 0::Int)
-#228 := (<= #167 0::Int)
-#212 := (= #167 0::Int)
-#200 := (not #152)
-#230 := [hypothesis]: #200
-#192 := (or #152 #141)
-#193 := [def-axiom]: #192
-#231 := [unit-resolution #193 #230]: #141
-#194 := (or #152 #128)
-#195 := [def-axiom]: #194
-#232 := [unit-resolution #195 #230]: #128
-#233 := (or #10 #129 #142)
-#234 := [th-lemma arith triangle-eq]: #233
-#235 := [unit-resolution #234 #232 #231]: #10
-#220 := (or #207 #212)
-#221 := [def-axiom]: #220
-#236 := [unit-resolution #221 #235]: #212
-#237 := (not #212)
-#238 := (or #237 #228)
-#239 := [th-lemma arith triangle-eq]: #238
-#240 := [unit-resolution #239 #236]: #228
-#226 := (<= #158 0::Int)
-#196 := (= #158 0::Int)
-#208 := (or #207 #196)
-#209 := [def-axiom]: #208
-#241 := [unit-resolution #209 #235]: #196
-#242 := (not #196)
-#243 := (or #242 #226)
-#244 := [th-lemma arith triangle-eq]: #243
-#245 := [unit-resolution #244 #241]: #226
-#247 := (not #228)
-#246 := (not #226)
-#248 := (or #225 #142 #246 #247)
-#249 := [th-lemma arith assign-bounds -1 3 1]: #248
-#250 := [unit-resolution #249 #231 #245 #240]: #225
-#224 := (<= #179 0::Int)
-#229 := (>= #167 0::Int)
-#251 := (or #237 #229)
-#252 := [th-lemma arith triangle-eq]: #251
-#253 := [unit-resolution #252 #236]: #229
-#227 := (>= #158 0::Int)
-#254 := (or #242 #227)
-#255 := [th-lemma arith triangle-eq]: #254
-#256 := [unit-resolution #255 #241]: #227
-#258 := (not #229)
-#257 := (not #227)
-#259 := (or #224 #129 #257 #258)
-#260 := [th-lemma arith assign-bounds -1 3 1]: #259
-#261 := [unit-resolution #260 #232 #256 #253]: #224
-#263 := (not #225)
-#262 := (not #224)
-#266 := (or #262 #263)
-#180 := (= #179 0::Int)
-#185 := (not #180)
-#22 := (- 3::Int)
-#21 := (- f3)
-#28 := (mod #21 #22)
-#29 := (- #28)
-#15 := (< 0::Int 3::Int)
-#17 := (< f3 0::Int)
-#18 := (and #17 #15)
-#14 := (< 0::Int f3)
-#16 := (and #14 #15)
-#19 := (or #16 #18)
-#30 := (ite #19 #27 #29)
-#31 := (ite #10 0::Int #30)
-#12 := (= 3::Int 0::Int)
-#32 := (ite #12 f3 #31)
-#23 := (div #21 #22)
-#24 := (ite #19 #20 #23)
-#13 := (or #10 #12)
-#25 := (ite #13 0::Int #24)
-#26 := (* #25 3::Int)
-#33 := (+ #26 #32)
-#34 := (= f3 #33)
-#35 := (not #34)
-#188 := (iff #35 #185)
-#65 := (and #15 #17)
-#68 := (or #16 #65)
-#106 := (ite #68 #27 #101)
-#109 := (ite #10 0::Int #106)
-#81 := (ite #68 #20 #78)
-#84 := (ite #10 0::Int #81)
-#90 := (* 3::Int #84)
-#119 := (+ #90 #109)
-#122 := (= f3 #119)
-#125 := (not #122)
-#186 := (iff #125 #185)
-#183 := (iff #122 #180)
-#161 := (* 3::Int #158)
-#170 := (+ #161 #167)
-#173 := (= f3 #170)
-#181 := (iff #173 #180)
-#182 := [rewrite]: #181
-#174 := (iff #122 #173)
-#171 := (= #119 #170)
-#168 := (= #109 #167)
-#165 := (= #106 #164)
-#153 := (iff #68 #152)
-#150 := (iff #65 #142)
-#1 := true
-#145 := (and true #142)
-#148 := (iff #145 #142)
+#132 := [monotonicity #122 #129]: #131
+#124 := (iff #26 #123)
+#117 := (iff #24 #116)
+#118 := [rewrite]: #117
+#125 := [monotonicity #118 #122]: #124
+#135 := [monotonicity #125 #132]: #134
+#180 := [monotonicity #135]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [quant-intro #189]: #191
+#176 := (iff #46 #175)
+#173 := (iff #45 #172)
+#170 := (= #44 #169)
+#167 := (= #43 #166)
+#164 := (= #42 #163)
+#161 := (= #41 #158)
+#155 := (- #152)
+#159 := (= #155 #158)
+#160 := [rewrite]: #159
+#156 := (= #41 #155)
+#153 := (= #40 #152)
+#98 := (= #32 #97)
+#99 := [rewrite]: #98
+#95 := (= #31 #94)
+#96 := [rewrite]: #95
+#154 := [monotonicity #96 #99]: #153
+#157 := [monotonicity #154]: #156
+#162 := [trans #157 #160]: #161
+#91 := (iff #29 #90)
+#88 := (iff #28 #86)
+#89 := [rewrite]: #88
+#92 := [monotonicity #89]: #91
+#165 := [monotonicity #92 #162]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [quant-intro #174]: #176
+#194 := [trans #177 #192]: #193
+#151 := [asserted]: #46
+#195 := [mp #151 #194]: #190
+#198 := [mp~ #195 #202]: #190
+#246 := [mp #198 #245]: #243
+#277 := [mp #246 #276]: #274
+#762 := [mp #277 #761]: #757
+#76 := -2::Int
+#70 := -3::Int
+#67 := -5::Int
+#73 := (f3 -5::Int -3::Int)
+#79 := (= #73 -2::Int)
+#82 := (not #79)
+#13 := 2::Int
+#14 := (- 2::Int)
+#10 := 3::Int
+#11 := (- 3::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#12 := (f3 #9 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#83 := (iff #16 #82)
+#80 := (iff #15 #79)
+#77 := (= #14 -2::Int)
+#78 := [rewrite]: #77
+#74 := (= #12 #73)
+#71 := (= #11 -3::Int)
+#72 := [rewrite]: #71
+#68 := (= #9 -5::Int)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#81 := [monotonicity #75 #78]: #80
+#84 := [monotonicity #81]: #83
+#66 := [asserted]: #16
+#87 := [mp #66 #84]: #82
+#667 := (not #757)
+#668 := (or #667 #79)
+#335 := (* -1::Int -3::Int)
+#420 := (* -1::Int -5::Int)
+#421 := (mod #420 #335)
+#422 := (+ #73 #421)
+#413 := (= #422 0::Int)
+#424 := (mod -5::Int -3::Int)
+#425 := (* -1::Int #424)
+#353 := (+ #73 #425)
+#426 := (= #353 0::Int)
+#423 := (>= -5::Int 0::Int)
+#427 := (<= -3::Int 0::Int)
+#406 := (or #427 #423)
+#741 := (not #406)
+#743 := (<= -5::Int 0::Int)
+#400 := (or #743 #427)
+#530 := (not #400)
+#737 := (or #530 #741)
+#411 := (ite #737 #426 #413)
+#412 := (= #73 0::Int)
+#744 := (= -5::Int 0::Int)
+#745 := (ite #744 #412 #411)
+#746 := (= -5::Int #73)
+#747 := (= -3::Int 0::Int)
+#742 := (ite #747 #746 #745)
+#669 := (or #667 #742)
+#670 := (iff #669 #668)
+#655 := (iff #668 #668)
+#657 := [rewrite]: #655
+#677 := (iff #742 #79)
+#403 := (= #73 -5::Int)
+#664 := (ite false #403 #79)
+#676 := (iff #664 #79)
+#672 := [rewrite]: #676
+#674 := (iff #742 #664)
+#665 := (iff #745 #79)
+#683 := (ite false #412 #79)
+#671 := (iff #683 #79)
+#673 := [rewrite]: #671
+#680 := (iff #745 #683)
+#589 := (iff #411 #79)
+#433 := 1::Int
+#694 := (= #73 1::Int)
+#585 := (ite false #694 #79)
+#587 := (iff #585 #79)
+#588 := [rewrite]: #587
+#578 := (iff #411 #585)
+#582 := (iff #413 #79)
+#572 := (+ 2::Int #73)
+#583 := (= #572 0::Int)
+#682 := (iff #583 #79)
+#567 := [rewrite]: #682
+#678 := (iff #413 #583)
+#533 := (= #422 #572)
+#689 := (+ #73 2::Int)
+#573 := (= #689 #572)
+#574 := [rewrite]: #573
+#687 := (= #422 #689)
+#686 := (= #421 2::Int)
+#700 := (mod 5::Int 3::Int)
+#532 := (= #700 2::Int)
+#685 := [rewrite]: #532
+#529 := (= #421 #700)
+#699 := (= #335 3::Int)
+#693 := [rewrite]: #699
+#692 := (= #420 5::Int)
+#698 := [rewrite]: #692
+#531 := [monotonicity #698 #693]: #529
+#688 := [trans #531 #685]: #686
+#690 := [monotonicity #688]: #687
+#681 := [trans #690 #574]: #533
+#679 := [monotonicity #681]: #678
+#584 := [trans #679 #567]: #582
+#697 := (iff #426 #694)
+#702 := (+ -1::Int #73)
+#550 := (= #702 0::Int)
+#695 := (iff #550 #694)
+#696 := [rewrite]: #695
+#551 := (iff #426 #550)
+#703 := (= #353 #702)
+#705 := (+ #73 -1::Int)
+#707 := (= #705 #702)
+#708 := [rewrite]: #707
+#706 := (= #353 #705)
+#715 := (= #425 -1::Int)
+#713 := (* -1::Int 1::Int)
+#714 := (= #713 -1::Int)
+#711 := [rewrite]: #714
+#428 := (= #425 #713)
+#434 := (= #424 1::Int)
+#712 := [rewrite]: #434
+#710 := [monotonicity #712]: #428
+#704 := [trans #710 #711]: #715
+#701 := [monotonicity #704]: #706
+#709 := [trans #701 #708]: #703
+#552 := [monotonicity #709]: #551
+#691 := [trans #552 #696]: #697
+#431 := (iff #737 false)
+#442 := (or false false)
+#717 := (iff #442 false)
+#721 := [rewrite]: #717
+#716 := (iff #737 #442)
+#719 := (iff #741 false)
+#1 := true
+#725 := (not true)
+#732 := (iff #725 false)
+#734 := [rewrite]: #732
+#341 := (iff #741 #725)
+#447 := (iff #406 true)
+#736 := (or true false)
+#445 := (iff #736 true)
+#446 := [rewrite]: #445
+#722 := (iff #406 #736)
+#735 := (iff #423 false)
+#733 := [rewrite]: #735
+#387 := (iff #427 true)
+#388 := [rewrite]: #387
+#723 := [monotonicity #388 #733]: #722
+#448 := [trans #723 #446]: #447
+#718 := [monotonicity #448]: #341
+#441 := [trans #718 #734]: #719
+#374 := (iff #530 false)
+#731 := (iff #530 #725)
+#729 := (iff #400 true)
+#389 := (or true true)
+#727 := (iff #389 true)
+#728 := [rewrite]: #727
+#390 := (iff #400 #389)
+#383 := (iff #743 true)
+#724 := [rewrite]: #383
+#726 := [monotonicity #724 #388]: #390
+#730 := [trans #726 #728]: #729
+#369 := [monotonicity #730]: #731
+#375 := [trans #369 #734]: #374
+#720 := [monotonicity #375 #441]: #716
+#432 := [trans #720 #721]: #431
+#586 := [monotonicity #432 #691 #584]: #578
+#590 := [trans #586 #588]: #589
+#399 := (iff #744 false)
+#740 := [rewrite]: #399
+#684 := [monotonicity #740 #590]: #680
+#662 := [trans #684 #673]: #665
+#398 := (iff #746 #403)
+#739 := [rewrite]: #398
+#748 := (iff #747 false)
+#738 := [rewrite]: #748
+#675 := [monotonicity #738 #739 #662]: #674
+#666 := [trans #675 #672]: #677
+#654 := [monotonicity #666]: #670
+#658 := [trans #654 #657]: #670
+#663 := [quant-inst #67 #70]: #669
+#659 := [mp #663 #658]: #668
+[unit-resolution #659 #87 #762]: false
+unsat
+0c710ae5525793136d2145b7da68378d3667fa91 322 0
+#2 := false
+#16 := 0::Int
+decl f4 :: Int
+#8 := f4
+#412 := (>= f4 0::Int)
+#732 := (<= f4 0::Int)
+#378 := (not #732)
+#721 := (not #412)
+#725 := (or #721 #378)
+#688 := (not #725)
+#9 := 3::Int
+#413 := (mod f4 3::Int)
+#82 := -1::Int
+#414 := (* -1::Int #413)
+decl f3 :: (-> Int Int Int)
+#10 := (f3 f4 3::Int)
+#342 := (+ #10 #414)
+#415 := (= #342 0::Int)
+#561 := (not #415)
+#518 := (<= #342 0::Int)
+#621 := (not #518)
+#629 := (>= #413 3::Int)
+#630 := (not #629)
+#1 := true
+#60 := [true-axiom]: true
+#617 := (or false #630)
+#618 := [th-lemma arith]: #617
+#619 := [unit-resolution #618 #60]: #630
+#620 := [hypothesis]: #518
+#67 := (>= #10 3::Int)
+#11 := (< #10 3::Int)
+#12 := (not #11)
+#74 := (iff #12 #67)
+#65 := (not #67)
+#69 := (not #65)
+#72 := (iff #69 #67)
+#73 := [rewrite]: #72
+#70 := (iff #12 #69)
+#66 := (iff #11 #65)
+#68 := [rewrite]: #66
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#62 := [asserted]: #12
+#76 := [mp #62 #75]: #67
+#615 := [th-lemma arith farkas -1 1 1 #76 #620 #619]: false
+#607 := [lemma #615]: #621
+#624 := (or #561 #518)
+#635 := [th-lemma arith triangle-eq]: #624
+#613 := [unit-resolution #635 #607]: #561
+#612 := (or #688 #415)
+#436 := -3::Int
+#409 := (* -1::Int f4)
+#707 := (mod #409 -3::Int)
+#431 := (+ #10 #707)
+#706 := (= #431 0::Int)
+#421 := (ite #725 #415 #706)
+#401 := (= #10 0::Int)
+#733 := (= f4 0::Int)
+#701 := (ite #733 #401 #421)
+#14 := (:var 0 Int)
+#13 := (:var 1 Int)
+#34 := (f3 #13 #14)
+#745 := (pattern #34)
+#86 := (* -1::Int #14)
+#83 := (* -1::Int #13)
+#141 := (mod #83 #86)
+#256 := (+ #34 #141)
+#257 := (= #256 0::Int)
+#35 := (mod #13 #14)
+#253 := (* -1::Int #35)
+#254 := (+ #34 #253)
+#255 := (= #254 0::Int)
+#115 := (>= #13 0::Int)
+#108 := (<= #14 0::Int)
+#200 := (or #108 #115)
+#201 := (not #200)
+#104 := (<= #13 0::Int)
+#198 := (or #104 #108)
+#199 := (not #198)
+#204 := (or #199 #201)
+#258 := (ite #204 #255 #257)
+#252 := (= #34 0::Int)
+#17 := (= #13 0::Int)
+#259 := (ite #17 #252 #258)
+#251 := (= #13 #34)
+#18 := (= #14 0::Int)
+#260 := (ite #18 #251 #259)
+#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #260)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#749 := (iff #263 #746)
+#747 := (iff #260 #260)
+#748 := [refl]: #747
+#750 := [quant-intro #748]: #749
+#147 := (* -1::Int #141)
+#220 := (ite #204 #35 #147)
+#223 := (ite #17 0::Int #220)
+#226 := (ite #18 #13 #223)
+#229 := (= #34 #226)
+#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #35 #147)
+#170 := (ite #17 0::Int #167)
+#173 := (ite #18 #13 #170)
+#176 := (= #34 #173)
+#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
+#233 := (iff #179 #232)
+#230 := (iff #176 #229)
+#227 := (= #173 #226)
+#224 := (= #170 #223)
+#221 := (= #167 #220)
+#205 := (iff #122 #204)
+#202 := (iff #119 #201)
+#203 := [rewrite]: #202
+#192 := (iff #112 #199)
+#193 := [rewrite]: #192
+#206 := [monotonicity #193 #203]: #205
+#222 := [monotonicity #206]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#190 := (~ #179 #179)
+#189 := (~ #176 #176)
+#186 := [refl]: #189
+#191 := [nnf-pos #186]: #190
+#28 := (- #14)
+#27 := (- #13)
+#36 := (mod #27 #28)
+#37 := (- #36)
+#21 := (< 0::Int #14)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#38 := (ite #25 #35 #37)
+#39 := (ite #17 0::Int #38)
+#40 := (ite #18 #13 #39)
+#41 := (= #34 #40)
+#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
+#182 := (iff #42 #179)
+#64 := (and #21 #23)
+#79 := (or #22 #64)
+#152 := (ite #79 #35 #147)
+#155 := (ite #17 0::Int #152)
+#158 := (ite #18 #13 #155)
+#161 := (= #34 #158)
+#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #64 #119)
+#117 := (iff #23 #116)
+#118 := [rewrite]: #117
+#110 := (iff #21 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #22 #112)
+#106 := (iff #20 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #42 #164)
+#162 := (iff #41 #161)
+#159 := (= #40 #158)
+#156 := (= #39 #155)
+#153 := (= #38 #152)
+#150 := (= #37 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
#149 := [rewrite]: #148
-#146 := (iff #65 #145)
-#143 := (iff #17 #142)
-#144 := [rewrite]: #143
-#132 := (iff #15 true)
-#133 := [rewrite]: #132
-#147 := [monotonicity #133 #144]: #146
-#151 := [trans #147 #149]: #150
-#139 := (iff #16 #129)
-#134 := (and #129 true)
-#137 := (iff #134 #129)
-#138 := [rewrite]: #137
-#135 := (iff #16 #134)
-#130 := (iff #14 #129)
-#131 := [rewrite]: #130
-#136 := [monotonicity #131 #133]: #135
-#140 := [trans #136 #138]: #139
-#154 := [monotonicity #140 #151]: #153
-#166 := [monotonicity #154]: #165
-#169 := [monotonicity #166]: #168
-#162 := (= #90 #161)
-#159 := (= #84 #158)
-#156 := (= #81 #155)
+#145 := (= #37 #144)
+#142 := (= #36 #141)
+#87 := (= #28 #86)
+#88 := [rewrite]: #87
+#84 := (= #27 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #25 #79)
+#77 := (iff #24 #64)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
#157 := [monotonicity #154]: #156
#160 := [monotonicity #157]: #159
#163 := [monotonicity #160]: #162
-#172 := [monotonicity #163 #169]: #171
-#175 := [monotonicity #172]: #174
-#184 := [trans #175 #182]: #183
-#187 := [monotonicity #184]: #186
-#126 := (iff #35 #125)
-#123 := (iff #34 #122)
-#120 := (= #33 #119)
-#117 := (= #32 #109)
-#112 := (ite false f3 #109)
-#115 := (= #112 #109)
-#116 := [rewrite]: #115
-#113 := (= #32 #112)
-#110 := (= #31 #109)
-#107 := (= #30 #106)
-#104 := (= #29 #101)
-#98 := (- #95)
-#102 := (= #98 #101)
-#103 := [rewrite]: #102
-#99 := (= #29 #98)
-#96 := (= #28 #95)
-#76 := (= #22 -3::Int)
-#77 := [rewrite]: #76
-#73 := (= #21 #72)
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #42
+#184 := [mp #140 #183]: #179
+#187 := [mp~ #184 #191]: #179
+#235 := [mp #187 #234]: #232
+#266 := [mp #235 #265]: #263
+#751 := [mp #266 #750]: #746
+#690 := (not #746)
+#691 := (or #690 #701)
+#324 := (* -1::Int 3::Int)
+#410 := (mod #409 #324)
+#411 := (+ #10 #410)
+#402 := (= #411 0::Int)
+#416 := (<= 3::Int 0::Int)
+#395 := (or #416 #412)
+#730 := (not #395)
+#389 := (or #732 #416)
+#519 := (not #389)
+#726 := (or #519 #730)
+#400 := (ite #726 #415 #402)
+#734 := (ite #733 #401 #400)
+#735 := (= f4 #10)
+#736 := (= 3::Int 0::Int)
+#731 := (ite #736 #735 #734)
+#696 := (or #690 #731)
+#692 := (iff #696 #691)
+#539 := (iff #691 #691)
+#540 := [rewrite]: #539
+#694 := (iff #731 #701)
+#699 := (ite false #735 #701)
+#704 := (iff #699 #701)
+#693 := [rewrite]: #704
+#703 := (iff #731 #699)
+#702 := (iff #734 #701)
+#422 := (iff #400 #421)
+#710 := (iff #402 #706)
+#705 := (= #411 #431)
+#708 := (= #410 #707)
+#437 := (= #324 -3::Int)
+#330 := [rewrite]: #437
+#430 := [monotonicity #330]: #708
+#709 := [monotonicity #430]: #705
+#420 := [monotonicity #709]: #710
+#434 := (iff #726 #725)
+#364 := (or #378 #721)
+#711 := (iff #364 #725)
+#712 := [rewrite]: #711
+#724 := (iff #726 #364)
+#723 := (iff #730 #721)
+#720 := (iff #395 #412)
+#716 := (or false #412)
+#719 := (iff #716 #412)
+#714 := [rewrite]: #719
+#717 := (iff #395 #716)
+#387 := (iff #416 false)
+#392 := [rewrite]: #387
+#718 := [monotonicity #392]: #717
+#358 := [trans #718 #714]: #720
+#363 := [monotonicity #358]: #723
+#379 := (iff #519 #378)
+#376 := (iff #389 #732)
+#728 := (or #732 false)
+#372 := (iff #728 #732)
+#713 := [rewrite]: #372
+#388 := (iff #389 #728)
+#729 := [monotonicity #392]: #388
+#377 := [trans #729 #713]: #376
+#715 := [monotonicity #377]: #379
+#722 := [monotonicity #715 #363]: #724
+#435 := [trans #722 #712]: #434
+#423 := [monotonicity #435 #420]: #422
+#417 := [monotonicity #423]: #702
+#737 := (iff #736 false)
+#727 := [rewrite]: #737
+#700 := [monotonicity #727 #417]: #703
+#695 := [trans #700 #693]: #694
+#698 := [monotonicity #695]: #692
+#541 := [trans #698 #540]: #692
+#697 := [quant-inst #8 #9]: #696
+#683 := [mp #697 #541]: #691
+#614 := [unit-resolution #683 #751]: #701
+#668 := (not #733)
+#667 := (not #701)
+#609 := (or #667 #668)
+#574 := (not #401)
+#684 := (<= #10 0::Int)
+#616 := (not #684)
+#646 := (or #616 #65)
+#647 := [th-lemma arith farkas 1 1]: #646
+#603 := [unit-resolution #647 #76]: #616
+#604 := (or #574 #684)
+#605 := [th-lemma arith triangle-eq]: #604
+#608 := [unit-resolution #605 #603]: #574
+#671 := (or #667 #668 #401)
+#556 := [def-axiom]: #671
+#610 := [unit-resolution #556 #608]: #609
+#611 := [unit-resolution #610 #614]: #668
+#571 := (or #667 #733 #421)
+#573 := [def-axiom]: #571
+#606 := [unit-resolution #573 #611 #614]: #421
+#675 := (not #421)
+#677 := (or #675 #688 #415)
+#678 := [def-axiom]: #677
+#585 := [unit-resolution #678 #606]: #612
+#586 := [unit-resolution #585 #613]: #688
+#686 := (or #725 #412)
+#680 := [def-axiom]: #686
+#587 := [unit-resolution #680 #586]: #412
+#681 := (or #725 #732)
+#687 := [def-axiom]: #681
+#480 := [unit-resolution #687 #586]: #732
+#591 := (or #733 #378 #721)
+#592 := [th-lemma arith triangle-eq]: #591
+#593 := [unit-resolution #592 #611]: #364
+[unit-resolution #593 #480 #587]: false
+unsat
+8e1905429e143174e0fcdce59027187ea0e3224c 340 0
+#2 := false
+#9 := 3::Int
+decl f3 :: (-> Int Int Int)
+decl f4 :: Int
+#8 := f4
+#10 := (f3 f4 3::Int)
+#439 := (mod #10 3::Int)
+#655 := (>= #439 3::Int)
+#656 := (not #655)
+#1 := true
+#62 := [true-axiom]: true
+#645 := (or false #656)
+#640 := [th-lemma arith]: #645
+#646 := [unit-resolution #640 #62]: #656
+#18 := 0::Int
+#107 := -1::Int
+#434 := (* -1::Int #10)
+#598 := (+ f4 #434)
+#599 := (<= #598 0::Int)
+#65 := (= f4 #10)
+#82 := (>= f4 3::Int)
+#80 := (not #82)
+#71 := (not #65)
+#87 := (or #71 #80)
+#92 := (not #87)
+#12 := (< f4 3::Int)
+#11 := (= #10 f4)
+#13 := (implies #11 #12)
+#14 := (not #13)
+#95 := (iff #14 #92)
+#72 := (or #12 #71)
+#77 := (not #72)
+#93 := (iff #77 #92)
+#90 := (iff #72 #87)
+#84 := (or #80 #71)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #72 #84)
+#81 := (iff #12 #80)
+#83 := [rewrite]: #81
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [monotonicity #91]: #93
+#78 := (iff #14 #77)
+#75 := (iff #13 #72)
+#68 := (implies #65 #12)
+#73 := (iff #68 #72)
#74 := [rewrite]: #73
-#97 := [monotonicity #74 #77]: #96
-#100 := [monotonicity #97]: #99
-#105 := [trans #100 #103]: #104
-#69 := (iff #19 #68)
-#66 := (iff #18 #65)
+#69 := (iff #13 #68)
+#66 := (iff #11 #65)
#67 := [rewrite]: #66
#70 := [monotonicity #67]: #69
-#108 := [monotonicity #70 #105]: #107
-#111 := [monotonicity #108]: #110
-#56 := (iff #12 false)
-#57 := [rewrite]: #56
-#114 := [monotonicity #57 #111]: #113
-#118 := [trans #114 #116]: #117
-#93 := (= #26 #90)
-#87 := (* #84 3::Int)
-#91 := (= #87 #90)
-#92 := [rewrite]: #91
-#88 := (= #26 #87)
-#85 := (= #25 #84)
-#82 := (= #24 #81)
-#79 := (= #23 #78)
-#80 := [monotonicity #74 #77]: #79
-#83 := [monotonicity #70 #80]: #82
-#63 := (iff #13 #10)
-#58 := (or #10 false)
-#61 := (iff #58 #10)
-#62 := [rewrite]: #61
-#59 := (iff #13 #58)
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#86 := [monotonicity #64 #83]: #85
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76]: #78
+#96 := [trans #79 #94]: #95
+#64 := [asserted]: #14
+#97 := [mp #64 #96]: #92
+#98 := [not-or-elim #97]: #65
+#632 := (or #71 #599)
+#628 := [th-lemma arith triangle-eq]: #632
+#629 := [unit-resolution #628 #98]: #599
+#99 := [not-or-elim #97]: #82
+#436 := (f3 #10 3::Int)
+#600 := (* -1::Int #436)
+#601 := (+ #10 #600)
+#602 := (<= #601 0::Int)
+#761 := (= #10 #436)
+#633 := (= #436 #10)
+#630 := [symm #98]: #11
+#634 := [monotonicity #630]: #633
+#635 := [symm #634]: #761
+#636 := (not #761)
+#631 := (or #636 #602)
+#637 := [th-lemma arith triangle-eq]: #631
+#610 := [unit-resolution #637 #635]: #602
+#367 := (* -1::Int #439)
+#440 := (+ #436 #367)
+#705 := (<= #440 0::Int)
+#437 := (= #440 0::Int)
+#736 := -3::Int
+#460 := (mod #434 -3::Int)
+#355 := (+ #436 #460)
+#455 := (= #355 0::Int)
+#441 := (>= #10 0::Int)
+#748 := (not #441)
+#414 := (<= #10 0::Int)
+#404 := (not #414)
+#749 := (or #404 #748)
+#734 := (ite #749 #437 #455)
+#758 := (= #436 0::Int)
+#759 := (= #10 0::Int)
+#445 := (ite #759 #758 #734)
+#16 := (:var 0 Int)
+#15 := (:var 1 Int)
+#36 := (f3 #15 #16)
+#770 := (pattern #36)
+#111 := (* -1::Int #16)
+#108 := (* -1::Int #15)
+#166 := (mod #108 #111)
+#281 := (+ #36 #166)
+#282 := (= #281 0::Int)
+#37 := (mod #15 #16)
+#278 := (* -1::Int #37)
+#279 := (+ #36 #278)
+#280 := (= #279 0::Int)
+#140 := (>= #15 0::Int)
+#133 := (<= #16 0::Int)
+#225 := (or #133 #140)
+#226 := (not #225)
+#129 := (<= #15 0::Int)
+#211 := (or #129 #133)
+#212 := (not #211)
+#229 := (or #212 #226)
+#283 := (ite #229 #280 #282)
+#277 := (= #36 0::Int)
+#19 := (= #15 0::Int)
+#284 := (ite #19 #277 #283)
+#276 := (= #15 #36)
+#20 := (= #16 0::Int)
+#285 := (ite #20 #276 #284)
+#771 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #770) #285)
+#288 := (forall (vars (?v0 Int) (?v1 Int)) #285)
+#774 := (iff #288 #771)
+#772 := (iff #285 #285)
+#773 := [refl]: #772
+#775 := [quant-intro #773]: #774
+#172 := (* -1::Int #166)
+#245 := (ite #229 #37 #172)
+#248 := (ite #19 0::Int #245)
+#251 := (ite #20 #15 #248)
+#254 := (= #36 #251)
+#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
+#289 := (iff #257 #288)
+#286 := (iff #254 #285)
+#287 := [rewrite]: #286
+#290 := [quant-intro #287]: #289
+#141 := (not #140)
+#134 := (not #133)
+#144 := (and #134 #141)
+#130 := (not #129)
+#137 := (and #130 #134)
+#147 := (or #137 #144)
+#192 := (ite #147 #37 #172)
+#195 := (ite #19 0::Int #192)
+#198 := (ite #20 #15 #195)
+#201 := (= #36 #198)
+#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
+#258 := (iff #204 #257)
+#255 := (iff #201 #254)
+#252 := (= #198 #251)
+#249 := (= #195 #248)
+#246 := (= #192 #245)
+#230 := (iff #147 #229)
+#227 := (iff #144 #226)
+#228 := [rewrite]: #227
+#219 := (iff #137 #212)
+#220 := [rewrite]: #219
+#231 := [monotonicity #220 #228]: #230
+#247 := [monotonicity #231]: #246
+#250 := [monotonicity #247]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [quant-intro #256]: #258
+#217 := (~ #204 #204)
+#216 := (~ #201 #201)
+#213 := [refl]: #216
+#218 := [nnf-pos #213]: #217
+#30 := (- #16)
+#29 := (- #15)
+#38 := (mod #29 #30)
+#39 := (- #38)
+#23 := (< 0::Int #16)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#40 := (ite #27 #37 #39)
+#41 := (ite #19 0::Int #40)
+#42 := (ite #20 #15 #41)
+#43 := (= #36 #42)
+#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
+#207 := (iff #44 #204)
+#101 := (and #23 #25)
+#104 := (or #24 #101)
+#177 := (ite #104 #37 #172)
+#180 := (ite #19 0::Int #177)
+#183 := (ite #20 #15 #180)
+#186 := (= #36 #183)
+#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
+#205 := (iff #189 #204)
+#202 := (iff #186 #201)
+#199 := (= #183 #198)
+#196 := (= #180 #195)
+#193 := (= #177 #192)
+#148 := (iff #104 #147)
+#145 := (iff #101 #144)
+#142 := (iff #25 #141)
+#143 := [rewrite]: #142
+#135 := (iff #23 #134)
+#136 := [rewrite]: #135
+#146 := [monotonicity #136 #143]: #145
+#138 := (iff #24 #137)
+#131 := (iff #22 #130)
+#132 := [rewrite]: #131
+#139 := [monotonicity #132 #136]: #138
+#149 := [monotonicity #139 #146]: #148
+#194 := [monotonicity #149]: #193
+#197 := [monotonicity #194]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [quant-intro #203]: #205
+#190 := (iff #44 #189)
+#187 := (iff #43 #186)
+#184 := (= #42 #183)
+#181 := (= #41 #180)
+#178 := (= #40 #177)
+#175 := (= #39 #172)
+#169 := (- #166)
+#173 := (= #169 #172)
+#174 := [rewrite]: #173
+#170 := (= #39 #169)
+#167 := (= #38 #166)
+#112 := (= #30 #111)
+#113 := [rewrite]: #112
+#109 := (= #29 #108)
+#110 := [rewrite]: #109
+#168 := [monotonicity #110 #113]: #167
+#171 := [monotonicity #168]: #170
+#176 := [trans #171 #174]: #175
+#105 := (iff #27 #104)
+#102 := (iff #26 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#179 := [monotonicity #106 #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [monotonicity #185]: #187
+#191 := [quant-intro #188]: #190
+#208 := [trans #191 #206]: #207
+#165 := [asserted]: #44
+#209 := [mp #165 #208]: #204
+#214 := [mp~ #209 #218]: #204
+#260 := [mp #214 #259]: #257
+#291 := [mp #260 #290]: #288
+#776 := [mp #291 #775]: #771
+#729 := (not #771)
+#718 := (or #729 #445)
+#349 := (* -1::Int 3::Int)
+#435 := (mod #434 #349)
+#427 := (+ #436 #435)
+#438 := (= #427 0::Int)
+#420 := (<= 3::Int 0::Int)
+#755 := (or #420 #441)
+#757 := (not #755)
+#544 := (or #414 #420)
+#751 := (not #544)
+#425 := (or #751 #757)
+#426 := (ite #425 #437 #438)
+#760 := (ite #759 #758 #426)
+#756 := (= 3::Int 0::Int)
+#762 := (ite #756 #761 #760)
+#719 := (or #729 #762)
+#715 := (iff #719 #718)
+#721 := (iff #718 #718)
+#722 := [rewrite]: #721
+#728 := (iff #762 #445)
+#448 := (ite false #761 #445)
+#442 := (iff #448 #445)
+#724 := [rewrite]: #442
+#726 := (iff #762 #448)
+#446 := (iff #760 #445)
+#731 := (iff #426 #734)
+#456 := (iff #438 #455)
+#732 := (= #427 #355)
+#461 := (= #435 #460)
+#737 := (= #349 -3::Int)
+#459 := [rewrite]: #737
+#462 := [monotonicity #459]: #461
+#733 := [monotonicity #462]: #732
+#730 := [monotonicity #733]: #456
+#747 := (iff #425 #749)
+#388 := (iff #757 #748)
+#383 := (iff #755 #441)
+#742 := (or false #441)
+#739 := (iff #742 #441)
+#745 := [rewrite]: #739
+#743 := (iff #755 #742)
+#417 := (iff #420 false)
+#753 := [rewrite]: #417
+#744 := [monotonicity #753]: #743
+#746 := [trans #744 #745]: #383
+#389 := [monotonicity #746]: #388
+#740 := (iff #751 #404)
+#402 := (iff #544 #414)
+#413 := (or #414 false)
+#738 := (iff #413 #414)
+#401 := [rewrite]: #738
+#754 := (iff #544 #413)
+#397 := [monotonicity #753]: #754
+#403 := [trans #397 #401]: #402
+#741 := [monotonicity #403]: #740
+#750 := [monotonicity #741 #389]: #747
+#735 := [monotonicity #750 #730]: #731
+#447 := [monotonicity #735]: #446
+#752 := (iff #756 false)
+#412 := [rewrite]: #752
+#727 := [monotonicity #412 #447]: #726
+#725 := [trans #727 #724]: #728
+#716 := [monotonicity #725]: #715
+#717 := [trans #716 #722]: #715
+#720 := [quant-inst #10 #9]: #719
+#723 := [mp #720 #717]: #718
+#611 := [unit-resolution #723 #776]: #445
+#587 := (not #759)
+#612 := (not #599)
+#505 := (or #404 #80 #612)
+#616 := [th-lemma arith assign-bounds 1 1]: #505
+#617 := [unit-resolution #616 #99 #629]: #404
+#618 := (or #587 #414)
+#623 := [th-lemma arith triangle-eq]: #618
+#619 := [unit-resolution #623 #617]: #587
+#586 := (not #445)
+#695 := (or #586 #759 #734)
+#597 := [def-axiom]: #695
+#620 := [unit-resolution #597 #619 #611]: #734
+#564 := (or #749 #414)
+#565 := [def-axiom]: #564
+#621 := [unit-resolution #565 #617]: #749
+#709 := (not #749)
+#707 := (not #734)
+#714 := (or #707 #709 #437)
+#543 := [def-axiom]: #714
+#624 := [unit-resolution #543 #621 #620]: #437
+#699 := (not #437)
+#625 := (or #699 #705)
+#626 := [th-lemma arith triangle-eq]: #625
+#622 := [unit-resolution #626 #624]: #705
+[th-lemma arith farkas 1 1 -1 1 1 #622 #610 #99 #629 #646]: false
+unsat
+554a2c1ef3c9bdd0bc388bdfa3186ab7a764500e 567 0
+#2 := false
+#19 := 0::Int
+decl f5 :: (-> Int Int Int)
+#9 := 1::Int
+decl f3 :: Int
+#8 := f3
+#12 := (f5 f3 1::Int)
+#77 := -1::Int
+#79 := (* -1::Int #12)
+decl f4 :: (-> Int Int Int)
+#10 := (f4 f3 1::Int)
+#78 := (* -1::Int #10)
+#80 := (+ #78 #79)
+#81 := (+ f3 #80)
+#423 := (>= #81 0::Int)
+#596 := (<= #12 0::Int)
+#667 := (= #12 0::Int)
+#751 := (= f3 0::Int)
+#746 := (>= f3 0::Int)
+#449 := (not #746)
+#414 := (<= f3 0::Int)
+#735 := (not #414)
+#635 := (or #735 #449 #751)
+#615 := (not #635)
+#582 := [hypothesis]: #615
+#609 := (or #635 #746)
+#610 := [def-axiom]: #609
+#583 := [unit-resolution #610 #582]: #746
+#612 := (or #635 #414)
+#608 := [def-axiom]: #612
+#584 := [unit-resolution #608 #582]: #414
+#570 := (not #751)
+#613 := (or #635 #570)
+#614 := [def-axiom]: #613
+#594 := [unit-resolution #614 #582]: #570
+#574 := (or #751 #735 #449)
+#595 := [th-lemma arith triangle-eq]: #574
+#550 := [unit-resolution #595 #594 #584 #583]: false
+#551 := [lemma #550]: #635
+#498 := (or #615 #667)
+#425 := (* -1::Int f3)
+#688 := (mod #425 -1::Int)
+#655 := (+ #12 #688)
+#636 := (= #655 0::Int)
+#618 := (ite #635 #667 #636)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#37 := (f5 #16 #17)
+#759 := (pattern #37)
+#101 := (* -1::Int #17)
+#98 := (* -1::Int #16)
+#156 := (mod #98 #101)
+#271 := (+ #37 #156)
+#272 := (= #271 0::Int)
+#38 := (mod #16 #17)
+#268 := (* -1::Int #38)
+#269 := (+ #37 #268)
+#270 := (= #269 0::Int)
+#130 := (>= #16 0::Int)
+#123 := (<= #17 0::Int)
+#215 := (or #123 #130)
+#216 := (not #215)
+#119 := (<= #16 0::Int)
+#213 := (or #119 #123)
+#214 := (not #213)
+#219 := (or #214 #216)
+#273 := (ite #219 #270 #272)
+#267 := (= #37 0::Int)
+#20 := (= #16 0::Int)
+#274 := (ite #20 #267 #273)
+#266 := (= #16 #37)
+#21 := (= #17 0::Int)
+#275 := (ite #21 #266 #274)
+#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#763 := (iff #278 #760)
+#761 := (iff #275 #275)
+#762 := [refl]: #761
+#764 := [quant-intro #762]: #763
+#162 := (* -1::Int #156)
+#235 := (ite #219 #38 #162)
+#238 := (ite #20 0::Int #235)
+#241 := (ite #21 #16 #238)
+#244 := (= #37 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#131 := (not #130)
+#124 := (not #123)
+#134 := (and #124 #131)
+#120 := (not #119)
+#127 := (and #120 #124)
+#137 := (or #127 #134)
+#182 := (ite #137 #38 #162)
+#185 := (ite #20 0::Int #182)
+#188 := (ite #21 #16 #185)
+#191 := (= #37 #188)
+#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
+#248 := (iff #194 #247)
+#245 := (iff #191 #244)
+#242 := (= #188 #241)
+#239 := (= #185 #238)
+#236 := (= #182 #235)
+#220 := (iff #137 #219)
+#217 := (iff #134 #216)
+#218 := [rewrite]: #217
+#207 := (iff #127 #214)
+#208 := [rewrite]: #207
+#221 := [monotonicity #208 #218]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#205 := (~ #194 #194)
+#204 := (~ #191 #191)
+#201 := [refl]: #204
+#206 := [nnf-pos #201]: #205
+#31 := (- #17)
+#30 := (- #16)
+#39 := (mod #30 #31)
+#40 := (- #39)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#41 := (ite #28 #38 #40)
+#42 := (ite #20 0::Int #41)
+#43 := (ite #21 #16 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#197 := (iff #45 #194)
+#92 := (and #24 #26)
+#95 := (or #25 #92)
+#167 := (ite #95 #38 #162)
+#170 := (ite #20 0::Int #167)
+#173 := (ite #21 #16 #170)
+#176 := (= #37 #173)
+#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
+#195 := (iff #179 #194)
+#192 := (iff #176 #191)
+#189 := (= #173 #188)
+#186 := (= #170 #185)
+#183 := (= #167 #182)
+#138 := (iff #95 #137)
+#135 := (iff #92 #134)
+#132 := (iff #26 #131)
+#133 := [rewrite]: #132
+#125 := (iff #24 #124)
+#126 := [rewrite]: #125
+#136 := [monotonicity #126 #133]: #135
+#128 := (iff #25 #127)
+#121 := (iff #23 #120)
+#122 := [rewrite]: #121
+#129 := [monotonicity #122 #126]: #128
+#139 := [monotonicity #129 #136]: #138
+#184 := [monotonicity #139]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [monotonicity #190]: #192
+#196 := [quant-intro #193]: #195
+#180 := (iff #45 #179)
+#177 := (iff #44 #176)
+#174 := (= #43 #173)
+#171 := (= #42 #170)
+#168 := (= #41 #167)
+#165 := (= #40 #162)
+#159 := (- #156)
+#163 := (= #159 #162)
+#164 := [rewrite]: #163
+#160 := (= #40 #159)
+#157 := (= #39 #156)
+#102 := (= #31 #101)
+#103 := [rewrite]: #102
+#99 := (= #30 #98)
+#100 := [rewrite]: #99
+#158 := [monotonicity #100 #103]: #157
+#161 := [monotonicity #158]: #160
+#166 := [trans #161 #164]: #165
+#96 := (iff #28 #95)
+#93 := (iff #27 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#169 := [monotonicity #97 #166]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#198 := [trans #181 #196]: #197
+#155 := [asserted]: #45
+#199 := [mp #155 #198]: #194
+#202 := [mp~ #199 #206]: #194
+#250 := [mp #202 #249]: #247
+#281 := [mp #250 #280]: #278
+#765 := [mp #281 #764]: #760
+#625 := (not #760)
+#620 := (or #625 #618)
+#424 := (* -1::Int 1::Int)
+#686 := (mod #425 #424)
+#683 := (+ #12 #686)
+#687 := (= #683 0::Int)
+#532 := (mod f3 1::Int)
+#674 := (* -1::Int #532)
+#676 := (+ #12 #674)
+#668 := (= #676 0::Int)
+#403 := (<= 1::Int 0::Int)
+#533 := (or #403 #746)
+#740 := (not #533)
+#415 := (or #414 #403)
+#747 := (not #415)
+#748 := (or #747 #740)
+#665 := (ite #748 #668 #687)
+#677 := (ite #751 #667 #665)
+#678 := (= f3 #12)
+#745 := (= 1::Int 0::Int)
+#679 := (ite #745 #678 #677)
+#626 := (or #625 #679)
+#600 := (iff #626 #620)
+#494 := (iff #620 #620)
+#605 := [rewrite]: #494
+#623 := (iff #679 #618)
+#345 := (or #735 #449)
+#646 := (or #345 #751)
+#647 := (ite #646 #667 #636)
+#619 := (iff #647 #618)
+#621 := (iff #646 #635)
+#617 := [rewrite]: #621
+#622 := [monotonicity #617]: #619
+#634 := (iff #679 #647)
+#628 := (ite false #678 #647)
+#632 := (iff #628 #647)
+#633 := [rewrite]: #632
+#630 := (iff #679 #628)
+#649 := (iff #677 #647)
+#640 := (ite #345 #667 #636)
+#643 := (ite #751 #667 #640)
+#648 := (iff #643 #647)
+#638 := [rewrite]: #648
+#644 := (iff #677 #643)
+#641 := (iff #665 #640)
+#637 := (iff #687 #636)
+#652 := (= #683 #655)
+#653 := (= #686 #688)
+#444 := (= #424 -1::Int)
+#445 := [rewrite]: #444
+#654 := [monotonicity #445]: #653
+#656 := [monotonicity #654]: #652
+#639 := [monotonicity #656]: #637
+#650 := (iff #668 #667)
+#659 := (= #676 #12)
+#658 := (+ #12 0::Int)
+#662 := (= #658 #12)
+#663 := [rewrite]: #662
+#660 := (= #676 #658)
+#673 := (= #674 0::Int)
+#669 := (* -1::Int 0::Int)
+#672 := (= #669 0::Int)
+#666 := [rewrite]: #672
+#670 := (= #674 #669)
+#675 := (= #532 0::Int)
+#680 := [rewrite]: #675
+#671 := [monotonicity #680]: #670
+#657 := [trans #671 #666]: #673
+#661 := [monotonicity #657]: #660
+#664 := [trans #661 #663]: #659
+#651 := [monotonicity #664]: #650
+#721 := (iff #748 #345)
+#450 := (iff #740 #449)
+#726 := (iff #533 #746)
+#378 := (or false #746)
+#739 := (iff #378 #746)
+#725 := [rewrite]: #739
+#738 := (iff #533 #378)
+#393 := (iff #403 false)
+#729 := [rewrite]: #393
+#736 := [monotonicity #729]: #738
+#448 := [trans #736 #725]: #726
+#451 := [monotonicity #448]: #450
+#737 := (iff #747 #735)
+#734 := (iff #415 #414)
+#730 := (or #414 false)
+#733 := (iff #730 #414)
+#728 := [rewrite]: #733
+#731 := (iff #415 #730)
+#732 := [monotonicity #729]: #731
+#372 := [trans #732 #728]: #734
+#377 := [monotonicity #372]: #737
+#722 := [monotonicity #377 #451]: #721
+#642 := [monotonicity #722 #651 #639]: #641
+#645 := [monotonicity #642]: #644
+#627 := [trans #645 #638]: #649
+#406 := (iff #745 false)
+#742 := [rewrite]: #406
+#631 := [monotonicity #742 #627]: #630
+#629 := [trans #631 #633]: #634
+#624 := [trans #629 #622]: #623
+#601 := [monotonicity #624]: #600
+#606 := [trans #601 #605]: #600
+#599 := [quant-inst #8 #9]: #626
+#607 := [mp #599 #606]: #620
+#505 := [unit-resolution #607 #765]: #618
+#602 := (not #618)
+#603 := (or #602 #615 #667)
+#598 := [def-axiom]: #603
+#501 := [unit-resolution #598 #505]: #498
+#502 := [unit-resolution #501 #551]: #667
+#579 := (not #667)
+#488 := (or #579 #596)
+#490 := [th-lemma arith triangle-eq]: #488
+#491 := [unit-resolution #490 #502]: #596
+#698 := (<= #10 0::Int)
+#750 := (= #10 0::Int)
+#453 := [hypothesis]: #570
+#702 := (not #345)
+#426 := (div f3 1::Int)
+#430 := (* -1::Int #426)
+#409 := (+ #10 #430)
+#744 := (= #409 0::Int)
+#577 := (not #744)
+#544 := (+ f3 #430)
+#549 := (>= #544 0::Int)
+#543 := (= #544 0::Int)
+#1 := true
+#63 := [true-axiom]: true
+#493 := (or false #543)
+#495 := [th-lemma arith]: #493
+#496 := [unit-resolution #495 #63]: #543
+#499 := (not #543)
+#500 := (or #499 #549)
+#504 := [th-lemma arith triangle-eq]: #500
+#497 := [unit-resolution #504 #496]: #549
+#534 := (<= #409 0::Int)
+#489 := [hypothesis]: #744
+#492 := (or #577 #534)
+#474 := [th-lemma arith triangle-eq]: #492
+#476 := [unit-resolution #474 #489]: #534
+#479 := (not #549)
+#478 := (not #534)
+#477 := (not #596)
+#480 := (or #423 #477 #478 #479)
+#481 := [th-lemma arith assign-bounds 1 1 -1]: #480
+#482 := [unit-resolution #481 #476 #491 #497]: #423
+#339 := (<= #81 0::Int)
+#531 := (<= #544 0::Int)
+#483 := (or #499 #531)
+#484 := [th-lemma arith triangle-eq]: #483
+#485 := [unit-resolution #484 #496]: #531
+#542 := (>= #12 0::Int)
+#486 := (or #579 #542)
+#475 := [th-lemma arith triangle-eq]: #486
+#487 := [unit-resolution #475 #502]: #542
+#535 := (>= #409 0::Int)
+#464 := (or #577 #535)
+#466 := [th-lemma arith triangle-eq]: #464
+#467 := [unit-resolution #466 #489]: #535
+#470 := (not #531)
+#469 := (not #535)
+#468 := (not #542)
+#471 := (or #339 #468 #469 #470)
+#472 := [th-lemma arith assign-bounds 1 1 -1]: #471
+#465 := [unit-resolution #472 #467 #487 #485]: #339
+#458 := (not #423)
+#473 := (not #339)
+#462 := (or #473 #458)
+#82 := (= #81 0::Int)
+#85 := (not #82)
+#11 := (* #10 1::Int)
+#13 := (+ #11 #12)
+#14 := (= f3 #13)
+#15 := (not #14)
+#88 := (iff #15 #85)
+#68 := (+ #10 #12)
+#71 := (= f3 #68)
+#74 := (not #71)
+#86 := (iff #74 #85)
+#83 := (iff #71 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#75 := (iff #15 #74)
+#72 := (iff #14 #71)
+#69 := (= #13 #68)
+#66 := (= #11 #10)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#76 := [monotonicity #73]: #75
+#89 := [trans #76 #87]: #88
+#65 := [asserted]: #15
+#90 := [mp #65 #89]: #85
+#459 := (or #82 #473 #458)
+#460 := [th-lemma arith triangle-eq]: #459
+#461 := [unit-resolution #460 #90]: #462
+#463 := [unit-resolution #461 #465 #482]: false
+#452 := [lemma #463]: #577
+#719 := (div #425 -1::Int)
+#724 := (* -1::Int #719)
+#436 := (+ #10 #724)
+#716 := (= #436 0::Int)
+#717 := (ite #345 #744 #716)
+#446 := (or #751 #717)
+#707 := (ite #751 #750 #717)
+#18 := (f4 #16 #17)
+#752 := (pattern #18)
+#104 := (div #98 #101)
+#255 := (* -1::Int #104)
+#256 := (+ #18 #255)
+#257 := (= #256 0::Int)
+#29 := (div #16 #17)
+#252 := (* -1::Int #29)
+#253 := (+ #18 #252)
+#254 := (= #253 0::Int)
+#258 := (ite #219 #254 #257)
+#251 := (= #18 0::Int)
+#22 := (or #20 #21)
+#259 := (ite #22 #251 #258)
+#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #259)
+#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
+#756 := (iff #262 #753)
+#754 := (iff #259 #259)
+#755 := [refl]: #754
+#757 := [quant-intro #755]: #756
+#222 := (ite #219 #29 #104)
+#225 := (ite #22 0::Int #222)
+#228 := (= #18 #225)
+#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#140 := (ite #137 #29 #104)
+#143 := (ite #22 0::Int #140)
+#146 := (= #18 #143)
+#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
+#232 := (iff #149 #231)
+#229 := (iff #146 #228)
+#226 := (= #143 #225)
+#223 := (= #140 #222)
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#211 := (~ #149 #149)
+#209 := (~ #146 #146)
+#210 := [refl]: #209
+#212 := [nnf-pos #210]: #211
+#32 := (div #30 #31)
+#33 := (ite #28 #29 #32)
+#34 := (ite #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#152 := (iff #36 #149)
+#107 := (ite #95 #29 #104)
+#110 := (ite #22 0::Int #107)
+#113 := (= #18 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#150 := (iff #116 #149)
+#147 := (iff #113 #146)
+#144 := (= #110 #143)
+#141 := (= #107 #140)
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [quant-intro #148]: #150
+#117 := (iff #36 #116)
+#114 := (iff #35 #113)
+#111 := (= #34 #110)
+#108 := (= #33 #107)
+#105 := (= #32 #104)
+#106 := [monotonicity #100 #103]: #105
+#109 := [monotonicity #97 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#153 := [trans #118 #151]: #152
+#91 := [asserted]: #36
+#154 := [mp #91 #153]: #149
+#203 := [mp~ #154 #212]: #149
+#234 := [mp #203 #233]: #231
+#265 := [mp #234 #264]: #262
+#758 := [mp #265 #757]: #753
+#704 := (not #753)
+#705 := (or #704 #707)
+#416 := (div #425 #424)
+#427 := (* -1::Int #416)
+#428 := (+ #10 #427)
+#429 := (= #428 0::Int)
+#749 := (ite #748 #744 #429)
+#741 := (or #751 #745)
+#401 := (ite #741 #750 #749)
+#710 := (or #704 #401)
+#706 := (iff #710 #705)
+#553 := (iff #705 #705)
+#554 := [rewrite]: #553
+#708 := (iff #401 #707)
+#714 := (iff #749 #717)
+#431 := (iff #429 #716)
+#437 := (= #428 #436)
+#434 := (= #427 #724)
+#723 := (= #416 #719)
+#720 := [monotonicity #445]: #723
+#435 := [monotonicity #720]: #434
+#715 := [monotonicity #435]: #437
+#713 := [monotonicity #715]: #431
+#718 := [monotonicity #722 #713]: #714
+#391 := (iff #741 #751)
+#402 := (or #751 false)
+#727 := (iff #402 #751)
+#390 := [rewrite]: #727
+#743 := (iff #741 #402)
+#386 := [monotonicity #742]: #743
+#392 := [trans #386 #390]: #391
+#709 := [monotonicity #392 #718]: #708
+#712 := [monotonicity #709]: #706
+#555 := [trans #712 #554]: #706
+#711 := [quant-inst #8 #9]: #710
+#697 := [mp #711 #555]: #705
+#454 := [unit-resolution #697 #758]: #707
+#685 := (not #707)
+#588 := (or #685 #751 #717)
+#581 := [def-axiom]: #588
+#455 := [unit-resolution #581 #454]: #446
+#456 := [unit-resolution #455 #453]: #717
+#692 := (not #717)
+#690 := (or #692 #702 #744)
+#693 := [def-axiom]: #690
+#447 := [unit-resolution #693 #456 #452]: #702
+#700 := (or #345 #414)
+#694 := [def-axiom]: #700
+#457 := [unit-resolution #694 #447]: #414
+#695 := (or #345 #746)
+#701 := [def-axiom]: #695
+#438 := [unit-resolution #701 #447]: #746
+#439 := [unit-resolution #595 #438 #457 #453]: false
+#440 := [lemma #439]: #751
+#432 := (or #570 #750)
+#585 := (or #685 #570 #750)
+#587 := [def-axiom]: #585
+#441 := [unit-resolution #587 #454]: #432
+#442 := [unit-resolution #441 #440]: #750
+#589 := (not #750)
+#433 := (or #589 #698)
+#443 := [th-lemma arith triangle-eq]: #433
+#410 := [unit-resolution #443 #442]: #698
+#412 := (or #570 #746)
+#413 := [th-lemma arith triangle-eq]: #412
+#404 := [unit-resolution #413 #440]: #746
+#417 := (not #698)
+#418 := (or #423 #417 #477 #449)
+#419 := [th-lemma arith assign-bounds 1 1 -1]: #418
+#420 := [unit-resolution #419 #404 #410 #491]: #423
+#699 := (>= #10 0::Int)
+#421 := (or #589 #699)
+#411 := [th-lemma arith triangle-eq]: #421
+#422 := [unit-resolution #411 #442]: #699
+#405 := (or #570 #414)
+#407 := [th-lemma arith triangle-eq]: #405
+#408 := [unit-resolution #407 #440]: #414
+#387 := (not #699)
+#389 := (or #339 #387 #468 #735)
+#394 := [th-lemma arith assign-bounds 1 1 -1]: #389
+#395 := [unit-resolution #394 #408 #422 #487]: #339
+[unit-resolution #461 #395 #420]: false
+unsat
+b7566ab9692699d99b59e9354d5e78d5af5e3d40 544 0
+#2 := false
+#19 := 0::Int
+decl f4 :: (-> Int Int Int)
+#9 := 3::Int
+decl f3 :: Int
+#8 := f3
+#10 := (f4 f3 3::Int)
+#701 := (>= #10 0::Int)
+#752 := (= #10 0::Int)
+#748 := (= f3 0::Int)
+#688 := (not #748)
+#560 := [hypothesis]: #688
+#743 := (<= f3 0::Int)
+#747 := (>= f3 0::Int)
+#451 := (not #747)
+#375 := (not #743)
+#454 := (or #375 #451)
+#704 := (not #454)
+#78 := -3::Int
+#80 := -1::Int
+#428 := (* -1::Int f3)
+#448 := (div #428 -3::Int)
+#723 := (* -1::Int #448)
+#438 := (+ #10 #723)
+#718 := (= #438 0::Int)
+#432 := (div f3 3::Int)
+#429 := (* -1::Int #432)
+#433 := (+ #10 #429)
+#412 := (= #433 0::Int)
+#716 := (ite #454 #412 #718)
+#562 := (or #748 #716)
+#721 := (ite #748 #752 #716)
+#17 := (:var 0 Int)
+#16 := (:var 1 Int)
+#18 := (f4 #16 #17)
+#755 := (pattern #18)
+#103 := (* -1::Int #17)
+#100 := (* -1::Int #16)
+#106 := (div #100 #103)
+#257 := (* -1::Int #106)
+#258 := (+ #18 #257)
+#259 := (= #258 0::Int)
+#29 := (div #16 #17)
+#254 := (* -1::Int #29)
+#255 := (+ #18 #254)
+#256 := (= #255 0::Int)
+#132 := (>= #16 0::Int)
+#125 := (<= #17 0::Int)
+#217 := (or #125 #132)
+#218 := (not #217)
+#121 := (<= #16 0::Int)
+#215 := (or #121 #125)
+#216 := (not #215)
+#221 := (or #216 #218)
+#260 := (ite #221 #256 #259)
+#253 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#22 := (or #20 #21)
+#261 := (ite #22 #253 #260)
+#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #261)
+#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
+#759 := (iff #264 #756)
+#757 := (iff #261 #261)
+#758 := [refl]: #757
+#760 := [quant-intro #758]: #759
+#224 := (ite #221 #29 #106)
+#227 := (ite #22 0::Int #224)
+#230 := (= #18 #227)
+#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
+#265 := (iff #233 #264)
+#262 := (iff #230 #261)
+#263 := [rewrite]: #262
+#266 := [quant-intro #263]: #265
+#133 := (not #132)
+#126 := (not #125)
+#136 := (and #126 #133)
+#122 := (not #121)
+#129 := (and #122 #126)
+#139 := (or #129 #136)
+#142 := (ite #139 #29 #106)
+#145 := (ite #22 0::Int #142)
+#148 := (= #18 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#234 := (iff #151 #233)
+#231 := (iff #148 #230)
+#228 := (= #145 #227)
+#225 := (= #142 #224)
+#222 := (iff #139 #221)
+#219 := (iff #136 #218)
+#220 := [rewrite]: #219
+#209 := (iff #129 #216)
+#210 := [rewrite]: #209
+#223 := [monotonicity #210 #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [quant-intro #232]: #234
+#213 := (~ #151 #151)
+#211 := (~ #148 #148)
+#212 := [refl]: #211
+#214 := [nnf-pos #212]: #213
+#31 := (- #17)
+#30 := (- #16)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (ite #28 #29 #32)
+#34 := (ite #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#154 := (iff #36 #151)
+#94 := (and #24 #26)
+#97 := (or #25 #94)
+#109 := (ite #97 #29 #106)
+#112 := (ite #22 0::Int #109)
+#115 := (= #18 #112)
+#118 := (forall (vars (?v0 Int) (?v1 Int)) #115)
+#152 := (iff #118 #151)
+#149 := (iff #115 #148)
+#146 := (= #112 #145)
+#143 := (= #109 #142)
+#140 := (iff #97 #139)
+#137 := (iff #94 #136)
+#134 := (iff #26 #133)
+#135 := [rewrite]: #134
+#127 := (iff #24 #126)
+#128 := [rewrite]: #127
+#138 := [monotonicity #128 #135]: #137
+#130 := (iff #25 #129)
+#123 := (iff #23 #122)
+#124 := [rewrite]: #123
+#131 := [monotonicity #124 #128]: #130
+#141 := [monotonicity #131 #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#119 := (iff #36 #118)
+#116 := (iff #35 #115)
+#113 := (= #34 #112)
+#110 := (= #33 #109)
+#107 := (= #32 #106)
+#104 := (= #31 #103)
+#105 := [rewrite]: #104
+#101 := (= #30 #100)
+#102 := [rewrite]: #101
+#108 := [monotonicity #102 #105]: #107
+#98 := (iff #28 #97)
+#95 := (iff #27 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#111 := [monotonicity #99 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#155 := [trans #120 #153]: #154
+#93 := [asserted]: #36
+#156 := [mp #93 #155]: #151
+#205 := [mp~ #156 #214]: #151
+#236 := [mp #205 #235]: #233
+#267 := [mp #236 #266]: #264
+#761 := [mp #267 #760]: #756
+#712 := (not #756)
+#707 := (or #712 #721)
+#427 := (* -1::Int 3::Int)
+#419 := (div #428 #427)
+#430 := (* -1::Int #419)
+#431 := (+ #10 #430)
+#359 := (= #431 0::Int)
+#749 := (<= 3::Int 0::Int)
+#406 := (or #749 #747)
+#536 := (not #406)
+#417 := (or #743 #749)
+#418 := (not #417)
+#750 := (or #418 #536)
+#751 := (ite #750 #412 #359)
+#753 := (= 3::Int 0::Int)
+#754 := (or #748 #753)
+#744 := (ite #754 #752 #751)
+#708 := (or #712 #744)
+#714 := (iff #708 #707)
+#715 := (iff #707 #707)
+#556 := [rewrite]: #715
+#710 := (iff #744 #721)
+#720 := (iff #751 #716)
+#719 := (iff #359 #718)
+#439 := (= #431 #438)
+#727 := (= #430 #723)
+#722 := (= #419 #448)
+#725 := (= #427 -3::Int)
+#447 := [rewrite]: #725
+#726 := [monotonicity #447]: #722
+#437 := [monotonicity #726]: #727
+#440 := [monotonicity #437]: #439
+#434 := [monotonicity #440]: #719
+#347 := (iff #750 #454)
+#452 := (iff #536 #451)
+#728 := (iff #406 #747)
+#380 := (or false #747)
+#739 := (iff #380 #747)
+#742 := [rewrite]: #739
+#381 := (iff #406 #380)
+#395 := (iff #749 false)
+#396 := [rewrite]: #395
+#741 := [monotonicity #396]: #381
+#729 := [trans #741 #742]: #728
+#453 := [monotonicity #729]: #452
+#738 := (iff #418 #375)
+#731 := (iff #417 #743)
+#732 := (or #743 false)
+#735 := (iff #732 #743)
+#736 := [rewrite]: #735
+#733 := (iff #417 #732)
+#734 := [monotonicity #396]: #733
+#737 := [trans #734 #736]: #731
+#740 := [monotonicity #737]: #738
+#724 := [monotonicity #740 #453]: #347
+#717 := [monotonicity #724 #434]: #720
+#393 := (iff #754 #748)
+#745 := (or #748 false)
+#389 := (iff #745 #748)
+#730 := [rewrite]: #389
+#405 := (iff #754 #745)
+#404 := (iff #753 false)
+#409 := [rewrite]: #404
+#746 := [monotonicity #409]: #405
+#394 := [trans #746 #730]: #393
+#711 := [monotonicity #394 #717]: #710
+#709 := [monotonicity #711]: #714
+#557 := [trans #709 #556]: #714
+#713 := [quant-inst #8 #9]: #708
+#558 := [mp #713 #557]: #707
+#561 := [unit-resolution #558 #761]: #721
+#685 := (not #721)
+#590 := (or #685 #748 #716)
+#591 := [def-axiom]: #590
+#563 := [unit-resolution #591 #561]: #562
+#564 := [unit-resolution #563 #560]: #716
+#538 := (mod #428 -3::Int)
+decl f5 :: (-> Int Int Int)
+#12 := (f5 f3 3::Int)
+#683 := (+ #12 #538)
+#674 := (= #683 0::Int)
+#706 := (mod f3 3::Int)
+#690 := (* -1::Int #706)
+#677 := (+ #12 #690)
+#679 := (= #677 0::Int)
+#676 := (ite #454 #679 #674)
+#523 := (or #748 #676)
+#668 := (= #12 0::Int)
+#663 := (ite #748 #668 #676)
+#37 := (f5 #16 #17)
+#762 := (pattern #37)
+#158 := (mod #100 #103)
+#273 := (+ #37 #158)
+#274 := (= #273 0::Int)
+#38 := (mod #16 #17)
+#270 := (* -1::Int #38)
+#271 := (+ #37 #270)
+#272 := (= #271 0::Int)
+#275 := (ite #221 #272 #274)
+#269 := (= #37 0::Int)
+#276 := (ite #20 #269 #275)
+#268 := (= #16 #37)
+#277 := (ite #21 #268 #276)
+#763 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #762) #277)
+#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
+#766 := (iff #280 #763)
+#764 := (iff #277 #277)
+#765 := [refl]: #764
+#767 := [quant-intro #765]: #766
+#164 := (* -1::Int #158)
+#237 := (ite #221 #38 #164)
+#240 := (ite #20 0::Int #237)
+#243 := (ite #21 #16 #240)
+#246 := (= #37 #243)
+#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
+#281 := (iff #249 #280)
+#278 := (iff #246 #277)
+#279 := [rewrite]: #278
+#282 := [quant-intro #279]: #281
+#184 := (ite #139 #38 #164)
+#187 := (ite #20 0::Int #184)
+#190 := (ite #21 #16 #187)
+#193 := (= #37 #190)
+#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
+#250 := (iff #196 #249)
+#247 := (iff #193 #246)
+#244 := (= #190 #243)
+#241 := (= #187 #240)
+#238 := (= #184 #237)
+#239 := [monotonicity #223]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [monotonicity #245]: #247
+#251 := [quant-intro #248]: #250
+#207 := (~ #196 #196)
+#206 := (~ #193 #193)
+#203 := [refl]: #206
+#208 := [nnf-pos #203]: #207
+#39 := (mod #30 #31)
+#40 := (- #39)
+#41 := (ite #28 #38 #40)
+#42 := (ite #20 0::Int #41)
+#43 := (ite #21 #16 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#199 := (iff #45 #196)
+#169 := (ite #97 #38 #164)
+#172 := (ite #20 0::Int #169)
+#175 := (ite #21 #16 #172)
+#178 := (= #37 #175)
+#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
+#197 := (iff #181 #196)
+#194 := (iff #178 #193)
+#191 := (= #175 #190)
+#188 := (= #172 #187)
+#185 := (= #169 #184)
+#186 := [monotonicity #141]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [quant-intro #195]: #197
+#182 := (iff #45 #181)
+#179 := (iff #44 #178)
+#176 := (= #43 #175)
+#173 := (= #42 #172)
+#170 := (= #41 #169)
+#167 := (= #40 #164)
+#161 := (- #158)
+#165 := (= #161 #164)
+#166 := [rewrite]: #165
+#162 := (= #40 #161)
+#159 := (= #39 #158)
+#160 := [monotonicity #102 #105]: #159
+#163 := [monotonicity #160]: #162
+#168 := [trans #163 #166]: #167
+#171 := [monotonicity #99 #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#200 := [trans #183 #198]: #199
+#157 := [asserted]: #45
+#201 := [mp #157 #200]: #196
+#204 := [mp~ #201 #208]: #196
+#252 := [mp #204 #251]: #249
+#283 := [mp #252 #282]: #280
+#768 := [mp #283 #767]: #763
+#658 := (not #763)
+#655 := (or #658 #663)
+#596 := (mod #428 #427)
+#689 := (+ #12 #596)
+#686 := (= #689 0::Int)
+#671 := (ite #750 #679 #686)
+#670 := (ite #748 #668 #671)
+#680 := (= f3 #12)
+#681 := (ite #753 #680 #670)
+#659 := (or #658 #681)
+#640 := (iff #659 #655)
+#643 := (iff #655 #655)
+#644 := [rewrite]: #643
+#656 := (iff #681 #663)
+#666 := (ite false #680 #663)
+#653 := (iff #666 #663)
+#654 := [rewrite]: #653
+#662 := (iff #681 #666)
+#664 := (iff #670 #663)
+#660 := (iff #671 #676)
+#675 := (iff #686 #674)
+#672 := (= #689 #683)
+#682 := (= #596 #538)
+#678 := [monotonicity #447]: #682
+#673 := [monotonicity #678]: #672
+#669 := [monotonicity #673]: #675
+#661 := [monotonicity #724 #669]: #660
+#665 := [monotonicity #661]: #664
+#667 := [monotonicity #409 #665]: #662
+#657 := [trans #667 #654]: #656
+#642 := [monotonicity #657]: #640
+#645 := [trans #642 #644]: #640
+#639 := [quant-inst #8 #9]: #659
+#646 := [mp #639 #645]: #655
+#619 := [unit-resolution #646 #768]: #663
+#620 := (not #663)
+#625 := (or #620 #748 #676)
+#626 := [def-axiom]: #625
+#524 := [unit-resolution #626 #619]: #523
+#525 := [unit-resolution #524 #560]: #676
+#694 := (not #716)
+#652 := (not #676)
+#489 := (or #704 #652 #694)
+#650 := (>= #677 0::Int)
+#565 := [hypothesis]: #676
+#566 := [hypothesis]: #454
+#630 := (or #652 #704 #679)
+#631 := [def-axiom]: #630
+#567 := [unit-resolution #631 #566 #565]: #679
+#635 := (not #679)
+#491 := (or #635 #650)
+#493 := [th-lemma arith triangle-eq]: #491
+#494 := [unit-resolution #493 #567]: #650
+#537 := (>= #433 0::Int)
+#547 := [hypothesis]: #716
+#695 := (or #694 #704 #412)
+#693 := [def-axiom]: #695
+#548 := [unit-resolution #693 #566 #547]: #412
+#579 := (not #412)
+#492 := (or #579 #537)
+#495 := [th-lemma arith triangle-eq]: #492
+#477 := [unit-resolution #495 #548]: #537
+#81 := (* -1::Int #12)
+#79 := (* -3::Int #10)
+#82 := (+ #79 #81)
+#83 := (+ f3 #82)
+#341 := (<= #83 0::Int)
+#479 := (not #341)
+#426 := (>= #83 0::Int)
+#555 := (not #426)
+#571 := [hypothesis]: #555
+#531 := (or #748 #426)
+#552 := (or #704 #426 #652 #694)
+#649 := (<= #677 0::Int)
+#568 := (or #635 #649)
+#569 := [th-lemma arith triangle-eq]: #568
+#570 := [unit-resolution #569 #567]: #649
+#613 := (* -3::Int #432)
+#616 := (+ #613 #690)
+#617 := (+ f3 #616)
+#599 := (>= #617 0::Int)
+#612 := (= #617 0::Int)
+#1 := true
+#63 := [true-axiom]: true
+#532 := (or false #612)
+#533 := [th-lemma arith]: #532
+#540 := [unit-resolution #533 #63]: #612
+#542 := (not #612)
+#543 := (or #542 #599)
+#544 := [th-lemma arith triangle-eq]: #543
+#546 := [unit-resolution #544 #540]: #599
+#535 := (<= #433 0::Int)
+#549 := (or #579 #535)
+#550 := [th-lemma arith triangle-eq]: #549
+#551 := [unit-resolution #550 #548]: #535
+#534 := [th-lemma arith farkas 3 -1 1 1 #551 #546 #571 #570]: false
+#522 := [lemma #534]: #552
+#527 := [unit-resolution #522 #525 #571 #564]: #704
+#702 := (or #454 #743)
+#703 := [def-axiom]: #702
+#528 := [unit-resolution #703 #527]: #743
+#697 := (or #454 #747)
+#698 := [def-axiom]: #697
+#529 := [unit-resolution #698 #527]: #747
+#372 := (or #748 #375 #451)
+#530 := [th-lemma arith triangle-eq]: #372
+#526 := [unit-resolution #530 #529 #528 #560]: false
+#510 := [lemma #526]: #531
+#513 := [unit-resolution #510 #571]: #748
+#517 := (or #688 #747)
+#519 := [th-lemma arith triangle-eq]: #517
+#520 := [unit-resolution #519 #513]: #747
+#647 := (<= #12 0::Int)
+#518 := (or #688 #668)
+#621 := (or #620 #688 #668)
+#622 := [def-axiom]: #621
+#521 := [unit-resolution #622 #619]: #518
+#509 := [unit-resolution #521 #513]: #668
+#627 := (not #668)
+#512 := (or #627 #647)
+#514 := [th-lemma arith triangle-eq]: #512
+#515 := [unit-resolution #514 #509]: #647
+#700 := (<= #10 0::Int)
+#511 := (or #688 #752)
+#573 := (or #685 #688 #752)
+#588 := [def-axiom]: #573
+#516 := [unit-resolution #588 #561]: #511
+#506 := [unit-resolution #516 #513]: #752
+#584 := (not #752)
+#496 := (or #584 #700)
+#498 := [th-lemma arith triangle-eq]: #496
+#499 := [unit-resolution #498 #506]: #700
+#502 := [th-lemma arith farkas -3 -1 -1 1 #499 #515 #571 #520]: false
+#503 := [lemma #502]: #426
+#482 := (or #479 #555)
+#84 := (= #83 0::Int)
+#87 := (not #84)
+#11 := (* #10 3::Int)
+#13 := (+ #11 #12)
+#14 := (= f3 #13)
+#15 := (not #14)
+#90 := (iff #15 #87)
+#66 := (* 3::Int #10)
+#69 := (+ #66 #12)
+#72 := (= f3 #69)
+#75 := (not #72)
+#88 := (iff #75 #87)
+#85 := (iff #72 #84)
+#86 := [rewrite]: #85
#89 := [monotonicity #86]: #88
-#94 := [trans #89 #92]: #93
-#121 := [monotonicity #94 #118]: #120
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124]: #126
-#189 := [trans #127 #187]: #188
-#55 := [asserted]: #35
-#190 := [mp #55 #189]: #185
-#264 := (or #180 #262 #263)
-#265 := [th-lemma arith triangle-eq]: #264
-#267 := [unit-resolution #265 #190]: #266
-#268 := [unit-resolution #267 #261 #250]: false
-#269 := [lemma #268]: #152
-#310 := [hypothesis]: #10
-#311 := (or #207 #128)
-#312 := [th-lemma arith triangle-eq]: #311
-#313 := [unit-resolution #312 #310]: #128
-#314 := (or #207 #141)
-#286 := [th-lemma arith triangle-eq]: #314
-#319 := [unit-resolution #286 #310]: #141
-#201 := (or #200 #129 #142)
-#202 := [def-axiom]: #201
-#323 := [unit-resolution #202 #319 #313 #269]: false
-#350 := [lemma #323]: #207
-#222 := (or #10 #213)
-#223 := [def-axiom]: #222
-#359 := [unit-resolution #223 #350]: #213
-#214 := (= #27 #164)
-#216 := (or #200 #214)
-#217 := [def-axiom]: #216
-#326 := [unit-resolution #217 #269]: #214
-#360 := [trans #326 #359]: #320
-#328 := (not #320)
-#361 := (or #328 #358)
-#362 := [th-lemma arith triangle-eq]: #361
-#363 := [unit-resolution #362 #360]: #358
-#280 := (* -1::Int #27)
-#279 := (* -3::Int #20)
-#281 := (+ #279 #280)
-#282 := (+ f3 #281)
-#351 := (>= #282 0::Int)
-#278 := (= #282 0::Int)
-#53 := [true-axiom]: true
-#332 := (or false #278)
-#333 := [th-lemma arith]: #332
-#334 := [unit-resolution #333 #53]: #278
-#335 := (not #278)
-#364 := (or #335 #351)
-#365 := [th-lemma arith triangle-eq]: #364
-#366 := [unit-resolution #365 #334]: #351
-#348 := (or #10 #224)
-#322 := (<= #321 0::Int)
-#324 := [hypothesis]: #207
-#325 := [unit-resolution #223 #324]: #213
-#327 := [trans #326 #325]: #320
-#329 := (or #328 #322)
-#330 := [th-lemma arith triangle-eq]: #329
-#331 := [unit-resolution #330 #327]: #322
-#285 := (<= #282 0::Int)
-#336 := (or #335 #285)
-#337 := [th-lemma arith triangle-eq]: #336
-#338 := [unit-resolution #337 #334]: #285
-#339 := [hypothesis]: #262
-#316 := (* -1::Int #158)
-#317 := (+ #20 #316)
-#318 := (<= #317 0::Int)
-#315 := (= #20 #158)
-#197 := (= #155 #158)
-#210 := (or #10 #197)
-#211 := [def-axiom]: #210
-#340 := [unit-resolution #211 #324]: #197
-#198 := (= #20 #155)
-#203 := (or #200 #198)
-#204 := [def-axiom]: #203
-#341 := [unit-resolution #204 #269]: #198
-#342 := [trans #341 #340]: #315
-#343 := (not #315)
-#344 := (or #343 #318)
-#345 := [th-lemma arith triangle-eq]: #344
-#346 := [unit-resolution #345 #342]: #318
-#347 := [th-lemma arith farkas 3 -1 1 1 #346 #339 #338 #331]: false
-#349 := [lemma #347]: #348
-#367 := [unit-resolution #349 #350]: #224
-#368 := [unit-resolution #267 #367]: #263
-#357 := (>= #317 0::Int)
-#369 := [unit-resolution #211 #350]: #197
-#370 := [trans #341 #369]: #315
-#371 := (or #343 #357)
-#372 := [th-lemma arith triangle-eq]: #371
-#373 := [unit-resolution #372 #370]: #357
-[th-lemma arith farkas 3 -1 1 1 #373 #368 #366 #363]: false
+#76 := (iff #15 #75)
+#73 := (iff #14 #72)
+#70 := (= #13 #69)
+#67 := (= #11 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#77 := [monotonicity #74]: #76
+#91 := [trans #77 #89]: #90
+#65 := [asserted]: #15
+#92 := [mp #65 #91]: #87
+#480 := (or #84 #479 #555)
+#481 := [th-lemma arith triangle-eq]: #480
+#483 := [unit-resolution #481 #92]: #482
+#484 := [unit-resolution #483 #503]: #479
+#507 := (<= #617 0::Int)
+#485 := (or #542 #507)
+#486 := [th-lemma arith triangle-eq]: #485
+#487 := [unit-resolution #486 #540]: #507
+#488 := [th-lemma arith farkas -1 1 3 1 #487 #484 #477 #494]: false
+#478 := [lemma #488]: #489
+#500 := [unit-resolution #478 #525 #564]: #704
+#508 := [unit-resolution #703 #500]: #743
+#501 := [unit-resolution #698 #500]: #747
+#504 := [unit-resolution #530 #501 #508 #560]: false
+#505 := [lemma #504]: #748
+#490 := [unit-resolution #516 #505]: #752
+#467 := (or #584 #701)
+#469 := [th-lemma arith triangle-eq]: #467
+#470 := [unit-resolution #469 #490]: #701
+#648 := (>= #12 0::Int)
+#471 := [unit-resolution #521 #505]: #668
+#472 := (or #627 #648)
+#473 := [th-lemma arith triangle-eq]: #472
+#474 := [unit-resolution #473 #471]: #648
+#475 := (or #688 #743)
+#468 := [th-lemma arith triangle-eq]: #475
+#476 := [unit-resolution #468 #505]: #743
+[th-lemma arith farkas -1/3 1/3 1/3 1 #476 #474 #484 #470]: false
unsat
cacbb4776a876130daed2cf13657b41ab1c7df25 75 0
#2 := false