# HG changeset patch # User boehmes # Date 1292833907 -3600 # Node ID 939f647f0c9eae3b5797e14a69e79d2669808e63 # Parent 0485186839a7b71f61313bb1b8fb4b61b820e384 updated SMT certificates diff -r 0485186839a7 -r 939f647f0c9e src/HOL/Boogie/Examples/VCC_Max.certs --- 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) +#13213 := (and #12224 #13208) +#13219 := (not #3121) +#13220 := (or #13219 #13213) +#13225 := (and #3121 #13220) +#12206 := (and #3116 #3117) +#12209 := (and #3116 #12206) +#13231 := (not #12209) +#13232 := (or #13231 #13225) #13241 := (or #13240 #13232) -#13246 := (and #12156 #13241) -#13253 := (or #13252 #13246) -#13258 := (and #12150 #13253) -#13265 := (or #13264 #13258) -#13270 := (and #12141 #13265) -#13276 := (not #3094) -#13277 := (or #13276 #13270) -#13286 := (or #13285 #13277) -#13295 := (or #13294 #13286) -#13304 := (or #13303 #13295) -#13313 := (or #13312 #13304) -#13321 := (not #3075) +#13250 := (or #13249 #13241) +#13259 := (or #13258 #13250) +#13268 := (or #13267 #13259) +#13277 := (or #13276 #13268) +#13282 := (and #12192 #13277) +#13289 := (or #13288 #13282) +#13294 := (and #12186 #13289) +#13301 := (or #13300 #13294) +#13306 := (and #12177 #13301) +#13312 := (not #3094) +#13313 := (or #13312 #13306) #13322 := (or #13321 #13313) #13331 := (or #13330 #13322) #13340 := (or #13339 #13331) -#12088 := (and #12082 #12085) -#12091 := (and #12076 #12088) -#12094 := (and #12073 #12091) -#12097 := (and #12070 #12094) -#12100 := (and #12066 #12097) -#13348 := (not #12100) #13349 := (or #13348 #13340) -#13357 := (not #3038) +#13357 := (not #3075) #13358 := (or #13357 #13349) -#13366 := (not #3037) #13367 := (or #13366 #13358) -#13375 := (not #3035) #13376 := (or #13375 #13367) -#13384 := (not #3031) +#12124 := (and #12118 #12121) +#12127 := (and #12112 #12124) +#12130 := (and #12109 #12127) +#12133 := (and #12106 #12130) +#12136 := (and #12102 #12133) +#13384 := (not #12136) #13385 := (or #13384 #13376) -#13393 := (not #3027) +#13393 := (not #3038) #13394 := (or #13393 #13385) -#13399 := (not #13394) -#14306 := (iff #13399 #14305) -#14303 := (iff #13394 #14300) -#14258 := (or #13413 #14177) -#14261 := (or #13285 #14258) -#14264 := (or #13294 #14261) -#14267 := (or #13303 #14264) -#14270 := (or #13312 #14267) -#14273 := (or #14189 #14270) -#14276 := (or #13330 #14273) -#14279 := (or #13339 #14276) -#14282 := (or #14195 #14279) -#14285 := (or #13472 #14282) -#14288 := (or #14205 #14285) -#14291 := (or #14227 #14288) -#14294 := (or #14241 #14291) -#14297 := (or #14255 #14294) -#14301 := (iff #14297 #14300) -#14302 := [rewrite]: #14301 -#14298 := (iff #13394 #14297) -#14295 := (iff #13385 #14294) -#14292 := (iff #13376 #14291) -#14289 := (iff #13367 #14288) -#14286 := (iff #13358 #14285) -#14283 := (iff #13349 #14282) -#14280 := (iff #13340 #14279) -#14277 := (iff #13331 #14276) -#14274 := (iff #13322 #14273) -#14271 := (iff #13313 #14270) -#14268 := (iff #13304 #14267) -#14265 := (iff #13295 #14264) -#14262 := (iff #13286 #14261) -#14259 := (iff #13277 #14258) -#14178 := (iff #13270 #14177) -#14175 := (iff #13265 #14174) -#14172 := (iff #13258 #14169) -#14166 := (and #12150 #14163) -#14170 := (iff #14166 #14169) -#14171 := [rewrite]: #14170 -#14167 := (iff #13258 #14166) -#14164 := (iff #13253 #14163) -#14161 := (iff #13246 #14158) -#14155 := (and #12156 #14150) -#14159 := (iff #14155 #14158) -#14160 := [rewrite]: #14159 -#14156 := (iff #13246 #14155) -#14153 := (iff #13241 #14150) -#14132 := (or false #14129) -#14135 := (or #13204 #14132) -#14138 := (or #13213 #14135) -#14141 := (or #13222 #14138) -#14144 := (or #13231 #14141) -#14147 := (or #13240 #14144) -#14151 := (iff #14147 #14150) -#14152 := [rewrite]: #14151 -#14148 := (iff #13241 #14147) -#14145 := (iff #13232 #14144) -#14142 := (iff #13223 #14141) -#14139 := (iff #13214 #14138) -#14136 := (iff #13205 #14135) -#14133 := (iff #13196 #14132) -#14130 := (iff #13189 #14129) -#14127 := (iff #13184 #14126) -#14124 := (iff #13177 #14123) -#14121 := (iff #13172 #14120) -#14118 := (iff #13165 #14115) -#14033 := (and #13473 #3109) -#14112 := (and #14033 #14107) -#14116 := (iff #14112 #14115) -#14117 := [rewrite]: #14116 -#14113 := (iff #13165 #14112) -#14110 := (iff #13160 #14107) -#14044 := (or #13485 #13914) -#14047 := (or #12988 #14044) -#14050 := (or #12997 #14047) -#14053 := (or #13006 #14050) -#14056 := (or #13015 #14053) -#14059 := (or #13024 #14056) -#14062 := (or #12366 #14059) -#14065 := (or #13938 #14062) -#14068 := (or #13938 #14065) -#14071 := (or #13485 #14068) -#14074 := (or #13485 #14071) -#14077 := (or #13485 #14074) -#14080 := (or #13485 #14077) -#14083 := (or #13955 #14080) -#14086 := (or #13989 #14083) -#14089 := (or #13995 #14086) -#14092 := (or #13485 #14089) -#14095 := (or #14007 #14092) -#14098 := (or #14017 #14095) -#14101 := (or #14030 #14098) -#14104 := (or #14041 #14101) -#14108 := (iff #14104 #14107) -#14109 := [rewrite]: #14108 -#14105 := (iff #13160 #14104) -#14102 := (iff #13151 #14101) -#14099 := (iff #13142 #14098) -#14096 := (iff #13133 #14095) -#14093 := (iff #13124 #14092) -#14090 := (iff #13116 #14089) -#14087 := (iff #13107 #14086) -#14084 := (iff #13098 #14083) -#14081 := (iff #13089 #14080) -#14078 := (iff #13074 #14077) -#14075 := (iff #13066 #14074) -#14072 := (iff #13058 #14071) -#14069 := (iff #13050 #14068) -#14066 := (iff #13042 #14065) -#14063 := (iff #13033 #14062) -#14060 := (iff #13025 #14059) -#14057 := (iff #13016 #14056) -#14054 := (iff #13007 #14053) -#14051 := (iff #12998 #14050) -#14048 := (iff #12989 #14047) -#14045 := (iff #12973 #14044) -#13915 := (iff #12967 #13914) -#13912 := (iff #12962 #13909) -#13891 := (or #13485 #13884) -#13894 := (or #13485 #13891) -#13897 := (or #13485 #13894) -#13900 := (or #13485 #13897) -#13903 := (or #13766 #13900) -#13906 := (or #13485 #13903) -#13910 := (iff #13906 #13909) -#13911 := [rewrite]: #13910 -#13907 := (iff #12962 #13906) -#13904 := (iff #12954 #13903) -#13901 := (iff #12945 #13900) -#13898 := (iff #12937 #13897) -#13895 := (iff #12358 #13894) -#13892 := (iff #12350 #13891) -#13885 := (iff #12344 #13884) -#13882 := (iff #12339 #13879) -#13855 := (or #12277 #13852) -#13858 := (or #12286 #13855) -#13861 := (or #12295 #13858) -#13864 := (or #12304 #13861) -#13867 := (or #13485 #13864) -#13870 := (or #13485 #13867) -#13873 := (or #13485 #13870) -#13876 := (or #12338 #13873) -#13880 := (iff #13876 #13879) -#13881 := [rewrite]: #13880 -#13877 := (iff #12339 #13876) -#13874 := (iff #12330 #13873) -#13871 := (iff #12322 #13870) -#13868 := (iff #12314 #13867) -#13865 := (iff #12305 #13864) -#13862 := (iff #12296 #13861) -#13859 := (iff #12287 #13858) -#13856 := (iff #12278 #13855) -#13853 := (iff #12271 #13852) -#13850 := (iff #12266 #13847) -#13844 := (or #13838 #13841) -#13848 := (iff #13844 #13847) -#13849 := [rewrite]: #13848 -#13845 := (iff #12266 #13844) -#13842 := (iff #12265 #13841) -#13822 := (iff #12257 #13821) -#13819 := (iff #12252 #13816) -#13810 := (or #13793 #13807) -#13813 := (or #5712 #13810) -#13817 := (iff #13813 #13816) -#13818 := [rewrite]: #13817 -#13814 := (iff #12252 #13813) -#13811 := (iff #12246 #13810) -#13808 := (iff #3169 #13807) -#13809 := [rewrite]: #13808 -#13803 := (iff #12245 #13793) -#13798 := (not #13795) -#13801 := (iff #13798 #13793) -#13802 := [rewrite]: #13801 -#13799 := (iff #12245 #13798) -#13796 := (iff #3168 #13795) -#13797 := [rewrite]: #13796 -#13800 := [monotonicity #13797]: #13799 -#13804 := [trans #13800 #13802]: #13803 -#13812 := [monotonicity #13804 #13809]: #13811 -#5713 := (iff #5703 #5712) -#4504 := (iff #455 #4503) -#4497 := (iff #454 #4496) -#4498 := [rewrite]: #4497 +#13402 := (not #3037) +#13403 := (or #13402 #13394) +#13411 := (not #3035) +#13412 := (or #13411 #13403) +#13420 := (not #3031) +#13421 := (or #13420 #13412) +#13429 := (not #3027) +#13430 := (or #13429 #13421) +#13435 := (not #13430) +#14342 := (iff #13435 #14341) +#14339 := (iff #13430 #14336) +#14294 := (or #13449 #14213) +#14297 := (or #13321 #14294) +#14300 := (or #13330 #14297) +#14303 := (or #13339 #14300) +#14306 := (or #13348 #14303) +#14309 := (or #14225 #14306) +#14312 := (or #13366 #14309) +#14315 := (or #13375 #14312) +#14318 := (or #14231 #14315) +#14321 := (or #13508 #14318) +#14324 := (or #14241 #14321) +#14327 := (or #14263 #14324) +#14330 := (or #14277 #14327) +#14333 := (or #14291 #14330) +#14337 := (iff #14333 #14336) +#14338 := [rewrite]: #14337 +#14334 := (iff #13430 #14333) +#14331 := (iff #13421 #14330) +#14328 := (iff #13412 #14327) +#14325 := (iff #13403 #14324) +#14322 := (iff #13394 #14321) +#14319 := (iff #13385 #14318) +#14316 := (iff #13376 #14315) +#14313 := (iff #13367 #14312) +#14310 := (iff #13358 #14309) +#14307 := (iff #13349 #14306) +#14304 := (iff #13340 #14303) +#14301 := (iff #13331 #14300) +#14298 := (iff #13322 #14297) +#14295 := (iff #13313 #14294) +#14214 := (iff #13306 #14213) +#14211 := (iff #13301 #14210) +#14208 := (iff #13294 #14205) +#14202 := (and #12186 #14199) +#14206 := (iff #14202 #14205) +#14207 := [rewrite]: #14206 +#14203 := (iff #13294 #14202) +#14200 := (iff #13289 #14199) +#14197 := (iff #13282 #14194) +#14191 := (and #12192 #14186) +#14195 := (iff #14191 #14194) +#14196 := [rewrite]: #14195 +#14192 := (iff #13282 #14191) +#14189 := (iff #13277 #14186) +#14168 := (or false #14165) +#14171 := (or #13240 #14168) +#14174 := (or #13249 #14171) +#14177 := (or #13258 #14174) +#14180 := (or #13267 #14177) +#14183 := (or #13276 #14180) +#14187 := (iff #14183 #14186) +#14188 := [rewrite]: #14187 +#14184 := (iff #13277 #14183) +#14181 := (iff #13268 #14180) +#14178 := (iff #13259 #14177) +#14175 := (iff #13250 #14174) +#14172 := (iff #13241 #14171) +#14169 := (iff #13232 #14168) +#14166 := (iff #13225 #14165) +#14163 := (iff #13220 #14162) +#14160 := (iff #13213 #14159) +#14157 := (iff #13208 #14156) +#14154 := (iff #13201 #14151) +#14069 := (and #13509 #3109) +#14148 := (and #14069 #14143) +#14152 := (iff #14148 #14151) +#14153 := [rewrite]: #14152 +#14149 := (iff #13201 #14148) +#14146 := (iff #13196 #14143) +#14080 := (or #13521 #13950) +#14083 := (or #13024 #14080) +#14086 := (or #13033 #14083) +#14089 := (or #13042 #14086) +#14092 := (or #13051 #14089) +#14095 := (or #13060 #14092) +#14098 := (or #12402 #14095) +#14101 := (or #13974 #14098) +#14104 := (or #13974 #14101) +#14107 := (or #13521 #14104) +#14110 := (or #13521 #14107) +#14113 := (or #13521 #14110) +#14116 := (or #13521 #14113) +#14119 := (or #13991 #14116) +#14122 := (or #14025 #14119) +#14125 := (or #14031 #14122) +#14128 := (or #13521 #14125) +#14131 := (or #14043 #14128) +#14134 := (or #14053 #14131) +#14137 := (or #14066 #14134) +#14140 := (or #14077 #14137) +#14144 := (iff #14140 #14143) +#14145 := [rewrite]: #14144 +#14141 := (iff #13196 #14140) +#14138 := (iff #13187 #14137) +#14135 := (iff #13178 #14134) +#14132 := (iff #13169 #14131) +#14129 := (iff #13160 #14128) +#14126 := (iff #13152 #14125) +#14123 := (iff #13143 #14122) +#14120 := (iff #13134 #14119) +#14117 := (iff #13125 #14116) +#14114 := (iff #13110 #14113) +#14111 := (iff #13102 #14110) +#14108 := (iff #13094 #14107) +#14105 := (iff #13086 #14104) +#14102 := (iff #13078 #14101) +#14099 := (iff #13069 #14098) +#14096 := (iff #13061 #14095) +#14093 := (iff #13052 #14092) +#14090 := (iff #13043 #14089) +#14087 := (iff #13034 #14086) +#14084 := (iff #13025 #14083) +#14081 := (iff #13009 #14080) +#13951 := (iff #13003 #13950) +#13948 := (iff #12998 #13945) +#13927 := (or #13521 #13920) +#13930 := (or #13521 #13927) +#13933 := (or #13521 #13930) +#13936 := (or #13521 #13933) +#13939 := (or #13802 #13936) +#13942 := (or #13521 #13939) +#13946 := (iff #13942 #13945) +#13947 := [rewrite]: #13946 +#13943 := (iff #12998 #13942) +#13940 := (iff #12990 #13939) +#13937 := (iff #12981 #13936) +#13934 := (iff #12973 #13933) +#13931 := (iff #12394 #13930) +#13928 := (iff #12386 #13927) +#13921 := (iff #12380 #13920) +#13918 := (iff #12375 #13915) +#13891 := (or #12313 #13888) +#13894 := (or #12322 #13891) +#13897 := (or #12331 #13894) +#13900 := (or #12340 #13897) +#13903 := (or #13521 #13900) +#13906 := (or #13521 #13903) +#13909 := (or #13521 #13906) +#13912 := (or #12374 #13909) +#13916 := (iff #13912 #13915) +#13917 := [rewrite]: #13916 +#13913 := (iff #12375 #13912) +#13910 := (iff #12366 #13909) +#13907 := (iff #12358 #13906) +#13904 := (iff #12350 #13903) +#13901 := (iff #12341 #13900) +#13898 := (iff #12332 #13897) +#13895 := (iff #12323 #13894) +#13892 := (iff #12314 #13891) +#13889 := (iff #12307 #13888) +#13886 := (iff #12302 #13883) +#13880 := (or #13874 #13877) +#13884 := (iff #13880 #13883) +#13885 := [rewrite]: #13884 +#13881 := (iff #12302 #13880) +#13878 := (iff #12301 #13877) +#13858 := (iff #12293 #13857) +#13855 := (iff #12288 #13852) +#13846 := (or #13829 #13843) +#13849 := (or #5738 #13846) +#13853 := (iff #13849 #13852) +#13854 := [rewrite]: #13853 +#13850 := (iff #12288 #13849) +#13847 := (iff #12282 #13846) +#13844 := (iff #3169 #13843) +#13845 := [rewrite]: #13844 +#13839 := (iff #12281 #13829) +#13834 := (not #13831) +#13837 := (iff #13834 #13829) +#13838 := [rewrite]: #13837 +#13835 := (iff #12281 #13834) +#13832 := (iff #3168 #13831) +#13833 := [rewrite]: #13832 +#13836 := [monotonicity #13833]: #13835 +#13840 := [trans #13836 #13838]: #13839 +#13848 := [monotonicity #13840 #13845]: #13847 +#5739 := (iff #5729 #5738) +#4524 := (iff #455 #4523) +#4517 := (iff #454 #4516) +#4518 := [rewrite]: #4517 #4200 := (iff #327 #4202) #4201 := [rewrite]: #4200 -#4505 := [monotonicity #4201 #4498]: #4504 -#5714 := [monotonicity #4505]: #5713 -#13815 := [monotonicity #5714 #13812]: #13814 -#13820 := [trans #13815 #13818]: #13819 -#13823 := [quant-intro #13820]: #13822 -#13843 := [monotonicity #13823]: #13842 -#13839 := (iff #3177 #13838) -#13836 := (iff #3176 #13833) -#13824 := (and #13795 #3173) -#13827 := (and #4496 #13824) -#13830 := (and #4202 #13827) -#13834 := (iff #13830 #13833) -#13835 := [rewrite]: #13834 -#13831 := (iff #3176 #13830) -#13828 := (iff #3175 #13827) -#13825 := (iff #3174 #13824) -#13826 := [monotonicity #13797]: #13825 -#13829 := [monotonicity #4498 #13826]: #13828 -#13832 := [monotonicity #4201 #13829]: #13831 -#13837 := [trans #13832 #13835]: #13836 -#13840 := [quant-intro #13837]: #13839 -#13846 := [monotonicity #13840 #13843]: #13845 -#13851 := [trans #13846 #13849]: #13850 -#13854 := [monotonicity #13823 #13851]: #13853 -#13857 := [monotonicity #13854]: #13856 -#13860 := [monotonicity #13857]: #13859 -#13863 := [monotonicity #13860]: #13862 -#13866 := [monotonicity #13863]: #13865 -#13486 := (iff #12313 #13485) -#13483 := (iff #12196 #13482) -#13479 := (iff #3143 #13480) -#13481 := [rewrite]: #13479 -#13476 := (iff #3136 #13477) -#13478 := [rewrite]: #13476 -#13484 := [monotonicity #13478 #13481]: #13483 -#13487 := [monotonicity #13484]: #13486 -#13869 := [monotonicity #13487 #13866]: #13868 -#13872 := [monotonicity #13487 #13869]: #13871 -#13875 := [monotonicity #13487 #13872]: #13874 -#13878 := [monotonicity #13875]: #13877 -#13883 := [trans #13878 #13881]: #13882 -#13886 := [monotonicity #13883]: #13885 -#13893 := [monotonicity #13487 #13886]: #13892 -#13896 := [monotonicity #13487 #13893]: #13895 -#13899 := [monotonicity #13487 #13896]: #13898 -#13902 := [monotonicity #13487 #13899]: #13901 -#13889 := (iff #12953 #13766) -#13887 := (iff #3347 #13765) -#13888 := [rewrite]: #13887 -#13890 := [monotonicity #13888]: #13889 -#13905 := [monotonicity #13890 #13902]: #13904 -#13908 := [monotonicity #13487 #13905]: #13907 -#13913 := [trans #13908 #13911]: #13912 -#13791 := (iff #12929 #13788) -#13776 := (or #13485 #13759) -#13779 := (or #13485 #13776) -#13782 := (or #13765 #13779) -#13785 := (or #13485 #13782) -#13789 := (iff #13785 #13788) -#13790 := [rewrite]: #13789 -#13786 := (iff #12929 #13785) -#13783 := (iff #12921 #13782) -#13780 := (iff #12912 #13779) -#13777 := (iff #12904 #13776) -#13762 := (iff #12898 #13759) -#13756 := (and #12545 #13753) -#13760 := (iff #13756 #13759) -#13761 := [rewrite]: #13760 -#13757 := (iff #12898 #13756) -#13754 := (iff #12893 #13753) -#13751 := (iff #12887 #13748) -#13745 := (and #12551 #13740) -#13749 := (iff #13745 #13748) -#13750 := [rewrite]: #13749 -#13746 := (iff #12887 #13745) -#13743 := (iff #12882 #13740) -#13734 := (or #13485 #13731) -#13737 := (or #12749 #13734) -#13741 := (iff #13737 #13740) -#13742 := [rewrite]: #13741 -#13738 := (iff #12882 #13737) -#13735 := (iff #12874 #13734) -#13732 := (iff #12868 #13731) -#13729 := (iff #12863 #13726) -#13623 := (or #13494 #13615) -#13705 := (or #13623 #12812) -#13708 := (or #12821 #13705) -#13711 := (or #13485 #13708) -#13714 := (or #13485 #13711) -#13717 := (or #13485 #13714) -#13720 := (or #13671 #13717) -#13723 := (or #13485 #13720) -#13727 := (iff #13723 #13726) -#13728 := [rewrite]: #13727 -#13724 := (iff #12863 #13723) -#13721 := (iff #12855 #13720) -#13718 := (iff #12846 #13717) -#13715 := (iff #12838 #13714) -#13712 := (iff #12830 #13711) -#13709 := (iff #12822 #13708) -#13706 := (iff #12813 #13705) -#13624 := (iff #12687 #13623) -#13618 := (iff #12680 #13615) -#13612 := (and #13589 #13607) -#13616 := (iff #13612 #13615) -#13617 := [rewrite]: #13616 -#13613 := (iff #12680 #13612) -#13610 := (iff #12675 #13607) -#13595 := (or #13511 #13579) -#13598 := (or #12656 #13595) -#13601 := (or #13586 #13598) -#13604 := (or #13592 #13601) -#13608 := (iff #13604 #13607) -#13609 := [rewrite]: #13608 -#13605 := (iff #12675 #13604) -#13602 := (iff #12666 #13601) -#13599 := (iff #12657 #13598) -#13596 := (iff #12648 #13595) -#13580 := (iff #12641 #13579) -#13577 := (iff #12636 #13576) -#13574 := (iff #12629 #13573) -#13571 := (iff #12624 #13570) -#13568 := (iff #12610 #13565) -#13562 := (and #13559 #12607) -#13566 := (iff #13562 #13565) -#13567 := [rewrite]: #13566 -#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 +#12987 := (iff #3350 #12986) +#12984 := (iff #3349 #12981) +#12978 := (implies #12232 #12973) +#12982 := (iff #12978 #12981) +#12983 := [rewrite]: #12982 +#12979 := (iff #3349 #12978) +#12976 := (iff #3348 #12973) +#12970 := (implies #12232 #12394) #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) +#12395 := (iff #12391 #12394) +#12396 := [rewrite]: #12395 +#12392 := (iff #3191 #12391) +#12389 := (iff #3190 #12386) +#12383 := (implies #12232 #12380) +#12387 := (iff #12383 #12386) +#12388 := [rewrite]: #12387 +#12384 := (iff #3190 #12383) +#12381 := (iff #3189 #12380) +#12378 := (iff #3188 #12375) +#12371 := (implies #10960 #12366) +#12376 := (iff #12371 #12375) +#12377 := [rewrite]: #12376 +#12372 := (iff #3188 #12371) +#12369 := (iff #3187 #12366) +#12363 := (implies #12232 #12358) +#12367 := (iff #12363 #12366) +#12368 := [rewrite]: #12367 +#12364 := (iff #3187 #12363) +#12361 := (iff #3186 #12358) +#12355 := (implies #12232 #12350) #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) -#23486 := (iff #22566 #23485) -#23483 := (iff #22560 #23482) -#23480 := (iff #22531 #23479) -#23477 := (iff #22530 #23476) -#23474 := (iff #22529 #23473) -#23471 := (iff #22522 #23468) -#23469 := (iff #22511 #22511) -#23470 := [refl]: #23469 -#23472 := [quant-intro #23470]: #23471 -#23475 := [monotonicity #23472]: #23474 -#23466 := (iff #22528 #23465) -#23463 := (iff #22507 #23460) -#23461 := (iff #22502 #22502) -#23462 := [refl]: #23461 -#23464 := [quant-intro #23462]: #23463 -#23467 := [monotonicity #23464]: #23466 -#23478 := [monotonicity #23467 #23475]: #23477 -#23481 := [monotonicity #23478]: #23480 -#23484 := [monotonicity #23481]: #23483 -#23487 := [monotonicity #23484]: #23486 -#23490 := [monotonicity #23487]: #23489 -#23493 := [monotonicity #23490]: #23492 -#23458 := (iff #22494 #23457) -#23455 := (iff #22493 #23454) -#23452 := (iff #22492 #23451) -#23449 := (iff #22486 #23448) -#23446 := (iff #22481 #23445) -#23443 := (iff #22480 #23442) -#23440 := (iff #22479 #23439) -#23437 := (iff #22473 #23436) -#23434 := (iff #22468 #23433) -#23431 := (iff #22467 #23430) -#23428 := (iff #22466 #23427) -#23425 := (iff #22460 #23424) -#23422 := (iff #22455 #23421) -#23419 := (iff #22454 #23418) -#23386 := (iff #22417 #23385) -#23383 := (iff #22411 #23382) -#23380 := (iff #22406 #23379) -#23377 := (iff #22405 #23376) -#23374 := (iff #22404 #23373) -#23371 := (iff #22396 #23370) -#23368 := (iff #22391 #23367) -#23365 := (iff #22390 #23364) -#23362 := (iff #22389 #23361) -#23359 := (iff #22383 #23358) -#23356 := (iff #22354 #23355) -#23353 := (iff #22353 #23352) -#23350 := (iff #22352 #23349) -#23347 := (iff #22346 #23344) -#23345 := (iff #22341 #22341) -#23346 := [refl]: #23345 -#23348 := [quant-intro #23346]: #23347 -#23351 := [monotonicity #23348]: #23350 -#23354 := [monotonicity #23351]: #23353 -#23357 := [monotonicity #23354]: #23356 -#23360 := [monotonicity #23357]: #23359 -#23363 := [monotonicity #23360]: #23362 -#23366 := [monotonicity #23363]: #23365 -#23369 := [monotonicity #23366]: #23368 -#23372 := [monotonicity #23369]: #23371 -#23375 := [monotonicity #23372]: #23374 -#23378 := [monotonicity #23375]: #23377 -#23381 := [monotonicity #23378]: #23380 -#23384 := [monotonicity #23381]: #23383 -#23387 := [monotonicity #23384]: #23386 -#23420 := [monotonicity #23387]: #23419 -#23423 := [monotonicity #23420]: #23422 -#23416 := (iff #22446 #23415) -#23413 := (iff #22445 #23412) -#23410 := (iff #22444 #23409) -#23407 := (iff #22437 #23406) -#23404 := (iff #22432 #23403) -#23401 := (iff #22431 #23400) -#23398 := (iff #22430 #23397) -#23395 := (iff #22424 #23394) -#23392 := (iff #22419 #23391) -#23389 := (iff #22418 #23388) -#23390 := [monotonicity #23387]: #23389 -#23393 := [monotonicity #23390]: #23392 -#23396 := [monotonicity #23393]: #23395 -#23399 := [monotonicity #23396]: #23398 -#23402 := [monotonicity #23399]: #23401 -#23405 := [monotonicity #23402]: #23404 -#23408 := [monotonicity #23405]: #23407 -#23411 := [monotonicity #23408]: #23410 -#23414 := [monotonicity #23411]: #23413 -#23417 := [monotonicity #23414]: #23416 -#23426 := [monotonicity #23417 #23423]: #23425 -#23429 := [monotonicity #23426]: #23428 -#23432 := [monotonicity #23429]: #23431 -#23435 := [monotonicity #23432]: #23434 -#23438 := [monotonicity #23435]: #23437 -#23441 := [monotonicity #23438]: #23440 -#23444 := [monotonicity #23441]: #23443 -#23447 := [monotonicity #23444]: #23446 -#23450 := [monotonicity #23447]: #23449 -#23453 := [monotonicity #23450]: #23452 -#23456 := [monotonicity #23453]: #23455 -#23459 := [monotonicity #23456]: #23458 -#23496 := [monotonicity #23459 #23493]: #23495 -#23499 := [monotonicity #23496]: #23498 -#23342 := (iff #22584 #23341) -#23339 := (iff #22323 #23336) -#23337 := (iff #22318 #22318) -#23338 := [refl]: #23337 -#23340 := [quant-intro #23338]: #23339 -#23343 := [monotonicity #23340]: #23342 -#23502 := [monotonicity #23343 #23499]: #23501 -#23505 := [monotonicity #23502]: #23504 -#23508 := [monotonicity #23505]: #23507 -#23511 := [monotonicity #23508]: #23510 -#23334 := (iff #22601 #23333) -#23331 := (iff #22312 #23328) -#23329 := (iff #22307 #22307) -#23330 := [refl]: #23329 -#23332 := [quant-intro #23330]: #23331 -#23335 := [monotonicity #23332]: #23334 -#23514 := [monotonicity #23335 #23511]: #23513 -#23517 := [monotonicity #23514]: #23516 -#23520 := [monotonicity #23517]: #23519 -#23523 := [monotonicity #23520]: #23522 -#23526 := [monotonicity #23523]: #23525 -#23529 := [monotonicity #23526]: #23528 -#23532 := [monotonicity #23529]: #23531 -#23535 := [monotonicity #23532]: #23534 -#23538 := [monotonicity #23535]: #23537 -#23541 := [monotonicity #23538]: #23540 -#23544 := [monotonicity #23541]: #23543 -#23547 := [monotonicity #23544]: #23546 -#23550 := [monotonicity #23547]: #23549 -#23553 := [monotonicity #23550]: #23552 -#23556 := [monotonicity #23553]: #23555 -#23559 := [monotonicity #23556]: #23558 -#23562 := [monotonicity #23559]: #23561 -#23565 := [monotonicity #23562]: #23564 -#23568 := [monotonicity #23565]: #23567 -#19060 := (and #18703 #18704) -#19063 := (not #19060) -#19066 := (or #19042 #19055 #19063) -#19069 := (not #19066) -#15985 := (and #3173 #4202 #13795 #15183) -#18726 := (not #15985) -#18729 := (forall (vars (?v0 Int)) #18726) -#14426 := (and #4202 #15183) -#14425 := (not #14426) -#15971 := (or #13793 #13807 #14425) -#15976 := (forall (vars (?v0 Int)) #15971) -#18733 := (and #15976 #18729) -#19075 := (or #18733 #19069) -#19083 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #19075) -#18912 := (and #18579 #18580) -#18915 := (not #18912) -#18918 := (or #18894 #18907 #18915) -#18921 := (not #18918) -#15872 := (or #13522 #13536 #14425) -#15877 := (forall (vars (?v0 Int)) #15872) -#18595 := (not #13565) -#18605 := (and #18595 #15877) -#18927 := (or #18605 #18921) -#18932 := (and #13514 #18927) -#18935 := (or #13519 #18932) -#18943 := (and #12586 #13489 #13498 #13506 #13582 #15864 #18935) -#18948 := (or #18558 #18561 #18943) -#18988 := (and #12803 #12806 #13477 #13480 #13489 #13672 #18948) -#18954 := (and #12539 #12548 #12554 #12557 #12560 #12565 #12568 #13480 #13489 #18948) -#18959 := (or #18520 #18529 #18954) -#18965 := (and #12539 #12542 #18959) -#18970 := (or #18520 #18523 #18965) -#18976 := (and #13477 #13480 #13671 #18970) -#18993 := (or #18976 #18988) -#18999 := (and #12539 #12548 #13477 #13480 #18993) -#19004 := (or #18520 #18529 #18999) -#19010 := (and #12539 #12542 #19004) -#19015 := (or #18520 #18523 #19010) -#19021 := (and #13477 #13480 #13766 #19015) -#19088 := (or #19021 #19083) -#15798 := (or #13958 #13972 #14425) -#15803 := (forall (vars (?v0 Int)) #15798) -#19094 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #15803 #15815 #15832 #15849 #19088) -#19099 := (or #13231 #13472 #19094) -#15784 := (or #13439 #13451 #14425) -#15789 := (forall (vars (?v0 Int)) #15784) -#19102 := (and #15789 #19099) -#18815 := (and #18442 #18443) -#18818 := (not #18815) -#18824 := (or #18450 #18451 #18818) -#18829 := (not #18824) -#19105 := (or #18829 #19102) -#19108 := (and #13433 #19105) -#19111 := (or #13436 #19108) -#19117 := (and #3109 #12144 #12153 #12159 #12162 #12165 #19111) -#19122 := (or #18409 #18418 #19117) -#19128 := (and #12144 #12147 #19122) -#19133 := (or #18409 #18412 #19128) -#19136 := (and #12141 #19133) -#19139 := (or #13264 #19136) -#22662 := (iff #19139 #22661) -#22659 := (iff #19136 #22656) -#22651 := (and #12141 #22648) -#22657 := (iff #22651 #22656) -#22658 := [rewrite]: #22657 -#22652 := (iff #19136 #22651) -#22649 := (iff #19133 #22648) -#22646 := (iff #19128 #22643) -#22638 := (and #12144 #12147 #22635) -#22644 := (iff #22638 #22643) -#22645 := [rewrite]: #22644 -#22639 := (iff #19128 #22638) -#22636 := (iff #19122 #22635) -#22633 := (iff #19117 #22630) -#22625 := (and #3109 #12144 #12153 #12159 #12162 #12165 #22622) -#22631 := (iff #22625 #22630) -#22632 := [rewrite]: #22631 -#22626 := (iff #19117 #22625) -#22623 := (iff #19111 #22622) -#22620 := (iff #19108 #22617) -#22612 := (and #13433 #22609) -#22618 := (iff #22612 #22617) -#22619 := [rewrite]: #22618 -#22613 := (iff #19108 #22612) -#22610 := (iff #19105 #22609) -#22607 := (iff #19102 #22604) -#22598 := (and #22312 #22595) -#22605 := (iff #22598 #22604) -#22606 := [rewrite]: #22605 -#22599 := (iff #19102 #22598) -#22596 := (iff #19099 #22595) -#22593 := (iff #19094 #22590) -#22576 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #22323 #15815 #15832 #15849 #22573) -#22591 := (iff #22576 #22590) -#22592 := [rewrite]: #22591 -#22577 := (iff #19094 #22576) -#22574 := (iff #19088 #22573) -#22571 := (iff #19083 #22568) -#22563 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #22560) -#22569 := (iff #22563 #22568) -#22570 := [rewrite]: #22569 -#22564 := (iff #19083 #22563) -#22561 := (iff #19075 #22560) -#22558 := (iff #19069 #22557) -#22555 := (iff #19066 #22552) -#22538 := (or #22536 #22537) -#22549 := (or #19042 #19055 #22538) -#22553 := (iff #22549 #22552) -#22554 := [rewrite]: #22553 -#22550 := (iff #19066 #22549) -#22547 := (iff #19063 #22538) -#22539 := (not #22538) -#22542 := (not #22539) -#22545 := (iff #22542 #22538) -#22546 := [rewrite]: #22545 -#22543 := (iff #19063 #22542) -#22540 := (iff #19060 #22539) -#22541 := [rewrite]: #22540 -#22544 := [monotonicity #22541]: #22543 -#22548 := [trans #22544 #22546]: #22547 -#22551 := [monotonicity #22548]: #22550 -#22556 := [trans #22551 #22554]: #22555 -#22559 := [monotonicity #22556]: #22558 -#22534 := (iff #18733 #22531) -#22525 := (and #22507 #22522) -#22532 := (iff #22525 #22531) -#22533 := [rewrite]: #22532 -#22526 := (iff #18733 #22525) -#22523 := (iff #18729 #22522) -#22520 := (iff #18726 #22511) -#22512 := (not #22511) -#22515 := (not #22512) -#22518 := (iff #22515 #22511) -#22519 := [rewrite]: #22518 -#22516 := (iff #18726 #22515) -#22513 := (iff #15985 #22512) -#22514 := [rewrite]: #22513 -#22517 := [monotonicity #22514]: #22516 -#22521 := [trans #22517 #22519]: #22520 -#22524 := [quant-intro #22521]: #22523 -#22508 := (iff #15976 #22507) -#22505 := (iff #15971 #22502) -#20215 := (or #5104 #19577) -#22499 := (or #13793 #13807 #20215) -#22503 := (iff #22499 #22502) -#22504 := [rewrite]: #22503 -#22500 := (iff #15971 #22499) -#20224 := (iff #14425 #20215) -#20216 := (not #20215) -#20219 := (not #20216) -#20222 := (iff #20219 #20215) -#20223 := [rewrite]: #20222 -#20220 := (iff #14425 #20219) -#20217 := (iff #14426 #20216) -#20218 := [rewrite]: #20217 -#20221 := [monotonicity #20218]: #20220 -#20225 := [trans #20221 #20223]: #20224 -#22501 := [monotonicity #20225]: #22500 -#22506 := [trans #22501 #22504]: #22505 -#22509 := [quant-intro #22506]: #22508 -#22527 := [monotonicity #22509 #22524]: #22526 -#22535 := [trans #22527 #22533]: #22534 -#22562 := [monotonicity #22535 #22559]: #22561 -#22565 := [monotonicity #22562]: #22564 -#22572 := [trans #22565 #22570]: #22571 -#22497 := (iff #19021 #22494) -#22489 := (and #13477 #13480 #13766 #22486) -#22495 := (iff #22489 #22494) -#22496 := [rewrite]: #22495 -#22490 := (iff #19021 #22489) -#22487 := (iff #19015 #22486) -#22484 := (iff #19010 #22481) -#22476 := (and #12539 #12542 #22473) -#22482 := (iff #22476 #22481) -#22483 := [rewrite]: #22482 -#22477 := (iff #19010 #22476) -#22474 := (iff #19004 #22473) -#22471 := (iff #18999 #22468) -#22463 := (and #12539 #12548 #13477 #13480 #22460) -#22469 := (iff #22463 #22468) -#22470 := [rewrite]: #22469 -#22464 := (iff #18999 #22463) -#22461 := (iff #18993 #22460) -#22458 := (iff #18988 #22455) -#22451 := (and #12803 #12806 #13477 #13480 #13489 #13672 #22411) -#22456 := (iff #22451 #22455) -#22457 := [rewrite]: #22456 -#22452 := (iff #18988 #22451) -#22412 := (iff #18948 #22411) -#22409 := (iff #18943 #22406) -#22399 := (and #12586 #13489 #13498 #13506 #13582 #15864 #22396) -#22407 := (iff #22399 #22406) -#22408 := [rewrite]: #22407 -#22400 := (iff #18943 #22399) -#22397 := (iff #18935 #22396) -#22394 := (iff #18932 #22391) -#22386 := (and #13514 #22383) -#22392 := (iff #22386 #22391) -#22393 := [rewrite]: #22392 -#22387 := (iff #18932 #22386) -#22384 := (iff #18927 #22383) -#22381 := (iff #18921 #22380) -#22378 := (iff #18918 #22375) -#22361 := (or #22359 #22360) -#22372 := (or #18894 #18907 #22361) -#22376 := (iff #22372 #22375) -#22377 := [rewrite]: #22376 -#22373 := (iff #18918 #22372) -#22370 := (iff #18915 #22361) -#22362 := (not #22361) -#22365 := (not #22362) -#22368 := (iff #22365 #22361) -#22369 := [rewrite]: #22368 -#22366 := (iff #18915 #22365) -#22363 := (iff #18912 #22362) -#22364 := [rewrite]: #22363 -#22367 := [monotonicity #22364]: #22366 -#22371 := [trans #22367 #22369]: #22370 -#22374 := [monotonicity #22371]: #22373 -#22379 := [trans #22374 #22377]: #22378 -#22382 := [monotonicity #22379]: #22381 -#22357 := (iff #18605 #22354) -#22349 := (and #22327 #22346) -#22355 := (iff #22349 #22354) -#22356 := [rewrite]: #22355 -#22350 := (iff #18605 #22349) -#22347 := (iff #15877 #22346) -#22344 := (iff #15872 #22341) -#22338 := (or #13522 #13536 #20215) -#22342 := (iff #22338 #22341) -#22343 := [rewrite]: #22342 -#22339 := (iff #15872 #22338) -#22340 := [monotonicity #20225]: #22339 -#22345 := [trans #22340 #22343]: #22344 -#22348 := [quant-intro #22345]: #22347 -#22336 := (iff #18595 #22327) -#22331 := (not #22328) -#22334 := (iff #22331 #22327) -#22335 := [rewrite]: #22334 -#22332 := (iff #18595 #22331) -#22329 := (iff #13565 #22328) -#22330 := [rewrite]: #22329 -#22333 := [monotonicity #22330]: #22332 -#22337 := [trans #22333 #22335]: #22336 -#22351 := [monotonicity #22337 #22348]: #22350 -#22358 := [trans #22351 #22356]: #22357 -#22385 := [monotonicity #22358 #22382]: #22384 -#22388 := [monotonicity #22385]: #22387 -#22395 := [trans #22388 #22393]: #22394 -#22398 := [monotonicity #22395]: #22397 -#22401 := [monotonicity #22398]: #22400 -#22410 := [trans #22401 #22408]: #22409 -#22413 := [monotonicity #22410]: #22412 -#22453 := [monotonicity #22413]: #22452 -#22459 := [trans #22453 #22457]: #22458 -#22449 := (iff #18976 #22446) -#22440 := (and #13477 #13480 #13671 #22437) -#22447 := (iff #22440 #22446) -#22448 := [rewrite]: #22447 -#22441 := (iff #18976 #22440) -#22438 := (iff #18970 #22437) -#22435 := (iff #18965 #22432) -#22427 := (and #12539 #12542 #22424) -#22433 := (iff #22427 #22432) -#22434 := [rewrite]: #22433 -#22428 := (iff #18965 #22427) -#22425 := (iff #18959 #22424) -#22422 := (iff #18954 #22419) -#22414 := (and #12539 #12548 #12554 #12557 #12560 #12565 #12568 #13480 #13489 #22411) -#22420 := (iff #22414 #22419) -#22421 := [rewrite]: #22420 -#22415 := (iff #18954 #22414) -#22416 := [monotonicity #22413]: #22415 -#22423 := [trans #22416 #22421]: #22422 -#22426 := [monotonicity #22423]: #22425 -#22429 := [monotonicity #22426]: #22428 -#22436 := [trans #22429 #22434]: #22435 -#22439 := [monotonicity #22436]: #22438 -#22442 := [monotonicity #22439]: #22441 -#22450 := [trans #22442 #22448]: #22449 -#22462 := [monotonicity #22450 #22459]: #22461 -#22465 := [monotonicity #22462]: #22464 -#22472 := [trans #22465 #22470]: #22471 -#22475 := [monotonicity #22472]: #22474 -#22478 := [monotonicity #22475]: #22477 -#22485 := [trans #22478 #22483]: #22484 -#22488 := [monotonicity #22485]: #22487 -#22491 := [monotonicity #22488]: #22490 -#22498 := [trans #22491 #22496]: #22497 -#22575 := [monotonicity #22498 #22572]: #22574 -#22324 := (iff #15803 #22323) -#22321 := (iff #15798 #22318) -#22315 := (or #13958 #13972 #20215) -#22319 := (iff #22315 #22318) -#22320 := [rewrite]: #22319 -#22316 := (iff #15798 #22315) -#22317 := [monotonicity #20225]: #22316 -#22322 := [trans #22317 #22320]: #22321 -#22325 := [quant-intro #22322]: #22324 -#22578 := [monotonicity #22325 #22575]: #22577 -#22594 := [trans #22578 #22592]: #22593 -#22597 := [monotonicity #22594]: #22596 -#22313 := (iff #15789 #22312) -#22310 := (iff #15784 #22307) -#22304 := (or #13439 #13451 #20215) -#22308 := (iff #22304 #22307) -#22309 := [rewrite]: #22308 -#22305 := (iff #15784 #22304) -#22306 := [monotonicity #20225]: #22305 -#22311 := [trans #22306 #22309]: #22310 -#22314 := [quant-intro #22311]: #22313 -#22600 := [monotonicity #22314 #22597]: #22599 -#22608 := [trans #22600 #22606]: #22607 -#22302 := (iff #18829 #22301) -#22299 := (iff #18824 #22296) -#22282 := (or #22280 #22281) -#22293 := (or #18450 #18451 #22282) -#22297 := (iff #22293 #22296) -#22298 := [rewrite]: #22297 -#22294 := (iff #18824 #22293) -#22291 := (iff #18818 #22282) -#22283 := (not #22282) -#22286 := (not #22283) -#22289 := (iff #22286 #22282) -#22290 := [rewrite]: #22289 -#22287 := (iff #18818 #22286) -#22284 := (iff #18815 #22283) -#22285 := [rewrite]: #22284 -#22288 := [monotonicity #22285]: #22287 -#22292 := [trans #22288 #22290]: #22291 -#22295 := [monotonicity #22292]: #22294 -#22300 := [trans #22295 #22298]: #22299 -#22303 := [monotonicity #22300]: #22302 -#22611 := [monotonicity #22303 #22608]: #22610 -#22614 := [monotonicity #22611]: #22613 -#22621 := [trans #22614 #22619]: #22620 -#22624 := [monotonicity #22621]: #22623 -#22627 := [monotonicity #22624]: #22626 -#22634 := [trans #22627 #22632]: #22633 -#22637 := [monotonicity #22634]: #22636 -#22640 := [monotonicity #22637]: #22639 -#22647 := [trans #22640 #22645]: #22646 -#22650 := [monotonicity #22647]: #22649 -#22653 := [monotonicity #22650]: #22652 -#22660 := [trans #22653 #22658]: #22659 -#22663 := [monotonicity #22660]: #22662 -#18705 := (and #18704 #18703) -#18706 := (not #18705) -#18709 := (+ #18708 #13805) -#18710 := (<= #18709 0::Int) -#18711 := (+ ?v0!15 #13406) -#18712 := (>= #18711 0::Int) -#18713 := (or #18712 #18710 #18706) -#18714 := (not #18713) -#18737 := (or #18714 #18733) -#18490 := (not #13485) -#18697 := (not #12277) -#18694 := (not #12286) -#18691 := (not #12295) -#18688 := (not #12304) -#18741 := (and #18688 #18691 #18694 #18697 #18490 #13769 #18737) -#15900 := (and #13498 #15864) -#15903 := (not #15900) -#18621 := (not #15903) -#18581 := (and #18580 #18579) -#18582 := (not #18581) -#18585 := (+ #18584 #13534) -#18586 := (<= #18585 0::Int) -#18587 := (+ ?v0!14 #13515) -#18588 := (>= #18587 0::Int) -#18589 := (or #18588 #18586 #18582) -#18590 := (not #18589) -#18609 := (or #18590 #18605) -#18575 := (not #13519) -#18613 := (and #18575 #18609) -#18617 := (or #13519 #18613) -#18570 := (not #13586) -#18567 := (not #13511) -#18564 := (not #12656) -#18624 := (and #18564 #18567 #18570 #18617 #18621) -#18628 := (or #18558 #18561 #18624) -#18555 := (not #13494) -#18655 := (not #12812) -#18652 := (not #12821) -#18660 := (and #18652 #18655 #18490 #18555 #13677 #18628) -#18552 := (not #13620) -#18549 := (not #12695) -#18546 := (not #12704) -#18543 := (not #12722) -#18540 := (not #12731) -#18537 := (not #12740) -#18532 := (not #12749) -#18632 := (and #18532 #18537 #18540 #18543 #18546 #18549 #18552 #18555 #18628) -#18636 := (or #18520 #18529 #18632) -#18526 := (not #12761) -#18640 := (and #18526 #18636) -#18644 := (or #18520 #18523 #18640) -#18648 := (and #18490 #13671 #18644) -#18664 := (or #18648 #18660) -#18668 := (and #18532 #18490 #18664) -#18672 := (or #18520 #18529 #18668) -#18676 := (and #18526 #18672) -#18680 := (or #18520 #18523 #18676) -#18684 := (and #18490 #13766 #18680) -#18745 := (or #18684 #18741) -#15854 := (and #14020 #15849) -#15857 := (not #15854) -#18515 := (not #15857) -#15837 := (and #13477 #15832) -#15840 := (not #15837) -#18512 := (not #15840) -#15820 := (and #13998 #15815) -#15823 := (not #15820) -#18509 := (not #15823) -#18499 := (not #14041) -#18496 := (not #13995) -#18493 := (not #13955) -#18487 := (not #12988) -#18484 := (not #12997) -#18481 := (not #13006) -#18478 := (not #13015) -#18475 := (not #13024) -#18472 := (not #13938) -#18469 := (not #15263) -#18749 := (and #18469 #18472 #18475 #18478 #18481 #18484 #18487 #18490 #18493 #18496 #18499 #15803 #18509 #18512 #18515 #18745) -#18753 := (or #13231 #14198 #18749) -#18757 := (and #15789 #18753) -#18444 := (and #18443 #18442) -#18445 := (not #18444) -#18452 := (or #18451 #18450 #18445) -#18453 := (not #18452) -#18761 := (or #18453 #18757) -#18438 := (not #13436) -#18765 := (and #18438 #18761) -#18769 := (or #13436 #18765) -#18433 := (not #13204) -#18430 := (not #13213) -#18427 := (not #13222) -#18424 := (not #13240) -#18421 := (not #13231) -#18773 := (and #18421 #18424 #18427 #18430 #18433 #18769) -#18777 := (or #18409 #18418 #18773) -#18415 := (not #13252) -#18781 := (and #18415 #18777) -#18785 := (or #18409 #18412 #18781) -#18406 := (not #13264) -#18789 := (and #18406 #18785) -#18793 := (or #13264 #18789) -#19140 := (iff #18793 #19139) -#19137 := (iff #18789 #19136) -#19134 := (iff #18785 #19133) -#19131 := (iff #18781 #19128) -#19125 := (and #12150 #19122) -#19129 := (iff #19125 #19128) -#19130 := [rewrite]: #19129 -#19126 := (iff #18781 #19125) -#19123 := (iff #18777 #19122) -#19120 := (iff #18773 #19117) -#19114 := (and #3109 #12156 #12159 #12162 #12165 #19111) -#19118 := (iff #19114 #19117) -#19119 := [rewrite]: #19118 -#19115 := (iff #18773 #19114) -#19112 := (iff #18769 #19111) -#19109 := (iff #18765 #19108) -#19106 := (iff #18761 #19105) -#19103 := (iff #18757 #19102) -#19100 := (iff #18753 #19099) -#19097 := (iff #18749 #19094) -#19091 := (and #12222 #12479 #12507 #12510 #12513 #12516 #12525 #13482 #13950 #13992 #14036 #15803 #15820 #15837 #15854 #19088) -#19095 := (iff #19091 #19094) -#19096 := [rewrite]: #19095 -#19092 := (iff #18749 #19091) -#19089 := (iff #18745 #19088) -#19086 := (iff #18741 #19083) -#19080 := (and #12233 #12236 #12239 #12242 #13482 #13765 #19075) -#19084 := (iff #19080 #19083) -#19085 := [rewrite]: #19084 -#19081 := (iff #18741 #19080) -#19078 := (iff #18737 #19075) -#19072 := (or #19069 #18733) -#19076 := (iff #19072 #19075) -#19077 := [rewrite]: #19076 -#19073 := (iff #18737 #19072) -#19070 := (iff #18714 #19069) -#19067 := (iff #18713 #19066) -#19064 := (iff #18706 #19063) -#19061 := (iff #18705 #19060) -#19062 := [rewrite]: #19061 -#19065 := [monotonicity #19062]: #19064 -#19058 := (iff #18710 #19055) -#19047 := (+ #13805 #18708) -#19050 := (<= #19047 0::Int) -#19056 := (iff #19050 #19055) -#19057 := [rewrite]: #19056 -#19051 := (iff #18710 #19050) -#19048 := (= #18709 #19047) -#19049 := [rewrite]: #19048 -#19052 := [monotonicity #19049]: #19051 -#19059 := [trans #19052 #19057]: #19058 -#19045 := (iff #18712 #19042) -#19034 := (+ #13406 ?v0!15) -#19037 := (>= #19034 0::Int) -#19043 := (iff #19037 #19042) -#19044 := [rewrite]: #19043 -#19038 := (iff #18712 #19037) -#19035 := (= #18711 #19034) -#19036 := [rewrite]: #19035 -#19039 := [monotonicity #19036]: #19038 -#19046 := [trans #19039 #19044]: #19045 -#19068 := [monotonicity #19046 #19059 #19065]: #19067 -#19071 := [monotonicity #19068]: #19070 -#19074 := [monotonicity #19071]: #19073 -#19079 := [trans #19074 #19077]: #19078 -#18846 := (iff #18490 #13482) -#18847 := [rewrite]: #18846 -#19032 := (iff #18697 #12242) -#19033 := [rewrite]: #19032 -#19030 := (iff #18694 #12239) -#19031 := [rewrite]: #19030 -#19028 := (iff #18691 #12236) -#19029 := [rewrite]: #19028 -#19026 := (iff #18688 #12233) -#19027 := [rewrite]: #19026 -#19082 := [monotonicity #19027 #19029 #19031 #19033 #18847 #13773 #19079]: #19081 -#19087 := [trans #19082 #19085]: #19086 -#19024 := (iff #18684 #19021) -#19018 := (and #13482 #13766 #19015) -#19022 := (iff #19018 #19021) -#19023 := [rewrite]: #19022 -#19019 := (iff #18684 #19018) -#19016 := (iff #18680 #19015) -#19013 := (iff #18676 #19010) -#19007 := (and #12545 #19004) -#19011 := (iff #19007 #19010) -#19012 := [rewrite]: #19011 -#19008 := (iff #18676 #19007) -#19005 := (iff #18672 #19004) -#19002 := (iff #18668 #18999) -#18996 := (and #12551 #13482 #18993) -#19000 := (iff #18996 #18999) -#19001 := [rewrite]: #19000 -#18997 := (iff #18668 #18996) -#18994 := (iff #18664 #18993) -#18991 := (iff #18660 #18988) -#18985 := (and #12803 #12806 #13482 #13491 #13672 #18948) -#18989 := (iff #18985 #18988) -#18990 := [rewrite]: #18989 -#18986 := (iff #18660 #18985) -#18949 := (iff #18628 #18948) -#18946 := (iff #18624 #18943) -#18940 := (and #12586 #13508 #13582 #18935 #15900) -#18944 := (iff #18940 #18943) -#18945 := [rewrite]: #18944 -#18941 := (iff #18624 #18940) -#18938 := (iff #18621 #15900) -#18939 := [rewrite]: #18938 -#18936 := (iff #18617 #18935) -#18933 := (iff #18613 #18932) -#18930 := (iff #18609 #18927) -#18924 := (or #18921 #18605) -#18928 := (iff #18924 #18927) -#18929 := [rewrite]: #18928 -#18925 := (iff #18609 #18924) -#18922 := (iff #18590 #18921) -#18919 := (iff #18589 #18918) -#18916 := (iff #18582 #18915) -#18913 := (iff #18581 #18912) -#18914 := [rewrite]: #18913 -#18917 := [monotonicity #18914]: #18916 -#18910 := (iff #18586 #18907) -#18899 := (+ #13534 #18584) -#18902 := (<= #18899 0::Int) -#18908 := (iff #18902 #18907) -#18909 := [rewrite]: #18908 -#18903 := (iff #18586 #18902) -#18900 := (= #18585 #18899) -#18901 := [rewrite]: #18900 -#18904 := [monotonicity #18901]: #18903 -#18911 := [trans #18904 #18909]: #18910 -#18897 := (iff #18588 #18894) -#18886 := (+ #13515 ?v0!14) -#18889 := (>= #18886 0::Int) -#18895 := (iff #18889 #18894) -#18896 := [rewrite]: #18895 -#18890 := (iff #18588 #18889) -#18887 := (= #18587 #18886) -#18888 := [rewrite]: #18887 -#18891 := [monotonicity #18888]: #18890 -#18898 := [trans #18891 #18896]: #18897 -#18920 := [monotonicity #18898 #18911 #18917]: #18919 -#18923 := [monotonicity #18920]: #18922 -#18926 := [monotonicity #18923]: #18925 -#18931 := [trans #18926 #18929]: #18930 -#18884 := (iff #18575 #13514) -#18885 := [rewrite]: #18884 -#18934 := [monotonicity #18885 #18931]: #18933 -#18937 := [monotonicity #18934]: #18936 -#18882 := (iff #18570 #13582) -#18883 := [rewrite]: #18882 -#18880 := (iff #18567 #13508) -#18881 := [rewrite]: #18880 -#18878 := (iff #18564 #12586) -#18879 := [rewrite]: #18878 -#18942 := [monotonicity #18879 #18881 #18883 #18937 #18939]: #18941 -#18947 := [trans #18942 #18945]: #18946 -#18950 := [monotonicity #18947]: #18949 -#18876 := (iff #18555 #13491) -#18877 := [rewrite]: #18876 -#18983 := (iff #18655 #12806) -#18984 := [rewrite]: #18983 -#18981 := (iff #18652 #12803) -#18982 := [rewrite]: #18981 -#18987 := [monotonicity #18982 #18984 #18847 #18877 #13681 #18950]: #18986 -#18992 := [trans #18987 #18990]: #18991 -#18979 := (iff #18648 #18976) -#18973 := (and #13482 #13671 #18970) -#18977 := (iff #18973 #18976) -#18978 := [rewrite]: #18977 -#18974 := (iff #18648 #18973) -#18971 := (iff #18644 #18970) -#18968 := (iff #18640 #18965) -#18962 := (and #12545 #18959) -#18966 := (iff #18962 #18965) -#18967 := [rewrite]: #18966 -#18963 := (iff #18640 #18962) -#18960 := (iff #18636 #18959) -#18957 := (iff #18632 #18954) -#18951 := (and #12551 #12554 #12557 #12560 #12565 #12568 #13480 #13491 #18948) -#18955 := (iff #18951 #18954) -#18956 := [rewrite]: #18955 -#18952 := (iff #18632 #18951) -#18874 := (iff #18552 #13480) -#18875 := [rewrite]: #18874 -#18872 := (iff #18549 #12568) -#18873 := [rewrite]: #18872 -#18870 := (iff #18546 #12565) -#18871 := [rewrite]: #18870 -#18868 := (iff #18543 #12560) -#18869 := [rewrite]: #18868 -#18866 := (iff #18540 #12557) -#18867 := [rewrite]: #18866 -#18864 := (iff #18537 #12554) -#18865 := [rewrite]: #18864 -#18862 := (iff #18532 #12551) -#18863 := [rewrite]: #18862 -#18953 := [monotonicity #18863 #18865 #18867 #18869 #18871 #18873 #18875 #18877 #18950]: #18952 -#18958 := [trans #18953 #18956]: #18957 -#18961 := [monotonicity #18958]: #18960 -#18860 := (iff #18526 #12545) -#18861 := [rewrite]: #18860 -#18964 := [monotonicity #18861 #18961]: #18963 -#18969 := [trans #18964 #18967]: #18968 -#18972 := [monotonicity #18969]: #18971 -#18975 := [monotonicity #18847 #18972]: #18974 -#18980 := [trans #18975 #18978]: #18979 -#18995 := [monotonicity #18980 #18992]: #18994 -#18998 := [monotonicity #18863 #18847 #18995]: #18997 -#19003 := [trans #18998 #19001]: #19002 -#19006 := [monotonicity #19003]: #19005 -#19009 := [monotonicity #18861 #19006]: #19008 -#19014 := [trans #19009 #19012]: #19013 -#19017 := [monotonicity #19014]: #19016 -#19020 := [monotonicity #18847 #19017]: #19019 -#19025 := [trans #19020 #19023]: #19024 -#19090 := [monotonicity #19025 #19087]: #19089 -#18858 := (iff #18515 #15854) -#18859 := [rewrite]: #18858 -#18856 := (iff #18512 #15837) -#18857 := [rewrite]: #18856 -#18854 := (iff #18509 #15820) -#18855 := [rewrite]: #18854 -#18852 := (iff #18499 #14036) -#18853 := [rewrite]: #18852 -#18850 := (iff #18496 #13992) -#18851 := [rewrite]: #18850 -#18848 := (iff #18493 #13950) -#18849 := [rewrite]: #18848 -#18844 := (iff #18487 #12525) -#18845 := [rewrite]: #18844 -#18842 := (iff #18484 #12516) -#18843 := [rewrite]: #18842 -#18840 := (iff #18481 #12513) -#18841 := [rewrite]: #18840 -#18838 := (iff #18478 #12510) -#18839 := [rewrite]: #18838 -#18836 := (iff #18475 #12507) -#18837 := [rewrite]: #18836 -#18834 := (iff #18472 #12479) -#18835 := [rewrite]: #18834 -#18832 := (iff #18469 #12222) -#18833 := [rewrite]: #18832 -#19093 := [monotonicity #18833 #18835 #18837 #18839 #18841 #18843 #18845 #18847 #18849 #18851 #18853 #18855 #18857 #18859 #19090]: #19092 -#19098 := [trans #19093 #19096]: #19097 -#19101 := [monotonicity #14202 #19098]: #19100 -#19104 := [monotonicity #19101]: #19103 -#18830 := (iff #18453 #18829) -#18827 := (iff #18452 #18824) -#18821 := (or #18451 #18450 #18818) -#18825 := (iff #18821 #18824) -#18826 := [rewrite]: #18825 -#18822 := (iff #18452 #18821) -#18819 := (iff #18445 #18818) -#18816 := (iff #18444 #18815) -#18817 := [rewrite]: #18816 -#18820 := [monotonicity #18817]: #18819 -#18823 := [monotonicity #18820]: #18822 -#18828 := [trans #18823 #18826]: #18827 -#18831 := [monotonicity #18828]: #18830 -#19107 := [monotonicity #18831 #19104]: #19106 -#18813 := (iff #18438 #13433) -#18814 := [rewrite]: #18813 -#19110 := [monotonicity #18814 #19107]: #19109 -#19113 := [monotonicity #19110]: #19112 -#18811 := (iff #18433 #12165) -#18812 := [rewrite]: #18811 -#18809 := (iff #18430 #12162) -#18810 := [rewrite]: #18809 -#18807 := (iff #18427 #12159) -#18808 := [rewrite]: #18807 -#18805 := (iff #18424 #12156) -#18806 := [rewrite]: #18805 -#18803 := (iff #18421 #3109) -#18804 := [rewrite]: #18803 -#19116 := [monotonicity #18804 #18806 #18808 #18810 #18812 #19113]: #19115 -#19121 := [trans #19116 #19119]: #19120 -#19124 := [monotonicity #19121]: #19123 -#18801 := (iff #18415 #12150) -#18802 := [rewrite]: #18801 -#19127 := [monotonicity #18802 #19124]: #19126 -#19132 := [trans #19127 #19130]: #19131 -#19135 := [monotonicity #19132]: #19134 -#18799 := (iff #18406 #12141) -#18800 := [rewrite]: #18799 -#19138 := [monotonicity #18800 #19135]: #19137 -#19141 := [monotonicity #19138]: #19140 -#15990 := (exists (vars (?v0 Int)) #15985) -#15979 := (not #15976) -#15993 := (or #15979 #15990) -#15996 := (and #15976 #15993) -#15999 := (or #12304 #12295 #12286 #12277 #13485 #13766 #15996) -#15880 := (not #15877) -#15886 := (or #13565 #15880) -#15891 := (and #15877 #15886) -#15894 := (or #13519 #15891) -#15897 := (and #13514 #15894) -#15909 := (or #12656 #13511 #13586 #15897 #15903) -#15914 := (and #13498 #15864 #15909) -#15940 := (or #12821 #12812 #13485 #13494 #13671 #15914) -#15917 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #15914) -#15920 := (and #12539 #12548 #15917) -#15923 := (or #12761 #15920) -#15926 := (and #12539 #12542 #15923) -#15932 := (or #13485 #13672 #15926) -#15945 := (and #15932 #15940) -#15948 := (or #12749 #13485 #15945) -#15951 := (and #12539 #12548 #15948) -#15954 := (or #12761 #15951) -#15957 := (and #12539 #12542 #15954) -#15963 := (or #13485 #13765 #15957) -#16002 := (and #15963 #15999) -#15806 := (not #15803) -#16008 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13995 #14041 #15806 #15823 #15840 #15857 #16002) -#16013 := (and #3109 #13473 #16008) -#15792 := (not #15789) -#16016 := (or #15792 #16013) -#16019 := (and #15789 #16016) -#16022 := (or #13436 #16019) -#16025 := (and #13433 #16022) -#16028 := (or #13231 #13240 #13222 #13213 #13204 #16025) -#16031 := (and #12144 #12153 #16028) -#16034 := (or #13252 #16031) -#16037 := (and #12144 #12147 #16034) -#16040 := (or #13264 #16037) -#16043 := (and #12141 #16040) -#16046 := (not #16043) -#18794 := (~ #16046 #18793) -#18790 := (not #16040) -#18791 := (~ #18790 #18789) -#18786 := (not #16037) -#18787 := (~ #18786 #18785) -#18782 := (not #16034) -#18783 := (~ #18782 #18781) -#18778 := (not #16031) -#18779 := (~ #18778 #18777) -#18774 := (not #16028) -#18775 := (~ #18774 #18773) -#18770 := (not #16025) -#18771 := (~ #18770 #18769) -#18766 := (not #16022) -#18767 := (~ #18766 #18765) -#18762 := (not #16019) -#18763 := (~ #18762 #18761) -#18758 := (not #16016) -#18759 := (~ #18758 #18757) -#18754 := (not #16013) -#18755 := (~ #18754 #18753) -#18750 := (not #16008) -#18751 := (~ #18750 #18749) -#18746 := (not #16002) -#18747 := (~ #18746 #18745) -#18742 := (not #15999) -#18743 := (~ #18742 #18741) -#18738 := (not #15996) -#18739 := (~ #18738 #18737) -#18734 := (not #15993) -#18735 := (~ #18734 #18733) -#18730 := (not #15990) -#18731 := (~ #18730 #18729) -#18727 := (~ #18726 #18726) -#18728 := [refl]: #18727 -#18732 := [nnf-neg #18728]: #18731 -#18723 := (not #15979) -#18724 := (~ #18723 #15976) -#18721 := (~ #15976 #15976) -#18719 := (~ #15971 #15971) -#18720 := [refl]: #18719 -#18722 := [nnf-pos #18720]: #18721 -#18725 := [nnf-neg #18722]: #18724 -#18736 := [nnf-neg #18725 #18732]: #18735 -#18715 := (~ #15979 #18714) -#18716 := [sk]: #18715 -#18740 := [nnf-neg #18716 #18736]: #18739 -#18700 := (~ #13769 #13769) -#18701 := [refl]: #18700 -#18491 := (~ #18490 #18490) -#18492 := [refl]: #18491 -#18698 := (~ #18697 #18697) -#18699 := [refl]: #18698 -#18695 := (~ #18694 #18694) -#18696 := [refl]: #18695 -#18692 := (~ #18691 #18691) -#18693 := [refl]: #18692 -#18689 := (~ #18688 #18688) -#18690 := [refl]: #18689 -#18744 := [nnf-neg #18690 #18693 #18696 #18699 #18492 #18701 #18740]: #18743 -#18685 := (not #15963) -#18686 := (~ #18685 #18684) -#18681 := (not #15957) -#18682 := (~ #18681 #18680) -#18677 := (not #15954) -#18678 := (~ #18677 #18676) -#18673 := (not #15951) -#18674 := (~ #18673 #18672) -#18669 := (not #15948) -#18670 := (~ #18669 #18668) -#18665 := (not #15945) -#18666 := (~ #18665 #18664) -#18661 := (not #15940) -#18662 := (~ #18661 #18660) -#18629 := (not #15914) -#18630 := (~ #18629 #18628) -#18625 := (not #15909) -#18626 := (~ #18625 #18624) -#18622 := (~ #18621 #18621) -#18623 := [refl]: #18622 -#18618 := (not #15897) -#18619 := (~ #18618 #18617) -#18614 := (not #15894) -#18615 := (~ #18614 #18613) -#18610 := (not #15891) -#18611 := (~ #18610 #18609) -#18606 := (not #15886) -#18607 := (~ #18606 #18605) -#18602 := (not #15880) -#18603 := (~ #18602 #15877) -#18600 := (~ #15877 #15877) -#18598 := (~ #15872 #15872) -#18599 := [refl]: #18598 -#18601 := [nnf-pos #18599]: #18600 -#18604 := [nnf-neg #18601]: #18603 -#18596 := (~ #18595 #18595) -#18597 := [refl]: #18596 -#18608 := [nnf-neg #18597 #18604]: #18607 -#18591 := (~ #15880 #18590) -#18592 := [sk]: #18591 -#18612 := [nnf-neg #18592 #18608]: #18611 -#18576 := (~ #18575 #18575) -#18577 := [refl]: #18576 -#18616 := [nnf-neg #18577 #18612]: #18615 -#18573 := (~ #13519 #13519) -#18574 := [refl]: #18573 -#18620 := [nnf-neg #18574 #18616]: #18619 -#18571 := (~ #18570 #18570) -#18572 := [refl]: #18571 -#18568 := (~ #18567 #18567) -#18569 := [refl]: #18568 -#18565 := (~ #18564 #18564) -#18566 := [refl]: #18565 -#18627 := [nnf-neg #18566 #18569 #18572 #18620 #18623]: #18626 -#18562 := (~ #18561 #18561) -#18563 := [refl]: #18562 -#18559 := (~ #18558 #18558) -#18560 := [refl]: #18559 -#18631 := [nnf-neg #18560 #18563 #18627]: #18630 -#18658 := (~ #13677 #13677) -#18659 := [refl]: #18658 -#18556 := (~ #18555 #18555) -#18557 := [refl]: #18556 -#18656 := (~ #18655 #18655) -#18657 := [refl]: #18656 -#18653 := (~ #18652 #18652) -#18654 := [refl]: #18653 -#18663 := [nnf-neg #18654 #18657 #18492 #18557 #18659 #18631]: #18662 -#18649 := (not #15932) -#18650 := (~ #18649 #18648) -#18645 := (not #15926) -#18646 := (~ #18645 #18644) -#18641 := (not #15923) -#18642 := (~ #18641 #18640) -#18637 := (not #15920) -#18638 := (~ #18637 #18636) -#18633 := (not #15917) -#18634 := (~ #18633 #18632) -#18553 := (~ #18552 #18552) -#18554 := [refl]: #18553 -#18550 := (~ #18549 #18549) -#18551 := [refl]: #18550 -#18547 := (~ #18546 #18546) -#18548 := [refl]: #18547 -#18544 := (~ #18543 #18543) -#18545 := [refl]: #18544 -#18541 := (~ #18540 #18540) -#18542 := [refl]: #18541 -#18538 := (~ #18537 #18537) -#18539 := [refl]: #18538 -#18533 := (~ #18532 #18532) -#18534 := [refl]: #18533 -#18635 := [nnf-neg #18534 #18539 #18542 #18545 #18548 #18551 #18554 #18557 #18631]: #18634 -#18530 := (~ #18529 #18529) -#18531 := [refl]: #18530 -#18521 := (~ #18520 #18520) -#18522 := [refl]: #18521 -#18639 := [nnf-neg #18522 #18531 #18635]: #18638 -#18527 := (~ #18526 #18526) -#18528 := [refl]: #18527 -#18643 := [nnf-neg #18528 #18639]: #18642 -#18524 := (~ #18523 #18523) -#18525 := [refl]: #18524 -#18647 := [nnf-neg #18522 #18525 #18643]: #18646 -#18535 := (~ #13671 #13671) -#18536 := [refl]: #18535 -#18651 := [nnf-neg #18492 #18536 #18647]: #18650 -#18667 := [nnf-neg #18651 #18663]: #18666 -#18671 := [nnf-neg #18534 #18492 #18667]: #18670 -#18675 := [nnf-neg #18522 #18531 #18671]: #18674 -#18679 := [nnf-neg #18528 #18675]: #18678 -#18683 := [nnf-neg #18522 #18525 #18679]: #18682 -#18518 := (~ #13766 #13766) -#18519 := [refl]: #18518 -#18687 := [nnf-neg #18492 #18519 #18683]: #18686 -#18748 := [nnf-neg #18687 #18744]: #18747 -#18516 := (~ #18515 #18515) -#18517 := [refl]: #18516 -#18513 := (~ #18512 #18512) -#18514 := [refl]: #18513 -#18510 := (~ #18509 #18509) -#18511 := [refl]: #18510 -#18506 := (not #15806) -#18507 := (~ #18506 #15803) -#18504 := (~ #15803 #15803) -#18502 := (~ #15798 #15798) -#18503 := [refl]: #18502 -#18505 := [nnf-pos #18503]: #18504 -#18508 := [nnf-neg #18505]: #18507 -#18500 := (~ #18499 #18499) -#18501 := [refl]: #18500 -#18497 := (~ #18496 #18496) -#18498 := [refl]: #18497 -#18494 := (~ #18493 #18493) -#18495 := [refl]: #18494 -#18488 := (~ #18487 #18487) -#18489 := [refl]: #18488 -#18485 := (~ #18484 #18484) -#18486 := [refl]: #18485 -#18482 := (~ #18481 #18481) -#18483 := [refl]: #18482 -#18479 := (~ #18478 #18478) -#18480 := [refl]: #18479 -#18476 := (~ #18475 #18475) -#18477 := [refl]: #18476 -#18473 := (~ #18472 #18472) -#18474 := [refl]: #18473 -#18470 := (~ #18469 #18469) -#18471 := [refl]: #18470 -#18752 := [nnf-neg #18471 #18474 #18477 #18480 #18483 #18486 #18489 #18492 #18495 #18498 #18501 #18508 #18511 #18514 #18517 #18748]: #18751 -#18467 := (~ #14198 #14198) -#18468 := [refl]: #18467 -#18465 := (~ #13231 #13231) -#18466 := [refl]: #18465 -#18756 := [nnf-neg #18466 #18468 #18752]: #18755 -#18462 := (not #15792) -#18463 := (~ #18462 #15789) -#18460 := (~ #15789 #15789) -#18458 := (~ #15784 #15784) -#18459 := [refl]: #18458 -#18461 := [nnf-pos #18459]: #18460 -#18464 := [nnf-neg #18461]: #18463 -#18760 := [nnf-neg #18464 #18756]: #18759 -#18454 := (~ #15792 #18453) -#18455 := [sk]: #18454 -#18764 := [nnf-neg #18455 #18760]: #18763 -#18439 := (~ #18438 #18438) -#18440 := [refl]: #18439 -#18768 := [nnf-neg #18440 #18764]: #18767 -#18436 := (~ #13436 #13436) -#18437 := [refl]: #18436 -#18772 := [nnf-neg #18437 #18768]: #18771 -#18434 := (~ #18433 #18433) -#18435 := [refl]: #18434 -#18431 := (~ #18430 #18430) -#18432 := [refl]: #18431 -#18428 := (~ #18427 #18427) -#18429 := [refl]: #18428 -#18425 := (~ #18424 #18424) -#18426 := [refl]: #18425 -#18422 := (~ #18421 #18421) -#18423 := [refl]: #18422 -#18776 := [nnf-neg #18423 #18426 #18429 #18432 #18435 #18772]: #18775 -#18419 := (~ #18418 #18418) -#18420 := [refl]: #18419 -#18410 := (~ #18409 #18409) -#18411 := [refl]: #18410 -#18780 := [nnf-neg #18411 #18420 #18776]: #18779 -#18416 := (~ #18415 #18415) -#18417 := [refl]: #18416 -#18784 := [nnf-neg #18417 #18780]: #18783 -#18413 := (~ #18412 #18412) -#18414 := [refl]: #18413 -#18788 := [nnf-neg #18411 #18414 #18784]: #18787 -#18407 := (~ #18406 #18406) -#18408 := [refl]: #18407 -#18792 := [nnf-neg #18408 #18788]: #18791 -#18404 := (~ #13264 #13264) -#18405 := [refl]: #18404 -#18795 := [nnf-neg #18405 #18792]: #18794 -#15288 := (or #12304 #12295 #12286 #12277 #13485 #13766 #13852) -#15293 := (and #13788 #15288) -#15299 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13989 #13995 #14007 #14017 #14030 #14041 #15293) -#15304 := (and #3109 #13473 #15299) -#15307 := (or #13469 #15304) -#15310 := (and #13466 #15307) -#15313 := (or #13436 #15310) -#15316 := (and #13433 #15313) -#15319 := (or #13231 #13240 #13222 #13213 #13204 #15316) -#15322 := (and #12144 #12153 #15319) -#15325 := (or #13252 #15322) -#15328 := (and #12144 #12147 #15325) -#15331 := (or #13264 #15328) -#15334 := (and #12141 #15331) -#15337 := (not #15334) -#16047 := (iff #15337 #16046) -#16044 := (iff #15334 #16043) -#16041 := (iff #15331 #16040) -#16038 := (iff #15328 #16037) -#16035 := (iff #15325 #16034) -#16032 := (iff #15322 #16031) -#16029 := (iff #15319 #16028) -#16026 := (iff #15316 #16025) -#16023 := (iff #15313 #16022) -#16020 := (iff #15310 #16019) -#16017 := (iff #15307 #16016) -#16014 := (iff #15304 #16013) -#16011 := (iff #15299 #16008) -#16005 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #15806 #13995 #15823 #15840 #15857 #14041 #16002) -#16009 := (iff #16005 #16008) -#16010 := [rewrite]: #16009 -#16006 := (iff #15299 #16005) -#16003 := (iff #15293 #16002) -#16000 := (iff #15288 #15999) -#15997 := (iff #13852 #15996) -#15994 := (iff #13847 #15993) -#15991 := (iff #13838 #15990) -#15988 := (iff #13833 #15985) -#15982 := (and #3173 #4202 #15183 #13795) -#15986 := (iff #15982 #15985) -#15987 := [rewrite]: #15986 -#15983 := (iff #13833 #15982) -#15178 := (iff #4496 #15183) -#15199 := -4294967295::Int -#15191 := (+ -4294967295::Int #202) -#15184 := (<= #15191 0::Int) -#15180 := (iff #15184 #15183) -#15181 := [rewrite]: #15180 -#15185 := (iff #4496 #15184) -#15186 := (= #4495 #15191) -#15192 := (+ #202 -4294967295::Int) -#15188 := (= #15192 #15191) -#15189 := [rewrite]: #15188 -#15193 := (= #4495 #15192) -#15194 := (= #4494 -4294967295::Int) -#15200 := (* -1::Int 4294967295::Int) -#15196 := (= #15200 -4294967295::Int) -#15197 := [rewrite]: #15196 -#15201 := (= #4494 #15200) -#7601 := (= f88 4294967295::Int) -#990 := 65536::Int -#1365 := (* 65536::Int 65536::Int) -#1370 := (- #1365 1::Int) -#1371 := (= f88 #1370) -#7602 := (iff #1371 #7601) -#7599 := (= #1370 4294967295::Int) -#1053 := 4294967296::Int -#7592 := (- 4294967296::Int 1::Int) -#7597 := (= #7592 4294967295::Int) -#7598 := [rewrite]: #7597 -#7594 := (= #1370 #7592) -#7563 := (= #1365 4294967296::Int) -#7564 := [rewrite]: #7563 -#7595 := [monotonicity #7564]: #7594 -#7600 := [trans #7595 #7598]: #7599 -#7603 := [monotonicity #7600]: #7602 -#7591 := [asserted]: #1371 -#7606 := [mp #7591 #7603]: #7601 -#15198 := [monotonicity #7606]: #15201 -#15195 := [trans #15198 #15197]: #15194 -#15190 := [monotonicity #15195]: #15193 -#15187 := [trans #15190 #15189]: #15186 -#15182 := [monotonicity #15187]: #15185 -#15179 := [trans #15182 #15181]: #15178 -#15984 := [monotonicity #15179]: #15983 -#15989 := [trans #15984 #15987]: #15988 -#15992 := [quant-intro #15989]: #15991 -#15980 := (iff #13841 #15979) -#15977 := (iff #13821 #15976) -#15974 := (iff #13816 #15971) -#15968 := (or #14425 #13793 #13807) -#15972 := (iff #15968 #15971) -#15973 := [rewrite]: #15972 -#15969 := (iff #13816 #15968) -#14422 := (iff #5712 #14425) -#14427 := (iff #4503 #14426) -#14424 := [monotonicity #15179]: #14427 -#14423 := [monotonicity #14424]: #14422 -#15970 := [monotonicity #14423]: #15969 -#15975 := [trans #15970 #15973]: #15974 -#15978 := [quant-intro #15975]: #15977 -#15981 := [monotonicity #15978]: #15980 -#15995 := [monotonicity #15981 #15992]: #15994 -#15998 := [monotonicity #15978 #15995]: #15997 -#16001 := [monotonicity #15998]: #16000 -#15966 := (iff #13788 #15963) -#15960 := (or #13485 #15957 #13765) -#15964 := (iff #15960 #15963) -#15965 := [rewrite]: #15964 -#15961 := (iff #13788 #15960) -#15958 := (iff #13759 #15957) -#15955 := (iff #13753 #15954) -#15952 := (iff #13748 #15951) -#15949 := (iff #13740 #15948) -#15946 := (iff #13731 #15945) -#15943 := (iff #13726 #15940) -#15937 := (or #12821 #12812 #13485 #13494 #15914 #13671) -#15941 := (iff #15937 #15940) -#15942 := [rewrite]: #15941 -#15938 := (iff #13726 #15937) -#15915 := (iff #13615 #15914) -#15912 := (iff #13607 #15909) -#15906 := (or #12656 #13511 #15897 #13586 #15903) -#15910 := (iff #15906 #15909) -#15911 := [rewrite]: #15910 -#15907 := (iff #13607 #15906) -#15904 := (iff #13592 #15903) -#15901 := (iff #13589 #15900) -#15867 := (iff #13500 #15864) -#15809 := (+ 4294967295::Int #13501) -#15860 := (>= #15809 1::Int) -#15865 := (iff #15860 #15864) -#15866 := [rewrite]: #15865 -#15861 := (iff #13500 #15860) -#15810 := (= #13502 #15809) -#15811 := [monotonicity #7606]: #15810 -#15862 := [monotonicity #15811]: #15861 -#15868 := [trans #15862 #15866]: #15867 -#15902 := [monotonicity #15868]: #15901 -#15905 := [monotonicity #15902]: #15904 -#15898 := (iff #13579 #15897) -#15895 := (iff #13576 #15894) -#15892 := (iff #13573 #15891) -#15889 := (iff #13570 #15886) -#15883 := (or #15880 #13565) -#15887 := (iff #15883 #15886) -#15888 := [rewrite]: #15887 -#15884 := (iff #13570 #15883) -#15881 := (iff #13553 #15880) -#15878 := (iff #13550 #15877) -#15875 := (iff #13545 #15872) -#15869 := (or #14425 #13522 #13536) -#15873 := (iff #15869 #15872) -#15874 := [rewrite]: #15873 -#15870 := (iff #13545 #15869) -#15871 := [monotonicity #14423]: #15870 -#15876 := [trans #15871 #15874]: #15875 -#15879 := [quant-intro #15876]: #15878 -#15882 := [monotonicity #15879]: #15881 -#15885 := [monotonicity #15882]: #15884 -#15890 := [trans #15885 #15888]: #15889 -#15893 := [monotonicity #15879 #15890]: #15892 -#15896 := [monotonicity #15893]: #15895 -#15899 := [monotonicity #15896]: #15898 -#15908 := [monotonicity #15899 #15905]: #15907 -#15913 := [trans #15908 #15911]: #15912 -#15916 := [monotonicity #15868 #15913]: #15915 -#15939 := [monotonicity #15916]: #15938 -#15944 := [trans #15939 #15942]: #15943 -#15935 := (iff #13696 #15932) -#15929 := (or #13485 #15926 #13672) -#15933 := (iff #15929 #15932) -#15934 := [rewrite]: #15933 -#15930 := (iff #13696 #15929) -#15927 := (iff #13666 #15926) -#15924 := (iff #13660 #15923) -#15921 := (iff #13655 #15920) -#15918 := (iff #13647 #15917) -#15919 := [monotonicity #15916]: #15918 -#15922 := [monotonicity #15919]: #15921 -#15925 := [monotonicity #15922]: #15924 -#15928 := [monotonicity #15925]: #15927 -#15931 := [monotonicity #15928]: #15930 -#15936 := [trans #15931 #15934]: #15935 -#15947 := [monotonicity #15936 #15944]: #15946 -#15950 := [monotonicity #15947]: #15949 -#15953 := [monotonicity #15950]: #15952 -#15956 := [monotonicity #15953]: #15955 -#15959 := [monotonicity #15956]: #15958 -#15962 := [monotonicity #15959]: #15961 -#15967 := [trans #15962 #15965]: #15966 -#16004 := [monotonicity #15967 #16001]: #16003 -#15858 := (iff #14030 #15857) -#15855 := (iff #14027 #15854) -#15852 := (iff #14023 #15849) -#15843 := (+ 255::Int #13970) -#15846 := (>= #15843 0::Int) -#15850 := (iff #15846 #15849) -#15851 := [rewrite]: #15850 -#15847 := (iff #14023 #15846) -#15844 := (= #14024 #15843) -#1375 := (= f90 255::Int) -#7605 := [asserted]: #1375 -#15845 := [monotonicity #7605]: #15844 -#15848 := [monotonicity #15845]: #15847 -#15853 := [trans #15848 #15851]: #15852 -#15856 := [monotonicity #15853]: #15855 -#15859 := [monotonicity #15856]: #15858 -#15841 := (iff #14017 #15840) -#15838 := (iff #14014 #15837) -#15835 := (iff #14010 #15832) -#15826 := (+ 4294967295::Int #13941) -#15829 := (>= #15826 0::Int) -#15833 := (iff #15829 #15832) -#15834 := [rewrite]: #15833 -#15830 := (iff #14010 #15829) -#15827 := (= #14011 #15826) -#15828 := [monotonicity #7606]: #15827 -#15831 := [monotonicity #15828]: #15830 -#15836 := [trans #15831 #15834]: #15835 -#15839 := [monotonicity #15836]: #15838 -#15842 := [monotonicity #15839]: #15841 -#15824 := (iff #14007 #15823) -#15821 := (iff #14004 #15820) -#15818 := (iff #14001 #15815) -#15812 := (>= #15809 0::Int) -#15816 := (iff #15812 #15815) -#15817 := [rewrite]: #15816 -#15813 := (iff #14001 #15812) -#15814 := [monotonicity #15811]: #15813 -#15819 := [trans #15814 #15817]: #15818 -#15822 := [monotonicity #15819]: #15821 -#15825 := [monotonicity #15822]: #15824 -#15807 := (iff #13989 #15806) -#15804 := (iff #13986 #15803) -#15801 := (iff #13981 #15798) -#15795 := (or #14425 #13958 #13972) -#15799 := (iff #15795 #15798) -#15800 := [rewrite]: #15799 -#15796 := (iff #13981 #15795) -#15797 := [monotonicity #14423]: #15796 -#15802 := [trans #15797 #15800]: #15801 -#15805 := [quant-intro #15802]: #15804 -#15808 := [monotonicity #15805]: #15807 -#16007 := [monotonicity #15808 #15825 #15842 #15859 #16004]: #16006 -#16012 := [trans #16007 #16010]: #16011 -#16015 := [monotonicity #16012]: #16014 -#15793 := (iff #13469 #15792) -#15790 := (iff #13466 #15789) -#15787 := (iff #13461 #15784) -#15781 := (or #14425 #13439 #13451) -#15785 := (iff #15781 #15784) -#15786 := [rewrite]: #15785 -#15782 := (iff #13461 #15781) -#15783 := [monotonicity #14423]: #15782 -#15788 := [trans #15783 #15786]: #15787 -#15791 := [quant-intro #15788]: #15790 -#15794 := [monotonicity #15791]: #15793 -#16018 := [monotonicity #15794 #16015]: #16017 -#16021 := [monotonicity #15791 #16018]: #16020 -#16024 := [monotonicity #16021]: #16023 -#16027 := [monotonicity #16024]: #16026 -#16030 := [monotonicity #16027]: #16029 -#16033 := [monotonicity #16030]: #16032 -#16036 := [monotonicity #16033]: #16035 -#16039 := [monotonicity #16036]: #16038 -#16042 := [monotonicity #16039]: #16041 -#16045 := [monotonicity #16042]: #16044 -#16048 := [monotonicity #16045]: #16047 -#14325 := (not #14177) -#15338 := (iff #14325 #15337) -#15335 := (iff #14177 #15334) -#15332 := (iff #14174 #15331) -#15329 := (iff #14169 #15328) -#15326 := (iff #14163 #15325) -#15323 := (iff #14158 #15322) -#15320 := (iff #14150 #15319) -#15317 := (iff #14129 #15316) -#15314 := (iff #14126 #15313) -#15311 := (iff #14123 #15310) -#15308 := (iff #14120 #15307) -#15305 := (iff #14115 #15304) -#15302 := (iff #14107 #15299) -#15296 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #15293 #13955 #13989 #13995 #14007 #14017 #14030 #14041) -#15300 := (iff #15296 #15299) -#15301 := [rewrite]: #15300 -#15297 := (iff #14107 #15296) -#15294 := (iff #13914 #15293) -#15291 := (iff #13909 #15288) -#15273 := (or #12304 #12295 #12286 #12277 #13485 #13852) -#15285 := (or #13485 #13766 #15273) -#15289 := (iff #15285 #15288) -#15290 := [rewrite]: #15289 -#15286 := (iff #13909 #15285) -#15283 := (iff #13884 #15273) -#15278 := (and true #15273) -#15281 := (iff #15278 #15273) -#15282 := [rewrite]: #15281 -#15279 := (iff #13884 #15278) -#15276 := (iff #13879 #15273) -#15270 := (or false #12304 #12295 #12286 #12277 #13485 #13852) -#15274 := (iff #15270 #15273) -#15275 := [rewrite]: #15274 -#15271 := (iff #13879 #15270) -#15268 := (iff #12338 false) -#15266 := (iff #12338 #3156) -#15004 := (iff #10924 true) -#10923 := [asserted]: #2542 -#10930 := [mp #10923 #10927]: #10924 -#15005 := [iff-true #10930]: #15004 -#15267 := [monotonicity #15005]: #15266 -#15269 := [trans #15267 #12221]: #15268 -#15272 := [monotonicity #15269]: #15271 -#15277 := [trans #15272 #15275]: #15276 -#15280 := [monotonicity #15005 #15277]: #15279 -#15284 := [trans #15280 #15282]: #15283 -#15287 := [monotonicity #15284]: #15286 -#15292 := [trans #15287 #15290]: #15291 -#15295 := [monotonicity #15292]: #15294 -#15264 := (iff #12366 #15263) -#15261 := (iff #12228 #12222) -#15256 := (and true #12222) -#15259 := (iff #15256 #12222) -#15260 := [rewrite]: #15259 -#15257 := (iff #12228 #15256) -#15240 := (iff #12109 true) -#15241 := [iff-true #14315]: #15240 -#15258 := [monotonicity #15241]: #15257 -#15262 := [trans #15258 #15260]: #15261 -#15265 := [monotonicity #15262]: #15264 -#15298 := [monotonicity #15265 #15295]: #15297 -#15303 := [trans #15298 #15301]: #15302 -#15306 := [monotonicity #15303]: #15305 -#15309 := [monotonicity #15306]: #15308 -#15312 := [monotonicity #15309]: #15311 -#15315 := [monotonicity #15312]: #15314 -#15318 := [monotonicity #15315]: #15317 -#15321 := [monotonicity #15318]: #15320 -#15324 := [monotonicity #15321]: #15323 -#15327 := [monotonicity #15324]: #15326 -#15330 := [monotonicity #15327]: #15329 -#15333 := [monotonicity #15330]: #15332 -#15336 := [monotonicity #15333]: #15335 -#15339 := [monotonicity #15336]: #15338 -#14326 := [not-or-elim #14310]: #14325 -#15340 := [mp #14326 #15339]: #15337 -#16049 := [mp #15340 #16048]: #16046 -#18796 := [mp~ #16049 #18795]: #18793 -#18797 := [mp #18796 #19141]: #19139 -#22664 := [mp #18797 #22663]: #22661 -#23569 := [mp #22664 #23568]: #23566 -#29167 := [unit-resolution #23569 #26960]: #23563 -#24793 := (or #23560 #23554) -#24794 := [def-axiom]: #24793 -#29168 := [unit-resolution #24794 #29167]: #23554 -#27003 := (f24 #3098) -decl f156 :: (-> S18 S18) -#24960 := (f156 #3040) -#27004 := (= #24960 #27003) -decl f39 :: (-> Int S20) -#24797 := (f39 #3076) -#27034 := (f128 #24797) -decl f81 :: (-> Int Int Int) -decl f151 :: (-> S18 Int) -#27032 := (f151 #24960) -#27033 := (f81 0::Int #27032) -#27041 := (+ #27033 #27034) -#27044 := (f54 #24960 #27041) -#27233 := (f24 #27044) -#27604 := (= #27233 #27003) -#27600 := (= #27003 #27233) -#27572 := (= #3098 #27044) -#27028 := (f77 #24797 0::Int #24960) -#27047 := (= #27028 #27044) -#27050 := (not #27047) -decl f150 :: (-> S20 S20 S1) -#27029 := (f150 #27028 #24797) -#27030 := (= f1 #27029) -#27031 := (not #27030) -#27056 := (or #27031 #27050) -#27061 := (not #27056) -#289 := (:var 1 Int) -#1622 := (f77 #60 #289 #275) -#1623 := (pattern #1622) -#1624 := (f150 #1622 #60) -#8354 := (= f1 #1624) -#21196 := (not #8354) -#1627 := (f151 #275) -#1628 := (f81 #289 #1627) -#1626 := (f128 #60) -#1629 := (+ #1626 #1628) -#1630 := (f54 #275 #1629) -#1631 := (= #1622 #1630) -#21195 := (not #1631) -#21197 := (or #21195 #21196) -#21198 := (not #21197) -#21201 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21198) -#8360 := (and #1631 #8354) -#8365 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8360) -#21202 := (iff #8365 #21201) -#21199 := (iff #8360 #21198) -#21200 := [rewrite]: #21199 -#21203 := [quant-intro #21200]: #21202 -#17329 := (~ #8365 #8365) -#17327 := (~ #8360 #8360) -#17328 := [refl]: #17327 -#17330 := [nnf-pos #17328]: #17329 -#1625 := (= #1624 f1) -#1632 := (and #1625 #1631) -#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632) -#8366 := (iff #1633 #8365) -#8363 := (iff #1632 #8360) -#8357 := (and #8354 #1631) -#8361 := (iff #8357 #8360) -#8362 := [rewrite]: #8361 -#8358 := (iff #1632 #8357) -#8355 := (iff #1625 #8354) -#8356 := [rewrite]: #8355 -#8359 := [monotonicity #8356]: #8358 -#8364 := [trans #8359 #8362]: #8363 -#8367 := [quant-intro #8364]: #8366 -#8353 := [asserted]: #1633 -#8370 := [mp #8353 #8367]: #8365 -#17331 := [mp~ #8370 #17330]: #8365 -#21204 := [mp #17331 #21203]: #21201 -#27451 := (not #21201) -#27452 := (or #27451 #27061) -#27035 := (+ #27034 #27033) -#27036 := (f54 #24960 #27035) -#27037 := (= #27028 #27036) -#27038 := (not #27037) -#27039 := (or #27038 #27031) -#27040 := (not #27039) -#27453 := (or #27451 #27040) -#27449 := (iff #27453 #27452) -#27456 := (iff #27452 #27452) -#27457 := [rewrite]: #27456 -#27062 := (iff #27040 #27061) -#27059 := (iff #27039 #27056) -#27053 := (or #27050 #27031) -#27057 := (iff #27053 #27056) -#27058 := [rewrite]: #27057 -#27054 := (iff #27039 #27053) -#27051 := (iff #27038 #27050) -#27048 := (iff #27037 #27047) -#27045 := (= #27036 #27044) -#27042 := (= #27035 #27041) -#27043 := [rewrite]: #27042 -#27046 := [monotonicity #27043]: #27045 -#27049 := [monotonicity #27046]: #27048 -#27052 := [monotonicity #27049]: #27051 -#27055 := [monotonicity #27052]: #27054 -#27060 := [trans #27055 #27058]: #27059 -#27063 := [monotonicity #27060]: #27062 -#27455 := [monotonicity #27063]: #27449 -#27458 := [trans #27455 #27457]: #27449 -#27454 := [quant-inst #24797 #161 #24960]: #27453 -#27459 := [mp #27454 #27458]: #27452 -#27562 := [unit-resolution #27459 #21204]: #27061 -#27468 := (or #27056 #27047) -#27466 := [def-axiom]: #27468 -#27568 := [unit-resolution #27466 #27562]: #27047 -#27570 := (= #3098 #27028) -#24961 := (= f19 #24960) -#1401 := (f136 #369 #202) -#1638 := (pattern #1401) -#1652 := (f156 #1401) -#8415 := (= #369 #1652) -#8419 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8415) -#17359 := (~ #8419 #8419) -#17357 := (~ #8415 #8415) -#17358 := [refl]: #17357 -#17360 := [nnf-pos #17358]: #17359 -#1653 := (= #1652 #369) -#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653) -#8420 := (iff #1654 #8419) -#8417 := (iff #1653 #8415) -#8418 := [rewrite]: #8417 -#8421 := [quant-intro #8418]: #8420 -#8414 := [asserted]: #1654 -#8424 := [mp #8414 #8421]: #8419 -#17361 := [mp~ #8424 #17360]: #8419 -#24964 := (not #8419) -#24965 := (or #24964 #24961) -#24966 := [quant-inst #50 #3036]: #24965 -#28486 := [unit-resolution #24966 #17361]: #24961 -#24798 := (= #3042 #24797) -#132 := (f40 #62) -#23175 := (pattern #132) -#133 := (f39 #132) -#3682 := (= #62 #133) -#23176 := (forall (vars (?v0 S20)) (:pat #23175) #3682) -#3685 := (forall (vars (?v0 S20)) #3682) -#23177 := (iff #3685 #23176) -#23179 := (iff #23176 #23176) -#23180 := [rewrite]: #23179 -#23178 := [rewrite]: #23177 -#23181 := [trans #23178 #23180]: #23177 -#16306 := (~ #3685 #3685) -#16296 := (~ #3682 #3682) -#16297 := [refl]: #16296 -#16362 := [nnf-pos #16297]: #16306 -#134 := (= #133 #62) -#135 := (forall (vars (?v0 S20)) #134) -#3686 := (iff #135 #3685) -#3683 := (iff #134 #3682) -#3684 := [rewrite]: #3683 -#3687 := [quant-intro #3684]: #3686 -#3681 := [asserted]: #135 -#3690 := [mp #3681 #3687]: #3685 -#16363 := [mp~ #3690 #16362]: #3685 -#23182 := [mp #16363 #23181]: #23176 -#24801 := (not #23176) -#24802 := (or #24801 #24798) -#24803 := [quant-inst #3042]: #24802 -#27569 := [unit-resolution #24803 #23182]: #24798 -#27571 := [monotonicity #27569 #28486]: #27570 -#27599 := [trans #27571 #27568]: #27572 -#27601 := [monotonicity #27599]: #27600 -#27591 := [symm #27601]: #27604 -#27234 := (= #24960 #27233) -#27497 := (or #25028 #27234) -#27503 := [quant-inst #24960 #27041]: #27497 -#27567 := [unit-resolution #27503 #23276]: #27234 -#27592 := [trans #27567 #27591]: #27004 -#27413 := (not #27004) -#26977 := (f59 #3098 #24960) -#26978 := (= f1 #26977) -#27006 := (iff #26978 #27004) -#1433 := (f24 #55) -#9184 := (= #275 #1433) -#11354 := (iff #9184 #11333) -#23258 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11354) -#11359 := (forall (vars (?v0 S20) (?v1 S18)) #11354) -#23261 := (iff #11359 #23258) -#23259 := (iff #11354 #11354) -#23260 := [refl]: #23259 -#23262 := [quant-intro #23260]: #23261 -#18251 := (~ #11359 #11359) -#18249 := (~ #11354 #11354) -#18250 := [refl]: #18249 -#18252 := [nnf-pos #18250]: #18251 -#1939 := (= #1433 #275) -#2736 := (iff #2731 #1939) -#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736) -#11360 := (iff #2737 #11359) -#11357 := (iff #2736 #11354) -#11350 := (iff #11333 #9184) -#11355 := (iff #11350 #11354) -#11356 := [rewrite]: #11355 -#11352 := (iff #2736 #11350) -#9185 := (iff #1939 #9184) -#9186 := [rewrite]: #9185 -#11353 := [monotonicity #11336 #9186]: #11352 -#11358 := [trans #11353 #11356]: #11357 -#11361 := [quant-intro #11358]: #11360 -#11349 := [asserted]: #2737 -#11364 := [mp #11349 #11361]: #11359 -#18253 := [mp~ #11364 #18252]: #11359 -#23263 := [mp #18253 #23262]: #23258 -#26174 := (not #23258) -#27419 := (or #26174 #27006) -#27005 := (iff #27004 #26978) -#27420 := (or #26174 #27005) -#27407 := (iff #27420 #27419) -#27409 := (iff #27419 #27419) -#27410 := [rewrite]: #27409 -#27007 := (iff #27005 #27006) -#27008 := [rewrite]: #27007 -#27408 := [monotonicity #27008]: #27407 -#27411 := [trans #27408 #27410]: #27407 -#27405 := [quant-inst #3098 #24960]: #27420 -#27406 := [mp #27405 #27411]: #27419 -#27530 := [unit-resolution #27406 #23263]: #27006 -#26985 := (not #26978) -#27563 := (iff #18409 #26985) -#27535 := (iff #12144 #26978) -#27533 := (iff #26978 #12144) -#27526 := (= #26977 #3099) -#28487 := (= #24960 f19) -#28488 := [symm #28486]: #28487 -#27532 := [monotonicity #28488]: #27526 -#27534 := [monotonicity #27532]: #27533 -#27536 := [symm #27534]: #27535 -#27564 := [monotonicity #27536]: #27563 -#27531 := [hypothesis]: #18409 -#27565 := [mp #27531 #27564]: #26985 -#27412 := (not #27006) -#27414 := (or #27412 #26978 #27413) -#27415 := [def-axiom]: #27414 -#27566 := [unit-resolution #27415 #27565 #27530]: #27413 -#27590 := [unit-resolution #27566 #27592]: false -#27593 := [lemma #27590]: #12144 -#27181 := (f54 #24960 #3043) -#27182 := (f77 #27181 0::Int #24960) -#27186 := (f35 f298 #27182) -#27187 := (= f1 #27186) -#27188 := (not #27187) -#28139 := (iff #18412 #27188) -#28109 := (iff #12147 #27187) -#28136 := (iff #27187 #12147) -#28133 := (= #27186 #3101) -#27752 := (= #27182 #3098) -#28494 := (= #27181 #3042) -#28492 := (= #3043 f299) -#25080 := (= f299 #3043) -#2762 := (f128 #2761) -#11409 := (= #202 #2762) -#23265 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11409) -#11413 := (forall (vars (?v0 S18) (?v1 Int)) #11409) -#23268 := (iff #11413 #23265) -#23266 := (iff #11409 #11409) -#23267 := [refl]: #23266 -#23269 := [quant-intro #23267]: #23268 -#18266 := (~ #11413 #11413) -#18264 := (~ #11409 #11409) -#18265 := [refl]: #18264 -#18267 := [nnf-pos #18265]: #18266 -#2763 := (= #2762 #202) -#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763) -#11414 := (iff #2764 #11413) -#11411 := (iff #2763 #11409) -#11412 := [rewrite]: #11411 -#11415 := [quant-intro #11412]: #11414 -#11408 := [asserted]: #2764 -#11418 := [mp #11408 #11415]: #11413 -#18268 := [mp~ #11418 #18267]: #11413 -#23270 := [mp #18268 #23269]: #23265 -#25034 := (not #23265) -#25085 := (or #25034 #25080) -#25086 := [quant-inst #50 #3041]: #25085 -#28491 := [unit-resolution #25086 #23270]: #25080 -#28493 := [symm #28491]: #28492 -#28495 := [monotonicity #28488 #28493]: #28494 -#28135 := [monotonicity #28495 #28488]: #27752 -#27928 := [monotonicity #28135]: #28133 -#28137 := [monotonicity #27928]: #28136 -#28138 := [symm #28137]: #28109 -#28111 := [monotonicity #28138]: #28139 -#27751 := [hypothesis]: #18412 -#28112 := [mp #27751 #28111]: #27188 -decl f148 :: (-> S29 S1) -#27183 := (f69 #3220 #27182) -#27184 := (f148 #27183) -#27185 := (= f1 #27184) -#27198 := (or #27185 #27188) -#27201 := (not #27198) -decl f33 :: (-> S18 S1) -#27194 := (f33 #24960) -#27195 := (= f1 #27194) -#2848 := (f33 f19) -#28526 := (= #2848 #27194) -#28523 := (= #27194 #2848) -#28524 := [monotonicity #28488]: #28523 -#28527 := [symm #28524]: #28526 -#11588 := (= f1 #2848) -#2849 := (= #2848 f1) -#11590 := (iff #2849 #11588) -#11591 := [rewrite]: #11590 -#11587 := [asserted]: #2849 -#11594 := [mp #11587 #11591]: #11588 -#28528 := [trans #11594 #28527]: #27195 -#27196 := (not #27195) -#28357 := (or #27196 #27201) -decl f26 :: (-> S20 S21 S1) -decl f27 :: (-> S19 S20 S21) -#26739 := (f27 f298 #26146) -decl f155 :: (-> S18 Int) -#24962 := (f155 #3040) -#27102 := (f136 #24960 #24962) -#27103 := (f54 #27102 #3043) -#27191 := (f26 #27103 #26739) -#27192 := (= f1 #27191) -#26740 := (f26 #26146 #26739) -#28128 := (= #26740 #27191) -#28366 := (= #27191 #26740) -#28055 := (= #27103 #26146) -#28363 := (= #27103 #3044) -#28152 := (= #27102 #3040) -#28151 := (= #24962 f297) -#24963 := (= f297 #24962) -#1649 := (f155 #1401) -#8408 := (= #202 #1649) -#8411 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8408) -#17354 := (~ #8411 #8411) -#17352 := (~ #8408 #8408) -#17353 := [refl]: #17352 -#17355 := [nnf-pos #17353]: #17354 -#1650 := (= #1649 #202) -#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650) -#8412 := (iff #1651 #8411) -#8409 := (iff #1650 #8408) -#8410 := [rewrite]: #8409 -#8413 := [quant-intro #8410]: #8412 -#8407 := [asserted]: #1651 -#8416 := [mp #8407 #8413]: #8411 -#17356 := [mp~ #8416 #17355]: #8411 -#24969 := (not #8411) -#24970 := (or #24969 #24963) -#24971 := [quant-inst #50 #3036]: #24970 -#28508 := [unit-resolution #24971 #17356]: #24963 -#27929 := [symm #28508]: #28151 -#28153 := [monotonicity #28488 #27929]: #28152 -#28364 := [monotonicity #28153]: #28363 -#28365 := [trans #28364 #28875]: #28055 -#28367 := [monotonicity #28365]: #28366 -#28129 := [symm #28367]: #28128 -#26741 := (= f1 #26740) -decl f64 :: (-> S19 S20 S21) -#26729 := (f64 f298 #26146) -#26730 := (f26 #62 #26729) -#26736 := (pattern #26730) -decl f209 :: (-> S18 S1) -#26733 := (f209 #26550) -#26734 := (= f1 #26733) -#26731 := (= f1 #26730) -#26732 := (not #26731) -decl f159 :: (-> S20 S21 S1) -decl f204 :: (-> S22 S21) -decl f22 :: (-> S19 S20 S22) -#26725 := (f22 f298 #26146) -#26726 := (f204 #26725) -#26727 := (f159 #62 #26726) -#26728 := (= f1 #26727) -#26746 := (or #26728 #26732 #26734) -#26749 := (forall (vars (?v3 S20)) (:pat #26736) #26746) -#26752 := (not #26749) -#26742 := (not #26741) -#26755 := (or #26613 #26742 #26752) -#26758 := (not #26755) -#28107 := (= #3096 #26680) -#28113 := [symm #26898]: #28107 -#28131 := [trans #26960 #28113]: #26681 -#26687 := (or #26689 #26679 #26697) -#26690 := [def-axiom]: #26687 -#28108 := [unit-resolution #26690 #28131 #26901]: #26679 -#26761 := (or #26700 #26758) +#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 +#22586 := (iff #19102 #22585) +#22583 := (iff #19099 #22574) +#22575 := (not #22574) +#22578 := (not #22575) +#22581 := (iff #22578 #22574) +#22582 := [rewrite]: #22581 +#22579 := (iff #19099 #22578) +#22576 := (iff #19096 #22575) +#22577 := [rewrite]: #22576 +#22580 := [monotonicity #22577]: #22579 +#22584 := [trans #22580 #22582]: #22583 +#22587 := [monotonicity #22584]: #22586 +#22592 := [trans #22587 #22590]: #22591 +#22595 := [monotonicity #22592]: #22594 +#22570 := (iff #18769 #22567) +#22561 := (and #22543 #22558) +#22568 := (iff #22561 #22567) +#22569 := [rewrite]: #22568 +#22562 := (iff #18769 #22561) +#22559 := (iff #18765 #22558) +#22556 := (iff #18762 #22547) +#22548 := (not #22547) +#22551 := (not #22548) +#22554 := (iff #22551 #22547) +#22555 := [rewrite]: #22554 +#22552 := (iff #18762 #22551) +#22549 := (iff #16021 #22548) +#22550 := [rewrite]: #22549 +#22553 := [monotonicity #22550]: #22552 +#22557 := [trans #22553 #22555]: #22556 +#22560 := [quant-intro #22557]: #22559 +#22544 := (iff #16012 #22543) +#22541 := (iff #16007 #22538) +#20251 := (or #5124 #19613) +#22535 := (or #13829 #13843 #20251) +#22539 := (iff #22535 #22538) +#22540 := [rewrite]: #22539 +#22536 := (iff #16007 #22535) +#20260 := (iff #14461 #20251) +#20252 := (not #20251) +#20255 := (not #20252) +#20258 := (iff #20255 #20251) +#20259 := [rewrite]: #20258 +#20256 := (iff #14461 #20255) +#20253 := (iff #14462 #20252) +#20254 := [rewrite]: #20253 +#20257 := [monotonicity #20254]: #20256 +#20261 := [trans #20257 #20259]: #20260 +#22537 := [monotonicity #20261]: #22536 +#22542 := [trans #22537 #22540]: #22541 +#22545 := [quant-intro #22542]: #22544 +#22563 := [monotonicity #22545 #22560]: #22562 +#22571 := [trans #22563 #22569]: #22570 +#22598 := [monotonicity #22571 #22595]: #22597 +#22601 := [monotonicity #22598]: #22600 +#22608 := [trans #22601 #22606]: #22607 +#22533 := (iff #19057 #22530) +#22525 := (and #13513 #13516 #13802 #22522) +#22531 := (iff #22525 #22530) +#22532 := [rewrite]: #22531 +#22526 := (iff #19057 #22525) +#22523 := (iff #19051 #22522) +#22520 := (iff #19046 #22517) +#22512 := (and #12575 #12578 #22509) +#22518 := (iff #22512 #22517) +#22519 := [rewrite]: #22518 +#22513 := (iff #19046 #22512) +#22510 := (iff #19040 #22509) +#22507 := (iff #19035 #22504) +#22499 := (and #12575 #12584 #13513 #13516 #22496) +#22505 := (iff #22499 #22504) +#22506 := [rewrite]: #22505 +#22500 := (iff #19035 #22499) +#22497 := (iff #19029 #22496) +#22494 := (iff #19024 #22491) +#22487 := (and #12839 #12842 #13513 #13516 #13525 #13708 #22447) +#22492 := (iff #22487 #22491) +#22493 := [rewrite]: #22492 +#22488 := (iff #19024 #22487) +#22448 := (iff #18984 #22447) +#22445 := (iff #18979 #22442) +#22435 := (and #12622 #13525 #13534 #13542 #13618 #15900 #22432) +#22443 := (iff #22435 #22442) +#22444 := [rewrite]: #22443 +#22436 := (iff #18979 #22435) +#22433 := (iff #18971 #22432) +#22430 := (iff #18968 #22427) +#22422 := (and #13550 #22419) +#22428 := (iff #22422 #22427) +#22429 := [rewrite]: #22428 +#22423 := (iff #18968 #22422) +#22420 := (iff #18963 #22419) +#22417 := (iff #18957 #22416) +#22414 := (iff #18954 #22411) +#22397 := (or #22395 #22396) +#22408 := (or #18930 #18943 #22397) +#22412 := (iff #22408 #22411) +#22413 := [rewrite]: #22412 +#22409 := (iff #18954 #22408) +#22406 := (iff #18951 #22397) +#22398 := (not #22397) +#22401 := (not #22398) +#22404 := (iff #22401 #22397) +#22405 := [rewrite]: #22404 +#22402 := (iff #18951 #22401) +#22399 := (iff #18948 #22398) +#22400 := [rewrite]: #22399 +#22403 := [monotonicity #22400]: #22402 +#22407 := [trans #22403 #22405]: #22406 +#22410 := [monotonicity #22407]: #22409 +#22415 := [trans #22410 #22413]: #22414 +#22418 := [monotonicity #22415]: #22417 +#22393 := (iff #18641 #22390) +#22385 := (and #22363 #22382) +#22391 := (iff #22385 #22390) +#22392 := [rewrite]: #22391 +#22386 := (iff #18641 #22385) +#22383 := (iff #15913 #22382) +#22380 := (iff #15908 #22377) +#22374 := (or #13558 #13572 #20251) +#22378 := (iff #22374 #22377) +#22379 := [rewrite]: #22378 +#22375 := (iff #15908 #22374) +#22376 := [monotonicity #20261]: #22375 +#22381 := [trans #22376 #22379]: #22380 +#22384 := [quant-intro #22381]: #22383 +#22372 := (iff #18631 #22363) +#22367 := (not #22364) +#22370 := (iff #22367 #22363) +#22371 := [rewrite]: #22370 +#22368 := (iff #18631 #22367) +#22365 := (iff #13601 #22364) +#22366 := [rewrite]: #22365 +#22369 := [monotonicity #22366]: #22368 +#22373 := [trans #22369 #22371]: #22372 +#22387 := [monotonicity #22373 #22384]: #22386 +#22394 := [trans #22387 #22392]: #22393 +#22421 := [monotonicity #22394 #22418]: #22420 +#22424 := [monotonicity #22421]: #22423 +#22431 := [trans #22424 #22429]: #22430 +#22434 := [monotonicity #22431]: #22433 +#22437 := [monotonicity #22434]: #22436 +#22446 := [trans #22437 #22444]: #22445 +#22449 := [monotonicity #22446]: #22448 +#22489 := [monotonicity #22449]: #22488 +#22495 := [trans #22489 #22493]: #22494 +#22485 := (iff #19012 #22482) +#22476 := (and #13513 #13516 #13707 #22473) +#22483 := (iff #22476 #22482) +#22484 := [rewrite]: #22483 +#22477 := (iff #19012 #22476) +#22474 := (iff #19006 #22473) +#22471 := (iff #19001 #22468) +#22463 := (and #12575 #12578 #22460) +#22469 := (iff #22463 #22468) +#22470 := [rewrite]: #22469 +#22464 := (iff #19001 #22463) +#22461 := (iff #18995 #22460) +#22458 := (iff #18990 #22455) +#22450 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #22447) +#22456 := (iff #22450 #22455) +#22457 := [rewrite]: #22456 +#22451 := (iff #18990 #22450) +#22452 := [monotonicity #22449]: #22451 +#22459 := [trans #22452 #22457]: #22458 +#22462 := [monotonicity #22459]: #22461 +#22465 := [monotonicity #22462]: #22464 +#22472 := [trans #22465 #22470]: #22471 +#22475 := [monotonicity #22472]: #22474 +#22478 := [monotonicity #22475]: #22477 +#22486 := [trans #22478 #22484]: #22485 +#22498 := [monotonicity #22486 #22495]: #22497 +#22501 := [monotonicity #22498]: #22500 +#22508 := [trans #22501 #22506]: #22507 +#22511 := [monotonicity #22508]: #22510 +#22514 := [monotonicity #22511]: #22513 +#22521 := [trans #22514 #22519]: #22520 +#22524 := [monotonicity #22521]: #22523 +#22527 := [monotonicity #22524]: #22526 +#22534 := [trans #22527 #22532]: #22533 +#22611 := [monotonicity #22534 #22608]: #22610 +#22360 := (iff #15839 #22359) +#22357 := (iff #15834 #22354) +#22351 := (or #13994 #14008 #20251) +#22355 := (iff #22351 #22354) +#22356 := [rewrite]: #22355 +#22352 := (iff #15834 #22351) +#22353 := [monotonicity #20261]: #22352 +#22358 := [trans #22353 #22356]: #22357 +#22361 := [quant-intro #22358]: #22360 +#22614 := [monotonicity #22361 #22611]: #22613 +#22630 := [trans #22614 #22628]: #22629 +#22633 := [monotonicity #22630]: #22632 +#22349 := (iff #15825 #22348) +#22346 := (iff #15820 #22343) +#22340 := (or #13475 #13487 #20251) +#22344 := (iff #22340 #22343) +#22345 := [rewrite]: #22344 +#22341 := (iff #15820 #22340) +#22342 := [monotonicity #20261]: #22341 +#22347 := [trans #22342 #22345]: #22346 +#22350 := [quant-intro #22347]: #22349 +#22636 := [monotonicity #22350 #22633]: #22635 +#22644 := [trans #22636 #22642]: #22643 +#22338 := (iff #18865 #22337) +#22335 := (iff #18860 #22332) +#22318 := (or #22316 #22317) +#22329 := (or #18486 #18487 #22318) +#22333 := (iff #22329 #22332) +#22334 := [rewrite]: #22333 +#22330 := (iff #18860 #22329) +#22327 := (iff #18854 #22318) +#22319 := (not #22318) +#22322 := (not #22319) +#22325 := (iff #22322 #22318) +#22326 := [rewrite]: #22325 +#22323 := (iff #18854 #22322) +#22320 := (iff #18851 #22319) +#22321 := [rewrite]: #22320 +#22324 := [monotonicity #22321]: #22323 +#22328 := [trans #22324 #22326]: #22327 +#22331 := [monotonicity #22328]: #22330 +#22336 := [trans #22331 #22334]: #22335 +#22339 := [monotonicity #22336]: #22338 +#22647 := [monotonicity #22339 #22644]: #22646 +#22650 := [monotonicity #22647]: #22649 +#22657 := [trans #22650 #22655]: #22656 +#22660 := [monotonicity #22657]: #22659 +#22663 := [monotonicity #22660]: #22662 +#22670 := [trans #22663 #22668]: #22669 +#22673 := [monotonicity #22670]: #22672 +#22676 := [monotonicity #22673]: #22675 +#22683 := [trans #22676 #22681]: #22682 +#22686 := [monotonicity #22683]: #22685 +#22689 := [monotonicity #22686]: #22688 +#22696 := [trans #22689 #22694]: #22695 +#22699 := [monotonicity #22696]: #22698 +#18741 := (and #18740 #18739) +#18742 := (not #18741) +#18745 := (+ #18744 #13841) +#18746 := (<= #18745 0::Int) +#18747 := (+ ?v0!15 #13442) +#18748 := (>= #18747 0::Int) +#18749 := (or #18748 #18746 #18742) +#18750 := (not #18749) +#18773 := (or #18750 #18769) +#18526 := (not #13521) +#18733 := (not #12313) +#18730 := (not #12322) +#18727 := (not #12331) +#18724 := (not #12340) +#18777 := (and #18724 #18727 #18730 #18733 #18526 #13805 #18773) +#15936 := (and #13534 #15900) +#15939 := (not #15936) +#18657 := (not #15939) +#18617 := (and #18616 #18615) +#18618 := (not #18617) +#18621 := (+ #18620 #13570) +#18622 := (<= #18621 0::Int) +#18623 := (+ ?v0!14 #13551) +#18624 := (>= #18623 0::Int) +#18625 := (or #18624 #18622 #18618) +#18626 := (not #18625) +#18645 := (or #18626 #18641) +#18611 := (not #13555) +#18649 := (and #18611 #18645) +#18653 := (or #13555 #18649) +#18606 := (not #13622) +#18603 := (not #13547) +#18600 := (not #12692) +#18660 := (and #18600 #18603 #18606 #18653 #18657) +#18664 := (or #18594 #18597 #18660) +#18591 := (not #13530) +#18691 := (not #12848) +#18688 := (not #12857) +#18696 := (and #18688 #18691 #18526 #18591 #13713 #18664) +#18588 := (not #13656) +#18585 := (not #12731) +#18582 := (not #12740) +#18579 := (not #12758) +#18576 := (not #12767) +#18573 := (not #12776) +#18568 := (not #12785) +#18668 := (and #18568 #18573 #18576 #18579 #18582 #18585 #18588 #18591 #18664) +#18672 := (or #18556 #18565 #18668) +#18562 := (not #12797) +#18676 := (and #18562 #18672) +#18680 := (or #18556 #18559 #18676) +#18684 := (and #18526 #13707 #18680) +#18700 := (or #18684 #18696) +#18704 := (and #18568 #18526 #18700) +#18708 := (or #18556 #18565 #18704) +#18712 := (and #18562 #18708) +#18716 := (or #18556 #18559 #18712) +#18720 := (and #18526 #13802 #18716) +#18781 := (or #18720 #18777) +#15890 := (and #14056 #15885) +#15893 := (not #15890) +#18551 := (not #15893) +#15873 := (and #13513 #15868) +#15876 := (not #15873) +#18548 := (not #15876) +#15856 := (and #14034 #15851) +#15859 := (not #15856) +#18545 := (not #15859) +#18535 := (not #14077) +#18532 := (not #14031) +#18529 := (not #13991) +#18523 := (not #13024) +#18520 := (not #13033) +#18517 := (not #13042) +#18514 := (not #13051) +#18511 := (not #13060) +#18508 := (not #13974) +#18505 := (not #15299) +#18785 := (and #18505 #18508 #18511 #18514 #18517 #18520 #18523 #18526 #18529 #18532 #18535 #15839 #18545 #18548 #18551 #18781) +#18789 := (or #13267 #14234 #18785) +#18793 := (and #15825 #18789) +#18480 := (and #18479 #18478) +#18481 := (not #18480) +#18488 := (or #18487 #18486 #18481) +#18489 := (not #18488) +#18797 := (or #18489 #18793) +#18474 := (not #13472) +#18801 := (and #18474 #18797) +#18805 := (or #13472 #18801) +#18469 := (not #13240) +#18466 := (not #13249) +#18463 := (not #13258) +#18460 := (not #13276) +#18457 := (not #13267) +#18809 := (and #18457 #18460 #18463 #18466 #18469 #18805) +#18813 := (or #18445 #18454 #18809) +#18451 := (not #13288) +#18817 := (and #18451 #18813) +#18821 := (or #18445 #18448 #18817) +#18442 := (not #13300) +#18825 := (and #18442 #18821) +#18829 := (or #13300 #18825) +#19176 := (iff #18829 #19175) +#19173 := (iff #18825 #19172) +#19170 := (iff #18821 #19169) +#19167 := (iff #18817 #19164) +#19161 := (and #12186 #19158) +#19165 := (iff #19161 #19164) +#19166 := [rewrite]: #19165 +#19162 := (iff #18817 #19161) +#19159 := (iff #18813 #19158) +#19156 := (iff #18809 #19153) +#19150 := (and #3109 #12192 #12195 #12198 #12201 #19147) +#19154 := (iff #19150 #19153) +#19155 := [rewrite]: #19154 +#19151 := (iff #18809 #19150) +#19148 := (iff #18805 #19147) +#19145 := (iff #18801 #19144) +#19142 := (iff #18797 #19141) +#19139 := (iff #18793 #19138) +#19136 := (iff #18789 #19135) +#19133 := (iff #18785 #19130) +#19127 := (and #12258 #12515 #12543 #12546 #12549 #12552 #12561 #13518 #13986 #14028 #14072 #15839 #15856 #15873 #15890 #19124) +#19131 := (iff #19127 #19130) +#19132 := [rewrite]: #19131 +#19128 := (iff #18785 #19127) +#19125 := (iff #18781 #19124) +#19122 := (iff #18777 #19119) +#19116 := (and #12269 #12272 #12275 #12278 #13518 #13801 #19111) +#19120 := (iff #19116 #19119) +#19121 := [rewrite]: #19120 +#19117 := (iff #18777 #19116) +#19114 := (iff #18773 #19111) +#19108 := (or #19105 #18769) +#19112 := (iff #19108 #19111) +#19113 := [rewrite]: #19112 +#19109 := (iff #18773 #19108) +#19106 := (iff #18750 #19105) +#19103 := (iff #18749 #19102) +#19100 := (iff #18742 #19099) +#19097 := (iff #18741 #19096) +#19098 := [rewrite]: #19097 +#19101 := [monotonicity #19098]: #19100 +#19094 := (iff #18746 #19091) +#19083 := (+ #13841 #18744) +#19086 := (<= #19083 0::Int) +#19092 := (iff #19086 #19091) +#19093 := [rewrite]: #19092 +#19087 := (iff #18746 #19086) +#19084 := (= #18745 #19083) +#19085 := [rewrite]: #19084 +#19088 := [monotonicity #19085]: #19087 +#19095 := [trans #19088 #19093]: #19094 +#19081 := (iff #18748 #19078) +#19070 := (+ #13442 ?v0!15) +#19073 := (>= #19070 0::Int) +#19079 := (iff #19073 #19078) +#19080 := [rewrite]: #19079 +#19074 := (iff #18748 #19073) +#19071 := (= #18747 #19070) +#19072 := [rewrite]: #19071 +#19075 := [monotonicity #19072]: #19074 +#19082 := [trans #19075 #19080]: #19081 +#19104 := [monotonicity #19082 #19095 #19101]: #19103 +#19107 := [monotonicity #19104]: #19106 +#19110 := [monotonicity #19107]: #19109 +#19115 := [trans #19110 #19113]: #19114 +#18882 := (iff #18526 #13518) +#18883 := [rewrite]: #18882 +#19068 := (iff #18733 #12278) +#19069 := [rewrite]: #19068 +#19066 := (iff #18730 #12275) +#19067 := [rewrite]: #19066 +#19064 := (iff #18727 #12272) +#19065 := [rewrite]: #19064 +#19062 := (iff #18724 #12269) +#19063 := [rewrite]: #19062 +#19118 := [monotonicity #19063 #19065 #19067 #19069 #18883 #13809 #19115]: #19117 +#19123 := [trans #19118 #19121]: #19122 +#19060 := (iff #18720 #19057) +#19054 := (and #13518 #13802 #19051) +#19058 := (iff #19054 #19057) +#19059 := [rewrite]: #19058 +#19055 := (iff #18720 #19054) +#19052 := (iff #18716 #19051) +#19049 := (iff #18712 #19046) +#19043 := (and #12581 #19040) +#19047 := (iff #19043 #19046) +#19048 := [rewrite]: #19047 +#19044 := (iff #18712 #19043) +#19041 := (iff #18708 #19040) +#19038 := (iff #18704 #19035) +#19032 := (and #12587 #13518 #19029) +#19036 := (iff #19032 #19035) +#19037 := [rewrite]: #19036 +#19033 := (iff #18704 #19032) +#19030 := (iff #18700 #19029) +#19027 := (iff #18696 #19024) +#19021 := (and #12839 #12842 #13518 #13527 #13708 #18984) +#19025 := (iff #19021 #19024) +#19026 := [rewrite]: #19025 +#19022 := (iff #18696 #19021) +#18985 := (iff #18664 #18984) +#18982 := (iff #18660 #18979) +#18976 := (and #12622 #13544 #13618 #18971 #15936) +#18980 := (iff #18976 #18979) +#18981 := [rewrite]: #18980 +#18977 := (iff #18660 #18976) +#18974 := (iff #18657 #15936) +#18975 := [rewrite]: #18974 +#18972 := (iff #18653 #18971) +#18969 := (iff #18649 #18968) +#18966 := (iff #18645 #18963) +#18960 := (or #18957 #18641) +#18964 := (iff #18960 #18963) +#18965 := [rewrite]: #18964 +#18961 := (iff #18645 #18960) +#18958 := (iff #18626 #18957) +#18955 := (iff #18625 #18954) +#18952 := (iff #18618 #18951) +#18949 := (iff #18617 #18948) +#18950 := [rewrite]: #18949 +#18953 := [monotonicity #18950]: #18952 +#18946 := (iff #18622 #18943) +#18935 := (+ #13570 #18620) +#18938 := (<= #18935 0::Int) +#18944 := (iff #18938 #18943) +#18945 := [rewrite]: #18944 +#18939 := (iff #18622 #18938) +#18936 := (= #18621 #18935) +#18937 := [rewrite]: #18936 +#18940 := [monotonicity #18937]: #18939 +#18947 := [trans #18940 #18945]: #18946 +#18933 := (iff #18624 #18930) +#18922 := (+ #13551 ?v0!14) +#18925 := (>= #18922 0::Int) +#18931 := (iff #18925 #18930) +#18932 := [rewrite]: #18931 +#18926 := (iff #18624 #18925) +#18923 := (= #18623 #18922) +#18924 := [rewrite]: #18923 +#18927 := [monotonicity #18924]: #18926 +#18934 := [trans #18927 #18932]: #18933 +#18956 := [monotonicity #18934 #18947 #18953]: #18955 +#18959 := [monotonicity #18956]: #18958 +#18962 := [monotonicity #18959]: #18961 +#18967 := [trans #18962 #18965]: #18966 +#18920 := (iff #18611 #13550) +#18921 := [rewrite]: #18920 +#18970 := [monotonicity #18921 #18967]: #18969 +#18973 := [monotonicity #18970]: #18972 +#18918 := (iff #18606 #13618) +#18919 := [rewrite]: #18918 +#18916 := (iff #18603 #13544) +#18917 := [rewrite]: #18916 +#18914 := (iff #18600 #12622) +#18915 := [rewrite]: #18914 +#18978 := [monotonicity #18915 #18917 #18919 #18973 #18975]: #18977 +#18983 := [trans #18978 #18981]: #18982 +#18986 := [monotonicity #18983]: #18985 +#18912 := (iff #18591 #13527) +#18913 := [rewrite]: #18912 +#19019 := (iff #18691 #12842) +#19020 := [rewrite]: #19019 +#19017 := (iff #18688 #12839) +#19018 := [rewrite]: #19017 +#19023 := [monotonicity #19018 #19020 #18883 #18913 #13717 #18986]: #19022 +#19028 := [trans #19023 #19026]: #19027 +#19015 := (iff #18684 #19012) +#19009 := (and #13518 #13707 #19006) +#19013 := (iff #19009 #19012) +#19014 := [rewrite]: #19013 +#19010 := (iff #18684 #19009) +#19007 := (iff #18680 #19006) +#19004 := (iff #18676 #19001) +#18998 := (and #12581 #18995) +#19002 := (iff #18998 #19001) +#19003 := [rewrite]: #19002 +#18999 := (iff #18676 #18998) +#18996 := (iff #18672 #18995) +#18993 := (iff #18668 #18990) +#18987 := (and #12587 #12590 #12593 #12596 #12601 #12604 #13516 #13527 #18984) +#18991 := (iff #18987 #18990) +#18992 := [rewrite]: #18991 +#18988 := (iff #18668 #18987) +#18910 := (iff #18588 #13516) +#18911 := [rewrite]: #18910 +#18908 := (iff #18585 #12604) +#18909 := [rewrite]: #18908 +#18906 := (iff #18582 #12601) +#18907 := [rewrite]: #18906 +#18904 := (iff #18579 #12596) +#18905 := [rewrite]: #18904 +#18902 := (iff #18576 #12593) +#18903 := [rewrite]: #18902 +#18900 := (iff #18573 #12590) +#18901 := [rewrite]: #18900 +#18898 := (iff #18568 #12587) +#18899 := [rewrite]: #18898 +#18989 := [monotonicity #18899 #18901 #18903 #18905 #18907 #18909 #18911 #18913 #18986]: #18988 +#18994 := [trans #18989 #18992]: #18993 +#18997 := [monotonicity #18994]: #18996 +#18896 := (iff #18562 #12581) +#18897 := [rewrite]: #18896 +#19000 := [monotonicity #18897 #18997]: #18999 +#19005 := [trans #19000 #19003]: #19004 +#19008 := [monotonicity #19005]: #19007 +#19011 := [monotonicity #18883 #19008]: #19010 +#19016 := [trans #19011 #19014]: #19015 +#19031 := [monotonicity #19016 #19028]: #19030 +#19034 := [monotonicity #18899 #18883 #19031]: #19033 +#19039 := [trans #19034 #19037]: #19038 +#19042 := [monotonicity #19039]: #19041 +#19045 := [monotonicity #18897 #19042]: #19044 +#19050 := [trans #19045 #19048]: #19049 +#19053 := [monotonicity #19050]: #19052 +#19056 := [monotonicity #18883 #19053]: #19055 +#19061 := [trans #19056 #19059]: #19060 +#19126 := [monotonicity #19061 #19123]: #19125 +#18894 := (iff #18551 #15890) +#18895 := [rewrite]: #18894 +#18892 := (iff #18548 #15873) +#18893 := [rewrite]: #18892 +#18890 := (iff #18545 #15856) +#18891 := [rewrite]: #18890 +#18888 := (iff #18535 #14072) +#18889 := [rewrite]: #18888 +#18886 := (iff #18532 #14028) +#18887 := [rewrite]: #18886 +#18884 := (iff #18529 #13986) +#18885 := [rewrite]: #18884 +#18880 := (iff #18523 #12561) +#18881 := [rewrite]: #18880 +#18878 := (iff #18520 #12552) +#18879 := [rewrite]: #18878 +#18876 := (iff #18517 #12549) +#18877 := [rewrite]: #18876 +#18874 := (iff #18514 #12546) +#18875 := [rewrite]: #18874 +#18872 := (iff #18511 #12543) +#18873 := [rewrite]: #18872 +#18870 := (iff #18508 #12515) +#18871 := [rewrite]: #18870 +#18868 := (iff #18505 #12258) +#18869 := [rewrite]: #18868 +#19129 := [monotonicity #18869 #18871 #18873 #18875 #18877 #18879 #18881 #18883 #18885 #18887 #18889 #18891 #18893 #18895 #19126]: #19128 +#19134 := [trans #19129 #19132]: #19133 +#19137 := [monotonicity #14238 #19134]: #19136 +#19140 := [monotonicity #19137]: #19139 +#18866 := (iff #18489 #18865) +#18863 := (iff #18488 #18860) +#18857 := (or #18487 #18486 #18854) +#18861 := (iff #18857 #18860) +#18862 := [rewrite]: #18861 +#18858 := (iff #18488 #18857) +#18855 := (iff #18481 #18854) +#18852 := (iff #18480 #18851) +#18853 := [rewrite]: #18852 +#18856 := [monotonicity #18853]: #18855 +#18859 := [monotonicity #18856]: #18858 +#18864 := [trans #18859 #18862]: #18863 +#18867 := [monotonicity #18864]: #18866 +#19143 := [monotonicity #18867 #19140]: #19142 +#18849 := (iff #18474 #13469) +#18850 := [rewrite]: #18849 +#19146 := [monotonicity #18850 #19143]: #19145 +#19149 := [monotonicity #19146]: #19148 +#18847 := (iff #18469 #12201) +#18848 := [rewrite]: #18847 +#18845 := (iff #18466 #12198) +#18846 := [rewrite]: #18845 +#18843 := (iff #18463 #12195) +#18844 := [rewrite]: #18843 +#18841 := (iff #18460 #12192) +#18842 := [rewrite]: #18841 +#18839 := (iff #18457 #3109) +#18840 := [rewrite]: #18839 +#19152 := [monotonicity #18840 #18842 #18844 #18846 #18848 #19149]: #19151 +#19157 := [trans #19152 #19155]: #19156 +#19160 := [monotonicity #19157]: #19159 +#18837 := (iff #18451 #12186) +#18838 := [rewrite]: #18837 +#19163 := [monotonicity #18838 #19160]: #19162 +#19168 := [trans #19163 #19166]: #19167 +#19171 := [monotonicity #19168]: #19170 +#18835 := (iff #18442 #12177) +#18836 := [rewrite]: #18835 +#19174 := [monotonicity #18836 #19171]: #19173 +#19177 := [monotonicity #19174]: #19176 +#16026 := (exists (vars (?v0 Int)) #16021) +#16015 := (not #16012) +#16029 := (or #16015 #16026) +#16032 := (and #16012 #16029) +#16035 := (or #12340 #12331 #12322 #12313 #13521 #13802 #16032) +#15916 := (not #15913) +#15922 := (or #13601 #15916) +#15927 := (and #15913 #15922) +#15930 := (or #13555 #15927) +#15933 := (and #13550 #15930) +#15945 := (or #12692 #13547 #13622 #15933 #15939) +#15950 := (and #13534 #15900 #15945) +#15976 := (or #12857 #12848 #13521 #13530 #13707 #15950) +#15953 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #15950) +#15956 := (and #12575 #12584 #15953) +#15959 := (or #12797 #15956) +#15962 := (and #12575 #12578 #15959) +#15968 := (or #13521 #13708 #15962) +#15981 := (and #15968 #15976) +#15984 := (or #12785 #13521 #15981) +#15987 := (and #12575 #12584 #15984) +#15990 := (or #12797 #15987) +#15993 := (and #12575 #12578 #15990) +#15999 := (or #13521 #13801 #15993) +#16038 := (and #15999 #16035) +#15842 := (not #15839) +#16044 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14031 #14077 #15842 #15859 #15876 #15893 #16038) +#16049 := (and #3109 #13509 #16044) +#15828 := (not #15825) +#16052 := (or #15828 #16049) +#16055 := (and #15825 #16052) +#16058 := (or #13472 #16055) +#16061 := (and #13469 #16058) +#16064 := (or #13267 #13276 #13258 #13249 #13240 #16061) +#16067 := (and #12180 #12189 #16064) +#16070 := (or #13288 #16067) +#16073 := (and #12180 #12183 #16070) +#16076 := (or #13300 #16073) +#16079 := (and #12177 #16076) +#16082 := (not #16079) +#18830 := (~ #16082 #18829) +#18826 := (not #16076) +#18827 := (~ #18826 #18825) +#18822 := (not #16073) +#18823 := (~ #18822 #18821) +#18818 := (not #16070) +#18819 := (~ #18818 #18817) +#18814 := (not #16067) +#18815 := (~ #18814 #18813) +#18810 := (not #16064) +#18811 := (~ #18810 #18809) +#18806 := (not #16061) +#18807 := (~ #18806 #18805) +#18802 := (not #16058) +#18803 := (~ #18802 #18801) +#18798 := (not #16055) +#18799 := (~ #18798 #18797) +#18794 := (not #16052) +#18795 := (~ #18794 #18793) +#18790 := (not #16049) +#18791 := (~ #18790 #18789) +#18786 := (not #16044) +#18787 := (~ #18786 #18785) +#18782 := (not #16038) +#18783 := (~ #18782 #18781) +#18778 := (not #16035) +#18779 := (~ #18778 #18777) +#18774 := (not #16032) +#18775 := (~ #18774 #18773) +#18770 := (not #16029) +#18771 := (~ #18770 #18769) +#18766 := (not #16026) +#18767 := (~ #18766 #18765) +#18763 := (~ #18762 #18762) +#18764 := [refl]: #18763 +#18768 := [nnf-neg #18764]: #18767 +#18759 := (not #16015) +#18760 := (~ #18759 #16012) +#18757 := (~ #16012 #16012) +#18755 := (~ #16007 #16007) +#18756 := [refl]: #18755 +#18758 := [nnf-pos #18756]: #18757 +#18761 := [nnf-neg #18758]: #18760 +#18772 := [nnf-neg #18761 #18768]: #18771 +#18751 := (~ #16015 #18750) +#18752 := [sk]: #18751 +#18776 := [nnf-neg #18752 #18772]: #18775 +#18736 := (~ #13805 #13805) +#18737 := [refl]: #18736 +#18527 := (~ #18526 #18526) +#18528 := [refl]: #18527 +#18734 := (~ #18733 #18733) +#18735 := [refl]: #18734 +#18731 := (~ #18730 #18730) +#18732 := [refl]: #18731 +#18728 := (~ #18727 #18727) +#18729 := [refl]: #18728 +#18725 := (~ #18724 #18724) +#18726 := [refl]: #18725 +#18780 := [nnf-neg #18726 #18729 #18732 #18735 #18528 #18737 #18776]: #18779 +#18721 := (not #15999) +#18722 := (~ #18721 #18720) +#18717 := (not #15993) +#18718 := (~ #18717 #18716) +#18713 := (not #15990) +#18714 := (~ #18713 #18712) +#18709 := (not #15987) +#18710 := (~ #18709 #18708) +#18705 := (not #15984) +#18706 := (~ #18705 #18704) +#18701 := (not #15981) +#18702 := (~ #18701 #18700) +#18697 := (not #15976) +#18698 := (~ #18697 #18696) +#18665 := (not #15950) +#18666 := (~ #18665 #18664) +#18661 := (not #15945) +#18662 := (~ #18661 #18660) +#18658 := (~ #18657 #18657) +#18659 := [refl]: #18658 +#18654 := (not #15933) +#18655 := (~ #18654 #18653) +#18650 := (not #15930) +#18651 := (~ #18650 #18649) +#18646 := (not #15927) +#18647 := (~ #18646 #18645) +#18642 := (not #15922) +#18643 := (~ #18642 #18641) +#18638 := (not #15916) +#18639 := (~ #18638 #15913) +#18636 := (~ #15913 #15913) +#18634 := (~ #15908 #15908) +#18635 := [refl]: #18634 +#18637 := [nnf-pos #18635]: #18636 +#18640 := [nnf-neg #18637]: #18639 +#18632 := (~ #18631 #18631) +#18633 := [refl]: #18632 +#18644 := [nnf-neg #18633 #18640]: #18643 +#18627 := (~ #15916 #18626) +#18628 := [sk]: #18627 +#18648 := [nnf-neg #18628 #18644]: #18647 +#18612 := (~ #18611 #18611) +#18613 := [refl]: #18612 +#18652 := [nnf-neg #18613 #18648]: #18651 +#18609 := (~ #13555 #13555) +#18610 := [refl]: #18609 +#18656 := [nnf-neg #18610 #18652]: #18655 +#18607 := (~ #18606 #18606) +#18608 := [refl]: #18607 +#18604 := (~ #18603 #18603) +#18605 := [refl]: #18604 +#18601 := (~ #18600 #18600) +#18602 := [refl]: #18601 +#18663 := [nnf-neg #18602 #18605 #18608 #18656 #18659]: #18662 +#18598 := (~ #18597 #18597) +#18599 := [refl]: #18598 +#18595 := (~ #18594 #18594) +#18596 := [refl]: #18595 +#18667 := [nnf-neg #18596 #18599 #18663]: #18666 +#18694 := (~ #13713 #13713) +#18695 := [refl]: #18694 +#18592 := (~ #18591 #18591) +#18593 := [refl]: #18592 +#18692 := (~ #18691 #18691) +#18693 := [refl]: #18692 +#18689 := (~ #18688 #18688) +#18690 := [refl]: #18689 +#18699 := [nnf-neg #18690 #18693 #18528 #18593 #18695 #18667]: #18698 +#18685 := (not #15968) +#18686 := (~ #18685 #18684) +#18681 := (not #15962) +#18682 := (~ #18681 #18680) +#18677 := (not #15959) +#18678 := (~ #18677 #18676) +#18673 := (not #15956) +#18674 := (~ #18673 #18672) +#18669 := (not #15953) +#18670 := (~ #18669 #18668) +#18589 := (~ #18588 #18588) +#18590 := [refl]: #18589 +#18586 := (~ #18585 #18585) +#18587 := [refl]: #18586 +#18583 := (~ #18582 #18582) +#18584 := [refl]: #18583 +#18580 := (~ #18579 #18579) +#18581 := [refl]: #18580 +#18577 := (~ #18576 #18576) +#18578 := [refl]: #18577 +#18574 := (~ #18573 #18573) +#18575 := [refl]: #18574 +#18569 := (~ #18568 #18568) +#18570 := [refl]: #18569 +#18671 := [nnf-neg #18570 #18575 #18578 #18581 #18584 #18587 #18590 #18593 #18667]: #18670 +#18566 := (~ #18565 #18565) +#18567 := [refl]: #18566 +#18557 := (~ #18556 #18556) +#18558 := [refl]: #18557 +#18675 := [nnf-neg #18558 #18567 #18671]: #18674 +#18563 := (~ #18562 #18562) +#18564 := [refl]: #18563 +#18679 := [nnf-neg #18564 #18675]: #18678 +#18560 := (~ #18559 #18559) +#18561 := [refl]: #18560 +#18683 := [nnf-neg #18558 #18561 #18679]: #18682 +#18571 := (~ #13707 #13707) +#18572 := [refl]: #18571 +#18687 := [nnf-neg #18528 #18572 #18683]: #18686 +#18703 := [nnf-neg #18687 #18699]: #18702 +#18707 := [nnf-neg #18570 #18528 #18703]: #18706 +#18711 := [nnf-neg #18558 #18567 #18707]: #18710 +#18715 := [nnf-neg #18564 #18711]: #18714 +#18719 := [nnf-neg #18558 #18561 #18715]: #18718 +#18554 := (~ #13802 #13802) +#18555 := [refl]: #18554 +#18723 := [nnf-neg #18528 #18555 #18719]: #18722 +#18784 := [nnf-neg #18723 #18780]: #18783 +#18552 := (~ #18551 #18551) +#18553 := [refl]: #18552 +#18549 := (~ #18548 #18548) +#18550 := [refl]: #18549 +#18546 := (~ #18545 #18545) +#18547 := [refl]: #18546 +#18542 := (not #15842) +#18543 := (~ #18542 #15839) +#18540 := (~ #15839 #15839) +#18538 := (~ #15834 #15834) +#18539 := [refl]: #18538 +#18541 := [nnf-pos #18539]: #18540 +#18544 := [nnf-neg #18541]: #18543 +#18536 := (~ #18535 #18535) +#18537 := [refl]: #18536 +#18533 := (~ #18532 #18532) +#18534 := [refl]: #18533 +#18530 := (~ #18529 #18529) +#18531 := [refl]: #18530 +#18524 := (~ #18523 #18523) +#18525 := [refl]: #18524 +#18521 := (~ #18520 #18520) +#18522 := [refl]: #18521 +#18518 := (~ #18517 #18517) +#18519 := [refl]: #18518 +#18515 := (~ #18514 #18514) +#18516 := [refl]: #18515 +#18512 := (~ #18511 #18511) +#18513 := [refl]: #18512 +#18509 := (~ #18508 #18508) +#18510 := [refl]: #18509 +#18506 := (~ #18505 #18505) +#18507 := [refl]: #18506 +#18788 := [nnf-neg #18507 #18510 #18513 #18516 #18519 #18522 #18525 #18528 #18531 #18534 #18537 #18544 #18547 #18550 #18553 #18784]: #18787 +#18503 := (~ #14234 #14234) +#18504 := [refl]: #18503 +#18501 := (~ #13267 #13267) +#18502 := [refl]: #18501 +#18792 := [nnf-neg #18502 #18504 #18788]: #18791 +#18498 := (not #15828) +#18499 := (~ #18498 #15825) +#18496 := (~ #15825 #15825) +#18494 := (~ #15820 #15820) +#18495 := [refl]: #18494 +#18497 := [nnf-pos #18495]: #18496 +#18500 := [nnf-neg #18497]: #18499 +#18796 := [nnf-neg #18500 #18792]: #18795 +#18490 := (~ #15828 #18489) +#18491 := [sk]: #18490 +#18800 := [nnf-neg #18491 #18796]: #18799 +#18475 := (~ #18474 #18474) +#18476 := [refl]: #18475 +#18804 := [nnf-neg #18476 #18800]: #18803 +#18472 := (~ #13472 #13472) +#18473 := [refl]: #18472 +#18808 := [nnf-neg #18473 #18804]: #18807 +#18470 := (~ #18469 #18469) +#18471 := [refl]: #18470 +#18467 := (~ #18466 #18466) +#18468 := [refl]: #18467 +#18464 := (~ #18463 #18463) +#18465 := [refl]: #18464 +#18461 := (~ #18460 #18460) +#18462 := [refl]: #18461 +#18458 := (~ #18457 #18457) +#18459 := [refl]: #18458 +#18812 := [nnf-neg #18459 #18462 #18465 #18468 #18471 #18808]: #18811 +#18455 := (~ #18454 #18454) +#18456 := [refl]: #18455 +#18446 := (~ #18445 #18445) +#18447 := [refl]: #18446 +#18816 := [nnf-neg #18447 #18456 #18812]: #18815 +#18452 := (~ #18451 #18451) +#18453 := [refl]: #18452 +#18820 := [nnf-neg #18453 #18816]: #18819 +#18449 := (~ #18448 #18448) +#18450 := [refl]: #18449 +#18824 := [nnf-neg #18447 #18450 #18820]: #18823 +#18443 := (~ #18442 #18442) +#18444 := [refl]: #18443 +#18828 := [nnf-neg #18444 #18824]: #18827 +#18440 := (~ #13300 #13300) +#18441 := [refl]: #18440 +#18831 := [nnf-neg #18441 #18828]: #18830 +#15324 := (or #12340 #12331 #12322 #12313 #13521 #13802 #13888) +#15329 := (and #13824 #15324) +#15335 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14025 #14031 #14043 #14053 #14066 #14077 #15329) +#15340 := (and #3109 #13509 #15335) +#15343 := (or #13505 #15340) +#15346 := (and #13502 #15343) +#15349 := (or #13472 #15346) +#15352 := (and #13469 #15349) +#15355 := (or #13267 #13276 #13258 #13249 #13240 #15352) +#15358 := (and #12180 #12189 #15355) +#15361 := (or #13288 #15358) +#15364 := (and #12180 #12183 #15361) +#15367 := (or #13300 #15364) +#15370 := (and #12177 #15367) +#15373 := (not #15370) +#16083 := (iff #15373 #16082) +#16080 := (iff #15370 #16079) +#16077 := (iff #15367 #16076) +#16074 := (iff #15364 #16073) +#16071 := (iff #15361 #16070) +#16068 := (iff #15358 #16067) +#16065 := (iff #15355 #16064) +#16062 := (iff #15352 #16061) +#16059 := (iff #15349 #16058) +#16056 := (iff #15346 #16055) +#16053 := (iff #15343 #16052) +#16050 := (iff #15340 #16049) +#16047 := (iff #15335 #16044) +#16041 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #15842 #14031 #15859 #15876 #15893 #14077 #16038) +#16045 := (iff #16041 #16044) +#16046 := [rewrite]: #16045 +#16042 := (iff #15335 #16041) +#16039 := (iff #15329 #16038) +#16036 := (iff #15324 #16035) +#16033 := (iff #13888 #16032) +#16030 := (iff #13883 #16029) +#16027 := (iff #13874 #16026) +#16024 := (iff #13869 #16021) +#16018 := (and #3173 #4202 #15219 #13831) +#16022 := (iff #16018 #16021) +#16023 := [rewrite]: #16022 +#16019 := (iff #13869 #16018) +#15214 := (iff #4516 #15219) +#15235 := -4294967295::Int +#15227 := (+ -4294967295::Int #202) +#15220 := (<= #15227 0::Int) +#15216 := (iff #15220 #15219) +#15217 := [rewrite]: #15216 +#15221 := (iff #4516 #15220) +#15222 := (= #4515 #15227) +#15228 := (+ #202 -4294967295::Int) +#15224 := (= #15228 #15227) +#15225 := [rewrite]: #15224 +#15229 := (= #4515 #15228) +#15230 := (= #4514 -4294967295::Int) +#15236 := (* -1::Int 4294967295::Int) +#15232 := (= #15236 -4294967295::Int) +#15233 := [rewrite]: #15232 +#15237 := (= #4514 #15236) +#7637 := (= f87 4294967295::Int) +#990 := 65536::Int +#1365 := (* 65536::Int 65536::Int) +#1370 := (- #1365 1::Int) +#1371 := (= f87 #1370) +#7638 := (iff #1371 #7637) +#7635 := (= #1370 4294967295::Int) +#1053 := 4294967296::Int +#7628 := (- 4294967296::Int 1::Int) +#7633 := (= #7628 4294967295::Int) +#7634 := [rewrite]: #7633 +#7630 := (= #1370 #7628) +#7599 := (= #1365 4294967296::Int) +#7600 := [rewrite]: #7599 +#7631 := [monotonicity #7600]: #7630 +#7636 := [trans #7631 #7634]: #7635 +#7639 := [monotonicity #7636]: #7638 +#7627 := [asserted]: #1371 +#7642 := [mp #7627 #7639]: #7637 +#15234 := [monotonicity #7642]: #15237 +#15231 := [trans #15234 #15233]: #15230 +#15226 := [monotonicity #15231]: #15229 +#15223 := [trans #15226 #15225]: #15222 +#15218 := [monotonicity #15223]: #15221 +#15215 := [trans #15218 #15217]: #15214 +#16020 := [monotonicity #15215]: #16019 +#16025 := [trans #16020 #16023]: #16024 +#16028 := [quant-intro #16025]: #16027 +#16016 := (iff #13877 #16015) +#16013 := (iff #13857 #16012) +#16010 := (iff #13852 #16007) +#16004 := (or #14461 #13829 #13843) +#16008 := (iff #16004 #16007) +#16009 := [rewrite]: #16008 +#16005 := (iff #13852 #16004) +#14458 := (iff #5738 #14461) +#14463 := (iff #4523 #14462) +#14460 := [monotonicity #15215]: #14463 +#14459 := [monotonicity #14460]: #14458 +#16006 := [monotonicity #14459]: #16005 +#16011 := [trans #16006 #16009]: #16010 +#16014 := [quant-intro #16011]: #16013 +#16017 := [monotonicity #16014]: #16016 +#16031 := [monotonicity #16017 #16028]: #16030 +#16034 := [monotonicity #16014 #16031]: #16033 +#16037 := [monotonicity #16034]: #16036 +#16002 := (iff #13824 #15999) +#15996 := (or #13521 #15993 #13801) +#16000 := (iff #15996 #15999) +#16001 := [rewrite]: #16000 +#15997 := (iff #13824 #15996) +#15994 := (iff #13795 #15993) +#15991 := (iff #13789 #15990) +#15988 := (iff #13784 #15987) +#15985 := (iff #13776 #15984) +#15982 := (iff #13767 #15981) +#15979 := (iff #13762 #15976) +#15973 := (or #12857 #12848 #13521 #13530 #15950 #13707) +#15977 := (iff #15973 #15976) +#15978 := [rewrite]: #15977 +#15974 := (iff #13762 #15973) +#15951 := (iff #13651 #15950) +#15948 := (iff #13643 #15945) +#15942 := (or #12692 #13547 #15933 #13622 #15939) +#15946 := (iff #15942 #15945) +#15947 := [rewrite]: #15946 +#15943 := (iff #13643 #15942) +#15940 := (iff #13628 #15939) +#15937 := (iff #13625 #15936) +#15903 := (iff #13536 #15900) +#15845 := (+ 4294967295::Int #13537) +#15896 := (>= #15845 1::Int) +#15901 := (iff #15896 #15900) +#15902 := [rewrite]: #15901 +#15897 := (iff #13536 #15896) +#15846 := (= #13538 #15845) +#15847 := [monotonicity #7642]: #15846 +#15898 := [monotonicity #15847]: #15897 +#15904 := [trans #15898 #15902]: #15903 +#15938 := [monotonicity #15904]: #15937 +#15941 := [monotonicity #15938]: #15940 +#15934 := (iff #13615 #15933) +#15931 := (iff #13612 #15930) +#15928 := (iff #13609 #15927) +#15925 := (iff #13606 #15922) +#15919 := (or #15916 #13601) +#15923 := (iff #15919 #15922) +#15924 := [rewrite]: #15923 +#15920 := (iff #13606 #15919) +#15917 := (iff #13589 #15916) +#15914 := (iff #13586 #15913) +#15911 := (iff #13581 #15908) +#15905 := (or #14461 #13558 #13572) +#15909 := (iff #15905 #15908) +#15910 := [rewrite]: #15909 +#15906 := (iff #13581 #15905) +#15907 := [monotonicity #14459]: #15906 +#15912 := [trans #15907 #15910]: #15911 +#15915 := [quant-intro #15912]: #15914 +#15918 := [monotonicity #15915]: #15917 +#15921 := [monotonicity #15918]: #15920 +#15926 := [trans #15921 #15924]: #15925 +#15929 := [monotonicity #15915 #15926]: #15928 +#15932 := [monotonicity #15929]: #15931 +#15935 := [monotonicity #15932]: #15934 +#15944 := [monotonicity #15935 #15941]: #15943 +#15949 := [trans #15944 #15947]: #15948 +#15952 := [monotonicity #15904 #15949]: #15951 +#15975 := [monotonicity #15952]: #15974 +#15980 := [trans #15975 #15978]: #15979 +#15971 := (iff #13732 #15968) +#15965 := (or #13521 #15962 #13708) +#15969 := (iff #15965 #15968) +#15970 := [rewrite]: #15969 +#15966 := (iff #13732 #15965) +#15963 := (iff #13702 #15962) +#15960 := (iff #13696 #15959) +#15957 := (iff #13691 #15956) +#15954 := (iff #13683 #15953) +#15955 := [monotonicity #15952]: #15954 +#15958 := [monotonicity #15955]: #15957 +#15961 := [monotonicity #15958]: #15960 +#15964 := [monotonicity #15961]: #15963 +#15967 := [monotonicity #15964]: #15966 +#15972 := [trans #15967 #15970]: #15971 +#15983 := [monotonicity #15972 #15980]: #15982 +#15986 := [monotonicity #15983]: #15985 +#15989 := [monotonicity #15986]: #15988 +#15992 := [monotonicity #15989]: #15991 +#15995 := [monotonicity #15992]: #15994 +#15998 := [monotonicity #15995]: #15997 +#16003 := [trans #15998 #16001]: #16002 +#16040 := [monotonicity #16003 #16037]: #16039 +#15894 := (iff #14066 #15893) +#15891 := (iff #14063 #15890) +#15888 := (iff #14059 #15885) +#15879 := (+ 255::Int #14006) +#15882 := (>= #15879 0::Int) +#15886 := (iff #15882 #15885) +#15887 := [rewrite]: #15886 +#15883 := (iff #14059 #15882) +#15880 := (= #14060 #15879) +#1375 := (= f89 255::Int) +#7641 := [asserted]: #1375 +#15881 := [monotonicity #7641]: #15880 +#15884 := [monotonicity #15881]: #15883 +#15889 := [trans #15884 #15887]: #15888 +#15892 := [monotonicity #15889]: #15891 +#15895 := [monotonicity #15892]: #15894 +#15877 := (iff #14053 #15876) +#15874 := (iff #14050 #15873) +#15871 := (iff #14046 #15868) +#15862 := (+ 4294967295::Int #13977) +#15865 := (>= #15862 0::Int) +#15869 := (iff #15865 #15868) +#15870 := [rewrite]: #15869 +#15866 := (iff #14046 #15865) +#15863 := (= #14047 #15862) +#15864 := [monotonicity #7642]: #15863 +#15867 := [monotonicity #15864]: #15866 +#15872 := [trans #15867 #15870]: #15871 +#15875 := [monotonicity #15872]: #15874 +#15878 := [monotonicity #15875]: #15877 +#15860 := (iff #14043 #15859) +#15857 := (iff #14040 #15856) +#15854 := (iff #14037 #15851) +#15848 := (>= #15845 0::Int) +#15852 := (iff #15848 #15851) +#15853 := [rewrite]: #15852 +#15849 := (iff #14037 #15848) +#15850 := [monotonicity #15847]: #15849 +#15855 := [trans #15850 #15853]: #15854 +#15858 := [monotonicity #15855]: #15857 +#15861 := [monotonicity #15858]: #15860 +#15843 := (iff #14025 #15842) +#15840 := (iff #14022 #15839) +#15837 := (iff #14017 #15834) +#15831 := (or #14461 #13994 #14008) +#15835 := (iff #15831 #15834) +#15836 := [rewrite]: #15835 +#15832 := (iff #14017 #15831) +#15833 := [monotonicity #14459]: #15832 +#15838 := [trans #15833 #15836]: #15837 +#15841 := [quant-intro #15838]: #15840 +#15844 := [monotonicity #15841]: #15843 +#16043 := [monotonicity #15844 #15861 #15878 #15895 #16040]: #16042 +#16048 := [trans #16043 #16046]: #16047 +#16051 := [monotonicity #16048]: #16050 +#15829 := (iff #13505 #15828) +#15826 := (iff #13502 #15825) +#15823 := (iff #13497 #15820) +#15817 := (or #14461 #13475 #13487) +#15821 := (iff #15817 #15820) +#15822 := [rewrite]: #15821 +#15818 := (iff #13497 #15817) +#15819 := [monotonicity #14459]: #15818 +#15824 := [trans #15819 #15822]: #15823 +#15827 := [quant-intro #15824]: #15826 +#15830 := [monotonicity #15827]: #15829 +#16054 := [monotonicity #15830 #16051]: #16053 +#16057 := [monotonicity #15827 #16054]: #16056 +#16060 := [monotonicity #16057]: #16059 +#16063 := [monotonicity #16060]: #16062 +#16066 := [monotonicity #16063]: #16065 +#16069 := [monotonicity #16066]: #16068 +#16072 := [monotonicity #16069]: #16071 +#16075 := [monotonicity #16072]: #16074 +#16078 := [monotonicity #16075]: #16077 +#16081 := [monotonicity #16078]: #16080 +#16084 := [monotonicity #16081]: #16083 +#14361 := (not #14213) +#15374 := (iff #14361 #15373) +#15371 := (iff #14213 #15370) +#15368 := (iff #14210 #15367) +#15365 := (iff #14205 #15364) +#15362 := (iff #14199 #15361) +#15359 := (iff #14194 #15358) +#15356 := (iff #14186 #15355) +#15353 := (iff #14165 #15352) +#15350 := (iff #14162 #15349) +#15347 := (iff #14159 #15346) +#15344 := (iff #14156 #15343) +#15341 := (iff #14151 #15340) +#15338 := (iff #14143 #15335) +#15332 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #15329 #13991 #14025 #14031 #14043 #14053 #14066 #14077) +#15336 := (iff #15332 #15335) +#15337 := [rewrite]: #15336 +#15333 := (iff #14143 #15332) +#15330 := (iff #13950 #15329) +#15327 := (iff #13945 #15324) +#15309 := (or #12340 #12331 #12322 #12313 #13521 #13888) +#15321 := (or #13521 #13802 #15309) +#15325 := (iff #15321 #15324) +#15326 := [rewrite]: #15325 +#15322 := (iff #13945 #15321) +#15319 := (iff #13920 #15309) +#15314 := (and true #15309) +#15317 := (iff #15314 #15309) +#15318 := [rewrite]: #15317 +#15315 := (iff #13920 #15314) +#15312 := (iff #13915 #15309) +#15306 := (or false #12340 #12331 #12322 #12313 #13521 #13888) +#15310 := (iff #15306 #15309) +#15311 := [rewrite]: #15310 +#15307 := (iff #13915 #15306) +#15304 := (iff #12374 false) +#15302 := (iff #12374 #3156) +#15040 := (iff #10960 true) +#10959 := [asserted]: #2542 +#10966 := [mp #10959 #10963]: #10960 +#15041 := [iff-true #10966]: #15040 +#15303 := [monotonicity #15041]: #15302 +#15305 := [trans #15303 #12257]: #15304 +#15308 := [monotonicity #15305]: #15307 +#15313 := [trans #15308 #15311]: #15312 +#15316 := [monotonicity #15041 #15313]: #15315 +#15320 := [trans #15316 #15318]: #15319 +#15323 := [monotonicity #15320]: #15322 +#15328 := [trans #15323 #15326]: #15327 +#15331 := [monotonicity #15328]: #15330 +#15300 := (iff #12402 #15299) +#15297 := (iff #12264 #12258) +#15292 := (and true #12258) +#15295 := (iff #15292 #12258) +#15296 := [rewrite]: #15295 +#15293 := (iff #12264 #15292) +#15276 := (iff #12145 true) +#15277 := [iff-true #14351]: #15276 +#15294 := [monotonicity #15277]: #15293 +#15298 := [trans #15294 #15296]: #15297 +#15301 := [monotonicity #15298]: #15300 +#15334 := [monotonicity #15301 #15331]: #15333 +#15339 := [trans #15334 #15337]: #15338 +#15342 := [monotonicity #15339]: #15341 +#15345 := [monotonicity #15342]: #15344 +#15348 := [monotonicity #15345]: #15347 +#15351 := [monotonicity #15348]: #15350 +#15354 := [monotonicity #15351]: #15353 +#15357 := [monotonicity #15354]: #15356 +#15360 := [monotonicity #15357]: #15359 +#15363 := [monotonicity #15360]: #15362 +#15366 := [monotonicity #15363]: #15365 +#15369 := [monotonicity #15366]: #15368 +#15372 := [monotonicity #15369]: #15371 +#15375 := [monotonicity #15372]: #15374 +#14362 := [not-or-elim #14346]: #14361 +#15376 := [mp #14362 #15375]: #15373 +#16085 := [mp #15376 #16084]: #16082 +#18832 := [mp~ #16085 #18831]: #18829 +#18833 := [mp #18832 #19177]: #19175 +#22700 := [mp #18833 #22699]: #22697 +#23605 := [mp #22700 #23604]: #23602 +#29129 := [unit-resolution #23605 #27033]: #23599 +#24829 := (or #23596 #23590) +#24830 := [def-axiom]: #24829 +#29130 := [unit-resolution #24830 #29129]: #23590 +#24825 := (or #23593 #18445 #18448 #23587) +#24826 := [def-axiom]: #24825 +#29134 := [unit-resolution #24826 #27642 #28798 #29130]: #23587 +#24815 := (or #23584 #23578) +#24816 := [def-axiom]: #24815 +#29135 := [unit-resolution #24816 #29134]: #23578 +#24809 := (or #23581 #18445 #18454 #23575) +#24810 := [def-axiom]: #24809 +#29136 := [unit-resolution #24810 #29135 #29128 #27642]: #23575 +#24787 := (or #23572 #3109) +#24788 := [def-axiom]: #24787 +#29137 := [unit-resolution #24788 #29136]: #3109 +#24799 := (or #23572 #23566) +#24800 := [def-axiom]: #24799 +#29663 := [unit-resolution #24800 #29136]: #23566 +#29664 := (or #23569 #23563) +#27310 := [hypothesis]: #13472 +#27311 := [th-lemma arith farkas 1 1 #14360 #27310]: false +#27312 := [lemma #27311]: #13469 +#24785 := (or #23569 #13472 #23563) +#24786 := [def-axiom]: #24785 +#29665 := [unit-resolution #24786 #27312]: #29664 +#29666 := [unit-resolution #29665 #29663]: #23563 +#24777 := (or #23560 #23554) +#24778 := [def-axiom]: #24777 +#29667 := [unit-resolution #24778 #29666]: #23554 +#27615 := (* -1::Int #3108) +#27616 := (+ f306 #27615) +#27617 := (>= #27616 0::Int) +#29138 := (or #13267 #27617) +#29139 := [th-lemma arith triangle-eq]: #29138 +#29140 := [unit-resolution #29139 #29137]: #27617 +#24455 := (not #18486) +#29141 := [hypothesis]: #22337 +#24456 := (or #22332 #24455) +#24457 := [def-axiom]: #24456 +#29142 := [unit-resolution #24457 #29141]: #24455 +#29102 := (+ #3108 #18484) +#29104 := (>= #29102 0::Int) +#29101 := (= #3108 #18483) +#29149 := (= #18483 #3108) +#29147 := (= #18482 #3098) +#29145 := (= ?v0!13 0::Int) +#24458 := (not #18487) +#24459 := (or #22332 #24458) +#24460 := [def-axiom]: #24459 +#29143 := [unit-resolution #24460 #29141]: #24458 +#24453 := (or #22332 #18479) +#24454 := [def-axiom]: #24453 +#29144 := [unit-resolution #24454 #29141]: #18479 +#29146 := [th-lemma arith eq-propagate 0 0 #29144 #29143]: #29145 +#29148 := [monotonicity #29146]: #29147 +#29150 := [monotonicity #29148]: #29149 +#29151 := [symm #29150]: #29101 +#29152 := (not #29101) +#29153 := (or #29152 #29104) +#29154 := [th-lemma arith triangle-eq]: #29153 +#29155 := [unit-resolution #29154 #29151]: #29104 +#29156 := [th-lemma arith farkas 1 -1 1 #29155 #29142 #29140]: false +#29157 := [lemma #29156]: #22332 +#24773 := (or #23557 #22337 #23551) #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 diff -r 0485186839a7 -r 939f647f0c9e src/HOL/SMT_Examples/SMT_Examples.certs --- 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 diff -r 0485186839a7 -r 939f647f0c9e src/HOL/SMT_Examples/SMT_Examples.thy --- 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) \ a*b > 0 \ 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 *} diff -r 0485186839a7 -r 939f647f0c9e src/HOL/SMT_Examples/SMT_Tests.certs --- 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