%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:45:58 EDT 2023
% Result : Theorem 0.89s 1.38s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.12 % Command : nanocop.sh %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 18 17:28:47 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.89/1.38
% 0.89/1.38 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.89/1.38 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.89/1.38 %-----------------------------------------------------
% 0.89/1.38 ncf(matrix, plain, [(11755 ^ _434076) ^ [] : [-(hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int))], (610 ^ _434076) ^ [_452563, _452565] : [_452565 = _452563, -(undefined(_452565) = undefined(_452563))], (616 ^ _434076) ^ [_452781, _452783] : [_452783 = _452781, -(succ(_452783) = succ(_452781))], (622 ^ _434076) ^ [_453027, _453029, _453031, _453033] : [-(legendre(_453033, _453029) = legendre(_453031, _453027)), _453033 = _453031, _453029 = _453027], (632 ^ _434076) ^ [_453358, _453360] : [_453360 = _453358, -(quadRes(_453360) = quadRes(_453358))], (638 ^ _434076) ^ [_453604, _453606, _453608, _453610] : [-(zcong(_453610, _453606) = zcong(_453608, _453604)), _453610 = _453608, _453606 = _453604], (648 ^ _434076) ^ [_453935, _453937] : [_453937 = _453935, -(nat_1(_453937) = nat_1(_453935))], (654 ^ _434076) ^ [_454153, _454155] : [_454155 = _454153, -(dvd_dvd(_454155) = dvd_dvd(_454153))], (660 ^ _434076) ^ [_454427, _454429, _454431, _454433, _454435, _454437] : [-(times_times(_454437, _454433, _454429) = times_times(_454435, _454431, _454427)), _454437 = _454435, _454433 = _454431, _454429 = _454427], (674 ^ _434076) ^ [_454887, _454889] : [_454889 = _454887, -(ord_less(_454889) = ord_less(_454887))], (680 ^ _434076) ^ [_455133, _455135, _455137, _455139] : [-(abs_abs(_455139, _455135) = abs_abs(_455137, _455133)), _455139 = _455137, _455135 = _455133], (690 ^ _434076) ^ [_455520, _455522, _455524, _455526, _455528, _455530] : [-(minus_minus(_455530, _455526, _455522) = minus_minus(_455528, _455524, _455520)), _455530 = _455528, _455526 = _455524, _455522 = _455520], (704 ^ _434076) ^ [_456008, _456010, _456012, _456014] : [-(fun(_456014, _456010) = fun(_456012, _456008)), _456014 = _456012, _456010 = _456008], (714 ^ _434076) ^ [_456339, _456341] : [_456341 = _456339, -(ord_less_eq(_456341) = ord_less_eq(_456339))], (720 ^ _434076) ^ [_456641, _456643, _456645, _456647, _456649, _456651, _456653, _456655] : [-(if(_456655, _456651, _456647, _456643) = if(_456653, _456649, _456645, _456641)), _456655 = _456653, _456651 = _456649, _456647 = _456645, _456643 = _456641], (738 ^ _434076) ^ [_457274, _457276, _457278, _457280] : [-(ti(_457280, _457276) = ti(_457278, _457274)), _457280 = _457278, _457276 = _457274], (748 ^ _434076) ^ [_457633, _457635, _457637, _457639] : [-(power_power(_457639, _457635) = power_power(_457637, _457633)), _457639 = _457637, _457635 = _457633], (758 ^ _434076) ^ [_458020, _458022, _458024, _458026, _458028, _458030] : [-(plus_plus(_458030, _458026, _458022) = plus_plus(_458028, _458024, _458020)), _458030 = _458028, _458026 = _458024, _458022 = _458020], (772 ^ _434076) ^ [_458480, _458482] : [_458482 = _458480, -(one_one(_458482) = one_one(_458480))], (778 ^ _434076) ^ [_458782, _458784, _458786, _458788, _458790, _458792, _458794, _458796] : [-(hAPP(_458796, _458792, _458788, _458784) = hAPP(_458794, _458790, _458786, _458782)), _458796 = _458794, _458792 = _458790, _458788 = _458786, _458784 = _458782], (796 ^ _434076) ^ [_459387, _459389] : [_459389 = _459387, -(semiring_1_of_nat(_459389) = semiring_1_of_nat(_459387))], (802 ^ _434076) ^ [_459633, _459635, _459637, _459639] : [-(number_number_of(_459639, _459635) = number_number_of(_459637, _459633)), _459639 = _459637, _459635 = _459633], (812 ^ _434076) ^ [_459964, _459966] : [_459966 = _459964, -(bit0(_459966) = bit0(_459964))], (818 ^ _434076) ^ [_460182, _460184] : [_460184 = _460182, -(bit1(_460184) = bit1(_460182))], (824 ^ _434076) ^ [_460380, _460382] : [_460382 = _460380, -(zero_zero(_460382) = zero_zero(_460380))], (2 ^ _434076) ^ [_434220] : [-(_434220 = _434220)], (4 ^ _434076) ^ [_434327, _434329] : [_434329 = _434327, -(_434327 = _434329)], (10 ^ _434076) ^ [_434531, _434533, _434535] : [-(_434535 = _434531), _434535 = _434533, _434533 = _434531], (20 ^ _434076) ^ [_434844, _434846] : [-(hBOOL(_434844)), _434846 = _434844, hBOOL(_434846)], (30 ^ _434076) ^ [_435139, _435141] : [-(semiri456707255roduct(_435139)), _435141 = _435139, semiri456707255roduct(_435141)], (40 ^ _434076) ^ [_435434, _435436] : [-(ordere223160158up_add(_435434)), _435436 = _435434, ordere223160158up_add(_435436)], (50 ^ _434076) ^ [_435729, _435731] : [-(ordere236663937imp_le(_435729)), _435731 = _435729, ordere236663937imp_le(_435731)], (60 ^ _434076) ^ [_436024, _436026] : [-(linord893533164strict(_436024)), _436026 = _436024, linord893533164strict(_436026)], (70 ^ _434076) ^ [_436319, _436321] : [-(linord626643107strict(_436319)), _436321 = _436319, linord626643107strict(_436321)], (80 ^ _434076) ^ [_436614, _436616] : [-(linord20386208strict(_436614)), _436616 = _436614, linord20386208strict(_436616)], (90 ^ _434076) ^ [_436909, _436911] : [-(ordere779506340up_add(_436909)), _436911 = _436909, ordere779506340up_add(_436911)], (100 ^ _434076) ^ [_437204, _437206] : [-(ordere142940540dd_abs(_437204)), _437206 = _437204, ordere142940540dd_abs(_437206)], (110 ^ _434076) ^ [_437499, _437501] : [-(ordere216010020id_add(_437499)), _437501 = _437499, ordere216010020id_add(_437501)], (120 ^ _434076) ^ [_437794, _437796] : [-(linord219039673up_add(_437794)), _437796 = _437794, linord219039673up_add(_437796)], (130 ^ _434076) ^ [_438089, _438091] : [-(cancel146912293up_add(_438089)), _438091 = _438089, cancel146912293up_add(_438091)], (140 ^ _434076) ^ [_438384, _438386] : [-(ring_11004092258visors(_438384)), _438386 = _438384, ring_11004092258visors(_438386)], (150 ^ _434076) ^ [_438679, _438681] : [-(ordere453448008miring(_438679)), _438681 = _438679, ordere453448008miring(_438681)], (160 ^ _434076) ^ [_438974, _438976] : [-(linord581940658strict(_438974)), _438976 = _438974, linord581940658strict(_438976)], (170 ^ _434076) ^ [_439269, _439271] : [-(ring_n68954251visors(_439269)), _439271 = _439269, ring_n68954251visors(_439271)], (180 ^ _434076) ^ [_439564, _439566] : [-(ordere1490568538miring(_439564)), _439566 = _439564, ordere1490568538miring(_439566)], (190 ^ _434076) ^ [_439859, _439861] : [-(linord1278240602ring_1(_439859)), _439861 = _439859, linord1278240602ring_1(_439861)], (200 ^ _434076) ^ [_440154, _440156] : [-(ordered_ab_group_add(_440154)), _440156 = _440154, ordered_ab_group_add(_440156)], (210 ^ _434076) ^ [_440449, _440451] : [-(cancel_semigroup_add(_440449)), _440451 = _440449, cancel_semigroup_add(_440451)], (220 ^ _434076) ^ [_440744, _440746] : [-(linordered_semiring(_440744)), _440746 = _440744, linordered_semiring(_440746)], (230 ^ _434076) ^ [_441039, _441041] : [-(linordered_semidom(_441039)), _441041 = _441039, linordered_semidom(_441041)], (240 ^ _434076) ^ [_441334, _441336] : [-(ab_semigroup_mult(_441334)), _441336 = _441334, ab_semigroup_mult(_441336)], (250 ^ _434076) ^ [_441629, _441631] : [-(comm_monoid_mult(_441629)), _441631 = _441629, comm_monoid_mult(_441631)], (260 ^ _434076) ^ [_441924, _441926] : [-(ab_semigroup_add(_441924)), _441926 = _441924, ab_semigroup_add(_441926)], (270 ^ _434076) ^ [_442219, _442221] : [-(ordered_semiring(_442219)), _442221 = _442219, ordered_semiring(_442221)], (280 ^ _434076) ^ [_442514, _442516] : [-(ordered_ring_abs(_442514)), _442516 = _442514, ordered_ring_abs(_442516)], (290 ^ _434076) ^ [_442809, _442811] : [-(no_zero_divisors(_442809)), _442811 = _442809, no_zero_divisors(_442811)], (300 ^ _434076) ^ [_443104, _443106] : [-(comm_monoid_add(_443104)), _443106 = _443104, comm_monoid_add(_443106)], (310 ^ _434076) ^ [_443399, _443401] : [-(linordered_ring(_443399)), _443401 = _443399, linordered_ring(_443401)], (320 ^ _434076) ^ [_443694, _443696] : [-(linordered_idom(_443694)), _443696 = _443694, linordered_idom(_443696)], (330 ^ _434076) ^ [_443989, _443991] : [-(comm_semiring_1(_443989)), _443991 = _443989, comm_semiring_1(_443991)], (340 ^ _434076) ^ [_444284, _444286] : [-(comm_semiring(_444284)), _444286 = _444284, comm_semiring(_444286)], (350 ^ _434076) ^ [_444579, _444581] : [-(semiring_char_0(_444579)), _444581 = _444579, semiring_char_0(_444581)], (360 ^ _434076) ^ [_444874, _444876] : [-(number_semiring(_444874)), _444876 = _444874, number_semiring(_444876)], (370 ^ _434076) ^ [_445169, _445171] : [-(ab_group_add(_445169)), _445171 = _445169, ab_group_add(_445171)], (380 ^ _434076) ^ [_445464, _445466] : [-(zero_neq_one(_445464)), _445466 = _445464, zero_neq_one(_445466)], (390 ^ _434076) ^ [_445759, _445761] : [-(ordered_ring(_445759)), _445761 = _445759, ordered_ring(_445761)], (400 ^ _434076) ^ [_446054, _446056] : [-(linorder(_446054)), _446056 = _446054, linorder(_446056)], (410 ^ _434076) ^ [_446349, _446351] : [-(monoid_mult(_446349)), _446351 = _446349, monoid_mult(_446351)], (420 ^ _434076) ^ [_446644, _446646] : [-(comm_ring_1(_446644)), _446646 = _446644, comm_ring_1(_446646)], (430 ^ _434076) ^ [_446939, _446941] : [-(monoid_add(_446939)), _446941 = _446939, monoid_add(_446941)], (440 ^ _434076) ^ [_447234, _447236] : [-(semiring_1(_447234)), _447236 = _447234, semiring_1(_447236)], (450 ^ _434076) ^ [_447529, _447531] : [-(semiring_0(_447529)), _447531 = _447529, semiring_0(_447531)], (460 ^ _434076) ^ [_447824, _447826] : [-(group_add(_447824)), _447826 = _447824, group_add(_447826)], (470 ^ _434076) ^ [_448119, _448121] : [-(mult_zero(_448119)), _448121 = _448119, mult_zero(_448121)], (480 ^ _434076) ^ [_448414, _448416] : [-(comm_ring(_448414)), _448416 = _448414, comm_ring(_448416)], (490 ^ _434076) ^ [_448709, _448711] : [-(order(_448709)), _448711 = _448709, order(_448711)], (500 ^ _434076) ^ [_449004, _449006] : [-(ring_char_0(_449004)), _449006 = _449004, ring_char_0(_449006)], (510 ^ _434076) ^ [_449299, _449301] : [-(number_ring(_449299)), _449301 = _449299, number_ring(_449301)], (520 ^ _434076) ^ [_449594, _449596] : [-(semiring(_449594)), _449596 = _449594, semiring(_449596)], (530 ^ _434076) ^ [_449889, _449891] : [-(ring_1(_449889)), _449891 = _449889, ring_1(_449891)], (540 ^ _434076) ^ [_450184, _450186] : [-(power(_450184)), _450186 = _450184, power(_450186)], (550 ^ _434076) ^ [_450479, _450481] : [-(zero(_450479)), _450481 = _450479, zero(_450481)], (560 ^ _434076) ^ [_450774, _450776] : [-(ring(_450774)), _450776 = _450774, ring(_450776)], (570 ^ _434076) ^ [_451069, _451071] : [-(idom(_451069)), _451071 = _451069, idom(_451071)], (580 ^ _434076) ^ [_451364, _451366] : [-(number(_451364)), _451366 = _451364, number(_451366)], (590 ^ _434076) ^ [_451659, _451661] : [-(one(_451659)), _451661 = _451659, one(_451661)], (600 ^ _434076) ^ [_451934, _451936] : [-(dvd(_451934)), _451936 = _451934, dvd(_451936)], (830 ^ _434076) ^ [_460736, _460738] : [ordere142940540dd_abs(_460736), -(abs_abs(_460736, ti(_460736, _460738)) = abs_abs(_460736, _460738))], (836 ^ _434076) ^ [_460962, _460964] : [ordere142940540dd_abs(_460962), -(ti(_460962, abs_abs(_460962, _460964)) = abs_abs(_460962, _460964))], (842 ^ _434076) ^ [_461202, _461204, _461206] : [group_add(_461202), -(minus_minus(_461202, ti(_461202, _461206), _461204) = minus_minus(_461202, _461206, _461204))], (848 ^ _434076) ^ [_461452, _461454, _461456] : [group_add(_461452), -(minus_minus(_461452, _461456, ti(_461452, _461454)) = minus_minus(_461452, _461456, _461454))], (854 ^ _434076) ^ [_461702, _461704, _461706] : [group_add(_461702), -(ti(_461702, minus_minus(_461702, _461706, _461704)) = minus_minus(_461702, _461706, _461704))], (860 ^ _434076) ^ [_461923, _461925] : [-(minus_minus(nat, ti(nat, _461925), _461923) = minus_minus(nat, _461925, _461923))], (862 ^ _434076) ^ [_462028, _462030] : [-(minus_minus(nat, _462030, ti(nat, _462028)) = minus_minus(nat, _462030, _462028))], (864 ^ _434076) ^ [_462133, _462135] : [-(ti(nat, minus_minus(nat, _462135, _462133)) = minus_minus(nat, _462135, _462133))], (866 ^ _434076) ^ [_462239] : [one(_462239), -(ti(_462239, one_one(_462239)) = one_one(_462239))], (872 ^ _434076) ^ [_462469, _462471, _462473] : [monoid_add(_462469), -(plus_plus(_462469, ti(_462469, _462473), _462471) = plus_plus(_462469, _462473, _462471))], (878 ^ _434076) ^ [_462719, _462721, _462723] : [monoid_add(_462719), -(plus_plus(_462719, _462723, ti(_462719, _462721)) = plus_plus(_462719, _462723, _462721))], (884 ^ _434076) ^ [_462969, _462971, _462973] : [monoid_add(_462969), -(ti(_462969, plus_plus(_462969, _462973, _462971)) = plus_plus(_462969, _462973, _462971))], (890 ^ _434076) ^ [_463219, _463221, _463223] : [ab_semigroup_add(_463219), -(plus_plus(_463219, ti(_463219, _463223), _463221) = plus_plus(_463219, _463223, _463221))], (896 ^ _434076) ^ [_463469, _463471, _463473] : [ab_semigroup_add(_463469), -(plus_plus(_463469, _463473, ti(_463469, _463471)) = plus_plus(_463469, _463473, _463471))], (902 ^ _434076) ^ [_463719, _463721, _463723] : [ab_semigroup_add(_463719), -(ti(_463719, plus_plus(_463719, _463723, _463721)) = plus_plus(_463719, _463723, _463721))], (908 ^ _434076) ^ [_463969, _463971, _463973] : [cancel_semigroup_add(_463969), -(plus_plus(_463969, ti(_463969, _463973), _463971) = plus_plus(_463969, _463973, _463971))], (914 ^ _434076) ^ [_464219, _464221, _464223] : [cancel_semigroup_add(_464219), -(plus_plus(_464219, _464223, ti(_464219, _464221)) = plus_plus(_464219, _464223, _464221))], (920 ^ _434076) ^ [_464469, _464471, _464473] : [cancel_semigroup_add(_464469), -(ti(_464469, plus_plus(_464469, _464473, _464471)) = plus_plus(_464469, _464473, _464471))], (926 ^ _434076) ^ [_464719, _464721, _464723] : [dvd(_464719), -(times_times(_464719, ti(_464719, _464723), _464721) = times_times(_464719, _464723, _464721))], (932 ^ _434076) ^ [_464969, _464971, _464973] : [dvd(_464969), -(times_times(_464969, _464973, ti(_464969, _464971)) = times_times(_464969, _464973, _464971))], (938 ^ _434076) ^ [_465219, _465221, _465223] : [dvd(_465219), -(ti(_465219, times_times(_465219, _465223, _465221)) = times_times(_465219, _465223, _465221))], (944 ^ _434076) ^ [_465469, _465471, _465473] : [power(_465469), -(times_times(_465469, ti(_465469, _465473), _465471) = times_times(_465469, _465473, _465471))], (950 ^ _434076) ^ [_465719, _465721, _465723] : [power(_465719), -(times_times(_465719, _465723, ti(_465719, _465721)) = times_times(_465719, _465723, _465721))], (956 ^ _434076) ^ [_465969, _465971, _465973] : [power(_465969), -(ti(_465969, times_times(_465969, _465973, _465971)) = times_times(_465969, _465973, _465971))], (962 ^ _434076) ^ [_466219, _466221, _466223] : [semiring(_466219), -(times_times(_466219, ti(_466219, _466223), _466221) = times_times(_466219, _466223, _466221))], (968 ^ _434076) ^ [_466469, _466471, _466473] : [semiring(_466469), -(times_times(_466469, _466473, ti(_466469, _466471)) = times_times(_466469, _466473, _466471))], (974 ^ _434076) ^ [_466719, _466721, _466723] : [semiring(_466719), -(ti(_466719, times_times(_466719, _466723, _466721)) = times_times(_466719, _466723, _466721))], (980 ^ _434076) ^ [_466969, _466971, _466973] : [no_zero_divisors(_466969), -(times_times(_466969, ti(_466969, _466973), _466971) = times_times(_466969, _466973, _466971))], (986 ^ _434076) ^ [_467219, _467221, _467223] : [no_zero_divisors(_467219), -(times_times(_467219, _467223, ti(_467219, _467221)) = times_times(_467219, _467223, _467221))], (992 ^ _434076) ^ [_467469, _467471, _467473] : [no_zero_divisors(_467469), -(ti(_467469, times_times(_467469, _467473, _467471)) = times_times(_467469, _467473, _467471))], (998 ^ _434076) ^ [_467719, _467721, _467723] : [mult_zero(_467719), -(times_times(_467719, ti(_467719, _467723), _467721) = times_times(_467719, _467723, _467721))], (1004 ^ _434076) ^ [_467969, _467971, _467973] : [mult_zero(_467969), -(times_times(_467969, _467973, ti(_467969, _467971)) = times_times(_467969, _467973, _467971))], (1010 ^ _434076) ^ [_468219, _468221, _468223] : [mult_zero(_468219), -(ti(_468219, times_times(_468219, _468223, _468221)) = times_times(_468219, _468223, _468221))], (1016 ^ _434076) ^ [_468469, _468471, _468473] : [ab_semigroup_mult(_468469), -(times_times(_468469, ti(_468469, _468473), _468471) = times_times(_468469, _468473, _468471))], (1022 ^ _434076) ^ [_468719, _468721, _468723] : [ab_semigroup_mult(_468719), -(times_times(_468719, _468723, ti(_468719, _468721)) = times_times(_468719, _468723, _468721))], (1028 ^ _434076) ^ [_468969, _468971, _468973] : [ab_semigroup_mult(_468969), -(ti(_468969, times_times(_468969, _468973, _468971)) = times_times(_468969, _468973, _468971))], (1034 ^ _434076) ^ [_469191] : [zero(_469191), -(ti(_469191, zero_zero(_469191)) = zero_zero(_469191))], (1040 ^ _434076) ^ [_469378] : [-(ti(_469378, undefined(_469378)) = undefined(_469378))], (1042 ^ _434076) ^ [_469505, _469507, _469509, _469511] : [-(if(_469511, ti(bool, _469509), _469507, _469505) = if(_469511, _469509, _469507, _469505))], (1044 ^ _434076) ^ [_469644, _469646, _469648, _469650] : [-(if(_469650, _469648, ti(_469650, _469646), _469644) = if(_469650, _469648, _469646, _469644))], (1046 ^ _434076) ^ [_469783, _469785, _469787, _469789] : [-(if(_469789, _469787, _469785, ti(_469789, _469783)) = if(_469789, _469787, _469785, _469783))], (1048 ^ _434076) ^ [_469922, _469924, _469926, _469928] : [-(ti(_469928, if(_469928, _469926, _469924, _469922)) = if(_469928, _469926, _469924, _469922))], (1050 ^ _434076) ^ [_470033, _470035] : [-(zcong(ti(int, _470035), _470033) = zcong(_470035, _470033))], (1052 ^ _434076) ^ [_470136, _470138] : [-(zcong(_470138, ti(int, _470136)) = zcong(_470138, _470136))], (1054 ^ _434076) ^ [_470239, _470241] : [-(ti(fun(int, bool), zcong(_470241, _470239)) = zcong(_470241, _470239))], (1056 ^ _434076) ^ [] : [-(ti(fun(int, bool), zprime) = zprime)], (1058 ^ _434076) ^ [_470381] : [-(bit0(ti(int, _470381)) = bit0(_470381))], (1060 ^ _434076) ^ [_470466] : [-(ti(int, bit0(_470466)) = bit0(_470466))], (1062 ^ _434076) ^ [_470551] : [-(bit1(ti(int, _470551)) = bit1(_470551))], (1064 ^ _434076) ^ [_470636] : [-(ti(int, bit1(_470636)) = bit1(_470636))], (1066 ^ _434076) ^ [] : [-(ti(int, min) = min)], (1068 ^ _434076) ^ [] : [-(ti(int, pls) = pls)], (1070 ^ _434076) ^ [_470827] : [-(nat_1(ti(int, _470827)) = nat_1(_470827))], (1072 ^ _434076) ^ [_470912] : [-(ti(nat, nat_1(_470912)) = nat_1(_470912))], (1074 ^ _434076) ^ [_471026, _471028] : [number(_471026), -(number_number_of(_471026, ti(int, _471028)) = number_number_of(_471026, _471028))], (1080 ^ _434076) ^ [_471252, _471254] : [number(_471252), -(ti(_471252, number_number_of(_471252, _471254)) = number_number_of(_471252, _471254))], (1086 ^ _434076) ^ [_471449] : [-(succ(ti(int, _471449)) = succ(_471449))], (1088 ^ _434076) ^ [_471534] : [-(ti(int, succ(_471534)) = succ(_471534))], (1090 ^ _434076) ^ [_471634] : [semiring_1(_471634), -(ti(fun(nat, _471634), semiring_1_of_nat(_471634)) = semiring_1_of_nat(_471634))], (1096 ^ _434076) ^ [_471842] : [order(_471842), -(ti(fun(_471842, fun(_471842, bool)), ord_less(_471842)) = ord_less(_471842))], (1102 ^ _434076) ^ [_472056] : [order(_472056), -(ti(fun(_472056, fun(_472056, bool)), ord_less_eq(_472056)) = ord_less_eq(_472056))], (1108 ^ _434076) ^ [_472284, _472286] : [power(_472284), -(power_power(_472284, ti(_472284, _472286)) = power_power(_472284, _472286))], (1114 ^ _434076) ^ [_472510, _472512] : [power(_472510), -(ti(fun(nat, _472510), power_power(_472510, _472512)) = power_power(_472510, _472512))], (1120 ^ _434076) ^ [_472727, _472729] : [-(legendre(ti(int, _472729), _472727) = legendre(_472729, _472727))], (1122 ^ _434076) ^ [_472830, _472832] : [-(legendre(_472832, ti(int, _472830)) = legendre(_472832, _472830))], (1124 ^ _434076) ^ [_472933, _472935] : [-(ti(int, legendre(_472935, _472933)) = legendre(_472935, _472933))], (1126 ^ _434076) ^ [_473022] : [-(quadRes(ti(int, _473022)) = quadRes(_473022))], (1128 ^ _434076) ^ [_473107] : [-(ti(fun(int, bool), quadRes(_473107)) = quadRes(_473107))], (1130 ^ _434076) ^ [_473207] : [dvd(_473207), -(ti(fun(_473207, fun(_473207, bool)), dvd_dvd(_473207)) = dvd_dvd(_473207))], (1136 ^ _434076) ^ [] : [-(ti(fun(int, bool), twoSqu658283162sum2sq) = twoSqu658283162sum2sq)], (1138 ^ _434076) ^ [] : [-(ti(bool, fFalse) = fFalse)], (1140 ^ _434076) ^ [] : [-(ti(bool, fTrue) = fTrue)], (1142 ^ _434076) ^ [_473608, _473610, _473612] : [order(_473608), -(hAPP(_473608, fun(_473608, bool), ti(fun(_473608, fun(_473608, bool)), _473612), _473610) = hAPP(_473608, fun(_473608, bool), _473612, _473610))], (1148 ^ _434076) ^ [_473886, _473888, _473890] : [order(_473886), -(hAPP(_473886, fun(_473886, bool), _473890, ti(_473886, _473888)) = hAPP(_473886, fun(_473886, bool), _473890, _473888))], (1154 ^ _434076) ^ [_474152, _474154, _474156] : [order(_474152), -(ti(fun(_474152, bool), hAPP(_474152, fun(_474152, bool), _474156, _474154)) = hAPP(_474152, fun(_474152, bool), _474156, _474154))], (1160 ^ _434076) ^ [_474424, _474426, _474428] : [order(_474424), -(hAPP(_474424, bool, ti(fun(_474424, bool), _474428), _474426) = hAPP(_474424, bool, _474428, _474426))], (1166 ^ _434076) ^ [_474684, _474686, _474688] : [order(_474684), -(hAPP(_474684, bool, _474688, ti(_474684, _474686)) = hAPP(_474684, bool, _474688, _474686))], (1172 ^ _434076) ^ [_474938, _474940, _474942] : [order(_474938), -(ti(bool, hAPP(_474938, bool, _474942, _474940)) = hAPP(_474938, bool, _474942, _474940))], (1178 ^ _434076) ^ [_475192, _475194, _475196] : [dvd(_475192), -(hAPP(_475192, fun(_475192, bool), ti(fun(_475192, fun(_475192, bool)), _475196), _475194) = hAPP(_475192, fun(_475192, bool), _475196, _475194))], (1184 ^ _434076) ^ [_475470, _475472, _475474] : [dvd(_475470), -(hAPP(_475470, fun(_475470, bool), _475474, ti(_475470, _475472)) = hAPP(_475470, fun(_475470, bool), _475474, _475472))], (1190 ^ _434076) ^ [_475736, _475738, _475740] : [dvd(_475736), -(ti(fun(_475736, bool), hAPP(_475736, fun(_475736, bool), _475740, _475738)) = hAPP(_475736, fun(_475736, bool), _475740, _475738))], (1196 ^ _434076) ^ [_476008, _476010, _476012] : [dvd(_476008), -(hAPP(_476008, bool, ti(fun(_476008, bool), _476012), _476010) = hAPP(_476008, bool, _476012, _476010))], (1202 ^ _434076) ^ [_476268, _476270, _476272] : [dvd(_476268), -(hAPP(_476268, bool, _476272, ti(_476268, _476270)) = hAPP(_476268, bool, _476272, _476270))], (1208 ^ _434076) ^ [_476522, _476524, _476526] : [dvd(_476522), -(ti(bool, hAPP(_476522, bool, _476526, _476524)) = hAPP(_476522, bool, _476526, _476524))], (1214 ^ _434076) ^ [_476776, _476778, _476780] : [power(_476776), -(hAPP(nat, _476776, ti(fun(nat, _476776), _476780), _476778) = hAPP(nat, _476776, _476780, _476778))], (1220 ^ _434076) ^ [_477036, _477038, _477040] : [power(_477036), -(hAPP(nat, _477036, _477040, ti(nat, _477038)) = hAPP(nat, _477036, _477040, _477038))], (1226 ^ _434076) ^ [_477290, _477292, _477294] : [power(_477290), -(ti(_477290, hAPP(nat, _477290, _477294, _477292)) = hAPP(nat, _477290, _477294, _477292))], (1232 ^ _434076) ^ [_477545] : [hBOOL(ti(bool, _477545)), -(hBOOL(_477545))], (1238 ^ _434076) ^ [_477703] : [hBOOL(_477703), -(hBOOL(ti(bool, _477703)))], (1244 ^ _434076) ^ [] : [-(ti(int, m) = m)], (1246 ^ _434076) ^ [] : [-(ti(int, m1) = m1)], (1248 ^ _434076) ^ [] : [-(ti(nat, n) = n)], (1250 ^ _434076) ^ [] : [-(ti(int, s1) = s1)], (1252 ^ _434076) ^ [] : [-(ti(int, s) = s)], (1254 ^ _434076) ^ [] : [-(ti(int, t) = t)], (1256 ^ _434076) ^ [] : [-(ti(nat, tn) = tn)], (1258 ^ _434076) ^ [] : [-(ti(int, x) = x)], (1260 ^ _434076) ^ [] : [-(ti(int, y) = y)], (1262 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (1264 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), one_one(int)), t)))], (1266 ^ _434076) ^ [_478480] : [linordered_idom(_478480), 1269 ^ _434076 : [(1270 ^ _434076) ^ [_478697, _478699] : [plus_plus(_478480, hAPP(nat, _478480, power_power(_478480, _478699), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _478480, power_power(_478480, _478697), number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_478480), 1273 ^ _434076 : [(1274 ^ _434076) ^ [] : [-(ti(_478480, _478699) = zero_zero(_478480))], (1276 ^ _434076) ^ [] : [-(ti(_478480, _478697) = zero_zero(_478480))]]], (1278 ^ _434076) ^ [_479008, _479010] : [-(plus_plus(_478480, hAPP(nat, _478480, power_power(_478480, _479010), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _478480, power_power(_478480, _479008), number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_478480)), ti(_478480, _479010) = zero_zero(_478480), ti(_478480, _479008) = zero_zero(_478480)]]], (1288 ^ _434076) ^ [_479376] : [semiring_1(_479376), -(hAPP(nat, _479376, power_power(_479376, one_one(_479376)), number_number_of(nat, bit0(bit1(pls)))) = one_one(_479376))], (1294 ^ _434076) ^ [_479588] : [semiring_1(_479588), -(hAPP(nat, _479588, power_power(_479588, zero_zero(_479588)), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_479588))], (1300 ^ _434076) ^ [_479800] : [ring_11004092258visors(_479800), 1303 ^ _434076 : [(1304 ^ _434076) ^ [_479975] : [hAPP(nat, _479800, power_power(_479800, _479975), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_479800), -(ti(_479800, _479975) = zero_zero(_479800))], (1310 ^ _434076) ^ [_480169] : [ti(_479800, _480169) = zero_zero(_479800), -(hAPP(nat, _479800, power_power(_479800, _480169), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_479800))]]], (1316 ^ _434076) ^ [_480404] : [number_ring(_480404), 1319 ^ _434076 : [(1320 ^ _434076) ^ [_480530] : [-(plus_plus(_480404, one_one(_480404), number_number_of(_480404, _480530)) = number_number_of(_480404, plus_plus(int, bit1(pls), _480530)))]]], (1322 ^ _434076) ^ [_480646] : [number_ring(_480646), 1325 ^ _434076 : [(1326 ^ _434076) ^ [_480772] : [-(plus_plus(_480646, number_number_of(_480646, _480772), one_one(_480646)) = number_number_of(_480646, plus_plus(int, _480772, bit1(pls))))]]], (1328 ^ _434076) ^ [_480888] : [number_ring(_480888), -(plus_plus(_480888, one_one(_480888), one_one(_480888)) = number_number_of(_480888, bit0(bit1(pls))))], (1334 ^ _434076) ^ [_481098] : [number_semiring(_481098), -(plus_plus(_481098, one_one(_481098), one_one(_481098)) = number_number_of(_481098, bit0(bit1(pls))))], (1340 ^ _434076) ^ [_481293] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, power_power(int, _481293), number_number_of(nat, bit0(bit1(pls))))), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, int, power_power(int, _481293), number_number_of(nat, bit0(bit0(bit1(pls))))))], (1342 ^ _434076) ^ [_481410] : [power(_481410), semiring_0(_481410), 1349 ^ _434076 : [(1350 ^ _434076) ^ [_481694] : [number_number_of(nat, _481694) = zero_zero(nat), -(hAPP(nat, _481410, power_power(_481410, zero_zero(_481410)), number_number_of(nat, _481694)) = one_one(_481410))], (1356 ^ _434076) ^ [_481894] : [-(number_number_of(nat, _481894) = zero_zero(nat)), -(hAPP(nat, _481410, power_power(_481410, zero_zero(_481410)), number_number_of(nat, _481894)) = zero_zero(_481410))]]], (1362 ^ _434076) ^ [_482140] : [number_ring(_482140), -(one_one(_482140) = number_number_of(_482140, bit1(pls)))], (1368 ^ _434076) ^ [_482338] : [number_ring(_482338), -(number_number_of(_482338, bit1(pls)) = one_one(_482338))], (1374 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)))], (1376 ^ _434076) ^ [_482603, _482605] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _482605), _482603))), -(ti(int, _482605) = ti(int, _482603)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _482603), _482605)))], (1386 ^ _434076) ^ [_482981, _482983] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, _482983)), number_number_of(int, _482981))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _482983), _482981)))], (1392 ^ _434076) ^ [_483191, _483193] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _483193), _483191)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, _483193)), number_number_of(int, _483191))))], (1398 ^ _434076) ^ [_483436, _483438] : [-(plus_plus(int, number_number_of(int, _483438), number_number_of(int, _483436)) = number_number_of(int, plus_plus(int, _483438, _483436)))], (1400 ^ _434076) ^ [_483548] : [number_ring(_483548), linordered_idom(_483548), 1407 ^ _434076 : [(1408 ^ _434076) ^ [_483839, _483841] : [hBOOL(hAPP(_483548, bool, hAPP(_483548, fun(_483548, bool), ord_less(_483548), number_number_of(_483548, _483841)), number_number_of(_483548, _483839))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _483841), _483839)))], (1414 ^ _434076) ^ [_484067, _484069] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _484069), _484067)), -(hBOOL(hAPP(_483548, bool, hAPP(_483548, fun(_483548, bool), ord_less(_483548), number_number_of(_483548, _484069)), number_number_of(_483548, _484067))))]]], (1420 ^ _434076) ^ [] : [-(zero_zero(int) = number_number_of(int, pls))], (1422 ^ _434076) ^ [_484390, _484392] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _484392)), _484390) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _484392), _484390)))], (1424 ^ _434076) ^ [_484510, _484512] : [-(hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _484512), _484510)) = hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _484512)), _484510))], (1426 ^ _434076) ^ [_484644, _484646, _484648] : [-(plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _484648), plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _484646), _484644)) = plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), plus_plus(nat, _484648, _484646)), _484644))], (1428 ^ _434076) ^ [_484771, _484773] : [-(plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _484773), hAPP(nat, int, semiring_1_of_nat(int), _484771)) = hAPP(nat, int, semiring_1_of_nat(int), plus_plus(nat, _484773, _484771)))], (1430 ^ _434076) ^ [] : [-(hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)) = one_one(int))], (1432 ^ _434076) ^ [] : [-(number_number_of(nat, pls) = zero_zero(nat))], (1434 ^ _434076) ^ [] : [-(zero_zero(nat) = number_number_of(nat, pls))], (1436 ^ _434076) ^ [_485077] : [hAPP(nat, int, semiring_1_of_nat(int), _485077) = zero_zero(int), -(_485077 = zero_zero(nat))], (1442 ^ _434076) ^ [_485243] : [_485243 = zero_zero(nat), -(hAPP(nat, int, semiring_1_of_nat(int), _485243) = zero_zero(int))], (1448 ^ _434076) ^ [] : [-(hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)) = zero_zero(int))], (1450 ^ _434076) ^ [] : [-(plus_plus(nat, one_one(nat), one_one(nat)) = number_number_of(nat, bit0(bit1(pls))))], (1452 ^ _434076) ^ [_485594, _485596] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_485596)), bit1(_485594))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _485596), _485594)))], (1458 ^ _434076) ^ [_485800, _485802] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _485802), _485800)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_485802)), bit1(_485800))))], (1464 ^ _434076) ^ [_486085, _486087] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_486087)), bit1(_486085))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _486087), _486085)))], (1470 ^ _434076) ^ [_486291, _486293] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _486293), _486291)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_486293)), bit1(_486291))))], (1476 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))], (1478 ^ _434076) ^ [_486628, _486630] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_486630)), bit0(_486628))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _486630), _486628)))], (1484 ^ _434076) ^ [_486834, _486836] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _486836), _486834)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_486836)), bit0(_486834))))], (1490 ^ _434076) ^ [_487119, _487121] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_487121)), bit0(_487119))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _487121), _487119)))], (1496 ^ _434076) ^ [_487325, _487327] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _487327), _487325)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_487327)), bit0(_487325))))], (1502 ^ _434076) ^ [_487595, _487597, _487599] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _487597), _487595)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, _487597, _487599)), plus_plus(int, _487595, _487599))))], (1508 ^ _434076) ^ [_487883, _487885] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _487883), pls)), -(plus_plus(nat, number_number_of(nat, _487883), number_number_of(nat, _487885)) = number_number_of(nat, _487885))], (1514 ^ _434076) ^ [_488089, _488091] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _488089), pls))), 1517 ^ _434076 : [(1518 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _488091), pls)), -(plus_plus(nat, number_number_of(nat, _488089), number_number_of(nat, _488091)) = number_number_of(nat, _488089))], (1524 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _488091), pls))), -(plus_plus(nat, number_number_of(nat, _488089), number_number_of(nat, _488091)) = number_number_of(nat, plus_plus(int, _488089, _488091)))]]], (1530 ^ _434076) ^ [] : [-(one_one(int) = number_number_of(int, bit1(pls)))], (1532 ^ _434076) ^ [] : [-(number_number_of(nat, bit1(pls)) = one_one(nat))], (1534 ^ _434076) ^ [] : [-(one_one(nat) = number_number_of(nat, bit1(pls)))], (1536 ^ _434076) ^ [_488819] : [number_ring(_488819), ring_char_0(_488819), 1543 ^ _434076 : [(1544 ^ _434076) ^ [_489093, _489095] : [number_number_of(_488819, _489095) = number_number_of(_488819, _489093), -(ti(int, _489095) = ti(int, _489093))], (1550 ^ _434076) ^ [_489287, _489289] : [ti(int, _489289) = ti(int, _489287), -(number_number_of(_488819, _489289) = number_number_of(_488819, _489287))]]], (1556 ^ _434076) ^ [_489524] : [number(_489524), 1559 ^ _434076 : [(1560 ^ _434076) ^ [_489715, _489717] : [number_number_of(_489524, _489717) = ti(_489524, _489715), -(ti(_489524, _489715) = number_number_of(_489524, _489717))], (1566 ^ _434076) ^ [_489909, _489911] : [ti(_489524, _489909) = number_number_of(_489524, _489911), -(number_number_of(_489524, _489911) = ti(_489524, _489909))]]], (1572 ^ _434076) ^ [_490187, _490189] : [bit1(_490189) = bit1(_490187), -(ti(int, _490189) = ti(int, _490187))], (1578 ^ _434076) ^ [_490369, _490371] : [ti(int, _490371) = ti(int, _490369), -(bit1(_490371) = bit1(_490369))], (1584 ^ _434076) ^ [_490630, _490632] : [bit0(_490632) = bit0(_490630), -(ti(int, _490632) = ti(int, _490630))], (1590 ^ _434076) ^ [_490812, _490814] : [ti(int, _490814) = ti(int, _490812), -(bit0(_490814) = bit0(_490812))], (1596 ^ _434076) ^ [_491030] : [linordered_idom(_491030), 1599 ^ _434076 : [(1600 ^ _434076) ^ [_491226] : [hBOOL(hAPP(_491030, bool, hAPP(_491030, fun(_491030, bool), ord_less(_491030), plus_plus(_491030, _491226, _491226)), zero_zero(_491030))), -(hBOOL(hAPP(_491030, bool, hAPP(_491030, fun(_491030, bool), ord_less(_491030), _491226), zero_zero(_491030))))], (1606 ^ _434076) ^ [_491462] : [hBOOL(hAPP(_491030, bool, hAPP(_491030, fun(_491030, bool), ord_less(_491030), _491462), zero_zero(_491030))), -(hBOOL(hAPP(_491030, bool, hAPP(_491030, fun(_491030, bool), ord_less(_491030), plus_plus(_491030, _491462, _491462)), zero_zero(_491030))))]]], (1612 ^ _434076) ^ [_491752, _491754, _491756] : [-(plus_plus(int, plus_plus(int, _491756, _491754), _491752) = plus_plus(int, _491756, plus_plus(int, _491754, _491752)))], (1614 ^ _434076) ^ [_491878, _491880, _491882] : [-(plus_plus(int, _491882, plus_plus(int, _491880, _491878)) = plus_plus(int, _491880, plus_plus(int, _491882, _491878)))], (1616 ^ _434076) ^ [_491990, _491992] : [-(plus_plus(int, _491992, _491990) = plus_plus(int, _491990, _491992))], (1618 ^ _434076) ^ [_492136, _492138] : [hAPP(nat, int, semiring_1_of_nat(int), _492138) = hAPP(nat, int, semiring_1_of_nat(int), _492136), -(_492138 = _492136)], (1624 ^ _434076) ^ [_492318, _492320] : [_492320 = _492318, -(hAPP(nat, int, semiring_1_of_nat(int), _492320) = hAPP(nat, int, semiring_1_of_nat(int), _492318))], (1630 ^ _434076) ^ [_492536] : [number_ring(_492536), linordered_idom(_492536), 1637 ^ _434076 : [(1638 ^ _434076) ^ [_492807] : [hBOOL(hAPP(_492536, bool, hAPP(_492536, fun(_492536, bool), ord_less(_492536), number_number_of(_492536, _492807)), zero_zero(_492536))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _492807), pls)))], (1644 ^ _434076) ^ [_493027] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _493027), pls)), -(hBOOL(hAPP(_492536, bool, hAPP(_492536, fun(_492536, bool), ord_less(_492536), number_number_of(_492536, _493027)), zero_zero(_492536))))]]], (1650 ^ _434076) ^ [_493290] : [number_ring(_493290), linordered_idom(_493290), 1657 ^ _434076 : [(1658 ^ _434076) ^ [_493556] : [hBOOL(hAPP(_493290, bool, hAPP(_493290, fun(_493290, bool), ord_less(_493290), zero_zero(_493290)), number_number_of(_493290, _493556))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _493556)))], (1664 ^ _434076) ^ [_493766] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _493766)), -(hBOOL(hAPP(_493290, bool, hAPP(_493290, fun(_493290, bool), ord_less(_493290), zero_zero(_493290)), number_number_of(_493290, _493766))))]]], (1670 ^ _434076) ^ [_494048] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_494048)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _494048), pls)))], (1676 ^ _434076) ^ [_494244] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _494244), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_494244)), pls)))], (1682 ^ _434076) ^ [_494519, _494521] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_494521)), bit0(_494519))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _494521), _494519)))], (1688 ^ _434076) ^ [_494725, _494727] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _494727), _494725)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_494727)), bit0(_494725))))], (1694 ^ _434076) ^ [_495010, _495012] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_495012)), bit0(_495010))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _495012), _495010)))], (1700 ^ _434076) ^ [_495216, _495218] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _495218), _495216)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_495218)), bit0(_495216))))], (1706 ^ _434076) ^ [_495487] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_495487)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _495487), pls)))], (1712 ^ _434076) ^ [_495683] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _495683), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_495683)), pls)))], (1718 ^ _434076) ^ [_495944] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), bit0(_495944))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _495944)))], (1724 ^ _434076) ^ [_496120] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _496120)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), bit0(_496120))))], (1730 ^ _434076) ^ [_496361] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_496361)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _496361), zero_zero(int))))], (1736 ^ _434076) ^ [_496557] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _496557), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_496557)), zero_zero(int))))], (1742 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))], (1744 ^ _434076) ^ [_496870] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_496870)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _496870), zero_zero(int))))], (1750 ^ _434076) ^ [_497066] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _497066), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_497066)), zero_zero(int))))], (1756 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), one_one(int))))], (1768 ^ _434076) ^ [_497702, _497704] : [1769 ^ _434076 : [(1770 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _497704), _497702))], (1772 ^ _434076) ^ [] : [ti(int, _497704) = ti(int, _497702)]], -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _497704), plus_plus(int, _497702, one_one(int)))))], (1758 ^ _434076) ^ [_497394, _497396] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _497396), plus_plus(int, _497394, one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _497396), _497394))), -(ti(int, _497396) = ti(int, _497394))], (1776 ^ _434076) ^ [_498014] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _498014)), zero_zero(int)))], (1778 ^ _434076) ^ [_498121] : [number_ring(_498121), linordered_idom(_498121), 1785 ^ _434076 : [(1786 ^ _434076) ^ [_498392] : [hBOOL(hAPP(_498121, bool, hAPP(_498121, fun(_498121, bool), ord_less(_498121), number_number_of(_498121, _498392)), one_one(_498121))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _498392), bit1(pls))))], (1792 ^ _434076) ^ [_498612] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _498612), bit1(pls))), -(hBOOL(hAPP(_498121, bool, hAPP(_498121, fun(_498121, bool), ord_less(_498121), number_number_of(_498121, _498612)), one_one(_498121))))]]], (1798 ^ _434076) ^ [_498875] : [number_ring(_498875), linordered_idom(_498875), 1805 ^ _434076 : [(1806 ^ _434076) ^ [_499141] : [hBOOL(hAPP(_498875, bool, hAPP(_498875, fun(_498875, bool), ord_less(_498875), one_one(_498875)), number_number_of(_498875, _499141))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(pls)), _499141)))], (1812 ^ _434076) ^ [_499351] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(pls)), _499351)), -(hBOOL(hAPP(_498875, bool, hAPP(_498875, fun(_498875, bool), ord_less(_498875), one_one(_498875)), number_number_of(_498875, _499351))))]]], (1818 ^ _434076) ^ [_499633] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, plus_plus(int, one_one(int), _499633), _499633)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _499633), zero_zero(int))))], (1824 ^ _434076) ^ [_499841] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _499841), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, plus_plus(int, one_one(int), _499841), _499841)), zero_zero(int))))], (1830 ^ _434076) ^ [_500085] : [linord219039673up_add(_500085), 1833 ^ _434076 : [(1834 ^ _434076) ^ [_500256] : [plus_plus(_500085, _500256, _500256) = zero_zero(_500085), -(ti(_500085, _500256) = zero_zero(_500085))], (1840 ^ _434076) ^ [_500442] : [ti(_500085, _500442) = zero_zero(_500085), -(plus_plus(_500085, _500442, _500442) = zero_zero(_500085))]]], (1846 ^ _434076) ^ [_500653] : [bit1(_500653) = pls], (1848 ^ _434076) ^ [_500732] : [pls = bit1(_500732)], (1850 ^ _434076) ^ [_500825, _500827] : [bit1(_500827) = bit0(_500825)], (1852 ^ _434076) ^ [_500922, _500924] : [bit0(_500924) = bit1(_500922)], (1854 ^ _434076) ^ [_501050] : [bit0(_501050) = pls, -(ti(int, _501050) = pls)], (1860 ^ _434076) ^ [_501216] : [ti(int, _501216) = pls, -(bit0(_501216) = pls)], (1866 ^ _434076) ^ [_501447] : [pls = bit0(_501447), -(pls = ti(int, _501447))], (1872 ^ _434076) ^ [_501613] : [pls = ti(int, _501613), -(pls = bit0(_501613))], (1878 ^ _434076) ^ [] : [-(bit0(pls) = pls)], (1880 ^ _434076) ^ [] : [-(pls = zero_zero(int))], (1882 ^ _434076) ^ [] : [zero_zero(int) = one_one(int)], (1884 ^ _434076) ^ [_501958] : [-(plus_plus(int, _501958, pls) = ti(int, _501958))], (1886 ^ _434076) ^ [_502043] : [-(plus_plus(int, pls, _502043) = ti(int, _502043))], (1888 ^ _434076) ^ [_502142, _502144] : [-(plus_plus(int, bit0(_502144), bit0(_502142)) = bit0(plus_plus(int, _502144, _502142)))], (1890 ^ _434076) ^ [_502236] : [-(bit0(_502236) = plus_plus(int, _502236, _502236))], (1892 ^ _434076) ^ [_502320] : [-(plus_plus(int, _502320, zero_zero(int)) = ti(int, _502320))], (1894 ^ _434076) ^ [_502405] : [-(plus_plus(int, zero_zero(int), _502405) = ti(int, _502405))], (1896 ^ _434076) ^ [_502505] : [number_semiring(_502505), -(number_number_of(_502505, pls) = zero_zero(_502505))], (1902 ^ _434076) ^ [_502703] : [number_ring(_502703), -(number_number_of(_502703, pls) = zero_zero(_502703))], (1908 ^ _434076) ^ [_502901] : [number_ring(_502901), -(zero_zero(_502901) = number_number_of(_502901, pls))], (1914 ^ _434076) ^ [_503099] : [number_ring(_503099), 1917 ^ _434076 : [(1918 ^ _434076) ^ [_503219] : [-(plus_plus(_503099, number_number_of(_503099, pls), _503219) = ti(_503099, _503219))]]], (1920 ^ _434076) ^ [_503329] : [number_ring(_503329), 1923 ^ _434076 : [(1924 ^ _434076) ^ [_503449] : [-(plus_plus(_503329, _503449, number_number_of(_503329, pls)) = ti(_503329, _503449))]]], (1926 ^ _434076) ^ [_503559] : [power(_503559), mult_zero(_503559), no_zero_divisors(_503559), zero_neq_one(_503559), 1941 ^ _434076 : [(1942 ^ _434076) ^ [_504016, _504018] : [hAPP(nat, _503559, power_power(_503559, _504018), number_number_of(nat, _504016)) = zero_zero(_503559), 1945 ^ _434076 : [(1946 ^ _434076) ^ [] : [-(ti(_503559, _504018) = zero_zero(_503559))], (1948 ^ _434076) ^ [] : [number_number_of(nat, _504016) = zero_zero(nat)]]], (1950 ^ _434076) ^ [_504306, _504308] : [-(hAPP(nat, _503559, power_power(_503559, _504308), number_number_of(nat, _504306)) = zero_zero(_503559)), ti(_503559, _504308) = zero_zero(_503559), -(number_number_of(nat, _504306) = zero_zero(nat))]]], (1960 ^ _434076) ^ [_504661] : [number_ring(_504661), 1963 ^ _434076 : [(1964 ^ _434076) ^ [_504834, _504836, _504838] : [-(plus_plus(_504661, number_number_of(_504661, _504838), plus_plus(_504661, number_number_of(_504661, _504836), _504834)) = plus_plus(_504661, number_number_of(_504661, plus_plus(int, _504838, _504836)), _504834))]]], (1966 ^ _434076) ^ [_504963] : [number_ring(_504963), 1969 ^ _434076 : [(1970 ^ _434076) ^ [_505109, _505111] : [-(plus_plus(_504963, number_number_of(_504963, _505111), number_number_of(_504963, _505109)) = number_number_of(_504963, plus_plus(int, _505111, _505109)))]]], (1972 ^ _434076) ^ [_505228] : [number_ring(_505228), 1975 ^ _434076 : [(1976 ^ _434076) ^ [_505374, _505376] : [-(number_number_of(_505228, plus_plus(int, _505376, _505374)) = plus_plus(_505228, number_number_of(_505228, _505376), number_number_of(_505228, _505374)))]]], (1978 ^ _434076) ^ [_505492, _505494] : [-(plus_plus(int, bit1(_505494), bit0(_505492)) = bit1(plus_plus(int, _505494, _505492)))], (1980 ^ _434076) ^ [_505600, _505602] : [-(plus_plus(int, bit0(_505602), bit1(_505600)) = bit1(plus_plus(int, _505602, _505600)))], (1982 ^ _434076) ^ [_505694] : [-(bit1(_505694) = plus_plus(int, plus_plus(int, one_one(int), _505694), _505694))], (1984 ^ _434076) ^ [_505781] : [plus_plus(int, plus_plus(int, one_one(int), _505781), _505781) = zero_zero(int)], (1986 ^ _434076) ^ [_505882] : [number_semiring(_505882), 1989 ^ _434076 : [(1990 ^ _434076) ^ [_506007] : [-(number_number_of(_505882, hAPP(nat, int, semiring_1_of_nat(int), _506007)) = hAPP(nat, _505882, semiring_1_of_nat(_505882), _506007))]]], (1992 ^ _434076) ^ [_506122] : [linordered_idom(_506122), 1995 ^ _434076 : [(1996 ^ _434076) ^ [_506313] : [hBOOL(hAPP(_506122, bool, hAPP(_506122, fun(_506122, bool), ord_less(_506122), zero_zero(_506122)), hAPP(nat, _506122, power_power(_506122, _506313), number_number_of(nat, bit0(bit1(pls)))))), ti(_506122, _506313) = zero_zero(_506122)], (2002 ^ _434076) ^ [_506536] : [-(ti(_506122, _506536) = zero_zero(_506122)), -(hBOOL(hAPP(_506122, bool, hAPP(_506122, fun(_506122, bool), ord_less(_506122), zero_zero(_506122)), hAPP(nat, _506122, power_power(_506122, _506536), number_number_of(nat, bit0(bit1(pls)))))))]]], (2008 ^ _434076) ^ [_506802] : [linordered_idom(_506802), 2011 ^ _434076 : [(2012 ^ _434076) ^ [_506937] : [hBOOL(hAPP(_506802, bool, hAPP(_506802, fun(_506802, bool), ord_less(_506802), hAPP(nat, _506802, power_power(_506802, _506937), number_number_of(nat, bit0(bit1(pls))))), zero_zero(_506802)))]]], (2014 ^ _434076) ^ [_507061] : [linordered_idom(_507061), 2017 ^ _434076 : [(2028 ^ _434076) ^ [_507654, _507656] : [2029 ^ _434076 : [(2030 ^ _434076) ^ [] : [-(ti(_507061, _507656) = zero_zero(_507061))], (2032 ^ _434076) ^ [] : [-(ti(_507061, _507654) = zero_zero(_507061))]], -(hBOOL(hAPP(_507061, bool, hAPP(_507061, fun(_507061, bool), ord_less(_507061), zero_zero(_507061)), plus_plus(_507061, hAPP(nat, _507061, power_power(_507061, _507656), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _507061, power_power(_507061, _507654), number_number_of(nat, bit0(bit1(pls))))))))], (2018 ^ _434076) ^ [_507296, _507298] : [hBOOL(hAPP(_507061, bool, hAPP(_507061, fun(_507061, bool), ord_less(_507061), zero_zero(_507061)), plus_plus(_507061, hAPP(nat, _507061, power_power(_507061, _507298), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _507061, power_power(_507061, _507296), number_number_of(nat, bit0(bit1(pls))))))), ti(_507061, _507298) = zero_zero(_507061), ti(_507061, _507296) = zero_zero(_507061)]]], (2036 ^ _434076) ^ [_508039] : [linordered_idom(_508039), 2039 ^ _434076 : [(2040 ^ _434076) ^ [_508205, _508207] : [hBOOL(hAPP(_508039, bool, hAPP(_508039, fun(_508039, bool), ord_less(_508039), plus_plus(_508039, hAPP(nat, _508039, power_power(_508039, _508207), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _508039, power_power(_508039, _508205), number_number_of(nat, bit0(bit1(pls)))))), zero_zero(_508039)))]]], (2042 ^ _434076) ^ [_508343] : [number_ring(_508343), 2045 ^ _434076 : [(2046 ^ _434076) ^ [_508474] : [-(number_number_of(_508343, bit0(_508474)) = plus_plus(_508343, plus_plus(_508343, zero_zero(_508343), number_number_of(_508343, _508474)), number_number_of(_508343, _508474)))]]], (2048 ^ _434076) ^ [_508595] : [number_ring(_508595), 2051 ^ _434076 : [(2052 ^ _434076) ^ [_508726] : [-(number_number_of(_508595, bit1(_508726)) = plus_plus(_508595, plus_plus(_508595, one_one(_508595), number_number_of(_508595, _508726)), number_number_of(_508595, _508726)))]]], (2054 ^ _434076) ^ [_508847] : [number_semiring(_508847), -(number_number_of(_508847, bit1(pls)) = one_one(_508847))], (2060 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), m1), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (2062 ^ _434076) ^ [_509098] : [2069 ^ _434076 : [(2070 ^ _434076) ^ [_509323] : [-(hBOOL(hAPP(_509098, bool, hAPP(_509098, fun(_509098, bool), ord_less(_509098), hAPP(nat, _509098, semiring_1_of_nat(_509098), _509323)), hAPP(nat, _509098, power_power(_509098, number_number_of(_509098, bit0(bit1(pls)))), _509323))))]], number_ring(_509098), linordered_idom(_509098)], (2072 ^ _434076) ^ [] : [-(number_number_of(int, bit0(bit1(pls))) = hAPP(nat, int, semiring_1_of_nat(int), number_number_of(nat, bit0(bit1(pls)))))], (2074 ^ _434076) ^ [] : [-(number_number_of(int, bit1(bit1(pls))) = hAPP(nat, int, semiring_1_of_nat(int), number_number_of(nat, bit1(bit1(pls)))))], (2076 ^ _434076) ^ [_509604, _509606] : [plus_plus(real, hAPP(nat, real, power_power(real, _509606), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, real, power_power(real, _509604), number_number_of(nat, bit0(bit1(pls))))) = zero_zero(real), 2079 ^ _434076 : [(2080 ^ _434076) ^ [] : [-(_509606 = zero_zero(real))], (2082 ^ _434076) ^ [] : [-(_509604 = zero_zero(real))]]], (2084 ^ _434076) ^ [_509881, _509883] : [-(plus_plus(real, hAPP(nat, real, power_power(real, _509883), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, real, power_power(real, _509881), number_number_of(nat, bit0(bit1(pls))))) = zero_zero(real)), _509883 = zero_zero(real), _509881 = zero_zero(real)], (2094 ^ _434076) ^ [_510208] : [linordered_semidom(_510208), 2097 ^ _434076 : [(2098 ^ _434076) ^ [_510395] : [hBOOL(hAPP(_510208, bool, hAPP(_510208, fun(_510208, bool), ord_less(_510208), zero_zero(_510208)), hAPP(nat, _510208, semiring_1_of_nat(_510208), _510395))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _510395)))], (2104 ^ _434076) ^ [_510613] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _510613)), -(hBOOL(hAPP(_510208, bool, hAPP(_510208, fun(_510208, bool), ord_less(_510208), zero_zero(_510208)), hAPP(nat, _510208, semiring_1_of_nat(_510208), _510613))))]]], (2110 ^ _434076) ^ [_510872] : [linordered_semidom(_510872), 2113 ^ _434076 : [(2114 ^ _434076) ^ [_511072, _511074] : [hBOOL(hAPP(_510872, bool, hAPP(_510872, fun(_510872, bool), ord_less(_510872), one_one(_510872)), _511072)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _511074)), -(hBOOL(hAPP(_510872, bool, hAPP(_510872, fun(_510872, bool), ord_less(_510872), one_one(_510872)), hAPP(nat, _510872, power_power(_510872, _511072), _511074))))]]], (2124 ^ _434076) ^ [_511462] : [power(_511462), semiring_0(_511462), 2131 ^ _434076 : [(2132 ^ _434076) ^ [_511734] : [_511734 = zero_zero(nat), -(hAPP(nat, _511462, power_power(_511462, zero_zero(_511462)), _511734) = one_one(_511462))], (2138 ^ _434076) ^ [_511922] : [-(_511922 = zero_zero(nat)), -(hAPP(nat, _511462, power_power(_511462, zero_zero(_511462)), _511922) = zero_zero(_511462))]]], (2144 ^ _434076) ^ [_512156] : [linordered_semidom(_512156), 2147 ^ _434076 : [(2148 ^ _434076) ^ [_512408, _512410, _512412] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _512410), _512408)), hBOOL(hAPP(_512156, bool, hAPP(_512156, fun(_512156, bool), ord_less(_512156), zero_zero(_512156)), _512412)), hBOOL(hAPP(_512156, bool, hAPP(_512156, fun(_512156, bool), ord_less(_512156), _512412), one_one(_512156))), -(hBOOL(hAPP(_512156, bool, hAPP(_512156, fun(_512156, bool), ord_less(_512156), hAPP(nat, _512156, power_power(_512156, _512412), _512408)), hAPP(nat, _512156, power_power(_512156, _512412), _512410))))]]], (2162 ^ _434076) ^ [_512959] : [linordered_semidom(_512959), -(hBOOL(hAPP(_512959, bool, hAPP(_512959, fun(_512959, bool), ord_less(_512959), zero_zero(_512959)), plus_plus(_512959, one_one(_512959), one_one(_512959)))))], (2168 ^ _434076) ^ [_513223, _513225, _513227] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _513225), _513223)), hBOOL(hAPP(int, bool, _513227, plus_plus(int, _513225, one_one(int)))), 2178 ^ _434076 : [(2179 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _513225), 2177 ^ [_513223, _513225, _513227])))], (2181 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, _513227, 2177 ^ [_513223, _513225, _513227])))], (2183 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _513227, plus_plus(int, 2177 ^ [_513223, _513225, _513227], one_one(int))))]], -(hBOOL(hAPP(int, bool, _513227, _513223)))], (2187 ^ _434076) ^ [] : [-(zero_zero(int) = hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))], (2189 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)))], (2191 ^ _434076) ^ [_514052] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514052), zero_zero(nat)))], (2193 ^ _434076) ^ [] : [zero_zero(real) = one_one(real)], (2195 ^ _434076) ^ [_514190] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514190), _514190))], (2197 ^ _434076) ^ [_514290, _514292] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _514292, _514290)), _514292))], (2199 ^ _434076) ^ [_514396, _514398] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _514398, _514396)), _514396))], (2201 ^ _434076) ^ [_514489] : [-(number_number_of(int, _514489) = ti(int, _514489))], (2213 ^ _434076) ^ [_514922, _514924] : [2214 ^ _434076 : [(2215 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514924), _514922))], (2217 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514922), _514924))]], _514924 = _514922], (2203 ^ _434076) ^ [_514631, _514633] : [-(_514633 = _514631), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514633), _514631))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _514631), _514633)))], (2221 ^ _434076) ^ [_515230, _515232] : [-(plus_plus(nat, _515232, _515230) = plus_plus(nat, _515230, _515232))], (2223 ^ _434076) ^ [_515346, _515348, _515350] : [-(plus_plus(nat, _515350, plus_plus(nat, _515348, _515346)) = plus_plus(nat, _515348, plus_plus(nat, _515350, _515346)))], (2225 ^ _434076) ^ [_515472, _515474, _515476] : [-(plus_plus(nat, plus_plus(nat, _515476, _515474), _515472) = plus_plus(nat, _515476, plus_plus(nat, _515474, _515472)))], (2227 ^ _434076) ^ [_515642, _515644, _515646] : [plus_plus(nat, _515646, _515644) = plus_plus(nat, _515646, _515642), -(_515644 = _515642)], (2233 ^ _434076) ^ [_515826, _515828, _515830] : [_515828 = _515826, -(plus_plus(nat, _515830, _515828) = plus_plus(nat, _515830, _515826))], (2239 ^ _434076) ^ [_516103, _516105, _516107] : [plus_plus(nat, _516107, _516105) = plus_plus(nat, _516103, _516105), -(_516107 = _516103)], (2245 ^ _434076) ^ [_516287, _516289, _516291] : [_516291 = _516287, -(plus_plus(nat, _516291, _516289) = plus_plus(nat, _516287, _516289))], (2251 ^ _434076) ^ [_516564, _516566, _516568] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _516568, _516566)), plus_plus(nat, _516568, _516564))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _516566), _516564)))], (2257 ^ _434076) ^ [_516784, _516786, _516788] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _516786), _516784)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _516788, _516786)), plus_plus(nat, _516788, _516784))))], (2263 ^ _434076) ^ [_517054, _517056] : [-(_517056 = _517054), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517056), _517054))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517054), _517056)))], (2273 ^ _434076) ^ [_517365] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517365), _517365))], (2275 ^ _434076) ^ [_517481, _517483] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517483), _517481)), _517481 = _517483], (2281 ^ _434076) ^ [_517710, _517712] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517712), _517710)), _517712 = _517710], (2287 ^ _434076) ^ [_517953, _517955, _517957] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517955), _517953)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _517955), plus_plus(nat, _517953, _517957))))], (2293 ^ _434076) ^ [_518227, _518229, _518231] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _518229), _518227)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _518229), plus_plus(nat, _518231, _518227))))], (2299 ^ _434076) ^ [_518501, _518503, _518505] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _518503), _518501)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _518503, _518505)), plus_plus(nat, _518501, _518505))))], (2305 ^ _434076) ^ [_518797, _518799, _518801, _518803] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _518799), _518797)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _518803), _518801)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _518799, _518803)), plus_plus(nat, _518797, _518801))))], (2315 ^ _434076) ^ [_519214, _519216, _519218, _519220] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _519216), _519214)), plus_plus(nat, _519220, _519214) = plus_plus(nat, _519216, _519218), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _519220), _519218)))], (2325 ^ _434076) ^ [_519599, _519601, _519603] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _519603, _519601)), _519599)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _519603), _519599)))], (2331 ^ _434076) ^ [_519873, _519875, _519877] : [2332 ^ _434076 : [(2333 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _519875), _519873)))], (2335 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _519877, _519873), _519875))]], 2338 ^ _434076 : [(2339 ^ _434076) ^ [] : [-(_519875 = _519873)], (2341 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _519877, _519873), _519875))]], 2344 ^ _434076 : [(2345 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _519873), _519875)))], (2347 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _519877, _519873), _519875))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _519877, _519873), _519875)))], (2351 ^ _434076) ^ [_520600] : [-(_520600 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _520600)))], (2357 ^ _434076) ^ [_520815, _520817] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _520817), _520815)), _520815 = zero_zero(nat)], (2363 ^ _434076) ^ [_521058, _521060, _521062] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _521058)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, power_power(nat, _521058), _521062)), hAPP(nat, nat, power_power(nat, _521058), _521060))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _521062), _521060)))], (2373 ^ _434076) ^ [_521413] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _521413), zero_zero(nat)))], (2385 ^ _434076) ^ [_521842, _521844] : [2386 ^ _434076 : [(2387 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _521844))], (2389 ^ _434076) ^ [] : [_521842 = zero_zero(nat)]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _521844), _521842))))], (2375 ^ _434076) ^ [_521558, _521560] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _521560), _521558))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _521560))), -(_521558 = zero_zero(nat))], (2403 ^ _434076) ^ [_522473, _522475] : [2404 ^ _434076 : [(2405 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522475))], (2407 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522473))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), plus_plus(nat, _522475, _522473))))], (2393 ^ _434076) ^ [_522189, _522191] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), plus_plus(nat, _522191, _522189))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522191))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522189)))], (2411 ^ _434076) ^ [_522806] : [-(_522806 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522806)))], (2417 ^ _434076) ^ [_522973] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _522973)), _522973 = zero_zero(nat)], (2423 ^ _434076) ^ [_523158] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _523158), zero_zero(nat)))], (2435 ^ _434076) ^ [_523587, _523589] : [2436 ^ _434076 : [(2437 ^ _434076) ^ [] : [_523587 = zero_zero(nat)], (2439 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _523589))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _523589), _523587))))], (2425 ^ _434076) ^ [_523303, _523305] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _523305), _523303))), -(_523303 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _523305)))], (2443 ^ _434076) ^ [_523934, _523936] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _523936)), hAPP(nat, int, semiring_1_of_nat(int), _523934))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _523936), _523934)))], (2449 ^ _434076) ^ [_524152, _524154] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _524154), _524152)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _524154)), hAPP(nat, int, semiring_1_of_nat(int), _524152))))], (2465 ^ _434076) ^ [_524745, _524747] : [2466 ^ _434076 : [(2467 ^ _434076) ^ [] : [number_number_of(nat, _524745) = zero_zero(nat)], (2469 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _524747))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _524747), number_number_of(nat, _524745)))))], (2455 ^ _434076) ^ [_524449, _524451] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _524451), number_number_of(nat, _524449)))), -(number_number_of(nat, _524449) = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _524451)))], (2473 ^ _434076) ^ [_525104, _525106] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _525106)), hAPP(nat, int, semiring_1_of_nat(int), _525104))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _525106), _525104)))], (2479 ^ _434076) ^ [_525322, _525324] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _525324), _525322)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _525324)), hAPP(nat, int, semiring_1_of_nat(int), _525322))))], (2485 ^ _434076) ^ [_525619, _525621] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), number_number_of(nat, _525621)), number_number_of(nat, _525619))), 2488 ^ _434076 : [(2495 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _525621), _525619)))], (2489 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _525621), _525619)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _525619)))]]], (2497 ^ _434076) ^ [_526019, _526021] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), number_number_of(nat, _526021)), number_number_of(nat, _526019)))), 2500 ^ _434076 : [(2501 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _526021), _526019)))], (2503 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _526019))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _526021), _526019))], (2509 ^ _434076) ^ [_526455] : [linordered_idom(_526455), 2512 ^ _434076 : [(2513 ^ _434076) ^ [_526649, _526651] : [-(ti(_526455, _526651) = ti(_526455, _526649)), -(hBOOL(hAPP(_526455, bool, hAPP(_526455, fun(_526455, bool), ord_less(_526455), _526651), _526649))), -(hBOOL(hAPP(_526455, bool, hAPP(_526455, fun(_526455, bool), ord_less(_526455), _526649), _526651)))]]], (2523 ^ _434076) ^ [_527039, _527041] : [plus_plus(nat, _527041, _527039) = _527041, -(_527039 = zero_zero(nat))], (2529 ^ _434076) ^ [_527286, _527288] : [plus_plus(nat, _527288, _527286) = zero_zero(nat), 2532 ^ _434076 : [(2533 ^ _434076) ^ [] : [-(_527288 = zero_zero(nat))], (2535 ^ _434076) ^ [] : [-(_527286 = zero_zero(nat))]]], (2537 ^ _434076) ^ [_527531, _527533] : [-(plus_plus(nat, _527533, _527531) = zero_zero(nat)), _527533 = zero_zero(nat), _527531 = zero_zero(nat)], (2547 ^ _434076) ^ [_527811] : [-(plus_plus(nat, _527811, zero_zero(nat)) = _527811)], (2549 ^ _434076) ^ [_527893] : [-(plus_plus(nat, zero_zero(nat), _527893) = _527893)], (2551 ^ _434076) ^ [_527990] : [monoid_mult(_527990), 2554 ^ _434076 : [(2555 ^ _434076) ^ [_528111] : [-(hAPP(nat, _527990, power_power(_527990, _528111), one_one(nat)) = ti(_527990, _528111))]]], (2557 ^ _434076) ^ [_528222] : [semiring_char_0(_528222), 2560 ^ _434076 : [(2561 ^ _434076) ^ [_528415, _528417] : [hAPP(nat, _528222, semiring_1_of_nat(_528222), _528417) = hAPP(nat, _528222, semiring_1_of_nat(_528222), _528415), -(_528417 = _528415)], (2567 ^ _434076) ^ [_528613, _528615] : [_528615 = _528613, -(hAPP(nat, _528222, semiring_1_of_nat(_528222), _528615) = hAPP(nat, _528222, semiring_1_of_nat(_528222), _528613))]]], (2573 ^ _434076) ^ [_528895, _528897] : [hAPP(nat, int, semiring_1_of_nat(int), _528897) = hAPP(nat, int, semiring_1_of_nat(int), _528895), -(_528897 = _528895)], (2579 ^ _434076) ^ [_529077, _529079] : [_529079 = _529077, -(hAPP(nat, int, semiring_1_of_nat(int), _529079) = hAPP(nat, int, semiring_1_of_nat(int), _529077))], (2585 ^ _434076) ^ [_529343, _529345, _529347] : [hBOOL(_529343), -(hAPP(nat, int, semiring_1_of_nat(int), _529347) = hAPP(nat, int, semiring_1_of_nat(int), if(nat, _529343, _529347, _529345)))], (2591 ^ _434076) ^ [_529539, _529541, _529543] : [-(hBOOL(_529539)), -(hAPP(nat, int, semiring_1_of_nat(int), _529541) = hAPP(nat, int, semiring_1_of_nat(int), if(nat, _529539, _529543, _529541)))], (2597 ^ _434076) ^ [_529803] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, _529803))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _529803)))], (2603 ^ _434076) ^ [_529981] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _529981)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, _529981))))], (2609 ^ _434076) ^ [_530224] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _530224))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _530224)))], (2615 ^ _434076) ^ [_530406] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _530406)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _530406))))], (2621 ^ _434076) ^ [_530624] : [zero_neq_one(_530624), one_one(_530624) = zero_zero(_530624)], (2627 ^ _434076) ^ [_530821] : [zero_neq_one(_530821), zero_zero(_530821) = one_one(_530821)], (2633 ^ _434076) ^ [_531018] : [ring_11004092258visors(_531018), 2636 ^ _434076 : [(2637 ^ _434076) ^ [_531187, _531189] : [-(ti(_531018, _531187) = zero_zero(_531018)), hAPP(nat, _531018, power_power(_531018, _531187), _531189) = zero_zero(_531018)]]], (2643 ^ _434076) ^ [_531430] : [monoid_mult(_531430), 2646 ^ _434076 : [(2647 ^ _434076) ^ [_531552] : [-(hAPP(nat, _531430, power_power(_531430, one_one(_531430)), _531552) = one_one(_531430))]]], (2649 ^ _434076) ^ [_531664] : [linordered_semidom(_531664), 2652 ^ _434076 : [(2653 ^ _434076) ^ [_531880, _531882] : [hBOOL(hAPP(_531664, bool, hAPP(_531664, fun(_531664, bool), ord_less(_531664), hAPP(nat, _531664, semiring_1_of_nat(_531664), _531882)), hAPP(nat, _531664, semiring_1_of_nat(_531664), _531880))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _531882), _531880)))], (2659 ^ _434076) ^ [_532124, _532126] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _532126), _532124)), -(hBOOL(hAPP(_531664, bool, hAPP(_531664, fun(_531664, bool), ord_less(_531664), hAPP(nat, _531664, semiring_1_of_nat(_531664), _532126)), hAPP(nat, _531664, semiring_1_of_nat(_531664), _532124))))]]], (2665 ^ _434076) ^ [_532409] : [linordered_semidom(_532409), 2668 ^ _434076 : [(2669 ^ _434076) ^ [_532596, _532598] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _532598), _532596)), -(hBOOL(hAPP(_532409, bool, hAPP(_532409, fun(_532409, bool), ord_less(_532409), hAPP(nat, _532409, semiring_1_of_nat(_532409), _532598)), hAPP(nat, _532409, semiring_1_of_nat(_532409), _532596))))]]], (2675 ^ _434076) ^ [_532879] : [linordered_semidom(_532879), 2678 ^ _434076 : [(2679 ^ _434076) ^ [_533066, _533068] : [hBOOL(hAPP(_532879, bool, hAPP(_532879, fun(_532879, bool), ord_less(_532879), hAPP(nat, _532879, semiring_1_of_nat(_532879), _533068)), hAPP(nat, _532879, semiring_1_of_nat(_532879), _533066))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _533068), _533066)))]]], (2685 ^ _434076) ^ [_533349] : [semiring_1(_533349), 2688 ^ _434076 : [(2689 ^ _434076) ^ [_533507, _533509] : [-(hAPP(nat, _533349, semiring_1_of_nat(_533349), plus_plus(nat, _533509, _533507)) = plus_plus(_533349, hAPP(nat, _533349, semiring_1_of_nat(_533349), _533509), hAPP(nat, _533349, semiring_1_of_nat(_533349), _533507)))]]], (2691 ^ _434076) ^ [_533638] : [semiring_1(_533638), -(hAPP(nat, _533638, semiring_1_of_nat(_533638), one_one(nat)) = one_one(_533638))], (2697 ^ _434076) ^ [_533844] : [semiring_1(_533844), 2700 ^ _434076 : [(2701 ^ _434076) ^ [_534003, _534005] : [-(hAPP(nat, _533844, semiring_1_of_nat(_533844), hAPP(nat, nat, power_power(nat, _534005), _534003)) = hAPP(nat, _533844, power_power(_533844, hAPP(nat, _533844, semiring_1_of_nat(_533844), _534005)), _534003))]]], (2703 ^ _434076) ^ [] : [-(one_one(int) = hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)))], (2705 ^ _434076) ^ [_534187, _534189] : [-(plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _534189), hAPP(nat, int, semiring_1_of_nat(int), _534187)) = hAPP(nat, int, semiring_1_of_nat(int), plus_plus(nat, _534189, _534187)))], (2707 ^ _434076) ^ [_534304, _534306] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _534306)), _534304) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _534306), _534304)))], (2709 ^ _434076) ^ [_534425] : [linordered_semidom(_534425), 2712 ^ _434076 : [(2713 ^ _434076) ^ [_534648, _534650, _534652] : [hBOOL(hAPP(_534425, bool, hAPP(_534425, fun(_534425, bool), ord_less(_534425), zero_zero(_534425)), _534648)), hBOOL(hAPP(_534425, bool, hAPP(_534425, fun(_534425, bool), ord_less(_534425), _534652), _534650)), -(hBOOL(hAPP(_534425, bool, hAPP(_534425, fun(_534425, bool), ord_less(_534425), _534652), plus_plus(_534425, _534648, _534650))))]]], (2723 ^ _434076) ^ [_535056] : [linordered_semidom(_535056), hBOOL(hAPP(_535056, bool, hAPP(_535056, fun(_535056, bool), ord_less(_535056), one_one(_535056)), zero_zero(_535056)))], (2729 ^ _434076) ^ [_535281] : [linordered_semidom(_535281), -(hBOOL(hAPP(_535281, bool, hAPP(_535281, fun(_535281, bool), ord_less(_535281), zero_zero(_535281)), one_one(_535281))))], (2735 ^ _434076) ^ [_535505] : [linordered_semidom(_535505), 2738 ^ _434076 : [(2739 ^ _434076) ^ [_535695, _535697] : [hBOOL(hAPP(_535505, bool, hAPP(_535505, fun(_535505, bool), ord_less(_535505), zero_zero(_535505)), _535695)), -(hBOOL(hAPP(_535505, bool, hAPP(_535505, fun(_535505, bool), ord_less(_535505), zero_zero(_535505)), hAPP(nat, _535505, power_power(_535505, _535695), _535697))))]]], (2745 ^ _434076) ^ [_535984] : [linordered_semidom(_535984), 2748 ^ _434076 : [(2749 ^ _434076) ^ [_536114] : [-(hBOOL(hAPP(_535984, bool, hAPP(_535984, fun(_535984, bool), ord_less(_535984), _536114), plus_plus(_535984, _536114, one_one(_535984)))))]]], (2751 ^ _434076) ^ [_536234] : [linordered_semidom(_536234), 2754 ^ _434076 : [(2755 ^ _434076) ^ [_536441, _536443, _536445] : [hBOOL(hAPP(_536234, bool, hAPP(_536234, fun(_536234, bool), ord_less(_536234), one_one(_536234)), _536441)), 2758 ^ _434076 : [(2759 ^ _434076) ^ [] : [hAPP(nat, _536234, power_power(_536234, _536441), _536445) = hAPP(nat, _536234, power_power(_536234, _536441), _536443), -(_536445 = _536443)], (2765 ^ _434076) ^ [] : [_536445 = _536443, -(hAPP(nat, _536234, power_power(_536234, _536441), _536445) = hAPP(nat, _536234, power_power(_536234, _536441), _536443))]]]]], (2771 ^ _434076) ^ [_537006] : [linordered_semidom(_537006), 2774 ^ _434076 : [(2775 ^ _434076) ^ [_537236, _537238, _537240] : [hBOOL(hAPP(_537006, bool, hAPP(_537006, fun(_537006, bool), ord_less(_537006), one_one(_537006)), _537236)), 2778 ^ _434076 : [(2779 ^ _434076) ^ [] : [hBOOL(hAPP(_537006, bool, hAPP(_537006, fun(_537006, bool), ord_less(_537006), hAPP(nat, _537006, power_power(_537006, _537236), _537240)), hAPP(nat, _537006, power_power(_537006, _537236), _537238))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _537240), _537238)))], (2785 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _537240), _537238)), -(hBOOL(hAPP(_537006, bool, hAPP(_537006, fun(_537006, bool), ord_less(_537006), hAPP(nat, _537006, power_power(_537006, _537236), _537240)), hAPP(nat, _537006, power_power(_537006, _537236), _537238))))]]]]], (2791 ^ _434076) ^ [_537870] : [linordered_semidom(_537870), 2794 ^ _434076 : [(2795 ^ _434076) ^ [_538100, _538102, _538104] : [hBOOL(hAPP(_537870, bool, hAPP(_537870, fun(_537870, bool), ord_less(_537870), one_one(_537870)), _538100)), hBOOL(hAPP(_537870, bool, hAPP(_537870, fun(_537870, bool), ord_less(_537870), hAPP(nat, _537870, power_power(_537870, _538100), _538104)), hAPP(nat, _537870, power_power(_537870, _538100), _538102))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _538104), _538102)))]]], (2805 ^ _434076) ^ [_538522] : [linordered_semidom(_538522), 2808 ^ _434076 : [(2809 ^ _434076) ^ [_538752, _538754, _538756] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _538754), _538752)), hBOOL(hAPP(_538522, bool, hAPP(_538522, fun(_538522, bool), ord_less(_538522), one_one(_538522)), _538756)), -(hBOOL(hAPP(_538522, bool, hAPP(_538522, fun(_538522, bool), ord_less(_538522), hAPP(nat, _538522, power_power(_538522, _538756), _538754)), hAPP(nat, _538522, power_power(_538522, _538756), _538752))))]]], (2819 ^ _434076) ^ [_539174] : [power(_539174), mult_zero(_539174), no_zero_divisors(_539174), zero_neq_one(_539174), 2834 ^ _434076 : [(2835 ^ _434076) ^ [_539625, _539627] : [hAPP(nat, _539174, power_power(_539174, _539627), _539625) = zero_zero(_539174), 2838 ^ _434076 : [(2839 ^ _434076) ^ [] : [-(ti(_539174, _539627) = zero_zero(_539174))], (2841 ^ _434076) ^ [] : [_539625 = zero_zero(nat)]]], (2843 ^ _434076) ^ [_539903, _539905] : [-(hAPP(nat, _539174, power_power(_539174, _539905), _539903) = zero_zero(_539174)), ti(_539174, _539905) = zero_zero(_539174), -(_539903 = zero_zero(nat))]]], (2853 ^ _434076) ^ [_540246] : [linordered_semidom(_540246), 2856 ^ _434076 : [(2857 ^ _434076) ^ [_540380] : [hBOOL(hAPP(_540246, bool, hAPP(_540246, fun(_540246, bool), ord_less(_540246), hAPP(nat, _540246, semiring_1_of_nat(_540246), _540380)), zero_zero(_540246)))]]], (2859 ^ _434076) ^ [_540503] : [power(_540503), 2862 ^ _434076 : [(2863 ^ _434076) ^ [_540623] : [-(hAPP(nat, _540503, power_power(_540503, _540623), zero_zero(nat)) = one_one(_540503))]]], (2865 ^ _434076) ^ [_540733] : [semiring_1(_540733), -(hAPP(nat, _540733, semiring_1_of_nat(_540733), zero_zero(nat)) = zero_zero(_540733))], (2871 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))))], (2873 ^ _434076) ^ [_540992] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _540992)), 2877 ^ _434076 : [(2878 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), 2876 ^ [_540992])))], (2880 ^ _434076) ^ [] : [-(ti(int, _540992) = hAPP(nat, int, semiring_1_of_nat(int), 2876 ^ [_540992]))]]], (2882 ^ _434076) ^ [_541375, _541377] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _541377), _541375)), 2886 ^ _434076 : [(2887 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), 2885 ^ [_541375, _541377])))], (2889 ^ _434076) ^ [] : [-(plus_plus(nat, _541377, 2885 ^ [_541375, _541377]) = _541375)]]], (2901 ^ _434076) ^ [_542069, _542071] : [2902 ^ _434076 : [(2903 ^ _434076) ^ [] : [_542071 = one_one(nat)], (2905 ^ _434076) ^ [] : [_542069 = zero_zero(nat)]], -(hAPP(nat, nat, power_power(nat, _542071), _542069) = one_one(nat))], (2891 ^ _434076) ^ [_541801, _541803] : [hAPP(nat, nat, power_power(nat, _541803), _541801) = one_one(nat), -(_541803 = one_one(nat)), -(_541801 = zero_zero(nat))], (2909 ^ _434076) ^ [_542357] : [comm_semiring_1(_542357), 2912 ^ _434076 : [(2913 ^ _434076) ^ [_542477] : [-(hAPP(nat, _542357, power_power(_542357, _542477), zero_zero(nat)) = one_one(_542357))]]], (2915 ^ _434076) ^ [_542587] : [linord219039673up_add(_542587), 2918 ^ _434076 : [(2919 ^ _434076) ^ [_542783] : [hBOOL(hAPP(_542587, bool, hAPP(_542587, fun(_542587, bool), ord_less(_542587), zero_zero(_542587)), plus_plus(_542587, _542783, _542783))), -(hBOOL(hAPP(_542587, bool, hAPP(_542587, fun(_542587, bool), ord_less(_542587), zero_zero(_542587)), _542783)))], (2925 ^ _434076) ^ [_543019] : [hBOOL(hAPP(_542587, bool, hAPP(_542587, fun(_542587, bool), ord_less(_542587), zero_zero(_542587)), _543019)), -(hBOOL(hAPP(_542587, bool, hAPP(_542587, fun(_542587, bool), ord_less(_542587), zero_zero(_542587)), plus_plus(_542587, _543019, _543019))))]]], (2931 ^ _434076) ^ [_543296] : [linord219039673up_add(_543296), 2934 ^ _434076 : [(2935 ^ _434076) ^ [_543492] : [hBOOL(hAPP(_543296, bool, hAPP(_543296, fun(_543296, bool), ord_less(_543296), plus_plus(_543296, _543492, _543492)), zero_zero(_543296))), -(hBOOL(hAPP(_543296, bool, hAPP(_543296, fun(_543296, bool), ord_less(_543296), _543492), zero_zero(_543296))))], (2941 ^ _434076) ^ [_543728] : [hBOOL(hAPP(_543296, bool, hAPP(_543296, fun(_543296, bool), ord_less(_543296), _543728), zero_zero(_543296))), -(hBOOL(hAPP(_543296, bool, hAPP(_543296, fun(_543296, bool), ord_less(_543296), plus_plus(_543296, _543728, _543728)), zero_zero(_543296))))]]], (2947 ^ _434076) ^ [_544005] : [ordere216010020id_add(_544005), 2950 ^ _434076 : [(2951 ^ _434076) ^ [_544213, _544215] : [hBOOL(hAPP(_544005, bool, hAPP(_544005, fun(_544005, bool), ord_less(_544005), zero_zero(_544005)), _544213)), hBOOL(hAPP(_544005, bool, hAPP(_544005, fun(_544005, bool), ord_less(_544005), zero_zero(_544005)), _544215)), -(hBOOL(hAPP(_544005, bool, hAPP(_544005, fun(_544005, bool), ord_less(_544005), zero_zero(_544005)), plus_plus(_544005, _544213, _544215))))]]], (2961 ^ _434076) ^ [_544619] : [ordere216010020id_add(_544619), 2964 ^ _434076 : [(2965 ^ _434076) ^ [_544827, _544829] : [hBOOL(hAPP(_544619, bool, hAPP(_544619, fun(_544619, bool), ord_less(_544619), _544827), zero_zero(_544619))), hBOOL(hAPP(_544619, bool, hAPP(_544619, fun(_544619, bool), ord_less(_544619), _544829), zero_zero(_544619))), -(hBOOL(hAPP(_544619, bool, hAPP(_544619, fun(_544619, bool), ord_less(_544619), plus_plus(_544619, _544827, _544829)), zero_zero(_544619))))]]], (2975 ^ _434076) ^ [_545233] : [zero(_545233), 2978 ^ _434076 : [(2979 ^ _434076) ^ [_545403] : [zero_zero(_545233) = ti(_545233, _545403), -(ti(_545233, _545403) = zero_zero(_545233))], (2985 ^ _434076) ^ [_545587] : [ti(_545233, _545587) = zero_zero(_545233), -(zero_zero(_545233) = ti(_545233, _545587))]]], (2991 ^ _434076) ^ [_545812] : [cancel_semigroup_add(_545812), 2994 ^ _434076 : [(2995 ^ _434076) ^ [_545995, _545997, _545999] : [plus_plus(_545812, _545999, _545997) = plus_plus(_545812, _545995, _545997), -(ti(_545812, _545999) = ti(_545812, _545995))]]], (3001 ^ _434076) ^ [_546238] : [cancel146912293up_add(_546238), 3004 ^ _434076 : [(3005 ^ _434076) ^ [_546421, _546423, _546425] : [plus_plus(_546238, _546425, _546423) = plus_plus(_546238, _546425, _546421), -(ti(_546238, _546423) = ti(_546238, _546421))]]], (3011 ^ _434076) ^ [_546664] : [cancel_semigroup_add(_546664), 3014 ^ _434076 : [(3015 ^ _434076) ^ [_546847, _546849, _546851] : [plus_plus(_546664, _546851, _546849) = plus_plus(_546664, _546851, _546847), -(ti(_546664, _546849) = ti(_546664, _546847))]]], (3021 ^ _434076) ^ [_547090] : [comm_semiring_1(_547090), 3024 ^ _434076 : [(3025 ^ _434076) ^ [_547281, _547283, _547285, _547287] : [-(plus_plus(_547090, plus_plus(_547090, _547287, _547285), plus_plus(_547090, _547283, _547281)) = plus_plus(_547090, plus_plus(_547090, _547287, _547283), plus_plus(_547090, _547285, _547281)))]]], (3027 ^ _434076) ^ [_547411] : [cancel_semigroup_add(_547411), 3030 ^ _434076 : [(3031 ^ _434076) ^ [_547623, _547625, _547627] : [plus_plus(_547411, _547627, _547625) = plus_plus(_547411, _547623, _547625), -(ti(_547411, _547627) = ti(_547411, _547623))], (3037 ^ _434076) ^ [_547827, _547829, _547831] : [ti(_547411, _547831) = ti(_547411, _547827), -(plus_plus(_547411, _547831, _547829) = plus_plus(_547411, _547827, _547829))]]], (3043 ^ _434076) ^ [_548072] : [cancel_semigroup_add(_548072), 3046 ^ _434076 : [(3047 ^ _434076) ^ [_548284, _548286, _548288] : [plus_plus(_548072, _548288, _548286) = plus_plus(_548072, _548288, _548284), -(ti(_548072, _548286) = ti(_548072, _548284))], (3053 ^ _434076) ^ [_548488, _548490, _548492] : [ti(_548072, _548490) = ti(_548072, _548488), -(plus_plus(_548072, _548492, _548490) = plus_plus(_548072, _548492, _548488))]]], (3059 ^ _434076) ^ [_548733] : [comm_semiring_1(_548733), 3062 ^ _434076 : [(3063 ^ _434076) ^ [_548897, _548899, _548901] : [-(plus_plus(_548733, plus_plus(_548733, _548901, _548899), _548897) = plus_plus(_548733, plus_plus(_548733, _548901, _548897), _548899))]]], (3065 ^ _434076) ^ [_549017] : [ab_semigroup_add(_549017), 3068 ^ _434076 : [(3069 ^ _434076) ^ [_549181, _549183, _549185] : [-(plus_plus(_549017, plus_plus(_549017, _549185, _549183), _549181) = plus_plus(_549017, _549185, plus_plus(_549017, _549183, _549181)))]]], (3071 ^ _434076) ^ [_549301] : [comm_semiring_1(_549301), 3074 ^ _434076 : [(3075 ^ _434076) ^ [_549465, _549467, _549469] : [-(plus_plus(_549301, plus_plus(_549301, _549469, _549467), _549465) = plus_plus(_549301, _549469, plus_plus(_549301, _549467, _549465)))]]], (3077 ^ _434076) ^ [_549585] : [comm_semiring_1(_549585), 3080 ^ _434076 : [(3081 ^ _434076) ^ [_549749, _549751, _549753] : [-(plus_plus(_549585, _549753, plus_plus(_549585, _549751, _549749)) = plus_plus(_549585, plus_plus(_549585, _549753, _549751), _549749))]]], (3083 ^ _434076) ^ [_549869] : [comm_semiring_1(_549869), 3086 ^ _434076 : [(3087 ^ _434076) ^ [_550033, _550035, _550037] : [-(plus_plus(_549869, _550037, plus_plus(_549869, _550035, _550033)) = plus_plus(_549869, _550035, plus_plus(_549869, _550037, _550033)))]]], (3089 ^ _434076) ^ [_550153] : [comm_semiring_1(_550153), 3092 ^ _434076 : [(3093 ^ _434076) ^ [_550290, _550292] : [-(plus_plus(_550153, _550292, _550290) = plus_plus(_550153, _550290, _550292))]]], (3095 ^ _434076) ^ [_550400] : [one(_550400), 3098 ^ _434076 : [(3099 ^ _434076) ^ [_550570] : [one_one(_550400) = ti(_550400, _550570), -(ti(_550400, _550570) = one_one(_550400))], (3105 ^ _434076) ^ [_550754] : [ti(_550400, _550754) = one_one(_550400), -(one_one(_550400) = ti(_550400, _550754))]]], (3111 ^ _434076) ^ [_550979] : [semiri456707255roduct(_550979), 3114 ^ _434076 : [(3115 ^ _434076) ^ [_551170, _551172] : [ti(_550979, _551172) = plus_plus(_550979, _551172, _551170), -(ti(_550979, _551170) = zero_zero(_550979))], (3121 ^ _434076) ^ [_551364, _551366] : [ti(_550979, _551364) = zero_zero(_550979), -(ti(_550979, _551366) = plus_plus(_550979, _551366, _551364))]]], (3127 ^ _434076) ^ [_551599] : [comm_monoid_add(_551599), 3130 ^ _434076 : [(3131 ^ _434076) ^ [_551718] : [-(plus_plus(_551599, _551718, zero_zero(_551599)) = ti(_551599, _551718))]]], (3133 ^ _434076) ^ [_551827] : [comm_semiring_1(_551827), 3136 ^ _434076 : [(3137 ^ _434076) ^ [_551946] : [-(plus_plus(_551827, _551946, zero_zero(_551827)) = ti(_551827, _551946))]]], (3139 ^ _434076) ^ [_552055] : [monoid_add(_552055), 3142 ^ _434076 : [(3143 ^ _434076) ^ [_552174] : [-(plus_plus(_552055, _552174, zero_zero(_552055)) = ti(_552055, _552174))]]], (3145 ^ _434076) ^ [_552283] : [linord219039673up_add(_552283), 3148 ^ _434076 : [(3149 ^ _434076) ^ [_552454] : [zero_zero(_552283) = plus_plus(_552283, _552454, _552454), -(ti(_552283, _552454) = zero_zero(_552283))], (3155 ^ _434076) ^ [_552640] : [ti(_552283, _552640) = zero_zero(_552283), -(zero_zero(_552283) = plus_plus(_552283, _552640, _552640))]]], (3161 ^ _434076) ^ [_552867] : [comm_monoid_add(_552867), 3164 ^ _434076 : [(3165 ^ _434076) ^ [_552986] : [-(plus_plus(_552867, zero_zero(_552867), _552986) = ti(_552867, _552986))]]], (3167 ^ _434076) ^ [_553095] : [comm_semiring_1(_553095), 3170 ^ _434076 : [(3171 ^ _434076) ^ [_553214] : [-(plus_plus(_553095, zero_zero(_553095), _553214) = ti(_553095, _553214))]]], (3173 ^ _434076) ^ [_553323] : [monoid_add(_553323), 3176 ^ _434076 : [(3177 ^ _434076) ^ [_553442] : [-(plus_plus(_553323, zero_zero(_553323), _553442) = ti(_553323, _553442))]]], (3179 ^ _434076) ^ [_553551] : [ordere236663937imp_le(_553551), 3182 ^ _434076 : [(3183 ^ _434076) ^ [_553756, _553758, _553760] : [hBOOL(hAPP(_553551, bool, hAPP(_553551, fun(_553551, bool), ord_less(_553551), plus_plus(_553551, _553760, _553758)), plus_plus(_553551, _553760, _553756))), -(hBOOL(hAPP(_553551, bool, hAPP(_553551, fun(_553551, bool), ord_less(_553551), _553758), _553756)))]]], (3189 ^ _434076) ^ [_554043] : [ordere236663937imp_le(_554043), 3192 ^ _434076 : [(3193 ^ _434076) ^ [_554248, _554250, _554252] : [hBOOL(hAPP(_554043, bool, hAPP(_554043, fun(_554043, bool), ord_less(_554043), plus_plus(_554043, _554252, _554250)), plus_plus(_554043, _554248, _554250))), -(hBOOL(hAPP(_554043, bool, hAPP(_554043, fun(_554043, bool), ord_less(_554043), _554252), _554248)))]]], (3199 ^ _434076) ^ [_554535] : [ordere223160158up_add(_554535), 3202 ^ _434076 : [(3203 ^ _434076) ^ [_554779, _554781, _554783, _554785] : [hBOOL(hAPP(_554535, bool, hAPP(_554535, fun(_554535, bool), ord_less(_554535), _554781), _554779)), hBOOL(hAPP(_554535, bool, hAPP(_554535, fun(_554535, bool), ord_less(_554535), _554785), _554783)), -(hBOOL(hAPP(_554535, bool, hAPP(_554535, fun(_554535, bool), ord_less(_554535), plus_plus(_554535, _554781, _554785)), plus_plus(_554535, _554779, _554783))))]]], (3213 ^ _434076) ^ [_555201] : [ordere223160158up_add(_555201), 3216 ^ _434076 : [(3217 ^ _434076) ^ [_555406, _555408, _555410] : [hBOOL(hAPP(_555201, bool, hAPP(_555201, fun(_555201, bool), ord_less(_555201), _555408), _555406)), -(hBOOL(hAPP(_555201, bool, hAPP(_555201, fun(_555201, bool), ord_less(_555201), plus_plus(_555201, _555410, _555408)), plus_plus(_555201, _555410, _555406))))]]], (3223 ^ _434076) ^ [_555693] : [ordere223160158up_add(_555693), 3226 ^ _434076 : [(3227 ^ _434076) ^ [_555898, _555900, _555902] : [hBOOL(hAPP(_555693, bool, hAPP(_555693, fun(_555693, bool), ord_less(_555693), _555900), _555898)), -(hBOOL(hAPP(_555693, bool, hAPP(_555693, fun(_555693, bool), ord_less(_555693), plus_plus(_555693, _555900, _555902)), plus_plus(_555693, _555898, _555902))))]]], (3233 ^ _434076) ^ [_556185] : [ordere236663937imp_le(_556185), 3236 ^ _434076 : [(3237 ^ _434076) ^ [_556419, _556421, _556423] : [hBOOL(hAPP(_556185, bool, hAPP(_556185, fun(_556185, bool), ord_less(_556185), plus_plus(_556185, _556423, _556421)), plus_plus(_556185, _556423, _556419))), -(hBOOL(hAPP(_556185, bool, hAPP(_556185, fun(_556185, bool), ord_less(_556185), _556421), _556419)))], (3243 ^ _434076) ^ [_556667, _556669, _556671] : [hBOOL(hAPP(_556185, bool, hAPP(_556185, fun(_556185, bool), ord_less(_556185), _556669), _556667)), -(hBOOL(hAPP(_556185, bool, hAPP(_556185, fun(_556185, bool), ord_less(_556185), plus_plus(_556185, _556671, _556669)), plus_plus(_556185, _556671, _556667))))]]], (3249 ^ _434076) ^ [_556956] : [ordere236663937imp_le(_556956), 3252 ^ _434076 : [(3253 ^ _434076) ^ [_557190, _557192, _557194] : [hBOOL(hAPP(_556956, bool, hAPP(_556956, fun(_556956, bool), ord_less(_556956), plus_plus(_556956, _557194, _557192)), plus_plus(_556956, _557190, _557192))), -(hBOOL(hAPP(_556956, bool, hAPP(_556956, fun(_556956, bool), ord_less(_556956), _557194), _557190)))], (3259 ^ _434076) ^ [_557438, _557440, _557442] : [hBOOL(hAPP(_556956, bool, hAPP(_556956, fun(_556956, bool), ord_less(_556956), _557442), _557438)), -(hBOOL(hAPP(_556956, bool, hAPP(_556956, fun(_556956, bool), ord_less(_556956), plus_plus(_556956, _557442, _557440)), plus_plus(_556956, _557438, _557440))))]]], (3265 ^ _434076) ^ [_557727] : [comm_semiring_1(_557727), 3268 ^ _434076 : [(3269 ^ _434076) ^ [_557848] : [-(hAPP(nat, _557727, power_power(_557727, _557848), one_one(nat)) = ti(_557727, _557848))]]], (3271 ^ _434076) ^ [_558002, _558004] : [hAPP(nat, nat, power_power(nat, _558004), _558002) = zero_zero(nat), 3274 ^ _434076 : [(3275 ^ _434076) ^ [] : [_558002 = zero_zero(nat)], (3277 ^ _434076) ^ [] : [-(_558004 = zero_zero(nat))]]], (3279 ^ _434076) ^ [_558256, _558258] : [-(hAPP(nat, nat, power_power(nat, _558258), _558256) = zero_zero(nat)), -(_558256 = zero_zero(nat)), _558258 = zero_zero(nat)], (3289 ^ _434076) ^ [_558576, _558578] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _558576)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _558578)), 3297 ^ _434076 : [(3298 ^ _434076) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), 3296 ^ [_558576, _558578])))], (3300 ^ _434076) ^ [] : [-(hAPP(nat, real, power_power(real, 3296 ^ [_558576, _558578]), _558576) = _558578)], (3302 ^ _434076) ^ [_559117] : [-(_559117 = 3296 ^ [_558576, _558578]), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _559117)), hAPP(nat, real, power_power(real, _559117), _558576) = _558578]]], (3312 ^ _434076) ^ [_559481, _559483] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _559481)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _559483)), 3320 ^ _434076 : [(3321 ^ _434076) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), 3319 ^ [_559481, _559483])))], (3323 ^ _434076) ^ [] : [-(hAPP(nat, real, power_power(real, 3319 ^ [_559481, _559483]), _559481) = _559483)]]], (3325 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), t)))], (3327 ^ _434076) ^ [_560036] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _560036), pls)), -(plus_plus(nat, number_number_of(nat, _560036), one_one(nat)) = one_one(nat))], (3333 ^ _434076) ^ [_560224] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _560224), pls))), -(plus_plus(nat, number_number_of(nat, _560224), one_one(nat)) = number_number_of(nat, succ(_560224)))], (3339 ^ _434076) ^ [_560481] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _560481), pls)), -(plus_plus(nat, one_one(nat), number_number_of(nat, _560481)) = one_one(nat))], (3345 ^ _434076) ^ [_560669] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _560669), pls))), -(plus_plus(nat, one_one(nat), number_number_of(nat, _560669)) = number_number_of(nat, succ(_560669)))], (3351 ^ _434076) ^ [_560905, _560907] : [-(hAPP(nat, int, power_power(int, plus_plus(int, _560907, _560905)), number_number_of(nat, bit1(bit1(pls)))) = plus_plus(int, plus_plus(int, plus_plus(int, hAPP(nat, int, power_power(int, _560907), number_number_of(nat, bit1(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), hAPP(nat, int, power_power(int, _560907), number_number_of(nat, bit0(bit1(pls))))), _560905)), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), _560907), hAPP(nat, int, power_power(int, _560905), number_number_of(nat, bit0(bit1(pls)))))), hAPP(nat, int, power_power(int, _560905), number_number_of(nat, bit1(bit1(pls))))))], (3353 ^ _434076) ^ [_561071, _561073] : [-(hAPP(nat, int, power_power(int, plus_plus(int, _561073, _561071)), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(int, plus_plus(int, hAPP(nat, int, power_power(int, _561073), number_number_of(nat, bit0(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit0(bit1(pls))), _561073), _561071)), hAPP(nat, int, power_power(int, _561071), number_number_of(nat, bit0(bit1(pls))))))], (3355 ^ _434076) ^ [] : [-(tn = minus_minus(nat, nat_1(t), one_one(nat)))], (3357 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), minus_minus(nat, nat_1(t), one_one(nat)))))], (3359 ^ _434076) ^ [_561316] : [ordered_ab_group_add(_561316), 3362 ^ _434076 : [(3363 ^ _434076) ^ [_561529, _561531] : [hBOOL(hAPP(_561316, bool, hAPP(_561316, fun(_561316, bool), ord_less_eq(_561316), _561531), _561529)), -(hBOOL(hAPP(_561316, bool, hAPP(_561316, fun(_561316, bool), ord_less_eq(_561316), minus_minus(_561316, _561531, _561529)), zero_zero(_561316))))], (3369 ^ _434076) ^ [_561767, _561769] : [hBOOL(hAPP(_561316, bool, hAPP(_561316, fun(_561316, bool), ord_less_eq(_561316), minus_minus(_561316, _561769, _561767)), zero_zero(_561316))), -(hBOOL(hAPP(_561316, bool, hAPP(_561316, fun(_561316, bool), ord_less_eq(_561316), _561769), _561767)))]]], (3375 ^ _434076) ^ [_562046] : [comm_semiring_1(_562046), 3378 ^ _434076 : [(3379 ^ _434076) ^ [_562183, _562185] : [-(times_times(_562046, _562185, _562183) = times_times(_562046, _562183, _562185))]]], (3381 ^ _434076) ^ [_562293] : [comm_semiring_1(_562293), 3384 ^ _434076 : [(3385 ^ _434076) ^ [_562457, _562459, _562461] : [-(times_times(_562293, _562461, times_times(_562293, _562459, _562457)) = times_times(_562293, _562459, times_times(_562293, _562461, _562457)))]]], (3387 ^ _434076) ^ [_562577] : [comm_semiring_1(_562577), 3390 ^ _434076 : [(3391 ^ _434076) ^ [_562741, _562743, _562745] : [-(times_times(_562577, _562745, times_times(_562577, _562743, _562741)) = times_times(_562577, times_times(_562577, _562745, _562743), _562741))]]], (3393 ^ _434076) ^ [_562861] : [ab_semigroup_mult(_562861), 3396 ^ _434076 : [(3397 ^ _434076) ^ [_563025, _563027, _563029] : [-(times_times(_562861, times_times(_562861, _563029, _563027), _563025) = times_times(_562861, _563029, times_times(_562861, _563027, _563025)))]]], (3399 ^ _434076) ^ [_563145] : [comm_semiring_1(_563145), 3402 ^ _434076 : [(3403 ^ _434076) ^ [_563309, _563311, _563313] : [-(times_times(_563145, times_times(_563145, _563313, _563311), _563309) = times_times(_563145, _563313, times_times(_563145, _563311, _563309)))]]], (3405 ^ _434076) ^ [_563429] : [comm_semiring_1(_563429), 3408 ^ _434076 : [(3409 ^ _434076) ^ [_563593, _563595, _563597] : [-(times_times(_563429, times_times(_563429, _563597, _563595), _563593) = times_times(_563429, times_times(_563429, _563597, _563593), _563595))]]], (3411 ^ _434076) ^ [_563713] : [comm_semiring_1(_563713), 3414 ^ _434076 : [(3415 ^ _434076) ^ [_563904, _563906, _563908, _563910] : [-(times_times(_563713, times_times(_563713, _563910, _563908), times_times(_563713, _563906, _563904)) = times_times(_563713, _563910, times_times(_563713, _563908, times_times(_563713, _563906, _563904))))]]], (3417 ^ _434076) ^ [_564034] : [comm_semiring_1(_564034), 3420 ^ _434076 : [(3421 ^ _434076) ^ [_564225, _564227, _564229, _564231] : [-(times_times(_564034, times_times(_564034, _564231, _564229), times_times(_564034, _564227, _564225)) = times_times(_564034, _564227, times_times(_564034, times_times(_564034, _564231, _564229), _564225)))]]], (3423 ^ _434076) ^ [_564355] : [comm_semiring_1(_564355), 3426 ^ _434076 : [(3427 ^ _434076) ^ [_564546, _564548, _564550, _564552] : [-(times_times(_564355, times_times(_564355, _564552, _564550), times_times(_564355, _564548, _564546)) = times_times(_564355, times_times(_564355, _564552, _564548), times_times(_564355, _564550, _564546)))]]], (3429 ^ _434076) ^ [_564676] : [ab_group_add(_564676), 3432 ^ _434076 : [(3433 ^ _434076) ^ [_564890, _564892, _564894, _564896] : [minus_minus(_564676, _564896, _564894) = minus_minus(_564676, _564892, _564890), 3436 ^ _434076 : [(3437 ^ _434076) ^ [] : [ti(_564676, _564896) = ti(_564676, _564894), -(ti(_564676, _564892) = ti(_564676, _564890))], (3443 ^ _434076) ^ [] : [ti(_564676, _564892) = ti(_564676, _564890), -(ti(_564676, _564896) = ti(_564676, _564894))]]]]], (3449 ^ _434076) ^ [_565443] : [ordered_ab_group_add(_565443), 3452 ^ _434076 : [(3453 ^ _434076) ^ [_565673, _565675, _565677, _565679] : [minus_minus(_565443, _565679, _565677) = minus_minus(_565443, _565675, _565673), 3456 ^ _434076 : [(3457 ^ _434076) ^ [] : [hBOOL(hAPP(_565443, bool, hAPP(_565443, fun(_565443, bool), ord_less_eq(_565443), _565679), _565677)), -(hBOOL(hAPP(_565443, bool, hAPP(_565443, fun(_565443, bool), ord_less_eq(_565443), _565675), _565673)))], (3463 ^ _434076) ^ [] : [hBOOL(hAPP(_565443, bool, hAPP(_565443, fun(_565443, bool), ord_less_eq(_565443), _565675), _565673)), -(hBOOL(hAPP(_565443, bool, hAPP(_565443, fun(_565443, bool), ord_less_eq(_565443), _565679), _565677)))]]]]], (3469 ^ _434076) ^ [_566274] : [number_semiring(_566274), 3472 ^ _434076 : [(3473 ^ _434076) ^ [_566455, _566457] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _566455)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _566457)), -(times_times(_566274, number_number_of(_566274, _566455), number_number_of(_566274, _566457)) = number_number_of(_566274, times_times(int, _566455, _566457)))]]], (3483 ^ _434076) ^ [_566792] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _566792), _566792)))], (3485 ^ _434076) ^ [_566893, _566895] : [-(times_times(int, _566895, _566893) = times_times(int, _566893, _566895))], (3487 ^ _434076) ^ [_567010, _567012] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567012), _567010))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567010), _567012)))], (3493 ^ _434076) ^ [_567256, _567258, _567260] : [-(times_times(int, times_times(int, _567260, _567258), _567256) = times_times(int, _567260, times_times(int, _567258, _567256)))], (3495 ^ _434076) ^ [_567397, _567399, _567401] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567399), _567397)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567397), _567401)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567399), _567401)))], (3505 ^ _434076) ^ [_567760, _567762] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567762), _567760)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _567760), _567762)), -(ti(int, _567762) = ti(int, _567760))], (3515 ^ _434076) ^ [_568093] : [number_ring(_568093), linordered_idom(_568093), 3522 ^ _434076 : [(3523 ^ _434076) ^ [_568384, _568386] : [hBOOL(hAPP(_568093, bool, hAPP(_568093, fun(_568093, bool), ord_less_eq(_568093), number_number_of(_568093, _568386)), number_number_of(_568093, _568384))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _568386), _568384)))], (3529 ^ _434076) ^ [_568612, _568614] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _568614), _568612)), -(hBOOL(hAPP(_568093, bool, hAPP(_568093, fun(_568093, bool), ord_less_eq(_568093), number_number_of(_568093, _568614)), number_number_of(_568093, _568612))))]]], (3535 ^ _434076) ^ [_568883] : [number_ring(_568883), 3538 ^ _434076 : [(3539 ^ _434076) ^ [_569029, _569031] : [-(number_number_of(_568883, times_times(int, _569031, _569029)) = times_times(_568883, number_number_of(_568883, _569031), number_number_of(_568883, _569029)))]]], (3541 ^ _434076) ^ [_569148] : [number_ring(_569148), 3544 ^ _434076 : [(3545 ^ _434076) ^ [_569294, _569296] : [-(times_times(_569148, number_number_of(_569148, _569296), number_number_of(_569148, _569294)) = number_number_of(_569148, times_times(int, _569296, _569294)))]]], (3547 ^ _434076) ^ [_569413] : [number_ring(_569413), 3550 ^ _434076 : [(3551 ^ _434076) ^ [_569586, _569588, _569590] : [-(times_times(_569413, number_number_of(_569413, _569590), times_times(_569413, number_number_of(_569413, _569588), _569586)) = times_times(_569413, number_number_of(_569413, times_times(int, _569590, _569588)), _569586))]]], (3553 ^ _434076) ^ [_569729, _569731] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _569729)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _569731)), 3560 ^ _434076 : [(3561 ^ _434076) ^ [] : [nat_1(_569729) = nat_1(_569731), -(ti(int, _569729) = ti(int, _569731))], (3567 ^ _434076) ^ [] : [ti(int, _569729) = ti(int, _569731), -(nat_1(_569729) = nat_1(_569731))]]], (3573 ^ _434076) ^ [_570310] : [3580 ^ _434076 : [(3581 ^ _434076) ^ [_570570, _570572, _570574] : [-(times_times(_570310, number_number_of(_570310, _570574), minus_minus(_570310, _570572, _570570)) = minus_minus(_570310, times_times(_570310, number_number_of(_570310, _570574), _570572), times_times(_570310, number_number_of(_570310, _570574), _570570)))]], number(_570310), ring(_570310)], (3583 ^ _434076) ^ [_570703] : [3590 ^ _434076 : [(3591 ^ _434076) ^ [_570963, _570965, _570967] : [-(times_times(_570703, minus_minus(_570703, _570967, _570965), number_number_of(_570703, _570963)) = minus_minus(_570703, times_times(_570703, _570967, number_number_of(_570703, _570963)), times_times(_570703, _570965, number_number_of(_570703, _570963))))]], number(_570703), ring(_570703)], (3593 ^ _434076) ^ [_571096] : [number_ring(_571096), 3596 ^ _434076 : [(3597 ^ _434076) ^ [_571242, _571244] : [-(number_number_of(_571096, minus_minus(int, _571244, _571242)) = minus_minus(_571096, number_number_of(_571096, _571244), number_number_of(_571096, _571242)))]]], (3599 ^ _434076) ^ [_571361] : [semiring_1(_571361), 3602 ^ _434076 : [(3603 ^ _434076) ^ [_571519, _571521] : [-(hAPP(nat, _571361, semiring_1_of_nat(_571361), times_times(nat, _571521, _571519)) = times_times(_571361, hAPP(nat, _571361, semiring_1_of_nat(_571361), _571521), hAPP(nat, _571361, semiring_1_of_nat(_571361), _571519)))]]], (3605 ^ _434076) ^ [_571650] : [linordered_semidom(_571650), 3608 ^ _434076 : [(3609 ^ _434076) ^ [_571866, _571868] : [hBOOL(hAPP(_571650, bool, hAPP(_571650, fun(_571650, bool), ord_less_eq(_571650), hAPP(nat, _571650, semiring_1_of_nat(_571650), _571868)), hAPP(nat, _571650, semiring_1_of_nat(_571650), _571866))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _571868), _571866)))], (3615 ^ _434076) ^ [_572110, _572112] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _572112), _572110)), -(hBOOL(hAPP(_571650, bool, hAPP(_571650, fun(_571650, bool), ord_less_eq(_571650), hAPP(nat, _571650, semiring_1_of_nat(_571650), _572112)), hAPP(nat, _571650, semiring_1_of_nat(_571650), _572110))))]]], (3621 ^ _434076) ^ [_572408, _572410, _572412] : [-(minus_minus(nat, minus_minus(nat, _572412, _572410), _572408) = minus_minus(nat, minus_minus(nat, _572412, _572408), _572410))], (3623 ^ _434076) ^ [_572569, _572571, _572573] : [hBOOL(_572569), -(nat_1(_572573) = nat_1(if(int, _572569, _572573, _572571)))], (3629 ^ _434076) ^ [_572753, _572755, _572757] : [-(hBOOL(_572753)), -(nat_1(_572755) = nat_1(if(int, _572753, _572757, _572755)))], (3635 ^ _434076) ^ [_572976] : [ordere453448008miring(_572976), 3638 ^ _434076 : [(3639 ^ _434076) ^ [_573228, _573230] : [-(hBOOL(hAPP(_572976, bool, hAPP(_572976, fun(_572976, bool), ord_less_eq(_572976), times_times(_572976, _573228, _573230)), zero_zero(_572976)))), 3640 ^ _434076 : [(3641 ^ _434076) ^ [] : [hBOOL(hAPP(_572976, bool, hAPP(_572976, fun(_572976, bool), ord_less_eq(_572976), zero_zero(_572976)), _573228)), hBOOL(hAPP(_572976, bool, hAPP(_572976, fun(_572976, bool), ord_less_eq(_572976), _573230), zero_zero(_572976)))], (3647 ^ _434076) ^ [] : [hBOOL(hAPP(_572976, bool, hAPP(_572976, fun(_572976, bool), ord_less_eq(_572976), _573228), zero_zero(_572976))), hBOOL(hAPP(_572976, bool, hAPP(_572976, fun(_572976, bool), ord_less_eq(_572976), zero_zero(_572976)), _573230))]]]]], (3655 ^ _434076) ^ [_573867] : [ordered_ring(_573867), 3658 ^ _434076 : [(3659 ^ _434076) ^ [_574119, _574121] : [-(hBOOL(hAPP(_573867, bool, hAPP(_573867, fun(_573867, bool), ord_less_eq(_573867), zero_zero(_573867)), times_times(_573867, _574119, _574121)))), 3660 ^ _434076 : [(3661 ^ _434076) ^ [] : [hBOOL(hAPP(_573867, bool, hAPP(_573867, fun(_573867, bool), ord_less_eq(_573867), zero_zero(_573867)), _574119)), hBOOL(hAPP(_573867, bool, hAPP(_573867, fun(_573867, bool), ord_less_eq(_573867), zero_zero(_573867)), _574121))], (3667 ^ _434076) ^ [] : [hBOOL(hAPP(_573867, bool, hAPP(_573867, fun(_573867, bool), ord_less_eq(_573867), _574119), zero_zero(_573867))), hBOOL(hAPP(_573867, bool, hAPP(_573867, fun(_573867, bool), ord_less_eq(_573867), _574121), zero_zero(_573867)))]]]]], (3675 ^ _434076) ^ [_574758] : [ordered_semiring(_574758), 3678 ^ _434076 : [(3679 ^ _434076) ^ [_575046, _575048, _575050, _575052] : [hBOOL(hAPP(_574758, bool, hAPP(_574758, fun(_574758, bool), ord_less_eq(_574758), _575048), _575046)), hBOOL(hAPP(_574758, bool, hAPP(_574758, fun(_574758, bool), ord_less_eq(_574758), _575052), _575050)), hBOOL(hAPP(_574758, bool, hAPP(_574758, fun(_574758, bool), ord_less_eq(_574758), zero_zero(_574758)), _575046)), hBOOL(hAPP(_574758, bool, hAPP(_574758, fun(_574758, bool), ord_less_eq(_574758), zero_zero(_574758)), _575052)), -(hBOOL(hAPP(_574758, bool, hAPP(_574758, fun(_574758, bool), ord_less_eq(_574758), times_times(_574758, _575048, _575052)), times_times(_574758, _575046, _575050))))]]], (3697 ^ _434076) ^ [_575734] : [ordered_semiring(_575734), 3700 ^ _434076 : [(3701 ^ _434076) ^ [_576022, _576024, _576026, _576028] : [hBOOL(hAPP(_575734, bool, hAPP(_575734, fun(_575734, bool), ord_less_eq(_575734), _576024), _576022)), hBOOL(hAPP(_575734, bool, hAPP(_575734, fun(_575734, bool), ord_less_eq(_575734), _576028), _576026)), hBOOL(hAPP(_575734, bool, hAPP(_575734, fun(_575734, bool), ord_less_eq(_575734), zero_zero(_575734)), _576024)), hBOOL(hAPP(_575734, bool, hAPP(_575734, fun(_575734, bool), ord_less_eq(_575734), zero_zero(_575734)), _576028)), -(hBOOL(hAPP(_575734, bool, hAPP(_575734, fun(_575734, bool), ord_less_eq(_575734), times_times(_575734, _576024, _576028)), times_times(_575734, _576022, _576026))))]]], (3719 ^ _434076) ^ [_576710] : [ordered_ring(_576710), 3722 ^ _434076 : [(3723 ^ _434076) ^ [_576937, _576939, _576941] : [hBOOL(hAPP(_576710, bool, hAPP(_576710, fun(_576710, bool), ord_less_eq(_576710), _576939), _576937)), hBOOL(hAPP(_576710, bool, hAPP(_576710, fun(_576710, bool), ord_less_eq(_576710), _576941), zero_zero(_576710))), -(hBOOL(hAPP(_576710, bool, hAPP(_576710, fun(_576710, bool), ord_less_eq(_576710), times_times(_576710, _576941, _576937)), times_times(_576710, _576941, _576939))))]]], (3733 ^ _434076) ^ [_577353] : [ordered_ring(_577353), 3736 ^ _434076 : [(3737 ^ _434076) ^ [_577580, _577582, _577584] : [hBOOL(hAPP(_577353, bool, hAPP(_577353, fun(_577353, bool), ord_less_eq(_577353), _577582), _577580)), hBOOL(hAPP(_577353, bool, hAPP(_577353, fun(_577353, bool), ord_less_eq(_577353), _577584), zero_zero(_577353))), -(hBOOL(hAPP(_577353, bool, hAPP(_577353, fun(_577353, bool), ord_less_eq(_577353), times_times(_577353, _577580, _577584)), times_times(_577353, _577582, _577584))))]]], (3747 ^ _434076) ^ [_577996] : [ordere1490568538miring(_577996), 3750 ^ _434076 : [(3751 ^ _434076) ^ [_578223, _578225, _578227] : [hBOOL(hAPP(_577996, bool, hAPP(_577996, fun(_577996, bool), ord_less_eq(_577996), _578225), _578223)), hBOOL(hAPP(_577996, bool, hAPP(_577996, fun(_577996, bool), ord_less_eq(_577996), zero_zero(_577996)), _578227)), -(hBOOL(hAPP(_577996, bool, hAPP(_577996, fun(_577996, bool), ord_less_eq(_577996), times_times(_577996, _578227, _578225)), times_times(_577996, _578227, _578223))))]]], (3761 ^ _434076) ^ [_578639] : [ordered_semiring(_578639), 3764 ^ _434076 : [(3765 ^ _434076) ^ [_578866, _578868, _578870] : [hBOOL(hAPP(_578639, bool, hAPP(_578639, fun(_578639, bool), ord_less_eq(_578639), _578868), _578866)), hBOOL(hAPP(_578639, bool, hAPP(_578639, fun(_578639, bool), ord_less_eq(_578639), zero_zero(_578639)), _578870)), -(hBOOL(hAPP(_578639, bool, hAPP(_578639, fun(_578639, bool), ord_less_eq(_578639), times_times(_578639, _578870, _578868)), times_times(_578639, _578870, _578866))))]]], (3775 ^ _434076) ^ [_579282] : [ordered_semiring(_579282), 3778 ^ _434076 : [(3779 ^ _434076) ^ [_579509, _579511, _579513] : [hBOOL(hAPP(_579282, bool, hAPP(_579282, fun(_579282, bool), ord_less_eq(_579282), _579511), _579509)), hBOOL(hAPP(_579282, bool, hAPP(_579282, fun(_579282, bool), ord_less_eq(_579282), zero_zero(_579282)), _579513)), -(hBOOL(hAPP(_579282, bool, hAPP(_579282, fun(_579282, bool), ord_less_eq(_579282), times_times(_579282, _579511, _579513)), times_times(_579282, _579509, _579513))))]]], (3789 ^ _434076) ^ [_579925] : [ordered_ring(_579925), 3792 ^ _434076 : [(3793 ^ _434076) ^ [_580133, _580135] : [hBOOL(hAPP(_579925, bool, hAPP(_579925, fun(_579925, bool), ord_less_eq(_579925), _580133), zero_zero(_579925))), hBOOL(hAPP(_579925, bool, hAPP(_579925, fun(_579925, bool), ord_less_eq(_579925), _580135), zero_zero(_579925))), -(hBOOL(hAPP(_579925, bool, hAPP(_579925, fun(_579925, bool), ord_less_eq(_579925), zero_zero(_579925)), times_times(_579925, _580133, _580135))))]]], (3803 ^ _434076) ^ [_580539] : [ordere453448008miring(_580539), 3806 ^ _434076 : [(3807 ^ _434076) ^ [_580747, _580749] : [hBOOL(hAPP(_580539, bool, hAPP(_580539, fun(_580539, bool), ord_less_eq(_580539), _580747), zero_zero(_580539))), hBOOL(hAPP(_580539, bool, hAPP(_580539, fun(_580539, bool), ord_less_eq(_580539), zero_zero(_580539)), _580749)), -(hBOOL(hAPP(_580539, bool, hAPP(_580539, fun(_580539, bool), ord_less_eq(_580539), times_times(_580539, _580747, _580749)), zero_zero(_580539))))]]], (3817 ^ _434076) ^ [_581153] : [ordere453448008miring(_581153), 3820 ^ _434076 : [(3821 ^ _434076) ^ [_581361, _581363] : [hBOOL(hAPP(_581153, bool, hAPP(_581153, fun(_581153, bool), ord_less_eq(_581153), zero_zero(_581153)), _581361)), hBOOL(hAPP(_581153, bool, hAPP(_581153, fun(_581153, bool), ord_less_eq(_581153), _581363), zero_zero(_581153))), -(hBOOL(hAPP(_581153, bool, hAPP(_581153, fun(_581153, bool), ord_less_eq(_581153), times_times(_581153, _581363, _581361)), zero_zero(_581153))))]]], (3831 ^ _434076) ^ [_581767] : [ordere453448008miring(_581767), 3834 ^ _434076 : [(3835 ^ _434076) ^ [_581975, _581977] : [hBOOL(hAPP(_581767, bool, hAPP(_581767, fun(_581767, bool), ord_less_eq(_581767), zero_zero(_581767)), _581975)), hBOOL(hAPP(_581767, bool, hAPP(_581767, fun(_581767, bool), ord_less_eq(_581767), _581977), zero_zero(_581767))), -(hBOOL(hAPP(_581767, bool, hAPP(_581767, fun(_581767, bool), ord_less_eq(_581767), times_times(_581767, _581975, _581977)), zero_zero(_581767))))]]], (3845 ^ _434076) ^ [_582395, _582397] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _582395)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _582397)), 3852 ^ _434076 : [(3853 ^ _434076) ^ [] : [nat_1(_582395) = nat_1(_582397), -(ti(int, _582395) = ti(int, _582397))], (3859 ^ _434076) ^ [] : [ti(int, _582395) = ti(int, _582397), -(nat_1(_582395) = nat_1(_582397))]]], (3865 ^ _434076) ^ [_582990, _582992] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _582990)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _582992)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), times_times(int, _582990, _582992))))], (3875 ^ _434076) ^ [_583307] : [ordere453448008miring(_583307), 3878 ^ _434076 : [(3879 ^ _434076) ^ [_583515, _583517] : [hBOOL(hAPP(_583307, bool, hAPP(_583307, fun(_583307, bool), ord_less_eq(_583307), zero_zero(_583307)), _583515)), hBOOL(hAPP(_583307, bool, hAPP(_583307, fun(_583307, bool), ord_less_eq(_583307), zero_zero(_583307)), _583517)), -(hBOOL(hAPP(_583307, bool, hAPP(_583307, fun(_583307, bool), ord_less_eq(_583307), zero_zero(_583307)), times_times(_583307, _583515, _583517))))]]], (3889 ^ _434076) ^ [_583921] : [ordered_ring(_583921), 3892 ^ _434076 : [(3893 ^ _434076) ^ [_584213, _584215, _584217, _584219, _584221] : [hBOOL(hAPP(_583921, bool, hAPP(_583921, fun(_583921, bool), ord_less_eq(_583921), plus_plus(_583921, times_times(_583921, _584221, _584219), _584217)), plus_plus(_583921, times_times(_583921, _584215, _584219), _584213))), -(hBOOL(hAPP(_583921, bool, hAPP(_583921, fun(_583921, bool), ord_less_eq(_583921), plus_plus(_583921, times_times(_583921, minus_minus(_583921, _584221, _584215), _584219), _584217)), _584213)))], (3899 ^ _434076) ^ [_584513, _584515, _584517, _584519, _584521] : [hBOOL(hAPP(_583921, bool, hAPP(_583921, fun(_583921, bool), ord_less_eq(_583921), plus_plus(_583921, times_times(_583921, minus_minus(_583921, _584521, _584515), _584519), _584517)), _584513)), -(hBOOL(hAPP(_583921, bool, hAPP(_583921, fun(_583921, bool), ord_less_eq(_583921), plus_plus(_583921, times_times(_583921, _584521, _584519), _584517)), plus_plus(_583921, times_times(_583921, _584515, _584519), _584513))))]]], (3905 ^ _434076) ^ [_584854] : [ring(_584854), 3908 ^ _434076 : [(3909 ^ _434076) ^ [_585121, _585123, _585125, _585127, _585129] : [plus_plus(_584854, times_times(_584854, _585129, _585127), _585125) = plus_plus(_584854, times_times(_584854, _585123, _585127), _585121), -(plus_plus(_584854, times_times(_584854, minus_minus(_584854, _585129, _585123), _585127), _585125) = ti(_584854, _585121))], (3915 ^ _434076) ^ [_585371, _585373, _585375, _585377, _585379] : [plus_plus(_584854, times_times(_584854, minus_minus(_584854, _585379, _585373), _585377), _585375) = ti(_584854, _585371), -(plus_plus(_584854, times_times(_584854, _585379, _585377), _585375) = plus_plus(_584854, times_times(_584854, _585373, _585377), _585371))]]], (3921 ^ _434076) ^ [_585662] : [ordered_ring(_585662), 3924 ^ _434076 : [(3925 ^ _434076) ^ [_585954, _585956, _585958, _585960, _585962] : [hBOOL(hAPP(_585662, bool, hAPP(_585662, fun(_585662, bool), ord_less_eq(_585662), plus_plus(_585662, times_times(_585662, _585962, _585960), _585958)), plus_plus(_585662, times_times(_585662, _585956, _585960), _585954))), -(hBOOL(hAPP(_585662, bool, hAPP(_585662, fun(_585662, bool), ord_less_eq(_585662), _585958), plus_plus(_585662, times_times(_585662, minus_minus(_585662, _585956, _585962), _585960), _585954))))], (3931 ^ _434076) ^ [_586254, _586256, _586258, _586260, _586262] : [hBOOL(hAPP(_585662, bool, hAPP(_585662, fun(_585662, bool), ord_less_eq(_585662), _586258), plus_plus(_585662, times_times(_585662, minus_minus(_585662, _586256, _586262), _586260), _586254))), -(hBOOL(hAPP(_585662, bool, hAPP(_585662, fun(_585662, bool), ord_less_eq(_585662), plus_plus(_585662, times_times(_585662, _586262, _586260), _586258)), plus_plus(_585662, times_times(_585662, _586256, _586260), _586254))))]]], (3937 ^ _434076) ^ [_586595] : [ring(_586595), 3940 ^ _434076 : [(3941 ^ _434076) ^ [_586862, _586864, _586866, _586868, _586870] : [plus_plus(_586595, times_times(_586595, _586870, _586868), _586866) = plus_plus(_586595, times_times(_586595, _586864, _586868), _586862), -(ti(_586595, _586866) = plus_plus(_586595, times_times(_586595, minus_minus(_586595, _586864, _586870), _586868), _586862))], (3947 ^ _434076) ^ [_587112, _587114, _587116, _587118, _587120] : [ti(_586595, _587116) = plus_plus(_586595, times_times(_586595, minus_minus(_586595, _587114, _587120), _587118), _587112), -(plus_plus(_586595, times_times(_586595, _587120, _587118), _587116) = plus_plus(_586595, times_times(_586595, _587114, _587118), _587112))]]], (3953 ^ _434076) ^ [_587403] : [ring(_587403), 3956 ^ _434076 : [(3957 ^ _434076) ^ [_587602, _587604, _587606, _587608] : [-(minus_minus(_587403, times_times(_587403, _587608, _587606), times_times(_587403, _587604, _587602)) = plus_plus(_587403, times_times(_587403, _587608, minus_minus(_587403, _587606, _587602)), times_times(_587403, minus_minus(_587403, _587608, _587604), _587602)))]]], (3959 ^ _434076) ^ [_587740] : [linord581940658strict(_587740), 3962 ^ _434076 : [(3963 ^ _434076) ^ [_588021, _588023] : [hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), times_times(_587740, _588023, _588021)), zero_zero(_587740))), 3968 ^ _434076 : [(3969 ^ _434076) ^ [] : [-(hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), zero_zero(_587740)), _588023)))], (3971 ^ _434076) ^ [] : [-(hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), _588021), zero_zero(_587740))))]], 3972 ^ _434076 : [(3973 ^ _434076) ^ [] : [-(hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), _588023), zero_zero(_587740))))], (3975 ^ _434076) ^ [] : [-(hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), zero_zero(_587740)), _588021)))]]], (3977 ^ _434076) ^ [_588607, _588609] : [-(hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), times_times(_587740, _588609, _588607)), zero_zero(_587740)))), 3978 ^ _434076 : [(3979 ^ _434076) ^ [] : [hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), zero_zero(_587740)), _588609)), hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), _588607), zero_zero(_587740)))], (3985 ^ _434076) ^ [] : [hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), _588609), zero_zero(_587740))), hBOOL(hAPP(_587740, bool, hAPP(_587740, fun(_587740, bool), ord_less_eq(_587740), zero_zero(_587740)), _588607))]]]]], (3993 ^ _434076) ^ [_589248] : [linord581940658strict(_589248), 3996 ^ _434076 : [(3997 ^ _434076) ^ [_589529, _589531] : [hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), times_times(_589248, _589531, _589529))), 4002 ^ _434076 : [(4003 ^ _434076) ^ [] : [-(hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), _589531)))], (4005 ^ _434076) ^ [] : [-(hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), _589529)))]], 4006 ^ _434076 : [(4007 ^ _434076) ^ [] : [-(hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), _589531), zero_zero(_589248))))], (4009 ^ _434076) ^ [] : [-(hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), _589529), zero_zero(_589248))))]]], (4011 ^ _434076) ^ [_590115, _590117] : [-(hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), times_times(_589248, _590117, _590115)))), 4012 ^ _434076 : [(4013 ^ _434076) ^ [] : [hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), _590117)), hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), zero_zero(_589248)), _590115))], (4019 ^ _434076) ^ [] : [hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), _590117), zero_zero(_589248))), hBOOL(hAPP(_589248, bool, hAPP(_589248, fun(_589248, bool), ord_less_eq(_589248), _590115), zero_zero(_589248)))]]]]], (4038 ^ _434076) ^ [_591180] : [4040 ^ _434076 : [(4041 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 4039 ^ [_591180])))], (4043 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _591180, nat_1(4039 ^ [_591180])))]], 4044 ^ _434076 : [(4045 ^ _434076) ^ [_591460] : [-(hBOOL(hAPP(nat, bool, _591180, _591460)))]]], (4027 ^ _434076) ^ [_590785] : [hBOOL(hAPP(nat, bool, _590785, 4028 ^ [_590785])), 4031 ^ _434076 : [(4032 ^ _434076) ^ [_590991] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _590991)), -(hBOOL(hAPP(nat, bool, _590785, nat_1(_590991))))]]], (4047 ^ _434076) ^ [_591596] : [4048 ^ _434076 : [(4049 ^ _434076) ^ [_591689] : [hBOOL(hAPP(nat, bool, _591596, _591689))]], 4051 ^ _434076 : [(4052 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 4050 ^ [_591596])))], (4054 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, _591596, nat_1(4050 ^ [_591596]))))]]], (4056 ^ _434076) ^ [_591947] : [-(hBOOL(hAPP(nat, bool, _591947, 4063 ^ [_591947]))), 4057 ^ _434076 : [(4058 ^ _434076) ^ [_592056] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _592056)), hBOOL(hAPP(nat, bool, _591947, nat_1(_592056)))]]], (4067 ^ _434076) ^ [_592378] : [linordered_ring(_592378), 4070 ^ _434076 : [(4071 ^ _434076) ^ [_592508] : [-(hBOOL(hAPP(_592378, bool, hAPP(_592378, fun(_592378, bool), ord_less_eq(_592378), zero_zero(_592378)), times_times(_592378, _592508, _592508))))]]], (4073 ^ _434076) ^ [_592628] : [ordered_ring(_592628), 4076 ^ _434076 : [(4077 ^ _434076) ^ [_592920, _592922, _592924, _592926, _592928] : [hBOOL(hAPP(_592628, bool, hAPP(_592628, fun(_592628, bool), ord_less(_592628), plus_plus(_592628, times_times(_592628, _592928, _592926), _592924)), plus_plus(_592628, times_times(_592628, _592922, _592926), _592920))), -(hBOOL(hAPP(_592628, bool, hAPP(_592628, fun(_592628, bool), ord_less(_592628), plus_plus(_592628, times_times(_592628, minus_minus(_592628, _592928, _592922), _592926), _592924)), _592920)))], (4083 ^ _434076) ^ [_593220, _593222, _593224, _593226, _593228] : [hBOOL(hAPP(_592628, bool, hAPP(_592628, fun(_592628, bool), ord_less(_592628), plus_plus(_592628, times_times(_592628, minus_minus(_592628, _593228, _593222), _593226), _593224)), _593220)), -(hBOOL(hAPP(_592628, bool, hAPP(_592628, fun(_592628, bool), ord_less(_592628), plus_plus(_592628, times_times(_592628, _593228, _593226), _593224)), plus_plus(_592628, times_times(_592628, _593222, _593226), _593220))))]]], (4089 ^ _434076) ^ [_593561] : [ordered_ring(_593561), 4092 ^ _434076 : [(4093 ^ _434076) ^ [_593853, _593855, _593857, _593859, _593861] : [hBOOL(hAPP(_593561, bool, hAPP(_593561, fun(_593561, bool), ord_less(_593561), plus_plus(_593561, times_times(_593561, _593861, _593859), _593857)), plus_plus(_593561, times_times(_593561, _593855, _593859), _593853))), -(hBOOL(hAPP(_593561, bool, hAPP(_593561, fun(_593561, bool), ord_less(_593561), _593857), plus_plus(_593561, times_times(_593561, minus_minus(_593561, _593855, _593861), _593859), _593853))))], (4099 ^ _434076) ^ [_594153, _594155, _594157, _594159, _594161] : [hBOOL(hAPP(_593561, bool, hAPP(_593561, fun(_593561, bool), ord_less(_593561), _594157), plus_plus(_593561, times_times(_593561, minus_minus(_593561, _594155, _594161), _594159), _594153))), -(hBOOL(hAPP(_593561, bool, hAPP(_593561, fun(_593561, bool), ord_less(_593561), plus_plus(_593561, times_times(_593561, _594161, _594159), _594157)), plus_plus(_593561, times_times(_593561, _594155, _594159), _594153))))]]], (4105 ^ _434076) ^ [_594494] : [ring_1(_594494), 4108 ^ _434076 : [(4109 ^ _434076) ^ [_594630] : [-(minus_minus(_594494, times_times(_594494, _594630, _594630), one_one(_594494)) = times_times(_594494, plus_plus(_594494, _594630, one_one(_594494)), minus_minus(_594494, _594630, one_one(_594494))))]]], (4111 ^ _434076) ^ [_594756] : [linord20386208strict(_594756), 4114 ^ _434076 : [(4115 ^ _434076) ^ [_594983, _594985, _594987] : [hBOOL(hAPP(_594756, bool, hAPP(_594756, fun(_594756, bool), ord_less_eq(_594756), times_times(_594756, _594987, _594985)), times_times(_594756, _594987, _594983))), hBOOL(hAPP(_594756, bool, hAPP(_594756, fun(_594756, bool), ord_less(_594756), zero_zero(_594756)), _594987)), -(hBOOL(hAPP(_594756, bool, hAPP(_594756, fun(_594756, bool), ord_less_eq(_594756), _594985), _594983)))]]], (4125 ^ _434076) ^ [_595399] : [linord20386208strict(_595399), 4128 ^ _434076 : [(4129 ^ _434076) ^ [_595626, _595628, _595630] : [hBOOL(hAPP(_595399, bool, hAPP(_595399, fun(_595399, bool), ord_less_eq(_595399), times_times(_595399, _595630, _595628)), times_times(_595399, _595626, _595628))), hBOOL(hAPP(_595399, bool, hAPP(_595399, fun(_595399, bool), ord_less(_595399), zero_zero(_595399)), _595628)), -(hBOOL(hAPP(_595399, bool, hAPP(_595399, fun(_595399, bool), ord_less_eq(_595399), _595630), _595626)))]]], (4139 ^ _434076) ^ [_596042] : [linord20386208strict(_596042), 4142 ^ _434076 : [(4143 ^ _434076) ^ [_596269, _596271, _596273] : [hBOOL(hAPP(_596042, bool, hAPP(_596042, fun(_596042, bool), ord_less(_596042), times_times(_596042, _596273, _596271)), times_times(_596042, _596273, _596269))), hBOOL(hAPP(_596042, bool, hAPP(_596042, fun(_596042, bool), ord_less_eq(_596042), zero_zero(_596042)), _596273)), -(hBOOL(hAPP(_596042, bool, hAPP(_596042, fun(_596042, bool), ord_less(_596042), _596271), _596269)))]]], (4153 ^ _434076) ^ [_596685] : [linordered_semiring(_596685), 4156 ^ _434076 : [(4157 ^ _434076) ^ [_596912, _596914, _596916] : [hBOOL(hAPP(_596685, bool, hAPP(_596685, fun(_596685, bool), ord_less(_596685), times_times(_596685, _596916, _596914)), times_times(_596685, _596916, _596912))), hBOOL(hAPP(_596685, bool, hAPP(_596685, fun(_596685, bool), ord_less_eq(_596685), zero_zero(_596685)), _596916)), -(hBOOL(hAPP(_596685, bool, hAPP(_596685, fun(_596685, bool), ord_less(_596685), _596914), _596912)))]]], (4167 ^ _434076) ^ [_597328] : [linord20386208strict(_597328), 4170 ^ _434076 : [(4171 ^ _434076) ^ [_597555, _597557, _597559] : [hBOOL(hAPP(_597328, bool, hAPP(_597328, fun(_597328, bool), ord_less(_597328), times_times(_597328, _597559, _597557)), times_times(_597328, _597555, _597557))), hBOOL(hAPP(_597328, bool, hAPP(_597328, fun(_597328, bool), ord_less_eq(_597328), zero_zero(_597328)), _597557)), -(hBOOL(hAPP(_597328, bool, hAPP(_597328, fun(_597328, bool), ord_less(_597328), _597559), _597555)))]]], (4181 ^ _434076) ^ [_597971] : [linordered_semiring(_597971), 4184 ^ _434076 : [(4185 ^ _434076) ^ [_598198, _598200, _598202] : [hBOOL(hAPP(_597971, bool, hAPP(_597971, fun(_597971, bool), ord_less(_597971), times_times(_597971, _598202, _598200)), times_times(_597971, _598198, _598200))), hBOOL(hAPP(_597971, bool, hAPP(_597971, fun(_597971, bool), ord_less_eq(_597971), zero_zero(_597971)), _598200)), -(hBOOL(hAPP(_597971, bool, hAPP(_597971, fun(_597971, bool), ord_less(_597971), _598202), _598198)))]]], (4195 ^ _434076) ^ [_598614] : [linord20386208strict(_598614), 4198 ^ _434076 : [(4199 ^ _434076) ^ [_598902, _598904, _598906, _598908] : [hBOOL(hAPP(_598614, bool, hAPP(_598614, fun(_598614, bool), ord_less_eq(_598614), _598904), _598902)), hBOOL(hAPP(_598614, bool, hAPP(_598614, fun(_598614, bool), ord_less(_598614), _598908), _598906)), hBOOL(hAPP(_598614, bool, hAPP(_598614, fun(_598614, bool), ord_less(_598614), zero_zero(_598614)), _598904)), hBOOL(hAPP(_598614, bool, hAPP(_598614, fun(_598614, bool), ord_less_eq(_598614), zero_zero(_598614)), _598908)), -(hBOOL(hAPP(_598614, bool, hAPP(_598614, fun(_598614, bool), ord_less(_598614), times_times(_598614, _598904, _598908)), times_times(_598614, _598902, _598906))))]]], (4217 ^ _434076) ^ [_599590] : [linord20386208strict(_599590), 4220 ^ _434076 : [(4221 ^ _434076) ^ [_599878, _599880, _599882, _599884] : [hBOOL(hAPP(_599590, bool, hAPP(_599590, fun(_599590, bool), ord_less(_599590), _599880), _599878)), hBOOL(hAPP(_599590, bool, hAPP(_599590, fun(_599590, bool), ord_less_eq(_599590), _599884), _599882)), hBOOL(hAPP(_599590, bool, hAPP(_599590, fun(_599590, bool), ord_less_eq(_599590), zero_zero(_599590)), _599880)), hBOOL(hAPP(_599590, bool, hAPP(_599590, fun(_599590, bool), ord_less(_599590), zero_zero(_599590)), _599884)), -(hBOOL(hAPP(_599590, bool, hAPP(_599590, fun(_599590, bool), ord_less(_599590), times_times(_599590, _599880, _599884)), times_times(_599590, _599878, _599882))))]]], (4239 ^ _434076) ^ [_600566] : [linord20386208strict(_600566), 4242 ^ _434076 : [(4243 ^ _434076) ^ [_600854, _600856, _600858, _600860] : [hBOOL(hAPP(_600566, bool, hAPP(_600566, fun(_600566, bool), ord_less(_600566), _600856), _600854)), hBOOL(hAPP(_600566, bool, hAPP(_600566, fun(_600566, bool), ord_less(_600566), _600860), _600858)), hBOOL(hAPP(_600566, bool, hAPP(_600566, fun(_600566, bool), ord_less_eq(_600566), zero_zero(_600566)), _600856)), hBOOL(hAPP(_600566, bool, hAPP(_600566, fun(_600566, bool), ord_less_eq(_600566), zero_zero(_600566)), _600860)), -(hBOOL(hAPP(_600566, bool, hAPP(_600566, fun(_600566, bool), ord_less(_600566), times_times(_600566, _600856, _600860)), times_times(_600566, _600854, _600858))))]]], (4261 ^ _434076) ^ [_601542] : [linord20386208strict(_601542), 4264 ^ _434076 : [(4265 ^ _434076) ^ [_601830, _601832, _601834, _601836] : [hBOOL(hAPP(_601542, bool, hAPP(_601542, fun(_601542, bool), ord_less(_601542), _601832), _601830)), hBOOL(hAPP(_601542, bool, hAPP(_601542, fun(_601542, bool), ord_less(_601542), _601836), _601834)), hBOOL(hAPP(_601542, bool, hAPP(_601542, fun(_601542, bool), ord_less(_601542), zero_zero(_601542)), _601830)), hBOOL(hAPP(_601542, bool, hAPP(_601542, fun(_601542, bool), ord_less_eq(_601542), zero_zero(_601542)), _601836)), -(hBOOL(hAPP(_601542, bool, hAPP(_601542, fun(_601542, bool), ord_less(_601542), times_times(_601542, _601832, _601836)), times_times(_601542, _601830, _601834))))]]], (4283 ^ _434076) ^ [_602518] : [linord581940658strict(_602518), 4286 ^ _434076 : [(4287 ^ _434076) ^ [_602745, _602747, _602749] : [hBOOL(hAPP(_602518, bool, hAPP(_602518, fun(_602518, bool), ord_less(_602518), _602745), zero_zero(_602518))), 4290 ^ _434076 : [(4291 ^ _434076) ^ [] : [hBOOL(hAPP(_602518, bool, hAPP(_602518, fun(_602518, bool), ord_less_eq(_602518), times_times(_602518, _602745, _602749)), times_times(_602518, _602745, _602747))), -(hBOOL(hAPP(_602518, bool, hAPP(_602518, fun(_602518, bool), ord_less_eq(_602518), _602747), _602749)))], (4297 ^ _434076) ^ [] : [hBOOL(hAPP(_602518, bool, hAPP(_602518, fun(_602518, bool), ord_less_eq(_602518), _602747), _602749)), -(hBOOL(hAPP(_602518, bool, hAPP(_602518, fun(_602518, bool), ord_less_eq(_602518), times_times(_602518, _602745, _602749)), times_times(_602518, _602745, _602747))))]]]]], (4303 ^ _434076) ^ [_603370] : [linord581940658strict(_603370), 4306 ^ _434076 : [(4307 ^ _434076) ^ [_603597, _603599, _603601] : [hBOOL(hAPP(_603370, bool, hAPP(_603370, fun(_603370, bool), ord_less(_603370), zero_zero(_603370)), _603597)), 4310 ^ _434076 : [(4311 ^ _434076) ^ [] : [hBOOL(hAPP(_603370, bool, hAPP(_603370, fun(_603370, bool), ord_less_eq(_603370), times_times(_603370, _603597, _603601)), times_times(_603370, _603597, _603599))), -(hBOOL(hAPP(_603370, bool, hAPP(_603370, fun(_603370, bool), ord_less_eq(_603370), _603601), _603599)))], (4317 ^ _434076) ^ [] : [hBOOL(hAPP(_603370, bool, hAPP(_603370, fun(_603370, bool), ord_less_eq(_603370), _603601), _603599)), -(hBOOL(hAPP(_603370, bool, hAPP(_603370, fun(_603370, bool), ord_less_eq(_603370), times_times(_603370, _603597, _603601)), times_times(_603370, _603597, _603599))))]]]]], (4323 ^ _434076) ^ [_604222] : [linordered_ring(_604222), 4326 ^ _434076 : [(4327 ^ _434076) ^ [_604379, _604381] : [-(hBOOL(hAPP(_604222, bool, hAPP(_604222, fun(_604222, bool), ord_less_eq(_604222), zero_zero(_604222)), plus_plus(_604222, times_times(_604222, _604381, _604381), times_times(_604222, _604379, _604379)))))]]], (4329 ^ _434076) ^ [_604509] : [linord581940658strict(_604509), 4332 ^ _434076 : [(4333 ^ _434076) ^ [_604732, _604734] : [hBOOL(hAPP(_604509, bool, hAPP(_604509, fun(_604509, bool), ord_less_eq(_604509), plus_plus(_604509, times_times(_604509, _604734, _604734), times_times(_604509, _604732, _604732))), zero_zero(_604509))), 4336 ^ _434076 : [(4337 ^ _434076) ^ [] : [-(ti(_604509, _604734) = zero_zero(_604509))], (4339 ^ _434076) ^ [] : [-(ti(_604509, _604732) = zero_zero(_604509))]]], (4341 ^ _434076) ^ [_605055, _605057] : [-(hBOOL(hAPP(_604509, bool, hAPP(_604509, fun(_604509, bool), ord_less_eq(_604509), plus_plus(_604509, times_times(_604509, _605057, _605057), times_times(_604509, _605055, _605055))), zero_zero(_604509)))), ti(_604509, _605057) = zero_zero(_604509), ti(_604509, _605055) = zero_zero(_604509)]]], (4351 ^ _434076) ^ [_605435] : [linordered_idom(_605435), 4354 ^ _434076 : [(4355 ^ _434076) ^ [_605663, _605665] : [hBOOL(hAPP(_605435, bool, hAPP(_605435, fun(_605435, bool), ord_less_eq(_605435), zero_zero(_605435)), _605663)), hBOOL(hAPP(_605435, bool, hAPP(_605435, fun(_605435, bool), ord_less_eq(_605435), zero_zero(_605435)), _605665)), hBOOL(hAPP(_605435, bool, hAPP(_605435, fun(_605435, bool), ord_less_eq(_605435), _605665), one_one(_605435))), -(hBOOL(hAPP(_605435, bool, hAPP(_605435, fun(_605435, bool), ord_less_eq(_605435), times_times(_605435, _605663, _605665)), _605663)))]]], (4369 ^ _434076) ^ [_606190] : [linordered_idom(_606190), 4372 ^ _434076 : [(4373 ^ _434076) ^ [_606418, _606420] : [hBOOL(hAPP(_606190, bool, hAPP(_606190, fun(_606190, bool), ord_less_eq(_606190), zero_zero(_606190)), _606418)), hBOOL(hAPP(_606190, bool, hAPP(_606190, fun(_606190, bool), ord_less_eq(_606190), zero_zero(_606190)), _606420)), hBOOL(hAPP(_606190, bool, hAPP(_606190, fun(_606190, bool), ord_less_eq(_606190), _606420), one_one(_606190))), -(hBOOL(hAPP(_606190, bool, hAPP(_606190, fun(_606190, bool), ord_less_eq(_606190), times_times(_606190, _606420, _606418)), _606418)))]]], (4387 ^ _434076) ^ [_606945] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _606945), zero_zero(int))), -(nat_1(_606945) = zero_zero(nat))], (4393 ^ _434076) ^ [_607186] : [nat_1(_607186) = zero_zero(nat), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _607186), zero_zero(int))))], (4399 ^ _434076) ^ [_607364] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _607364), zero_zero(int))), -(nat_1(_607364) = zero_zero(nat))], (4405 ^ _434076) ^ [_607578] : [linordered_semidom(_607578), 4408 ^ _434076 : [(4409 ^ _434076) ^ [_607808, _607810, _607812] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _607810), _607808)), hBOOL(hAPP(_607578, bool, hAPP(_607578, fun(_607578, bool), ord_less_eq(_607578), one_one(_607578)), _607812)), -(hBOOL(hAPP(_607578, bool, hAPP(_607578, fun(_607578, bool), ord_less_eq(_607578), hAPP(nat, _607578, power_power(_607578, _607812), _607810)), hAPP(nat, _607578, power_power(_607578, _607812), _607808))))]]], (4419 ^ _434076) ^ [_608250] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _608250)), -(hAPP(nat, int, semiring_1_of_nat(int), nat_1(_608250)) = ti(int, _608250))], (4425 ^ _434076) ^ [_608434] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _608434))), -(hAPP(nat, int, semiring_1_of_nat(int), nat_1(_608434)) = zero_zero(int))], (4431 ^ _434076) ^ [_608694, _608696] : [hAPP(nat, int, semiring_1_of_nat(int), _608696) = ti(int, _608694), 4434 ^ _434076 : [(4435 ^ _434076) ^ [] : [-(_608696 = nat_1(_608694))], (4437 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _608694)))]]], (4439 ^ _434076) ^ [_608959, _608961] : [-(hAPP(nat, int, semiring_1_of_nat(int), _608961) = ti(int, _608959)), _608961 = nat_1(_608959), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _608959))], (4449 ^ _434076) ^ [_609274] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _609274)), -(hAPP(nat, int, semiring_1_of_nat(int), nat_1(_609274)) = ti(int, _609274))], (4455 ^ _434076) ^ [_609492] : [group_add(_609492), 4458 ^ _434076 : [(4459 ^ _434076) ^ [_609683, _609685] : [minus_minus(_609492, _609685, _609683) = zero_zero(_609492), -(ti(_609492, _609685) = ti(_609492, _609683))], (4465 ^ _434076) ^ [_609877, _609879] : [ti(_609492, _609879) = ti(_609492, _609877), -(minus_minus(_609492, _609879, _609877) = zero_zero(_609492))]]], (4471 ^ _434076) ^ [_610112] : [ab_group_add(_610112), 4474 ^ _434076 : [(4475 ^ _434076) ^ [_610303, _610305] : [ti(_610112, _610305) = ti(_610112, _610303), -(minus_minus(_610112, _610305, _610303) = zero_zero(_610112))], (4481 ^ _434076) ^ [_610497, _610499] : [minus_minus(_610112, _610499, _610497) = zero_zero(_610112), -(ti(_610112, _610499) = ti(_610112, _610497))]]], (4487 ^ _434076) ^ [_610732] : [group_add(_610732), 4490 ^ _434076 : [(4491 ^ _434076) ^ [_610848] : [-(minus_minus(_610732, _610848, _610848) = zero_zero(_610732))]]], (4493 ^ _434076) ^ [_610954] : [group_add(_610954), 4496 ^ _434076 : [(4497 ^ _434076) ^ [_611073] : [-(minus_minus(_610954, _611073, zero_zero(_610954)) = ti(_610954, _611073))]]], (4499 ^ _434076) ^ [_611182] : [ordered_ab_group_add(_611182), 4502 ^ _434076 : [(4503 ^ _434076) ^ [_611412, _611414, _611416, _611418] : [minus_minus(_611182, _611418, _611416) = minus_minus(_611182, _611414, _611412), 4506 ^ _434076 : [(4507 ^ _434076) ^ [] : [hBOOL(hAPP(_611182, bool, hAPP(_611182, fun(_611182, bool), ord_less(_611182), _611418), _611416)), -(hBOOL(hAPP(_611182, bool, hAPP(_611182, fun(_611182, bool), ord_less(_611182), _611414), _611412)))], (4513 ^ _434076) ^ [] : [hBOOL(hAPP(_611182, bool, hAPP(_611182, fun(_611182, bool), ord_less(_611182), _611414), _611412)), -(hBOOL(hAPP(_611182, bool, hAPP(_611182, fun(_611182, bool), ord_less(_611182), _611418), _611416)))]]]]], (4519 ^ _434076) ^ [_612013] : [ab_group_add(_612013), 4522 ^ _434076 : [(4523 ^ _434076) ^ [_612204, _612206, _612208, _612210] : [-(minus_minus(_612013, plus_plus(_612013, _612210, _612208), plus_plus(_612013, _612206, _612204)) = plus_plus(_612013, minus_minus(_612013, _612210, _612206), minus_minus(_612013, _612208, _612204)))]]], (4525 ^ _434076) ^ [_612334] : [group_add(_612334), 4528 ^ _434076 : [(4529 ^ _434076) ^ [_612474, _612476] : [-(minus_minus(_612334, plus_plus(_612334, _612476, _612474), _612474) = ti(_612334, _612476))]]], (4531 ^ _434076) ^ [_612587] : [group_add(_612587), 4534 ^ _434076 : [(4535 ^ _434076) ^ [_612727, _612729] : [-(plus_plus(_612587, minus_minus(_612587, _612729, _612727), _612727) = ti(_612587, _612729))]]], (4537 ^ _434076) ^ [_612840] : [mult_zero(_612840), 4540 ^ _434076 : [(4541 ^ _434076) ^ [_612958] : [-(times_times(_612840, zero_zero(_612840), _612958) = zero_zero(_612840))]]], (4543 ^ _434076) ^ [_613066] : [mult_zero(_613066), 4546 ^ _434076 : [(4547 ^ _434076) ^ [_613184] : [-(times_times(_613066, _613184, zero_zero(_613066)) = zero_zero(_613066))]]], (4549 ^ _434076) ^ [_613292] : [ring_n68954251visors(_613292), 4552 ^ _434076 : [(4563 ^ _434076) ^ [_613789, _613791] : [4564 ^ _434076 : [(4565 ^ _434076) ^ [] : [ti(_613292, _613791) = zero_zero(_613292)], (4567 ^ _434076) ^ [] : [ti(_613292, _613789) = zero_zero(_613292)]], -(times_times(_613292, _613791, _613789) = zero_zero(_613292))], (4553 ^ _434076) ^ [_613493, _613495] : [times_times(_613292, _613495, _613493) = zero_zero(_613292), -(ti(_613292, _613495) = zero_zero(_613292)), -(ti(_613292, _613493) = zero_zero(_613292))]]], (4571 ^ _434076) ^ [_614108] : [no_zero_divisors(_614108), 4574 ^ _434076 : [(4575 ^ _434076) ^ [_614286, _614288] : [-(ti(_614108, _614286) = zero_zero(_614108)), -(ti(_614108, _614288) = zero_zero(_614108)), times_times(_614108, _614286, _614288) = zero_zero(_614108)]]], (4585 ^ _434076) ^ [_614627] : [no_zero_divisors(_614627), 4588 ^ _434076 : [(4589 ^ _434076) ^ [_614799, _614801] : [times_times(_614627, _614801, _614799) = zero_zero(_614627), -(ti(_614627, _614801) = zero_zero(_614627)), -(ti(_614627, _614799) = zero_zero(_614627))]]], (4599 ^ _434076) ^ [_615134] : [comm_semiring_1(_615134), 4602 ^ _434076 : [(4603 ^ _434076) ^ [_615252] : [-(times_times(_615134, _615252, zero_zero(_615134)) = zero_zero(_615134))]]], (4605 ^ _434076) ^ [_615360] : [comm_semiring_1(_615360), 4608 ^ _434076 : [(4609 ^ _434076) ^ [_615478] : [-(times_times(_615360, zero_zero(_615360), _615478) = zero_zero(_615360))]]], (4611 ^ _434076) ^ [_615600, _615602] : [minus_minus(nat, _615602, _615600) = zero_zero(nat), minus_minus(nat, _615600, _615602) = zero_zero(nat), -(_615602 = _615600)], (4621 ^ _434076) ^ [_615886] : [-(minus_minus(nat, _615886, _615886) = zero_zero(nat))], (4623 ^ _434076) ^ [_615968] : [-(minus_minus(nat, _615968, zero_zero(nat)) = _615968)], (4625 ^ _434076) ^ [_616050] : [-(minus_minus(nat, zero_zero(nat), _616050) = zero_zero(nat))], (4627 ^ _434076) ^ [_616147] : [comm_semiring(_616147), 4630 ^ _434076 : [(4631 ^ _434076) ^ [_616315, _616317, _616319] : [-(times_times(_616147, plus_plus(_616147, _616319, _616317), _616315) = plus_plus(_616147, times_times(_616147, _616319, _616315), times_times(_616147, _616317, _616315)))]]], (4633 ^ _434076) ^ [_616439] : [semiring(_616439), 4636 ^ _434076 : [(4637 ^ _434076) ^ [_616634, _616636, _616638, _616640] : [-(plus_plus(_616439, times_times(_616439, _616640, _616638), plus_plus(_616439, times_times(_616439, _616636, _616638), _616634)) = plus_plus(_616439, times_times(_616439, plus_plus(_616439, _616640, _616636), _616638), _616634))]]], (4639 ^ _434076) ^ [_616768] : [semiri456707255roduct(_616768), 4642 ^ _434076 : [(4653 ^ _434076) ^ [_617383, _617385, _617387, _617389] : [4654 ^ _434076 : [(4655 ^ _434076) ^ [] : [ti(_616768, _617389) = ti(_616768, _617385)], (4657 ^ _434076) ^ [] : [ti(_616768, _617387) = ti(_616768, _617383)]], -(plus_plus(_616768, times_times(_616768, _617389, _617387), times_times(_616768, _617385, _617383)) = plus_plus(_616768, times_times(_616768, _617389, _617383), times_times(_616768, _617385, _617387)))], (4643 ^ _434076) ^ [_617027, _617029, _617031, _617033] : [plus_plus(_616768, times_times(_616768, _617033, _617031), times_times(_616768, _617029, _617027)) = plus_plus(_616768, times_times(_616768, _617033, _617027), times_times(_616768, _617029, _617031)), -(ti(_616768, _617033) = ti(_616768, _617029)), -(ti(_616768, _617031) = ti(_616768, _617027))]]], (4661 ^ _434076) ^ [_617758] : [comm_semiring_1(_617758), 4664 ^ _434076 : [(4665 ^ _434076) ^ [_617926, _617928, _617930] : [-(plus_plus(_617758, times_times(_617758, _617930, _617928), times_times(_617758, _617926, _617928)) = times_times(_617758, plus_plus(_617758, _617930, _617926), _617928))]]], (4667 ^ _434076) ^ [_618050] : [comm_semiring_1(_618050), 4670 ^ _434076 : [(4671 ^ _434076) ^ [_618218, _618220, _618222] : [-(times_times(_618050, plus_plus(_618050, _618222, _618220), _618218) = plus_plus(_618050, times_times(_618050, _618222, _618218), times_times(_618050, _618220, _618218)))]]], (4673 ^ _434076) ^ [_618342] : [semiri456707255roduct(_618342), 4676 ^ _434076 : [(4687 ^ _434076) ^ [_618969, _618971, _618973, _618975] : [-(plus_plus(_618342, times_times(_618342, _618971, _618975), times_times(_618342, _618969, _618973)) = plus_plus(_618342, times_times(_618342, _618971, _618973), times_times(_618342, _618969, _618975))), 4690 ^ _434076 : [(4691 ^ _434076) ^ [] : [ti(_618342, _618971) = ti(_618342, _618969)], (4693 ^ _434076) ^ [] : [ti(_618342, _618975) = ti(_618342, _618973)]]], (4677 ^ _434076) ^ [_618607, _618609, _618611, _618613] : [plus_plus(_618342, times_times(_618342, _618609, _618613), times_times(_618342, _618607, _618611)) = plus_plus(_618342, times_times(_618342, _618609, _618611), times_times(_618342, _618607, _618613)), -(ti(_618342, _618609) = ti(_618342, _618607)), -(ti(_618342, _618613) = ti(_618342, _618611))]]], (4695 ^ _434076) ^ [_619350] : [comm_semiring_1(_619350), 4698 ^ _434076 : [(4699 ^ _434076) ^ [_619518, _619520, _619522] : [-(times_times(_619350, _619522, plus_plus(_619350, _619520, _619518)) = plus_plus(_619350, times_times(_619350, _619522, _619520), times_times(_619350, _619522, _619518)))]]], (4701 ^ _434076) ^ [_619627] : [-(nat_1(hAPP(nat, int, semiring_1_of_nat(int), _619627)) = _619627)], (4703 ^ _434076) ^ [_619727] : [comm_monoid_mult(_619727), 4706 ^ _434076 : [(4707 ^ _434076) ^ [_619846] : [-(times_times(_619727, _619846, one_one(_619727)) = ti(_619727, _619846))]]], (4709 ^ _434076) ^ [_619955] : [comm_semiring_1(_619955), 4712 ^ _434076 : [(4713 ^ _434076) ^ [_620074] : [-(times_times(_619955, _620074, one_one(_619955)) = ti(_619955, _620074))]]], (4715 ^ _434076) ^ [_620183] : [monoid_mult(_620183), 4718 ^ _434076 : [(4719 ^ _434076) ^ [_620302] : [-(times_times(_620183, _620302, one_one(_620183)) = ti(_620183, _620302))]]], (4721 ^ _434076) ^ [_620411] : [comm_monoid_mult(_620411), 4724 ^ _434076 : [(4725 ^ _434076) ^ [_620530] : [-(times_times(_620411, one_one(_620411), _620530) = ti(_620411, _620530))]]], (4727 ^ _434076) ^ [_620639] : [comm_semiring_1(_620639), 4730 ^ _434076 : [(4731 ^ _434076) ^ [_620758] : [-(times_times(_620639, one_one(_620639), _620758) = ti(_620639, _620758))]]], (4733 ^ _434076) ^ [_620867] : [monoid_mult(_620867), 4736 ^ _434076 : [(4737 ^ _434076) ^ [_620986] : [-(times_times(_620867, one_one(_620867), _620986) = ti(_620867, _620986))]]], (4739 ^ _434076) ^ [_621095] : [ordere236663937imp_le(_621095), 4742 ^ _434076 : [(4743 ^ _434076) ^ [_621300, _621302, _621304] : [hBOOL(hAPP(_621095, bool, hAPP(_621095, fun(_621095, bool), ord_less_eq(_621095), plus_plus(_621095, _621304, _621302)), plus_plus(_621095, _621304, _621300))), -(hBOOL(hAPP(_621095, bool, hAPP(_621095, fun(_621095, bool), ord_less_eq(_621095), _621302), _621300)))]]], (4749 ^ _434076) ^ [_621587] : [ordere236663937imp_le(_621587), 4752 ^ _434076 : [(4753 ^ _434076) ^ [_621792, _621794, _621796] : [hBOOL(hAPP(_621587, bool, hAPP(_621587, fun(_621587, bool), ord_less_eq(_621587), plus_plus(_621587, _621796, _621794)), plus_plus(_621587, _621792, _621794))), -(hBOOL(hAPP(_621587, bool, hAPP(_621587, fun(_621587, bool), ord_less_eq(_621587), _621796), _621792)))]]], (4759 ^ _434076) ^ [_622079] : [ordere779506340up_add(_622079), 4762 ^ _434076 : [(4763 ^ _434076) ^ [_622323, _622325, _622327, _622329] : [hBOOL(hAPP(_622079, bool, hAPP(_622079, fun(_622079, bool), ord_less_eq(_622079), _622325), _622323)), hBOOL(hAPP(_622079, bool, hAPP(_622079, fun(_622079, bool), ord_less_eq(_622079), _622329), _622327)), -(hBOOL(hAPP(_622079, bool, hAPP(_622079, fun(_622079, bool), ord_less_eq(_622079), plus_plus(_622079, _622325, _622329)), plus_plus(_622079, _622323, _622327))))]]], (4773 ^ _434076) ^ [_622745] : [ordere779506340up_add(_622745), 4776 ^ _434076 : [(4777 ^ _434076) ^ [_622950, _622952, _622954] : [hBOOL(hAPP(_622745, bool, hAPP(_622745, fun(_622745, bool), ord_less_eq(_622745), _622952), _622950)), -(hBOOL(hAPP(_622745, bool, hAPP(_622745, fun(_622745, bool), ord_less_eq(_622745), plus_plus(_622745, _622954, _622952)), plus_plus(_622745, _622954, _622950))))]]], (4783 ^ _434076) ^ [_623237] : [ordere779506340up_add(_623237), 4786 ^ _434076 : [(4787 ^ _434076) ^ [_623442, _623444, _623446] : [hBOOL(hAPP(_623237, bool, hAPP(_623237, fun(_623237, bool), ord_less_eq(_623237), _623444), _623442)), -(hBOOL(hAPP(_623237, bool, hAPP(_623237, fun(_623237, bool), ord_less_eq(_623237), plus_plus(_623237, _623444, _623446)), plus_plus(_623237, _623442, _623446))))]]], (4793 ^ _434076) ^ [_623729] : [ordere236663937imp_le(_623729), 4796 ^ _434076 : [(4797 ^ _434076) ^ [_623963, _623965, _623967] : [hBOOL(hAPP(_623729, bool, hAPP(_623729, fun(_623729, bool), ord_less_eq(_623729), plus_plus(_623729, _623967, _623965)), plus_plus(_623729, _623967, _623963))), -(hBOOL(hAPP(_623729, bool, hAPP(_623729, fun(_623729, bool), ord_less_eq(_623729), _623965), _623963)))], (4803 ^ _434076) ^ [_624211, _624213, _624215] : [hBOOL(hAPP(_623729, bool, hAPP(_623729, fun(_623729, bool), ord_less_eq(_623729), _624213), _624211)), -(hBOOL(hAPP(_623729, bool, hAPP(_623729, fun(_623729, bool), ord_less_eq(_623729), plus_plus(_623729, _624215, _624213)), plus_plus(_623729, _624215, _624211))))]]], (4809 ^ _434076) ^ [_624500] : [ordere236663937imp_le(_624500), 4812 ^ _434076 : [(4813 ^ _434076) ^ [_624734, _624736, _624738] : [hBOOL(hAPP(_624500, bool, hAPP(_624500, fun(_624500, bool), ord_less_eq(_624500), plus_plus(_624500, _624738, _624736)), plus_plus(_624500, _624734, _624736))), -(hBOOL(hAPP(_624500, bool, hAPP(_624500, fun(_624500, bool), ord_less_eq(_624500), _624738), _624734)))], (4819 ^ _434076) ^ [_624982, _624984, _624986] : [hBOOL(hAPP(_624500, bool, hAPP(_624500, fun(_624500, bool), ord_less_eq(_624500), _624986), _624982)), -(hBOOL(hAPP(_624500, bool, hAPP(_624500, fun(_624500, bool), ord_less_eq(_624500), plus_plus(_624500, _624986, _624984)), plus_plus(_624500, _624982, _624984))))]]], (4825 ^ _434076) ^ [_625299, _625301, _625303] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _625301), _625299)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _625301, _625303)), _625299)))], (4831 ^ _434076) ^ [_625573, _625575, _625577] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _625575), _625573)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _625575), _625577)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _625577, _625573)), minus_minus(nat, _625577, _625575))))], (4841 ^ _434076) ^ [_625938] : [monoid_mult(_625938), 4844 ^ _434076 : [(4845 ^ _434076) ^ [_626091, _626093] : [-(times_times(_625938, hAPP(nat, _625938, power_power(_625938, _626093), _626091), _626093) = times_times(_625938, _626093, hAPP(nat, _625938, power_power(_625938, _626093), _626091)))]]], (4847 ^ _434076) ^ [_626217] : [comm_monoid_mult(_626217), 4850 ^ _434076 : [(4851 ^ _434076) ^ [_626397, _626399, _626401] : [-(hAPP(nat, _626217, power_power(_626217, times_times(_626217, _626401, _626399)), _626397) = times_times(_626217, hAPP(nat, _626217, power_power(_626217, _626401), _626397), hAPP(nat, _626217, power_power(_626217, _626399), _626397)))]]], (4853 ^ _434076) ^ [_626533] : [comm_semiring_1(_626533), 4856 ^ _434076 : [(4857 ^ _434076) ^ [_626713, _626715, _626717] : [-(hAPP(nat, _626533, power_power(_626533, times_times(_626533, _626717, _626715)), _626713) = times_times(_626533, hAPP(nat, _626533, power_power(_626533, _626717), _626713), hAPP(nat, _626533, power_power(_626533, _626715), _626713)))]]], (4859 ^ _434076) ^ [_626848, _626850] : [-(minus_minus(nat, plus_plus(nat, _626850, _626848), _626848) = _626850)], (4861 ^ _434076) ^ [_626950, _626952] : [-(minus_minus(nat, plus_plus(nat, _626952, _626950), _626952) = _626950)], (4863 ^ _434076) ^ [_627066, _627068, _627070] : [-(minus_minus(nat, minus_minus(nat, _627070, _627068), _627066) = minus_minus(nat, _627070, plus_plus(nat, _627068, _627066)))], (4865 ^ _434076) ^ [_627192, _627194, _627196] : [-(minus_minus(nat, plus_plus(nat, _627196, _627194), plus_plus(nat, _627196, _627192)) = minus_minus(nat, _627194, _627192))], (4867 ^ _434076) ^ [_627318, _627320, _627322] : [-(minus_minus(nat, plus_plus(nat, _627322, _627320), plus_plus(nat, _627318, _627320)) = minus_minus(nat, _627322, _627318))], (4869 ^ _434076) ^ [_627416] : [-(times_times(int, pls, _627416) = pls)], (4871 ^ _434076) ^ [_627512, _627514] : [-(times_times(int, bit0(_627514), _627512) = bit0(times_times(int, _627514, _627512)))], (4873 ^ _434076) ^ [_627662, _627664] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_627664)), bit1(_627662))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _627664), _627662)))], (4879 ^ _434076) ^ [_627868, _627870] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _627870), _627868)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_627870)), bit1(_627868))))], (4885 ^ _434076) ^ [_628153, _628155] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_628155)), bit1(_628153))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _628155), _628153)))], (4891 ^ _434076) ^ [_628359, _628361] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _628361), _628359)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_628361)), bit1(_628359))))], (4897 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), pls)))], (4899 ^ _434076) ^ [_628697, _628699] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_628699)), bit0(_628697))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _628699), _628697)))], (4905 ^ _434076) ^ [_628903, _628905] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _628905), _628903)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_628905)), bit0(_628903))))], (4911 ^ _434076) ^ [_629188, _629190] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_629190)), bit0(_629188))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _629190), _629188)))], (4917 ^ _434076) ^ [_629394, _629396] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _629396), _629394)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_629396)), bit0(_629394))))], (4923 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), zero_zero(int))))], (4925 ^ _434076) ^ [_629674] : [-(times_times(int, one_one(int), _629674) = ti(int, _629674))], (4927 ^ _434076) ^ [_629759] : [-(times_times(int, _629759, one_one(int)) = ti(int, _629759))], (4929 ^ _434076) ^ [_629902, _629904] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _629904), _629902)), 4932 ^ _434076 : [(4933 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _629904), _629902)))], (4935 ^ _434076) ^ [] : [ti(int, _629904) = ti(int, _629902)]]], (4937 ^ _434076) ^ [_630188, _630190] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _630190), _630188))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _630190), _630188)), -(ti(int, _630190) = ti(int, _630188))], (4947 ^ _434076) ^ [_630539, _630541, _630543] : [-(times_times(int, _630543, plus_plus(int, _630541, _630539)) = plus_plus(int, times_times(int, _630543, _630541), times_times(int, _630543, _630539)))], (4949 ^ _434076) ^ [_630669, _630671, _630673] : [-(times_times(int, plus_plus(int, _630673, _630671), _630669) = plus_plus(int, times_times(int, _630673, _630669), times_times(int, _630671, _630669)))], (4951 ^ _434076) ^ [_630814, _630816, _630818] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _630816), _630814)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, _630818, _630816)), plus_plus(int, _630818, _630814))))], (4957 ^ _434076) ^ [_631067, _631069] : [-(times_times(int, number_number_of(int, _631069), number_number_of(int, _631067)) = number_number_of(int, times_times(int, _631069, _631067)))], (4959 ^ _434076) ^ [_631222, _631224] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), number_number_of(int, _631224)), number_number_of(int, _631222))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _631224), _631222)))], (4965 ^ _434076) ^ [_631432, _631434] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _631434), _631432)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), number_number_of(int, _631434)), number_number_of(int, _631432))))], (4971 ^ _434076) ^ [_631678] : [linord1278240602ring_1(_631678), 4974 ^ _434076 : [(4975 ^ _434076) ^ [_632001, _632003, _632005, _632007, _632009] : [hBOOL(hAPP(_631678, bool, hAPP(_631678, fun(_631678, bool), ord_less_eq(_631678), _632003), _632001)), hBOOL(hAPP(_631678, bool, hAPP(_631678, fun(_631678, bool), ord_less_eq(_631678), _632005), _632001)), hBOOL(hAPP(_631678, bool, hAPP(_631678, fun(_631678, bool), ord_less_eq(_631678), zero_zero(_631678)), _632007)), hBOOL(hAPP(_631678, bool, hAPP(_631678, fun(_631678, bool), ord_less_eq(_631678), zero_zero(_631678)), _632009)), plus_plus(_631678, _632007, _632009) = one_one(_631678), -(hBOOL(hAPP(_631678, bool, hAPP(_631678, fun(_631678, bool), ord_less_eq(_631678), plus_plus(_631678, times_times(_631678, _632007, _632003), times_times(_631678, _632009, _632005))), _632001)))]]], (4997 ^ _434076) ^ [_632846, _632848] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _632846)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _632848)), 5004 ^ _434076 : [(5005 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_632846)), nat_1(_632848))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _632846), _632848)))], (5011 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _632846), _632848)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_632846)), nat_1(_632848))))]]], (5017 ^ _434076) ^ [_633477, _633479] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _633477)), 5020 ^ _434076 : [(5021 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_633477)), nat_1(_633479))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _633477), _633479)))], (5027 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _633477), _633479)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_633477)), nat_1(_633479))))]]], (5033 ^ _434076) ^ [_633997] : [number_ring(_633997), linordered_idom(_633997), 5040 ^ _434076 : [(5041 ^ _434076) ^ [_634263] : [hBOOL(hAPP(_633997, bool, hAPP(_633997, fun(_633997, bool), ord_less_eq(_633997), zero_zero(_633997)), number_number_of(_633997, _634263))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _634263)))], (5047 ^ _434076) ^ [_634473] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _634473)), -(hBOOL(hAPP(_633997, bool, hAPP(_633997, fun(_633997, bool), ord_less_eq(_633997), zero_zero(_633997)), number_number_of(_633997, _634473))))]]], (5053 ^ _434076) ^ [_634726] : [number_ring(_634726), linordered_idom(_634726), 5060 ^ _434076 : [(5061 ^ _434076) ^ [_634997] : [hBOOL(hAPP(_634726, bool, hAPP(_634726, fun(_634726, bool), ord_less_eq(_634726), number_number_of(_634726, _634997)), zero_zero(_634726))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _634997), pls)))], (5067 ^ _434076) ^ [_635217] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _635217), pls)), -(hBOOL(hAPP(_634726, bool, hAPP(_634726, fun(_634726, bool), ord_less_eq(_634726), number_number_of(_634726, _635217)), zero_zero(_634726))))]]], (5073 ^ _434076) ^ [_635480] : [linordered_semidom(_635480), 5076 ^ _434076 : [(5077 ^ _434076) ^ [_635732, _635734, _635736] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _635734), _635732)), hBOOL(hAPP(_635480, bool, hAPP(_635480, fun(_635480, bool), ord_less_eq(_635480), zero_zero(_635480)), _635736)), hBOOL(hAPP(_635480, bool, hAPP(_635480, fun(_635480, bool), ord_less_eq(_635480), _635736), one_one(_635480))), -(hBOOL(hAPP(_635480, bool, hAPP(_635480, fun(_635480, bool), ord_less_eq(_635480), hAPP(nat, _635480, power_power(_635480, _635736), _635732)), hAPP(nat, _635480, power_power(_635480, _635736), _635734))))]]], (5091 ^ _434076) ^ [_636283] : [linordered_semidom(_636283), 5094 ^ _434076 : [(5095 ^ _434076) ^ [_636513, _636515, _636517] : [hBOOL(hAPP(_636283, bool, hAPP(_636283, fun(_636283, bool), ord_less(_636283), one_one(_636283)), _636513)), 5098 ^ _434076 : [(5099 ^ _434076) ^ [] : [hBOOL(hAPP(_636283, bool, hAPP(_636283, fun(_636283, bool), ord_less_eq(_636283), hAPP(nat, _636283, power_power(_636283, _636513), _636517)), hAPP(nat, _636283, power_power(_636283, _636513), _636515))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _636517), _636515)))], (5105 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _636517), _636515)), -(hBOOL(hAPP(_636283, bool, hAPP(_636283, fun(_636283, bool), ord_less_eq(_636283), hAPP(nat, _636283, power_power(_636283, _636513), _636517)), hAPP(nat, _636283, power_power(_636283, _636513), _636515))))]]]]], (5111 ^ _434076) ^ [_637147] : [linordered_semidom(_637147), 5114 ^ _434076 : [(5115 ^ _434076) ^ [_637377, _637379, _637381] : [hBOOL(hAPP(_637147, bool, hAPP(_637147, fun(_637147, bool), ord_less(_637147), one_one(_637147)), _637377)), hBOOL(hAPP(_637147, bool, hAPP(_637147, fun(_637147, bool), ord_less_eq(_637147), hAPP(nat, _637147, power_power(_637147, _637377), _637381)), hAPP(nat, _637147, power_power(_637147, _637377), _637379))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _637381), _637379)))]]], (5141 ^ _434076) ^ [_638296, _638298] : [-(_638298 = nat_1(_638296)), 5144 ^ _434076 : [(5145 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _638296)))], (5147 ^ _434076) ^ [] : [ti(int, _638296) = hAPP(nat, int, semiring_1_of_nat(int), _638298)]], 5148 ^ _434076 : [(5149 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _638296))], (5151 ^ _434076) ^ [] : [_638298 = zero_zero(nat)]]], (5125 ^ _434076) ^ [_637842, _637844] : [_637844 = nat_1(_637842), 5128 ^ _434076 : [(5129 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _637842)), -(ti(int, _637842) = hAPP(nat, int, semiring_1_of_nat(int), _637844))], (5135 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _637842))), -(_637844 = zero_zero(nat))]]], (5171 ^ _434076) ^ [_639267, _639269] : [-(nat_1(_639269) = _639267), 5174 ^ _434076 : [(5175 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _639269)))], (5177 ^ _434076) ^ [] : [ti(int, _639269) = hAPP(nat, int, semiring_1_of_nat(int), _639267)]], 5178 ^ _434076 : [(5179 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _639269))], (5181 ^ _434076) ^ [] : [_639267 = zero_zero(nat)]]], (5155 ^ _434076) ^ [_638813, _638815] : [nat_1(_638815) = _638813, 5158 ^ _434076 : [(5159 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _638815)), -(ti(int, _638815) = hAPP(nat, int, semiring_1_of_nat(int), _638813))], (5165 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _638815))), -(_638813 = zero_zero(nat))]]], (5185 ^ _434076) ^ [_639755, _639757] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _639755)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _639757)), -(plus_plus(nat, nat_1(_639755), nat_1(_639757)) = nat_1(plus_plus(int, _639755, _639757)))], (5195 ^ _434076) ^ [_640098, _640100] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _640098)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _640100)), -(nat_1(plus_plus(int, _640098, _640100)) = plus_plus(nat, nat_1(_640098), nat_1(_640100)))], (5205 ^ _434076) ^ [_640470, _640472] : [hAPP(nat, int, semiring_1_of_nat(int), _640472) = number_number_of(int, _640470), 5208 ^ _434076 : [(5209 ^ _434076) ^ [] : [-(_640472 = nat_1(number_number_of(int, _640470)))], (5211 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _640470))))]]], (5213 ^ _434076) ^ [_640747, _640749] : [-(hAPP(nat, int, semiring_1_of_nat(int), _640749) = number_number_of(int, _640747)), _640749 = nat_1(number_number_of(int, _640747)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _640747)))], (5223 ^ _434076) ^ [_641088, _641090] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _641088)), -(hAPP(nat, nat, power_power(nat, nat_1(_641088)), _641090) = nat_1(hAPP(nat, int, power_power(int, _641088), _641090)))], (5229 ^ _434076) ^ [_641346, _641348] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _641346)), -(nat_1(hAPP(nat, int, power_power(int, _641346), _641348)) = hAPP(nat, nat, power_power(nat, nat_1(_641346)), _641348))], (5235 ^ _434076) ^ [_641590] : [linord626643107strict(_641590), 5238 ^ _434076 : [(5239 ^ _434076) ^ [_641913, _641915, _641917, _641919, _641921] : [hBOOL(hAPP(_641590, bool, hAPP(_641590, fun(_641590, bool), ord_less(_641590), _641915), _641913)), hBOOL(hAPP(_641590, bool, hAPP(_641590, fun(_641590, bool), ord_less(_641590), _641917), _641913)), hBOOL(hAPP(_641590, bool, hAPP(_641590, fun(_641590, bool), ord_less_eq(_641590), zero_zero(_641590)), _641919)), hBOOL(hAPP(_641590, bool, hAPP(_641590, fun(_641590, bool), ord_less_eq(_641590), zero_zero(_641590)), _641921)), plus_plus(_641590, _641919, _641921) = one_one(_641590), -(hBOOL(hAPP(_641590, bool, hAPP(_641590, fun(_641590, bool), ord_less(_641590), plus_plus(_641590, times_times(_641590, _641919, _641915), times_times(_641590, _641921, _641917))), _641913)))]]], (5261 ^ _434076) ^ [_642758, _642760] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _642758)), 5264 ^ _434076 : [(5265 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_642758)), _642760)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _642758), hAPP(nat, int, semiring_1_of_nat(int), _642760))))], (5271 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _642758), hAPP(nat, int, semiring_1_of_nat(int), _642760))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_642758)), _642760)))]]], (5277 ^ _434076) ^ [_643287] : [number_ring(_643287), linordered_idom(_643287), 5284 ^ _434076 : [(5285 ^ _434076) ^ [_643553] : [hBOOL(hAPP(_643287, bool, hAPP(_643287, fun(_643287, bool), ord_less_eq(_643287), one_one(_643287)), number_number_of(_643287, _643553))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(pls)), _643553)))], (5291 ^ _434076) ^ [_643763] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(pls)), _643763)), -(hBOOL(hAPP(_643287, bool, hAPP(_643287, fun(_643287, bool), ord_less_eq(_643287), one_one(_643287)), number_number_of(_643287, _643763))))]]], (5297 ^ _434076) ^ [_644016] : [number_ring(_644016), linordered_idom(_644016), 5304 ^ _434076 : [(5305 ^ _434076) ^ [_644287] : [hBOOL(hAPP(_644016, bool, hAPP(_644016, fun(_644016, bool), ord_less_eq(_644016), number_number_of(_644016, _644287)), one_one(_644016))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _644287), bit1(pls))))], (5311 ^ _434076) ^ [_644507] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _644507), bit1(pls))), -(hBOOL(hAPP(_644016, bool, hAPP(_644016, fun(_644016, bool), ord_less_eq(_644016), number_number_of(_644016, _644507)), one_one(_644016))))]]], (5317 ^ _434076) ^ [_644770] : [monoid_mult(_644770), 5320 ^ _434076 : [(5321 ^ _434076) ^ [_644948, _644950] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _644948)), -(times_times(_644770, hAPP(nat, _644770, power_power(_644770, _644950), minus_minus(nat, _644948, one_one(nat))), _644950) = hAPP(nat, _644770, power_power(_644770, _644950), _644948))]]], (5327 ^ _434076) ^ [_645213] : [ordered_ab_group_add(_645213), 5330 ^ _434076 : [(5331 ^ _434076) ^ [_645426, _645428] : [hBOOL(hAPP(_645213, bool, hAPP(_645213, fun(_645213, bool), ord_less(_645213), _645428), _645426)), -(hBOOL(hAPP(_645213, bool, hAPP(_645213, fun(_645213, bool), ord_less(_645213), minus_minus(_645213, _645428, _645426)), zero_zero(_645213))))], (5337 ^ _434076) ^ [_645664, _645666] : [hBOOL(hAPP(_645213, bool, hAPP(_645213, fun(_645213, bool), ord_less(_645213), minus_minus(_645213, _645666, _645664)), zero_zero(_645213))), -(hBOOL(hAPP(_645213, bool, hAPP(_645213, fun(_645213, bool), ord_less(_645213), _645666), _645664)))]]], (5343 ^ _434076) ^ [] : [-(zero_zero(nat) = nat_1(zero_zero(int)))], (5345 ^ _434076) ^ [] : [-(nat_1(zero_zero(int)) = zero_zero(nat))], (5347 ^ _434076) ^ [_646049] : [linordered_ring(_646049), 5350 ^ _434076 : [(5351 ^ _434076) ^ [_646180] : [hBOOL(hAPP(_646049, bool, hAPP(_646049, fun(_646049, bool), ord_less(_646049), times_times(_646049, _646180, _646180)), zero_zero(_646049)))]]], (5353 ^ _434076) ^ [_646300] : [linord581940658strict(_646300), 5356 ^ _434076 : [(5357 ^ _434076) ^ [_646598, _646600, _646602] : [hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), times_times(_646300, _646602, _646600)), times_times(_646300, _646598, _646600))), 5362 ^ _434076 : [(5363 ^ _434076) ^ [] : [-(hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), zero_zero(_646300)), _646600)))], (5365 ^ _434076) ^ [] : [-(hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _646602), _646598)))]], 5366 ^ _434076 : [(5367 ^ _434076) ^ [] : [-(hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _646600), zero_zero(_646300))))], (5369 ^ _434076) ^ [] : [-(hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _646598), _646602)))]]], (5371 ^ _434076) ^ [_647194, _647196, _647198] : [-(hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), times_times(_646300, _647198, _647196)), times_times(_646300, _647194, _647196)))), 5372 ^ _434076 : [(5373 ^ _434076) ^ [] : [hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), zero_zero(_646300)), _647196)), hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _647198), _647194))], (5379 ^ _434076) ^ [] : [hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _647196), zero_zero(_646300))), hBOOL(hAPP(_646300, bool, hAPP(_646300, fun(_646300, bool), ord_less(_646300), _647194), _647198))]]]]], (5387 ^ _434076) ^ [_647847] : [linord581940658strict(_647847), 5390 ^ _434076 : [(5391 ^ _434076) ^ [_648145, _648147, _648149] : [hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), times_times(_647847, _648149, _648147)), times_times(_647847, _648149, _648145))), 5396 ^ _434076 : [(5397 ^ _434076) ^ [] : [-(hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), zero_zero(_647847)), _648149)))], (5399 ^ _434076) ^ [] : [-(hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648147), _648145)))]], 5400 ^ _434076 : [(5401 ^ _434076) ^ [] : [-(hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648149), zero_zero(_647847))))], (5403 ^ _434076) ^ [] : [-(hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648145), _648147)))]]], (5405 ^ _434076) ^ [_648741, _648743, _648745] : [-(hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), times_times(_647847, _648745, _648743)), times_times(_647847, _648745, _648741)))), 5406 ^ _434076 : [(5407 ^ _434076) ^ [] : [hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), zero_zero(_647847)), _648745)), hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648743), _648741))], (5413 ^ _434076) ^ [] : [hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648745), zero_zero(_647847))), hBOOL(hAPP(_647847, bool, hAPP(_647847, fun(_647847, bool), ord_less(_647847), _648741), _648743))]]]]], (5421 ^ _434076) ^ [_649394] : [linord581940658strict(_649394), 5424 ^ _434076 : [(5425 ^ _434076) ^ [_649621, _649623, _649625] : [hBOOL(hAPP(_649394, bool, hAPP(_649394, fun(_649394, bool), ord_less(_649394), zero_zero(_649394)), _649621)), 5428 ^ _434076 : [(5429 ^ _434076) ^ [] : [hBOOL(hAPP(_649394, bool, hAPP(_649394, fun(_649394, bool), ord_less(_649394), times_times(_649394, _649621, _649625)), times_times(_649394, _649621, _649623))), -(hBOOL(hAPP(_649394, bool, hAPP(_649394, fun(_649394, bool), ord_less(_649394), _649625), _649623)))], (5435 ^ _434076) ^ [] : [hBOOL(hAPP(_649394, bool, hAPP(_649394, fun(_649394, bool), ord_less(_649394), _649625), _649623)), -(hBOOL(hAPP(_649394, bool, hAPP(_649394, fun(_649394, bool), ord_less(_649394), times_times(_649394, _649621, _649625)), times_times(_649394, _649621, _649623))))]]]]], (5441 ^ _434076) ^ [_650246] : [linord20386208strict(_650246), 5444 ^ _434076 : [(5445 ^ _434076) ^ [_650454, _650456] : [hBOOL(hAPP(_650246, bool, hAPP(_650246, fun(_650246, bool), ord_less(_650246), zero_zero(_650246)), _650454)), hBOOL(hAPP(_650246, bool, hAPP(_650246, fun(_650246, bool), ord_less(_650246), zero_zero(_650246)), _650456)), -(hBOOL(hAPP(_650246, bool, hAPP(_650246, fun(_650246, bool), ord_less(_650246), zero_zero(_650246)), times_times(_650246, _650454, _650456))))]]], (5455 ^ _434076) ^ [_650860] : [linord20386208strict(_650860), 5458 ^ _434076 : [(5459 ^ _434076) ^ [_651068, _651070] : [hBOOL(hAPP(_650860, bool, hAPP(_650860, fun(_650860, bool), ord_less(_650860), zero_zero(_650860)), _651068)), hBOOL(hAPP(_650860, bool, hAPP(_650860, fun(_650860, bool), ord_less(_650860), _651070), zero_zero(_650860))), -(hBOOL(hAPP(_650860, bool, hAPP(_650860, fun(_650860, bool), ord_less(_650860), times_times(_650860, _651068, _651070)), zero_zero(_650860))))]]], (5469 ^ _434076) ^ [_651474] : [linord20386208strict(_651474), 5472 ^ _434076 : [(5473 ^ _434076) ^ [_651682, _651684] : [hBOOL(hAPP(_651474, bool, hAPP(_651474, fun(_651474, bool), ord_less(_651474), zero_zero(_651474)), _651682)), hBOOL(hAPP(_651474, bool, hAPP(_651474, fun(_651474, bool), ord_less(_651474), _651684), zero_zero(_651474))), -(hBOOL(hAPP(_651474, bool, hAPP(_651474, fun(_651474, bool), ord_less(_651474), times_times(_651474, _651684, _651682)), zero_zero(_651474))))]]], (5483 ^ _434076) ^ [_652088] : [linord20386208strict(_652088), 5486 ^ _434076 : [(5487 ^ _434076) ^ [_652296, _652298] : [hBOOL(hAPP(_652088, bool, hAPP(_652088, fun(_652088, bool), ord_less(_652088), zero_zero(_652088)), times_times(_652088, _652298, _652296))), hBOOL(hAPP(_652088, bool, hAPP(_652088, fun(_652088, bool), ord_less(_652088), zero_zero(_652088)), _652298)), -(hBOOL(hAPP(_652088, bool, hAPP(_652088, fun(_652088, bool), ord_less(_652088), zero_zero(_652088)), _652296)))]]], (5497 ^ _434076) ^ [_652702] : [linord20386208strict(_652702), 5500 ^ _434076 : [(5501 ^ _434076) ^ [_652910, _652912] : [hBOOL(hAPP(_652702, bool, hAPP(_652702, fun(_652702, bool), ord_less(_652702), zero_zero(_652702)), times_times(_652702, _652912, _652910))), hBOOL(hAPP(_652702, bool, hAPP(_652702, fun(_652702, bool), ord_less(_652702), zero_zero(_652702)), _652910)), -(hBOOL(hAPP(_652702, bool, hAPP(_652702, fun(_652702, bool), ord_less(_652702), zero_zero(_652702)), _652912)))]]], (5511 ^ _434076) ^ [_653316] : [linord581940658strict(_653316), 5514 ^ _434076 : [(5515 ^ _434076) ^ [_653543, _653545, _653547] : [hBOOL(hAPP(_653316, bool, hAPP(_653316, fun(_653316, bool), ord_less(_653316), _653543), zero_zero(_653316))), 5518 ^ _434076 : [(5519 ^ _434076) ^ [] : [hBOOL(hAPP(_653316, bool, hAPP(_653316, fun(_653316, bool), ord_less(_653316), times_times(_653316, _653543, _653547)), times_times(_653316, _653543, _653545))), -(hBOOL(hAPP(_653316, bool, hAPP(_653316, fun(_653316, bool), ord_less(_653316), _653545), _653547)))], (5525 ^ _434076) ^ [] : [hBOOL(hAPP(_653316, bool, hAPP(_653316, fun(_653316, bool), ord_less(_653316), _653545), _653547)), -(hBOOL(hAPP(_653316, bool, hAPP(_653316, fun(_653316, bool), ord_less(_653316), times_times(_653316, _653543, _653547)), times_times(_653316, _653543, _653545))))]]]]], (5531 ^ _434076) ^ [_654168] : [linord20386208strict(_654168), 5534 ^ _434076 : [(5535 ^ _434076) ^ [_654376, _654378] : [hBOOL(hAPP(_654168, bool, hAPP(_654168, fun(_654168, bool), ord_less(_654168), _654376), zero_zero(_654168))), hBOOL(hAPP(_654168, bool, hAPP(_654168, fun(_654168, bool), ord_less(_654168), zero_zero(_654168)), _654378)), -(hBOOL(hAPP(_654168, bool, hAPP(_654168, fun(_654168, bool), ord_less(_654168), times_times(_654168, _654376, _654378)), zero_zero(_654168))))]]], (5545 ^ _434076) ^ [_654782] : [linord581940658strict(_654782), 5548 ^ _434076 : [(5549 ^ _434076) ^ [_654990, _654992] : [hBOOL(hAPP(_654782, bool, hAPP(_654782, fun(_654782, bool), ord_less(_654782), _654990), zero_zero(_654782))), hBOOL(hAPP(_654782, bool, hAPP(_654782, fun(_654782, bool), ord_less(_654782), _654992), zero_zero(_654782))), -(hBOOL(hAPP(_654782, bool, hAPP(_654782, fun(_654782, bool), ord_less(_654782), zero_zero(_654782)), times_times(_654782, _654990, _654992))))]]], (5559 ^ _434076) ^ [_655396] : [linord20386208strict(_655396), 5562 ^ _434076 : [(5563 ^ _434076) ^ [_655623, _655625, _655627] : [hBOOL(hAPP(_655396, bool, hAPP(_655396, fun(_655396, bool), ord_less(_655396), _655625), _655623)), hBOOL(hAPP(_655396, bool, hAPP(_655396, fun(_655396, bool), ord_less(_655396), zero_zero(_655396)), _655627)), -(hBOOL(hAPP(_655396, bool, hAPP(_655396, fun(_655396, bool), ord_less(_655396), times_times(_655396, _655625, _655627)), times_times(_655396, _655623, _655627))))]]], (5573 ^ _434076) ^ [_656039] : [linord20386208strict(_656039), 5576 ^ _434076 : [(5577 ^ _434076) ^ [_656266, _656268, _656270] : [hBOOL(hAPP(_656039, bool, hAPP(_656039, fun(_656039, bool), ord_less(_656039), _656268), _656266)), hBOOL(hAPP(_656039, bool, hAPP(_656039, fun(_656039, bool), ord_less(_656039), zero_zero(_656039)), _656270)), -(hBOOL(hAPP(_656039, bool, hAPP(_656039, fun(_656039, bool), ord_less(_656039), times_times(_656039, _656270, _656268)), times_times(_656039, _656270, _656266))))]]], (5587 ^ _434076) ^ [_656682] : [linord893533164strict(_656682), 5590 ^ _434076 : [(5591 ^ _434076) ^ [_656909, _656911, _656913] : [hBOOL(hAPP(_656682, bool, hAPP(_656682, fun(_656682, bool), ord_less(_656682), _656911), _656909)), hBOOL(hAPP(_656682, bool, hAPP(_656682, fun(_656682, bool), ord_less(_656682), zero_zero(_656682)), _656913)), -(hBOOL(hAPP(_656682, bool, hAPP(_656682, fun(_656682, bool), ord_less(_656682), times_times(_656682, _656913, _656911)), times_times(_656682, _656913, _656909))))]]], (5601 ^ _434076) ^ [_657325] : [linord581940658strict(_657325), 5604 ^ _434076 : [(5605 ^ _434076) ^ [_657552, _657554, _657556] : [hBOOL(hAPP(_657325, bool, hAPP(_657325, fun(_657325, bool), ord_less(_657325), _657554), _657552)), hBOOL(hAPP(_657325, bool, hAPP(_657325, fun(_657325, bool), ord_less(_657325), _657556), zero_zero(_657325))), -(hBOOL(hAPP(_657325, bool, hAPP(_657325, fun(_657325, bool), ord_less(_657325), times_times(_657325, _657552, _657556)), times_times(_657325, _657554, _657556))))]]], (5615 ^ _434076) ^ [_657968] : [linord581940658strict(_657968), 5618 ^ _434076 : [(5619 ^ _434076) ^ [_658195, _658197, _658199] : [hBOOL(hAPP(_657968, bool, hAPP(_657968, fun(_657968, bool), ord_less(_657968), _658197), _658195)), hBOOL(hAPP(_657968, bool, hAPP(_657968, fun(_657968, bool), ord_less(_657968), _658199), zero_zero(_657968))), -(hBOOL(hAPP(_657968, bool, hAPP(_657968, fun(_657968, bool), ord_less(_657968), times_times(_657968, _658199, _658195)), times_times(_657968, _658199, _658197))))]]], (5629 ^ _434076) ^ [_658596] : [-(nat_1(number_number_of(int, _658596)) = number_number_of(nat, _658596))], (5631 ^ _434076) ^ [_658682] : [-(number_number_of(nat, _658682) = nat_1(number_number_of(int, _658682)))], (5633 ^ _434076) ^ [_658783] : [linord581940658strict(_658783), 5636 ^ _434076 : [(5637 ^ _434076) ^ [_658992, _658994] : [plus_plus(_658783, times_times(_658783, _658994, _658994), times_times(_658783, _658992, _658992)) = zero_zero(_658783), 5640 ^ _434076 : [(5641 ^ _434076) ^ [] : [-(ti(_658783, _658994) = zero_zero(_658783))], (5643 ^ _434076) ^ [] : [-(ti(_658783, _658992) = zero_zero(_658783))]]], (5645 ^ _434076) ^ [_659287, _659289] : [-(plus_plus(_658783, times_times(_658783, _659289, _659289), times_times(_658783, _659287, _659287)) = zero_zero(_658783)), ti(_658783, _659289) = zero_zero(_658783), ti(_658783, _659287) = zero_zero(_658783)]]], (5655 ^ _434076) ^ [_659639] : [semiri456707255roduct(_659639), 5658 ^ _434076 : [(5659 ^ _434076) ^ [_659897, _659899, _659901, _659903, _659905] : [-(ti(_659639, _659897) = zero_zero(_659639)), plus_plus(_659639, _659901, times_times(_659639, _659897, _659905)) = plus_plus(_659639, _659899, times_times(_659639, _659897, _659903)), ti(_659639, _659901) = ti(_659639, _659899), -(ti(_659639, _659905) = ti(_659639, _659903))]]], (5673 ^ _434076) ^ [] : [-(one_one(nat) = nat_1(one_one(int)))], (5675 ^ _434076) ^ [_660460] : [linordered_semidom(_660460), 5678 ^ _434076 : [(5679 ^ _434076) ^ [_660668, _660670] : [hBOOL(hAPP(_660460, bool, hAPP(_660460, fun(_660460, bool), ord_less(_660460), one_one(_660460)), _660668)), hBOOL(hAPP(_660460, bool, hAPP(_660460, fun(_660460, bool), ord_less(_660460), one_one(_660460)), _660670)), -(hBOOL(hAPP(_660460, bool, hAPP(_660460, fun(_660460, bool), ord_less(_660460), one_one(_660460)), times_times(_660460, _660668, _660670))))]]], (5689 ^ _434076) ^ [_661074] : [linord219039673up_add(_661074), 5692 ^ _434076 : [(5693 ^ _434076) ^ [_661270] : [hBOOL(hAPP(_661074, bool, hAPP(_661074, fun(_661074, bool), ord_less_eq(_661074), zero_zero(_661074)), plus_plus(_661074, _661270, _661270))), -(hBOOL(hAPP(_661074, bool, hAPP(_661074, fun(_661074, bool), ord_less_eq(_661074), zero_zero(_661074)), _661270)))], (5699 ^ _434076) ^ [_661506] : [hBOOL(hAPP(_661074, bool, hAPP(_661074, fun(_661074, bool), ord_less_eq(_661074), zero_zero(_661074)), _661506)), -(hBOOL(hAPP(_661074, bool, hAPP(_661074, fun(_661074, bool), ord_less_eq(_661074), zero_zero(_661074)), plus_plus(_661074, _661506, _661506))))]]], (5705 ^ _434076) ^ [_661783] : [linord219039673up_add(_661783), 5708 ^ _434076 : [(5709 ^ _434076) ^ [_661979] : [hBOOL(hAPP(_661783, bool, hAPP(_661783, fun(_661783, bool), ord_less_eq(_661783), plus_plus(_661783, _661979, _661979)), zero_zero(_661783))), -(hBOOL(hAPP(_661783, bool, hAPP(_661783, fun(_661783, bool), ord_less_eq(_661783), _661979), zero_zero(_661783))))], (5715 ^ _434076) ^ [_662215] : [hBOOL(hAPP(_661783, bool, hAPP(_661783, fun(_661783, bool), ord_less_eq(_661783), _662215), zero_zero(_661783))), -(hBOOL(hAPP(_661783, bool, hAPP(_661783, fun(_661783, bool), ord_less_eq(_661783), plus_plus(_661783, _662215, _662215)), zero_zero(_661783))))]]], (5721 ^ _434076) ^ [_662492] : [ordere216010020id_add(_662492), 5724 ^ _434076 : [(5725 ^ _434076) ^ [_662700, _662702] : [hBOOL(hAPP(_662492, bool, hAPP(_662492, fun(_662492, bool), ord_less_eq(_662492), zero_zero(_662492)), _662700)), hBOOL(hAPP(_662492, bool, hAPP(_662492, fun(_662492, bool), ord_less_eq(_662492), zero_zero(_662492)), _662702)), -(hBOOL(hAPP(_662492, bool, hAPP(_662492, fun(_662492, bool), ord_less_eq(_662492), zero_zero(_662492)), plus_plus(_662492, _662700, _662702))))]]], (5735 ^ _434076) ^ [_663106] : [ordere216010020id_add(_663106), 5738 ^ _434076 : [(5739 ^ _434076) ^ [_663322, _663324] : [hBOOL(hAPP(_663106, bool, hAPP(_663106, fun(_663106, bool), ord_less_eq(_663106), zero_zero(_663106)), _663322)), hBOOL(hAPP(_663106, bool, hAPP(_663106, fun(_663106, bool), ord_less_eq(_663106), zero_zero(_663106)), _663324)), 5746 ^ _434076 : [(5747 ^ _434076) ^ [] : [plus_plus(_663106, _663322, _663324) = zero_zero(_663106), 5750 ^ _434076 : [(5751 ^ _434076) ^ [] : [-(ti(_663106, _663322) = zero_zero(_663106))], (5753 ^ _434076) ^ [] : [-(ti(_663106, _663324) = zero_zero(_663106))]]], (5755 ^ _434076) ^ [] : [-(plus_plus(_663106, _663322, _663324) = zero_zero(_663106)), ti(_663106, _663322) = zero_zero(_663106), ti(_663106, _663324) = zero_zero(_663106)]]]]], (5765 ^ _434076) ^ [_664160] : [ordere216010020id_add(_664160), 5768 ^ _434076 : [(5769 ^ _434076) ^ [_664383, _664385, _664387] : [hBOOL(hAPP(_664160, bool, hAPP(_664160, fun(_664160, bool), ord_less_eq(_664160), zero_zero(_664160)), _664383)), hBOOL(hAPP(_664160, bool, hAPP(_664160, fun(_664160, bool), ord_less_eq(_664160), _664387), _664385)), -(hBOOL(hAPP(_664160, bool, hAPP(_664160, fun(_664160, bool), ord_less_eq(_664160), _664387), plus_plus(_664160, _664383, _664385))))]]], (5779 ^ _434076) ^ [_664791] : [ordere216010020id_add(_664791), 5782 ^ _434076 : [(5783 ^ _434076) ^ [_665014, _665016, _665018] : [hBOOL(hAPP(_664791, bool, hAPP(_664791, fun(_664791, bool), ord_less_eq(_664791), zero_zero(_664791)), _665014)), hBOOL(hAPP(_664791, bool, hAPP(_664791, fun(_664791, bool), ord_less_eq(_664791), _665018), _665016)), -(hBOOL(hAPP(_664791, bool, hAPP(_664791, fun(_664791, bool), ord_less_eq(_664791), _665018), plus_plus(_664791, _665016, _665014))))]]], (5793 ^ _434076) ^ [_665422] : [ordere216010020id_add(_665422), 5796 ^ _434076 : [(5797 ^ _434076) ^ [_665630, _665632] : [hBOOL(hAPP(_665422, bool, hAPP(_665422, fun(_665422, bool), ord_less_eq(_665422), _665630), zero_zero(_665422))), hBOOL(hAPP(_665422, bool, hAPP(_665422, fun(_665422, bool), ord_less_eq(_665422), _665632), zero_zero(_665422))), -(hBOOL(hAPP(_665422, bool, hAPP(_665422, fun(_665422, bool), ord_less_eq(_665422), plus_plus(_665422, _665630, _665632)), zero_zero(_665422))))]]], (5807 ^ _434076) ^ [_666036] : [ordere223160158up_add(_666036), 5810 ^ _434076 : [(5811 ^ _434076) ^ [_666280, _666282, _666284, _666286] : [hBOOL(hAPP(_666036, bool, hAPP(_666036, fun(_666036, bool), ord_less(_666036), _666282), _666280)), hBOOL(hAPP(_666036, bool, hAPP(_666036, fun(_666036, bool), ord_less_eq(_666036), _666286), _666284)), -(hBOOL(hAPP(_666036, bool, hAPP(_666036, fun(_666036, bool), ord_less(_666036), plus_plus(_666036, _666282, _666286)), plus_plus(_666036, _666280, _666284))))]]], (5821 ^ _434076) ^ [_666702] : [ordere223160158up_add(_666702), 5824 ^ _434076 : [(5825 ^ _434076) ^ [_666946, _666948, _666950, _666952] : [hBOOL(hAPP(_666702, bool, hAPP(_666702, fun(_666702, bool), ord_less_eq(_666702), _666948), _666946)), hBOOL(hAPP(_666702, bool, hAPP(_666702, fun(_666702, bool), ord_less(_666702), _666952), _666950)), -(hBOOL(hAPP(_666702, bool, hAPP(_666702, fun(_666702, bool), ord_less(_666702), plus_plus(_666702, _666948, _666952)), plus_plus(_666702, _666946, _666950))))]]], (5835 ^ _434076) ^ [_667368] : [linordered_semidom(_667368), hBOOL(hAPP(_667368, bool, hAPP(_667368, fun(_667368, bool), ord_less_eq(_667368), one_one(_667368)), zero_zero(_667368)))], (5841 ^ _434076) ^ [_667593] : [linordered_semidom(_667593), -(hBOOL(hAPP(_667593, bool, hAPP(_667593, fun(_667593, bool), ord_less_eq(_667593), zero_zero(_667593)), one_one(_667593))))], (5847 ^ _434076) ^ [_667817] : [5854 ^ _434076 : [(5855 ^ _434076) ^ [_668077, _668079, _668081] : [-(times_times(_667817, number_number_of(_667817, _668081), plus_plus(_667817, _668079, _668077)) = plus_plus(_667817, times_times(_667817, number_number_of(_667817, _668081), _668079), times_times(_667817, number_number_of(_667817, _668081), _668077)))]], number(_667817), semiring(_667817)], (5857 ^ _434076) ^ [_668210] : [5864 ^ _434076 : [(5865 ^ _434076) ^ [_668470, _668472, _668474] : [-(times_times(_668210, plus_plus(_668210, _668474, _668472), number_number_of(_668210, _668470)) = plus_plus(_668210, times_times(_668210, _668474, number_number_of(_668210, _668470)), times_times(_668210, _668472, number_number_of(_668210, _668470))))]], number(_668210), semiring(_668210)], (5867 ^ _434076) ^ [_668603] : [comm_semiring_1(_668603), 5870 ^ _434076 : [(5871 ^ _434076) ^ [_668729] : [-(plus_plus(_668603, _668729, _668729) = times_times(_668603, plus_plus(_668603, one_one(_668603), one_one(_668603)), _668729))]]], (5873 ^ _434076) ^ [_668845] : [comm_semiring_1(_668845), 5876 ^ _434076 : [(5877 ^ _434076) ^ [_668992, _668994] : [-(plus_plus(_668845, _668994, times_times(_668845, _668992, _668994)) = times_times(_668845, plus_plus(_668845, _668992, one_one(_668845)), _668994))]]], (5879 ^ _434076) ^ [_669112] : [comm_semiring_1(_669112), 5882 ^ _434076 : [(5883 ^ _434076) ^ [_669259, _669261] : [-(plus_plus(_669112, times_times(_669112, _669261, _669259), _669259) = times_times(_669112, plus_plus(_669112, _669261, one_one(_669112)), _669259))]]], (5885 ^ _434076) ^ [_669379] : [number(_669379), linorder(_669379), 5892 ^ _434076 : [(5893 ^ _434076) ^ [_669683, _669685] : [hBOOL(hAPP(_669379, bool, hAPP(_669379, fun(_669379, bool), ord_less_eq(_669379), number_number_of(_669379, _669685)), number_number_of(_669379, _669683))), hBOOL(hAPP(_669379, bool, hAPP(_669379, fun(_669379, bool), ord_less(_669379), number_number_of(_669379, _669683)), number_number_of(_669379, _669685)))], (5899 ^ _434076) ^ [_669934, _669936] : [-(hBOOL(hAPP(_669379, bool, hAPP(_669379, fun(_669379, bool), ord_less(_669379), number_number_of(_669379, _669934)), number_number_of(_669379, _669936)))), -(hBOOL(hAPP(_669379, bool, hAPP(_669379, fun(_669379, bool), ord_less_eq(_669379), number_number_of(_669379, _669936)), number_number_of(_669379, _669934))))]]], (5905 ^ _434076) ^ [_670230] : [linordered_semidom(_670230), 5908 ^ _434076 : [(5909 ^ _434076) ^ [_670420, _670422] : [hBOOL(hAPP(_670230, bool, hAPP(_670230, fun(_670230, bool), ord_less_eq(_670230), zero_zero(_670230)), _670420)), -(hBOOL(hAPP(_670230, bool, hAPP(_670230, fun(_670230, bool), ord_less_eq(_670230), zero_zero(_670230)), hAPP(nat, _670230, power_power(_670230, _670420), _670422))))]]], (5915 ^ _434076) ^ [_670709] : [linordered_semidom(_670709), 5918 ^ _434076 : [(5919 ^ _434076) ^ [_670944, _670946, _670948] : [hBOOL(hAPP(_670709, bool, hAPP(_670709, fun(_670709, bool), ord_less_eq(_670709), _670946), _670944)), hBOOL(hAPP(_670709, bool, hAPP(_670709, fun(_670709, bool), ord_less_eq(_670709), zero_zero(_670709)), _670946)), -(hBOOL(hAPP(_670709, bool, hAPP(_670709, fun(_670709, bool), ord_less_eq(_670709), hAPP(nat, _670709, power_power(_670709, _670946), _670948)), hAPP(nat, _670709, power_power(_670709, _670944), _670948))))]]], (5929 ^ _434076) ^ [_671419, _671421] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), minus_minus(nat, _671421, _671419))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _671419), _671421)))], (5935 ^ _434076) ^ [_671615, _671617] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _671615), _671617)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), minus_minus(nat, _671617, _671615))))], (5941 ^ _434076) ^ [_671861, _671863] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _671861)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _671863)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _671863, _671861)), _671863)))], (5951 ^ _434076) ^ [_672187, _672189] : [-(minus_minus(nat, _672189, plus_plus(nat, _672189, _672187)) = zero_zero(nat))], (5953 ^ _434076) ^ [_672290] : [linordered_semidom(_672290), 5956 ^ _434076 : [(5957 ^ _434076) ^ [_672480, _672482] : [hBOOL(hAPP(_672290, bool, hAPP(_672290, fun(_672290, bool), ord_less_eq(_672290), one_one(_672290)), _672480)), -(hBOOL(hAPP(_672290, bool, hAPP(_672290, fun(_672290, bool), ord_less_eq(_672290), one_one(_672290)), hAPP(nat, _672290, power_power(_672290, _672480), _672482))))]]], (5963 ^ _434076) ^ [_672826, _672828, _672830] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _672830), minus_minus(nat, _672828, _672826))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _672830, _672826)), _672828)))], (5969 ^ _434076) ^ [_673046, _673048, _673050] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, _673050, _673046)), _673048)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _673050), minus_minus(nat, _673048, _673046))))], (5975 ^ _434076) ^ [_673316, _673318] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _673318), _673316))), -(plus_plus(nat, _673316, minus_minus(nat, _673318, _673316)) = _673318)], (5981 ^ _434076) ^ [_673549] : [linordered_semidom(_673549), 5984 ^ _434076 : [(5985 ^ _434076) ^ [_673682] : [-(hBOOL(hAPP(_673549, bool, hAPP(_673549, fun(_673549, bool), ord_less_eq(_673549), zero_zero(_673549)), hAPP(nat, _673549, semiring_1_of_nat(_673549), _673682))))]]], (5987 ^ _434076) ^ [_673805] : [linordered_semidom(_673805), 5990 ^ _434076 : [(5991 ^ _434076) ^ [_673938] : [-(hBOOL(hAPP(_673805, bool, hAPP(_673805, fun(_673805, bool), ord_less_eq(_673805), zero_zero(_673805)), hAPP(nat, _673805, semiring_1_of_nat(_673805), _673938))))]]], (5993 ^ _434076) ^ [_674061] : [monoid_mult(_674061), 5996 ^ _434076 : [(5997 ^ _434076) ^ [_674241, _674243, _674245] : [-(hAPP(nat, _674061, power_power(_674061, _674245), plus_plus(nat, _674243, _674241)) = times_times(_674061, hAPP(nat, _674061, power_power(_674061, _674245), _674243), hAPP(nat, _674061, power_power(_674061, _674245), _674241)))]]], (5999 ^ _434076) ^ [_674377] : [comm_semiring_1(_674377), 6002 ^ _434076 : [(6003 ^ _434076) ^ [_674557, _674559, _674561] : [-(times_times(_674377, hAPP(nat, _674377, power_power(_674377, _674561), _674559), hAPP(nat, _674377, power_power(_674377, _674561), _674557)) = hAPP(nat, _674377, power_power(_674377, _674561), plus_plus(nat, _674559, _674557)))]]], (6005 ^ _434076) ^ [_674722] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), bit1(_674722))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _674722)))], (6011 ^ _434076) ^ [_674898] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _674898)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), bit1(_674898))))], (6017 ^ _434076) ^ [_675153, _675155] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_675155)), bit1(_675153))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _675155), _675153)))], (6023 ^ _434076) ^ [_675359, _675361] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _675361), _675359)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_675361)), bit1(_675359))))], (6029 ^ _434076) ^ [_675644, _675646] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_675646)), bit1(_675644))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _675646), _675644)))], (6035 ^ _434076) ^ [_675850, _675852] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _675852), _675850)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_675852)), bit1(_675850))))], (6041 ^ _434076) ^ [_676121] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), bit0(_676121))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _676121)))], (6047 ^ _434076) ^ [_676297] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _676297)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), bit0(_676297))))], (6053 ^ _434076) ^ [_676538] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_676538)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _676538), pls)))], (6059 ^ _434076) ^ [_676734] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _676734), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_676734)), pls)))], (6065 ^ _434076) ^ [_676980, _676982] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _676980)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), times_times(int, _676980, _676982))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _676982)))], (6075 ^ _434076) ^ [_677325, _677327, _677329] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _677327), _677325)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _677329)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), times_times(int, _677329, _677327)), times_times(int, _677329, _677325))))], (6085 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), one_one(int))))], (6087 ^ _434076) ^ [_677747, _677749] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _677747)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _677749)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), plus_plus(int, _677747, _677749))))], (6097 ^ _434076) ^ [_678064] : [semiring_1(_678064), 6100 ^ _434076 : [(6101 ^ _434076) ^ [_678234] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _678234)), -(hAPP(nat, _678064, semiring_1_of_nat(_678064), nat_1(times_times(int, number_number_of(int, bit0(bit1(pls))), _678234))) = plus_plus(_678064, hAPP(nat, _678064, semiring_1_of_nat(_678064), nat_1(_678234)), hAPP(nat, _678064, semiring_1_of_nat(_678064), nat_1(_678234))))]]], (6107 ^ _434076) ^ [_678557, _678559, _678561, _678563] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _678559), _678557)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _678563), _678561)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, _678559, _678563)), plus_plus(int, _678557, _678561))))], (6117 ^ _434076) ^ [_678917] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _678917))))], (6130 ^ _434076) ^ [_679452] : [6131 ^ _434076 : [(6132 ^ _434076) ^ [_679548] : [hBOOL(hAPP(int, bool, _679452, hAPP(nat, int, semiring_1_of_nat(int), _679548)))]], 6134 ^ _434076 : [(6135 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 6133 ^ [_679452])))], (6137 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, _679452, 6133 ^ [_679452])))]]], (6119 ^ _434076) ^ [_679048] : [-(hBOOL(hAPP(int, bool, _679048, hAPP(nat, int, semiring_1_of_nat(int), 6126 ^ [_679048])))), 6120 ^ _434076 : [(6121 ^ _434076) ^ [_679160] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _679160)), hBOOL(hAPP(int, bool, _679048, _679160))]]], (6139 ^ _434076) ^ [_679872] : [6141 ^ _434076 : [(6142 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 6140 ^ [_679872])))], (6144 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _679872, 6140 ^ [_679872]))]], 6145 ^ _434076 : [(6146 ^ _434076) ^ [_680151] : [-(hBOOL(hAPP(int, bool, _679872, hAPP(nat, int, semiring_1_of_nat(int), _680151))))]]], (6148 ^ _434076) ^ [_680227] : [hBOOL(hAPP(int, bool, _680227, hAPP(nat, int, semiring_1_of_nat(int), 6149 ^ [_680227]))), 6152 ^ _434076 : [(6153 ^ _434076) ^ [_680446] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _680446)), -(hBOOL(hAPP(int, bool, _680227, _680446)))]]], (6159 ^ _434076) ^ [_680652] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _680652))))], (6161 ^ _434076) ^ [_680768, _680770] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _680768)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, power_power(int, _680768), _680770))))], (6167 ^ _434076) ^ [_681039, _681041] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _681041), _681039)), -(ti(int, _681039) = plus_plus(int, _681041, hAPP(nat, int, semiring_1_of_nat(int), 6170 ^ [_681039, _681041])))], (6174 ^ _434076) ^ [_681312, _681314] : [6175 ^ _434076 : [(6176 ^ _434076) ^ [_681403] : [ti(int, _681312) = plus_plus(int, _681314, hAPP(nat, int, semiring_1_of_nat(int), _681403))]], -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _681314), _681312)))], (6180 ^ _434076) ^ [_681587, _681589, _681591] : [-(hAPP(nat, int, power_power(int, _681591), plus_plus(nat, _681589, _681587)) = times_times(int, hAPP(nat, int, power_power(int, _681591), _681589), hAPP(nat, int, power_power(int, _681591), _681587)))], (6182 ^ _434076) ^ [_681716] : [number_semiring(_681716), 6185 ^ _434076 : [(6186 ^ _434076) ^ [_681865] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _681865)), -(plus_plus(_681716, one_one(_681716), number_number_of(_681716, _681865)) = number_number_of(_681716, succ(_681865)))]]], (6192 ^ _434076) ^ [_682104] : [number_semiring(_682104), 6195 ^ _434076 : [(6196 ^ _434076) ^ [_682253] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _682253)), -(plus_plus(_682104, number_number_of(_682104, _682253), one_one(_682104)) = number_number_of(_682104, succ(_682253)))]]], (6202 ^ _434076) ^ [_682492] : [comm_semiring_1(_682492), 6205 ^ _434076 : [(6206 ^ _434076) ^ [_682653, _682655] : [-(hAPP(nat, _682492, power_power(_682492, _682655), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _682653)) = times_times(_682492, hAPP(nat, _682492, power_power(_682492, _682655), _682653), hAPP(nat, _682492, power_power(_682492, _682655), _682653)))]]], (6208 ^ _434076) ^ [_682787] : [number_ring(_682787), 6211 ^ _434076 : [(6212 ^ _434076) ^ [_682960, _682962, _682964] : [-(plus_plus(_682787, number_number_of(_682787, _682964), minus_minus(_682787, number_number_of(_682787, _682962), _682960)) = minus_minus(_682787, number_number_of(_682787, plus_plus(int, _682964, _682962)), _682960))]]], (6214 ^ _434076) ^ [_683103, _683105] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _683103)), 6217 ^ _434076 : [(6218 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_683105)), nat_1(_683103))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _683105), _683103)))], (6224 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _683105), _683103)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_683105)), nat_1(_683103))))]]], (6230 ^ _434076) ^ [_683666, _683668] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_683668)), nat_1(_683666))), 6233 ^ _434076 : [(6234 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _683666)))], (6236 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _683668), _683666)))]]], (6238 ^ _434076) ^ [_683955, _683957] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), nat_1(_683957)), nat_1(_683955)))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _683955)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _683957), _683955))], (6248 ^ _434076) ^ [_684294] : [linordered_ring(_684294), 6251 ^ _434076 : [(6252 ^ _434076) ^ [_684452, _684454] : [hBOOL(hAPP(_684294, bool, hAPP(_684294, fun(_684294, bool), ord_less(_684294), plus_plus(_684294, times_times(_684294, _684454, _684454), times_times(_684294, _684452, _684452))), zero_zero(_684294)))]]], (6254 ^ _434076) ^ [_684582] : [linord581940658strict(_684582), 6257 ^ _434076 : [(6268 ^ _434076) ^ [_685151, _685153] : [6269 ^ _434076 : [(6270 ^ _434076) ^ [] : [-(ti(_684582, _685153) = zero_zero(_684582))], (6272 ^ _434076) ^ [] : [-(ti(_684582, _685151) = zero_zero(_684582))]], -(hBOOL(hAPP(_684582, bool, hAPP(_684582, fun(_684582, bool), ord_less(_684582), zero_zero(_684582)), plus_plus(_684582, times_times(_684582, _685153, _685153), times_times(_684582, _685151, _685151)))))], (6258 ^ _434076) ^ [_684809, _684811] : [hBOOL(hAPP(_684582, bool, hAPP(_684582, fun(_684582, bool), ord_less(_684582), zero_zero(_684582)), plus_plus(_684582, times_times(_684582, _684811, _684811), times_times(_684582, _684809, _684809)))), ti(_684582, _684811) = zero_zero(_684582), ti(_684582, _684809) = zero_zero(_684582)]]], (6276 ^ _434076) ^ [_685563, _685565] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _685565), nat_1(_685563))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _685565)), _685563)))], (6282 ^ _434076) ^ [_685775, _685777] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _685777)), _685775)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _685777), nat_1(_685775))))], (6288 ^ _434076) ^ [_686023] : [ordere216010020id_add(_686023), 6291 ^ _434076 : [(6292 ^ _434076) ^ [_686231, _686233] : [hBOOL(hAPP(_686023, bool, hAPP(_686023, fun(_686023, bool), ord_less(_686023), zero_zero(_686023)), _686231)), hBOOL(hAPP(_686023, bool, hAPP(_686023, fun(_686023, bool), ord_less_eq(_686023), zero_zero(_686023)), _686233)), -(hBOOL(hAPP(_686023, bool, hAPP(_686023, fun(_686023, bool), ord_less(_686023), zero_zero(_686023)), plus_plus(_686023, _686231, _686233))))]]], (6302 ^ _434076) ^ [_686637] : [ordere216010020id_add(_686637), 6305 ^ _434076 : [(6306 ^ _434076) ^ [_686845, _686847] : [hBOOL(hAPP(_686637, bool, hAPP(_686637, fun(_686637, bool), ord_less_eq(_686637), zero_zero(_686637)), _686845)), hBOOL(hAPP(_686637, bool, hAPP(_686637, fun(_686637, bool), ord_less(_686637), zero_zero(_686637)), _686847)), -(hBOOL(hAPP(_686637, bool, hAPP(_686637, fun(_686637, bool), ord_less(_686637), zero_zero(_686637)), plus_plus(_686637, _686845, _686847))))]]], (6316 ^ _434076) ^ [_687251] : [ordere216010020id_add(_687251), 6319 ^ _434076 : [(6320 ^ _434076) ^ [_687474, _687476, _687478] : [hBOOL(hAPP(_687251, bool, hAPP(_687251, fun(_687251, bool), ord_less(_687251), zero_zero(_687251)), _687474)), hBOOL(hAPP(_687251, bool, hAPP(_687251, fun(_687251, bool), ord_less_eq(_687251), _687478), _687476)), -(hBOOL(hAPP(_687251, bool, hAPP(_687251, fun(_687251, bool), ord_less(_687251), _687478), plus_plus(_687251, _687474, _687476))))]]], (6330 ^ _434076) ^ [_687882] : [ordere216010020id_add(_687882), 6333 ^ _434076 : [(6334 ^ _434076) ^ [_688105, _688107, _688109] : [hBOOL(hAPP(_687882, bool, hAPP(_687882, fun(_687882, bool), ord_less_eq(_687882), zero_zero(_687882)), _688105)), hBOOL(hAPP(_687882, bool, hAPP(_687882, fun(_687882, bool), ord_less(_687882), _688109), _688107)), -(hBOOL(hAPP(_687882, bool, hAPP(_687882, fun(_687882, bool), ord_less(_687882), _688109), plus_plus(_687882, _688105, _688107))))]]], (6344 ^ _434076) ^ [_688513] : [ordere216010020id_add(_688513), 6347 ^ _434076 : [(6348 ^ _434076) ^ [_688721, _688723] : [hBOOL(hAPP(_688513, bool, hAPP(_688513, fun(_688513, bool), ord_less(_688513), _688721), zero_zero(_688513))), hBOOL(hAPP(_688513, bool, hAPP(_688513, fun(_688513, bool), ord_less_eq(_688513), _688723), zero_zero(_688513))), -(hBOOL(hAPP(_688513, bool, hAPP(_688513, fun(_688513, bool), ord_less(_688513), plus_plus(_688513, _688721, _688723)), zero_zero(_688513))))]]], (6358 ^ _434076) ^ [_689127] : [ordere216010020id_add(_689127), 6361 ^ _434076 : [(6362 ^ _434076) ^ [_689335, _689337] : [hBOOL(hAPP(_689127, bool, hAPP(_689127, fun(_689127, bool), ord_less_eq(_689127), _689335), zero_zero(_689127))), hBOOL(hAPP(_689127, bool, hAPP(_689127, fun(_689127, bool), ord_less(_689127), _689337), zero_zero(_689127))), -(hBOOL(hAPP(_689127, bool, hAPP(_689127, fun(_689127, bool), ord_less(_689127), plus_plus(_689127, _689335, _689337)), zero_zero(_689127))))]]], (6372 ^ _434076) ^ [_689741] : [linordered_semidom(_689741), 6375 ^ _434076 : [(6376 ^ _434076) ^ [_689976, _689978, _689980] : [hBOOL(hAPP(_689741, bool, hAPP(_689741, fun(_689741, bool), ord_less(_689741), hAPP(nat, _689741, power_power(_689741, _689980), _689978)), hAPP(nat, _689741, power_power(_689741, _689976), _689978))), hBOOL(hAPP(_689741, bool, hAPP(_689741, fun(_689741, bool), ord_less_eq(_689741), zero_zero(_689741)), _689976)), -(hBOOL(hAPP(_689741, bool, hAPP(_689741, fun(_689741, bool), ord_less(_689741), _689980), _689976)))]]], (6386 ^ _434076) ^ [_690408] : [linordered_semidom(_690408), 6389 ^ _434076 : [(6390 ^ _434076) ^ [_690602, _690604] : [hBOOL(hAPP(_690408, bool, hAPP(_690408, fun(_690408, bool), ord_less(_690408), one_one(_690408)), _690602)), -(hBOOL(hAPP(_690408, bool, hAPP(_690408, fun(_690408, bool), ord_less(_690408), one_one(_690408)), times_times(_690408, _690602, hAPP(nat, _690408, power_power(_690408, _690602), _690604)))))]]], (6396 ^ _434076) ^ [_690899] : [linordered_semidom(_690899), 6399 ^ _434076 : [(6400 ^ _434076) ^ [_691099, _691101] : [hBOOL(hAPP(_690899, bool, hAPP(_690899, fun(_690899, bool), ord_less(_690899), one_one(_690899)), _691099)), -(hBOOL(hAPP(_690899, bool, hAPP(_690899, fun(_690899, bool), ord_less(_690899), hAPP(nat, _690899, power_power(_690899, _691099), _691101)), times_times(_690899, _691099, hAPP(nat, _690899, power_power(_690899, _691099), _691101)))))]]], (6406 ^ _434076) ^ [_691408] : [number_ring(_691408), 6409 ^ _434076 : [(6410 ^ _434076) ^ [_691528] : [-(times_times(_691408, _691528, number_number_of(_691408, bit1(pls))) = ti(_691408, _691528))]]], (6412 ^ _434076) ^ [_691638] : [number_ring(_691638), 6415 ^ _434076 : [(6416 ^ _434076) ^ [_691758] : [-(times_times(_691638, number_number_of(_691638, bit1(pls)), _691758) = ti(_691638, _691758))]]], (6434 ^ _434076) ^ [_692494, _692496, _692498] : [-(hBOOL(hAPP(nat, bool, _692498, minus_minus(nat, _692496, _692494)))), 6437 ^ _434076 : [(6438 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _692496), _692494)))], (6440 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _692498, zero_zero(nat)))]], 6442 ^ _434076 : [(6443 ^ _434076) ^ [] : [-(_692496 = plus_plus(nat, _692494, 6441 ^ [_692494, _692496, _692498]))], (6445 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _692498, 6441 ^ [_692494, _692496, _692498]))]]], (6418 ^ _434076) ^ [_691925, _691927, _691929] : [hBOOL(hAPP(nat, bool, _691929, minus_minus(nat, _691927, _691925))), 6421 ^ _434076 : [(6422 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _691927), _691925)), -(hBOOL(hAPP(nat, bool, _691929, zero_zero(nat))))], (6428 ^ _434076) ^ [_692289] : [_691927 = plus_plus(nat, _691925, _692289), -(hBOOL(hAPP(nat, bool, _691929, _692289)))]]], (6465 ^ _434076) ^ [_693715, _693717, _693719] : [-(hBOOL(hAPP(nat, bool, _693719, minus_minus(nat, _693717, _693715)))), 6468 ^ _434076 : [(6469 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _693717), _693715)))], (6471 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _693719, zero_zero(nat)))]], 6473 ^ _434076 : [(6474 ^ _434076) ^ [] : [-(_693717 = plus_plus(nat, _693715, 6472 ^ [_693715, _693717, _693719]))], (6476 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _693719, 6472 ^ [_693715, _693717, _693719]))]]], (6449 ^ _434076) ^ [_693154, _693156, _693158] : [hBOOL(hAPP(nat, bool, _693158, minus_minus(nat, _693156, _693154))), 6452 ^ _434076 : [(6453 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _693156), _693154)), -(hBOOL(hAPP(nat, bool, _693158, zero_zero(nat))))], (6459 ^ _434076) ^ [_693512] : [_693156 = plus_plus(nat, _693154, _693512), -(hBOOL(hAPP(nat, bool, _693158, _693512)))]]], (6480 ^ _434076) ^ [_694339] : [zero_zero(nat) = number_number_of(nat, _694339), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _694339), pls)))], (6486 ^ _434076) ^ [_694519] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _694519), pls)), -(zero_zero(nat) = number_number_of(nat, _694519))], (6492 ^ _434076) ^ [_694764] : [number_number_of(nat, _694764) = zero_zero(nat), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _694764), pls)))], (6498 ^ _434076) ^ [_694944] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _694944), pls)), -(number_number_of(nat, _694944) = zero_zero(nat))], (6504 ^ _434076) ^ [_695189] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), bit1(_695189))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _695189)))], (6510 ^ _434076) ^ [_695365] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _695365)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), bit1(_695365))))], (6516 ^ _434076) ^ [_695606] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_695606)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _695606), pls)))], (6522 ^ _434076) ^ [_695802] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _695802), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_695802)), pls)))], (6528 ^ _434076) ^ [_696077, _696079] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_696079)), bit1(_696077))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _696079), _696077)))], (6534 ^ _434076) ^ [_696283, _696285] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _696285), _696283)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_696285)), bit1(_696283))))], (6540 ^ _434076) ^ [_696568, _696570] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_696570)), bit1(_696568))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _696570), _696568)))], (6546 ^ _434076) ^ [_696774, _696776] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _696776), _696774)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_696776)), bit1(_696774))))], (6552 ^ _434076) ^ [_697059, _697061] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_697061)), bit0(_697059))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _697061), _697059)))], (6558 ^ _434076) ^ [_697265, _697267] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _697267), _697265)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_697267)), bit0(_697265))))], (6564 ^ _434076) ^ [_697550, _697552] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_697552)), bit0(_697550))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _697552), _697550)))], (6570 ^ _434076) ^ [_697756, _697758] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _697758), _697756)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_697758)), bit0(_697756))))], (6576 ^ _434076) ^ [_697997, _697999] : [-(times_times(int, bit1(_697999), _697997) = plus_plus(int, bit0(times_times(int, _697999, _697997)), _697997))], (6578 ^ _434076) ^ [_698122, _698124] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _698122)), 6581 ^ _434076 : [(6582 ^ _434076) ^ [] : [times_times(int, _698122, _698124) = one_one(int), 6585 ^ _434076 : [(6586 ^ _434076) ^ [] : [-(ti(int, _698122) = one_one(int))], (6588 ^ _434076) ^ [] : [-(ti(int, _698124) = one_one(int))]]], (6590 ^ _434076) ^ [] : [-(times_times(int, _698122, _698124) = one_one(int)), ti(int, _698122) = one_one(int), ti(int, _698124) = one_one(int)]]], (6600 ^ _434076) ^ [_698793] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), _698793)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _698793)))], (6606 ^ _434076) ^ [_698965] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _698965)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), _698965)))], (6612 ^ _434076) ^ [_699202] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _699202)), zero_zero(int))), -(_699202 = zero_zero(nat))], (6618 ^ _434076) ^ [_699386] : [_699386 = zero_zero(nat), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _699386)), zero_zero(int))))], (6624 ^ _434076) ^ [] : [-(succ(pls) = bit1(pls))], (6626 ^ _434076) ^ [_699644] : [-(succ(bit0(_699644)) = bit1(_699644))], (6628 ^ _434076) ^ [_699728] : [-(succ(bit1(_699728)) = bit0(succ(_699728)))], (6630 ^ _434076) ^ [_699872, _699874] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _699874), plus_plus(int, _699872, one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _699874), _699872)))], (6636 ^ _434076) ^ [_700078, _700080] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _700080), _700078)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _700080), plus_plus(int, _700078, one_one(int)))))], (6642 ^ _434076) ^ [_700363, _700365] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, _700365, one_one(int))), _700363)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _700365), _700363)))], (6648 ^ _434076) ^ [_700569, _700571] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _700571), _700569)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, _700571, one_one(int))), _700569)))], (6654 ^ _434076) ^ [_700825, _700827] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _700827), _700825)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, _700827, one_one(int))), _700825)))], (6660 ^ _434076) ^ [_701050] : [-(succ(_701050) = plus_plus(int, _701050, one_one(int)))], (6662 ^ _434076) ^ [_701149] : [number_ring(_701149), 6665 ^ _434076 : [(6666 ^ _434076) ^ [_701325, _701327] : [-(hAPP(nat, _701149, power_power(_701149, minus_minus(_701149, _701327, _701325)), number_number_of(nat, bit0(bit1(pls)))) = minus_minus(_701149, plus_plus(_701149, hAPP(nat, _701149, power_power(_701149, _701327), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _701149, power_power(_701149, _701325), number_number_of(nat, bit0(bit1(pls))))), times_times(_701149, times_times(_701149, number_number_of(_701149, bit0(bit1(pls))), _701327), _701325)))]]], (6668 ^ _434076) ^ [_701503] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), nat_1(_701503))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _701503)))], (6674 ^ _434076) ^ [_701679] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _701679)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), nat_1(_701679))))], (6680 ^ _434076) ^ [] : [-(number_number_of(nat, bit1(bit1(pls))) = nat_1(number_number_of(int, bit1(bit1(pls)))))], (6698 ^ _434076) ^ [_702538, _702540] : [-(hBOOL(hAPP(nat, bool, _702540, nat_1(_702538)))), 6702 ^ _434076 : [(6703 ^ _434076) ^ [] : [-(ti(int, _702538) = hAPP(nat, int, semiring_1_of_nat(int), 6701 ^ [_702538, _702540]))], (6705 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _702540, 6701 ^ [_702538, _702540]))]], 6706 ^ _434076 : [(6707 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _702538), zero_zero(int))))], (6709 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, _702540, zero_zero(nat)))]]], (6682 ^ _434076) ^ [_701987, _701989] : [hBOOL(hAPP(nat, bool, _701989, nat_1(_701987))), 6685 ^ _434076 : [(6686 ^ _434076) ^ [_702193] : [ti(int, _701987) = hAPP(nat, int, semiring_1_of_nat(int), _702193), -(hBOOL(hAPP(nat, bool, _701989, _702193)))], (6692 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _701987), zero_zero(int))), -(hBOOL(hAPP(nat, bool, _701989, zero_zero(nat))))]]], (6713 ^ _434076) ^ [_703119] : [linordered_semidom(_703119), 6716 ^ _434076 : [(6717 ^ _434076) ^ [_703341, _703343] : [hBOOL(hAPP(_703119, bool, hAPP(_703119, fun(_703119, bool), ord_less(_703119), zero_zero(_703119)), _703341)), hBOOL(hAPP(_703119, bool, hAPP(_703119, fun(_703119, bool), ord_less(_703119), _703341), one_one(_703119))), -(hBOOL(hAPP(_703119, bool, hAPP(_703119, fun(_703119, bool), ord_less(_703119), times_times(_703119, _703341, hAPP(nat, _703119, power_power(_703119, _703341), _703343))), hAPP(nat, _703119, power_power(_703119, _703341), _703343))))]]], (6727 ^ _434076) ^ [_703775] : [number_ring(_703775), 6730 ^ _434076 : [(6731 ^ _434076) ^ [_703905] : [-(times_times(_703775, plus_plus(_703775, one_one(_703775), one_one(_703775)), number_number_of(_703775, _703905)) = number_number_of(_703775, bit0(_703905)))]]], (6733 ^ _434076) ^ [_704025] : [linordered_semidom(_704025), 6736 ^ _434076 : [(6737 ^ _434076) ^ [_704270, _704272, _704274] : [hAPP(nat, _704025, power_power(_704025, _704274), _704272) = hAPP(nat, _704025, power_power(_704025, _704270), _704272), hBOOL(hAPP(_704025, bool, hAPP(_704025, fun(_704025, bool), ord_less_eq(_704025), zero_zero(_704025)), _704274)), hBOOL(hAPP(_704025, bool, hAPP(_704025, fun(_704025, bool), ord_less_eq(_704025), zero_zero(_704025)), _704270)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _704272)), -(ti(_704025, _704274) = ti(_704025, _704270))]]], (6755 ^ _434076) ^ [_704892] : [monoid_mult(_704892), 6758 ^ _434076 : [(6759 ^ _434076) ^ [_705018] : [-(hAPP(nat, _704892, power_power(_704892, _705018), number_number_of(nat, bit1(bit1(pls)))) = times_times(_704892, times_times(_704892, _705018, _705018), _705018))]]], (6761 ^ _434076) ^ [_705134] : [number_semiring(_705134), 6764 ^ _434076 : [(6765 ^ _434076) ^ [_705315, _705317] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _705315)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _705317)), -(plus_plus(_705134, number_number_of(_705134, _705315), number_number_of(_705134, _705317)) = number_number_of(_705134, plus_plus(int, _705315, _705317)))]]], (6775 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, bit1(bit1(pls))))))], (6777 ^ _434076) ^ [_705720] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _705720)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), _705720))))], (6783 ^ _434076) ^ [_705962, _705964, _705966] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _705964), _705962)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _705966)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), times_times(int, hAPP(nat, int, semiring_1_of_nat(int), _705966), _705964)), times_times(int, hAPP(nat, int, semiring_1_of_nat(int), _705966), _705962))))], (6793 ^ _434076) ^ [_706337] : [number_ring(_706337), 6796 ^ _434076 : [(6797 ^ _434076) ^ [_706461] : [-(number_number_of(_706337, succ(_706461)) = plus_plus(_706337, one_one(_706337), number_number_of(_706337, _706461)))]]], (6799 ^ _434076) ^ [_706574, _706576] : [-(plus_plus(int, bit1(_706576), bit1(_706574)) = bit0(plus_plus(int, _706576, succ(_706574))))], (6801 ^ _434076) ^ [] : [-(number_number_of(nat, bit0(bit1(pls))) = nat_1(number_number_of(int, bit0(bit1(pls)))))], (6803 ^ _434076) ^ [_706738] : [number_ring(_706738), 6806 ^ _434076 : [(6807 ^ _434076) ^ [_706859] : [-(times_times(_706738, _706859, number_number_of(_706738, bit0(bit1(pls)))) = plus_plus(_706738, _706859, _706859))]]], (6809 ^ _434076) ^ [_706970] : [number_semiring(_706970), 6812 ^ _434076 : [(6813 ^ _434076) ^ [_707091] : [-(times_times(_706970, _707091, number_number_of(_706970, bit0(bit1(pls)))) = plus_plus(_706970, _707091, _707091))]]], (6815 ^ _434076) ^ [_707202] : [number_ring(_707202), 6818 ^ _434076 : [(6819 ^ _434076) ^ [_707323] : [-(times_times(_707202, number_number_of(_707202, bit0(bit1(pls))), _707323) = plus_plus(_707202, _707323, _707323))]]], (6821 ^ _434076) ^ [_707434] : [number_semiring(_707434), 6824 ^ _434076 : [(6825 ^ _434076) ^ [_707555] : [-(times_times(_707434, number_number_of(_707434, bit0(bit1(pls))), _707555) = plus_plus(_707434, _707555, _707555))]]], (6827 ^ _434076) ^ [_707666] : [linordered_semidom(_707666), 6830 ^ _434076 : [(6831 ^ _434076) ^ [_707911, _707913, _707915] : [hBOOL(hAPP(_707666, bool, hAPP(_707666, fun(_707666, bool), ord_less(_707666), _707913), _707911)), hBOOL(hAPP(_707666, bool, hAPP(_707666, fun(_707666, bool), ord_less_eq(_707666), zero_zero(_707666)), _707913)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _707915)), -(hBOOL(hAPP(_707666, bool, hAPP(_707666, fun(_707666, bool), ord_less(_707666), hAPP(nat, _707666, power_power(_707666, _707913), _707915)), hAPP(nat, _707666, power_power(_707666, _707911), _707915))))]]], (6845 ^ _434076) ^ [_708448] : [monoid_mult(_708448), 6848 ^ _434076 : [(6849 ^ _434076) ^ [_708570] : [-(hAPP(nat, _708448, power_power(_708448, _708570), number_number_of(nat, bit0(bit1(pls)))) = times_times(_708448, _708570, _708570))]]], (6851 ^ _434076) ^ [_708682] : [comm_semiring_1(_708682), 6854 ^ _434076 : [(6855 ^ _434076) ^ [_708804] : [-(times_times(_708682, _708804, _708804) = hAPP(nat, _708682, power_power(_708682, _708804), number_number_of(nat, bit0(bit1(pls)))))]]], (6857 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, bit0(bit1(pls))))))], (6859 ^ _434076) ^ [_708954] : [-(times_times(int, _708954, hAPP(nat, int, power_power(int, _708954), number_number_of(nat, bit0(bit1(pls))))) = hAPP(nat, int, power_power(int, _708954), number_number_of(nat, bit1(bit1(pls)))))], (6861 ^ _434076) ^ [_709052] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _709052), hAPP(nat, int, power_power(int, _709052), number_number_of(nat, bit0(bit1(pls)))))))], (6863 ^ _434076) ^ [_709162] : [6870 ^ _434076 : [(6871 ^ _434076) ^ [_709376] : [-(hAPP(nat, _709162, power_power(_709162, number_number_of(_709162, _709376)), number_number_of(nat, bit0(bit1(pls)))) = times_times(_709162, number_number_of(_709162, _709376), number_number_of(_709162, _709376)))]], monoid_mult(_709162), number(_709162)], (6873 ^ _434076) ^ [_709497] : [linordered_idom(_709497), 6876 ^ _434076 : [(6877 ^ _434076) ^ [_709631] : [-(hBOOL(hAPP(_709497, bool, hAPP(_709497, fun(_709497, bool), ord_less_eq(_709497), zero_zero(_709497)), hAPP(nat, _709497, power_power(_709497, _709631), number_number_of(nat, bit0(bit1(pls)))))))]]], (6879 ^ _434076) ^ [_709755] : [linordered_semidom(_709755), 6882 ^ _434076 : [(6883 ^ _434076) ^ [_709971, _709973] : [hBOOL(hAPP(_709755, bool, hAPP(_709755, fun(_709755, bool), ord_less_eq(_709755), hAPP(nat, _709755, power_power(_709755, _709973), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, _709755, power_power(_709755, _709971), number_number_of(nat, bit0(bit1(pls)))))), hBOOL(hAPP(_709755, bool, hAPP(_709755, fun(_709755, bool), ord_less_eq(_709755), zero_zero(_709755)), _709971)), -(hBOOL(hAPP(_709755, bool, hAPP(_709755, fun(_709755, bool), ord_less_eq(_709755), _709973), _709971)))]]], (6893 ^ _434076) ^ [_710393] : [linordered_semidom(_710393), 6896 ^ _434076 : [(6897 ^ _434076) ^ [_710609, _710611] : [hAPP(nat, _710393, power_power(_710393, _710611), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, _710393, power_power(_710393, _710609), number_number_of(nat, bit0(bit1(pls)))), hBOOL(hAPP(_710393, bool, hAPP(_710393, fun(_710393, bool), ord_less_eq(_710393), zero_zero(_710393)), _710611)), hBOOL(hAPP(_710393, bool, hAPP(_710393, fun(_710393, bool), ord_less_eq(_710393), zero_zero(_710393)), _710609)), -(ti(_710393, _710611) = ti(_710393, _710609))]]], (6911 ^ _434076) ^ [_711112] : [number_ring(_711112), 6914 ^ _434076 : [(6915 ^ _434076) ^ [_711316] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _711316))), -(hAPP(nat, _711112, semiring_1_of_nat(_711112), number_number_of(nat, _711316)) = number_number_of(_711112, _711316))], (6921 ^ _434076) ^ [_711520] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _711520)))), -(hAPP(nat, _711112, semiring_1_of_nat(_711112), number_number_of(nat, _711520)) = zero_zero(_711112))]]], (6927 ^ _434076) ^ [_711766] : [number_semiring(_711766), 6930 ^ _434076 : [(6931 ^ _434076) ^ [_711942, _711944] : [-(hAPP(nat, _711766, power_power(_711766, plus_plus(_711766, _711944, _711942)), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(_711766, plus_plus(_711766, hAPP(nat, _711766, power_power(_711766, _711944), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _711766, power_power(_711766, _711942), number_number_of(nat, bit0(bit1(pls))))), times_times(_711766, times_times(_711766, number_number_of(_711766, bit0(bit1(pls))), _711944), _711942)))]]], (6933 ^ _434076) ^ [_712091] : [linordered_semidom(_712091), 6936 ^ _434076 : [(6937 ^ _434076) ^ [_712307, _712309] : [hBOOL(hAPP(_712091, bool, hAPP(_712091, fun(_712091, bool), ord_less(_712091), hAPP(nat, _712091, power_power(_712091, _712309), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, _712091, power_power(_712091, _712307), number_number_of(nat, bit0(bit1(pls)))))), hBOOL(hAPP(_712091, bool, hAPP(_712091, fun(_712091, bool), ord_less_eq(_712091), zero_zero(_712091)), _712307)), -(hBOOL(hAPP(_712091, bool, hAPP(_712091, fun(_712091, bool), ord_less(_712091), _712309), _712307)))]]], (6947 ^ _434076) ^ [_712729] : [linordered_idom(_712729), 6950 ^ _434076 : [(6951 ^ _434076) ^ [_712894, _712896] : [-(hBOOL(hAPP(_712729, bool, hAPP(_712729, fun(_712729, bool), ord_less_eq(_712729), zero_zero(_712729)), plus_plus(_712729, hAPP(nat, _712729, power_power(_712729, _712896), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _712729, power_power(_712729, _712894), number_number_of(nat, bit0(bit1(pls))))))))]]], (6953 ^ _434076) ^ [_713032] : [linordered_idom(_713032), 6956 ^ _434076 : [(6957 ^ _434076) ^ [_713263, _713265] : [hBOOL(hAPP(_713032, bool, hAPP(_713032, fun(_713032, bool), ord_less_eq(_713032), plus_plus(_713032, hAPP(nat, _713032, power_power(_713032, _713265), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _713032, power_power(_713032, _713263), number_number_of(nat, bit0(bit1(pls)))))), zero_zero(_713032))), 6960 ^ _434076 : [(6961 ^ _434076) ^ [] : [-(ti(_713032, _713265) = zero_zero(_713032))], (6963 ^ _434076) ^ [] : [-(ti(_713032, _713263) = zero_zero(_713032))]]], (6965 ^ _434076) ^ [_713602, _713604] : [-(hBOOL(hAPP(_713032, bool, hAPP(_713032, fun(_713032, bool), ord_less_eq(_713032), plus_plus(_713032, hAPP(nat, _713032, power_power(_713032, _713604), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, _713032, power_power(_713032, _713602), number_number_of(nat, bit0(bit1(pls)))))), zero_zero(_713032)))), ti(_713032, _713604) = zero_zero(_713032), ti(_713032, _713602) = zero_zero(_713032)]]], (6975 ^ _434076) ^ [_713998] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _713998)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _713998), number_number_of(int, bit0(bit1(pls))))), -(ti(int, _713998) = zero_zero(int)), -(ti(int, _713998) = one_one(int))], (6989 ^ _434076) ^ [_714411, _714413] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _714411)), -(hAPP(nat, int, power_power(int, _714413), nat_1(_714411)) = times_times(int, _714413, hAPP(nat, int, power_power(int, _714413), minus_minus(nat, nat_1(_714411), one_one(nat)))))], (6995 ^ _434076) ^ [_714699, _714701, _714703] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _714699)), ti(int, _714699) = plus_plus(int, _714703, times_times(int, _714699, _714701)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _714703)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _714701), one_one(int))))], (7009 ^ _434076) ^ [_715171, _715173, _715175] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _715171)), ti(int, _715171) = plus_plus(int, _715175, times_times(int, _715171, _715173)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _715175), _715171)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), _715173)))], (7023 ^ _434076) ^ [_715615] : [power(_715615), 7026 ^ _434076 : [(7027 ^ _434076) ^ [_715833, _715835] : [_715833 = zero_zero(nat), -(hAPP(nat, _715615, power_power(_715615, _715835), _715833) = one_one(_715615))], (7033 ^ _434076) ^ [_716023, _716025] : [-(_716023 = zero_zero(nat)), -(hAPP(nat, _715615, power_power(_715615, _716025), _716023) = times_times(_715615, _716025, hAPP(nat, _715615, power_power(_715615, _716025), minus_minus(nat, _716023, one_one(nat)))))]]], (7039 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (7041 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))))], (7043 ^ _434076) ^ [_716421, _716423, _716425] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), plus_plus(int, times_times(int, _716425, _716423), _716421))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _716421), _716425)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _716425)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _716423)))], (7057 ^ _434076) ^ [_716895, _716897, _716899] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, times_times(int, _716899, _716897), _716895)), zero_zero(int))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _716895)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _716899)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _716897), zero_zero(int))))], (7071 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))))))], (7073 ^ _434076) ^ [_717388] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), zero_zero(nat)), _717388)))], (7075 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (7077 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), t), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (7079 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t))))], (7081 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (7083 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))))], (7087 ^ _434076) ^ [] : [-(plus_plus(int, hAPP(nat, int, power_power(int, 7084 ^ []), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, 7085 ^ []), number_number_of(nat, bit0(bit1(pls))))) = times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))], (7089 ^ _434076) ^ [] : [-(plus_plus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), one_one(int)) = times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t))], (7091 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zprime, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (7093 ^ _434076) ^ [] : [t = one_one(int), -(plus_plus(int, hAPP(nat, int, power_power(int, 7096 ^ []), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, 7097 ^ []), number_number_of(nat, bit0(bit1(pls))))) = plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))], (7101 ^ _434076) ^ [_718241] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _718241), _718241)))], (7103 ^ _434076) ^ [_718328] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _718328), times_times(nat, _718328, _718328))))], (7105 ^ _434076) ^ [_718419] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _718419), times_times(nat, _718419, times_times(nat, _718419, _718419)))))], (7107 ^ _434076) ^ [_718528, _718530] : [-(times_times(nat, _718530, _718528) = times_times(nat, _718528, _718530))], (7109 ^ _434076) ^ [_718645, _718647] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _718647), _718645))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _718645), _718647)))], (7115 ^ _434076) ^ [_718891, _718893, _718895] : [-(times_times(nat, times_times(nat, _718895, _718893), _718891) = times_times(nat, _718895, times_times(nat, _718893, _718891)))], (7117 ^ _434076) ^ [_719018, _719020] : [_719020 = _719018, -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719020), _719018)))], (7123 ^ _434076) ^ [_719260, _719262, _719264] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719262), _719260)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _719262, _719264)), times_times(nat, _719260, _719264))))], (7129 ^ _434076) ^ [_719542, _719544, _719546] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719544), _719542)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _719546, _719544)), times_times(nat, _719546, _719542))))], (7135 ^ _434076) ^ [_719824, _719826, _719828] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719826), _719824)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719824), _719828)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _719826), _719828)))], (7145 ^ _434076) ^ [_720187, _720189] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _720189), _720187)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _720187), _720189)), -(_720189 = _720187)], (7155 ^ _434076) ^ [_720550, _720552, _720554, _720556] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _720552), _720550)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _720556), _720554)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _720552, _720556)), times_times(nat, _720550, _720554))))], (7165 ^ _434076) ^ [_720968, _720970] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _720970), _720968)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), minus_minus(real, _720970, _720968)), zero_zero(real))))], (7171 ^ _434076) ^ [_721174, _721176] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), minus_minus(real, _721176, _721174)), zero_zero(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _721176), _721174)))], (7187 ^ _434076) ^ [_721794, _721796, _721798] : [7188 ^ _434076 : [(7189 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _721796)))], (7191 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _721798), _721794))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _721798, _721796)), times_times(nat, _721794, _721796))))], (7177 ^ _434076) ^ [_721473, _721475, _721477] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _721477, _721475)), times_times(nat, _721473, _721475))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _721475)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _721477), _721473)))], (7205 ^ _434076) ^ [_722513, _722515, _722517] : [7206 ^ _434076 : [(7207 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _722517)))], (7209 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _722515), _722513))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _722517, _722515)), times_times(nat, _722517, _722513))))], (7195 ^ _434076) ^ [_722192, _722194, _722196] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _722196, _722194)), times_times(nat, _722196, _722192))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _722196)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _722194), _722192)))], (7213 ^ _434076) ^ [_722882, _722884, _722886] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _722882)), 7216 ^ _434076 : [(7217 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), times_times(real, _722886, _722882)), times_times(real, _722884, _722882))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _722886), _722884)))], (7223 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _722886), _722884)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), times_times(real, _722886, _722882)), times_times(real, _722884, _722882))))]]], (7229 ^ _434076) ^ [_723458, _723460, _723462] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _723458)), 7232 ^ _434076 : [(7233 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), times_times(real, _723458, _723462)), times_times(real, _723458, _723460))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _723462), _723460)))], (7239 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _723462), _723460)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), times_times(real, _723458, _723462)), times_times(real, _723458, _723460))))]]], (7245 ^ _434076) ^ [_724020, _724022] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _724022), _724020)), -(minus_minus(int, hAPP(nat, int, semiring_1_of_nat(int), _724020), hAPP(nat, int, semiring_1_of_nat(int), _724022)) = hAPP(nat, int, semiring_1_of_nat(int), minus_minus(nat, _724020, _724022)))], (7251 ^ _434076) ^ [_724265] : [-(minus_minus(int, _724265, pls) = ti(int, _724265))], (7253 ^ _434076) ^ [_724364, _724366] : [-(minus_minus(int, bit0(_724366), bit0(_724364)) = bit0(minus_minus(int, _724366, _724364)))], (7255 ^ _434076) ^ [_724486, _724488, _724490] : [-(times_times(int, minus_minus(int, _724490, _724488), _724486) = minus_minus(int, times_times(int, _724490, _724486), times_times(int, _724488, _724486)))], (7257 ^ _434076) ^ [_724616, _724618, _724620] : [-(times_times(int, _724620, minus_minus(int, _724618, _724616)) = minus_minus(int, times_times(int, _724620, _724618), times_times(int, _724620, _724616)))], (7259 ^ _434076) ^ [_724718] : [-(times_times(nat, zero_zero(nat), _724718) = zero_zero(nat))], (7261 ^ _434076) ^ [_724800] : [-(times_times(nat, _724800, zero_zero(nat)) = zero_zero(nat))], (7273 ^ _434076) ^ [_725200, _725202] : [7274 ^ _434076 : [(7275 ^ _434076) ^ [] : [_725202 = zero_zero(nat)], (7277 ^ _434076) ^ [] : [_725200 = zero_zero(nat)]], -(times_times(nat, _725202, _725200) = zero_zero(nat))], (7263 ^ _434076) ^ [_724940, _724942] : [times_times(nat, _724942, _724940) = zero_zero(nat), -(_724942 = zero_zero(nat)), -(_724940 = zero_zero(nat))], (7291 ^ _434076) ^ [_725815, _725817, _725819] : [7292 ^ _434076 : [(7293 ^ _434076) ^ [] : [_725817 = _725815], (7295 ^ _434076) ^ [] : [_725819 = zero_zero(nat)]], -(times_times(nat, _725819, _725817) = times_times(nat, _725819, _725815))], (7281 ^ _434076) ^ [_725537, _725539, _725541] : [times_times(nat, _725541, _725539) = times_times(nat, _725541, _725537), -(_725539 = _725537), -(_725541 = zero_zero(nat))], (7309 ^ _434076) ^ [_726446, _726448, _726450] : [7310 ^ _434076 : [(7311 ^ _434076) ^ [] : [_726450 = _726446], (7313 ^ _434076) ^ [] : [_726448 = zero_zero(nat)]], -(times_times(nat, _726450, _726448) = times_times(nat, _726446, _726448))], (7299 ^ _434076) ^ [_726168, _726170, _726172] : [times_times(nat, _726172, _726170) = times_times(nat, _726168, _726170), -(_726172 = _726168), -(_726170 = zero_zero(nat))], (7317 ^ _434076) ^ [_726742] : [comm_semiring_1(_726742), 7320 ^ _434076 : [(7321 ^ _434076) ^ [_726918, _726920, _726922] : [-(hAPP(nat, _726742, power_power(_726742, hAPP(nat, _726742, power_power(_726742, _726922), _726920)), _726918) = hAPP(nat, _726742, power_power(_726742, _726922), times_times(nat, _726920, _726918)))]]], (7323 ^ _434076) ^ [_727050] : [monoid_mult(_727050), 7326 ^ _434076 : [(7327 ^ _434076) ^ [_727226, _727228, _727230] : [-(hAPP(nat, _727050, power_power(_727050, _727230), times_times(nat, _727228, _727226)) = hAPP(nat, _727050, power_power(_727050, hAPP(nat, _727050, power_power(_727050, _727230), _727228)), _727226))]]], (7329 ^ _434076) ^ [_727343] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), zero_zero(nat)), _727343)))], (7331 ^ _434076) ^ [_727469] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _727469), zero_zero(nat))), -(_727469 = zero_zero(nat))], (7337 ^ _434076) ^ [_727643] : [_727643 = zero_zero(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _727643), zero_zero(nat))))], (7343 ^ _434076) ^ [_727881, _727883, _727885] : [-(_727881 = zero_zero(real)), 7346 ^ _434076 : [(7347 ^ _434076) ^ [] : [times_times(real, _727881, _727885) = times_times(real, _727881, _727883), -(_727885 = _727883)], (7353 ^ _434076) ^ [] : [_727885 = _727883, -(times_times(real, _727881, _727885) = times_times(real, _727881, _727883))]]], (7359 ^ _434076) ^ [_728398, _728400, _728402] : [-(_728398 = zero_zero(real)), 7362 ^ _434076 : [(7363 ^ _434076) ^ [] : [times_times(real, _728402, _728398) = times_times(real, _728400, _728398), -(_728402 = _728400)], (7369 ^ _434076) ^ [] : [_728402 = _728400, -(times_times(real, _728402, _728398) = times_times(real, _728400, _728398))]]], (7375 ^ _434076) ^ [_728901, _728903] : [7376 ^ _434076 : [(7377 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _728903), _728901))], (7379 ^ _434076) ^ [] : [_728903 = _728901]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _728903), _728901)))], (7383 ^ _434076) ^ [_729221, _729223] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _729223), _729221)), -(_729223 = _729221), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _729223), _729221)))], (7393 ^ _434076) ^ [_729559, _729561] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _729561), _729559)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _729561), _729559)))], (7409 ^ _434076) ^ [_730122, _730124] : [7410 ^ _434076 : [(7411 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _730124), _730122))], (7413 ^ _434076) ^ [] : [_730124 = _730122]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _730124), _730122)))], (7399 ^ _434076) ^ [_729834, _729836] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _729836), _729834)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _729836), _729834))), -(_729836 = _729834)], (7417 ^ _434076) ^ [_730473, _730475] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _730475), _730473)), 7420 ^ _434076 : [(7421 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _730475), _730473)))], (7423 ^ _434076) ^ [] : [_730475 = _730473]]], (7425 ^ _434076) ^ [_730747, _730749] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _730749), _730747))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _730749), _730747)), -(_730749 = _730747)], (7435 ^ _434076) ^ [_731116, _731118] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _731118), _731116)), 7438 ^ _434076 : [(7439 ^ _434076) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _731118), _731116)))], (7441 ^ _434076) ^ [] : [_731118 = _731116]]], (7443 ^ _434076) ^ [_731390, _731392] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _731392), _731390))), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _731392), _731390)), -(_731392 = _731390)], (7463 ^ _434076) ^ [_732047, _732049] : [7464 ^ _434076 : [(7465 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _732049), _732047))], (7467 ^ _434076) ^ [] : [_732049 = _732047]], -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _732049), _732047)))], (7453 ^ _434076) ^ [_731759, _731761] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _731761), _731759)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _731761), _731759))), -(_731761 = _731759)], (7471 ^ _434076) ^ [_732368, _732370, _732372] : [-(times_times(nat, plus_plus(nat, _732372, _732370), _732368) = plus_plus(nat, times_times(nat, _732372, _732368), times_times(nat, _732370, _732368)))], (7473 ^ _434076) ^ [_732498, _732500, _732502] : [-(times_times(nat, _732502, plus_plus(nat, _732500, _732498)) = plus_plus(nat, times_times(nat, _732502, _732500), times_times(nat, _732502, _732498)))], (7475 ^ _434076) ^ [_732643, _732645, _732647] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _732647, _732645)), _732643)), 7478 ^ _434076 : [(7479 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _732647), _732643)))], (7481 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _732645), _732643)))]]], (7483 ^ _434076) ^ [_733016, _733018, _733020] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _733020, _733018)), _733016)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _733020), _733016)))], (7489 ^ _434076) ^ [_733290, _733292, _733294] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _733294, _733292)), _733290)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _733292), _733290)))], (7495 ^ _434076) ^ [_733578, _733580, _733582, _733584] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _733580), _733578)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _733584), _733582)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _733580, _733584)), plus_plus(nat, _733578, _733582))))], (7505 ^ _434076) ^ [_733981, _733983, _733985] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _733983), _733981)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _733983, _733985)), plus_plus(nat, _733981, _733985))))], (7511 ^ _434076) ^ [_734263, _734265, _734267] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _734265), _734263)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _734265), plus_plus(nat, _734267, _734263))))], (7517 ^ _434076) ^ [_734537, _734539, _734541] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _734539), _734537)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _734539), plus_plus(nat, _734537, _734541))))], (7523 ^ _434076) ^ [_734840, _734842, _734844] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _734844, _734842)), plus_plus(nat, _734844, _734840))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _734842), _734840)))], (7529 ^ _434076) ^ [_735060, _735062, _735064] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _735062), _735060)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _735064, _735062)), plus_plus(nat, _735064, _735060))))], (7535 ^ _434076) ^ [_735359, _735361] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _735361), _735359)), -(_735359 = plus_plus(nat, _735361, 7538 ^ [_735359, _735361]))], (7542 ^ _434076) ^ [_735608, _735610] : [7543 ^ _434076 : [(7544 ^ _434076) ^ [_735691] : [_735608 = plus_plus(nat, _735610, _735691)]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _735610), _735608)))], (7548 ^ _434076) ^ [_735853, _735855] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _735855), plus_plus(nat, _735855, _735853))))], (7550 ^ _434076) ^ [_735960, _735962] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _735962), plus_plus(nat, _735960, _735962))))], (7552 ^ _434076) ^ [_736111, _736113] : [times_times(nat, _736113, _736111) = one_one(nat), 7555 ^ _434076 : [(7556 ^ _434076) ^ [] : [-(_736113 = one_one(nat))], (7558 ^ _434076) ^ [] : [-(_736111 = one_one(nat))]]], (7560 ^ _434076) ^ [_736356, _736358] : [-(times_times(nat, _736358, _736356) = one_one(nat)), _736358 = one_one(nat), _736356 = one_one(nat)], (7570 ^ _434076) ^ [_736694, _736696] : [times_times(nat, _736696, _736694) = one_one(nat), 7573 ^ _434076 : [(7574 ^ _434076) ^ [] : [-(_736696 = one_one(nat))], (7576 ^ _434076) ^ [] : [-(_736694 = one_one(nat))]]], (7578 ^ _434076) ^ [_736939, _736941] : [-(times_times(nat, _736941, _736939) = one_one(nat)), _736941 = one_one(nat), _736939 = one_one(nat)], (7588 ^ _434076) ^ [_737219] : [-(times_times(nat, _737219, one_one(nat)) = _737219)], (7590 ^ _434076) ^ [_737359, _737361] : [one_one(nat) = times_times(nat, _737361, _737359), 7593 ^ _434076 : [(7594 ^ _434076) ^ [] : [-(_737361 = one_one(nat))], (7596 ^ _434076) ^ [] : [-(_737359 = one_one(nat))]]], (7598 ^ _434076) ^ [_737604, _737606] : [-(one_one(nat) = times_times(nat, _737606, _737604)), _737606 = one_one(nat), _737604 = one_one(nat)], (7608 ^ _434076) ^ [_737884] : [-(times_times(nat, one_one(nat), _737884) = _737884)], (7610 ^ _434076) ^ [_737994, _737996, _737998] : [-(times_times(nat, minus_minus(nat, _737998, _737996), _737994) = minus_minus(nat, times_times(nat, _737998, _737994), times_times(nat, _737996, _737994)))], (7612 ^ _434076) ^ [_738124, _738126, _738128] : [-(times_times(nat, _738128, minus_minus(nat, _738126, _738124)) = minus_minus(nat, times_times(nat, _738128, _738126), times_times(nat, _738128, _738124)))], (7614 ^ _434076) ^ [_738226] : [-(times_times(real, one_one(real), _738226) = _738226)], (7616 ^ _434076) ^ [_738351, _738353, _738355] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _738353), _738351)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _738353), _738355)), 7623 ^ _434076 : [(7624 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _738351, _738353)), minus_minus(nat, _738355, _738353))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _738351), _738355)))], (7630 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _738351), _738355)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _738351, _738353)), minus_minus(nat, _738355, _738353))))]]], (7636 ^ _434076) ^ [_739048, _739050, _739052] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _739050), _739048)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _739050), _739052)), -(minus_minus(nat, minus_minus(nat, _739048, _739050), minus_minus(nat, _739052, _739050)) = minus_minus(nat, _739048, _739052))], (7646 ^ _434076) ^ [_739439, _739441, _739443] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _739441), _739439)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _739441), _739443)), 7653 ^ _434076 : [(7654 ^ _434076) ^ [] : [minus_minus(nat, _739439, _739441) = minus_minus(nat, _739443, _739441), -(_739439 = _739443)], (7660 ^ _434076) ^ [] : [_739439 = _739443, -(minus_minus(nat, _739439, _739441) = minus_minus(nat, _739443, _739441))]]], (7666 ^ _434076) ^ [_740068, _740070] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _740070), _740068)), -(minus_minus(nat, _740068, minus_minus(nat, _740068, _740070)) = _740070)], (7672 ^ _434076) ^ [_740326, _740328, _740330] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _740328), _740326)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _740328, _740330)), minus_minus(nat, _740326, _740330))))], (7678 ^ _434076) ^ [_740608, _740610, _740612] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _740610), _740608)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _740612, _740608)), minus_minus(nat, _740612, _740610))))], (7684 ^ _434076) ^ [_740861, _740863] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _740863, _740861)), _740863)))], (7686 ^ _434076) ^ [_740982, _740984, _740986] : [-(times_times(real, plus_plus(real, _740986, _740984), _740982) = plus_plus(real, times_times(real, _740986, _740982), times_times(real, _740984, _740982)))], (7688 ^ _434076) ^ [_741112, _741114, _741116] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, power_power(int, _741116), _741114)), _741112) = hAPP(nat, int, power_power(int, _741116), times_times(nat, _741114, _741112)))], (7690 ^ _434076) ^ [_741265, _741267, _741269] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _741267), _741265)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), plus_plus(real, _741269, _741267)), plus_plus(real, _741269, _741265))))], (7696 ^ _434076) ^ [_741518, _741520] : [-(minus_minus(int, bit1(_741520), bit1(_741518)) = bit0(minus_minus(int, _741520, _741518)))], (7698 ^ _434076) ^ [_741626, _741628] : [-(minus_minus(int, bit1(_741628), bit0(_741626)) = bit1(minus_minus(int, _741628, _741626)))], (7700 ^ _434076) ^ [_741720] : [-(minus_minus(int, pls, bit0(_741720)) = bit0(minus_minus(int, pls, _741720)))], (7702 ^ _434076) ^ [_741839, _741841] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _741839)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _741839), _741841)), -(ti(int, _741839) = minus_minus(int, _741841, one_one(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _741839), minus_minus(int, _741841, one_one(int)))))], (7716 ^ _434076) ^ [_742325, _742327] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _742327), _742325)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), minus_minus(int, _742327, _742325)), zero_zero(int))))], (7722 ^ _434076) ^ [_742531, _742533] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), minus_minus(int, _742533, _742531)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _742533), _742531)))], (7728 ^ _434076) ^ [_742801, _742803, _742805] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _742803), _742801)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _742805)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _742805, _742803)), times_times(nat, _742805, _742801))))], (7738 ^ _434076) ^ [_743184, _743186, _743188] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _743186), _743184)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _743188)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _743186, _743188)), times_times(nat, _743184, _743188))))], (7748 ^ _434076) ^ [_743596, _743598, _743600] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _743600, _743598)), times_times(nat, _743596, _743598))), 7751 ^ _434076 : [(7752 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _743598)))], (7754 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _743600), _743596)))]]], (7756 ^ _434076) ^ [_743901, _743903, _743905] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _743905, _743903)), times_times(nat, _743901, _743903)))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _743903)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _743905), _743901))], (7766 ^ _434076) ^ [_744315, _744317, _744319] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _744319, _744317)), times_times(nat, _744319, _744315))), 7769 ^ _434076 : [(7770 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _744319)))], (7772 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _744317), _744315)))]]], (7774 ^ _434076) ^ [_744620, _744622, _744624] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _744624, _744622)), times_times(nat, _744624, _744620)))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _744624)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _744622), _744620))], (7784 ^ _434076) ^ [_745020, _745022] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), times_times(nat, _745022, _745020))), 7787 ^ _434076 : [(7788 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _745022)))], (7790 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _745020)))]]], (7792 ^ _434076) ^ [_745289, _745291] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), times_times(nat, _745291, _745289)))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _745291)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _745289))], (7802 ^ _434076) ^ [_745637] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), times_times(real, _745637, _745637)))), -(_745637 = zero_zero(real))], (7808 ^ _434076) ^ [_745812] : [_745812 = zero_zero(real), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), times_times(real, _745812, _745812)))], (7814 ^ _434076) ^ [_746049, _746051, _746053] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _746049)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _746053), _746051)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), times_times(real, _746049, _746053)), times_times(real, _746049, _746051))))], (7824 ^ _434076) ^ [_746418, _746420] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _746418)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _746420)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), times_times(real, _746418, _746420))))], (7834 ^ _434076) ^ [_746763, _746765, _746767] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _746763)), 7837 ^ _434076 : [(7838 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), times_times(real, _746767, _746763)), times_times(real, _746765, _746763))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _746767), _746765)))], (7844 ^ _434076) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _746767), _746765)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), times_times(real, _746767, _746763)), times_times(real, _746765, _746763))))]]], (7850 ^ _434076) ^ [_747325, _747327] : [_747327 = times_times(nat, _747327, _747325), -(_747325 = one_one(nat)), -(_747327 = zero_zero(nat))], (7860 ^ _434076) ^ [_747662, _747664] : [minus_minus(nat, _747664, _747662) = zero_zero(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _747664), _747662)))], (7866 ^ _434076) ^ [_747850, _747852] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _747852), _747850)), -(minus_minus(nat, _747852, _747850) = zero_zero(nat))], (7872 ^ _434076) ^ [_748088, _748090] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _748090), _748088)), -(minus_minus(nat, _748090, _748088) = zero_zero(nat))], (7878 ^ _434076) ^ [_748353, _748355] : [plus_plus(real, times_times(real, _748355, _748355), times_times(real, _748353, _748353)) = zero_zero(real), 7881 ^ _434076 : [(7882 ^ _434076) ^ [] : [-(_748355 = zero_zero(real))], (7884 ^ _434076) ^ [] : [-(_748353 = zero_zero(real))]]], (7886 ^ _434076) ^ [_748614, _748616] : [-(plus_plus(real, times_times(real, _748616, _748616), times_times(real, _748614, _748614)) = zero_zero(real)), _748616 = zero_zero(real), _748614 = zero_zero(real)], (7896 ^ _434076) ^ [_748953, _748955, _748957] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _748955), _748953)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _748957), _748955)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _748955, _748957)), minus_minus(nat, _748953, _748957))))], (7906 ^ _434076) ^ [_749346, _749348, _749350] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _749348), _749346)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _749348), _749350)), 7913 ^ _434076 : [(7914 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _749346, _749348)), minus_minus(nat, _749350, _749348))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _749346), _749350)))], (7920 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _749346), _749350)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), minus_minus(nat, _749346, _749348)), minus_minus(nat, _749350, _749348))))]]], (7926 ^ _434076) ^ [_750014, _750016] : [-(times_times(int, hAPP(nat, int, semiring_1_of_nat(int), _750016), hAPP(nat, int, semiring_1_of_nat(int), _750014)) = hAPP(nat, int, semiring_1_of_nat(int), times_times(nat, _750016, _750014)))], (7928 ^ _434076) ^ [_750131, _750133] : [-(times_times(int, hAPP(nat, int, semiring_1_of_nat(int), _750133), hAPP(nat, int, semiring_1_of_nat(int), _750131)) = hAPP(nat, int, semiring_1_of_nat(int), times_times(nat, _750133, _750131)))], (7930 ^ _434076) ^ [_750248, _750250] : [-(hAPP(nat, int, semiring_1_of_nat(int), times_times(nat, _750250, _750248)) = times_times(int, hAPP(nat, int, semiring_1_of_nat(int), _750250), hAPP(nat, int, semiring_1_of_nat(int), _750248)))], (7932 ^ _434076) ^ [_750394, _750396, _750398] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _750396), _750394)), -(minus_minus(nat, _750398, minus_minus(nat, _750394, _750396)) = minus_minus(nat, plus_plus(nat, _750398, _750396), _750394))], (7938 ^ _434076) ^ [_750703, _750705, _750707] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _750707, _750705)), _750703)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _750707), plus_plus(nat, _750703, _750705))))], (7944 ^ _434076) ^ [_750923, _750925, _750927] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _750927), plus_plus(nat, _750923, _750925))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), minus_minus(nat, _750927, _750925)), _750923)))], (7950 ^ _434076) ^ [_751207, _751209, _751211] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _751209), _751207)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _751211), minus_minus(nat, plus_plus(nat, _751207, _751211), _751209))))], (7956 ^ _434076) ^ [_751475, _751477] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _751477), _751475)), -(plus_plus(nat, _751477, minus_minus(nat, _751475, _751477)) = _751475)], (7962 ^ _434076) ^ [_751733, _751735, _751737] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _751735), _751733)), -(plus_plus(nat, _751737, minus_minus(nat, _751733, _751735)) = minus_minus(nat, plus_plus(nat, _751737, _751733), _751735))], (7968 ^ _434076) ^ [_752013, _752015, _752017] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _752015), _752013)), 7971 ^ _434076 : [(7972 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _752017), minus_minus(nat, _752013, _752015))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _752017, _752015)), _752013)))], (7978 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, _752017, _752015)), _752013)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _752017), minus_minus(nat, _752013, _752015))))]]], (7984 ^ _434076) ^ [_752585, _752587] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _752587), _752585)), -(plus_plus(nat, minus_minus(nat, _752585, _752587), _752587) = _752585)], (7990 ^ _434076) ^ [_752843, _752845, _752847] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _752845), _752843)), 7993 ^ _434076 : [(7994 ^ _434076) ^ [] : [minus_minus(nat, _752843, _752845) = _752847, -(_752843 = plus_plus(nat, _752847, _752845))], (8000 ^ _434076) ^ [] : [_752843 = plus_plus(nat, _752847, _752845), -(minus_minus(nat, _752843, _752845) = _752847)]]], (8006 ^ _434076) ^ [_753375, _753377, _753379] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _753377), _753375)), -(minus_minus(nat, plus_plus(nat, _753379, _753375), _753377) = plus_plus(nat, _753379, minus_minus(nat, _753375, _753377)))], (8012 ^ _434076) ^ [_753655, _753657, _753659] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _753657), _753655)), -(plus_plus(nat, minus_minus(nat, _753655, _753657), _753659) = minus_minus(nat, plus_plus(nat, _753655, _753659), _753657))], (8018 ^ _434076) ^ [_753935, _753937, _753939] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _753937), _753935)), -(minus_minus(nat, plus_plus(nat, _753935, _753939), _753937) = plus_plus(nat, minus_minus(nat, _753935, _753937), _753939))], (8024 ^ _434076) ^ [_754230, _754232] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _754232)), hAPP(nat, int, semiring_1_of_nat(int), _754230))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _754232), _754230)))], (8030 ^ _434076) ^ [_754448, _754450] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _754450), _754448)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _754450)), hAPP(nat, int, semiring_1_of_nat(int), _754448))))], (8036 ^ _434076) ^ [_754745, _754747] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _754747)), hAPP(nat, int, semiring_1_of_nat(int), _754745))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _754747), _754745)))], (8042 ^ _434076) ^ [_754963, _754965] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _754965), _754963)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _754965)), hAPP(nat, int, semiring_1_of_nat(int), _754963))))], (8048 ^ _434076) ^ [_755231, _755233] : [hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, _755231)), hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, _755233)), -(hBOOL(hAPP(int, bool, twoSqu658283162sum2sq, times_times(int, _755231, _755233))))], (8058 ^ _434076) ^ [_755591, _755593] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _755593), minus_minus(int, _755591, one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _755593), _755591)))], (8064 ^ _434076) ^ [_755797, _755799] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _755799), _755797)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _755799), minus_minus(int, _755797, one_one(int)))))], (8080 ^ _434076) ^ [_756402, _756404] : [8081 ^ _434076 : [(8082 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _756404), _756402))], (8084 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _756404), pls))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), number_number_of(nat, _756404)), number_number_of(nat, _756402))))], (8070 ^ _434076) ^ [_756082, _756084] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), number_number_of(nat, _756084)), number_number_of(nat, _756082))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _756084), _756082))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _756084), pls)))], (8088 ^ _434076) ^ [_756742] : [ring_1(_756742), 8091 ^ _434076 : [(8092 ^ _434076) ^ [_756930, _756932] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _756932), _756930)), -(hAPP(nat, _756742, semiring_1_of_nat(_756742), minus_minus(nat, _756930, _756932)) = minus_minus(_756742, hAPP(nat, _756742, semiring_1_of_nat(_756742), _756930), hAPP(nat, _756742, semiring_1_of_nat(_756742), _756932)))]]], (8098 ^ _434076) ^ [_757229, _757231] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _757229)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _757231)), 8105 ^ _434076 : [(8106 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), nat_1(_757229)), nat_1(_757231))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _757229), _757231)))], (8112 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _757229), _757231)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), nat_1(_757229)), nat_1(_757231))))]]], (8118 ^ _434076) ^ [_757860, _757862] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _757860)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _757860), _757862)), -(nat_1(minus_minus(int, _757862, _757860)) = minus_minus(nat, nat_1(_757862), nat_1(_757860)))], (8128 ^ _434076) ^ [_758213, _758215] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _758213)), -(nat_1(times_times(int, _758213, _758215)) = times_times(nat, nat_1(_758213), nat_1(_758215)))], (8134 ^ _434076) ^ [_758459, _758461] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _758459)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _758461)), -(times_times(nat, nat_1(_758459), nat_1(_758461)) = nat_1(times_times(int, _758459, _758461)))], (8144 ^ _434076) ^ [_758822, _758824] : [_758822 = zero_zero(nat), -(times_times(nat, _758822, _758824) = zero_zero(nat))], (8150 ^ _434076) ^ [_758992, _758994] : [-(_758992 = zero_zero(nat)), -(times_times(nat, _758992, _758994) = plus_plus(nat, _758994, times_times(nat, minus_minus(nat, _758992, one_one(nat)), _758994)))], (8156 ^ _434076) ^ [_759239, _759241] : [8157 ^ _434076 : [(8158 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _759239))], (8160 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _759241))]], 8161 ^ _434076 : [(8162 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), nat_1(_759239)), nat_1(_759241))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _759239), _759241)))], (8168 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _759239), _759241)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), nat_1(_759239)), nat_1(_759241))))]]], (8174 ^ _434076) ^ [_759875, _759877] : [_759875 = zero_zero(nat), -(hAPP(nat, nat, power_power(nat, _759877), _759875) = one_one(nat))], (8180 ^ _434076) ^ [_760053, _760055] : [-(_760053 = zero_zero(nat)), -(hAPP(nat, nat, power_power(nat, _760055), _760053) = times_times(nat, _760055, hAPP(nat, nat, power_power(nat, _760055), minus_minus(nat, _760053, one_one(nat)))))], (8186 ^ _434076) ^ [_760302] : [monoid_mult(_760302), 8189 ^ _434076 : [(8190 ^ _434076) ^ [_760459, _760461] : [-(hAPP(nat, _760302, power_power(_760302, _760461), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _760459)) = hAPP(nat, _760302, power_power(_760302, hAPP(nat, _760302, power_power(_760302, _760461), _760459)), number_number_of(nat, bit0(bit1(pls)))))]]], (8192 ^ _434076) ^ [_760574] : [-(times_times(nat, number_number_of(nat, bit0(bit1(pls))), _760574) = plus_plus(nat, _760574, _760574))], (8194 ^ _434076) ^ [_760660] : [-(times_times(nat, _760660, number_number_of(nat, bit0(bit1(pls)))) = plus_plus(nat, _760660, _760660))], (8196 ^ _434076) ^ [_760809, _760811, _760813] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _760809), pls)), -(times_times(nat, number_number_of(nat, _760809), times_times(nat, number_number_of(nat, _760813), _760811)) = zero_zero(nat))], (8202 ^ _434076) ^ [_761023, _761025, _761027] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _761023), pls))), -(times_times(nat, number_number_of(nat, _761023), times_times(nat, number_number_of(nat, _761027), _761025)) = times_times(nat, number_number_of(nat, times_times(int, _761023, _761027)), _761025))], (8208 ^ _434076) ^ [_761332, _761334] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _761332), pls)), -(times_times(nat, number_number_of(nat, _761332), number_number_of(nat, _761334)) = zero_zero(nat))], (8214 ^ _434076) ^ [_761532, _761534] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _761532), pls))), -(times_times(nat, number_number_of(nat, _761532), number_number_of(nat, _761534)) = number_number_of(nat, times_times(int, _761532, _761534)))], (8220 ^ _434076) ^ [_761770] : [-(times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), hAPP(nat, real, power_power(real, _761770), number_number_of(nat, bit0(bit1(pls))))) = hAPP(nat, real, power_power(real, times_times(real, number_number_of(real, bit0(bit1(pls))), _761770)), number_number_of(nat, bit0(bit1(pls)))))], (8222 ^ _434076) ^ [_761872] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), one_one(real)), hAPP(nat, real, power_power(real, number_number_of(real, bit0(bit1(pls)))), _761872))))], (8224 ^ _434076) ^ [_762002, _762004, _762006] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _762004), _762002)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _762006), _762002)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _762004), _762006))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _762006), _762004)))], (8238 ^ _434076) ^ [_762462, _762464] : [-(times_times(int, plus_plus(int, _762464, _762462), minus_minus(int, _762464, _762462)) = minus_minus(int, hAPP(nat, int, power_power(int, _762464), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, _762462), number_number_of(nat, bit0(bit1(pls))))))], (8240 ^ _434076) ^ [_762589] : [linordered_idom(_762589), 8243 ^ _434076 : [(8244 ^ _434076) ^ [_762772, _762774] : [hBOOL(hAPP(_762589, bool, hAPP(_762589, fun(_762589, bool), ord_less_eq(_762589), hAPP(nat, _762589, power_power(_762589, _762774), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _762772))), zero_zero(_762589))), -(ti(_762589, _762774) = zero_zero(_762589))]]], (8250 ^ _434076) ^ [_763047] : [linordered_idom(_763047), 8253 ^ _434076 : [(8254 ^ _434076) ^ [_763204, _763206] : [-(hBOOL(hAPP(_763047, bool, hAPP(_763047, fun(_763047, bool), ord_less_eq(_763047), zero_zero(_763047)), hAPP(nat, _763047, power_power(_763047, _763206), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _763204)))))]]], (8256 ^ _434076) ^ [_763333, _763335] : [-(minus_minus(nat, hAPP(nat, nat, power_power(nat, _763335), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, nat, power_power(nat, _763333), number_number_of(nat, bit0(bit1(pls))))) = times_times(nat, plus_plus(nat, _763335, _763333), minus_minus(nat, _763335, _763333)))], (8258 ^ _434076) ^ [_763459, _763461] : [-(hAPP(nat, int, power_power(int, minus_minus(int, _763461, _763459)), number_number_of(nat, bit1(bit1(pls)))) = minus_minus(int, plus_plus(int, minus_minus(int, hAPP(nat, int, power_power(int, _763461), number_number_of(nat, bit1(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), hAPP(nat, int, power_power(int, _763461), number_number_of(nat, bit0(bit1(pls))))), _763459)), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), _763461), hAPP(nat, int, power_power(int, _763459), number_number_of(nat, bit0(bit1(pls)))))), hAPP(nat, int, power_power(int, _763459), number_number_of(nat, bit1(bit1(pls))))))], (8260 ^ _434076) ^ [_763625, _763627] : [-(hAPP(nat, int, power_power(int, minus_minus(int, _763627, _763625)), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(int, minus_minus(int, hAPP(nat, int, power_power(int, _763627), number_number_of(nat, bit0(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit0(bit1(pls))), _763627), _763625)), hAPP(nat, int, power_power(int, _763625), number_number_of(nat, bit0(bit1(pls))))))], (8262 ^ _434076) ^ [_763834, _763836, _763838, _763840, _763842, _763844] : [plus_plus(int, times_times(int, _763844, _763842), _763840) = plus_plus(int, times_times(int, _763838, _763836), _763834), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), plus_plus(int, times_times(int, _763838, _763836), _763834)), zero_zero(int))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _763840), _763844)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _763834)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _763838)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _763838), _763844)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _763836), _763842)))], (8288 ^ _434076) ^ [_764771, _764773, _764775, _764777, _764779] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, times_times(int, _764779, _764777), _764775)), plus_plus(int, times_times(int, _764779, _764773), _764771))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _764771), zero_zero(int))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _764779), _764771)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _764779), _764775)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _764773), _764777)))], (8306 ^ _434076) ^ [_765480, _765482, _765484, _765486, _765488, _765490] : [plus_plus(int, times_times(int, _765490, _765488), _765486) = plus_plus(int, times_times(int, _765484, _765482), _765480), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), plus_plus(int, times_times(int, _765484, _765482), _765480))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _765480), _765484)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _765486)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _765484)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _765484), _765490)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _765488), _765482)))], (8332 ^ _434076) ^ [_766407, _766409, _766411, _766413, _766415] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, times_times(int, _766415, _766413), _766411)), plus_plus(int, times_times(int, _766415, _766409), _766407))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _766411)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _766411), _766415)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _766407), _766415)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _766413), _766409)))], (8350 ^ _434076) ^ [] : [-(plus_plus(int, hAPP(nat, int, power_power(int, x), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, y), number_number_of(nat, bit0(bit1(pls))))) = times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))], (8352 ^ _434076) ^ [_767089] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, bit0(bit1(pls)))), _767089)), -(minus_minus(nat, nat_1(_767089), number_number_of(nat, bit0(bit1(pls)))) = nat_1(minus_minus(int, _767089, number_number_of(int, bit0(bit1(pls))))))], (8358 ^ _434076) ^ [_767311] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, bit0(bit1(pls)))), _767311)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), nat_1(minus_minus(int, _767311, number_number_of(int, bit0(bit1(pls))))))))], (8365 ^ _434076) ^ [] : [-(plus_plus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), one_one(int)) = times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), 8363 ^ []))], (8367 ^ _434076) ^ [_767610] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _767610), _767610)))], (8369 ^ _434076) ^ [_767711, _767713] : [-(times_times(real, _767713, _767711) = times_times(real, _767711, _767713))], (8371 ^ _434076) ^ [_767828, _767830] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _767830), _767828))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _767828), _767830)))], (8377 ^ _434076) ^ [_768074, _768076, _768078] : [-(times_times(real, times_times(real, _768078, _768076), _768074) = times_times(real, _768078, times_times(real, _768076, _768074)))], (8379 ^ _434076) ^ [_768215, _768217, _768219] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _768217), _768215)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _768215), _768219)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _768217), _768219)))], (8389 ^ _434076) ^ [_768578, _768580] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _768580), _768578)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _768578), _768580)), -(_768580 = _768578)], (8399 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))))], (8401 ^ _434076) ^ [_768980, _768982, _768984] : [minus_minus(int, _768984, _768982) = ti(int, _768980), -(ti(int, _768984) = plus_plus(int, _768980, _768982))], (8407 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))), plus_plus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), one_one(int)))))], (8409 ^ _434076) ^ [_769262, _769264] : [-(hAPP(nat, real, power_power(real, plus_plus(real, _769264, _769262)), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(real, plus_plus(real, hAPP(nat, real, power_power(real, _769264), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, real, power_power(real, _769262), number_number_of(nat, bit0(bit1(pls))))), times_times(real, times_times(real, number_number_of(real, bit0(bit1(pls))), _769264), _769262)))], (8411 ^ _434076) ^ [] : [-(minus_minus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)) = plus_plus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), one_one(int)))], (8413 ^ _434076) ^ [_769454] : [comm_semiring_1(_769454), 8416 ^ _434076 : [(8417 ^ _434076) ^ [_769580] : [-(hBOOL(hAPP(_769454, bool, hAPP(_769454, fun(_769454, bool), dvd_dvd(_769454), _769580), zero_zero(_769454))))]]], (8419 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))), minus_minus(int, hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)))))], (8421 ^ _434076) ^ [] : [-(legendre(number_number_of(int, min), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))) = one_one(int))], (8423 ^ _434076) ^ [_769830, _769832, _769834] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _769834), minus_minus(int, _769832, _769830))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _769834), _769830)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _769834), _769832)))], (8433 ^ _434076) ^ [_770215, _770217, _770219] : [hBOOL(hAPP(int, bool, zprime, _770215)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _770215), times_times(int, _770219, _770217))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _770215), _770219))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _770215), _770217)))], (8447 ^ _434076) ^ [_770674] : [comm_semiring_1(_770674), 8450 ^ _434076 : [(8451 ^ _434076) ^ [_770875, _770877, _770879] : [hBOOL(hAPP(_770674, bool, hAPP(_770674, fun(_770674, bool), dvd_dvd(_770674), times_times(_770674, _770879, _770877)), _770875)), -(hBOOL(hAPP(_770674, bool, hAPP(_770674, fun(_770674, bool), dvd_dvd(_770674), _770877), _770875)))]]], (8457 ^ _434076) ^ [_771154] : [comm_semiring_1(_771154), 8460 ^ _434076 : [(8461 ^ _434076) ^ [_771355, _771357, _771359] : [hBOOL(hAPP(_771154, bool, hAPP(_771154, fun(_771154, bool), dvd_dvd(_771154), times_times(_771154, _771359, _771357)), _771355)), -(hBOOL(hAPP(_771154, bool, hAPP(_771154, fun(_771154, bool), dvd_dvd(_771154), _771359), _771355)))]]], (8467 ^ _434076) ^ [_771634] : [dvd(_771634), 8470 ^ _434076 : [(8471 ^ _434076) ^ [_771821, _771823, _771825] : [_771825 = times_times(_771634, _771823, _771821), -(hBOOL(hAPP(_771634, bool, hAPP(_771634, fun(_771634, bool), dvd_dvd(_771634), _771823), _771825)))]]], (8477 ^ _434076) ^ [_772072] : [comm_semiring_1(_772072), 8480 ^ _434076 : [(8481 ^ _434076) ^ [_772316, _772318, _772320, _772322] : [hBOOL(hAPP(_772072, bool, hAPP(_772072, fun(_772072, bool), dvd_dvd(_772072), _772318), _772316)), hBOOL(hAPP(_772072, bool, hAPP(_772072, fun(_772072, bool), dvd_dvd(_772072), _772322), _772320)), -(hBOOL(hAPP(_772072, bool, hAPP(_772072, fun(_772072, bool), dvd_dvd(_772072), times_times(_772072, _772318, _772322)), times_times(_772072, _772316, _772320))))]]], (8491 ^ _434076) ^ [_772738] : [comm_semiring_1(_772738), 8494 ^ _434076 : [(8495 ^ _434076) ^ [_772939, _772941, _772943] : [hBOOL(hAPP(_772738, bool, hAPP(_772738, fun(_772738, bool), dvd_dvd(_772738), _772941), _772939)), -(hBOOL(hAPP(_772738, bool, hAPP(_772738, fun(_772738, bool), dvd_dvd(_772738), _772941), times_times(_772738, _772943, _772939))))]]], (8501 ^ _434076) ^ [_773218] : [comm_semiring_1(_773218), 8504 ^ _434076 : [(8505 ^ _434076) ^ [_773419, _773421, _773423] : [hBOOL(hAPP(_773218, bool, hAPP(_773218, fun(_773218, bool), dvd_dvd(_773218), _773421), _773419)), -(hBOOL(hAPP(_773218, bool, hAPP(_773218, fun(_773218, bool), dvd_dvd(_773218), _773421), times_times(_773218, _773419, _773423))))]]], (8511 ^ _434076) ^ [_773698] : [comm_semiring_1(_773698), 8514 ^ _434076 : [(8515 ^ _434076) ^ [_773845, _773847] : [-(hBOOL(hAPP(_773698, bool, hAPP(_773698, fun(_773698, bool), dvd_dvd(_773698), _773847), times_times(_773698, _773845, _773847))))]]], (8517 ^ _434076) ^ [_773965] : [comm_semiring_1(_773965), 8520 ^ _434076 : [(8521 ^ _434076) ^ [_774112, _774114] : [-(hBOOL(hAPP(_773965, bool, hAPP(_773965, fun(_773965, bool), dvd_dvd(_773965), _774114), times_times(_773965, _774114, _774112))))]]], (8523 ^ _434076) ^ [_774232] : [comm_ring_1(_774232), 8526 ^ _434076 : [(8527 ^ _434076) ^ [_774453, _774455, _774457] : [hBOOL(hAPP(_774232, bool, hAPP(_774232, fun(_774232, bool), dvd_dvd(_774232), _774455), _774453)), hBOOL(hAPP(_774232, bool, hAPP(_774232, fun(_774232, bool), dvd_dvd(_774232), _774455), _774457)), -(hBOOL(hAPP(_774232, bool, hAPP(_774232, fun(_774232, bool), dvd_dvd(_774232), _774455), minus_minus(_774232, _774453, _774457))))]]], (8537 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), min)))], (8539 ^ _434076) ^ [_774924, _774926] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _774926), _774924)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _774924), zero_zero(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _774926), _774924)))], (8549 ^ _434076) ^ [_775292, _775294, _775296] : [hBOOL(hAPP(int, bool, zprime, _775292)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _775292), hAPP(nat, int, power_power(int, _775296), _775294))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _775292), _775296)))], (8559 ^ _434076) ^ [_775647] : [idom(_775647), 8562 ^ _434076 : [(8573 ^ _434076) ^ [_776248, _776250, _776252] : [8574 ^ _434076 : [(8575 ^ _434076) ^ [] : [ti(_775647, _776252) = zero_zero(_775647)], (8577 ^ _434076) ^ [] : [hBOOL(hAPP(_775647, bool, hAPP(_775647, fun(_775647, bool), dvd_dvd(_775647), _776250), _776248))]], -(hBOOL(hAPP(_775647, bool, hAPP(_775647, fun(_775647, bool), dvd_dvd(_775647), times_times(_775647, _776252, _776250)), times_times(_775647, _776252, _776248))))], (8563 ^ _434076) ^ [_775892, _775894, _775896] : [hBOOL(hAPP(_775647, bool, hAPP(_775647, fun(_775647, bool), dvd_dvd(_775647), times_times(_775647, _775896, _775894)), times_times(_775647, _775896, _775892))), -(ti(_775647, _775896) = zero_zero(_775647)), -(hBOOL(hAPP(_775647, bool, hAPP(_775647, fun(_775647, bool), dvd_dvd(_775647), _775894), _775892)))]]], (8581 ^ _434076) ^ [_776625] : [idom(_776625), 8584 ^ _434076 : [(8595 ^ _434076) ^ [_777226, _777228, _777230] : [8596 ^ _434076 : [(8597 ^ _434076) ^ [] : [ti(_776625, _777228) = zero_zero(_776625)], (8599 ^ _434076) ^ [] : [hBOOL(hAPP(_776625, bool, hAPP(_776625, fun(_776625, bool), dvd_dvd(_776625), _777230), _777226))]], -(hBOOL(hAPP(_776625, bool, hAPP(_776625, fun(_776625, bool), dvd_dvd(_776625), times_times(_776625, _777230, _777228)), times_times(_776625, _777226, _777228))))], (8585 ^ _434076) ^ [_776870, _776872, _776874] : [hBOOL(hAPP(_776625, bool, hAPP(_776625, fun(_776625, bool), dvd_dvd(_776625), times_times(_776625, _776874, _776872)), times_times(_776625, _776870, _776872))), -(ti(_776625, _776872) = zero_zero(_776625)), -(hBOOL(hAPP(_776625, bool, hAPP(_776625, fun(_776625, bool), dvd_dvd(_776625), _776874), _776870)))]]], (8603 ^ _434076) ^ [_777603] : [comm_semiring_1(_777603), 8606 ^ _434076 : [(8607 ^ _434076) ^ [_777811, _777813, _777815] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _777813), _777811)), -(hBOOL(hAPP(_777603, bool, hAPP(_777603, fun(_777603, bool), dvd_dvd(_777603), hAPP(nat, _777603, power_power(_777603, _777815), _777813)), hAPP(nat, _777603, power_power(_777603, _777815), _777811))))]]], (8613 ^ _434076) ^ [_778104] : [comm_semiring_1(_778104), 8616 ^ _434076 : [(8617 ^ _434076) ^ [_778351, _778353, _778355, _778357] : [hBOOL(hAPP(_778104, bool, hAPP(_778104, fun(_778104, bool), dvd_dvd(_778104), _778353), _778351)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _778357), _778355)), -(hBOOL(hAPP(_778104, bool, hAPP(_778104, fun(_778104, bool), dvd_dvd(_778104), hAPP(nat, _778104, power_power(_778104, _778353), _778357)), hAPP(nat, _778104, power_power(_778104, _778351), _778355))))]]], (8627 ^ _434076) ^ [_778779] : [comm_semiring_1(_778779), 8630 ^ _434076 : [(8631 ^ _434076) ^ [_779026, _779028, _779030, _779032] : [hBOOL(hAPP(_778779, bool, hAPP(_778779, fun(_778779, bool), dvd_dvd(_778779), hAPP(nat, _778779, power_power(_778779, _779030), _779028)), _779026)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _779032), _779028)), -(hBOOL(hAPP(_778779, bool, hAPP(_778779, fun(_778779, bool), dvd_dvd(_778779), hAPP(nat, _778779, power_power(_778779, _779030), _779032)), _779026)))]]], (8641 ^ _434076) ^ [_779468, _779470] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _779468)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _779468), _779470)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _779470), _779468))], (8651 ^ _434076) ^ [_779826, _779828, _779830] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), times_times(int, _779830, _779828)), times_times(int, _779830, _779826))), -(ti(int, _779830) = zero_zero(int)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _779828), _779826)))], (8661 ^ _434076) ^ [_780196, _780198] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _780196)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _780198)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _780196), _780198)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _780198), _780196)), -(ti(int, _780196) = ti(int, _780198))], (8679 ^ _434076) ^ [_780780, _780782, _780784] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _780784), plus_plus(int, _780782, times_times(int, _780784, _780780)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _780784), _780782)))], (8685 ^ _434076) ^ [_781000, _781002, _781004] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781004), _781002)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781004), plus_plus(int, _781002, times_times(int, _781004, _781000)))))], (8691 ^ _434076) ^ [_781312, _781314, _781316, _781318, _781320] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781314), _781312)), 8694 ^ _434076 : [(8695 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781314), plus_plus(int, _781318, _781316))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781314), plus_plus(int, plus_plus(int, _781318, times_times(int, _781320, _781312)), _781316))))], (8701 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781314), plus_plus(int, plus_plus(int, _781318, times_times(int, _781320, _781312)), _781316))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _781314), plus_plus(int, _781318, _781316))))]]], (8707 ^ _434076) ^ [_781955] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), bit1(_781955))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _781955)))], (8713 ^ _434076) ^ [_782131] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _782131)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), bit1(_782131))))], (8719 ^ _434076) ^ [_782372] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_782372)), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _782372), min)))], (8725 ^ _434076) ^ [_782568] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _782568), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit1(_782568)), min)))], (8731 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)))], (8733 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), min))], (8735 ^ _434076) ^ [_782934] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), bit0(_782934))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _782934)))], (8741 ^ _434076) ^ [_783110] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _783110)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), bit0(_783110))))], (8747 ^ _434076) ^ [_783351] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), bit1(_783351))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), _783351)))], (8753 ^ _434076) ^ [_783527] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), _783527)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), bit1(_783527))))], (8759 ^ _434076) ^ [_783768] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_783768)), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _783768), min)))], (8765 ^ _434076) ^ [_783964] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _783964), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit1(_783964)), min)))], (8771 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), zero_zero(int))))], (8773 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), pls)))], (8775 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), min))], (8777 ^ _434076) ^ [_784383] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_784383)), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _784383), min)))], (8783 ^ _434076) ^ [_784579] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _784579), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), bit0(_784579)), min)))], (8789 ^ _434076) ^ [] : [number_number_of(int, pls) = number_number_of(int, min)], (8791 ^ _434076) ^ [_784863] : [comm_semiring_1(_784863), 8794 ^ _434076 : [(8795 ^ _434076) ^ [_785080, _785082, _785084] : [hBOOL(hAPP(_784863, bool, hAPP(_784863, fun(_784863, bool), dvd_dvd(_784863), _785082), _785080)), hBOOL(hAPP(_784863, bool, hAPP(_784863, fun(_784863, bool), dvd_dvd(_784863), _785080), _785084)), -(hBOOL(hAPP(_784863, bool, hAPP(_784863, fun(_784863, bool), dvd_dvd(_784863), _785082), _785084)))]]], (8805 ^ _434076) ^ [_785476] : [comm_semiring_1(_785476), 8808 ^ _434076 : [(8809 ^ _434076) ^ [_785600] : [-(hBOOL(hAPP(_785476, bool, hAPP(_785476, fun(_785476, bool), dvd_dvd(_785476), _785600), _785600)))]]], (8811 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), min))], (8813 ^ _434076) ^ [_785750] : [min = bit0(_785750)], (8815 ^ _434076) ^ [_785829] : [bit0(_785829) = min], (8817 ^ _434076) ^ [] : [min = pls], (8819 ^ _434076) ^ [] : [pls = min], (8821 ^ _434076) ^ [] : [-(bit1(min) = min)], (8823 ^ _434076) ^ [_786110] : [min = bit1(_786110), -(min = ti(int, _786110))], (8829 ^ _434076) ^ [_786276] : [min = ti(int, _786276), -(min = bit1(_786276))], (8835 ^ _434076) ^ [_786507] : [bit1(_786507) = min, -(ti(int, _786507) = min)], (8841 ^ _434076) ^ [_786673] : [ti(int, _786673) = min, -(bit1(_786673) = min)], (8847 ^ _434076) ^ [_786875] : [comm_semiring_1(_786875), 8850 ^ _434076 : [(8851 ^ _434076) ^ [_787088, _787090, _787092] : [hBOOL(hAPP(_786875, bool, hAPP(_786875, fun(_786875, bool), dvd_dvd(_786875), _787090), _787088)), -(hBOOL(hAPP(_786875, bool, hAPP(_786875, fun(_786875, bool), dvd_dvd(_786875), hAPP(nat, _786875, power_power(_786875, _787090), _787092)), hAPP(nat, _786875, power_power(_786875, _787088), _787092))))]]], (8857 ^ _434076) ^ [_787391] : [comm_semiring_1(_787391), 8860 ^ _434076 : [(8861 ^ _434076) ^ [_787517] : [-(hBOOL(hAPP(_787391, bool, hAPP(_787391, fun(_787391, bool), dvd_dvd(_787391), one_one(_787391)), _787517)))]]], (8863 ^ _434076) ^ [_787633] : [comm_semiring_1(_787633), 8866 ^ _434076 : [(8867 ^ _434076) ^ [_787854, _787856, _787858] : [hBOOL(hAPP(_787633, bool, hAPP(_787633, fun(_787633, bool), dvd_dvd(_787633), _787856), _787854)), hBOOL(hAPP(_787633, bool, hAPP(_787633, fun(_787633, bool), dvd_dvd(_787633), _787856), _787858)), -(hBOOL(hAPP(_787633, bool, hAPP(_787633, fun(_787633, bool), dvd_dvd(_787633), _787856), plus_plus(_787633, _787854, _787858))))]]], (8877 ^ _434076) ^ [_788258] : [comm_semiring_1(_788258), 8880 ^ _434076 : [(8881 ^ _434076) ^ [_788410] : [hBOOL(hAPP(_788258, bool, hAPP(_788258, fun(_788258, bool), dvd_dvd(_788258), zero_zero(_788258)), _788410)), -(ti(_788258, _788410) = zero_zero(_788258))]]], (8887 ^ _434076) ^ [] : [-(succ(min) = pls)], (8889 ^ _434076) ^ [_788693] : [-(minus_minus(int, _788693, min) = succ(_788693))], (8891 ^ _434076) ^ [_788806, _788808] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _788808), _788806)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _788806)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _788808), _788806)))], (8901 ^ _434076) ^ [_789163, _789165, _789167] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _789163)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _789167), _789165)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _789167), hAPP(nat, int, power_power(int, _789165), _789163))))], (8911 ^ _434076) ^ [_789547] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), bit0(_789547))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _789547)))], (8917 ^ _434076) ^ [_789723] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), _789723)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), min), bit0(_789723))))], (8923 ^ _434076) ^ [_789964] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_789964)), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _789964), min)))], (8929 ^ _434076) ^ [_790160] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _790160), min)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), bit0(_790160)), min)))], (8935 ^ _434076) ^ [_790377] : [-(minus_minus(int, pls, bit1(_790377)) = bit1(minus_minus(int, min, _790377)))], (8937 ^ _434076) ^ [_790467] : [-(minus_minus(int, min, bit1(_790467)) = bit0(minus_minus(int, min, _790467)))], (8939 ^ _434076) ^ [_790557] : [-(minus_minus(int, min, bit0(_790557)) = bit1(minus_minus(int, min, _790557)))], (8941 ^ _434076) ^ [_790705, _790707] : [times_times(int, _790707, _790705) = one_one(int), 8946 ^ _434076 : [(8947 ^ _434076) ^ [] : [-(ti(int, _790707) = one_one(int))], (8949 ^ _434076) ^ [] : [-(ti(int, _790705) = one_one(int))]], 8950 ^ _434076 : [(8951 ^ _434076) ^ [] : [-(ti(int, _790707) = number_number_of(int, min))], (8953 ^ _434076) ^ [] : [-(ti(int, _790705) = number_number_of(int, min))]]], (8955 ^ _434076) ^ [_791139, _791141] : [-(times_times(int, _791141, _791139) = one_one(int)), 8956 ^ _434076 : [(8957 ^ _434076) ^ [] : [ti(int, _791141) = one_one(int), ti(int, _791139) = one_one(int)], (8963 ^ _434076) ^ [] : [ti(int, _791141) = number_number_of(int, min), ti(int, _791139) = number_number_of(int, min)]]], (8971 ^ _434076) ^ [_791635, _791637] : [times_times(int, _791637, _791635) = one_one(int), -(ti(int, _791637) = one_one(int)), -(ti(int, _791637) = number_number_of(int, min))], (8981 ^ _434076) ^ [_791983, _791985, _791987, _791989] : [hBOOL(hAPP(int, bool, zprime, _791983)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _791983), _791985))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, power_power(int, _791983), _791989)), times_times(int, _791987, _791985))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, power_power(int, _791983), _791989)), _791987)))], (8995 ^ _434076) ^ [_792532, _792534, _792536, _792538] : [hBOOL(hAPP(int, bool, zprime, _792532)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _792532), _792534))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, power_power(int, _792532), _792538)), times_times(int, _792534, _792536))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, power_power(int, _792532), _792538)), _792536)))], (9009 ^ _434076) ^ [_793039] : [comm_semiring_1(_793039), 9012 ^ _434076 : [(9013 ^ _434076) ^ [_793226, _793228] : [9014 ^ _434076 : [(9015 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _793226))], (9017 ^ _434076) ^ [] : [ti(_793039, _793228) = one_one(_793039)]], -(hBOOL(hAPP(_793039, bool, hAPP(_793039, fun(_793039, bool), dvd_dvd(_793039), _793228), hAPP(nat, _793039, power_power(_793039, _793228), _793226))))]]], (9021 ^ _434076) ^ [_793601, _793603, _793605] : [hBOOL(hAPP(int, bool, zprime, _793601)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _793601), hAPP(nat, int, power_power(int, _793605), _793603))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _793603)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _793601), _793605)))], (9035 ^ _434076) ^ [_794057] : [number_ring(_794057), 9038 ^ _434076 : [(9039 ^ _434076) ^ [_794184] : [-(hAPP(nat, _794057, power_power(_794057, number_number_of(_794057, min)), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _794184)) = one_one(_794057))]]], (9041 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, quadRes(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))), number_number_of(int, min))))], (9043 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9045 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, quadRes(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))), number_number_of(int, min)))), legendre(number_number_of(int, min), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))) = one_one(int)], (9051 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, s1), number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9053 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), s)))], (9055 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), s), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9057 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(s1, s), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9060 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, 9058 ^ []), number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9062 ^ _434076) ^ [_794877, _794879, _794881] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _794879), _794877)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _794879, _794881)), times_times(nat, _794877, _794881))))], (9068 ^ _434076) ^ [_795159, _795161, _795163] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _795161), _795159)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _795163, _795161)), times_times(nat, _795163, _795159))))], (9074 ^ _434076) ^ [_795441, _795443, _795445] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _795443), _795441)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _795443), _795445)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _795443), minus_minus(nat, _795441, _795445))))], (9084 ^ _434076) ^ [_795841, _795843] : [hBOOL(hAPP(int, bool, zcong(_795843, zero_zero(int)), _795841)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _795841), _795843)))], (9090 ^ _434076) ^ [_796035, _796037] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _796035), _796037)), -(hBOOL(hAPP(int, bool, zcong(_796037, zero_zero(int)), _796035)))], (9096 ^ _434076) ^ [_796308, _796310] : [hBOOL(hAPP(int, bool, zcong(_796310, zero_zero(int)), _796308)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _796308), _796310)))], (9102 ^ _434076) ^ [_796502, _796504] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _796502), _796504)), -(hBOOL(hAPP(int, bool, zcong(_796504, zero_zero(int)), _796502)))], (9108 ^ _434076) ^ [_796746, _796748] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _796746)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _796746), _796748)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _796748), _796746))], (9118 ^ _434076) ^ [_797090, _797092] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _797092), _797090)), -(_797090 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _797092), _797090)))], (9138 ^ _434076) ^ [_797783, _797785, _797787] : [9139 ^ _434076 : [(9140 ^ _434076) ^ [] : [_797785 = zero_zero(nat)], (9142 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _797787), _797783))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _797787, _797785)), times_times(nat, _797783, _797785))))], (9128 ^ _434076) ^ [_797469, _797471, _797473] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _797473, _797471)), times_times(nat, _797469, _797471))), -(_797471 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _797473), _797469)))], (9146 ^ _434076) ^ [_798143, _798145, _798147] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798147), minus_minus(nat, _798145, _798143))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798147), _798143)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _798143), _798145)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798147), _798145)))], (9160 ^ _434076) ^ [_798639, _798641, _798643] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798643), minus_minus(nat, _798641, _798639))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798643), _798641)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _798639), _798641)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _798643), _798639)))], (9174 ^ _434076) ^ [_799135, _799137, _799139] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), hAPP(nat, nat, power_power(nat, _799139), _799137)), hAPP(nat, nat, power_power(nat, _799135), _799137))), -(_799137 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _799139), _799135)))], (9184 ^ _434076) ^ [_799529, _799531, _799533] : [-(_799529 = zero_zero(nat)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), hAPP(nat, nat, power_power(nat, _799533), _799529)), _799531)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _799533), _799531)))], (9194 ^ _434076) ^ [_799922, _799924] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _799924)), hAPP(nat, int, semiring_1_of_nat(int), _799922))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _799924), _799922)))], (9200 ^ _434076) ^ [_800140, _800142] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _800142), _800140)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _800142)), hAPP(nat, int, semiring_1_of_nat(int), _800140))))], (9206 ^ _434076) ^ [_800437, _800439] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _800439), _800437)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _800439)), hAPP(nat, int, semiring_1_of_nat(int), _800437))))], (9212 ^ _434076) ^ [_800655, _800657] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _800657)), hAPP(nat, int, semiring_1_of_nat(int), _800655))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _800657), _800655)))], (9218 ^ _434076) ^ [_800937, _800939, _800941] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _800939), _800937)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), hAPP(nat, nat, power_power(nat, _800939), _800941)), hAPP(nat, nat, power_power(nat, _800937), _800941))))], (9224 ^ _434076) ^ [_801236] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801236), one_one(nat))), -(_801236 = one_one(nat))], (9230 ^ _434076) ^ [_801410] : [_801410 = one_one(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801410), one_one(nat))))], (9236 ^ _434076) ^ [_801663, _801665] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801665), plus_plus(nat, _801663, _801665))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801665), _801663)))], (9242 ^ _434076) ^ [_801869, _801871] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801871), _801869)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _801871), plus_plus(nat, _801869, _801871))))], (9248 ^ _434076) ^ [_802139, _802141, _802143] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _802141), _802139)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _802141), plus_plus(nat, _802139, _802143))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _802141), _802143)))], (9258 ^ _434076) ^ [_802481] : [-(hBOOL(hAPP(int, bool, zcong(_802481, zero_zero(int)), _802481)))], (9260 ^ _434076) ^ [_802623, _802625, _802627, _802629] : [hBOOL(hAPP(int, bool, zcong(_802627, _802625), _802623)), -(hBOOL(hAPP(int, bool, zcong(plus_plus(int, _802627, _802629), plus_plus(int, _802625, _802629)), _802623)))], (9266 ^ _434076) ^ [_802931, _802933, _802935, _802937, _802939] : [hBOOL(hAPP(int, bool, zcong(_802935, _802933), _802931)), ti(int, _802933) = ti(int, _802937), hBOOL(hAPP(int, bool, zcong(_802937, _802939), _802931)), -(hBOOL(hAPP(int, bool, zcong(_802935, _802939), _802931)))], (9280 ^ _434076) ^ [_803443, _803445, _803447, _803449] : [hBOOL(hAPP(int, bool, zcong(_803447, _803445), _803443)), -(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _803447), _803449), hAPP(nat, int, power_power(int, _803445), _803449)), _803443)))], (9286 ^ _434076) ^ [_803739, _803741, _803743] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _803739)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _803741)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _803743)), hBOOL(hAPP(int, bool, zcong(_803739, _803741), _803743)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _803739), _803743)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _803741), _803743)), -(ti(int, _803739) = ti(int, _803741))], (9312 ^ _434076) ^ [_804506, _804508] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _804506)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _804506), _804508)), hBOOL(hAPP(int, bool, zcong(_804506, zero_zero(int)), _804508))], (9322 ^ _434076) ^ [_804888, _804890, _804892, _804894, _804896] : [hBOOL(hAPP(int, bool, zcong(_804892, _804890), _804888)), 9325 ^ _434076 : [(9326 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, zcong(_804896, times_times(int, _804892, _804894)), _804888)), -(hBOOL(hAPP(int, bool, zcong(_804896, times_times(int, _804890, _804894)), _804888)))], (9332 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, zcong(_804896, times_times(int, _804890, _804894)), _804888)), -(hBOOL(hAPP(int, bool, zcong(_804896, times_times(int, _804892, _804894)), _804888)))]]], (9338 ^ _434076) ^ [_805518, _805520, _805522, _805524, _805526] : [hBOOL(hAPP(int, bool, zcong(_805522, _805520), _805518)), 9341 ^ _434076 : [(9342 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, zcong(_805526, times_times(int, _805524, _805522)), _805518)), -(hBOOL(hAPP(int, bool, zcong(_805526, times_times(int, _805524, _805520)), _805518)))], (9348 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, zcong(_805526, times_times(int, _805524, _805520)), _805518)), -(hBOOL(hAPP(int, bool, zcong(_805526, times_times(int, _805524, _805522)), _805518)))]]], (9354 ^ _434076) ^ [_806106, _806108] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _806106)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _806106), _806108)), hBOOL(hAPP(int, bool, zcong(_806106, zero_zero(int)), _806108)), -(ti(int, _806106) = zero_zero(int))], (9368 ^ _434076) ^ [_806554, _806556, _806558] : [hBOOL(hAPP(int, bool, zprime, _806554)), -(hBOOL(hAPP(int, bool, zcong(_806556, zero_zero(int)), _806554))), -(hBOOL(hAPP(int, bool, zcong(_806558, zero_zero(int)), _806554))), hBOOL(hAPP(int, bool, zcong(times_times(int, _806556, _806558), zero_zero(int)), _806554))], (9382 ^ _434076) ^ [_807021, _807023] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _807023), _807021)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _807021)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _807023), _807021)))], (9392 ^ _434076) ^ [_807378, _807380, _807382] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _807382, _807380)), times_times(nat, _807382, _807378))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _807382)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _807380), _807378)))], (9402 ^ _434076) ^ [_807761, _807763, _807765] : [hBOOL(hAPP(int, bool, zprime, _807761)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _807763)), hBOOL(hAPP(int, bool, zcong(times_times(int, _807763, _807765), zero_zero(int)), _807761)), -(hBOOL(hAPP(int, bool, zcong(_807763, zero_zero(int)), _807761))), -(hBOOL(hAPP(int, bool, zcong(_807765, zero_zero(int)), _807761)))], (9420 ^ _434076) ^ [_808337, _808339, _808341] : [hBOOL(hAPP(int, bool, zprime, _808337)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _808339)), hBOOL(hAPP(int, bool, zcong(times_times(int, _808339, _808341), zero_zero(int)), _808337)), -(hBOOL(hAPP(int, bool, zcong(_808339, zero_zero(int)), _808337))), -(hBOOL(hAPP(int, bool, zcong(_808341, zero_zero(int)), _808337)))], (9438 ^ _434076) ^ [_808933, _808935, _808937, _808939] : [_808939 = plus_plus(nat, times_times(nat, _808937, _808935), _808933), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _808933)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _808933), _808935)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _808935), _808939))], (9452 ^ _434076) ^ [_809410, _809412] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _809410)), 9455 ^ _434076 : [(9456 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _809410, _809412)), _809410)), -(_809412 = one_one(nat))], (9462 ^ _434076) ^ [] : [_809412 = one_one(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _809410, _809412)), _809410)))]]], (9468 ^ _434076) ^ [_809917, _809919] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _809917)), 9471 ^ _434076 : [(9472 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _809919, _809917)), _809917)), -(_809919 = one_one(nat))], (9478 ^ _434076) ^ [] : [_809919 = one_one(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _809919, _809917)), _809917)))]]], (9484 ^ _434076) ^ [_810424, _810426] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _810424)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _810426)), 9491 ^ _434076 : [(9492 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(_810424)), nat_1(_810426))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _810424), _810426)))], (9498 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _810424), _810426)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(_810424)), nat_1(_810426))))]]], (9504 ^ _434076) ^ [_811069, _811071, _811073] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), hAPP(nat, nat, power_power(nat, _811073), _811071)), hAPP(nat, nat, power_power(nat, _811073), _811069))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), one_one(nat)), _811073)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _811071), _811069)))], (9530 ^ _434076) ^ [_811967, _811969] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(_811969)), _811967))), 9533 ^ _434076 : [(9534 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _811969)))], (9536 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _811969), hAPP(nat, int, semiring_1_of_nat(int), _811967)))]], 9537 ^ _434076 : [(9538 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _811969))], (9540 ^ _434076) ^ [] : [_811967 = zero_zero(nat)]]], (9514 ^ _434076) ^ [_811483, _811485] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(_811485)), _811483)), 9517 ^ _434076 : [(9518 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _811485)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _811485), hAPP(nat, int, semiring_1_of_nat(int), _811483))))], (9524 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _811485))), -(_811483 = zero_zero(nat))]]], (9544 ^ _434076) ^ [_812485, _812487] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, bit0(bit1(pls)))), _812485)), hBOOL(hAPP(int, bool, zcong(_812487, number_number_of(int, min)), _812485)), hBOOL(hAPP(int, bool, zcong(_812487, one_one(int)), _812485))], (9554 ^ _434076) ^ [_812835, _812837, _812839] : [-(hBOOL(hAPP(int, bool, zcong(_812837, zero_zero(int)), _812835))), hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _812839), number_number_of(nat, bit0(bit1(pls)))), _812837), _812835)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _812835), _812839))], (9564 ^ _434076) ^ [_813210, _813212] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _813212), _813210)), -(_813210 = zero_zero(nat)), -(_813210 = _813212), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _813212)), _813210)))], (9578 ^ _434076) ^ [_813630] : [hBOOL(hAPP(int, bool, zprime, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), _813630), one_one(int)))), -(legendre(number_number_of(int, min), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), _813630), one_one(int))) = one_one(int))], (9584 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, s), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, s1), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9587 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 9585 ^ [])))], (9589 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), 9585 ^ []), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9591 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(s1, 9585 ^ []), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9593 ^ _434076) ^ [_814202] : [-(ti(int, _814202) = ti(int, 9585 ^ [])), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _814202)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _814202), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))), hBOOL(hAPP(int, bool, zcong(s1, _814202), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (9607 ^ _434076) ^ [_814599] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _814599), _814599)))], (9610 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 9608 ^ [])))], (9612 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), 9608 ^ []), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9614 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, zcong(s1, 9608 ^ []), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))))], (9616 ^ _434076) ^ [_814949, _814951] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _814951), _814949)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _814949), _814951))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _814949), _814951)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _814951), _814949)))], (9630 ^ _434076) ^ [_815432, _815434, _815436] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815434), _815432)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815432), _815434))), 9645 ^ _434076 : [(9646 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815434), _815436)))], (9648 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815436), _815434))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815432), _815436)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _815436), _815432)))], (9650 ^ _434076) ^ [_816121, _816123] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816123), _816121)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816121), _816123))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816121), _816123)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816123), _816121)))], (9664 ^ _434076) ^ [_816604, _816606, _816608] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816606), _816604)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816604), _816606))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816604), _816608)), 9675 ^ _434076 : [(9676 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816606), _816608)))], (9678 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _816608), _816606))]]], (9680 ^ _434076) ^ [_817193, _817195, _817197] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817195), _817193)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817193), _817195))), _817193 = _817197, 9691 ^ _434076 : [(9692 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817195), _817197)))], (9694 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817197), _817195))]]], (9696 ^ _434076) ^ [_817764, _817766, _817768] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817766), _817764)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817764), _817766))), -(hBOOL(_817768)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817764), _817766)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _817766), _817764)))], (9714 ^ _434076) ^ [_818337, _818339] : [_818337 = _818339, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _818339), _818337)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _818337), _818339)))], (9724 ^ _434076) ^ [_818676, _818678] : [_818678 = _818676, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _818678), _818676)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _818676), _818678)))], (9734 ^ _434076) ^ [_819015, _819017] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819017), _819015)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819015), _819017))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819015), _819017)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819017), _819015)))], (9748 ^ _434076) ^ [_819484, _819486] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819486), _819484))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819486), _819484)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819484), _819486)))], (9758 ^ _434076) ^ [_819840, _819842] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819842), _819840)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819840), _819842))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819840), _819842)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _819842), _819840)))], (9772 ^ _434076) ^ [_820309, _820311] : [_820311 = _820309, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820311), _820309)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820309), _820311)))], (9782 ^ _434076) ^ [_820662, _820664, _820666] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820664), _820662)), 9793 ^ _434076 : [(9794 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820664), _820666)))], (9796 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820666), _820664))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820662), _820666)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _820666), _820662)))], (9798 ^ _434076) ^ [_821249, _821251, _821253] : [_821251 = _821249, 9809 ^ _434076 : [(9810 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821251), _821253)))], (9812 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821253), _821251))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821249), _821253)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821253), _821249)))], (9814 ^ _434076) ^ [_821818, _821820, _821822] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821820), _821818)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821818), _821822)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _821820), _821822)))], (9824 ^ _434076) ^ [_822181, _822183] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822183), _822181)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822181), _822183)), -(_822183 = _822181)], (9834 ^ _434076) ^ [_822516, _822518] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822518), _822516)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822516), _822518)), -(_822518 = _822516)], (9844 ^ _434076) ^ [_822865, _822867, _822869] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822867), _822865)), _822865 = _822869, -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _822867), _822869)))], (9854 ^ _434076) ^ [_823224, _823226, _823228] : [_823226 = _823224, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _823224), _823228)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _823226), _823228)))], (9864 ^ _434076) ^ [_823569, _823571] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _823571), _823569)), -(_823571 = _823569), 9871 ^ _434076 : [(9872 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _823571), _823569)))], (9874 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _823569), _823571))]]], (9876 ^ _434076) ^ [_824001, _824003] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824003), _824001)), 9881 ^ _434076 : [(9882 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824003), _824001)))], (9884 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824001), _824003))]], -(_824003 = _824001)], (9888 ^ _434076) ^ [_824431, _824433] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824433), _824431)), 9891 ^ _434076 : [(9892 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824431), _824433)), -(_824431 = _824433)], (9898 ^ _434076) ^ [] : [_824431 = _824433, -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824431), _824433)))]]], (9904 ^ _434076) ^ [_824936, _824938] : [_824938 = _824936, -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _824938), _824936)))], (9910 ^ _434076) ^ [_825164, _825166] : [-(_825166 = _825164), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825166), _825164)), 9917 ^ _434076 : [(9918 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825166), _825164)))], (9920 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825164), _825166))]]], (9922 ^ _434076) ^ [_825625, _825627] : [9929 ^ _434076 : [(9930 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825627), _825625)))], (9932 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825625), _825627))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825627), _825625)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _825625), _825627)))], (9934 ^ _434076) ^ [_826027, _826029] : [9941 ^ _434076 : [(9942 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826029), _826027)))], (9944 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826027), _826029))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826029), _826027)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826027), _826029)))], (9946 ^ _434076) ^ [_826508, _826510] : [9953 ^ _434076 : [(9954 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826510), _826508)))], (9956 ^ _434076) ^ [] : [_826510 = _826508]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826510), _826508)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826508), _826510)))], (9958 ^ _434076) ^ [_826892, _826894] : [9965 ^ _434076 : [(9966 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826894), _826892)))], (9968 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826892), _826894))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _826894), _826892)), -(_826894 = _826892)], (9970 ^ _434076) ^ [_827355, _827357] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827357), _827355)), 9975 ^ _434076 : [(9976 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827357), _827355)))], (9978 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827355), _827357))]], -(_827357 = _827355)], (9982 ^ _434076) ^ [_827737, _827739] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827739), _827737))), 9983 ^ _434076 : [(9990 ^ _434076) ^ [] : [_827739 = _827737], (9984 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827739), _827737)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _827737), _827739)))]]], (9994 ^ _434076) ^ [_828198, _828200] : [_828200 = _828198, 9997 ^ _434076 : [(9998 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828200), _828198)))], (10000 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828198), _828200)))]]], (10002 ^ _434076) ^ [_828471, _828473] : [-(_828473 = _828471), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828473), _828471)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828471), _828473))], (10012 ^ _434076) ^ [_828794] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828794), _828794)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _828794), _828794)))], (10028 ^ _434076) ^ [_829352, _829354] : [_829354 = _829352, 10031 ^ _434076 : [(10032 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _829354), _829352)))], (10034 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _829352), _829354)))]]], (10018 ^ _434076) ^ [_829065, _829067] : [-(_829067 = _829065), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _829067), _829065)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _829065), _829067))], (10036 ^ _434076) ^ [_829689, _829691, _829693] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, bit0(bit1(pls)))), _829689)), hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, number_number_of(int, min)), _829693), hAPP(nat, int, power_power(int, number_number_of(int, min)), _829691)), _829689)), -(hAPP(nat, int, power_power(int, number_number_of(int, min)), _829693) = hAPP(nat, int, power_power(int, number_number_of(int, min)), _829691))], (10046 ^ _434076) ^ [_830046] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, bit0(bit1(pls)))), _830046)), hBOOL(hAPP(int, bool, zcong(one_one(int), number_number_of(int, min)), _830046))], (10052 ^ _434076) ^ [_830253] : [-(hAPP(nat, int, power_power(int, number_number_of(int, min)), _830253) = one_one(int)), -(hAPP(nat, int, power_power(int, number_number_of(int, min)), _830253) = number_number_of(int, min))], (10058 ^ _434076) ^ [_830498, _830500] : [hBOOL(hAPP(int, bool, zcong(_830500, zero_zero(int)), _830498)), -(legendre(_830500, _830498) = zero_zero(int))], (10064 ^ _434076) ^ [_830680, _830682] : [-(hBOOL(hAPP(int, bool, zcong(_830682, zero_zero(int)), _830680))), 10067 ^ _434076 : [(10068 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, quadRes(_830680), _830682)), -(legendre(_830682, _830680) = one_one(int))], (10074 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, quadRes(_830680), _830682))), -(legendre(_830682, _830680) = number_number_of(int, min))]]], (10080 ^ _434076) ^ [_831230, _831232] : [hBOOL(hAPP(int, bool, quadRes(_831232), _831230)), -(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, 10083 ^ [_831230, _831232]), number_number_of(nat, bit0(bit1(pls)))), _831230), _831232)))], (10087 ^ _434076) ^ [_831506, _831508] : [10088 ^ _434076 : [(10089 ^ _434076) ^ [_831597] : [hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _831597), number_number_of(nat, bit0(bit1(pls)))), _831506), _831508))]], -(hBOOL(hAPP(int, bool, quadRes(_831508), _831506)))], (10093 ^ _434076) ^ [_831782, _831784] : [hBOOL(hAPP(int, bool, zprime, _831782)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _831782), _831784))), -(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _831784), nat_1(minus_minus(int, _831782, one_one(int)))), one_one(int)), _831782)))], (10103 ^ _434076) ^ [_832152, _832154] : [hBOOL(hAPP(int, bool, zprime, _832152)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _832154)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _832154), _832152)), hBOOL(hAPP(int, bool, zcong(times_times(int, _832154, _832154), one_one(int)), _832152)), -(ti(int, _832154) = one_one(int)), -(ti(int, _832154) = minus_minus(int, _832152, one_one(int)))], (10125 ^ _434076) ^ [_832823, _832825, _832827, _832829] : [hBOOL(hAPP(int, bool, zcong(_832827, _832825), _832823)), hBOOL(hAPP(int, bool, zcong(_832825, _832829), _832823)), -(hBOOL(hAPP(int, bool, zcong(_832827, _832829), _832823)))], (10135 ^ _434076) ^ [_833169, _833171] : [-(hBOOL(hAPP(int, bool, zcong(_833171, _833171), _833169)))], (10137 ^ _434076) ^ [_833328, _833330, _833332] : [hBOOL(hAPP(int, bool, zcong(_833332, _833330), _833328)), -(hBOOL(hAPP(int, bool, zcong(_833330, _833332), _833328)))], (10143 ^ _434076) ^ [_833524, _833526, _833528] : [hBOOL(hAPP(int, bool, zcong(_833526, _833528), _833524)), -(hBOOL(hAPP(int, bool, zcong(_833528, _833526), _833524)))], (10149 ^ _434076) ^ [_833756] : [order(_833756), 10152 ^ _434076 : [(10153 ^ _434076) ^ [_833948, _833950] : [hBOOL(hAPP(_833756, bool, hAPP(_833756, fun(_833756, bool), ord_less_eq(_833756), _833950), _833948)), -(ti(_833756, _833950) = ti(_833756, _833948)), -(hBOOL(hAPP(_833756, bool, hAPP(_833756, fun(_833756, bool), ord_less(_833756), _833950), _833948)))]]], (10163 ^ _434076) ^ [_834364, _834366] : [hBOOL(hAPP(int, bool, zcong(_834366, _834364), zero_zero(int))), -(ti(int, _834366) = ti(int, _834364))], (10169 ^ _434076) ^ [_834552, _834554] : [ti(int, _834554) = ti(int, _834552), -(hBOOL(hAPP(int, bool, zcong(_834554, _834552), zero_zero(int))))], (10175 ^ _434076) ^ [_834775, _834777] : [-(hBOOL(hAPP(int, bool, zcong(_834777, _834775), one_one(int))))], (10177 ^ _434076) ^ [_834890, _834892, _834894] : [-(hBOOL(hAPP(int, bool, zcong(times_times(int, _834894, _834892), times_times(int, _834890, _834892)), _834892)))], (10179 ^ _434076) ^ [_835044, _835046, _835048, _835050] : [hBOOL(hAPP(int, bool, zcong(_835048, _835046), _835044)), -(hBOOL(hAPP(int, bool, zcong(times_times(int, _835048, _835050), times_times(int, _835046, _835050)), _835044)))], (10185 ^ _434076) ^ [_835338, _835340, _835342, _835344] : [hBOOL(hAPP(int, bool, zcong(_835342, _835340), _835338)), -(hBOOL(hAPP(int, bool, zcong(times_times(int, _835344, _835342), times_times(int, _835344, _835340)), _835338)))], (10191 ^ _434076) ^ [_835646, _835648, _835650, _835652, _835654] : [hBOOL(hAPP(int, bool, zcong(_835650, _835648), _835646)), hBOOL(hAPP(int, bool, zcong(_835654, _835652), _835646)), -(hBOOL(hAPP(int, bool, zcong(times_times(int, _835650, _835654), times_times(int, _835648, _835652)), _835646)))], (10201 ^ _434076) ^ [_836075, _836077, _836079, _836081, _836083] : [hBOOL(hAPP(int, bool, zcong(_836079, _836077), _836075)), hBOOL(hAPP(int, bool, zcong(_836083, _836081), _836075)), -(hBOOL(hAPP(int, bool, zcong(plus_plus(int, _836079, _836083), plus_plus(int, _836077, _836081)), _836075)))], (10211 ^ _434076) ^ [_836504, _836506, _836508, _836510, _836512] : [hBOOL(hAPP(int, bool, zcong(_836508, _836506), _836504)), hBOOL(hAPP(int, bool, zcong(_836512, _836510), _836504)), -(hBOOL(hAPP(int, bool, zcong(minus_minus(int, _836508, _836512), minus_minus(int, _836506, _836510)), _836504)))], (10221 ^ _434076) ^ [_836905, _836907, _836909] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _836905)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _836905), _836907)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _836909)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _836909), _836905)), hBOOL(hAPP(int, bool, zcong(_836905, _836909), _836907))], (10239 ^ _434076) ^ [_837522, _837524, _837526, _837528, _837530, _837532, _837534] : [-(plus_plus(int, times_times(int, minus_minus(int, _837534, times_times(int, _837532, _837530)), _837528), times_times(int, minus_minus(int, _837526, times_times(int, _837532, _837524)), _837522)) = minus_minus(int, plus_plus(int, times_times(int, _837534, _837528), times_times(int, _837526, _837522)), times_times(int, _837532, plus_plus(int, times_times(int, _837530, _837528), times_times(int, _837524, _837522)))))], (10241 ^ _434076) ^ [_837744, _837746, _837748] : [hBOOL(hAPP(int, bool, zcong(_837748, _837746), _837744)), -(ti(int, _837746) = plus_plus(int, _837748, times_times(int, _837744, 10244 ^ [_837744, _837746, _837748])))], (10248 ^ _434076) ^ [_838022, _838024, _838026] : [10249 ^ _434076 : [(10250 ^ _434076) ^ [_838112] : [ti(int, _838024) = plus_plus(int, _838026, times_times(int, _838022, _838112))]], -(hBOOL(hAPP(int, bool, zcong(_838026, _838024), _838022)))], (10254 ^ _434076) ^ [_838341, _838343, _838345] : [hBOOL(hAPP(int, bool, zcong(_838345, _838343), _838341)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _838341), minus_minus(int, _838345, _838343))))], (10260 ^ _434076) ^ [_838549, _838551, _838553] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _838549), minus_minus(int, _838553, _838551))), -(hBOOL(hAPP(int, bool, zcong(_838553, _838551), _838549)))], (10266 ^ _434076) ^ [_838807, _838809] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _838809), minus_minus(int, _838807, one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _838809), _838807)))], (10272 ^ _434076) ^ [_839061, _839063] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _839061)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _839061), _839063)), hBOOL(hAPP(int, bool, zcong(_839061, zero_zero(int)), _839063)), -(ti(int, _839061) = zero_zero(int))], (10286 ^ _434076) ^ [_839509, _839511, _839513] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _839509)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _839509), _839511)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _839513)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _839513), _839511)), hBOOL(hAPP(int, bool, zcong(_839509, _839513), _839511)), -(ti(int, _839509) = ti(int, _839513))], (10308 ^ _434076) ^ [_840189, _840191, _840193] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _840189)), hBOOL(hAPP(int, bool, zprime, _840191)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _840191), times_times(int, _840189, _840193))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _840191), _840189))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _840191), _840193)))], (10346 ^ _434076) ^ [_841427] : [-(hBOOL(hAPP(int, bool, zprime, _841427))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), one_one(int)), _841427)), 10352 ^ _434076 : [(10353 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 10351 ^ [_841427])))], (10355 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), 10351 ^ [_841427]), _841427)))], (10357 ^ _434076) ^ [] : [ti(int, 10351 ^ [_841427]) = one_one(int)], (10359 ^ _434076) ^ [] : [ti(int, 10351 ^ [_841427]) = ti(int, _841427)]]], (10326 ^ _434076) ^ [_840778] : [hBOOL(hAPP(int, bool, zprime, _840778)), 10329 ^ _434076 : [(10330 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), one_one(int)), _840778)))], (10332 ^ _434076) ^ [_841031] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _841031)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _841031), _840778)), -(ti(int, _841031) = one_one(int)), -(ti(int, _841031) = ti(int, _840778))]]], (10363 ^ _434076) ^ [_842102, _842104] : [hBOOL(hAPP(int, bool, zprime, _842102)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _842104)), hBOOL(hAPP(int, bool, zcong(times_times(int, _842104, _842104), one_one(int)), _842102)), -(hBOOL(hAPP(int, bool, zcong(_842104, one_one(int)), _842102))), -(hBOOL(hAPP(int, bool, zcong(_842104, minus_minus(int, _842102, one_one(int))), _842102)))], (10397 ^ _434076) ^ [_843234, _843236, _843238] : [-(hBOOL(hAPP(int, bool, _843238, hAPP(nat, int, semiring_1_of_nat(int), minus_minus(nat, _843236, _843234))))), 10400 ^ _434076 : [(10401 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _843234), _843236)))], (10403 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _843238, minus_minus(int, hAPP(nat, int, semiring_1_of_nat(int), _843236), hAPP(nat, int, semiring_1_of_nat(int), _843234))))]], 10404 ^ _434076 : [(10405 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _843236), _843234)))], (10407 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _843238, zero_zero(int)))]]], (10381 ^ _434076) ^ [_842697, _842699, _842701] : [hBOOL(hAPP(int, bool, _842701, hAPP(nat, int, semiring_1_of_nat(int), minus_minus(nat, _842699, _842697)))), 10384 ^ _434076 : [(10385 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _842697), _842699)), -(hBOOL(hAPP(int, bool, _842701, minus_minus(int, hAPP(nat, int, semiring_1_of_nat(int), _842699), hAPP(nat, int, semiring_1_of_nat(int), _842697)))))], (10391 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _842699), _842697)), -(hBOOL(hAPP(int, bool, _842701, zero_zero(int))))]]], (10411 ^ _434076) ^ [_843791] : [hBOOL(hAPP(int, bool, zprime, _843791)), -(ti(int, _843791) = number_number_of(int, bit0(bit1(pls)))), -(ti(int, _843791) = number_number_of(int, bit1(bit1(pls)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), number_number_of(int, bit1(bit0(bit1(pls))))), _843791)))], (10425 ^ _434076) ^ [_844213, _844215, _844217] : [10426 ^ _434076 : [(10427 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _844213)))], (10429 ^ _434076) ^ [] : [10430 ^ _434076 : [(10431 ^ _434076) ^ [] : [-(hBOOL(_844215))], (10433 ^ _434076) ^ [] : [hBOOL(_844217)]], 10434 ^ _434076 : [(10435 ^ _434076) ^ [] : [-(hBOOL(_844217))], (10437 ^ _434076) ^ [] : [hBOOL(_844215)]]]], 10438 ^ _434076 : [(10439 ^ _434076) ^ [] : [10446 ^ _434076 : [(10447 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _844213)))], (10449 ^ _434076) ^ [] : [-(hBOOL(_844217))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _844213)), hBOOL(_844215)], (10451 ^ _434076) ^ [] : [10458 ^ _434076 : [(10459 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _844213)))], (10461 ^ _434076) ^ [] : [-(hBOOL(_844215))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _844213)), hBOOL(_844217)]]], (10463 ^ _434076) ^ [_845372, _845374, _845376] : [10464 ^ _434076 : [(10465 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _845372)))], (10467 ^ _434076) ^ [] : [10468 ^ _434076 : [(10469 ^ _434076) ^ [] : [-(hBOOL(_845374))], (10471 ^ _434076) ^ [] : [hBOOL(_845376)]], 10472 ^ _434076 : [(10473 ^ _434076) ^ [] : [-(hBOOL(_845376))], (10475 ^ _434076) ^ [] : [hBOOL(_845374)]]]], 10476 ^ _434076 : [(10477 ^ _434076) ^ [] : [10478 ^ _434076 : [(10479 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _845372)))], (10481 ^ _434076) ^ [] : [hBOOL(_845374)]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _845372)), -(hBOOL(_845376))], (10489 ^ _434076) ^ [] : [10490 ^ _434076 : [(10491 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _845372)))], (10493 ^ _434076) ^ [] : [hBOOL(_845376)]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _845372)), -(hBOOL(_845374))]]], (10501 ^ _434076) ^ [_846531, _846533, _846535] : [-(ti(int, _846531) = zero_zero(int)), 10504 ^ _434076 : [(10505 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _846535), _846533)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), times_times(int, _846531, _846535)), times_times(int, _846531, _846533))))], (10511 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), times_times(int, _846531, _846535)), times_times(int, _846531, _846533))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _846535), _846533)))]]], (10517 ^ _434076) ^ [_847080] : [dvd(_847080), semiring_0(_847080), 10524 ^ _434076 : [(10525 ^ _434076) ^ [_847390, _847392] : [10526 ^ _434076 : [(10527 ^ _434076) ^ [_847507] : [hBOOL(hAPP(_847080, bool, _847392, times_times(_847080, _847390, _847507)))]], 10529 ^ _434076 : [(10530 ^ _434076) ^ [] : [-(hBOOL(hAPP(_847080, bool, hAPP(_847080, fun(_847080, bool), dvd_dvd(_847080), _847390), plus_plus(_847080, 10528 ^ [_847080, _847390, _847392], zero_zero(_847080)))))], (10532 ^ _434076) ^ [] : [-(hBOOL(hAPP(_847080, bool, _847392, 10528 ^ [_847080, _847390, _847392])))]]], (10534 ^ _434076) ^ [_847825, _847827] : [-(hBOOL(hAPP(_847080, bool, _847827, times_times(_847080, _847825, 10541 ^ [_847080, _847825, _847827])))), 10535 ^ _434076 : [(10536 ^ _434076) ^ [_847958] : [hBOOL(hAPP(_847080, bool, hAPP(_847080, fun(_847080, bool), dvd_dvd(_847080), _847825), plus_plus(_847080, _847958, zero_zero(_847080)))), hBOOL(hAPP(_847080, bool, _847827, _847958))]]]]], (10545 ^ _434076) ^ [_848355] : [comm_ring(_848355), dvd(_848355), 10552 ^ _434076 : [(10553 ^ _434076) ^ [_848681, _848683, _848685] : [hBOOL(hAPP(_848355, bool, hAPP(_848355, fun(_848355, bool), dvd_dvd(_848355), _848683), _848681)), 10556 ^ _434076 : [(10557 ^ _434076) ^ [_848948, _848950] : [hBOOL(hAPP(_848355, bool, hAPP(_848355, fun(_848355, bool), dvd_dvd(_848355), _848683), plus_plus(_848355, _848950, _848685))), -(hBOOL(hAPP(_848355, bool, hAPP(_848355, fun(_848355, bool), dvd_dvd(_848355), _848683), plus_plus(_848355, minus_minus(_848355, _848950, times_times(_848355, _848948, _848681)), _848685))))], (10563 ^ _434076) ^ [_849230, _849232] : [hBOOL(hAPP(_848355, bool, hAPP(_848355, fun(_848355, bool), dvd_dvd(_848355), _848683), plus_plus(_848355, minus_minus(_848355, _849232, times_times(_848355, _849230, _848681)), _848685))), -(hBOOL(hAPP(_848355, bool, hAPP(_848355, fun(_848355, bool), dvd_dvd(_848355), _848683), plus_plus(_848355, _849232, _848685))))]]]]], (10569 ^ _434076) ^ [_849560] : [comm_ring(_849560), dvd(_849560), 10576 ^ _434076 : [(10577 ^ _434076) ^ [_849890, _849892, _849894] : [hBOOL(hAPP(_849560, bool, hAPP(_849560, fun(_849560, bool), dvd_dvd(_849560), _849892), _849890)), 10580 ^ _434076 : [(10581 ^ _434076) ^ [_850161, _850163] : [-(hBOOL(hAPP(_849560, bool, hAPP(_849560, fun(_849560, bool), dvd_dvd(_849560), _849892), plus_plus(_849560, _850163, _849894)))), hBOOL(hAPP(_849560, bool, hAPP(_849560, fun(_849560, bool), dvd_dvd(_849560), _849892), plus_plus(_849560, minus_minus(_849560, _850163, times_times(_849560, _850161, _849890)), _849894)))], (10587 ^ _434076) ^ [_850447, _850449] : [-(hBOOL(hAPP(_849560, bool, hAPP(_849560, fun(_849560, bool), dvd_dvd(_849560), _849892), plus_plus(_849560, minus_minus(_849560, _850449, times_times(_849560, _850447, _849890)), _849894)))), hBOOL(hAPP(_849560, bool, hAPP(_849560, fun(_849560, bool), dvd_dvd(_849560), _849892), plus_plus(_849560, _850449, _849894)))]]]]], (10593 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, pls))))], (10595 ^ _434076) ^ [_850877, _850879] : [hBOOL(hAPP(int, bool, zcong(times_times(int, _850879, minus_minus(int, _850877, one_one(int))), one_one(int)), _850877)), -(hBOOL(hAPP(int, bool, zcong(_850879, minus_minus(int, _850877, one_one(int))), _850877)))], (10601 ^ _434076) ^ [_851091, _851093] : [hBOOL(hAPP(int, bool, zcong(_851093, minus_minus(int, _851091, one_one(int))), _851091)), -(hBOOL(hAPP(int, bool, zcong(times_times(int, _851093, minus_minus(int, _851091, one_one(int))), one_one(int)), _851091)))], (10607 ^ _434076) ^ [_851383, _851385, _851387, _851389] : [hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _851387), _851385), one_one(int)), _851383)), -(hBOOL(hAPP(int, bool, zcong(hAPP(nat, int, power_power(int, _851387), times_times(nat, _851385, _851389)), one_one(int)), _851383)))], (10613 ^ _434076) ^ [_851659] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _851659))), 10616 ^ _434076 : [(10617 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, bit0(_851659)))))], (10619 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, bit1(_851659)))))]]], (10623 ^ _434076) ^ [] : [-(ti(int, 10621 ^ []) = minus_minus(int, y, times_times(int, 10620 ^ [], plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (10625 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), times_times(int, number_number_of(int, bit0(bit1(pls))), abs_abs(int, 10621 ^ []))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (10629 ^ _434076) ^ [] : [-(ti(int, 10627 ^ []) = minus_minus(int, x, times_times(int, 10626 ^ [], plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (10631 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), times_times(int, number_number_of(int, bit0(bit1(pls))), abs_abs(int, 10627 ^ []))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (10633 ^ _434076) ^ [_852484, _852486] : [-(ti(int, _852484) = zero_zero(int)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _852486), _852484)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), abs_abs(int, _852486)), abs_abs(int, _852484))))], (10643 ^ _434076) ^ [_852825, _852827] : [-(nat_1(abs_abs(int, times_times(int, _852827, _852825))) = times_times(nat, nat_1(abs_abs(int, _852827)), nat_1(abs_abs(int, _852825))))], (10645 ^ _434076) ^ [_852943] : [linordered_idom(_852943), 10648 ^ _434076 : [(10649 ^ _434076) ^ [_853113, _853115] : [abs_abs(_852943, _853115) = abs_abs(_852943, _853113), -(hBOOL(hAPP(_852943, bool, hAPP(_852943, fun(_852943, bool), dvd_dvd(_852943), _853115), _853113)))]]], (10655 ^ _434076) ^ [_853362] : [linordered_idom(_853362), 10658 ^ _434076 : [(10659 ^ _434076) ^ [_853572, _853574] : [hBOOL(hAPP(_853362, bool, hAPP(_853362, fun(_853362, bool), dvd_dvd(_853362), abs_abs(_853362, _853574)), _853572)), -(hBOOL(hAPP(_853362, bool, hAPP(_853362, fun(_853362, bool), dvd_dvd(_853362), _853574), _853572)))], (10665 ^ _434076) ^ [_853804, _853806] : [hBOOL(hAPP(_853362, bool, hAPP(_853362, fun(_853362, bool), dvd_dvd(_853362), _853806), _853804)), -(hBOOL(hAPP(_853362, bool, hAPP(_853362, fun(_853362, bool), dvd_dvd(_853362), abs_abs(_853362, _853806)), _853804)))]]], (10671 ^ _434076) ^ [_854077] : [linordered_idom(_854077), 10674 ^ _434076 : [(10675 ^ _434076) ^ [_854287, _854289] : [hBOOL(hAPP(_854077, bool, hAPP(_854077, fun(_854077, bool), dvd_dvd(_854077), _854289), abs_abs(_854077, _854287))), -(hBOOL(hAPP(_854077, bool, hAPP(_854077, fun(_854077, bool), dvd_dvd(_854077), _854289), _854287)))], (10681 ^ _434076) ^ [_854519, _854521] : [hBOOL(hAPP(_854077, bool, hAPP(_854077, fun(_854077, bool), dvd_dvd(_854077), _854521), _854519)), -(hBOOL(hAPP(_854077, bool, hAPP(_854077, fun(_854077, bool), dvd_dvd(_854077), _854521), abs_abs(_854077, _854519))))]]], (10687 ^ _434076) ^ [_854806, _854808] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _854808), _854806)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _854806), _854808)), -(abs_abs(int, _854808) = abs_abs(int, _854806))], (10697 ^ _434076) ^ [_855168] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _855168), one_one(int))), -(abs_abs(int, _855168) = one_one(int))], (10703 ^ _434076) ^ [_855348] : [abs_abs(int, _855348) = one_one(int), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _855348), one_one(int))))], (10709 ^ _434076) ^ [_855564] : [linordered_idom(_855564), 10712 ^ _434076 : [(10713 ^ _434076) ^ [_855744, _855746] : [hBOOL(hAPP(_855564, bool, hAPP(_855564, fun(_855564, bool), ord_less_eq(_855564), zero_zero(_855564)), _855744)), -(times_times(_855564, abs_abs(_855564, _855746), _855744) = abs_abs(_855564, times_times(_855564, _855746, _855744)))]]], (10719 ^ _434076) ^ [_856013] : [ordered_ring_abs(_856013), 10722 ^ _434076 : [(10723 ^ _434076) ^ [_856262, _856264] : [-(abs_abs(_856013, times_times(_856013, _856262, _856264)) = times_times(_856013, abs_abs(_856013, _856262), abs_abs(_856013, _856264))), 10726 ^ _434076 : [(10727 ^ _434076) ^ [] : [hBOOL(hAPP(_856013, bool, hAPP(_856013, fun(_856013, bool), ord_less_eq(_856013), zero_zero(_856013)), _856262))], (10729 ^ _434076) ^ [] : [hBOOL(hAPP(_856013, bool, hAPP(_856013, fun(_856013, bool), ord_less_eq(_856013), _856262), zero_zero(_856013)))]], 10730 ^ _434076 : [(10731 ^ _434076) ^ [] : [hBOOL(hAPP(_856013, bool, hAPP(_856013, fun(_856013, bool), ord_less_eq(_856013), zero_zero(_856013)), _856264))], (10733 ^ _434076) ^ [] : [hBOOL(hAPP(_856013, bool, hAPP(_856013, fun(_856013, bool), ord_less_eq(_856013), _856264), zero_zero(_856013)))]]]]], (10737 ^ _434076) ^ [_856878] : [linordered_idom(_856878), 10740 ^ _434076 : [(10741 ^ _434076) ^ [_857034, _857036] : [-(hBOOL(hAPP(_856878, bool, hAPP(_856878, fun(_856878, bool), ord_less_eq(_856878), zero_zero(_856878)), hAPP(nat, _856878, power_power(_856878, abs_abs(_856878, _857036)), _857034))))]]], (10743 ^ _434076) ^ [_857163] : [ordere142940540dd_abs(_857163), 10746 ^ _434076 : [(10747 ^ _434076) ^ [_857377, _857379, _857381, _857383] : [-(hBOOL(hAPP(_857163, bool, hAPP(_857163, fun(_857163, bool), ord_less_eq(_857163), abs_abs(_857163, minus_minus(_857163, plus_plus(_857163, _857383, _857381), plus_plus(_857163, _857379, _857377)))), plus_plus(_857163, abs_abs(_857163, minus_minus(_857163, _857383, _857379)), abs_abs(_857163, minus_minus(_857163, _857381, _857377))))))]]], (10749 ^ _434076) ^ [_857530] : [ordere142940540dd_abs(_857530), 10752 ^ _434076 : [(10753 ^ _434076) ^ [_857690, _857692] : [-(hBOOL(hAPP(_857530, bool, hAPP(_857530, fun(_857530, bool), ord_less_eq(_857530), abs_abs(_857530, minus_minus(_857530, _857692, _857690))), plus_plus(_857530, abs_abs(_857530, _857692), abs_abs(_857530, _857690)))))]]], (10755 ^ _434076) ^ [_857823] : [-(abs_abs(_857823, number_number_of(_857823, min)) = one_one(_857823)), number_ring(_857823), linordered_idom(_857823)], (10765 ^ _434076) ^ [_858110] : [ordere142940540dd_abs(_858110), -(abs_abs(_858110, zero_zero(_858110)) = zero_zero(_858110))], (10771 ^ _434076) ^ [_858312] : [ordere142940540dd_abs(_858312), 10774 ^ _434076 : [(10775 ^ _434076) ^ [_858482] : [abs_abs(_858312, _858482) = zero_zero(_858312), -(ti(_858312, _858482) = zero_zero(_858312))], (10781 ^ _434076) ^ [_858666] : [ti(_858312, _858666) = zero_zero(_858312), -(abs_abs(_858312, _858666) = zero_zero(_858312))]]], (10787 ^ _434076) ^ [_858891] : [ordere142940540dd_abs(_858891), 10790 ^ _434076 : [(10791 ^ _434076) ^ [_859043, _859045] : [-(abs_abs(_858891, plus_plus(_858891, abs_abs(_858891, _859045), abs_abs(_858891, _859043))) = plus_plus(_858891, abs_abs(_858891, _859045), abs_abs(_858891, _859043)))]]], (10793 ^ _434076) ^ [_859168] : [linordered_idom(_859168), -(abs_abs(_859168, one_one(_859168)) = one_one(_859168))], (10799 ^ _434076) ^ [_859370] : [linordered_idom(_859370), 10802 ^ _434076 : [(10803 ^ _434076) ^ [_859521, _859523] : [-(abs_abs(_859370, hAPP(nat, _859370, power_power(_859370, _859523), _859521)) = hAPP(nat, _859370, power_power(_859370, abs_abs(_859370, _859523)), _859521))]]], (10805 ^ _434076) ^ [_859645] : [linordered_idom(_859645), 10808 ^ _434076 : [(10809 ^ _434076) ^ [_859772] : [-(abs_abs(_859645, hAPP(nat, _859645, semiring_1_of_nat(_859645), _859772)) = hAPP(nat, _859645, semiring_1_of_nat(_859645), _859772))]]], (10811 ^ _434076) ^ [_859874] : [-(abs_abs(int, hAPP(nat, int, semiring_1_of_nat(int), _859874)) = hAPP(nat, int, semiring_1_of_nat(int), _859874))], (10813 ^ _434076) ^ [_859980] : [ordere142940540dd_abs(_859980), 10816 ^ _434076 : [(10817 ^ _434076) ^ [_860099] : [-(abs_abs(_859980, abs_abs(_859980, _860099)) = abs_abs(_859980, _860099))]]], (10819 ^ _434076) ^ [_860222, _860224] : [abs_abs(int, times_times(int, _860224, _860222)) = one_one(int), -(abs_abs(int, _860224) = one_one(int))], (10825 ^ _434076) ^ [_860438] : [ordere142940540dd_abs(_860438), 10828 ^ _434076 : [(10829 ^ _434076) ^ [_860598, _860600] : [-(hBOOL(hAPP(_860438, bool, hAPP(_860438, fun(_860438, bool), ord_less_eq(_860438), minus_minus(_860438, abs_abs(_860438, _860600), abs_abs(_860438, _860598))), abs_abs(_860438, minus_minus(_860438, _860598, _860600)))))]]], (10831 ^ _434076) ^ [_860731] : [ordere142940540dd_abs(_860731), 10834 ^ _434076 : [(10835 ^ _434076) ^ [_860891, _860893] : [-(hBOOL(hAPP(_860731, bool, hAPP(_860731, fun(_860731, bool), ord_less_eq(_860731), minus_minus(_860731, abs_abs(_860731, _860893), abs_abs(_860731, _860891))), abs_abs(_860731, minus_minus(_860731, _860893, _860891)))))]]], (10837 ^ _434076) ^ [_861024] : [ordere142940540dd_abs(_861024), 10840 ^ _434076 : [(10841 ^ _434076) ^ [_861187, _861189] : [-(hBOOL(hAPP(_861024, bool, hAPP(_861024, fun(_861024, bool), ord_less_eq(_861024), abs_abs(_861024, minus_minus(_861024, abs_abs(_861024, _861189), abs_abs(_861024, _861187)))), abs_abs(_861024, minus_minus(_861024, _861189, _861187)))))]]], (10843 ^ _434076) ^ [_861323] : [ordere142940540dd_abs(_861323), 10846 ^ _434076 : [(10847 ^ _434076) ^ [_861483, _861485] : [-(hBOOL(hAPP(_861323, bool, hAPP(_861323, fun(_861323, bool), ord_less_eq(_861323), abs_abs(_861323, plus_plus(_861323, _861485, _861483))), plus_plus(_861323, abs_abs(_861323, _861485), abs_abs(_861323, _861483)))))]]], (10849 ^ _434076) ^ [_861616] : [linordered_idom(_861616), 10852 ^ _434076 : [(10853 ^ _434076) ^ [_861872, _861874, _861876, _861878] : [hBOOL(hAPP(_861616, bool, hAPP(_861616, fun(_861616, bool), ord_less(_861616), abs_abs(_861616, _861874)), _861872)), hBOOL(hAPP(_861616, bool, hAPP(_861616, fun(_861616, bool), ord_less(_861616), abs_abs(_861616, _861878)), _861876)), -(hBOOL(hAPP(_861616, bool, hAPP(_861616, fun(_861616, bool), ord_less(_861616), times_times(_861616, abs_abs(_861616, _861874), abs_abs(_861616, _861878))), times_times(_861616, _861872, _861876))))]]], (10863 ^ _434076) ^ [_862318] : [ordere142940540dd_abs(_862318), 10866 ^ _434076 : [(10867 ^ _434076) ^ [_862471] : [hBOOL(hAPP(_862318, bool, hAPP(_862318, fun(_862318, bool), ord_less(_862318), zero_zero(_862318)), _862471)), -(abs_abs(_862318, _862471) = ti(_862318, _862471))]]], (10873 ^ _434076) ^ [_862718] : [ordere142940540dd_abs(_862718), 10876 ^ _434076 : [(10877 ^ _434076) ^ [_862904] : [hBOOL(hAPP(_862718, bool, hAPP(_862718, fun(_862718, bool), ord_less(_862718), zero_zero(_862718)), abs_abs(_862718, _862904))), ti(_862718, _862904) = zero_zero(_862718)], (10883 ^ _434076) ^ [_863117] : [-(ti(_862718, _863117) = zero_zero(_862718)), -(hBOOL(hAPP(_862718, bool, hAPP(_862718, fun(_862718, bool), ord_less(_862718), zero_zero(_862718)), abs_abs(_862718, _863117))))]]], (10889 ^ _434076) ^ [_863373] : [ordere142940540dd_abs(_863373), 10892 ^ _434076 : [(10893 ^ _434076) ^ [_863503] : [hBOOL(hAPP(_863373, bool, hAPP(_863373, fun(_863373, bool), ord_less(_863373), abs_abs(_863373, _863503)), zero_zero(_863373)))]]], (10895 ^ _434076) ^ [_863622] : [ordere142940540dd_abs(_863622), 10898 ^ _434076 : [(10899 ^ _434076) ^ [_863775] : [hBOOL(hAPP(_863622, bool, hAPP(_863622, fun(_863622, bool), ord_less_eq(_863622), zero_zero(_863622)), _863775)), -(abs_abs(_863622, _863775) = ti(_863622, _863775))]]], (10905 ^ _434076) ^ [_864022] : [ordere142940540dd_abs(_864022), 10908 ^ _434076 : [(10909 ^ _434076) ^ [_864206] : [hBOOL(hAPP(_864022, bool, hAPP(_864022, fun(_864022, bool), ord_less_eq(_864022), abs_abs(_864022, _864206)), zero_zero(_864022))), -(ti(_864022, _864206) = zero_zero(_864022))], (10915 ^ _434076) ^ [_864418] : [ti(_864022, _864418) = zero_zero(_864022), -(hBOOL(hAPP(_864022, bool, hAPP(_864022, fun(_864022, bool), ord_less_eq(_864022), abs_abs(_864022, _864418)), zero_zero(_864022))))]]], (10921 ^ _434076) ^ [_864671] : [ordere142940540dd_abs(_864671), 10924 ^ _434076 : [(10925 ^ _434076) ^ [_864800] : [-(hBOOL(hAPP(_864671, bool, hAPP(_864671, fun(_864671, bool), ord_less_eq(_864671), zero_zero(_864671)), abs_abs(_864671, _864800))))]]], (10927 ^ _434076) ^ [_864919] : [ordere142940540dd_abs(_864919), 10930 ^ _434076 : [(10931 ^ _434076) ^ [_865062, _865064] : [-(abs_abs(_864919, minus_minus(_864919, _865064, _865062)) = abs_abs(_864919, minus_minus(_864919, _865062, _865064)))]]], (10933 ^ _434076) ^ [_865178] : [linordered_idom(_865178), 10936 ^ _434076 : [(10937 ^ _434076) ^ [_865324, _865326] : [-(abs_abs(_865178, times_times(_865178, _865326, _865324)) = times_times(_865178, abs_abs(_865178, _865326), abs_abs(_865178, _865324)))]]], (10939 ^ _434076) ^ [_865443] : [linordered_idom(_865443), 10942 ^ _434076 : [(10943 ^ _434076) ^ [_865567] : [-(times_times(_865443, abs_abs(_865443, _865567), abs_abs(_865443, _865567)) = times_times(_865443, _865567, _865567))]]], (10945 ^ _434076) ^ [_865681] : [ordere142940540dd_abs(_865681), 10948 ^ _434076 : [(10949 ^ _434076) ^ [_865808] : [-(hBOOL(hAPP(_865681, bool, hAPP(_865681, fun(_865681, bool), ord_less_eq(_865681), _865808), abs_abs(_865681, _865808))))]]], (10951 ^ _434076) ^ [_865925] : [ordere142940540dd_abs(_865925), 10954 ^ _434076 : [(10955 ^ _434076) ^ [_866106, _866108] : [hBOOL(hAPP(_865925, bool, hAPP(_865925, fun(_865925, bool), ord_less_eq(_865925), abs_abs(_865925, _866108)), _866106)), -(hBOOL(hAPP(_865925, bool, hAPP(_865925, fun(_865925, bool), ord_less_eq(_865925), _866108), _866106)))]]], (10961 ^ _434076) ^ [_866376, _866378] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, power_power(int, abs_abs(int, _866378)), _866376))))], (10963 ^ _434076) ^ [_866515] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), abs_abs(int, _866515)), one_one(int))), -(ti(int, _866515) = zero_zero(int))], (10969 ^ _434076) ^ [_866701] : [ti(int, _866701) = zero_zero(int), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), abs_abs(int, _866701)), one_one(int))))], (10985 ^ _434076) ^ [_867212] : [10986 ^ _434076 : [(10987 ^ _434076) ^ [] : [ti(int, _867212) = one_one(int)], (10989 ^ _434076) ^ [] : [ti(int, _867212) = number_number_of(int, min)]], -(abs_abs(int, _867212) = one_one(int))], (10975 ^ _434076) ^ [_866952] : [abs_abs(int, _866952) = one_one(int), -(ti(int, _866952) = one_one(int)), -(ti(int, _866952) = number_number_of(int, min))], (10993 ^ _434076) ^ [_867494] : [11000 ^ _434076 : [(11001 ^ _434076) ^ [_867703] : [-(abs_abs(_867494, hAPP(nat, _867494, power_power(_867494, number_number_of(_867494, min)), _867703)) = one_one(_867494))]], number_ring(_867494), linordered_idom(_867494)], (11003 ^ _434076) ^ [_867804] : [-(abs_abs(int, hAPP(nat, int, power_power(int, _867804), number_number_of(nat, bit1(bit1(pls))))) = hAPP(nat, int, power_power(int, abs_abs(int, _867804)), number_number_of(nat, bit1(bit1(pls)))))], (11015 ^ _434076) ^ [_868251, _868253] : [11016 ^ _434076 : [(11017 ^ _434076) ^ [] : [-(ti(int, _868253) = zero_zero(int))], (11019 ^ _434076) ^ [] : [_868251 = zero_zero(nat)]], -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, abs_abs(int, _868253)), _868251))))], (11005 ^ _434076) ^ [_867962, _867964] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, abs_abs(int, _867964)), _867962))), ti(int, _867964) = zero_zero(int), -(_867962 = zero_zero(nat))], (11023 ^ _434076) ^ [_868576, _868578] : [-(ti(int, _868576) = zero_zero(int)), 11026 ^ _434076 : [(11027 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), times_times(int, _868576, _868578)), _868576)), -(abs_abs(int, _868578) = one_one(int))], (11033 ^ _434076) ^ [] : [abs_abs(int, _868578) = one_one(int), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), times_times(int, _868576, _868578)), _868576)))]]], (11039 ^ _434076) ^ [_869122, _869124] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _869124)), _869122)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _869124), nat_1(abs_abs(int, _869122)))))], (11045 ^ _434076) ^ [_869340, _869342] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _869342), nat_1(abs_abs(int, _869340)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), hAPP(nat, int, semiring_1_of_nat(int), _869342)), _869340)))], (11051 ^ _434076) ^ [_869637, _869639] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _869639), hAPP(nat, int, semiring_1_of_nat(int), _869637))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(abs_abs(int, _869639))), _869637)))], (11057 ^ _434076) ^ [_869855, _869857] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), nat_1(abs_abs(int, _869857))), _869855)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), dvd_dvd(int), _869857), hAPP(nat, int, semiring_1_of_nat(int), _869855))))], (11063 ^ _434076) ^ [_870109] : [linordered_idom(_870109), 11066 ^ _434076 : [(11067 ^ _434076) ^ [_870238] : [-(abs_abs(_870109, hAPP(nat, _870109, power_power(_870109, _870238), number_number_of(nat, bit0(bit1(pls))))) = hAPP(nat, _870109, power_power(_870109, _870238), number_number_of(nat, bit0(bit1(pls)))))]]], (11069 ^ _434076) ^ [_870357] : [linordered_idom(_870357), 11072 ^ _434076 : [(11073 ^ _434076) ^ [_870486] : [-(hAPP(nat, _870357, power_power(_870357, abs_abs(_870357, _870486)), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, _870357, power_power(_870357, _870486), number_number_of(nat, bit0(bit1(pls)))))]]], (11075 ^ _434076) ^ [_870590] : [-(abs_abs(int, hAPP(nat, int, power_power(int, _870590), number_number_of(nat, bit0(bit1(pls))))) = hAPP(nat, int, power_power(int, abs_abs(int, _870590)), number_number_of(nat, bit0(bit1(pls)))))], (11077 ^ _434076) ^ [_870748, _870750] : [hAPP(nat, int, power_power(int, _870750), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, int, power_power(int, _870748), number_number_of(nat, bit0(bit1(pls)))), -(abs_abs(int, _870750) = abs_abs(int, _870748))], (11083 ^ _434076) ^ [_870954, _870956] : [abs_abs(int, _870956) = abs_abs(int, _870954), -(hAPP(nat, int, power_power(int, _870956), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, int, power_power(int, _870954), number_number_of(nat, bit0(bit1(pls)))))], (11089 ^ _434076) ^ [_871196] : [hAPP(nat, int, power_power(int, _871196), number_number_of(nat, bit0(bit1(pls)))) = one_one(int), -(abs_abs(int, _871196) = one_one(int))], (11095 ^ _434076) ^ [_871436, _871438, _871440] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _871436)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _871440), plus_plus(int, _871438, times_times(int, plus_plus(int, abs_abs(int, minus_minus(int, _871438, _871440)), one_one(int)), _871436)))))], (11101 ^ _434076) ^ [_871730, _871732, _871734] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _871730)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), minus_minus(int, _871734, times_times(int, plus_plus(int, abs_abs(int, minus_minus(int, _871734, _871732)), one_one(int)), _871730))), _871732)))], (11107 ^ _434076) ^ [_872010, _872012] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _872010)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), times_times(int, number_number_of(int, bit0(bit1(pls))), abs_abs(int, minus_minus(int, _872012, times_times(int, 11110 ^ [_872010, _872012], _872010))))), _872010)))], (11114 ^ _434076) ^ [_872371, _872373, _872375] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _872371)), 11120 ^ _434076 : [(11121 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, _872373, 11119 ^ [_872371, _872373, _872375])))], (11123 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _872373, minus_minus(int, 11119 ^ [_872371, _872373, _872375], _872371)))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _872375)), 11128 ^ _434076 : [(11129 ^ _434076) ^ [_872912] : [hBOOL(hAPP(int, bool, _872373, _872912)), -(hBOOL(hAPP(int, bool, _872373, minus_minus(int, _872912, times_times(int, _872375, _872371)))))]]], (11135 ^ _434076) ^ [_873156] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), plus_plus(real, abs_abs(real, _873156), one_one(real))), _873156))], (11137 ^ _434076) ^ [_873250] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), plus_plus(real, one_one(real), abs_abs(real, _873250)))))], (11139 ^ _434076) ^ [_873354] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), abs_abs(real, _873354)), one_one(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), hAPP(nat, real, power_power(real, _873354), number_number_of(nat, bit0(bit1(pls))))), one_one(real))))], (11145 ^ _434076) ^ [_873616, _873618] : [-(hBOOL(hAPP(nat, bool, _873616, zero_zero(nat)))), hBOOL(hAPP(nat, bool, _873616, _873618)), 11153 ^ _434076 : [(11154 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 11152 ^ [_873616, _873618]), _873618)))], (11162 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, _873616, plus_plus(nat, 11152 ^ [_873616, _873618], one_one(nat)))))], (11156 ^ _434076) ^ [_874108] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _874108), 11152 ^ [_873616, _873618])), hBOOL(hAPP(nat, bool, _873616, _874108))]]], (11164 ^ _434076) ^ [_874457, _874459, _874461] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _874457)), 11170 ^ _434076 : [(11171 ^ _434076) ^ [] : [-(hBOOL(hAPP(int, bool, _874459, 11169 ^ [_874457, _874459, _874461])))], (11173 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, _874459, plus_plus(int, 11169 ^ [_874457, _874459, _874461], _874457)))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _874461)), 11178 ^ _434076 : [(11179 ^ _434076) ^ [_874998] : [hBOOL(hAPP(int, bool, _874459, _874998)), -(hBOOL(hAPP(int, bool, _874459, plus_plus(int, _874998, times_times(int, _874461, _874457)))))]]], (11185 ^ _434076) ^ [_875314, _875316, _875318, _875320, _875322] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _875316), _875314)), 11188 ^ _434076 : [(11189 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, _875314, _875322), _875320)), plus_plus(nat, times_times(nat, _875316, _875322), _875318))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, minus_minus(nat, _875314, _875316), _875322), _875320)), _875318)))], (11195 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, minus_minus(nat, _875314, _875316), _875322), _875320)), _875318)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, _875314, _875322), _875320)), plus_plus(nat, times_times(nat, _875316, _875322), _875318))))]]], (11201 ^ _434076) ^ [_876020, _876022, _876024, _876026, _876028] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _876022), _876020)), 11204 ^ _434076 : [(11205 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, _876022, _876028), _876026)), plus_plus(nat, times_times(nat, _876020, _876028), _876024))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _876026), plus_plus(nat, times_times(nat, minus_minus(nat, _876020, _876022), _876028), _876024))))], (11211 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _876026), plus_plus(nat, times_times(nat, minus_minus(nat, _876020, _876022), _876028), _876024))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), plus_plus(nat, times_times(nat, _876022, _876028), _876026)), plus_plus(nat, times_times(nat, _876020, _876028), _876024))))]]], (11227 ^ _434076) ^ [_877005, _877007, _877009] : [11228 ^ _434076 : [(11229 ^ _434076) ^ [] : [_877009 = zero_zero(nat)], (11231 ^ _434076) ^ [] : [_877007 = _877005]], -(times_times(nat, _877009, _877007) = times_times(nat, _877009, _877005))], (11217 ^ _434076) ^ [_876727, _876729, _876731] : [times_times(nat, _876731, _876729) = times_times(nat, _876731, _876727), -(_876731 = zero_zero(nat)), -(_876729 = _876727)], (11235 ^ _434076) ^ [_877328, _877330, _877332, _877334] : [-(plus_plus(nat, times_times(nat, _877334, _877332), plus_plus(nat, times_times(nat, _877330, _877332), _877328)) = plus_plus(nat, times_times(nat, plus_plus(nat, _877334, _877330), _877332), _877328))], (11237 ^ _434076) ^ [_877483, _877485, _877487] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _877483)), 11240 ^ _434076 : [(11241 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _877483, _877487)), times_times(nat, _877483, _877485))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _877487), _877485)))], (11247 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _877487), _877485)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), times_times(nat, _877483, _877487)), times_times(nat, _877483, _877485))))]]], (11253 ^ _434076) ^ [_878059, _878061, _878063] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _878059)), 11256 ^ _434076 : [(11257 ^ _434076) ^ [] : [times_times(nat, _878059, _878063) = times_times(nat, _878059, _878061), -(_878063 = _878061)], (11263 ^ _434076) ^ [] : [_878063 = _878061, -(times_times(nat, _878059, _878063) = times_times(nat, _878059, _878061))]]], (11279 ^ _434076) ^ [_878924, _878926, _878928] : [11280 ^ _434076 : [(11281 ^ _434076) ^ [] : [_878928 = zero_zero(nat)], (11283 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _878926), _878924))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _878928, _878926)), times_times(nat, _878928, _878924))))], (11269 ^ _434076) ^ [_878610, _878612, _878614] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _878614, _878612)), times_times(nat, _878614, _878610))), -(_878614 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _878612), _878610)))], (11287 ^ _434076) ^ [_879284, _879286, _879288] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _879284)), 11290 ^ _434076 : [(11291 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _879284, _879288)), times_times(nat, _879284, _879286))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _879288), _879286)))], (11297 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), _879288), _879286)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), dvd_dvd(nat), times_times(nat, _879284, _879288)), times_times(nat, _879284, _879286))))]]], (11303 ^ _434076) ^ [_879860, _879862, _879864] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _879860)), 11306 ^ _434076 : [(11307 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _879860, _879864)), times_times(nat, _879860, _879862))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _879864), _879862)))], (11313 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _879864), _879862)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), times_times(nat, _879860, _879864)), times_times(nat, _879860, _879862))))]]], (11319 ^ _434076) ^ [_880464, _880466, _880468, _880470, _880472] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _880466), _880464)), 11322 ^ _434076 : [(11323 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, _880464, _880472), _880470)), plus_plus(nat, times_times(nat, _880466, _880472), _880468))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, minus_minus(nat, _880464, _880466), _880472), _880470)), _880468)))], (11329 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, minus_minus(nat, _880464, _880466), _880472), _880470)), _880468)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, _880464, _880472), _880470)), plus_plus(nat, times_times(nat, _880466, _880472), _880468))))]]], (11335 ^ _434076) ^ [_881170, _881172, _881174, _881176, _881178] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _881172), _881170)), -(minus_minus(nat, plus_plus(nat, times_times(nat, _881170, _881178), _881176), plus_plus(nat, times_times(nat, _881172, _881178), _881174)) = minus_minus(nat, plus_plus(nat, times_times(nat, minus_minus(nat, _881170, _881172), _881178), _881176), _881174))], (11341 ^ _434076) ^ [_881530, _881532, _881534, _881536, _881538] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _881532), _881530)), 11344 ^ _434076 : [(11345 ^ _434076) ^ [] : [plus_plus(nat, times_times(nat, _881530, _881538), _881536) = plus_plus(nat, times_times(nat, _881532, _881538), _881534), -(plus_plus(nat, times_times(nat, minus_minus(nat, _881530, _881532), _881538), _881536) = _881534)], (11351 ^ _434076) ^ [] : [plus_plus(nat, times_times(nat, minus_minus(nat, _881530, _881532), _881538), _881536) = _881534, -(plus_plus(nat, times_times(nat, _881530, _881538), _881536) = plus_plus(nat, times_times(nat, _881532, _881538), _881534))]]], (11357 ^ _434076) ^ [_882182, _882184, _882186, _882188, _882190] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _882184), _882182)), 11360 ^ _434076 : [(11361 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, _882184, _882190), _882188)), plus_plus(nat, times_times(nat, _882182, _882190), _882186))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _882188), plus_plus(nat, times_times(nat, minus_minus(nat, _882182, _882184), _882190), _882186))))], (11367 ^ _434076) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _882188), plus_plus(nat, times_times(nat, minus_minus(nat, _882182, _882184), _882190), _882186))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), plus_plus(nat, times_times(nat, _882184, _882190), _882188)), plus_plus(nat, times_times(nat, _882182, _882190), _882186))))]]], (11373 ^ _434076) ^ [_882888, _882890, _882892, _882894, _882896] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _882890), _882888)), -(minus_minus(nat, plus_plus(nat, times_times(nat, _882890, _882896), _882894), plus_plus(nat, times_times(nat, _882888, _882896), _882892)) = minus_minus(nat, _882894, plus_plus(nat, times_times(nat, minus_minus(nat, _882888, _882890), _882896), _882892)))], (11379 ^ _434076) ^ [_883248, _883250, _883252, _883254, _883256] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _883250), _883248)), 11382 ^ _434076 : [(11383 ^ _434076) ^ [] : [plus_plus(nat, times_times(nat, _883250, _883256), _883254) = plus_plus(nat, times_times(nat, _883248, _883256), _883252), -(_883254 = plus_plus(nat, times_times(nat, minus_minus(nat, _883248, _883250), _883256), _883252))], (11389 ^ _434076) ^ [] : [_883254 = plus_plus(nat, times_times(nat, minus_minus(nat, _883248, _883250), _883256), _883252), -(plus_plus(nat, times_times(nat, _883250, _883256), _883254) = plus_plus(nat, times_times(nat, _883248, _883256), _883252))]]], (11395 ^ _434076) ^ [_883872, _883874, _883876] : [11397 ^ _434076 : [(11398 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 11396 ^ [_883872, _883874, _883876]), _883872)))], (11400 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), abs_abs(int, minus_minus(int, hAPP(nat, int, _883874, plus_plus(nat, 11396 ^ [_883872, _883874, _883876], one_one(nat))), hAPP(nat, int, _883874, 11396 ^ [_883872, _883874, _883876])))), one_one(int)))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, _883874, zero_zero(nat))), _883876)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _883876), hAPP(nat, int, _883874, _883872))), 11410 ^ _434076 : [(11411 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), 11409 ^ [_883872, _883874, _883876]), _883872)))], (11413 ^ _434076) ^ [] : [-(hAPP(nat, int, _883874, 11409 ^ [_883872, _883874, _883876]) = ti(int, _883876))]]], (11435 ^ _434076) ^ [] : [-(semiri456707255roduct(int))], (11437 ^ _434076) ^ [] : [-(ordere223160158up_add(int))], (11439 ^ _434076) ^ [] : [-(ordere236663937imp_le(int))], (11441 ^ _434076) ^ [] : [-(linord893533164strict(int))], (11443 ^ _434076) ^ [] : [-(linord626643107strict(int))], (11445 ^ _434076) ^ [] : [-(linord20386208strict(int))], (11447 ^ _434076) ^ [] : [-(ordere779506340up_add(int))], (11449 ^ _434076) ^ [] : [-(ordere142940540dd_abs(int))], (11451 ^ _434076) ^ [] : [-(ordere216010020id_add(int))], (11453 ^ _434076) ^ [] : [-(linord219039673up_add(int))], (11455 ^ _434076) ^ [] : [-(cancel146912293up_add(int))], (11457 ^ _434076) ^ [] : [-(ring_11004092258visors(int))], (11459 ^ _434076) ^ [] : [-(ordere453448008miring(int))], (11461 ^ _434076) ^ [] : [-(linord581940658strict(int))], (11463 ^ _434076) ^ [] : [-(ring_n68954251visors(int))], (11465 ^ _434076) ^ [] : [-(ordere1490568538miring(int))], (11467 ^ _434076) ^ [] : [-(linord1278240602ring_1(int))], (11469 ^ _434076) ^ [] : [-(ordered_ab_group_add(int))], (11471 ^ _434076) ^ [] : [-(cancel_semigroup_add(int))], (11473 ^ _434076) ^ [] : [-(linordered_semiring(int))], (11475 ^ _434076) ^ [] : [-(linordered_semidom(int))], (11477 ^ _434076) ^ [] : [-(ab_semigroup_mult(int))], (11479 ^ _434076) ^ [] : [-(comm_monoid_mult(int))], (11481 ^ _434076) ^ [] : [-(ab_semigroup_add(int))], (11483 ^ _434076) ^ [] : [-(ordered_semiring(int))], (11485 ^ _434076) ^ [] : [-(ordered_ring_abs(int))], (11487 ^ _434076) ^ [] : [-(no_zero_divisors(int))], (11489 ^ _434076) ^ [] : [-(comm_monoid_add(int))], (11491 ^ _434076) ^ [] : [-(linordered_ring(int))], (11493 ^ _434076) ^ [] : [-(linordered_idom(int))], (11495 ^ _434076) ^ [] : [-(comm_semiring_1(int))], (11497 ^ _434076) ^ [] : [-(comm_semiring(int))], (11499 ^ _434076) ^ [] : [-(semiring_char_0(int))], (11501 ^ _434076) ^ [] : [-(number_semiring(int))], (11503 ^ _434076) ^ [] : [-(ab_group_add(int))], (11505 ^ _434076) ^ [] : [-(zero_neq_one(int))], (11507 ^ _434076) ^ [] : [-(ordered_ring(int))], (11509 ^ _434076) ^ [] : [-(linorder(int))], (11511 ^ _434076) ^ [] : [-(monoid_mult(int))], (11513 ^ _434076) ^ [] : [-(comm_ring_1(int))], (11515 ^ _434076) ^ [] : [-(monoid_add(int))], (11517 ^ _434076) ^ [] : [-(semiring_1(int))], (11519 ^ _434076) ^ [] : [-(semiring_0(int))], (11521 ^ _434076) ^ [] : [-(group_add(int))], (11523 ^ _434076) ^ [] : [-(mult_zero(int))], (11525 ^ _434076) ^ [] : [-(comm_ring(int))], (11527 ^ _434076) ^ [] : [-(order(int))], (11529 ^ _434076) ^ [] : [-(ring_char_0(int))], (11531 ^ _434076) ^ [] : [-(number_ring(int))], (11533 ^ _434076) ^ [] : [-(semiring(int))], (11535 ^ _434076) ^ [] : [-(ring_1(int))], (11537 ^ _434076) ^ [] : [-(power(int))], (11539 ^ _434076) ^ [] : [-(zero(int))], (11541 ^ _434076) ^ [] : [-(ring(int))], (11543 ^ _434076) ^ [] : [-(idom(int))], (11545 ^ _434076) ^ [] : [-(number(int))], (11547 ^ _434076) ^ [] : [-(one(int))], (11549 ^ _434076) ^ [] : [-(dvd(int))], (11551 ^ _434076) ^ [] : [-(semiri456707255roduct(nat))], (11553 ^ _434076) ^ [] : [-(ordere223160158up_add(nat))], (11555 ^ _434076) ^ [] : [-(ordere236663937imp_le(nat))], (11557 ^ _434076) ^ [] : [-(linord893533164strict(nat))], (11559 ^ _434076) ^ [] : [-(linord20386208strict(nat))], (11561 ^ _434076) ^ [] : [-(ordere779506340up_add(nat))], (11563 ^ _434076) ^ [] : [-(ordere216010020id_add(nat))], (11565 ^ _434076) ^ [] : [-(cancel146912293up_add(nat))], (11567 ^ _434076) ^ [] : [-(ordere453448008miring(nat))], (11569 ^ _434076) ^ [] : [-(ordere1490568538miring(nat))], (11571 ^ _434076) ^ [] : [-(cancel_semigroup_add(nat))], (11573 ^ _434076) ^ [] : [-(linordered_semiring(nat))], (11575 ^ _434076) ^ [] : [-(linordered_semidom(nat))], (11577 ^ _434076) ^ [] : [-(ab_semigroup_mult(nat))], (11579 ^ _434076) ^ [] : [-(comm_monoid_mult(nat))], (11581 ^ _434076) ^ [] : [-(ab_semigroup_add(nat))], (11583 ^ _434076) ^ [] : [-(ordered_semiring(nat))], (11585 ^ _434076) ^ [] : [-(no_zero_divisors(nat))], (11587 ^ _434076) ^ [] : [-(comm_monoid_add(nat))], (11589 ^ _434076) ^ [] : [-(comm_semiring_1(nat))], (11591 ^ _434076) ^ [] : [-(comm_semiring(nat))], (11593 ^ _434076) ^ [] : [-(semiring_char_0(nat))], (11595 ^ _434076) ^ [] : [-(number_semiring(nat))], (11597 ^ _434076) ^ [] : [-(zero_neq_one(nat))], (11599 ^ _434076) ^ [] : [-(linorder(nat))], (11601 ^ _434076) ^ [] : [-(monoid_mult(nat))], (11603 ^ _434076) ^ [] : [-(monoid_add(nat))], (11605 ^ _434076) ^ [] : [-(semiring_1(nat))], (11607 ^ _434076) ^ [] : [-(semiring_0(nat))], (11609 ^ _434076) ^ [] : [-(mult_zero(nat))], (11611 ^ _434076) ^ [] : [-(order(nat))], (11613 ^ _434076) ^ [] : [-(semiring(nat))], (11615 ^ _434076) ^ [] : [-(power(nat))], (11617 ^ _434076) ^ [] : [-(zero(nat))], (11619 ^ _434076) ^ [] : [-(number(nat))], (11621 ^ _434076) ^ [] : [-(one(nat))], (11623 ^ _434076) ^ [] : [-(dvd(nat))], (11625 ^ _434076) ^ [] : [-(order(bool))], (11627 ^ _434076) ^ [] : [-(semiri456707255roduct(real))], (11629 ^ _434076) ^ [] : [-(ordere223160158up_add(real))], (11631 ^ _434076) ^ [] : [-(ordere236663937imp_le(real))], (11633 ^ _434076) ^ [] : [-(linord893533164strict(real))], (11635 ^ _434076) ^ [] : [-(linord626643107strict(real))], (11637 ^ _434076) ^ [] : [-(linord20386208strict(real))], (11639 ^ _434076) ^ [] : [-(ordere779506340up_add(real))], (11641 ^ _434076) ^ [] : [-(ordere142940540dd_abs(real))], (11643 ^ _434076) ^ [] : [-(ordere216010020id_add(real))], (11645 ^ _434076) ^ [] : [-(linord219039673up_add(real))], (11647 ^ _434076) ^ [] : [-(cancel146912293up_add(real))], (11649 ^ _434076) ^ [] : [-(ring_11004092258visors(real))], (11651 ^ _434076) ^ [] : [-(ordere453448008miring(real))], (11653 ^ _434076) ^ [] : [-(linord581940658strict(real))], (11655 ^ _434076) ^ [] : [-(ring_n68954251visors(real))], (11657 ^ _434076) ^ [] : [-(ordere1490568538miring(real))], (11659 ^ _434076) ^ [] : [-(linord1278240602ring_1(real))], (11661 ^ _434076) ^ [] : [-(ordered_ab_group_add(real))], (11663 ^ _434076) ^ [] : [-(cancel_semigroup_add(real))], (11665 ^ _434076) ^ [] : [-(linordered_semiring(real))], (11667 ^ _434076) ^ [] : [-(linordered_semidom(real))], (11669 ^ _434076) ^ [] : [-(ab_semigroup_mult(real))], (11671 ^ _434076) ^ [] : [-(comm_monoid_mult(real))], (11673 ^ _434076) ^ [] : [-(ab_semigroup_add(real))], (11675 ^ _434076) ^ [] : [-(ordered_semiring(real))], (11677 ^ _434076) ^ [] : [-(ordered_ring_abs(real))], (11679 ^ _434076) ^ [] : [-(no_zero_divisors(real))], (11681 ^ _434076) ^ [] : [-(comm_monoid_add(real))], (11683 ^ _434076) ^ [] : [-(linordered_ring(real))], (11685 ^ _434076) ^ [] : [-(linordered_idom(real))], (11687 ^ _434076) ^ [] : [-(comm_semiring_1(real))], (11689 ^ _434076) ^ [] : [-(comm_semiring(real))], (11691 ^ _434076) ^ [] : [-(semiring_char_0(real))], (11693 ^ _434076) ^ [] : [-(number_semiring(real))], (11695 ^ _434076) ^ [] : [-(ab_group_add(real))], (11697 ^ _434076) ^ [] : [-(zero_neq_one(real))], (11699 ^ _434076) ^ [] : [-(ordered_ring(real))], (11701 ^ _434076) ^ [] : [-(linorder(real))], (11703 ^ _434076) ^ [] : [-(monoid_mult(real))], (11705 ^ _434076) ^ [] : [-(comm_ring_1(real))], (11707 ^ _434076) ^ [] : [-(monoid_add(real))], (11709 ^ _434076) ^ [] : [-(semiring_1(real))], (11711 ^ _434076) ^ [] : [-(semiring_0(real))], (11713 ^ _434076) ^ [] : [-(group_add(real))], (11715 ^ _434076) ^ [] : [-(mult_zero(real))], (11717 ^ _434076) ^ [] : [-(comm_ring(real))], (11719 ^ _434076) ^ [] : [-(order(real))], (11721 ^ _434076) ^ [] : [-(ring_char_0(real))], (11723 ^ _434076) ^ [] : [-(number_ring(real))], (11725 ^ _434076) ^ [] : [-(semiring(real))], (11727 ^ _434076) ^ [] : [-(ring_1(real))], (11729 ^ _434076) ^ [] : [-(power(real))], (11731 ^ _434076) ^ [] : [-(zero(real))], (11733 ^ _434076) ^ [] : [-(ring(real))], (11735 ^ _434076) ^ [] : [-(idom(real))], (11737 ^ _434076) ^ [] : [-(number(real))], (11739 ^ _434076) ^ [] : [-(one(real))], (11741 ^ _434076) ^ [] : [-(dvd(real))], (11743 ^ _434076) ^ [_893923, _893925] : [-(ti(_893925, ti(_893925, _893923)) = ti(_893925, _893923))], (11745 ^ _434076) ^ [_894040, _894042, _894044] : [-(if(_894044, fTrue, _894042, _894040) = ti(_894044, _894042))], (11747 ^ _434076) ^ [_894158, _894160, _894162] : [-(if(_894162, fFalse, _894160, _894158) = ti(_894162, _894158))], (11749 ^ _434076) ^ [_894243] : [-(ti(bool, _894243) = fTrue), -(ti(bool, _894243) = fFalse)], (11415 ^ _434076) ^ [_884831, _884833, _884835] : [11417 ^ _434076 : [(11418 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 11416 ^ [_884831, _884833, _884835]), _884831)))], (11420 ^ _434076) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), abs_abs(int, minus_minus(int, hAPP(nat, int, _884833, plus_plus(nat, 11416 ^ [_884831, _884833, _884835], one_one(nat))), hAPP(nat, int, _884833, 11416 ^ [_884831, _884833, _884835])))), one_one(int)))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, _884833, zero_zero(nat))), _884835)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _884835), hAPP(nat, int, _884833, _884831))), 11430 ^ _434076 : [(11431 ^ _434076) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), 11429 ^ [_884831, _884833, _884835]), _884831)))], (11433 ^ _434076) ^ [] : [-(hAPP(nat, int, _884833, 11429 ^ [_884831, _884833, _884835]) = ti(int, _884835))]]]], input).
% 0.89/1.39 ncf('1',plain,[linordered_idom(int), 1996 : hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))), 1996 : ti(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))) = zero_zero(int)],start(1992 ^ 0,bind([[_506122, _506313], [int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))]]))).
% 0.89/1.39 ncf('1.1',plain,[-(linordered_idom(int))],extension(11493 ^ 1)).
% 0.89/1.39 ncf('1.2',plain,[-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))))), 2739 : hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))), 2739 : linordered_semidom(int)],extension(2735 ^ 3,bind([[_535505, _535695, _535697], [int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), number_number_of(nat, bit0(bit1(pls)))]]))).
% 0.89/1.39 ncf('1.2.1',plain,[-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))))],extension(1262 ^ 6)).
% 0.89/1.39 ncf('1.2.2',plain,[-(linordered_semidom(int))],extension(11475 ^ 4)).
% 0.89/1.39 ncf('1.3',plain,[-(ti(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))) = zero_zero(int)), 1304 : hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int), 1304 : ring_11004092258visors(int)],extension(1300 ^ 3,bind([[_479800, _479975], [int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))]]))).
% 0.89/1.39 ncf('1.3.1',plain,[-(hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int))],extension(11755 ^ 6)).
% 0.89/1.39 ncf('1.3.2',plain,[-(ring_11004092258visors(int))],extension(11457 ^ 4)).
% 0.89/1.39 %-----------------------------------------------------
% 0.89/1.39 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------