%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n010.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 11:45:56 EDT 2023

% Result   : Theorem 101.38s 98.61s
% Output   : Proof 101.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% 0.04/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 16:44:27 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 101.38/98.61  
% 101.38/98.61  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 101.38/98.61  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 101.38/98.61  %-----------------------------------------------------
% 101.38/98.61  ncf(matrix, plain, [(5916 ^ _768566) ^ [] : [ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int))], (456 ^ _768566) ^ [_782722, _782724] : [_782724 = _782722, -(undefined(_782724) = undefined(_782722))], (462 ^ _768566) ^ [_782968, _782970, _782972, _782974] : [-(legendre(_782974, _782970) = legendre(_782972, _782968)), _782974 = _782972, _782970 = _782968], (472 ^ _768566) ^ [_783355, _783357, _783359, _783361, _783363, _783365] : [-(minus_minus(_783365, _783361, _783357) = minus_minus(_783363, _783359, _783355)), _783365 = _783363, _783361 = _783359, _783357 = _783355], (486 ^ _768566) ^ [_783871, _783873, _783875, _783877, _783879, _783881] : [-(times_times(_783881, _783877, _783873) = times_times(_783879, _783875, _783871)), _783881 = _783879, _783877 = _783875, _783873 = _783871], (500 ^ _768566) ^ [_784359, _784361, _784363, _784365] : [-(ti(_784365, _784361) = ti(_784363, _784359)), _784365 = _784363, _784361 = _784359], (510 ^ _768566) ^ [_784746, _784748, _784750, _784752, _784754, _784756] : [-(plus_plus(_784756, _784752, _784748) = plus_plus(_784754, _784750, _784746)), _784756 = _784754, _784752 = _784750, _784748 = _784746], (524 ^ _768566) ^ [_785262, _785264, _785266, _785268, _785270, _785272] : [-(power_power(_785272, _785268, _785264) = power_power(_785270, _785266, _785262)), _785272 = _785270, _785268 = _785266, _785264 = _785262], (538 ^ _768566) ^ [_785750, _785752, _785754, _785756] : [-(number_number_of(_785756, _785752) = number_number_of(_785754, _785750)), _785756 = _785754, _785752 = _785750], (548 ^ _768566) ^ [_786081, _786083] : [_786083 = _786081, -(bit0(_786083) = bit0(_786081))], (554 ^ _768566) ^ [_786299, _786301] : [_786301 = _786299, -(bit1(_786301) = bit1(_786299))], (560 ^ _768566) ^ [_786517, _786519] : [_786519 = _786517, -(one_one(_786519) = one_one(_786517))], (566 ^ _768566) ^ [_786715, _786717] : [_786717 = _786715, -(zero_zero(_786717) = zero_zero(_786715))], (2 ^ _768566) ^ [_768710] : [-(_768710 = _768710)], (4 ^ _768566) ^ [_768817, _768819] : [_768819 = _768817, -(_768817 = _768819)], (10 ^ _768566) ^ [_769021, _769023, _769025] : [-(_769025 = _769021), _769025 = _769023, _769023 = _769021], (20 ^ _768566) ^ [_769334, _769336] : [-(twoSqu420862341sum2sq(_769334)), _769336 = _769334, twoSqu420862341sum2sq(_769336)], (30 ^ _768566) ^ [_769629, _769631] : [-(zprime(_769629)), _769631 = _769629, zprime(_769631)], (40 ^ _768566) ^ [_769952, _769954, _769956, _769958] : [-(quadRes(_769956, _769952)), quadRes(_769958, _769954), _769958 = _769956, _769954 = _769952], (54 ^ _768566) ^ [_770424, _770426, _770428, _770430, _770432, _770434] : [-(zcong(_770432, _770428, _770424)), zcong(_770434, _770430, _770426), _770434 = _770432, _770430 = _770428, _770426 = _770424], (72 ^ _768566) ^ [_771033, _771035, _771037, _771039, _771041, _771043] : [-(dvd_dvd(_771041, _771037, _771033)), dvd_dvd(_771043, _771039, _771035), _771043 = _771041, _771039 = _771037, _771035 = _771033], (90 ^ _768566) ^ [_771642, _771644, _771646, _771648, _771650, _771652] : [-(ord_less_eq(_771650, _771646, _771642)), ord_less_eq(_771652, _771648, _771644), _771652 = _771650, _771648 = _771646, _771644 = _771642], (108 ^ _768566) ^ [_772195, _772197] : [-(semiri456707255roduct(_772195)), _772197 = _772195, semiri456707255roduct(_772197)], (118 ^ _768566) ^ [_772490, _772492] : [-(linord626643107strict(_772490)), _772492 = _772490, linord626643107strict(_772492)], (128 ^ _768566) ^ [_772785, _772787] : [-(linord219039673up_add(_772785)), _772787 = _772785, linord219039673up_add(_772787)], (138 ^ _768566) ^ [_773080, _773082] : [-(ring_11004092258visors(_773080)), _773082 = _773080, ring_11004092258visors(_773082)], (148 ^ _768566) ^ [_773375, _773377] : [-(ordere453448008miring(_773375)), _773377 = _773375, ordere453448008miring(_773377)], (158 ^ _768566) ^ [_773670, _773672] : [-(linord581940658strict(_773670)), _773672 = _773670, linord581940658strict(_773672)], (168 ^ _768566) ^ [_773965, _773967] : [-(ring_n68954251visors(_773965)), _773967 = _773965, ring_n68954251visors(_773967)], (178 ^ _768566) ^ [_774260, _774262] : [-(linordered_semidom(_774260)), _774262 = _774260, linordered_semidom(_774262)], (188 ^ _768566) ^ [_774555, _774557] : [-(comm_monoid_mult(_774555)), _774557 = _774555, comm_monoid_mult(_774557)], (198 ^ _768566) ^ [_774850, _774852] : [-(no_zero_divisors(_774850)), _774852 = _774850, no_zero_divisors(_774852)], (208 ^ _768566) ^ [_775145, _775147] : [-(linordered_ring(_775145)), _775147 = _775145, linordered_ring(_775147)], (218 ^ _768566) ^ [_775440, _775442] : [-(linordered_idom(_775440)), _775442 = _775440, linordered_idom(_775442)], (228 ^ _768566) ^ [_775735, _775737] : [-(comm_semiring_1(_775735)), _775737 = _775735, comm_semiring_1(_775737)], (238 ^ _768566) ^ [_776030, _776032] : [-(comm_semiring(_776030)), _776032 = _776030, comm_semiring(_776032)], (248 ^ _768566) ^ [_776325, _776327] : [-(number_semiring(_776325)), _776327 = _776325, number_semiring(_776327)], (258 ^ _768566) ^ [_776620, _776622] : [-(ab_group_add(_776620)), _776622 = _776620, ab_group_add(_776622)], (268 ^ _768566) ^ [_776915, _776917] : [-(zero_neq_one(_776915)), _776917 = _776915, zero_neq_one(_776917)], (278 ^ _768566) ^ [_777210, _777212] : [-(ordered_ring(_777210)), _777212 = _777210, ordered_ring(_777212)], (288 ^ _768566) ^ [_777505, _777507] : [-(linorder(_777505)), _777507 = _777505, linorder(_777507)], (298 ^ _768566) ^ [_777800, _777802] : [-(monoid_mult(_777800)), _777802 = _777800, monoid_mult(_777802)], (308 ^ _768566) ^ [_778095, _778097] : [-(comm_ring_1(_778095)), _778097 = _778095, comm_ring_1(_778097)], (318 ^ _768566) ^ [_778390, _778392] : [-(semiring_1(_778390)), _778392 = _778390, semiring_1(_778392)], (328 ^ _768566) ^ [_778685, _778687] : [-(semiring_0(_778685)), _778687 = _778685, semiring_0(_778687)], (338 ^ _768566) ^ [_778980, _778982] : [-(mult_zero(_778980)), _778982 = _778980, mult_zero(_778982)], (348 ^ _768566) ^ [_779275, _779277] : [-(order(_779275)), _779277 = _779275, order(_779277)], (358 ^ _768566) ^ [_779570, _779572] : [-(ring_char_0(_779570)), _779572 = _779570, ring_char_0(_779572)], (368 ^ _768566) ^ [_779865, _779867] : [-(number_ring(_779865)), _779867 = _779865, number_ring(_779867)], (378 ^ _768566) ^ [_780160, _780162] : [-(semiring(_780160)), _780162 = _780160, semiring(_780162)], (388 ^ _768566) ^ [_780455, _780457] : [-(ring_1(_780455)), _780457 = _780455, ring_1(_780457)], (398 ^ _768566) ^ [_780750, _780752] : [-(power(_780750)), _780752 = _780750, power(_780752)], (408 ^ _768566) ^ [_781045, _781047] : [-(ring(_781045)), _781047 = _781045, ring(_781047)], (418 ^ _768566) ^ [_781340, _781342] : [-(number(_781340)), _781342 = _781340, number(_781342)], (428 ^ _768566) ^ [_781635, _781637] : [-(dvd(_781635)), _781637 = _781635, dvd(_781637)], (438 ^ _768566) ^ [_781966, _781968, _781970, _781972, _781974, _781976] : [-(ord_less(_781974, _781970, _781966)), ord_less(_781976, _781972, _781968), _781976 = _781974, _781972 = _781970, _781968 = _781966], (572 ^ _768566) ^ [_786998, _787000, _787002] : [ab_group_add(_786998), -(minus_minus(_786998, ti(_786998, _787002), _787000) = minus_minus(_786998, _787002, _787000))], (578 ^ _768566) ^ [_787248, _787250, _787252] : [ab_group_add(_787248), -(minus_minus(_787248, _787252, ti(_787248, _787250)) = minus_minus(_787248, _787252, _787250))], (584 ^ _768566) ^ [_787498, _787500, _787502] : [ab_group_add(_787498), -(ti(_787498, minus_minus(_787498, _787502, _787500)) = minus_minus(_787498, _787502, _787500))], (590 ^ _768566) ^ [_787719, _787721] : [-(minus_minus(nat, ti(nat, _787721), _787719) = minus_minus(nat, _787721, _787719))], (592 ^ _768566) ^ [_787824, _787826] : [-(minus_minus(nat, _787826, ti(nat, _787824)) = minus_minus(nat, _787826, _787824))], (594 ^ _768566) ^ [_787929, _787931] : [-(ti(nat, minus_minus(nat, _787931, _787929)) = minus_minus(nat, _787931, _787929))], (596 ^ _768566) ^ [_788035] : [zero_neq_one(_788035), -(ti(_788035, one_one(_788035)) = one_one(_788035))], (602 ^ _768566) ^ [_788237] : [power(_788237), -(ti(_788237, one_one(_788237)) = one_one(_788237))], (608 ^ _768566) ^ [_788467, _788469, _788471] : [semiring(_788467), -(plus_plus(_788467, ti(_788467, _788471), _788469) = plus_plus(_788467, _788471, _788469))], (614 ^ _768566) ^ [_788717, _788719, _788721] : [semiring(_788717), -(plus_plus(_788717, _788721, ti(_788717, _788719)) = plus_plus(_788717, _788721, _788719))], (620 ^ _768566) ^ [_788967, _788969, _788971] : [semiring(_788967), -(ti(_788967, plus_plus(_788967, _788971, _788969)) = plus_plus(_788967, _788971, _788969))], (626 ^ _768566) ^ [_789217, _789219, _789221] : [ab_group_add(_789217), -(plus_plus(_789217, ti(_789217, _789221), _789219) = plus_plus(_789217, _789221, _789219))], (632 ^ _768566) ^ [_789467, _789469, _789471] : [ab_group_add(_789467), -(plus_plus(_789467, _789471, ti(_789467, _789469)) = plus_plus(_789467, _789471, _789469))], (638 ^ _768566) ^ [_789717, _789719, _789721] : [ab_group_add(_789717), -(ti(_789717, plus_plus(_789717, _789721, _789719)) = plus_plus(_789717, _789721, _789719))], (644 ^ _768566) ^ [_789967, _789969, _789971] : [dvd(_789967), -(times_times(_789967, ti(_789967, _789971), _789969) = times_times(_789967, _789971, _789969))], (650 ^ _768566) ^ [_790217, _790219, _790221] : [dvd(_790217), -(times_times(_790217, _790221, ti(_790217, _790219)) = times_times(_790217, _790221, _790219))], (656 ^ _768566) ^ [_790467, _790469, _790471] : [dvd(_790467), -(ti(_790467, times_times(_790467, _790471, _790469)) = times_times(_790467, _790471, _790469))], (662 ^ _768566) ^ [_790717, _790719, _790721] : [semiring(_790717), -(times_times(_790717, ti(_790717, _790721), _790719) = times_times(_790717, _790721, _790719))], (668 ^ _768566) ^ [_790967, _790969, _790971] : [semiring(_790967), -(times_times(_790967, _790971, ti(_790967, _790969)) = times_times(_790967, _790971, _790969))], (674 ^ _768566) ^ [_791217, _791219, _791221] : [semiring(_791217), -(ti(_791217, times_times(_791217, _791221, _791219)) = times_times(_791217, _791221, _791219))], (680 ^ _768566) ^ [_791467, _791469, _791471] : [no_zero_divisors(_791467), -(times_times(_791467, ti(_791467, _791471), _791469) = times_times(_791467, _791471, _791469))], (686 ^ _768566) ^ [_791717, _791719, _791721] : [no_zero_divisors(_791717), -(times_times(_791717, _791721, ti(_791717, _791719)) = times_times(_791717, _791721, _791719))], (692 ^ _768566) ^ [_791967, _791969, _791971] : [no_zero_divisors(_791967), -(ti(_791967, times_times(_791967, _791971, _791969)) = times_times(_791967, _791971, _791969))], (698 ^ _768566) ^ [_792217, _792219, _792221] : [mult_zero(_792217), -(times_times(_792217, ti(_792217, _792221), _792219) = times_times(_792217, _792221, _792219))], (704 ^ _768566) ^ [_792467, _792469, _792471] : [mult_zero(_792467), -(times_times(_792467, _792471, ti(_792467, _792469)) = times_times(_792467, _792471, _792469))], (710 ^ _768566) ^ [_792717, _792719, _792721] : [mult_zero(_792717), -(ti(_792717, times_times(_792717, _792721, _792719)) = times_times(_792717, _792721, _792719))], (716 ^ _768566) ^ [_792967, _792969, _792971] : [power(_792967), -(times_times(_792967, ti(_792967, _792971), _792969) = times_times(_792967, _792971, _792969))], (722 ^ _768566) ^ [_793217, _793219, _793221] : [power(_793217), -(times_times(_793217, _793221, ti(_793217, _793219)) = times_times(_793217, _793221, _793219))], (728 ^ _768566) ^ [_793467, _793469, _793471] : [power(_793467), -(ti(_793467, times_times(_793467, _793471, _793469)) = times_times(_793467, _793471, _793469))], (734 ^ _768566) ^ [_793689] : [zero_neq_one(_793689), -(ti(_793689, zero_zero(_793689)) = zero_zero(_793689))], (740 ^ _768566) ^ [_793891] : [no_zero_divisors(_793891), -(ti(_793891, zero_zero(_793891)) = zero_zero(_793891))], (746 ^ _768566) ^ [_794093] : [mult_zero(_794093), -(ti(_794093, zero_zero(_794093)) = zero_zero(_794093))], (752 ^ _768566) ^ [_794295] : [linord219039673up_add(_794295), -(ti(_794295, zero_zero(_794295)) = zero_zero(_794295))], (758 ^ _768566) ^ [_794482] : [-(ti(_794482, undefined(_794482)) = undefined(_794482))], (760 ^ _768566) ^ [_794639, _794641, _794643] : [zcong(ti(int, _794643), _794641, _794639), -(zcong(_794643, _794641, _794639))], (766 ^ _768566) ^ [_794817, _794819, _794821] : [zcong(_794821, _794819, _794817), -(zcong(ti(int, _794821), _794819, _794817))], (772 ^ _768566) ^ [_795088, _795090, _795092] : [zcong(_795092, ti(int, _795090), _795088), -(zcong(_795092, _795090, _795088))], (778 ^ _768566) ^ [_795266, _795268, _795270] : [zcong(_795270, _795268, _795266), -(zcong(_795270, ti(int, _795268), _795266))], (784 ^ _768566) ^ [_795537, _795539, _795541] : [zcong(_795541, _795539, ti(int, _795537)), -(zcong(_795541, _795539, _795537))], (790 ^ _768566) ^ [_795715, _795717, _795719] : [zcong(_795719, _795717, _795715), -(zcong(_795719, _795717, ti(int, _795715)))], (796 ^ _768566) ^ [_795958] : [zprime(ti(int, _795958)), -(zprime(_795958))], (802 ^ _768566) ^ [_796116] : [zprime(_796116), -(zprime(ti(int, _796116)))], (808 ^ _768566) ^ [_796295] : [-(bit0(ti(int, _796295)) = bit0(_796295))], (810 ^ _768566) ^ [_796380] : [-(ti(int, bit0(_796380)) = bit0(_796380))], (812 ^ _768566) ^ [_796465] : [-(bit1(ti(int, _796465)) = bit1(_796465))], (814 ^ _768566) ^ [_796550] : [-(ti(int, bit1(_796550)) = bit1(_796550))], (816 ^ _768566) ^ [] : [-(ti(int, min) = min)], (818 ^ _768566) ^ [] : [-(ti(int, pls) = pls)], (820 ^ _768566) ^ [_796770, _796772] : [number(_796770), -(number_number_of(_796770, ti(int, _796772)) = number_number_of(_796770, _796772))], (826 ^ _768566) ^ [_796996, _796998] : [number(_796996), -(ti(_796996, number_number_of(_796996, _796998)) = number_number_of(_796996, _796998))], (832 ^ _768566) ^ [_797236, _797238, _797240] : [order(_797236), 835 ^ _768566 : [(836 ^ _768566) ^ [] : [ord_less(_797236, ti(_797236, _797240), _797238), -(ord_less(_797236, _797240, _797238))], (842 ^ _768566) ^ [] : [ord_less(_797236, _797240, _797238), -(ord_less(_797236, ti(_797236, _797240), _797238))]]], (848 ^ _768566) ^ [_797739, _797741, _797743] : [order(_797739), 851 ^ _768566 : [(852 ^ _768566) ^ [] : [ord_less(_797739, _797743, ti(_797739, _797741)), -(ord_less(_797739, _797743, _797741))], (858 ^ _768566) ^ [] : [ord_less(_797739, _797743, _797741), -(ord_less(_797739, _797743, ti(_797739, _797741)))]]], (864 ^ _768566) ^ [_798242, _798244, _798246] : [order(_798242), 867 ^ _768566 : [(868 ^ _768566) ^ [] : [ord_less_eq(_798242, ti(_798242, _798246), _798244), -(ord_less_eq(_798242, _798246, _798244))], (874 ^ _768566) ^ [] : [ord_less_eq(_798242, _798246, _798244), -(ord_less_eq(_798242, ti(_798242, _798246), _798244))]]], (880 ^ _768566) ^ [_798745, _798747, _798749] : [order(_798745), 883 ^ _768566 : [(884 ^ _768566) ^ [] : [ord_less_eq(_798745, _798749, ti(_798745, _798747)), -(ord_less_eq(_798745, _798749, _798747))], (890 ^ _768566) ^ [] : [ord_less_eq(_798745, _798749, _798747), -(ord_less_eq(_798745, _798749, ti(_798745, _798747)))]]], (896 ^ _768566) ^ [_799248, _799250, _799252] : [power(_799248), -(power_power(_799248, ti(_799248, _799252), _799250) = power_power(_799248, _799252, _799250))], (902 ^ _768566) ^ [_799498, _799500, _799502] : [power(_799498), -(power_power(_799498, _799502, ti(nat, _799500)) = power_power(_799498, _799502, _799500))], (908 ^ _768566) ^ [_799748, _799750, _799752] : [power(_799748), -(ti(_799748, power_power(_799748, _799752, _799750)) = power_power(_799748, _799752, _799750))], (914 ^ _768566) ^ [_799969, _799971] : [-(legendre(ti(int, _799971), _799969) = legendre(_799971, _799969))], (916 ^ _768566) ^ [_800072, _800074] : [-(legendre(_800074, ti(int, _800072)) = legendre(_800074, _800072))], (918 ^ _768566) ^ [_800175, _800177] : [-(ti(int, legendre(_800177, _800175)) = legendre(_800177, _800175))], (920 ^ _768566) ^ [_800322, _800324] : [quadRes(ti(int, _800324), _800322), -(quadRes(_800324, _800322))], (926 ^ _768566) ^ [_800490, _800492] : [quadRes(_800492, _800490), -(quadRes(ti(int, _800492), _800490))], (932 ^ _768566) ^ [_800737, _800739] : [quadRes(_800739, ti(int, _800737)), -(quadRes(_800739, _800737))], (938 ^ _768566) ^ [_800905, _800907] : [quadRes(_800907, _800905), -(quadRes(_800907, ti(int, _800905)))], (944 ^ _768566) ^ [_801137, _801139, _801141] : [dvd(_801137), 947 ^ _768566 : [(948 ^ _768566) ^ [] : [dvd_dvd(_801137, ti(_801137, _801141), _801139), -(dvd_dvd(_801137, _801141, _801139))], (954 ^ _768566) ^ [] : [dvd_dvd(_801137, _801141, _801139), -(dvd_dvd(_801137, ti(_801137, _801141), _801139))]]], (960 ^ _768566) ^ [_801640, _801642, _801644] : [dvd(_801640), 963 ^ _768566 : [(964 ^ _768566) ^ [] : [dvd_dvd(_801640, _801644, ti(_801640, _801642)), -(dvd_dvd(_801640, _801644, _801642))], (970 ^ _768566) ^ [] : [dvd_dvd(_801640, _801644, _801642), -(dvd_dvd(_801640, _801644, ti(_801640, _801642)))]]], (976 ^ _768566) ^ [_802144] : [twoSqu420862341sum2sq(ti(int, _802144)), -(twoSqu420862341sum2sq(_802144))], (982 ^ _768566) ^ [_802302] : [twoSqu420862341sum2sq(_802302), -(twoSqu420862341sum2sq(ti(int, _802302)))], (988 ^ _768566) ^ [] : [-(ti(int, m) = m)], (990 ^ _768566) ^ [] : [-(ti(int, s1) = s1)], (992 ^ _768566) ^ [] : [-(ti(int, s) = s)], (994 ^ _768566) ^ [] : [-(ti(int, t) = t)], (996 ^ _768566) ^ [] : [-(ord_less(int, t, zero_zero(int)))], (998 ^ _768566) ^ [] : [-(ord_less(int, t, one_one(int)))], (1000 ^ _768566) ^ [] : [-(ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int))))], (1002 ^ _768566) ^ [] : [-(plus_plus(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))], (1004 ^ _768566) ^ [] : [t = zero_zero(int), -(plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)) = zero_zero(int))], (1010 ^ _768566) ^ [] : [ord_less_eq(int, one_one(int), t)], (1012 ^ _768566) ^ [] : [-(ord_less(int, zero_zero(int), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (1014 ^ _768566) ^ [_803144] : [linordered_idom(_803144), 1017 ^ _768566 : [(1018 ^ _768566) ^ [_803289, _803291] : [ord_less(_803144, plus_plus(_803144, power_power(_803144, _803291, number_number_of(nat, bit0(bit1(pls)))), power_power(_803144, _803289, number_number_of(nat, bit0(bit1(pls))))), zero_zero(_803144))]]], (1020 ^ _768566) ^ [_803406] : [linordered_idom(_803406), 1023 ^ _768566 : [(1034 ^ _768566) ^ [_803936, _803938] : [1035 ^ _768566 : [(1036 ^ _768566) ^ [] : [-(ti(_803406, _803938) = zero_zero(_803406))], (1038 ^ _768566) ^ [] : [-(ti(_803406, _803936) = zero_zero(_803406))]], -(ord_less(_803406, zero_zero(_803406), plus_plus(_803406, power_power(_803406, _803938, number_number_of(nat, bit0(bit1(pls)))), power_power(_803406, _803936, number_number_of(nat, bit0(bit1(pls)))))))], (1024 ^ _768566) ^ [_803620, _803622] : [ord_less(_803406, zero_zero(_803406), plus_plus(_803406, power_power(_803406, _803622, number_number_of(nat, bit0(bit1(pls)))), power_power(_803406, _803620, number_number_of(nat, bit0(bit1(pls)))))), ti(_803406, _803622) = zero_zero(_803406), ti(_803406, _803620) = zero_zero(_803406)]]], (1042 ^ _768566) ^ [_804279] : [linordered_idom(_804279), 1045 ^ _768566 : [(1046 ^ _768566) ^ [_804488, _804490] : [plus_plus(_804279, power_power(_804279, _804490, number_number_of(nat, bit0(bit1(pls)))), power_power(_804279, _804488, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_804279), 1049 ^ _768566 : [(1050 ^ _768566) ^ [] : [-(ti(_804279, _804490) = zero_zero(_804279))], (1052 ^ _768566) ^ [] : [-(ti(_804279, _804488) = zero_zero(_804279))]]], (1054 ^ _768566) ^ [_804783, _804785] : [-(plus_plus(_804279, power_power(_804279, _804785, number_number_of(nat, bit0(bit1(pls)))), power_power(_804279, _804783, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_804279)), ti(_804279, _804785) = zero_zero(_804279), ti(_804279, _804783) = zero_zero(_804279)]]], (1064 ^ _768566) ^ [_805135] : [linordered_idom(_805135), 1067 ^ _768566 : [(1068 ^ _768566) ^ [_805253] : [ord_less(_805135, power_power(_805135, _805253, number_number_of(nat, bit0(bit1(pls)))), zero_zero(_805135))]]], (1070 ^ _768566) ^ [_805360] : [linordered_idom(_805360), 1073 ^ _768566 : [(1074 ^ _768566) ^ [_805534] : [ord_less(_805360, zero_zero(_805360), power_power(_805360, _805534, number_number_of(nat, bit0(bit1(pls))))), ti(_805360, _805534) = zero_zero(_805360)], (1080 ^ _768566) ^ [_805723] : [-(ti(_805360, _805723) = zero_zero(_805360)), -(ord_less(_805360, zero_zero(_805360), power_power(_805360, _805723, number_number_of(nat, bit0(bit1(pls))))))]]], (1086 ^ _768566) ^ [_805955] : [semiring_1(_805955), -(power_power(_805955, one_one(_805955), number_number_of(nat, bit0(bit1(pls)))) = one_one(_805955))], (1092 ^ _768566) ^ [_806159] : [semiring_1(_806159), -(power_power(_806159, zero_zero(_806159), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_806159))], (1098 ^ _768566) ^ [_806363] : [ring_11004092258visors(_806363), 1101 ^ _768566 : [(1102 ^ _768566) ^ [_806534] : [power_power(_806363, _806534, number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_806363), -(ti(_806363, _806534) = zero_zero(_806363))], (1108 ^ _768566) ^ [_806720] : [ti(_806363, _806720) = zero_zero(_806363), -(power_power(_806363, _806720, number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_806363))]]], (1114 ^ _768566) ^ [_806947] : [number_ring(_806947), 1117 ^ _768566 : [(1118 ^ _768566) ^ [_807073] : [-(plus_plus(_806947, one_one(_806947), number_number_of(_806947, _807073)) = number_number_of(_806947, plus_plus(int, bit1(pls), _807073)))]]], (1120 ^ _768566) ^ [_807189] : [number_ring(_807189), 1123 ^ _768566 : [(1124 ^ _768566) ^ [_807315] : [-(plus_plus(_807189, number_number_of(_807189, _807315), one_one(_807189)) = number_number_of(_807189, plus_plus(int, _807315, bit1(pls))))]]], (1126 ^ _768566) ^ [] : [-(ord_less(int, t, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (1129 ^ _768566) ^ [] : [-(plus_plus(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)), 1127 ^ []))], (1131 ^ _768566) ^ [] : [-(zprime(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (1133 ^ _768566) ^ [] : [-(twoSqu420862341sum2sq(times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t)))], (1135 ^ _768566) ^ [_807671] : [-(ord_less_eq(int, _807671, _807671))], (1137 ^ _768566) ^ [_807750] : [-(number_number_of(int, _807750) = ti(int, _807750))], (1139 ^ _768566) ^ [_807848, _807850] : [-(times_times(int, _807850, _807848) = times_times(int, _807848, _807850))], (1141 ^ _768566) ^ [_807965, _807967] : [-(ord_less_eq(int, _807967, _807965)), -(ord_less_eq(int, _807965, _807967))], (1147 ^ _768566) ^ [_808165, _808167] : [-(times_times(int, number_number_of(int, _808167), number_number_of(int, _808165)) = number_number_of(int, times_times(int, _808167, _808165)))], (1149 ^ _768566) ^ [_808320, _808322] : [ord_less_eq(int, number_number_of(int, _808322), number_number_of(int, _808320)), -(ord_less_eq(int, _808322, _808320))], (1155 ^ _768566) ^ [_808498, _808500] : [ord_less_eq(int, _808500, _808498), -(ord_less_eq(int, number_number_of(int, _808500), number_number_of(int, _808498)))], (1161 ^ _768566) ^ [_808712] : [number_ring(_808712), linordered_idom(_808712), 1168 ^ _768566 : [(1169 ^ _768566) ^ [_808982, _808984] : [ord_less_eq(_808712, number_number_of(_808712, _808984), number_number_of(_808712, _808982)), -(ord_less_eq(int, _808984, _808982))], (1175 ^ _768566) ^ [_809168, _809170] : [ord_less_eq(int, _809170, _809168), -(ord_less_eq(_808712, number_number_of(_808712, _809170), number_number_of(_808712, _809168)))]]], (1181 ^ _768566) ^ [_809410, _809412, _809414] : [-(times_times(int, times_times(int, _809414, _809412), _809410) = times_times(int, _809414, times_times(int, _809412, _809410)))], (1183 ^ _768566) ^ [_809551, _809553, _809555] : [ord_less_eq(int, _809553, _809551), ord_less_eq(int, _809551, _809555), -(ord_less_eq(int, _809553, _809555))], (1193 ^ _768566) ^ [_809866, _809868] : [ord_less_eq(int, _809868, _809866), ord_less_eq(int, _809866, _809868), -(ti(int, _809868) = ti(int, _809866))], (1203 ^ _768566) ^ [_810180, _810182, _810184] : [-(power_power(int, _810184, plus_plus(nat, _810182, _810180)) = times_times(int, power_power(int, _810184, _810182), power_power(int, _810184, _810180)))], (1205 ^ _768566) ^ [_810340, _810342] : [ord_less_eq(int, bit1(_810342), bit1(_810340)), -(ord_less_eq(int, _810342, _810340))], (1211 ^ _768566) ^ [_810514, _810516] : [ord_less_eq(int, _810516, _810514), -(ord_less_eq(int, bit1(_810516), bit1(_810514)))], (1217 ^ _768566) ^ [_810767, _810769] : [ord_less_eq(int, bit1(_810769), bit1(_810767)), -(ord_less_eq(int, _810769, _810767))], (1223 ^ _768566) ^ [_810941, _810943] : [ord_less_eq(int, _810943, _810941), -(ord_less_eq(int, bit1(_810943), bit1(_810941)))], (1229 ^ _768566) ^ [] : [-(ord_less_eq(int, pls, pls))], (1231 ^ _768566) ^ [_811247, _811249] : [ord_less_eq(int, bit0(_811249), bit0(_811247)), -(ord_less_eq(int, _811249, _811247))], (1237 ^ _768566) ^ [_811421, _811423] : [ord_less_eq(int, _811423, _811421), -(ord_less_eq(int, bit0(_811423), bit0(_811421)))], (1243 ^ _768566) ^ [_811674, _811676] : [ord_less_eq(int, bit0(_811676), bit0(_811674)), -(ord_less_eq(int, _811676, _811674))], (1249 ^ _768566) ^ [_811848, _811850] : [ord_less_eq(int, _811850, _811848), -(ord_less_eq(int, bit0(_811850), bit0(_811848)))], (1255 ^ _768566) ^ [_812101, _812103] : [ord_less(int, _812103, _812101), 1258 ^ _768566 : [(1259 ^ _768566) ^ [] : [-(ord_less_eq(int, _812103, _812101))], (1261 ^ _768566) ^ [] : [ti(int, _812103) = ti(int, _812101)]]], (1263 ^ _768566) ^ [_812355, _812357] : [-(ord_less(int, _812357, _812355)), ord_less_eq(int, _812357, _812355), -(ti(int, _812357) = ti(int, _812355))], (1273 ^ _768566) ^ [_812689, _812691, _812693] : [ord_less_eq(int, _812691, _812689), -(ord_less_eq(int, plus_plus(int, _812693, _812691), plus_plus(int, _812693, _812689)))], (1279 ^ _768566) ^ [_812940] : [number_number_of(nat, _812940) = zero_zero(nat), -(ord_less_eq(int, _812940, pls))], (1285 ^ _768566) ^ [_813104] : [ord_less_eq(int, _813104, pls), -(number_number_of(nat, _813104) = zero_zero(nat))], (1291 ^ _768566) ^ [_813333] : [zero_zero(nat) = number_number_of(nat, _813333), -(ord_less_eq(int, _813333, pls))], (1297 ^ _768566) ^ [_813497] : [ord_less_eq(int, _813497, pls), -(zero_zero(nat) = number_number_of(nat, _813497))], (1303 ^ _768566) ^ [_813697] : [number_semiring(_813697), 1306 ^ _768566 : [(1307 ^ _768566) ^ [_813872, _813874] : [ord_less_eq(int, pls, _813872), ord_less_eq(int, pls, _813874), -(times_times(_813697, number_number_of(_813697, _813872), number_number_of(_813697, _813874)) = number_number_of(_813697, times_times(int, _813872, _813874)))]]], (1317 ^ _768566) ^ [_814212] : [number_ring(_814212), 1320 ^ _768566 : [(1321 ^ _768566) ^ [_814385, _814387, _814389] : [-(times_times(_814212, number_number_of(_814212, _814389), times_times(_814212, number_number_of(_814212, _814387), _814385)) = times_times(_814212, number_number_of(_814212, times_times(int, _814389, _814387)), _814385))]]], (1323 ^ _768566) ^ [_814514] : [number_ring(_814514), 1326 ^ _768566 : [(1327 ^ _768566) ^ [_814660, _814662] : [-(times_times(_814514, number_number_of(_814514, _814662), number_number_of(_814514, _814660)) = number_number_of(_814514, times_times(int, _814662, _814660)))]]], (1329 ^ _768566) ^ [_814779] : [number_ring(_814779), 1332 ^ _768566 : [(1333 ^ _768566) ^ [_814925, _814927] : [-(number_number_of(_814779, times_times(int, _814927, _814925)) = times_times(_814779, number_number_of(_814779, _814927), number_number_of(_814779, _814925)))]]], (1335 ^ _768566) ^ [_815044] : [linord581940658strict(_815044), 1338 ^ _768566 : [(1339 ^ _768566) ^ [_815254, _815256] : [ord_less_eq(_815044, plus_plus(_815044, times_times(_815044, _815256, _815256), times_times(_815044, _815254, _815254)), zero_zero(_815044)), 1342 ^ _768566 : [(1343 ^ _768566) ^ [] : [-(ti(_815044, _815256) = zero_zero(_815044))], (1345 ^ _768566) ^ [] : [-(ti(_815044, _815254) = zero_zero(_815044))]]], (1347 ^ _768566) ^ [_815551, _815553] : [-(ord_less_eq(_815044, plus_plus(_815044, times_times(_815044, _815553, _815553), times_times(_815044, _815551, _815551)), zero_zero(_815044))), ti(_815044, _815553) = zero_zero(_815044), ti(_815044, _815551) = zero_zero(_815044)]]], (1357 ^ _768566) ^ [_815905] : [linordered_ring(_815905), 1360 ^ _768566 : [(1361 ^ _768566) ^ [_816049, _816051] : [-(ord_less_eq(_815905, zero_zero(_815905), plus_plus(_815905, times_times(_815905, _816051, _816051), times_times(_815905, _816049, _816049))))]]], (1363 ^ _768566) ^ [_816166] : [number_ring(_816166), linordered_idom(_816166), 1370 ^ _768566 : [(1371 ^ _768566) ^ [_816416] : [ord_less_eq(_816166, number_number_of(_816166, _816416), zero_zero(_816166)), -(ord_less_eq(int, _816416, pls))], (1377 ^ _768566) ^ [_816594] : [ord_less_eq(int, _816594, pls), -(ord_less_eq(_816166, number_number_of(_816166, _816594), zero_zero(_816166)))]]], (1383 ^ _768566) ^ [_816815] : [number_ring(_816815), linordered_idom(_816815), 1390 ^ _768566 : [(1391 ^ _768566) ^ [_817065] : [ord_less_eq(_816815, zero_zero(_816815), number_number_of(_816815, _817065)), -(ord_less_eq(int, pls, _817065))], (1397 ^ _768566) ^ [_817243] : [ord_less_eq(int, pls, _817243), -(ord_less_eq(_816815, zero_zero(_816815), number_number_of(_816815, _817243)))]]], (1403 ^ _768566) ^ [_817493] : [ord_less(nat, zero_zero(nat), number_number_of(nat, _817493)), -(ord_less(int, pls, _817493))], (1409 ^ _768566) ^ [_817659] : [ord_less(int, pls, _817659), -(ord_less(nat, zero_zero(nat), number_number_of(nat, _817659)))], (1415 ^ _768566) ^ [_817861] : [number(_817861), linorder(_817861), 1422 ^ _768566 : [(1423 ^ _768566) ^ [_818139, _818141] : [ord_less_eq(_817861, number_number_of(_817861, _818141), number_number_of(_817861, _818139)), ord_less(_817861, number_number_of(_817861, _818139), number_number_of(_817861, _818141))], (1429 ^ _768566) ^ [_818338, _818340] : [-(ord_less(_817861, number_number_of(_817861, _818338), number_number_of(_817861, _818340))), -(ord_less_eq(_817861, number_number_of(_817861, _818340), number_number_of(_817861, _818338)))]]], (1435 ^ _768566) ^ [_818611] : [ord_less_eq(int, pls, bit1(_818611)), -(ord_less_eq(int, pls, _818611))], (1441 ^ _768566) ^ [_818775] : [ord_less_eq(int, pls, _818775), -(ord_less_eq(int, pls, bit1(_818775)))], (1447 ^ _768566) ^ [_819018, _819020] : [ord_less_eq(int, bit0(_819020), bit1(_819018)), -(ord_less_eq(int, _819020, _819018))], (1453 ^ _768566) ^ [_819192, _819194] : [ord_less_eq(int, _819194, _819192), -(ord_less_eq(int, bit0(_819194), bit1(_819192)))], (1459 ^ _768566) ^ [_819445, _819447] : [ord_less_eq(int, bit0(_819447), bit1(_819445)), -(ord_less_eq(int, _819447, _819445))], (1465 ^ _768566) ^ [_819619, _819621] : [ord_less_eq(int, _819621, _819619), -(ord_less_eq(int, bit0(_819621), bit1(_819619)))], (1471 ^ _768566) ^ [_819858] : [ord_less_eq(int, bit0(_819858), pls), -(ord_less_eq(int, _819858, pls))], (1477 ^ _768566) ^ [_820022] : [ord_less_eq(int, _820022, pls), -(ord_less_eq(int, bit0(_820022), pls))], (1483 ^ _768566) ^ [_820251] : [ord_less_eq(int, pls, bit0(_820251)), -(ord_less_eq(int, pls, _820251))], (1489 ^ _768566) ^ [_820415] : [ord_less_eq(int, pls, _820415), -(ord_less_eq(int, pls, bit0(_820415)))], (1495 ^ _768566) ^ [_820657, _820659, _820661, _820663] : [ord_less(int, _820659, _820657), ord_less_eq(int, _820663, _820661), -(ord_less(int, plus_plus(int, _820659, _820663), plus_plus(int, _820657, _820661)))], (1505 ^ _768566) ^ [] : [-(number_number_of(nat, pls) = zero_zero(nat))], (1507 ^ _768566) ^ [] : [-(zero_zero(nat) = number_number_of(nat, pls))], (1509 ^ _768566) ^ [_821090] : [number_ring(_821090), linordered_idom(_821090), 1516 ^ _768566 : [(1517 ^ _768566) ^ [_821340] : [ord_less_eq(_821090, number_number_of(_821090, _821340), one_one(_821090)), -(ord_less_eq(int, _821340, bit1(pls)))], (1523 ^ _768566) ^ [_821518] : [ord_less_eq(int, _821518, bit1(pls)), -(ord_less_eq(_821090, number_number_of(_821090, _821518), one_one(_821090)))]]], (1529 ^ _768566) ^ [_821739] : [number_ring(_821739), linordered_idom(_821739), 1536 ^ _768566 : [(1537 ^ _768566) ^ [_821989] : [ord_less_eq(_821739, one_one(_821739), number_number_of(_821739, _821989)), -(ord_less_eq(int, bit1(pls), _821989))], (1543 ^ _768566) ^ [_822167] : [ord_less_eq(int, bit1(pls), _822167), -(ord_less_eq(_821739, one_one(_821739), number_number_of(_821739, _822167)))]]], (1549 ^ _768566) ^ [] : [-(plus_plus(nat, one_one(nat), one_one(nat)) = number_number_of(nat, bit0(bit1(pls))))], (1551 ^ _768566) ^ [_822426] : [-(times_times(int, pls, _822426) = pls)], (1553 ^ _768566) ^ [_822522, _822524] : [-(times_times(int, bit0(_822524), _822522) = bit0(times_times(int, _822524, _822522)))], (1555 ^ _768566) ^ [_822672, _822674] : [ord_less(int, number_number_of(int, _822674), number_number_of(int, _822672)), -(ord_less(int, _822674, _822672))], (1561 ^ _768566) ^ [_822850, _822852] : [ord_less(int, _822852, _822850), -(ord_less(int, number_number_of(int, _822852), number_number_of(int, _822850)))], (1567 ^ _768566) ^ [_823049] : [-(times_times(int, _823049, one_one(int)) = ti(int, _823049))], (1569 ^ _768566) ^ [_823134] : [-(times_times(int, one_one(int), _823134) = ti(int, _823134))], (1571 ^ _768566) ^ [_823233, _823235] : [-(plus_plus(int, number_number_of(int, _823235), number_number_of(int, _823233)) = number_number_of(int, plus_plus(int, _823235, _823233)))], (1573 ^ _768566) ^ [_823358, _823360, _823362] : [-(times_times(int, plus_plus(int, _823362, _823360), _823358) = plus_plus(int, times_times(int, _823362, _823358), times_times(int, _823360, _823358)))], (1575 ^ _768566) ^ [_823488, _823490, _823492] : [-(times_times(int, _823492, plus_plus(int, _823490, _823488)) = plus_plus(int, times_times(int, _823492, _823490), times_times(int, _823492, _823488)))], (1577 ^ _768566) ^ [_823634] : [ord_less_eq(int, bit1(_823634), pls), -(ord_less(int, _823634, pls))], (1583 ^ _768566) ^ [_823798] : [ord_less(int, _823798, pls), -(ord_less_eq(int, bit1(_823798), pls))], (1589 ^ _768566) ^ [_824027] : [ord_less(int, pls, bit1(_824027)), -(ord_less_eq(int, pls, _824027))], (1595 ^ _768566) ^ [_824191] : [ord_less_eq(int, pls, _824191), -(ord_less(int, pls, bit1(_824191)))], (1601 ^ _768566) ^ [_824434, _824436] : [ord_less_eq(int, bit1(_824436), bit0(_824434)), -(ord_less(int, _824436, _824434))], (1607 ^ _768566) ^ [_824608, _824610] : [ord_less(int, _824610, _824608), -(ord_less_eq(int, bit1(_824610), bit0(_824608)))], (1613 ^ _768566) ^ [_824861, _824863] : [ord_less_eq(int, bit1(_824863), bit0(_824861)), -(ord_less(int, _824863, _824861))], (1619 ^ _768566) ^ [_825035, _825037] : [ord_less(int, _825037, _825035), -(ord_less_eq(int, bit1(_825037), bit0(_825035)))], (1625 ^ _768566) ^ [_825288, _825290] : [ord_less(int, bit0(_825290), bit1(_825288)), -(ord_less_eq(int, _825290, _825288))], (1631 ^ _768566) ^ [_825462, _825464] : [ord_less_eq(int, _825464, _825462), -(ord_less(int, bit0(_825464), bit1(_825462)))], (1637 ^ _768566) ^ [_825715, _825717] : [ord_less(int, bit0(_825717), bit1(_825715)), -(ord_less_eq(int, _825717, _825715))], (1643 ^ _768566) ^ [_825889, _825891] : [ord_less_eq(int, _825891, _825889), -(ord_less(int, bit0(_825891), bit1(_825889)))], (1649 ^ _768566) ^ [_826142, _826144] : [ord_less(nat, number_number_of(nat, _826144), number_number_of(nat, _826142)), 1652 ^ _768566 : [(1659 ^ _768566) ^ [] : [-(ord_less(int, _826144, _826142))], (1653 ^ _768566) ^ [] : [ord_less(int, _826144, _826142), -(ord_less(int, pls, _826142))]]], (1661 ^ _768566) ^ [_826488, _826490] : [-(ord_less(nat, number_number_of(nat, _826490), number_number_of(nat, _826488))), 1664 ^ _768566 : [(1665 ^ _768566) ^ [] : [-(ord_less(int, _826490, _826488))], (1667 ^ _768566) ^ [] : [ord_less(int, pls, _826488)]], ord_less(int, _826490, _826488)], (1673 ^ _768566) ^ [_826899] : [ord_less_eq(int, one_one(int), _826899), -(ord_less(int, zero_zero(int), _826899))], (1679 ^ _768566) ^ [_827059] : [ord_less(int, zero_zero(int), _827059), -(ord_less_eq(int, one_one(int), _827059))], (1685 ^ _768566) ^ [] : [-(number_number_of(nat, bit1(pls)) = one_one(nat))], (1687 ^ _768566) ^ [] : [-(one_one(nat) = number_number_of(nat, bit1(pls)))], (1689 ^ _768566) ^ [_827375, _827377] : [ord_less(int, _827377, _827375), -(ord_less_eq(int, plus_plus(int, _827377, one_one(int)), _827375))], (1695 ^ _768566) ^ [_827626, _827628] : [ord_less_eq(int, plus_plus(int, _827628, one_one(int)), _827626), -(ord_less(int, _827628, _827626))], (1701 ^ _768566) ^ [_827800, _827802] : [ord_less(int, _827802, _827800), -(ord_less_eq(int, plus_plus(int, _827802, one_one(int)), _827800))], (1707 ^ _768566) ^ [_828053, _828055] : [ord_less(int, _828055, plus_plus(int, _828053, one_one(int))), -(ord_less_eq(int, _828055, _828053))], (1713 ^ _768566) ^ [_828227, _828229] : [ord_less_eq(int, _828229, _828227), -(ord_less(int, _828229, plus_plus(int, _828227, one_one(int))))], (1719 ^ _768566) ^ [_828437] : [number_semiring(_828437), 1722 ^ _768566 : [(1723 ^ _768566) ^ [_828612, _828614] : [ord_less_eq(int, pls, _828612), ord_less_eq(int, pls, _828614), -(plus_plus(_828437, number_number_of(_828437, _828612), number_number_of(_828437, _828614)) = number_number_of(_828437, plus_plus(int, _828612, _828614)))]]], (1733 ^ _768566) ^ [_828986, _828988] : [ord_less(int, _828986, pls), -(plus_plus(nat, number_number_of(nat, _828986), number_number_of(nat, _828988)) = number_number_of(nat, _828988))], (1739 ^ _768566) ^ [_829176, _829178] : [-(ord_less(int, _829176, pls)), 1742 ^ _768566 : [(1743 ^ _768566) ^ [] : [ord_less(int, _829178, pls), -(plus_plus(nat, number_number_of(nat, _829176), number_number_of(nat, _829178)) = number_number_of(nat, _829176))], (1749 ^ _768566) ^ [] : [-(ord_less(int, _829178, pls)), -(plus_plus(nat, number_number_of(nat, _829176), number_number_of(nat, _829178)) = number_number_of(nat, plus_plus(int, _829176, _829178)))]]], (1755 ^ _768566) ^ [_829699] : [ord_less_eq(int, zero_zero(int), _829699), -(ord_less(int, zero_zero(int), plus_plus(int, one_one(int), _829699)))], (1761 ^ _768566) ^ [_829901] : [number_ring(_829901), ring_char_0(_829901), 1768 ^ _768566 : [(1769 ^ _768566) ^ [_830175, _830177] : [number_number_of(_829901, _830177) = number_number_of(_829901, _830175), -(ti(int, _830177) = ti(int, _830175))], (1775 ^ _768566) ^ [_830369, _830371] : [ti(int, _830371) = ti(int, _830369), -(number_number_of(_829901, _830371) = number_number_of(_829901, _830369))]]], (1781 ^ _768566) ^ [_830606] : [number(_830606), 1784 ^ _768566 : [(1785 ^ _768566) ^ [_830797, _830799] : [number_number_of(_830606, _830799) = ti(_830606, _830797), -(ti(_830606, _830797) = number_number_of(_830606, _830799))], (1791 ^ _768566) ^ [_830991, _830993] : [ti(_830606, _830991) = number_number_of(_830606, _830993), -(number_number_of(_830606, _830993) = ti(_830606, _830991))]]], (1797 ^ _768566) ^ [_831269, _831271] : [bit1(_831271) = bit1(_831269), -(ti(int, _831271) = ti(int, _831269))], (1803 ^ _768566) ^ [_831451, _831453] : [ti(int, _831453) = ti(int, _831451), -(bit1(_831453) = bit1(_831451))], (1809 ^ _768566) ^ [_831712, _831714] : [bit0(_831714) = bit0(_831712), -(ti(int, _831714) = ti(int, _831712))], (1815 ^ _768566) ^ [_831894, _831896] : [ti(int, _831896) = ti(int, _831894), -(bit0(_831896) = bit0(_831894))], (1821 ^ _768566) ^ [_832126, _832128] : [-(ord_less(int, _832128, _832126)), -(ti(int, _832128) = ti(int, _832126)), -(ord_less(int, _832126, _832128))], (1831 ^ _768566) ^ [_832429] : [linord581940658strict(_832429), 1834 ^ _768566 : [(1835 ^ _768566) ^ [_832638, _832640] : [plus_plus(_832429, times_times(_832429, _832640, _832640), times_times(_832429, _832638, _832638)) = zero_zero(_832429), 1838 ^ _768566 : [(1839 ^ _768566) ^ [] : [-(ti(_832429, _832640) = zero_zero(_832429))], (1841 ^ _768566) ^ [] : [-(ti(_832429, _832638) = zero_zero(_832429))]]], (1843 ^ _768566) ^ [_832933, _832935] : [-(plus_plus(_832429, times_times(_832429, _832935, _832935), times_times(_832429, _832933, _832933)) = zero_zero(_832429)), ti(_832429, _832935) = zero_zero(_832429), ti(_832429, _832933) = zero_zero(_832429)]]], (1853 ^ _768566) ^ [_833285] : [1860 ^ _768566 : [(1861 ^ _768566) ^ [_833545, _833547, _833549] : [-(times_times(_833285, plus_plus(_833285, _833549, _833547), number_number_of(_833285, _833545)) = plus_plus(_833285, times_times(_833285, _833549, number_number_of(_833285, _833545)), times_times(_833285, _833547, number_number_of(_833285, _833545))))]], number(_833285), semiring(_833285)], (1863 ^ _768566) ^ [_833678] : [1870 ^ _768566 : [(1871 ^ _768566) ^ [_833938, _833940, _833942] : [-(times_times(_833678, number_number_of(_833678, _833942), plus_plus(_833678, _833940, _833938)) = plus_plus(_833678, times_times(_833678, number_number_of(_833678, _833942), _833940), times_times(_833678, number_number_of(_833678, _833942), _833938)))]], number(_833678), semiring(_833678)], (1873 ^ _768566) ^ [_834084, _834086, _834088] : [-(plus_plus(int, plus_plus(int, _834088, _834086), _834084) = plus_plus(int, _834088, plus_plus(int, _834086, _834084)))], (1875 ^ _768566) ^ [_834210, _834212, _834214] : [-(plus_plus(int, _834214, plus_plus(int, _834212, _834210)) = plus_plus(int, _834212, plus_plus(int, _834214, _834210)))], (1877 ^ _768566) ^ [_834322, _834324] : [-(plus_plus(int, _834324, _834322) = plus_plus(int, _834322, _834324))], (1879 ^ _768566) ^ [] : [-(zero_zero(int) = number_number_of(int, pls))], (1881 ^ _768566) ^ [_834506, _834508, _834510] : [ord_less(int, _834508, _834506), ord_less(int, zero_zero(int), _834510), -(ord_less(int, times_times(int, _834510, _834508), times_times(int, _834510, _834506)))], (1891 ^ _768566) ^ [_834823] : [linordered_semidom(_834823), 1894 ^ _768566 : [(1895 ^ _768566) ^ [_835005, _835007] : [power_power(_834823, _835007, number_number_of(nat, bit0(bit1(pls)))) = power_power(_834823, _835005, number_number_of(nat, bit0(bit1(pls)))), ord_less_eq(_834823, zero_zero(_834823), _835007), ord_less_eq(_834823, zero_zero(_834823), _835005), -(ti(_834823, _835007) = ti(_834823, _835005))]]], (1909 ^ _768566) ^ [_835440] : [linordered_semidom(_835440), 1912 ^ _768566 : [(1913 ^ _768566) ^ [_835609, _835611] : [ord_less_eq(_835440, power_power(_835440, _835611, number_number_of(nat, bit0(bit1(pls)))), power_power(_835440, _835609, number_number_of(nat, bit0(bit1(pls))))), ord_less_eq(_835440, zero_zero(_835440), _835609), -(ord_less_eq(_835440, _835611, _835609))]]], (1923 ^ _768566) ^ [_835937] : [linordered_idom(_835937), 1926 ^ _768566 : [(1927 ^ _768566) ^ [_836054] : [-(ord_less_eq(_835937, zero_zero(_835937), power_power(_835937, _836054, number_number_of(nat, bit0(bit1(pls))))))]]], (1929 ^ _768566) ^ [_836161] : [linordered_semidom(_836161), 1932 ^ _768566 : [(1933 ^ _768566) ^ [_836330, _836332] : [ord_less(_836161, power_power(_836161, _836332, number_number_of(nat, bit0(bit1(pls)))), power_power(_836161, _836330, number_number_of(nat, bit0(bit1(pls))))), ord_less_eq(_836161, zero_zero(_836161), _836330), -(ord_less(_836161, _836332, _836330))]]], (1943 ^ _768566) ^ [_836658] : [linordered_idom(_836658), 1946 ^ _768566 : [(1947 ^ _768566) ^ [_836868, _836870] : [ord_less_eq(_836658, plus_plus(_836658, power_power(_836658, _836870, number_number_of(nat, bit0(bit1(pls)))), power_power(_836658, _836868, number_number_of(nat, bit0(bit1(pls))))), zero_zero(_836658)), 1950 ^ _768566 : [(1951 ^ _768566) ^ [] : [-(ti(_836658, _836870) = zero_zero(_836658))], (1953 ^ _768566) ^ [] : [-(ti(_836658, _836868) = zero_zero(_836658))]]], (1955 ^ _768566) ^ [_837165, _837167] : [-(ord_less_eq(_836658, plus_plus(_836658, power_power(_836658, _837167, number_number_of(nat, bit0(bit1(pls)))), power_power(_836658, _837165, number_number_of(nat, bit0(bit1(pls))))), zero_zero(_836658))), ti(_836658, _837167) = zero_zero(_836658), ti(_836658, _837165) = zero_zero(_836658)]]], (1965 ^ _768566) ^ [_837519] : [linordered_idom(_837519), 1968 ^ _768566 : [(1969 ^ _768566) ^ [_837663, _837665] : [-(ord_less_eq(_837519, zero_zero(_837519), plus_plus(_837519, power_power(_837519, _837665, number_number_of(nat, bit0(bit1(pls)))), power_power(_837519, _837663, number_number_of(nat, bit0(bit1(pls)))))))]]], (1971 ^ _768566) ^ [_837780] : [linord581940658strict(_837780), 1974 ^ _768566 : [(1985 ^ _768566) ^ [_838310, _838312] : [1986 ^ _768566 : [(1987 ^ _768566) ^ [] : [-(ti(_837780, _838312) = zero_zero(_837780))], (1989 ^ _768566) ^ [] : [-(ti(_837780, _838310) = zero_zero(_837780))]], -(ord_less(_837780, zero_zero(_837780), plus_plus(_837780, times_times(_837780, _838312, _838312), times_times(_837780, _838310, _838310))))], (1975 ^ _768566) ^ [_837994, _837996] : [ord_less(_837780, zero_zero(_837780), plus_plus(_837780, times_times(_837780, _837996, _837996), times_times(_837780, _837994, _837994))), ti(_837780, _837996) = zero_zero(_837780), ti(_837780, _837994) = zero_zero(_837780)]]], (1993 ^ _768566) ^ [_838653] : [linordered_ring(_838653), 1996 ^ _768566 : [(1997 ^ _768566) ^ [_838798, _838800] : [ord_less(_838653, plus_plus(_838653, times_times(_838653, _838800, _838800), times_times(_838653, _838798, _838798)), zero_zero(_838653))]]], (1999 ^ _768566) ^ [_838915] : [number_ring(_838915), 2002 ^ _768566 : [(2003 ^ _768566) ^ [_839035] : [-(times_times(_838915, number_number_of(_838915, bit1(pls)), _839035) = ti(_838915, _839035))]]], (2005 ^ _768566) ^ [_839145] : [number_ring(_839145), 2008 ^ _768566 : [(2009 ^ _768566) ^ [_839265] : [-(times_times(_839145, _839265, number_number_of(_839145, bit1(pls))) = ti(_839145, _839265))]]], (2011 ^ _768566) ^ [] : [-(one_one(int) = number_number_of(int, bit1(pls)))], (2013 ^ _768566) ^ [_839427, _839429] : [-(times_times(int, bit1(_839429), _839427) = plus_plus(int, bit0(times_times(int, _839429, _839427)), _839427))], (2015 ^ _768566) ^ [_839552, _839554] : [ord_less(int, zero_zero(int), _839552), 2018 ^ _768566 : [(2019 ^ _768566) ^ [] : [times_times(int, _839552, _839554) = one_one(int), 2022 ^ _768566 : [(2023 ^ _768566) ^ [] : [-(ti(int, _839552) = one_one(int))], (2025 ^ _768566) ^ [] : [-(ti(int, _839554) = one_one(int))]]], (2027 ^ _768566) ^ [] : [-(times_times(int, _839552, _839554) = one_one(int)), ti(int, _839552) = one_one(int), ti(int, _839554) = one_one(int)]]], (2037 ^ _768566) ^ [_840188] : [linord219039673up_add(_840188), 2040 ^ _768566 : [(2041 ^ _768566) ^ [_840359] : [plus_plus(_840188, _840359, _840359) = zero_zero(_840188), -(ti(_840188, _840359) = zero_zero(_840188))], (2047 ^ _768566) ^ [_840545] : [ti(_840188, _840545) = zero_zero(_840188), -(plus_plus(_840188, _840545, _840545) = zero_zero(_840188))]]], (2053 ^ _768566) ^ [_840756] : [bit1(_840756) = pls], (2055 ^ _768566) ^ [_840835] : [pls = bit1(_840835)], (2057 ^ _768566) ^ [_840928, _840930] : [bit1(_840930) = bit0(_840928)], (2059 ^ _768566) ^ [_841025, _841027] : [bit0(_841027) = bit1(_841025)], (2061 ^ _768566) ^ [_841153] : [bit0(_841153) = pls, -(ti(int, _841153) = pls)], (2067 ^ _768566) ^ [_841319] : [ti(int, _841319) = pls, -(bit0(_841319) = pls)], (2073 ^ _768566) ^ [_841550] : [pls = bit0(_841550), -(pls = ti(int, _841550))], (2079 ^ _768566) ^ [_841716] : [pls = ti(int, _841716), -(pls = bit0(_841716))], (2085 ^ _768566) ^ [] : [-(bit0(pls) = pls)], (2087 ^ _768566) ^ [] : [-(pls = zero_zero(int))], (2089 ^ _768566) ^ [_842067, _842069] : [ord_less(int, bit1(_842069), bit1(_842067)), -(ord_less(int, _842069, _842067))], (2095 ^ _768566) ^ [_842241, _842243] : [ord_less(int, _842243, _842241), -(ord_less(int, bit1(_842243), bit1(_842241)))], (2101 ^ _768566) ^ [_842494, _842496] : [ord_less(int, bit1(_842496), bit1(_842494)), -(ord_less(int, _842496, _842494))], (2107 ^ _768566) ^ [_842668, _842670] : [ord_less(int, _842670, _842668), -(ord_less(int, bit1(_842670), bit1(_842668)))], (2113 ^ _768566) ^ [] : [ord_less(int, pls, pls)], (2115 ^ _768566) ^ [_842973, _842975] : [ord_less(int, bit0(_842975), bit0(_842973)), -(ord_less(int, _842975, _842973))], (2121 ^ _768566) ^ [_843147, _843149] : [ord_less(int, _843149, _843147), -(ord_less(int, bit0(_843149), bit0(_843147)))], (2127 ^ _768566) ^ [_843400, _843402] : [ord_less(int, bit0(_843402), bit0(_843400)), -(ord_less(int, _843402, _843400))], (2133 ^ _768566) ^ [_843574, _843576] : [ord_less(int, _843576, _843574), -(ord_less(int, bit0(_843576), bit0(_843574)))], (2139 ^ _768566) ^ [] : [zero_zero(int) = one_one(int)], (2141 ^ _768566) ^ [_843821] : [-(plus_plus(int, _843821, pls) = ti(int, _843821))], (2143 ^ _768566) ^ [_843906] : [-(plus_plus(int, pls, _843906) = ti(int, _843906))], (2145 ^ _768566) ^ [_844005, _844007] : [-(plus_plus(int, bit0(_844007), bit0(_844005)) = bit0(plus_plus(int, _844007, _844005)))], (2147 ^ _768566) ^ [_844099] : [-(bit0(_844099) = plus_plus(int, _844099, _844099))], (2149 ^ _768566) ^ [_844183] : [-(plus_plus(int, _844183, zero_zero(int)) = ti(int, _844183))], (2151 ^ _768566) ^ [_844268] : [-(plus_plus(int, zero_zero(int), _844268) = ti(int, _844268))], (2153 ^ _768566) ^ [_844396, _844398, _844400] : [ord_less(int, _844398, _844396), -(ord_less(int, plus_plus(int, _844398, _844400), plus_plus(int, _844396, _844400)))], (2159 ^ _768566) ^ [_844618] : [number_ring(_844618), 2162 ^ _768566 : [(2163 ^ _768566) ^ [_844748] : [-(times_times(_844618, plus_plus(_844618, one_one(_844618), one_one(_844618)), number_number_of(_844618, _844748)) = number_number_of(_844618, bit0(_844748)))]]], (2165 ^ _768566) ^ [_844868] : [monoid_mult(_844868), 2168 ^ _768566 : [(2169 ^ _768566) ^ [_844990] : [-(power_power(_844868, _844990, number_number_of(nat, bit1(bit1(pls)))) = times_times(_844868, times_times(_844868, _844990, _844990), _844990))]]], (2171 ^ _768566) ^ [_845102] : [number_semiring(_845102), 2174 ^ _768566 : [(2175 ^ _768566) ^ [_845223] : [-(times_times(_845102, number_number_of(_845102, bit0(bit1(pls))), _845223) = plus_plus(_845102, _845223, _845223))]]], (2177 ^ _768566) ^ [_845334] : [number_ring(_845334), 2180 ^ _768566 : [(2181 ^ _768566) ^ [_845455] : [-(times_times(_845334, number_number_of(_845334, bit0(bit1(pls))), _845455) = plus_plus(_845334, _845455, _845455))]]], (2183 ^ _768566) ^ [_845566] : [number_semiring(_845566), 2186 ^ _768566 : [(2187 ^ _768566) ^ [_845687] : [-(times_times(_845566, _845687, number_number_of(_845566, bit0(bit1(pls)))) = plus_plus(_845566, _845687, _845687))]]], (2189 ^ _768566) ^ [_845798] : [number_ring(_845798), 2192 ^ _768566 : [(2193 ^ _768566) ^ [_845919] : [-(times_times(_845798, _845919, number_number_of(_845798, bit0(bit1(pls)))) = plus_plus(_845798, _845919, _845919))]]], (2195 ^ _768566) ^ [_846030] : [monoid_mult(_846030), 2198 ^ _768566 : [(2199 ^ _768566) ^ [_846148] : [-(power_power(_846030, _846148, number_number_of(nat, bit0(bit1(pls)))) = times_times(_846030, _846148, _846148))]]], (2201 ^ _768566) ^ [_846256] : [linordered_idom(_846256), 2204 ^ _768566 : [(2205 ^ _768566) ^ [_846426] : [ord_less(_846256, plus_plus(_846256, _846426, _846426), zero_zero(_846256)), -(ord_less(_846256, _846426, zero_zero(_846256)))], (2211 ^ _768566) ^ [_846610] : [ord_less(_846256, _846610, zero_zero(_846256)), -(ord_less(_846256, plus_plus(_846256, _846610, _846610), zero_zero(_846256)))]]], (2217 ^ _768566) ^ [_846835] : [number_semiring(_846835), -(number_number_of(_846835, pls) = zero_zero(_846835))], (2223 ^ _768566) ^ [_847033] : [number_ring(_847033), -(number_number_of(_847033, pls) = zero_zero(_847033))], (2229 ^ _768566) ^ [_847231] : [number_ring(_847231), -(zero_zero(_847231) = number_number_of(_847231, pls))], (2235 ^ _768566) ^ [_847429] : [number_ring(_847429), 2238 ^ _768566 : [(2239 ^ _768566) ^ [_847549] : [-(plus_plus(_847429, number_number_of(_847429, pls), _847549) = ti(_847429, _847549))]]], (2241 ^ _768566) ^ [_847659] : [number_ring(_847659), 2244 ^ _768566 : [(2245 ^ _768566) ^ [_847779] : [-(plus_plus(_847659, _847779, number_number_of(_847659, pls)) = ti(_847659, _847779))]]], (2247 ^ _768566) ^ [_847889] : [number_ring(_847889), linordered_idom(_847889), 2254 ^ _768566 : [(2255 ^ _768566) ^ [_848159, _848161] : [ord_less(_847889, number_number_of(_847889, _848161), number_number_of(_847889, _848159)), -(ord_less(int, _848161, _848159))], (2261 ^ _768566) ^ [_848345, _848347] : [ord_less(int, _848347, _848345), -(ord_less(_847889, number_number_of(_847889, _848347), number_number_of(_847889, _848345)))]]], (2267 ^ _768566) ^ [_848574] : [number_ring(_848574), 2270 ^ _768566 : [(2271 ^ _768566) ^ [_848747, _848749, _848751] : [-(plus_plus(_848574, number_number_of(_848574, _848751), plus_plus(_848574, number_number_of(_848574, _848749), _848747)) = plus_plus(_848574, number_number_of(_848574, plus_plus(int, _848751, _848749)), _848747))]]], (2273 ^ _768566) ^ [_848876] : [number_ring(_848876), 2276 ^ _768566 : [(2277 ^ _768566) ^ [_849022, _849024] : [-(plus_plus(_848876, number_number_of(_848876, _849024), number_number_of(_848876, _849022)) = number_number_of(_848876, plus_plus(int, _849024, _849022)))]]], (2279 ^ _768566) ^ [_849141] : [number_ring(_849141), 2282 ^ _768566 : [(2283 ^ _768566) ^ [_849287, _849289] : [-(number_number_of(_849141, plus_plus(int, _849289, _849287)) = plus_plus(_849141, number_number_of(_849141, _849289), number_number_of(_849141, _849287)))]]], (2285 ^ _768566) ^ [_849435] : [ord_less(int, bit1(_849435), pls), -(ord_less(int, _849435, pls))], (2291 ^ _768566) ^ [_849599] : [ord_less(int, _849599, pls), -(ord_less(int, bit1(_849599), pls))], (2297 ^ _768566) ^ [_849842, _849844] : [ord_less(int, bit1(_849844), bit0(_849842)), -(ord_less(int, _849844, _849842))], (2303 ^ _768566) ^ [_850016, _850018] : [ord_less(int, _850018, _850016), -(ord_less(int, bit1(_850018), bit0(_850016)))], (2309 ^ _768566) ^ [_850269, _850271] : [ord_less(int, bit1(_850271), bit0(_850269)), -(ord_less(int, _850271, _850269))], (2315 ^ _768566) ^ [_850443, _850445] : [ord_less(int, _850445, _850443), -(ord_less(int, bit1(_850445), bit0(_850443)))], (2321 ^ _768566) ^ [_850682] : [ord_less(int, bit1(_850682), zero_zero(int)), -(ord_less(int, _850682, zero_zero(int)))], (2327 ^ _768566) ^ [_850846] : [ord_less(int, _850846, zero_zero(int)), -(ord_less(int, bit1(_850846), zero_zero(int)))], (2333 ^ _768566) ^ [_851075] : [ord_less(int, bit0(_851075), pls), -(ord_less(int, _851075, pls))], (2339 ^ _768566) ^ [_851239] : [ord_less(int, _851239, pls), -(ord_less(int, bit0(_851239), pls))], (2345 ^ _768566) ^ [_851468] : [ord_less(int, pls, bit0(_851468)), -(ord_less(int, pls, _851468))], (2351 ^ _768566) ^ [_851632] : [ord_less(int, pls, _851632), -(ord_less(int, pls, bit0(_851632)))], (2357 ^ _768566) ^ [] : [ord_less(int, pls, zero_zero(int))], (2359 ^ _768566) ^ [_851913] : [ord_less(int, bit0(_851913), zero_zero(int)), -(ord_less(int, _851913, zero_zero(int)))], (2365 ^ _768566) ^ [_852077] : [ord_less(int, _852077, zero_zero(int)), -(ord_less(int, bit0(_852077), zero_zero(int)))], (2371 ^ _768566) ^ [_852276, _852278] : [-(plus_plus(int, bit1(_852278), bit0(_852276)) = bit1(plus_plus(int, _852278, _852276)))], (2373 ^ _768566) ^ [_852384, _852386] : [-(plus_plus(int, bit0(_852386), bit1(_852384)) = bit1(plus_plus(int, _852386, _852384)))], (2375 ^ _768566) ^ [] : [-(ord_less(int, zero_zero(int), one_one(int)))], (2377 ^ _768566) ^ [_852531] : [-(bit1(_852531) = plus_plus(int, plus_plus(int, one_one(int), _852531), _852531))], (2379 ^ _768566) ^ [_852618] : [plus_plus(int, plus_plus(int, one_one(int), _852618), _852618) = zero_zero(int)], (2391 ^ _768566) ^ [_853038, _853040] : [2392 ^ _768566 : [(2393 ^ _768566) ^ [] : [ord_less(int, _853040, _853038)], (2395 ^ _768566) ^ [] : [ti(int, _853040) = ti(int, _853038)]], -(ord_less(int, _853040, plus_plus(int, _853038, one_one(int))))], (2381 ^ _768566) ^ [_852762, _852764] : [ord_less(int, _852764, plus_plus(int, _852762, one_one(int))), -(ord_less(int, _852764, _852762)), -(ti(int, _852764) = ti(int, _852762))], (2399 ^ _768566) ^ [_853334] : [2406 ^ _768566 : [(2407 ^ _768566) ^ [_853544] : [-(power_power(_853334, number_number_of(_853334, _853544), number_number_of(nat, bit0(bit1(pls)))) = times_times(_853334, number_number_of(_853334, _853544), number_number_of(_853334, _853544)))]], monoid_mult(_853334), number(_853334)], (2409 ^ _768566) ^ [_853661] : [number_semiring(_853661), 2412 ^ _768566 : [(2413 ^ _768566) ^ [_853825, _853827] : [-(power_power(_853661, plus_plus(_853661, _853827, _853825), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(_853661, plus_plus(_853661, power_power(_853661, _853827, number_number_of(nat, bit0(bit1(pls)))), power_power(_853661, _853825, number_number_of(nat, bit0(bit1(pls))))), times_times(_853661, times_times(_853661, number_number_of(_853661, bit0(bit1(pls))), _853827), _853825)))]]], (2415 ^ _768566) ^ [_853962] : [number_ring(_853962), 2418 ^ _768566 : [(2419 ^ _768566) ^ [_854093] : [-(number_number_of(_853962, bit0(_854093)) = plus_plus(_853962, plus_plus(_853962, zero_zero(_853962), number_number_of(_853962, _854093)), number_number_of(_853962, _854093)))]]], (2421 ^ _768566) ^ [_854214] : [number_ring(_854214), 2424 ^ _768566 : [(2425 ^ _768566) ^ [_854345] : [-(number_number_of(_854214, bit1(_854345)) = plus_plus(_854214, plus_plus(_854214, one_one(_854214), number_number_of(_854214, _854345)), number_number_of(_854214, _854345)))]]], (2427 ^ _768566) ^ [_854466] : [number_semiring(_854466), -(number_number_of(_854466, bit1(pls)) = one_one(_854466))], (2433 ^ _768566) ^ [_854664] : [number_ring(_854664), -(number_number_of(_854664, bit1(pls)) = one_one(_854664))], (2439 ^ _768566) ^ [_854862] : [number_ring(_854862), -(one_one(_854862) = number_number_of(_854862, bit1(pls)))], (2445 ^ _768566) ^ [_855089] : [ord_less(int, plus_plus(int, plus_plus(int, one_one(int), _855089), _855089), zero_zero(int)), -(ord_less(int, _855089, zero_zero(int)))], (2451 ^ _768566) ^ [_855265] : [ord_less(int, _855265, zero_zero(int)), -(ord_less(int, plus_plus(int, plus_plus(int, one_one(int), _855265), _855265), zero_zero(int)))], (2457 ^ _768566) ^ [_855477] : [number_ring(_855477), linordered_idom(_855477), 2464 ^ _768566 : [(2465 ^ _768566) ^ [_855727] : [ord_less(_855477, number_number_of(_855477, _855727), zero_zero(_855477)), -(ord_less(int, _855727, pls))], (2471 ^ _768566) ^ [_855905] : [ord_less(int, _855905, pls), -(ord_less(_855477, number_number_of(_855477, _855905), zero_zero(_855477)))]]], (2477 ^ _768566) ^ [_856126] : [number_ring(_856126), linordered_idom(_856126), 2484 ^ _768566 : [(2485 ^ _768566) ^ [_856376] : [ord_less(_856126, zero_zero(_856126), number_number_of(_856126, _856376)), -(ord_less(int, pls, _856376))], (2491 ^ _768566) ^ [_856554] : [ord_less(int, pls, _856554), -(ord_less(_856126, zero_zero(_856126), number_number_of(_856126, _856554)))]]], (2497 ^ _768566) ^ [_856775] : [number_semiring(_856775), -(plus_plus(_856775, one_one(_856775), one_one(_856775)) = number_number_of(_856775, bit0(bit1(pls))))], (2503 ^ _768566) ^ [_856985] : [number_ring(_856985), -(plus_plus(_856985, one_one(_856985), one_one(_856985)) = number_number_of(_856985, bit0(bit1(pls))))], (2509 ^ _768566) ^ [_857195] : [number_ring(_857195), linordered_idom(_857195), 2516 ^ _768566 : [(2517 ^ _768566) ^ [_857445] : [ord_less(_857195, number_number_of(_857195, _857445), one_one(_857195)), -(ord_less(int, _857445, bit1(pls)))], (2523 ^ _768566) ^ [_857623] : [ord_less(int, _857623, bit1(pls)), -(ord_less(_857195, number_number_of(_857195, _857623), one_one(_857195)))]]], (2529 ^ _768566) ^ [_857844] : [number_ring(_857844), linordered_idom(_857844), 2536 ^ _768566 : [(2537 ^ _768566) ^ [_858094] : [ord_less(_857844, one_one(_857844), number_number_of(_857844, _858094)), -(ord_less(int, bit1(pls), _858094))], (2543 ^ _768566) ^ [_858272] : [ord_less(int, bit1(pls), _858272), -(ord_less(_857844, one_one(_857844), number_number_of(_857844, _858272)))]]], (2549 ^ _768566) ^ [] : [-(dvd_dvd(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int))))], (2551 ^ _768566) ^ [_858545, _858547] : [-(power_power(int, plus_plus(int, _858547, _858545), number_number_of(nat, bit1(bit1(pls)))) = plus_plus(int, plus_plus(int, plus_plus(int, power_power(int, _858547, number_number_of(nat, bit1(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), power_power(int, _858547, number_number_of(nat, bit0(bit1(pls))))), _858545)), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), _858547), power_power(int, _858545, number_number_of(nat, bit0(bit1(pls)))))), power_power(int, _858545, number_number_of(nat, bit1(bit1(pls))))))], (2553 ^ _768566) ^ [_858691, _858693] : [-(power_power(int, plus_plus(int, _858693, _858691), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(int, plus_plus(int, power_power(int, _858693, number_number_of(nat, bit0(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit0(bit1(pls))), _858693), _858691)), power_power(int, _858691, number_number_of(nat, bit0(bit1(pls))))))], (2555 ^ _768566) ^ [_858818] : [ord_less_eq(int, zero_zero(int), _858818), ord_less(int, _858818, number_number_of(int, bit0(bit1(pls)))), -(ti(int, _858818) = zero_zero(int)), -(ti(int, _858818) = one_one(int))], (2569 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), s))], (2571 ^ _768566) ^ [] : [-(ord_less(int, s, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2573 ^ _768566) ^ [] : [-(zcong(s1, s, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2575 ^ _768566) ^ [_859343] : [-(times_times(int, _859343, power_power(int, _859343, number_number_of(nat, bit0(bit1(pls))))) = power_power(int, _859343, number_number_of(nat, bit1(bit1(pls)))))], (2577 ^ _768566) ^ [_859433] : [-(ord_less_eq(int, _859433, power_power(int, _859433, number_number_of(nat, bit0(bit1(pls))))))], (2579 ^ _768566) ^ [_859559, _859561, _859563] : [ord_less(int, zero_zero(int), _859559), ti(int, _859559) = plus_plus(int, _859563, times_times(int, _859559, _859561)), ord_less(int, _859563, _859559), -(ord_less_eq(int, one_one(int), _859561))], (2593 ^ _768566) ^ [_860003, _860005, _860007] : [ord_less(int, zero_zero(int), _860003), ti(int, _860003) = plus_plus(int, _860007, times_times(int, _860003, _860005)), ord_less_eq(int, zero_zero(int), _860007), -(ord_less_eq(int, _860005, one_one(int)))], (2607 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), number_number_of(int, bit0(bit1(pls)))))], (2609 ^ _768566) ^ [_860472] : [comm_semiring_1(_860472), 2612 ^ _768566 : [(2613 ^ _768566) ^ [_860621, _860623] : [-(power_power(_860472, _860623, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _860621)) = times_times(_860472, power_power(_860472, _860623, _860621), power_power(_860472, _860623, _860621)))]]], (2615 ^ _768566) ^ [] : [-(zcong(power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), 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))))], (2618 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), 2616 ^ []))], (2620 ^ _768566) ^ [] : [-(ord_less(int, 2616 ^ [], plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2622 ^ _768566) ^ [] : [-(zcong(s1, 2616 ^ [], plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2624 ^ _768566) ^ [_861045] : [-(ti(int, _861045) = ti(int, 2616 ^ [])), ord_less_eq(int, zero_zero(int), _861045), ord_less(int, _861045, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))), zcong(s1, _861045, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)))], (2639 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), 2637 ^ []))], (2641 ^ _768566) ^ [] : [-(ord_less(int, 2637 ^ [], plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2643 ^ _768566) ^ [] : [-(zcong(s1, 2637 ^ [], plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (2645 ^ _768566) ^ [] : [-(zcong(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))))], (2657 ^ _768566) ^ [_862000, _862002] : [2658 ^ _768566 : [(2659 ^ _768566) ^ [] : [_862000 = zero_zero(nat)], (2661 ^ _768566) ^ [] : [ord_less(nat, zero_zero(nat), _862002)]], -(ord_less(nat, zero_zero(nat), power_power(nat, _862002, _862000)))], (2647 ^ _768566) ^ [_861736, _861738] : [ord_less(nat, zero_zero(nat), power_power(nat, _861738, _861736)), -(_861736 = zero_zero(nat)), -(ord_less(nat, zero_zero(nat), _861738))], (2665 ^ _768566) ^ [_862312, _862314, _862316] : [zprime(_862312), dvd_dvd(int, _862312, power_power(int, _862316, _862314)), -(dvd_dvd(int, _862312, _862316))], (2675 ^ _768566) ^ [_862617] : [comm_semiring_1(_862617), 2678 ^ _768566 : [(2679 ^ _768566) ^ [_862781, _862783, _862785] : [-(power_power(_862617, power_power(_862617, _862785, _862783), _862781) = power_power(_862617, _862785, times_times(nat, _862783, _862781)))]]], (2681 ^ _768566) ^ [_862943, _862945, _862947, _862949] : [zprime(_862943), -(dvd_dvd(int, _862943, _862945)), dvd_dvd(int, power_power(int, _862943, _862949), times_times(int, _862947, _862945)), -(dvd_dvd(int, power_power(int, _862943, _862949), _862947))], (2695 ^ _768566) ^ [_863418, _863420, _863422, _863424] : [zprime(_863418), -(dvd_dvd(int, _863418, _863420)), dvd_dvd(int, power_power(int, _863418, _863424), times_times(int, _863420, _863422)), -(dvd_dvd(int, power_power(int, _863418, _863424), _863422))], (2709 ^ _768566) ^ [_863864, _863866, _863868] : [-(power_power(int, power_power(int, _863868, _863866), _863864) = power_power(int, _863868, times_times(nat, _863866, _863864)))], (2711 ^ _768566) ^ [_863991, _863993] : [ord_less(int, zero_zero(int), _863991), ord_less(int, _863991, _863993), dvd_dvd(int, _863993, _863991)], (2721 ^ _768566) ^ [_864297, _864299] : [ord_less_eq(int, zero_zero(int), _864297), ord_less_eq(int, zero_zero(int), _864299), dvd_dvd(int, _864297, _864299), dvd_dvd(int, _864299, _864297), -(ti(int, _864297) = ti(int, _864299))], (2739 ^ _768566) ^ [_864808, _864810, _864812] : [dvd_dvd(int, times_times(int, _864812, _864810), times_times(int, _864812, _864808)), -(ti(int, _864812) = zero_zero(int)), -(dvd_dvd(int, _864810, _864808))], (2749 ^ _768566) ^ [_865189, _865191, _865193] : [dvd_dvd(int, _865193, plus_plus(int, _865191, times_times(int, _865193, _865189))), -(dvd_dvd(int, _865193, _865191))], (2755 ^ _768566) ^ [_865377, _865379, _865381] : [dvd_dvd(int, _865381, _865379), -(dvd_dvd(int, _865381, plus_plus(int, _865379, times_times(int, _865381, _865377))))], (2761 ^ _768566) ^ [_865657, _865659, _865661, _865663, _865665] : [dvd_dvd(int, _865659, _865657), 2764 ^ _768566 : [(2765 ^ _768566) ^ [] : [dvd_dvd(int, _865659, plus_plus(int, _865663, _865661)), -(dvd_dvd(int, _865659, plus_plus(int, plus_plus(int, _865663, times_times(int, _865665, _865657)), _865661)))], (2771 ^ _768566) ^ [] : [dvd_dvd(int, _865659, plus_plus(int, plus_plus(int, _865663, times_times(int, _865665, _865657)), _865661)), -(dvd_dvd(int, _865659, plus_plus(int, _865663, _865661)))]]], (2777 ^ _768566) ^ [] : [-(zprime(number_number_of(int, bit0(bit1(pls)))))], (2779 ^ _768566) ^ [_866274, _866276] : [dvd_dvd(int, _866276, _866274), ord_less(int, zero_zero(int), _866274), -(ord_less_eq(int, _866276, _866274))], (2789 ^ _768566) ^ [_866579, _866581] : [twoSqu420862341sum2sq(_866579), twoSqu420862341sum2sq(_866581), -(twoSqu420862341sum2sq(times_times(int, _866579, _866581)))], (2809 ^ _768566) ^ [_867181, _867183] : [2810 ^ _768566 : [(2811 ^ _768566) ^ [] : [ord_less_eq(int, _867183, _867181)], (2813 ^ _768566) ^ [] : [ord_less_eq(int, _867183, pls)]], -(ord_less_eq(nat, number_number_of(nat, _867183), number_number_of(nat, _867181)))], (2799 ^ _768566) ^ [_866909, _866911] : [ord_less_eq(nat, number_number_of(nat, _866911), number_number_of(nat, _866909)), -(ord_less_eq(int, _866911, _866909)), -(ord_less_eq(int, _866911, pls))], (2817 ^ _768566) ^ [_867473] : [comm_semiring_1(_867473), 2820 ^ _768566 : [(2821 ^ _768566) ^ [_867664, _867666, _867668, _867670] : [-(times_times(_867473, times_times(_867473, _867670, _867668), times_times(_867473, _867666, _867664)) = times_times(_867473, times_times(_867473, _867670, _867666), times_times(_867473, _867668, _867664)))]]], (2823 ^ _768566) ^ [_867794] : [comm_semiring_1(_867794), 2826 ^ _768566 : [(2827 ^ _768566) ^ [_867985, _867987, _867989, _867991] : [-(times_times(_867794, times_times(_867794, _867991, _867989), times_times(_867794, _867987, _867985)) = times_times(_867794, _867987, times_times(_867794, times_times(_867794, _867991, _867989), _867985)))]]], (2829 ^ _768566) ^ [_868115] : [comm_semiring_1(_868115), 2832 ^ _768566 : [(2833 ^ _768566) ^ [_868306, _868308, _868310, _868312] : [-(times_times(_868115, times_times(_868115, _868312, _868310), times_times(_868115, _868308, _868306)) = times_times(_868115, _868312, times_times(_868115, _868310, times_times(_868115, _868308, _868306))))]]], (2835 ^ _768566) ^ [_868436] : [comm_semiring_1(_868436), 2838 ^ _768566 : [(2839 ^ _768566) ^ [_868600, _868602, _868604] : [-(times_times(_868436, times_times(_868436, _868604, _868602), _868600) = times_times(_868436, times_times(_868436, _868604, _868600), _868602))]]], (2841 ^ _768566) ^ [_868720] : [comm_semiring_1(_868720), 2844 ^ _768566 : [(2845 ^ _768566) ^ [_868884, _868886, _868888] : [-(times_times(_868720, times_times(_868720, _868888, _868886), _868884) = times_times(_868720, _868888, times_times(_868720, _868886, _868884)))]]], (2847 ^ _768566) ^ [_869004] : [comm_semiring_1(_869004), 2850 ^ _768566 : [(2851 ^ _768566) ^ [_869168, _869170, _869172] : [-(times_times(_869004, _869172, times_times(_869004, _869170, _869168)) = times_times(_869004, times_times(_869004, _869172, _869170), _869168))]]], (2853 ^ _768566) ^ [_869288] : [comm_semiring_1(_869288), 2856 ^ _768566 : [(2857 ^ _768566) ^ [_869452, _869454, _869456] : [-(times_times(_869288, _869456, times_times(_869288, _869454, _869452)) = times_times(_869288, _869454, times_times(_869288, _869456, _869452)))]]], (2859 ^ _768566) ^ [_869572] : [comm_semiring_1(_869572), 2862 ^ _768566 : [(2863 ^ _768566) ^ [_869709, _869711] : [-(times_times(_869572, _869711, _869709) = times_times(_869572, _869709, _869711))]]], (2865 ^ _768566) ^ [_869819] : [comm_semiring_1(_869819), 2868 ^ _768566 : [(2869 ^ _768566) ^ [_869956, _869958] : [-(plus_plus(_869819, _869958, _869956) = plus_plus(_869819, _869956, _869958))]]], (2871 ^ _768566) ^ [_870066] : [comm_semiring_1(_870066), 2874 ^ _768566 : [(2875 ^ _768566) ^ [_870230, _870232, _870234] : [-(plus_plus(_870066, _870234, plus_plus(_870066, _870232, _870230)) = plus_plus(_870066, _870232, plus_plus(_870066, _870234, _870230)))]]], (2877 ^ _768566) ^ [_870350] : [comm_semiring_1(_870350), 2880 ^ _768566 : [(2881 ^ _768566) ^ [_870514, _870516, _870518] : [-(plus_plus(_870350, _870518, plus_plus(_870350, _870516, _870514)) = plus_plus(_870350, plus_plus(_870350, _870518, _870516), _870514))]]], (2883 ^ _768566) ^ [_870634] : [comm_semiring_1(_870634), 2886 ^ _768566 : [(2887 ^ _768566) ^ [_870798, _870800, _870802] : [-(plus_plus(_870634, plus_plus(_870634, _870802, _870800), _870798) = plus_plus(_870634, _870802, plus_plus(_870634, _870800, _870798)))]]], (2889 ^ _768566) ^ [_870918] : [comm_semiring_1(_870918), 2892 ^ _768566 : [(2893 ^ _768566) ^ [_871082, _871084, _871086] : [-(plus_plus(_870918, plus_plus(_870918, _871086, _871084), _871082) = plus_plus(_870918, plus_plus(_870918, _871086, _871082), _871084))]]], (2895 ^ _768566) ^ [_871202] : [comm_semiring_1(_871202), 2898 ^ _768566 : [(2899 ^ _768566) ^ [_871393, _871395, _871397, _871399] : [-(plus_plus(_871202, plus_plus(_871202, _871399, _871397), plus_plus(_871202, _871395, _871393)) = plus_plus(_871202, plus_plus(_871202, _871399, _871395), plus_plus(_871202, _871397, _871393)))]]], (2901 ^ _768566) ^ [_871523] : [comm_semiring_1(_871523), 2904 ^ _768566 : [(2905 ^ _768566) ^ [_871640] : [-(power_power(_871523, _871640, one_one(nat)) = ti(_871523, _871640))]]], (2917 ^ _768566) ^ [_872066, _872068] : [2918 ^ _768566 : [(2919 ^ _768566) ^ [] : [number_number_of(nat, _872066) = zero_zero(nat)], (2921 ^ _768566) ^ [] : [ord_less(nat, zero_zero(nat), _872068)]], -(ord_less(nat, zero_zero(nat), power_power(nat, _872068, number_number_of(nat, _872066))))], (2907 ^ _768566) ^ [_871790, _871792] : [ord_less(nat, zero_zero(nat), power_power(nat, _871792, number_number_of(nat, _871790))), -(number_number_of(nat, _871790) = zero_zero(nat)), -(ord_less(nat, zero_zero(nat), _871792))], (2925 ^ _768566) ^ [_872347] : [-(times_times(nat, _872347, number_number_of(nat, bit0(bit1(pls)))) = plus_plus(nat, _872347, _872347))], (2927 ^ _768566) ^ [_872433] : [-(times_times(nat, number_number_of(nat, bit0(bit1(pls))), _872433) = plus_plus(nat, _872433, _872433))], (2929 ^ _768566) ^ [_872568, _872570] : [ord_less(int, _872568, pls), -(times_times(nat, number_number_of(nat, _872568), number_number_of(nat, _872570)) = zero_zero(nat))], (2935 ^ _768566) ^ [_872752, _872754] : [-(ord_less(int, _872752, pls)), -(times_times(nat, number_number_of(nat, _872752), number_number_of(nat, _872754)) = number_number_of(nat, times_times(int, _872752, _872754)))], (2941 ^ _768566) ^ [_873037, _873039, _873041] : [ord_less(int, _873037, pls), -(times_times(nat, number_number_of(nat, _873037), times_times(nat, number_number_of(nat, _873041), _873039)) = zero_zero(nat))], (2947 ^ _768566) ^ [_873235, _873237, _873239] : [-(ord_less(int, _873235, pls)), -(times_times(nat, number_number_of(nat, _873235), times_times(nat, number_number_of(nat, _873239), _873237)) = times_times(nat, number_number_of(nat, times_times(int, _873235, _873239)), _873237))], (2953 ^ _768566) ^ [_873494] : [monoid_mult(_873494), 2956 ^ _768566 : [(2957 ^ _768566) ^ [_873639, _873641] : [-(power_power(_873494, _873641, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _873639)) = power_power(_873494, power_power(_873494, _873641, _873639), number_number_of(nat, bit0(bit1(pls)))))]]], (2959 ^ _768566) ^ [_873757] : [linordered_idom(_873757), 2962 ^ _768566 : [(2963 ^ _768566) ^ [_873923, _873925] : [ord_less_eq(_873757, power_power(_873757, _873925, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _873923)), zero_zero(_873757)), -(ti(_873757, _873925) = zero_zero(_873757))]]], (2969 ^ _768566) ^ [_874164] : [comm_semiring_1(_874164), 2972 ^ _768566 : [(2973 ^ _768566) ^ [_874282] : [-(times_times(_874164, zero_zero(_874164), _874282) = zero_zero(_874164))]]], (2975 ^ _768566) ^ [_874390] : [comm_semiring_1(_874390), 2978 ^ _768566 : [(2979 ^ _768566) ^ [_874508] : [-(times_times(_874390, _874508, zero_zero(_874390)) = zero_zero(_874390))]]], (2981 ^ _768566) ^ [_874616] : [comm_semiring_1(_874616), 2984 ^ _768566 : [(2985 ^ _768566) ^ [_874735] : [-(plus_plus(_874616, zero_zero(_874616), _874735) = ti(_874616, _874735))]]], (2987 ^ _768566) ^ [_874844] : [comm_semiring_1(_874844), 2990 ^ _768566 : [(2991 ^ _768566) ^ [_874963] : [-(plus_plus(_874844, _874963, zero_zero(_874844)) = ti(_874844, _874963))]]], (2993 ^ _768566) ^ [_875072] : [semiri456707255roduct(_875072), 2996 ^ _768566 : [(2997 ^ _768566) ^ [_875263, _875265] : [ti(_875072, _875265) = plus_plus(_875072, _875265, _875263), -(ti(_875072, _875263) = zero_zero(_875072))], (3003 ^ _768566) ^ [_875457, _875459] : [ti(_875072, _875457) = zero_zero(_875072), -(ti(_875072, _875459) = plus_plus(_875072, _875459, _875457))]]], (3009 ^ _768566) ^ [_875692] : [comm_semiring_1(_875692), 3012 ^ _768566 : [(3013 ^ _768566) ^ [_875860, _875862, _875864] : [-(times_times(_875692, _875864, plus_plus(_875692, _875862, _875860)) = plus_plus(_875692, times_times(_875692, _875864, _875862), times_times(_875692, _875864, _875860)))]]], (3015 ^ _768566) ^ [_875984] : [semiri456707255roduct(_875984), 3018 ^ _768566 : [(3029 ^ _768566) ^ [_876611, _876613, _876615, _876617] : [-(plus_plus(_875984, times_times(_875984, _876613, _876617), times_times(_875984, _876611, _876615)) = plus_plus(_875984, times_times(_875984, _876613, _876615), times_times(_875984, _876611, _876617))), 3032 ^ _768566 : [(3033 ^ _768566) ^ [] : [ti(_875984, _876613) = ti(_875984, _876611)], (3035 ^ _768566) ^ [] : [ti(_875984, _876617) = ti(_875984, _876615)]]], (3019 ^ _768566) ^ [_876249, _876251, _876253, _876255] : [plus_plus(_875984, times_times(_875984, _876251, _876255), times_times(_875984, _876249, _876253)) = plus_plus(_875984, times_times(_875984, _876251, _876253), times_times(_875984, _876249, _876255)), -(ti(_875984, _876251) = ti(_875984, _876249)), -(ti(_875984, _876255) = ti(_875984, _876253))]]], (3037 ^ _768566) ^ [_876992] : [comm_semiring_1(_876992), 3040 ^ _768566 : [(3041 ^ _768566) ^ [_877160, _877162, _877164] : [-(times_times(_876992, plus_plus(_876992, _877164, _877162), _877160) = plus_plus(_876992, times_times(_876992, _877164, _877160), times_times(_876992, _877162, _877160)))]]], (3043 ^ _768566) ^ [_877284] : [comm_semiring_1(_877284), 3046 ^ _768566 : [(3047 ^ _768566) ^ [_877452, _877454, _877456] : [-(plus_plus(_877284, times_times(_877284, _877456, _877454), times_times(_877284, _877452, _877454)) = times_times(_877284, plus_plus(_877284, _877456, _877452), _877454))]]], (3049 ^ _768566) ^ [_877576] : [semiri456707255roduct(_877576), 3052 ^ _768566 : [(3063 ^ _768566) ^ [_878191, _878193, _878195, _878197] : [3064 ^ _768566 : [(3065 ^ _768566) ^ [] : [ti(_877576, _878197) = ti(_877576, _878193)], (3067 ^ _768566) ^ [] : [ti(_877576, _878195) = ti(_877576, _878191)]], -(plus_plus(_877576, times_times(_877576, _878197, _878195), times_times(_877576, _878193, _878191)) = plus_plus(_877576, times_times(_877576, _878197, _878191), times_times(_877576, _878193, _878195)))], (3053 ^ _768566) ^ [_877835, _877837, _877839, _877841] : [plus_plus(_877576, times_times(_877576, _877841, _877839), times_times(_877576, _877837, _877835)) = plus_plus(_877576, times_times(_877576, _877841, _877835), times_times(_877576, _877837, _877839)), -(ti(_877576, _877841) = ti(_877576, _877837)), -(ti(_877576, _877839) = ti(_877576, _877835))]]], (3071 ^ _768566) ^ [_878566] : [comm_semiring_1(_878566), 3074 ^ _768566 : [(3075 ^ _768566) ^ [_878685] : [-(times_times(_878566, one_one(_878566), _878685) = ti(_878566, _878685))]]], (3077 ^ _768566) ^ [_878794] : [comm_semiring_1(_878794), 3080 ^ _768566 : [(3081 ^ _768566) ^ [_878913] : [-(times_times(_878794, _878913, one_one(_878794)) = ti(_878794, _878913))]]], (3083 ^ _768566) ^ [_879022] : [comm_semiring_1(_879022), 3086 ^ _768566 : [(3087 ^ _768566) ^ [_879190, _879192, _879194] : [-(power_power(_879022, times_times(_879022, _879194, _879192), _879190) = times_times(_879022, power_power(_879022, _879194, _879190), power_power(_879022, _879192, _879190)))]]], (3089 ^ _768566) ^ [_879314] : [comm_semiring_1(_879314), 3092 ^ _768566 : [(3093 ^ _768566) ^ [_879482, _879484, _879486] : [-(times_times(_879314, power_power(_879314, _879486, _879484), power_power(_879314, _879486, _879482)) = power_power(_879314, _879486, plus_plus(nat, _879484, _879482)))]]], (3095 ^ _768566) ^ [_879606] : [comm_semiring_1(_879606), 3098 ^ _768566 : [(3099 ^ _768566) ^ [_879722] : [-(power_power(_879606, _879722, zero_zero(nat)) = one_one(_879606))]]], (3101 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), zero_zero(int)))], (3103 ^ _768566) ^ [_879881] : [linordered_idom(_879881), 3106 ^ _768566 : [(3107 ^ _768566) ^ [_880021, _880023] : [-(ord_less_eq(_879881, zero_zero(_879881), power_power(_879881, _880023, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _880021))))]]], (3109 ^ _768566) ^ [_880134] : [semiri456707255roduct(_880134), 3112 ^ _768566 : [(3113 ^ _768566) ^ [_880392, _880394, _880396, _880398, _880400] : [-(ti(_880134, _880392) = zero_zero(_880134)), plus_plus(_880134, _880396, times_times(_880134, _880392, _880400)) = plus_plus(_880134, _880394, times_times(_880134, _880392, _880398)), ti(_880134, _880396) = ti(_880134, _880394), -(ti(_880134, _880400) = ti(_880134, _880398))]]], (3127 ^ _768566) ^ [_880902] : [comm_semiring_1(_880902), 3130 ^ _768566 : [(3131 ^ _768566) ^ [_881028] : [-(plus_plus(_880902, _881028, _881028) = times_times(_880902, plus_plus(_880902, one_one(_880902), one_one(_880902)), _881028))]]], (3133 ^ _768566) ^ [_881144] : [comm_semiring_1(_881144), 3136 ^ _768566 : [(3137 ^ _768566) ^ [_881291, _881293] : [-(plus_plus(_881144, _881293, times_times(_881144, _881291, _881293)) = times_times(_881144, plus_plus(_881144, _881291, one_one(_881144)), _881293))]]], (3139 ^ _768566) ^ [_881411] : [comm_semiring_1(_881411), 3142 ^ _768566 : [(3143 ^ _768566) ^ [_881558, _881560] : [-(plus_plus(_881411, times_times(_881411, _881560, _881558), _881558) = times_times(_881411, plus_plus(_881411, _881560, one_one(_881411)), _881558))]]], (3145 ^ _768566) ^ [_881678] : [power(_881678), mult_zero(_881678), no_zero_divisors(_881678), zero_neq_one(_881678), 3160 ^ _768566 : [(3161 ^ _768566) ^ [_882131, _882133] : [power_power(_881678, _882133, number_number_of(nat, _882131)) = zero_zero(_881678), 3164 ^ _768566 : [(3165 ^ _768566) ^ [] : [-(ti(_881678, _882133) = zero_zero(_881678))], (3167 ^ _768566) ^ [] : [number_number_of(nat, _882131) = zero_zero(nat)]]], (3169 ^ _768566) ^ [_882413, _882415] : [-(power_power(_881678, _882415, number_number_of(nat, _882413)) = zero_zero(_881678)), ti(_881678, _882415) = zero_zero(_881678), -(number_number_of(nat, _882413) = zero_zero(nat))]]], (3179 ^ _768566) ^ [_882774, _882776] : [ord_less(int, zero_zero(int), _882774), ord_less(int, zero_zero(int), times_times(int, _882774, _882776)), -(ord_less(int, zero_zero(int), _882776))], (3189 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), one_one(int)))], (3191 ^ _768566) ^ [_883140, _883142] : [ord_less_eq(int, zero_zero(int), _883140), ord_less_eq(int, zero_zero(int), _883142), -(ord_less_eq(int, zero_zero(int), times_times(int, _883140, _883142)))], (3201 ^ _768566) ^ [_883453, _883455] : [ord_less_eq(int, zero_zero(int), _883453), ord_less_eq(int, zero_zero(int), _883455), -(ord_less_eq(int, zero_zero(int), plus_plus(int, _883453, _883455)))], (3211 ^ _768566) ^ [_883766, _883768] : [ord_less_eq(int, zero_zero(int), _883766), -(ord_less_eq(int, zero_zero(int), power_power(int, _883766, _883768)))], (3217 ^ _768566) ^ [_883974] : [power(_883974), semiring_0(_883974), 3224 ^ _768566 : [(3225 ^ _768566) ^ [_884250] : [number_number_of(nat, _884250) = zero_zero(nat), -(power_power(_883974, zero_zero(_883974), number_number_of(nat, _884250)) = one_one(_883974))], (3231 ^ _768566) ^ [_884442] : [-(number_number_of(nat, _884442) = zero_zero(nat)), -(power_power(_883974, zero_zero(_883974), number_number_of(nat, _884442)) = zero_zero(_883974))]]], (3237 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), number_number_of(int, bit1(bit1(pls)))))], (3239 ^ _768566) ^ [_884761, _884763, _884765] : [ord_less_eq(int, zero_zero(int), plus_plus(int, times_times(int, _884765, _884763), _884761)), ord_less(int, _884761, _884765), ord_less(int, zero_zero(int), _884765), -(ord_less_eq(int, zero_zero(int), _884763))], (3253 ^ _768566) ^ [_885201, _885203, _885205] : [ord_less(int, plus_plus(int, times_times(int, _885205, _885203), _885201), zero_zero(int)), ord_less_eq(int, zero_zero(int), _885201), ord_less(int, zero_zero(int), _885205), -(ord_less_eq(int, _885203, zero_zero(int)))], (3267 ^ _768566) ^ [_885669, _885671, _885673, _885675, _885677] : [ord_less_eq(int, plus_plus(int, times_times(int, _885677, _885675), _885673), plus_plus(int, times_times(int, _885677, _885671), _885669)), ord_less_eq(int, zero_zero(int), _885673), ord_less(int, _885673, _885677), ord_less(int, _885669, _885677), -(ord_less_eq(int, _885675, _885671))], (3285 ^ _768566) ^ [_886298, _886300, _886302, _886304, _886306, _886308] : [plus_plus(int, times_times(int, _886308, _886306), _886304) = plus_plus(int, times_times(int, _886302, _886300), _886298), ord_less_eq(int, zero_zero(int), plus_plus(int, times_times(int, _886302, _886300), _886298)), ord_less(int, _886298, _886302), ord_less_eq(int, zero_zero(int), _886304), ord_less(int, zero_zero(int), _886302), ord_less_eq(int, _886302, _886308), -(ord_less_eq(int, _886306, _886300))], (3311 ^ _768566) ^ [_887159, _887161, _887163, _887165, _887167] : [ord_less_eq(int, plus_plus(int, times_times(int, _887167, _887165), _887163), plus_plus(int, times_times(int, _887167, _887161), _887159)), ord_less_eq(int, _887159, zero_zero(int)), ord_less(int, _887167, _887159), ord_less(int, _887167, _887163), -(ord_less_eq(int, _887161, _887165))], (3329 ^ _768566) ^ [_887788, _887790, _887792, _887794, _887796, _887798] : [plus_plus(int, times_times(int, _887798, _887796), _887794) = plus_plus(int, times_times(int, _887792, _887790), _887788), ord_less(int, plus_plus(int, times_times(int, _887792, _887790), _887788), zero_zero(int)), ord_less(int, _887794, _887798), ord_less_eq(int, zero_zero(int), _887788), ord_less(int, zero_zero(int), _887792), ord_less_eq(int, _887792, _887798), -(ord_less_eq(int, _887790, _887796))], (3355 ^ _768566) ^ [_888578] : [-(power_power(int, power_power(int, _888578, number_number_of(nat, bit0(bit1(pls)))), number_number_of(nat, bit0(bit1(pls)))) = power_power(int, _888578, number_number_of(nat, bit0(bit0(bit1(pls))))))], (3357 ^ _768566) ^ [_888683] : [comm_semiring_1(_888683), 3360 ^ _768566 : [(3361 ^ _768566) ^ [_888801] : [-(times_times(_888683, _888801, _888801) = power_power(_888683, _888801, number_number_of(nat, bit0(bit1(pls)))))]]], (3363 ^ _768566) ^ [] : [-(zcong(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))))], (3365 ^ _768566) ^ [_888990, _888992, _888994] : [-(zcong(_888992, zero_zero(int), _888990)), zcong(power_power(int, _888994, number_number_of(nat, bit0(bit1(pls)))), _888992, _888990), dvd_dvd(int, _888990, _888994)], (3395 ^ _768566) ^ [_889932] : [-(zprime(_889932)), ord_less(int, one_one(int), _889932), 3401 ^ _768566 : [(3402 ^ _768566) ^ [] : [-(ord_less_eq(int, zero_zero(int), 3400 ^ [_889932]))], (3404 ^ _768566) ^ [] : [-(dvd_dvd(int, 3400 ^ [_889932], _889932))], (3406 ^ _768566) ^ [] : [ti(int, 3400 ^ [_889932]) = one_one(int)], (3408 ^ _768566) ^ [] : [ti(int, 3400 ^ [_889932]) = ti(int, _889932)]]], (3375 ^ _768566) ^ [_889332] : [zprime(_889332), 3378 ^ _768566 : [(3379 ^ _768566) ^ [] : [-(ord_less(int, one_one(int), _889332))], (3381 ^ _768566) ^ [_889558] : [ord_less_eq(int, zero_zero(int), _889558), dvd_dvd(int, _889558, _889332), -(ti(int, _889558) = one_one(int)), -(ti(int, _889558) = ti(int, _889332))]]], (3412 ^ _768566) ^ [_890544] : [zprime(_890544), -(ti(int, _890544) = number_number_of(int, bit0(bit1(pls)))), -(ti(int, _890544) = number_number_of(int, bit1(bit1(pls)))), -(ord_less_eq(int, number_number_of(int, bit1(bit0(bit1(pls)))), _890544))], (3426 ^ _768566) ^ [] : [-(ord_less(nat, zero_zero(nat), number_number_of(nat, bit0(bit1(pls)))))], (3429 ^ _768566) ^ [] : [-(zcong(power_power(int, 3427 ^ [], 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))))], (3431 ^ _768566) ^ [] : [-(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))], (3433 ^ _768566) ^ [] : [-(bit1(min) = min)], (3435 ^ _768566) ^ [_891207] : [min = bit1(_891207), -(min = ti(int, _891207))], (3441 ^ _768566) ^ [_891373] : [min = ti(int, _891373), -(min = bit1(_891373))], (3447 ^ _768566) ^ [_891604] : [bit1(_891604) = min, -(ti(int, _891604) = min)], (3453 ^ _768566) ^ [_891770] : [ti(int, _891770) = min, -(bit1(_891770) = min)], (3459 ^ _768566) ^ [] : [min = pls], (3461 ^ _768566) ^ [] : [pls = min], (3463 ^ _768566) ^ [_892060] : [min = bit0(_892060)], (3465 ^ _768566) ^ [_892139] : [bit0(_892139) = min], (3467 ^ _768566) ^ [] : [ord_less(int, min, min)], (3469 ^ _768566) ^ [] : [-(ord_less_eq(int, min, min))], (3471 ^ _768566) ^ [_892368] : [ord_less(int, bit1(_892368), min), -(ord_less(int, _892368, min))], (3477 ^ _768566) ^ [_892532] : [ord_less(int, _892532, min), -(ord_less(int, bit1(_892532), min))], (3483 ^ _768566) ^ [_892761] : [ord_less(int, min, bit1(_892761)), -(ord_less(int, min, _892761))], (3489 ^ _768566) ^ [_892925] : [ord_less(int, min, _892925), -(ord_less(int, min, bit1(_892925)))], (3495 ^ _768566) ^ [] : [ord_less(int, pls, min)], (3497 ^ _768566) ^ [] : [-(ord_less(int, min, pls))], (3499 ^ _768566) ^ [_893259] : [ord_less(int, min, bit0(_893259)), -(ord_less(int, min, _893259))], (3505 ^ _768566) ^ [_893423] : [ord_less(int, min, _893423), -(ord_less(int, min, bit0(_893423)))], (3511 ^ _768566) ^ [] : [-(ord_less(int, min, zero_zero(int)))], (3513 ^ _768566) ^ [_893705] : [ord_less_eq(int, min, bit1(_893705)), -(ord_less_eq(int, min, _893705))], (3519 ^ _768566) ^ [_893869] : [ord_less_eq(int, min, _893869), -(ord_less_eq(int, min, bit1(_893869)))], (3525 ^ _768566) ^ [_894098] : [ord_less_eq(int, bit1(_894098), min), -(ord_less_eq(int, _894098, min))], (3531 ^ _768566) ^ [_894262] : [ord_less_eq(int, _894262, min), -(ord_less_eq(int, bit1(_894262), min))], (3537 ^ _768566) ^ [] : [-(ord_less_eq(int, min, pls))], (3539 ^ _768566) ^ [] : [ord_less_eq(int, pls, min)], (3541 ^ _768566) ^ [_894596] : [ord_less_eq(int, bit0(_894596), min), -(ord_less_eq(int, _894596, min))], (3547 ^ _768566) ^ [_894760] : [ord_less_eq(int, _894760, min), -(ord_less_eq(int, bit0(_894760), min))], (3553 ^ _768566) ^ [] : [number_number_of(int, pls) = number_number_of(int, min)], (3555 ^ _768566) ^ [_895041] : [ord_less(int, bit0(_895041), min), -(ord_less_eq(int, _895041, min))], (3561 ^ _768566) ^ [_895205] : [ord_less_eq(int, _895205, min), -(ord_less(int, bit0(_895205), min))], (3567 ^ _768566) ^ [_895434] : [ord_less_eq(int, min, bit0(_895434)), -(ord_less(int, min, _895434))], (3573 ^ _768566) ^ [_895598] : [ord_less(int, min, _895598), -(ord_less_eq(int, min, bit0(_895598)))], (3579 ^ _768566) ^ [_895841, _895843] : [times_times(int, _895843, _895841) = one_one(int), 3584 ^ _768566 : [(3585 ^ _768566) ^ [] : [-(ti(int, _895843) = one_one(int))], (3587 ^ _768566) ^ [] : [-(ti(int, _895841) = one_one(int))]], 3588 ^ _768566 : [(3589 ^ _768566) ^ [] : [-(ti(int, _895843) = number_number_of(int, min))], (3591 ^ _768566) ^ [] : [-(ti(int, _895841) = number_number_of(int, min))]]], (3593 ^ _768566) ^ [_896275, _896277] : [-(times_times(int, _896277, _896275) = one_one(int)), 3594 ^ _768566 : [(3595 ^ _768566) ^ [] : [ti(int, _896277) = one_one(int), ti(int, _896275) = one_one(int)], (3601 ^ _768566) ^ [] : [ti(int, _896277) = number_number_of(int, min), ti(int, _896275) = number_number_of(int, min)]]], (3609 ^ _768566) ^ [_896771, _896773] : [times_times(int, _896773, _896771) = one_one(int), -(ti(int, _896773) = one_one(int)), -(ti(int, _896773) = number_number_of(int, min))], (3619 ^ _768566) ^ [_897134, _897136, _897138] : [zcong(_897138, _897136, _897134), -(zcong(_897136, _897138, _897134))], (3625 ^ _768566) ^ [_897306, _897308, _897310] : [zcong(_897308, _897310, _897306), -(zcong(_897310, _897308, _897306))], (3631 ^ _768566) ^ [_897513, _897515] : [-(zcong(_897515, _897515, _897513))], (3633 ^ _768566) ^ [_897651, _897653, _897655, _897657] : [zcong(_897655, _897653, _897651), zcong(_897653, _897657, _897651), -(zcong(_897655, _897657, _897651))], (3643 ^ _768566) ^ [_897962] : [order(_897962), 3646 ^ _768566 : [(3647 ^ _768566) ^ [_898128, _898130] : [ord_less_eq(_897962, _898130, _898128), -(ti(_897962, _898130) = ti(_897962, _898128)), -(ord_less(_897962, _898130, _898128))]]], (3657 ^ _768566) ^ [_898477, _898479, _898481] : [ord_less(int, _898479, _898477), ord_less(int, _898481, _898477), -(ord_less_eq(int, _898479, _898481)), -(ord_less_eq(int, _898481, _898479))], (3671 ^ _768566) ^ [_898917, _898919] : [zcong(_898919, _898917, zero_zero(int)), -(ti(int, _898919) = ti(int, _898917))], (3677 ^ _768566) ^ [_899093, _899095] : [ti(int, _899095) = ti(int, _899093), -(zcong(_899095, _899093, zero_zero(int)))], (3683 ^ _768566) ^ [_899304, _899306] : [-(zcong(_899306, _899304, one_one(int)))], (3685 ^ _768566) ^ [_899413, _899415, _899417] : [-(zcong(times_times(int, _899417, _899415), times_times(int, _899413, _899415), _899415))], (3687 ^ _768566) ^ [_899561, _899563, _899565, _899567] : [zcong(_899565, _899563, _899561), -(zcong(times_times(int, _899565, _899567), times_times(int, _899563, _899567), _899561))], (3693 ^ _768566) ^ [_899831, _899833, _899835, _899837] : [zcong(_899835, _899833, _899831), -(zcong(times_times(int, _899837, _899835), times_times(int, _899837, _899833), _899831))], (3699 ^ _768566) ^ [_900115, _900117, _900119, _900121, _900123] : [zcong(_900119, _900117, _900115), zcong(_900123, _900121, _900115), -(zcong(times_times(int, _900119, _900123), times_times(int, _900117, _900121), _900115))], (3709 ^ _768566) ^ [_900508, _900510, _900512, _900514, _900516] : [zcong(_900512, _900510, _900508), zcong(_900516, _900514, _900508), -(zcong(plus_plus(int, _900512, _900516), plus_plus(int, _900510, _900514), _900508))], (3719 ^ _768566) ^ [_900845] : [number_ring(_900845), 3722 ^ _768566 : [(3723 ^ _768566) ^ [_900968] : [-(power_power(_900845, number_number_of(_900845, min), times_times(nat, number_number_of(nat, bit0(bit1(pls))), _900968)) = one_one(_900845))]]], (3725 ^ _768566) ^ [_901109, _901111, _901113] : [ord_less(int, zero_zero(int), _901109), ord_less(int, _901109, _901111), ord_less(int, zero_zero(int), _901113), ord_less(int, _901113, _901109), zcong(_901109, _901113, _901111)], (3743 ^ _768566) ^ [_901658, _901660, _901662] : [zcong(_901662, _901660, _901658), -(ti(int, _901660) = plus_plus(int, _901662, times_times(int, _901658, 3746 ^ [_901658, _901660, _901662])))], (3750 ^ _768566) ^ [_901924, _901926, _901928] : [3751 ^ _768566 : [(3752 ^ _768566) ^ [_902008] : [ti(int, _901926) = plus_plus(int, _901928, times_times(int, _901924, _902008))]], -(zcong(_901928, _901926, _901924))], (3756 ^ _768566) ^ [_902159] : [-(times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), power_power(real, _902159, number_number_of(nat, bit0(bit1(pls))))) = power_power(real, times_times(real, number_number_of(real, bit0(bit1(pls))), _902159), number_number_of(nat, bit0(bit1(pls)))))], (3758 ^ _768566) ^ [_902282, _902284] : [ord_less_eq(int, zero_zero(int), _902282), ord_less(int, _902282, _902284), zcong(_902282, zero_zero(int), _902284), -(ti(int, _902282) = zero_zero(int))], (3772 ^ _768566) ^ [_902696, _902698, _902700] : [ord_less_eq(int, zero_zero(int), _902696), ord_less(int, _902696, _902698), ord_less_eq(int, zero_zero(int), _902700), ord_less(int, _902700, _902698), zcong(_902696, _902700, _902698), -(ti(int, _902696) = ti(int, _902700))], (3794 ^ _768566) ^ [_903334, _903336, _903338, _903340] : [zcong(power_power(int, _903338, _903336), one_one(int), _903334), -(zcong(power_power(int, _903338, times_times(nat, _903336, _903340)), one_one(int), _903334))], (3800 ^ _768566) ^ [_903598, _903600, _903602] : [ord_less_eq(int, zero_zero(int), _903598), zprime(_903600), dvd_dvd(int, _903600, times_times(int, _903598, _903602)), -(dvd_dvd(int, _903600, _903598)), -(dvd_dvd(int, _903600, _903602))], (3818 ^ _768566) ^ [] : [-(quadRes(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), number_number_of(int, min)))], (3820 ^ _768566) ^ [] : [-(dvd_dvd(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), minus_minus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min))))], (3822 ^ _768566) ^ [_904228, _904230, _904232] : [ord_less(int, number_number_of(int, bit0(bit1(pls))), _904228), zcong(power_power(int, number_number_of(int, min), _904232), power_power(int, number_number_of(int, min), _904230), _904228), -(power_power(int, number_number_of(int, min), _904232) = power_power(int, number_number_of(int, min), _904230))], (3832 ^ _768566) ^ [_904573, _904575] : [ord_less(int, number_number_of(int, bit0(bit1(pls))), _904573), zcong(_904575, number_number_of(int, min), _904573), zcong(_904575, one_one(int), _904573)], (3842 ^ _768566) ^ [] : [-(minus_minus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), number_number_of(int, min)) = plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)))], (3844 ^ _768566) ^ [] : [-(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)], (3850 ^ _768566) ^ [_905066] : [-(ord_less(real, zero_zero(real), times_times(real, _905066, _905066))), -(_905066 = zero_zero(real))], (3856 ^ _768566) ^ [_905235] : [_905235 = zero_zero(real), ord_less(real, zero_zero(real), times_times(real, _905235, _905235))], (3862 ^ _768566) ^ [_905494, _905496, _905498, _905500, _905502] : [zcong(_905498, _905496, _905494), zcong(_905502, _905500, _905494), -(zcong(minus_minus(int, _905498, _905502), minus_minus(int, _905496, _905500), _905494))], (3872 ^ _768566) ^ [_905859, _905861, _905863] : [dvd_dvd(int, _905863, minus_minus(int, _905861, _905859)), dvd_dvd(int, _905863, _905859), -(dvd_dvd(int, _905863, _905861))], (3882 ^ _768566) ^ [_906181, _906183, _906185] : [-(times_times(int, _906185, minus_minus(int, _906183, _906181)) = minus_minus(int, times_times(int, _906185, _906183), times_times(int, _906185, _906181)))], (3884 ^ _768566) ^ [_906311, _906313, _906315] : [-(times_times(int, minus_minus(int, _906315, _906313), _906311) = minus_minus(int, times_times(int, _906315, _906311), times_times(int, _906313, _906311)))], (3886 ^ _768566) ^ [_906427, _906429] : [-(minus_minus(int, bit0(_906429), bit0(_906427)) = bit0(minus_minus(int, _906429, _906427)))], (3888 ^ _768566) ^ [_906521] : [-(minus_minus(int, _906521, pls) = ti(int, _906521))], (3890 ^ _768566) ^ [_906649, _906651, _906653] : [minus_minus(int, _906653, _906651) = ti(int, _906649), -(ti(int, _906653) = plus_plus(int, _906649, _906651))], (3896 ^ _768566) ^ [_906879] : [number_ring(_906879), 3899 ^ _768566 : [(3900 ^ _768566) ^ [_907025, _907027] : [-(number_number_of(_906879, minus_minus(int, _907027, _907025)) = minus_minus(_906879, number_number_of(_906879, _907027), number_number_of(_906879, _907025)))]]], (3902 ^ _768566) ^ [_907144] : [3909 ^ _768566 : [(3910 ^ _768566) ^ [_907404, _907406, _907408] : [-(times_times(_907144, number_number_of(_907144, _907408), minus_minus(_907144, _907406, _907404)) = minus_minus(_907144, times_times(_907144, number_number_of(_907144, _907408), _907406), times_times(_907144, number_number_of(_907144, _907408), _907404)))]], number(_907144), ring(_907144)], (3912 ^ _768566) ^ [_907537] : [3919 ^ _768566 : [(3920 ^ _768566) ^ [_907797, _907799, _907801] : [-(times_times(_907537, minus_minus(_907537, _907801, _907799), number_number_of(_907537, _907797)) = minus_minus(_907537, times_times(_907537, _907801, number_number_of(_907537, _907797)), times_times(_907537, _907799, number_number_of(_907537, _907797))))]], number(_907537), ring(_907537)], (3922 ^ _768566) ^ [_907929, _907931] : [-(minus_minus(int, bit1(_907931), bit0(_907929)) = bit1(minus_minus(int, _907931, _907929)))], (3924 ^ _768566) ^ [_908037, _908039] : [-(minus_minus(int, bit1(_908039), bit1(_908037)) = bit0(minus_minus(int, _908039, _908037)))], (3926 ^ _768566) ^ [_908131] : [-(minus_minus(int, pls, bit0(_908131)) = bit0(minus_minus(int, pls, _908131)))], (3928 ^ _768566) ^ [_908279, _908281] : [ord_less(int, _908281, _908279), -(ord_less(int, minus_minus(int, _908281, _908279), zero_zero(int)))], (3934 ^ _768566) ^ [_908453, _908455] : [ord_less(int, minus_minus(int, _908455, _908453), zero_zero(int)), -(ord_less(int, _908455, _908453))], (3940 ^ _768566) ^ [_908732, _908734, _908736, _908738, _908740, _908742, _908744] : [-(plus_plus(int, times_times(int, minus_minus(int, _908744, times_times(int, _908742, _908740)), _908738), times_times(int, minus_minus(int, _908736, times_times(int, _908742, _908734)), _908732)) = minus_minus(int, plus_plus(int, times_times(int, _908744, _908738), times_times(int, _908736, _908732)), times_times(int, _908742, plus_plus(int, times_times(int, _908740, _908738), times_times(int, _908734, _908732)))))], (3942 ^ _768566) ^ [_908954, _908956, _908958] : [zcong(_908958, _908956, _908954), -(dvd_dvd(int, _908954, minus_minus(int, _908958, _908956)))], (3948 ^ _768566) ^ [_909134, _909136, _909138] : [dvd_dvd(int, _909134, minus_minus(int, _909138, _909136)), -(zcong(_909138, _909136, _909134))], (3954 ^ _768566) ^ [_909350] : [number_ring(_909350), 3957 ^ _768566 : [(3958 ^ _768566) ^ [_909523, _909525, _909527] : [-(plus_plus(_909350, number_number_of(_909350, _909527), minus_minus(_909350, number_number_of(_909350, _909525), _909523)) = minus_minus(_909350, number_number_of(_909350, plus_plus(int, _909527, _909525)), _909523))]]], (3960 ^ _768566) ^ [_909666, _909668] : [ord_less(int, zero_zero(int), _909666), ord_less(int, _909666, _909668), -(ti(int, _909666) = minus_minus(int, _909668, one_one(int))), -(ord_less(int, _909666, minus_minus(int, _909668, one_one(int))))], (3974 ^ _768566) ^ [_910114, _910116] : [ord_less_eq(int, _910116, minus_minus(int, _910114, one_one(int))), -(ord_less(int, _910116, _910114))], (3980 ^ _768566) ^ [_910288, _910290] : [ord_less(int, _910290, _910288), -(ord_less_eq(int, _910290, minus_minus(int, _910288, one_one(int))))], (3986 ^ _768566) ^ [_910483] : [-(minus_minus(int, pls, bit1(_910483)) = bit1(minus_minus(int, min, _910483)))], (3988 ^ _768566) ^ [_910573] : [-(minus_minus(int, min, bit1(_910573)) = bit0(minus_minus(int, min, _910573)))], (3990 ^ _768566) ^ [_910663] : [-(minus_minus(int, min, bit0(_910663)) = bit1(minus_minus(int, min, _910663)))], (3992 ^ _768566) ^ [_910811, _910813] : [zcong(times_times(int, _910813, minus_minus(int, _910811, one_one(int))), one_one(int), _910811), -(zcong(_910813, minus_minus(int, _910811, one_one(int)), _910811))], (3998 ^ _768566) ^ [_911001, _911003] : [zcong(_911003, minus_minus(int, _911001, one_one(int)), _911001), -(zcong(times_times(int, _911003, minus_minus(int, _911001, one_one(int))), one_one(int), _911001))], (4004 ^ _768566) ^ [_911283, _911285, _911287, _911289, _911291] : [zcong(_911287, _911285, _911283), ti(int, _911285) = ti(int, _911289), zcong(_911289, _911291, _911283), -(zcong(_911287, _911291, _911283))], (4018 ^ _768566) ^ [_911731, _911733] : [zprime(_911731), ord_less(int, zero_zero(int), _911733), ord_less(int, _911733, _911731), zcong(times_times(int, _911733, _911733), one_one(int), _911731), -(ti(int, _911733) = one_one(int)), -(ti(int, _911733) = minus_minus(int, _911731, one_one(int)))], (4040 ^ _768566) ^ [_912330, _912332] : [zprime(_912330), ord_less(int, zero_zero(int), _912332), zcong(times_times(int, _912332, _912332), one_one(int), _912330), -(zcong(_912332, one_one(int), _912330)), -(zcong(_912332, minus_minus(int, _912330, one_one(int)), _912330))], (4058 ^ _768566) ^ [_912815, _912817] : [-(times_times(int, plus_plus(int, _912817, _912815), minus_minus(int, _912817, _912815)) = minus_minus(int, power_power(int, _912817, number_number_of(nat, bit0(bit1(pls)))), power_power(int, _912815, number_number_of(nat, bit0(bit1(pls))))))], (4060 ^ _768566) ^ [_912919] : [-(zcong(_912919, zero_zero(int), _912919))], (4062 ^ _768566) ^ [_913069, _913071, _913073, _913075, _913077] : [zcong(_913073, _913071, _913069), 4065 ^ _768566 : [(4066 ^ _768566) ^ [] : [zcong(_913077, times_times(int, _913075, _913073), _913069), -(zcong(_913077, times_times(int, _913075, _913071), _913069))], (4072 ^ _768566) ^ [] : [zcong(_913077, times_times(int, _913075, _913071), _913069), -(zcong(_913077, times_times(int, _913075, _913073), _913069))]]], (4078 ^ _768566) ^ [_913651, _913653, _913655, _913657, _913659] : [zcong(_913655, _913653, _913651), 4081 ^ _768566 : [(4082 ^ _768566) ^ [] : [zcong(_913659, times_times(int, _913655, _913657), _913651), -(zcong(_913659, times_times(int, _913653, _913657), _913651))], (4088 ^ _768566) ^ [] : [zcong(_913659, times_times(int, _913653, _913657), _913651), -(zcong(_913659, times_times(int, _913655, _913657), _913651))]]], (4094 ^ _768566) ^ [_914219, _914221, _914223, _914225] : [zcong(_914223, _914221, _914219), -(zcong(plus_plus(int, _914223, _914225), plus_plus(int, _914221, _914225), _914219))], (4100 ^ _768566) ^ [_914489, _914491, _914493, _914495] : [zcong(_914493, _914491, _914489), -(zcong(power_power(int, _914493, _914495), power_power(int, _914491, _914495), _914489))], (4106 ^ _768566) ^ [_914717] : [number_ring(_914717), 4109 ^ _768566 : [(4110 ^ _768566) ^ [_914881, _914883] : [-(power_power(_914717, minus_minus(_914717, _914883, _914881), number_number_of(nat, bit0(bit1(pls)))) = minus_minus(_914717, plus_plus(_914717, power_power(_914717, _914883, number_number_of(nat, bit0(bit1(pls)))), power_power(_914717, _914881, number_number_of(nat, bit0(bit1(pls))))), times_times(_914717, times_times(_914717, number_number_of(_914717, bit0(bit1(pls))), _914883), _914881)))]]], (4112 ^ _768566) ^ [_915017, _915019] : [-(power_power(int, minus_minus(int, _915019, _915017), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(int, minus_minus(int, power_power(int, _915019, number_number_of(nat, bit0(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit0(bit1(pls))), _915019), _915017)), power_power(int, _915017, number_number_of(nat, bit0(bit1(pls))))))], (4114 ^ _768566) ^ [_915143, _915145] : [-(power_power(int, minus_minus(int, _915145, _915143), number_number_of(nat, bit1(bit1(pls)))) = minus_minus(int, plus_plus(int, minus_minus(int, power_power(int, _915145, number_number_of(nat, bit1(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), power_power(int, _915145, number_number_of(nat, bit0(bit1(pls))))), _915143)), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), _915145), power_power(int, _915143, number_number_of(nat, bit0(bit1(pls)))))), power_power(int, _915143, number_number_of(nat, bit1(bit1(pls))))))], (4116 ^ _768566) ^ [_915318, _915320, _915322] : [ord_less(int, zero_zero(int), _915318), ord_less(int, zero_zero(int), _915320), ord_less(int, zero_zero(int), _915322), zcong(_915318, _915320, _915322), ord_less(int, _915318, _915322), ord_less(int, _915320, _915322), -(ti(int, _915318) = ti(int, _915320))], (4142 ^ _768566) ^ [_916023, _916025] : [ord_less(int, zero_zero(int), _916023), ord_less(int, _916023, _916025), zcong(_916023, zero_zero(int), _916025)], (4152 ^ _768566) ^ [_916329, _916331] : [dvd_dvd(int, _916331, _916329), -(ord_less_eq(int, _916329, zero_zero(int))), -(ord_less_eq(int, _916331, _916329))], (4162 ^ _768566) ^ [_916664, _916666] : [zcong(_916666, zero_zero(int), _916664), -(dvd_dvd(int, _916664, _916666))], (4168 ^ _768566) ^ [_916830, _916832] : [dvd_dvd(int, _916830, _916832), -(zcong(_916832, zero_zero(int), _916830))], (4174 ^ _768566) ^ [_917075, _917077] : [zcong(_917077, zero_zero(int), _917075), -(dvd_dvd(int, _917075, _917077))], (4180 ^ _768566) ^ [_917241, _917243] : [dvd_dvd(int, _917241, _917243), -(zcong(_917243, zero_zero(int), _917241))], (4186 ^ _768566) ^ [_917471, _917473, _917475] : [zprime(_917471), dvd_dvd(int, _917471, times_times(int, _917475, _917473)), -(dvd_dvd(int, _917471, _917475)), -(dvd_dvd(int, _917471, _917473))], (4200 ^ _768566) ^ [_917886, _917888] : [ord_less_eq(int, zero_zero(int), _917886), ord_less(int, _917886, _917888), zcong(_917886, zero_zero(int), _917888), -(ti(int, _917886) = zero_zero(int))], (4214 ^ _768566) ^ [_918300, _918302, _918304] : [ord_less(nat, zero_zero(nat), _918300), dvd_dvd(int, _918304, _918302), -(dvd_dvd(int, _918304, power_power(int, _918302, _918300)))], (4224 ^ _768566) ^ [_918609] : [-(power_power(int, number_number_of(int, min), _918609) = one_one(int)), -(power_power(int, number_number_of(int, min), _918609) = number_number_of(int, min))], (4230 ^ _768566) ^ [_918844, _918846, _918848] : [zprime(_918844), -(zcong(_918846, zero_zero(int), _918844)), -(zcong(_918848, zero_zero(int), _918844)), zcong(times_times(int, _918846, _918848), zero_zero(int), _918844)], (4244 ^ _768566) ^ [_919279, _919281, _919283] : [zprime(_919279), ord_less(int, zero_zero(int), _919281), zcong(times_times(int, _919281, _919283), zero_zero(int), _919279), -(zcong(_919281, zero_zero(int), _919279)), -(zcong(_919283, zero_zero(int), _919279))], (4262 ^ _768566) ^ [_919809, _919811, _919813] : [zprime(_919809), ord_less(int, zero_zero(int), _919811), zcong(times_times(int, _919811, _919813), zero_zero(int), _919809), -(zcong(_919811, zero_zero(int), _919809)), -(zcong(_919813, zero_zero(int), _919809))], (4280 ^ _768566) ^ [_920333, _920335, _920337] : [zprime(_920333), dvd_dvd(int, _920333, power_power(int, _920337, _920335)), ord_less(nat, zero_zero(nat), _920335), -(dvd_dvd(int, _920333, _920337))], (4294 ^ _768566) ^ [_920733] : [zprime(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), _920733), one_one(int))), -(legendre(number_number_of(int, min), plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), _920733), one_one(int))) = one_one(int))], (4300 ^ _768566) ^ [_920959] : [ord_less(int, number_number_of(int, bit0(bit1(pls))), _920959), zcong(one_one(int), number_number_of(int, min), _920959)], (4306 ^ _768566) ^ [_921188, _921190] : [zcong(_921190, zero_zero(int), _921188), -(legendre(_921190, _921188) = zero_zero(int))], (4312 ^ _768566) ^ [_921358, _921360] : [-(zcong(_921360, zero_zero(int), _921358)), 4315 ^ _768566 : [(4316 ^ _768566) ^ [] : [quadRes(_921358, _921360), -(legendre(_921360, _921358) = one_one(int))], (4322 ^ _768566) ^ [] : [-(quadRes(_921358, _921360)), -(legendre(_921360, _921358) = number_number_of(int, min))]]], (4328 ^ _768566) ^ [_921872, _921874] : [quadRes(_921874, _921872), -(zcong(power_power(int, 4331 ^ [_921872, _921874], number_number_of(nat, bit0(bit1(pls)))), _921872, _921874))], (4335 ^ _768566) ^ [_922106, _922108] : [4336 ^ _768566 : [(4337 ^ _768566) ^ [_922181] : [zcong(power_power(int, _922181, number_number_of(nat, bit0(bit1(pls)))), _922106, _922108)]], -(quadRes(_922108, _922106))], (4341 ^ _768566) ^ [_922335, _922337] : [-(power_power(real, plus_plus(real, _922337, _922335), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(real, plus_plus(real, power_power(real, _922337, number_number_of(nat, bit0(bit1(pls)))), power_power(real, _922335, number_number_of(nat, bit0(bit1(pls))))), times_times(real, times_times(real, number_number_of(real, bit0(bit1(pls))), _922337), _922335)))], (4343 ^ _768566) ^ [_922496, _922498] : [_922496 = zero_zero(nat), -(times_times(nat, _922496, _922498) = zero_zero(nat))], (4349 ^ _768566) ^ [_922666, _922668] : [-(_922666 = zero_zero(nat)), -(times_times(nat, _922666, _922668) = plus_plus(nat, _922668, times_times(nat, minus_minus(nat, _922666, one_one(nat)), _922668)))], (4355 ^ _768566) ^ [_922933, _922935] : [_922933 = zero_zero(nat), -(power_power(nat, _922935, _922933) = one_one(nat))], (4361 ^ _768566) ^ [_923103, _923105] : [-(_923103 = zero_zero(nat)), -(power_power(nat, _923105, _923103) = times_times(nat, _923105, power_power(nat, _923105, minus_minus(nat, _923103, one_one(nat)))))], (4367 ^ _768566) ^ [_923335, _923337] : [-(minus_minus(nat, power_power(nat, _923337, number_number_of(nat, bit0(bit1(pls)))), power_power(nat, _923335, number_number_of(nat, bit0(bit1(pls))))) = times_times(nat, plus_plus(nat, _923337, _923335), minus_minus(nat, _923337, _923335)))], (4369 ^ _768566) ^ [_923497, _923499] : [plus_plus(real, power_power(real, _923499, number_number_of(nat, bit0(bit1(pls)))), power_power(real, _923497, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(real), 4372 ^ _768566 : [(4373 ^ _768566) ^ [] : [-(_923499 = zero_zero(real))], (4375 ^ _768566) ^ [] : [-(_923497 = zero_zero(real))]]], (4377 ^ _768566) ^ [_923758, _923760] : [-(plus_plus(real, power_power(real, _923760, number_number_of(nat, bit0(bit1(pls)))), power_power(real, _923758, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(real)), _923760 = zero_zero(real), _923758 = zero_zero(real)], (4387 ^ _768566) ^ [] : [zero_zero(real) = one_one(real)], (4389 ^ _768566) ^ [_924164, _924166] : [ord_less_eq(real, _924166, _924164), -(ord_less_eq(real, minus_minus(real, _924166, _924164), zero_zero(real)))], (4395 ^ _768566) ^ [_924338, _924340] : [ord_less_eq(real, minus_minus(real, _924340, _924338), zero_zero(real)), -(ord_less_eq(real, _924340, _924338))], (4401 ^ _768566) ^ [_924591, _924593] : [ord_less(real, _924593, _924591), 4404 ^ _768566 : [(4405 ^ _768566) ^ [] : [-(ord_less_eq(real, _924593, _924591))], (4407 ^ _768566) ^ [] : [_924593 = _924591]]], (4409 ^ _768566) ^ [_924833, _924835] : [-(ord_less(real, _924835, _924833)), ord_less_eq(real, _924835, _924833), -(_924835 = _924833)], (4429 ^ _768566) ^ [_925426, _925428] : [4430 ^ _768566 : [(4431 ^ _768566) ^ [] : [ord_less(real, _925428, _925426)], (4433 ^ _768566) ^ [] : [_925428 = _925426]], -(ord_less_eq(real, _925428, _925426))], (4419 ^ _768566) ^ [_925170, _925172] : [ord_less_eq(real, _925172, _925170), -(ord_less(real, _925172, _925170)), -(_925172 = _925170)], (4437 ^ _768566) ^ [_925715, _925717, _925719] : [-(times_times(real, times_times(real, _925719, _925717), _925715) = times_times(real, _925719, times_times(real, _925717, _925715)))], (4439 ^ _768566) ^ [_925827, _925829] : [-(times_times(real, _925829, _925827) = times_times(real, _925827, _925829))], (4441 ^ _768566) ^ [_925915] : [-(times_times(real, one_one(real), _925915) = _925915)], (4443 ^ _768566) ^ [_926040, _926042, _926044] : [ord_less_eq(real, _926042, _926040), -(ord_less_eq(real, plus_plus(real, _926044, _926042), plus_plus(real, _926044, _926040)))], (4449 ^ _768566) ^ [_926262] : [ab_group_add(_926262), 4452 ^ _768566 : [(4453 ^ _768566) ^ [_926453, _926455, _926457, _926459] : [-(minus_minus(_926262, plus_plus(_926262, _926459, _926457), plus_plus(_926262, _926455, _926453)) = plus_plus(_926262, minus_minus(_926262, _926459, _926455), minus_minus(_926262, _926457, _926453)))]]], (4455 ^ _768566) ^ [_926611, _926613, _926615] : [-(_926611 = zero_zero(real)), 4458 ^ _768566 : [(4459 ^ _768566) ^ [] : [times_times(real, _926611, _926615) = times_times(real, _926611, _926613), -(_926615 = _926613)], (4465 ^ _768566) ^ [] : [_926615 = _926613, -(times_times(real, _926611, _926615) = times_times(real, _926611, _926613))]]], (4471 ^ _768566) ^ [_927128, _927130, _927132] : [-(_927128 = zero_zero(real)), 4474 ^ _768566 : [(4475 ^ _768566) ^ [] : [times_times(real, _927132, _927128) = times_times(real, _927130, _927128), -(_927132 = _927130)], (4481 ^ _768566) ^ [] : [_927132 = _927130, -(times_times(real, _927132, _927128) = times_times(real, _927130, _927128))]]], (4487 ^ _768566) ^ [_927660, _927662] : [times_times(nat, _927662, _927660) = one_one(nat), 4490 ^ _768566 : [(4491 ^ _768566) ^ [] : [-(_927662 = one_one(nat))], (4493 ^ _768566) ^ [] : [-(_927660 = one_one(nat))]]], (4495 ^ _768566) ^ [_927905, _927907] : [-(times_times(nat, _927907, _927905) = one_one(nat)), _927907 = one_one(nat), _927905 = one_one(nat)], (4505 ^ _768566) ^ [_928213, _928215, _928217] : [-(times_times(real, plus_plus(real, _928217, _928215), _928213) = plus_plus(real, times_times(real, _928217, _928213), times_times(real, _928215, _928213)))], (4507 ^ _768566) ^ [_928373, _928375] : [power_power(nat, _928375, _928373) = zero_zero(nat), 4510 ^ _768566 : [(4511 ^ _768566) ^ [] : [_928373 = zero_zero(nat)], (4513 ^ _768566) ^ [] : [-(_928375 = zero_zero(nat))]]], (4515 ^ _768566) ^ [_928619, _928621] : [-(power_power(nat, _928621, _928619) = zero_zero(nat)), -(_928619 = zero_zero(nat)), _928621 = zero_zero(nat)], (4525 ^ _768566) ^ [_928917] : [ring(_928917), 4528 ^ _768566 : [(4529 ^ _768566) ^ [_929116, _929118, _929120, _929122] : [-(minus_minus(_928917, times_times(_928917, _929122, _929120), times_times(_928917, _929118, _929116)) = plus_plus(_928917, times_times(_928917, _929122, minus_minus(_928917, _929120, _929116)), times_times(_928917, minus_minus(_928917, _929122, _929118), _929116)))]]], (4531 ^ _768566) ^ [_929282, _929284, _929286] : [ord_less(real, zero_zero(real), _929282), 4534 ^ _768566 : [(4535 ^ _768566) ^ [] : [ord_less_eq(real, times_times(real, _929286, _929282), times_times(real, _929284, _929282)), -(ord_less_eq(real, _929286, _929284))], (4541 ^ _768566) ^ [] : [ord_less_eq(real, _929286, _929284), -(ord_less_eq(real, times_times(real, _929286, _929282), times_times(real, _929284, _929282)))]]], (4547 ^ _768566) ^ [_929804, _929806, _929808] : [ord_less(real, zero_zero(real), _929804), 4550 ^ _768566 : [(4551 ^ _768566) ^ [] : [ord_less_eq(real, times_times(real, _929804, _929808), times_times(real, _929804, _929806)), -(ord_less_eq(real, _929808, _929806))], (4557 ^ _768566) ^ [] : [ord_less_eq(real, _929808, _929806), -(ord_less_eq(real, times_times(real, _929804, _929808), times_times(real, _929804, _929806)))]]], (4563 ^ _768566) ^ [_930326, _930328, _930330] : [ord_less(real, zero_zero(real), _930326), ord_less(real, _930330, _930328), -(ord_less(real, times_times(real, _930326, _930330), times_times(real, _930326, _930328)))], (4573 ^ _768566) ^ [_930657, _930659] : [ord_less(real, zero_zero(real), _930657), ord_less(real, zero_zero(real), _930659), -(ord_less(real, zero_zero(real), times_times(real, _930657, _930659)))], (4583 ^ _768566) ^ [_930984, _930986, _930988] : [ord_less(real, zero_zero(real), _930984), 4586 ^ _768566 : [(4587 ^ _768566) ^ [] : [ord_less(real, times_times(real, _930988, _930984), times_times(real, _930986, _930984)), -(ord_less(real, _930988, _930986))], (4593 ^ _768566) ^ [] : [ord_less(real, _930988, _930986), -(ord_less(real, times_times(real, _930988, _930984), times_times(real, _930986, _930984)))]]], (4599 ^ _768566) ^ [_931521, _931523] : [plus_plus(real, times_times(real, _931523, _931523), times_times(real, _931521, _931521)) = zero_zero(real), 4602 ^ _768566 : [(4603 ^ _768566) ^ [] : [-(_931523 = zero_zero(real))], (4605 ^ _768566) ^ [] : [-(_931521 = zero_zero(real))]]], (4607 ^ _768566) ^ [_931782, _931784] : [-(plus_plus(real, times_times(real, _931784, _931784), times_times(real, _931782, _931782)) = zero_zero(real)), _931784 = zero_zero(real), _931782 = zero_zero(real)], (4627 ^ _768566) ^ [_932396, _932398] : [4628 ^ _768566 : [(4629 ^ _768566) ^ [] : [_932398 = one_one(nat)], (4631 ^ _768566) ^ [] : [_932396 = zero_zero(nat)]], -(power_power(nat, _932398, _932396) = one_one(nat))], (4617 ^ _768566) ^ [_932136, _932138] : [power_power(nat, _932138, _932136) = one_one(nat), -(_932138 = one_one(nat)), -(_932136 = zero_zero(nat))], (4635 ^ _768566) ^ [_932676] : [ring_1(_932676), 4638 ^ _768566 : [(4639 ^ _768566) ^ [_932812] : [-(minus_minus(_932676, times_times(_932676, _932812, _932812), one_one(_932676)) = times_times(_932676, plus_plus(_932676, _932812, one_one(_932676)), minus_minus(_932676, _932812, one_one(_932676))))]]], (4641 ^ _768566) ^ [_932938] : [monoid_mult(_932938), 4644 ^ _768566 : [(4645 ^ _768566) ^ [_933105, _933107] : [ord_less(nat, zero_zero(nat), _933105), -(times_times(_932938, power_power(_932938, _933107, minus_minus(nat, _933105, one_one(nat))), _933107) = power_power(_932938, _933107, _933105))]]], (4651 ^ _768566) ^ [_933333] : [-(ord_less_eq(real, one_one(real), power_power(real, number_number_of(real, bit0(bit1(pls))), _933333)))], (4653 ^ _768566) ^ [_933431] : [power(_933431), 4656 ^ _768566 : [(4657 ^ _768566) ^ [_933637, _933639] : [_933637 = zero_zero(nat), -(power_power(_933431, _933639, _933637) = one_one(_933431))], (4663 ^ _768566) ^ [_933819, _933821] : [-(_933819 = zero_zero(nat)), -(power_power(_933431, _933821, _933819) = times_times(_933431, _933821, power_power(_933431, _933821, minus_minus(nat, _933819, one_one(nat)))))]]], (4669 ^ _768566) ^ [_934065] : [linordered_semidom(_934065), 4672 ^ _768566 : [(4673 ^ _768566) ^ [_934260, _934262, _934264] : [ord_less(_934065, _934262, _934260), ord_less_eq(_934065, zero_zero(_934065), _934262), ord_less(nat, zero_zero(nat), _934264), -(ord_less(_934065, power_power(_934065, _934262, _934264), power_power(_934065, _934260, _934264)))]]], (4687 ^ _768566) ^ [_934682] : [-(ord_less_eq(real, _934682, _934682))], (4689 ^ _768566) ^ [_934790, _934792] : [-(ord_less_eq(real, _934792, _934790)), -(ord_less_eq(real, _934790, _934792))], (4695 ^ _768566) ^ [_935019, _935021, _935023] : [ord_less_eq(real, _935021, _935019), ord_less_eq(real, _935019, _935023), -(ord_less_eq(real, _935021, _935023))], (4705 ^ _768566) ^ [_935334, _935336] : [ord_less_eq(real, _935336, _935334), ord_less_eq(real, _935334, _935336), -(_935336 = _935334)], (4715 ^ _768566) ^ [_935623] : [ring_11004092258visors(_935623), 4718 ^ _768566 : [(4719 ^ _768566) ^ [_935788, _935790] : [-(ti(_935623, _935788) = zero_zero(_935623)), power_power(_935623, _935788, _935790) = zero_zero(_935623)]]], (4725 ^ _768566) ^ [_936023] : [comm_monoid_mult(_936023), 4728 ^ _768566 : [(4729 ^ _768566) ^ [_936191, _936193, _936195] : [-(power_power(_936023, times_times(_936023, _936195, _936193), _936191) = times_times(_936023, power_power(_936023, _936195, _936191), power_power(_936023, _936193, _936191)))]]], (4731 ^ _768566) ^ [_936315] : [monoid_mult(_936315), 4734 ^ _768566 : [(4735 ^ _768566) ^ [_936460, _936462] : [-(times_times(_936315, power_power(_936315, _936462, _936460), _936462) = times_times(_936315, _936462, power_power(_936315, _936462, _936460)))]]], (4737 ^ _768566) ^ [_936578] : [monoid_mult(_936578), 4740 ^ _768566 : [(4741 ^ _768566) ^ [_936696] : [-(power_power(_936578, one_one(_936578), _936696) = one_one(_936578))]]], (4743 ^ _768566) ^ [_936804] : [comm_semiring_1(_936804), 4746 ^ _768566 : [(4747 ^ _768566) ^ [_936983, _936985, _936987] : [dvd_dvd(_936804, _936985, _936983), -(dvd_dvd(_936804, power_power(_936804, _936985, _936987), power_power(_936804, _936983, _936987)))]]], (4753 ^ _768566) ^ [_937218] : [monoid_mult(_937218), 4756 ^ _768566 : [(4757 ^ _768566) ^ [_937382, _937384, _937386] : [-(power_power(_937218, _937386, times_times(nat, _937384, _937382)) = power_power(_937218, power_power(_937218, _937386, _937384), _937382))]]], (4759 ^ _768566) ^ [_937502] : [monoid_mult(_937502), 4762 ^ _768566 : [(4763 ^ _768566) ^ [_937619] : [-(power_power(_937502, _937619, one_one(nat)) = ti(_937502, _937619))]]], (4765 ^ _768566) ^ [_937726] : [linordered_semidom(_937726), 4768 ^ _768566 : [(4769 ^ _768566) ^ [_937914, _937916, _937918] : [ord_less_eq(_937726, _937916, _937914), ord_less_eq(_937726, zero_zero(_937726), _937916), -(ord_less_eq(_937726, power_power(_937726, _937916, _937918), power_power(_937726, _937914, _937918)))]]], (4779 ^ _768566) ^ [_938252] : [linordered_semidom(_938252), 4782 ^ _768566 : [(4783 ^ _768566) ^ [_938412, _938414] : [ord_less_eq(_938252, zero_zero(_938252), _938412), -(ord_less_eq(_938252, zero_zero(_938252), power_power(_938252, _938412, _938414)))]]], (4789 ^ _768566) ^ [_938641] : [linordered_semidom(_938641), 4792 ^ _768566 : [(4793 ^ _768566) ^ [_938801, _938803] : [ord_less(_938641, zero_zero(_938641), _938801), -(ord_less(_938641, zero_zero(_938641), power_power(_938641, _938801, _938803)))]]], (4799 ^ _768566) ^ [_939030] : [linordered_semidom(_939030), 4802 ^ _768566 : [(4803 ^ _768566) ^ [_939190, _939192] : [ord_less_eq(_939030, one_one(_939030), _939190), -(ord_less_eq(_939030, one_one(_939030), power_power(_939030, _939190, _939192)))]]], (4809 ^ _768566) ^ [_939419] : [linordered_semidom(_939419), 4812 ^ _768566 : [(4813 ^ _768566) ^ [_939605, _939607, _939609] : [ord_less(_939419, one_one(_939419), _939605), 4816 ^ _768566 : [(4817 ^ _768566) ^ [] : [power_power(_939419, _939605, _939609) = power_power(_939419, _939605, _939607), -(_939609 = _939607)], (4823 ^ _768566) ^ [] : [_939609 = _939607, -(power_power(_939419, _939605, _939609) = power_power(_939419, _939605, _939607))]]]]], (4829 ^ _768566) ^ [_940120] : [power(_940120), mult_zero(_940120), no_zero_divisors(_940120), zero_neq_one(_940120), 4844 ^ _768566 : [(4845 ^ _768566) ^ [_940567, _940569] : [power_power(_940120, _940569, _940567) = zero_zero(_940120), 4848 ^ _768566 : [(4849 ^ _768566) ^ [] : [-(ti(_940120, _940569) = zero_zero(_940120))], (4851 ^ _768566) ^ [] : [_940567 = zero_zero(nat)]]], (4853 ^ _768566) ^ [_940837, _940839] : [-(power_power(_940120, _940839, _940837) = zero_zero(_940120)), ti(_940120, _940839) = zero_zero(_940120), -(_940837 = zero_zero(nat))]]], (4863 ^ _768566) ^ [_941172] : [power(_941172), 4866 ^ _768566 : [(4867 ^ _768566) ^ [_941288] : [-(power_power(_941172, _941288, zero_zero(nat)) = one_one(_941172))]]], (4869 ^ _768566) ^ [_941394] : [monoid_mult(_941394), 4872 ^ _768566 : [(4873 ^ _768566) ^ [_941562, _941564, _941566] : [-(power_power(_941394, _941566, plus_plus(nat, _941564, _941562)) = times_times(_941394, power_power(_941394, _941566, _941564), power_power(_941394, _941566, _941562)))]]], (4875 ^ _768566) ^ [_941686] : [comm_semiring_1(_941686), 4878 ^ _768566 : [(4879 ^ _768566) ^ [_941891, _941893, _941895, _941897] : [dvd_dvd(_941686, power_power(_941686, _941895, _941893), _941891), ord_less_eq(nat, _941897, _941893), -(dvd_dvd(_941686, power_power(_941686, _941895, _941897), _941891))]]], (4889 ^ _768566) ^ [_942235] : [comm_semiring_1(_942235), 4892 ^ _768566 : [(4893 ^ _768566) ^ [_942440, _942442, _942444, _942446] : [dvd_dvd(_942235, _942442, _942440), ord_less_eq(nat, _942446, _942444), -(dvd_dvd(_942235, power_power(_942235, _942442, _942446), power_power(_942235, _942440, _942444)))]]], (4903 ^ _768566) ^ [_942784] : [comm_semiring_1(_942784), 4906 ^ _768566 : [(4907 ^ _768566) ^ [_942963, _942965, _942967] : [ord_less_eq(nat, _942965, _942963), -(dvd_dvd(_942784, power_power(_942784, _942967, _942965), power_power(_942784, _942967, _942963)))]]], (4913 ^ _768566) ^ [_943226, _943228, _943230] : [ord_less(nat, zero_zero(nat), _943226), ord_less(nat, power_power(nat, _943226, _943230), power_power(nat, _943226, _943228)), -(ord_less(nat, _943230, _943228))], (4933 ^ _768566) ^ [_943850, _943852] : [4934 ^ _768566 : [(4935 ^ _768566) ^ [] : [ord_less(nat, zero_zero(nat), _943852)], (4937 ^ _768566) ^ [] : [_943850 = zero_zero(nat)]], -(ord_less(nat, zero_zero(nat), power_power(nat, _943852, _943850)))], (4923 ^ _768566) ^ [_943586, _943588] : [ord_less(nat, zero_zero(nat), power_power(nat, _943588, _943586)), -(ord_less(nat, zero_zero(nat), _943588)), -(_943586 = zero_zero(nat))], (4941 ^ _768566) ^ [_944134] : [linordered_semidom(_944134), 4944 ^ _768566 : [(4945 ^ _768566) ^ [_944322, _944324, _944326] : [ord_less(_944134, power_power(_944134, _944326, _944324), power_power(_944134, _944322, _944324)), ord_less_eq(_944134, zero_zero(_944134), _944322), -(ord_less(_944134, _944326, _944322))]]], (4955 ^ _768566) ^ [_944660] : [linordered_semidom(_944660), 4958 ^ _768566 : [(4959 ^ _768566) ^ [_944826, _944828] : [ord_less(_944660, one_one(_944660), _944826), -(ord_less(_944660, power_power(_944660, _944826, _944828), times_times(_944660, _944826, power_power(_944660, _944826, _944828))))]]], (4965 ^ _768566) ^ [_945067] : [linordered_semidom(_945067), 4968 ^ _768566 : [(4969 ^ _768566) ^ [_945231, _945233] : [ord_less(_945067, one_one(_945067), _945231), -(ord_less(_945067, one_one(_945067), times_times(_945067, _945231, power_power(_945067, _945231, _945233))))]]], (4975 ^ _768566) ^ [_945468] : [power(_945468), semiring_0(_945468), 4982 ^ _768566 : [(4983 ^ _768566) ^ [_945732] : [_945732 = zero_zero(nat), -(power_power(_945468, zero_zero(_945468), _945732) = one_one(_945468))], (4989 ^ _768566) ^ [_945912] : [-(_945912 = zero_zero(nat)), -(power_power(_945468, zero_zero(_945468), _945912) = zero_zero(_945468))]]], (4995 ^ _768566) ^ [_946138] : [linordered_semidom(_946138), 4998 ^ _768566 : [(4999 ^ _768566) ^ [_946326, _946328, _946330] : [ord_less(nat, _946328, _946326), ord_less(_946138, one_one(_946138), _946330), -(ord_less(_946138, power_power(_946138, _946330, _946328), power_power(_946138, _946330, _946326)))]]], (5009 ^ _768566) ^ [_946664] : [linordered_semidom(_946664), 5012 ^ _768566 : [(5013 ^ _768566) ^ [_946852, _946854, _946856] : [ord_less(_946664, one_one(_946664), _946852), ord_less(_946664, power_power(_946664, _946852, _946856), power_power(_946664, _946852, _946854)), -(ord_less(nat, _946856, _946854))]]], (5023 ^ _768566) ^ [_947190] : [linordered_semidom(_947190), 5026 ^ _768566 : [(5027 ^ _768566) ^ [_947378, _947380, _947382] : [ord_less(_947190, one_one(_947190), _947378), 5030 ^ _768566 : [(5031 ^ _768566) ^ [] : [ord_less(_947190, power_power(_947190, _947378, _947382), power_power(_947190, _947378, _947380)), -(ord_less(nat, _947382, _947380))], (5037 ^ _768566) ^ [] : [ord_less(nat, _947382, _947380), -(ord_less(_947190, power_power(_947190, _947378, _947382), power_power(_947190, _947378, _947380)))]]]]], (5043 ^ _768566) ^ [_947899] : [linordered_semidom(_947899), 5046 ^ _768566 : [(5047 ^ _768566) ^ [_948087, _948089, _948091] : [ord_less_eq(nat, _948089, _948087), ord_less_eq(_947899, one_one(_947899), _948091), -(ord_less_eq(_947899, power_power(_947899, _948091, _948089), power_power(_947899, _948091, _948087)))]]], (5057 ^ _768566) ^ [_948425] : [linordered_semidom(_948425), 5060 ^ _768566 : [(5061 ^ _768566) ^ [_948600, _948602] : [ord_less(_948425, zero_zero(_948425), _948600), ord_less(_948425, _948600, one_one(_948425)), -(ord_less(_948425, times_times(_948425, _948600, power_power(_948425, _948600, _948602)), power_power(_948425, _948600, _948602)))]]], (5071 ^ _768566) ^ [_948940] : [linordered_semidom(_948940), 5074 ^ _768566 : [(5075 ^ _768566) ^ [_949137, _949139, _949141] : [ord_less(nat, _949139, _949137), ord_less(_948940, zero_zero(_948940), _949141), ord_less(_948940, _949141, one_one(_948940)), -(ord_less(_948940, power_power(_948940, _949141, _949137), power_power(_948940, _949141, _949139)))]]], (5089 ^ _768566) ^ [_949578] : [linordered_semidom(_949578), 5092 ^ _768566 : [(5093 ^ _768566) ^ [_949786, _949788, _949790] : [power_power(_949578, _949790, _949788) = power_power(_949578, _949786, _949788), ord_less_eq(_949578, zero_zero(_949578), _949790), ord_less_eq(_949578, zero_zero(_949578), _949786), ord_less(nat, zero_zero(nat), _949788), -(ti(_949578, _949790) = ti(_949578, _949786))]]], (5111 ^ _768566) ^ [_950334] : [linordered_semidom(_950334), 5114 ^ _768566 : [(5115 ^ _768566) ^ [_950531, _950533, _950535] : [ord_less_eq(nat, _950533, _950531), ord_less_eq(_950334, zero_zero(_950334), _950535), ord_less_eq(_950334, _950535, one_one(_950334)), -(ord_less_eq(_950334, power_power(_950334, _950535, _950531), power_power(_950334, _950535, _950533)))]]], (5129 ^ _768566) ^ [_950972] : [linordered_semidom(_950972), 5132 ^ _768566 : [(5133 ^ _768566) ^ [_951160, _951162, _951164] : [ord_less(_950972, one_one(_950972), _951160), ord_less_eq(_950972, power_power(_950972, _951160, _951164), power_power(_950972, _951160, _951162)), -(ord_less_eq(nat, _951164, _951162))]]], (5143 ^ _768566) ^ [_951498] : [linordered_semidom(_951498), 5146 ^ _768566 : [(5147 ^ _768566) ^ [_951686, _951688, _951690] : [ord_less(_951498, one_one(_951498), _951686), 5150 ^ _768566 : [(5151 ^ _768566) ^ [] : [ord_less_eq(_951498, power_power(_951498, _951686, _951690), power_power(_951498, _951686, _951688)), -(ord_less_eq(nat, _951690, _951688))], (5157 ^ _768566) ^ [] : [ord_less_eq(nat, _951690, _951688), -(ord_less_eq(_951498, power_power(_951498, _951686, _951690), power_power(_951498, _951686, _951688)))]]]]], (5163 ^ _768566) ^ [_952207] : [linordered_semidom(_952207), 5166 ^ _768566 : [(5167 ^ _768566) ^ [_952374, _952376] : [ord_less(_952207, one_one(_952207), _952374), ord_less(nat, zero_zero(nat), _952376), -(ord_less(_952207, one_one(_952207), power_power(_952207, _952374, _952376)))]]], (5177 ^ _768566) ^ [_952698] : [comm_semiring_1(_952698), 5180 ^ _768566 : [(5181 ^ _768566) ^ [_952865, _952867] : [5182 ^ _768566 : [(5183 ^ _768566) ^ [] : [ord_less(nat, zero_zero(nat), _952865)], (5185 ^ _768566) ^ [] : [ti(_952698, _952867) = one_one(_952698)]], -(dvd_dvd(_952698, _952867, power_power(_952698, _952867, _952865)))]]], (5189 ^ _768566) ^ [_953172] : [linord626643107strict(_953172), 5192 ^ _768566 : [(5193 ^ _768566) ^ [_953430, _953432, _953434, _953436, _953438] : [ord_less(_953172, _953432, _953430), ord_less(_953172, _953434, _953430), ord_less_eq(_953172, zero_zero(_953172), _953436), ord_less_eq(_953172, zero_zero(_953172), _953438), plus_plus(_953172, _953436, _953438) = one_one(_953172), -(ord_less(_953172, plus_plus(_953172, times_times(_953172, _953436, _953432), times_times(_953172, _953438, _953434)), _953430))]]], (5215 ^ _768566) ^ [_954145, _954147] : [ord_less(nat, zero_zero(nat), _954145), ord_less(real, zero_zero(real), _954147), 5223 ^ _768566 : [(5224 ^ _768566) ^ [] : [-(ord_less(real, zero_zero(real), 5222 ^ [_954145, _954147]))], (5226 ^ _768566) ^ [] : [-(power_power(real, 5222 ^ [_954145, _954147], _954145) = _954147)], (5228 ^ _768566) ^ [_954639] : [-(_954639 = 5222 ^ [_954145, _954147]), ord_less(real, zero_zero(real), _954639), power_power(real, _954639, _954145) = _954147]]], (5238 ^ _768566) ^ [_954975] : [comm_semiring_1(_954975), 5241 ^ _768566 : [(5242 ^ _768566) ^ [_955088] : [-(dvd_dvd(_954975, _955088, zero_zero(_954975)))]]], (5244 ^ _768566) ^ [_955205, _955207] : [dvd_dvd(nat, _955207, _955205), -(_955205 = zero_zero(nat)), -(ord_less_eq(nat, _955207, _955205))], (5254 ^ _768566) ^ [_955523, _955525, _955527] : [dvd_dvd(nat, _955525, _955523), -(dvd_dvd(nat, power_power(nat, _955525, _955527), power_power(nat, _955523, _955527)))], (5260 ^ _768566) ^ [_955773, _955775, _955777] : [dvd_dvd(nat, _955775, _955773), -(dvd_dvd(nat, times_times(nat, _955777, _955775), times_times(nat, _955777, _955773)))], (5266 ^ _768566) ^ [_956023, _956025, _956027] : [dvd_dvd(nat, _956025, _956023), -(dvd_dvd(nat, times_times(nat, _956025, _956027), times_times(nat, _956023, _956027)))], (5272 ^ _768566) ^ [_956273, _956275, _956277] : [dvd_dvd(nat, _956275, _956273), dvd_dvd(nat, _956275, plus_plus(nat, _956273, _956277)), -(dvd_dvd(nat, _956275, _956277))], (5292 ^ _768566) ^ [_956921, _956923, _956925] : [5293 ^ _768566 : [(5294 ^ _768566) ^ [] : [_956923 = zero_zero(nat)], (5296 ^ _768566) ^ [] : [dvd_dvd(nat, _956925, _956921)]], -(dvd_dvd(nat, times_times(nat, _956925, _956923), times_times(nat, _956921, _956923)))], (5282 ^ _768566) ^ [_956639, _956641, _956643] : [dvd_dvd(nat, times_times(nat, _956643, _956641), times_times(nat, _956639, _956641)), -(_956641 = zero_zero(nat)), -(dvd_dvd(nat, _956643, _956639))], (5300 ^ _768566) ^ [_957249, _957251, _957253] : [dvd_dvd(nat, power_power(nat, _957253, _957251), power_power(nat, _957249, _957251)), -(_957251 = zero_zero(nat)), -(dvd_dvd(nat, _957253, _957249))], (5310 ^ _768566) ^ [_957595, _957597, _957599] : [-(_957595 = zero_zero(nat)), dvd_dvd(nat, power_power(nat, _957599, _957595), _957597), -(dvd_dvd(nat, _957599, _957597))], (5320 ^ _768566) ^ [_957905] : [linordered_idom(_957905), 5323 ^ _768566 : [(5324 ^ _768566) ^ [_958073, _958075] : [-(ti(_957905, _958075) = ti(_957905, _958073)), -(ord_less(_957905, _958075, _958073)), -(ord_less(_957905, _958073, _958075))]]], (5334 ^ _768566) ^ [_958397] : [comm_semiring_1(_958397), 5337 ^ _768566 : [(5338 ^ _768566) ^ [_958575, _958577, _958579] : [dvd_dvd(_958397, _958577, _958575), dvd_dvd(_958397, _958575, _958579), -(dvd_dvd(_958397, _958577, _958579))]]], (5348 ^ _768566) ^ [_958893] : [comm_semiring_1(_958893), 5351 ^ _768566 : [(5352 ^ _768566) ^ [_959004] : [-(dvd_dvd(_958893, _959004, _959004))]]], (5354 ^ _768566) ^ [_959147, _959149, _959151, _959153] : [_959153 = plus_plus(nat, times_times(nat, _959151, _959149), _959147), ord_less(nat, zero_zero(nat), _959147), ord_less(nat, _959147, _959149), dvd_dvd(nat, _959149, _959153)], (5368 ^ _768566) ^ [_959600, _959602, _959604] : [dvd_dvd(nat, power_power(nat, _959604, _959602), power_power(nat, _959604, _959600)), ord_less(nat, one_one(nat), _959604), -(ord_less_eq(nat, _959602, _959600))], (5378 ^ _768566) ^ [_959917] : [mult_zero(_959917), 5381 ^ _768566 : [(5382 ^ _768566) ^ [_960035] : [-(times_times(_959917, zero_zero(_959917), _960035) = zero_zero(_959917))]]], (5384 ^ _768566) ^ [_960143] : [mult_zero(_960143), 5387 ^ _768566 : [(5388 ^ _768566) ^ [_960261] : [-(times_times(_960143, _960261, zero_zero(_960143)) = zero_zero(_960143))]]], (5390 ^ _768566) ^ [_960369] : [ring_n68954251visors(_960369), 5393 ^ _768566 : [(5404 ^ _768566) ^ [_960866, _960868] : [5405 ^ _768566 : [(5406 ^ _768566) ^ [] : [ti(_960369, _960868) = zero_zero(_960369)], (5408 ^ _768566) ^ [] : [ti(_960369, _960866) = zero_zero(_960369)]], -(times_times(_960369, _960868, _960866) = zero_zero(_960369))], (5394 ^ _768566) ^ [_960570, _960572] : [times_times(_960369, _960572, _960570) = zero_zero(_960369), -(ti(_960369, _960572) = zero_zero(_960369)), -(ti(_960369, _960570) = zero_zero(_960369))]]], (5412 ^ _768566) ^ [_961185] : [no_zero_divisors(_961185), 5415 ^ _768566 : [(5416 ^ _768566) ^ [_961363, _961365] : [-(ti(_961185, _961363) = zero_zero(_961185)), -(ti(_961185, _961365) = zero_zero(_961185)), times_times(_961185, _961363, _961365) = zero_zero(_961185)]]], (5426 ^ _768566) ^ [_961704] : [no_zero_divisors(_961704), 5429 ^ _768566 : [(5430 ^ _768566) ^ [_961876, _961878] : [times_times(_961704, _961878, _961876) = zero_zero(_961704), -(ti(_961704, _961878) = zero_zero(_961704)), -(ti(_961704, _961876) = zero_zero(_961704))]]], (5440 ^ _768566) ^ [_962211] : [zero_neq_one(_962211), one_one(_962211) = zero_zero(_962211)], (5446 ^ _768566) ^ [_962408] : [zero_neq_one(_962408), zero_zero(_962408) = one_one(_962408)], (5452 ^ _768566) ^ [_962605] : [comm_semiring(_962605), 5455 ^ _768566 : [(5456 ^ _768566) ^ [_962773, _962775, _962777] : [-(times_times(_962605, plus_plus(_962605, _962777, _962775), _962773) = plus_plus(_962605, times_times(_962605, _962777, _962773), times_times(_962605, _962775, _962773)))]]], (5458 ^ _768566) ^ [_962897] : [semiring(_962897), 5461 ^ _768566 : [(5462 ^ _768566) ^ [_963092, _963094, _963096, _963098] : [-(plus_plus(_962897, times_times(_962897, _963098, _963096), plus_plus(_962897, times_times(_962897, _963094, _963096), _963092)) = plus_plus(_962897, times_times(_962897, plus_plus(_962897, _963098, _963094), _963096), _963092))]]], (5464 ^ _768566) ^ [_963226] : [comm_semiring_1(_963226), 5467 ^ _768566 : [(5468 ^ _768566) ^ [_963365] : [dvd_dvd(_963226, zero_zero(_963226), _963365), -(ti(_963226, _963365) = zero_zero(_963226))]]], (5474 ^ _768566) ^ [_963584] : [comm_semiring_1(_963584), 5477 ^ _768566 : [(5478 ^ _768566) ^ [_963759, _963761, _963763] : [dvd_dvd(_963584, times_times(_963584, _963763, _963761), _963759), -(dvd_dvd(_963584, _963761, _963759))]]], (5484 ^ _768566) ^ [_963986] : [comm_semiring_1(_963986), 5487 ^ _768566 : [(5488 ^ _768566) ^ [_964161, _964163, _964165] : [dvd_dvd(_963986, times_times(_963986, _964165, _964163), _964161), -(dvd_dvd(_963986, _964165, _964161))]]], (5494 ^ _768566) ^ [_964388] : [dvd(_964388), 5497 ^ _768566 : [(5498 ^ _768566) ^ [_964562, _964564, _964566] : [_964566 = times_times(_964388, _964564, _964562), -(dvd_dvd(_964388, _964564, _964566))]]], (5504 ^ _768566) ^ [_964787] : [comm_semiring_1(_964787), 5507 ^ _768566 : [(5508 ^ _768566) ^ [_964992, _964994, _964996, _964998] : [dvd_dvd(_964787, _964994, _964992), dvd_dvd(_964787, _964998, _964996), -(dvd_dvd(_964787, times_times(_964787, _964994, _964998), times_times(_964787, _964992, _964996)))]]], (5518 ^ _768566) ^ [_965336] : [comm_semiring_1(_965336), 5521 ^ _768566 : [(5522 ^ _768566) ^ [_965511, _965513, _965515] : [dvd_dvd(_965336, _965513, _965511), -(dvd_dvd(_965336, _965513, times_times(_965336, _965515, _965511)))]]], (5528 ^ _768566) ^ [_965738] : [comm_semiring_1(_965738), 5531 ^ _768566 : [(5532 ^ _768566) ^ [_965913, _965915, _965917] : [dvd_dvd(_965738, _965915, _965913), -(dvd_dvd(_965738, _965915, times_times(_965738, _965913, _965917)))]]], (5538 ^ _768566) ^ [_966140] : [comm_semiring_1(_966140), 5541 ^ _768566 : [(5542 ^ _768566) ^ [_966274, _966276] : [-(dvd_dvd(_966140, _966276, times_times(_966140, _966274, _966276)))]]], (5544 ^ _768566) ^ [_966381] : [comm_semiring_1(_966381), 5547 ^ _768566 : [(5548 ^ _768566) ^ [_966515, _966517] : [-(dvd_dvd(_966381, _966517, times_times(_966381, _966517, _966515)))]]], (5550 ^ _768566) ^ [_966622] : [comm_semiring_1(_966622), 5553 ^ _768566 : [(5554 ^ _768566) ^ [_966804, _966806, _966808] : [dvd_dvd(_966622, _966806, _966804), dvd_dvd(_966622, _966806, _966808), -(dvd_dvd(_966622, _966806, plus_plus(_966622, _966804, _966808)))]]], (5564 ^ _768566) ^ [_967130] : [comm_semiring_1(_967130), 5567 ^ _768566 : [(5568 ^ _768566) ^ [_967243] : [-(dvd_dvd(_967130, one_one(_967130), _967243))]]], (5570 ^ _768566) ^ [_967346] : [comm_ring_1(_967346), 5573 ^ _768566 : [(5574 ^ _768566) ^ [_967528, _967530, _967532] : [dvd_dvd(_967346, _967530, _967528), dvd_dvd(_967346, _967530, _967532), -(dvd_dvd(_967346, _967530, minus_minus(_967346, _967528, _967532)))]]], (5584 ^ _768566) ^ [_967868, _967870] : [dvd_dvd(nat, _967870, _967868), -(_967868 = zero_zero(nat)), -(_967868 = _967870), -(ord_less_eq(nat, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _967870), _967868))], (5598 ^ _768566) ^ [_968256] : [linordered_ring(_968256), 5601 ^ _768566 : [(5602 ^ _768566) ^ [_968373] : [-(ord_less_eq(_968256, zero_zero(_968256), times_times(_968256, _968373, _968373)))]]], (5604 ^ _768566) ^ [_968480] : [linord581940658strict(_968480), 5607 ^ _768566 : [(5608 ^ _768566) ^ [_968696, _968698] : [ord_less_eq(_968480, zero_zero(_968480), times_times(_968480, _968698, _968696)), 5613 ^ _768566 : [(5614 ^ _768566) ^ [] : [-(ord_less_eq(_968480, zero_zero(_968480), _968698))], (5616 ^ _768566) ^ [] : [-(ord_less_eq(_968480, zero_zero(_968480), _968696))]], 5617 ^ _768566 : [(5618 ^ _768566) ^ [] : [-(ord_less_eq(_968480, _968698, zero_zero(_968480)))], (5620 ^ _768566) ^ [] : [-(ord_less_eq(_968480, _968696, zero_zero(_968480)))]]], (5622 ^ _768566) ^ [_969152, _969154] : [-(ord_less_eq(_968480, zero_zero(_968480), times_times(_968480, _969154, _969152))), 5623 ^ _768566 : [(5624 ^ _768566) ^ [] : [ord_less_eq(_968480, zero_zero(_968480), _969154), ord_less_eq(_968480, zero_zero(_968480), _969152)], (5630 ^ _768566) ^ [] : [ord_less_eq(_968480, _969154, zero_zero(_968480)), ord_less_eq(_968480, _969152, zero_zero(_968480))]]]]], (5638 ^ _768566) ^ [_969663] : [linord581940658strict(_969663), 5641 ^ _768566 : [(5642 ^ _768566) ^ [_969879, _969881] : [ord_less_eq(_969663, times_times(_969663, _969881, _969879), zero_zero(_969663)), 5647 ^ _768566 : [(5648 ^ _768566) ^ [] : [-(ord_less_eq(_969663, zero_zero(_969663), _969881))], (5650 ^ _768566) ^ [] : [-(ord_less_eq(_969663, _969879, zero_zero(_969663)))]], 5651 ^ _768566 : [(5652 ^ _768566) ^ [] : [-(ord_less_eq(_969663, _969881, zero_zero(_969663)))], (5654 ^ _768566) ^ [] : [-(ord_less_eq(_969663, zero_zero(_969663), _969879))]]], (5656 ^ _768566) ^ [_970335, _970337] : [-(ord_less_eq(_969663, times_times(_969663, _970337, _970335), zero_zero(_969663))), 5657 ^ _768566 : [(5658 ^ _768566) ^ [] : [ord_less_eq(_969663, zero_zero(_969663), _970337), ord_less_eq(_969663, _970335, zero_zero(_969663))], (5664 ^ _768566) ^ [] : [ord_less_eq(_969663, _970337, zero_zero(_969663)), ord_less_eq(_969663, zero_zero(_969663), _970335)]]]]], (5672 ^ _768566) ^ [_970846] : [ordere453448008miring(_970846), 5675 ^ _768566 : [(5676 ^ _768566) ^ [_971015, _971017] : [ord_less_eq(_970846, zero_zero(_970846), _971015), ord_less_eq(_970846, zero_zero(_970846), _971017), -(ord_less_eq(_970846, zero_zero(_970846), times_times(_970846, _971015, _971017)))]]], (5686 ^ _768566) ^ [_971343] : [ordere453448008miring(_971343), 5689 ^ _768566 : [(5690 ^ _768566) ^ [_971512, _971514] : [ord_less_eq(_971343, zero_zero(_971343), _971512), ord_less_eq(_971343, _971514, zero_zero(_971343)), -(ord_less_eq(_971343, times_times(_971343, _971512, _971514), zero_zero(_971343)))]]], (5700 ^ _768566) ^ [_971840] : [ordere453448008miring(_971840), 5703 ^ _768566 : [(5704 ^ _768566) ^ [_972009, _972011] : [ord_less_eq(_971840, zero_zero(_971840), _972009), ord_less_eq(_971840, _972011, zero_zero(_971840)), -(ord_less_eq(_971840, times_times(_971840, _972011, _972009), zero_zero(_971840)))]]], (5714 ^ _768566) ^ [_972337] : [ordere453448008miring(_972337), 5717 ^ _768566 : [(5718 ^ _768566) ^ [_972506, _972508] : [ord_less_eq(_972337, _972506, zero_zero(_972337)), ord_less_eq(_972337, zero_zero(_972337), _972508), -(ord_less_eq(_972337, times_times(_972337, _972506, _972508), zero_zero(_972337)))]]], (5742 ^ _768566) ^ [] : [-(semiri456707255roduct(int))], (5744 ^ _768566) ^ [] : [-(linord626643107strict(int))], (5746 ^ _768566) ^ [] : [-(linord219039673up_add(int))], (5748 ^ _768566) ^ [] : [-(ring_11004092258visors(int))], (5750 ^ _768566) ^ [] : [-(ordere453448008miring(int))], (5752 ^ _768566) ^ [] : [-(linord581940658strict(int))], (5754 ^ _768566) ^ [] : [-(ring_n68954251visors(int))], (5756 ^ _768566) ^ [] : [-(linordered_semidom(int))], (5758 ^ _768566) ^ [] : [-(comm_monoid_mult(int))], (5760 ^ _768566) ^ [] : [-(no_zero_divisors(int))], (5762 ^ _768566) ^ [] : [-(linordered_ring(int))], (5764 ^ _768566) ^ [] : [-(linordered_idom(int))], (5766 ^ _768566) ^ [] : [-(comm_semiring_1(int))], (5768 ^ _768566) ^ [] : [-(comm_semiring(int))], (5770 ^ _768566) ^ [] : [-(number_semiring(int))], (5772 ^ _768566) ^ [] : [-(ab_group_add(int))], (5774 ^ _768566) ^ [] : [-(zero_neq_one(int))], (5776 ^ _768566) ^ [] : [-(ordered_ring(int))], (5778 ^ _768566) ^ [] : [-(linorder(int))], (5780 ^ _768566) ^ [] : [-(monoid_mult(int))], (5782 ^ _768566) ^ [] : [-(comm_ring_1(int))], (5784 ^ _768566) ^ [] : [-(semiring_1(int))], (5786 ^ _768566) ^ [] : [-(semiring_0(int))], (5788 ^ _768566) ^ [] : [-(mult_zero(int))], (5790 ^ _768566) ^ [] : [-(order(int))], (5792 ^ _768566) ^ [] : [-(ring_char_0(int))], (5794 ^ _768566) ^ [] : [-(number_ring(int))], (5796 ^ _768566) ^ [] : [-(semiring(int))], (5798 ^ _768566) ^ [] : [-(ring_1(int))], (5800 ^ _768566) ^ [] : [-(power(int))], (5802 ^ _768566) ^ [] : [-(ring(int))], (5804 ^ _768566) ^ [] : [-(number(int))], (5806 ^ _768566) ^ [] : [-(dvd(int))], (5808 ^ _768566) ^ [] : [-(semiri456707255roduct(nat))], (5810 ^ _768566) ^ [] : [-(ordere453448008miring(nat))], (5812 ^ _768566) ^ [] : [-(linordered_semidom(nat))], (5814 ^ _768566) ^ [] : [-(comm_monoid_mult(nat))], (5816 ^ _768566) ^ [] : [-(no_zero_divisors(nat))], (5818 ^ _768566) ^ [] : [-(comm_semiring_1(nat))], (5820 ^ _768566) ^ [] : [-(comm_semiring(nat))], (5822 ^ _768566) ^ [] : [-(number_semiring(nat))], (5824 ^ _768566) ^ [] : [-(zero_neq_one(nat))], (5826 ^ _768566) ^ [] : [-(linorder(nat))], (5828 ^ _768566) ^ [] : [-(monoid_mult(nat))], (5830 ^ _768566) ^ [] : [-(semiring_1(nat))], (5832 ^ _768566) ^ [] : [-(semiring_0(nat))], (5834 ^ _768566) ^ [] : [-(mult_zero(nat))], (5836 ^ _768566) ^ [] : [-(order(nat))], (5838 ^ _768566) ^ [] : [-(semiring(nat))], (5840 ^ _768566) ^ [] : [-(power(nat))], (5842 ^ _768566) ^ [] : [-(number(nat))], (5844 ^ _768566) ^ [] : [-(dvd(nat))], (5846 ^ _768566) ^ [] : [-(order(bool))], (5848 ^ _768566) ^ [] : [-(semiri456707255roduct(real))], (5850 ^ _768566) ^ [] : [-(linord626643107strict(real))], (5852 ^ _768566) ^ [] : [-(linord219039673up_add(real))], (5854 ^ _768566) ^ [] : [-(ring_11004092258visors(real))], (5856 ^ _768566) ^ [] : [-(ordere453448008miring(real))], (5858 ^ _768566) ^ [] : [-(linord581940658strict(real))], (5860 ^ _768566) ^ [] : [-(ring_n68954251visors(real))], (5862 ^ _768566) ^ [] : [-(linordered_semidom(real))], (5864 ^ _768566) ^ [] : [-(comm_monoid_mult(real))], (5866 ^ _768566) ^ [] : [-(no_zero_divisors(real))], (5868 ^ _768566) ^ [] : [-(linordered_ring(real))], (5870 ^ _768566) ^ [] : [-(linordered_idom(real))], (5872 ^ _768566) ^ [] : [-(comm_semiring_1(real))], (5874 ^ _768566) ^ [] : [-(comm_semiring(real))], (5876 ^ _768566) ^ [] : [-(number_semiring(real))], (5878 ^ _768566) ^ [] : [-(ab_group_add(real))], (5880 ^ _768566) ^ [] : [-(zero_neq_one(real))], (5882 ^ _768566) ^ [] : [-(ordered_ring(real))], (5884 ^ _768566) ^ [] : [-(linorder(real))], (5886 ^ _768566) ^ [] : [-(monoid_mult(real))], (5888 ^ _768566) ^ [] : [-(comm_ring_1(real))], (5890 ^ _768566) ^ [] : [-(semiring_1(real))], (5892 ^ _768566) ^ [] : [-(semiring_0(real))], (5894 ^ _768566) ^ [] : [-(mult_zero(real))], (5896 ^ _768566) ^ [] : [-(order(real))], (5898 ^ _768566) ^ [] : [-(ring_char_0(real))], (5900 ^ _768566) ^ [] : [-(number_ring(real))], (5902 ^ _768566) ^ [] : [-(semiring(real))], (5904 ^ _768566) ^ [] : [-(ring_1(real))], (5906 ^ _768566) ^ [] : [-(power(real))], (5908 ^ _768566) ^ [] : [-(ring(real))], (5910 ^ _768566) ^ [] : [-(number(real))], (5912 ^ _768566) ^ [] : [-(dvd(real))], (5914 ^ _768566) ^ [_977868, _977870] : [-(ti(_977870, ti(_977870, _977868)) = ti(_977870, _977868))], (5728 ^ _768566) ^ [_972834] : [ordered_ring(_972834), 5731 ^ _768566 : [(5732 ^ _768566) ^ [_973003, _973005] : [ord_less_eq(_972834, _973003, zero_zero(_972834)), ord_less_eq(_972834, _973005, zero_zero(_972834)), -(ord_less_eq(_972834, zero_zero(_972834), times_times(_972834, _973003, _973005)))]]]], input).
% 101.38/98.61  ncf('1',plain,[ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int))],start(5916 ^ 0)).
% 101.38/98.61  ncf('1.1',plain,[-(ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int))), ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int))), int = int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t) = plus_plus(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)), zero_zero(int)) = zero_zero(int)],extension(438 ^ 1,bind([[_781966, _781968, _781970, _781972, _781974, _781976], [zero_zero(int), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int)), plus_plus(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), int, int]]))).
% 101.38/98.61  ncf('1.1.1',plain,[-(ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int))))],extension(1000 ^ 2)).
% 101.38/98.61  ncf('1.1.2',plain,[-(int = int)],extension(2 ^ 2,bind([[_768710], [int]]))).
% 101.38/98.61  ncf('1.1.3',plain,[-(times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t) = plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int))), plus_plus(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)],extension(4 ^ 2,bind([[_768817, _768819], [times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int))]]))).
% 101.38/98.61  ncf('1.1.3.1',plain,[-(plus_plus(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))],extension(1002 ^ 3)).
% 101.38/98.61  ncf('1.1.4',plain,[-(times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int)) = zero_zero(int)), comm_semiring_1(int)],extension(2975 ^ 2,bind([[_874390, _874508], [int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))]]))).
% 101.38/98.61  ncf('1.1.4.1',plain,[-(comm_semiring_1(int))],extension(5766 ^ 3)).
% 101.38/98.61  %-----------------------------------------------------
% 101.38/98.61  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------