%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:45:58 EDT 2023
% Result : Theorem 0.62s 1.39s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.13 % Command : nanocop.sh %s %d
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 17:01:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.62/1.39
% 0.62/1.39 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.62/1.39 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/1.39 %-----------------------------------------------------
% 0.62/1.39 ncf(matrix, plain, [(6388 ^ _76106) ^ [] : [-(hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(int))], (420 ^ _76106) ^ [_81496, _81498] : [_81498 = _81496, -(undefined(_81498) = undefined(_81496))], (426 ^ _76106) ^ [_81581, _81583] : [_81583 = _81581, -(ord_less_eq(_81583) = ord_less_eq(_81581))], (432 ^ _76106) ^ [_81666, _81668] : [_81668 = _81666, -(times_times(_81668) = times_times(_81666))], (438 ^ _76106) ^ [_81751, _81753] : [_81753 = _81751, -(ord_less(_81753) = ord_less(_81751))], (444 ^ _76106) ^ [_81836, _81838, _81840, _81842] : [-(fun(_81842, _81838) = fun(_81840, _81836)), _81842 = _81840, _81838 = _81836], (454 ^ _76106) ^ [_81985, _81987] : [_81987 = _81985, -((if _81987) = (if _81985))], (460 ^ _76106) ^ [_82070, _82072, _82074, _82076] : [-(ti(_82076, _82072) = ti(_82074, _82070)), _82076 = _82074, _82072 = _82070], (470 ^ _76106) ^ [_82219, _82221, _82223, _82225] : [-(power_power(_82225, _82221) = power_power(_82223, _82219)), _82225 = _82223, _82221 = _82219], (480 ^ _76106) ^ [_82368, _82370, _82372, _82374] : [-(plus_plus(_82374, _82370) = plus_plus(_82372, _82368)), _82374 = _82372, _82370 = _82368], (490 ^ _76106) ^ [_82517, _82519] : [_82519 = _82517, -(one_one(_82519) = one_one(_82517))], (496 ^ _76106) ^ [_82602, _82604] : [_82604 = _82602, -(semiring_1_of_nat(_82604) = semiring_1_of_nat(_82602))], (502 ^ _76106) ^ [_82687, _82689, _82691, _82693] : [-(number_number_of(_82693, _82689) = number_number_of(_82691, _82687)), _82693 = _82691, _82689 = _82687], (530 ^ _76106) ^ [_83133, _83135] : [_83135 = _83133, -(zero_zero(_83135) = zero_zero(_83133))], (512 ^ _76106) ^ [_82836, _82838, _82840, _82842, _82844, _82846, _82848, _82850] : [-(hAPP(_82850, _82846, _82842, _82838) = hAPP(_82848, _82844, _82840, _82836)), _82850 = _82848, _82846 = _82844, _82842 = _82840, _82838 = _82836], (2 ^ _76106) ^ [_76136] : [-(_76136 = _76136)], (4 ^ _76106) ^ [_76159, _76161] : [_76161 = _76159, -(_76159 = _76161)], (10 ^ _76106) ^ [_76232, _76234, _76236] : [-(_76236 = _76232), _76236 = _76234, _76234 = _76232], (20 ^ _76106) ^ [_76369, _76371] : [-(hBOOL(_76369)), _76371 = _76369, hBOOL(_76371)], (30 ^ _76106) ^ [_76494, _76496] : [-(semiri456707255roduct(_76494)), _76496 = _76494, semiri456707255roduct(_76496)], (40 ^ _76106) ^ [_76619, _76621] : [-(ordere223160158up_add(_76619)), _76621 = _76619, ordere223160158up_add(_76621)], (50 ^ _76106) ^ [_76744, _76746] : [-(ordere236663937imp_le(_76744)), _76746 = _76744, ordere236663937imp_le(_76746)], (60 ^ _76106) ^ [_76869, _76871] : [-(linord893533164strict(_76869)), _76871 = _76869, linord893533164strict(_76871)], (70 ^ _76106) ^ [_76994, _76996] : [-(linord20386208strict(_76994)), _76996 = _76994, linord20386208strict(_76996)], (80 ^ _76106) ^ [_77119, _77121] : [-(ordere779506340up_add(_77119)), _77121 = _77119, ordere779506340up_add(_77121)], (90 ^ _76106) ^ [_77244, _77246] : [-(ordere216010020id_add(_77244)), _77246 = _77244, ordere216010020id_add(_77246)], (100 ^ _76106) ^ [_77369, _77371] : [-(linord219039673up_add(_77369)), _77371 = _77369, linord219039673up_add(_77371)], (110 ^ _76106) ^ [_77494, _77496] : [-(cancel146912293up_add(_77494)), _77496 = _77494, cancel146912293up_add(_77496)], (120 ^ _76106) ^ [_77619, _77621] : [-(ring_11004092258visors(_77619)), _77621 = _77619, ring_11004092258visors(_77621)], (130 ^ _76106) ^ [_77744, _77746] : [-(linord581940658strict(_77744)), _77746 = _77744, linord581940658strict(_77746)], (140 ^ _76106) ^ [_77869, _77871] : [-(cancel_semigroup_add(_77869)), _77871 = _77869, cancel_semigroup_add(_77871)], (150 ^ _76106) ^ [_77994, _77996] : [-(linordered_semiring(_77994)), _77996 = _77994, linordered_semiring(_77996)], (160 ^ _76106) ^ [_78119, _78121] : [-(linordered_semidom(_78119)), _78121 = _78119, linordered_semidom(_78121)], (170 ^ _76106) ^ [_78244, _78246] : [-(dense_linorder(_78244)), _78246 = _78244, dense_linorder(_78246)], (180 ^ _76106) ^ [_78369, _78371] : [-(ab_semigroup_add(_78369)), _78371 = _78369, ab_semigroup_add(_78371)], (190 ^ _76106) ^ [_78494, _78496] : [-(no_zero_divisors(_78494)), _78496 = _78494, no_zero_divisors(_78496)], (200 ^ _76106) ^ [_78619, _78621] : [-(comm_monoid_add(_78619)), _78621 = _78619, comm_monoid_add(_78621)], (210 ^ _76106) ^ [_78744, _78746] : [-(linordered_ring(_78744)), _78746 = _78744, linordered_ring(_78746)], (220 ^ _76106) ^ [_78869, _78871] : [-(linordered_idom(_78869)), _78871 = _78869, linordered_idom(_78871)], (230 ^ _76106) ^ [_78994, _78996] : [-(comm_semiring_1(_78994)), _78996 = _78994, comm_semiring_1(_78996)], (240 ^ _76106) ^ [_79119, _79121] : [-(semiring_char_0(_79119)), _79121 = _79119, semiring_char_0(_79121)], (250 ^ _76106) ^ [_79244, _79246] : [-(number_semiring(_79244)), _79246 = _79244, number_semiring(_79246)], (260 ^ _76106) ^ [_79369, _79371] : [-(zero_neq_one(_79369)), _79371 = _79369, zero_neq_one(_79371)], (270 ^ _76106) ^ [_79494, _79496] : [-(preorder(_79494)), _79496 = _79494, preorder(_79496)], (280 ^ _76106) ^ [_79619, _79621] : [-(linorder(_79619)), _79621 = _79619, linorder(_79621)], (290 ^ _76106) ^ [_79744, _79746] : [-(monoid_mult(_79744)), _79746 = _79744, monoid_mult(_79746)], (300 ^ _76106) ^ [_79869, _79871] : [-(monoid_add(_79869)), _79871 = _79869, monoid_add(_79871)], (310 ^ _76106) ^ [_79994, _79996] : [-(semiring_1(_79994)), _79996 = _79994, semiring_1(_79996)], (320 ^ _76106) ^ [_80119, _80121] : [-(semiring_0(_80119)), _80121 = _80119, semiring_0(_80121)], (330 ^ _76106) ^ [_80244, _80246] : [-(mult_zero(_80244)), _80246 = _80244, mult_zero(_80246)], (340 ^ _76106) ^ [_80369, _80371] : [-(order(_80369)), _80371 = _80369, order(_80371)], (350 ^ _76106) ^ [_80494, _80496] : [-(ring_char_0(_80494)), _80496 = _80494, ring_char_0(_80496)], (360 ^ _76106) ^ [_80619, _80621] : [-(number_ring(_80619)), _80621 = _80619, number_ring(_80621)], (370 ^ _76106) ^ [_80744, _80746] : [-(ord(_80744)), _80746 = _80744, ord(_80746)], (380 ^ _76106) ^ [_80869, _80871] : [-(power(_80869)), _80871 = _80869, power(_80871)], (390 ^ _76106) ^ [_80994, _80996] : [-(zero(_80994)), _80996 = _80994, zero(_80996)], (400 ^ _76106) ^ [_81119, _81121] : [-(number(_81119)), _81121 = _81119, number(_81121)], (410 ^ _76106) ^ [_81240, _81242] : [-(one(_81240)), _81242 = _81240, one(_81242)], (536 ^ _76106) ^ [_83249] : [one(_83249), -(ti(_83249, one_one(_83249)) = one_one(_83249))], (542 ^ _76106) ^ [_83336, _83338] : [monoid_add(_83336), -(plus_plus(_83336, ti(_83336, _83338)) = plus_plus(_83336, _83338))], (548 ^ _76106) ^ [_83429, _83431] : [monoid_add(_83429), -(ti(fun(_83429, _83429), plus_plus(_83429, _83431)) = plus_plus(_83429, _83431))], (554 ^ _76106) ^ [_83528, _83530] : [ab_semigroup_add(_83528), -(plus_plus(_83528, ti(_83528, _83530)) = plus_plus(_83528, _83530))], (560 ^ _76106) ^ [_83621, _83623] : [ab_semigroup_add(_83621), -(ti(fun(_83621, _83621), plus_plus(_83621, _83623)) = plus_plus(_83621, _83623))], (566 ^ _76106) ^ [_83720, _83722] : [cancel_semigroup_add(_83720), -(plus_plus(_83720, ti(_83720, _83722)) = plus_plus(_83720, _83722))], (572 ^ _76106) ^ [_83813, _83815] : [cancel_semigroup_add(_83813), -(ti(fun(_83813, _83813), plus_plus(_83813, _83815)) = plus_plus(_83813, _83815))], (578 ^ _76106) ^ [_83912] : [linordered_semiring(_83912), -(ti(fun(_83912, fun(_83912, _83912)), times_times(_83912)) = times_times(_83912))], (584 ^ _76106) ^ [_84011] : [zero(_84011), -(ti(_84011, zero_zero(_84011)) = zero_zero(_84011))], (590 ^ _76106) ^ [_84098] : [-(ti(_84098, undefined(_84098)) = undefined(_84098))], (592 ^ _76106) ^ [_84128] : [-(ti(fun(bool, fun(_84128, fun(_84128, _84128))), (if _84128)) = (if _84128))], (594 ^ _76106) ^ [] : [-(ti(fun(int, int), bit0) = bit0)], (596 ^ _76106) ^ [] : [-(ti(fun(int, int), bit1) = bit1)], (598 ^ _76106) ^ [] : [-(ti(int, pls) = pls)], (600 ^ _76106) ^ [_84221, _84223] : [number(_84221), -(number_number_of(_84221, ti(int, _84223)) = number_number_of(_84221, _84223))], (606 ^ _76106) ^ [_84314, _84316] : [number(_84314), -(ti(_84314, number_number_of(_84314, _84316)) = number_number_of(_84314, _84316))], (612 ^ _76106) ^ [] : [-(ti(fun(int, int), succ) = succ)], (614 ^ _76106) ^ [_84425] : [semiring_1(_84425), -(ti(fun(nat, _84425), semiring_1_of_nat(_84425)) = semiring_1_of_nat(_84425))], (620 ^ _76106) ^ [] : [-(ti(fun(real, real), sqrt) = sqrt)], (622 ^ _76106) ^ [_84536] : [ord(_84536), -(ti(fun(_84536, fun(_84536, bool)), ord_less(_84536)) = ord_less(_84536))], (628 ^ _76106) ^ [_84635] : [ord(_84635), -(ti(fun(_84635, fun(_84635, bool)), ord_less_eq(_84635)) = ord_less_eq(_84635))], (634 ^ _76106) ^ [_84734, _84736] : [power(_84734), -(power_power(_84734, ti(_84734, _84736)) = power_power(_84734, _84736))], (640 ^ _76106) ^ [_84827, _84829] : [power(_84827), -(ti(fun(nat, _84827), power_power(_84827, _84829)) = power_power(_84827, _84829))], (646 ^ _76106) ^ [] : [-(ti(bool, fFalse) = fFalse)], (648 ^ _76106) ^ [] : [-(ti(bool, fTrue) = fTrue)], (650 ^ _76106) ^ [_84962, _84964, _84966, _84968] : [ord(_84962), -(hAPP(_84968, _84962, ti(fun(_84968, _84962), _84966), _84964) = hAPP(_84968, _84962, _84966, _84964))], (656 ^ _76106) ^ [_85073, _85075, _85077, _85079] : [ord(_85073), -(hAPP(_85079, _85073, _85077, ti(_85079, _85075)) = hAPP(_85079, _85073, _85077, _85075))], (662 ^ _76106) ^ [_85178, _85180, _85182, _85184] : [ord(_85178), -(ti(_85178, hAPP(_85184, _85178, _85182, _85180)) = hAPP(_85184, _85178, _85182, _85180))], (668 ^ _76106) ^ [_85283, _85285, _85287] : [power(_85283), -(hAPP(nat, _85283, ti(fun(nat, _85283), _85287), _85285) = hAPP(nat, _85283, _85287, _85285))], (674 ^ _76106) ^ [_85392, _85394, _85396] : [power(_85392), -(hAPP(nat, _85392, _85396, ti(nat, _85394)) = hAPP(nat, _85392, _85396, _85394))], (680 ^ _76106) ^ [_85495, _85497, _85499] : [power(_85495), -(ti(_85495, hAPP(nat, _85495, _85499, _85497)) = hAPP(nat, _85495, _85499, _85497))], (686 ^ _76106) ^ [_85598, _85600, _85602] : [-(hAPP(bool, fun(_85602, fun(_85602, _85602)), ti(fun(bool, fun(_85602, fun(_85602, _85602))), _85600), _85598) = hAPP(bool, fun(_85602, fun(_85602, _85602)), _85600, _85598))], (688 ^ _76106) ^ [_85659, _85661, _85663] : [-(hAPP(bool, fun(_85663, fun(_85663, _85663)), _85661, ti(bool, _85659)) = hAPP(bool, fun(_85663, fun(_85663, _85663)), _85661, _85659))], (690 ^ _76106) ^ [_85711, _85713, _85715] : [-(ti(fun(_85715, fun(_85715, _85715)), hAPP(bool, fun(_85715, fun(_85715, _85715)), _85713, _85711)) = hAPP(bool, fun(_85715, fun(_85715, _85715)), _85713, _85711))], (692 ^ _76106) ^ [_85769, _85771, _85773] : [-(hAPP(_85773, fun(_85773, _85773), ti(fun(_85773, fun(_85773, _85773)), _85771), _85769) = hAPP(_85773, fun(_85773, _85773), _85771, _85769))], (694 ^ _76106) ^ [_85821, _85823, _85825] : [-(hAPP(_85825, fun(_85825, _85825), _85823, ti(_85825, _85821)) = hAPP(_85825, fun(_85825, _85825), _85823, _85821))], (696 ^ _76106) ^ [_85867, _85869, _85871] : [-(ti(fun(_85871, _85871), hAPP(_85871, fun(_85871, _85871), _85869, _85867)) = hAPP(_85871, fun(_85871, _85871), _85869, _85867))], (698 ^ _76106) ^ [_85916, _85918, _85920] : [-(hAPP(_85920, _85920, ti(fun(_85920, _85920), _85918), _85916) = hAPP(_85920, _85920, _85918, _85916))], (700 ^ _76106) ^ [_85959, _85961, _85963] : [-(hAPP(_85963, _85963, _85961, ti(_85963, _85959)) = hAPP(_85963, _85963, _85961, _85959))], (702 ^ _76106) ^ [_85999, _86001, _86003] : [-(ti(_86003, hAPP(_86003, _86003, _86001, _85999)) = hAPP(_86003, _86003, _86001, _85999))], (704 ^ _76106) ^ [_86051] : [hBOOL(ti(bool, _86051)), -(hBOOL(_86051))], (710 ^ _76106) ^ [_86124] : [hBOOL(_86124), -(hBOOL(ti(bool, _86124)))], (716 ^ _76106) ^ [] : [-(ti(int, m1) = m1)], (718 ^ _76106) ^ [] : [-(ti(nat, n) = n)], (720 ^ _76106) ^ [] : [-(ti(int, t) = t)], (722 ^ _76106) ^ [] : [-(ti(nat, tn) = tn)], (724 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (726 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), one_one(int)), t)))], (728 ^ _76106) ^ [_86311] : [linordered_idom(_86311), 731 ^ _76106 : [(732 ^ _76106) ^ [_86432, _86434] : [hAPP(_86311, _86311, plus_plus(_86311, hAPP(nat, _86311, power_power(_86311, _86434), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _86311, power_power(_86311, _86432), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))) = zero_zero(_86311), 735 ^ _76106 : [(736 ^ _76106) ^ [] : [-(ti(_86311, _86434) = zero_zero(_86311))], (738 ^ _76106) ^ [] : [-(ti(_86311, _86432) = zero_zero(_86311))]]], (740 ^ _76106) ^ [_86605, _86607] : [-(hAPP(_86311, _86311, plus_plus(_86311, hAPP(nat, _86311, power_power(_86311, _86607), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _86311, power_power(_86311, _86605), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))) = zero_zero(_86311)), ti(_86311, _86607) = zero_zero(_86311), ti(_86311, _86605) = zero_zero(_86311)]]], (750 ^ _76106) ^ [_86816] : [semiring_1(_86816), -(hAPP(nat, _86816, power_power(_86816, one_one(_86816)), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = one_one(_86816))], (756 ^ _76106) ^ [_86913] : [semiring_1(_86913), -(hAPP(nat, _86913, power_power(_86913, zero_zero(_86913)), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(_86913))], (762 ^ _76106) ^ [_87010] : [ring_11004092258visors(_87010), 765 ^ _76106 : [(766 ^ _76106) ^ [_87096] : [hAPP(nat, _87010, power_power(_87010, _87096), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(_87010), -(ti(_87010, _87096) = zero_zero(_87010))], (772 ^ _76106) ^ [_87199] : [ti(_87010, _87199) = zero_zero(_87010), -(hAPP(nat, _87010, power_power(_87010, _87199), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(_87010))]]], (778 ^ _76106) ^ [_87312] : [number_ring(_87312), 781 ^ _76106 : [(782 ^ _76106) ^ [_87388] : [-(hAPP(_87312, _87312, plus_plus(_87312, one_one(_87312)), number_number_of(_87312, _87388)) = number_number_of(_87312, hAPP(int, int, plus_plus(int, hAPP(int, int, bit1, pls)), _87388)))]]], (784 ^ _76106) ^ [_87436] : [number_ring(_87436), 787 ^ _76106 : [(788 ^ _76106) ^ [_87515] : [-(hAPP(_87436, _87436, plus_plus(_87436, number_number_of(_87436, _87515)), one_one(_87436)) = number_number_of(_87436, hAPP(int, int, plus_plus(int, _87515), hAPP(int, int, bit1, pls))))]]], (790 ^ _76106) ^ [_87566] : [number_ring(_87566), -(hAPP(_87566, _87566, plus_plus(_87566, one_one(_87566)), one_one(_87566)) = number_number_of(_87566, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))], (796 ^ _76106) ^ [_87669] : [number_semiring(_87669), -(hAPP(_87669, _87669, plus_plus(_87669, one_one(_87669)), one_one(_87669)) = number_number_of(_87669, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))], (802 ^ _76106) ^ [_87772] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, power_power(int, _87772), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = hAPP(nat, int, power_power(int, _87772), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))], (804 ^ _76106) ^ [_87819] : [power(_87819), semiring_0(_87819), 811 ^ _76106 : [(812 ^ _76106) ^ [_87982] : [number_number_of(nat, _87982) = zero_zero(nat), -(hAPP(nat, _87819, power_power(_87819, zero_zero(_87819)), number_number_of(nat, _87982)) = one_one(_87819))], (818 ^ _76106) ^ [_88089] : [-(number_number_of(nat, _88089) = zero_zero(nat)), -(hAPP(nat, _87819, power_power(_87819, zero_zero(_87819)), number_number_of(nat, _88089)) = zero_zero(_87819))]]], (824 ^ _76106) ^ [_88149] : [number_ring(_88149), -(one_one(_88149) = number_number_of(_88149, hAPP(int, int, bit1, pls)))], (830 ^ _76106) ^ [_88232] : [number_ring(_88232), -(number_number_of(_88232, hAPP(int, int, bit1, pls)) = one_one(_88232))], (836 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)))], (838 ^ _76106) ^ [_88329, _88331] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88331), _88329))), -(_88331 = _88329), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88329), _88331)))], (848 ^ _76106) ^ [_88405, _88407] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, _88407)), number_number_of(int, _88405))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88407), _88405)))], (854 ^ _76106) ^ [_88526, _88528] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88528), _88526)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), number_number_of(int, _88528)), number_number_of(int, _88526))))], (860 ^ _76106) ^ [_88653, _88655] : [-(hAPP(int, int, plus_plus(int, number_number_of(int, _88655)), number_number_of(int, _88653)) = number_number_of(int, hAPP(int, int, plus_plus(int, _88655), _88653)))], (862 ^ _76106) ^ [_88703] : [number_ring(_88703), linordered_idom(_88703), 869 ^ _76106 : [(870 ^ _76106) ^ [_88859, _88861] : [hBOOL(hAPP(_88703, bool, hAPP(_88703, fun(_88703, bool), ord_less(_88703), number_number_of(_88703, _88861)), number_number_of(_88703, _88859))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88861), _88859)))], (876 ^ _76106) ^ [_88992, _88994] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _88994), _88992)), -(hBOOL(hAPP(_88703, bool, hAPP(_88703, fun(_88703, bool), ord_less(_88703), number_number_of(_88703, _88994)), number_number_of(_88703, _88992))))]]], (882 ^ _76106) ^ [] : [-(zero_zero(int) = number_number_of(int, pls))], (884 ^ _76106) ^ [_89155, _89157] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _89157)), _89155) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _89157), _89155)))], (886 ^ _76106) ^ [_89206, _89208] : [-(hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _89208), _89206)) = hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _89208)), _89206))], (888 ^ _76106) ^ [_89257, _89259, _89261] : [-(hAPP(int, int, plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _89261)), hAPP(int, int, plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _89259)), _89257)) = hAPP(int, int, plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, plus_plus(nat, _89261), _89259))), _89257))], (890 ^ _76106) ^ [_89331, _89333] : [-(hAPP(int, int, plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _89333)), hAPP(nat, int, semiring_1_of_nat(int), _89331)) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, plus_plus(nat, _89333), _89331)))], (892 ^ _76106) ^ [] : [-(hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)) = one_one(int))], (894 ^ _76106) ^ [] : [-(number_number_of(nat, pls) = zero_zero(nat))], (896 ^ _76106) ^ [] : [-(zero_zero(nat) = number_number_of(nat, pls))], (898 ^ _76106) ^ [_89453] : [hAPP(nat, int, semiring_1_of_nat(int), _89453) = zero_zero(int), -(_89453 = zero_zero(nat))], (904 ^ _76106) ^ [_89534] : [_89534 = zero_zero(nat), -(hAPP(nat, int, semiring_1_of_nat(int), _89534) = zero_zero(int))], (910 ^ _76106) ^ [] : [-(hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)) = zero_zero(int))], (912 ^ _76106) ^ [] : [-(hAPP(nat, nat, plus_plus(nat, one_one(nat)), one_one(nat)) = number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))], (914 ^ _76106) ^ [_89672, _89674] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _89674)), hAPP(int, int, bit1, _89672))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _89674), _89672)))], (920 ^ _76106) ^ [_89801, _89803] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _89803), _89801)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _89803)), hAPP(int, int, bit1, _89801))))], (926 ^ _76106) ^ [_89951, _89953] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _89953)), hAPP(int, int, bit1, _89951))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _89953), _89951)))], (932 ^ _76106) ^ [_90080, _90082] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90082), _90080)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _90082)), hAPP(int, int, bit1, _90080))))], (938 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))], (940 ^ _76106) ^ [_90254, _90256] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _90256)), hAPP(int, int, bit0, _90254))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90256), _90254)))], (946 ^ _76106) ^ [_90383, _90385] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90385), _90383)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _90385)), hAPP(int, int, bit0, _90383))))], (952 ^ _76106) ^ [_90533, _90535] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _90535)), hAPP(int, int, bit0, _90533))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90535), _90533)))], (958 ^ _76106) ^ [_90662, _90664] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90664), _90662)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _90664)), hAPP(int, int, bit0, _90662))))], (964 ^ _76106) ^ [_90797, _90799, _90801] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90799), _90797)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, plus_plus(int, _90799), _90801)), hAPP(int, int, plus_plus(int, _90797), _90801))))], (970 ^ _76106) ^ [_90953, _90955] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _90953), pls)), -(hAPP(nat, nat, plus_plus(nat, number_number_of(nat, _90953)), number_number_of(nat, _90955)) = number_number_of(nat, _90955))], (976 ^ _76106) ^ [_91077, _91079] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _91077), pls))), 979 ^ _76106 : [(980 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _91079), pls)), -(hAPP(nat, nat, plus_plus(nat, number_number_of(nat, _91077)), number_number_of(nat, _91079)) = number_number_of(nat, _91077))], (986 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _91079), pls))), -(hAPP(nat, nat, plus_plus(nat, number_number_of(nat, _91077)), number_number_of(nat, _91079)) = number_number_of(nat, hAPP(int, int, plus_plus(int, _91077), _91079)))]]], (992 ^ _76106) ^ [] : [-(one_one(int) = number_number_of(int, hAPP(int, int, bit1, pls)))], (994 ^ _76106) ^ [] : [-(number_number_of(nat, hAPP(int, int, bit1, pls)) = one_one(nat))], (996 ^ _76106) ^ [] : [-(one_one(nat) = number_number_of(nat, hAPP(int, int, bit1, pls)))], (998 ^ _76106) ^ [_91436] : [number_ring(_91436), ring_char_0(_91436), 1005 ^ _76106 : [(1006 ^ _76106) ^ [_91569, _91571] : [number_number_of(_91436, _91571) = number_number_of(_91436, _91569), -(_91571 = _91569)], (1012 ^ _76106) ^ [_91656, _91658] : [_91658 = _91656, -(number_number_of(_91436, _91658) = number_number_of(_91436, _91656))]]], (1018 ^ _76106) ^ [_91755] : [number(_91755), 1021 ^ _76106 : [(1022 ^ _76106) ^ [_91846, _91848] : [number_number_of(_91755, _91848) = ti(_91755, _91846), -(ti(_91755, _91846) = number_number_of(_91755, _91848))], (1028 ^ _76106) ^ [_91945, _91947] : [ti(_91755, _91945) = number_number_of(_91755, _91947), -(number_number_of(_91755, _91947) = ti(_91755, _91945))]]], (1034 ^ _76106) ^ [_92069, _92071] : [hAPP(int, int, bit1, _92071) = hAPP(int, int, bit1, _92069), -(_92071 = _92069)], (1040 ^ _76106) ^ [_92162, _92164] : [_92164 = _92162, -(hAPP(int, int, bit1, _92164) = hAPP(int, int, bit1, _92162))], (1046 ^ _76106) ^ [_92276, _92278] : [hAPP(int, int, bit0, _92278) = hAPP(int, int, bit0, _92276), -(_92278 = _92276)], (1052 ^ _76106) ^ [_92369, _92371] : [_92371 = _92369, -(hAPP(int, int, bit0, _92371) = hAPP(int, int, bit0, _92369))], (1058 ^ _76106) ^ [_92468] : [linordered_idom(_92468), 1061 ^ _76106 : [(1062 ^ _76106) ^ [_92579] : [hBOOL(hAPP(_92468, bool, hAPP(_92468, fun(_92468, bool), ord_less(_92468), hAPP(_92468, _92468, plus_plus(_92468, _92579), _92579)), zero_zero(_92468))), -(hBOOL(hAPP(_92468, bool, hAPP(_92468, fun(_92468, bool), ord_less(_92468), _92579), zero_zero(_92468))))], (1068 ^ _76106) ^ [_92732] : [hBOOL(hAPP(_92468, bool, hAPP(_92468, fun(_92468, bool), ord_less(_92468), _92732), zero_zero(_92468))), -(hBOOL(hAPP(_92468, bool, hAPP(_92468, fun(_92468, bool), ord_less(_92468), hAPP(_92468, _92468, plus_plus(_92468, _92732), _92732)), zero_zero(_92468))))]]], (1074 ^ _76106) ^ [_92895, _92897, _92899] : [-(hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, _92899), _92897)), _92895) = hAPP(int, int, plus_plus(int, _92899), hAPP(int, int, plus_plus(int, _92897), _92895)))], (1076 ^ _76106) ^ [_92954, _92956, _92958] : [-(hAPP(int, int, plus_plus(int, _92958), hAPP(int, int, plus_plus(int, _92956), _92954)) = hAPP(int, int, plus_plus(int, _92956), hAPP(int, int, plus_plus(int, _92958), _92954)))], (1078 ^ _76106) ^ [_93013, _93015] : [-(hAPP(int, int, plus_plus(int, _93015), _93013) = hAPP(int, int, plus_plus(int, _93013), _93015))], (1080 ^ _76106) ^ [_93069, _93071] : [hAPP(nat, int, semiring_1_of_nat(int), _93071) = hAPP(nat, int, semiring_1_of_nat(int), _93069), -(_93071 = _93069)], (1086 ^ _76106) ^ [_93162, _93164] : [_93164 = _93162, -(hAPP(nat, int, semiring_1_of_nat(int), _93164) = hAPP(nat, int, semiring_1_of_nat(int), _93162))], (1092 ^ _76106) ^ [_93261] : [number_ring(_93261), linordered_idom(_93261), 1099 ^ _76106 : [(1100 ^ _76106) ^ [_93408] : [hBOOL(hAPP(_93261, bool, hAPP(_93261, fun(_93261, bool), ord_less(_93261), number_number_of(_93261, _93408)), zero_zero(_93261))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _93408), pls)))], (1106 ^ _76106) ^ [_93537] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _93537), pls)), -(hBOOL(hAPP(_93261, bool, hAPP(_93261, fun(_93261, bool), ord_less(_93261), number_number_of(_93261, _93537)), zero_zero(_93261))))]]], (1112 ^ _76106) ^ [_93678] : [number_ring(_93678), linordered_idom(_93678), 1119 ^ _76106 : [(1120 ^ _76106) ^ [_93820] : [hBOOL(hAPP(_93678, bool, hAPP(_93678, fun(_93678, bool), ord_less(_93678), zero_zero(_93678)), number_number_of(_93678, _93820))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _93820)))], (1126 ^ _76106) ^ [_93939] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _93939)), -(hBOOL(hAPP(_93678, bool, hAPP(_93678, fun(_93678, bool), ord_less(_93678), zero_zero(_93678)), number_number_of(_93678, _93939))))]]], (1132 ^ _76106) ^ [_94082] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94082)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94082), pls)))], (1138 ^ _76106) ^ [_94199] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94199), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94199)), pls)))], (1144 ^ _76106) ^ [_94337, _94339] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94339)), hAPP(int, int, bit0, _94337))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94339), _94337)))], (1150 ^ _76106) ^ [_94466, _94468] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94468), _94466)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94468)), hAPP(int, int, bit0, _94466))))], (1156 ^ _76106) ^ [_94616, _94618] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94618)), hAPP(int, int, bit0, _94616))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94618), _94616)))], (1162 ^ _76106) ^ [_94745, _94747] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94747), _94745)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _94747)), hAPP(int, int, bit0, _94745))))], (1168 ^ _76106) ^ [_94892] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _94892)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _94892), pls)))], (1174 ^ _76106) ^ [_95009] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95009), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _95009)), pls)))], (1180 ^ _76106) ^ [_95144] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), hAPP(int, int, bit0, _95144))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _95144)))], (1186 ^ _76106) ^ [_95241] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _95241)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), hAPP(int, int, bit0, _95241))))], (1192 ^ _76106) ^ [_95356] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _95356)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95356), zero_zero(int))))], (1198 ^ _76106) ^ [_95473] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95473), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, _95473)), zero_zero(int))))], (1204 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))], (1206 ^ _76106) ^ [_95632] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _95632)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95632), zero_zero(int))))], (1212 ^ _76106) ^ [_95749] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95749), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _95749)), zero_zero(int))))], (1218 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), one_one(int))))], (1230 ^ _76106) ^ [_96043, _96045] : [1231 ^ _76106 : [(1232 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _96045), _96043))], (1234 ^ _76106) ^ [] : [_96045 = _96043]], -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _96045), hAPP(int, int, plus_plus(int, _96043), one_one(int)))))], (1220 ^ _76106) ^ [_95905, _95907] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95907), hAPP(int, int, plus_plus(int, _95905), one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _95907), _95905))), -(_95907 = _95905)], (1238 ^ _76106) ^ [_96221] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _96221)), zero_zero(int)))], (1240 ^ _76106) ^ [_96258] : [number_ring(_96258), linordered_idom(_96258), 1247 ^ _76106 : [(1248 ^ _76106) ^ [_96405] : [hBOOL(hAPP(_96258, bool, hAPP(_96258, fun(_96258, bool), ord_less(_96258), number_number_of(_96258, _96405)), one_one(_96258))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _96405), hAPP(int, int, bit1, pls))))], (1254 ^ _76106) ^ [_96534] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _96534), hAPP(int, int, bit1, pls))), -(hBOOL(hAPP(_96258, bool, hAPP(_96258, fun(_96258, bool), ord_less(_96258), number_number_of(_96258, _96534)), one_one(_96258))))]]], (1260 ^ _76106) ^ [_96675] : [number_ring(_96675), linordered_idom(_96675), 1267 ^ _76106 : [(1268 ^ _76106) ^ [_96817] : [hBOOL(hAPP(_96675, bool, hAPP(_96675, fun(_96675, bool), ord_less(_96675), one_one(_96675)), number_number_of(_96675, _96817))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, pls)), _96817)))], (1274 ^ _76106) ^ [_96936] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit1, pls)), _96936)), -(hBOOL(hAPP(_96675, bool, hAPP(_96675, fun(_96675, bool), ord_less(_96675), one_one(_96675)), number_number_of(_96675, _96936))))]]], (1280 ^ _76106) ^ [_97079] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, one_one(int)), _97079)), _97079)), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _97079), zero_zero(int))))], (1286 ^ _76106) ^ [_97212] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _97212), zero_zero(int))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, one_one(int)), _97212)), _97212)), zero_zero(int))))], (1292 ^ _76106) ^ [_97351] : [linord219039673up_add(_97351), 1295 ^ _76106 : [(1296 ^ _76106) ^ [_97437] : [hAPP(_97351, _97351, plus_plus(_97351, _97437), _97437) = zero_zero(_97351), -(ti(_97351, _97437) = zero_zero(_97351))], (1302 ^ _76106) ^ [_97540] : [ti(_97351, _97540) = zero_zero(_97351), -(hAPP(_97351, _97351, plus_plus(_97351, _97540), _97540) = zero_zero(_97351))]]], (1308 ^ _76106) ^ [_97662] : [hAPP(int, int, bit1, _97662) = pls], (1310 ^ _76106) ^ [_97699] : [pls = hAPP(int, int, bit1, _97699)], (1312 ^ _76106) ^ [_97739, _97741] : [hAPP(int, int, bit1, _97741) = hAPP(int, int, bit0, _97739)], (1314 ^ _76106) ^ [_97786, _97788] : [hAPP(int, int, bit0, _97788) = hAPP(int, int, bit1, _97786)], (1316 ^ _76106) ^ [_97833] : [hAPP(int, int, bit0, _97833) = pls, -(_97833 = pls)], (1322 ^ _76106) ^ [_97914] : [_97914 = pls, -(hAPP(int, int, bit0, _97914) = pls)], (1328 ^ _76106) ^ [_98013] : [pls = hAPP(int, int, bit0, _98013), -(pls = _98013)], (1334 ^ _76106) ^ [_98094] : [pls = _98094, -(pls = hAPP(int, int, bit0, _98094))], (1340 ^ _76106) ^ [] : [-(hAPP(int, int, bit0, pls) = pls)], (1342 ^ _76106) ^ [] : [-(pls = zero_zero(int))], (1344 ^ _76106) ^ [] : [zero_zero(int) = one_one(int)], (1346 ^ _76106) ^ [_98241] : [-(hAPP(int, int, plus_plus(int, _98241), pls) = _98241)], (1348 ^ _76106) ^ [_98272] : [-(hAPP(int, int, plus_plus(int, pls), _98272) = _98272)], (1350 ^ _76106) ^ [_98300, _98302] : [-(hAPP(int, int, plus_plus(int, hAPP(int, int, bit0, _98302)), hAPP(int, int, bit0, _98300)) = hAPP(int, int, bit0, hAPP(int, int, plus_plus(int, _98302), _98300)))], (1352 ^ _76106) ^ [_98356] : [-(hAPP(int, int, bit0, _98356) = hAPP(int, int, plus_plus(int, _98356), _98356))], (1354 ^ _76106) ^ [_98392] : [-(hAPP(int, int, plus_plus(int, _98392), zero_zero(int)) = _98392)], (1356 ^ _76106) ^ [_98423] : [-(hAPP(int, int, plus_plus(int, zero_zero(int)), _98423) = _98423)], (1358 ^ _76106) ^ [_98451] : [number_semiring(_98451), -(number_number_of(_98451, pls) = zero_zero(_98451))], (1364 ^ _76106) ^ [_98534] : [number_ring(_98534), -(number_number_of(_98534, pls) = zero_zero(_98534))], (1370 ^ _76106) ^ [_98617] : [number_ring(_98617), -(zero_zero(_98617) = number_number_of(_98617, pls))], (1376 ^ _76106) ^ [_98700] : [number_ring(_98700), 1379 ^ _76106 : [(1380 ^ _76106) ^ [_98769] : [-(hAPP(_98700, _98700, plus_plus(_98700, number_number_of(_98700, pls)), _98769) = ti(_98700, _98769))]]], (1382 ^ _76106) ^ [_98810] : [number_ring(_98810), 1385 ^ _76106 : [(1386 ^ _76106) ^ [_98879] : [-(hAPP(_98810, _98810, plus_plus(_98810, _98879), number_number_of(_98810, pls)) = ti(_98810, _98879))]]], (1388 ^ _76106) ^ [_98920] : [power(_98920), mult_zero(_98920), no_zero_divisors(_98920), zero_neq_one(_98920), 1403 ^ _76106 : [(1404 ^ _76106) ^ [_99172, _99174] : [hAPP(nat, _98920, power_power(_98920, _99174), number_number_of(nat, _99172)) = zero_zero(_98920), 1407 ^ _76106 : [(1408 ^ _76106) ^ [] : [-(ti(_98920, _99174) = zero_zero(_98920))], (1410 ^ _76106) ^ [] : [number_number_of(nat, _99172) = zero_zero(nat)]]], (1412 ^ _76106) ^ [_99323, _99325] : [-(hAPP(nat, _98920, power_power(_98920, _99325), number_number_of(nat, _99323)) = zero_zero(_98920)), ti(_98920, _99325) = zero_zero(_98920), -(number_number_of(nat, _99323) = zero_zero(nat))]]], (1422 ^ _76106) ^ [_99513] : [number_ring(_99513), 1425 ^ _76106 : [(1426 ^ _76106) ^ [_99619, _99621, _99623] : [-(hAPP(_99513, _99513, plus_plus(_99513, number_number_of(_99513, _99623)), hAPP(_99513, _99513, plus_plus(_99513, number_number_of(_99513, _99621)), _99619)) = hAPP(_99513, _99513, plus_plus(_99513, number_number_of(_99513, hAPP(int, int, plus_plus(int, _99623), _99621))), _99619))]]], (1428 ^ _76106) ^ [_99691] : [number_ring(_99691), 1431 ^ _76106 : [(1432 ^ _76106) ^ [_99776, _99778] : [-(hAPP(_99691, _99691, plus_plus(_99691, number_number_of(_99691, _99778)), number_number_of(_99691, _99776)) = number_number_of(_99691, hAPP(int, int, plus_plus(int, _99778), _99776)))]]], (1434 ^ _76106) ^ [_99830] : [number_ring(_99830), 1437 ^ _76106 : [(1438 ^ _76106) ^ [_99915, _99917] : [-(number_number_of(_99830, hAPP(int, int, plus_plus(int, _99917), _99915)) = hAPP(_99830, _99830, plus_plus(_99830, number_number_of(_99830, _99917)), number_number_of(_99830, _99915)))]]], (1440 ^ _76106) ^ [_99969, _99971] : [-(hAPP(int, int, plus_plus(int, hAPP(int, int, bit1, _99971)), hAPP(int, int, bit0, _99969)) = hAPP(int, int, bit1, hAPP(int, int, plus_plus(int, _99971), _99969)))], (1442 ^ _76106) ^ [_100025, _100027] : [-(hAPP(int, int, plus_plus(int, hAPP(int, int, bit0, _100027)), hAPP(int, int, bit1, _100025)) = hAPP(int, int, bit1, hAPP(int, int, plus_plus(int, _100027), _100025)))], (1444 ^ _76106) ^ [_100081] : [-(hAPP(int, int, bit1, _100081) = hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, one_one(int)), _100081)), _100081))], (1446 ^ _76106) ^ [_100131] : [hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, one_one(int)), _100131)), _100131) = zero_zero(int)], (1448 ^ _76106) ^ [_100167] : [number_semiring(_100167), 1451 ^ _76106 : [(1452 ^ _76106) ^ [_100237] : [-(number_number_of(_100167, hAPP(nat, int, semiring_1_of_nat(int), _100237)) = hAPP(nat, _100167, semiring_1_of_nat(_100167), _100237))]]], (1454 ^ _76106) ^ [_100279] : [linordered_idom(_100279), 1457 ^ _76106 : [(1458 ^ _76106) ^ [_100381] : [hBOOL(hAPP(_100279, bool, hAPP(_100279, fun(_100279, bool), ord_less(_100279), zero_zero(_100279)), hAPP(nat, _100279, power_power(_100279, _100381), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), ti(_100279, _100381) = zero_zero(_100279)], (1464 ^ _76106) ^ [_100511] : [-(ti(_100279, _100511) = zero_zero(_100279)), -(hBOOL(hAPP(_100279, bool, hAPP(_100279, fun(_100279, bool), ord_less(_100279), zero_zero(_100279)), hAPP(nat, _100279, power_power(_100279, _100511), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))))]]], (1470 ^ _76106) ^ [_100580] : [linordered_idom(_100580), 1473 ^ _76106 : [(1474 ^ _76106) ^ [_100663] : [hBOOL(hAPP(_100580, bool, hAPP(_100580, fun(_100580, bool), ord_less(_100580), hAPP(nat, _100580, power_power(_100580, _100663), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), zero_zero(_100580)))]]], (1476 ^ _76106) ^ [_100714] : [linordered_idom(_100714), 1479 ^ _76106 : [(1490 ^ _76106) ^ [_101083, _101085] : [1491 ^ _76106 : [(1492 ^ _76106) ^ [] : [-(ti(_100714, _101085) = zero_zero(_100714))], (1494 ^ _76106) ^ [] : [-(ti(_100714, _101083) = zero_zero(_100714))]], -(hBOOL(hAPP(_100714, bool, hAPP(_100714, fun(_100714, bool), ord_less(_100714), zero_zero(_100714)), hAPP(_100714, _100714, plus_plus(_100714, hAPP(nat, _100714, power_power(_100714, _101085), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _100714, power_power(_100714, _101083), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))))], (1480 ^ _76106) ^ [_100853, _100855] : [hBOOL(hAPP(_100714, bool, hAPP(_100714, fun(_100714, bool), ord_less(_100714), zero_zero(_100714)), hAPP(_100714, _100714, plus_plus(_100714, hAPP(nat, _100714, power_power(_100714, _100855), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _100714, power_power(_100714, _100853), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))), ti(_100714, _100855) = zero_zero(_100714), ti(_100714, _100853) = zero_zero(_100714)]]], (1498 ^ _76106) ^ [_101212] : [linordered_idom(_101212), 1501 ^ _76106 : [(1502 ^ _76106) ^ [_101319, _101321] : [hBOOL(hAPP(_101212, bool, hAPP(_101212, fun(_101212, bool), ord_less(_101212), hAPP(_101212, _101212, plus_plus(_101212, hAPP(nat, _101212, power_power(_101212, _101321), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _101212, power_power(_101212, _101319), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), zero_zero(_101212)))]]], (1504 ^ _76106) ^ [_101388] : [number_ring(_101388), 1507 ^ _76106 : [(1508 ^ _76106) ^ [_101475] : [-(number_number_of(_101388, hAPP(int, int, bit0, _101475)) = hAPP(_101388, _101388, plus_plus(_101388, hAPP(_101388, _101388, plus_plus(_101388, zero_zero(_101388)), number_number_of(_101388, _101475))), number_number_of(_101388, _101475)))]]], (1510 ^ _76106) ^ [_101534] : [number_ring(_101534), 1513 ^ _76106 : [(1514 ^ _76106) ^ [_101621] : [-(number_number_of(_101534, hAPP(int, int, bit1, _101621)) = hAPP(_101534, _101534, plus_plus(_101534, hAPP(_101534, _101534, plus_plus(_101534, one_one(_101534)), number_number_of(_101534, _101621))), number_number_of(_101534, _101621)))]]], (1516 ^ _76106) ^ [_101680] : [number_semiring(_101680), -(number_number_of(_101680, hAPP(int, int, bit1, pls)) = one_one(_101680))], (1522 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), m1), hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))))], (1524 ^ _76106) ^ [_101781] : [1531 ^ _76106 : [(1532 ^ _76106) ^ [_101916] : [-(hBOOL(hAPP(_101781, bool, hAPP(_101781, fun(_101781, bool), ord_less(_101781), hAPP(nat, _101781, semiring_1_of_nat(_101781), _101916)), hAPP(nat, _101781, power_power(_101781, number_number_of(_101781, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), _101916))))]], number_ring(_101781), linordered_idom(_101781)], (1534 ^ _76106) ^ [] : [-(number_number_of(int, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))) = hAPP(nat, int, semiring_1_of_nat(int), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))], (1536 ^ _76106) ^ [] : [-(number_number_of(int, hAPP(int, int, bit1, hAPP(int, int, bit1, pls))) = hAPP(nat, int, semiring_1_of_nat(int), number_number_of(nat, hAPP(int, int, bit1, hAPP(int, int, bit1, pls)))))], (1538 ^ _76106) ^ [_102026, _102028] : [hAPP(real, real, plus_plus(real, hAPP(nat, real, power_power(real, _102028), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, real, power_power(real, _102026), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))) = zero_zero(real), 1541 ^ _76106 : [(1542 ^ _76106) ^ [] : [-(_102028 = zero_zero(real))], (1544 ^ _76106) ^ [] : [-(_102026 = zero_zero(real))]]], (1546 ^ _76106) ^ [_102173, _102175] : [-(hAPP(real, real, plus_plus(real, hAPP(nat, real, power_power(real, _102175), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, real, power_power(real, _102173), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))) = zero_zero(real)), _102175 = zero_zero(real), _102173 = zero_zero(real)], (1556 ^ _76106) ^ [_102352] : [linordered_semidom(_102352), 1559 ^ _76106 : [(1560 ^ _76106) ^ [_102450] : [hBOOL(hAPP(_102352, bool, hAPP(_102352, fun(_102352, bool), ord_less(_102352), zero_zero(_102352)), hAPP(nat, _102352, semiring_1_of_nat(_102352), _102450))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _102450)))], (1566 ^ _76106) ^ [_102577] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _102577)), -(hBOOL(hAPP(_102352, bool, hAPP(_102352, fun(_102352, bool), ord_less(_102352), zero_zero(_102352)), hAPP(nat, _102352, semiring_1_of_nat(_102352), _102577))))]]], (1572 ^ _76106) ^ [_102714] : [linordered_semidom(_102714), 1575 ^ _76106 : [(1576 ^ _76106) ^ [_102828, _102830] : [hBOOL(hAPP(_102714, bool, hAPP(_102714, fun(_102714, bool), ord_less(_102714), one_one(_102714)), _102828)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _102830)), -(hBOOL(hAPP(_102714, bool, hAPP(_102714, fun(_102714, bool), ord_less(_102714), one_one(_102714)), hAPP(nat, _102714, power_power(_102714, _102828), _102830))))]]], (1586 ^ _76106) ^ [_103053] : [power(_103053), semiring_0(_103053), 1593 ^ _76106 : [(1594 ^ _76106) ^ [_103204] : [_103204 = zero_zero(nat), -(hAPP(nat, _103053, power_power(_103053, zero_zero(_103053)), _103204) = one_one(_103053))], (1600 ^ _76106) ^ [_103299] : [-(_103299 = zero_zero(nat)), -(hAPP(nat, _103053, power_power(_103053, zero_zero(_103053)), _103299) = zero_zero(_103053))]]], (1606 ^ _76106) ^ [_103353] : [linordered_semidom(_103353), 1609 ^ _76106 : [(1610 ^ _76106) ^ [_103505, _103507, _103509] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _103507), _103505)), hBOOL(hAPP(_103353, bool, hAPP(_103353, fun(_103353, bool), ord_less(_103353), zero_zero(_103353)), _103509)), hBOOL(hAPP(_103353, bool, hAPP(_103353, fun(_103353, bool), ord_less(_103353), _103509), one_one(_103353))), -(hBOOL(hAPP(_103353, bool, hAPP(_103353, fun(_103353, bool), ord_less(_103353), hAPP(nat, _103353, power_power(_103353, _103509), _103505)), hAPP(nat, _103353, power_power(_103353, _103509), _103507))))]]], (1624 ^ _76106) ^ [_103844] : [linordered_semidom(_103844), -(hBOOL(hAPP(_103844, bool, hAPP(_103844, fun(_103844, bool), ord_less(_103844), zero_zero(_103844)), hAPP(_103844, _103844, plus_plus(_103844, one_one(_103844)), one_one(_103844)))))], (1630 ^ _76106) ^ [_103973, _103975, _103977] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _103975), _103973)), hBOOL(hAPP(int, bool, _103977, hAPP(int, int, plus_plus(int, _103975), one_one(int)))), 1640 ^ _76106 : [(1641 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _103975), 1639 ^ [_103973, _103975, _103977])))], (1643 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, _103977, 1639 ^ [_103973, _103975, _103977])))], (1645 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, _103977, hAPP(int, int, plus_plus(int, 1639 ^ [_103973, _103975, _103977]), one_one(int))))]], -(hBOOL(hAPP(int, bool, _103977, _103973)))], (1649 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)))], (1651 ^ _76106) ^ [_104416] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104416), zero_zero(nat)))], (1653 ^ _76106) ^ [] : [zero_zero(real) = one_one(real)], (1655 ^ _76106) ^ [_104481] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104481), _104481))], (1657 ^ _76106) ^ [_104525, _104527] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _104527), _104525)), _104527))], (1659 ^ _76106) ^ [_104579, _104581] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _104581), _104579)), _104579))], (1661 ^ _76106) ^ [_104621] : [-(number_number_of(int, _104621) = _104621)], (1673 ^ _76106) ^ [_104713, _104715] : [1674 ^ _76106 : [(1675 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104715), _104713))], (1677 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104713), _104715))]], _104715 = _104713], (1663 ^ _76106) ^ [_104656, _104658] : [-(_104658 = _104656), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104658), _104656))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _104656), _104658)))], (1681 ^ _76106) ^ [_104867, _104869] : [-(hAPP(nat, nat, plus_plus(nat, _104869), _104867) = hAPP(nat, nat, plus_plus(nat, _104867), _104869))], (1683 ^ _76106) ^ [_104908, _104910, _104912] : [-(hAPP(nat, nat, plus_plus(nat, _104912), hAPP(nat, nat, plus_plus(nat, _104910), _104908)) = hAPP(nat, nat, plus_plus(nat, _104910), hAPP(nat, nat, plus_plus(nat, _104912), _104908)))], (1685 ^ _76106) ^ [_104967, _104969, _104971] : [-(hAPP(nat, nat, plus_plus(nat, hAPP(nat, nat, plus_plus(nat, _104971), _104969)), _104967) = hAPP(nat, nat, plus_plus(nat, _104971), hAPP(nat, nat, plus_plus(nat, _104969), _104967)))], (1687 ^ _76106) ^ [_105044, _105046, _105048] : [hAPP(nat, nat, plus_plus(nat, _105048), _105046) = hAPP(nat, nat, plus_plus(nat, _105048), _105044), -(_105046 = _105044)], (1693 ^ _76106) ^ [_105151, _105153, _105155] : [_105153 = _105151, -(hAPP(nat, nat, plus_plus(nat, _105155), _105153) = hAPP(nat, nat, plus_plus(nat, _105155), _105151))], (1699 ^ _76106) ^ [_105282, _105284, _105286] : [hAPP(nat, nat, plus_plus(nat, _105286), _105284) = hAPP(nat, nat, plus_plus(nat, _105282), _105284), -(_105286 = _105282)], (1705 ^ _76106) ^ [_105389, _105391, _105393] : [_105393 = _105389, -(hAPP(nat, nat, plus_plus(nat, _105393), _105391) = hAPP(nat, nat, plus_plus(nat, _105389), _105391))], (1711 ^ _76106) ^ [_105520, _105522, _105524] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _105524), _105522)), hAPP(nat, nat, plus_plus(nat, _105524), _105520))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105522), _105520)))], (1717 ^ _76106) ^ [_105663, _105665, _105667] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105665), _105663)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _105667), _105665)), hAPP(nat, nat, plus_plus(nat, _105667), _105663))))], (1723 ^ _76106) ^ [_105808, _105810] : [-(_105810 = _105808), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105810), _105808))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105808), _105810)))], (1733 ^ _76106) ^ [_105878] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105878), _105878))], (1735 ^ _76106) ^ [_105910, _105912] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _105912), _105910)), _105910 = _105912], (1741 ^ _76106) ^ [_106006, _106008] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106008), _106006)), _106008 = _106006], (1747 ^ _76106) ^ [_106102, _106104, _106106] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106104), _106102)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106104), hAPP(nat, nat, plus_plus(nat, _106102), _106106))))], (1753 ^ _76106) ^ [_106233, _106235, _106237] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106235), _106233)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106235), hAPP(nat, nat, plus_plus(nat, _106237), _106233))))], (1759 ^ _76106) ^ [_106364, _106366, _106368] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106366), _106364)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _106366), _106368)), hAPP(nat, nat, plus_plus(nat, _106364), _106368))))], (1765 ^ _76106) ^ [_106511, _106513, _106515, _106517] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106513), _106511)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106517), _106515)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _106513), _106517)), hAPP(nat, nat, plus_plus(nat, _106511), _106515))))], (1775 ^ _76106) ^ [_106734, _106736, _106738, _106740] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106736), _106734)), hAPP(nat, nat, plus_plus(nat, _106740), _106734) = hAPP(nat, nat, plus_plus(nat, _106736), _106738), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106740), _106738)))], (1785 ^ _76106) ^ [_106939, _106941, _106943] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, plus_plus(nat, _106943), _106941)), _106939)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _106943), _106939)))], (1791 ^ _76106) ^ [_107070, _107072, _107074] : [1792 ^ _76106 : [(1793 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _107072), _107070)))], (1795 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _107074, _107070), _107072))]], 1798 ^ _76106 : [(1799 ^ _76106) ^ [] : [-(_107072 = _107070)], (1801 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _107074, _107070), _107072))]], 1804 ^ _76106 : [(1805 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _107070), _107072)))], (1807 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _107074, _107070), _107072))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), _107074, _107070), _107072)))], (1811 ^ _76106) ^ [_107460] : [-(_107460 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _107460)))], (1817 ^ _76106) ^ [_107498, _107500] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _107500), _107498)), _107498 = zero_zero(nat)], (1823 ^ _76106) ^ [_107594, _107596, _107598] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _107594)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, power_power(nat, _107594), _107598)), hAPP(nat, nat, power_power(nat, _107594), _107596))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _107598), _107596)))], (1833 ^ _76106) ^ [_107812] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _107812), zero_zero(nat)))], (1845 ^ _76106) ^ [_107977, _107979] : [1846 ^ _76106 : [(1847 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _107979))], (1849 ^ _76106) ^ [] : [_107977 = zero_zero(nat)]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _107979), _107977))))], (1835 ^ _76106) ^ [_107859, _107861] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _107861), _107859))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _107861))), -(_107859 = zero_zero(nat))], (1863 ^ _76106) ^ [_108267, _108269] : [1864 ^ _76106 : [(1865 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108269))], (1867 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108267))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, plus_plus(nat, _108269), _108267))))], (1853 ^ _76106) ^ [_108141, _108143] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, plus_plus(nat, _108143), _108141))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108143))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108141)))], (1871 ^ _76106) ^ [_108430] : [-(_108430 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108430)))], (1877 ^ _76106) ^ [_108464] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108464)), _108464 = zero_zero(nat)], (1883 ^ _76106) ^ [_108559] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _108559), zero_zero(nat)))], (1895 ^ _76106) ^ [_108724, _108726] : [1896 ^ _76106 : [(1897 ^ _76106) ^ [] : [_108724 = zero_zero(nat)], (1899 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108726))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _108726), _108724))))], (1885 ^ _76106) ^ [_108606, _108608] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _108608), _108606))), -(_108606 = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _108608)))], (1903 ^ _76106) ^ [_108888, _108890] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _108890)), hAPP(nat, int, semiring_1_of_nat(int), _108888))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _108890), _108888)))], (1909 ^ _76106) ^ [_109017, _109019] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _109019), _109017)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _109019)), hAPP(nat, int, semiring_1_of_nat(int), _109017))))], (1925 ^ _76106) ^ [_109297, _109299] : [1926 ^ _76106 : [(1927 ^ _76106) ^ [] : [number_number_of(nat, _109297) = zero_zero(nat)], (1929 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _109299))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _109299), number_number_of(nat, _109297)))))], (1915 ^ _76106) ^ [_109167, _109169] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), hAPP(nat, nat, power_power(nat, _109169), number_number_of(nat, _109167)))), -(number_number_of(nat, _109167) = zero_zero(nat)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _109169)))], (1933 ^ _76106) ^ [_109473, _109475] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _109475)), hAPP(nat, int, semiring_1_of_nat(int), _109473))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _109475), _109473)))], (1939 ^ _76106) ^ [_109602, _109604] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _109604), _109602)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, semiring_1_of_nat(int), _109604)), hAPP(nat, int, semiring_1_of_nat(int), _109602))))], (1945 ^ _76106) ^ [_109752, _109754] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), number_number_of(nat, _109754)), number_number_of(nat, _109752))), 1948 ^ _76106 : [(1955 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _109754), _109752)))], (1949 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _109754), _109752)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _109752)))]]], (1957 ^ _76106) ^ [_109983, _109985] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), number_number_of(nat, _109985)), number_number_of(nat, _109983)))), 1960 ^ _76106 : [(1961 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _109985), _109983)))], (1963 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _109983))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _109985), _109983))], (1969 ^ _76106) ^ [_110221] : [linordered_idom(_110221), 1972 ^ _76106 : [(1973 ^ _76106) ^ [_110327, _110329] : [-(ti(_110221, _110329) = ti(_110221, _110327)), -(hBOOL(hAPP(_110221, bool, hAPP(_110221, fun(_110221, bool), ord_less(_110221), _110329), _110327))), -(hBOOL(hAPP(_110221, bool, hAPP(_110221, fun(_110221, bool), ord_less(_110221), _110327), _110329)))]]], (1983 ^ _76106) ^ [_110408, _110410] : [hAPP(nat, nat, plus_plus(nat, _110410), _110408) = _110410, -(_110408 = zero_zero(nat))], (1989 ^ _76106) ^ [_110516, _110518] : [hAPP(nat, nat, plus_plus(nat, _110518), _110516) = zero_zero(nat), 1992 ^ _76106 : [(1993 ^ _76106) ^ [] : [-(_110518 = zero_zero(nat))], (1995 ^ _76106) ^ [] : [-(_110516 = zero_zero(nat))]]], (1997 ^ _76106) ^ [_110631, _110633] : [-(hAPP(nat, nat, plus_plus(nat, _110633), _110631) = zero_zero(nat)), _110633 = zero_zero(nat), _110631 = zero_zero(nat)], (2007 ^ _76106) ^ [_110778] : [-(hAPP(nat, nat, plus_plus(nat, _110778), zero_zero(nat)) = _110778)], (2009 ^ _76106) ^ [_110809] : [-(hAPP(nat, nat, plus_plus(nat, zero_zero(nat)), _110809) = _110809)], (2011 ^ _76106) ^ [_110837] : [monoid_mult(_110837), 2014 ^ _76106 : [(2015 ^ _76106) ^ [_110903] : [-(hAPP(nat, _110837, power_power(_110837, _110903), one_one(nat)) = ti(_110837, _110903))]]], (2017 ^ _76106) ^ [_110941] : [semiring_char_0(_110941), 2020 ^ _76106 : [(2021 ^ _76106) ^ [_111034, _111036] : [hAPP(nat, _110941, semiring_1_of_nat(_110941), _111036) = hAPP(nat, _110941, semiring_1_of_nat(_110941), _111034), -(_111036 = _111034)], (2027 ^ _76106) ^ [_111137, _111139] : [_111139 = _111137, -(hAPP(nat, _110941, semiring_1_of_nat(_110941), _111139) = hAPP(nat, _110941, semiring_1_of_nat(_110941), _111137))]]], (2033 ^ _76106) ^ [_111265, _111267] : [hAPP(nat, int, semiring_1_of_nat(int), _111267) = hAPP(nat, int, semiring_1_of_nat(int), _111265), -(_111267 = _111265)], (2039 ^ _76106) ^ [_111358, _111360] : [_111360 = _111358, -(hAPP(nat, int, semiring_1_of_nat(int), _111360) = hAPP(nat, int, semiring_1_of_nat(int), _111358))], (2045 ^ _76106) ^ [_111469, _111471, _111473] : [hBOOL(_111469), -(hAPP(nat, int, semiring_1_of_nat(int), _111473) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, hAPP(nat, fun(nat, nat), hAPP(bool, fun(nat, fun(nat, nat)), (if nat), _111469), _111473), _111471)))], (2051 ^ _76106) ^ [_111590, _111592, _111594] : [-(hBOOL(_111590)), -(hAPP(nat, int, semiring_1_of_nat(int), _111592) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, hAPP(nat, fun(nat, nat), hAPP(bool, fun(nat, fun(nat, nat)), (if nat), _111590), _111594), _111592)))], (2057 ^ _76106) ^ [_111666] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, _111666))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _111666)))], (2063 ^ _76106) ^ [_111759] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), _111759)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, _111759))))], (2069 ^ _76106) ^ [_111870] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _111870))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _111870)))], (2075 ^ _76106) ^ [_111967] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _111967)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _111967))))], (2081 ^ _76106) ^ [_112070] : [zero_neq_one(_112070), one_one(_112070) = zero_zero(_112070)], (2087 ^ _76106) ^ [_112152] : [zero_neq_one(_112152), zero_zero(_112152) = one_one(_112152)], (2093 ^ _76106) ^ [_112234] : [ring_11004092258visors(_112234), 2096 ^ _76106 : [(2097 ^ _76106) ^ [_112316, _112318] : [-(ti(_112234, _112316) = zero_zero(_112234)), hAPP(nat, _112234, power_power(_112234, _112316), _112318) = zero_zero(_112234)]]], (2103 ^ _76106) ^ [_112424] : [monoid_mult(_112424), 2106 ^ _76106 : [(2107 ^ _76106) ^ [_112491] : [-(hAPP(nat, _112424, power_power(_112424, one_one(_112424)), _112491) = one_one(_112424))]]], (2109 ^ _76106) ^ [_112530] : [linordered_semidom(_112530), 2112 ^ _76106 : [(2113 ^ _76106) ^ [_112646, _112648] : [hBOOL(hAPP(_112530, bool, hAPP(_112530, fun(_112530, bool), ord_less(_112530), hAPP(nat, _112530, semiring_1_of_nat(_112530), _112648)), hAPP(nat, _112530, semiring_1_of_nat(_112530), _112646))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _112648), _112646)))], (2119 ^ _76106) ^ [_112795, _112797] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _112797), _112795)), -(hBOOL(hAPP(_112530, bool, hAPP(_112530, fun(_112530, bool), ord_less(_112530), hAPP(nat, _112530, semiring_1_of_nat(_112530), _112797)), hAPP(nat, _112530, semiring_1_of_nat(_112530), _112795))))]]], (2125 ^ _76106) ^ [_112954] : [linordered_semidom(_112954), 2128 ^ _76106 : [(2129 ^ _76106) ^ [_113055, _113057] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _113057), _113055)), -(hBOOL(hAPP(_112954, bool, hAPP(_112954, fun(_112954, bool), ord_less(_112954), hAPP(nat, _112954, semiring_1_of_nat(_112954), _113057)), hAPP(nat, _112954, semiring_1_of_nat(_112954), _113055))))]]], (2135 ^ _76106) ^ [_113212] : [linordered_semidom(_113212), 2138 ^ _76106 : [(2139 ^ _76106) ^ [_113313, _113315] : [hBOOL(hAPP(_113212, bool, hAPP(_113212, fun(_113212, bool), ord_less(_113212), hAPP(nat, _113212, semiring_1_of_nat(_113212), _113315)), hAPP(nat, _113212, semiring_1_of_nat(_113212), _113313))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _113315), _113313)))]]], (2145 ^ _76106) ^ [_113470] : [semiring_1(_113470), 2148 ^ _76106 : [(2149 ^ _76106) ^ [_113567, _113569] : [-(hAPP(nat, _113470, semiring_1_of_nat(_113470), hAPP(nat, nat, plus_plus(nat, _113569), _113567)) = hAPP(_113470, _113470, plus_plus(_113470, hAPP(nat, _113470, semiring_1_of_nat(_113470), _113569)), hAPP(nat, _113470, semiring_1_of_nat(_113470), _113567)))]]], (2151 ^ _76106) ^ [_113633] : [semiring_1(_113633), -(hAPP(nat, _113633, semiring_1_of_nat(_113633), one_one(nat)) = one_one(_113633))], (2157 ^ _76106) ^ [_113724] : [semiring_1(_113724), 2160 ^ _76106 : [(2161 ^ _76106) ^ [_113814, _113816] : [-(hAPP(nat, _113724, semiring_1_of_nat(_113724), hAPP(nat, nat, power_power(nat, _113816), _113814)) = hAPP(nat, _113724, power_power(_113724, hAPP(nat, _113724, semiring_1_of_nat(_113724), _113816)), _113814))]]], (2163 ^ _76106) ^ [] : [-(one_one(int) = hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)))], (2165 ^ _76106) ^ [_113891, _113893] : [-(hAPP(int, int, plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), _113893)), hAPP(nat, int, semiring_1_of_nat(int), _113891)) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, plus_plus(nat, _113893), _113891)))], (2167 ^ _76106) ^ [_113947, _113949] : [-(hAPP(nat, int, power_power(int, hAPP(nat, int, semiring_1_of_nat(int), _113949)), _113947) = hAPP(nat, int, semiring_1_of_nat(int), hAPP(nat, nat, power_power(nat, _113949), _113947)))], (2169 ^ _76106) ^ [_113998] : [linordered_semidom(_113998), 2172 ^ _76106 : [(2173 ^ _76106) ^ [_114125, _114127, _114129] : [hBOOL(hAPP(_113998, bool, hAPP(_113998, fun(_113998, bool), ord_less(_113998), zero_zero(_113998)), _114125)), hBOOL(hAPP(_113998, bool, hAPP(_113998, fun(_113998, bool), ord_less(_113998), _114129), _114127)), -(hBOOL(hAPP(_113998, bool, hAPP(_113998, fun(_113998, bool), ord_less(_113998), _114129), hAPP(_113998, _113998, plus_plus(_113998, _114125), _114127))))]]], (2183 ^ _76106) ^ [_114370] : [linordered_semidom(_114370), hBOOL(hAPP(_114370, bool, hAPP(_114370, fun(_114370, bool), ord_less(_114370), one_one(_114370)), zero_zero(_114370)))], (2189 ^ _76106) ^ [_114480] : [linordered_semidom(_114480), -(hBOOL(hAPP(_114480, bool, hAPP(_114480, fun(_114480, bool), ord_less(_114480), zero_zero(_114480)), one_one(_114480))))], (2195 ^ _76106) ^ [_114589] : [linordered_semidom(_114589), 2198 ^ _76106 : [(2199 ^ _76106) ^ [_114693, _114695] : [hBOOL(hAPP(_114589, bool, hAPP(_114589, fun(_114589, bool), ord_less(_114589), zero_zero(_114589)), _114693)), -(hBOOL(hAPP(_114589, bool, hAPP(_114589, fun(_114589, bool), ord_less(_114589), zero_zero(_114589)), hAPP(nat, _114589, power_power(_114589, _114693), _114695))))]]], (2205 ^ _76106) ^ [_114856] : [linordered_semidom(_114856), 2208 ^ _76106 : [(2209 ^ _76106) ^ [_114935] : [-(hBOOL(hAPP(_114856, bool, hAPP(_114856, fun(_114856, bool), ord_less(_114856), _114935), hAPP(_114856, _114856, plus_plus(_114856, _114935), one_one(_114856)))))]]], (2211 ^ _76106) ^ [_114986] : [linordered_semidom(_114986), 2214 ^ _76106 : [(2215 ^ _76106) ^ [_115093, _115095, _115097] : [hBOOL(hAPP(_114986, bool, hAPP(_114986, fun(_114986, bool), ord_less(_114986), one_one(_114986)), _115093)), 2218 ^ _76106 : [(2219 ^ _76106) ^ [] : [hAPP(nat, _114986, power_power(_114986, _115093), _115097) = hAPP(nat, _114986, power_power(_114986, _115093), _115095), -(_115097 = _115095)], (2225 ^ _76106) ^ [] : [_115097 = _115095, -(hAPP(nat, _114986, power_power(_114986, _115093), _115097) = hAPP(nat, _114986, power_power(_114986, _115093), _115095))]]]]], (2231 ^ _76106) ^ [_115396] : [linordered_semidom(_115396), 2234 ^ _76106 : [(2235 ^ _76106) ^ [_115526, _115528, _115530] : [hBOOL(hAPP(_115396, bool, hAPP(_115396, fun(_115396, bool), ord_less(_115396), one_one(_115396)), _115526)), 2238 ^ _76106 : [(2239 ^ _76106) ^ [] : [hBOOL(hAPP(_115396, bool, hAPP(_115396, fun(_115396, bool), ord_less(_115396), hAPP(nat, _115396, power_power(_115396, _115526), _115530)), hAPP(nat, _115396, power_power(_115396, _115526), _115528))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _115530), _115528)))], (2245 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _115530), _115528)), -(hBOOL(hAPP(_115396, bool, hAPP(_115396, fun(_115396, bool), ord_less(_115396), hAPP(nat, _115396, power_power(_115396, _115526), _115530)), hAPP(nat, _115396, power_power(_115396, _115526), _115528))))]]]]], (2251 ^ _76106) ^ [_115898] : [linordered_semidom(_115898), 2254 ^ _76106 : [(2255 ^ _76106) ^ [_116028, _116030, _116032] : [hBOOL(hAPP(_115898, bool, hAPP(_115898, fun(_115898, bool), ord_less(_115898), one_one(_115898)), _116028)), hBOOL(hAPP(_115898, bool, hAPP(_115898, fun(_115898, bool), ord_less(_115898), hAPP(nat, _115898, power_power(_115898, _116028), _116032)), hAPP(nat, _115898, power_power(_115898, _116028), _116030))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _116032), _116030)))]]], (2265 ^ _76106) ^ [_116279] : [linordered_semidom(_116279), 2268 ^ _76106 : [(2269 ^ _76106) ^ [_116409, _116411, _116413] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _116411), _116409)), hBOOL(hAPP(_116279, bool, hAPP(_116279, fun(_116279, bool), ord_less(_116279), one_one(_116279)), _116413)), -(hBOOL(hAPP(_116279, bool, hAPP(_116279, fun(_116279, bool), ord_less(_116279), hAPP(nat, _116279, power_power(_116279, _116413), _116411)), hAPP(nat, _116279, power_power(_116279, _116413), _116409))))]]], (2279 ^ _76106) ^ [_116758] : [power(_116758), mult_zero(_116758), no_zero_divisors(_116758), zero_neq_one(_116758), 2294 ^ _76106 : [(2295 ^ _76106) ^ [_117209, _117211] : [hAPP(nat, _116758, power_power(_116758, _117211), _117209) = zero_zero(_116758), 2298 ^ _76106 : [(2299 ^ _76106) ^ [] : [-(ti(_116758, _117211) = zero_zero(_116758))], (2301 ^ _76106) ^ [] : [_117209 = zero_zero(nat)]]], (2303 ^ _76106) ^ [_117487, _117489] : [-(hAPP(nat, _116758, power_power(_116758, _117489), _117487) = zero_zero(_116758)), ti(_116758, _117489) = zero_zero(_116758), -(_117487 = zero_zero(nat))]]], (2313 ^ _76106) ^ [_117830] : [linordered_semidom(_117830), 2316 ^ _76106 : [(2317 ^ _76106) ^ [_117964] : [hBOOL(hAPP(_117830, bool, hAPP(_117830, fun(_117830, bool), ord_less(_117830), hAPP(nat, _117830, semiring_1_of_nat(_117830), _117964)), zero_zero(_117830)))]]], (2319 ^ _76106) ^ [_118087] : [power(_118087), 2322 ^ _76106 : [(2323 ^ _76106) ^ [_118207] : [-(hAPP(nat, _118087, power_power(_118087, _118207), zero_zero(nat)) = one_one(_118087))]]], (2325 ^ _76106) ^ [_118317] : [semiring_1(_118317), -(hAPP(nat, _118317, semiring_1_of_nat(_118317), zero_zero(nat)) = zero_zero(_118317))], (2331 ^ _76106) ^ [] : [-(zero_zero(int) = hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))], (2333 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))], (2335 ^ _76106) ^ [_118629] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _118629)), 2339 ^ _76106 : [(2340 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), 2338 ^ [_118629])))], (2342 ^ _76106) ^ [] : [-(_118629 = hAPP(nat, int, semiring_1_of_nat(int), 2338 ^ [_118629]))]]], (2344 ^ _76106) ^ [_119003, _119005] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _119005), _119003)), 2348 ^ _76106 : [(2349 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), 2347 ^ [_119003, _119005])))], (2351 ^ _76106) ^ [] : [-(hAPP(nat, nat, plus_plus(nat, _119005), 2347 ^ [_119003, _119005]) = _119003)]]], (2363 ^ _76106) ^ [_119709, _119711] : [2364 ^ _76106 : [(2365 ^ _76106) ^ [] : [_119711 = one_one(nat)], (2367 ^ _76106) ^ [] : [_119709 = zero_zero(nat)]], -(hAPP(nat, nat, power_power(nat, _119711), _119709) = one_one(nat))], (2353 ^ _76106) ^ [_119441, _119443] : [hAPP(nat, nat, power_power(nat, _119443), _119441) = one_one(nat), -(_119443 = one_one(nat)), -(_119441 = zero_zero(nat))], (2371 ^ _76106) ^ [_119997] : [comm_semiring_1(_119997), 2374 ^ _76106 : [(2375 ^ _76106) ^ [_120117] : [-(hAPP(nat, _119997, power_power(_119997, _120117), zero_zero(nat)) = one_one(_119997))]]], (2377 ^ _76106) ^ [_120227] : [linord219039673up_add(_120227), 2380 ^ _76106 : [(2381 ^ _76106) ^ [_120427] : [hBOOL(hAPP(_120227, bool, hAPP(_120227, fun(_120227, bool), ord_less(_120227), zero_zero(_120227)), hAPP(_120227, _120227, plus_plus(_120227, _120427), _120427))), -(hBOOL(hAPP(_120227, bool, hAPP(_120227, fun(_120227, bool), ord_less(_120227), zero_zero(_120227)), _120427)))], (2387 ^ _76106) ^ [_120671] : [hBOOL(hAPP(_120227, bool, hAPP(_120227, fun(_120227, bool), ord_less(_120227), zero_zero(_120227)), _120671)), -(hBOOL(hAPP(_120227, bool, hAPP(_120227, fun(_120227, bool), ord_less(_120227), zero_zero(_120227)), hAPP(_120227, _120227, plus_plus(_120227, _120671), _120671))))]]], (2393 ^ _76106) ^ [_120956] : [linord219039673up_add(_120956), 2396 ^ _76106 : [(2397 ^ _76106) ^ [_121156] : [hBOOL(hAPP(_120956, bool, hAPP(_120956, fun(_120956, bool), ord_less(_120956), hAPP(_120956, _120956, plus_plus(_120956, _121156), _121156)), zero_zero(_120956))), -(hBOOL(hAPP(_120956, bool, hAPP(_120956, fun(_120956, bool), ord_less(_120956), _121156), zero_zero(_120956))))], (2403 ^ _76106) ^ [_121400] : [hBOOL(hAPP(_120956, bool, hAPP(_120956, fun(_120956, bool), ord_less(_120956), _121400), zero_zero(_120956))), -(hBOOL(hAPP(_120956, bool, hAPP(_120956, fun(_120956, bool), ord_less(_120956), hAPP(_120956, _120956, plus_plus(_120956, _121400), _121400)), zero_zero(_120956))))]]], (2409 ^ _76106) ^ [_121685] : [zero(_121685), 2412 ^ _76106 : [(2413 ^ _76106) ^ [_121855] : [zero_zero(_121685) = ti(_121685, _121855), -(ti(_121685, _121855) = zero_zero(_121685))], (2419 ^ _76106) ^ [_122039] : [ti(_121685, _122039) = zero_zero(_121685), -(zero_zero(_121685) = ti(_121685, _122039))]]], (2425 ^ _76106) ^ [_122264] : [cancel_semigroup_add(_122264), 2428 ^ _76106 : [(2429 ^ _76106) ^ [_122455, _122457, _122459] : [hAPP(_122264, _122264, plus_plus(_122264, _122459), _122457) = hAPP(_122264, _122264, plus_plus(_122264, _122455), _122457), -(ti(_122264, _122459) = ti(_122264, _122455))]]], (2435 ^ _76106) ^ [_122714] : [cancel146912293up_add(_122714), 2438 ^ _76106 : [(2439 ^ _76106) ^ [_122905, _122907, _122909] : [hAPP(_122714, _122714, plus_plus(_122714, _122909), _122907) = hAPP(_122714, _122714, plus_plus(_122714, _122909), _122905), -(ti(_122714, _122907) = ti(_122714, _122905))]]], (2445 ^ _76106) ^ [_123164] : [cancel_semigroup_add(_123164), 2448 ^ _76106 : [(2449 ^ _76106) ^ [_123355, _123357, _123359] : [hAPP(_123164, _123164, plus_plus(_123164, _123359), _123357) = hAPP(_123164, _123164, plus_plus(_123164, _123359), _123355), -(ti(_123164, _123357) = ti(_123164, _123355))]]], (2455 ^ _76106) ^ [_123614] : [comm_semiring_1(_123614), 2458 ^ _76106 : [(2459 ^ _76106) ^ [_123829, _123831, _123833, _123835] : [-(hAPP(_123614, _123614, plus_plus(_123614, hAPP(_123614, _123614, plus_plus(_123614, _123835), _123833)), hAPP(_123614, _123614, plus_plus(_123614, _123831), _123829)) = hAPP(_123614, _123614, plus_plus(_123614, hAPP(_123614, _123614, plus_plus(_123614, _123835), _123831)), hAPP(_123614, _123614, plus_plus(_123614, _123833), _123829)))]]], (2461 ^ _76106) ^ [_123983] : [cancel_semigroup_add(_123983), 2464 ^ _76106 : [(2465 ^ _76106) ^ [_124203, _124205, _124207] : [hAPP(_123983, _123983, plus_plus(_123983, _124207), _124205) = hAPP(_123983, _123983, plus_plus(_123983, _124203), _124205), -(ti(_123983, _124207) = ti(_123983, _124203))], (2471 ^ _76106) ^ [_124423, _124425, _124427] : [ti(_123983, _124427) = ti(_123983, _124423), -(hAPP(_123983, _123983, plus_plus(_123983, _124427), _124425) = hAPP(_123983, _123983, plus_plus(_123983, _124423), _124425))]]], (2477 ^ _76106) ^ [_124684] : [cancel_semigroup_add(_124684), 2480 ^ _76106 : [(2481 ^ _76106) ^ [_124904, _124906, _124908] : [hAPP(_124684, _124684, plus_plus(_124684, _124908), _124906) = hAPP(_124684, _124684, plus_plus(_124684, _124908), _124904), -(ti(_124684, _124906) = ti(_124684, _124904))], (2487 ^ _76106) ^ [_125124, _125126, _125128] : [ti(_124684, _125126) = ti(_124684, _125124), -(hAPP(_124684, _124684, plus_plus(_124684, _125128), _125126) = hAPP(_124684, _124684, plus_plus(_124684, _125128), _125124))]]], (2493 ^ _76106) ^ [_125385] : [comm_semiring_1(_125385), 2496 ^ _76106 : [(2497 ^ _76106) ^ [_125565, _125567, _125569] : [-(hAPP(_125385, _125385, plus_plus(_125385, hAPP(_125385, _125385, plus_plus(_125385, _125569), _125567)), _125565) = hAPP(_125385, _125385, plus_plus(_125385, hAPP(_125385, _125385, plus_plus(_125385, _125569), _125565)), _125567))]]], (2499 ^ _76106) ^ [_125701] : [ab_semigroup_add(_125701), 2502 ^ _76106 : [(2503 ^ _76106) ^ [_125881, _125883, _125885] : [-(hAPP(_125701, _125701, plus_plus(_125701, hAPP(_125701, _125701, plus_plus(_125701, _125885), _125883)), _125881) = hAPP(_125701, _125701, plus_plus(_125701, _125885), hAPP(_125701, _125701, plus_plus(_125701, _125883), _125881)))]]], (2505 ^ _76106) ^ [_126017] : [comm_semiring_1(_126017), 2508 ^ _76106 : [(2509 ^ _76106) ^ [_126197, _126199, _126201] : [-(hAPP(_126017, _126017, plus_plus(_126017, hAPP(_126017, _126017, plus_plus(_126017, _126201), _126199)), _126197) = hAPP(_126017, _126017, plus_plus(_126017, _126201), hAPP(_126017, _126017, plus_plus(_126017, _126199), _126197)))]]], (2511 ^ _76106) ^ [_126333] : [comm_semiring_1(_126333), 2514 ^ _76106 : [(2515 ^ _76106) ^ [_126513, _126515, _126517] : [-(hAPP(_126333, _126333, plus_plus(_126333, _126517), hAPP(_126333, _126333, plus_plus(_126333, _126515), _126513)) = hAPP(_126333, _126333, plus_plus(_126333, hAPP(_126333, _126333, plus_plus(_126333, _126517), _126515)), _126513))]]], (2517 ^ _76106) ^ [_126649] : [comm_semiring_1(_126649), 2520 ^ _76106 : [(2521 ^ _76106) ^ [_126829, _126831, _126833] : [-(hAPP(_126649, _126649, plus_plus(_126649, _126833), hAPP(_126649, _126649, plus_plus(_126649, _126831), _126829)) = hAPP(_126649, _126649, plus_plus(_126649, _126831), hAPP(_126649, _126649, plus_plus(_126649, _126833), _126829)))]]], (2523 ^ _76106) ^ [_126965] : [comm_semiring_1(_126965), 2526 ^ _76106 : [(2527 ^ _76106) ^ [_127110, _127112] : [-(hAPP(_126965, _126965, plus_plus(_126965, _127112), _127110) = hAPP(_126965, _126965, plus_plus(_126965, _127110), _127112))]]], (2529 ^ _76106) ^ [_127228] : [one(_127228), 2532 ^ _76106 : [(2533 ^ _76106) ^ [_127398] : [one_one(_127228) = ti(_127228, _127398), -(ti(_127228, _127398) = one_one(_127228))], (2539 ^ _76106) ^ [_127582] : [ti(_127228, _127582) = one_one(_127228), -(one_one(_127228) = ti(_127228, _127582))]]], (2545 ^ _76106) ^ [_127807] : [semiri456707255roduct(_127807), 2548 ^ _76106 : [(2549 ^ _76106) ^ [_128002, _128004] : [ti(_127807, _128004) = hAPP(_127807, _127807, plus_plus(_127807, _128004), _128002), -(ti(_127807, _128002) = zero_zero(_127807))], (2555 ^ _76106) ^ [_128204, _128206] : [ti(_127807, _128204) = zero_zero(_127807), -(ti(_127807, _128206) = hAPP(_127807, _127807, plus_plus(_127807, _128206), _128204))]]], (2561 ^ _76106) ^ [_128447] : [comm_monoid_add(_128447), 2564 ^ _76106 : [(2565 ^ _76106) ^ [_128570] : [-(hAPP(_128447, _128447, plus_plus(_128447, _128570), zero_zero(_128447)) = ti(_128447, _128570))]]], (2567 ^ _76106) ^ [_128683] : [comm_semiring_1(_128683), 2570 ^ _76106 : [(2571 ^ _76106) ^ [_128806] : [-(hAPP(_128683, _128683, plus_plus(_128683, _128806), zero_zero(_128683)) = ti(_128683, _128806))]]], (2573 ^ _76106) ^ [_128919] : [monoid_add(_128919), 2576 ^ _76106 : [(2577 ^ _76106) ^ [_129042] : [-(hAPP(_128919, _128919, plus_plus(_128919, _129042), zero_zero(_128919)) = ti(_128919, _129042))]]], (2579 ^ _76106) ^ [_129155] : [linord219039673up_add(_129155), 2582 ^ _76106 : [(2583 ^ _76106) ^ [_129330] : [zero_zero(_129155) = hAPP(_129155, _129155, plus_plus(_129155, _129330), _129330), -(ti(_129155, _129330) = zero_zero(_129155))], (2589 ^ _76106) ^ [_129524] : [ti(_129155, _129524) = zero_zero(_129155), -(zero_zero(_129155) = hAPP(_129155, _129155, plus_plus(_129155, _129524), _129524))]]], (2595 ^ _76106) ^ [_129759] : [comm_monoid_add(_129759), 2598 ^ _76106 : [(2599 ^ _76106) ^ [_129882] : [-(hAPP(_129759, _129759, plus_plus(_129759, zero_zero(_129759)), _129882) = ti(_129759, _129882))]]], (2601 ^ _76106) ^ [_129995] : [comm_semiring_1(_129995), 2604 ^ _76106 : [(2605 ^ _76106) ^ [_130118] : [-(hAPP(_129995, _129995, plus_plus(_129995, zero_zero(_129995)), _130118) = ti(_129995, _130118))]]], (2607 ^ _76106) ^ [_130231] : [monoid_add(_130231), 2610 ^ _76106 : [(2611 ^ _76106) ^ [_130354] : [-(hAPP(_130231, _130231, plus_plus(_130231, zero_zero(_130231)), _130354) = ti(_130231, _130354))]]], (2613 ^ _76106) ^ [_130467] : [ordere236663937imp_le(_130467), 2616 ^ _76106 : [(2617 ^ _76106) ^ [_130680, _130682, _130684] : [hBOOL(hAPP(_130467, bool, hAPP(_130467, fun(_130467, bool), ord_less(_130467), hAPP(_130467, _130467, plus_plus(_130467, _130684), _130682)), hAPP(_130467, _130467, plus_plus(_130467, _130684), _130680))), -(hBOOL(hAPP(_130467, bool, hAPP(_130467, fun(_130467, bool), ord_less(_130467), _130682), _130680)))]]], (2623 ^ _76106) ^ [_130983] : [ordere236663937imp_le(_130983), 2626 ^ _76106 : [(2627 ^ _76106) ^ [_131196, _131198, _131200] : [hBOOL(hAPP(_130983, bool, hAPP(_130983, fun(_130983, bool), ord_less(_130983), hAPP(_130983, _130983, plus_plus(_130983, _131200), _131198)), hAPP(_130983, _130983, plus_plus(_130983, _131196), _131198))), -(hBOOL(hAPP(_130983, bool, hAPP(_130983, fun(_130983, bool), ord_less(_130983), _131200), _131196)))]]], (2633 ^ _76106) ^ [_131499] : [ordere223160158up_add(_131499), 2636 ^ _76106 : [(2637 ^ _76106) ^ [_131751, _131753, _131755, _131757] : [hBOOL(hAPP(_131499, bool, hAPP(_131499, fun(_131499, bool), ord_less(_131499), _131753), _131751)), hBOOL(hAPP(_131499, bool, hAPP(_131499, fun(_131499, bool), ord_less(_131499), _131757), _131755)), -(hBOOL(hAPP(_131499, bool, hAPP(_131499, fun(_131499, bool), ord_less(_131499), hAPP(_131499, _131499, plus_plus(_131499, _131753), _131757)), hAPP(_131499, _131499, plus_plus(_131499, _131751), _131755))))]]], (2647 ^ _76106) ^ [_132189] : [ordere223160158up_add(_132189), 2650 ^ _76106 : [(2651 ^ _76106) ^ [_132402, _132404, _132406] : [hBOOL(hAPP(_132189, bool, hAPP(_132189, fun(_132189, bool), ord_less(_132189), _132404), _132402)), -(hBOOL(hAPP(_132189, bool, hAPP(_132189, fun(_132189, bool), ord_less(_132189), hAPP(_132189, _132189, plus_plus(_132189, _132406), _132404)), hAPP(_132189, _132189, plus_plus(_132189, _132406), _132402))))]]], (2657 ^ _76106) ^ [_132705] : [ordere223160158up_add(_132705), 2660 ^ _76106 : [(2661 ^ _76106) ^ [_132918, _132920, _132922] : [hBOOL(hAPP(_132705, bool, hAPP(_132705, fun(_132705, bool), ord_less(_132705), _132920), _132918)), -(hBOOL(hAPP(_132705, bool, hAPP(_132705, fun(_132705, bool), ord_less(_132705), hAPP(_132705, _132705, plus_plus(_132705, _132920), _132922)), hAPP(_132705, _132705, plus_plus(_132705, _132918), _132922))))]]], (2667 ^ _76106) ^ [_133221] : [ordere236663937imp_le(_133221), 2670 ^ _76106 : [(2671 ^ _76106) ^ [_133463, _133465, _133467] : [hBOOL(hAPP(_133221, bool, hAPP(_133221, fun(_133221, bool), ord_less(_133221), hAPP(_133221, _133221, plus_plus(_133221, _133467), _133465)), hAPP(_133221, _133221, plus_plus(_133221, _133467), _133463))), -(hBOOL(hAPP(_133221, bool, hAPP(_133221, fun(_133221, bool), ord_less(_133221), _133465), _133463)))], (2677 ^ _76106) ^ [_133727, _133729, _133731] : [hBOOL(hAPP(_133221, bool, hAPP(_133221, fun(_133221, bool), ord_less(_133221), _133729), _133727)), -(hBOOL(hAPP(_133221, bool, hAPP(_133221, fun(_133221, bool), ord_less(_133221), hAPP(_133221, _133221, plus_plus(_133221, _133731), _133729)), hAPP(_133221, _133221, plus_plus(_133221, _133731), _133727))))]]], (2683 ^ _76106) ^ [_134032] : [ordere236663937imp_le(_134032), 2686 ^ _76106 : [(2687 ^ _76106) ^ [_134274, _134276, _134278] : [hBOOL(hAPP(_134032, bool, hAPP(_134032, fun(_134032, bool), ord_less(_134032), hAPP(_134032, _134032, plus_plus(_134032, _134278), _134276)), hAPP(_134032, _134032, plus_plus(_134032, _134274), _134276))), -(hBOOL(hAPP(_134032, bool, hAPP(_134032, fun(_134032, bool), ord_less(_134032), _134278), _134274)))], (2693 ^ _76106) ^ [_134538, _134540, _134542] : [hBOOL(hAPP(_134032, bool, hAPP(_134032, fun(_134032, bool), ord_less(_134032), _134542), _134538)), -(hBOOL(hAPP(_134032, bool, hAPP(_134032, fun(_134032, bool), ord_less(_134032), hAPP(_134032, _134032, plus_plus(_134032, _134542), _134540)), hAPP(_134032, _134032, plus_plus(_134032, _134538), _134540))))]]], (2699 ^ _76106) ^ [_134843] : [comm_semiring_1(_134843), 2702 ^ _76106 : [(2703 ^ _76106) ^ [_134964] : [-(hAPP(nat, _134843, power_power(_134843, _134964), one_one(nat)) = ti(_134843, _134964))]]], (2705 ^ _76106) ^ [_135118, _135120] : [hAPP(nat, nat, power_power(nat, _135120), _135118) = zero_zero(nat), 2708 ^ _76106 : [(2709 ^ _76106) ^ [] : [_135118 = zero_zero(nat)], (2711 ^ _76106) ^ [] : [-(_135120 = zero_zero(nat))]]], (2713 ^ _76106) ^ [_135372, _135374] : [-(hAPP(nat, nat, power_power(nat, _135374), _135372) = zero_zero(nat)), -(_135372 = zero_zero(nat)), _135374 = zero_zero(nat)], (2723 ^ _76106) ^ [_135678] : [ordere216010020id_add(_135678), 2726 ^ _76106 : [(2727 ^ _76106) ^ [_135890, _135892] : [hBOOL(hAPP(_135678, bool, hAPP(_135678, fun(_135678, bool), ord_less(_135678), _135890), zero_zero(_135678))), hBOOL(hAPP(_135678, bool, hAPP(_135678, fun(_135678, bool), ord_less(_135678), _135892), zero_zero(_135678))), -(hBOOL(hAPP(_135678, bool, hAPP(_135678, fun(_135678, bool), ord_less(_135678), hAPP(_135678, _135678, plus_plus(_135678, _135890), _135892)), zero_zero(_135678))))]]], (2737 ^ _76106) ^ [_136304] : [ordere216010020id_add(_136304), 2740 ^ _76106 : [(2741 ^ _76106) ^ [_136516, _136518] : [hBOOL(hAPP(_136304, bool, hAPP(_136304, fun(_136304, bool), ord_less(_136304), zero_zero(_136304)), _136516)), hBOOL(hAPP(_136304, bool, hAPP(_136304, fun(_136304, bool), ord_less(_136304), zero_zero(_136304)), _136518)), -(hBOOL(hAPP(_136304, bool, hAPP(_136304, fun(_136304, bool), ord_less(_136304), zero_zero(_136304)), hAPP(_136304, _136304, plus_plus(_136304, _136516), _136518))))]]], (2751 ^ _76106) ^ [_136944, _136946] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _136944)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _136946)), 2759 ^ _76106 : [(2760 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), 2758 ^ [_136944, _136946])))], (2762 ^ _76106) ^ [] : [-(hAPP(nat, real, power_power(real, 2758 ^ [_136944, _136946]), _136944) = _136946)], (2764 ^ _76106) ^ [_137485] : [-(_137485 = 2758 ^ [_136944, _136946]), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _137485)), hAPP(nat, real, power_power(real, _137485), _136944) = _136946]]], (2774 ^ _76106) ^ [_137849, _137851] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _137849)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _137851)), 2782 ^ _76106 : [(2783 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), 2781 ^ [_137849, _137851])))], (2785 ^ _76106) ^ [] : [-(hAPP(nat, real, power_power(real, 2781 ^ [_137849, _137851]), _137849) = _137851)]]], (2787 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), t)))], (2789 ^ _76106) ^ [_138404] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _138404), pls)), -(hAPP(nat, nat, plus_plus(nat, number_number_of(nat, _138404)), one_one(nat)) = one_one(nat))], (2795 ^ _76106) ^ [_138600] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _138600), pls))), -(hAPP(nat, nat, plus_plus(nat, number_number_of(nat, _138600)), one_one(nat)) = number_number_of(nat, hAPP(int, int, succ, _138600)))], (2801 ^ _76106) ^ [_138871] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _138871), pls)), -(hAPP(nat, nat, plus_plus(nat, one_one(nat)), number_number_of(nat, _138871)) = one_one(nat))], (2807 ^ _76106) ^ [_139061] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _139061), pls))), -(hAPP(nat, nat, plus_plus(nat, one_one(nat)), number_number_of(nat, _139061)) = number_number_of(nat, hAPP(int, int, succ, _139061)))], (2813 ^ _76106) ^ [_139306] : [ordere236663937imp_le(_139306), 2816 ^ _76106 : [(2817 ^ _76106) ^ [_139548, _139550, _139552] : [hBOOL(hAPP(_139306, bool, hAPP(_139306, fun(_139306, bool), ord_less_eq(_139306), hAPP(_139306, _139306, plus_plus(_139306, _139552), _139550)), hAPP(_139306, _139306, plus_plus(_139306, _139548), _139550))), -(hBOOL(hAPP(_139306, bool, hAPP(_139306, fun(_139306, bool), ord_less_eq(_139306), _139552), _139548)))], (2823 ^ _76106) ^ [_139812, _139814, _139816] : [hBOOL(hAPP(_139306, bool, hAPP(_139306, fun(_139306, bool), ord_less_eq(_139306), _139816), _139812)), -(hBOOL(hAPP(_139306, bool, hAPP(_139306, fun(_139306, bool), ord_less_eq(_139306), hAPP(_139306, _139306, plus_plus(_139306, _139816), _139814)), hAPP(_139306, _139306, plus_plus(_139306, _139812), _139814))))]]], (2829 ^ _76106) ^ [_140117] : [ordere236663937imp_le(_140117), 2832 ^ _76106 : [(2833 ^ _76106) ^ [_140359, _140361, _140363] : [hBOOL(hAPP(_140117, bool, hAPP(_140117, fun(_140117, bool), ord_less_eq(_140117), hAPP(_140117, _140117, plus_plus(_140117, _140363), _140361)), hAPP(_140117, _140117, plus_plus(_140117, _140363), _140359))), -(hBOOL(hAPP(_140117, bool, hAPP(_140117, fun(_140117, bool), ord_less_eq(_140117), _140361), _140359)))], (2839 ^ _76106) ^ [_140623, _140625, _140627] : [hBOOL(hAPP(_140117, bool, hAPP(_140117, fun(_140117, bool), ord_less_eq(_140117), _140625), _140623)), -(hBOOL(hAPP(_140117, bool, hAPP(_140117, fun(_140117, bool), ord_less_eq(_140117), hAPP(_140117, _140117, plus_plus(_140117, _140627), _140625)), hAPP(_140117, _140117, plus_plus(_140117, _140627), _140623))))]]], (2845 ^ _76106) ^ [_140928] : [ordere779506340up_add(_140928), 2848 ^ _76106 : [(2849 ^ _76106) ^ [_141141, _141143, _141145] : [hBOOL(hAPP(_140928, bool, hAPP(_140928, fun(_140928, bool), ord_less_eq(_140928), _141143), _141141)), -(hBOOL(hAPP(_140928, bool, hAPP(_140928, fun(_140928, bool), ord_less_eq(_140928), hAPP(_140928, _140928, plus_plus(_140928, _141143), _141145)), hAPP(_140928, _140928, plus_plus(_140928, _141141), _141145))))]]], (2855 ^ _76106) ^ [_141444] : [ordere779506340up_add(_141444), 2858 ^ _76106 : [(2859 ^ _76106) ^ [_141657, _141659, _141661] : [hBOOL(hAPP(_141444, bool, hAPP(_141444, fun(_141444, bool), ord_less_eq(_141444), _141659), _141657)), -(hBOOL(hAPP(_141444, bool, hAPP(_141444, fun(_141444, bool), ord_less_eq(_141444), hAPP(_141444, _141444, plus_plus(_141444, _141661), _141659)), hAPP(_141444, _141444, plus_plus(_141444, _141661), _141657))))]]], (2865 ^ _76106) ^ [_141960] : [ordere779506340up_add(_141960), 2868 ^ _76106 : [(2869 ^ _76106) ^ [_142212, _142214, _142216, _142218] : [hBOOL(hAPP(_141960, bool, hAPP(_141960, fun(_141960, bool), ord_less_eq(_141960), _142214), _142212)), hBOOL(hAPP(_141960, bool, hAPP(_141960, fun(_141960, bool), ord_less_eq(_141960), _142218), _142216)), -(hBOOL(hAPP(_141960, bool, hAPP(_141960, fun(_141960, bool), ord_less_eq(_141960), hAPP(_141960, _141960, plus_plus(_141960, _142214), _142218)), hAPP(_141960, _141960, plus_plus(_141960, _142212), _142216))))]]], (2879 ^ _76106) ^ [_142650] : [ordere236663937imp_le(_142650), 2882 ^ _76106 : [(2883 ^ _76106) ^ [_142863, _142865, _142867] : [hBOOL(hAPP(_142650, bool, hAPP(_142650, fun(_142650, bool), ord_less_eq(_142650), hAPP(_142650, _142650, plus_plus(_142650, _142867), _142865)), hAPP(_142650, _142650, plus_plus(_142650, _142863), _142865))), -(hBOOL(hAPP(_142650, bool, hAPP(_142650, fun(_142650, bool), ord_less_eq(_142650), _142867), _142863)))]]], (2889 ^ _76106) ^ [_143166] : [ordere236663937imp_le(_143166), 2892 ^ _76106 : [(2893 ^ _76106) ^ [_143379, _143381, _143383] : [hBOOL(hAPP(_143166, bool, hAPP(_143166, fun(_143166, bool), ord_less_eq(_143166), hAPP(_143166, _143166, plus_plus(_143166, _143383), _143381)), hAPP(_143166, _143166, plus_plus(_143166, _143383), _143379))), -(hBOOL(hAPP(_143166, bool, hAPP(_143166, fun(_143166, bool), ord_less_eq(_143166), _143381), _143379)))]]], (2899 ^ _76106) ^ [_143682] : [linordered_semidom(_143682), 2902 ^ _76106 : [(2903 ^ _76106) ^ [_143912, _143914, _143916] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _143914), _143912)), hBOOL(hAPP(_143682, bool, hAPP(_143682, fun(_143682, bool), ord_less_eq(_143682), one_one(_143682)), _143916)), -(hBOOL(hAPP(_143682, bool, hAPP(_143682, fun(_143682, bool), ord_less_eq(_143682), hAPP(nat, _143682, power_power(_143682, _143916), _143914)), hAPP(nat, _143682, power_power(_143682, _143916), _143912))))]]], (2913 ^ _76106) ^ [_144377, _144379] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _144379)), hAPP(int, int, bit1, _144377))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _144379), _144377)))], (2919 ^ _76106) ^ [_144595, _144597] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _144597), _144595)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _144597)), hAPP(int, int, bit1, _144595))))], (2925 ^ _76106) ^ [_144892, _144894] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _144894)), hAPP(int, int, bit1, _144892))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _144894), _144892)))], (2931 ^ _76106) ^ [_145110, _145112] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _145112), _145110)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _145112)), hAPP(int, int, bit1, _145110))))], (2937 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), pls)))], (2939 ^ _76106) ^ [_145460, _145462] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _145462)), hAPP(int, int, bit0, _145460))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _145462), _145460)))], (2945 ^ _76106) ^ [_145678, _145680] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _145680), _145678)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _145680)), hAPP(int, int, bit0, _145678))))], (2951 ^ _76106) ^ [_145975, _145977] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _145977)), hAPP(int, int, bit0, _145975))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _145977), _145975)))], (2957 ^ _76106) ^ [_146193, _146195] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146195), _146193)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _146195)), hAPP(int, int, bit0, _146193))))], (2963 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), zero_zero(int))))], (2965 ^ _76106) ^ [_146485] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146485), _146485)))], (2967 ^ _76106) ^ [_146601, _146603] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146603), _146601))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146601), _146603)))], (2973 ^ _76106) ^ [_146862, _146864, _146866] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146864), _146862)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146862), _146866)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _146864), _146866)))], (2983 ^ _76106) ^ [_147225, _147227] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _147227), _147225)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _147225), _147227)), -(_147227 = _147225)], (2993 ^ _76106) ^ [_147546] : [number_ring(_147546), linordered_idom(_147546), 3000 ^ _76106 : [(3001 ^ _76106) ^ [_147837, _147839] : [hBOOL(hAPP(_147546, bool, hAPP(_147546, fun(_147546, bool), ord_less_eq(_147546), number_number_of(_147546, _147839)), number_number_of(_147546, _147837))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _147839), _147837)))], (3007 ^ _76106) ^ [_148065, _148067] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _148067), _148065)), -(hBOOL(hAPP(_147546, bool, hAPP(_147546, fun(_147546, bool), ord_less_eq(_147546), number_number_of(_147546, _148067)), number_number_of(_147546, _148065))))]]], (3013 ^ _76106) ^ [_148336] : [linordered_semidom(_148336), 3016 ^ _76106 : [(3017 ^ _76106) ^ [_148552, _148554] : [hBOOL(hAPP(_148336, bool, hAPP(_148336, fun(_148336, bool), ord_less_eq(_148336), hAPP(nat, _148336, semiring_1_of_nat(_148336), _148554)), hAPP(nat, _148336, semiring_1_of_nat(_148336), _148552))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _148554), _148552)))], (3023 ^ _76106) ^ [_148796, _148798] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _148798), _148796)), -(hBOOL(hAPP(_148336, bool, hAPP(_148336, fun(_148336, bool), ord_less_eq(_148336), hAPP(nat, _148336, semiring_1_of_nat(_148336), _148798)), hAPP(nat, _148336, semiring_1_of_nat(_148336), _148796))))]]], (3029 ^ _76106) ^ [_149124, _149126] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _149126), _149124)), 3032 ^ _76106 : [(3033 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _149126), _149124)))], (3035 ^ _76106) ^ [] : [_149126 = _149124]]], (3037 ^ _76106) ^ [_149398, _149400] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _149400), _149398))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _149400), _149398)), -(_149400 = _149398)], (3047 ^ _76106) ^ [_149752, _149754, _149756] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _149754), _149752)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, plus_plus(int, _149756), _149754)), hAPP(int, int, plus_plus(int, _149756), _149752))))], (3053 ^ _76106) ^ [_150065, _150067] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), number_number_of(int, _150067)), number_number_of(int, _150065))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _150067), _150065)))], (3059 ^ _76106) ^ [_150275, _150277] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _150277), _150275)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), number_number_of(int, _150277)), number_number_of(int, _150275))))], (3065 ^ _76106) ^ [_150521] : [number_ring(_150521), linordered_idom(_150521), 3072 ^ _76106 : [(3073 ^ _76106) ^ [_150787] : [hBOOL(hAPP(_150521, bool, hAPP(_150521, fun(_150521, bool), ord_less_eq(_150521), zero_zero(_150521)), number_number_of(_150521, _150787))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _150787)))], (3079 ^ _76106) ^ [_150997] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _150997)), -(hBOOL(hAPP(_150521, bool, hAPP(_150521, fun(_150521, bool), ord_less_eq(_150521), zero_zero(_150521)), number_number_of(_150521, _150997))))]]], (3085 ^ _76106) ^ [_151250] : [number_ring(_151250), linordered_idom(_151250), 3092 ^ _76106 : [(3093 ^ _76106) ^ [_151521] : [hBOOL(hAPP(_151250, bool, hAPP(_151250, fun(_151250, bool), ord_less_eq(_151250), number_number_of(_151250, _151521)), zero_zero(_151250))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _151521), pls)))], (3099 ^ _76106) ^ [_151741] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _151741), pls)), -(hBOOL(hAPP(_151250, bool, hAPP(_151250, fun(_151250, bool), ord_less_eq(_151250), number_number_of(_151250, _151741)), zero_zero(_151250))))]]], (3105 ^ _76106) ^ [_152004] : [linordered_semidom(_152004), 3108 ^ _76106 : [(3109 ^ _76106) ^ [_152256, _152258, _152260] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _152258), _152256)), hBOOL(hAPP(_152004, bool, hAPP(_152004, fun(_152004, bool), ord_less_eq(_152004), zero_zero(_152004)), _152260)), hBOOL(hAPP(_152004, bool, hAPP(_152004, fun(_152004, bool), ord_less_eq(_152004), _152260), one_one(_152004))), -(hBOOL(hAPP(_152004, bool, hAPP(_152004, fun(_152004, bool), ord_less_eq(_152004), hAPP(nat, _152004, power_power(_152004, _152260), _152256)), hAPP(nat, _152004, power_power(_152004, _152260), _152258))))]]], (3123 ^ _76106) ^ [_152807] : [linordered_semidom(_152807), 3126 ^ _76106 : [(3127 ^ _76106) ^ [_153037, _153039, _153041] : [hBOOL(hAPP(_152807, bool, hAPP(_152807, fun(_152807, bool), ord_less(_152807), one_one(_152807)), _153037)), 3130 ^ _76106 : [(3131 ^ _76106) ^ [] : [hBOOL(hAPP(_152807, bool, hAPP(_152807, fun(_152807, bool), ord_less_eq(_152807), hAPP(nat, _152807, power_power(_152807, _153037), _153041)), hAPP(nat, _152807, power_power(_152807, _153037), _153039))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _153041), _153039)))], (3137 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _153041), _153039)), -(hBOOL(hAPP(_152807, bool, hAPP(_152807, fun(_152807, bool), ord_less_eq(_152807), hAPP(nat, _152807, power_power(_152807, _153037), _153041)), hAPP(nat, _152807, power_power(_152807, _153037), _153039))))]]]]], (3143 ^ _76106) ^ [_153671] : [linordered_semidom(_153671), 3146 ^ _76106 : [(3147 ^ _76106) ^ [_153901, _153903, _153905] : [hBOOL(hAPP(_153671, bool, hAPP(_153671, fun(_153671, bool), ord_less(_153671), one_one(_153671)), _153901)), hBOOL(hAPP(_153671, bool, hAPP(_153671, fun(_153671, bool), ord_less_eq(_153671), hAPP(nat, _153671, power_power(_153671, _153901), _153905)), hAPP(nat, _153671, power_power(_153671, _153901), _153903))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _153905), _153903)))]]], (3157 ^ _76106) ^ [_154323] : [number_ring(_154323), linordered_idom(_154323), 3164 ^ _76106 : [(3165 ^ _76106) ^ [_154589] : [hBOOL(hAPP(_154323, bool, hAPP(_154323, fun(_154323, bool), ord_less_eq(_154323), one_one(_154323)), number_number_of(_154323, _154589))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, pls)), _154589)))], (3171 ^ _76106) ^ [_154799] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, pls)), _154799)), -(hBOOL(hAPP(_154323, bool, hAPP(_154323, fun(_154323, bool), ord_less_eq(_154323), one_one(_154323)), number_number_of(_154323, _154799))))]]], (3177 ^ _76106) ^ [_155052] : [number_ring(_155052), linordered_idom(_155052), 3184 ^ _76106 : [(3185 ^ _76106) ^ [_155323] : [hBOOL(hAPP(_155052, bool, hAPP(_155052, fun(_155052, bool), ord_less_eq(_155052), number_number_of(_155052, _155323)), one_one(_155052))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _155323), hAPP(int, int, bit1, pls))))], (3191 ^ _76106) ^ [_155543] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _155543), hAPP(int, int, bit1, pls))), -(hBOOL(hAPP(_155052, bool, hAPP(_155052, fun(_155052, bool), ord_less_eq(_155052), number_number_of(_155052, _155543)), one_one(_155052))))]]], (3197 ^ _76106) ^ [_155806] : [linord219039673up_add(_155806), 3200 ^ _76106 : [(3201 ^ _76106) ^ [_156006] : [hBOOL(hAPP(_155806, bool, hAPP(_155806, fun(_155806, bool), ord_less_eq(_155806), zero_zero(_155806)), hAPP(_155806, _155806, plus_plus(_155806, _156006), _156006))), -(hBOOL(hAPP(_155806, bool, hAPP(_155806, fun(_155806, bool), ord_less_eq(_155806), zero_zero(_155806)), _156006)))], (3207 ^ _76106) ^ [_156250] : [hBOOL(hAPP(_155806, bool, hAPP(_155806, fun(_155806, bool), ord_less_eq(_155806), zero_zero(_155806)), _156250)), -(hBOOL(hAPP(_155806, bool, hAPP(_155806, fun(_155806, bool), ord_less_eq(_155806), zero_zero(_155806)), hAPP(_155806, _155806, plus_plus(_155806, _156250), _156250))))]]], (3213 ^ _76106) ^ [_156535] : [linord219039673up_add(_156535), 3216 ^ _76106 : [(3217 ^ _76106) ^ [_156735] : [hBOOL(hAPP(_156535, bool, hAPP(_156535, fun(_156535, bool), ord_less_eq(_156535), hAPP(_156535, _156535, plus_plus(_156535, _156735), _156735)), zero_zero(_156535))), -(hBOOL(hAPP(_156535, bool, hAPP(_156535, fun(_156535, bool), ord_less_eq(_156535), _156735), zero_zero(_156535))))], (3223 ^ _76106) ^ [_156979] : [hBOOL(hAPP(_156535, bool, hAPP(_156535, fun(_156535, bool), ord_less_eq(_156535), _156979), zero_zero(_156535))), -(hBOOL(hAPP(_156535, bool, hAPP(_156535, fun(_156535, bool), ord_less_eq(_156535), hAPP(_156535, _156535, plus_plus(_156535, _156979), _156979)), zero_zero(_156535))))]]], (3229 ^ _76106) ^ [_157264] : [ordere216010020id_add(_157264), 3232 ^ _76106 : [(3233 ^ _76106) ^ [_157476, _157478] : [hBOOL(hAPP(_157264, bool, hAPP(_157264, fun(_157264, bool), ord_less_eq(_157264), zero_zero(_157264)), _157476)), hBOOL(hAPP(_157264, bool, hAPP(_157264, fun(_157264, bool), ord_less_eq(_157264), zero_zero(_157264)), _157478)), -(hBOOL(hAPP(_157264, bool, hAPP(_157264, fun(_157264, bool), ord_less_eq(_157264), zero_zero(_157264)), hAPP(_157264, _157264, plus_plus(_157264, _157476), _157478))))]]], (3243 ^ _76106) ^ [_157890] : [ordere216010020id_add(_157890), 3246 ^ _76106 : [(3247 ^ _76106) ^ [_158110, _158112] : [hBOOL(hAPP(_157890, bool, hAPP(_157890, fun(_157890, bool), ord_less_eq(_157890), zero_zero(_157890)), _158110)), hBOOL(hAPP(_157890, bool, hAPP(_157890, fun(_157890, bool), ord_less_eq(_157890), zero_zero(_157890)), _158112)), 3254 ^ _76106 : [(3255 ^ _76106) ^ [] : [hAPP(_157890, _157890, plus_plus(_157890, _158110), _158112) = zero_zero(_157890), 3258 ^ _76106 : [(3259 ^ _76106) ^ [] : [-(ti(_157890, _158110) = zero_zero(_157890))], (3261 ^ _76106) ^ [] : [-(ti(_157890, _158112) = zero_zero(_157890))]]], (3263 ^ _76106) ^ [] : [-(hAPP(_157890, _157890, plus_plus(_157890, _158110), _158112) = zero_zero(_157890)), ti(_157890, _158110) = zero_zero(_157890), ti(_157890, _158112) = zero_zero(_157890)]]]]], (3273 ^ _76106) ^ [_158960] : [ordere216010020id_add(_158960), 3276 ^ _76106 : [(3277 ^ _76106) ^ [_159187, _159189, _159191] : [hBOOL(hAPP(_158960, bool, hAPP(_158960, fun(_158960, bool), ord_less_eq(_158960), zero_zero(_158960)), _159187)), hBOOL(hAPP(_158960, bool, hAPP(_158960, fun(_158960, bool), ord_less_eq(_158960), _159191), _159189)), -(hBOOL(hAPP(_158960, bool, hAPP(_158960, fun(_158960, bool), ord_less_eq(_158960), _159191), hAPP(_158960, _158960, plus_plus(_158960, _159187), _159189))))]]], (3287 ^ _76106) ^ [_159603] : [ordere216010020id_add(_159603), 3290 ^ _76106 : [(3291 ^ _76106) ^ [_159830, _159832, _159834] : [hBOOL(hAPP(_159603, bool, hAPP(_159603, fun(_159603, bool), ord_less_eq(_159603), zero_zero(_159603)), _159830)), hBOOL(hAPP(_159603, bool, hAPP(_159603, fun(_159603, bool), ord_less_eq(_159603), _159834), _159832)), -(hBOOL(hAPP(_159603, bool, hAPP(_159603, fun(_159603, bool), ord_less_eq(_159603), _159834), hAPP(_159603, _159603, plus_plus(_159603, _159832), _159830))))]]], (3301 ^ _76106) ^ [_160246] : [ordere216010020id_add(_160246), 3304 ^ _76106 : [(3305 ^ _76106) ^ [_160458, _160460] : [hBOOL(hAPP(_160246, bool, hAPP(_160246, fun(_160246, bool), ord_less_eq(_160246), _160458), zero_zero(_160246))), hBOOL(hAPP(_160246, bool, hAPP(_160246, fun(_160246, bool), ord_less_eq(_160246), _160460), zero_zero(_160246))), -(hBOOL(hAPP(_160246, bool, hAPP(_160246, fun(_160246, bool), ord_less_eq(_160246), hAPP(_160246, _160246, plus_plus(_160246, _160458), _160460)), zero_zero(_160246))))]]], (3315 ^ _76106) ^ [_160872] : [ordere223160158up_add(_160872), 3318 ^ _76106 : [(3319 ^ _76106) ^ [_161124, _161126, _161128, _161130] : [hBOOL(hAPP(_160872, bool, hAPP(_160872, fun(_160872, bool), ord_less(_160872), _161126), _161124)), hBOOL(hAPP(_160872, bool, hAPP(_160872, fun(_160872, bool), ord_less_eq(_160872), _161130), _161128)), -(hBOOL(hAPP(_160872, bool, hAPP(_160872, fun(_160872, bool), ord_less(_160872), hAPP(_160872, _160872, plus_plus(_160872, _161126), _161130)), hAPP(_160872, _160872, plus_plus(_160872, _161124), _161128))))]]], (3329 ^ _76106) ^ [_161562] : [ordere223160158up_add(_161562), 3332 ^ _76106 : [(3333 ^ _76106) ^ [_161814, _161816, _161818, _161820] : [hBOOL(hAPP(_161562, bool, hAPP(_161562, fun(_161562, bool), ord_less_eq(_161562), _161816), _161814)), hBOOL(hAPP(_161562, bool, hAPP(_161562, fun(_161562, bool), ord_less(_161562), _161820), _161818)), -(hBOOL(hAPP(_161562, bool, hAPP(_161562, fun(_161562, bool), ord_less(_161562), hAPP(_161562, _161562, plus_plus(_161562, _161816), _161820)), hAPP(_161562, _161562, plus_plus(_161562, _161814), _161818))))]]], (3343 ^ _76106) ^ [_162252] : [linordered_semidom(_162252), hBOOL(hAPP(_162252, bool, hAPP(_162252, fun(_162252, bool), ord_less_eq(_162252), one_one(_162252)), zero_zero(_162252)))], (3349 ^ _76106) ^ [_162477] : [linordered_semidom(_162477), -(hBOOL(hAPP(_162477, bool, hAPP(_162477, fun(_162477, bool), ord_less_eq(_162477), zero_zero(_162477)), one_one(_162477))))], (3355 ^ _76106) ^ [_162701] : [number(_162701), linorder(_162701), 3362 ^ _76106 : [(3363 ^ _76106) ^ [_163005, _163007] : [hBOOL(hAPP(_162701, bool, hAPP(_162701, fun(_162701, bool), ord_less_eq(_162701), number_number_of(_162701, _163007)), number_number_of(_162701, _163005))), hBOOL(hAPP(_162701, bool, hAPP(_162701, fun(_162701, bool), ord_less(_162701), number_number_of(_162701, _163005)), number_number_of(_162701, _163007)))], (3369 ^ _76106) ^ [_163256, _163258] : [-(hBOOL(hAPP(_162701, bool, hAPP(_162701, fun(_162701, bool), ord_less(_162701), number_number_of(_162701, _163256)), number_number_of(_162701, _163258)))), -(hBOOL(hAPP(_162701, bool, hAPP(_162701, fun(_162701, bool), ord_less_eq(_162701), number_number_of(_162701, _163258)), number_number_of(_162701, _163256))))]]], (3375 ^ _76106) ^ [_163552] : [linordered_semidom(_163552), 3378 ^ _76106 : [(3379 ^ _76106) ^ [_163742, _163744] : [hBOOL(hAPP(_163552, bool, hAPP(_163552, fun(_163552, bool), ord_less_eq(_163552), zero_zero(_163552)), _163742)), -(hBOOL(hAPP(_163552, bool, hAPP(_163552, fun(_163552, bool), ord_less_eq(_163552), zero_zero(_163552)), hAPP(nat, _163552, power_power(_163552, _163742), _163744))))]]], (3385 ^ _76106) ^ [_164031] : [linordered_semidom(_164031), 3388 ^ _76106 : [(3389 ^ _76106) ^ [_164266, _164268, _164270] : [hBOOL(hAPP(_164031, bool, hAPP(_164031, fun(_164031, bool), ord_less_eq(_164031), _164268), _164266)), hBOOL(hAPP(_164031, bool, hAPP(_164031, fun(_164031, bool), ord_less_eq(_164031), zero_zero(_164031)), _164268)), -(hBOOL(hAPP(_164031, bool, hAPP(_164031, fun(_164031, bool), ord_less_eq(_164031), hAPP(nat, _164031, power_power(_164031, _164268), _164270)), hAPP(nat, _164031, power_power(_164031, _164266), _164270))))]]], (3399 ^ _76106) ^ [_164698] : [linordered_semidom(_164698), 3402 ^ _76106 : [(3403 ^ _76106) ^ [_164888, _164890] : [hBOOL(hAPP(_164698, bool, hAPP(_164698, fun(_164698, bool), ord_less_eq(_164698), one_one(_164698)), _164888)), -(hBOOL(hAPP(_164698, bool, hAPP(_164698, fun(_164698, bool), ord_less_eq(_164698), one_one(_164698)), hAPP(nat, _164698, power_power(_164698, _164888), _164890))))]]], (3409 ^ _76106) ^ [_165177] : [linordered_semidom(_165177), 3412 ^ _76106 : [(3413 ^ _76106) ^ [_165310] : [-(hBOOL(hAPP(_165177, bool, hAPP(_165177, fun(_165177, bool), ord_less_eq(_165177), zero_zero(_165177)), hAPP(nat, _165177, semiring_1_of_nat(_165177), _165310))))]]], (3415 ^ _76106) ^ [_165433] : [linordered_semidom(_165433), 3418 ^ _76106 : [(3419 ^ _76106) ^ [_165566] : [-(hBOOL(hAPP(_165433, bool, hAPP(_165433, fun(_165433, bool), ord_less_eq(_165433), zero_zero(_165433)), hAPP(nat, _165433, semiring_1_of_nat(_165433), _165566))))]]], (3421 ^ _76106) ^ [_165718] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), hAPP(int, int, bit1, _165718))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _165718)))], (3427 ^ _76106) ^ [_165900] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _165900)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), hAPP(int, int, bit1, _165900))))], (3433 ^ _76106) ^ [_166161, _166163] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _166163)), hAPP(int, int, bit1, _166161))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _166163), _166161)))], (3439 ^ _76106) ^ [_166379, _166381] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _166381), _166379)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _166381)), hAPP(int, int, bit1, _166379))))], (3445 ^ _76106) ^ [_166676, _166678] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _166678)), hAPP(int, int, bit1, _166676))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _166678), _166676)))], (3451 ^ _76106) ^ [_166894, _166896] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _166896), _166894)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _166896)), hAPP(int, int, bit1, _166894))))], (3457 ^ _76106) ^ [_167177] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), hAPP(int, int, bit0, _167177))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _167177)))], (3463 ^ _76106) ^ [_167359] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _167359)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), hAPP(int, int, bit0, _167359))))], (3469 ^ _76106) ^ [_167606] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _167606)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _167606), pls)))], (3475 ^ _76106) ^ [_167808] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _167808), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit0, _167808)), pls)))], (3481 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), one_one(int))))], (3483 ^ _76106) ^ [_168113, _168115] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _168113)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _168115)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(int, int, plus_plus(int, _168113), _168115))))], (3493 ^ _76106) ^ [_168480, _168482, _168484, _168486] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _168482), _168480)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _168486), _168484)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, plus_plus(int, _168482), _168486)), hAPP(int, int, plus_plus(int, _168480), _168484))))], (3503 ^ _76106) ^ [_168856] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _168856))))], (3516 ^ _76106) ^ [_169391] : [3517 ^ _76106 : [(3518 ^ _76106) ^ [_169487] : [hBOOL(hAPP(int, bool, _169391, hAPP(nat, int, semiring_1_of_nat(int), _169487)))]], 3520 ^ _76106 : [(3521 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 3519 ^ [_169391])))], (3523 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, _169391, 3519 ^ [_169391])))]]], (3505 ^ _76106) ^ [_168987] : [-(hBOOL(hAPP(int, bool, _168987, hAPP(nat, int, semiring_1_of_nat(int), 3512 ^ [_168987])))), 3506 ^ _76106 : [(3507 ^ _76106) ^ [_169099] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _169099)), hBOOL(hAPP(int, bool, _168987, _169099))]]], (3525 ^ _76106) ^ [_169811] : [3527 ^ _76106 : [(3528 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), 3526 ^ [_169811])))], (3530 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, _169811, 3526 ^ [_169811]))]], 3531 ^ _76106 : [(3532 ^ _76106) ^ [_170090] : [-(hBOOL(hAPP(int, bool, _169811, hAPP(nat, int, semiring_1_of_nat(int), _170090))))]]], (3534 ^ _76106) ^ [_170166] : [hBOOL(hAPP(int, bool, _170166, hAPP(nat, int, semiring_1_of_nat(int), 3535 ^ [_170166]))), 3538 ^ _76106 : [(3539 ^ _76106) ^ [_170385] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _170385)), -(hBOOL(hAPP(int, bool, _170166, _170385)))]]], (3545 ^ _76106) ^ [_170591] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), _170591))))], (3547 ^ _76106) ^ [_170707, _170709] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _170707)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, power_power(int, _170707), _170709))))], (3553 ^ _76106) ^ [_170978, _170980] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _170980), _170978)), -(_170978 = hAPP(int, int, plus_plus(int, _170980), hAPP(nat, int, semiring_1_of_nat(int), 3556 ^ [_170978, _170980])))], (3560 ^ _76106) ^ [_171254, _171256] : [3561 ^ _76106 : [(3562 ^ _76106) ^ [_171346] : [_171254 = hAPP(int, int, plus_plus(int, _171256), hAPP(nat, int, semiring_1_of_nat(int), _171346))]], -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _171256), _171254)))], (3566 ^ _76106) ^ [_171518] : [number_semiring(_171518), 3569 ^ _76106 : [(3570 ^ _76106) ^ [_171674] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _171674)), -(hAPP(_171518, _171518, plus_plus(_171518, one_one(_171518)), number_number_of(_171518, _171674)) = number_number_of(_171518, hAPP(int, int, succ, _171674)))]]], (3576 ^ _76106) ^ [_171927] : [number_semiring(_171927), 3579 ^ _76106 : [(3580 ^ _76106) ^ [_172083] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _172083)), -(hAPP(_171927, _171927, plus_plus(_171927, number_number_of(_171927, _172083)), one_one(_171927)) = number_number_of(_171927, hAPP(int, int, succ, _172083)))]]], (3586 ^ _76106) ^ [_172336] : [ordere216010020id_add(_172336), 3589 ^ _76106 : [(3590 ^ _76106) ^ [_172548, _172550] : [hBOOL(hAPP(_172336, bool, hAPP(_172336, fun(_172336, bool), ord_less(_172336), zero_zero(_172336)), _172548)), hBOOL(hAPP(_172336, bool, hAPP(_172336, fun(_172336, bool), ord_less_eq(_172336), zero_zero(_172336)), _172550)), -(hBOOL(hAPP(_172336, bool, hAPP(_172336, fun(_172336, bool), ord_less(_172336), zero_zero(_172336)), hAPP(_172336, _172336, plus_plus(_172336, _172548), _172550))))]]], (3600 ^ _76106) ^ [_172962] : [ordere216010020id_add(_172962), 3603 ^ _76106 : [(3604 ^ _76106) ^ [_173174, _173176] : [hBOOL(hAPP(_172962, bool, hAPP(_172962, fun(_172962, bool), ord_less_eq(_172962), zero_zero(_172962)), _173174)), hBOOL(hAPP(_172962, bool, hAPP(_172962, fun(_172962, bool), ord_less(_172962), zero_zero(_172962)), _173176)), -(hBOOL(hAPP(_172962, bool, hAPP(_172962, fun(_172962, bool), ord_less(_172962), zero_zero(_172962)), hAPP(_172962, _172962, plus_plus(_172962, _173174), _173176))))]]], (3614 ^ _76106) ^ [_173588] : [ordere216010020id_add(_173588), 3617 ^ _76106 : [(3618 ^ _76106) ^ [_173815, _173817, _173819] : [hBOOL(hAPP(_173588, bool, hAPP(_173588, fun(_173588, bool), ord_less(_173588), zero_zero(_173588)), _173815)), hBOOL(hAPP(_173588, bool, hAPP(_173588, fun(_173588, bool), ord_less_eq(_173588), _173819), _173817)), -(hBOOL(hAPP(_173588, bool, hAPP(_173588, fun(_173588, bool), ord_less(_173588), _173819), hAPP(_173588, _173588, plus_plus(_173588, _173815), _173817))))]]], (3628 ^ _76106) ^ [_174231] : [ordere216010020id_add(_174231), 3631 ^ _76106 : [(3632 ^ _76106) ^ [_174458, _174460, _174462] : [hBOOL(hAPP(_174231, bool, hAPP(_174231, fun(_174231, bool), ord_less_eq(_174231), zero_zero(_174231)), _174458)), hBOOL(hAPP(_174231, bool, hAPP(_174231, fun(_174231, bool), ord_less(_174231), _174462), _174460)), -(hBOOL(hAPP(_174231, bool, hAPP(_174231, fun(_174231, bool), ord_less(_174231), _174462), hAPP(_174231, _174231, plus_plus(_174231, _174458), _174460))))]]], (3642 ^ _76106) ^ [_174874] : [ordere216010020id_add(_174874), 3645 ^ _76106 : [(3646 ^ _76106) ^ [_175086, _175088] : [hBOOL(hAPP(_174874, bool, hAPP(_174874, fun(_174874, bool), ord_less(_174874), _175086), zero_zero(_174874))), hBOOL(hAPP(_174874, bool, hAPP(_174874, fun(_174874, bool), ord_less_eq(_174874), _175088), zero_zero(_174874))), -(hBOOL(hAPP(_174874, bool, hAPP(_174874, fun(_174874, bool), ord_less(_174874), hAPP(_174874, _174874, plus_plus(_174874, _175086), _175088)), zero_zero(_174874))))]]], (3656 ^ _76106) ^ [_175500] : [ordere216010020id_add(_175500), 3659 ^ _76106 : [(3660 ^ _76106) ^ [_175712, _175714] : [hBOOL(hAPP(_175500, bool, hAPP(_175500, fun(_175500, bool), ord_less_eq(_175500), _175712), zero_zero(_175500))), hBOOL(hAPP(_175500, bool, hAPP(_175500, fun(_175500, bool), ord_less(_175500), _175714), zero_zero(_175500))), -(hBOOL(hAPP(_175500, bool, hAPP(_175500, fun(_175500, bool), ord_less(_175500), hAPP(_175500, _175500, plus_plus(_175500, _175712), _175714)), zero_zero(_175500))))]]], (3670 ^ _76106) ^ [_176126] : [linordered_semidom(_176126), 3673 ^ _76106 : [(3674 ^ _76106) ^ [_176361, _176363, _176365] : [hBOOL(hAPP(_176126, bool, hAPP(_176126, fun(_176126, bool), ord_less(_176126), hAPP(nat, _176126, power_power(_176126, _176365), _176363)), hAPP(nat, _176126, power_power(_176126, _176361), _176363))), hBOOL(hAPP(_176126, bool, hAPP(_176126, fun(_176126, bool), ord_less_eq(_176126), zero_zero(_176126)), _176361)), -(hBOOL(hAPP(_176126, bool, hAPP(_176126, fun(_176126, bool), ord_less(_176126), _176365), _176361)))]]], (3684 ^ _76106) ^ [_176822] : [zero_zero(nat) = number_number_of(nat, _176822), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _176822), pls)))], (3690 ^ _76106) ^ [_177002] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _177002), pls)), -(zero_zero(nat) = number_number_of(nat, _177002))], (3696 ^ _76106) ^ [_177247] : [number_number_of(nat, _177247) = zero_zero(nat), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _177247), pls)))], (3702 ^ _76106) ^ [_177427] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _177427), pls)), -(number_number_of(nat, _177427) = zero_zero(nat))], (3708 ^ _76106) ^ [_177672] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), hAPP(int, int, bit1, _177672))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _177672)))], (3714 ^ _76106) ^ [_177854] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _177854)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), hAPP(int, int, bit1, _177854))))], (3720 ^ _76106) ^ [_178101] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _178101)), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _178101), pls)))], (3726 ^ _76106) ^ [_178303] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _178303), pls)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _178303)), pls)))], (3732 ^ _76106) ^ [_178584, _178586] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _178586)), hAPP(int, int, bit1, _178584))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _178586), _178584)))], (3738 ^ _76106) ^ [_178802, _178804] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _178804), _178802)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _178804)), hAPP(int, int, bit1, _178802))))], (3744 ^ _76106) ^ [_179099, _179101] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _179101)), hAPP(int, int, bit1, _179099))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _179101), _179099)))], (3750 ^ _76106) ^ [_179317, _179319] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _179319), _179317)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(int, int, bit0, _179319)), hAPP(int, int, bit1, _179317))))], (3756 ^ _76106) ^ [_179614, _179616] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _179616)), hAPP(int, int, bit0, _179614))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _179616), _179614)))], (3762 ^ _76106) ^ [_179832, _179834] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _179834), _179832)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _179834)), hAPP(int, int, bit0, _179832))))], (3768 ^ _76106) ^ [_180129, _180131] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _180131)), hAPP(int, int, bit0, _180129))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _180131), _180129)))], (3774 ^ _76106) ^ [_180347, _180349] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _180349), _180347)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, _180349)), hAPP(int, int, bit0, _180347))))], (3780 ^ _76106) ^ [_180630] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), _180630)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _180630)))], (3786 ^ _76106) ^ [_180802] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), _180802)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), _180802)))], (3792 ^ _76106) ^ [_181039] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _181039)), zero_zero(int))), -(_181039 = zero_zero(nat))], (3798 ^ _76106) ^ [_181223] : [_181223 = zero_zero(nat), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _181223)), zero_zero(int))))], (3804 ^ _76106) ^ [] : [-(hAPP(int, int, succ, pls) = hAPP(int, int, bit1, pls))], (3806 ^ _76106) ^ [_181481] : [-(hAPP(int, int, succ, hAPP(int, int, bit0, _181481)) = hAPP(int, int, bit1, _181481))], (3808 ^ _76106) ^ [_181574] : [-(hAPP(int, int, succ, hAPP(int, int, bit1, _181574)) = hAPP(int, int, bit0, hAPP(int, int, succ, _181574)))], (3810 ^ _76106) ^ [_181730, _181732] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _181732), hAPP(int, int, plus_plus(int, _181730), one_one(int)))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _181732), _181730)))], (3816 ^ _76106) ^ [_181944, _181946] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _181946), _181944)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _181946), hAPP(int, int, plus_plus(int, _181944), one_one(int)))))], (3822 ^ _76106) ^ [_182237, _182239] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, plus_plus(int, _182239), one_one(int))), _182237)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _182239), _182237)))], (3828 ^ _76106) ^ [_182451, _182453] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _182453), _182451)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, plus_plus(int, _182453), one_one(int))), _182451)))], (3834 ^ _76106) ^ [_182715, _182717] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _182717), _182715)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, plus_plus(int, _182717), one_one(int))), _182715)))], (3840 ^ _76106) ^ [_182948] : [-(hAPP(int, int, succ, _182948) = hAPP(int, int, plus_plus(int, _182948), one_one(int)))], (3842 ^ _76106) ^ [_183054] : [linordered_semidom(_183054), 3845 ^ _76106 : [(3846 ^ _76106) ^ [_183299, _183301, _183303] : [hAPP(nat, _183054, power_power(_183054, _183303), _183301) = hAPP(nat, _183054, power_power(_183054, _183299), _183301), hBOOL(hAPP(_183054, bool, hAPP(_183054, fun(_183054, bool), ord_less_eq(_183054), zero_zero(_183054)), _183303)), hBOOL(hAPP(_183054, bool, hAPP(_183054, fun(_183054, bool), ord_less_eq(_183054), zero_zero(_183054)), _183299)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _183301)), -(ti(_183054, _183303) = ti(_183054, _183299))]]], (3864 ^ _76106) ^ [_183921] : [number_semiring(_183921), 3867 ^ _76106 : [(3868 ^ _76106) ^ [_184110, _184112] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _184110)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), _184112)), -(hAPP(_183921, _183921, plus_plus(_183921, number_number_of(_183921, _184110)), number_number_of(_183921, _184112)) = number_number_of(_183921, hAPP(int, int, plus_plus(int, _184110), _184112)))]]], (3878 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, hAPP(int, int, bit1, hAPP(int, int, bit1, pls))))))], (3880 ^ _76106) ^ [_184531] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _184531)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, plus_plus(int, one_one(int)), _184531))))], (3886 ^ _76106) ^ [_184747] : [number_ring(_184747), 3889 ^ _76106 : [(3890 ^ _76106) ^ [_184878] : [-(number_number_of(_184747, hAPP(int, int, succ, _184878)) = hAPP(_184747, _184747, plus_plus(_184747, one_one(_184747)), number_number_of(_184747, _184878)))]]], (3892 ^ _76106) ^ [_184998, _185000] : [-(hAPP(int, int, plus_plus(int, hAPP(int, int, bit1, _185000)), hAPP(int, int, bit1, _184998)) = hAPP(int, int, bit0, hAPP(int, int, plus_plus(int, _185000), hAPP(int, int, succ, _184998))))], (3894 ^ _76106) ^ [_185129] : [linordered_semidom(_185129), 3897 ^ _76106 : [(3898 ^ _76106) ^ [_185374, _185376, _185378] : [hBOOL(hAPP(_185129, bool, hAPP(_185129, fun(_185129, bool), ord_less(_185129), _185376), _185374)), hBOOL(hAPP(_185129, bool, hAPP(_185129, fun(_185129, bool), ord_less_eq(_185129), zero_zero(_185129)), _185376)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), _185378)), -(hBOOL(hAPP(_185129, bool, hAPP(_185129, fun(_185129, bool), ord_less(_185129), hAPP(nat, _185129, power_power(_185129, _185376), _185378)), hAPP(nat, _185129, power_power(_185129, _185374), _185378))))]]], (3912 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))], (3914 ^ _76106) ^ [_185949] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _185949), hAPP(nat, int, power_power(int, _185949), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))))], (3916 ^ _76106) ^ [_186059] : [linordered_idom(_186059), 3919 ^ _76106 : [(3920 ^ _76106) ^ [_186193] : [-(hBOOL(hAPP(_186059, bool, hAPP(_186059, fun(_186059, bool), ord_less_eq(_186059), zero_zero(_186059)), hAPP(nat, _186059, power_power(_186059, _186193), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))))]]], (3922 ^ _76106) ^ [_186317] : [linordered_semidom(_186317), 3925 ^ _76106 : [(3926 ^ _76106) ^ [_186533, _186535] : [hBOOL(hAPP(_186317, bool, hAPP(_186317, fun(_186317, bool), ord_less_eq(_186317), hAPP(nat, _186317, power_power(_186317, _186535), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _186317, power_power(_186317, _186533), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), hBOOL(hAPP(_186317, bool, hAPP(_186317, fun(_186317, bool), ord_less_eq(_186317), zero_zero(_186317)), _186533)), -(hBOOL(hAPP(_186317, bool, hAPP(_186317, fun(_186317, bool), ord_less_eq(_186317), _186535), _186533)))]]], (3936 ^ _76106) ^ [_186955] : [linordered_semidom(_186955), 3939 ^ _76106 : [(3940 ^ _76106) ^ [_187171, _187173] : [hAPP(nat, _186955, power_power(_186955, _187173), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = hAPP(nat, _186955, power_power(_186955, _187171), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), hBOOL(hAPP(_186955, bool, hAPP(_186955, fun(_186955, bool), ord_less_eq(_186955), zero_zero(_186955)), _187173)), hBOOL(hAPP(_186955, bool, hAPP(_186955, fun(_186955, bool), ord_less_eq(_186955), zero_zero(_186955)), _187171)), -(ti(_186955, _187173) = ti(_186955, _187171))]]], (3954 ^ _76106) ^ [_187674] : [number_ring(_187674), 3957 ^ _76106 : [(3958 ^ _76106) ^ [_187878] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _187878))), -(hAPP(nat, _187674, semiring_1_of_nat(_187674), number_number_of(nat, _187878)) = number_number_of(_187674, _187878))], (3964 ^ _76106) ^ [_188082] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _188082)))), -(hAPP(nat, _187674, semiring_1_of_nat(_187674), number_number_of(nat, _188082)) = zero_zero(_187674))]]], (3970 ^ _76106) ^ [_188328] : [linordered_semidom(_188328), 3973 ^ _76106 : [(3974 ^ _76106) ^ [_188544, _188546] : [hBOOL(hAPP(_188328, bool, hAPP(_188328, fun(_188328, bool), ord_less(_188328), hAPP(nat, _188328, power_power(_188328, _188546), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _188328, power_power(_188328, _188544), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), hBOOL(hAPP(_188328, bool, hAPP(_188328, fun(_188328, bool), ord_less_eq(_188328), zero_zero(_188328)), _188544)), -(hBOOL(hAPP(_188328, bool, hAPP(_188328, fun(_188328, bool), ord_less(_188328), _188546), _188544)))]]], (3984 ^ _76106) ^ [_188966] : [linordered_idom(_188966), 3987 ^ _76106 : [(3988 ^ _76106) ^ [_189135, _189137] : [-(hBOOL(hAPP(_188966, bool, hAPP(_188966, fun(_188966, bool), ord_less_eq(_188966), zero_zero(_188966)), hAPP(_188966, _188966, plus_plus(_188966, hAPP(nat, _188966, power_power(_188966, _189137), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _188966, power_power(_188966, _189135), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))))]]], (3990 ^ _76106) ^ [_189277] : [linordered_idom(_189277), 3993 ^ _76106 : [(3994 ^ _76106) ^ [_189512, _189514] : [hBOOL(hAPP(_189277, bool, hAPP(_189277, fun(_189277, bool), ord_less_eq(_189277), hAPP(_189277, _189277, plus_plus(_189277, hAPP(nat, _189277, power_power(_189277, _189514), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _189277, power_power(_189277, _189512), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), zero_zero(_189277))), 3997 ^ _76106 : [(3998 ^ _76106) ^ [] : [-(ti(_189277, _189514) = zero_zero(_189277))], (4000 ^ _76106) ^ [] : [-(ti(_189277, _189512) = zero_zero(_189277))]]], (4002 ^ _76106) ^ [_189859, _189861] : [-(hBOOL(hAPP(_189277, bool, hAPP(_189277, fun(_189277, bool), ord_less_eq(_189277), hAPP(_189277, _189277, plus_plus(_189277, hAPP(nat, _189277, power_power(_189277, _189861), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, _189277, power_power(_189277, _189859), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), zero_zero(_189277)))), ti(_189277, _189861) = zero_zero(_189277), ti(_189277, _189859) = zero_zero(_189277)]]], (4012 ^ _76106) ^ [_190263] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _190263)), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), _190263), number_number_of(int, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), -(_190263 = zero_zero(int)), -(_190263 = one_one(int))], (4026 ^ _76106) ^ [_190650] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, _190650))), 4029 ^ _76106 : [(4030 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, hAPP(int, int, bit0, _190650)))))], (4032 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, hAPP(int, int, bit1, _190650)))))]]], (4034 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), number_number_of(int, pls))))], (4036 ^ _76106) ^ [_191028] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _191028)), -(_191028 = hAPP(nat, int, semiring_1_of_nat(int), 4039 ^ [_191028]))], (4043 ^ _76106) ^ [_191292] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _191292)), -(_191292 = hAPP(nat, int, semiring_1_of_nat(int), 4046 ^ [_191292]))], (4050 ^ _76106) ^ [_191547] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), zero_zero(nat)), _191547)))], (4052 ^ _76106) ^ [_191629] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), zero_zero(nat)), _191629)))], (4054 ^ _76106) ^ [_191755] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _191755), zero_zero(nat))), -(_191755 = zero_zero(nat))], (4060 ^ _76106) ^ [_191929] : [_191929 = zero_zero(nat), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _191929), zero_zero(nat))))], (4066 ^ _76106) ^ [_192153, _192155] : [4067 ^ _76106 : [(4068 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _192155), _192153))], (4070 ^ _76106) ^ [] : [_192155 = _192153]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _192155), _192153)))], (4074 ^ _76106) ^ [_192473, _192475] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _192475), _192473)), -(_192475 = _192473), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _192475), _192473)))], (4084 ^ _76106) ^ [_192811, _192813] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _192813), _192811)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _192813), _192811)))], (4100 ^ _76106) ^ [_193374, _193376] : [4101 ^ _76106 : [(4102 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _193376), _193374))], (4104 ^ _76106) ^ [] : [_193376 = _193374]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _193376), _193374)))], (4090 ^ _76106) ^ [_193086, _193088] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _193088), _193086)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _193088), _193086))), -(_193088 = _193086)], (4108 ^ _76106) ^ [_193725, _193727] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _193727), _193725)), 4111 ^ _76106 : [(4112 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _193727), _193725)))], (4114 ^ _76106) ^ [] : [_193727 = _193725]]], (4116 ^ _76106) ^ [_193999, _194001] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _194001), _193999))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194001), _193999)), -(_194001 = _193999)], (4126 ^ _76106) ^ [_194310] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194310), _194310)))], (4128 ^ _76106) ^ [_194426, _194428] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194428), _194426))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194426), _194428)))], (4134 ^ _76106) ^ [_194673, _194675] : [_194675 = _194673, -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194675), _194673)))], (4140 ^ _76106) ^ [_194915, _194917, _194919] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194917), _194915)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194915), _194919)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _194917), _194919)))], (4150 ^ _76106) ^ [_195278, _195280] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _195280), _195278)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _195278), _195280)), -(_195280 = _195278)], (4170 ^ _76106) ^ [_195930, _195932] : [4171 ^ _76106 : [(4172 ^ _76106) ^ [] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _195932), _195930))], (4174 ^ _76106) ^ [] : [_195932 = _195930]], -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _195932), _195930)))], (4160 ^ _76106) ^ [_195642, _195644] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _195644), _195642)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _195644), _195642))), -(_195644 = _195642)], (4178 ^ _76106) ^ [_196281, _196283] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _196283), _196281)), 4181 ^ _76106 : [(4182 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _196283), _196281)))], (4184 ^ _76106) ^ [] : [_196283 = _196281]]], (4186 ^ _76106) ^ [_196555, _196557] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _196557), _196555))), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _196557), _196555)), -(_196557 = _196555)], (4196 ^ _76106) ^ [_196880, _196882] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _196882), hAPP(nat, nat, plus_plus(nat, _196880), _196882))))], (4198 ^ _76106) ^ [_196991, _196993] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _196993), hAPP(nat, nat, plus_plus(nat, _196993), _196991))))], (4200 ^ _76106) ^ [_197146, _197148] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _197148), _197146)), -(_197146 = hAPP(nat, nat, plus_plus(nat, _197148), 4203 ^ [_197146, _197148]))], (4207 ^ _76106) ^ [_197407, _197409] : [4208 ^ _76106 : [(4209 ^ _76106) ^ [_197494] : [_197407 = hAPP(nat, nat, plus_plus(nat, _197409), _197494)]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _197409), _197407)))], (4213 ^ _76106) ^ [_197718, _197720, _197722] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _197722), _197720)), hAPP(nat, nat, plus_plus(nat, _197722), _197718))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _197720), _197718)))], (4219 ^ _76106) ^ [_197954, _197956, _197958] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _197956), _197954)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _197958), _197956)), hAPP(nat, nat, plus_plus(nat, _197958), _197954))))], (4225 ^ _76106) ^ [_198254, _198256, _198258] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _198256), _198254)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _198256), hAPP(nat, nat, plus_plus(nat, _198254), _198258))))], (4231 ^ _76106) ^ [_198536, _198538, _198540] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _198538), _198536)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _198538), hAPP(nat, nat, plus_plus(nat, _198540), _198536))))], (4237 ^ _76106) ^ [_198818, _198820, _198822] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _198820), _198818)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _198820), _198822)), hAPP(nat, nat, plus_plus(nat, _198818), _198822))))], (4243 ^ _76106) ^ [_199130, _199132, _199134, _199136] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _199132), _199130)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _199136), _199134)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _199132), _199136)), hAPP(nat, nat, plus_plus(nat, _199130), _199134))))], (4253 ^ _76106) ^ [_199549, _199551, _199553] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _199553), _199551)), _199549)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _199551), _199549)))], (4259 ^ _76106) ^ [_199831, _199833, _199835] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _199835), _199833)), _199831)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _199835), _199831)))], (4265 ^ _76106) ^ [_200113, _200115, _200117] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, _200117), _200115)), _200113)), 4268 ^ _76106 : [(4269 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _200117), _200113)))], (4271 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _200115), _200113)))]]], (4273 ^ _76106) ^ [_200494, _200496, _200498] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _200496), _200494)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), hAPP(real, real, plus_plus(real, _200498), _200496)), hAPP(real, real, plus_plus(real, _200498), _200494))))], (4279 ^ _76106) ^ [_200807, _200809] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _200809)), hAPP(nat, int, semiring_1_of_nat(int), _200807))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _200809), _200807)))], (4285 ^ _76106) ^ [_201025, _201027] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _201027), _201025)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _201027)), hAPP(nat, int, semiring_1_of_nat(int), _201025))))], (4291 ^ _76106) ^ [_201322, _201324] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _201324)), hAPP(nat, int, semiring_1_of_nat(int), _201322))), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _201324), _201322)))], (4297 ^ _76106) ^ [_201540, _201542] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _201542), _201540)), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), _201542)), hAPP(nat, int, semiring_1_of_nat(int), _201540))))], (4313 ^ _76106) ^ [_202157, _202159] : [4314 ^ _76106 : [(4315 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _202159), _202157))], (4317 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _202159), pls))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), number_number_of(nat, _202159)), number_number_of(nat, _202157))))], (4303 ^ _76106) ^ [_201837, _201839] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), number_number_of(nat, _201839)), number_number_of(nat, _201837))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _201839), _201837))), -(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _201839), pls)))], (4321 ^ _76106) ^ [_202482] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), one_one(real)), hAPP(nat, real, power_power(real, number_number_of(real, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), _202482))))], (4323 ^ _76106) ^ [_202612, _202614, _202616] : [4324 ^ _76106 : [(4325 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _202612)))], (4327 ^ _76106) ^ [] : [4328 ^ _76106 : [(4329 ^ _76106) ^ [] : [-(hBOOL(_202614))], (4331 ^ _76106) ^ [] : [hBOOL(_202616)]], 4332 ^ _76106 : [(4333 ^ _76106) ^ [] : [-(hBOOL(_202616))], (4335 ^ _76106) ^ [] : [hBOOL(_202614)]]]], 4336 ^ _76106 : [(4337 ^ _76106) ^ [] : [4344 ^ _76106 : [(4345 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _202612)))], (4347 ^ _76106) ^ [] : [-(hBOOL(_202616))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _202612)), hBOOL(_202614)], (4349 ^ _76106) ^ [] : [4356 ^ _76106 : [(4357 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _202612)))], (4359 ^ _76106) ^ [] : [-(hBOOL(_202614))]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _202612)), hBOOL(_202616)]]], (4361 ^ _76106) ^ [_203771, _203773, _203775] : [4362 ^ _76106 : [(4363 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _203771)))], (4365 ^ _76106) ^ [] : [4366 ^ _76106 : [(4367 ^ _76106) ^ [] : [-(hBOOL(_203773))], (4369 ^ _76106) ^ [] : [hBOOL(_203775)]], 4370 ^ _76106 : [(4371 ^ _76106) ^ [] : [-(hBOOL(_203775))], (4373 ^ _76106) ^ [] : [hBOOL(_203773)]]]], 4374 ^ _76106 : [(4375 ^ _76106) ^ [] : [4376 ^ _76106 : [(4377 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _203771)))], (4379 ^ _76106) ^ [] : [hBOOL(_203773)]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _203771)), -(hBOOL(_203775))], (4387 ^ _76106) ^ [] : [4388 ^ _76106 : [(4389 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _203771)))], (4391 ^ _76106) ^ [] : [hBOOL(_203775)]], hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _203771)), -(hBOOL(_203773))]]], (4399 ^ _76106) ^ [_204916, _204918] : [-(hBOOL(hAPP(nat, bool, _204916, zero_zero(nat)))), hBOOL(hAPP(nat, bool, _204916, _204918)), 4407 ^ _76106 : [(4408 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 4406 ^ [_204916, _204918]), _204918)))], (4416 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, _204916, hAPP(nat, nat, plus_plus(nat, 4406 ^ [_204916, _204918]), one_one(nat)))))], (4410 ^ _76106) ^ [_205416] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _205416), 4406 ^ [_204916, _204918])), hBOOL(hAPP(nat, bool, _204916, _205416))]]], (4418 ^ _76106) ^ [_205741] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), _205741)), -(_205741 = hAPP(nat, int, semiring_1_of_nat(int), 4421 ^ [_205741]))], (4425 ^ _76106) ^ [_206039, _206041, _206043] : [4428 ^ _76106 : [(4429 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 4426 ^ [_206039, _206041, _206043]), 4427 ^ [_206039, _206041, _206043])))], (4431 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, _206039, 4426 ^ [_206039, _206041, _206043])), hAPP(nat, nat, _206039, 4427 ^ [_206039, _206041, _206043])))]], -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, plus_plus(nat, hAPP(nat, nat, _206039, _206043)), _206041)), hAPP(nat, nat, _206039, hAPP(nat, nat, plus_plus(nat, _206043), _206041)))))], (4435 ^ _76106) ^ [_206664] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _206664), _206664)))], (4437 ^ _76106) ^ [_206780, _206782] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _206782), _206780))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _206780), _206782)))], (4443 ^ _76106) ^ [_207041, _207043, _207045] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _207043), _207041)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _207041), _207045)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _207043), _207045)))], (4453 ^ _76106) ^ [_207404, _207406] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _207406), _207404)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), _207404), _207406)), -(_207406 = _207404)], (4463 ^ _76106) ^ [_207753, _207755, _207757] : [hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _207755), _207753)), hBOOL(hAPP(int, bool, _207757, _207755)), 4473 ^ _76106 : [(4474 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), _207755), 4472 ^ [_207753, _207755, _207757])))], (4476 ^ _76106) ^ [] : [-(hBOOL(hAPP(int, bool, _207757, 4472 ^ [_207753, _207755, _207757])))], (4478 ^ _76106) ^ [] : [hBOOL(hAPP(int, bool, _207757, hAPP(int, int, plus_plus(int, 4472 ^ [_207753, _207755, _207757]), one_one(int))))]], -(hBOOL(hAPP(int, bool, _207757, _207753)))], (4482 ^ _76106) ^ [_208510, _208512] : [-(hBOOL(hAPP(nat, bool, _208510, zero_zero(nat)))), hBOOL(hAPP(nat, bool, _208510, _208512)), 4490 ^ _76106 : [(4491 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), 4489 ^ [_208510, _208512]), _208512)))], (4499 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, _208510, 4489 ^ [_208510, _208512])))], (4493 ^ _76106) ^ [_208994] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), _208994), 4489 ^ [_208510, _208512])), hBOOL(hAPP(nat, bool, _208510, _208994))]]], (4501 ^ _76106) ^ [_209339, _209341, _209343] : [4504 ^ _76106 : [(4505 ^ _76106) ^ [] : [-(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), 4502 ^ [_209339, _209341, _209343]), 4503 ^ [_209339, _209341, _209343])))], (4507 ^ _76106) ^ [] : [hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), hAPP(nat, nat, _209339, 4502 ^ [_209339, _209341, _209343])), hAPP(nat, nat, _209339, 4503 ^ [_209339, _209341, _209343])))]], hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), _209343), _209341)), -(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), hAPP(nat, nat, _209339, _209343)), hAPP(nat, nat, _209339, _209341))))], (4515 ^ _76106) ^ [_210058] : [preorder(_210058), 4518 ^ _76106 : [(4519 ^ _76106) ^ [_210182] : [-(hBOOL(hAPP(_210058, bool, hAPP(_210058, fun(_210058, bool), ord_less_eq(_210058), _210182), _210182)))]]], (4521 ^ _76106) ^ [_210296] : [linorder(_210296), 4524 ^ _76106 : [(4525 ^ _76106) ^ [_210476, _210478] : [-(hBOOL(hAPP(_210296, bool, hAPP(_210296, fun(_210296, bool), ord_less_eq(_210296), _210478), _210476))), -(hBOOL(hAPP(_210296, bool, hAPP(_210296, fun(_210296, bool), ord_less_eq(_210296), _210476), _210478)))]]], (4531 ^ _76106) ^ [_210758, _210760] : [ord(_210758), 4534 ^ _76106 : [(4535 ^ _76106) ^ [_210981, _210983, _210985] : [hBOOL(hAPP(fun(_210760, _210758), bool, hAPP(fun(_210760, _210758), fun(fun(_210760, _210758), bool), ord_less_eq(fun(_210760, _210758)), _210983), _210981)), -(hBOOL(hAPP(_210758, bool, hAPP(_210758, fun(_210758, bool), ord_less_eq(_210758), hAPP(_210760, _210758, _210983, _210985)), hAPP(_210760, _210758, _210981, _210985))))]]], (4541 ^ _76106) ^ [_211304] : [order(_211304), 4544 ^ _76106 : [(4545 ^ _76106) ^ [_211521, _211523, _211525] : [hBOOL(hAPP(_211304, bool, hAPP(_211304, fun(_211304, bool), ord_less_eq(_211304), _211523), _211521)), hBOOL(hAPP(_211304, bool, hAPP(_211304, fun(_211304, bool), ord_less_eq(_211304), _211525), _211523)), -(hBOOL(hAPP(_211304, bool, hAPP(_211304, fun(_211304, bool), ord_less_eq(_211304), _211525), _211521)))]]], (4555 ^ _76106) ^ [_211917] : [order(_211917), 4558 ^ _76106 : [(4559 ^ _76106) ^ [_212107, _212109] : [hBOOL(hAPP(_211917, bool, hAPP(_211917, fun(_211917, bool), ord_less_eq(_211917), _212109), _212107)), hBOOL(hAPP(_211917, bool, hAPP(_211917, fun(_211917, bool), ord_less_eq(_211917), _212107), _212109)), -(ti(_211917, _212107) = ti(_211917, _212109))]]], (4569 ^ _76106) ^ [_212477] : [preorder(_212477), 4572 ^ _76106 : [(4573 ^ _76106) ^ [_212694, _212696, _212698] : [hBOOL(hAPP(_212477, bool, hAPP(_212477, fun(_212477, bool), ord_less_eq(_212477), _212696), _212694)), hBOOL(hAPP(_212477, bool, hAPP(_212477, fun(_212477, bool), ord_less_eq(_212477), _212694), _212698)), -(hBOOL(hAPP(_212477, bool, hAPP(_212477, fun(_212477, bool), ord_less_eq(_212477), _212696), _212698)))]]], (4583 ^ _76106) ^ [_213090] : [order(_213090), 4586 ^ _76106 : [(4587 ^ _76106) ^ [_213280, _213282] : [hBOOL(hAPP(_213090, bool, hAPP(_213090, fun(_213090, bool), ord_less_eq(_213090), _213282), _213280)), hBOOL(hAPP(_213090, bool, hAPP(_213090, fun(_213090, bool), ord_less_eq(_213090), _213280), _213282)), -(ti(_213090, _213282) = ti(_213090, _213280))]]], (4597 ^ _76106) ^ [_213650] : [order(_213650), 4600 ^ _76106 : [(4601 ^ _76106) ^ [_213859, _213861, _213863] : [hBOOL(hAPP(_213650, bool, hAPP(_213650, fun(_213650, bool), ord_less_eq(_213650), _213861), _213859)), ti(_213650, _213861) = ti(_213650, _213863), -(hBOOL(hAPP(_213650, bool, hAPP(_213650, fun(_213650, bool), ord_less_eq(_213650), _213863), _213859)))]]], (4611 ^ _76106) ^ [_214239] : [ord(_214239), 4614 ^ _76106 : [(4615 ^ _76106) ^ [_214442, _214444, _214446] : [hBOOL(hAPP(_214239, bool, hAPP(_214239, fun(_214239, bool), ord_less_eq(_214239), _214444), _214442)), _214442 = _214446, -(hBOOL(hAPP(_214239, bool, hAPP(_214239, fun(_214239, bool), ord_less_eq(_214239), _214444), _214446)))]]], (4625 ^ _76106) ^ [_214810] : [order(_214810), 4628 ^ _76106 : [(4629 ^ _76106) ^ [_215019, _215021, _215023] : [ti(_214810, _215021) = ti(_214810, _215019), hBOOL(hAPP(_214810, bool, hAPP(_214810, fun(_214810, bool), ord_less_eq(_214810), _215023), _215019)), -(hBOOL(hAPP(_214810, bool, hAPP(_214810, fun(_214810, bool), ord_less_eq(_214810), _215023), _215021)))]]], (4639 ^ _76106) ^ [_215399] : [ord(_215399), 4642 ^ _76106 : [(4643 ^ _76106) ^ [_215602, _215604, _215606] : [_215604 = _215602, hBOOL(hAPP(_215399, bool, hAPP(_215399, fun(_215399, bool), ord_less_eq(_215399), _215602), _215606)), -(hBOOL(hAPP(_215399, bool, hAPP(_215399, fun(_215399, bool), ord_less_eq(_215399), _215604), _215606)))]]], (4653 ^ _76106) ^ [_215970] : [order(_215970), 4656 ^ _76106 : [(4657 ^ _76106) ^ [_216160, _216162] : [hBOOL(hAPP(_215970, bool, hAPP(_215970, fun(_215970, bool), ord_less_eq(_215970), _216162), _216160)), 4660 ^ _76106 : [(4661 ^ _76106) ^ [] : [hBOOL(hAPP(_215970, bool, hAPP(_215970, fun(_215970, bool), ord_less_eq(_215970), _216160), _216162)), -(ti(_215970, _216160) = ti(_215970, _216162))], (4667 ^ _76106) ^ [] : [ti(_215970, _216160) = ti(_215970, _216162), -(hBOOL(hAPP(_215970, bool, hAPP(_215970, fun(_215970, bool), ord_less_eq(_215970), _216160), _216162)))]]]]], (4673 ^ _76106) ^ [_216731, _216733] : [ord(_216731), 4676 ^ _76106 : [(4677 ^ _76106) ^ [_216954, _216956, _216958] : [hBOOL(hAPP(fun(_216733, _216731), bool, hAPP(fun(_216733, _216731), fun(fun(_216733, _216731), bool), ord_less_eq(fun(_216733, _216731)), _216956), _216954)), -(hBOOL(hAPP(_216731, bool, hAPP(_216731, fun(_216731, bool), ord_less_eq(_216731), hAPP(_216733, _216731, _216956, _216958)), hAPP(_216733, _216731, _216954, _216958))))]]], (4683 ^ _76106) ^ [_217277] : [preorder(_217277), 4686 ^ _76106 : [(4687 ^ _76106) ^ [_217441, _217443] : [_217443 = _217441, -(hBOOL(hAPP(_217277, bool, hAPP(_217277, fun(_217277, bool), ord_less_eq(_217277), _217443), _217441)))]]], (4693 ^ _76106) ^ [_217678] : [order(_217678), 4696 ^ _76106 : [(4697 ^ _76106) ^ [_217897, _217899] : [ti(_217678, _217899) = ti(_217678, _217897), 4700 ^ _76106 : [(4701 ^ _76106) ^ [] : [-(hBOOL(hAPP(_217678, bool, hAPP(_217678, fun(_217678, bool), ord_less_eq(_217678), _217899), _217897)))], (4703 ^ _76106) ^ [] : [-(hBOOL(hAPP(_217678, bool, hAPP(_217678, fun(_217678, bool), ord_less_eq(_217678), _217897), _217899)))]]], (4705 ^ _76106) ^ [_218212, _218214] : [-(ti(_217678, _218214) = ti(_217678, _218212)), hBOOL(hAPP(_217678, bool, hAPP(_217678, fun(_217678, bool), ord_less_eq(_217678), _218214), _218212)), hBOOL(hAPP(_217678, bool, hAPP(_217678, fun(_217678, bool), ord_less_eq(_217678), _218212), _218214))]]], (4715 ^ _76106) ^ [_218584] : [linorder(_218584), 4718 ^ _76106 : [(4719 ^ _76106) ^ [_218762, _218764] : [-(hBOOL(hAPP(_218584, bool, hAPP(_218584, fun(_218584, bool), ord_less_eq(_218584), _218764), _218762))), -(hBOOL(hAPP(_218584, bool, hAPP(_218584, fun(_218584, bool), ord_less_eq(_218584), _218762), _218764)))]]], (4725 ^ _76106) ^ [_219042, _219044] : [ord(_219042), 4728 ^ _76106 : [(4729 ^ _76106) ^ [_219280, _219282] : [hBOOL(hAPP(fun(_219044, _219042), bool, hAPP(fun(_219044, _219042), fun(fun(_219044, _219042), bool), ord_less_eq(fun(_219044, _219042)), _219282), _219280)), 4732 ^ _76106 : [(4733 ^ _76106) ^ [_219484] : [-(hBOOL(hAPP(_219042, bool, hAPP(_219042, fun(_219042, bool), ord_less_eq(_219042), hAPP(_219044, _219042, _219282, _219484)), hAPP(_219044, _219042, _219280, _219484))))]]], (4735 ^ _76106) ^ [_219580, _219582] : [hBOOL(hAPP(_219042, bool, hAPP(_219042, fun(_219042, bool), ord_less_eq(_219042), hAPP(_219044, _219042, _219582, 4736 ^ [_219042, _219044, _219580, _219582])), hAPP(_219044, _219042, _219580, 4736 ^ [_219042, _219044, _219580, _219582]))), -(hBOOL(hAPP(fun(_219044, _219042), bool, hAPP(fun(_219044, _219042), fun(fun(_219044, _219042), bool), ord_less_eq(fun(_219044, _219042)), _219582), _219580)))]]], (4742 ^ _76106) ^ [_220003] : [linorder(_220003), 4745 ^ _76106 : [(4746 ^ _76106) ^ [_220197, _220199] : [-(hBOOL(hAPP(_220003, bool, hAPP(_220003, fun(_220003, bool), ord_less(_220003), _220199), _220197))), -(ti(_220003, _220199) = ti(_220003, _220197)), -(hBOOL(hAPP(_220003, bool, hAPP(_220003, fun(_220003, bool), ord_less(_220003), _220197), _220199)))]]], (4756 ^ _76106) ^ [_220573] : [preorder(_220573), 4759 ^ _76106 : [(4760 ^ _76106) ^ [_220753, _220755] : [hBOOL(hAPP(_220573, bool, hAPP(_220573, fun(_220573, bool), ord_less(_220573), _220755), _220753)), hBOOL(hAPP(_220573, bool, hAPP(_220573, fun(_220573, bool), ord_less(_220573), _220753), _220755))]]], (4766 ^ _76106) ^ [_221019] : [order(_221019), 4769 ^ _76106 : [(4770 ^ _76106) ^ [_221236, _221238, _221240] : [hBOOL(hAPP(_221019, bool, hAPP(_221019, fun(_221019, bool), ord_less(_221019), _221238), _221236)), hBOOL(hAPP(_221019, bool, hAPP(_221019, fun(_221019, bool), ord_less(_221019), _221240), _221238)), -(hBOOL(hAPP(_221019, bool, hAPP(_221019, fun(_221019, bool), ord_less(_221019), _221240), _221236)))]]], (4780 ^ _76106) ^ [_221632] : [preorder(_221632), 4783 ^ _76106 : [(4784 ^ _76106) ^ [_221849, _221851, _221853] : [hBOOL(hAPP(_221632, bool, hAPP(_221632, fun(_221632, bool), ord_less(_221632), _221851), _221849)), hBOOL(hAPP(_221632, bool, hAPP(_221632, fun(_221632, bool), ord_less(_221632), _221849), _221853)), -(hBOOL(hAPP(_221632, bool, hAPP(_221632, fun(_221632, bool), ord_less(_221632), _221851), _221853)))]]], (4794 ^ _76106) ^ [_222245] : [order(_222245), 4797 ^ _76106 : [(4798 ^ _76106) ^ [_222454, _222456, _222458] : [hBOOL(hAPP(_222245, bool, hAPP(_222245, fun(_222245, bool), ord_less(_222245), _222456), _222454)), ti(_222245, _222456) = ti(_222245, _222458), -(hBOOL(hAPP(_222245, bool, hAPP(_222245, fun(_222245, bool), ord_less(_222245), _222458), _222454)))]]], (4808 ^ _76106) ^ [_222834] : [ord(_222834), 4811 ^ _76106 : [(4812 ^ _76106) ^ [_223037, _223039, _223041] : [hBOOL(hAPP(_222834, bool, hAPP(_222834, fun(_222834, bool), ord_less(_222834), _223039), _223037)), _223037 = _223041, -(hBOOL(hAPP(_222834, bool, hAPP(_222834, fun(_222834, bool), ord_less(_222834), _223039), _223041)))]]], (4822 ^ _76106) ^ [_223405] : [order(_223405), 4825 ^ _76106 : [(4826 ^ _76106) ^ [_223614, _223616, _223618] : [ti(_223405, _223616) = ti(_223405, _223614), hBOOL(hAPP(_223405, bool, hAPP(_223405, fun(_223405, bool), ord_less(_223405), _223618), _223614)), -(hBOOL(hAPP(_223405, bool, hAPP(_223405, fun(_223405, bool), ord_less(_223405), _223618), _223616)))]]], (4836 ^ _76106) ^ [_223994] : [ord(_223994), 4839 ^ _76106 : [(4840 ^ _76106) ^ [_224197, _224199, _224201] : [_224199 = _224197, hBOOL(hAPP(_223994, bool, hAPP(_223994, fun(_223994, bool), ord_less(_223994), _224197), _224201)), -(hBOOL(hAPP(_223994, bool, hAPP(_223994, fun(_223994, bool), ord_less(_223994), _224199), _224201)))]]], (4850 ^ _76106) ^ [_224565] : [order(_224565), 4853 ^ _76106 : [(4854 ^ _76106) ^ [_224745, _224747] : [hBOOL(hAPP(_224565, bool, hAPP(_224565, fun(_224565, bool), ord_less(_224565), _224747), _224745)), hBOOL(hAPP(_224565, bool, hAPP(_224565, fun(_224565, bool), ord_less(_224565), _224745), _224747))]]], (4860 ^ _76106) ^ [_225011] : [preorder(_225011), 4863 ^ _76106 : [(4864 ^ _76106) ^ [_225191, _225193] : [hBOOL(hAPP(_225011, bool, hAPP(_225011, fun(_225011, bool), ord_less(_225011), _225193), _225191)), hBOOL(hAPP(_225011, bool, hAPP(_225011, fun(_225011, bool), ord_less(_225011), _225191), _225193))]]], (4870 ^ _76106) ^ [_225457] : [preorder(_225457), 4873 ^ _76106 : [(4874 ^ _76106) ^ [_225659, _225661, _225663] : [hBOOL(hAPP(_225457, bool, hAPP(_225457, fun(_225457, bool), ord_less(_225457), _225661), _225659)), hBOOL(hAPP(_225457, bool, hAPP(_225457, fun(_225457, bool), ord_less(_225457), _225659), _225661)), -(hBOOL(_225663))]]], (4884 ^ _76106) ^ [_226025] : [order(_226025), 4887 ^ _76106 : [(4888 ^ _76106) ^ [_226197, _226199] : [hBOOL(hAPP(_226025, bool, hAPP(_226025, fun(_226025, bool), ord_less(_226025), _226199), _226197)), ti(_226025, _226197) = ti(_226025, _226199)]]], (4894 ^ _76106) ^ [_226447] : [order(_226447), 4897 ^ _76106 : [(4898 ^ _76106) ^ [_226619, _226621] : [hBOOL(hAPP(_226447, bool, hAPP(_226447, fun(_226447, bool), ord_less(_226447), _226621), _226619)), ti(_226447, _226621) = ti(_226447, _226619)]]], (4904 ^ _76106) ^ [_226869] : [preorder(_226869), 4907 ^ _76106 : [(4908 ^ _76106) ^ [_227049, _227051] : [hBOOL(hAPP(_226869, bool, hAPP(_226869, fun(_226869, bool), ord_less(_226869), _227051), _227049)), hBOOL(hAPP(_226869, bool, hAPP(_226869, fun(_226869, bool), ord_less(_226869), _227049), _227051))]]], (4914 ^ _76106) ^ [_227315] : [preorder(_227315), 4917 ^ _76106 : [(4918 ^ _76106) ^ [_227495, _227497] : [hBOOL(hAPP(_227315, bool, hAPP(_227315, fun(_227315, bool), ord_less(_227315), _227497), _227495)), hBOOL(hAPP(_227315, bool, hAPP(_227315, fun(_227315, bool), ord_less(_227315), _227495), _227497))]]], (4924 ^ _76106) ^ [_227761] : [order(_227761), 4927 ^ _76106 : [(4928 ^ _76106) ^ [_227933, _227935] : [hBOOL(hAPP(_227761, bool, hAPP(_227761, fun(_227761, bool), ord_less(_227761), _227935), _227933)), ti(_227761, _227935) = ti(_227761, _227933)]]], (4934 ^ _76106) ^ [_228183] : [linorder(_228183), 4937 ^ _76106 : [(4938 ^ _76106) ^ [_228377, _228379] : [-(ti(_228183, _228379) = ti(_228183, _228377)), -(hBOOL(hAPP(_228183, bool, hAPP(_228183, fun(_228183, bool), ord_less(_228183), _228379), _228377))), -(hBOOL(hAPP(_228183, bool, hAPP(_228183, fun(_228183, bool), ord_less(_228183), _228377), _228379)))]]], (4948 ^ _76106) ^ [_228753] : [linorder(_228753), 4951 ^ _76106 : [(4952 ^ _76106) ^ [_228947, _228949] : [-(hBOOL(hAPP(_228753, bool, hAPP(_228753, fun(_228753, bool), ord_less(_228753), _228949), _228947))), 4955 ^ _76106 : [(4956 ^ _76106) ^ [] : [-(hBOOL(hAPP(_228753, bool, hAPP(_228753, fun(_228753, bool), ord_less(_228753), _228947), _228949))), -(ti(_228753, _228947) = ti(_228753, _228949))], (4962 ^ _76106) ^ [] : [ti(_228753, _228947) = ti(_228753, _228949), hBOOL(hAPP(_228753, bool, hAPP(_228753, fun(_228753, bool), ord_less(_228753), _228947), _228949))]]]]], (4968 ^ _76106) ^ [_229509] : [linorder(_229509), 4971 ^ _76106 : [(4972 ^ _76106) ^ [_229699, _229701] : [-(hBOOL(hAPP(_229509, bool, hAPP(_229509, fun(_229509, bool), ord_less(_229509), _229701), _229699))), -(ti(_229509, _229701) = ti(_229509, _229699)), -(hBOOL(hAPP(_229509, bool, hAPP(_229509, fun(_229509, bool), ord_less(_229509), _229699), _229701)))]]], (4982 ^ _76106) ^ [_230071] : [linorder(_230071), 4985 ^ _76106 : [(4996 ^ _76106) ^ [_230627, _230629] : [4997 ^ _76106 : [(4998 ^ _76106) ^ [] : [hBOOL(hAPP(_230071, bool, hAPP(_230071, fun(_230071, bool), ord_less(_230071), _230627), _230629))], (5000 ^ _76106) ^ [] : [ti(_230071, _230629) = ti(_230071, _230627)]], hBOOL(hAPP(_230071, bool, hAPP(_230071, fun(_230071, bool), ord_less(_230071), _230629), _230627))], (4986 ^ _76106) ^ [_230292, _230294] : [-(hBOOL(hAPP(_230071, bool, hAPP(_230071, fun(_230071, bool), ord_less(_230071), _230294), _230292))), -(hBOOL(hAPP(_230071, bool, hAPP(_230071, fun(_230071, bool), ord_less(_230071), _230292), _230294))), -(ti(_230071, _230294) = ti(_230071, _230292))]]], (5004 ^ _76106) ^ [_230983] : [linorder(_230983), 5007 ^ _76106 : [(5018 ^ _76106) ^ [_231539, _231541] : [5019 ^ _76106 : [(5020 ^ _76106) ^ [] : [hBOOL(hAPP(_230983, bool, hAPP(_230983, fun(_230983, bool), ord_less(_230983), _231541), _231539))], (5022 ^ _76106) ^ [] : [hBOOL(hAPP(_230983, bool, hAPP(_230983, fun(_230983, bool), ord_less(_230983), _231539), _231541))]], ti(_230983, _231541) = ti(_230983, _231539)], (5008 ^ _76106) ^ [_231204, _231206] : [-(ti(_230983, _231206) = ti(_230983, _231204)), -(hBOOL(hAPP(_230983, bool, hAPP(_230983, fun(_230983, bool), ord_less(_230983), _231206), _231204))), -(hBOOL(hAPP(_230983, bool, hAPP(_230983, fun(_230983, bool), ord_less(_230983), _231204), _231206)))]]], (5026 ^ _76106) ^ [_231895] : [preorder(_231895), 5029 ^ _76106 : [(5030 ^ _76106) ^ [_232020] : [hBOOL(hAPP(_231895, bool, hAPP(_231895, fun(_231895, bool), ord_less(_231895), _232020), _232020))]]], (5032 ^ _76106) ^ [_232134] : [linorder(_232134), 5035 ^ _76106 : [(5036 ^ _76106) ^ [_232343, _232345] : [-(hBOOL(hAPP(_232134, bool, hAPP(_232134, fun(_232134, bool), ord_less(_232134), _232345), _232343))), -(hBOOL(hAPP(_232134, bool, hAPP(_232134, fun(_232134, bool), ord_less_eq(_232134), _232343), _232345)))], (5042 ^ _76106) ^ [_232572, _232574] : [hBOOL(hAPP(_232134, bool, hAPP(_232134, fun(_232134, bool), ord_less_eq(_232134), _232572), _232574)), hBOOL(hAPP(_232134, bool, hAPP(_232134, fun(_232134, bool), ord_less(_232134), _232574), _232572))]]], (5048 ^ _76106) ^ [_232840] : [linorder(_232840), 5051 ^ _76106 : [(5052 ^ _76106) ^ [_233049, _233051] : [-(hBOOL(hAPP(_232840, bool, hAPP(_232840, fun(_232840, bool), ord_less_eq(_232840), _233051), _233049))), -(hBOOL(hAPP(_232840, bool, hAPP(_232840, fun(_232840, bool), ord_less(_232840), _233049), _233051)))], (5058 ^ _76106) ^ [_233278, _233280] : [hBOOL(hAPP(_232840, bool, hAPP(_232840, fun(_232840, bool), ord_less(_232840), _233278), _233280)), hBOOL(hAPP(_232840, bool, hAPP(_232840, fun(_232840, bool), ord_less_eq(_232840), _233280), _233278))]]], (5064 ^ _76106) ^ [_233546] : [linorder(_233546), 5067 ^ _76106 : [(5068 ^ _76106) ^ [_233724, _233726] : [-(hBOOL(hAPP(_233546, bool, hAPP(_233546, fun(_233546, bool), ord_less_eq(_233546), _233726), _233724))), -(hBOOL(hAPP(_233546, bool, hAPP(_233546, fun(_233546, bool), ord_less(_233546), _233724), _233726)))]]], (5074 ^ _76106) ^ [_233990] : [order(_233990), 5077 ^ _76106 : [(5078 ^ _76106) ^ [_234211, _234213] : [hBOOL(hAPP(_233990, bool, hAPP(_233990, fun(_233990, bool), ord_less(_233990), _234213), _234211)), 5081 ^ _76106 : [(5082 ^ _76106) ^ [] : [-(hBOOL(hAPP(_233990, bool, hAPP(_233990, fun(_233990, bool), ord_less_eq(_233990), _234213), _234211)))], (5084 ^ _76106) ^ [] : [ti(_233990, _234213) = ti(_233990, _234211)]]], (5086 ^ _76106) ^ [_234527, _234529] : [-(hBOOL(hAPP(_233990, bool, hAPP(_233990, fun(_233990, bool), ord_less(_233990), _234529), _234527))), hBOOL(hAPP(_233990, bool, hAPP(_233990, fun(_233990, bool), ord_less_eq(_233990), _234529), _234527)), -(ti(_233990, _234529) = ti(_233990, _234527))]]], (5096 ^ _76106) ^ [_234902] : [preorder(_234902), 5099 ^ _76106 : [(5100 ^ _76106) ^ [_235131, _235133] : [hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less(_234902), _235133), _235131)), 5103 ^ _76106 : [(5104 ^ _76106) ^ [] : [-(hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less_eq(_234902), _235133), _235131)))], (5106 ^ _76106) ^ [] : [hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less_eq(_234902), _235131), _235133))]]], (5108 ^ _76106) ^ [_235463, _235465] : [-(hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less(_234902), _235465), _235463))), hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less_eq(_234902), _235465), _235463)), -(hBOOL(hAPP(_234902, bool, hAPP(_234902, fun(_234902, bool), ord_less_eq(_234902), _235463), _235465)))]]], (5118 ^ _76106) ^ [_235854] : [order(_235854), 5121 ^ _76106 : [(5132 ^ _76106) ^ [_236405, _236407] : [5133 ^ _76106 : [(5134 ^ _76106) ^ [] : [hBOOL(hAPP(_235854, bool, hAPP(_235854, fun(_235854, bool), ord_less(_235854), _236407), _236405))], (5136 ^ _76106) ^ [] : [ti(_235854, _236407) = ti(_235854, _236405)]], -(hBOOL(hAPP(_235854, bool, hAPP(_235854, fun(_235854, bool), ord_less_eq(_235854), _236407), _236405)))], (5122 ^ _76106) ^ [_236073, _236075] : [hBOOL(hAPP(_235854, bool, hAPP(_235854, fun(_235854, bool), ord_less_eq(_235854), _236075), _236073)), -(hBOOL(hAPP(_235854, bool, hAPP(_235854, fun(_235854, bool), ord_less(_235854), _236075), _236073))), -(ti(_235854, _236075) = ti(_235854, _236073))]]], (5140 ^ _76106) ^ [_236760] : [linorder(_236760), 5143 ^ _76106 : [(5144 ^ _76106) ^ [_236940, _236942] : [-(hBOOL(hAPP(_236760, bool, hAPP(_236760, fun(_236760, bool), ord_less(_236760), _236942), _236940))), -(hBOOL(hAPP(_236760, bool, hAPP(_236760, fun(_236760, bool), ord_less_eq(_236760), _236940), _236942)))]]], (5150 ^ _76106) ^ [_237208] : [linorder(_237208), 5153 ^ _76106 : [(5154 ^ _76106) ^ [_237388, _237390] : [-(hBOOL(hAPP(_237208, bool, hAPP(_237208, fun(_237208, bool), ord_less_eq(_237208), _237390), _237388))), -(hBOOL(hAPP(_237208, bool, hAPP(_237208, fun(_237208, bool), ord_less(_237208), _237388), _237390)))]]], (5160 ^ _76106) ^ [_237656] : [linorder(_237656), 5163 ^ _76106 : [(5164 ^ _76106) ^ [_237848, _237850] : [-(hBOOL(hAPP(_237656, bool, hAPP(_237656, fun(_237656, bool), ord_less(_237656), _237850), _237848))), 5167 ^ _76106 : [(5168 ^ _76106) ^ [] : [hBOOL(hAPP(_237656, bool, hAPP(_237656, fun(_237656, bool), ord_less_eq(_237656), _237850), _237848)), -(ti(_237656, _237850) = ti(_237656, _237848))], (5174 ^ _76106) ^ [] : [ti(_237656, _237850) = ti(_237656, _237848), -(hBOOL(hAPP(_237656, bool, hAPP(_237656, fun(_237656, bool), ord_less_eq(_237656), _237850), _237848)))]]]]], (5180 ^ _76106) ^ [_238408] : [order(_238408), 5183 ^ _76106 : [(5184 ^ _76106) ^ [_238600, _238602] : [-(ti(_238408, _238602) = ti(_238408, _238600)), hBOOL(hAPP(_238408, bool, hAPP(_238408, fun(_238408, bool), ord_less_eq(_238408), _238602), _238600)), -(hBOOL(hAPP(_238408, bool, hAPP(_238408, fun(_238408, bool), ord_less(_238408), _238602), _238600)))]]], (5194 ^ _76106) ^ [_238973] : [order(_238973), 5197 ^ _76106 : [(5198 ^ _76106) ^ [_239165, _239167] : [-(ti(_238973, _239167) = ti(_238973, _239165)), hBOOL(hAPP(_238973, bool, hAPP(_238973, fun(_238973, bool), ord_less_eq(_238973), _239165), _239167)), -(hBOOL(hAPP(_238973, bool, hAPP(_238973, fun(_238973, bool), ord_less(_238973), _239165), _239167)))]]], (5208 ^ _76106) ^ [_239538] : [linorder(_239538), 5211 ^ _76106 : [(5212 ^ _76106) ^ [_239718, _239720] : [hBOOL(hAPP(_239538, bool, hAPP(_239538, fun(_239538, bool), ord_less_eq(_239538), _239720), _239718)), hBOOL(hAPP(_239538, bool, hAPP(_239538, fun(_239538, bool), ord_less(_239538), _239718), _239720))]]], (5218 ^ _76106) ^ [_239984] : [preorder(_239984), 5221 ^ _76106 : [(5222 ^ _76106) ^ [_240162, _240164] : [hBOOL(hAPP(_239984, bool, hAPP(_239984, fun(_239984, bool), ord_less(_239984), _240164), _240162)), -(hBOOL(hAPP(_239984, bool, hAPP(_239984, fun(_239984, bool), ord_less_eq(_239984), _240164), _240162)))]]], (5228 ^ _76106) ^ [_240427] : [linorder(_240427), 5231 ^ _76106 : [(5232 ^ _76106) ^ [_240619, _240621] : [hBOOL(hAPP(_240427, bool, hAPP(_240427, fun(_240427, bool), ord_less_eq(_240427), _240621), _240619)), 5235 ^ _76106 : [(5236 ^ _76106) ^ [] : [-(hBOOL(hAPP(_240427, bool, hAPP(_240427, fun(_240427, bool), ord_less(_240427), _240621), _240619))), -(ti(_240427, _240621) = ti(_240427, _240619))], (5242 ^ _76106) ^ [] : [ti(_240427, _240621) = ti(_240427, _240619), hBOOL(hAPP(_240427, bool, hAPP(_240427, fun(_240427, bool), ord_less(_240427), _240621), _240619))]]]]], (5248 ^ _76106) ^ [_241178] : [order(_241178), 5251 ^ _76106 : [(5252 ^ _76106) ^ [_241368, _241370] : [hBOOL(hAPP(_241178, bool, hAPP(_241178, fun(_241178, bool), ord_less_eq(_241178), _241370), _241368)), -(hBOOL(hAPP(_241178, bool, hAPP(_241178, fun(_241178, bool), ord_less(_241178), _241370), _241368))), -(ti(_241178, _241370) = ti(_241178, _241368))]]], (5262 ^ _76106) ^ [_241739] : [order(_241739), 5265 ^ _76106 : [(5266 ^ _76106) ^ [_241931, _241933] : [hBOOL(hAPP(_241739, bool, hAPP(_241739, fun(_241739, bool), ord_less_eq(_241739), _241933), _241931)), -(ti(_241739, _241933) = ti(_241739, _241931)), -(hBOOL(hAPP(_241739, bool, hAPP(_241739, fun(_241739, bool), ord_less(_241739), _241933), _241931)))]]], (5276 ^ _76106) ^ [_242304] : [order(_242304), 5279 ^ _76106 : [(5280 ^ _76106) ^ [_242496, _242498] : [hBOOL(hAPP(_242304, bool, hAPP(_242304, fun(_242304, bool), ord_less_eq(_242304), _242498), _242496)), -(ti(_242304, _242496) = ti(_242304, _242498)), -(hBOOL(hAPP(_242304, bool, hAPP(_242304, fun(_242304, bool), ord_less(_242304), _242498), _242496)))]]], (5290 ^ _76106) ^ [_242869] : [preorder(_242869), 5293 ^ _76106 : [(5294 ^ _76106) ^ [_243086, _243088, _243090] : [hBOOL(hAPP(_242869, bool, hAPP(_242869, fun(_242869, bool), ord_less(_242869), _243088), _243086)), hBOOL(hAPP(_242869, bool, hAPP(_242869, fun(_242869, bool), ord_less_eq(_242869), _243086), _243090)), -(hBOOL(hAPP(_242869, bool, hAPP(_242869, fun(_242869, bool), ord_less(_242869), _243088), _243090)))]]], (5304 ^ _76106) ^ [_243482] : [order(_243482), 5307 ^ _76106 : [(5308 ^ _76106) ^ [_243699, _243701, _243703] : [hBOOL(hAPP(_243482, bool, hAPP(_243482, fun(_243482, bool), ord_less(_243482), _243701), _243699)), hBOOL(hAPP(_243482, bool, hAPP(_243482, fun(_243482, bool), ord_less_eq(_243482), _243703), _243701)), -(hBOOL(hAPP(_243482, bool, hAPP(_243482, fun(_243482, bool), ord_less(_243482), _243703), _243699)))]]], (5318 ^ _76106) ^ [_244095] : [preorder(_244095), 5321 ^ _76106 : [(5322 ^ _76106) ^ [_244312, _244314, _244316] : [hBOOL(hAPP(_244095, bool, hAPP(_244095, fun(_244095, bool), ord_less_eq(_244095), _244314), _244312)), hBOOL(hAPP(_244095, bool, hAPP(_244095, fun(_244095, bool), ord_less(_244095), _244312), _244316)), -(hBOOL(hAPP(_244095, bool, hAPP(_244095, fun(_244095, bool), ord_less(_244095), _244314), _244316)))]]], (5332 ^ _76106) ^ [_244708] : [order(_244708), 5335 ^ _76106 : [(5336 ^ _76106) ^ [_244925, _244927, _244929] : [hBOOL(hAPP(_244708, bool, hAPP(_244708, fun(_244708, bool), ord_less_eq(_244708), _244927), _244925)), hBOOL(hAPP(_244708, bool, hAPP(_244708, fun(_244708, bool), ord_less(_244708), _244929), _244927)), -(hBOOL(hAPP(_244708, bool, hAPP(_244708, fun(_244708, bool), ord_less(_244708), _244929), _244925)))]]], (5346 ^ _76106) ^ [_245335, _245337] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _245335)), hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _245337)), 5354 ^ _76106 : [(5355 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), 5353 ^ [_245335, _245337])))], (5357 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), 5353 ^ [_245335, _245337]), _245335)))], (5359 ^ _76106) ^ [] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), 5353 ^ [_245335, _245337]), _245337)))]]], (5361 ^ _76106) ^ [_245934] : [dense_linorder(_245934), 5364 ^ _76106 : [(5365 ^ _76106) ^ [_246137, _246139] : [5367 ^ _76106 : [(5368 ^ _76106) ^ [] : [-(hBOOL(hAPP(_245934, bool, hAPP(_245934, fun(_245934, bool), ord_less(_245934), 5366 ^ [_245934, _246137, _246139]), _246137)))], (5370 ^ _76106) ^ [] : [hBOOL(hAPP(_245934, bool, hAPP(_245934, fun(_245934, bool), ord_less_eq(_245934), 5366 ^ [_245934, _246137, _246139]), _246139))]], -(hBOOL(hAPP(_245934, bool, hAPP(_245934, fun(_245934, bool), ord_less_eq(_245934), _246137), _246139)))]]], (5374 ^ _76106) ^ [_246627, _246629] : [ord(_246627), 5377 ^ _76106 : [(5378 ^ _76106) ^ [_246896, _246898] : [hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less(fun(_246629, _246627)), _246898), _246896)), 5381 ^ _76106 : [(5382 ^ _76106) ^ [] : [-(hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less_eq(fun(_246629, _246627)), _246898), _246896)))], (5384 ^ _76106) ^ [] : [hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less_eq(fun(_246629, _246627)), _246896), _246898))]]], (5386 ^ _76106) ^ [_247310, _247312] : [-(hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less(fun(_246629, _246627)), _247312), _247310))), hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less_eq(fun(_246629, _246627)), _247312), _247310)), -(hBOOL(hAPP(fun(_246629, _246627), bool, hAPP(fun(_246629, _246627), fun(fun(_246629, _246627), bool), ord_less_eq(fun(_246629, _246627)), _247310), _247312)))]]], (5396 ^ _76106) ^ [_247799, _247801] : [ord(_247799), 5399 ^ _76106 : [(5400 ^ _76106) ^ [_248008, _248010] : [hBOOL(hAPP(_247799, bool, hAPP(_247799, fun(_247799, bool), ord_less_eq(_247799), hAPP(_247801, _247799, _248010, 5401 ^ [_247799, _247801, _248008, _248010])), hAPP(_247801, _247799, _248008, 5401 ^ [_247799, _247801, _248008, _248010]))), -(hBOOL(hAPP(fun(_247801, _247799), bool, hAPP(fun(_247801, _247799), fun(fun(_247801, _247799), bool), ord_less_eq(fun(_247801, _247799)), _248010), _248008)))]]], (5407 ^ _76106) ^ [_248429] : [linorder(_248429), 5411 ^ _76106 : [(5412 ^ _76106) ^ [_248698, _248700] : [hBOOL(hAPP(_248429, bool, hAPP(_248429, fun(_248429, bool), ord_less(_248429), 5410 ^ [_248429, _248700]), _248698)), hBOOL(hAPP(_248429, bool, hAPP(_248429, fun(_248429, bool), ord_less_eq(_248429), _248698), _248700))]]], (5418 ^ _76106) ^ [_248978] : [dense_linorder(_248978), 5421 ^ _76106 : [(5422 ^ _76106) ^ [_249240, _249242, _249244] : [hBOOL(hAPP(_248978, bool, hAPP(_248978, fun(_248978, bool), ord_less(_248978), _249242), _249240)), 5428 ^ _76106 : [(5429 ^ _76106) ^ [] : [-(hBOOL(hAPP(_248978, bool, hAPP(_248978, fun(_248978, bool), ord_less(_248978), _249242), 5427 ^ [_248978, _249240, _249242, _249244])))], (5431 ^ _76106) ^ [] : [-(hBOOL(hAPP(_248978, bool, hAPP(_248978, fun(_248978, bool), ord_less(_248978), 5427 ^ [_248978, _249240, _249242, _249244]), _249240)))], (5433 ^ _76106) ^ [] : [hBOOL(hAPP(_248978, bool, hAPP(_248978, fun(_248978, bool), ord_less_eq(_248978), 5427 ^ [_248978, _249240, _249242, _249244]), _249244))]], -(hBOOL(hAPP(_248978, bool, hAPP(_248978, fun(_248978, bool), ord_less_eq(_248978), _249240), _249244)))]]], (5437 ^ _76106) ^ [_250008, _250010] : [order(_250008), order(_250010), 5444 ^ _76106 : [(5445 ^ _76106) ^ [_250405, _250407, _250409, _250411] : [hBOOL(hAPP(_250008, bool, hAPP(_250008, fun(_250008, bool), ord_less(_250008), _250407), _250405)), hBOOL(hAPP(_250010, bool, hAPP(_250010, fun(_250010, bool), ord_less_eq(_250010), _250411), hAPP(_250008, _250010, _250409, _250407))), 5456 ^ _76106 : [(5457 ^ _76106) ^ [] : [-(hBOOL(hAPP(_250008, bool, hAPP(_250008, fun(_250008, bool), ord_less(_250008), 5455 ^ [_250008, _250010, _250405, _250407, _250409, _250411]), 5454 ^ [_250008, _250010, _250405, _250407, _250409, _250411])))], (5459 ^ _76106) ^ [] : [hBOOL(hAPP(_250010, bool, hAPP(_250010, fun(_250010, bool), ord_less(_250010), hAPP(_250008, _250010, _250409, 5455 ^ [_250008, _250010, _250405, _250407, _250409, _250411])), hAPP(_250008, _250010, _250409, 5454 ^ [_250008, _250010, _250405, _250407, _250409, _250411])))]], -(hBOOL(hAPP(_250010, bool, hAPP(_250010, fun(_250010, bool), ord_less(_250010), _250411), hAPP(_250008, _250010, _250409, _250405))))]]], (5463 ^ _76106) ^ [_251424] : [linorder(_251424), 5467 ^ _76106 : [(5468 ^ _76106) ^ [_251689, _251691] : [hBOOL(hAPP(_251424, bool, hAPP(_251424, fun(_251424, bool), ord_less(_251424), _251689), 5466 ^ [_251424, _251691])), -(hBOOL(hAPP(_251424, bool, hAPP(_251424, fun(_251424, bool), ord_less_eq(_251424), _251689), _251691)))]]], (5474 ^ _76106) ^ [_251968] : [linorder(_251968), 5478 ^ _76106 : [(5479 ^ _76106) ^ [_252233, _252235] : [hBOOL(hAPP(_251968, bool, hAPP(_251968, fun(_251968, bool), ord_less(_251968), 5477 ^ [_251968, _252235]), _252233)), -(hBOOL(hAPP(_251968, bool, hAPP(_251968, fun(_251968, bool), ord_less_eq(_251968), _252235), _252233)))]]], (5485 ^ _76106) ^ [_252526, _252528] : [order(_252526), order(_252528), 5492 ^ _76106 : [(5493 ^ _76106) ^ [_252923, _252925, _252927, _252929] : [hBOOL(hAPP(_252526, bool, hAPP(_252526, fun(_252526, bool), ord_less_eq(_252526), _252925), _252923)), hBOOL(hAPP(_252528, bool, hAPP(_252528, fun(_252528, bool), ord_less(_252528), _252929), hAPP(_252526, _252528, _252927, _252925))), 5504 ^ _76106 : [(5505 ^ _76106) ^ [] : [-(hBOOL(hAPP(_252526, bool, hAPP(_252526, fun(_252526, bool), ord_less_eq(_252526), 5503 ^ [_252526, _252528, _252923, _252925, _252927, _252929]), 5502 ^ [_252526, _252528, _252923, _252925, _252927, _252929])))], (5507 ^ _76106) ^ [] : [hBOOL(hAPP(_252528, bool, hAPP(_252528, fun(_252528, bool), ord_less_eq(_252528), hAPP(_252526, _252528, _252927, 5503 ^ [_252526, _252528, _252923, _252925, _252927, _252929])), hAPP(_252526, _252528, _252927, 5502 ^ [_252526, _252528, _252923, _252925, _252927, _252929])))]], -(hBOOL(hAPP(_252528, bool, hAPP(_252528, fun(_252528, bool), ord_less(_252528), _252929), hAPP(_252526, _252528, _252927, _252923))))]]], (5511 ^ _76106) ^ [_253956, _253958] : [order(_253956), order(_253958), 5518 ^ _76106 : [(5519 ^ _76106) ^ [_254353, _254355, _254357, _254359] : [hBOOL(hAPP(_253958, bool, hAPP(_253958, fun(_253958, bool), ord_less(_253958), _254355), _254353)), hBOOL(hAPP(_253956, bool, hAPP(_253956, fun(_253956, bool), ord_less_eq(_253956), hAPP(_253958, _253956, _254359, _254353)), _254357)), 5530 ^ _76106 : [(5531 ^ _76106) ^ [] : [-(hBOOL(hAPP(_253958, bool, hAPP(_253958, fun(_253958, bool), ord_less(_253958), 5528 ^ [_253956, _253958, _254353, _254355, _254357, _254359]), 5529 ^ [_253956, _253958, _254353, _254355, _254357, _254359])))], (5533 ^ _76106) ^ [] : [hBOOL(hAPP(_253956, bool, hAPP(_253956, fun(_253956, bool), ord_less(_253956), hAPP(_253958, _253956, _254359, 5528 ^ [_253956, _253958, _254353, _254355, _254357, _254359])), hAPP(_253958, _253956, _254359, 5529 ^ [_253956, _253958, _254353, _254355, _254357, _254359])))]], -(hBOOL(hAPP(_253956, bool, hAPP(_253956, fun(_253956, bool), ord_less(_253956), hAPP(_253958, _253956, _254359, _254355)), _254357)))]]], (5537 ^ _76106) ^ [_255372] : [linorder(_255372), 5541 ^ _76106 : [(5542 ^ _76106) ^ [_255641, _255643] : [hBOOL(hAPP(_255372, bool, hAPP(_255372, fun(_255372, bool), ord_less(_255372), _255641), 5540 ^ [_255372, _255643])), hBOOL(hAPP(_255372, bool, hAPP(_255372, fun(_255372, bool), ord_less_eq(_255372), _255643), _255641))]]], (5548 ^ _76106) ^ [_255935, _255937] : [order(_255935), ord(_255937), 5555 ^ _76106 : [(5556 ^ _76106) ^ [_256332, _256334, _256336, _256338] : [hBOOL(hAPP(_255935, bool, hAPP(_255935, fun(_255935, bool), ord_less_eq(_255935), hAPP(_255937, _255935, _256336, _256334)), _256332)), hBOOL(hAPP(_255937, bool, hAPP(_255937, fun(_255937, bool), ord_less(_255937), _256338), _256334)), 5567 ^ _76106 : [(5568 ^ _76106) ^ [] : [-(hBOOL(hAPP(_255937, bool, hAPP(_255937, fun(_255937, bool), ord_less(_255937), 5566 ^ [_255935, _255937, _256332, _256334, _256336, _256338]), 5565 ^ [_255935, _255937, _256332, _256334, _256336, _256338])))], (5570 ^ _76106) ^ [] : [hBOOL(hAPP(_255935, bool, hAPP(_255935, fun(_255935, bool), ord_less(_255935), hAPP(_255937, _255935, _256336, 5566 ^ [_255935, _255937, _256332, _256334, _256336, _256338])), hAPP(_255937, _255935, _256336, 5565 ^ [_255935, _255937, _256332, _256334, _256336, _256338])))]], -(hBOOL(hAPP(_255935, bool, hAPP(_255935, fun(_255935, bool), ord_less(_255935), hAPP(_255937, _255935, _256336, _256338)), _256332)))]]], (5574 ^ _76106) ^ [_257365, _257367] : [order(_257365), order(_257367), 5581 ^ _76106 : [(5582 ^ _76106) ^ [_257762, _257764, _257766, _257768] : [hBOOL(hAPP(_257367, bool, hAPP(_257367, fun(_257367, bool), ord_less_eq(_257367), _257764), _257762)), hBOOL(hAPP(_257365, bool, hAPP(_257365, fun(_257365, bool), ord_less(_257365), hAPP(_257367, _257365, _257768, _257762)), _257766)), 5593 ^ _76106 : [(5594 ^ _76106) ^ [] : [-(hBOOL(hAPP(_257367, bool, hAPP(_257367, fun(_257367, bool), ord_less_eq(_257367), 5591 ^ [_257365, _257367, _257762, _257764, _257766, _257768]), 5592 ^ [_257365, _257367, _257762, _257764, _257766, _257768])))], (5596 ^ _76106) ^ [] : [hBOOL(hAPP(_257365, bool, hAPP(_257365, fun(_257365, bool), ord_less_eq(_257365), hAPP(_257367, _257365, _257768, 5591 ^ [_257365, _257367, _257762, _257764, _257766, _257768])), hAPP(_257367, _257365, _257768, 5592 ^ [_257365, _257367, _257762, _257764, _257766, _257768])))]], -(hBOOL(hAPP(_257365, bool, hAPP(_257365, fun(_257365, bool), ord_less(_257365), hAPP(_257367, _257365, _257768, _257764)), _257766)))]]], (5600 ^ _76106) ^ [_258795, _258797] : [order(_258795), order(_258797), 5607 ^ _76106 : [(5608 ^ _76106) ^ [_259192, _259194, _259196, _259198] : [hBOOL(hAPP(_258797, bool, hAPP(_258797, fun(_258797, bool), ord_less(_258797), _259196), hAPP(_258795, _258797, _259194, _259192))), hBOOL(hAPP(_258795, bool, hAPP(_258795, fun(_258795, bool), ord_less_eq(_258795), _259192), _259198)), 5619 ^ _76106 : [(5620 ^ _76106) ^ [] : [-(hBOOL(hAPP(_258795, bool, hAPP(_258795, fun(_258795, bool), ord_less_eq(_258795), 5617 ^ [_258795, _258797, _259192, _259194, _259196, _259198]), 5618 ^ [_258795, _258797, _259192, _259194, _259196, _259198])))], (5622 ^ _76106) ^ [] : [hBOOL(hAPP(_258797, bool, hAPP(_258797, fun(_258797, bool), ord_less_eq(_258797), hAPP(_258795, _258797, _259194, 5617 ^ [_258795, _258797, _259192, _259194, _259196, _259198])), hAPP(_258795, _258797, _259194, 5618 ^ [_258795, _258797, _259192, _259194, _259196, _259198])))]], -(hBOOL(hAPP(_258797, bool, hAPP(_258797, fun(_258797, bool), ord_less(_258797), _259196), hAPP(_258795, _258797, _259194, _259198))))]]], (5626 ^ _76106) ^ [_260225, _260227] : [order(_260225), order(_260227), 5633 ^ _76106 : [(5634 ^ _76106) ^ [_260622, _260624, _260626, _260628] : [hBOOL(hAPP(_260225, bool, hAPP(_260225, fun(_260225, bool), ord_less(_260225), hAPP(_260227, _260225, _260626, _260624)), _260622)), hBOOL(hAPP(_260227, bool, hAPP(_260227, fun(_260227, bool), ord_less_eq(_260227), _260628), _260624)), 5645 ^ _76106 : [(5646 ^ _76106) ^ [] : [-(hBOOL(hAPP(_260227, bool, hAPP(_260227, fun(_260227, bool), ord_less_eq(_260227), 5644 ^ [_260225, _260227, _260622, _260624, _260626, _260628]), 5643 ^ [_260225, _260227, _260622, _260624, _260626, _260628])))], (5648 ^ _76106) ^ [] : [hBOOL(hAPP(_260225, bool, hAPP(_260225, fun(_260225, bool), ord_less_eq(_260225), hAPP(_260227, _260225, _260626, 5644 ^ [_260225, _260227, _260622, _260624, _260626, _260628])), hAPP(_260227, _260225, _260626, 5643 ^ [_260225, _260227, _260622, _260624, _260626, _260628])))]], -(hBOOL(hAPP(_260225, bool, hAPP(_260225, fun(_260225, bool), ord_less(_260225), hAPP(_260227, _260225, _260626, _260628)), _260622)))]]], (5652 ^ _76106) ^ [_261655, _261657] : [order(_261655), order(_261657), 5659 ^ _76106 : [(5660 ^ _76106) ^ [_262052, _262054, _262056, _262058] : [hBOOL(hAPP(_261657, bool, hAPP(_261657, fun(_261657, bool), ord_less_eq(_261657), _262056), hAPP(_261655, _261657, _262054, _262052))), hBOOL(hAPP(_261655, bool, hAPP(_261655, fun(_261655, bool), ord_less(_261655), _262052), _262058)), 5671 ^ _76106 : [(5672 ^ _76106) ^ [] : [-(hBOOL(hAPP(_261655, bool, hAPP(_261655, fun(_261655, bool), ord_less(_261655), 5669 ^ [_261655, _261657, _262052, _262054, _262056, _262058]), 5670 ^ [_261655, _261657, _262052, _262054, _262056, _262058])))], (5674 ^ _76106) ^ [] : [hBOOL(hAPP(_261657, bool, hAPP(_261657, fun(_261657, bool), ord_less(_261657), hAPP(_261655, _261657, _262054, 5669 ^ [_261655, _261657, _262052, _262054, _262056, _262058])), hAPP(_261655, _261657, _262054, 5670 ^ [_261655, _261657, _262052, _262054, _262056, _262058])))]], -(hBOOL(hAPP(_261657, bool, hAPP(_261657, fun(_261657, bool), ord_less(_261657), _262056), hAPP(_261655, _261657, _262054, _262058))))]]], (5678 ^ _76106) ^ [_263070, _263072] : [-(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), zero_zero(real)), hAPP(real, real, sqrt, hAPP(real, real, plus_plus(real, hAPP(nat, real, power_power(real, _263072), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(nat, real, power_power(real, _263070), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))))))], (5680 ^ _76106) ^ [_263197, _263199] : [-(hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, _263199), _263197)), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, hAPP(nat, int, power_power(int, _263199), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), hAPP(int, int, hAPP(int, fun(int, int), times_times(int), hAPP(int, int, hAPP(int, fun(int, int), times_times(int), number_number_of(int, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), _263199)), _263197))), hAPP(nat, int, power_power(int, _263197), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))], (5682 ^ _76106) ^ [_263354, _263356] : [-(hAPP(int, int, hAPP(int, fun(int, int), times_times(int), hAPP(int, int, bit1, _263356)), _263354) = hAPP(int, int, plus_plus(int, hAPP(int, int, bit0, hAPP(int, int, hAPP(int, fun(int, int), times_times(int), _263356), _263354))), _263354))], (5684 ^ _76106) ^ [_263487] : [linord20386208strict(_263487), 5687 ^ _76106 : [(5688 ^ _76106) ^ [_263736, _263738, _263740] : [hBOOL(hAPP(_263487, bool, hAPP(_263487, fun(_263487, bool), ord_less_eq(_263487), hAPP(_263487, _263487, hAPP(_263487, fun(_263487, _263487), times_times(_263487), _263740), _263738)), hAPP(_263487, _263487, hAPP(_263487, fun(_263487, _263487), times_times(_263487), _263740), _263736))), hBOOL(hAPP(_263487, bool, hAPP(_263487, fun(_263487, bool), ord_less(_263487), zero_zero(_263487)), _263740)), -(hBOOL(hAPP(_263487, bool, hAPP(_263487, fun(_263487, bool), ord_less_eq(_263487), _263738), _263736)))]]], (5698 ^ _76106) ^ [_264196] : [linord20386208strict(_264196), 5701 ^ _76106 : [(5702 ^ _76106) ^ [_264445, _264447, _264449] : [hBOOL(hAPP(_264196, bool, hAPP(_264196, fun(_264196, bool), ord_less_eq(_264196), hAPP(_264196, _264196, hAPP(_264196, fun(_264196, _264196), times_times(_264196), _264449), _264447)), hAPP(_264196, _264196, hAPP(_264196, fun(_264196, _264196), times_times(_264196), _264445), _264447))), hBOOL(hAPP(_264196, bool, hAPP(_264196, fun(_264196, bool), ord_less(_264196), zero_zero(_264196)), _264447)), -(hBOOL(hAPP(_264196, bool, hAPP(_264196, fun(_264196, bool), ord_less_eq(_264196), _264449), _264445)))]]], (5712 ^ _76106) ^ [_264905] : [linord20386208strict(_264905), 5715 ^ _76106 : [(5716 ^ _76106) ^ [_265154, _265156, _265158] : [hBOOL(hAPP(_264905, bool, hAPP(_264905, fun(_264905, bool), ord_less(_264905), hAPP(_264905, _264905, hAPP(_264905, fun(_264905, _264905), times_times(_264905), _265158), _265156)), hAPP(_264905, _264905, hAPP(_264905, fun(_264905, _264905), times_times(_264905), _265158), _265154))), hBOOL(hAPP(_264905, bool, hAPP(_264905, fun(_264905, bool), ord_less_eq(_264905), zero_zero(_264905)), _265158)), -(hBOOL(hAPP(_264905, bool, hAPP(_264905, fun(_264905, bool), ord_less(_264905), _265156), _265154)))]]], (5726 ^ _76106) ^ [_265614] : [linordered_semiring(_265614), 5729 ^ _76106 : [(5730 ^ _76106) ^ [_265863, _265865, _265867] : [hBOOL(hAPP(_265614, bool, hAPP(_265614, fun(_265614, bool), ord_less(_265614), hAPP(_265614, _265614, hAPP(_265614, fun(_265614, _265614), times_times(_265614), _265867), _265865)), hAPP(_265614, _265614, hAPP(_265614, fun(_265614, _265614), times_times(_265614), _265867), _265863))), hBOOL(hAPP(_265614, bool, hAPP(_265614, fun(_265614, bool), ord_less_eq(_265614), zero_zero(_265614)), _265867)), -(hBOOL(hAPP(_265614, bool, hAPP(_265614, fun(_265614, bool), ord_less(_265614), _265865), _265863)))]]], (5740 ^ _76106) ^ [_266323] : [linord20386208strict(_266323), 5743 ^ _76106 : [(5744 ^ _76106) ^ [_266572, _266574, _266576] : [hBOOL(hAPP(_266323, bool, hAPP(_266323, fun(_266323, bool), ord_less(_266323), hAPP(_266323, _266323, hAPP(_266323, fun(_266323, _266323), times_times(_266323), _266576), _266574)), hAPP(_266323, _266323, hAPP(_266323, fun(_266323, _266323), times_times(_266323), _266572), _266574))), hBOOL(hAPP(_266323, bool, hAPP(_266323, fun(_266323, bool), ord_less_eq(_266323), zero_zero(_266323)), _266574)), -(hBOOL(hAPP(_266323, bool, hAPP(_266323, fun(_266323, bool), ord_less(_266323), _266576), _266572)))]]], (5754 ^ _76106) ^ [_267032] : [linordered_semiring(_267032), 5757 ^ _76106 : [(5758 ^ _76106) ^ [_267281, _267283, _267285] : [hBOOL(hAPP(_267032, bool, hAPP(_267032, fun(_267032, bool), ord_less(_267032), hAPP(_267032, _267032, hAPP(_267032, fun(_267032, _267032), times_times(_267032), _267285), _267283)), hAPP(_267032, _267032, hAPP(_267032, fun(_267032, _267032), times_times(_267032), _267281), _267283))), hBOOL(hAPP(_267032, bool, hAPP(_267032, fun(_267032, bool), ord_less_eq(_267032), zero_zero(_267032)), _267283)), -(hBOOL(hAPP(_267032, bool, hAPP(_267032, fun(_267032, bool), ord_less(_267032), _267285), _267281)))]]], (5768 ^ _76106) ^ [_267741] : [linord20386208strict(_267741), 5771 ^ _76106 : [(5772 ^ _76106) ^ [_268051, _268053, _268055, _268057] : [hBOOL(hAPP(_267741, bool, hAPP(_267741, fun(_267741, bool), ord_less_eq(_267741), _268053), _268051)), hBOOL(hAPP(_267741, bool, hAPP(_267741, fun(_267741, bool), ord_less(_267741), _268057), _268055)), hBOOL(hAPP(_267741, bool, hAPP(_267741, fun(_267741, bool), ord_less(_267741), zero_zero(_267741)), _268053)), hBOOL(hAPP(_267741, bool, hAPP(_267741, fun(_267741, bool), ord_less_eq(_267741), zero_zero(_267741)), _268057)), -(hBOOL(hAPP(_267741, bool, hAPP(_267741, fun(_267741, bool), ord_less(_267741), hAPP(_267741, _267741, hAPP(_267741, fun(_267741, _267741), times_times(_267741), _268053), _268057)), hAPP(_267741, _267741, hAPP(_267741, fun(_267741, _267741), times_times(_267741), _268051), _268055))))]]], (5790 ^ _76106) ^ [_268783] : [linord20386208strict(_268783), 5793 ^ _76106 : [(5794 ^ _76106) ^ [_269093, _269095, _269097, _269099] : [hBOOL(hAPP(_268783, bool, hAPP(_268783, fun(_268783, bool), ord_less(_268783), _269095), _269093)), hBOOL(hAPP(_268783, bool, hAPP(_268783, fun(_268783, bool), ord_less_eq(_268783), _269099), _269097)), hBOOL(hAPP(_268783, bool, hAPP(_268783, fun(_268783, bool), ord_less_eq(_268783), zero_zero(_268783)), _269095)), hBOOL(hAPP(_268783, bool, hAPP(_268783, fun(_268783, bool), ord_less(_268783), zero_zero(_268783)), _269099)), -(hBOOL(hAPP(_268783, bool, hAPP(_268783, fun(_268783, bool), ord_less(_268783), hAPP(_268783, _268783, hAPP(_268783, fun(_268783, _268783), times_times(_268783), _269095), _269099)), hAPP(_268783, _268783, hAPP(_268783, fun(_268783, _268783), times_times(_268783), _269093), _269097))))]]], (5812 ^ _76106) ^ [_269825] : [linord20386208strict(_269825), 5815 ^ _76106 : [(5816 ^ _76106) ^ [_270135, _270137, _270139, _270141] : [hBOOL(hAPP(_269825, bool, hAPP(_269825, fun(_269825, bool), ord_less(_269825), _270137), _270135)), hBOOL(hAPP(_269825, bool, hAPP(_269825, fun(_269825, bool), ord_less(_269825), _270141), _270139)), hBOOL(hAPP(_269825, bool, hAPP(_269825, fun(_269825, bool), ord_less_eq(_269825), zero_zero(_269825)), _270137)), hBOOL(hAPP(_269825, bool, hAPP(_269825, fun(_269825, bool), ord_less_eq(_269825), zero_zero(_269825)), _270141)), -(hBOOL(hAPP(_269825, bool, hAPP(_269825, fun(_269825, bool), ord_less(_269825), hAPP(_269825, _269825, hAPP(_269825, fun(_269825, _269825), times_times(_269825), _270137), _270141)), hAPP(_269825, _269825, hAPP(_269825, fun(_269825, _269825), times_times(_269825), _270135), _270139))))]]], (5834 ^ _76106) ^ [_270867] : [linord20386208strict(_270867), 5837 ^ _76106 : [(5838 ^ _76106) ^ [_271177, _271179, _271181, _271183] : [hBOOL(hAPP(_270867, bool, hAPP(_270867, fun(_270867, bool), ord_less(_270867), _271179), _271177)), hBOOL(hAPP(_270867, bool, hAPP(_270867, fun(_270867, bool), ord_less(_270867), _271183), _271181)), hBOOL(hAPP(_270867, bool, hAPP(_270867, fun(_270867, bool), ord_less(_270867), zero_zero(_270867)), _271177)), hBOOL(hAPP(_270867, bool, hAPP(_270867, fun(_270867, bool), ord_less_eq(_270867), zero_zero(_270867)), _271183)), -(hBOOL(hAPP(_270867, bool, hAPP(_270867, fun(_270867, bool), ord_less(_270867), hAPP(_270867, _270867, hAPP(_270867, fun(_270867, _270867), times_times(_270867), _271179), _271183)), hAPP(_270867, _270867, hAPP(_270867, fun(_270867, _270867), times_times(_270867), _271177), _271181))))]]], (5856 ^ _76106) ^ [_271909] : [linord581940658strict(_271909), 5859 ^ _76106 : [(5860 ^ _76106) ^ [_272158, _272160, _272162] : [hBOOL(hAPP(_271909, bool, hAPP(_271909, fun(_271909, bool), ord_less(_271909), _272158), zero_zero(_271909))), 5863 ^ _76106 : [(5864 ^ _76106) ^ [] : [hBOOL(hAPP(_271909, bool, hAPP(_271909, fun(_271909, bool), ord_less_eq(_271909), hAPP(_271909, _271909, hAPP(_271909, fun(_271909, _271909), times_times(_271909), _272158), _272162)), hAPP(_271909, _271909, hAPP(_271909, fun(_271909, _271909), times_times(_271909), _272158), _272160))), -(hBOOL(hAPP(_271909, bool, hAPP(_271909, fun(_271909, bool), ord_less_eq(_271909), _272160), _272162)))], (5870 ^ _76106) ^ [] : [hBOOL(hAPP(_271909, bool, hAPP(_271909, fun(_271909, bool), ord_less_eq(_271909), _272160), _272162)), -(hBOOL(hAPP(_271909, bool, hAPP(_271909, fun(_271909, bool), ord_less_eq(_271909), hAPP(_271909, _271909, hAPP(_271909, fun(_271909, _271909), times_times(_271909), _272158), _272162)), hAPP(_271909, _271909, hAPP(_271909, fun(_271909, _271909), times_times(_271909), _272158), _272160))))]]]]], (5876 ^ _76106) ^ [_272849] : [linord581940658strict(_272849), 5879 ^ _76106 : [(5880 ^ _76106) ^ [_273098, _273100, _273102] : [hBOOL(hAPP(_272849, bool, hAPP(_272849, fun(_272849, bool), ord_less(_272849), zero_zero(_272849)), _273098)), 5883 ^ _76106 : [(5884 ^ _76106) ^ [] : [hBOOL(hAPP(_272849, bool, hAPP(_272849, fun(_272849, bool), ord_less_eq(_272849), hAPP(_272849, _272849, hAPP(_272849, fun(_272849, _272849), times_times(_272849), _273098), _273102)), hAPP(_272849, _272849, hAPP(_272849, fun(_272849, _272849), times_times(_272849), _273098), _273100))), -(hBOOL(hAPP(_272849, bool, hAPP(_272849, fun(_272849, bool), ord_less_eq(_272849), _273102), _273100)))], (5890 ^ _76106) ^ [] : [hBOOL(hAPP(_272849, bool, hAPP(_272849, fun(_272849, bool), ord_less_eq(_272849), _273102), _273100)), -(hBOOL(hAPP(_272849, bool, hAPP(_272849, fun(_272849, bool), ord_less_eq(_272849), hAPP(_272849, _272849, hAPP(_272849, fun(_272849, _272849), times_times(_272849), _273098), _273102)), hAPP(_272849, _272849, hAPP(_272849, fun(_272849, _272849), times_times(_272849), _273098), _273100))))]]]]], (5896 ^ _76106) ^ [_273789] : [linord581940658strict(_273789), 5899 ^ _76106 : [(5910 ^ _76106) ^ [_274436, _274438] : [5911 ^ _76106 : [(5912 ^ _76106) ^ [] : [-(ti(_273789, _274438) = zero_zero(_273789))], (5914 ^ _76106) ^ [] : [-(ti(_273789, _274436) = zero_zero(_273789))]], -(hBOOL(hAPP(_273789, bool, hAPP(_273789, fun(_273789, bool), ord_less(_273789), zero_zero(_273789)), hAPP(_273789, _273789, plus_plus(_273789, hAPP(_273789, _273789, hAPP(_273789, fun(_273789, _273789), times_times(_273789), _274438), _274438)), hAPP(_273789, _273789, hAPP(_273789, fun(_273789, _273789), times_times(_273789), _274436), _274436)))))], (5900 ^ _76106) ^ [_274042, _274044] : [hBOOL(hAPP(_273789, bool, hAPP(_273789, fun(_273789, bool), ord_less(_273789), zero_zero(_273789)), hAPP(_273789, _273789, plus_plus(_273789, hAPP(_273789, _273789, hAPP(_273789, fun(_273789, _273789), times_times(_273789), _274044), _274044)), hAPP(_273789, _273789, hAPP(_273789, fun(_273789, _273789), times_times(_273789), _274042), _274042)))), ti(_273789, _274044) = zero_zero(_273789), ti(_273789, _274042) = zero_zero(_273789)]]], (5918 ^ _76106) ^ [_274857] : [linordered_ring(_274857), 5921 ^ _76106 : [(5922 ^ _76106) ^ [_275041, _275043] : [hBOOL(hAPP(_274857, bool, hAPP(_274857, fun(_274857, bool), ord_less(_274857), hAPP(_274857, _274857, plus_plus(_274857, hAPP(_274857, _274857, hAPP(_274857, fun(_274857, _274857), times_times(_274857), _275043), _275043)), hAPP(_274857, _274857, hAPP(_274857, fun(_274857, _274857), times_times(_274857), _275041), _275041))), zero_zero(_274857)))]]], (5924 ^ _76106) ^ [_275197] : [linordered_semidom(_275197), 5927 ^ _76106 : [(5928 ^ _76106) ^ [_275408, _275410] : [hBOOL(hAPP(_275197, bool, hAPP(_275197, fun(_275197, bool), ord_less(_275197), one_one(_275197)), _275408)), -(hBOOL(hAPP(_275197, bool, hAPP(_275197, fun(_275197, bool), ord_less(_275197), hAPP(nat, _275197, power_power(_275197, _275408), _275410)), hAPP(_275197, _275197, hAPP(_275197, fun(_275197, _275197), times_times(_275197), _275408), hAPP(nat, _275197, power_power(_275197, _275408), _275410)))))]]], (5934 ^ _76106) ^ [_275739] : [linordered_semidom(_275739), 5937 ^ _76106 : [(5938 ^ _76106) ^ [_275944, _275946] : [hBOOL(hAPP(_275739, bool, hAPP(_275739, fun(_275739, bool), ord_less(_275739), one_one(_275739)), _275944)), -(hBOOL(hAPP(_275739, bool, hAPP(_275739, fun(_275739, bool), ord_less(_275739), one_one(_275739)), hAPP(_275739, _275739, hAPP(_275739, fun(_275739, _275739), times_times(_275739), _275944), hAPP(nat, _275739, power_power(_275739, _275944), _275946)))))]]], (5944 ^ _76106) ^ [_276263] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _276263)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), hAPP(real, real, sqrt, _276263))))], (5950 ^ _76106) ^ [_276479] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _276479)), hAPP(real, real, sqrt, _276479) = zero_zero(real)], (5956 ^ _76106) ^ [_276717] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), hAPP(real, real, sqrt, _276717)), zero_zero(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _276717), zero_zero(real))))], (5962 ^ _76106) ^ [_276919] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _276919), zero_zero(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), hAPP(real, real, sqrt, _276919)), zero_zero(real))))], (5968 ^ _76106) ^ [_277186] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), hAPP(real, real, sqrt, _277186))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _277186)))], (5974 ^ _76106) ^ [_277368] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), _277368)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), hAPP(real, real, sqrt, _277368))))], (5980 ^ _76106) ^ [_277615] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), hAPP(real, real, sqrt, _277615)), one_one(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _277615), one_one(real))))], (5986 ^ _76106) ^ [_277817] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), _277817), one_one(real))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), hAPP(real, real, sqrt, _277817)), one_one(real))))], (5992 ^ _76106) ^ [_278084] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), one_one(real)), hAPP(real, real, sqrt, _278084))), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), one_one(real)), _278084)))], (5998 ^ _76106) ^ [_278266] : [hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), one_one(real)), _278266)), -(hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), one_one(real)), hAPP(real, real, sqrt, _278266))))], (6004 ^ _76106) ^ [_278484] : [linord581940658strict(_278484), 6007 ^ _76106 : [(6008 ^ _76106) ^ [_278733, _278735, _278737] : [hBOOL(hAPP(_278484, bool, hAPP(_278484, fun(_278484, bool), ord_less(_278484), _278735), _278733)), hBOOL(hAPP(_278484, bool, hAPP(_278484, fun(_278484, bool), ord_less(_278484), _278737), zero_zero(_278484))), -(hBOOL(hAPP(_278484, bool, hAPP(_278484, fun(_278484, bool), ord_less(_278484), hAPP(_278484, _278484, hAPP(_278484, fun(_278484, _278484), times_times(_278484), _278737), _278733)), hAPP(_278484, _278484, hAPP(_278484, fun(_278484, _278484), times_times(_278484), _278737), _278735))))]]], (6018 ^ _76106) ^ [_279193] : [linord581940658strict(_279193), 6021 ^ _76106 : [(6022 ^ _76106) ^ [_279442, _279444, _279446] : [hBOOL(hAPP(_279193, bool, hAPP(_279193, fun(_279193, bool), ord_less(_279193), _279444), _279442)), hBOOL(hAPP(_279193, bool, hAPP(_279193, fun(_279193, bool), ord_less(_279193), _279446), zero_zero(_279193))), -(hBOOL(hAPP(_279193, bool, hAPP(_279193, fun(_279193, bool), ord_less(_279193), hAPP(_279193, _279193, hAPP(_279193, fun(_279193, _279193), times_times(_279193), _279442), _279446)), hAPP(_279193, _279193, hAPP(_279193, fun(_279193, _279193), times_times(_279193), _279444), _279446))))]]], (6032 ^ _76106) ^ [_279902] : [linord893533164strict(_279902), 6035 ^ _76106 : [(6036 ^ _76106) ^ [_280151, _280153, _280155] : [hBOOL(hAPP(_279902, bool, hAPP(_279902, fun(_279902, bool), ord_less(_279902), _280153), _280151)), hBOOL(hAPP(_279902, bool, hAPP(_279902, fun(_279902, bool), ord_less(_279902), zero_zero(_279902)), _280155)), -(hBOOL(hAPP(_279902, bool, hAPP(_279902, fun(_279902, bool), ord_less(_279902), hAPP(_279902, _279902, hAPP(_279902, fun(_279902, _279902), times_times(_279902), _280155), _280153)), hAPP(_279902, _279902, hAPP(_279902, fun(_279902, _279902), times_times(_279902), _280155), _280151))))]]], (6046 ^ _76106) ^ [_280611] : [linord20386208strict(_280611), 6049 ^ _76106 : [(6050 ^ _76106) ^ [_280860, _280862, _280864] : [hBOOL(hAPP(_280611, bool, hAPP(_280611, fun(_280611, bool), ord_less(_280611), _280862), _280860)), hBOOL(hAPP(_280611, bool, hAPP(_280611, fun(_280611, bool), ord_less(_280611), zero_zero(_280611)), _280864)), -(hBOOL(hAPP(_280611, bool, hAPP(_280611, fun(_280611, bool), ord_less(_280611), hAPP(_280611, _280611, hAPP(_280611, fun(_280611, _280611), times_times(_280611), _280864), _280862)), hAPP(_280611, _280611, hAPP(_280611, fun(_280611, _280611), times_times(_280611), _280864), _280860))))]]], (6060 ^ _76106) ^ [_281320] : [linord20386208strict(_281320), 6063 ^ _76106 : [(6064 ^ _76106) ^ [_281569, _281571, _281573] : [hBOOL(hAPP(_281320, bool, hAPP(_281320, fun(_281320, bool), ord_less(_281320), _281571), _281569)), hBOOL(hAPP(_281320, bool, hAPP(_281320, fun(_281320, bool), ord_less(_281320), zero_zero(_281320)), _281573)), -(hBOOL(hAPP(_281320, bool, hAPP(_281320, fun(_281320, bool), ord_less(_281320), hAPP(_281320, _281320, hAPP(_281320, fun(_281320, _281320), times_times(_281320), _281571), _281573)), hAPP(_281320, _281320, hAPP(_281320, fun(_281320, _281320), times_times(_281320), _281569), _281573))))]]], (6074 ^ _76106) ^ [_282029] : [linord581940658strict(_282029), 6077 ^ _76106 : [(6078 ^ _76106) ^ [_282248, _282250] : [hBOOL(hAPP(_282029, bool, hAPP(_282029, fun(_282029, bool), ord_less(_282029), _282248), zero_zero(_282029))), hBOOL(hAPP(_282029, bool, hAPP(_282029, fun(_282029, bool), ord_less(_282029), _282250), zero_zero(_282029))), -(hBOOL(hAPP(_282029, bool, hAPP(_282029, fun(_282029, bool), ord_less(_282029), zero_zero(_282029)), hAPP(_282029, _282029, hAPP(_282029, fun(_282029, _282029), times_times(_282029), _282248), _282250))))]]], (6088 ^ _76106) ^ [_282676] : [linord20386208strict(_282676), 6091 ^ _76106 : [(6092 ^ _76106) ^ [_282895, _282897] : [hBOOL(hAPP(_282676, bool, hAPP(_282676, fun(_282676, bool), ord_less(_282676), _282895), zero_zero(_282676))), hBOOL(hAPP(_282676, bool, hAPP(_282676, fun(_282676, bool), ord_less(_282676), zero_zero(_282676)), _282897)), -(hBOOL(hAPP(_282676, bool, hAPP(_282676, fun(_282676, bool), ord_less(_282676), hAPP(_282676, _282676, hAPP(_282676, fun(_282676, _282676), times_times(_282676), _282895), _282897)), zero_zero(_282676))))]]], (6102 ^ _76106) ^ [_283323] : [linord581940658strict(_283323), 6105 ^ _76106 : [(6106 ^ _76106) ^ [_283572, _283574, _283576] : [hBOOL(hAPP(_283323, bool, hAPP(_283323, fun(_283323, bool), ord_less(_283323), _283572), zero_zero(_283323))), 6109 ^ _76106 : [(6110 ^ _76106) ^ [] : [hBOOL(hAPP(_283323, bool, hAPP(_283323, fun(_283323, bool), ord_less(_283323), hAPP(_283323, _283323, hAPP(_283323, fun(_283323, _283323), times_times(_283323), _283572), _283576)), hAPP(_283323, _283323, hAPP(_283323, fun(_283323, _283323), times_times(_283323), _283572), _283574))), -(hBOOL(hAPP(_283323, bool, hAPP(_283323, fun(_283323, bool), ord_less(_283323), _283574), _283576)))], (6116 ^ _76106) ^ [] : [hBOOL(hAPP(_283323, bool, hAPP(_283323, fun(_283323, bool), ord_less(_283323), _283574), _283576)), -(hBOOL(hAPP(_283323, bool, hAPP(_283323, fun(_283323, bool), ord_less(_283323), hAPP(_283323, _283323, hAPP(_283323, fun(_283323, _283323), times_times(_283323), _283572), _283576)), hAPP(_283323, _283323, hAPP(_283323, fun(_283323, _283323), times_times(_283323), _283572), _283574))))]]]]], (6122 ^ _76106) ^ [_284263] : [linord20386208strict(_284263), 6125 ^ _76106 : [(6126 ^ _76106) ^ [_284482, _284484] : [hBOOL(hAPP(_284263, bool, hAPP(_284263, fun(_284263, bool), ord_less(_284263), zero_zero(_284263)), hAPP(_284263, _284263, hAPP(_284263, fun(_284263, _284263), times_times(_284263), _284484), _284482))), hBOOL(hAPP(_284263, bool, hAPP(_284263, fun(_284263, bool), ord_less(_284263), zero_zero(_284263)), _284482)), -(hBOOL(hAPP(_284263, bool, hAPP(_284263, fun(_284263, bool), ord_less(_284263), zero_zero(_284263)), _284484)))]]], (6136 ^ _76106) ^ [_284924, _284926] : [preorder(_284924), -(preorder(fun(_284926, _284924)))], (6142 ^ _76106) ^ [_285136, _285138] : [order(_285136), -(order(fun(_285138, _285136)))], (6148 ^ _76106) ^ [_285348, _285350] : [ord(_285348), -(ord(fun(_285350, _285348)))], (6154 ^ _76106) ^ [] : [-(semiri456707255roduct(int))], (6156 ^ _76106) ^ [] : [-(ordere223160158up_add(int))], (6158 ^ _76106) ^ [] : [-(ordere236663937imp_le(int))], (6160 ^ _76106) ^ [] : [-(linord893533164strict(int))], (6162 ^ _76106) ^ [] : [-(linord20386208strict(int))], (6164 ^ _76106) ^ [] : [-(ordere779506340up_add(int))], (6166 ^ _76106) ^ [] : [-(ordere216010020id_add(int))], (6168 ^ _76106) ^ [] : [-(linord219039673up_add(int))], (6170 ^ _76106) ^ [] : [-(cancel146912293up_add(int))], (6172 ^ _76106) ^ [] : [-(ring_11004092258visors(int))], (6174 ^ _76106) ^ [] : [-(linord581940658strict(int))], (6176 ^ _76106) ^ [] : [-(cancel_semigroup_add(int))], (6178 ^ _76106) ^ [] : [-(linordered_semiring(int))], (6180 ^ _76106) ^ [] : [-(linordered_semidom(int))], (6182 ^ _76106) ^ [] : [-(ab_semigroup_add(int))], (6184 ^ _76106) ^ [] : [-(no_zero_divisors(int))], (6186 ^ _76106) ^ [] : [-(comm_monoid_add(int))], (6188 ^ _76106) ^ [] : [-(linordered_ring(int))], (6190 ^ _76106) ^ [] : [-(linordered_idom(int))], (6192 ^ _76106) ^ [] : [-(comm_semiring_1(int))], (6194 ^ _76106) ^ [] : [-(semiring_char_0(int))], (6196 ^ _76106) ^ [] : [-(number_semiring(int))], (6198 ^ _76106) ^ [] : [-(zero_neq_one(int))], (6200 ^ _76106) ^ [] : [-(preorder(int))], (6202 ^ _76106) ^ [] : [-(linorder(int))], (6204 ^ _76106) ^ [] : [-(monoid_mult(int))], (6206 ^ _76106) ^ [] : [-(monoid_add(int))], (6208 ^ _76106) ^ [] : [-(semiring_1(int))], (6210 ^ _76106) ^ [] : [-(semiring_0(int))], (6212 ^ _76106) ^ [] : [-(mult_zero(int))], (6214 ^ _76106) ^ [] : [-(order(int))], (6216 ^ _76106) ^ [] : [-(ring_char_0(int))], (6218 ^ _76106) ^ [] : [-(number_ring(int))], (6220 ^ _76106) ^ [] : [-(ord(int))], (6222 ^ _76106) ^ [] : [-(power(int))], (6224 ^ _76106) ^ [] : [-(zero(int))], (6226 ^ _76106) ^ [] : [-(number(int))], (6228 ^ _76106) ^ [] : [-(one(int))], (6230 ^ _76106) ^ [] : [-(semiri456707255roduct(nat))], (6232 ^ _76106) ^ [] : [-(ordere223160158up_add(nat))], (6234 ^ _76106) ^ [] : [-(ordere236663937imp_le(nat))], (6236 ^ _76106) ^ [] : [-(linord893533164strict(nat))], (6238 ^ _76106) ^ [] : [-(linord20386208strict(nat))], (6240 ^ _76106) ^ [] : [-(ordere779506340up_add(nat))], (6242 ^ _76106) ^ [] : [-(ordere216010020id_add(nat))], (6244 ^ _76106) ^ [] : [-(cancel146912293up_add(nat))], (6246 ^ _76106) ^ [] : [-(cancel_semigroup_add(nat))], (6248 ^ _76106) ^ [] : [-(linordered_semiring(nat))], (6250 ^ _76106) ^ [] : [-(linordered_semidom(nat))], (6252 ^ _76106) ^ [] : [-(ab_semigroup_add(nat))], (6254 ^ _76106) ^ [] : [-(no_zero_divisors(nat))], (6256 ^ _76106) ^ [] : [-(comm_monoid_add(nat))], (6258 ^ _76106) ^ [] : [-(comm_semiring_1(nat))], (6260 ^ _76106) ^ [] : [-(semiring_char_0(nat))], (6262 ^ _76106) ^ [] : [-(number_semiring(nat))], (6264 ^ _76106) ^ [] : [-(zero_neq_one(nat))], (6266 ^ _76106) ^ [] : [-(preorder(nat))], (6268 ^ _76106) ^ [] : [-(linorder(nat))], (6270 ^ _76106) ^ [] : [-(monoid_mult(nat))], (6272 ^ _76106) ^ [] : [-(monoid_add(nat))], (6274 ^ _76106) ^ [] : [-(semiring_1(nat))], (6276 ^ _76106) ^ [] : [-(semiring_0(nat))], (6278 ^ _76106) ^ [] : [-(mult_zero(nat))], (6280 ^ _76106) ^ [] : [-(order(nat))], (6282 ^ _76106) ^ [] : [-(ord(nat))], (6284 ^ _76106) ^ [] : [-(power(nat))], (6286 ^ _76106) ^ [] : [-(zero(nat))], (6288 ^ _76106) ^ [] : [-(number(nat))], (6290 ^ _76106) ^ [] : [-(one(nat))], (6292 ^ _76106) ^ [] : [-(preorder(bool))], (6294 ^ _76106) ^ [] : [-(order(bool))], (6296 ^ _76106) ^ [] : [-(ord(bool))], (6298 ^ _76106) ^ [] : [-(semiri456707255roduct(real))], (6300 ^ _76106) ^ [] : [-(ordere223160158up_add(real))], (6302 ^ _76106) ^ [] : [-(ordere236663937imp_le(real))], (6304 ^ _76106) ^ [] : [-(linord893533164strict(real))], (6306 ^ _76106) ^ [] : [-(linord20386208strict(real))], (6308 ^ _76106) ^ [] : [-(ordere779506340up_add(real))], (6310 ^ _76106) ^ [] : [-(ordere216010020id_add(real))], (6312 ^ _76106) ^ [] : [-(linord219039673up_add(real))], (6314 ^ _76106) ^ [] : [-(cancel146912293up_add(real))], (6316 ^ _76106) ^ [] : [-(ring_11004092258visors(real))], (6318 ^ _76106) ^ [] : [-(linord581940658strict(real))], (6320 ^ _76106) ^ [] : [-(cancel_semigroup_add(real))], (6322 ^ _76106) ^ [] : [-(linordered_semiring(real))], (6324 ^ _76106) ^ [] : [-(linordered_semidom(real))], (6326 ^ _76106) ^ [] : [-(dense_linorder(real))], (6328 ^ _76106) ^ [] : [-(ab_semigroup_add(real))], (6330 ^ _76106) ^ [] : [-(no_zero_divisors(real))], (6332 ^ _76106) ^ [] : [-(comm_monoid_add(real))], (6334 ^ _76106) ^ [] : [-(linordered_ring(real))], (6336 ^ _76106) ^ [] : [-(linordered_idom(real))], (6338 ^ _76106) ^ [] : [-(comm_semiring_1(real))], (6340 ^ _76106) ^ [] : [-(semiring_char_0(real))], (6342 ^ _76106) ^ [] : [-(number_semiring(real))], (6344 ^ _76106) ^ [] : [-(zero_neq_one(real))], (6346 ^ _76106) ^ [] : [-(preorder(real))], (6348 ^ _76106) ^ [] : [-(linorder(real))], (6350 ^ _76106) ^ [] : [-(monoid_mult(real))], (6352 ^ _76106) ^ [] : [-(monoid_add(real))], (6354 ^ _76106) ^ [] : [-(semiring_1(real))], (6356 ^ _76106) ^ [] : [-(semiring_0(real))], (6358 ^ _76106) ^ [] : [-(mult_zero(real))], (6360 ^ _76106) ^ [] : [-(order(real))], (6362 ^ _76106) ^ [] : [-(ring_char_0(real))], (6364 ^ _76106) ^ [] : [-(number_ring(real))], (6366 ^ _76106) ^ [] : [-(ord(real))], (6368 ^ _76106) ^ [] : [-(power(real))], (6370 ^ _76106) ^ [] : [-(zero(real))], (6372 ^ _76106) ^ [] : [-(number(real))], (6374 ^ _76106) ^ [] : [-(one(real))], (6376 ^ _76106) ^ [_291428, _291430] : [-(ti(_291430, ti(_291430, _291428)) = ti(_291430, _291428))], (6378 ^ _76106) ^ [_291545, _291547, _291549] : [-(hAPP(_291549, _291549, hAPP(_291549, fun(_291549, _291549), hAPP(bool, fun(_291549, fun(_291549, _291549)), (if _291549), fTrue), _291547), _291545) = ti(_291549, _291547))], (6380 ^ _76106) ^ [_291684, _291686, _291688] : [-(hAPP(_291688, _291688, hAPP(_291688, fun(_291688, _291688), hAPP(bool, fun(_291688, fun(_291688, _291688)), (if _291688), fFalse), _291686), _291684) = ti(_291688, _291684))], (6382 ^ _76106) ^ [_291790] : [-(ti(bool, _291790) = fTrue), -(ti(bool, _291790) = fFalse)]], input).
% 0.62/1.39 ncf('1',plain,[linordered_idom(int), 1458 : hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))))), 1458 : ti(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))) = zero_zero(int)],start(1454 ^ 0,bind([[_100279, _100381], [int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))]]))).
% 0.62/1.39 ncf('1.1',plain,[-(linordered_idom(int))],extension(6190 ^ 1)).
% 0.62/1.39 ncf('1.2',plain,[-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))))), 2199 : hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))), 2199 : linordered_semidom(int)],extension(2195 ^ 3,bind([[_114589, _114693, _114695], [int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))]]))).
% 0.62/1.39 ncf('1.2.1',plain,[-(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))))],extension(724 ^ 6)).
% 0.62/1.39 ncf('1.2.2',plain,[-(linordered_semidom(int))],extension(6180 ^ 4)).
% 0.62/1.39 ncf('1.3',plain,[-(ti(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))) = zero_zero(int)), 766 : hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(int), 766 : ring_11004092258visors(int)],extension(762 ^ 3,bind([[_87010, _87096], [int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))]]))).
% 0.62/1.39 ncf('1.3.1',plain,[-(hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))) = zero_zero(int))],extension(6388 ^ 6)).
% 0.62/1.39 ncf('1.3.2',plain,[-(ring_11004092258visors(int))],extension(6172 ^ 4)).
% 0.62/1.39 %-----------------------------------------------------
% 0.62/1.39 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------